Write a quadratic function in standard form whose graph has the given characteristics.

The pre-image ABC in order to become the reflection at A'B'C' is reflected across the x-axis.

The pre-image ABC in order to become A"B"C" both are CONGRUENT, because the image and pre-image are BOTH RIGID.

**Please note that the rules for the transformation from ABC to A"B"C" were not provided**

The amount earned as commission in the month of June is $2700

From the question, we have the following parameters that can be used in our computation:

Commission percentage = 5%

Total sales in the month of June = $54000

The amount earned as commission in the month of June is then calculated as

Amount = Commission percentage x Total sales in the month of June

Substitute the known values in the above equation

So, we have

Amount = 5% x 54000

Evaluate

Amount = 2700

Hence, the commission amount is $2700

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This can be solved using ratio and proportions.

What is ratio?

A ratio in mathematics illustrates how many times one number contains another. For example, if a dish of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the proportion of lemons to oranges is 6:8 (or 3:4), while the proportion of oranges to overall fruit is 8:14. (or 4:7). A ratio's numbers can be any quantity, such as a count of persons or things, or measures of lengths, weights, time, and so forth. In most situations, both numbers must be positive. A ratio in mathematics illustrates how many times one number contains another.

First, we find the ratio of trees planted to trees cut

= 48/8 = 6

So, no. of trees to be planted when 5 trees are cut = 5x6 = 30

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Division stops after a certain number of steps as the remainder becomes zero and When division continues as there is a remainder after every step.

a division is a process of splitting a specific amount into equal parts.

We can stop the long division process when converting a fraction to a decimal number.

There can be two situations in converting fractions to decimals:

When division stops after a certain number of steps as the remainder becomes zero.

When division continues as there is a remainder after every step.

Hence When division stops after a certain number of steps as the remainder becomes zero and When division continues as there is a remainder after every step.

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From the information given,

MAD for the heights of some sixth graders = 1.2

MAD for the heights of some seventh graders = 1

Number of times = MAD of data1/MAD of data 2 = 1.2/1

The answer is 1.2

Solution

We are given the equation

We want to find y when x = -3. We only need to put x = -3

Therefore, the answer is

In the small triangle

There are a right angle and an acute angle of measure 53 degrees

Since the sum of the angles of a triangle is 180 degrees

Then 90 + 53 + < 1 = 180 degrees

Then 143 + < 1 = 180

Subtract 143 from both sides

Then < 1 = 37 degrees

Since <2 is an exterior angle of the small triangle

Then its measure = the sum of <1 and 90 degrees

Then < 2 = 37 + 90 = 127 degrees

In the triangle of angles 2, n3 and 30

< 2 + < 3 + 30 = 180

127 + < 3 + 30 = 180

Add 127 and 30

157 + <3 = 180

<3 = 23

The answer is < 2 = 127 degrees and < 3 = 23 degrees

Hello!

What is an x-intercept:

 ⇒ value of x when the value of y equals '0'

       [tex]8x + 5y=25\\8x+5(0)=25\\8x=25\\\\x=\dfrac{25}{8}[/tex]

  x-intercept is 25/8

What is a y-intercept:

 ⇒ value of y when the value of x equals '0'

       [tex]8x+5y=25\\8(0)+5y=25\\5y=25\\y=5[/tex]

   y-intercept is 5

Hope that helps!

The measure of "a" in the above-given right-angled triangle is 32°

Note that a triangle is a three-sided polygon that is sometimes (but not always) referred to as the trigon. Every triangle has three sides and three angles, which may or may not be the same.

Key properties of a right-angled triangle to note are:

To solve for "a" recall the following. It is given that:

AB = BC

∠BEC=90°

∠DCE=42°

Because CD bisects ∠ACB, Hence,

∠ACD = ∠DCB = x.............................1

∠DCE= ∠BCE + ∠DCB .....................2

= ∠BCE + x = 42° ................................3

To find  ∠A, we use deductive reasoning to state:

∠A +∠E +∠ACD + ∠DCB + ∠BCE = 180° (Sum of Interior Angles)

Recall equation 1 hence, replacing ∠ACD with ∠DCB we have:

∠A +∠E +∠DCB + ∠DCB + ∠BCE = 180°

Recall equation 2, where ∠DCB = x, hence

∠A +∠E +x + x + ∠BCE = 180°

Recall equation three where 3 where  ∠BCE + x = 42°, hence

∠A +∠E +x + (x + ∠BCE) = 180°

⇒ ∠A +∠E + x + 42° = 180°

Recall that ∠E = 90° so

⇒ ∠A +90° + x + 42° = 180° (Collect like terms)

