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Lelechka [254]
3 years ago
6

The table shows a proportional relationship between x and y.

Mathematics
1 answer:
Free_Kalibri [48]3 years ago
8 0

Answer:

D

Step-by-step explanation:

if y is 4 then x is -12 Because 4 times -3 is -12

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Please show the working and answer. you can take a picture for the working.
baherus [9]

Answer:

(a) The area of the triangle is approximately 39.0223 cm²

(b) ∠SQR is approximately 55.582°

Step-by-step explanation:

(a) By sin rule, we have;

SQ/(sin(∠SPQ)) = PQ/(sin(∠PSQ)), which gives;

5.4/(sin(52°)) = 6.8/(sin(∠PSQ))

∴ (sin(∠PSQ)) = (6.8/5.4) × (sin(52°)) ≈ 0.9923

∠PSQ = sin⁻¹(0.9923) ≈ 82.88976°

Similarly, we have;

5.4/(sin(52°)) = SP/(sin(180 - 52 - 82.88976))

Where, 180 - 52 - 82.88976 = ∠PQS = 45.11024

SP = 5.4/(sin(52°))×(sin(180 - 52 - 82.88976)) ≈ 4.8549

Given that RS : SP = 2 : 1, we have;

RS = 2 × SP = 2 × 4.8549 ≈ 9.7098

We have by cosine rule, \overline {RQ}² =  \overline {SQ}² +  \overline {SR}² - 2 × \overline {SQ} × \overline {SR} × cos(∠QSR)

∠QSR and ∠PSQ are supplementary angles, therefore;

∠QSR = 180° - ∠PSQ = 180° - 82.88976° = 97.11024°

∠QSR = 97.11024°

Therefore;

\overline {RQ}² =  5.4² +  9.7098² - 2 ×  5.4×9.7098× cos(97.11024)

\overline {RQ}² ≈ 136.42

\overline {RQ} = √(136.42) ≈ 11.6799

The area of the triangle = 1/2 ×\overline {PQ} × \overline {PR} × sin(∠SPQ)

By substituting the values, we have;

1/2 ×\overline {PQ} × \overline {PR} × sin(∠SPQ)

1/2 × 6.8 × (4.8549 + 9.7098) × sin(52°) ≈ 39.0223 cm²

The area of the triangle ≈ 39.0223 cm²

(b) By sin rule, we have;

\overline {RS}/(sin(∠SQR)) = \overline {RQ}/(sin(∠QSR))

By substituting, we have;

9.7098/(sin(∠SQR)) = 11.6799/(sin(97.11024))

sin(∠SQR) = 9.7098/(11.6799/(sin(97.11024))) ≈ 0.82493

∠SQR = sin⁻¹(0.82493) ≈ 55.582°.

8 0
3 years ago
PLEASE HELP ME!! GIVING BRAINLIEST AND 5 STARS
Marizza181 [45]
4(x+2)=4x+8
2(x-1)=2x-2
2(x+1)=2x+2

You use disruptive property when solving equations like this.
6 0
2 years ago
What is the lcd of 8/15 11/30 and 3/5
pogonyaev

Answer:

LCD(8/ 15 , 11/ 30 , 3/ 5 ) = LCM(15, 30, 5) = 2×3×5 = 30

Step-by-step explanation:

7 0
2 years ago
a recipe uses 1 1/4 cups of milk to make 10 servings. if the same amount of milk is used for each serving how mant servings can
laiz [17]

Answer:

I believe its 36

Step-by-step explanation:

so what i id is a took apart the answer, if 1 1/4 if 10 cups the 1/4 1/4 1/4 1/4 1/4 would also be 10 cups, so now i know that 1/4 = 2 servings

eso i took 3. 1/4 and that gave me 6 and now add the previous which is 10 so its 16 and i have   2 cups left

from here i knew 1 cup and 1/4 is 10 so subtract 1/4 which is -2 servings and you have 8 and 8+8 is 16 so

then i added

16+16= 36

which leads to my final answer of 36

Im so sorry if im wronge but if its right please give brainlest

7 0
2 years ago
The length of a rectangular picture is 5 inches more than three times the width. Find the dimensions of the picture if its perim
luda_lava [24]

Answer:

<h3>Length = 29 inches</h3><h3>Width = 8 inches</h3><h3 />

Step-by-step explanation:

Perimeter of a rectangle = 2l + 2w

where

l is the length of the rectangle

w is the width

From the question

length of a rectangular picture is 5 inches more than three times the width is written as

l = 5 + 3w

Now substitute this into the above equation

Perimeter = 74 inches

74 = 2(5 + 3w) + 2w

74 = 10 + 6w + 2w

8w = 74 - 10

8w = 64

Divide both sides by 8

w = 8 inches

Substitute w = 8 into l = 5 + 3w

That's

l = 5 + 3(8)

l = 5 + 24

l = 29 inches

<h3>Length = 29 inches</h3><h3>Width = 8 inches</h3>

Hope this helps you

4 0
3 years ago
Read 2 more answers
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