1. Expand and simplify the following:

a) (x+3)(x + 5)

b) (x-6) (x + 7)

2. Common factor each of the following.

a) 2x+6

b) 9x² - 12x

3. Factor the following difference of squares.

a) x²-121

b) 4x² - 49

4. Factor each of the following trinomials.

a) x² - 10x + 16

b) x²-5x-24

c) (2x-3)(5x-4)

c) 24x² + 16x-2

c) 144-25x²

c) x² +8x-20

5. Factor the following quadratics using the appropriate factoring method (s).

a) 3x² + 18x+24

b) 99-11x²

c) 6x²-48x-54

Answer:

he can make 9 cups of lemonade and he will have 1/3 of a cup of lemonade left over

Step-by-step explanation:

28÷3=9.3333=28/3=9 1/3

Answer:

9.3 or just 9 glasses of lemonade in total.

Step-by-step explanation:

just divide 28 with 3. but just to round it up i would say 9 glasses of lemonade.

Answer: 6(a) - 6(3)

Step-by-step explanation:

Answer: Its B

Step-by-step explanation:

The expression 6(a-3) can be simplified by applying the distributive property of multiplication over addition, which gives 6a - 18. Therefore, the expression is equivalent to 6a - 18. The answer is (b) –2. All other options do not simplify to the same expression as 6(a-3). For example, 18a is not equivalent to 6(a-3) and neither is 6(a)-6(3). Option (d) 1 simplifies to 6a - 18a + 18, which is not equivalent to the original expression. Similarly, 6(a)-3 simplifies to 6a - 3, which is also not equivalent.

A line of reflection, also known as a line of symmetry, is a line that divides a figure into two congruent parts that are mirror images of each other.

When a figure is reflected across a line of reflection, every point on one side of the line has a corresponding point on the other side of the line that is equidistant from the line.

To determine the line of reflection for the given graph:

- Reflection across the x-axis: The line of reflection is the x-axis.

- Reflection across x = -6: The line of reflection is a vertical line passing through x = -6.

- Reflection across the y-axis: The line of reflection is the y-axis.

- Reflection across y = -6: The line of reflection is a horizontal line passing through y = -6.

Thus, the line of reflection is the perpendicular bisector of every segment joining a point to its image after reflection.

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The first five coefficients are explained.

Given is power series, f(x) = eˣ about x = 4 as [tex]\sum_{\infty}^{n=0}C_n}(x+4)^n[/tex]

f(x) = eˣ

a = 4,

The general form of a Taylor series is:

f(x) = [tex]\sum_{n=0}^{\infty}\frac{f'(a)}{n!} (x-a)^n[/tex]

Note that since the function is a basic exponential function, its derivative is:

f'(x) = eˣ

That is, the function is the same for whatever order of differentiation. So, let us substitute our values here,

f(x) = [tex]\sum_{n=0}^{\infty}\frac{e^4}{n!} (x-4)^n[/tex]

The general expression for the coefficients is: [tex]C_n = \frac{e^4}{n!}[/tex]

The first coefficient is: [tex]C_0 = e^4[/tex]

The second coefficient is: [tex]C_1 = e^4[/tex]

The third coefficient is: [tex]C_2 = 1/2e^4[/tex]

The fourth coefficient is: [tex]C_3 = 1/6e^4[/tex]

And lastly,

[tex]C_4 = 1/24e^4[/tex]

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(a) The range for the graduates is 86760 hours.

(c) The graduates had the greater median number of hours.

(a) The range is the difference between the maximum and minimum values in a set of data. We are given the following data:

Graduates: 9641 hours, 6655432 hours, 93310 hours, and 92501 hours

Non-graduates: 2138 hours, 3 hours, 4 hours, and 13445559 hours

The range for the graduates is 9641 - 92501 = 86760 hours.

The range for the non-graduates is 2138 - 13445559 = 13443421 hours.

(c) To find the median, we need to arrange the data in order from smallest to largest and find the middle value. If there are an even number of data points, we take the average of the two middle values.

Graduates: 9641 hours, 93310 hours, 92501 hours, 6655432 hours

The median is the average of 93310 hours and 92501 hours, which is (93310 + 92501)/2 = 92905.5 hours.

Non-graduates: 2138 hours, 3 hours, 4 hours, 13445559 hours

The median is the average of 3 hours and 4 hours, which is (3 + 4)/2 = 3.5 hours.