⇒ ∠A + x = 180° - 90° - 42° = 48°; Hence

∠A + x = 48°...........................4

Recall that in Δ ABC

AB =  BC (given)  

Hence, ABC is an Isosceles triangle. Since this is true, then

⇒ ∠A = ∠ACB = 2x ...........................5 (Two angles opposite the equal sides are equal)

Substituting 2x in equation 5 into equation 4, we have
2x + x = 48°

3x = 48

x = 48/3

x = 16°

Recall that

∠A = 2x...........equation 5, hence,

∠A = 2 * 16

∠A = 32°

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The probability is 0.9999

Given that the mean is 17.6 inches

standard deviation is 3.3/37 = 0.089

We have:

z(18.9)

Now, we have

P(x > 18.9) = P(z > 14.6067)

= 0.9999

z(0.394) = 0.6532

Hello! First, let's write some important information contained in the exercise:

committee = 6 students

class: 28 students:

- 10 males

- 18 females

Let's consider the rule: At least three females must be on the committee, so we have some cases, look:

_F_ * _F_ * _F_ * __ * __ * __

3 females and 3 males

_F_ * _F_ * _F_ * _M_ * _M_ * _M_

4 females and 2 males

_F_ * _F_ * _F_ * _F_ * _M_ * _M_

5 females and 1 male

_F_ * _F_ * _F_ * _F_ * _F_ * _M_

6 females and 0 male

_F_ * _F_ * _F_ * _F_ * _F_ * _F_

Now, we have to use the formula below and find the number of possible combinations:

Let's calculate each option below:

3 females:

3 males:

3 females and 3 males: 816 * 120 = 97920

4 females:

2 males:

4 females and 2 males: 3060* 45 = 137700

5 females:

1 male:

5 females and 1 male = 8568 * 10 = 85680

6 females and 0 male:

6 females and 0 male: 18564 * 1 = 18564

To finish the exercise, we have to sum the four options:

97920 + 137700 + 85680 + 18564 = 339864

So, right answer A: 339864.

Explanation

Part A: The quotient of y and seven is eight.

Answer: y/7 =8

Part B: Thrice a number is eighteen

Answer: 3x = 18

Part C: The sum of twice a number and five is nine

Answer: 2x+5 =9

Part D: A number decreased by seven is twenty- eight

Answer: x-7 =28

Answer:

Step-by-step explanation:

f(x)=|5x|    

f(2)= |5(2)|      Substitute 2 for x

f(2)= 10   Answer

Answer:

f(2) = | 5 • 2 | = | 10 | = 10

Step-by-step explanation:

Replace x with 2 then solve with the absolute value

Answer:

Step-by-step explanation:

x/7=12

Solution

For this case we have the following:

g = 12 and h=19

And we want to find 3h(h-g)

If we replace we got:

3*19 (19-12) =57*7=399

Then the answer would be:

D. 399​

The form of quadratic is:

Since (0,6) is given, we know c = 6, thus we have:

Point 2 is (2,8), replace x and y and find equation:

Putting point 2 (3,0), we have:

Solving the 2 simulatenous equations for a and b, we get:

a = -3

b = 7

Now u have all the values, a, b, and c.

Just put it in the general form of parabola :

y = -3x^2 + 7x + 6

[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{3}x^2\stackrel{\stackrel{b}{\downarrow }}{+6}x\stackrel{\stackrel{c}{\downarrow }}{+1} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 6}{2(3)}~~~~ ,~~~~ 1-\cfrac{ (6)^2}{4(3)}\right) \implies \left( - \cfrac{ 6 }{ 6 }~~,~~1 - \cfrac{ 36 }{ 12 } \right) \\\\\\ (-1~~,~~1-3)\implies {\Large \begin{array}{llll} (-1~~,~~-2) \end{array}}[/tex]

Considering the definition of an equation, the equation 0.925p= p - 599 models the following situation: the sale prices of the motorcycles in both dealers are equal.

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values appear in addition to certain known data.

The solution of a equation means determining the value that satisfies it and the equality is true. To solve an equation, keep in mind:

Being "p" the motorcycle’s original price, you know that:

If the sale prices are equal, the equation in this case is:

Sale price A= Sale price B

0.925p= p - 599

Finally, the equation 0.925p= p - 599 represent the situation.

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f(x) = (x + 1)^3

g(x) = cubic root x + 1

f(g)(x) =

result

f(g(-64)) = -8

Answer:

-5  < x < 17/5

Step-by-step explanation:

add three onto all sides -10 < 5x < 17

then divide all sides by -5  < x < 17/5

Given the following question:

Part A:

75 dollars to spend on gaS

Gas per gallon costs $2.80

With 75 dollars you can buy "26.8 gallons of gas."

