When written in standard form, the product
of (3 + x) and (2x - 5) is
3x - 2
2x² + x - 15
2x² - 11x - 15
6x - 15 + 2x² - 5x

Let's denote the three numbers A, B, and C.

Given that the highest common factor (HCF) of these three numbers is 8 and their sum is 80, we can consider possible combinations of numbers that satisfy these conditions.

Since the HCF is 8, all three numbers must be divisible by 8. Additionally, the sum of the numbers is 80, so we need to find combinations of three numbers that satisfy both conditions.

Let's list the possible combinations:

These are the four possible sets of three numbers that satisfy the given conditions: (8, 16, 56), (16, 8, 56), (24, 8, 48), and (8, 24, 48).

Answer:

Step-by-step explanation:

The data in the table shows quantity increase with the price increase and we want to analyze the relationship between price and quantity.

The data indicates a positive slope if we keep price on x-axis and quantity on y- axis.

Option C is reflecting this and correctly highlighted.

Answer:

Option C

Step-by-step explanation:

Because as we can see y is increasing with respect to x

So the slope is positive

The line should go up rightwards

Hence option C is correct

Answer:

Step-by-step explanation:

The correct equation that shows a step in the process of completing the square on the given quadratic y = x^2 + 8x – 3 is y = x^2 + 8x + 16 – 3 – 16. Completing the square involves adding and subtracting a constant term in order to create a perfect square trinomial. In this case, the constant term added is (8/2)^2 = 16, which is half the coefficient of the x-term squared. This step transforms the quadratic into the form (x + a)^2 + b, where a represents half of the x-term coefficient and b represents the constant term.

By adding 16 to the equation to create a perfect square trinomial, we need to subtract 16 afterward to maintain the equation’s balance. Thus, the equation becomes:

y = x^2 + 8x + 16 - 3 - 16

Simplifying further:

y = (x + 4)^2 - 19

Therefore, the correct equation is:

y = (x + 4)^2 - 19

Answer:

the number of adult ticket sold is 570

Explanation:

Let x represent the number of adult ticket and y represent the number of child's ticket.

Given that he charges $5 for an adult's ticket and $2 for a child's ticket.

For one event, he sold 785 tickets.

So, we have;

he sold 785 tickets for $3280.

Then;

let us solve by substitution.

make y the subject of formula in equation 1 and substitute to equation 2;

substituting to equation 2;

Therefore, since x represent the number of adult tickets sold, then the number of adult ticket sold is 570

1.

Since you earn 1.25 points every 1-8 minutes, it would take you 4000 (1-8 minutes) in order for you to get 5000 points.

I'll be looking for the range, so we'll find how long it would take for one minute, then eight minutes.

4000 x 1 = 4000 minutes (2 days, 18 hours and 40 minutes)

4000 x 8 = 32000 minutes (22 days, 5 hours and 20 minutes)

It will take anywhere from 2 days, 18 hours and 40 minutes to 22 days, 5 hours and 20 minutes.

2.

Since you earn 3 points every 1-8 minutes, it would take you 1666.666... (1-8 minutes), which would be 1667 since you don't earn points every third of a second, it's only every second, in order for you to get 5000 points.

Same thing, we'll find it for one minute and then eight minutes.

1667 x 1 = 1667 minutes (1 day, 3 hours and 47 minutes)

1667 x 8 = 13336 minutes (9 days, 6 hours and 16 minutes)

It will take you anywhere from 1 day, 3 hours and 47 minutes to 9 days, 6 hours and 16 minutes.

The present value (PV) of the investment today is approximately $2,965.05.

To find the present value (PV) of the investment today, we need to calculate the present value of each individual contribution and then sum them up. We can use the formula for the present value of an annuity to do this calculation.

The formula for the present value of an annuity is given by:

PV = C * [(1 - (1 + r)^(-n)) / r]

Where:

PV = Present Value

C = Cash flow per period

r = Interest rate per period

n = Number of periods

In this case, the cash flow per period (C) is $500, the interest rate per period (r) is 10.5% (or 0.105), and the number of periods (n) is 20 years.

Let's plug in these values into the formula and calculate the present value (PV):

PV = $500 * [(1 - (1 + 0.105)^(-20)) / 0.105]

Using a calculator, we can evaluate the expression inside the brackets:

PV = $500 * [(1 - 0.376889) / 0.105]

Simplifying further:

PV = $500 * [0.623111 / 0.105]

PV = $500 * 5.930105

PV = $2,965.05

Therefore, the present value (PV) of the investment today is approximately $2,965.05.

