If 150° and 3a are supplementary angles, find the value of a. ​

Answer:

y = 5/4x-15

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b where m is the slope and b is the y intercept

y = 5/4x+b

Substitute the point into the equation and solve for b

-5 = 5/4(8)+b

-5 = 10+b

Subtract 10 from each side

-5-10 = b

-15 = b

y = 5/4x-15

Step-by-step explanation:

y-y'=m(x-x')

y-(-5)=5/4(x-8)

y+5=5x/4-10

4(y+5)=4(5x/4)-10(4)

4y+20=5x-40

4y-5x=-40-20

4y-5x=-60

5x-4y-60=0

y=5x/4-15

Answer:

22+g=65

Step-by-step explanation:

take the 22 add (sum) to g (the variable) and have them = 65

Answer:

x ≥ -30

Step-by-step explanation:

The equation is 3 - x / 2 ≤ 18.

First, subtract 3 on both sides:

- x / 2 ≤ 15.

Multiply by -2 on both sides and swap the less than or equal to sign:

x ≥ -30

Hope this helps!

Answer:

B) Rays AB and AE

Step-by-step explanation:

Though A-F, A-D, and A-C all meet at one point on line B-E, point A, they aren't a part of it. Point A on line B-E marks the "midpoint" of it, and therefore, ray A-E and A-B are part of line B-E.

Answer:

[tex]x=\frac{4\sqrt{3}}{3}[/tex]

Step-by-step explanation:

From the figure attached,

ΔABC is an equilateral triangle.

Therefore, by the property of the equilateral triangle,

Measure of each angle = 60°

By applying tangent rule in the right triangle ADC,

[tex]\text{tan}(60^{\circ})=\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]

[tex]\sqrt{3}=\frac{4}{x}[/tex]

[tex]x=\frac{4}{\sqrt{3}}[/tex]

[tex]x=\frac{4}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3} }[/tex]

[tex]x=\frac{4\sqrt{3}}{3}[/tex]

Answer:

56

Step-by-step explanation:

that is the procedure above

The missing segment in the image below is 8.

The missing segment is the side length of the small triangle that is formed by the two red lines and the green line. We can find the length of this side length by using the Pythagorean Theorem.

The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is the missing segment, and the other two sides are 4 and 5.

missing [tex]segment^2[/tex] = [tex]4^2[/tex] + [tex]5^2[/tex]

missing [tex]segment^2[/tex] = 16 + 25

missing [tex]segment^2[/tex] = 41

missing segment = √41

Therefore, the missing segment is √41.

Here are the steps in detail:

Identify the small triangle that is formed by the two red lines and the green line.

Label the sides of the triangle with the letters A, B, and C, where C is the missing segment.

Substitute the known side lengths into the Pythagorean Theorem.

Solve for the length of the missing segment.

To learn more about segment here:

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Answer:

...-243, 729, -2187

Step-by-step explanation:

-3, 9, -27, 81, -243, 729, -2187

Everytime ×(-3)

-3×(-3)=9

9×(-3)=-27

-27×(-3)=81

Etc.

The value of COS Cx sin A by the given data is V3/4.

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

Trigonometric ratio can be defined in terms of ratios of perpendicular, bases and hypotenuse. These are defined only in right angled triangles (triangles whose one angle is of 90 degree measure).

We are given that;

AB = 1, AC = 2 and BC = V3

Now,

To find the value of cos C x sin A, we need to use the trigonometric ratios of the right triangle.

We know that cos C = adjacent/hypotenuse = AB/AC = 1/2 and sin A = opposite/hypotenuse = BC/AC = V3/2.

cos C x sin A = (1/2) x (V3/2) = V3/4.

Therefore, by the trigonometric ratio the answer will be V3/4.

Learn more about trigonometric ratios;

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Answer:

There were 44 students in each bus.

Step-by-step explanation:

357 - 5 = 352

352/8 = 44

Answer:

Step-by-step explanation:

Total students = 357

Total buses filled = 8

No of students traveled in car = 5

Remaining students = 357 - 5 = 352

Students in each bus = 352 ÷ 8 = 44 students

Answer:

$14722.14

Step-by-step explanation:

We are given that

In 2015

The value of jewel=$17500

Rate of appreciation, r=2.5%

We have to find the initial value of the jewel when it was first bought.

Time, n=7 years

Final value=[tex]Initial\;value (r/100+1)^n[/tex]

Using the formula

[tex]17500=Initial\;value(2.5/100+1)^7[/tex]

[tex]17500=Initial\;value(1.025)^7[/tex]

[tex]Initial\;value=\frac{17500}{(1.025)^7}[/tex]

Initial value=$14722.14

Hence, the the initial value of the jewel when it was first bought=$14722.14

Answer: When f(x)=g(x) , x equal to -2 or -1

Step-by-step explanation:

Step-by-step explanation:

[tex]x + 3y = 7 \\ 2x + 4y = 8 \\ x = 7 - 3y \\ 2(7 - 3y) + 4y = 8 \\ 14 - 6y + 4y = 8 \\ 14 - 2y = 8 \\ - 2y = - 6 \\ y = 3 \\ x = 7 - 3(3) \\ x = 7 - 9 \\ x = - 2[/tex]

Answer:

2x+3y=7x4

x+4y=8x3

8x+12y=27

3x+12y=24

8x-3x =5x

+12y-+12y=0

27-24=3

5x/5 3/5x

answer = x = 3/5

y=1.85

Answer:

cannot be determined

Step-by-step explanation:

We do not know if any of the angles are equal and are only given two sides.

