Answer:
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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).
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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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
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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Factorize the equation
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]
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
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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The sum of three times a number and nine is 12 
Answer:
1
Step-by-step explanation:
let the number be n
3n + 9 = 12
3n = 12 - 9 = 3
n= 3/3
n= 1
I don’t understand this question
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).
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].
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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List the domain and range of the relation.
{(5,-3), (2.2), (0, -3), (2.1) (5,3)}
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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Is the relation a function yes or no circle the order pairs that cause the relation to not be a function
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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Which of the following represents "the square of the sum of a number and 4 is 36"?
Ox²+42=36
(x+4)2 = 36
Ox²+4=36
Answer:
[tex](x + 4)^{2}[/tex] = 36
Step-by-step explanation:
So the "sum of a number and 4" is what gets squared and that together is equal to 36.
Confused on Math
Solve the Systems
x+2y+2z=-2
2x-y-2z=-5
x+2y+4z=0
x=?
y=?
z=?
Answer:
Step-by-step explanation:
slope of (-8,-3) and (-1,-2)
Solution :-
As we know that,
m = y_2 - y_1 / x_2 - x_1Therefore ,
>> 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.Rewrite, using the distributive
property.
4(2x + 5) = [?]x + [ ]
Step-by-step explanation:
8x+20 is the answer ......
just need help with some of them at least 5 questions please already did the first one. i put 90 points please help.
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 equationsFrom 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
2¹
= 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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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}.
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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The length of a rectangle is nine more than triple the width. If the perimeter is 154 inches, find the dimensions.
Answer:
Length = 60 inches
Width = 17 inches
Step-by-step explanation:
Let width = w
Length = 3w + 9
Perimeter = 154
Perimeter = 2(length + width)
2(3w + 9 + w) = 154
8w + 18 = 154
8w = 154 - 18
8w = 136
w = 136/8
w = 17 inches
Length = 3w + 9 = 3(17) + 9 = 60 inches
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.
Answer:
$95.88
Step-by-step explanation:
multiply 6 by 17 and get 102
multiply 102 by 0.94 and get 95.88
Which expression shows another way to write -2/5 divided by 3/2?
The expression that shows another way to write -2/5 divided by 3/2 will be -2/5 ÷ 3/2.
How to calculate the value?It should be noted that an expression simply shows the relationship between the variables.
Therefore, the expression that shows another way to write -2/5 divided by 3/2 will be:
= -2/5 ÷ 3/2
= -2/5 × 2/3
= -4/15.
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25 25
4
2º
A
=
25.
=
C=
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
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?
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 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
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.
it is math for evaluating functions please help
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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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?
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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Can somebody help me if you know what this is
Answer:The LCM of 15 and 20 is 60.
Step-by-step explanation: I used the internet/gggle
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
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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-5•g(4)-1 If g(x)=1-3/4x
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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Find the lengths of UV and ST and determine whether they are congruent.
Hint: Congruent line segments have the same length.
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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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
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.
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.
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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