Identify coordinate point C.

(1, 5)
(6, 7)
(7, 3)
(0, 2)

Answer:

x = 3

Step-by-step explanation:

Angle S and Angle T are consecutive interior angles. Therefore, we know that T + S = 180°.

First, we need to solve for T, and since angles S and T are consecutive interior angles, we know that T + S = 180°. If we reorganize the equation to include the things we know (S = 105°), then we get 180° - 105° = 75°. So T is 75°.

Now, we use T = 75° and the information given to us in the picture to set up an equation. 75 = 24x + 3. Now, we can find x by isolating it. Do this by:

1) Subtracting 3 from both sides to give you 72 = 24x. We do this to get rid of the 3 from the "x side", but we must also do it to the other to keep the equation true. This moves the 3 from the "x side" to the other since we're trying to isolate x.

2) Divide 24 by both sides to get 3 = x. We use the same logic as we did for 3, except this time we divide since that's the opposite of multiplying.

In conclusion, x = 3.

Answer:

[tex]3,10,29,66,127,218[/tex]

Step-by-step explanation:

[tex]f(n) = n^3 +2\\\\f(1) = 1^3 +2 = 1+2=3\\\\f(2) =2^3 +2 = 8+2=10\\\\f(3)=3^3 +2 = 27+2 = 29\\\\f(4) = 4^3 +2 = 64 +2 = 66\\\\f(5) = 5^3 +2 = 125+2 = 127\\\\f(6) = 6^3 +2 = 216+2 = 218[/tex]

Answer:

If I am not mistaking it should be -7.5

Step-by-step explanation:

Answer:

  b = -15/2

  y = -3x -15/2

Step-by-step explanation:

The value of the y-intercept can be found from a point and the slope of the line by solving the slope-intercept equation for the intercept.

__

  y = mx + b . . . . . . . equation of a line with slope m and y-intercept b

  y -mx = b . . . . . . . . subtract mx from both sides

For the point (x, y) = (-2, -3/2) and slope m = -3, the value of b is ...

  b = -3/2 -(-3)(-2) = -3/2 -6

  b = -15/2 . . . . . the value of b for this line

__

Then the equation for the line is ...

  y = mx +b

  y = -3x -15/2

Answer:

  3 and 1/2 half-cups

Step-by-step explanation:

We are asked to find the number of half-cups that will equal 1 3/4 cups.

__

Let the desired number be represented by n. Then we require ...

  n × 1/2 = 1 3/4 . . . . some number of 1/2-cups will give 1 3/4 cups

Using a common denominator, we have ...

  n × 2/4 = 7/4

Multiplying by the inverse of the coefficient of n gives ...

  n × 2/4 × 4/2 = 7/4 × 4/2

  n = 7/2 = 3 1/2 . . . . . simplify

That is, Donna can measure 1 3/4 cups of sugar by using her 1/2-cup measure 3 times, and filling it half-full for the final 1/4 cup she needs.

She needs 3 1/2 half-cups to get the correct amount.

Answer:

64in

Step-by-step explanation:

for a four sided figure, you do base x height. volume isn't squared in Math.

Reason:

Rewrite the given equation into [tex](x-6)^2 + (y-(-5))^2 = 5^2[/tex]

I changed the y+5 into y-(-5), and also replaced 25 with [tex]5^2[/tex]

Then compare that to the circle template of [tex](x-h)^2 + (y-k)^2 = r^2[/tex]

We see that h = 6 and k = -5 to give a center of (h,k) = (6, -5)

Side note: the radius is r = 5 units

Answer:

BOD = 189 °

Step-by-step explanation:

that is the answer above

The vertical asymptotes are x = 2 and horizontal asymptotes are y = 3 and the parent graph is shifted two to the right and three to the top.

It's a two-dimensional geometry curve with two components that are both symmetric. In other words, the number of points in two-dimensional geometry that have a constant difference between them and two fixed points in the plane can be defined.

We have a graph of a hyperbola:

[tex]\rm y=\dfrac{\left3x+14\right}{x-2}[/tex]

The above equation represents the hyperbola.

