Answer:√16 and 6.39 are rational numbers because they can be expressed as a ratio and a fraction.
(-2/3)(6/7)
Please show work if possible!
Determining the Input Value to Produce the Same Output Value for Two Graphed Functions A coordinate plane with 2 lines. The first line is labeled y equals f(x) and passes through (negative 1, 2), (0, 2), and (2, 2). The second line is labeled y equals g(x) and passes through (negative 0.5, negative 2), points at (0, negative 1), and (1, 1). The lines intersect at (1.5, 2). Use the graph to determine the input value for which f(x) = g(x) is true. x = 0.5 x = 1 x = 1.5 x = 2
Y equals f(x) is written on the first line, The second line, marked y = g(x). When the input is for either of the two functions, the result is x=0 and return the output is same value.
Given that,
Y equals f(x) is written on the first line, which also passes through (-1, 2), (0, 2), and (2, 2). The second line, marked y = g(x), points at (0, -1), passes through (-0.5, -2), and (1, 1). The lines come together at (1.5, 2).
We have to find the input value for which f(x) = g(x) is true using the graph. x = 0.5, x = 1, x = 1.5, x = 2.
The final two actions:
f(x)=-2/3(x+1)
g(x)=1/3(x-2)
The output are equation
f(x)=g(x)
-2/3(x+1)=1/3(x-2)
-2(x+1)=1(x-2)
-2x-2=x-2
-2x-x=-2+2
-x=0
x=0
When x = 0 is used as an input, the first two functions always return the same results.
f(x) traverses (-1,2), (0,2), and (2,2)
The paths that g(x) takes are (-0.5,-2), (0,-1), (1,1)
Therefore, When the input is for either of the two functions, the result is x=0 and return the output is same value.
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make it simple its x=1.5
Find the range and standard deviation of the set of data.
12,9,5,13,21
Answer: range = 16 standard deviation = 5
Step-by-step explanation:
Find the value of unknown
The value of x is 52° and the value of y is 104 ° as calculated using the chord properties of a circle.
A circle is defined as the locus of a moving point such that the distance of the point from a fixed point is always same.
A chord is a straight line joining any two points on a circle.The diameter is the largest chord.The angle subtended by the diameter at the center is always 90° .In the given figure AC is the diameter of the circle.
We know that the angle subtended by the chord is always 90°.
∴∠CBA = 90°
Now in ΔABC
∠ABC+∠BCA+ ∠CAB =180° (sum of all angles of a triangle is always 180°)
or, 90° + 38° + x° = 180°
or, 128° + x° =180°
or, x = 52°
Again in ΔDBC ,
DB=DC (radius of the circle)
∴∠DCB = ∠DBC (base angles of an isosceles triangles are equal)
∴∠DBC = 38°
Again in ΔDBC
∠DBC+∠BCD+ ∠CDB = 180° (sum of all angles of a triangle is always 180°)
or, y = 180° - 76°
or, y = 104°
Therefore the value of x is 52° and the value of y is 104 ° .
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Find the equation to the line below.
y=4/5x +?
Answer:
y =x - 1
Step-by-step explanation:
Slope intercept of a line: y =mx + bHere, m is the slope and b is the y-intercept.
Plot any two points on the line. (5,4) & (0,-1)
[tex]\sf \boxed{Slope =\dfrac{y_2-y_2}{x_2-x_1}}[/tex]
[tex]\sf =\dfrac{-1-4}{0-5}\\\\=\dfrac{-5}{-5}\\\\=1[/tex]
m = 1
At y-intercept x = 0. So, the -1 is the y-intercept.
m = 1 & b = -1
y = 1x + (-1)
Find B if A=70° and a + b = 80°
Answer:
B=30°
Step-by-step explanation:
Recall that the sum of interior angles of a triangle equals to 180°. So basically
[tex]A+B+\alpha+\beta=180^{\circ}[/tex]
[tex] \implies B + {70}^{ \circ} + {80}^{ \circ} = {180}^{ \circ} \\ \implies B = {180}^{ \circ} - {150}^{ \circ} \\ \implies B = \boxed{{30}^{ \circ} }[/tex]
A 28% income tax on a 80,000 income
Answer:
22,400
Step-by-step explanation:
80,000 x .28
Drag the purple points to show the location of G, H, and I after a 90° clockwise rotation around (0, 0) Then enter the coordinates of G', H, and I' in the table.
