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3 years ago

Find the value of x. I Need to show the equations please, and show my work

Mathematics

2 answers:

defon3 years ago

6 0

Answer:

Step-by-step explanation:

since both equations are set with a right angle, the equation must be equal to 90 degrees. So you set the equation as

13+x+4x+2=90

add the x variables together and the constants separately

15+5x=90

then subtract 15 from both sides.

15+5x=90

-15 -15

5x=75

then divide 5 from both sides.

75/5= 15

so x is 15 :).

Volgvan3 years ago

4 0

Answer:

It shows a 90° angle split into 2 separate angles so,

$13 + x + 4x + 2 = 90\\\\5x + 15 = 90\\\\5x = 75\\\\x = 15$

Basically, the total angle measure of the given angles [90°, (13 + x)°, and (4x + 2°) equals 180°. Take away 90 from 180 and you get 90, then solve for x using what's left: 13 + x + 4x + 2 = 90. You get x = 15.

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Field book of an land is given in the figure. It is divided into 4 plots . Plot I is a right triangle , plot II is an equilatera

Kazeer [188]

Answer:

Total area = 237.09 cm²

Step-by-step explanation:

Given question is incomplete; here is the complete question.

Field book of an agricultural land is given in the figure. It is divided into 4 plots. Plot I is a right triangle, plot II is an equilateral triangle, plot III is a rectangle and plot IV is a trapezium, Find the area of each plot and the total area of the field. ( use √3 =1.73)

From the figure attached,

Area of the right triangle I = $\frac{1}{2}(\text{Base})\times (\text{Height})$

Area of ΔADC = $\frac{1}{2}(\text{CD})(\text{AD})$

= $\frac{1}{2}(\sqrt{(AC)^2-(AD)^2})(\text{AD})$

= $\frac{1}{2}(\sqrt{(13)^2-(19-7)^2} )(19-7)$

= $\frac{1}{2}(\sqrt{169-144})(12)$

= $\frac{1}{2}(5)(12)$

= 30 cm²

Area of equilateral triangle II = $\frac{\sqrt{3} }{4}(\text{Side})^2$

Area of equilateral triangle II = $\frac{\sqrt{3}}{4}(13)^2$

= $\frac{(1.73)(169)}{4}$

= 73.0925

≈ 73.09 cm²

Area of rectangle III = Length × width

= CF × CD

= 7 × 5

= 35 cm²

Area of trapezium EFGH = $\frac{1}{2}(\text{EF}+\text{GH})(\text{FJ})$

Since, GH = GJ + JK + KH

17 = $\sqrt{9^{2}-x^{2}}+5+\sqrt{(15)^2-x^{2}}$

12 = $\sqrt{81-x^2}+\sqrt{225-x^2}$

144 = (81 - x²) + (225 - x²) + 2 $\sqrt{(81-x^2)(225-x^2)}$

144 - 306 = -2x² + $2\sqrt{(81-x^2)(225-x^2)}$

-81 = -x² + $\sqrt{(81-x^2)(225-x^2)}$

(x² - 81)² = (81 - x²)(225 - x²)

x⁴ + 6561 - 162x² = 18225 - 306x² + x⁴

144x² - 11664 = 0

x² = 81

x = 9 cm

Now area of plot IV = $\frac{1}{2}(5+17)(9)$

= 99 cm²

Total Area of the land = 30 + 73.09 + 35 + 99

= 237.09 cm²

7 0

3 years ago

Which inequalities are true? Check all that apply. Three-fifths < 0 Four-sixths greater-than one-half Nine-elevenths < 1 T

Kipish [7]

$\frac{3}{5} < 0$

$\frac{8}{16} > \frac{1}{2}\\\\$

Solution:

We have to find the inequalities that are true

Option 1

$\frac{3}{5} < 0\\\\0.6 < 0$

0.6 is not less than 0

Thus this inequality is not true

Option 2

$\frac{4}{6} > \frac{1}{2}\\\\0.667 > 0.5$

0.667 is greater than 0.5

Thus this inequality is true

Option 3

$\frac{9}{11} < 1\\\\0.818 < 1$

0.818 is less than 1

Thus this inequality is true

Option 4

$\frac{8}{16} > \frac{1}{2}\\\\$

0.5 = 0.5

Thus the above inequality is not true

6 0

3 years ago

Graph the circle (x-1)2+(y-8)2=4

Ludmilka [50]

Answer:

Use desmos graphing calculator

Step-by-step explanation:

7 0

3 years ago

Isabel received 4/7 of the 210 votes for cast for class treasurer. How many votes did she receive? Write your answer in simplest

KengaRu [80]

Answer:

120 votes

Step-by-step explanation:

So one way to solve this is by creating an equation to solve for x.

So we are given 4/7, that will be one side of the equation.

And we are trying to figure out how many votes out of the 210 she received, so on the other side of the equation we will have x/210, since we are solving for x.

So 4/7 = x/210

We want to get x alone, so we can multiply 4/7 by 210, which equals 120.

So x equals 120!

8 0

3 years ago

In a game, if you roll a 6 on a 6-sided number cube, you lose a turn.

Julli [10]

A) the probability is 1 in 6 (1/6); there are six numbers and only one is 6, therefore 1 in 6
B) the probability is 5 in 6 (5/6); there are 6 numbers and only one is not 6, therefore 5 in 6
C) the probability of rolling a 6 is 1 in 6 and the probability of not rolling a 6 is 5 in 6
D) the probability is again 1 in 6 (1/6); 120 divided by 6 is 20, and 20/120 simplifies to 1/6
thats the best i can do to explain

4 0

3 years ago