what are the factors of 15​

let's take a peek at the picture above, hmmm let's notice the vertex is at (-1 , 2), now let's get a point besides the vertex hmmm let's see it passes through (-2 , -1).

So we can reword that as what's the equation of a quadratic whose vertex is at (-1 , 2) and it passes through (-2 , -1)?

\(~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{a~is~negative}{op ens~\cap}\qquad \stackrel{a~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\)

\(\begin{cases} h=-1\\ k=2\\ \end{cases}\implies y=a(~~x-(-1)~~)^2 + 2\hspace{4em}\textit{we also know that} \begin{cases} x=-2\\ y=-1 \end{cases} \\\\\\ -1=a( ~~-2-(-1) ~~ )^2 + 2\implies -3=a(-2+1)^2\implies -3=a \\\\\\ ~\hfill~ {\Large \begin{array}{llll} y=-3(x+1)^2 + 2 \end{array}} ~\hfill~\)

Answer:

y = -3(x + 1)^2 + 2

Step-by-step explanation:

y = a(x - h)^2 + k is the vertex form of a quadratic, where

Finding (h, k):

We see from the graph that the vertex is a maximum and its coordinates are (-1, 2).  Thus h is -1 and k is 2.  Since h becomes negative, it will be 1 in the parentheses: (x - (-1) = (x + 1).

Finding a:

In order to find a, we will need to plug in a point on the parabola for (x, y) and (-1, 2) for h and k.  We see that (0, -1) lies on the parabola so we can use this point for (x, y).

-1 = a(0 - (-1))^2 + 2

-1 = a(0 + 1)^2 + 2

-3 = a(1)^2

-3 = a

Thus, a = -3.

Thus, the exact equation in vertex form of the parabola is:

y = -3(x + 1)^2 + 2

I attached a picture from Desmos Graphing Calculator that shows how the equation I provided works and contains the two points you marked on the parabola, including (-1, 2) aka the maximum, and (0, -1) aka the y-intercept.

Answer:

A=b/2

Step-by-step explanation:

you're simplifying both ends of an equation.

Answer:

A scale drawing with a 1: 0,8 scale will have sides that measure 2.24, 1.6, and 3.2.

Step-by-step explanation:

A scale drawing refers to a drawing that has been made bigger or smaller but preserves the proportions of a drawing.

How to make the scale drawing of the sign?

The first step is to decide the scale. In this case, the best scale is 1:0.8, which means the new drawing is 0.2 smaller. This scale is ideal because this sign is slightly bigger than regular signs.

Draw the sign by multiplying each side by the scale (0,8).

Answer:

Cory bought 6.30 gallons of gas at the gas station.

Step-by-step explanation:

total amount = cost of snacks + amount spent on gas

\($\$ 24.00=\$ 6.50+\$ 2.78 \mathrm{~g}$\)

\($\$ 2.78 \mathrm{~g}=\$ 24.00-\$ 6.50$\)

\($\$ 2.78 \mathrm{~g}=\$ 17.50$\)

\($g=\frac{\$ 17.50}{\$ 2.78}$\)

\($g=6.30$\)

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Answer:

perimeter = 25.62 units

Step-by-step explanation:

Let the quadrilateral be ABCD

A = (1, 5), B = (6, 5), C= (1, 11) , D = (6, 11)

To find the perimeter we need to add the lengths of sides AB , BC, CD, and AD.

Lets find the length of all sides using distance formula;

\(distance = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\)

\(AB = \sqrt{(1-6)^2+(5-5)^2} = \sqrt{25} = 5units\\\\BC= \sqrt{(6-1)^2+(5-11)^2} = \sqrt{25+36} =\sqrt{61} units\\\\CD=\sqrt{(1-6)^2 + (11-11)^2} = \sqrt{25} = 5units\\\\AD = \sqrt{(1-6)^2+(5-11)^2} = \sqrt{25+36} = \sqrt{61}units\)

Perimeter = AB + BC + CD + AD

               \(=10 + 2\sqrt{61} units\) = 25.62 units

The correct statement is: g(x) is translated up 5 units compared to f(x).

The correct answer is A.

The correct answer is A.

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The best use for a sign chart when graphing rational functions is Option D: To check whether F(x) is positive or negative for values of x.

A sign chart, also known as an interval chart, is a tool used to determine the sign (positive or negative) of a function over different intervals. When graphing rational functions, it is essential to identify the intervals where the function is positive or negative.

By constructing a sign chart for the rational function, you can analyze the behavior of the function and determine its sign over different intervals. This information is crucial for sketching an accurate graph of the rational function.

