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1 year ago

Find the value of each variable.

Mathematics

1 answer:

Harrizon [31]1 year ago

8 0

Step-by-step explanation:

b is per the identity of angles on parallel lines when intersected by one inclined line the same as the 40° angle.

so,

b = 40°

due to the parallel nature of the 2 lines there is a symmetry effect for such shapes inscribed a circle. the upper and the lower triangle must be similar. and when applying a vertical line through the central crossing point, everything to the left is mirrored by everything on the right.

so, angle c must be equal to angle b.

c = 40°

and as the sum of all angles in a triangle is always 180°, d is then

d = 180 - 40 - 40 = 100°

the interior angle of the arc angle a is the supplementary angle of d (together they are 180°), because together with d they cover the full down side of the top-left to bottom-right line.

interior angle to a = 180 - 100 = 80°

due to the symmetry again, the arc angle opposite to a is the same as a.

as we know, the interior angle to a pair of opposing arc angles is the mean value of the 2 angles.

so, we have

(a + a)/2 = 80

2a/2 = 80

a = 80°

there might (and actually should) be some more direct approaches for "a" out of the other pieces of information, but that was the most straight one right out of my mind, and I don't spend time on finding additional shortcuts, when I have already a working approach.

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Solve for x: - 6 < x - 1 < 9

dusya [7]

Answer:

-5<x<10

Step-by-step explanation: in these types of questions you have to leave x alone which means you have to do the following:

-6<x-1<9

when we throw -1 to the left side the solution would be like this -6+1=5

and when we throw it to the right side the solution would be 9+1=10

which means;

-5<x<10

8 0

2 years ago

Convert 3 miles to feet. A. 15,840 feet B. 1,584 feet C. 3,279 feet D. 9,372 feet

andreev551 [17]

Answer:

A. 15,840 feet

Step-by-step explanation:

1 mile = 5,280 feet (I think "five tomatoes" is helpful: five tomatoes --> five-two-eight-oh)

multiply both sides of equation by 3: 1 * 3 = 5,280 * 3

simplify: 3 miles = 15,840 feet, which means A is the answer

7 0

2 years ago

Solve the system by submission -5y-10=x<br> x+9y=-2

Sonbull [250]

Answer: =−20

y=2

Step-by-step explanation:

Solve for xx in -5y-10=x−5y−10=x.

x=-5y-10

x=−5y−10

2 Substitute x=-5y-10x=−5y−10 into x+9y=-2x+9y=−2.

4y-10=-2

4y−10=−2

3 Solve for yy in 4y-10=-24y−10=−2.

y=2

4 Substitute y=2y=2 into x=-5y-10x=−5y−10.

x=-20

x=−20

5 Therefore,

\begin{aligned}&x=-20\\&y=2\end{aligned}

x=−20

y=2

8 0

2 years ago

[02.06]<br> Solve and graph the absolute value inequality: (2x + 1/ s 5. (1 point)

solong [7]

Step-by-step explanation:

We are given with the inequality |2x + 1| ≤ 5 and asked to solve the equation. In this case, we take first the positive side, that is 2x + 1 ≤ 5. this is equal to 2x ≤ 4 or x ≤ 2. For the negative side, the equality is -5 ≤ 2x + 1. This is equal to -6 ≤ 2x or -3 ≤ x. Hence the solution is -3 ≤ x ≤ 2. The answer is B. closed dots on -3 and 2 with shading in between. The equal in ≤ means closed dots.

7 0

1 year ago

Read 2 more answers

Solve the polynomial equation

ExtremeBDS [4]

Hey there!

You can solve this by squaring both sides to first cancel out the square root on the left. Then, you can eliminate each term as your normally would.

$2 \sqrt{x} =x-3$

$(2 \sqrt{x})^{2} = (x-3)^{2}$

$(4x) = (x-3)(x-3)$

$4x = x^{2} -6x+9$

$x^{2} -10x+9$

Now, you're given the opportunity to find your solution using the quadratic formula. That formula is:

$\frac{-b_-^+ \sqrt{b^2-4ac} }{2a}$

You can find out a, b, and c by comparing your new equation to the standard form. Luckily, we just put our equation into standard form:

$ax^{2} + bx + c$

$x^{2} -10x+9$

$a = 1 \\ b = -10 \\ c = 9$

To find your solution, plug these numbers into the quadratic formula and solve.

$\frac{-b_-^+ \sqrt{b^2-4ac} }{2a}$

$\frac{10_-^+ \sqrt{-10^2-4(9)}}{2}$

Remember to use PEMDAS when solving these problems.

$\frac{10_-^+ \sqrt{100-36}}{2}$

$\frac{10_-^+ \sqrt{64}}{2}$

$\frac{10_-^+ 8}{2}$

Now, solve this final bit by adding the top terms then subtracting them for two different answers.

$\frac{10 + 8}{2} = 9$

$\frac{10- 8}{2} = 1$

Don't assume that both of these are correct. The very last step is to plug both of these into the original problem you were given and see if they make the equation true.

$2 \sqrt{9} =9-3$
$2*3=6$
$6=6$

$2 \sqrt{1} =1-3$
$2*1=-2$
$2 \neq -2$

So (finally), your answer will be x = 9.

Hope this helped you out! :-)

7 0

2 years ago