I don’t know how to find the median and the mode HELPP

Answer:

[tex]\textsf{Vertex form}: \quad y=\dfrac{1}{36}(x+3)^2+1[/tex]

[tex]\textsf{Standard form}: \quad y=\dfrac{1}{36}x^2+\dfrac{1}{6}x+\dfrac{5}{4}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]

Given:

Substitute the given vertex and point into the formula and solve for a:

[tex]\begin{aligned}y&=a(x-h)^2+k\\\\\implies 2&=a(-9-(-3))^2+1\\2&=a(-6)^2+1\\2&=36a+1\\36a&=1\\a&=\dfrac{1}{36}\end{aligned}[/tex]

Therefore, the equation of the parabola in vertex form is:

[tex]\boxed{y=\dfrac{1}{36}(x+3)^2+1}[/tex]

In standard form:

[tex]\implies y=\dfrac{1}{36}(x+3)(x+3)+1[/tex]

[tex]\implies y=\dfrac{1}{36}(x^2+6x+9)+1[/tex]

[tex]\implies y=\dfrac{1}{36}x^2+\dfrac{6}{36}x+\dfrac{9}{36}+1[/tex]

[tex]\implies y=\dfrac{1}{36}x^2+\dfrac{1}{6}x+\dfrac{5}{4}[/tex]

Answer:

  18.7 miles

Step-by-step explanation:

You want to know how far Kendall can ride her bike in 2 hours if she rides at the speed of 7 miles in 45 minutes.

The question assumes that distance is proportional to time, so the distance (d) of interest can be written in the proportion ...

   miles/minutes = 7/45 = d/120 . . . . . . 120 minutes is 2 hours

Multiplying by 120, we have ...

  d = 120(7/45) = 7(8/3) = 18 2/3 ≈ 18.7

Kendall can ride about 18.7 miles in 2 hours.

the zeros of the graph tell us the time needed for the tank to be drain.

(2t-7)(2t-9)

The sales tax rate of an item which cost $430 and tax of $8.60 is 2%

Sales tax refers to local or state tax imposed as a percentage of the selling price of goods or services payable by the customer. The tax is not recognized as the seller's earnings as the seller only collects the tax and transmits it to local or state authorities.

Sales tax rate = Sales tax / Cost of item before tax × 100

= $8.60 / $430 × 100

= 0.02 × 100

= 2%

In conclusion, the sales tax rate of the item is given by 2%.

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Answer:

Your answer is [tex]y = 2x - 2[/tex]

Step-by-step explanation:

Just test it out on all of them, it fits.

The best estimate of the diameter of the moon is 3.474×10⁶.

The best estimate of the diameter will be calculated by converting the number into scientific notation. To convert the number into scientific notation it is broken into two parts.

First number is coefficient which has to range between 1 and 10. So, as per the digits, 3.474 will be the coefficient.

The 10 will be written along with exponent. There are three digits after the decimal followed by three zeroes. Therefore, the 10 and exponent will be written as 10⁶.

So, the complete number estimating the diameter of moon is 3.474×10⁶.

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The integers are 71 and 72 respectively

An algebraic expression can be defined as an expression that is composed of terms, variables, coefficients, factors and constants.

They are also known to be composed of mathematical operations such as;

From the information given , we have;

x + 1 + x + 2 = 143

collect like terms

2x = 143 - 3

Subtract like terms

2x = 140

Make 'x' the subject

x = 140/2

x = 70

The numbers are;

x + 1  = 70 + 1  = 71

x + 2 = 70 + 2 = 72

Hence, the numbers are 71 and 72

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The perimeter of a geometric figure is the sum of it's side lengths.

We have a pentagon with side lengths equal to:

x, x, x, 3x, and 3x

a)

The perimeter of this pentagon is:

P = x + x + x + 3x + 3x

Since the perimeter is given as 54 cm:

x + x + x + 3x + 3x = 54

Answer: Option A

b) Solve the equation in part a)

Collecting all like terms:

9x = 54

Dividing by 9:

x = 54 / 9

x = 6 cm

c) Find the length of each side.

The sides are

x=9 cm

x=9 cm

x=9 cm

3x=27 cm

3x=27 cm

Given the polynomial:

The x-intercepts are the points in which the polynomial crosses the x-axis. That is, are the points (x, 0).

To find these points, use the quadratic formula according to the steps below.

Step 01: Substitute the values in the quadratic formula.

For a equation y = ax² + bx + c, the x-intercepts are:

In this question,

a = 1

b = 16

c = 64

Substituting the values:

Step 02: Solve the equation above.