The sign chart helps identify intervals where the function is positive (above the x-axis) or negative (below the x-axis), which directly impacts the shape and position of the graph. It provides information about the regions where the function is increasing or decreasing.

The best use for a sign chart when graphing rational functions is Option D: To check whether F(x) is positive or negative for values of x. Options A, B, and C are not the best uses for a sign chart when graphing rational functions. Checking whether the function is a straight or curved line (Option A), the slope (Option B).

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Given statement solution is :- It takes 4 months to pay off the card, and the total amount paid, including interest, is $1600.

To determine the number of months it takes to pay off the credit card and the total amount paid, including interest, we can follow these steps:

Step 1: Calculate the monthly interest rate.

The APR (Annual Percentage Rate) is given as 9.5%. To find the monthly interest rate, we divide this by 12 (the number of months in a year):

Monthly interest rate = 9.5% / 12 = 0.0079167

Step 2: Determine the monthly payment.

The monthly payment is given as $400.

Step 3: Calculate the interest and principal paid each month.

The interest paid each month can be calculated by multiplying the monthly interest rate by the current balance.

Principal paid = Monthly payment - Interest paid

Step 4: Track the remaining balance each month.

Starting with the initial balance of $1,367.90, subtract the principal paid each month to determine the new balance.

Step 5: Repeat Steps 3 and 4 until the balance reaches zero.

Continue calculating the interest and principal paid each month, updating the balance, until the remaining balance becomes zero.

Step 6: Determine the total number of months and the total amount paid.

Count the number of months it takes to reach a balance of zero. Multiply the number of months by the monthly payment ($400) to find the total amount paid.

Let's calculate the number of months and the total amount paid, including interest:

Month 1:

Interest paid = 0.0079167 * $1,367.90 = $10.84

Principal paid = $400 - $10.84 = $389.16

New balance = $1,367.90 - $389.16 = $978.74

Month 2:

Interest paid = 0.0079167 * $978.74 = $7.75

Principal paid = $400 - $7.75 = $392.25

New balance = $978.74 - $392.25 = $586.49

Month 3:

Interest paid = 0.0079167 * $586.49 = $4.64

Principal paid = $400 - $4.64 = $395.36

New balance = $586.49 - $395.36 = $191.13

Month 4:

Interest paid = 0.0079167 * $191.13 = $1.51

Principal paid = $400 - $1.51 = $398.49

New balance = $191.13 - $398.49 = -$207.36 (Paid off)

It takes 4 months to pay off the credit card. Now, let's calculate the total amount paid, including interest:

Total amount paid = 4 * $400 = $1600

Therefore, it takes 4 months to pay off the card, and the total amount paid, including interest, is $1600.

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Step-by-step explanation:

To compare the two amounts of fabric, we need to express them with a common denominator:

15/2 = 30/4

7 1/2 = 15/2

Now we can compare the two amounts:

30/4 > 15/2

This is true because 30/4 is equal to 7.5 yards, which is greater than 7.5 yards (or 15/2 yards) of silver fabric.

Therefore, Ms. Thompson needs more red fabric than silver fabric.

Answer:

Yes, one inch is a twlefth of a ft which is a porportion of a feet

Step-by-step explanation:

Answer:  its not a perfect square.

Step-by-step explanation:

We need to assume the sample was randomly selected because we are making inferences about parameters.

In mathematics, the parameter is a variable for which the range of possible values identifies a collection of distinct cases in a problem. Any equation expressed in terms of parameters is a parametric equation. The general equation of a straight line in slope-intercept form, y = mx+b, in which m and b are parameters, is an example of a parametric equation.

In statistics, the parameter in a function is a variable whose value is sought by means of evidence from samples. The resulting assigned value is the estimate or statistic.

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Answer:

The surface area of the cube is equal to 216 cm².

General Formulas and Concepts:
Geometry

Surface Area Formula [Cube]:
\(\displaystyle \text{SA} = 6a^2\)

Step-by-step explanation:

Step 1: Define

Identify given variables.

a = 6 cm

Step 2: Find Surface Area

∴ we have found the surface area of the cube to be 216 cm².

---

Topic: Geometry

The surface area of a 3D figure is the sum of the area of its faces.

We know the following:

Since all faces in a cube have the same area, the surface area of a cube is:

\(\boxed{(\text{side})^{2} + (\text{side})^{2} + (\text{side})^{2} + (\text{side})^{2} + (\text{side})^{2} + (\text{side})x^{2} = 6(\text{side})^{2}}\)

Therefore, the surface area of a cube must be known as 6(side)².

