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4 years ago

If DF = 9x -39 find EF

Mathematics

2 answers:

Klio2033 [76]4 years ago

7 0

|DF| = |DE| + |EF|

|DF| = 9x -36

|DE| = 47

|EF| = 3x+10

Substitute:

9x - 39 = 47 + 3x + 10

9x - 39 = 3x + 57 |+39

9x = 3x + 96 |-3x

6x = 96 |:6

x = 16

Put the value of x to the equation |EF| = 3x + 10

|EF| = (3)(16) + 10 = 48 + 10 = 58

Answer: |EF| = 58

tekilochka [14]4 years ago

5 0

Answer: The required length of EF is 58 units.

Step-by-step explanation: Given that DF = 9x - 39, DE = 47 units and EF = 3x + 10.

We are to find the length of EF.

We have

$DE+EF=DF\\\\\Rightarrow 47+(3x+10)=9x-39\\\\\Rightarrow 3x+57=9x-39\\\\\Rightarrow 9x-3x=57+39\\\\\Rightarrow 6x=96\\\\\Rightarrow x=\dfrac{96}{6}\\\\\Rightarrow x=16.$

Therefore, the length of EF is given by

$EF=3\imes16+10=48+10=58.$

Thus, the required length of EF is 58 units.

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Answer:

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Step-by-step explanation:

Given that,

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3 years ago

Jorden leaves home for school on his bike everyday at 6:00 AM, traveling at 32 km/h. one day he forgot his homework, which his m

densk [106]

Answer:

She caught up with Jordan at 6:39 AM

Step-by-step explanation:

We solve this question making linear functions for the distances that Jorden and his mom have driven, and then we equalize them to find the moment they caught up.

Jorden leaves home for school on his bike everyday at 6:00 AM, traveling at 32 km/h.

Her mom will have left 15 minutes after he left, when he will already have traveled $\frac{15*32}{60} = \frac{32}{4} = 8\text{km}$

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His mom goes after him starting from home, so the initial position is 0, with a velocity of 52 km/h. So her position can be modeled by the following function:

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She catches up t minutes after 6:15 AM.

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3 years ago

A soup can in the shape of a right circular cylinder is to be made from two materials. The material for the side of the can cost

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Answer:

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Let the radius of the can is 'r' and height of the can is 'h'.

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Now the function that represents the cost to construct the can will be

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Now we place the value of h in the equation (1) from equation (2)

$C=0.054\pi r^{2}+0.03\pi r(\frac{16}{\pi r^{2}})$

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Now for C' = 0

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3 years ago

50 POINTS EACH HEEEEELP !!!!!

Phoenix [80]

Hello there,

The <em>answer is </em>A' (-3,2).

<h3>Step-by-step explanation:-</h3>

From the image shown on the xy-plane, the coordinate of point A is at (3,-2).

The rule for rotation by 180° about the origin is (x,y)→(-x, -y), where (x,y) is the coordinate of image and (-x, -y) is the coordinate of the resulting pre-image.

Given the coordinate point A(3,-2), if this coordinate is rotated 180°, the resulting point A' will be located at (-3,-(-2)) = (-3,2).

Therefore, the answer will be <u>A'(-3,2)</u>

✍️ <em>by </em><em>Benjemin</em> ☺️

8 0

3 years ago

Read 2 more answers

A dog pen in the shape of a rectangle is to be built using one wall of a house as a side. If 132 feet

diamong [38]

This is a very poorly written question. im assuming the house wall is at least 130 ft since there is no information given about it.

each set of side lengths has three elements, the long side and the two short sides. we're asked to list all whole number possibilities so start anywhere, the two short sides being 1ft
(1 1 130). the long side has to be the difference of 132 and the length of both short sides.

the area is one of the short sides times the ling side, in the first case 1*130=130 sqft

continuing the list

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122÷4=30.5

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(31 31 70) area = 2170

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(34 34 64) area = 2176

so the area is decreasing now which means the maximum area is found when thw long side is 66 feet and the short sides are 33 feet.

as far as listing all possibilities, you see the pattern i started, i leave the rest to you

6 0

3 years ago