Answer:The value of coordinates G', H', and F' are (1,6) , ( 7,3) and (4 , 0) respectively.What are coordinates?A pair of numbers that employ the horizontal and vertical distinctions from the two reference axes to represent a point's placement on a coordinate plane. typically expressed by the x-value and y-value pairs (x,y).Coordinates are always written in the form of small brackets the first term will be x and the second term will be y.For example (5,3) here 5 will be for the x and 3 will be for the y.Another example is (9,0) here 9 is for x and 0 is for y.
Step-by-step explanation:
1. Solve the following polynomial equations by factoring
b. x4+4x3-8x-32=0
[tex]x^4+4x^3-8x-32=0[/tex]
Can be factoried into:
[tex](x^3-8)(x+4)=0\\[/tex]
Now you're looking for which values of x will make the equations in the brackets equal to 0, since as long as one is equal to 0, they will be multiplied into 0.
First we'll do:
[tex]x^3-8=0[/tex]
We're looking for what number cubed is equal to 8, which is 2.
Note: -2 is also a possibility, but if you plug it in, you'll see that it doesn't work.
Second we'll do:
[tex]x+4=0[/tex]
This one's pretty easy, x will be -4.
So your solutions are:
x = 2, -4
The solutions of the polynomial [tex]x^{4}[/tex] + 4x³ - 8x - 32 = 0 are 2 and -4.
What is a polynomial?Polynomials are sums of terms of the form k⋅xⁿ.
where k is any number
n is a positive integer.
Example:
2x + 4x - 7 is a polynomial
We have,
[tex]x^{4}[/tex] + 4x³ - 8x - 32 = 0 _______(1)
Divide into two parts.
[tex]x^{4}[/tex] + 4x³
-8x - 32
Take out the common from each part.
x³ ( x + 4 )
- 8 ( x + 4 )
Now,
We have,
x³ ( x + 4 ) - 8 ( x + 4 ) = 0
We can write this as:
(x³ - 8) (x + 4) = 0
Now,
We need to find the x values.
x³ - 8 = 0
x³ = 8
x = ±2
Put x = 2 in (1)
[tex]x^{4}[/tex] + 4x³ - 8x - 32 = 0
x = 2
16 + 32 - 16 - 32
0 = 0
x = 2 is satisfied
Put x = -2 in (1)
16 - 32 + 16 - 32 = 0
-64 ≠ 0
x = -2 is not satisfied
x + 4 = 0
x = -4 putting in (1)
256 - 256 + 32 - 32 = 0
0 = 0
x = -4 is satisfied
Thus the solutions of the polynomial [tex]x^{4}[/tex] + 4x³ - 8x - 32 = 0 are 2 and -4.
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Write the slope, intercept form of the equation of the line describe
Through (3,-2) and parallel to y=-x+5
Answer:
y = - x + 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - x + 5 ← is in slope- intercept form
with slope m = - 1
• Parallel lines have equal slopes , then
y = - x + c ← is the partial equation of the parallel line
to find c substitute (3, - 2 ) into the partial equation
- 2 = - 3 + c ⇒ c = - 2 + 3 = 1
y = - x + 1 ← equation of parallel line
A) The derivative of f(x) = 6x ^ 2 is given by f^ prime (x)=lim h——>0 ________=____.
B) The derivative of f(x) = 2x ^ 2 - 7x + 8 is given by f () lim h—->______=____.
Here we go ~
A.) Derivative of 6x² :
[tex]\qquad \sf \dashrightarrow \:f {}^{ \prime}(x) = \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{f(x + h) - f(x)}{h} [/tex]
[tex]\qquad \sf \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{6(x + h) {}^{2} - 6(x) {}^{2} }{h} [/tex]
[tex]\qquad \sf \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{6(x {}^{2} + 2xh + h {}^{2} ) {}^{} - 6(x) {}^{2} }{h} [/tex]
[tex]\qquad \sf \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{ \cancel{6x {}^{2}} + 12xh +6 h {}^{2} {}^{} - \cancel{6x{}^{2}} }{h} [/tex]
[tex]\qquad \sf \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{ 12xh +6 h {}^{2} {}^{} }{h} [/tex]
[tex]\qquad \sf \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{ \cancel{ h}( 12x +6h ) {}^{} {}^{} }{ \cancel{h}} [/tex]
[tex]\qquad \sf \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: 12x + 6h[/tex]
[tex]\qquad \sf \dashrightarrow \: 12x + 0[/tex]
[tex]\qquad \sf \dashrightarrow \: f {}^{ \prime} (x) = 12x[/tex]
B.) The derivative of f(x) = 2x² -7x + 8 :
[tex]\qquad \sf \dashrightarrow \:f {}^{ \prime}(x) = \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{f(x + h) - f(x)}{h} [/tex]
[tex]\qquad \sf \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{ 2(x + h) {}^{2} - 7(x + h) + 8 - (2 {x}^{2} - 7x + 8)}{h} [/tex]
[tex]\qquad \sf \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{ 2(x {}^{2} + 2xh + {h}^{2} ) {}^{} - \cancel{7x} + 7h+ \cancel8 - 2 {x}^{2} + \cancel{7x } - \cancel 8)}{h} [/tex]
[tex]\qquad \sf \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{ \cancel{ 2x {}^{2}} + 4xh + 2{h}^{2} {}^{} - 7h - \cancel{2 {x}^{2}} }{h} [/tex]
[tex]\qquad \sf \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{ \cancel {h}( 4x + 2{h}^{} {}^{} - 7) }{ \cancel{h} }[/tex]
[tex]\qquad \sf \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: 4x + 2{h}^{} {}^{} - 7[/tex]
[tex]\qquad \sf \dashrightarrow \: 4x - 0 - 7[/tex]
[tex]\qquad \sf \dashrightarrow \: f {}^{ \prime} (x) = 4x - 7[/tex]
Given:
p: x – 5 =10
q: 4x + 1 = 61
Which is the inverse of p → q?
