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Solnce55 [7]
3 years ago
7

Given ^MNO = ^PQR,

Mathematics
1 answer:
Nataly_w [17]3 years ago
6 0

Answer:

Part 1) PQ=10\ units

Part 2) PR=7\ units

Step-by-step explanation:

<u><em>The correct question is</em></u>

The triangles MNO and PQR are congruent. (MNO≅PQR)

Find the lengths of PQ and PR.

we know that

If two figures are congruent, then its corresponding sides are congruent

In this problem

MN and PQ are corresponding sides

MO and PR are corresponding sides

NO and QR are corresponding sides

therefore

MN≅PQ

MO≅PR

NO≅QR

step 1

Find the value  of y

we have

MN = 6 +2y\\ PQ = 3y + 4

equate the equations

3y + 4=6 +2y

solve for y

3y-2y=6-4

y=2

step 2

Find the length of PQ

PQ = 3y + 4

substitute the value of y

PQ = 3(2) + 4=10\ units

step 3

Find the value  of x

we have

MO = 2x + 1\\PR = 10 - x

equate the equations

2x+1=10-x

solve for x

2x+x=10-1

3x=9

x=3

step 4

Find the length of PR

PR = 10 - x

substitute the value of x

PR = 10-3=7\ units

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Surface area of cube = 6 * (side)^2
side^2 = surface area / 6
side = sqrt (surface area / 6)

For the cube with area 1200 square inches:
side = sqrt(surface area / 6)
side = sqrt(1200 / 6) 
side = 14.1421 inches

For the cube with area 768 square inches:
side = sqrt(surface area / 6) 
side = sqrt(768 / 6) 
side = 11.3137 inches

difference between the two lengths = 14.1421 - 11.3137 = 2.8284 inches

Based on the above calculations, the side of the cube with surface area 1200 square inches is  2.8284  inches longer than the side of the cube with surface area 768 square inches
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3 years ago
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Answer:

a) 900 dollars

b) 5900 dollars

Step-by-step explanation:

The complete question is

A new bank customer with $5,000 wants to open a money market account. The bank is offering a simple interest rate of 1.8%. a. How much interest will the customer earn in 10 years? b. What will the account balance be after 10 years?

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FULL POINTS AND BRAINLIEST
HACTEHA [7]

Answer:

2) y = 0.95x + 4

3) slope: height increases by 0.95 units as x increases by 1 unit

intercept: initial height

Step-by-step explanation:

Using (20,23) and (40,42)

Slope: (42 - 23)/(40 - 20)

0.95

y = 0.95x+ c

23 = 0.95(20) + c

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3 years ago
Polly buys 14 cupcakes for a party. The bakery puts them into boxes that hold 4 cupcakes each.
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Answer:

Part a) The number of boxes needed will be 4

part b) The fraction of the box that is empty is \frac{1}{2}

Part c) Are needed 2 cupcakes to fill the last box

Step-by-step explanation:

Part a) How many boxes will be needed for Polly to bring all the cupcakes to the party?

To find out the number of boxes needed, divide the total number of cupcakes by 4 (maximum number of cupcakes that fit in each box).

so

\frac{14}{4}=3.5\ box

Round up

The number of boxes needed will be 4

Part b) If the bakery completely fills as many boxes as possible, what fraction of the last box is empty?

we know that

The maximum number of cupcakes per box is 4

The first three boxes have 4 cupcakes

The last box has

14-3(4)=2\ cupcakes

The fraction of the box that is empty is equal to the number of cupcakes missing to fill the box divided by the cupcake capacity of the box

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Part c) How many more cupcakes are needed to fill this box

Subtract the number of cupcakes in the box from the cupcake capacity of the box

The last box has 2 cupcakes

The cupcake capacity of the box is 4

so

4-2=2\ cupcakes

therefore

Are needed 2 cupcakes to fill the last box

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How to identify vertical angles
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Answer:

You identify them by examining them and if you examine them, eventually you will identify.

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