Given: RT ≅ TV and ST ≅ TU
Prove: RSVU is a parallelogram.

Quadrilateral R S V U is shown. Diagonals are drawn from point R to point V and from point S to point U and intersect at point T. The lengths of R T and T V are congruent. The lengths of U T and T S are congruent.


Statements

Reasons
1. RT ≅ TV;
ST ≅ TU 1. given
2. ∠RTS and ∠VTU are vert. ∠s;
∠RTU and ∠VTS are vert. ∠s 2. definition of vertical angles
3. ∠RTS ≅ ∠VTU;
∠RTU ≅ ∠VTS 3. vertical angles are congruent
4. ? 4. SAS congruency theorem
5. ∠VRS ≅ ∠RVU; ∠USR ≅ ∠SUV;
∠VRU ≅ ∠RVS; ∠RUS ≅ ∠USV 5. CPCTC
6. ∠VRS and ∠RVU, ∠USR and ∠SUV, ∠VRU and ∠RVS, ∠RUS and ∠USV are each a pair of alternate interior angles 6. definition of alternate interior angles
7. RS ∥ UV and RU ∥ SV 7. converse of the parallelogram diagonal theorem
8. RSVU is a parallelogram 8. definition of parallelogram
What is the missing statement in step 4?

△RTS ≅ △VTU and △RTU ≅ △VTS
△RTS ≅ △RVS and △RTU ≅ △STV
△VRS ≅ △VRU and △USR ≅ △USV
△VUR ≅ △VUS and △UVS ≅ △SRU

Answer:

342 sprouts are planted outside.

Step-by-step explanation:

500 sprouts

500*0.10=50

500-50=450

450*0.20=90

450-90=360

360*0.05=18

360-18=342

Answer:

Step-by-step explanation:

There are three terms. So, 14x² + 3x -15 is a trinomial

Answer:

22.3923

Step-by-step explanation:

Calculated based on 2 given angles and 1 given side.

∠A = 180° - B - C = 1.309 rad = 5/12π = 75°

a = b·sin(A)/sin(B) = 22.3923

c = b·sin(C)/sin(B) = 23.18222

Answer:

this would be 90 because you would need to multiply to answer it

Step-by-step explanation:

Answer:

3.67

Step-by-step explanation:

Because, 9% is literally just 9/100

and when you multiply that by 245 then you get 3.67

Answer:

=

3

6

Step-by-step explanation:

+

+

2

+

4

+

1

=

1

0

0

{\color{#c92786}{p}}+{\color{#c92786}{p}}+\frac{p}{2}+\frac{p}{4}+1=100

p+p+2p​+4p​+1=100

2

+

2

+

4

+

1

=

1

0

0.         2

+

2

+

4

+

1

=

1

0

0

2p+\frac{p}{2}+\frac{p}{4}+1=100

2p+2p​+4p​+1=100

2

+

2

+

4

+

1

−

1

=

1

0

0

−

1.              Subtract the numbers

Subtract the numbers

2

+

2

+

4

=

9

=

3

6

.        

Answer:

answer is a

the height of the water increases 2 inches per minute

Answer:

The height of the water increases 2 inches per minute.

Step-by-step explanation:

Answer:

0.3x1.71=0.513

Answer:

0.513 is the 100% correct answer for this question. Hope this helps! :)

Step-by-step explanation:

Answer: 4 miles

Step-by-step explanation:

The circumference of a circle can be calculated by using the formula:

= 2πr

where,

π = 22/7

r = radius = 7/11 miles

Therefore, circumference = 2πr

= 2 × 22/7 × 7/11

= 4 miles

Th circumference is 4 miles.

Answer:

X = 33.3 percent

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

no of rulers each student gets,=,no of rulers ÷ no of students

........=83÷s OR

83/s

Answer:

B. 0.067

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Number of arrangements:

The number of possible arrangements of n elements is given by:

[tex]A_{n} = n![/tex]

Desired outcomes

First red(10 - (5+2) = 3 possible)

Last red(2 possible).