We cannot determine if the two triangles are similar

Answer:

119?

Step-by-step explanation:

Answer:

-23/9  or -2 5/9

Step-by-step explanation:

w+(-x) - 2/3

Let w = -5/9  and x = 4/3

-5/9+(- 4/3) - 2/3

Get a common denominator of 9

-5/9 - 4/3 *3/3 - 2/3 *3/3

-5/9 - 12/9 - 6/9

-23/9

-2 5/9

Answer:

-2 5/9

Step-by-step explanation:

Answer:

17 lb I guess 8 don't think the question is full

Step-by-step explanation:

the question is half

9514 1404 393

Answer:

  5.7·10^-3

Step-by-step explanation:

The expanded scale shows point P lies 7/10 of the way between 5 and 6 times 10^-3. Its value is 5.7·10^-3.

Answer:

second x -1,-3,-5 y 1 3 5 for proportional relation

Answer:

32 = <4

Step-by-step explanation:

The exterior angle of a  triangle is equal to the sum of the opposite interior angles

15+17 = <4

32 = <4

Answer:

d talking into microphone

Answer:

Hello,

answer B

2

Step-by-step explanation:

[tex]\dfrac{2}{x} -\dfrac{x}{x+5} =\dfrac{10}{x^2+5x} \\\\we\ suppose\ x\neq 0\ and\ x\neq -5\\\\\text{Reducing to the same denominator}\\\dfrac{2(x+5)-x^2}{x(x+5)} =\dfrac{10}{x^2+5x} \\\\Simplify\ by\ x^2+5x\\\\2x+10-x^2=10\\\\-x^2+2x=0\\\\-x(x-2)=0\\\\roots\ are\ 2 \ and\ 0\ (to\ be\ excluded)\\\\Root=2\\[/tex]

Answer:

[tex]\text{1) }\\\text{Circumference: }24\pi \text{ m}},\\\text{Length of bolded arc: }18\pi \text{ m}\\\\\text{3)}\\\text{Circumference. }4\pi \text{ mi},\\\text{Length of bolded arc: } \frac{3\pi}{2}\text{ mi}[/tex]

Step-by-step explanation:

The circumference of a circle with radius [tex]r[/tex] is given by [tex]C=2\pi r[/tex]. The length of an arc is makes up part of this circumference, and is directly proportion to the central angle of the arc. Since there are 360 degrees in a circle, the length of an arc with central angle [tex]\theta^{\circ}[/tex] is equal to [tex]2\pi r\cdot \frac{\theta}{360}[/tex].

Formulas at a glance:

Question 1:

The radius of the circle is 12 m. Therefore, the circumference is:

[tex]C=2\pi r,\\C=2(\pi)(12)=\boxed{24\pi\text{ m}}[/tex]

The measure of the central angle of the bolded arc is 270 degrees. Therefore, the measure of the bolded arc is equal to:

[tex]\ell_{arc}=24\pi \cdot \frac{270}{360},\\\\\ell_{arc}=24\pi \cdot \frac{3}{4},\\\\\ell_{arc}=\boxed{18\pi\text{ m}}[/tex]

Question 2:

In the circle shown, the radius is marked as 2 miles. Substituting [tex]r=2[/tex] into our circumference formula, we get:

[tex]C=2(\pi)(2),\\C=\boxed{4\pi\text{ mi}}[/tex]

The measure of the central angle of the bolded arc is 135 degrees. Its length must then be:

[tex]\ell_{arc}=4\pi \cdot \frac{135}{360},\\\ell_{arc}=1.5\pi=\boxed{\frac{3\pi}{2}\text{ mi}}[/tex]

Answer:

The Tasty Beans Coffee House being planned for the corner of SE 12th and Main will ruin a perfectly nice neighborhood. Besides the fact that Tasty Beans already has coffee shops all over the city, it will pull business away from local coffee houses that have been here for decades. In addition, there is already a parking problem on that street, and the new business will just add to the congestion. They're planning a drive-up window, too, and that will mean a steady stream of traffic in a very high-volume area. Ask anyone walking down the street, and they'll tell you this is a bad idea. I speak for my whole neighborhood when I say, "Go away, Tasty Beans!"

Step-by-step explanation:

Answer: 1:3

Step-by-step explanation:

The odds are 2/6 because you’re given 2 choices from the 6 side die you can then simplify that fraction to 1:3

Answer:

61

Step-by-step explanation:

45/3 = 15

2*8 = 16

15+16-12+42 = 61

Answer:

15 + 16 + 30

and that is in total 61

Step-by-step explanation:

45/3 = 15

2×8 = 16

-12 + 42 = 30

you simplify an expression by calculating the part expressions, to be left only with the main terms and main operations.

Answer:

i can help you i know this answer

Answer:

5 cm

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

let h be the hypotenuse , then

h² = 3² + 4² = 9 + 16 = 25 ( take the square root of both sides )

h = [tex]\sqrt{25}[/tex] = 5