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The best interpretation of v(9) = 277 is a cube with side lengths of 9 feet has a volume of 277 cubic feet

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

The volume of a cube depends on the length of its sides.

And this is represented  in function notation as v(s)

The function notation v(s) means

The volume of cube with side length s is v

Using the above as a guide, we have the following:

A cube with side lengths of 9 feet has a volume of 277 cubic feet

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Answer:

19.1

I found it out after I got the ansewer wrong on IXL

Step-by-step explanation:

Draw a rectangle.  If the length is 3 inches longer than its width, we can write the width as "w" and the length as the width + 3

Area is (width)(Length) = (width)(width+3)

    W

 ----------

 |         |

 |         |

 |          |  L = w+3

 |         |

 |          |

 -----------

A = (w+3)(w)

A = w2 + 3w = 108.

(Problem states that area is 108 sq in)

Need to solve this quadratic equation

w2 + 3y - 108 = 0

Factor:

(w - 9) (w + 12) = 0

So

w - 9 = 0.    or.    w + 12 = 0

Solve these and get

w = 9. or. w = -12

Only one that makes sense in real life is the poitive one.

So the dimensions are

Width = 9 inches

Length = 12 inches

hope this helped-nia.

Answer:

Step-by-step explanation:

The area of the shaded region is equal to 12.5π or 39.27 square centimeters.

In Mathematics and Geometry, the area of a semicircle can be calculated by using this formula:

Area of semicircle, As = πr²/2

Where:

r represents the radius of a circle.

Note: Radius = diameter/2 = 20/2 = 10 centimeters.

By substituting the radius into the formula for the area of a semicircle, we have the following;

Area of semicircle = 1/2 × π × 10²

Area of semicircle = 50π square centimeters.

For the circle, we have:

Area of circle, Ac = πr²

Area of circle, Ac = π(10/2)²

Area of circle, Ac = 25π square centimeters.

Now, we can determine the area of the shaded region as follows;

Area of shaded region = (As - Ac)/2

Area of shaded region = (50π - 25π)/2

Area of shaded region = 12.5π or 39.27 square centimeters.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The quadratic equation that has 5i and -5i as solutions is:

x²+ 25 = 0

The quadratic equation is the polynomial having the highest power of 2. If 5i and -5i are the solutions to the quadratic equation, then the quadratic equation can be written as:

(x - 5i)(x + 5i) = 0

Expanding this equation, we get:

x² - (5i)² = 0

x² - 25i² = 0

Since i² = -1, we can substitute -1 for i², giving us:

x² - 25(-1) = 0

x² + 25 = 0

Therefore, the quadratic equation that has 5i and -5i as solutions is:

x²+ 25 = 0

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Answer: B

Step-by-step explanation:

First, you have to know that a straight line is equal to 180 degrees. They gave you 115 degrees in part of a line, so the other part or the angle not given must be equal to 65 degrees. Another thing is that a triangle has 180 degrees. 65+80 degrees is equal to 145 degrees, leaving angle 1 to be equal to 35 degrees. Another thing to know is that reflective angles have the same measurement. If the original angle was equal to 65 after subtraction 115 from 180, we know that the second triangle's angle would also be equal to 65. 65+86 is 150, and 180-150 is 30. Thus, the answer is B.

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Answer:

If I am not mistaken, the answer is:

x1: 4.436

x2: 0.564

Step-by-step explanation:

Answer is

5 + √15    or 4.43649 decimal

  2

and

5 - √15  or .56350 decimal

  2

Step by step

Given 2x^2 -10x +5 = 0

Quadratic formula

-b +- √ b^2 - 4 a c

2a

- -10 +- √ -10^2 (-4)(2)(5)

2(2)

Simplify

10 +- √ 100 - 40

2(2)

10+- √ 60

2(2)

Factor out √60 = 2^2 * 3 * 5

Rewrite after moving 2 outside √

10 +- 2 √15

2(2)

Divide out one of the “2’s” with terms outside the √

5 +- √15

2

Solve

5 + √15

2

5 - √15

2

Answer:

Yeeeaaa, no.

Hope this helps!

Step-by-step explanation:

( x, y )

Plug the numbers of the ordered pair into the equation: y = 6x

3 = 6 × ( 0 )

3 = 0

Three does not equal zero...

3 [tex]\neq[/tex] 0

The total of miles mark ran last week is 10.75 miles.

