The equations of the transformed graphs are [tex]f(x) = \frac 23\sqrt{x - 3}[/tex], [tex]f(x) = 8\sqrt{x }-3[/tex], [tex]f(x) = \sqrt{\frac x7} + 5[/tex] and [tex]f(x) = \sqrt{-x} - 10[/tex]
How to transform the functions?The function #1
The function is given as::
[tex]f(x) = \sqrt{x}[/tex]
It is shifted right by 3 units.
So, we have:
[tex]f(x) = \sqrt{x - 3}[/tex]
It is shrunk vertically by a factor of 2/3
[tex]f(x) = \frac 23\sqrt{x - 3}[/tex]
Hence, the equation of the transformed graph is [tex]f(x) = \frac 23\sqrt{x - 3}[/tex]
The function #2
The function is given as::
[tex]f(x) = \sqrt{x}[/tex]
It is stretched vertically by a factor of 8
[tex]f(x) = 8\sqrt{x }[/tex]
It is shifted down by 3 units.
So, we have:
[tex]f(x) = 8\sqrt{x }-3[/tex]
Hence, the equation of the transformed graph is [tex]f(x) = 8\sqrt{x }-3[/tex]
The function #3
The function is given as::
[tex]f(x) = \sqrt{x}[/tex]
It is stretched horizontally by a factor of 7
[tex]f(x) = \sqrt{\frac x7}[/tex]
It is shifted up by 5 units.
So, we have:
[tex]f(x) = \sqrt{\frac x7} + 5[/tex]
Hence, the equation of the transformed graph is [tex]f(x) = \sqrt{\frac x7} + 5[/tex]
The function #4
The function is given as::
[tex]f(x) = \sqrt{x}[/tex]
It is reflected across the y-axis
[tex]f(x) = \sqrt{-x}[/tex]
It is shifted down by 10 units.
So, we have:
[tex]f(x) = \sqrt{-x} - 10[/tex]
Hence, the equation of the transformed graph is [tex]f(x) = \sqrt{-x} - 10[/tex]
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A map has the scale 1/3inch = 8 miles. If city a and city b are 12 inches apart on my map then how far apart are the city’s in real life
PLEASE HELP ASAP I NEED TO PASS SUMMER SCHOOL ASAP
ILL MARK BRAINLIEST
236,181 + 150,486
Answer:
236,181+150,486=386,667
Julio es un alumno que faltó a las clases por ayudar a su familia a elaborar y vender quesos. Decidió sacar fotocopias al cuaderno de su compañero. Si cada fotocopia vale S/ 0.30 y debe calcular cuánto dinero necesita para pagar las fotocopias. Identifica cada variable, expresa como función, grafica y responde: ¿Cuánto pagará por 29 copias?
Es urgente por favor
Aplicando el concepto de precio unitario, concluimos que Julio debe pagar 8.70 soles peruanos por la producción de 29 fotocopias de los apuntes de un compañero.
¿Cuánto dinero debe pagar Julio por las fotocopias?
En esta situación, Julio debe pagar por 29 fotocopias de los apuntes de un compañero suyo. El monto a pagar es el producto del número de copias y el coste unitario de cada fotocopia, es decir:
x = (0.30 PEN) · (29)
x = 8.70 PEN
Aplicando el concepto de precio unitario, concluimos que Julio debe pagar 8.70 soles peruanos por la producción de 29 fotocopias de los apuntes de un compañero.
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Find the measure of
Answer:
B. 30
Step-by-step explanation:
3x + 2x + x = 180 (angle sum of a triangle is 180)
6x = 180
x = 30
Answer:
B. 30
Step-by-step explanation:
3x + 2x + x = 180
6x = 180
x = 180/6
x = 30
I have redone this one assignment like 5 times and I keep getting it wrong help
A linear function f(x) on a table. How do I find a solution for the value of f(4)?
