The sum of two numbers is 4. Three times the larger number plus two times the smaller number is 26. Find the numbers.
The larger number is and the smaller number is

Answers

Answer 1

The larger integer number is 18 and the smaller integer number is -14.

Integers are the subset of Rational numbers which contains all numbers except fraction and decimals

Numbers are the building blocks of mathematics. Numbers are used to count ,measure or label quantities.

The different types of numbers are:

Real numbers: 89.26 , -847 , 4/5irrational numbers √2 ,√3 imaginary numbers (5 + 9i) Integers -89 , 65 , 45

Let the smaller number be x. The sum of the numbers is 4 .

So the larger number is 4 - x

Again given that sum of three times the larger number and 2 times the smaller number is 26.

∴3 ( 4-x )+ 2x = 26

or, 12 -3x +2 x = 26

or, -x = 26-12

or, x = -14

Therefore the larger number is 4-(-14)= 18

Hence the larger integer number is 18 and the smaller number is -14 .

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Related Questions

On his road trip, Leon stops to refuel and get some snacks. He has the following purchases:
12 gallons of gas at of $2.89 per gallon
2 granola bars for $1.59 each
1 apple for $0.89
2 bottles of vitamin water for $1.39 each
Leon must pay 7.5% sales tax on everything but the gas, which already has tax included in the per gallon price. If
Leon paid $44.64, then he
for his purchase.
a. did not pay enough
b. paid the correct amount
C.
paid $2.60 too much
d.
paid $3.11 too much
Please select the best answer from the choices provided

Answers

Let’s transform this word problem into an equation. We’ll use a function formula to model the problem.

y=12(2.89)+(2(1.59)+.89+2(1.39))+.075p

This is a function, meaning that y=output (total cost), which we are given is 44.64, so y=44.64. Also notice that there is a variable “p.” This variable “p” simply means the price disregarding gas. We substitute y in and solve the equation using PEMDAS.

44.64=34.68+(3.18+.89+2.78)+.075p

44.64=34.68+(6.85)+.075(6.85)

Now, you see that “p” was replaced with the price disregarding gas, so we need to find the sales tax (7.5%=.075) of the food products and add that to the whole equation.

44.64=34.68+6.85+.51375

44.64=34.68+7.36375

44.68≠42.043

Notice that after simplifying, the equation is an inequality; therefore, we must subtract 44.68-42.043=2.637, and rounding down to the nearest tenth of 2.60.

Your answer is that Leon overpaid by $2.60

The correct option is that;

C. Leon overpaid for his purchase by $2.60 if he paid $44.64.

What is the difference between a sales tax and a use tax?

The vendor, who is acting as the state's agent, collects the sales tax and remits it to the state on behalf of the final customer. The use tax, on the other hand, is self-assessed and paid by the final customer.

Given that;

Purchase fuel = 12 Gallons per $2.89 per gallons (including Tax)

2 Granola Bar for $1.59 per bar

1  apple for $0.89

2 bottles of vitamin water for $1.39

The sales Tax rate is 7.5%

Required to calculate the difference amount of Actual Paid and Actual Purchase =?

Fuel = 12 x 2.89 = $34.68 (including tax)

Granola Bar = 2 x 1.59 = $3.18

Apple = 1 x 0.89 = $0.89

Vitamin Water = 2 x 1.39 = $2.78

Total Purchase excluding fuel without tax is,

= $3.18 + $0.89 + $2.78

= $6.85.

Adding sale tax on  $6.85 at the rate of 7.5% = $7.36

Hence, Total Purchase including Tax is,

$7.36 + $34.68 = $42.04

Thus, there is a clear difference that Leon paid 2.60 more than his actual purchase. He paid $ 44.64 and his actual purchase is 42.04 the difference between that is $2.60.

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Dave and Sandy Hartranft are frequent flyers with a particular . They often from City A to City a of 840 On particular tripthey wirdand the flight takes 2 hoursThe return trip, with the wind behind them, only takes 1 1/2 * t hoursthe wind speed is the same on tripthe wind and find the speed of the plane in still air The wind speed ismph The speed of the plane ismph

Answers

It should be noted that the wind speed is 70km per hour and the plane speed is 490km per hour.

