1 The trinomial x? - X-6 can be factored as the product of 2 linear factors, in the form (x + a)(x + b). What is the polynomial sum of these 2 factors? A, 2x - 1 B. 2x + 1 C. 2x - 5 D. 2 x + S E. 2.x = 6 geo

Sally's average annual percentage gain is approximately 5.26%.

To calculate Sally's average annual percentage gain, we can use the formula:

Average Annual Percentage Gain = (Profit / Initial Investment) * (1 / Time) * 100

Profit = $2500

Initial Investment = $19000

Time = 2.5 years

Substituting the values into the formula:

Average Annual Percentage Gain = (2500 / 19000) * (1 / 2.5) * 100

= (0.1316) * (0.4) * 100

= 5.26

Therefore, Sally's average annual percentage gain is approximately 5.26%.

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Answer:

D) 22

Step-by-step explanation:

y-1= -7(x-3)

y= -7x+21+1

x=0 ⇒ y-intercept is equal to:

So y -intercept is 22, option D

Answer:

22

Step-by-step explanation:

y-1 = -7(x-3)

This is point slope form

Distribute

y-1 = -7x +21

Add 1 to each side

y-1+1 = -7x+21+1

y = -7x+22

This is slope intercept form where y = mx+b and b is the y intercept

22 is the y intercept

Answer:

Could you show me the expression?

Step-by-step explanation:

Answer:

f(1) = 1

Step-by-step explanation:

To go 1 on the x-axis and check to see where it is on the y-axis. In this case, when x = 1, y = 1.

Therefore, f(1) = 1.

Answer: 7x + 1

Step-by-step explanation:

(6x-4)+(x+5)

Step 1: Remove Parentheses:

              6x-4+x+5

Step 2: Combine Like Terms:

             7x +1

Answer:

only god knows

Step-by-step explanation:

because they didn't give us an answer on how many text messages anyone sent

Answer:

Step-by-step explanation:

x + x + 90 = 180

2x + 90 = 180

2x = 90

x = 45

There can 120 ways 5 friends can stand in a line.

What is Permutation?

Permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters.

How to determine this

How many different ways of 5 friends

i.e  5! = 5 * 4 * 3 * 2 *1

= 120 ways

Therefore, the numbers of ways for 5 friends is 120 ways

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Answer:

(1.5, 0.5)

Step-by-step explanation:

(5, 3) and (-2, -2)

5 - 2 / 2 = 1.5

-2 + 3 / 2 = 0.5

The linear equation written in the slope-intercept form is:

y = (-3/5)*x

The correct option is C.

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Here we can see that the line crosses through the poin (0, 0), so the y-intercept is 0.

b = 0

y = a*x + 0

y = a*x

To find the value of a, we can use another point on the graph.

We can see that the linear equation passes through (5, - 3), replacing these values:

-3 = a*5

-3/5 = a

Then the linear equation is just:

y = (-3/5)*x

The correct option is C.

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Answer: \(4\pi r^{2}\)

Step-by-step explanation:

Area of a circle is pi r squared

Given statement solution is :- The present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

To calculate the present value of an investment with compound interest, we can use the formula for the present value of an annuity:

PV = A *\((1 - (1 + r)^(-n)) / r\)

Where:

PV = Present value

A = Annual payment or cash flow

r = Interest rate per period

n = Number of periods

In this case, the annual payment (A) is R13,000, the interest rate (r) is 10% per year, and the investment is made for 8 years (n).

Using the formula and substituting the given values, we can calculate the present value:

PV = \(13000 * (1 - (1 + 0.10)^(-8)) / 0.10\)

Calculating this expression:

PV = \(13000 * (1 - 1.10^(-8)) / 0.10\)

= 13000 * (1 - 0.46318) / 0.10

= 13000 * 0.53682 / 0.10

= 6977.66 / 0.10

= 69776.6

Therefore, the present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

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Answer:

13.75 m/sec

Step-by-step explanation:

Since the 'per second' part stays the same, simply multiply 22 kilometers by the reciprocal of 1.6:

\(22(\frac{1}{1.6})\)

then simplify the fraction:

\(= 22(\frac{10}{16})\)

\(= 22(\frac{5}{8})\)

and solve to get

\(= 13 \frac{3}{4}\) miles per second as the answer.

or optionally:

13.75 m/sec

Answer:

a) -2+6

b) -2 + (-6)

Step-by-step explanation:

do like previous man

Answer:

-2+6

Step-by-step explanation:

Answer:

b or a

Step-by-step explanation:

a) Probability of occurrence of evant A is equals to the 7/10.

