Answer:
(2, 6)
Step-by-step explanation:
Point G has a coordinate of x = 5, and y = 4, that is (5, 4).
If Lynn plots point G, such that:
G is 3 units to the left of point F, the x-coordinate of point G = 5 - 3 = 2
G is 2 units above point F, the y-coordinate of point G = 4 + 2 = 6.
Therefore, Lynn plotted point G at x = 2, and y = 6. Which is (2, 6)
Answer:2,6
Step-by-step explanation:5-3=2 4+2=6 2,6
)
X
4.8 m
6.5 m
A) 9.4 m
C) 4.4 m
B) 10.4 m
D) 8.1 m
Answer:
makes no sense
Step-by-step explanation:
Vehicles generally decrease in value around 14% per year. If you buy a vehicle priced at $39,500 , this can be modeled by the equation A=39500(0.86)t . Estimate the value of the vehicle after 4 years. Round to the nearest cent and do not round until the final calculation.
Rounding to the nearest cent, the estimated value of the vehicle after 4 years is approximately $23,726.20..
To estimate the value of the vehicle after 4 years, we can use the given equation A = 39500(0.86)^t, where A represents the value of the vehicle and t represents the number of years.
Substituting t = 4 into the equation:
A = 39500(0.86)^4
A ≈ 39500(0.5996)
A ≈ 23726.20
Rounding to the nearest cent, the estimated value of the vehicle after 4 years is approximately $23,726.20.
This estimation is based on the assumption that the vehicle's value decreases by 14% each year. The equation A = 39500(0.86)^t models the exponential decay of the vehicle's value over time. By raising the decay factor of 0.86 to the power of 4, we account for the 4-year period. The final result suggests that the value of the vehicle would be around $23,726.20 after 4 years of ownership.
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y = 3x - 2. What is the slope?
Answer:the slope is 3
Source: trust me bro
Write two equations in standard form for two lines that will have the same solution as 4x-5y=7
Answer:
7-4x/y=5
7+5y/x=4
Step-by-step explanation:
hope it's helpful
Answer:
8x - 10y = 14 is the first one
12x - 15y = 21 is the second :)
Step-by-step explanation:
im pretty sure its correct and i hope i could help !! :)
HELP PLEASE!! i’m giving 15 points for this!!
Answer:The picture did not load
Step-by-step explanation:Sorry
Q3. Given that the area of sector below is 85cm^2 work out its radius, marked p on the
diagram.
Give your answer correct to 1 decimal place
The radius of the circle, marked p on the diagram, is approximately 5.8 cm.
What is radius?Radius is a term used in geometry to describe the distance from the center of a circle to any point on the circumference. It is a line segment that has its two endpoints at the center of the circle and at any point on the circumference.
The area of a sector is equal to the fraction of the circle's area that the sector occupies multiplied by the area of the entire circle.
Therefore, the area of the sector is equal to (θ/360) × πr^2.
Since the area of the sector is given as 85 cm^2, we can rearrange the equation to get:
85 = (θ/360) × πr^2
Rearranging further, we get:
r^2 = (85 × 360)/(πθ)
Taking the square root of both sides, we get:
r = √((85 × 360)/(πθ))
Since the angle θ is not given, we cannot solve for r. However, we can approximate the angle θ to be equal to 360° since the sector occupies the entire circle.
Therefore, the radius of the circle is equal to:
r = √((85 × 360)/(π × 360))
r = √(85/π)
r ≈ 5.8 cm
Therefore, the radius of the circle, marked p on the diagram, is approximately 5.8 cm.
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(GIVING BRAINLIYEST)
7. what is the volume of these 2 objects
figure #1
smaller part
4x7x2= 56m
larger part
4x3x7= 84m
84+56= 140m³
figure #2
smaller part
2x4x3= 24m
larger part
4x4x12= 192m
192+24= 216in³
Answer:
3 is 140i think 4 is 396 (sorry if im wrong about 4)
Step-by-step explanation:
Suppose that continuous random variables X and Y have a joint probability density function given by: f X,Y
(x,y)={ c⋅x 2 y,0,0≤x≤2;0≤y≤2 otherwise 1. Define the mode of a continuous random variable to be the point at which the density is maximized, if such a point exists. What is the mode of YY?