How to illustrate the information?

Based on the information given, the following an be illustrated.

Let P = speed of plane

Let w = speed of wind

The appropriate equation will be:

(P + W) (3/2) = 840 ....... i

(P - W) × 2 = (840 / 2) ...... ii

P + W = 560 .....i

P - W = 420 ......ii

Subtract the equations

2P = 980

P = 980 / 2 = 490

P + W = 560

490 + W = 560

W = 560 - 490

W = 70

Therefore, the wind speed is 70km per hour and the plane speed is 490km per hour.

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find the prime factors of 6912 and cube root​

Answers

The prime factors of 6912 are 2 and 3 and the cube root of 6912 is approximately 19.05 (rounded to 2 decimal places) .

Prime numbers are numbers which do not have any factors other than 1 and itself. For example 7 is a prime number, 37 is a prime number as the factors of 7 are 1 and 7 and the factors of 37 are 1 and 37.

Prime factorization of a number is given by writing all the prime factors of as number in multiplication form.

The prime factorization of 6912 gives:

6912 = 2 × 2 × 2 ×2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 = 2⁸ × 3³

Hence the prime factors of 6912 are 2 and 3.

The cube root of 6912 = 19.0488... ≈ 19.05 (rounded to 2 decimal places)

Therefore the cube root of 6912 is approximately 19.05 .

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The electoral college is in place so that states with a greater population have more influence in a presidential election. The higher populated states have more votes. For example, Washington is roughly 3 times as populated as Idaho, so Washigton’s number of electoral college votes is 300% of Idaho’s number. If Idaho has 4 electoral college votes, how many votes does Washington have? Percent formula

Answers

Answer: 12 electoral college votes

Step-by-step explanation:

4*100%=

4*100/100=

400/100=4

4*300%=

4*300/100=

1200/100=12 votes

25 25
4

A
=
25.
=
C=

Answers

Answer:

a = 2

b = 3

c= 8

Step-by-step explanation:

a) 4 = [tex]2^{2}[/tex]  We want to have all of the bases the same in the powers, so we will convert 4 to a base of 2.

b) When we divide with powers with the same baes, we subtract the exponents.  (5-2 =3)

c) [tex]2^{3}[/tex] means 2x2x2 or 8

The sum of three times a number and nine is 12 

Answers

Answer:

1

Step-by-step explanation:

let the number be n

3n + 9 = 12

3n = 12 - 9 = 3

n= 3/3

n= 1

a rectangular room measures 17 feet by 6 feet. find the cost of installing a strip of wallpaper around the room if the wallpaper costs $0.94 foot.

Answers

Answer:

$95.88

Step-by-step explanation:

multiply 6 by 17 and get 102

multiply 102 by 0.94 and get 95.88

Write a compound inequality that represents the following phrase.
all real numbers that are between -4 and 5, inclusive

Write a compound inequality that represents the phrase. Choose the correct answer below.
A:[tex]-4\leq n\ \textless \ 5[/tex]
B:[tex]-4\ \textless \ n\ \textless \ 5[/tex]
C:[tex]-4\ \textless \ n\leq 5[/tex]
D:[tex]-4\leq n\leq 5[/tex]

Answers

The compound inequality that represents the set of real numbers that are between -4 and 5 inclusive is the option;

D: -4 ≤ n ≤ 5

How can the compound inequality be found?

A compound inequality comprises of a sentence that makes two inequality statements that are joined by either the word 'and' or 'or'.

Given that the inequality represents the set of all real numbers that are between -4 and 5, and -4 < 5, the required set of numbers is therefore of the form;

[tex] - 4 \: \leftrightarrow \: 5[/tex]

The expression of the required set of numbers as inequalities is therefore;

-4 ≤ n and n ≤ 5

The compound inequality is therefore;

D: -4 ≤ n ≤ 5

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it is math for evaluating functions please help

Answers

The domain of the given function is; (0, 2)

The range of the given function is; (-2, 6)

What is the range and domain of the given function?

