can you answer this for me please

Can You Answer This For Me Please

Answers

Answer 1

The length of LN for the triangle is 18.

What are triangles?

A triangle is a three-sided polygon because it has three edges and three vertices. The most important attribute of a triangle is the sum of its internal angles to 180 degrees

Given triangle JKL,

and MN is parallel to JK,

taking ΔJKL and ΔLMN

∠L = ∠L  (common angle)

because MN is parallel to JK, so corresponding angles are equal,

so ∠K = ∠N

and ∠J = ∠M

ΔJKL ≈ ΔLMN(triangles are similar)

since both triangles are similar the ratio of their corresponding sides is equal,

JL/LM = JK/MN = LK/LN

and JK = 55 and LK = 33

and MN = 12 + LN

JK/MN = LK/LN

substitute the values

55/(12 + LN) = 33/LN

55LN = 33(12 + LN)

55LN - 33LN = 396

22LN = 396

LN = 396/22

LN = 18

Hence the length of LN is 18.

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Related Questions

6. Which of the following is the additive
inverse of -(2 − 9)?


A. -7
B. -1/7
C. 1/7
D. 7

Answers

Answer:

A. -7

That's it

a cube has a volume of 1000 cm cube calculate the surface area of the cube

Answers

Answer:

600 cm²

Step-by-step explanation:

let x = length of a side of the cube

all sides are equal in a cube

Volume = x³ = 1000 cm³

x = ∛1000 = 10 cm

Area of 1 side = 10cm x 10cm = 100 cm²

There are 6 equal sides in a cube

SA = 6(100) =  600 cm²

help please I neeeeeeed help

Answers

The answer is D

-1 is your y-int
2/1 is your slope

Final answer: y=2x-1

Which of the following points is closest to (4,0)?
50 points each?

Answers

Answer: Its point B, its closer to the vertices of 4.

Step-by-step explanation:

(7/2,1.87)

the distance between the points

(4,0)and (0,3)

would be:

√(3−0)2+(4−0)2=√9+16=√25=5

what is gcf for 24x^5 and 10x​

Answers

answer = there are three photos. all answer in three photos

9 miles for every 1/2 hour and 6 miles for every 20 minutes tell whether the missing values are equivalent and justify

Answers

9 miles for every ½ hour and 6 miles for every 20 minutes can be considered equivalent because they represent the same speed, just measured in different units.

To see this, we can convert the units to a common unit, such as miles per hour.

First, let's convert the 6 miles in 20 minutes to miles per hour:

[tex] \frac{6}{20} \times 60[/tex]= 18 miles/hour

Next, let's compare this speed to the 9 miles per ½ hour:

[tex] \frac{9}{ \frac{1}{2} } = \frac{9}{ \frac{1}{2} } \times \frac{1}{ \frac{1}{2} } = 18[/tex]

Since both speeds are equal to 18 miles per hour, we can conclude that they are equivalent. This means that the missing values are also equivalent.

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Need real answer with solution please i need it quickly. No random answers

Answers

If you differentiate each piece with respect to x, you'd get

    [tex]\frac{d}{dx}(x)\cdot y + x \cdot \frac{d}{dx}(y) + \frac{d}{dx}(2x)+\frac{d}{dx}(3x^2)=\frac{d}{dx}(4)[/tex]

which becomes

    [tex]1\cdot y + x \cdot \frac{dy}{dx} + 2+6x^1=0[/tex]

which is equivalent to B.

The answer is B.

What is the solution to the inequality of 7w+63>=150

Answers

Answer:

w ≥ 87/7

Step-by-step explanation:

Step 1: Subtract 63 from both sides.

7w+63−63≥150−63

7w≥87

Step 2: Divide both sides by 7.

7w/7  ≥  87/7

w ≥ 87/7

Help find the length

Answers

The length of the side D'E' is 9 units for the given translated triangle D'E'F'.

What is a transformation?

A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.

As we know that the translation does change the change location but it can't change the shape of the figure.

According to the given question, triangle DEF is translated as 6 units right and 6 units up.