Part B:

We know we can travel 230 miles with 26.8 gallons of gas, now we have to find out how many miles can we travel PER gallon of gas.

"10.4 miles" per gallon

The parent function is given as:

f(x) = x²

y = x²

The graph is reflected across the x - axis

The x axis remains the same but the y axis is negated

g(x) = -x²

It is translated 4 units left

The function g(x) becomes

g(x) = -(x - 4)²

It is the translated 2 units down

g(x) = -(x - 4)² - 2

Simplifying the above equation:

g(x) = - (x² - 8x + 16) - 2

g(x) = -x² + 8x - 16 - 2

g(x) = -x² + 8x - 18

The population after 5 years is approximately 337,465 people

The population of the city is 250,000

Annual growth rate is 6%

The population after t years is:

After 5 years, t = 5 and the population becomes:

The population after 5 years is approximately 337,465 people

Hello there. To solve this question, we'll need to remember how to find the variance and standard deviation of a data set.

First, given a data set with values:

The variance can be calculated by the formula:

In this case, μ is the arithmetic mean of the data set and x_i is the i-th element of the data set.

The data set given is:

{4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 9}

To calculate the mean, we add every term and divide by the number of terms:

Now, we calculate the square of the difference between every term and mean.

Notice we have some repeated terms, we rewrite the sum like this:

Adding the terms and calculating the squares, we have:

This is the variance of the values of this data set. We can round it up to the nearest tenth as 1.6

The standard deviation is the square root of the variance.

Then, we calculate:

Again, rounding it to the nearest tenth, we have 1.3;

The final answer is: The variance of this data set is 1.6 and its standard deviation is 1.3.

Solving the second question:

We apply the same formula. First, find the mean of the values:

Now, as every term is different from each other, we apply the formula and get the following:

Calculating the difference, squaring it, adding the values and dividing by 9, we get:

Variance is approximately equal to 4.84

The Standard deviation is the square root of the variance, namely 2.2

From the given table, it is found that:

a. The average population decline was of 2,250 deer a year.

b. The population would have reached 225 thousand deer during the years of 2017 and 2018.

The average rate of change of a function is given by the change in the output divided by the change in the input of the function. Hence, over an interval [a,b], the average rate of change is given as follows:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

In 1984 and 2018, the populations are given as follows:

Hence the rate of change is given as follows:

r = (173.5 - 250)/34 = -2.25.

(2.25 thousand = 2,250).

For item b, the following linear function is built:

y = 230.5 - 1.45x.

The amount would be of 225 when:

230.5 - 1.45x = 225

1.45x = 5.5.

x = 5.5/1.45

x = 3.79.

Hence between the years of 2017 and 2018.

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The total number of ways she can hang the painting is 720 after applying the concept of permutation and combination.

The variety of possible arrangements of a set is its permutation however order is important in permutations but not in combinations.

It is given that:

Alicia wants to place her ten paintings side by side on the wall.

We can get the factorial of 6 and use that knowledge to calculate how many ways there are to multiply 6 by multiplying it by all positive integers that are more than or equal to that number, in this case, 6.

Alicia can arrange her six paintings:

6! = 6x5x4x3x2x1

6! = 720

Thus, the total number of ways she can hang the painting is 720 after applying the concept of permutation and combination.

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Answer:

  U'(12, 15)

Step-by-step explanation:

Given point U(4, 5) is part of figure STUVW that is dilated by a factor of 3 about the origin, you want the coordinates of U'.

Dilation about the origin multiplies each coordinate value by the scale factor:

  U' = 3U

  U' = 3(4, 5) = (12, 15)

The coordinates of U' are (12, 15).

Problem

Henry purchased compact disks for $112. The compact discs cost $16 each.

Which of the following equations could you use to find how many compact disks, x, Henry purchased?

Solution

We can set up the following notation:

x= number of disks

total cost = (number of disks)* (unitary price)

Total cost = $112

number of disks =x

unitary price = $16

Replacing we got:

112 = x*16

For this case the correct equation would be given by:

$112 = $16x

The given figure can be divided into a rectangle and a triangle

The rectangle has the dimensions 10 m by 12 m

so, the area of the rectangle = 10 x 12 = 120 square meters

Now, we will find the area of the triangle:

Base = 12 - 10 1/4 = 1 3/4 m

Height = 15 - 10 = 5 m

Area = 1/2 x base x height =

So, the total area =