x | f(x)
3 | -3.5
4 |
5 | 5.5
6 | 10
7 | 14.5
Aria paid $75,000 for her house. its property value increased by 2.2% per year. when aria sold her house after eleven years, how much was it worth, to the nearest hundred dollars?a.$133,700b.$95,400c.$95,300d.$93,100 please select the best answer from the choices providedabcd
Answer:
D
Step-by-step explanation:
Converting percent to decimal : 2.2/100 = 0.022
Finding 2.2$ of $75k : 75,000 x 0.022 = $1,650 (also the increase in one year)
Finding how much it was worth after 11 years :
(75,000 x 0.022) x 11 = $18,150 or 1,650 x 11 = $18,150
Now add the product to the regular amount to find out the answer:
75,000 + 18,150 = $93,150 (which is how much it increased after 11 years)
100 cubed as a power of 10
Answer:
100
Step-by-step explanation:
10^2 is 100 therefore it is 100
Emma read the statement “the quotient of six and a number, x, is the same as negative two times the difference of x and 4.5.” She translated it as shown below. 6 x = negative 2 x minus 4.5 What errors did Emma make? Select two options. She should have used division to represent the quotient of six and x. She should not have included an equal sign. She should have used parentheses to show that Negative 2 is multiplied by (x minus 4.5). She should have subtracted the difference (x minus 4.5) from Negative 2. She should have used parentheses to show that Negative 2 is multiplied by (4.5 minus x).
The errors Emma made are
She should have used division to represent the quotient of six and xShe should have used parentheses to show that - 2 is multiplied by (x - 4.5)Writing an expression as an equationFrom the question, we are to determine the errors that Emma made
The given statement is
"The quotient of six and a number, x, is the same as negative two times the difference of x and 4.5"
"The quotient of six and a number, x", can be expressed as
6/x
"Two times the difference of x and 4.5", can be expressed as
2(x - 4.5)
Hence, the errors Emma made are
She should have used division to represent the quotient of six and xShe should have used parentheses to show that - 2 is multiplied by (x - 4.5)Learn more on Writing an expression as an equation here: https://brainly.com/question/13155862
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(05.05 HC) Figure ABCD has vertices A(-3, 2), B(2, 2), C(2, -4), and D(-3, -2). What is the area of Figure ABCD?
Answer:
I don't know how to answer this, sorry!
Step-by-step explanation:
.
In each part (a)-(d) below, some additional assumptions about the
picture are given. In each problem, determine whether the given
assumptions are enough to prove that the two triangles are similar; and
if so, what the correct correspondence of vertices is. If the two triangles
must be similar, prove this result by describing a sequence of similarity
transformations that maps one triangle to the other. If not, explain why
not.
a. The lengths AX and XD satisfy the equation 2AX = 3XD.
AX
b. The lengths AX, BX, CX, and DX satisfy the equation A
c. Lines AB and CD are parallel.
d. Angle XAB is congruent to angle XCD.
=
DX
CX
In the triangle, the fact that wee are given 2AX = 3XD isn't enough to prove similarity.
How to explain the triangle?a. In the question, we are given 2AX = 3XD. An arbitrary triangle AXB can be drawn where one extends AX and choose a point D on the extended line in order for 2AX = 3XD. Also, extend BX and choose a point C on the line so that 2BX = XC. Even though they both satisfy the condition, they're not similar.
b. We are given that AX/BX = DX/CX. When this is rearranged, we'll have AX/DX = BX/CX. In this case, let AX/DX = k. DX and AX will align upon rotation of 180°. The triangle can then be dilated by a factor of k. This brings about the mapping of triangle DXC to AXB. Therefore, the original triangle DXC is similar to AXB.
c. Lines AB and CD are parallel. Here, the dilation moves line CD onto line AB. Here, since the dilation moves D to a point on ray XA, D must move to A. Therefore, the rotation of triangle DXC is similar to AXB. Therefore, DXC is similar to AXB.
d. Here, angle XAB is congruent to angle XCD. This shows similarity and in this case, XCD is similar to XAB.
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Please I need help with this 2 calc questionssss. Thank you
Question 14
As we approaching from the negative side, [tex]|x-3|=3-x[/tex].
So, we have [tex]\lim_{x \to 3^{-}}=\frac{3-x}{x-3}=\frac{-(x-3)}{x-3}=\boxed{-1}[/tex]
and thus the limit exists at x=3.
Question 15
For the top part of the function, [tex](9-9)^{2}=0[/tex]
For the bottom part of the function, [tex]9-9=0[/tex]
As both one-sided limits are equal, L = 0, and thus the limit exists at x=9.