2. What value of cc makes this a valid probability density function?
3. What is the expected value of YY, E[Y]E[Y]?
4. What is the variance of YY, V[Y]V[Y]?
And , the Y's variance is \(V[Y] = E[Y^2] - (E[Y])^2 = 2 - 1^2 = 1.\)To find the mode of Y, we need to find the value of y that maximizes the joint probability density function\(f_X, Y(x,y).\)
To do this, we can fix x to be a particular value and then find the value of y that maximizes \(f_X, Y(x,y).\)
For any fixed x between 0 and 2, the function\(f_X, Y(x,y)\) is maximized at y = 1, since this is the only value of y that depends on x and maximizes the function\(cx^2y.\) Therefore, the mode of Y is 1.
To find the value of c that makes this a valid probability density function, we need to ensure that the integral of \(f_X, Y(x,y)\)over the entire sky-plane is equal to 1. We can set up the integral as follows:
integral from 0 to 2 of (integral from 0 to 2 of cx^2y dy) dx
= integral from 0 to \(2 of [c*x^2/2 * y^2]\)evaluated from 0 to 2 dx
= integral from 0 to 2 of \(c*x^2 x2d\)
= [2c/3 * x^3] evaluated from 0 to 2
= (16c/3)
For this to equal 1, we must have c = 3/16. Therefore, the valid probability density function is:
f_X,Y(x,y) = { (3/16)x^2y, 0 <= x <= 2, 0 <= y <= 2; 0, otherwise }
To find the expected value of Y, we need to integrate Y times the joint probability density function f_X, Y(x,y) over the entire xy-plane:
E[Y] = integral from 0 to 2 of (integral from 0 to 2 of y*f_X, Y(x,y) dy) dx
= integral from 0 to 2 of \([(3/16)*x^2/2 * y^2]\) evaluated from 0 to 2 dx
= integral from 0 to 2 of (3/16)*x^2 dx
= [3/16 * x^3/3] evaluated from 0 to 2
= 1
Therefore, the expected value of Y is 1.
To find the variance of Y, we first need to find the second moment of Y by integrating Y^2 times the joint probability density function f_X, Y(x,y) over the entire xy-plane:
E[Y^2] = integral from 0 to 2 of (integral from 0 to 2 of y^2*f_X, Y(x, y) dy) dx
= integral from \(0 to 2 of [(3/16)*x^2/3 * y^3]\) evaluated from 0 to 2 dx
= integral from \(0 to 2 of (3/8)*x^2 dx\)
= \([3/8 * x^3/3]\) evaluated from 0 to 2
= 2
And , the Y's variance is
\(V[Y] = E[Y^2] - (E[Y])^2 = 2 - 1^2 = 1.\)
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Wyatt was out at a restaurant for dinner when the bill came. He wanted to leave a tip of 19%. What number should he multiply the cost of the meal by to find the total plus tip in one step?
Answer:
The cost of the meal should be multiplied by 1.19.---------------------------------------
Let the cost of the meal be x.
Adding a tip of 19%:
x + 19% = x + 0.19x = x (1 + 0.19) = 1.19xAnswer:
Wyatt should multiply with 1.19.
Step-by-step explanation:
Forming the expression,
→ 1 + (19% of 1)
Now the required number is,
→ 1 + (19% of 1)
→ 1 + ((19/100) × 1)
→ 1 + (19/100)
→ 1 + 0.19 = 1.19
Hence, required number is 1.19.
Evaluate this expression.
3^-2
Answer:Exact Form: one over 9
1
9
Step-by-step explanation: ,..
If t = 45 and s = 9, what does t + s equal?
Answer:
it will 54
Step-by-step explanation:
1. If t= 45 then t+s it you put the t into the equation. So it will be
45 + s
2. And put s=9 into the equation. It will be
45 + 9
3. Just add them together
45 + 9 = 54
Answer: 54
Answer:
54
Step-by-step explanation:
We know t = 45 and s = 9, so all we have to do is substitute these values to each corresponding variable in the expression t + s.
t + s =
45 + 9 =
54
So, t + s is equal to 54
Hope this helps!
Write an expression, in terms of h, for the perimeter of this triangle.
Simplify your answer fully.
