The measurement of ∠ F = 53 °.
Given,
Triangle EFG is dilated with a scale factor of 4 to create Δ E ' F ' G ' .
The measure of ∠ F ' is 53 °.
To find the measurement of angle F.
We know that a dilation creates similar figures i.e. it preserves the measure of angles.
Therefore, if Triangle EFG is dilated to form Δ E ' F ' G ', then the measure of ∠ F' = measure of ∠ F [Corresponding angles remains same]
⇒ The measure of ∠ F' = measure of ∠ F = 53 °
Hence, The measurement of ∠ F = 53 °.
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A cookie recipe calls for 3/4 of a cup of flour and makes 2dozen cookies. How many cookies can Julia make if she has 12cups of flour and wants to use it all
Given that 3/4 of a cup of flour is used to cook 2 dozen cookies,
[tex]\frac{3}{4}\text{ cup of flour}\equiv2\text{ dozen cookies}[/tex]Consider the conversion,
[tex]1\text{ dozen}=12\text{ units}[/tex]So it follows that,
[tex]\frac{3}{4}\text{ cup of flour}\equiv2\cdot12=24\text{ cookies}[/tex]Multiply both sides by 4/3 as follows,
[tex]\begin{gathered} \frac{3}{4}\cdot\frac{4}{3}\text{ cups of flour}\equiv24\cdot\frac{4}{3}\text{ cookies} \\ 1\text{ cup of flour}\equiv32\text{ cookies} \end{gathered}[/tex]So, 32 cookies can be cooked using 1 cup pf flour.
Given that Julia has 12 cups of flour, so the number of cookies that she can cook, is calculated as,
[tex]12\text{ cups of flour}\equiv32\cdot12=384\text{ cookies.}[/tex]Thus, Julia can make 384 cookies if she uses 12 cups of flour.
Which relation is a function? choose all the correct answers.[1] (1, 0), (3, 0), (1, 1), (3, 1) (1, 3) [2] (1, 1), (2, 2), (3, 3), (4, 4), (5, 8)[3] (2, 7), (6, 5), (4, 4), (3, 3), (2, 1)[4] (9, −3), (9, 3), (4, −2), (4, 2), (0, 0)
A relation is a function if an input value has only one output value. This means that a value of x must have only one value of y. Looking at the options,
1) for x = 1, there are different values of y. They include y = 0, 1, 3
for x = 3, y = 0, 1
This means that it is not a function
2) No value of x has more than one value of y. Thus, no input has more than one output. This means that it is a function
3) for x = 2, there are different values of y. They include y = 7, 1
This means that it is not a function
4) for x = 9, there are different values of y. They include y = - 3, 3
for x = 2, there are different values of y. They include y = - 2, 2
This means that it is not a function
Thus, the correct option is
[2] (1, 1), (2, 2), (3, 3), (4, 4), (5, 8)
express the quadratic function f(x)=3x^2 + 6x - 2 in the form a(x + h)^2 + k where a,h and k are constants
Answer:
Explanation:
Given:
[tex]f(x)=3x^2+6x-2[/tex]First, we do completing the square on the given function to express it into vertex form. So,
We write it in the form:
[tex]\begin{gathered} x^2+2ax+a^2 \\ \end{gathered}[/tex]And, factor out 3: So,
[tex]\begin{gathered} 3(x^2+2x-\frac{2}{3}) \\ \text{where:} \\ 2a=2\text{ or a=1} \\ \text{Hence} \\ 3(x^2-2x-\frac{2}{3}+1^2-1^2) \end{gathered}[/tex]Since:
[tex]\begin{gathered} x^2+2ax+a^2=(x+a)^2 \\ So, \\ x^2+2x+1^2=(x+1)^2 \end{gathered}[/tex]Then,
[tex]\begin{gathered} 3(x^2-2x-\frac{2}{3}+1^2-1^2) \\ =3((x+1)^2-\frac{2}{3}-1^2) \\ \text{Simplify} \\ f(x)=3(x+1)^2-2-3 \\ f(x)=3(x+1)^2-5 \end{gathered}[/tex]Therefore, the answer is:
[tex]f(x)=3(x+1)^2-5[/tex]Is my answer correct help please
Answer:
No, the correct answer is C.