\({\text{Given side length of cube:} \ |\text{6 centimeters}|\)

Substitute the side length in the surface area formula and simplify:

\(\implies 6(6)^{2}\)

\(\implies 6(6)(6)\)

\(\implies \boxed{216 \ \text{cm}^{2}}\)

Therefore, the surface area of the cube is 216 cm².

\(\overline{===============================================}\)

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Answer:

Step-by-step explanation:

i am working on the assumption that nobody does all three of them

i got 4 because including the people that do swimming and park, the total number of people that do swimming is 22.

the same logic goes for cycling: including the people that do swimming and visit the national park, the total is 23.

so that means that find how many people do swimming and cycling, we have to add the people doing only swimming, with the people doing both swimming and park and then subtract that answer from 22 which gives you 4

Answer:FOR ALL MY POINTS write an argumentative essay on why dog parks are "helpful or harmful"

READ PROMPT

Step-by-step explanation:

A single outlier does not affect the values of the quartiles.

An outlier is a number that is way smaller or way larger than that of other numbers in a data set. An outlier does not affect the values of the upper and lower quartiles. This is an advantage of the upper and lower quartiles over range.

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The jeweler made 7 bracelets and 9 necklaces .

In the question ,

it is given that

amount of gold in each bracelet is \(=\) 6 grams

amount of gold in each necklace is \(=\) 24 grams .

let the number of bracelets \(=\) "b" .

let the number of necklaces \(=\) "n" .

since the total number of necklace and bracelet is 16 .

the equation is b + n = 16

so , b = 16 - n

also given that total gold used is 258 grams .

so the equation is 6b + 24n = 258

Substituting b= 16 - n in the equation ,

we get , 6*(16 - n) + 24n = 258

96 - 6n + 24n = 258

96 + 18n = 258

18n = 258 - 96

18n = 162

n = 162/18

n = 9

and b = 16 - 9 = 7

Therefore , The jeweler made 7 bracelets and 9 necklaces .

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Answer:

350 ml

Step-by-step explanation:

70% of 500 ml = 0.7*500 ml = 350 ml

Answer:

350 ml

Step-by-step explanation:

70% of 500 ml = 0.7*500 ml = 350 ml

The arc length can be calculated by using the following formula

theta, is the central angle of the arc in radians, and r is the radius

We have been given that the radius is 18, and the central angle is 150 degrees. To find the arc length, let us start by converting the angle to radians. We can do this by multiplying 150 by the ratio between radians and degrees (pi/180). This works because 180 degrees is equal to pi radians (so the fraction is equal to 1):

So, the sector is 5pi/6 radians. Now, we can solve this by multiplying this by the radius of the circle:

Therefore, the answer is C, or 15pi

The different sums are possible are 18.

As, the number of different sums possible is given by the equation:

Number of different sums = n x m

In other words, we multiply the number of outcomes for the first spinner by the number of outcomes for the second spinner to get the total number of unique sums.

So, the different sums are possible

= 2 x 3 x 3

= 18

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When two or more variables vary jointly, their product is always constant. In this case, if 'a' varies jointly with 'b' and 'c' it means that their product is always constant, so abc = k, where k is a constant value.

When a variable 'a' varies inversely as the square of another variable 'd', it means that a*1/d^2 = k, where k is a constant value.

So, if 'b' is tripled, 'c' is doubled and 'd' is doubled, we can see the effect on 'a' by substituting the new values into the equations.

abc = k => a3b2c = k

a1/d^2 = k => a1/(2d)^2 = k

So the effect on 'a' if 'b' is tripled, 'c' is doubled, and 'd' is doubled is that it will be divided by 4.

a3b2c = a1/(2d)^2 => a = k / (3b2c*(2d)^2) = (k/(12bcd^2))

So a = k/(12bcd^2) = a/4.

Therefore, the value of 'a' is decreased by a factor of 4.

Answer:

True i guess

Step-by-step explanation:

Answer: 172 ounces

Step-by-step explanation:

We are given 10 pounds and 12 ounces to convert to ounces.

There are 16 ounces in 1 pound.

We can create a proportion to find out how much ounces 10 pounds is.

10 pounds / x ounces = 1 pound / 16 ounces

We need to solve for x by isolating the variable x.

10/x = 1/16

10 = x/16

10 * 16 = x

160 ounces = x

so 10 pounds is equivalent to 160 ounces. But we are not done yet.

We were asked to convert 10 pounds and 12 ounces.

So add together the ounces to find the total ounces:

160 ounces + 12 ounces = 172 ounces.

We can conclude that with 95 percent confidence, the sample means will fall within the interval of approximately (0.9534, 0.9566).

To determine the interval within which 95 percent of the sample means will fall, we need to calculate the margin of error using the standard deviation and the desired level of confidence.

