determine the value of x which r || s. then find m<1 and m<2.
m<1 = 60-4x
m<2= 80-12x

[tex] \frac{1}{12} \times \frac{1}{3} \\ = \frac{1 \times 1}{12 \times 3} \\ = \frac{1}{36} [/tex]

[tex]\displaystyle \frac{4x+3}{5} ^{/9}=\frac{8x-1}{9} ^{/5} \\\\\\ 36x+27=40x-5 \\\\ 40x-36x=27+5\\\\ 4x=32 \\\\ \boxed{x=8 }[/tex]

Step-by-step explanation:

Given fractional expression:

(4x+3)/5 = (8x-1)/9

By doing cross multiplication, we get

⇛4x(9) + 3(9) = 8x(5) - 1(5)

⇛36x + 27 = 40x - 5

Now, combine the like terms in one side.

⇛27x - 40x = -5 + 36

⇛-13x = 31

⇛x = 31/-13 Ans.

The option that gives the correct value of the second term is;

Option B; -73728x¹¹y

We are given the expression;

(2x - 3y)¹²

Now we want to find the second term using binomial expansion.

(x + y)² = x² + 2xy + y²

(x - y)³ = x³ - 3x²y + 3xy² + y³

(x - y)⁴ = x⁴ - 4x³y + 6x²y² - 4xy³ + y⁴

(x - y)¹² = x¹² - x¹¹y + x¹⁰y² - x⁹y³ + ....

Now applying this same system above to our question gives us;

(2x - 3y)¹² = 4096x¹² - 73728x¹¹y + 608256x¹⁰y² - 3041280x⁹y³ + ........

Thus, our second term here is; -73728x¹¹y

In conclusion, the correct option that gives the second term is Option B.

Read more at; https://brainly.com/question/24102756

Answer:

8

Step-by-step explanation:

rectangle length is 2-3w

w=2

3 x 2=6 - 2=4

l x w

4 x 2 =8

Answer:

76

Step-by-step explanation:

PQRS is a Rhombus.

Property of Rhombus : -

All sides are equal.

So,

PQ = QR = RN = NP

RN = 5x + 16

QR = 9x - 32

QR = RN

5x + 16 = 9x - 32

9x - 32 = 5x + 16

9x - 5x = 16 + 32

4x = 48

x = 48 / 4

x = 12

Substitute x = 12 in RN,

RN = 5x + 16

= 5 ( 12 ) + 16

= 60 + 16

RN = 76

Since,

PQ = QR = RN = NP

Therefore,

PQ = 76

The sine law of triangles can be proved by dividing the triangle into right-triangles.

Option (c) proves the first equality in the law of sines​

From the question, we have:

h equals to the distance from point C to segment AB

The sine of angle is:

[tex]\mathbf{sin(\theta) = \frac{Opposite}{Hypotenuse}}[/tex]

For angle at A, we have:

[tex]\mathbe{\theta = A}[/tex]

[tex]\mathbf{Hypotenuse = b}\\\mathbf{Opposite = h}[/tex]

So, we have:

[tex]\mathbf{sin(\theta) = \frac{Opposite}{Hypotenuse}}[/tex]

Substitute values for Opposite, Hypotenuse and theta

[tex]\mathbf{sin A = \frac{h}{b}}[/tex]

Similarly

[tex]\mathbf{sin B = \frac{h}{a}}[/tex]

Make h the subject

[tex]\mathbf{h = a\ sinB}[/tex]

Substitute [tex]\mathbf{h = a\ sinB}[/tex] in [tex]\mathbf{sin A = \frac{h}{b}}[/tex]

[tex]\mathbf{sin A = \frac{a\ sinB}{b}}[/tex]

Divide both sides by a

[tex]\mathbf{\frac{sin A}{a} = \frac{sinB}{b}}[/tex]

Hence, the correct option is (c).

Read more about proof of sine law at:

https://brainly.com/question/4637169

Answer:

40

Step-by-step explanation:

0.28÷0.007

=280÷7

=40

_________

[tex] \: [/tex]

0,28 ÷ 0,007 = ...

[tex] = \frac{28}{100} \div \frac{7}{1.000} [/tex]

[tex] = \frac{28}{100} \times \frac{1.000}{7} [/tex]

[tex] = \frac{28.0 \cancel{00}}{7 \cancel{00}} [/tex]

[tex] = \frac{280}{7} [/tex]

[tex] \longmapsto \boxed{ \bold{ \red{40}}}[/tex]

Answer:

x= -7

The whole thing is just an awkward mirror but the lower triangle has an angle that is 1 degree smaller so the whole lower section is going to be bigger or smaller and the angle that mirrors the 80 degree angle is now 79 degrees which makes the other angle on that line 1 degree bigger which would be 101 so you put it in the expession to make it the equation -12x+17=101 and you solve for x which you would then get -7.