This means there are no changes in the dimensions.

So D'E' =  DE

Thus, D'E' = 9 units

The length of the side D'E' is 9 units

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What is the area of a circle with a diameter of 14 meters? Leave the answer in terms of π.

A. 49π square meters
B. 7π square meters
C. 196π square meters
D. 14π square meters

Answers

Answer:

A

Step-by-step explanation:

the area (A) of a circle is calculated as

A = πr² ( r is the radius )

given diameter = 14 then r = 14 ÷ 2 = 7

A = π × 7² = 49π m²

Answer:

49π

Step-by-step explanation:

area of circle=pie*radius²

and radius=diameter/2

therefore

r=14/2

=7m

Area =π*7²

Area=49π

(2x + 3) + (4x - 7)

2x + 3 + 4x - 7

2x + 4x + 3 - 7

Answers

1. -4
2. -4
3. -4
They all have the same answer
All of these equal out to -4.

A circle with a radius of 14 feet is cut into 8 equal pieces. How many square feet are 3 of the pieces? Use 22 over 7 for π.

A. 1,155 square feet
B. 231 square feet
C. 22 square feet
D. 11 square feet

Answers

The requried area of 3 of the pieces is 231 square feet. Option B is correct.

What is the area of the circle?

The area of a circle is the amount of space enclosed by the circle in a two-dimensional plane. It is given by the formula:

A = πr²

where "A" is the area of the circle, "r" is the radius of the circle, and "π" (pi) is a mathematical constant with an approximate value of 3.14159.

Here,
The area of a full circle with a radius of 14 feet is given by:

A = πr²

A = (22/7) × (14)²

A = (22/7) × 196

A = 616 square feet (rounded to the nearest whole number)

If the circle is cut into 8 equal pieces, each piece will have an area of:

616 ÷ 8 = 77 square feet

Therefore, 3 pieces will have an area of 3 × 77 = 231 square feet.

Thus, the requried area of 3 of the pieces is 231 square feet. Option B is correct.

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PLEASE HELP ASAP
Determine the slope of the line.

Answers

Answer:

4/3

Step-by-step explanation:

sorry if I'm wrong

4/3

rise over run so up is rise side is run 4/3

find the midpoint of segment CD. C = (-3, -2) D =0, -5)

Answers

Answer:

(-1.5,-3.5)

Step-by-step explanation:

midpoint=(x1+x2)/2,(y1+y2)/2

-3+0/2, -2+( -5)/2

(-1.5,-3.5)

PLease HELP ME!!!
Questions and Answers are in the link below

Answers

The equation can be used to solve for x is 90-52 = (12x - 10)°

How to determine which equation can be used to solve for x?

Angle geometry is a branch of mathematics that deals with the study of angles and their properties in two-dimensional figures such as circles, triangles, and polygons.

In the diagram, since vertically opposite angles are equal. Thus, we can say:

∠UTW =  ∠VTZ

90 - 52 = (12x - 10)°

38 = 12x - 10

12x = 38 + 10

12x = 48

x = 48/12

x = 4

Therefore, the equation is 90-52 = (12x-10)°

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ara sells apples at a farmers market she begins the day with 35 1/2 pounds of apples she sells half of the apples in the mornning 4/19 of the apples in the afternoon and 1/4 of the apples in the evening how many pounds of apples dose she have left

Answers

She has 1 61/152 pounds of apples left

How to determine how many pounds of apples she has left?

Fractions are represented as numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing

In order to find how many pounds of apples she has left, subtract the apple she sold from the apple she begins with. That is:

Apple left = 35 1/2 - (35 1/2 * 1/2) - (35 1/2 *4/19) - (35 1/2 * 1/4 )

Apple left = 1 61/152

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7. A rancher has 1000 m of fencing to enclose two rectangular corrals. The corrals have the same dimensions and one side in common. What dimensions will maximize the enclosed area? X y​

Answers

The dimensions that will maximize the enclosed area are 125 meters by 250 meters

What dimensions will maximize the enclosed area?

