An arithmetic sequence begins with 72, 64, 56, 48, 40 …

Which option below represents the formula for the sequence?

f(n) = 72 + 8(n − 1)
f(n) = 72 − 8(n − 1)
f(n) = 64 + 8(n − 1)
f(n) = 64 − 8(n)

Answer:

113.04 cm

Step-by-step explanation:

We know the formula to find the area of a circle is

\(A= pi(r^{2})\)

And we are told to use 3.14 instead of pi so what we have now is,

\(A=3.14(r^{2})\)

We are also told the radius, r, is 6. So our equation now looks like this,

\(A=3.14(6^{2})\\\\6^{2}\)is the same as 36, because 6x6 is 36.

Now we have,

\(A=3.14(36)\)  

Which equals 113.04 and that is the area!

Hope that helps and have a great day!

Answer:

slope is 7 and point on line is (1, 4 )

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

given line A has equation in point- slope form of

y - 4 = 7(x - 1) , then

slope of line is 7 and a point on the line is (1, 4 )

Answer:

x=15

Step-by-step explanation:

Answer:

integer

Step-by-step explanation:

Answer:

The family traveled at 45 miles per hour.

Step-by-step explanation:

The equation for the line in point-(1, 1) is y = -0.5x + 0.5.

Given that the slope of the line below is -0.5. We are to enter the equation for the line in point-(1, 1).The equation for the slope-intercept form of the line is y = mx + c where m is the slope and c is the y-intercept.

Now, the slope of the line is given as -0.5.Therefore, the equation for the slope-intercept form of the line is y = -0.5x + c. Now we need to find the value of c for the equation of the line.

To find the value of c, substitute the values of x and y in the equation of the slope-intercept form of the line.

Given that the point is (-1,1), x=-1 and y=1y = -0.5x + c⇒ 1 = (-0.5) (-1) + c⇒ 1 = 0.5 + c⇒ c = 1 - 0.5⇒ c = 0.5

Therefore, the equation for the line in point-(1, 1) is y = -0.5x + 0.5.The slope of a line refers to how steep the line is and is used to describe its direction. Slope is defined as the vertical change between two points divided by the horizontal change between them.A positive slope moves up and to the right, while a negative slope moves down and to the right. If a line has a slope of zero, it is said to be a horizontal line.

The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept, or the point at which the line crosses the y-axis. To find the equation of a line with a given slope and a point, we can use the point-slope form of a linear equation.

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Answer:

good evening good evening good evening good evening

The pounds of the Earl Grey tea and Orange Pekoe tea are required from selling the new blend versus selling the other types is 225 pounds and 75 pounds.

Let x = amount of Earl Grey tea to mix

so, 300-x = amount of Orange Pekoe tea to mix

After putting the equations together,

6x+4(300-x)=5.5*300

6x+1200-4x=1650

2x=450

x=225

So amount of Earl Grey tea to mix is 225 pounds

amount of Orange Pekoe tea to mix = 300-x

300-225 = 75

So the amount of Orange Pekoe tea to mix is 75 pounds.

Amount of Earl Grey tea to mix=225 pounds

Amount of Orange Pekoe tea to mix=75 pounds

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Answer:

Skewed right center around varies from 12 to 30. Possible outliers 12, 14, 15, 16.

The distribution of quiz scores is skewed right with a center around 24 and varies from 12 to 30. There are possible outliers at 12, 14, 15, and 16.

The dot plot is skewed to the right because majority of the data occur to the right of the dot plot.

An outlier is a number that is way smaller or way larger than that of other numbers in a data set. Outliers usually occur with a frequency of one. Looking at the dot plot, it can be seen that the numbers that range from 12 to 16 have only one dot.

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Answer:

2.5x100÷340000=

5x340000/1000

The maximum amount you can earn is $540

a. y = 13.50x , 10 <= x <= 40
b. x = 10, y = 135; x = 20, y= 270; x = 30, y = 405; x = 40, y = 540
c. Domain: 10 <= x <= 40; Range: 0 <= y <= 540
d. The minimum amount you can earn in a week with this job is $135. The maximum amount you can earn is $540.