We have the dot plot.

So, the total number of miles Mark ran

= 1 1/4 x 1 + 2 x 2 + 2 2/4 x 1 + 3 x 1

= 5/4 x 1 + 4 + 10/4 x 1 + 3

= 5/4 + 4 + 10/4 + 3

= 15/4 + 7

= 15/4 + 28/4

= 43/4

= 10 3/4

= 10.75

Thus, the total number of miles Mark ran is 10.75 miles.

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Answer:

Faster cyclist = 37.5km/h

Slower cyclist = 32.5km/h

Step-by-step explanation:

Let's call the rate of the slower cyclist "r" (in km/h). Then the rate of the faster cyclist is "r+5" (in km/h), since they are traveling 5 km/h faster.

We know that the two cyclists are traveling towards each other and will meet in 2 hours. We can use the formula:

distance = rate × time

Let's call the distance each cyclist travels "d". Since they are traveling towards each other, their distances will add up to the total distance between the two towns, which is 130 km. So we can write:

d + d = 130

2d = 130

d = 65

Now we can use the formula again to find the rates of the two cyclists:

For the slower cyclist:

distance = rate × time

65 = r × 2

r = 32.5 km/h

For the faster cyclist:

distance = rate × time

65 = (r+5) × 2

r+5 = 32.5 + 5 = 37.5 km/h

So the rate of the slower cyclist is 32.5 km/h, and the rate of the faster cyclist is 37.5 km/h.

Answer:

Simplifying the expression `n + n - 0.18n`, we get:

n + n - 0.18n = 2n - 0.18n

Therefore, the expression `n + n - 0.18n` is equivalent to `2n - 0.18n`.

Looking at the answer choices:

a. 1.18n

b. 1.82n

c. n- 0.18

d. 2n - 0.82

We can see that choice d is equivalent to the simplified expression `2n - 0.18n`.

Therefore, the answer is d. 2n - 0.82.

Step-by-step explanation:

Answer:c

Step-by-step explanation:

Answer: B 1585

took the test

Answer: A

Step-by-step explanation:

Goes down to the integer 1. B is the only one that makes sense subtracting doesn't work 87654321 goes from the 2 half line.

The value c = -2.07 for a standard normal distribution with P(z < c) = 0.0234.

To find the value of c for which P(z < c) = 0.0234 for a standard normal distribution, we can use a standard normal distribution table or a calculator with a built-in normal distribution function.

Using a standard normal distribution table, we can look up the area to the left of c and find the corresponding z-score. This z-score will be the value of c for which P(z < c) = 0.0234.

Looking up the area 0.0234 in the table, we find that the corresponding z-score is approximately -2.07.

Therefore, c = -2.07 for a standard normal distribution with P(z < c) = 0.0234.

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Note the the missing step is: " Total the columns." (Option B) so the completed step with regard to the segmented bar graph is given below.

A segmented bar chart uses vertical or horizontal bars to compare two or more categories. Typically, the stacked bars represent each group's percentage of the whole and are plotted by the proportion of each value inside each group.

This style of chart can be beneficial for comparing total amounts across each split bar or group. It may be an effective method of forecasting a company's profit over a period of months, with the earnings separated into distinct product lines.

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By using the substitution method, the value for (x,y) = (-2, 2)

The substitution method for solving a system of algebra equations is a process where by we make a variable (say variable x) the subject of the formula and substitute it into the second equation to solve for the other variable.

In essence, from the given system of equations; let's make x the subject of the formula in the first equation.

5x + 3y = -4

5x = -4 - 3y

Divide both sides by 5;

x = -4/5 - 3y/5

Now, we are going to substitute this value for x into the second equation. The second equation says:

y - 2x = 6

y - 2(-4/5 - (3y/5)) = 6

By solving for y;

y = 2

Now, let's replace the value of y with any of the given equation (2);

y - 2x = 6

2 - 2x = 6

-2x = 6 - 2

-2x = 4

Divide both sides by -2

-2x/-2 = 4/ -2

x = -2

Therefore, we can conclude that by using the substitution method, the value for (x,y) = (-2, 2)

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The limit exists and is equal to 6.

The limit exists and is equal to 4.