Middle 8 arranged in any way.

So

[tex]D = 3*A_{8}*2 = 3*8!*2 = 241920[/tex]

Total outcomes:

Arrangements of 10 elements. So

[tex]T = A_{10} = 10! = 3628800[/tex]

What is the probability that the first and last blouse are both red?

[tex]p = \frac{D}{T} = \frac{241920}{3628800} = 0.067[/tex]

The correct answer is given by option B.

Answer:

g(-2) = -5

Step-by-step explanation:

We are given the following function:

[tex]g(x) = \sqrt[3]{x - 123}[/tex]

Find g( - 2).

This means that we find g when [tex]x = -2[/tex]. So

[tex]g(-2) = \sqrt[3]{-2 - 123} = \sqrt[3]{-125} = \sqrt[3]{-5^3} = -5[/tex]

So

g(-2) = -5

Answer:

$86.8

Step-by-step explanation:

Given that,

Principal, P = $80

Rate of interest, R = 8.5%

We need to find the money he will have in 1 year. As the interest is not compounded, it must be simple interest. The simple interest can be calculated by the formula,

[tex]I=\dfrac{PRT}{100}\\\\I=\dfrac{80\times 8.5\times 1}{100}\\\\=\$ 6.8[/tex]

We know that,

Amount = Principal + interest

= $80 + $6.8

= $86.8

Hence, the amount will become $86.8.

Answer:

y = 3cos(81x)

Step-by-step explanation:

Hello!

Here is the foundational equation to find sine and cosine:

y = A sin(B(x + C)) + D

Any cosine function can be written as a sine function. y = A sin(Bx) and y = A cos(Bx). The number, A, in front of sine or cosine changes the height of the graph. The value A (in front of sin or cos) affects the amplitude (height). B is the period by which the width of the wavelengths are measrured. C is known as the phase shift, which is positive to the left on graph. D is the vertical shift of function.

The amplitude changes the heaight of the cosine function by 3 units. The period is indicated as 81 and , but usually we must first use the equation that is the usual given: period = [tex]\frac{2\pi }{|B|}[/tex] . B must always have an absolute sign to have a psotive value. In this case, the period was given to us.

So, the final equation looks like this:

y = 3cos(81x)

Hope this helps!

Answer:

750 miles

Step-by-step explanation:

Given that,

The rental costs 350 per week plus 20 cents per mile.

Becky can spend no more than $500.

Let he travel x miles. We can form an equation as follows :

350 + 0.2x = 500

0.2x = 500-350

0.2x = 150

x = 750 miles

Hence, she can travel 750 miles.

Answer:

the answer is B 4/9.... I need 20 characters smh.

Answer:

4/9

Step-by-step explanation:

there are 4 numbers below ten and 9 numbers total

The direction of both forces will be on the positive x-axis. And the resultant force is 185.64 Newtons.

The product of the mass and acceleration is known as force.

Peyton and Tanner were lifting a large boulder and relocating it within their property.

Peyton is pushing the boulder with a force of 110 newtons at an angle of 55° with respect to the positive x-axis.

Tanner is pulling the boulder with a force of 165 newtons at an angle of 42° with respect to the positive x-axis.

The direction of both forces will be on the positive x-axis.

The pushing force will be

→ 110 × cos 55° = 63.09 N

The pulling force will be

→ 165 × cos 42° = 122.62 N

Then the resultant force will be

Resultant force = 63.02 + 122.62 = 185.64 N

More about the force link is given below.

https://brainly.com/question/13191643

Answer:

52

Step-by-step explanation:

find the area of each individual piece

top and bottom dimensions are 4 X 3- so each one is 12 inches squared

the left and right side dimensions are 4 X 2- each one is 8

the front and back dimensions are 3 X 2 each one is 6

Surface area- add all together

12+12+8+8+6+6= 52 in squared

Answer:

142

Step-by-step explanation:

hope this help love y all!