7
14-6h
3h+3
Answer:
P = 24 - 3h-----------------------------------
It is assumed the sides of the triangle are7, 14 - 6h and 3h + 3Perimeter is the sum of three sidesP = a + b + cP = 7 + 14 - 6h + 3h + 3 = (7 + 14 + 3) + (3h - 6h) = 24 - 3hAnswer:
Perimeter = -3h + 24
Step-by-step explanation:
Forming the expression,
→ 7 + (14 - 6h) + (3h + 3)
Let's simplify the expression,
→ 7 + (14 - 6h) + (3h + 3)
→ 7 + 14 - 6h + 3h + 3
→ (-6h + 3h) + (7 + 14 + 3)
→ -3h + 24
Hence, answer is -3h + 24.
Warm-Up
Jug
Use the diagram below to answer the questions.
Intro
K
P
M
Which are shown on the diagram? Check all that apply.
O
OKM
Ojk
OPK
OLJK
COM
Dong
KM, JK, PK, and MJ are shown on the diagram.
Then the correct options are B, C, D, and F.
Since, Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.
A line segment in mathematics has two different points on it that define its boundaries.
All the line segments will be
JK, JM, KM, MP, PK, and KL
The triangle KPM.
And the angle will be ∠LKJ, ∠PKM. ∠KMP. and ∠MPK.
Then the correct options are B, C, D, and F.
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3,998-(-7)= can you please help me with this problem
Answer:
4005
Step-by-step explanation:
3,998 - (-7) = ?
Two negative signs will make a positive sign.
3,998 - (-7) = 3998 + 7 = 4005
So, the answer is 4005
The time married men with children spend on child care averages 6.0 hours per week. You belong to a professional group on family practices that would like to do its own study to determine if the time married men in your area spend on child care per week differs from the reported mean of 6.0 hours per week. A sample of 40 married couples will be used with the data collected showing the hours per week the husband spends on child care. The sample data are contained in the table below. 1.4 4.9 8.5 5.2 10.2 2.6 7.2 2.6 11.1 10.6 2.3 7.8 1.8 8.7 2.1 4.5 5.3 3.5 8.8 6.7 2.9 10.8 8.4 4.9 5.7 9.8 0.9 11.9 3.5 8.7 6.5 6.5 2.0 9.7 a. What are the hypotheses if your group would like to determine if the population mean number of hours married men are spending in child care differs from the mean reported in your area? H : HA: # Ag b. What is the sample mean (to 1 decimal)? Calculate the value of the test statistic (to 2 decimals). What is the p-value? greater than .207 c. Select your own level of significance. What is your conclusion? Do not reject the null. We don't have enough evidence to disprove the reported time.
The null hypothesis (H0) would be that the population mean number of hours married men in your area spend on child care per week is equal to the reported mean of 6.0 hours per week.
The population mean number is equal to the reported mean according to null hypothesis. The alternative hypothesis (HA) would be that the population mean differs from the reported mean.
H0: μ = 6.0 hours/week
HA: μ ≠ 6.0 hours/week
b. To find the sample mean, we need to add up all of the values in the sample and divide by the number of values. The sample mean is 6.34 hours/week.
To calculate the test statistic, we can use the formula:
t = (x' - μ0) / (s / √n)
where x' is the sample mean, μ0 is the hypothesized mean (in this case, 6.0 hours/week), s is the sample standard deviation, and n is the sample size.
Plugging in the values, we get:
t = (6.34 - 6.0) / (3.23 / √40) = 0.34 / (0.53 / 6.32) = 0.34 / 0.08 = 4.25
The p-value is the probability of getting a result as extreme as the one we observed, given that the null hypothesis is true. In this case, we would need to use a t-distribution table or a computer program to find the p-value, since the sample size is small and the population standard deviation is unknown.
c. If we select a level of significance of 0.05, then we can use the p-value to make a decision about the null hypothesis. If the p-value is less than 0.05, we would reject the null hypothesis and conclude that the population mean differs from the reported mean. If the p-value is greater than 0.05, we do not have enough evidence to reject the null hypothesis and would conclude that the population mean is likely to be the same as the reported mean.
In this case, the p-value is greater than 0.207, so we do not have enough evidence to reject the null hypothesis. We would conclude that the population mean number of hours married men in your area spend on child care per week is likely to be the same as the reported mean of 6.0 hours per week.
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The functions f(x) and h(x) share a common x-intercept.
f(x) = x2+4x
It is true that the functions f(x) and h(x) share a common x-intercept.