What are the exact steps to solve for the x-intercepts of f(x)= −4x2 + 4x + 8? What about −9 = x2 + 6x? Please explain thoroughly
Answer:
x-intercepts: (-1, 0) and (2, 0)
x-intercept: (-3, 0)
Step-by-step explanation:
Given quadratic function:
[tex]f(x)=-4x^2+4x+8[/tex]
The x-intercepts of a quadratic function are the points at which the curve crosses the x-axis ⇒ when y = 0
Therefore, to find the x-intercepts of the given function, set the function to zero:
[tex]\implies -4x^2+4x+8=0[/tex]
Factor out -4:
[tex]\implies -4(x^2-x-2)=0[/tex]
Divide both sides by -4
[tex]\implies x^2-x-2=0[/tex]
Rewrite the middle term as -2x + x:
[tex]\implies x^2-2x+x-2=0[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(x-2)+1(x-2)=0[/tex]
Factor out the common term (x - 2):
[tex]\implies (x+1)(x-2)=0[/tex]
Zero Product Property: If a ⋅ b = 0 then either a = 0 or b = 0 (or both).
Using the Zero Product Property, set each factor equal to zero and solve for x (if possible):
[tex]\begin{aligned}(x+1) & = 0 & \quad \textsf{ or } \quad \quad (x-2) & = 0\\\implies x & = -1 & \implies x & = 2\end{aligned}[/tex]
Therefore, the x-intercepts are (-1, 0) and (2, 0).
---------------------------------------------------------------------------------------
Given quadratic equation:
[tex]-9 = x^2 + 6x[/tex]
Add 9 to both sides:
[tex]\implies x^2+6x+9=0[/tex]
Rewrite the middle term as 3x + 3x:
[tex]\implies x^2+3x+3x+9[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(x+3)+3(x+3)=0[/tex]
Factor out the common term (x + 3):
[tex]\implies (x+3)(x+3)=0[/tex]
[tex]\implies (x+3)^2=0[/tex]
Square root both sides:
[tex]\implies (x+3)=0[/tex]
Solve for x:
[tex]\implies x=-3[/tex]
Therefore, the x-intercept is (-3, 0).
As the function has a repeated factor (multiplicity of two), the curve will touch the x-axis at (-3, 0) and bounce off.
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options.
x2 + (y – 3)2 = 36
x2 + (y – 5)2 = 6
(x – 4)² + y² = 36
(x + 6)² + y² = 144
x2 + (y + 8)2 = 36
From the given options A and option D are the possible equations will be;
x² + (y – 3)² = 36
or, x² + (y + 8)² = 36
What is Circle?A circle is a round 2-dimensional shape. It is a closed shape with a distance from center to circumference termed as radius 'r' and distance from one point on the circumference to another point passing through center termed as diameter 'd'.
Here, General equation of circle
(x - a)² + (y - b)² = r²
where, (a, b) are the coordinates of center
and r is the radius of circle.
Now, given data; Diameter = 12 units
Radius = 6 units
center lies on y-axis so coordinates will be (0, b)
Equation of given circle
x² + (y - b)² = 6²
x² + (y - b) = 36
where, b may be any value on y-axis.
Thus, from the given options A and option D are the possible equations will be;
x² + (y – 3)² = 36
or, x² + (y + 8)² = 36
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The question is down below 30 points
also I home school and have permission to post this question
The ratios for the surface area, volume and width respectively are:
Ratio of SA = 9:196.Ratio of V = 27:2,744.Ratio of W = 3:14.What is ratio?Ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.
In this exercise, we are given the scale factor for this canoe is 3:14. Thus, the ratio of the surface area of the canoe model to the surface area of the original model would squared as follows:
Ratio of SA = 3²/14²
Ratio of SA = 9/196
Ratio of SA = 9:196.
For the volume, we would take the cube:
Ratio of V = 3³/14³
Ratio of V = 27/2,744
Ratio of V = 27:2,744.
For the width, we have:
Ratio of W = 3/14
Ratio of W = 3:14.
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cos 0 = . Find tan 0.
Answer:
b
Step-by-step explanation:
15/8
Pls help! I need to finish quickly.
The inverse of the function f(x) = 2x + 5 is; f⁻¹(x) = (x - 5)/2
How to find the Inverse of a Function?An inverse function in mathematics is function which reverses the another function.
