After a reflection of the figure, the image vertices are A'(5, 1), B'(3, –1), and C'(7, –1). What is the line of reflection?




After a reflection of the figure, the image vertices are A'(5, 1), B'(3, –1), and C'(7, –1). What is the line of reflection?




y = 2x

y = –x

x = 2


y = 2

Answer:

C )  ( x - 2 ) ( x + 4 ) ( x - 6 )

Step-by-step explanation:

.

Answer:

Step-by-step explanation:

2 subtraction symbols equals a plus

so the answer is 9

Answer:

11

Step-by-step explanation:

The height is 11 inches.

Answer:

D. About 9.4 units

Step-by-step explanation:

\(ab = \sqrt{ {(9 - 4)}^{2} + {(10 - 2)}^{2} } \\ ab = \sqrt{ {(5)}^{2} + {(8)}^{2} } \\ ab = \sqrt{25 + 64} \\ ab = \sqrt{89} \\ ab = 9.43398 \: units\)

Multiply to get the answer:

Convert to scientific notation and find the ratio of the second number by the first:

Divide:

Answer:

\( x_{1} = 2, ▪︎ x_{2} = -2\)

Step-by-step explanation:

\( {x}^{2} = 4 (mod6)\)

\( {x}^{2} = 4\)

\( x =±2 \)

\( x_{1} = 2, ▪︎ x_{2} = -2\)

Answer:

Step-by-step explanation:

There is only one intercepting point, it means one solution.

Assuming that we have two data sets, a and b, with means of 20 and 30, respectively, and the same standard deviation of 5, we can conclude that neither data set is more spread out than the other.

Suppose you have two data sets A and B, with means of 20 and 30, respectively, and the same standard deviation of 5. To determine which data set is more spread out, we need to compare the variance of the two data sets. Since the variance is the square of the standard deviation, we can compare the variances of the two data sets. Using the formula, Var = s², we can calculate the variances of data set A and B.

\(Var(A) = (5)^2 = 25\\Var(B) = (5)^2 = 25\)

Both data sets have the same variance, indicating that they have the same amount of spread, or convergence. Therefore, we can conclude that no data set is more spread out than the other.

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Answer:

where is the graph?

Step-by-step explanation:

this is so easy it's: 1015

your welcome

Thus, the obtained area of sector for the given circle is found as 43.96 in².

Two radii that meet at the centre to form a sector define a circle. The sector is the portion of the circle created by these two radii. Knowing a circle's central angle assessment and radius measurement are both crucial for solving circle-related difficulties.

The curved portion that runs along the circle's perimeter and joins the ends of a two radii that make up a sector is known as the sector arc.

given data:

Formula for the area of sector:

area of sector = Ф /360 * (πr²)

area of sector = 140/360 * (3.14 *6²)

area of sector = 7/18 * 3.14 *36

area of sector = 43.96 in²

Thus, the obtained area of sector for the given circle is found as 43.96 in².

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Answer:

|3x + 1| + 6 < 2

|3x+1| < -4

Absolute value cannot be less than 0

No Solution for x in real numbers

Step-by-step explanation:

Answer:

The choice a.

\(B = \frac{3v}{h} \)

Step-by-step explanation:

\(v = \frac{1}{3} Bh \\ \\ v = \frac{Bh}{3} \\ \\ Bh = 3v \\ \\B = \frac{3v}{h} \)

I hope I helped you^_^

Answer:

Option D

Step-by-step explanation:

The triangle ABJ is equitorial

So area

Then mBJ is a arc which is 1/6th of circle

Area.

So area of unshaded region

Answer:

\(\textsf{d.} \quad r^2\left(\dfrac{\pi}{6}- \dfrac{\sqrt{3}}{4}\right)\)

Step-by-step explanation:

To find the area of the unshaded region, subtract the area of ΔJGB from the area of sector JGB.

The measure of an arc is equal to its corresponding central angle measure.  Therefore, the central angle of sector JGB is 60°.

As the two sides of ΔJGB adjacent the central angle are the radii of the circle (and therefore equal in length), ∠GJB = ∠GBJ.  

Interior angles of a triangle sum to 180°.  Therefore, all interior angles of ΔJGB are 60° which makes it an equilateral triangle.

