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4 years ago

Given m||n, find the value of x. 135

Mathematics

1 answer:

Viefleur [7K]4 years ago

7 0

Answer: Option C.

Step-by-step explanation:

Let as consider the complete question is same as question shown in the below figure.

In the figure m║n.

If a transversal line intersect two parallel lines then same sided interior angles are supplementary angles and their sum is 180 degrees.

$3x+x=180^{\circ}$

$4x=180^{\circ}$

Divide both sides by 4.

$x=\dfrac{180^{\circ}}{4}$

$x=45^{\circ}$

The value of x is 45 degrees.

Therefore, the correct option is C.

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A cake recipe calls for two eggs per cake. Sydney used 20 eggs in this recipe for a bake sale. How many cakes did she bake?

Alex787 [66]

20 / 2 = 10

Sydney baked 10 cakes :D

8 0

4 years ago

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CDs R Us sells books on tape and on Cd. Tapes sell for $10 and Cds sell for $15.

jeyben [28]

Answer:

10 tapes and 6 Cds

Step-by-step explanation:

As tapes sell for $10 and CD sell for $15, let t be the number of tapes bought and c the number of cds, we can write an equation for the expenditure in the form:

10c + 16t = expenditure

We also n=know she spent 220, so:

10c + 16t = 220

As she bought 16 items, the sum of CD and tapes must be equal to 16. So:

c + t = 16

If we take this last equation and subtract t in both sides:

c = 16 - t

We got the number of CD depending on the number of tapes. We can replace this in the first equation to get t:

10 [16 - t] + 16t = 220

160 - 10 t +16t = 220

160 + 6t = 220

If we subtract 160 in both sides

6t = 220 - 160

6t = 60

Dividing both by 6:

t = 60/6 = 10

So, she purchased 10 tapes. As in total she purchased 16 items she must have purchased 6 cds.

Solution: She purchased 10 tapes and 6 CDs

4 0

4 years ago

A bakery uses 37 1/2 cups of flour to make 25 loaves of bread each day. Write a fraction that shows how many 1/4 cups of flour a

Elanso [62]

Answer: 74/25

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

You are given the polar curve r = e^θ

galina1969 [7]

The tangent to $r(\theta)=e^\theta$ has slope $\frac{\mathrm dy}{\mathrm dx}$ , where

$\begin{cases}x(\theta)=r(\theta)\cos\theta\\y(\theta)=r(\theta)=\sin\theta\end{cases}$

By the chain rule, we have

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\frac{\mathrm dy}{\mathrm d\theta}}{\frac{\mathrm dx}{\mathrm d\theta}}$

and by the product rule,

$\dfrac{\mathrm dx}{\mathrm d\theta}=\dfrac{\mathrm dr}{\mathrm d\theta}\cos\theta-r(\theta)\sin\theta$

$\dfrac{\mathrm dy}{\mathrm d\theta}=\dfrac{\mathrm dr}{\mathrm d\theta}\sin\theta+r(\theta)\cos\theta$

so that with $\frac{\mathrm dr}{\mathrm d\theta}=e^\theta$ , we get

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{e^\theta\sin\theta+e^\theta\cos\theta}{e^\theta\cos\theta-e^\theta\sin\theta}=\dfrac{\sin\theta+\cos\theta}{\cos\theta-\sin\theta}=-\dfrac{1+\sin(2\theta)}{\cos(2\theta)}$

The tangent line is horizontal when the slope is 0; this happens for

$-\dfrac{1+\sin(2\theta)}{\cos(2\theta)}=0\implies\sin(2\theta)=-1\implies2\theta=-\dfrac\pi2+2n\pi\implies\theta=-\dfrac\pi4+n\pi$

where $n$ is any integer. In the interval $0\le\theta\le2\pi$ , this happens for $n=1,2$ , or

$\theta=\dfrac{3\pi}4\text{ and }\theta=\dfrac{7\pi}4$

i.e at the points

$(r,\theta)=\left(e^{3\pi/4},\dfrac{3\pi}4\right)$

and

$(r,\theta)=\left(e^{7\pi/4},\dfrac{7\pi}4\right)$

8 0

3 years ago

How many solutions does the system have?

siniylev [52]

If you would like to know how many solutions does the system of two equations have, you can calculate this using the following steps:

x = -4y + 4 ... x + 4y = 4 /*(2)
2x + 8y = 8
____________
2x + 8y = 8
<span>2x + 8y = 8
</span>____________
0 = 0

The correct result would be infinitely many solutions.

4 0

3 years ago