Represent the dimensions with x and y

So, we have the following equations

Perimeter = 4x + 2y = 1000

Area = 2xy

So, we have

2x + y = 500

This gives

y = 500 - 2x

So, we have

Area = 2x(500 - 2x)

Expand

Area = 1000x - 4x^2

Differentiate and set to 0

1000 - 8x = 0

So, we have

8x = 1000

Divide

x = 125

Recall that

y = 500 - 2x

y = 500 - 2 * 125

y = 250

Hence, the dimension is 125 by 250

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The equation and the graph represent two functions. Use the equation y=4 and the graph to answer the questions.
When x is 4, is the output of the equation or graph greater?
What value for x produces the same output in both the graph and the equation?

Answers

When x is 4, the output of the equation is greater.

The value for x that produces the same output in both the graph and the equation is equal to 6.

What is a proportional relationship?

In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios, a straight line, and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

k is the constant of proportionality.y and x represent the variables in a proportional relationship.

Generally speaking, the graph of any proportional relationship such as the linear equation (y = 4) is characterized by a straight line that crosses the y-coordinate as shown in the image attached below.

By critically observing the graphs, we can reasonably infer and logically deduce that they would produce the same output (range) at the ordered pair (4, 6).

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Calculate the area. ​

Answers

Answer:

1.) 55.3896

2.) 30.1754

Step-by-step explanation:

Follow steps in the image. (didn't know if you had to round, so i just left the numbers as they are.)

-Hope this helped

1 ]

Given:-

[tex] \rm{π = \bold{3.14}}[/tex][tex] \rm{radius= \bold{4.2in}}[/tex]

[tex] \: [/tex]

To Find:-

[tex] \rm{Area \: of \: the \: circle= \: ?}[/tex]

[tex] \: [/tex]

By using formula:-

[tex] \pmb{ \boxed{ \rm{Area \: of \: circle = \bold{ πr²}}}}[/tex]

[tex] \: [/tex]

Solution:-

[tex] \rm{Area \: of \: circle = πr²} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \rm{= 3.14×(4.2)²} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \rm{=3.14× 17.64} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \underline{ \boxed{\rm{ \red{= 55.3896}}}}[/tex]

———————————————————————

2]

Given:-

[tex] \rm{π = \bold{3.14}}[/tex][tex] \rm \:{diameter ( d ) =\bold {6.2yd}}[/tex]

[tex] \: [/tex]

To find:-

[tex] \rm \: Area \: of \: the \: circle= \: ? [/tex]

[tex] \: [/tex]

By using formula:-

[tex] \pmb{ \rm{ \boxed{Area \: of \: circle = \frac{(π×d²)}{4} }}}[/tex]

[tex] \: [/tex]

Solution:-

[tex] \rm{Area \: of \: circle = \rm{\frac{(π×d²)}{4} } }\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: = \rm{\frac{3.14×38.44}{4} }\\ \: \: \:\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \rm{ = \cancel\frac{120.7016}{4} }\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \underline{ \boxed{\rm{ \green{=30.1754}}}}[/tex]

[tex] \: [/tex]

hope it helps!:)

NO LINKS!!
Please help me with #8 and 9

Answers

Answer:

8.  TN = 22 units

9.  RT = √(165) units

Step-by-step explanation:

It appears that point T is the circumcenter of triangle MNP.

A circumcenter of a triangle is:

The center of a circle that passes through each vertex of a triangle. The point at which the perpendicular bisectors of the sides of the triangle intersect.

As a perpendicular bisector is a line that divides another line segment into two equal parts at a right angle, then:

MR = RNNS = SPPQ = QM

As point T is the circumcenter, ΔMTN, ΔNTP and ΔMTP are isosceles triangles and MT, TP and TN are the radius of the circumcircle.