Area of an equilateral triangle:

\(\sf A=\dfrac{\sqrt{3}}{4}a^2 \quad \textsf{(where a is the side length)}\)

As the side length of the given equilateral triangle is the radius (r):

\(\implies \sf Area\:of\:triangle=\dfrac{\sqrt{3}}{4}r^2\)

To find the area of the sector, first convert degrees to radians by multiplying the degrees by π/180 :

\(\implies 60^{\circ}=60 \times \dfrac{ \pi}{180}=\dfrac{\pi}{3}\:\:\sf radians\)

Area of a sector of a circle

\(\textsf{A}=\dfrac12 r^2 \theta \quad \textsf{(where r is the radius and the angle }\theta \textsf{ is in radians)}\)

Substituting the angle in radians, the area of the sector is:

\(\implies \sf A=\dfrac{1}{2}r^2\left(\dfrac{\pi}{3}\right)\)

\(\implies \sf A=\dfrac{\pi}6}r^2\)

Area of the unshaded region:

\(\begin{aligned}\textsf{Area of unshaded region} & =\textsf{Area of sector} - \textsf{Area of triangle}\\\\& = \dfrac{\pi}{6}r^2 - \dfrac{\sqrt{3}}{4}r^2\\\\& = r^2\left(\dfrac{\pi}{6}- \dfrac{\sqrt{3}}{4}\right)\end{aligned}\)

Therefore, the solution is option D.

Answer:

P(-5) = 109

Step-by-step explanation:

     If the polynomial p(x) is divided by the linear polynomial (x-a), the remainder is p(a).

   Dividend = divisor * quotient + remainder.

   p(x) = (x-a) * q(x) + p(a)

Here, q(x) is the quotient and p(a) is the remainder.

      P(x) = 4x² - x + 4

     P(-5) = 4*(-5)² - 1*(-5) + 4

              = 4*25 + 5 + 4

              = 100 + 5 + 4

              = 109

The product, of (2 + i)(4 - 2i) in form of a + bi is 0i + 10

A complex number is a combination of real values and imaginary values. It is denoted by z = a + ib, where a, b are real numbers and i is an imaginary number.

Given that, (2 + i)(4 - 2i), we need to find the product, in form of a + bi.

(2 + i)(4 - 2i)

= 8-4i+4i+2

= 10

We can write it as, 0i + 10

Hence the product, of (2 + i)(4 - 2i) in form of a + bi is 0i + 10

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We must know the following exponent rules to help us solve this question:

\(3^p=\dfrac{\sqrt[3]{9}}{3}\)

⇒ Rewrite \(\sqrt[3]{9}\) as \(9^\frac{1}{3}\):

\(3^p=\dfrac{(3^2)^\frac{1}{3}}{3}\)

⇒ Multiply:

\(3^p=\dfrac{3^\frac{2}{3}}{3}\)

⇒ Subtract:

\(3^p=3^{\frac{2}{3}-1}\)

\(p=\dfrac{2}{3}-1\\\\p=-\dfrac{1}{3}\)

\(p=-\dfrac{1}{3}\)

Answer:48

Step-by-step explanation:

Answers:

B) There are 3 terms in the simplified product.

E) The final simplified product is –3y2 + 37y – 84.

The true statements are:

B. The simplified product has three terms

E. –3y2 + 37y – 84 is the final simplified product.

Given the polynomial expression, –3(y – 5)² – 9 + 7y, to simplify, do the following:

–3(y – 5)(y – 5) – 9 + 7y

-3y² + 30y - 75 - 9 + 7y

Combine like terms

-3y² + 37y - 84 (three terms)

Therefore, the statements that are true are:

B. The simplified product has three terms

E. –3y2 + 37y – 84 is the final simplified product

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Answer:

8x +4y

Step-by-step explanation:

6x + 3y + 2x + y

1) add similar variables together.

2) 6x + 2x = 8x

    3y + (1)y = 4y.

3) y by itself basically means 1y, since in front of every variable theres an invisible 1.

6x + 3y + 2x + y

Simplified: 4 · ( 2x + y)

Answer= 11y

To find the approximate length of the cylinder's radius, we can use the formula for the volume of a cylinder, which is given by V = πr²h. By rearranging the formula and substituting the known values, we can solve for the radius of the cylinder.

The volume of the clay block is given as 450 in³, and the height of the cylinder is 10 in. We can set up the equation V = πr²h and substitute the known values: 450 = πr²(10). By rearranging the equation, we have r² = 45/π.

To find the approximate length of the radius, we can take the square root of both sides: r ≈ √(45/π). Evaluating this expression using a calculator, we can determine the approximate length of the cylinder's radius.