We can write the above equation as:

[tex]\rm y=3+\dfrac{\left20\right}{x-2}[/tex]

The vertical asymptotes: x = 2

The horizontal asymptotes: y = 3

Thus, the vertical asymptotes are x = 2 and horizontal asymptotes are y = 3 and the parent graph is shifted two to the right and three to the top.

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Answer:

Likely

Step-by-step explanation:

It is not guaranteed, but it is not impossible. There is a higher chance of it happening compared to it not happening, so it it likely.

Answer:

x = 129°

Step-by-step explanation:

∠ ABD and ∠ DBC are a linear pair and sum to 180° , then

y + ∠ DBC = 180°

107° + ∠ DBC = 180° ( subtract 107° from both sides )

∠ DBC = 73°

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles , then

x = ∠ DBC + z = 73° + 56° = 129°

Answer:

scale factor = 4

Step-by-step explanation:

the scale factor is the ratio of corresponding sides, image to original

scale factor = [tex]\frac{8}{2}[/tex] = 4

Answer:

multiply the probability of the first event by the second.

Step-by-step explanation:

Use the specific multiplication rule formula. Just multiply the probability of the first event by the second. For example, if the probability of event A is 2/9 and the probability of event B is 3/9 then the probability of both events happening at the same time is (2/9)*(3/9) = 6/81 = 2/27.

Answer:

[tex]\frac{1}{26} * \frac{1}{26} = \frac{1}{676} = .00148.[/tex]

Step-by-step explanation:

Multiply the probability of P by the probability of Q.

In which the probability of P is equal to [tex]\frac{R}{Total NumberOf LettersInAlphabet} = \frac{1}{26}[/tex]

In which the probability of Q is equal to [tex]\frac{P}{Total NumberOf LettersInAlphabet} = \frac{1}{26}[/tex]

There's a 1 in 676 chance that you'd randomly pick R, put the tile back in, and then pick P in a sack of 26 letters of the latin alphabet.

The probability that he does not wait for more than five minutes all 5 days this week is 0.16807

The probability that he waits for more than 5 minutes is:

p = 30%

This means that the probability that he does not wait for more than 5 minutes is

q = 70%

If he does not wait for more than five minutes all 5 days this week, the probability is:

P = q^5

This gives

P = (70%)^5

Evaluate

P = 0.16807

Hence, the probability that he does not wait for more than five minutes all 5 days this week is 0.16807

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Answer:

(1, 0 ) and (0, - 8 )

Step-by-step explanation:

8x - y = 8 → (1)

8x² - y = 8 → (2)

since both equations are equal to 8 then equate the left sides

8x² - y = 8x - y ( subtract 8x - y from both sides )

8x² - 8x = 0 ← factor out 8x from each term

8x(x - 1) = 0

equate each factor to zero and solve for x

8x = 0 ⇒ x = 0

x - 1 = 0 ⇒ x = 1

substitute these values into (1) and solve for y

x = 0 : 8(0) - y = 8 ⇒ y = - 8 ⇒  (0, - 8 )

x = 1 : 8(1) - y = 8 ⇒ y = 0 ⇒ (1, 0 )

The area of the shaded region = area of semicircle - area of triangle ACB = 11.32 cm².

Area of a triangle = 1/2(base)(height).

Area of a semi-circle = 1/2(πr²).

m∠ACB is a right triangle based on the central angle theorem. Therefore, ΔACB is a right triangle.

Radius of circle = OC = 4 cm

CB = 4 cm

Diameter AB = 2(4) = 8 cm

Using the Pythagorean theorem, find AC in ΔACB:

AC = √(AB² - CB²)

AC = √(8² - 4²)

AC ≈ 6.9 cm

Area of ΔACB = 1/2(CB)(AC)

Area of ΔACB = 1/2(4)(6.9)

Area of ΔACB ≈ 13.8 cm²

Area of semicircle = 1/2(πr²) = 1/2(π)(4²)

Area of semicircle ≈ 25.12 cm²

Area of the shaded region = area of semicircle - area of triangle ACB = 25.12 - 13.8

Area of the shaded region = 11.32 cm²

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Answer:

y = 108

Step-by-step explanation:

2x + 16 = 3x -12 (as you can see the F shape and are on straight lines and AB is parallel to CD) .