We want to evaluate the function f(x) = 4x - 2 for x = 0, 1 and 2.

Step 1;

f(0) = 4(0) - 2

f(1) = 4(1) - 2

f(2) = 4(2) - 2

Step 2;

f(0) = 0 - 2 = -2

f(1) = 4 - 2 = 2

f(2) = 8 - 2 = 6

The domain is the set of all possible input values which is (0, 2)

The range is the set of all possible output values which is (-2, 6)

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The mapping diagram shows a relation.

A mapping diagram shows a relation, using arrows, between inputs and outputs for the following ordered pairs: (negative 6, 0), (2, 1), (negative 7, negative 4), (11, 2), (3, 2).

What is the domain of the relation?

{x| x = –4 , 0, 1, 2}.
{x| x = –7, –6, 2, 3, 11}.
{y| y = –4, 0, 1, 2}.
{y| y = –7, –6, 2, 3, 11}.

Answers

The domain of the given relation is: {x| x = –7, –6, 2, 3, 11}.

What is a domain?

A domain can be defined as the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain is the set of all possible input numerical values to a function and the domain of a graph comprises all the input numerical values which are shown on the x-axis.

Additionally, the horizontal extent of a graph represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.

In this context, we can reasonably infer and logically deduce that the domain of the given relation include the following: {x| x = –7, –6, 2, 3, 11}.

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-5•g(4)-1 If g(x)=1-3/4x

Answers

The value of -5*g(4)-1 is 9.

It is a question of functions.

Here, g is a function of x.

Function

A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

Let X and Y be any two non-empty sets; mapping from X to Y will be a function only when every element in set X has one end, only one image in set Y.

Given that:-

g(x) = 1 - (3/4)x

We have to find the value of  -5*g(4)-1

First we will find g(4),

g(4) = 1 - (3/4)*(4) = 1 - 3 = -2

-5*g(4) - 1 = -5*(-2) - 1 = 10 - 1 = 9

Hence, the value of -5*g(4) - 1  is 9.

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just need help with some of them at least 5 questions please already did the first one. i put 90 points please help.

Answers

2. The solution to the given system of equation is x = 1 and y = 6

3. The solution to the given system of equations is x = 1, y = 2

4. The simplified form of the expression is y²

5. The simplified form of the expression is 2

8. the subtraction of the polynomials yields -2x³ + 3x² + 9x - 11

9. The multiplication yields x² - 4x - 96

10. The factored form of the expression is (x + 6)(x- 6)

11. The solutions to the given quadratic equation are x = 5 and x = -6

Solving system of equations

From the question, we are to solve the given system of equations

The given system of equation is

y = 10 - 4x      --------- (1)

2x + 3y = 20  --------- (2)

Substitute equation (1) into equation (2)

2x + 3y = 20

2x + 3(10 -4x) = 20

2x + 30 - 12x = 20

2x - 12x = 20 - 30

-10x = -10

x = -10/-10

x = 1

Substitute the value of x into equation (1)

y = 10 - 4x

y = 10 - 4(1)

y = 10 - 4

y = 6

Hence, the solution to the given system of equation is x = 1 and y = 6

3.

From the question, we are to solve the system of equations using the elimination method

The given system of equations is

5x + 2y = 9

-5x + 4y = 3

Add the two equations

5x + 2y = 9

-5x + 4y = 3

----------------------

0x + 6y = 12

6y = 12

y = 12/6

y = 2

Substitute the value of y into the first equation

5x + 2y = 9

5x + 2(2) = 9

5x + 4 = 9

5x = 9 - 4

5x = 5

x = 5/5

x = 1

Hence, the solution to the given system of equations is x = 1, y = 2

4. From the question, we are to simplify the expression

y⁻⁴(y³)²

First, multiply the exponents in (y³)²

(y³)² = y ³ ˣ ²

= y⁶

Thus,

The expression becomes y⁻⁴y⁶

Applying the multiplication law of indices

y⁻⁴y⁶ = y⁻⁴ ⁺ ⁶

= y²

Hence, the simplified form of the expression is y²

5.