P(not getting a white or a blue shirt), P(Aᶜ ) is equals the 3/10.

Probability of occurrence of evant B is equal to the 1/2.

b) The events A and B are not mutually exclusive

c) Mike's preference is to getting a white shirt with his size L.

We have a probabality based problem. Probability is defined as chance of occurrence of an event or result. It can be calculate as favourable outcomes divided by total possible outcomes. There is total number of avaliabile shirts = 20 i.e., total possible outcomes = 20

Mike is interested in getting a white or a blue shirt in size L. Let us consider two events :

A : Getting a white or a blue shirt

B: Getting a shirt in size L

a) Number of favourable outcomes to getting white or a blue shirt = 9 white or 5 blues

Probability ( Getting a white or a blue shirt) , P(A)

= 9/20 + 5/20 + 0 = 14/20 = 7/10

P(not Getting a white or a blue shirt), P(Aᶜ )

= 1 - P(A) = 1 - 7/10 = 3/10

ii) The number of favourable outcomes for event B, n(B) = 10

So, Probability of getting a shirt in size L, P(B)

= 10/20 = 1/2

b) Mutually exclusive events are defined as the events that can't happen at the same time. In other words AnB = 0 . Here, we see there is total 14 shirts which are in white or blue colors and 10 are in size L , So there is possibility that shirt is white or blue in colour and in size L , i.e, An B ≠0

So, events A and B are not mutually exclusive.

c) Event ,n( A u B )= n(A) + n(B) - n(A n B)

On the basis of all details, we conclude that Mike's preference is to choose white shirt with size L .

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The h the price of a hamburger and f the price of an order of french fries is h = (11/2) - (f/2) and f = 11 − 2h.

Let h be the price of a hamburger and f be the price of an order of french fries.

        3h + 4f = 22.75

        2h + 1f = 11

Therefore, the system of equations that can be used to find the prices of a hamburger and an order of french fries are:

3h + 4f = 22.75

2h + 1f = 11

The specific equations I provided are only applicable to the problem of finding the prices of hamburgers and french fries at Hamberger Hut based on the given information.

For other problems, different equations may be needed to model the situation and solve for the unknown variables.

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Answer:

the answer is 2 hours

Step-by-step explanation:

\((x-2)(5x+6)\\\\=x(5x+6) -2(5x+6)\\\\= 5x^2 +6x -10x -12 \\\\=5x^2 -4x-12\)

5x-10x+6x-12

-`9x-12

i believe so

When the converted costs are compared, the earlier edition of the history book is more expensive.

The consumer price index measures the changes in price of a basket of good. It is used to measure inflation.

Converted price of the earlier edition = (CPI in 1992 / CPI in 1999) x later edition of the book

(140.3 / 166.3) x $43 = $36.28

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The missing value 'x' in the two-way relative frequency table is 0.36.

To convert the two-way table to a two-way relative frequency table, we need to calculate the relative frequencies for each category. Relative frequency is calculated by dividing the frequency of a particular category by the total count in that row or column.

Let's denote the missing value as 'x'. To find the value of 'x', we need to ensure that the sum of the relative frequencies in each row and each column adds up to 1.

First, let's calculate the relative frequencies for each category:

Likes hockey: The total count in this row is 12 + 18 = 30.

Relative frequency of "Likes hockey" = 12/30 = 0.4

Relative frequency of "Doesn't like hockey" = 18/30 = 0.6

Likes baseball: The total count in this column is 12 + 14 = 26.

Relative frequency of "Likes baseball" = 12/26 ≈ 0.4615

Relative frequency of "Doesn't like baseball" = 14/26 ≈ 0.5385

To ensure that the relative frequencies add up to 1, we can set up the following equations:

0.4 + x = 1 (sum of relative frequencies in the "Likes hockey" row)

0.4615 + 0.5385 + x = 1 (sum of relative frequencies in the "Likes baseball" column)

Simplifying the equations, we have:

x = 0.6 (1 - 0.4) = 0.6 * 0.6 = 0.36

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Answer:

Step-by-step explanation:

To get the y values all you need to do is substitute the x value in the equation y=-2/3x+7.

For example:

y=-2/3(-6)=7

-2/3x6=-4

-4+7=3

(-6,3)

You can double check your work by filling the x and y coordinates in the equation and when solved if it it true you know you were correct.