How to obtain the x-intercepts of a function?On the definition of a function, the x-intercept is given by the value/values of x for which the function assumes a value of zero.
Function f(x) is defined as follows:
x² + 4x.
Hence the x-intercepts are obtained as follows:
x² + 4x = 0
x(x + 4) = 0
x = 0 and x + 4 = 0 -> x = -4.
On a graph, the x-intercept of a function is the value of x at which the graph of the function crosses the x-axis.
Hence the x-intercept of function h(x) is given as follows:
x = -4.
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Which data set could be represented by
the box plot shown below?
H
0 2 4 6 8
Choose 1 answer:
A
Creating box plots
B
C
D
10 12 14 16 18 20
3, 4, 8, 9, 9, 12, 12, 13, 13, 16, 18
3, 4, 7, 9, 9, 10, 12, 13, 13, 16, 18
3, 4, 8, 9, 9, 10, 12, 13, 13, 16, 18
2, 4, 7, 9, 9, 10, 12, 13, 13, 16, 18
The given box plot represented by the data sets in option A and B.
From the given box plot, we have
Minimum value = 3
Maximum value = 18
First quartile (Q1) = 7
Third quartile (Q3) = 13
Median = 10
Option A:
3, 4, 8, 9, 9, 12, 12, 13, 13, 16, 18
Median = 12
First quartile (Q1) = 8
Third quartile (Q3) = 13
Option B:
3, 4, 7, 9, 9, 10, 12, 13, 13, 16, 18
Median = 10
First quartile (Q1) = 7
Third quartile (Q3) = 13
Option C:
3, 4, 8, 9, 9, 10, 12, 13, 13, 16, 18
Median = 10
First quartile (Q1) = 8
Third quartile (Q3) = 13
Option D:
2, 4, 7, 9, 9, 10, 12, 13, 13, 16, 18
Median = 10
First quartile (Q1) = 7
Third quartile (Q3) = 13
Therefore, the correct options are B and D.
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21 cans of tomato paste of the same size have weight of 7300 grams. What is the weight of 5 cans.
Answer:
answer is 347.6
Step-by-step explanation:
21/7300= 347.6
Kevin has a ratio of 2 wrong answers to 7 correct answers on his math test. If he got 6 questions wrong, then how many did he answer correctly
Answer:
21
Step-by-step explanation:
2:7 Ratio
Since he got 6 wrong it 6:?
6/2 = 3
3*7=21
6:21
He got 21 right
what is the probability of 26/100 19/100 and 55/100
Answer:
1/3
Step-by-step explanation:
Hope this helps
Answer:
1/3
Step-by-step explanation:
E
Can anyone graph this problem in the picture
Answer:
The graph would be dotted at -2, and shaded in everything less than -2. Its the same thing as y=-2, but your adding a dotted line, and shading in everything less than/below -2.
Step-by-step explanation:
-Hope this helped
Answer:
see image
Step-by-step explanation:
If you are working with number lines, then put an open circle or round parenthesis on or over the -2 and draw an arrow to the left.
But more likely, if you are already graphing lines on the x-y-coordinate plane and are now learning about inequalities, the use a dashed horizontal line through -2 and shade below. See image.
Decide whether the rates are equivalent. Maria saves $50 in 4 months.
Ralph saves $60 in 5 months
Answer:
The rates are not equivalent since Maria saves $0.50 more per month than Ralph.
Step-by-step explanation:
We can determine if two rates are equivalent by comparing the rates at which they save per month.
Maria's savings per month:
Both 50 and 4 can be divided by 2, which gives us 25/2. As a regular number, this becomes 12.5/1 which means Maria saves $12.5 per month.
Ralph's savings per month:
Both 60 and 5 can be divided by 5, which gives us 12. Thus, Ralph saves $12 per month.
Thus, the rates are not equivalent as Maria saves $0.50 more per month than Ralph.
A portfolio manager generates a 5% return in Year 1, a 12% return in Year 2, a negative 6% return in Year 3, and a return of 2% (nonannualized) in the first quarter in Year 4. The annualized return for the entire period is the closest to __________.
The annualized return for the entire period is the closest to 10.5%.
To calculate the annualized return for the entire period, we need to consider the returns for each year and the return in the first quarter of Year 4. Since the returns are given for each period, we can use the geometric mean to calculate the annualized return.