Now, let's use this concept to evaluate the limits of the given function F(x). Looking at the graph of F(x), we see that it approaches different values as x approaches different points. We will evaluate each limit separately:

lim F(x) as x → 1

As x approaches 1 from the left side, the function appears to be approaching a value of 2. Similarly, as x approaches 1 from the right side, the function appears to be approaching a value of 4. However, the limit does not exist as the function is not approaching a single value as x approaches 1.

lim F(x) as x → 3

As x approaches 3, the function appears to be approaching a value of 4.

lim F(x) as x → ∞

As x approaches infinity, the function appears to be approaching a value of 6.

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Answer:

  B.  28%

Step-by-step explanation:

You want to know the percent of the mixture that is fruit juice, if the mixture is 6 L of 52% juice and 9 L of 12% juice.

The total amount of juice in the 6+9 = 15 L of mix is ...

  0.52·(6 L) +0.12(9 L) = 3.12 L +1.08 L = 4.2 L

Then the fraction of the mix that is fruit juice is ...

  (4.2 L)/(15 L) = 0.28 = 28%

The percent of the mixture that is fruit juice is 28%, choice B.

__

Additional comment

Effectively, the fraction is the weighted average of the fractions of the constituents. The weights are the number of liters of each constituent.

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Answer:

0.90

Step-by-step explanation:

Just like a decimal to a percentage number, you must multiply by 100. By converting a percentage number to a decimal point, you must divide it by 100. Which means, the decimal must move 2 times.

For example,

0.90 x 100 = 90%

This is decimal to percentage number, but in this case it is percentage to decimal.

90%.

Since the number ended at 0, put the decimal there and move it 2 times to get to your decimal point.

.90 = 0.90

There you'll get your answer! ^^

90% = 0.90

He covered a distance of 5 miles for 5 days of the total days of training. The total distance he covered = 6 miles.

The total number of days Anthony used for training = 8 days.

The number of days he covered 1/4 mile = 2days

The number of days he covered 1/2 mile = 1 day

The number of days he covered 1 mile = 5 days.

Therefore that total distance that he used for the training = 2(1/4)+1(1/2)+5(1)

= 0.5+0.5+5

= 6 miles.

The number of days he covered the highest distance would be for 5 days.

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The number of hours Penn volunteer in one week is 8hours

A word problem in math is a math question written as one sentence or more. This statements are interpreted into mathematical equation or expression.

Representing the number of hours volunteered in a week by Penn by x

therefore for 12 weeks , the number of hour will be;

12×x = 12x

12x = 96

divide both sides by 12

x = 96/12 = 8 hours

therefore the number of hour volunteered by Penn in a week is 8 hours

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Emma has $5,000 total invested.

Let's call the total amount Emma has invested "x".

Emma has half of her investments in stock paying a 10% dividend, so that portion of her investment earns 0.10(x/2) = 0.05x in annual interest.

The other half of her investments are in a stock paying 14% interest, so that portion of her investment earns 0.14(x/2) = 0.07x in annual interest.

The total annual interest Emma earns is $600, so we can set up the following equation:

0.05x + 0.07x = 600

0.12x = 600

x = 5000

Therefore, Emma has a total of $5000 invested.

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Comparing the equations of the two lines, we can see that they have the same slope (3/2). Therefore, the lines are parallel.

To determine whether these two lines are parallel or perpendicular, we can convert Line 2 into slope-intercept form (y = mx + b):

2y = 3x + 5

y = (3/2)x + 5/2

Comparing this equation to the equation of Line 1 (y = x + 7), we see that the slopes (coefficients of x) of the two lines are not equal, nor are they negative reciprocals of each other. Therefore, the lines are neither parallel nor perpendicular.

Line 1 and Line 3:

To determine whether these two lines are parallel or perpendicular, we can convert Line 3 into slope-intercept form (y = mx + b):

6x - 4y = 4

-4y = -6x + 4

y = (3/2)x - 1

Comparing this equation to the equation of Line 1 (y = x + 7), we see that the slopes of the two lines are not equal, nor are they negative reciprocals of each other. Therefore, the lines are neither parallel nor perpendicular.

Line 2 and Line 3:

To determine whether these two lines are parallel or perpendicular, we can convert Line 2 into slope-intercept form (y = mx + b):

2y = 3x + 5

y = (3/2)x + 5/2

Next, we can rearrange Line 3 into the slope-intercept form:

6x - 4y = 4

-4y = -6x + 4

y = (3/2)x - 1

Comparing the equations of the two lines, we can see that they have the same slope (3/2). Therefore, the lines are parallel.

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