From the question, we are to simplify

∛8

First, express 8 in exponent form

8 = 2³

Thus,

The expression becomes

∛2³

Applying one of the laws of indices,

∛2³ = (2³)¹/³

Multiplying the exponents, we get

= 2

8.

From the question, we are to subtract the polynomial

(3x² + 5x - 8) - (2x³  - 4x + 3)

Subtracting

(3x² + 5x - 8) - (2x³  - 4x + 3)

3x² + 5x - 8 -(2x³  - 4x + 3)

Open the parentheses by distributing negative

3x² + 5x - 8 -2x³  + 4x - 3

Collect like terms

-2x³ + 3x² + 5x + 4x - 8 - 3

Simplify

-2x³ + 3x² + 9x - 11

Hence, the subtraction of the polynomials yields -2x³ + 3x² + 9x - 11

9.

From the question we are to multiply

(x + 8)(x - 12)

Applying the distributive property

x(x -12) +8(x -12)

x² - 12x + 8x - 96

Simplifying

x² - 4x - 96

10.

From the question, we are to factor

x² - 36

This can be written as

x² - 6²

From the rule of difference of two squares, we have that

a² - b² = (a + b)(a - b)

Thus,

x² - 6² = (x + 6)(x- 6)

11.

From the question, we are to find the solutions for

x² - x - 30 = 0

Solve by factoring

x² - x - 30 = 0

x² + 6x - 5x - 30 = 0

x(x + 6) -5(x + 6) = 0

(x - 5)(x + 6)  = 0

∴ x - 5 = 0 and x + 6 = 0

x = 5 and x = -6

Hence, the solutions to the given quadratic equation are x = 5 and x = -6

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Jayden is standing in a stadium and has the option of running up a staircase or down a staircase for exercise. The function f(x)=\frac{1}{25}\big(\left|6x\right|+5x\big)f(x)= 25 1 ​ (∣6x∣+5x) will determine how many calories Jayden will burn if he runs up xx steps. Use a negative value for xx if he runs down the stairs. Find and interpret the given function values and determine an appropriate domain for the function.

Answers

The interpretation of the value of the function, [tex]f(x) = \frac{1}{25} \times \left( \left |6 \cdot x \right | + 5 \cdot x \right)[/tex], when x = 30 is that by running up 30 steps, Jayden burns [tex] 13 \frac{1}{3} [/tex] calories.

The domain of the function is the set of all real numbers

How can the values of the function be interpreted?

The given function is presented as follows;

[tex]f(x) = \frac{1}{25} \times \left( \left |6 \cdot x \right | + 5 \cdot x \right)[/tex]

Where;

f(x) = The number of calories burnt

x = The number of steps Jayden runs

The value of x is negative while running down the stairs

Therefore;

[tex]f(30) = \frac{1}{25} \times \left( \left |6 \times 30 \right | + 5 \times 30 \right) = 13 \frac{1}{3} [/tex]

[tex]f(30) = 13 \frac{1}{3} [/tex]

The interpretation of the above function equation is that the amount of calories Jayden burns when she runs 30 steps up the stairs is [tex] 13 \frac{1}{3} [/tex]

Given that 6•x > 5•x, the function is always positive, and has a minimum value of zero, the function can take any value for x.

The domain of the function is therefore, -∞ ≤ x ≤ ∞, which is the set of all real numbers.

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Brianna and Aisha start a small business making handmade soaps to sell at fairs and local stores.
Brianna can make 50 bars of soap in 40 hours, and Aisha can make 50 bars of soap in 75 hours. How long will it take Aisha to make 50 bars of soap?

Answers

Answer: 75 hours

Step-by-step explanation:

"Aisha can make 50 bars of soap in 75 hours"

The division is one of the four fundamental arithmetic operations. The time it will take to make 50 soap bars if they both work together is 25.4543 hours.