Step-by-step explanation:
Five less than a number m = m - 5. and not 5 - m, so false.
a can of juice is 5.5 inches high and its base has a diameter or 6 inches what is the volume of the can? round to the nearest hundredth
According to the problem, the can of juice has the form of a cylinder, so we have to use the following formula
[tex]V=\pi(r)^2h[/tex]Where the radius is half the diameter, r = 3 in, h = 5.5 in, and pi = 3.14. Replacing these values, we have
[tex]V=3.14\cdot(3in)^2\cdot5.5in=155.43in^3[/tex]Hence, the volume of the can is 155.43 cubic inches.perform the calculation then round to the appropriate number of significant digits
The given expression is,
[tex]\frac{308.45}{1.12}[/tex]On division we get,
[tex]\frac{308.45}{1.12}=275.4017[/tex]On rounding we get, 275.402.
Find the length of line segment MN. Round to the nearest hundredths place.
First, look th the graph and set the coordinate of the points:
M = (mx,my)= (-1,2)
N = (nx,ny)= (4,0)
Now, apply the distance formula:
[tex]\text{Distance =}\sqrt[]{(mx-nx)^2+(my-ny)^2}[/tex]Replace with the coordinates:
[tex]D\text{ =}\sqrt[]{(-1-4)^2+(2-0)^2}[/tex][tex]D=\sqrt[]{(-5)^2+2^2}=\sqrt[]{25+4}=\sqrt[]{29}\text{ =5.3}9[/tex]Distance: 5.39
Trent earns scores of 60, 90, and 72 on three chapter tests for a certain class. His homework grade is 68 and his grade for a class project is 64. The overall average for the course is computed as follows: the average of the three chapter tests makes up 50% of the course grade; homework accounts for 10% of the grade; the project accounts for 20%; and the final exam accounts for 20%. What scores can Trent earn on the final exam to pass the course if he needs a "C" or better? A "C" or better requires an overall score of 70 or better, and 100 is the highest score that can be earned on the final exam. Assume that only whole-number scores are given. To obtain a "C" or better, Trent needs to score between and Inclusive.
A: 90% - 100%
B: 80% - 89%
C: 70% - 79%
D: 60% - 69%
F: 0% - 59%
Using the data provided:
[tex]0.5(\frac{60+90+72}{3})+0.1(68)+0.2(64)+0.2(x)\ge70[/tex]Where:
x = Score of the final exam in order to get at least a C.
Solve for x:
[tex]\begin{gathered} 37+6.8+12.8+0.2x\ge70 \\ 56.6+0.2x\ge70 \\ 0.2x\ge70-56.6 \\ 0.2x\ge13.4 \\ x\ge\frac{13.4}{0.2} \\ x\ge67 \end{gathered}[/tex]He needs to score between 67 and 100
After every score in a sample is multiplied by 5,the mean is found to be M = 40.What was the value for the original mean?
Since each of the data value is multiplied by 5, the new mean will be 5 times the original mean.
To get the original mean, we need to divide by 5.
Therefore the original mean is given by:
[tex]\frac{40}{5}=8[/tex]Answer: 8
Justin earns a base salary of $1500 per month at
the jewelry shop. He also earns a 3% commission
on all sales. If Just sold $82,975 worth of jewelry
last month, how much would he make for the
month including his base salary and commission?
The total salary earned by the Justin including the commission is $3959.25.
What exactly is the commission?A commission is extra money earned based on job performance.Members believe to be paid a specified amount of money depending on achievement marketed, sessions closed, recruits placed, and so on—when they agree to a commission-based position as well as commission framework (more by signing the agreement).For the given question;
The base salary of Justin is $1500.
The commission earned by Justin is 3%.
The jewelry of worth $82,975 last month.
Let x be the total commission earned.
Then,
3% of 82,975 = x
x = 3× 82,975 / 100
x = $2489.25
Total salary = base salary + commission
Total salary = $1500 + $2489.25
Total salary = $3959.25
Thus, the total salary earned by the Justin including the commission is $3959.25.
