Point P is the center of dilation. Triangle S T U is dilated to create triangle S prime T prime U prime. The length of P T is 2. The length of T T prime is 10.

Which statements justify that the dilation of triangle STU is an enlargement increasing its size by the magnitude of the scale factor? Select two options.
The triangle pre-image is closer to the point of dilation than the image.
The triangle image is closer to the point of dilation than the pre-image.
The value of the scale factor, One-sixth, is between 0 and 1.
The value of the scale factor, 6, is greater than 1.
The vertices of the pre-image are collinear with the vertices of the imag

ΔRSP ≅ ΔQSP by SAS. Therefore, PR ≅ PQ by CPCTC theorem.

If two triangles are congruent, the CPCTC theorem states that all corresponding parts of the two triangles would also be congruent to each other.

Since S is the midpoint of QR, therefore, RS ≅ QS (one pair of congruent sides)

∠RSP ≅ ∠QSP [right angles] (one pair of congruent included angles)

SP ≅ SP based on the reflexive property (one pair of congruent sides)

Therefore, ΔRSP ≅ ΔQSP by SAS.

Conclusively, PR ≅ PQ by CPCTC theorem.

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Closed-end

You can answer "yes" or "no" to the completed question. Or, the number of answers is limited (eg A, B, C, or all of the above). Closed-end questions are often suitable for voting, as response rates are high when users don't have to type too much.

Closed-end questions are defined as question types that require respondents to choose from a specific set of predefined answers. B. Between "yes/no" or fixed multiple-choice questions. In a typical scenario, closed-end questions are used to collect quantitative data from respondents.

An indefinite definition represents a situation or question with a predetermined number of results. An example of a closed ending is the question "Do you need help?" This usually has only four answers-yes, no, maybe, or not.

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Answer:

Step-by-step explanation:

If she offers to 9, but 2 reject, that means she paid for 7 friends.

If each friend costs $4, multiply 4 by 7.

The answer is $28

Hope this helps! (:

The points on the graph of the inverse variation are of the form:

(x, 8/x)

An inverse variation function is written as:

y = k/x.

Here we know that k = 8.

y = 8/x

Then the points (x, y) on the graph of the function are of the form:

(x, 8/x).

So evaluating in different values of x, we can get different points on the graph:

And so on.

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The transformation that's illustrated in the diagram is translation.

It should be noted that transformation simply means the manipulation of that moves a shape from a space to another.

In this case, the transformation that's illustrated in the diagram is translation. This is the sliding of try shape across certain number of spaces.

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Answer:

38

Step-by-step explanation:

Let x be the number of pencils bought.

Let y be the number of pens bought.

Given information from the question:

x = y - equation 1

2.9y - 1.2x = 32.30 - equation 2

From here we can use the substitution method in solving simultaneous equations to find x and y. We will substitute equation 1 into equation 2.

2.9y - 1.2y = 32.30

1.7y = 32.30

y = [tex]\frac{32.3}{1.7} \\= 19[/tex]

Now since we know number of pens = number of pencils,

x = 19

Total Pencils and Pens bought = x + y = 19 + 19 = 38

Answer:

19

Step-by-step explanation:

hope it helps.good day.

Answer: Second option from the top

Step-by-step explanation:

   First, we will simplify the given inequalities.

2x + 7 ≥ 1

2x ≥ -6

   x ≥ -3

-

8 - [tex]\frac{x}{3}[/tex] ≤ 5

- [tex]\frac{x}{3}[/tex] ≤ 5

- [tex]\frac{x}{3}[/tex] ≤ -3

   x ≥ 9

   Now, we will graph them. See attached.

Answer:

1/5

Step-by-step explanation:

The slope-intercept form looks like [tex]y=mx+b[/tex] where b is the y-intercept and m is the slope. m is the slope because if you increase x by 1, the value y increases by m, and if you increase x by 1 again, the y-value will increase by the value of m, because it's being multiplied. b is the y-intercept since the y-intercept is when x=0 so mx will become m(0) which is just 0 leaving b by it self. In this case you have y=1/5x so if you were to start with 0 as x the value of y is 0. Now increase it by 1 so x becomes 1, the value of y becomes 1/5x, now increase it by 1 again so x becomes 2, the value of y is 2/5x, so as you can see the function is just increasing by 1/5 so that's the slope, so essentially whatever the coefficient of x is (the number in front of the variable x), is the slope

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Answer:  [tex]\textsf{Slope = 1/5}[/tex]

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Given:  [tex]\textsf{y = 1/5x}[/tex]

Find: [tex]\textsf{The slope of the line}[/tex]

Solution:  In order to determine the slope of the line we need to see how the slope-intercept form compares to this expressions.  The slope-intercept form is y = mx + b where m is the slope and b is the y-intercept.  In this case we have no y-intercept therefore we do not have a b. However, our slope is equal to 1/5 as it fits perfectly with the form that was provided.

