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3 years ago

Find the missing angle.

Mathematics

1 answer:

Sphinxa [80]3 years ago

5 0

Answer:

$m\angle XYV=135^{\circ}$

Step-by-step explanation:

Notice that $m\angle XYV=m\angle XYW+m\angle VYW$ .

The diagram already marks $m\angle VYW=80^{\circ}$ , so we just need to find $m\angle XYW$ .

$\angle TYU$ and $\angle XYW$ are vertical angles, which means they are equal in measure.

Therefore,

$m\angle TYU=m\angle XYW=6x+7$

Since there are $180^{\circ}$ on each side of a line, we have the following equation:

$m\angle XYW+m\angle VYW+m\angle UYV=180^{\circ},\\6x+7+13+4x+80=180,\\10x+20=100,\\10x=80,\\x=8$ .

Plugging in $x=8$ , we have:

$m\angle XYW=6(8)+7=55^{\circ}$ .

Therefore,

$m\angle XYV=55^{\circ}+80^{\circ},\\m\angle XYV=\fbox{$135^{\circ}$}$ .

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8/2(2+2)=? 100 points to the best answer!

Effectus [21]

Answer:

Step-by-step explanation:

8/2(2+2)

- According to the rules of BEDMAS, solve the values inside the bracket.

8/2 (4)

- Simplify the fraction outside the bracket.

4(4)

- Multiply the two values.

= 16

7 0

3 years ago

Read 2 more answers

A pigpen is to be enclosed using 640 m of fencing along three of its sides, the fourth side being a barn. Determine the dimensio

Basile [38]

Answer:

$W_{max}=480m\\ L_{max}=160m$

Step-by-step explanation:

Since we know we only have 640 feet of fence available, we know that L + W + L = 640, $\implies$ 2L + W = 640. This allows us to represent the width, W, in terms of L: W = 640 – 2L

Remember, the area of a rectangle is equal to the product of its width and length, therefore,

$A_{\rm pigpen}=L(640-2L)\implies 640L-2L^2$

Notice that, quadratic has been vertically reflected, since the coefficient on the squared term is negative, so the graph will open downwards, and the vertex will be a maximum value for the area.

recall,

$x_{max}=-b/2a$
$f(x)_{max}=f(x_{max})$

Since our function is A(L)=640L-2L², we get

a=-2
b=640

plug in the value of a and b into the first formula:

$L_{max}=-(640)/2(-2)\implies 160$

$A(L)_{max}=640(160)-2(160)^2\implies 76800$

hence,the dimensions of the pen that will maximize the area are L=160m and W=76800/160=480m

and we're done!

3 0

3 years ago

Find the center and the radius of the circle with the equation: x2+6x+y2+4y+12=0

Andrews [41]

Answer:

centre = (- 3, - 2) , radius = 1

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Given

x² + 6x + y² + 4y + 12 = 0 ( subtract 12 from both sides )

x² + 6x + y² + 4y = - 12

Use the method of completing the square on the x and y terms

add ( half the coefficient of the x/ y terms )² to both sides

x² + 2(3)x + 9 + y² + 2(2)y + 4 = - 12 + 9 + 4

(x + 3)² + (y + 2)² = 1 ← in standard form

with centre = (- (- 3), - (- 2)) and r² = 1, that is

centre = (- 3, - 2) and radius = 1

8 0

3 years ago

Alice earns simple interest on a principal of $1,400 at an annual interest rate of 6% for the period of 3 years. What equation s

Greeley [361]

The amount of interest is $252. The equations or represent the relation relationship between p, (r), (t) and (i).

Step-by-step explanation:

The formula of simple interest is

Where, principal amount (p), rate of interest (r), period of investment in years (t), and interest earned (i).

The principal amount is $1,400, interest rate of 6% and the time period of 3 years.

The amount of interest is

Therefore the amount of interest is $252.

The equations or represent the relation relationship between p, (r), (t) and (i).

5 0

3 years ago

Read 2 more answers

Solve a=2b-c for b Can someone help me

Sauron [17]

Answer:

$b=\frac{a}{2} +\frac{c}{2}$

Explanation:

While solving literal equations could be quite overwelhming, simply solve it by using normal equation solving methods.

For example, if you were to solve 2x + 3 = 9

You would add 3 on both sides and divide both sides by 2 to determine x.

Do the same thing for literal equations, and if in doubts, plug in numbers to check your work.

Step-by-step explanation:

For this problem, add c on both sides, we do this because we are aiming to eliminate the c from both sides.

a+c =2b

In order to find the value of b, divide both sides by 2, we do this because we want to get rid of the coefficient.

This should leave you with the answer of b=a/2 + c/2

3 0

3 years ago