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3 years ago

How do I solve this with Substitution?

Mathematics

1 answer:

TiliK225 [7]3 years ago

8 0

They give you an "x =" statement so you plug in the right side of the equals sign into the first equation wherever x appears. So...

y = 10 - 2(y - 4)
y = 10 - 2y + 8
y = 18 - 2y
y + 2y = 18
3y = 18
y = 6

Now we plug in this result for the y-value into the "x =" statement.

x = 6 - 4
x = 2

Your answer is (2, 6)

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Trapezoid MNPQ is similar to Trapezoid RSTU. What is the length of the "x" on the misside side NP ? Also, what is the length of

ivolga24 [154]

Answer:

$x = 15$

$y = 25$

Step-by-step explanation:

Given

See attachment for MNPQ and RSTU

Required

Find x and y

To solve this question, we make use of equivalent ratios of corresponding side lengths.

The ratio of corresponding sides are:

$MN : RS$

$NP : ST$

$PQ : TU$

$MQ : RU$

From the attachment, we have:

$MN : RS \to 18 : 30$

$NP : ST \to x : 25$

$PQ : TU \to 15 : y$

To solve for x, we equate $MN : RS$ and $NP : ST$

$18 : 30 = x : 25$

Express as fraction

$\frac{18 }{ 30 }= \frac{x }{ 25}$

Make x the subject

$x = 25 * \frac{18 }{ 30 }$

$x = \frac{25 * 18 }{ 30 }$

$x = \frac{450}{ 30 }$

$x = 15$

To solve for y, we equate $MN : RS$ and $PQ : TU$

$18 : 30 = 15 : y$

Express as fraction

$\frac{18 }{ 30 }= \frac{15 }{ y}$

Make y the subject

$y = 15 * \frac{30 }{ 18 }$

$y = \frac{15 *30}{ 18 }$

$y = \frac{450}{ 18 }$

$y = 25$

8 0

3 years ago

-4(10-a)=36 what the steps

SpyIntel [72]

Hey there!☺

$Answer:\boxed{a=19}$

$Explanation:$

$-4(10-a)=36$ Equation

−4(10 − a) = 36 Simplify both sides

(−4)(10) + (−4)(−a) = 36 Distribute

−40 + 4a = 36

4a − 40 = 36

4a - 40 + 40 = 36 + 40 Add 40 to both sides

4a = 76

4a/4 = 76/4 Divide both sides by 4

76/4 = 19 Simplify 76/4

a = 19

Hope this helps!

8 0

3 years ago

Macy is painting a design that contains two repeating patterns. One pattern repeats every 8 inches. The other repeats every 12 i

spayn [35]

Answer:

8-inch pattern is fully printed 28 times.

12-inch pattern is fully printed 19 times.

Patterns start at the same place 9 times

Step-by-step explanation:

1. 19 feet is 228 inches.

2. 8-inch pattern is fully printed 28 times.

3. 12-inch pattern is fully printed 19 times.

4. 8-inch patterns starts at`0,8,16,24,32,40,48...

5. 12-inch pattern starts at 0,12,24,48...

6. As you see they start at the same place after 24 inches.

7. 228/24=9.5, => They start at the same place 9 times.

3 0

3 years ago

Evaluate the integral of the quotient of the cosine of x and the square root of the quantity 1 plus sine x, dx.

VMariaS [17]

Answer:

∫((cos(x)*dx)/(√(1+sin(x)))) = 2√(1 + sin(x)) + c.

Step-by-step explanation:

In order to solve this question, it is important to notice that the derivative of the expression (1 + sin(x)) is present in the numerator, which is cos(x). This means that the question can be solved using the u-substitution method.

Let u = 1 + sin(x).

This means du/dx = cos(x). This implies dx = du/cos(x).

Substitute u = 1 + sin(x) and dx = du/cos(x) in the integral.

∫((cos(x)*dx)/(√(1+sin(x)))) = ∫((cos(x)*du)/(cos(x)*√(u))) = ∫((du)/(√(u)))

= ∫(u^(-1/2) * du). Integrating:

(u^(-1/2+1))/(-1/2+1) + c = (u^(1/2))/(1/2) + c = 2u^(1/2) + c = 2√u + c.

Put u = 1 + sin(x). Therefore, 2√(1 + sin(x)) + c. Therefore:

∫((cos(x)*dx)/(√(1+sin(x)))) = 2√(1 + sin(x)) + c!!!

4 0

3 years ago

Read 2 more answers

Idk the answer to this question please help me

erica [24]

2/3 x 42/3
hope this helps

7 0

3 years ago