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3 years ago

Look at the figure below. What is the measure of Angle ACB

Mathematics

1 answer:

Kazeer [188]3 years ago

4 0

Hey there!

Since these angles share the same vertex (point where the lines that make the angle meet), they are congruent (they have the same value). Therefore, we can write the following equation.

4x-12=2x+48

We add 12 to both sides.

4x=2x+60

We subtract 2x from both sides.

2x=60

We divide both sides by 2.

x=30

Now, we can plug this in to find the measure of angle ACB. Whenever you see an angle that is named with three letters, the middle one is its vertex and the other two are the end points.

m∠ACB=4(30)-12

m∠ACB=120-12

m∠ACB=108

I hope that this helps! Have a wonderful day!

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HELP HELP HELP Quick algebra 1 questions

beks73 [17]

Hello:

Okay, this problem should be taken in a series of steps:

What is the slope's formula?

$\rm\hookrightarrow \frac{y_2-y_1}{x_2-x_1}$

(x₁,y₁) -- first point
(x₂,y₂) -- second point

Okay, now let's use this knowledge

10. (5,-19) and (-5,21)

$Slope = \frac{21--19}{-5-5} =\frac{40}{-10}=-4$

11. (12,1) and (12, -1)

$Slope = \frac{-1-1}{12-12} =\frac{-2}{0}$

12. (8,7) and (4,7)

$Slope = \frac{7-7}{4-7} =0$

Answer:

Question 10: -4
Question 11: undefined
Question 12: 0

Hopefully that helps!

5 0

2 years ago

Hey guys I have a hard time with these questions. Can someone explain it to me? :)

frutty [35]

The slope would be 0

This is basically how you do it if you need more help let me know

6 0

3 years ago

Read 2 more answers

A rectangular parking lot has a length that is 5 yards greater than the width the area of the parking lot is 300 yd.² find the l

ArbitrLikvidat [17]

Answer:

width=5yd and length=10yd

Step-by-step explanation:

To solve this problem, you need to start by asking what you do and don't know (always where to start with word problems)

We know that Area (A) = Length (L) * Width (W)

You know Area (A) = 50 sq. yds.

You don't know anything about the width, so let's just say Width (W) = x

And you know that the length is 5 yds longer than the width, so L = W + 5yd and, since W = x, we can say L = x + 5yd

Now, we recall that A = L * W, and, since A = 50, we can say 50 sq yd = L * W.

Well, now just plug in. What does W equal and L equal?

From above we plug in and can say that 50 sq yd = x * (x + 5 yd).

Multiply it out and you get 50 = x^2 + 5x (removing units for a moment so they don't clutter the lines).

Now there are a number of ways to solve this. You can tell (because of the "x^2") that it is quadratic. So let's get it equal to zero:

0 = x^2 + 5x - 50

Now you can factor it, use your quadratic formula, or (if you hated yourself) do it as a completing the square problem. I'm going to factor.

I can see from going through a list in my head that the factors 10 and -5 multiply to -50 and add to 5, so I know that

0 = x^2 + 5x - 50 = (x + 10)(x - 5)

And so you know that x = -10 or 5.

Well, you know the parking lot cannot be -10 yd long. So we must say that W = x = 5, and, since L = W + 5, then L = 5+5 = 10. So your width is 5 yd and length is 10 yd.

<h2>mark me brainlist</h2>

6 0

2 years ago

Complete the square to determine the minimum or maximum value of the function defined by the expression.

Alekssandra [29.7K]

The minimum value at -1 ⇒ D

Step-by-step explanation:

The completing square form of ax² + bx + c is a(x - h)² + k, where

$h=\frac{-b}{2a}$
k is the value of of the expression when x = h
k is minimum if a > 0 and maximum if a < 0

∵ The expression is x² + 4x + 3

∴ a = 1 , b = 4 , c = 3

- Use the rule above to find h

∵ $h=\frac{-4}{2(1)}$

∴ h = -2

- To find k substitute x by the value of h

∵ k = (-2)² + 4(-2) + 3 = 4 - 8 + 3

∴ k = -1

- Substitute h and k in the form of the completing square

∵ a(x - h)² + k = 1(x - -2)² + (-1)

∴ a(x - h)² + k = (x + 2)² - 1

∴ x² + 4x + 3 = (x + 2)² - 1

∵ The completing square is (x + 2)² - 1

∵ a = 1 ⇒ greater than zero

∴ The value is minimum

- The minimum value is the value of k

∵ k = -1

∴ The minimum value of the function is -1

The minimum value at -1

Learn more:

You can learn more about the quadratic function in brainly.com/question/9390381

#LearnwithBrainly

3 0

3 years ago

Determine whether the series is arithmetic or geometric. Then evaluate the finite series for the specified number of terms. 10 +

Salsk061 [2.6K]

Answer:

10 + 7 + 4 + . . .; n = 5

The series is arithmetic

Common difference between terms = (-3)

10 - 3 = 7

7 - 3 = 4

Or:

10 + (-3) = 7

7 + (-3) = 4

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

Another example:

Arithmetic:

5, 9, 13, 17

common difference = 4

5 + 4 = 9

9 + 4 = 13

Geometric:

4, 8, 16, 32

4 × 2 = 8

8 × 2 = 16

16 × 2 = 32

common ratio = 2

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

10 + 7 + 4 + . . .; n = 5

a₁ = 10

a₂ = 7

a₄ = a₃ + d = 4 + (-3) = 4 - 3 = 1 (d = common difference)

a₅ = a₄ - 3 = 1 - 3 = -2

Or with formula:

$d=a_{n} -a_{n-1}$

d = a₂ - a₁ = 7 - 10 = -3

aₙ = a₁ + (n - 1)d

fourth term = a₄ = 10 + (4 - 1)(-3) = 10 + 3(-3) = 10 + (-9) = 10 - 9 = 1

fifth term = a₅ = 10 + (5 - 1)(-3) = 10 + 4(-3) = 10 + (-12) = 10 - 12 = -2

Sum of the finite series (if n = 5):

$S_{n} =\frac{n(a_{1} +a_{n} )}{2} \\S_{5} =\frac{5(a_{1} +a_{5} )}{2} \\S_{5} =\frac{5(10 +(-2) )}{2} \\S_{5} =\frac{5(8 )}{2} =\frac{40}{2} =20$

Manual count: S₅ = 10 + 7 + 4 + 1 + (-2) = 20

7 0

2 years ago