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Write an equation for the line through the point (x0,y0) with a slope of M in point slope form. Enter X0 and Y0 as y0. Use X and Y for variables names. Your equation should be of the form y=….
The equation of the line in point slope form is y = M(x - x₀) + y₀ .
The Point slope form of the line passing through the point (x₁,y₁) with slope m is given by the formula
(y - y₁) = m(x - x₁)
In the question ,
it is given that
the required line passes through the points (x₀ , y₀)
and the slope is M .
So, the point slope form equation of the line will be
( y - y₀) = M(x - x₀)
y - y₀ = M(x - x₀)
y = M(x - x₀) + y₀
Therefore , the equation of the line in point slope form is y = M(x - x₀) + y₀ .
The given question is incomplete , the complete question is
Write an equation for the line through the point (x₀,y₀) with a slope of M in point slope form. Your equation should be in the form of y = ... ?
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Real world compositions: A manufacturer sells a lawn mower to a store at $75 over the manufacturing cost. The store then sells the lawn mower for 140% of the price paid to the manufacturer. Determine the function of the price of a lawn mower in terms of the cost to manufacture the mower. What price will a customer pay for this mower if the manufacturer's cost was $230? Solve using composite functions
From the information provided, the lawn mower is sold at a price which is $75 over the cost of manufacture.
If the cost of manufacture is x, then we would have;
[tex]f(x)=x+75[/tex]Also, the store now sells the lawn mower for 140% of the price paid to the manufacturer. Therefore, we would have;
[tex]g(x)=f(x)1.4[/tex]Hence, if the manufacturer's cost is $230, the customer would be paying g(x). When the cost x is now given as 230, we wou;d have;
[tex]\begin{gathered} f(230)=230+75 \\ f(230)=305 \\ \text{Hence;} \\ g(x)=f(x)1.4 \\ g(x)=305\times1.4 \\ g(x)=427 \end{gathered}[/tex]ANSWER:
The function of the price is;
[tex]f(x)=x+75[/tex]The price a customer pays when the cost of manufacturing is $230 would now be $427
Real estate prices in a Denver neighborhood areNormally distributed with a mean price of $187,500 and astandard deviation of $12,500.ALDenver Neighborhood Real Estate Pricing
First, find the z-score of the two values $150,000 and $225,000
[tex]\begin{gathered} \text{z-score for }x_1 \\ z=\frac{x-\mu}{\sigma} \\ z=\frac{150000-187500}{12500} \\ z=\frac{-37500}{12500} \\ z_1=-3 \\ \; \\ \text{z-score for }x_2 \\ z=\frac{x-\mu}{\sigma} \\ z=\frac{225000-187500}{12500} \\ z=\frac{37500}{12500} \\ z_2=3 \end{gathered}[/tex]Since the z-scores are both 3 standard deviations away from the mean, by Emperical rule, we conclude that about 99.7% of the homes will be priced between $150,000 and $225,000.
You start driving north for 5 miles, turn right, and drive east for another 12 miles. At the end of driving, what is your straight line dissonance from you r starting point?
You start driving north for 5 miles, turn right, and drive east for another 12 miles
The angle between north and east = 90
So, x is the hypotenuse of the triangle
[tex]x=\sqrt[]{5^2+12^2}=\sqrt[]{25+144}=\sqrt[]{169}=13[/tex]so, the length = 13 miles
Graph the function. Plot five points on the graph of the function as follows.
Dylan’s boat can carry 40 people across a river. Last month, 2504 people road on Dylan’s boat. What is the least number of trips that Dylan could have made across that river.
The required least number of trips that Dylan would have made across the river is 62.
Given that,
Dylan’s boat can carry 40 people across a river. Last month, 2504 people rode on Dylan’s boat. What is the least number of trips that Dylan could have made across that river is to be determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
Total people road = 2504
Maximum people can road at single trip = 40
Least number of trip = 2504 / 40
Least number of trip = 62
Thus, the required least number of trips that Dylan would have made across the river is 62.