Now we solve for x :

Subtract 2x from both sides :

16 = x - 12

Now we add 12 to both sides :

28 = x

Angle 3x-12 and y add up to 180 as they are on a straight line :

3x-12 + y = 180

Substitute x and solve for y :

3(28) - 12 + y = 180

84 - 12 + y = 180

72 + y = 180

y = 108  

Hope this helped and have a good day

Answer:

-22

Step-by-step explanation:

each mark decreases by three, two marks down from 16 would be 16+3+3; which equals 22, and it has to be negative

hope this helped!

Answer:

-13/20

Step-by-step explanation:

-0.65 can be written as -65/100. To simplify, divide both numerator and denominator with 5. 65/5=13.  100/5=20

And you get -13/20 for your answer.

Answer:

3

Step-by-step explanation:

Put both expressions equal to each other.

2x+4=3x+1

Solve:

2x+4=3x+1

4-1=3x-2x

3=1x

x=3

Answer:

The first choice

Step-by-step explanation:

7/8 x + 3/4 = -6

6 (x/8) + 3/4 = -6

For the function y = |x| + 2, it shows a vertical translation of the parent function up by 2 units.

The parent function for the graph of the modulus is given as g(x) = |x|

For the function y = |x| + 2, it shows a vertical translation of the parent function up by 2 units.

For the graph, there will be s shift down the graph by 2 units from the graph of the parent function as shown;

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Answer:

The answer is

[tex]2 \cos(100) + i \sin(100) [/tex]

Step-by-step explanation:

This is a complex number,

[tex]a + bi[/tex]

First, convert this to de movire form.

[tex]r( \cos( \alpha ) + i \sin( \alpha ) [/tex]

where

[tex]r = \sqrt{ {a}^{2} + {b}^{2} } [/tex]

and

[tex] \alpha = \tan {}^{ - 1} ( \frac{b}{a} ) [/tex]

[tex]a = 4[/tex]

[tex]b = - 4 \sqrt{ 3} i[/tex]

[tex]r = \sqrt{ {4}^{2} + ( - 4 \sqrt{3}) {}^{2} } [/tex]

[tex]r = \sqrt{16 + 48} [/tex]

[tex]r = \sqrt{64} = 8[/tex]

and

[tex] \alpha = \tan {}^{ - 1} ( \frac{ - 4 \sqrt{3} }{4} ) [/tex]

[tex] \alpha = \tan {}^{ - 1} ( - \sqrt{3} ) [/tex]

Here, our a is positive and b is negative so our angle in degrees must lie in the fourth quadrant, that angle is 300 degrees.

So

[tex] \alpha = 300[/tex]

So our initially form is

[tex]8( \cos(300) + i \sin(300) )[/tex]

Now, we use the roots of unity formula. To do this, we first take the cube root of the modulus, 8,

[tex] \sqrt[3]{8} = 2[/tex]

Next, since cos and sin have a period of 360 we add 360 to each degree then we divide it by 3.

[tex] \sqrt[3]{8} ( \cos( \frac{300 + 360n}{3} ) + \sin( \frac{300 + 360n}{3} ) [/tex]

[tex]2 \cos(100 + 120n) + i \sin(100 + 120n) [/tex]

Since 100 is in the second quadrant, we let n=0,

[tex]2 \cos(100) + i \sin(100) [/tex]

The margin of error is inversely proportional to the sample size. As the sample size increases, the margin of error decreases.

The probability or the chances of error while choosing or calculating a sample in a survey is called the margin of error.

The margin of error is given as

[tex]\rm ME = z\times \sqrt{\dfrac{p(1-p)}{n}}[/tex]

We know that margin of error is inversely proportional to the sample size.

As the sample size increases, the margin of error decreases.

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Answer:

B

Step-by-step explanation:

To rotate triangle ABC about the origin 90° clockwise we would follow the rule (x,y) → (y,-x), where the y-value of the original point becomes the new x-value and the x-value of the original point becomes the new y-value with the opposite sign.

Step-by-step explanation:

(2x + 3)(2x + 3)

4x² + 6x + 6x + 9

4x² + 12x + 9