Begin by solving the square and the multiplications:

Now, subtract the values inside the root.

Solve the root:

And find the values of x:

Answer: The x-intercepts are: (-8, 0), (-8, 0).

The growth rate of real gdp per capita from 2019 to 2020 is 40%

Given,

The real gdp of an economy in 2019 = 100 billion = 100, 000, 000, 000

The real gdp of an economy in 2020 = 240 billion = 240, 000, 000, 000

The population in 2019 = 15 million = 15, 000, 000

The population in 2020 = 15 million = 15, 000, 000

Growth rate of real gdp per capita =( increased gdp × 100) / (initial gdp)

Here,

Initial gdp = 100,000,000,000 / 15,000,000 = 6666.67

Increased gdp = 240,000,000,000 / 15, 000, 000 = 16000

Now,

Growth rate of real gdp per capita =( increased gdp × 100) / (initial gdp)

Growth rate of real gdp per capita = (16000 × 100) / 6666.67 = 240

That is,

The growth rate of real gdp per capita from 2019 to 2020 is 40%

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The probability that Dave will select a gray T-shirt is 13 / 25.

The odds in favor of picking a gray T-shirt is 13 : 25

Probability is used to calculate the odds that are in favor or against a random event happening. The odds in favor or against a random event happening has a probability value that lies between 0 and 1. The higher the odds that are in favor of the event happening, the closer the probability value would be to 1.

The probability that Dave will select a gray T-shirt = number of gray T-shirts / total number of T-shirts

13 / 25

Ratio is used to compare two or more numbers together.

The odds in favor of picking a gray T-shirt = number of gray T-shirt : total number of T-shirts = 13 : 25

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John's account balance after considering the withdrawal and the overdrawn fee is -$35

What does it mean for an account to be overdrawn?

An account is overdrawn if the money withdrawn from it is more than the account balance, in this scenario, the check presented whose value is $110 is more than the account balance, which was the account by which the account was opened initially, hence, John's account can be said to be overdrawn.

Account balance=initial balance-amount withdrawn-overdrawn fee

Note overdrawn fee and amount withdrawn would be shown as negative values because they are obligations against the account balance

initial balance=$100

amount withdrawn=$110

overdrawn fee=$25

Account balance=$100-$110-$25

Account balance=-$35

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Answer:

x²-2

Explanation:

Let the number be x.

The square of the number = x²

If 2 is subtracted from the square of the number, we have:

Therefore, an algebraic expression for the statement "2 is subtracted from the square of a number" is x²-2.

Explanation:

Equation A

In order to complete the square remember that

first, equal the expression divide all the expressions by 2,

then, we can find "a" using the second portion of the definition

then,

add 1 on both sides

rewrite as a square expression on the left,

multiply both sides by 2

bring all to the left side and equal to f(x)

Donna is right. 115° angle and ∠3 are supplementary.

From the figure, we are discussing about the 115° angle and ∠3.

Donna says that m∠3 = 65° because the 115° angle and ∠3 are supplementary. That is their sum = 180°.

From the figure, it is clear that the 115° angle and ∠2 are supplementary.

So ∠2 = 180° -115° = 65°.

Now ∠2 and ∠3 are corresponding angles formed between the parallel lines m and q. Since corresponding angles are equal, m∠2 = m∠3.

Thus m∠3 = 65°.

Thus 115° + m∠3 = 115° + 65° = 180°

As the sum of the 115° angle and m∠3 = 180°, they are supplementary.

Hence Donna is correct.

Luis said that 115° and ∠3 are alternate but they are not. Alternate angles are those which are formed in the interior and on the opposite sides of the transversal cutting two parallel lines. They are of same size. But here, m∠3 ≠ 115°.

So Luis is not right.

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Answer:

Explanation:

Here, we want to get the measure of the other three angles in a parallelogram

The angle rules in a parallelogram are:

i) Opposite angles are equal to each other

ii) The two adjacent angles add up to 180 degrees

From what we have, one of the angles is 24 degrees

The measure of the last two angles would be:

The amount that he borrow (PV)  if interest rate is 13% (interest rate) per annum compounded monthly (P/YR)​ is: $12,235.90.

First step is find to  the number of months

n = 20 months / 12

n = 1.66666666

Now let find the amount borrowed

A= P/ ( 1+ r) ^ n

Where:

A = Amount

P = Principal

r = interest rate

n =  time

Hence.

