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dimaraw [331]
3 years ago
10

A line passes through (−1, 5) and (1, 3). Which answer is the equation of the line?

Mathematics
1 answer:
UNO [17]3 years ago
4 0

Answer:

d) x+y = 4

Step-by-step explanation:

(−1, 5) and (1, 3)

y = mx + b

m = (3 - 5) / (1 - (-1)) = -2 / 2 = -1

b = y - mx = 3 - ((-1) x 1) = 4

equation:  y = -x + 4

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The isosceles trapezoids, ABCD and EFGH, are similar quadrilaterals. The scale factor between the trapezoids is 2:3, = 6 centime
Bingel [31]

Answer:

Part A) see the explanation

Part B) see the explanation

Part C) The perimeter of trapezoid ABCD is 32 centimeters and the perimeter of trapezoid EFGH is 48 centimeters

Step-by-step explanation:

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

The isosceles trapezoids, ABCD and EFGH, are similar quadrilaterals. The scale factor between the trapezoids is 2:3, GH = 6 centimeters, AD = 8 centimeters, and AB is three times the length of DC

Part A) Write a similarity statement for each of the four pair of corresponding sides

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional

The corresponding sides are

AB and EF

BC and FG

CD and GH

AD and EH

so

\frac{AB}{EF}=\frac{BC}{FG}=\frac{CD}{GH}=\frac{AD}{EH}

Part B) Write a congruence statement for each of the four pair of corresponding angles.

we know that

If two figures are similar, then its corresponding angles are congruent

The corresponding angles are

∠A and ∠E

∠B and ∠F

∠C and ∠G

∠D and ∠H

so

∠A ≅ ∠E

∠B ≅ ∠F

∠C ≅ ∠G

∠D ≅ ∠H

Part C) Determine the perimeter for each of the isosceles trapezoids

we have

The scale factor between the trapezoids is 2:3, GH = 6 centimeters, AD = 8 centimeters, and AB is three times the length of DC

step 1

Find the measure of CD

Remember that

The ratio between corresponding sides is proportional and this ratio is the scale factor

Let

z ----> the scale factor

z=\frac{2}{3}

so

\frac{2}{3}=\frac{CD}{GH}}

we have

GH=6\ cm

substitute

\frac{2}{3}=\frac{CD}{6}}\\\\CD=4\ cm

step 2

Find the measure of AB

Remember that

AB is three times the length of DC

so

AB=3DC

DC=CD=4\ cm

substitute

AB=3(4)=12\ cm

step 3

Find the measure of BC

Remember that in an isosceles trapezoid, the legs are equal

so

BC=AD

we have

AD=8\ cm

therefore

BC=8\ cm

step 4

Find the perimeter of trapezoid ABCD

P=AB+BC+CD+AD

substitute the values

P=12+8+4+8=32\ cm

step 5

Find the perimeter of trapezoid EFGH

we know that

If two figures are similar, then the ratio of its perimeters is equal to the scale factor

Let

z ---> the scale factor

x ----> the perimeter of trapezoid ABCD

y ----> the perimeter of trapezoid EFGH

so

z=\frac{x}{y}

we have

z=\frac{2}{3}

x=32\ cm

substitute

\frac{2}{3}=\frac{32}{y}

y=32(3)/2=48\ cm

therefore

The perimeter of trapezoid EFGH is 48 centimeters

3 0
2 years ago
Marsha has some math exercises to do for homework. She did one half during study period and two thirds of those remaining while
Paha777 [63]

Answer: She has 1 5/6 exercises for homework.

Step-by-step explanation:

1/2 + 2/3 = 1 1/6

2 * 3 = 6 3 * 2 = 6

1 * 3 = 3 2 * 2 = 4

4 + 3/ 3 + 3

7/6 = 1 1/6

So, she finished 1 1/6 of her problems.

3 - 1 1/6 = 1 5/6

3 - 1 = 2

2 - 1/6 = 1 5/6

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10.) If a system of equations are dependent what is unique about the lines 2 point
MrRa [10]

Step-by-step explanation:

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There’s no photo so we can’t help you sorry :(
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Which decimals are less than –0.8? choose all answers that are correct.
sergey [27]
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