Therefore:

MT = TP = TN

Question 8

To find the length of TN, find the value of x by equating the given expressions for MP and TP:

[tex]\implies \sf MT = TP[/tex]

[tex]\implies 6x - 56 = 3x - 17[/tex]

[tex]\implies 3x = 39[/tex]

[tex]\implies x = 13[/tex]

Substitute the found value of x into the expression for TP:

[tex]\implies \textsf{TP} = 3(13) - 17[/tex]

[tex]\implies \textsf{TP} = 22[/tex]

Therefore, as TN = TP then TN = 22 units.

Question 9

First find the value of x by equating the given expressions for TN and TP:

[tex]\implies \sf TN=TP[/tex]

[tex]\implies 4x-17=x+10[/tex]

[tex]\implies 3x=27[/tex]

[tex]\implies x=9[/tex]

Substitute the found value of x into the expression for TN:

[tex]\implies \textsf{TN} = 4(9) - 17[/tex]

[tex]\implies \textsf{TN} = 19[/tex]

As RT is the perpendicular bisector of MN, then ΔTRN is a right triangle where ∠TRN is 90°.

Given:

RN = 14TN = 19

To calculate the length of RT, use Pythagoras Theorem:

[tex]\implies \sf RN^2+RT^2=TN^2[/tex]

[tex]\implies \sf RT=\sqrt{TN^2-RN^2}[/tex]

[tex]\implies \sf RT=\sqrt{19^2-14^2}[/tex]

[tex]\implies \sf RT=\sqrt{165}[/tex]

Consider the complex number -i√5.
What is the real part?

Answers

Answer: The real part of the complex number is 0.

Step-by-step explanation:

Complex numbers are always in the format: a + bi

On the given complex number, -i√5 , it is representing the "bi" part of the standard complex number expression.

We are looking for the real part. The real part is the real number. Since -i√5 doesn't show a real part, we can infer that its real part is 0.

If you rewrite the expression with 0 as the real number, it is equivalent to the principle of the original:

0 + -i√5

This concept is similar to the idea:

y = mx + b

if the equation said:

y = 3x

we know that b is 0, although its not stated. This principle is used in complex numbers.

Thank you.

OK guys, so this is a problem if someone can give me this answer I’ll be so happy. I need it right away. Please respond quick .


I Sally buys 5 dolls and 1 purse for $21.
Donna buys 7 dolls and 1  purse for 27$

Answers

Answer:

ok one doll is 3 dollars and one purse is 6 dollars

and for the bottom I got 84 so I don't know I'm sorry

Step-by-step explanation:

Answer:

1. The unit price for a doll is three dollars. The unit price for a purse is six dollars.

2. One doll costs three. One purse costs six.

3. Polly spends $24 on the 2 dolls and 3 purses.

Step-by-step explanation:

Doing some calculations, 1 doll costs three dollars and 1 purse costs six dollars.

5 x 3 + 6 = 21

7 x 3 + 1  = 27

If Polly buys 2 dolls and 3 purses, that means she spends six dollars on the dolls and eighteen dollars on the purses.

(2 x 3) + (3 x 6) = $24

Polly spends $24 on 2 dolls and 3 purses.

Hope This Helps!

PLEASE HELP‼️‼️
EXTRA POINTS‼️

Answers

The equations of the functions are

y = -7(x - 4)(x + 2) --- in standard form and in vertex form, it is y = -7(x - 1)^2 + 63. The point is not on the liney = 4(x - 5)(x + 5) --- in standard form and in vertex form, it is y = -4x^2 - 100. The point is on the line

How to determine the equation

Function (a)

From the question, we have the following parameters that can be used in our computation:

x-intercepts = (4, 0) and (-2, 0)

This means that

y = a(x - 4)(x + 2)

Also, we have point (5, -7)

This means that

a(5 - 4)(5 + 2) = -7

So, we have

a =  -7

The equation becomes

y = -7(x - 4)(x + 2) --- in standard form

In vertex form, it is

y = -7(x - 1)^2 + 63

To test the point (2, 15), we have

y = -7(2 - 1)^2 + 63

Evaluate

y = 56 ---- false

Function (b)

From the question, we have the following parameters that can be used in our computation:

x-intercepts = (5, 0) and (-5, 0)

This means that

y = a(x - 5)(x + 5)

Also, we have point (-4, -36)

This means that

a(-4 - 5)(-4 + 5) = 36

So, we have

a =  4

The equation becomes

y = 4(x - 5)(x + 5) --- in standard form

In vertex form, it is

y = 4x^2 - 100

To test the point (3, -64), we have

y = 4 * 3^2 - 100

Evaluate

y = -64 ---- true

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Please help, 25 points!