If x – 5 ≠ 10, then 4x + 1 ≠ 61.
If 4x + 1 ≠ 61, then x – 5 ≠ 10.
If x – 5 = 10, then 4x + 1 = 61.
If 4x + 1 = 61, then x – 5 = 10.
The inverse of the statement p → q is "If x – 5 ≠ 10 then
4x + 1 ≠ 61"
How to determine the inverse of the statement?The statement is given as
p: x – 5 =10
q: 4x + 1 = 61
The inverse of a statement is such that:
The hypothesis and conclusion are negated.
This means that a conditional statement referred to as p → q would have the inverse of -p → -q.
When the above rule is applied on the statement
p: x – 5 ≠ 10
q: 4x + 1 ≠ 61
This means that the inverse of the statement p → q is "If x – 5 ≠ 10 then
4x + 1 ≠ 61"
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Answer:
A
MF up there wont tell u but its A
Find the HCF:
3x³ + 15x² and 2x³ - 50x
H.C.F of 3x³+15x² and 2x³-50x is x(x+5)
What is Number system?A number system is defined as a system of writing to express numbers.
The greatest common divisor of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers.
3x³ + 15x²
Factorize the given expression by taking out 3x²
3x²(x+5)
and the expression 2x³ - 50x
2x(x²-25)
2x(x+5)(x-5)
H.C.F of 3x³+15x² and 2x³-50x is x(x+5)
Hence, H.C.F of 3x³+15x² and 2x³-50x is x(x+5)
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Let f(x) = x^2 + 2 and g(x) = -3. Find f(x) • g(x).
A. X^3-6x^2+12x-6
B. X^3-5x^2+8x-6
C. X^3-3x^2+6x-6
D. X^3-2x^2+5x-6
Solve the inequality and express your answer in interval notation.
x^2+ 12x+7<0
The solution in interval form is given as (-∞, -6-√29
] or [-6+√29, ∞)
Inequality expressionGiven the quadratic inequality below;
x^2+ 12x+7<0
Using the general formula
x = -12±√12²-4(1)(7)/2(1)
x = -12±√144-28/2
x = -6±√116/2
x = -6±√29
Hence the solution in interval form is given as (-∞, -6-√29
] or [-6+√29, ∞)
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A map is drawn to a scale of 1/2 inch = 20 miles How many miles apart are two cities that are 3 1/4 inches apart on the map?
Work Shown:
1/2 = 0.5
1/4 = 0.25
0.5 inch = 20 miles, which is the given scale
1 inch = 40 miles, after multiplying both sides by 2
3.25 inches = 130 miles after multiplying both sides by 3.25
Find the equation the line with a slope of 2 and that passes
through the point (1, 6).
Enter your answer in slope-intercept form, y = mx + b
Answer:
y = 2x +4
Step-by-step explanation:
Equation of a line in slope-intercept form is
y = mx + b
where m is the slope and b is the y-intercept, the point at which the line crosses the y axis (at x = 0)
Given slope is 2 we get the equation as
y = 2x + b
We have to solve for b by plugging in the x and y values for point(1,6)
Thus we get y = 6 = 2(1) + b
Or 6 = 2 + b
b= 6-2 = 4
Equation in slope-intercept form is
y = 2x +4
Hi!
