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3 years ago

Explain how to find the value of x. Be sure to include the postulates, definitions and theorems that justify your answer.

Mathematics

1 answer:

Black_prince [1.1K]3 years ago

7 0

Answer: x = 12

Step-by-step explanation:

We can see two triangles rectangles, we will use the angle S to solve this, as this angle is common to both triangles.

We know that:

cos(S) = adj cathetus/hipotenuse.

Then we have, for the triangle SRT.

Cos(S) = 9/SR.

for the big triangle, SQR, we have:

Cos(S) = SR/(9 + 16)

now we can find the quotient of those two equations and get:

cos(S)/cos(S) = 9/Sr*(9+16)/SR

SR^2 = 9*(25)

SR = 15.

Now with this side we can find the value of x.

We can use the Pythagorean theorem in the triangle SRT, where the sum of the squared cathetus is equal to the hypotenuse:

9^2 + x^2 = 15^2

x = √(15^2 - 9^2) = 12

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Please help I am horrible at math! Ye is riding home from a friend's house. After 5 minutes he is 4 miles from home, after 15 mi

vesna_86 [32]

Answer:

y=-0.2x+5. Correct choice: A)

Step-by-step explanation:

Modeling With Equations

Let's call x the number of minutes and y the distance from home. The correct model should meet both conditions:

After 5 minutes, Ye is 4 miles from home. This is the ordered pair (5,4)

After 15 minutes, Ye is 2 miles from home. This is the ordered pair (15,2)

A) y=-0.2x+5. Testing the first point (5,4): y=-0.2*5+5=4. Correct

Testing the second point (15,2): y=-0.2*15+5=2. Correct

This is the correct choice.

B) y=11/7x-27/7. Testing the first point: (5,4) y=11/7*5-27/7=4. Correct

Testing the second point (15,2). y=11/7*15-27/7=138/7. Incorrect

Incorrect choice.

C) This equation is equal to the choice B), thus this one is incorrect.

D) y=5x-0.2. The first point (5,4) yields to:

4=5*5-0.2=24.8 Incorrect.

6 0

3 years ago

Read 2 more answers

Joe bought 16 pounds of flour for $7. How many pounds of flour did he get per dollar?

wolverine [178]

Answer:

112

Step-by-step explanation:

7 0

3 years ago

Tom has a water tank that holds 5 gallons of water.Tom uses water from a full tank to fill 6 bottles that each hold 16 ounces an

REY [17]

1/2 Gallon is equal to 64 ounces
16 x 6 = 96
96 + 64 = 160
5 gallons is equal to 640
640 - 160 = 480

7 0

4 years ago

Determine which graph has the line of best fit drawn and explain why.

Nina [5.8K]

Answer:

graph c

Step-by-step explanation:

because it is a more perfect line through the dots then the others, thats how you can always tell

5 0

3 years ago

If the volume of a box is 2x3 + 4x2 − 30xwhich of the dimensions are possible with the given x-value?

Kipish [7]

The possible value of x = 4, dimensions 8 by 9 by 1 (option D), if the volume of a box is $2 x^{3} + 4 x^{2} -30x$ .

Step-by-step explanation:

The given is,

$2 x^{3} + 4 x^{2} -30x$ ................................(1)

Step:1

Check for option A,

x = 1, dimensions 8 by 9 by 1

From the equation (1),

Volume = $2 (1^{3}) + 4 (1^{2} )-30(1)$

$=2+4-30$ = -24...................(2)

From the dimensions,

Volume = ( 8 × 9 × 1 )

= 72............................................(3)

From equation (2) and (3)

-24 ≠ 72

So, X=1; dimensions 8 by 9 by 1 is not possible.

Check for option B,

x = 1, dimensions 2 by 5 by 3

From the equation (1),

Volume = $2 (1^{3}) + 4 (1^{2} )-30(1)$

$=2+4-30$ = -24...................(4)

From the dimensions,

Volume = ( 2 × 5 × 3 )

= 30.........................................(5)

From equation (4) and (5)

-24 ≠ 30

So, X=1; dimensions 2 by 5 by 3 is not possible.

Check for option C,

x = 4, dimensions 2 by 5 by 3

From the equation (1),

Volume = $2 (4^{3}) + 4 (4^{2} )-30(4)$

$=2(64)+4(16)-30(4)$

$= 128+64-120$

= 72.............................................(6)

From the dimensions,

Volume = ( 2 × 5 × 3 )

= 30............................................(7)

From equation (6) and (7)

72 ≠ 30

So, X=4; dimensions 2 by 5 by 3 is not possible.

Check for option C,

x = 4, dimensions 8 by 9 by 1

From the equation (1),

Volume = $2 (4^{3}) + 4 (4^{2} )-30(4)$

$=2(64)+4(16)-30(4)$

$= 128+64-120$

= 72............................................(8)

From the dimensions,

Volume = ( 8 × 9 × 1 )

= 72............................................(9)

From equation (8) and (9)

72 = 72

So, X=4; dimensions 8 by 9 by 3 is possible.

Result:

The possible value of x = 4, dimensions 8 by 9 by 1 (option D), if the volume of a box is $2 x^{3} + 4 x^{2} -30x$ .

4 0

3 years ago