The formula for calculating the geometric mean return is:
Geometric Mean Return = [(1 + R1) * (1 + R2) * (1 + R3) * (1 + R4)]^(1/n) - 1
Where R1, R2, R3, and R4 are the returns for each respective period, and n is the number of periods.
Given the returns:
Year 1 return: 5% or 0.05
Year 2 return: 12% or 0.12
Year 3 return: -6% or -0.06
First quarter of Year 4 return: 2% or 0.02
Using the formula, we can calculate the annualized return:
Annualized Return = [(1 + 0.05) * (1 + 0.12) * (1 - 0.06) * (1 + 0.02)]^(1/3) - 1
Annualized Return = (1.05 * 1.12 * 0.94 * 1.02)^(1/3) - 1
Annualized Return = 1.121485^(1/3) - 1
Annualized Return ≈ 0.105 or 10.5%
Therefore, the annualized return for the entire period is approximately 10.5%.
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Help ASAP NEED HELP
Answer:
Its C
Step-by-step explanation:
first you would do the square which would be 3x3 which is 9 next you would do the rectangle which is 9x3 which is 27
9+27=36
Several batches of stew were made yesterday. Each batch required 1 and two-thirds pounds of meat. All together, 10 and StartFraction 5 over 6 EndFraction pounds of meat was used. Janice tried to find the number of batches of stew made. Her work is shown below.
10 and StartFraction 5 over 6 EndFraction divided by 1 and two-thirds = StartFraction 65 over 6 EndFraction divided by five halves = StartFraction 65 over 6 EndFraction times StartFraction 2 over 5 EndFraction = StartFraction 130 over 30 EndFraction = 4 and one-third
When she checked the answer by estimating, it did not make sense. What error did Janice make?
Janice converted a mixed number to the wrong improper fraction.
Janice added the numerators and denominators instead of multiplying.
Janice did not change the division problem to multiplication.
Janice did not convert the improper fraction to a mixed number correctly in the answer.
Mark this and return
The error that Janice made is that she did not convert the improper fraction StartFraction 130 over 30 EndFraction to a mixed number correctly in her final answer.
The error that Janice made can be identified by analyzing her calculations. Let's examine each step she took:
Step 1: 10 and StartFraction 5 over 6 EndFraction divided by 1 and two-thirds
In this step, Janice correctly converted the mixed number to an improper fraction, which becomes 10 and StartFraction 5 over 6 EndFraction = StartFraction 65 over 6 EndFraction.
Step 2: StartFraction 65 over 6 EndFraction divided by five halves
In this step, Janice attempted to divide the fractions. However, she made an error by adding the numerators and denominators instead of multiplying. This is incorrect. The correct operation for dividing fractions is to multiply the first fraction by the reciprocal of the second fraction. The reciprocal of five halves is two fifths.
Step 3: StartFraction 65 over 6 EndFraction times StartFraction 2 over 5 EndFraction
Here, Janice multiplied the fractions correctly. The product of these fractions is StartFraction 130 over 30 EndFraction.
Step 4: StartFraction 130 over 30 EndFraction = 4 and one-third
In this step, Janice attempted to convert the improper fraction to a mixed number. However, she made another error in her calculation. The fraction StartFraction 130 over 30 EndFraction is not equal to 4 and one-third. The correct conversion would yield 4 and two-sixths or 4 and one-third.
Therefore, the error that Janice made is that she did not convert the improper fraction StartFraction 130 over 30 EndFraction to a mixed number correctly in her final answer.
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4. Suppose y varies directly with x. If y = 6 when x = -2, find x when y = 15.
Answer:
x is -7.5 or -14/2 or -7½
Step-by-step explanation:
- Supposing y varies directly with x
\( { \tt{y \: \alpha \: x}} \\ \: \: \: \: { \tt{y = kx}} \)
[k is a constant of proportionality (k ≠ 0)]
- When y is 6, x is -2
\( \: \: \: \: \: \: \: \: \: { \tt{6 = (k \times ^{ - }2) }} \\ { \tt{6 = - 2k}} \\ { \tt{k = - 3 \: \: }}\)
- Therefore, the equation is;
\({ \boxed{ \tt{y = - 2x}}}\)
- What is x when y is 15
\({ \tt{15 = - 2x}} \\ { \tt{x = - 7.5}}\)
The value of x is -5
The equation for a direct variation is y = kx, where k is the constant of variation. Since we know that y = 6 when x = -2, we can solve for k:
k = y/x
k = 6/-2
k = -3
Therefore, the equation for this direct variation is y = -3x. To find x when y = 15, Substitute k = -3 and y = 15 into the equation
15 = -3x
Then solve x,
x = \(\frac{-15}{3}\)
x = -5
Therefore, when y = 15, x = -5.