What is Division?

The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.


Given that Brianna can make 50 bars of soap in 40 hours, and Aisha can make 50 bars of soap in 75 hours. Therefore, we can write,

Soaps Made Briana in an hour = 50 bars/40 hours

                                                   = 1.25 soap bars per hour

Soaps Made Aisha in an hour = 50 bars/75hours

                                                   = 0.7143 soap bars per hour

Now, together the number of soap bars they can make in an hour is,

Number of soap bars in an hour = 1.25 + 0.7143 soap bars per hour

                                                      = 1.9643 soap bars per hour

Further, the time it will take to make 50 soap bars if they both work together is,

Time is taken = Number of soaps/ Number of soaps in an hour

                       = 50 soap / 1.9643 soap bars per hour

                       = 25.4543 hours

Hence, the time it will take to make 50 soap bars if they both work together is 25.4543 hours.

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For the stem-and-leaf plot below, what are the maximum and minimum entries?

1 | 3 4
1 | 6 6 6 7 8 9
2 | 0 1 1 2 3 4 4 5 6 6
2 | 7 7 7 8 8 9 9 9
3 | 0 1 1 2 3 4 4 5 5
3 | 6 6 6 7 8 8 9 9
4 | 1 3

Answers

Depending on what the | means sometimes it can be a indication on a decimal but assume you just combine the numbers into a 2 digit number. If so:
Min: 12
Max: 43

Rewrite, using the distributive
property.
4(2x + 5) = [?]x + [ ]

Answers

Step-by-step explanation:

8x+20 is the answer ......

Find the lengths of UV and ST and determine whether they are congruent.
Hint: Congruent line segments have the same length.

Answers

The length of both UV and ST is [tex]3\sqrt{2}[/tex] and hence they both are congruent.

Here, we are given two lines- UV and ST.

We can find the length of the lines using distance formula. According to distance formula, distance between two points- (x1, y1) and (x2, y2) is given as-

[tex]\sqrt{(x2-x1)^{2} + (y2 - y1)^{2} }[/tex]

Here, for UV,

the two endpoints are- (1,0) and (4,3)

thus, the length of UV will be-

[tex]\sqrt{(4-1)^{2} + (3 - 0)^{2} }[/tex]

= [tex]\sqrt{(3)^{2} + (3 )^{2} }[/tex]

= [tex]\sqrt{9 + 9 }[/tex]

= [tex]\sqrt{18}[/tex]

= [tex]3\sqrt{2}[/tex]

Similarly, the two endpoints of ST are- (-2,-1) and (1,-4)

thus, the length of UV will be-

[tex]\sqrt{(1+2)^{2} + (-4 +1)^{2} }[/tex]

= [tex]\sqrt{(3)^{2} + (-3)^{2} }[/tex]

= [tex]\sqrt{9 + 9 }[/tex]

= [tex]\sqrt{18}[/tex]

= [tex]3\sqrt{2}[/tex]

So we can see that UV = ST = [tex]3\sqrt{2}[/tex], which means that both of them are congruent. Hence, option 1 is the correct answer.

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Your question was incomplete. Check for the missing figure below.

Given [tex]$\triangle RST \cong \triangle XYZ$[/tex]. Points [tex]$P$[/tex] and [tex]$W$[/tex] lie on [tex]$ST$[/tex] and [tex]$YZ$[/tex], respectively. Which of the following statements are true?
A) If [tex]$P$[/tex] is the midpoint of [tex]$\overline {ST}$[/tex] and [tex]$W$[/tex] is the midpoint of [tex]$\overline {YZ},$[/tex] then [tex]$\triangle RSP\cong \triangle XYW$[/tex].

B) If [tex]$\overline {RP}$[/tex] bisects [tex]$\angle SRT$ and [tex]$\overline {XW}$[/tex] bisects [tex]$\angle YXZ$[/tex], then [tex]$\triangle RSP\cong \triangle XYW$[/tex].

C) If [tex]$RP=XW$[/tex], then [tex]$\triangle RSP\cong \triangle XYW$[/tex].