A = 15,000 / ( 1+ 0.13) ^ 1.66666666

A = 15,000 / (1.13)^ 1.66666666

A = 15,000 /  1.2259

A = $12,235.90

Therefore $12,235.90 is the amount borrowed.

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The equation of the parabola from its focus and vertex is 5x = 4y² .

A parabola is a mirror-symmetrical, roughly U-shaped planar curve. The same curves can be defined by a number of seemingly unrelated mathematical definitions, which all correspond to it.

A line and a point (the focus) are two components of one definition of a parabola (the directrix). There is less emphasis on the directrix. The parabola is the location of the endpoints in that plane that are equally spaced away from the directrix and the focus.

Another approach to define a parabola is as a conic section formed by the union of a right circular conical area with a plane parallel to another axis perpendicular to the conical surface.

from the figure the parabola is opening on the right side.

Hence the general equation of the parabola is is y² = 4ax

Now from the focus we get 4a = 5

or, a = 5/4

Hence the equation of the parabola is 5x = 4y².

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When we want to determine the midpoint of two points on a line segment, we must first determine the coordinates of the two points. Then we divide the sum of the abscissa [tex](x)[/tex] by [tex]2[/tex] to find the abscissa of the midpoint and divide the sum of the ordinates [tex](y)[/tex] by [tex]2[/tex] to find the ordinate of the midpoint.

Let the coordinates of our midpoint be [tex]F(a,b)[/tex].

We found our midpoint.

1) Gathering the data

3 pencils ----------- $0.45

Using proportions, it is found that the number of people that each asked is given as follows:

a) Rasheed: 571 people.

b) Kamal: 667 people.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using basic arithmetic operations, especially multiplication and division, with the unit rates or percentages of the problem.

For Rasheed, since he was counting people with silver cars, we have that 21% of the n people is equivalent to 120 people, hence the number of people n is calculated as follows:

0.21n = 120

n = 120/0.21

n = 571 people. (rounding)

For Kamal, since he was counting people with blue cars, we have that 18% of the n people is equivalent to 120 people, hence the number of people n is calculated as follows:

0.18n = 120

n = 120/0.18

n = 667 people. (rounding)

The percentages of car colors in the UK are mussing and are given as follows:

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Answer:

(-5, 2)

Explanation:

If a point (x,y) is reflected in the line y=x, the x-coordinate and y-coordinate change places.

That is:

Therefore, the image of (2, -5) when reflected in the line y=x is:

there is a zero at x = 1 (option D)

Explanation:

a) The graph shows it is going up (increasing towards both the y axis and x axis).

This graph will give a positive leading coefficient.

As a result, the equation will have a positive leading coefficient not a negative one.

b) zeros of a polynomial are the values of x when the line crossses the x axis.

From our graph, the line doesn't cross the x axis at x = 6.

As a result, there is no zero of -6.

Multiplicity tells us the number of times the number of times a factor occurs.

Since part of the statement is wrong, it makes the whole statement wrong

c) The degree of this graph is odd. Its equation is 3rd degree

d) From the graph, the line crosses the x axis at x = 1 (2nd tick line)

Each tick line represents 0.5

The zero is the value of x when it crosses the x axis

As a result the polynomial has a zero at x = 1

The correct option is there is a zero at x = 1 (option D)

The exponent multiplies the logarithm of the base

So:

The answer is option C

This is the correct answer, this is because it only function that the inverse is correctly represented

SOLUTION:

Step 1:

In this question, we are given the following:

Certain pieces of antique furniture increased very rapidly in price in the 1970s and 1980s.

For example, the value of a particular rocking chair is well approximated by:

where V is in dollars and t is the number of years since 1975.

Find the rate, in dollars per year, at which the price is increasing.

Step 2:

Next,

Now, we need to evaluate:

Hence, the rate, in dollars per year since 1975, at which the price is increasing is:





Answer: y-1=3(x-3)

this in the correct answer.  you take one point on the line and substitues x and y of the point into the equation.  M is your slope.  y-y1=m(x-x1)

Recall the definitions of the magnitude and direction of a vector:

The triangles are not similar.

Triangles that are comparable to one another are those that have an equal number of corresponding sides and corresponding angles.

If the respective sides of two triangles are proportional and the corresponding angles are congruent, then the triangles are said to be comparable. To put it another way, similar triangles have the same shape but may differ in size. In addition, if the corresponding sides of the triangles are identical in length, the triangles are congruent.

Here, the ratio of the sides are not similar

AB/AC= 4/10 = 2/5

DE/DF= 8/19

Hence, 2/5≠8/19

therefore, the triangles are not similar.

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