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Please anyone that can help me
Answer:
\(|\frac{x}{y} |\)
Step-by-step explanation:
Pre-SolvingWe are given the following expression: \(\sqrt\frac{x^3y^5}{xy^7}\), where x > 0 and y > 0.
We want to simplify it.
To do that, we can first simplify what is under the radical, then take the square root of what is left.
Recall that when simplifying exponents, we don't want any negative or non-integer radicals left.
SolvingTo simplify what is under the radical, we can remember the rule where \(\frac{a^n}{a^m} = a^{n-m}\).
So, that means that \(\frac{x^3}{x} = x^2\) and \(\frac{y^5}{y^7} = y^{-2}\) .
Under the radical, we now have:
\(\sqrt{x^2y^{-2}}\)
Now, we take the square root of both exponents to get:
\(|xy^{-1}|\)
The reason why we need the absolute value signs is because we know that x > 0 and y > 0, but when we take the square root of of \(x^2\) and \(y^{-2}\) , the values of x and y can be either positive or negative, so by taking the absolute value, we ensure that the value is positive.
However, we aren't done yet; remember that we don't want any radicals to be negative, and the integer of y is negative.
Recall that if \(a^{-n}\), that is equal to \(\frac{1}{a^n}\).
So, by using that,
\(|x * \frac{1}{y} |\)
This can be simplified to:
\(|\frac{x}{y} |\)
50 POINTS
Ron has a homeowner’s insurance policy, which covers theft, with a deductible of d dollars. Two bicycles, worth b dollars each, and some tools, worth t dollars, were stolen from his garage. If the value of the stolen items was greater than the deductible, represent the amount of money the insurance company will pay algebraically.
Algebraically, the amount of money the insurance company will pay, represented as P, is equal to the total value of the stolen items (2b + t) minus the deductible (d).
Let's denote the amount of money the insurance company will pay as P. In this scenario, if the value of the stolen items is greater than the deductible, the insurance company will cover the loss, and Ron will receive compensation for the stolen items.
The total value of the stolen items can be calculated by adding the value of the bicycles (2b) and the value of the tools (t). So, the total value of the stolen items is 2b + t.
If the total value of the stolen items is greater than the deductible (d), then the insurance company will pay the difference between the total value and the deductible. Mathematically, this can be represented as:
P = (2b + t) - d
Therefore, algebraically, the amount of money the insurance company will pay, represented as P, is equal to the total value of the stolen items (2b + t) minus the deductible (d).
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Which graph represents f(x)= | x+3|
The graph of the function looks like V. And the vertex of the function will be at (-3, 0).
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
The function is given below.
f(x) = |x + 3|
Then the graph of the function looks like V. And the vertex of the function will be at (-3, 0).
The graph of the function is given below.
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HELP PLEASEEEEEEE!!!!!
The similar shapes EFGH and JKLM have the measurement of angle Z equal to 65°, the length x = 27.5 and the length of y = 12
What are similar shapesSimilar shapes are two or more shapes that have the same shape, but different sizes. In other words, they have the same angles, but their sides are proportional to each other. When two shapes are similar, one can be obtained from the other by uniformly scaling (enlarging or reducing) the shape.
Given that the shape EFGH is a smaller shape of JKLM, and they are similar, then:
the measure of angle Z is equal to 65°
the side EF corresponds to JK and side FG corresponds to KL, so:
8/20 = 11/x
x = (11 × 20)/8 {cross multiplication}
x = 27.5
the side EF corresponds to JK and EH corresponds to JM, so:
8/20 = y/30
y = (30 × 8)/20 {cross multiplication}
y = 12
Therefore, the similar shapes EFGH and JKLM have the measurement of angle Z equal to 65°, the length x = 27.5 and the length of y = 12
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