D) If [tex]$\overline {RP}\perp\overline {ST}$[/tex] and [tex]$\overline {XW}\perp\overline{YZ}$[/tex], then [tex]$\triangle RSP\cong \triangle XYW$[/tex].

Answers

The triangles ΔRST and ΔXYZ are congruent, then all the same construction make triangles congruent. All the options are correct.

What is the triangle?

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

If two triangles are congruent, then the ratio of the corresponding sides will be one.

The triangles ΔRST ≅ ΔXYZ. Points P and W lie on ST and YZ, respectively.

The diagram is given below.

A) If P is the midpoint of ST and W is the midpoint of YZ then ΔRSP ≅ ΔXYW is true.

B) If RP bisects ∠SRT and XW bisects ∠YXZ, then ΔRSP ≅ ΔXYW is true.

C) If RP = XW, then ΔRSP ΔXYW is true.

D) If RP ⊥ ST and XW ⊥ YZ, then ΔRSP ≅ ΔXYW is true.

All the options are correct.

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What size heater will be required to heat the water in a swimming pool from
70°F to 72 °F in 1 hour if the appliance is 100% efficient and the pool holds
20,000 gallons of water?
A. 166,000 Btu/h
B. 332,000 Btu/h
C. 86,000 Btu/h
D. 224,000 Btu/h


Ps. the answer is B but i want an explanation on how to work through the problem

Answers

Answer:

B

Step-by-step explanation:

the British thermal unit (BTU or Btu) is a unit of heat; it is defined as the amount of heat required to raise the temperature of one pound of water by one degree Fahrenheit.

and it is outdated. your teacher and the manufacturer should use joules as metric.

1 BTU ≈ 1055 joules

anyway, so, the solution has several parts.

we need to find how many pounds of water are in a gallon.

and then multiply by the amount of gallons (20 000) and the amount of degrees (2 from 70 to 72).

and after a little search on the internet we get

1 gallon of water = 8.34 pounds

so, we need to warm

20000×8.34 pounds of water by 2 degrees F.

that is

20000 × 8.34 × 2 = 333,600 BTU

if we use only the rounded value of pounds per gallons (8.3), this would be

20000 × 8.3 × 2 = 332,000 BTU

so in any case, B is the right answer (as being the closest to the real result), which is the situation with any size classification of devices : reality is somewhere close by, but never meets the exact specifications.

A mining company owns two mines. These mines produce an ore that can be graded into two classes: regular grade and low grade. The company must produce

at least 420 tons of regular-grade and 480 tons of low-grade ore per week. The first mine produces 6 tons of regular-grade and 16 tons of low-grade ore per

hour. The second mine produces 18 tons of regular-grade and 8 tons of low-grade ore per hour. The operating cost of the first mine is $20,500 per hour, and the

operating cost of the second mine is $10,200 per hour. The first mine can be operated no more than 55 hours a week, and the second mine can be operated no

more than 36 hours a week. How many hours per week should each mine be operated to minimize the cost?

Answers

The number of hours to operate the mines to minimize cost are Mine 1 hour = 26.5 hours and Mine 2 hour = 14.5 hours

How to determine the number of hours?

The given parameters can be represented using the following table of values

                              Mine 1 (x)              Mine 2 (y)   Available

Regular grade          6                            18             420

Low grade               16                             8              480

Operating cost      20500                     10200

Time                        55                              36

From the table, we understand that we are to minimize cost

This means that:

Objective function: C = 20500x + 10200y

Subject to:

6x + 18y >= 420

16x + 8y >= 540

Next, we plot the constraints on a graph (see attachment)

From the graph, we have

(x, y) = (26.5, 14.5)

This means that

Mine 1 hour = 26.5 hours

Mine 2 hour = 14.5 hours

Hence, the number of hours to operate the mines to minimize cost are Mine 1 hour = 26.5 hours and Mine 2 hour = 14.5 hours

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What is the domain of the function y = 3 l n x graphed below?