Answers

Answer:

3a + 3b

Step-by-step explanation:

The distributive property of multiplication over addition is

a(b + c) = ab + ac

Here we have

3(a + b)

We apply the distributive property and get

3 × a + 3 × b

which simplifies to

3a + 3b

4. Dr. Olson's receptionist will receive a 5% raise in June. How much will be withheld each two weeks for Social Security after the raise?

Answers

Answer:

y=3x+5

Step-by-step explanation:

qqqqqqqqqqqqqqqqssssssssss

Sets A, B, and C are subsets of the universal set U.
These sets are defined as follows.
U= {f, g, h, p, q, r, x, y, z)
A={g, h, q, r, z
:}
B={q, r, x, y, z)
C = {h, p, q,y}
Find (An B)' U C'.
Write your answer in roster form or as Ø.
(An B)' UC' = []

Answers

As sets A, B, and C are subsets of the universal set U, the value of A’ ∪ B’ U C'  = {f}.

What is De Morgans law?

Demorgan's law can be utilised in set theory and boolean algebra to make mathematical formulations simpler. Let's say that the universal set U has two subsets, A and B. A' is A's complement, and B' is set B's complement.

Given that, (An B)' UC'.

Using the De Morgan's law we have:

(A ∩ B)’ = A’ ∪ B’.

Substituting this in (An B)' UC'. we have:

A’ ∪ B’ U C'

A' = {f, p, x, y}

B' = {f, g, h, p}

C' = {f, g, x, z}

A’ ∪ B’ U C'  = {f}

As sets A, B, and C are subsets of the universal set U, the value of A’ ∪ B’ U C'  = {f}.

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A shop has a sale of
1
3
off all items in stock.
If the original price of a dress is £27, what would be its sale price?

Answers

The sales price of the item is £18

How to determine the sales price

From the question, we have the following parameters that can be used in our computation:

Discount = 1/3

Original price = 27

This means that

Sales price = original price * (1 - discount)

Substitute the known values in the above equation, so, we have the following representation

Sales price = 27 * (1 - 1/3)

Evaluate

Sales price = 18

Hence, the sales price is #18

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Find a and b, such that a+b=18, and a/b is close to 1/2.
What is the answer for A
And B

Answers

The value of a is 6 and b is 12.

What is equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

given:

a + b= 18.......(1)

a/b= 1/2

or, a= b/2......(2)

Put the value of a from equation (2) in (1) we get

b/2 + b= 18

3b/2 = 18

3b= 36

b= 36/3

b= 12

and, a= b/2 = 12/2 = 6

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Using a proportion, what is 60% of 20? 12 120 1.2 240

Answers

=60/100 ×20=60/5=1260% of 20

=12

a small business owner is applying for a small business loan and has been approved for a $50,000 loan with a 6.15% annual interest. the first loan is a simple interest rate, the second loan compounds interest quarterly, and the third loan compounds interest continuously. the small business owner plans to pay off the loan in three years and 7 months. Determine the total value of the loan with the quarterly compounded interest.

Answers

The total value of the loan with the quarterly compounded interest

is $117599.

What is compound interest?

Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.

We know the formula for compound interest is,

A = P(1 + r/100)ⁿ.

Where, A = amount, P = principle, r = rate, and n = time in years.

The formula for compound interest compounded quarterly is,

A = P(1 + (r/4)/100)ⁿ.

[tex]A = 50000(1 + 6.15/100)^{4\times\frac{43}{12}}[/tex].

[tex]A = 5000(1 + 0.0615)^{14.33}[/tex].

[tex]A = 5000(1.0615)^{14.33}[/tex].