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By permutation, in 95040  ways we can choose a starting lineup consisting of a center, a power forward, a shooting forward, a point guard, and a shooting guard

A permutation is a set up of things in a certain sequence. Here, the members of sets or their constituent parts are sorted in a linear or sequential manner.

Take the number of possibilities for each event and multiply it by itself X times, where X is the total number of events in the sequence, to find the number of permutations. For instance, four-character PINs have a total of 10 possible combinations because each digit can vary from 0 to 9.

\(12^P_{5} = \frac{12!}{(12-5)!} =\frac{12!}{5!} = 12 X 11 X 10 X 9 X 8 = 95040\)

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The Total surface of triangular prism  is 112 inches.

To calculate the surface area of a triangular prism, you need the measurements of the base and the height of the triangular faces, as well as the length of the prism.

The given measurements are;

Base ; 5 inches and  4 inches

height is 8 inches

Length of the prism is 2 inches.

To find the total surface area, we sum up the areas of all the faces:

Total surface area = area of triangular  faces + area of rectangular faces + area of lateral faces.

area of triangular faces = 5 inches × 4 inches = 20 inches.

area of the two faces = 20 ×2 =40

Area rectangular faces = 5 inches × 8 inches/ 2 = 40 inches.

Area of lateral faces = 8 inches ×2 = 16 square inches

for the two lateral faces is 16 × 2 = 32 square inches.

Total surface area = 40 square inches + 40 inches + 32 square inches = 112 square inches.

The Total surface of triangular prism  is 112 inches.

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Answer:

Jen has X cats.

Sister has 3x-2 cats.

3x-2 = 4

X = 2

Step-by-step explanation:

Answer:

what grade is this?

Answer:

14.82

Step-by-step explanation:

what is the coordinate of the vertex for the following parabola:

-8 ( x - 5 ) = ( y + 1 ) ² (5, -1)

what is the coordinate of the focus for the following parabola:

-8 ( x - 5 ) = ( y + 1 ) ² (3, -1)

The vertex of the equation of a parabola \(- 8 (x - 5) = (y + 1)^2\) by compared with the standard form of the equation of a parabola \(x = a (y - k)^2 + h\) is,

⇒ (h, k) = (5, - 1)

Where, \((h, k)\) is the vertex of the parabola.

We have to give that,

The equation of a parabola is,

\(- 8 (x - 5) = (y + 1)^2\)

The standard form of the equation of a parabola is,

\(x = a (y - k)^2 + h\)

Where, \((h, k)\) is the vertex of the parabola.

Here, The equation of a parabola is,

\(- 8 (x - 5) = (y + 1)^2\)

It can be written as,

\((x - 5) = \frac{(y + 1)^2}{-8}\)

Add 5 on both sides,

\(x = \frac{(y + 1)^2}{-8} + 5\)

Now, compare with the standard form of the equation of a parabola,

h = 5

k = - 1

Therefore, the vertex of the parabola is, (5, - 1).

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Answer:

The area of the shaded region is, \(24mm^{2}\)

Step-by-step explanation:

First we have to calculate the area of ΔABC and ΔXYZ.

Area of ΔABC = \(\frac{1}2}\)×\(Base\)×\(Height\)

Area of ΔABC = \(\frac{1}{2}\)×\(5mm\)×\(12mm\)

Area of ΔABC =\(30mm^{2}\)

and,

Area of ΔXYZ = \(\frac{1}{2}\)×\(Base\)×\(Height\)

Area of ΔXYZ = \(\frac{1}{2} X3mmX4mm\)

Area of ΔXYZ = \(6mm^{2}\)

Now we have to calculate the area of the shaded region.

Area of the shaded region = Area of ΔABC - Area of ΔXYZ

Area of the shaded region = \(30mm^{2} - 6mm^{2}\)

Area of the shaded region = \(24mm^{2}\)

Therefore, the area of the shaded region is, \(24mm^{2}\)

11.5 and 15 are the values that are part of the solution set of the inequality.