On a coordinate plane, a curve starts in quadrant 4 and then increases up into quadrant 1. It crosses the x-axis at (1, 0).

Answers

The domain of the function y = 3 ln x is (0, ∞) .

In mathematics, the logarithmic function is the inverse of power.The domain of a function is the set of inputs or x-values ​​on which the function is defined.

The graph of the function y = 3ln x is given below .

Then , coordinate point (1, 0)

The logarithmic function y = log x has the domain x > 0 (or) (0, ∞).

This is a logarithmic function. An important property of logarithms is that the domain cannot be denied. The same is true for x=0, since the logarithm of negative numbers is undefined.

The image attached shows the graph of this function, there you can notice its domain restriction.

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Is the relation a function yes or no circle the order pairs that cause the relation to not be a function

Answers

For the relations (tables) from left to right we have:

1) Is not a function, because the input 5 is mapped into two different values.

2) Is not a function, because the input -1 is mapped into two different values.

3) It is a function.

4) It is a function (the input x = 7 appears twice, but both times is mapped into the same output).

How to know if the relations are functions or not?

A relation is an operation that maps elements from one set called the domain (set of the inputs) into elements of another set, called the range (set of the outputs).

Now, a relation is a function only if each element of the domain is mapped into only one element of the range. So, if you see the same input in a table two times (related to two different outputs) then that table does not represent a function.

Then, for the tables reading from left to right, we have:

1) Is not a function, because the input 5 is mapped into two different values.

2) Is not a function, because the input -1 is mapped into two different values.

3) It is a function.

4) It is a function (the input x = 7 appears twice, but both times is mapped into the same output).

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I don’t understand this question

Answers

Answer:

This relation is not a function.

Step-by-step explanation:

Function

A relation is a function when each input (x-value) has a single output (y-value).

A function is one-to-one if each output (y-values) corresponds to exactly one input (x-values).

A function is many-to-one if some outputs (y-values) correspond to more than one (many) inputs (x-values).

In the given relation, one input value (x = 4) corresponds to two output values.  Therefore, this relation is not a function.

(See attached Relation Arrow Diagram).

Confused on Math
Solve the Systems
x+2y+2z=-2
2x-y-2z=-5
x+2y+4z=0
x=?
y=?
z=?

Answers

Answer:

Step-by-step explanation:

If angle YXZ measures 90 degrees, which statement is true?
(answers are below)

segment XZ is perpendicular to segment WY

WX =XY

segment XZ is a perpendicular bisector of segment WY

X is the midpoint of segment WY

Answers

The statement that is true is: A. segment XZ is perpendicular to segment WY.

What is a Perpendicular Lines?

When two lines intersect at a point to form right angles (90 degrees), both lines are said to be perpendicular to each other.

We are told that angle YXZ is equal to 90 degrees. This is the angle formed at the point where segment XZ intersects segment WY at point X.

This means that both lines are perpendicular to each other.

Therefore, the statement that is true is: A. segment XZ is perpendicular to segment WY.

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PLEASE HELP FAST I ONLY HAVE ONE HOUR!!!!!!

Answers

The interpretation of the y-intercept of the model is (d) when the attendance is 0, the number of wins is 15.2

How to interpret the y-intercept of the model?

The equation of the linear regression model is given as

y = 4.9x + 15.2

The y-intercept of the model implies that

x = 0

Substitute x = 0 in the equation of the linear regression model given as

y = 4.9x + 15.2

So, we have

y = 4.9 x 0 + 15.2

Evaluate the product

So, we have

y = 0 + 15.2

Evaluate the sum

So, we have

y = 15.2

Hence, the interpretation of the y-intercept of the model is (d) when the attendance is 0, the number of wins is 15.2

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-2x + 14y = -29
x-7y=19
elimination process

Answers

Answer:

no solution

Step-by-step explanation:

Multiplying the second equation by 2 gives 2x-14y=38.

Adding this to the first equation, we get 0=9, and thus there is no solution.