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1Choose the equation that matches the table below.X-101331521Ny-5-27O y = -7x+5O y = 5xOy=3x-2Oy=x-2
Given:
The coordinates are:
Find-:
The equation of a line
Explanation-:
The general equation is:
[tex]y=mx+c[/tex]Where,
[tex]\begin{gathered} m=\text{ Slope} \\ \\ (x,y)=\text{ Coordintes of line} \\ \\ c=\text{ y-intercept} \end{gathered}[/tex]The formula of the slope is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Choose any two points from the chart is:
[tex]\begin{gathered} (x_1,y_1)=(-1,-5) \\ \\ (x_2,y_2)=(0,-2) \end{gathered}[/tex]Then the slope is:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ m=\frac{-2-(-5)}{0-(-1)} \\ \\ m=\frac{-2+5}{0+1} \\ \\ m=\frac{3}{1} \\ \\ m=3 \end{gathered}[/tex]If the slope of the line is 3, then the equation becomes:
[tex]\begin{gathered} y=mx+c \\ \\ y=3x+c \end{gathered}[/tex]The value of "c" is:
Choose any one point.
[tex](x,y)=(0,-2)[/tex]The value of "c" is:
[tex]\begin{gathered} y=3x+c \\ \\ (x,y)=(0,-2) \\ \\ -2=3(0)+c \\ \\ -2=0+c \\ \\ c=-2 \end{gathered}[/tex]The equation of line is:
[tex]\begin{gathered} y=mx+c \\ \\ y=3x+(-2) \\ \\ y=3x-2 \end{gathered}[/tex]The equation of line is y = 3x-2
A boat is heading towards a lighthouse, whose beacon-light is 140 feet above the water. The boat’s crew measures the angle of elevation to the beacon, 10∘∘ . What is the ship’s horizontal distance from the lighthouse (and the shore)? Round your answer to the nearest tenth of a foot if necessary.
see the figure below to better understand the problem
we have that
tan(10∘)=140/x -----> by TOA
solve for x
x=140/tan(10∘)
x=794 ft
therefore
The answer is 794 feetAnswer:
Step-by-step explanation:
tan 10=140/x
x=140 / tan 10
x=794
Other than no solutions to use interval notation to Express the solution set and then graph the solution set on the number line
Answer
[tex]7(4x-4)-12x<4(1+4x)-3[/tex]Open the bracket
[tex]\begin{gathered} 28x-28-12x<4+16x-3 \\ collect\text{ the like terms} \\ 28x-12x_{}-16x<4-3+28 \\ 16x-16x<1+28 \\ 0<29 \end{gathered}[/tex]True for all x
[tex](-\infty,\infty)[/tex]How do you solve this?
Answer: B
Step-by-step explanation:
Answer: The answer is B
Step-by-step explanation:
Which of the following distribution belongs to discrete distribution?Even distributionOdd distributionInteger distributionReal numbers distribution
Explanation:
Discrete probability distribution:
It counts the occurrences that have countable or finite outcomes.
As the even numbers, odd numbers are countably infinite .
The real numbers are not countable.
So, the discrete distributions are Integer distribution.
A rectangle has an area ofx² + 9x + 14Find the expressions that represent the dimensions of the rectangle.O (x - 2) and (x - 7)O (x + 3) and (x + 6)(x + 2) and (x + 7)O (x + 1) and (x + 14)
x² + 9x + 14
The area of a rectangle is the product of the length and the width.