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The vocabulary for a is called the apothem

The area of the regular polygon is \(2419.68 cm^2.\)

a = 7√3 cm

s = 14 cm

The perimeter of the polygon is:

P = ns

where n is the number of sides of the polygon. We can find n using the formula:

\(n = 360 / (180 - (360 / 2n))\)

where n is the number of sides. Substituting the given value for s, we get:

\(n = 360 / (180 - (360 / 2*7)) = 14\)

Therefore, the polygon has 14 sides.

a = \(\sqrt{31.820 cm)^2 - (14 cm/2)^2}\))

= 24.615 cm

A = (1/2) * apothem * perimeter

\((\frac{1}{2} ) * 24.615 cm * 196 cm \\=\\ 2419.68 cm^2\)

Therefore, the area of the regular polygon is \(2419.68 cm^2.\)\(2419.68 cm^2.\)

In summary,

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hello

if i'm right, what you're trying to ask is

Answer:

4/3

Step-by-step explanation:

To find the slope you use the equation y2 - y1 / x2 - x1. This means you take the y variable from your 1st point and subtract it from the y variable from the 2 one. ex: 1 - (-3) = 4 And then put it over the x variable from the first one subtracted from the x variable of the second one ex: 5 - 2 = 3 -> 4/3. If possible, simplify, but if it's like this one you don't have to.

Answer:

The mass of wood is 4309.65 kg.

Step-by-step explanation:

Volume of a cylinder is:

\(V = \pi r^{2} h\)

Where \(r\) is the radius of base of cylinder

and \(h\) is the height of the cylinder

\(r=\dfrac{d}{2}\)

\(d\) is the diameter of base of cylinder.

A tree's trunk is in the shape of cylinder only. And we are given the following details:

\(d = 0.5m\\\Rightarrow r = \dfrac{0.5}{2} m\)

\(h =36 m\)

\(V = \pi (\dfrac{0.5}{2})^2 \times 36\\\Rightarrow V = 7.065\ m^3\)

Density of wood of tree = 610 kg per cubic meter

Mass of trunk = Volume \(\times\) density

\(\Rightarrow 610 \times 7.065\\\Rightarrow 4309.65\ kg\)

Hence, mass of trunk is 4309.65 kg.

The probability that either event A or B will occur is 43/60

Using the parameters given

n(A) = 29

n(B) = 14

Total number of events = 29+17+14 = 60

The probability of each event :

P(A) = 29/60

P(B) = 14/60

P(A or B ) = P(A) + P(B)

P(A or B ) = 29/60 + 14/60

P(A or B ) = 43/60

Therefore, the probability of A or B is 43/60

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It should be noted that the expression that can be used to identify the x-values for which f(x)>-2 will be -2 <= x <= 2. This is illustrated in the graph.

It should be noted that a graph is a diagram that is used to show the relationship that exists between the data presented or the information.

In this case, ut should be noted that the expression that can be used to identify the x-values for which f(x)>-2 will be -2 <= x <= 2. This is illustrated in the graph.

The graph is attached below.

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The answer is:

Work/explanation:

Bear in mind that the sum of all the angles in a triangle is 180°.

Given two angles, we can easily find the third one.

Let's call it x.

Next, we set up an equation:

\(\sf{54+87+x=180}\)

\(\sf{141+x=180}\)

Subtract 141 on each side.

\(\sf{x=180-141}\)

\(\sf{x=39}\)

Answer:

454%

Step-by-step explanation:

i think this is corrrect hope it helps

Answer:

The answer should be 454%

Step-by-step explanation:

Lmk if this helped

Answer:

Unreduced: (4) + (5 • x) + (-9) + (4 • x)

Reduced: 9x – 5

Answer: $40,000 - $45,000

Step-by-step explanation:

Given the histogram above :

The median salary is located in the 50th percentile on the graph. Hence, locating the 50% mark on the vertical y axis named cumulative frequency, the corresponding value on the x_axis gives the median value.

Hence, for the problem above. The 50% cumulative frequency mark corresponds to 40 - 45bar on the x axis

Hence, the median salary = $40,000 - $45,000

Answer:

A.)$40,000–$45,000

Step-by-step explanation:

Got it right on edge

Answer:

12.

Step-by-step explanation:

if to re-write the given condition, then

\(\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;\)

it is clear, the required constant is 12 (12 per hour).

The numerical value of x in angle ABD is 9 as angle ABC is divided into two equal halves.

An angle bisector divided an angle into two equal halves.

From the diagram:

Line BD divides angle ABC into two equal halves.

Angle ABD = ( 3x - 7 ) degrees

Angle DBC = 20 degrees

Since angle ABD and DBC are equal haves;

Angle ABD = Angle DBC

Plug in the values:

( 3x - 7 ) = 20

Solve for x:

3x - 7 = 20

Add 7 to both sides:

3x - 7 + 7 = 20 + 7

3x = 27

x = 27/3

x = 9

Therefore, the value of x is 9.