List the domain and range of the relation.
{(5,-3), (2.2), (0, -3), (2.1) (5,3)}

Answers

The domain of the relation is x = {5, 2, 0, 2, 5} and the range is y = {-3, 2, -3, 1, 3}

The domain of a function is the set of inputs that are accepted by the function. The range, also known as the codomain, is the set of all the output values of the function.

Here, we are given a relation with the following set of solutions-  

{(5,-3), (2,2), (0, -3), (2,1) (5,3)}

We know that all x values will form the domain and all the y values will make up the range.

Here the x values are: 5, 2, 0, 2, 5

and the y values are: -3, 2, -3, 1, 3

Thus, the domain of the relation is x = {5, 2, 0, 2, 5} and the range is y = {-3, 2, -3, 1, 3}

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slope of (-8,-3) and (-1,-2)

Answers

Solution :-

As we know that,

m = y_2 - y_1 / x_2 - x_1

Therefore ,

>> m = -2 - (-3) / -1 - (-8)

>> m = -2 + 3 / -1 + 8

>> m = 1 / 7

We have that the data are:

(x₁ = -8, y₁ = -3) and (x₂ = -1, y₂ = -2)

The slope is equal to the change in and with respect to change in X, or what rises when moving forward.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{Change \ in \ y}{Change \ in \ x} \ \longmapsto \ \ m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} } \end{gathered}$}}[/tex]

The change in X is equal to the subtraction in the X coordinate (also called advance), and the change in and is equal to the subtraction in the coordinate and (also called elevation).

Introduce the values of x and y In the equation to find the slope.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{-2-(-3)}{-1-(-8) } } \end{gathered}$}}[/tex]

[tex]\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{1}{7} } \end{gathered}$}}}[/tex]

The slope of (-8, -3) and (-1, -2) is 1/7.

Factorize the equation

Answers

Answer:

[tex]\sqrt{x^2+2}\left(x^2+x+2\right)^2[/tex]

Step-by-step explanation:

Given equation:

[tex](x^2+2)^{\frac{5}{2}}+2x(x^2+2)^{\frac{3}{2}}+x^2\sqrt{x^2+2}[/tex]

[tex]\textsf{Rewrite the exponents }\frac{5}{2} \textsf{ as } \left(\frac{1}{2} \cdot 5\right)\textsf{ and }\frac{3}{2} \textsf{ as }\left(\frac{1}{2} \cdot 3\right):[/tex]

[tex]\implies (x^2+2)^{\frac{1}{2} \cdot 5}+2x(x^2+2)^{\frac{1}{2}\cdot 3}+x^2\sqrt{x^2+2}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c:[/tex]

[tex]\implies \left((x^2+2)^{\frac{1}{2}}\right)^5+2x\left((x^2+2)^{\frac{1}{2}}\right)^3+x^2\sqrt{x^2+2}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{\frac{1}{2}}=\sqrt{a}:[/tex]

[tex]\implies \left(\sqrt{x^2+2}\right)^5+2x\left(\sqrt{x^2+2}\right)^3+x^2\sqrt{x^2+2}[/tex]

Factor out [tex]\sqrt{x^2+2}[/tex] from each of the three terms:

[tex]\implies \sqrt{x^2+2}\left[\left(\sqrt{x^2+2}\right)^4+2x\left(\sqrt{x^2+2}\right)^2+x^2\right][/tex]

[tex]\textsf{Factor the expression in the parentheses using} \quad a^2+2ab+b^2=(a+b)^2.[/tex]

[tex]\textsf{Let }a=\left(\sqrt{x^2+2}\right)^2 \textsf {and }b=x:[/tex]

[tex]\implies \sqrt{x^2+2}\left(\left(\sqrt{x^2+2}\right)^2+x\right)^2[/tex]

[tex]\textsf{Apply exponent rule} \quad \sqrt{a^2}=a:[/tex]

[tex]\implies \sqrt{x^2+2}\left(x^2+2+x\right)^2[/tex]

[tex]\implies \sqrt{x^2+2}\left(x^2+x+2\right)^2[/tex]

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