We want to find the inverse of the function; f(x) = 2x + 5
Thus;
Step 1; y = 2x + 5
Step 2; Subtract 5 from both sides to get;
y - 5 = 2x
Step 3; Since we want to find the inverse of f(x), then we now have;
x - 5 = 2y
Step 4: Divide both sides by 2 to get;
(x - 5)/2 = y
Step 5; Thus, we have;
f⁻¹(x) = (x - 5)/2
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Ross has $750 in a bank account that earns 9% in annual interest. Select an equation that represents this scenario.
PLS HELP
The step function f(x) is graphed. -54-3 -2 -1 4 3 EXO 4 4 y 1 CHELLEREN 2 3 What is the value of f(0)? O -2 O -1 0 0 1
Answer: -2
Step-by-step explanation:
When x = 0, y = -2.
So, f(0) = -2.
Dan was getting rs. 100 for 5 years at an interest rate of 5%. Find the accumulated value of annuity at the end of 5 years
The future value of the annuity after the end of 5 years is $552.56.
Given that, r =5%= 0.05, 5 years = 5 yearly payments, so n = 5, and P = $100.
What is the annuity formula?The formula to find the annuity formula [tex]FV=\frac{P \times ((1+r)^{n}-1 )}{r}[/tex].
Now, [tex]FV=\frac{100 \times ((1+0.05)^{5}-1 )}{0.05}[/tex]
⇒FV = 100 × 55.256
⇒FV = $552.56
Therefore, the future value of the annuity after the end of 5 years is $552.56.
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Solve using the distributive property of whole numbers.
27,345 x 113 x-27,345 x 13
Answer:
2,734,500
Step-by-step explanation:
27,345 × 113 - 27,345 × 13 ← factor out 27,345 from each term
= 27,345(113 - 13)
= 27,345 × 100
= 2,734,500
The junior class sold 75% of the raffle tickets. They started with 100 raffle tickets.
How many tickets have been sold?
Answer:
75
Step-by-step explanation:
Since they sold 75% of the raffle tickets and the total is 100 raffle tickets, you simply need to find 75% of 100. To find x% of a, you simply convert x% to a decimal by dividing by 100 and then multiplying it by a. So the general formula to find x% of a would be: [tex]a*\frac{x}{100}[/tex]. In this case a=100, and x=75. So you have the equation: [tex]100*\frac{75}{100} = \frac{100 * 75}{100}=\frac{75}{1} = 75[/tex]
Answer: 75 tickets
Step-by-step explanation:
- percentages are out of 100, they are a rate, number, or amount in each hundred
- for example, (10/100) x 100 (because it’s out of 100) = 10%
- or it could be (6/40) x 100 (because it’s out of 100) = 15%
- so because they started with 100 tickets, it’s just (75/100) x 100 =75
hope this helps :)
Select the procedure that can be used to show the converse of the Pythagorean theorem using side lengths chosen from 3 feet, 4 feet, 5 feet, and 6 feet.
A. Knowing that 32 + 42 = 52, draw the 3-foot side and the 4-foot side with a right angle between them. The 5-foot side will fit to form a right triangle.
B. Knowing that 32 + 52 ≠ 62, draw the 3-foot side and the 5-foot side with a right angle between them. The 6-foot side will fit to form a right triangle.
C. Knowing that 32 + 42 = 52, draw any two of the sides with a right angle between them. The third side will fit to form a right triangle.
D. Knowing that 42 + 52 < 62, draw the 4-foot side and the 5-foot side with a right angle between them. The 6-foot side will fit to form a right triangle.
Using Pythagoras theorem, we know that 3² + 4² = 5², draw the 3-foot side and the 4-foot side with a right angle between them. The 5-foot side will fit to form a right triangle
How to use Pythagoras theorem to prove a right triangle?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
Therefore,
c²= a²+ b²
where
c = hypotenuse sidea and b are the other legs.Therefore,
3² + 4² = 5²
Hence,
Knowing that 3² + 4² = 5², draw the 3-foot side and the 4-foot side with a right angle between them. The 5-foot side will fit to form a right triangle
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You work as an assistant for a local musical theatre group, the Main Street Theatre Company. The company is putting on a production of Les Misérables this year, and they need your help planning it.
All the roles have now been cast, and the lead actors playing the following parts are gathered around a large circular table for their first read: Jean Valjean, Inspector Javert, Thénardier, Enjolras, Marius, Fantine, adult Cosette, adult Éponine, and Madame Thénardier. It is your job to seat these 9 actors, the 3 producers, and the director around the table.
If the 9 actors must sit together, how many ways are there to seat the 13 people around the table?