The inverse of any function F(x) is also a function.

A function is an abecedarian notion in mathematics and computer programming. In both contexts, a function is a regulation or relationship that maps input values to corresponding output values. It takes one or more input values, performs a set of operations or calculations, and produces a single output value.

There are many types of functions such as trigonometric function, logarithmic function, exponential function, and so on.

If a function f(x) gives output y then its inverse will be [tex]f^{-1}(y)[/tex] and will return x as output.

So, the statement is true.

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1) Because [tex]\angle AOC[/tex] is a central angle, the answer is 50 degrees.

2) By the inscribed angle theorem, the answer is 25 degrees.

Answer:

The 2 numbers are 3 and 5.

Step-by-step explanation:

x + y = 8

1/x + 1/y = 8/15

From first equation  y = 8 - x so

1/x + 1 / (8-x) = 8/15

Multiply through by the LCM 15x(8-x):-

15(8 - x) + 15x =  8x(8-x)

120 - 15x + 15x = 64x - 8x^2

8x^2 - 64x + 120 = 0

x^2 - 8x + 15 = 0

(x - 3)(x - 5) = 0

x = 3 or  5

so y = 8-3 = 5 or 3.

The value of x will be 33 units approximately. Thus, option A is correct.

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

We need to find the value of x

so first

Tan 60 = Perpendicular / 11√6

Perpendicular = 1.732 (11√6)

Perpendicular = 46.66

Then,

Sin 45 = Perpendicular / x

Sin 45 = 46.66/ x

x = 33.00

So, the value of x will be 33 units approximately.

Thus, option A is correct.

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Answer:

Step-by-step explanation:

Let "a number" be x.

"3/7 of a number" means (3/7)x

"32 less" means - 32

Thus, "32 less than 3/7 of a number" means (3/7)x -32

"is 11/35 of that number" means = (11/35)x

Put these together and we get:

(3/7)x -32 = (11/35)x

(3/7)x - (11/35)x = 32   Rearrang to get the x on one side

We need to change "(3/7)x - (11/35)" so that the two terms have a common denominator.

If we multiply the first term by (5/5) [which is equal to 1], we get:  

(5/5)(3/7)x or

(15/35)x

We can now write:

(15/35)x - (11/35)x = 32

(4/35)x = 32

Multiply both sides by (35/4)

(35/4)(4/35)x = (35/4)(32)

x = (35)(8)

x = 280

The triangle will be computed based on the information illustrated below.

The steps needed for the construction will be:

Draw a segment XY.

Locate B, C on XY such that BC = 4.5cm.

Construct a line segment such that B = 90°.

With C as center and radius 7cm, draw a arc cutting BD at A.

Then, the required triangle ABC will be gotten.

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The area of a right-angle triangle is half the product of the base of the triangle and the height of the triangle. The area of the triangle is 90 units².

The area of a right-angle triangle is half the product of the base of the triangle and the height of the triangle.

[tex]\rm{ Area \triangle = \dfrac{1}{2} \times base \times height\\[/tex]

For the given triangle if the hypotenuse is assumed as the base, and the altitude is assumed as the height of the triangle, then the area of the triangle will be,

Area of the triangle = 0.5 × 15 units × 12units

                                 = 90 units²

Hence, the area of the triangle is 90 units².

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Answer:

P = 55°

K = 27°

Step-by-step explanation:

55° + 98° + c = 180°

153° + c = 180°

c = 27°

since C is opposite K, K = 27°

Since 55° is opposite P, P = 55°

We can check this by adding up the values of P, K, and 98

27°+55°+98° = 180°

Answer:

I don't see a list of equations.  See the attached image for an equation that works well.

Step-by-step explanation:

Option A and D. The statements that are correct here are

If the two points UT and QP are parallel, then UT is going to be the half of QP. This would be due to a scale factor of 1/2.

Then at a midpoint T is that of PR. SU is parallel to RP. SU is half of RP due to as scale factor of 1/2.

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Answer: A and D E2020

Step-by-step explanation:

E2020 geometry B!! :)

Answer:

Step-by-step explanation:

  [tex]\sf f(x) = \dfrac{1}{Sin \ x}[/tex]

f(x) does not contain values where sin x = 0. Sin x is 0 at integral multiples of π.

Domain = R - nπ , n is integers.

The range of Sin x is [-1 , 1] and in this range we cannot find 1/sin x .

Range = (-∞, -1] U [1,∞)

[tex]\sf f(x) =\dfrac{1}{Cos x}[/tex]

f(x) does not contain values where Cos x  = 0 . Cos x is 0 at integral of multiples of (π/2)

   [tex]\sf Domiain =R -\dfrac{(2n+1)\pi }{2}[/tex]

The range of Cos x is [-1,1] and in this range we cannot find 1/Cos x.