Answer:

3

Step-by-step explanation:

3+1=5

Answer:

if she goes 5 days a week then she will pay 45 dollars

she only had 2 pay 20$ one time and she pays 5 dollars each visit and she goes 5 times a week

5x5 is 25 and plus 20 will be 45 just within only that weel

Answer:

The answer is C i.e an=4n-7

9514 1404 393

Answer:

  5

Step-by-step explanation:

We presume the figure is a rectangular pyramid and that there are two hidden faces, one on the bottom and one at the back.

We can see 3 faces, so adding the two we presume we can't see, there are a total of 5 faces on this polyhedron.

Answer: -7/5x

To find slope, you use the formula (THE FORMULA IS IN A PICTURE ATTACHED BELOW)

So by following this formula we would get

-3 - 4               -7

---------      =  -----------

8 - 3                 5

So the slope is -7/5x; BTW most teachers prefer if the answer is still in a fraction not a decimal because it is often easier to graph.

We want to find the slope of the line that passes through the points (3, 4) and (8, -3). We will see that the slope is equal to -7/5

We know that for a line that passes through the points (x₁, y₁) and (x₂, y₂) the slope is given by:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

In this case, we know that the line passes through (3, 4) and (8, -3), then the slope is just:

[tex]a = \frac{-3 - 4}{8 - 3} = \frac{-7}{5}[/tex]

So we can see that the slope of that line is equal to -7/5.

If you want to learn more, you can read:

https://brainly.com/question/16180119

Answer:

28/45????????????????

Step-by-step explanation:

Answer:

Step-by-step explanation: The equation is s = 9.8 – 9.8e-0.88t and we need to find the speed if t or time = 2 so to solve this equation algebraically you would;

[tex]s = 9.8-9.8e-0.88(2)[/tex]

[tex]s = 9.8-9.8e-1.76[/tex]

[tex]s = 8.04-9.8e[/tex]

and after graphing it you would get

[tex]-18.5991619189[/tex]

which after rounding and using absolute value would be

[tex]s=18.6[/tex]

Answer:

the answer to the question is c

The equivalent expression to the equation is A = √ ( x² - 9 )

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.

It displays the similarity of the connections between the phrases on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are examples of the parts of an equation. When creating an equation, the "=" symbol and terms on both sides are necessary.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = √ ( x + 3 ) .√( x - 3 )

Now , on simplifying the roots of the equation , we get

A = √ ( x + 3 ) ( x - 3 )

The value of ( a + b ) ( a - b ) = a² - b²

So , on further simplification , we get

A = √ ( x² - 9 )

Therefore , the equivalent expression of A is √ ( x² - 9 )

Hence , the equation is A = √ ( x² - 9 )

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ7

Answer:

True

Step-by-step explanation:

I took the test!

Answer:

true is the answer

There are an infinite number of triangles which can be constructed with angles measuring this.

There are an infinite number of lengths the sides of the triangles can be while the angles stay the same measure.

9514 1404 393

Answer:

  BE = 266 2/3

  PE = 233 1/3

Step-by-step explanation:

Part A: The figure has 3 triangles, all similar. In order of shortest-to-longest side lengths, they are ...

  ΔBPE ~ ΔBCG ~ ΔGRE

__

Part B: They can be declared similar by the AA postulate. For BPE and BCG, the angles at B are vertical angles, so are congruent. The angles at C and G are alternate interior angles, so are congruent.

For triangles BPE and GRE, angle E is congruent to itself, The angles at R and P are corresponding angles, so are congruent.

(Remember, GRPC is a parallelogram, so any line in the figure is a transversal crossing parallel lines.)

__

Part C:

From parts A and B, we know ΔBPE ~ ΔBCG. Corresponding sides are proportional:

  BP/BC = BE/BG = PE/CG

  200/300 = BE/400 = PE/350

  BE = (400)(2/3) = 266 2/3

  PE = (350)(2/3) = 233 1/3