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umka21 [38]
3 years ago
15

Find the value of x

Mathematics
1 answer:
balu736 [363]3 years ago
6 0

Equals 180 because the exterior angle in question is equal to the sum of the other two angles in the triangle. In other words, the other two angles in the triangle (the ones that add up to form the exterior angle) must combine with the angle in the bottom right corner to make a 180 degree angle.

-----------------------------------

Add whole numbers.

2x + 1 + 37 + 118 = 180

Add whole number (if there is any).

2x + 38 +118 = 180

Subtract 156 from both sides to have one side have a variable.

2x + 156 = 180

     -156     -156

Divide both sides by 2 because you don't need the whole number with the variable.

2x = 24

---    ----

2       2

You get the answer as 12.

x = 12

Check:

2(12) + 1 + 37 + 118 = 180

24 + 1 + 37 + 118 = 180

25 + 37 + 118 = 180

62 + 118 = 180

180 = 180

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Evaluate the double integral.
Fynjy0 [20]

Answer:

\iint_D 8y^2 \ dA = \dfrac{88}{3}

Step-by-step explanation:

The equation of the line through the point (x_o,y_o) & (x_1,y_1) can be represented by:

y-y_o = m(x - x_o)

Making m the subject;

m = \dfrac{y_1 - y_0}{x_1-x_0}

∴

we need to carry out the equation of the line through (0,1) and (1,2)

i.e

y - 1 = m(x - 0)

y - 1 = mx

where;

m= \dfrac{2-1}{1-0}

m = 1

Thus;

y - 1 = (1)x

y - 1 = x ---- (1)

The equation of the line through (1,2) & (4,1) is:

y -2 = m (x - 1)

where;

m = \dfrac{1-2}{4-1}

m = \dfrac{-1}{3}

∴

y-2 = -\dfrac{1}{3}(x-1)

-3(y-2) = x - 1

-3y + 6 = x - 1

x = -3y + 7

Thus: for equation of two lines

x = y - 1

x = -3y + 7

i.e.

y - 1 = -3y + 7

y + 3y = 1 + 7

4y = 8

y = 2

Now, y ranges from 1 → 2 & x ranges from y - 1 to -3y + 7

∴

\iint_D 8y^2 \ dA = \int^2_1 \int ^{-3y+7}_{y-1} \ 8y^2 \ dxdy

\iint_D 8y^2 \ dA =8 \int^2_1 \int ^{-3y+7}_{y-1} \ y^2 \ dxdy

\iint_D 8y^2 \ dA =8 \int^2_1  \bigg ( \int^{-3y+7}_{y-1} \ dx \bigg)   dy

\iint_D 8y^2 \ dA =8 \int^2_1  \bigg ( [xy^2]^{-3y+7}_{y-1} \bigg ) \ dy

\iint_D 8y^2 \ dA =8 \int^2_1  \bigg ( [y^2(-3y+7-y+1)]\bigg ) \ dy

\iint_D 8y^2 \ dA =8 \int^2_1  \bigg ([y^2(-4y+8)] \bigg ) \ dy

\iint_D 8y^2 \ dA =8 \int^2_1  \bigg ( -4y^3+8y^2 \bigg ) \ dy

\iint_D 8y^2 \ dA =8 \bigg [\dfrac{ -4y^4}{4}+\dfrac{8y^3}{3} \bigg ]^2_1

\iint_D 8y^2 \ dA =8 \bigg [ -y^4+\dfrac{8y^3}{3} \bigg ]^2_1

\iint_D 8y^2 \ dA =8 \bigg [ -2^4+\dfrac{8(2)^3}{3} + 1^4- \dfrac{8\times (1)^3}{3}\bigg]

\iint_D 8y^2 \ dA =8 \bigg [ -16+\dfrac{64}{3} + 1- \dfrac{8}{3}\bigg]

\iint_D 8y^2 \ dA =8 \bigg [ -15+ \dfrac{64-8}{3}\bigg]

\iint_D 8y^2 \ dA =8 \bigg [ -15+ \dfrac{56}{3}\bigg]

\iint_D 8y^2 \ dA =8 \bigg [  \dfrac{-45+56}{3}\bigg]

\iint_D 8y^2 \ dA =8 \bigg [  \dfrac{11}{3}\bigg]

\iint_D 8y^2 \ dA = \dfrac{88}{3}

4 0
2 years ago
1. A bag contains red apples and yellow apples. The ratio of red apples to yellow apples in the bag is 9 to 4. How many apples a
andre [41]

Answer:

?

Step-by-step explanation:

You can’t know that, because you don’t know how many total apples there are.

6 0
2 years ago
which graph represnts a line with a slope ot -2/3 and a y-intercept equal to that of the line y=2/3x-2?
tia_tia [17]
The graph will be as shown in attached figure

4 0
3 years ago
Tori uses the greatest common factor and the distributive property to rewrite this sum:
vovikov84 [41]
12(2+7)

12 is the GCF for 24 with 12 x2 =24 and 12 is the GCF for 84 with 12 x7= 84.
6 0
3 years ago
Read 2 more answers
2x+7y=-20, y=3x+7. solve using elimination
Setler79 [48]

Answer:

(x,y) = (-3,-2)

Step-by-step explanation: Please brainliest!

8 0
2 years ago
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