To get the x value, you need to fill in the y in the equation y=-2/3x+7

for example:

5=-2/3x+7

-2=-2/3x

3=x

(3,5)

y=-2/3x+7

y=-2/3(15)+7

y=-10+7

y=-3

(15,-3)

y=-2/3x+7

15=-2/3x+7

8=-2/3x

-12=x

(-12,15)

Answer:

(9, 6)

Step-by-step explanation:

Midpoint formula is:

Having coordinates of one end- and midpoint (-5, 12) and (2, 9):

we get the coordinates of the missing endpoint with coordinates (x₂, y₂):

So the missing point is: (9, 6)

Answer:

\(A = 89.1327\)

Step-by-step explanation:

1. Approach

To solve this problem, one must divide the figure up into two smaller figures. Calculate the areas of these smaller figures, and then finally, add up the result. The given figure can be divided into a square and a semi-circle. One can solve for the area of the square using the formula (\(length*width=area\)). One can solve for the area of the semicircle by solving for the area of the circle, and then dividing it by (2).

2. Solve for the area of the square

This is the easier part, all one has to do is multiply the length of the square by the width;

\(length * width = area\\\\8 * 8 = area\\\\64 = area\)

3. Solve for the area of the semi-circle

The formula for the area of a circle is;

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

Where coefficient (\(pi\)) represent the values (\(3.1415...\)), parameter (\(r\)) represent the radius of the circle, and (\(A\)) represents the area.

In the problem, one is given the diameter of the semicircle. The diameter is the largest cord (a line that is drawn in a circle) in the circle, this cord will pass through the center of the circle. The radius is the distance from the center of the circle to the outer edge of the circle. The radius, by its definition will always be half of the diameter. It is given that the diameter of the given circle is (\(8\)), therefore the radius is (\(4\)), because (\(8\)÷\(2=4\)).

Substitute in the values and solve;

\((pi)(4)^2 = A\\\\3.1415*(16)=A\\\\50.2655=A\)

Don't forget to divide this in half, because the given figure is a semi-circle, not a circle;

\(25.1327\)

4. Putting it together

Now add the value for the area of the semi-circle, with the value for the area of the square;

\(square + semi-circle = Total\ area\\\\64 + 25.1327 = Total\ area\\\\89.1327 = Total\ area\)

Answer:

2(x - \(\frac{7}{4}\) )² - \(\frac{9}{8}\)

Step-by-step explanation:

Given

2x² - 7x + 5

The coefficient of the x² term must be 1, thus factor out 2 from 2x² - 7x

= 2(x² - \(\frac{7}{2}\) x ) + 5

To complete the square

add/ subtract ( half the coefficient of the x- term )² to x² - \(\frac{7}{2}\) x

= 2(x² + 2(- \(\frac{7}{4}\) )x + \(\frac{49}{16}\) - \(\frac{49}{16}\) ) + 5

= 2(x - \(\frac{7}{4}\) )² - \(\frac{98}{16}\) + 5

= 2(x - \(\frac{7}{4}\) )² - \(\frac{18}{16}\)

= 2(x - \(\frac{7}{4}\) )² - \(\frac{9}{8}\)

Answer:

g(x) = 2(x - 1.75)^2 - 1.125.

Step-by-step explanation:

g(x) = 2x^2 – 7x + 5

First take the 2 out of the first  terms:

g(x) = 2(x^2 - 3.5x) + 5

Now complete the square on the expression in the parentheses:

g(x) = 2 [ (x - 1.75)^2 - 1.75^2] + 5

g(x) = 2 [ (x - 1.75)^2 - 3.0625] + 5

g(x) = 2(x - 1.75)^2 - 6.125 + 5

g(x) = 2(x - 1.75)^2 - 1.125.

Answer:

Step-by-step explanation:

a.12÷36/7=7/3

12*7/36

84/36

7/3

b.let the number be x

x*1/2=x/2

x*1/2

x/2

A- True

12÷36/7 = 2.333...

7/3 = 2.333....

Hence it's true

B- True

Consider Any random number eg 10

multiplying it by 1/2 gives 5

and dividing by 2 also gives 5

hence it's true.

C- False

3/2 = 1.5

multiplying it to any number will produce half of the number more.

Answer:

A, B, and E. Hope this helps!

Answer:

The number of smoking rooms \(N_s = \frac{480(100-x)}{100}\), in which x is the percentage of non-smoking rooms.

Step-by-step explanation:

We are given a percentage of rooms that are non smoking, lets say x%, and (100-x)% will be smoking rooms. The number of rooms which are smoking is the total number of 480, multiplied by (100-x) and divided by 100.

Then:

\(N_s = \frac{480(100-x)}{100}\)