Apply the Point-Slope formula:
[tex]\textsl{y-y1=m(x-x1)}[/tex]◈Where:
y₁ -> the y-coordinate of the pointm -> slopex₁ -> x-coordinate◈We know that:
y₁ -> 6m -> 2x₁ -> 1◈Plug in the values:
[tex]\boldsymbol{y-6=2(x-1)}[/tex](simplify) [tex]\boldsymbol{y-6=2x-2}[/tex](add 6 to both sides) [tex]\boldsymbol{y=2x+4}[/tex][tex]\bigstar\textsf{\textbf{Solution: \boxed{\textsf{\textbf{2x+4}}}}}[/tex]
Have a great day!
I hope this helped!
-stargazing
Find the distance of the line segment below.
___ units
Answer:
let (5,4)=(x1,y1)
(-3,-2)=(x2,y2)
now, by using distance formula
we get distance between line segment =10 unit
therefore distance =10 units ans
Solution,
As the formula...
[tex] = \sqrt{( - 3 - 5 {)}^{2} + ( - 2 - 4 {)}^{2} } [/tex]
[tex] = \sqrt{( - 8 {)}^{2} + ( - 6 {)}^{2} } [/tex]
[tex] = \sqrt{64 + 36} [/tex]
[tex] = \sqrt{100} [/tex]
= 10 units...
☘☘☘....
Select the best answer for the question.
12. Which set is an example of like fractions?
A. 1/2 and 3/2
B.2/1 and 2/3
C. 10/10 and 5/5
D. 7/4 and 4/7
Answer:
A. 1/2 and 3/2
Step-by-step explanation:
You want to identify like fractions among the sets {1/2, 3/2}, {2/1, 2/3}, {10/10, 5/5}, and {7/4, 4/7}.
Like fractionsLike fractions are fractions that have the same denominator. Among the sets offered, the only one with denominators the same is ...
{1/2, 3/2}
Country A produces about six times the amount of diamonds in carats produced in country B.If the total produced in both countries is 28,000,000 carats
The diamonds produced by country A and B are 24,000,000 and 4,000,000 carats respectively.
Here, we are given that Country A produces about six times the amount of diamonds in carats produced in country B.
Let the diamonds produced by country B be x
Then, the diamonds produced by country A will be 6x
The total diamonds produced by the two countries = 28,000,000
Thus, we can get the following equation-
x + 6x = 28,000,000
7x = 28,000,000
x = 28,000,000/ 7
x = 4,000,000
⇒ 6x = 24,000,000
Thus, the diamonds produced by country A and B are 24,000,000 and 4,000,000 carats respectively.
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To swimmers Angie aTwo swimmers Angie and Beth from different states wanted to find out who had the fastest time for the 50 m freestyle when compared to her team which swimmer had the fastest time when compared to her team
Using z-scores, it is found that due to the lower z-score, Beth had the fastest time when compared to her team.
What is the missing information?This problem is incomplete, but researching on the internet, we have that:
Angie had a time of 26.2 seconds, while her team had a mean time of 27.2 seconds with a standard deviation of 0.8 seconds.Beth had a time of 27.3 seconds, while her team had a mean time of 30.1 seconds with a standard deviation of 1.4 seconds.What are z-scores?The z-score of a measure X in a distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.For this problem, lower times means that the swimmer is faster, hence the swimmer that had the fastest time when compared to her team is the swimmer with the lowest z-score.
Angie's z-score is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (26.2 - 27.2)/0.8
Z = -1.25.
Beth's z-score is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (27.3 - 30.1)/1.4
Z = -2.
Due to the lower z-score, Beth had the fastest time when compared to her team.
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Find the sum. 2 3/8 + 4 4/8
For a total accumulated amount of $3688.86, a principal of $2000, and a time period of 5 years, use the compound interest formula to find r, if interest is compounded
monthly.
r=
The interest rate required to get a total amount of $3,688.86 from compound interest on a principal of $2,000.00 compounded 12 times per year over 5 years is 12.306% per year.
Given,
The total amount (A)= $3688.86
Principal (P) = $2000
time period (t) = 5 years.
compounded monthly (n) = 12
rate of interest per year = ?
we know that r=n[(A/P)¹/ⁿt -1]
substitute the above values.
r = 12 × [(3688.86/2000)¹/⁽¹²⁾⁽⁵⁾ - 1]
r = 12 × [(1.84443)¹/⁶⁰ - 1]
r = 12 × 0.0102
r = 0.12306
Now convert r to R as a percentage.
R = r × 100
R = 0.12306 × 100
R = 12.306%
Hence the rate of interest compounded monthly is 12.306%
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The expense function is E= 15q+750.
A) What is the price per item?