Option A)9 is the correct answer.

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Answer: 168

Step-by-step explanation:

First, let's count the types of selection:

We can select:

Type of car: a compact car, a midsize, a sport utility vehicle, and a light truck (4 options)

Pack: standard, custom, or sport styling, (3 options)

type of transmission: Manual or automatic (2 options)

Color: (7 options)

The total number of combinations is equal to the product of the number of options in each selection:

C = 4*3*2*7 = 168

Answer:

3

Step-by-step explanation:

You have to equate them so...

5v+2=8v-7

I hope this helps you!

The area of the shaded part is 704mm²

The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles.

The area of the shaded part = area of the whole shape - area of the unshaded part

Area of the whole shape = l×w

= 54 × 16

= 864mm²

Area(1) of the unshaded part = 1/2bh

= 1/2 ×16×8

= 64mm²

Area( 2) of the unshaded part = 1/2bh

= 1/2 ×8 × 8

= 32mm²

Area(3) of the unshaded part = l×w

= 8×8 = 64mm²

therefore the total area of the unshaded part =

64+32+64 = 160mm²

therefore the area of the shaded part = 864-160 =

704mm²

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The variance of Billy's grades obtained from his test scores is 15.76

The variance is a measure of variability or spread a dataset. The variance can be calculated from the sum of the square of the differences of the data points from the mean divided by the number or count of the data points.

The variance of Billy's test scores can be calculated by finding the mean or the average of the scores, then finding the sum of the squares of the differences of each score from the mean as follows;

The mean score = (89 + 88 + 93 + 90 + 81)/5 = 88.2

The square of the differences of the values from the mean can be calculated as follows;

(89 - 88.2)² = 0.64, (88 - 88.2)² = 0.04, (93 - 88.2)² = 23.04, (90 - 88.2)² = 3.24, and (81 - 88.2)² = 51.84

The sum of the square of the differences is therefore;

0.64 + 0.04 + 23.04 + 3.24 + 51.84 = 78.8

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The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.

To determine the sequence of transformations, let's break down the given function:

1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.

2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.

3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.

4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.

5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.

In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.

Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.

After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)

This example helps illustrate the effect of the transformations on the graph of the function.

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Answer:

3 flowerbeds and 5 lawns.

Step-by-step explanation:

I promise.

we have that

If the distance varies directly as the square of the time

then the equation is equal to

where k is the constant of proportionality

step 1

Find the value of k

we have

d=280 ft and t=5 sec

substitute

280=k(5^2)

k=280/25

k=11.2

The equation is equal to

d=11.2t^2

step 2

Find the value of d when the value of t is 6 sec

substitute the given value in the equation

d=11.2(6^2)

d=403.2 ft

Round to the nearest integer

d=403 ft

(2x+4y=16).....1

(2x-4y=0).....2

then take equation 1 plus 2

4x=16

x=4

then take equation 2 to solve for y

2x-4y=0

(2×4)-4y=0

y=2

therefore answer is D. (4,2)

The result of the unknown variable x is equivalent to 7

Linear equations are equation that has a leading degree of 1. Given the expression below:

5(3x − 15) + 16 = 5x + 11

Expand the expression

5(3x) - 5(15) + 16 = 5x + 11

15x - 75 + 16 = 5x + 11

15x - 5x - 59 - 11 = 0

10x - 70 = 0

10x = 70

Divide both sides by 10

10x/10 = 70/10

x = 7

Hence the value of x makes the equation true is 7

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The limit of [f(x) - f(2)]/[x - 2] as x approaches 2 is 20

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

f(x) = 5(x2 – 1)

Rewrite as

f(x) = 5(x² – 1)

The limit is given as

[f(x) - f(2)]/[x - 2]

Calculate f(2)

So, we have

f(2) = 5(2² – 1)

Evaluate

f(2) = 15

Substitute f(2) = 15 in [f(x) - f(2)]/[x - 2]

So, we have

[f(x) - f(2)]/[x - 2] = [5(x² – 1) - 15]/[x - 2]

Open the brackets

[f(x) - f(2)]/[x - 2] = [5x² – 5 - 15]/[x - 2]

Evaluate the like terms

[f(x) - f(2)]/[x - 2] = [5x² – 20]/[x - 2]

Factorize

[f(x) - f(2)]/[x - 2] = [5(x² – 4)]/[x - 2]

Express as difference of two squares

[f(x) - f(2)]/[x - 2] = [5(x – 2)(x + 2)]/[x - 2]

Divide

[f(x) - f(2)]/[x - 2] = 5(x + 2)

Limit x to 2

[f(x) - f(2)]/[x - 2] = 5(2 + 2)

Evaluate

[f(x) - f(2)]/[x - 2] = 20

Hence, the limit is 20

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