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Answer:

The missing angle is 50 and x=6

Step-by-step explanation:

So if all three angles of a triangle add up to 180 degrees, you would simply subtract 180-70-60 to find the missing angle, and from there you put in the equation 8x+2=50, you would do a step by step process get the x by itself on one side. first subtract 2 from both sides to remove it from one, making the equation 8x=48 and than divide both sides by 8 to remove it from the x making the answer x=6. :3

Answer:

x=6

Step-by-step explanation:

Ok so to do this you need to know if you add up all the sides of a triangle [This is for triangles] you get 180 every time.

So you already have two given angels. 70 and 60.

Lets make it an equation.

70+60+8x+2=180

It looks long and hard but we can simplify this if we go ahead and add up all the common factors. In this case would be all the numbers with no variables.

132+8x=180

You don't add the 180 because its on the opposite side of the equation.

Now you need to get the variable alone. To do that you need to do the opposite operation. In this case, that would be subtraction

132(-132)+8x=180(-132)

8x=48

Divide the 8.

x=6

8(6)+2=50

Answer:

the top one now!

Step-by-step explanation:

The distribution for the random variable follows the binomial distribution with p = 0.5.

The random variable representing the number of red cards observed in these four trials follows the binomial distribution with a probability of success of 0.5. Therefore, the correct answer is (b) the binomial distribution with p = 0.5.

Each trial consists of choosing one card from the set of 10 cards, and the probability of selecting a red card is 0.5 since there are 5 red cards out of 10 total cards. The trials are independent because after each selection, the chosen card is replaced, so the probability of selecting a red card remains the same for each trial.

The binomial distribution is suitable for situations where there are a fixed number of independent trials, and each trial has two possible outcomes (success or failure) with a constant probability of success. In this case, the random variable represents the number of successes (red cards) observed in four trials.

The probability mass function (PMF) for the binomial distribution is given by:

P(X = k) = C(n, k) * p^k * (1-p)^(n-k)

Where X is the random variable, k is the number of successes, n is the number of trials, p is the probability of success, and C(n, k) represents the binomial coefficient.

n = 4 (four trials), p = 0.5 (probability of selecting a red card), and we are interested in finding P(X = k) for different values of k (0, 1, 2, 3, 4) representing the number of red cards observed in the four trials.

The distribution for the random variable follows the binomial distribution with p = 0.5.

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Answer:

27

Step-by-step explanation:

15.75/0.60=26.25

if we round it up, Erin needs to sell 27 cookies

Circle: Graph upwards/down wards

The given equation is in the form of a quadratic function y = ax^2 + bx + c, where a = -1/2, b = 0, and c = 8. This is a downward-opening parabola since the coefficient of x^2 is negative.

the graph of the function is shaped like a "U" and opens downwards.

Vertical Axis of Symmetry

The vertical axis of symmetry is given by the equation x = -b/2a. Here, b = 0 and a = -1/2. Therefore, the axis of symmetry is x = 0.

Vertex (plug in axis of symmetry)

To find the vertex of the parabola, we need to plug in the value of the axis of symmetry into the equation for x and solve for y. Since the axis of symmetry is x = 0, we have:

x = 0

y = -1/2x^2 + 8

y = -1/2(0)^2 + 8

y = 8

Therefore, the vertex of the parabola is (0, 8).

Y-intercept (plug in 0)

To find the y-intercept, we need to plug in x = 0 into the equation and solve for y. Therefore, we have:

x = 0

y = -1/2x^2 + 8

y = -1/2(0)^2 + 8

y = 8

Therefore, the y-intercept is (0, 8).

X-intercepts (Solve by Square Rooting)

To find the x-intercepts, we need to set y = 0 in the equation and solve for x. Therefore, we have:

0 = -1/2x^2 + 8

1/2x^2 = 8

x^2 = 16

x = ±4

Therefore, the x-intercepts are (-4, 0) and (4, 0).

Graph the equation below:

The graph of the equation y = -1/2x^2 + 8 is a downward-opening parabola with vertex at (0, 8) and x-intercepts at (-4, 0) and (4, 0). The y-intercept is (0, 8). The vertical axis of symmetry is x = 0. The graph would look like:

          8 |

            |    

            |        

            |    /\    

            |   /  \  

            |  /    \  

            | /      \

       ---- + ------- + ----

          -4      0      4

Note that the points (0, 8), (-4, 0), and (4, 0) are on the graph, and the axis of symmetry is a vertical line passing through the vertex.

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Answerh

Step-by-step explanation:

huh

Answer: is not a function