Answer:

∠8 is 105° and ∠7 is 75°

Step-by-step explanation:

Angles 4 and 8 are corresponding angles, and are congruent.

Angles 8 and 7 are a linear pair

Answer:

8 millimeters 4x where x is 2 millimeters

Answer:

a. The real GDP increases by $200,000.

a. The real GDP increases by $150,000.

Step-by-step explanation:

a. What is the eventual effect on real GDP if the government increases its purchases of goods and services by $50,000?

Eventual effect on real GDP = Amount of increase in government spending * (1 /(1 - MPC)) = $50,000 * (1 / (1 – 0.75)) = $200,000

Therefore, the real GDP increases by $200,000.

a. What is the eventual effect on real GDP if the government, instead of changing its spending, increases transfers by $50,000?

Eventual effect on real GDP = (Amount of increase in government transfers * (1 /(1 - MPC))) - Amount of increase in government transfers = ($50,000 * (1 / (1 – 0.75))) - $50,000 = $150,000

Therefore, the real GDP increases by $150,000.

10 quarters 6 nickels 18 dimes

Answer:

24,000

Step-by-step explanation:

615 ≈ 600

38 ≈ 40

600 × 40 = 24,000

Therefore, 615 × 38 ≈ 24,000

Answer:

x=45 y=60

Step-by-step explanation:

the picture is kinda blurry but if im seeing it correctly its ^^^

9514 1404 393

Answer:

  C

Step-by-step explanation:

Judging by the answers, the lines have slopes of 7/3 and 2/5. (We could verify this by close examination of the graph.) The shading is above (greater than) the line with the smaller slope value (2/5), and below (less than) the line with the steeper slope value (7/3).

That means we're looking for a pair of inequalities with the symbols ...

  y ≥ 2/5x ...

  y ≤ 7/3x ...

This combination is found in choice C.

Answer:

D. ∠2 and ∠8

Step-by-step explanation:

common sense lol

Answer:

250

Step-by-step explanation:

As a decimal 253 and 19/23 can be written as 253.73

If we think about 253.73 being closer to 250 or 260, we can see that it is closer to 250, so that is the nearest ten we will round to.

Even if it is too difficult to convert to a decimal, if we round 19/23 to 23/23, our number becomes 254. The nearest ten is still 250.

Answer:

2/15

Step-by-step explanation:

1/3 x 2/5

= ( 1 x 2 ) / ( 3 x 5 )

= 2/15

Answer:

2/15

Step-by-step explanation:

1/3*2/5

(1*2)/(3*5)

2/15

Answer:

0.72

Step-by-step explanation:

64 hundredths= 0.64

8 hundredths= 0.08

0.64 + 0.08 = 0.72

Answer:

.72

Step-by-step explanation:

You just add 64 and 8 (equal to 72) and make sure it's in the hundredths (.00) Hope this is helpful.

Answer:

-7/4 < -2/3 < 0 < 0.6 < 3/4 < 3

Step-by-step explanation:

Answer:

yes because are slopes are the same

Answer:

4 blue balloons.

Step-by-step explanation:

Answer: 14

Step-by-step explanation: 4 + 3 = 7  and there are 21 balloons 21 - 7 = 14. and thats how you get 14

Using an exponential equation, it is found that it will be 7.3 years before the value is doubled.

The equation for an increasing exponential function is given by:

[tex]A(t) = A(0)(1 + r)^t[/tex]

In which:

In this problem:

The doubling time is t for which [tex]A(t) = 2A(0)[/tex], then:

[tex]A(t) = A(0)(1.1)^t[/tex]

[tex]2A(0) = A(0)(1.1)^t[/tex]

[tex](1.1)^t = 2[/tex]

[tex]\log{(1.1)^t} = \log{2}[/tex]

[tex]t\log{1.1} = \log{2}[/tex]

[tex]t = \frac{\log{2}}{\log{1.1}}[/tex]

[tex]t = 7.3[/tex]

It will be 7.3 years before the value is doubled.

A similar problem is given at https://brainly.com/question/23008760

Your answer should be 724 cents, in dollars that is $7.24

Step-by-step explanation:

from the cents is shoes be 724 and the dollars souls be $7.24

See the picture above for the solution.

Answer:

3 1/8

Step-by-step explanation:

3 3/4 and 1/6 percent of the water evaporated

3 3/4 as a inproper fraction 15/4  

15/4  * 1/6= 15/24 = 5/8

so we have to subtract 5/8 from 15/ 4

15/4*2/2= 30/8

30/8-5/8= 25/8

Answer:

3 1/8

Step-by-step explanation:

Answer:

978

explanation is a calculator