The formula to calculate the margin of error is given by:

Margin of Error = Z * (Standard Deviation / √n)

Where:

Z is the critical value corresponding to the desired level of confidence

Standard Deviation is the standard deviation of the population

n is the sample size

Since the sample size is 41 and we want to find the interval at a 95 percent confidence level, we need to find the critical value corresponding to a 95 percent confidence level.

The critical value can be found using a standard normal distribution table or a calculator. For a 95 percent confidence level, the critical value is approximately 1.96.

Now we can calculate the margin of error:

Margin of Error = 1.96 * (0.0050 / √41)

Calculating this, we find:

Margin of Error ≈ 0.001624

To find the interval within which 95 percent of the sample means will fall, we need to subtract and add the margin of error to the true mean:

Interval = True Mean ± Margin of Error

Interval = 0.9550 ± 0.001624

Calculating this, we find:

Interval ≈ (0.9534, 0.9566)

Therefore, we can conclude that with 95 percent confidence, the sample means will fall within the interval of approximately (0.9534, 0.9566).

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Answer:

4!

Step-by-step explanation:

20/5=4

14. The trigonometric equation (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45° = 4

15. In the trigonometric equation 2(cos²θ - sin²θ) = 1, θ = 15°

A trigonometric equation is an equation that contains a trigonometric ration.

14. To find the value of (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45°, we proceed as follows

Since we have the trigonometric equation (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45°,

We know that sin47° = sin(90 - 43°) = cos43°. So, substituting this into the equation, we have that

(sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45° = (cos43°/cos43°)² + (cos43°/cos43°)² - 4cos²45°

= 1² + 1² - 4cos²45°

We know that cos45° = 1/√2. So, we have

1² + 1² - 4cos²45° = 1² + 1² - 4(1/√2)²

= 1 + 1 + 4/2

= 2 + 2

= 4

So, (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45° = 4

15. If 2(cos²θ - sin²θ) = 1 and θ is a positive acute angle, we need to find the value of θ. We proceed as follows

Since we have the trigonometric equation 2(cos²θ - sin²θ) = 1

We know that cos2θ = cos²θ - sin²θ. so, substituting this into the equation, we have that

2(cos²θ - sin²θ) = 1

2(cos2θ) = 1

cos2θ = 1/2

Taking inverse cosine, we have that

2θ = cos⁻¹(1/2)

2θ = 30°

θ = 30°/2

θ = 15°

So, θ = 15°

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Solution:

Note that:

Using cross multiplication:

Using the division property of equality.

Each day, Cornell ate 11/60 gallons of soup.

The amount of gallons of soup Cornell ate each day was 11/60

When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get.

Thus, if 10 mangoes are there, and 2 people, then 10 ÷ 2 is the number of mangoes each person would get, which is 5.

Division, thus, can be interpreted as equally dividing the number that is being divided in total \(x\) parts, where \(x\) is the number of parts the given number is divided.

Thus, \(a \div b\) = a divided in b equal parts.

Also, we can write: \(a \div b = a \times \dfrac{1}{b}\)

(it is since a = a times 1 so \(a/b = 1 \times (a/b) = (1/b) \times a\))

For the given case, we're given that:

Total amount of soup Cornell ate in 5 days = 11/12 gallons.
Cornell ate equal amount of soup each day.

Due to this equal amount of soup eating, we can use division.

The amount of soup Cornell ate each day = 11/12 divided in  5 equal parts

The amount of soup Cornell ate each day = \(\dfrac{11}{12} \div 5 = \dfrac{11}{12} \times {1}{5} = \dfrac{11}{60}\)

Thus, the amount of gallons of soup Cornell ate each day was 11/60

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Answer:

Step-by-step explanation:

An absolute value is the distance a number is from 0 on the number line. So, regardless if it is a negative or a positive number, the distance from that number to 0 will always be positive. For example, -5 is 5 units away from 0, and 5 is also 5 units from zero. They have the same absolute value, even though one is negative and the other is positive.

Answer:

You can describe absolute value as a number's (Negative or positive) distance from zero.

Step-by-step explanation:

Say you have 4 and -4. 4's absolute value is four because it is four number units away from zero. -4 is a negative number but its absolute value would still be positive four because it is still four number units away from zero even though those number units are negative.

Answer:

7^9

Step-by-step explanation:

when dividing you take away powers.

Answer:

7 to the power of 9

Step-by-step explanation:

7 by it self is 7 to the power of 1, and when you are dividing a power to subtract the power on top, so 10-1=9 and the answer is 7 to the power of 9 or 7^9

Answer:

B is the answer to the problem