[tex]A = 5000\times2.352[/tex].

A = $117,599.

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What are the main similarities and differences between Judaism, Christianity and Islam? hydroxide is not a suitable base for deprotonating an alkyne, why? use pka values to support your answer. matt and sara are regulars at culver's. they have strong positive belief about the restaurant, and tend to get offended if someone complains about the service. culver's, according to them, indisputably offers the quickest service in town. this is an example of: que elementos se tienen en cuenta para afirmar que la cartografia,como disciplina,nacio en grecia? suppose p and q are polynomial functions. if and q(0), find p(0). The development of today's consumer culture requires that people continually desire and purchase new goods and services. This contrasts with the frugality and modesty of the so-called "Protestant ethic" of the past and represents a shift in cultural values. Which of the following bears the MOST responsibility for this shift?a) the marketing and educational industriesb) the advertising and financial services industriesc) the credit card and fashion industriesd) the banking and loan industries What was the analogy of the history of punishment that the presenter used? A. Rollercoaster B. Merry-go-round. C. Carousel D. Pendulum. the graph of the loanable funds market is different than that of the money market in which of the following ways? Two cars A and B are moving at speeds of 60 km/h and 80km/h respectively .what is the speed of car A relative to car B if the two cars are moving on the same direction What was Flints response to the Virginia Tech research findings? EASY 100 POINTS, WILL MARK BRAINLEST TO FIRST ANSWER,Data was collected on the weight, in ounces, of kittens for the first three months after birth. A line of fit was drawn through the scatter plot and had the equation w = 3.25 + 0.3d, where w is the weight of the kitten in ounces and d is the age of the kitten in days.What is the w-intercept of the line of fit and its meaning in terms of the scenario?A, 3.25; a kitten who is just born is predicted to weigh 3.25 ouncesB,0.3; a kitten who is just born is predicted to weigh 0.3 ouncesC, 3.25; for each additional day after the kitten is born, its weight is predicted to increase by 3.25 ouncesD, 0.3; for each additional day after the kitten is born, its weight is predicted to increase by 0.3 ounces What are the arguments of those who believe that President Truman's decision to use atomic weapons to end the war was justified? a trauma-informed approach to human trafficking means . a. notifying authorities that the victim suffered trauma b. educating dental office and hospital personnel on the victim rights c. having a plan of action in place that everyone in the office can follow d. alerting the fbi that you may have a trafficking situation 2. dentists and healthcare workers are mandated to report child abuse. any person under the age of is considered a child and under federal law must be reported, if child abuse is suspected. human trafficking is child abuse. a. 18 b. 17 c. 16 d. 15 3. the trafficking victims protection act of 2000 provides all of the following mandates except which one: a. extends protection to persons internationally and domestically. b. prohibits all forms of human trafficking. c. prescribes punishment for perpetrators involved in human trafficking. d. victims are not entitled to the same rights as refugees. 4. healthcare providers who report a trafficking victim are protected from . a. prosecution only b. criminal liability c. civil and criminal liability d. civil liability Write a formula for the function obtained when the graph is shifted as described. When typing exponents use the carrot key ^ by pressing SHIFT and 6. For example x squared can be typed as x^2. Do not put spaces between your characters and remember to use parentheses in the appropriate places!f(x)=x^3 is shifted up 3 unit and to the left 7 units.The new equations f(x)=Answer What is 5/7 times 10/11 as a fraction in simplest form The vertices of a rectangle are at (1, 5), (3, 5), (3, 7), and (1, 7). What is the length of the shorter side of the rectangle? Enter your answer in the box Blake puts eight marbles in the bag cold puts nine marbles in the bag then Blake takes out seven marbles from the bag how many marbles are in the bag now the sum of direct materials and direct labor is called cost. true or false Fred wants to buy a new car. If he puts $7,000 in a savings account that earns 8% interest each year,how long will it take for Fred to have $30,100 for a new car.a. Write the exponential equation.b. Solve the problem. Round up to the nearest whole number. What idea was Madison expressing in the excerpt