Inequality is defined as relationship between non-equal numbers or expressions. The solution of an inequality is the set of values that satisfies the given inequality.

To determine the solution set of the given inequality, isolate the variable to one side and simplify.

-4x + 24 < -2x + 2

-4x + 2x < -24 + 2

-2x < -22

22 < 2x

11 < x

Hence, the solution set of the given inequality is the set of numbers greater than 11. Among the given choices, 11.5 and 15 are both greater than 11.

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A right trapezoid is a quadrilateral that has exactly one pair of perpendicular lines, one pair of parallel sides, and no sides with equal lengths.

A quadrilateral is a polygon that has four sides and four angles. Types of quadrilaterals are trapezium, square, rectangle and so on.

A right trapezoid is a quadrilateral that has exactly one pair of perpendicular lines, one pair of parallel sides, and no sides with equal lengths.

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Answer:

Step-by-step explanation:

You basicly want to use A=pe^rt to find the amount of money you now have. A is the total amount of money you have after a certian period of time (T) while your money grows at a steady rate (R). (E) is an irrational number 2.71828. (P) is the amount of money you started with. Your precentage is your rate and this means you earn 9% of what you have per year. The way the problem would be set up A=1500(2.71828)^(.09)(2). This problem allows for exponential growth to occur because your two variables are time and the amount you have in that time.

1.

\( 2x {}^{2} + 17x + 35 \\ = 2x {}^{2} + 10x + 7x + 35 \\ = 2x(x + 5) + 7(x + 5) \\ = (2x + 7)(x + 5)\)

2.

\(2y {}^{2} - 5y - 3 \\ = 2y {}^{2} -6y + y - 3 \\ = 2y(y - 3) + 1(y - 3) \\ = (2y + 1)(y - 3)\)

3.

\(3x {}^{2} - 8x + 4 \\ = 3x {}^{2} - 6x - 2x + 4 \\ = 3x(x - 2)( - 2)(x - 2) \\ = (3x - 2)(x - 2)\)

Answer:

n is greater than - 6.

Step-by-step explanation:

4+n>-2

subtract 4 on both sides

4-4+n>-2-4

n>-6

n is greater than - 6

The coffee distributor should mix 56 pounds of Mexican Shade Grown coffee blend and 34 pounds of Terraza coffee blend to create a 90-pound coffee blend that can sell for $10.99 per pound.

Let's assume x represents the number of pounds of Mexican Shade Grown coffee blend that need to be mixed, and y represents the number of pounds of Terraza coffee blend.

From the given information, we can set up the following equations:

1) The total weight of the coffee blend: x + y = 90

2) The total cost of the coffee blend: (9.10x) + (14.10y) = 10.99 * 90

Simplifying equation 2:

9.10x + 14.10y = 989.10

Now, we can solve this system of equations to find the values of x and y.

Multiplying equation 1 by 9.10 to eliminate decimals, we get:

9.10x + 9.10y = 819

Subtracting this equation from equation 2:

(9.10x + 14.10y) - (9.10x + 9.10y) = 989.10 - 819

Simplifying:

14.10y - 9.10y = 170.10

5y = 170.10

y = 170.10 / 5

y = 34

Now, substitute the value of y into equation 1 to solve for x:

x + 34 = 90

x = 90 - 34

x = 56

Therefore, the coffee distributor should mix 56 pounds of Mexican Shade Grown coffee blend and 34 pounds of Terraza coffee blend to create a 90-pound coffee blend that can sell for $10.99 per pound.

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Answer: (3x^3)^3 = 3^3 (x^3)^3 = 27 (x^3)^3 = 27^3x3 = 27^9

27^9

Answer:

27x^9

Step-by-step explanation:

Distribute.

3^3 (x^3)^3

27 (x^3)^3

Power of a power.

27x^3 times 3

Multiply.

27x^9

Answer:

X=6

Step-by-step explanation:

1. 6(2x-10)+22=3x+16

2. 12x-60+22=3x+16

Is that the answer you are looking for

Answer:

-3

Step-by-step explanation:

it is the only one without a variable