Factorizing the expression
x² + 9x + 14 = x² + 7x + 2x + 14
= x(x + 7) + 2(x + 7)
= (x + 7)(x + 2)
Hence the dimensions are (x + 2) and (x + 7)
Convert the following rectangular equation to polar form.Assume a>0 3x^2+3y^2-4x+2y=0
The given equation is,
[tex]3x^2+3y^2-4x+2y=0[/tex]The polar form of the equation can be determined by using the substitution
[tex]\begin{gathered} x=r\cos \theta \\ y=r\sin \theta \end{gathered}[/tex]using the substitution,
[tex]\begin{gathered} 3(x^2+y^2)-4x+2y=0 \\ 3(r^2\cos ^2\theta+r^2\sin ^2\theta)-4r\cos \theta+2r\sin \theta=0 \\ 3r^2-4rcos\theta+2r\sin \theta=0 \\ r(3r-4\cos \theta+2\sin \theta)=0 \\ r=0\text{ and }(3r-4\cos \theta+2\sin \theta)=0 \\ (3r-4\cos \theta+2\sin \theta)=0 \end{gathered}[/tex]Thus, the above equation gives the required polar form of the circle.
in the figure below, when the sun angle of elevation is 50°, the tree casts a shadow 80 feet long which can be used to find the height of the tree?
We can use the tangent of 50º. The height is approximately 95.34 ft
1) We can trace a right triangle over that mark and calculate that height, using a trigonometric ratio.
2) As we have the adjacent leg to that 50º angle and the opposite leg, we can use the tangent of 50º to find that height out.
[tex]\begin{gathered} \tan (50)=\frac{x}{80} \\ x=80\cdot\tan (50) \\ x\approx\text{ 95.34} \end{gathered}[/tex]3) Hence the answer is
We can use the tangent of 50º. The height is approximately 95.34 ft
I have an image can I show it to you?
Answer:
Rhombus
Explanation:
Looking at the given figure, the correct option is a Rhombus because the figure is a quadrilateral and all of its sides have the same length, opposites sides are parallel and opposite angles are equal.
Line segment AB has a midpoint C.If AC=17 and AB = 5x-6, then find the value of x
From that diagram that is drawn above, C is the midpoint of the line AB:
AC = 17
AB = 5x - 6
Since C is the midpoint of AB;
AB = 2AC = 2CB:
5x - 6 = 2(17)
5x - 6 = 34
5x = 34 + 6
5x = 40
x = 40/5
x = 8
Company operates stores under multiple banners in 13 states in the United States
Given:
Banners in 13 states in united states:
Total states in united state is 50.
(A)
Do not have store is:
[tex]\begin{gathered} =50-13 \\ =37 \end{gathered}[/tex]So in 37 states Company not operates any store.
(B)
Fraction do not have a store operates :
[tex]\begin{gathered} =\frac{37}{50} \\ =0.75 \end{gathered}[/tex]Geometry ? What is the coordinate of G if triangle E’F’G’ is created by dilating EFG with a scale factor of 4 about the origin
In order to dilate the figure around the origin by a scale of 4, we need to multiply the coordinates of each point by 4. This is done below:
[tex]\begin{gathered} F^{\prime}=(4\cdot-1,4\cdot2)=(-4,8) \\ G^{\prime}=(4\cdot2,4\cdot-2)=(8,-8) \\ E^{\prime}^{}=(4\cdot-2,,4\cdot0)=(-8,0) \end{gathered}[/tex]The coordinates are: F'(-4, 8), G'(8,-8) and E'(-8,0).
Show that (3 * 8 * x)⁷ = 6⁷ * 4⁷ * x⁷
Answer:
Q.E.D.
Explanation:
Given the expression
[tex](3\times8\times x)^7[/tex]We want to show that it is equal to the right-hand side.
Now, we note that: 8 = 2 x 4
Substituting 8 = 2 x 4, we have:
[tex]=(3\times2\times4\times x)^7[/tex]We then go further to get:
[tex]=(6\times4\times x)^7[/tex]Distributing the exponent, we have:
[tex]=6^7\times4^7\times x^7[/tex]This is the given right-hand side of the equation as required.
I need help with this question! I tried to work the question out but the answer I got is not an answer choice.
Given:
The given expression is
[tex]2\times72-3\times8+6\times5+4[/tex]Required:
We have to find the value of the given expression.
Explanation:
[tex]\begin{gathered} 2\times72-3\times8+6\times5+4 \\ =144-24+30+4 \end{gathered}[/tex][tex]\begin{gathered} =120+30+4 \\ =150+4 \end{gathered}[/tex][tex]=154[/tex]Final answer:
Hence the final answer is