B) What is the variable cost of 100 units?
C) What is the fixed expense?
D) What is the expense if you needed 100 units?
The price per item is 765.
The variable cost of 100 units is 1500.
The fixed expense is 750.
The expense for 100 units is 2250
What is the fixed cost and variable cost?Fixed costs are costs that do not vary with output. e,g, rent, mortgage payments. Variable cost change with the unit of output.
The variable cost of 100 units = variable cost per unit x number of units
15 x 100 = 1500
The expense for 100 units = fixed cost + total variable cost
750 + 1500 = 2250
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After 30 baseball games Aaron Smith had 24 hits. If after 100 games he had 80 hits, what is his average hits per baseball game?
Aaron Smith would has average hits per baseball game as 0.79 hits per game.
What is the interpretation of average?Average provides ill information in case of skewed data.
Arithmetic mean is the best central measure available for representing the values of a data set. It is also called average of the values of the considered data set. It serves as predicted value(in case no other information of the data is available) of that data set.
WE have been given that After 30 baseball games Aaron Smith had 24 hits. If after 100 games he had 80 hits, then he would has average hits per baseball game;
Average = Hits in game / number of games
Average = 24- 80 / 30-100
Average = 56 / 70
Average = 0.79 hits per game
Hence, Aaron Smith would has average hits per baseball game as 0.79 hits per game.
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∠J and ∠E are congruent. If ∠J = (6x + 4)° and ∠E = (2x + 32)°, then what is the value of ∠E?
Answer: 46
Step-by-step explanation:
Since we know that angles J and E are congruent, we can do the equation 6x + 4 = 2x +32. We then solve for x which gives us 7. After that, we plug in the 7 into the equation for E which would be = 2(7) + 32. Once we solve that, we end up with 46.
Sally is running laps around a track. She runs 12 laps to warm up. Then she runs 13² laps.
How many laps does Sally run in all? Move numbers to the boxes to show the answer.
Answer:
181
Step-by-step explanation:
Sally is running laps around a track. She runs 12 laps to warm up. Then she runs 13² laps.
First write the equation. we know she alr ran 12 laps so its going to be +12
to 13^2. so the equation will be 12+13^2 then using PEMDAS we know that we have to do the exponents first so 13^2 is just 13 * 13 which is 169. so now the equation is 169+12 now just add. the answer is 181
=?
२०
21090 (x -1 ) + 109.07 = 1
)
The value of "x" which will satisfy the equation [{21090(x -1 ) + 109.07 } = 1] is 1.01.
As per the question statement, we are provided with an equation [tex][{21090(x -1 ) + 109.07 } = 1][/tex].
We are required to solve the above mentioned equation for "x", such that the value of x when substituted in the equation, satisfies the same.
To solve this question, we will simply use the methods of rearranging and opening up of brackets, as shown below.
[tex][{21090(x -1 ) + 109.07 } = 1] \\or, 21090x - 21090+109.07=1\\or, 21090x - (21090-109.07)=1\\or, 21090x - 20980.93=1\\or, 21090x=(1+20980.93)\\or, 21090x=20981.93\\or,x=\frac{21090}{20981.93}\\or,x=1.00515\\or,x=1.01[/tex]
Therefore, the value of "x" which will satisfy the equation
[{21090(x -1 ) + 109.07 } = 1] is 1.01.
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The circle below has center P, and its radius is 6in. Given that =m∠QPR170°, find the length of the major arc QSR.
The length of the major arc QSR is 39.77 inches
How to find the length of the major arc QSR?The given parameters are:
m∠QPR = 170 degree
Radius, r = 6 inches
The length of the major arc QSR is calculated as:
Arc length = (360 - Angle/360) * 2πr
Substitute the known values in the above equation
Arc length = (360 - 170/360) * 2 * 3.14 * 6
Evaluate the difference
Arc length = (190/180) * 2 * 3.14 * 6
Evaluate the product
Arc length = 39.77
Hence, the length of the major arc QSR is 39.77 inches
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7.) Given 9x-27y = 81
D.) Does the line RISE or fall?
E.) Why?
Answer: rises; your slope is positive
Every single time your slope is positive, your line goes upward.
Every time your slope is negative, however, your line goes downward.
Rearrange 9x - 27y = 81 to -27y = -9x + 81 because we want to put our equation into slope intercept so that we can eventually get our 'y' all by itself.
Divide by -27 for every variable.
Your slope intercept form should now look like this; y = 1/3x - 3
Now that we're completely done or that we have 'y' by itself, it's safe to say that our answer is 1/3, which is, also, positive.
Hope this helps, dawg.