Range =  (-∞, -1] U [1,∞)

#1

No

#2

We can see f(1) has 3 values so it's not a function as it's failed in vertical line test

#3

f(10) has two values -2 and 11

So not a function

#4

As per definition of function

So it's not a function

Answer: $13361.76

Step-by-step explanation:

Amount = initial balance(1 + annual rate/periods per year)^(periods per year*years)

A = 3000(1+0.1/12)^12*15

A = 3000(1.0083)^180

A = 3000(4.4275)

A = 13361.76

Hope this helps!

The probability that a randomly selected customer will order a chicken sandwich or french fries is 36%

The given parameters are:

P(Chicken) = 56%

P(Sandwich) = 43%

P(Both) = 30%

The required probability is:

P = P(Chicken) + P(Sandwich) - P(Both)

This gives

P = 56% + 43% - 30%

Evaluate

P = 36%

Hence, the probability that a randomly selected customer will order a chicken sandwich or french fries is 36%

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Jorge will receive 9 hours in time off from work.

How many hours will Jorge get to take time off?

It is given that, Jorge has done overtime for 6 hours in this week. As per the Fair Labor Standards Act, for 6 hours of overtime work, he must be paid one and a half times the pay he gets per hour.

Instead of receiving an overtime pay for working 6 hours extra, Jorge decides to receive paid leaves from work, that is, he will get one and a half of the total hours for which he worked overtime.

As a result, the time off he receives from work = [tex]1\frac{1}{2} (6)[/tex] hours

[tex]=\frac{3}{2}(6) = 9 hours[/tex]

Thus, Jorge gets 9 hours in time off from work in return. The time that he earns for the overtime is equivalent to the pay he was supposed to receive for the overtime work.

What is Fair Labor Standards Act?

The Fair Labor Standards Act (FLSA) specifies standards for minimum wage, over-time compensation, recordkeeping, and youth employment that are applicable to workers in the private sector and in federal, state, and municipal governments.

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Answer: x = 15

Step-by-step explanation:

Hi!

These are supplementary angles, which means they both add up to 180°

Therefore,

9x+10 + 1x + 20 = 180

to solve, combine like terms

10x + 30 = 180

Then subtract 30 from both sides

10x = 150

now divide 10 from both sides leaving x by itself

x = 15

Hope this helps and have a nice day!

Answer: x = 15

Step-by-step explanation:

Hi!

These are supplementary angles, which means they both add up to 180°

Therefore,

9x+10 + 1x + 20 = 180

to solve, combine like terms

10x + 30 = 180

Then subtract 30 from both sides

10x = 150

now divide 10 from both sides leaving x by itself

x = 15

Hope this helps and have a nice day!

Answer:

How To Protect Against Predatory Lending

1) Consider alternatives to borrowing

2) Borrow federal first

3) Check your credit before applying for private loans

4) Shop around when looking for a loan

Explanation:

Definition: "Imposing unfair and abusive loan terms on borrowers." - FDIC

Answer:

x=22

Step-by-step explanation:

7x+6=160.

Lets start by moving 6 over to the other side. We can do this by subtracting 6 from both sides of the equation.

7x+6-6=160-6

7x=154

Now, let's isolate x by getting rid of the 7. The 7 is being multiplied with x, so to get rid of it we have to divide both sides by 7.

7x/7 = 154/7

x=22

Look Below :

Step-by-step explanation:

160 - 6 = 7x

154 = 7x

Or

7x = 154

x = 22

Answer:

? = 45

Step-by-step explanation:

the inner and outer triangles are similar ( AA postulate )

Then the ratios of corresponding sides are in proportion, that is

[tex]\frac{56}{56+24}[/tex] = [tex]\frac{105}{105+?}[/tex]  , that is

[tex]\frac{56}{80}[/tex] = [tex]\frac{105}{105+?}[/tex] ( divide numerator/denominator by 8 to simplify left side )

[tex]\frac{7}{10}[/tex] = [tex]\frac{105}{105+?}[/tex] ( cross- multiply )

7(105 + ? )  = 1050 ← distribute parenthesis on left side

735 + 7? = 1050 ( subtract 735 from both sides )

7? = 315 ( divide both sides by 7 )

? = 45

Here use general math mind

F(x) has more than one x inetercept .

Domain is for real numbers

Four unique numbers?

Lets see

[tex]\sf f(x)=\begin{cases}\sf (x+2)²,x\neq \left\{0,-1,1,2,3\right\}\\ \sf 0,x=0\\ \sf 1,x=-1\\ \sf 9,x=1\\ \sf 16,x=4\\ \sf 25,x=5\end{cases}[/tex]

For -2

For 0 it's (0,0)

And for extra ,it's discontinuous on x=0

[tex]10^2 + b^2=15^2\\\\100+b^2=225\\\\b^2=125\\\\b =\sqrt{125}\\\\b \approx \boxed{11.2}[/tex]