8,709,120
362,880
6,227,020,800
259,459,200
There are 8,709,120 ways to arrange the people around the table
How to determine the number of ways?The given parameters are:
People = 13
Actors = 9
If the actors must seat together, then the actors must be grouped as 1.
The 9 actors can be arranged in 9! ways
Now, we have 1 group + 4 individuals.
This equals 5 people (in theory)
The 5 people can be arranged in 5! ways
So, the number of ways is
Ways= 9! * 5!
Evaluate
Ways = 8,709,120
Hence, there are 8,709,120 ways to arrange the people around the table
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Keisha borrowed money from a bank to buy a fishing boat.
She took out a personal, amortized loan for $19,500, at an interest rate of 4.75%, with monthly payments for a term of 5 years.
(a) Find Keisha's monthly payment.
(b) If Keisha pays the monthly payment each month for the full term,
find her total amount to repay the loan.
$0
(c) If Keisha pays the monthly payment each month for the full term,
find the total amount of interest she will pay.
$0
Answer:
Your $19,513 loan has 60 monthly payments of $366.00 at 4.75%.
If you make all of your payments on this loan, and do not prepay any of the principal, the total interest for this loan is $2,447.26.
Step-by-step explanation:Loan Summary
Total payments $21,960.26
Total interest paid $2,447.26
Loan amount $19,513
Monthly payment $366.00
Interest rate 4.75%
Term 60 monthly payments
Solve inequality
58 - 10xs 20 + 9x.
Answer:
x>=2 so B
Hope this helps :)
If 5(x-6y) = 50y,what is the value of x in terms of y? PLS EXPLAIn
E. 16y
F. 15y
G. 11 2/5y
H.11y
EXPLAIN CORRECT ANSWER AND EXPLANATION GETS BRAINIEST
Answer:
E. 16y
Step-by-step explanation:
Given equation:
5(x - 6y) = 50y
Expand the brackets using
Distributive Property for subtraction: a(b - c) = ab - ac
⇒ 5 · x - 5 · 6y = 50y
⇒ 5x - 30y = 50y
Add 30y to both sides:
⇒ 5x - 30y + 30y = 50y + 30y
⇒ 5x = 80y
Divide both sides by 5:
⇒ 5x ÷ 5 = 80y ÷ 5
⇒ x = 16y
A chocolate bar measures 40 mm wide, 80 mm long, and 5 and 1 over 2 mm high. Will’s Wrapping Company is making a wrapper to cover the chocolate bar. Use the correct net and determine how much paper will be needed to make the wrapper.
Answer:
7720 mm²
Step-by-step explanation:
area = 2 × 80 mm × 40 mm + 2 × 80 mm × 5.5 mm + 2 × 40 mm × 5.5 mm
area = 7720 mm²
PLEASE NEED HELP
2 graphs. Graph A: a dotted line goes from (1, 0) to (1, 0.25), is solid and horizontal to (2, 0.25), is dotted to (2, negative 0.1875), is solid and horizontal to (6, negative 0.1875), and then is dotted to (6, 0). Graph B. A line goes from (negative 5, 0) to (negative 3, 0.25), and then decreases to (3, 0).
Which statement about the graphs is true?
Graph A is a valid density curve because the part of the graph from 2 to 6 is below the horizontal axis.
Graph A is not a valid density curve because the part of the graph from 1 to 2 is above the horizontal axis.
Graph B is not a valid density curve because part of the horizontal axis has negative values.
Graph B is a valid density curve because the curve is above the horizontal axis, and the area under the curve is 1.
Pictures posted below
Answer: Graph B is a valid density curve because the curve is above the horizontal axis, and the area under the curve is 1.
The last statement "Graph B is a valid density curve because the curve is above the horizontal axis, and the area under the curve is 1." is the correct statement.
A few fundamental principles apply to density curves:
A density curve's area beneath it represents probability.A density curve's area under it equals one.Base x height in a uniform density curve equals one.The likelihood that x = a will never occur.The likelihood that x < a is the same as that of x ≤ a.Following the rules above, we can see from graph B that the curve is above the horizontal axis. That shows that the probabilities are positive which is a necessity. Moreover, the area under the curve must also be 1. That is also satisfied.
Hence, the last statement "Graph B is a valid density curve because the curve is above the horizontal axis, and the area under the curve is 1." is the correct statement.
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