Factor completely.

x^2−2x−24


Enter your answer in the box.

Answer:

The correct answer is the amount the average person spends in a month on gasoline.

Step-by-step explanation:

When comparing the amounts spent on the purchase of two items, we must need to see the price difference between the products first, then we will see the consumption of those products. Here the two items that are being compared have different purchase prices. A cup of Coffee is far cheaper than purchasing a tank of gasoline. If coffee is purchased on daily basis, even then the amount spent on purchasing coffee would be much lesser than the amount spent on buying the gasoline. For example, the cup of coffee costs $1 and a tank of gasoline costs $50. If coffee is purchased daily, then monthly amount spent on it will be $30, and if gasoline is purchased twice in a month, the amount spent on it will be $100. So an average person spends more amount on gasoline than on purchasing coffee.

Answer:

Part A: Data summary is given in the table

Part B: out of the total 100 students, 15 students do not like either tennis or track

[tex]\frac{15}{100}[/tex]  = 0.15

0.15 × [tex]\frac{100}{100}[/tex] = 15%

Part C:

Total no. of students that dislike track = 60

Total no. of students that dislike tennis = 40

According to the survey results, more people dislike track.

Answer:

Step-by-step explanation:

Given that in a survey of 100 students,  60 liked tennis, out of this 60, 15 also liked track

i.e. people who like tennis and track = 15

people who liked only tennis = 45

Peoplewho like track = 40

a)                                     Like tennis    Do not like tennis    Total

Like track                             15                     25                       40

do not like track                  45                     15                       60

Total                                     60                     40                     100

B) Percentage of the survey respondents did not like either tennis or track

= [tex]\frac{15}{100} =15%[/tex]

C) Dislike for tennis

Answer:

7k -7

Step-by-step explanation:

-k-(-8k+7)

Distribute the minus sign to all terms in the parentheses

-k--8k-7

Ad negative negative is a positive

-k + 8k -7

Combine like terms

7k -7

Answer:

The answer is 7k-7

Step-by-step explanation:

Hope this helps!!!

Answer:

Step-by-step explanation:

The Ruler Postulate:

A distance between a number A and a number B:

AB = |B - A|

We have A = -60, and B = 13. Substitute:

|13 - (-60)| = |13 + 60| = |73| = 73

1÷81 because you square it

9^ -2 = 1/9^2 = 1/81

The frequency  is    1 /period =    1 / [ 2 pi ]

Final answer:

The frequency of the function f(x) = 2cos(x) - 4 is 1/(2π), meaning the function completes one full cycle every 2π units along the x-axis.

Explanation:

The frequency of a function in mathematics describes how often the function repeats its pattern over a certain interval. In the case of the function f(x) = 2cos(x) - 4, the frequency is determined by the coefficient of x inside the cosine function. The standard form of the cosine function is cos(bx), where the frequency is |b|/(2π), because a sine or cosine function oscillates between +1 and -1 every 2π radians, as denoted in Figure 16.10.

In this instance, b = 1 since there is no coefficient multiplying x inside the cosine. Therefore, the frequency of the function f(x) is |1|/(2π), which simplifies to 1/(2π). This frequency means that the function completes one full cycle every 2π units along the x-axis.

Answer:

20

Step-by-step explanation:

Answer:

x=21.4

Step-by-step explanation:

As we know the values of:

Perpendicular=10

Angle=25 degrees

And

Base=x

As the triangle is a right angled triangle, we will use the trigonometric ratios to find the value of x. As we have to find base and we know the values of perpendicular and angle, we will use a ratio that will include base and perpendicular.

So,

tan ⁡x=Perpendicular/Base

tan⁡ 25=10/x

x=10/tan ⁡25  

x=10/0.4663

x=21.4454

Rounding off to the nearest tenth

x=21.4

Answer:

see below

Step-by-step explanation:

the pattern between the numbers is that you add;

4+1=5

5+2=7

7+3=10

10+4=14

14+5=19

19+6=25

hope this helps

You add 6 to 19 in order to get to 25

The value of the constant in the equation is 0.4

An equation is a mathematical statement that shows the equality of two expressions. It consists of two sides, with an equal sign (=) separating them.

The expressions on either side of the equation can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. Equations can be used to solve for an unknown value, model real-world situations, or describe relationships between different quantities.

We have the equation: Height = Constant/Width

This implies, Constant = Height * Width

Since the graph represents the plot of Height against Width, just pick any point and multiply the values to get the Constant. That is:

Constant = 0.5 * 0.8 = 0.4

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Answer:

Final step: Division Property of Inequality

Step-by-step explanation:

–2(5 – 4x) < 6x-4

-10 + 4x < 6x - 4          :  Distributive property

4x < 6x + 6                 :  Addition Property of Inequality (Add 10 to both sides)

-2x < 6                         :  Subtraction Property of Inequality (Subtract 6x from both sides)

  x > - 3                        :  Division Property of Inequality (Divide both sides by -2, flip the symbol sign)

Answer

I don't see the options here so the final step is Division Property of Inequality

The equation of the line parallel to y= (1/2) x−4 and passing through (-4, 2) is y= (1/2) x+4. The equation of the line perpendicular is y=−2x−6.

1. To find the slope of a line parallel to the given line y = (1/2)x - 4, we use the fact that parallel lines have the same slope. Therefore, the parallel line will also have a slope of 1/2.
2. Now, we can use point-slope form of linear equation, given by
[tex]y-y_1 =m(x-x_1),[/tex] where [tex](x_1 , y_1)[/tex] is a point on the line, m is the slope.
3. For the parallel line passing through (-4, 2),substitute [tex]x_1=-4, y_1 =2,[/tex] and m=1/2 into the point-slope form:
y−2= (1/2) (x+4)
4. Now, let's simplify equation to get in slope-intercept form (y=mx+b):
y−2= (1/2) x+2
5. Add 2 to both sides:
y= (1/2) x+4
6. So, the equation of the line parallel to y= (1/2) x−4 and passing through (-4, 2) is y= (1/2) x+4.
7. Now, to find the slope of a line perpendicular to the given line, we use the fact that perpendicular slopes are negative reciprocals. The slope of y= (1/2) x−4 is 1/2, so the perpendicular slope is -2.
8. Now, use the point-slope form again to find the equation of the line perpendicular to y= (1/2) x−4 and passing through (-4, 2):
y−2=−2(x+4)
9. Simplify:
y−2=−2x−8
10. Add 2 to both sides:
y=−2x−6
11. So, the equation of the line perpendicular to y= (1/2) x−4 and passing through (-4, 2) is y=−2x−6.

Complete and correct question:

Consider the graph of the line y = one-halfx – 4 and the point (−4, 2). The slope of a line parallel to the given line is . A point on the line parallel to the given line, passing through (−4, 2), is . The slope of a line perpendicular to the given line is . A point on the line perpendicular to the given line, passing through (−4, 2), is .

The value of tan 25° to the nearest hundredth​ is: 0.47

There are three main trigonometric ratios which are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

We want to find tan 25° to the nearest hundredth​

The value of tan 25 degrees in decimal is 0.466307658

Approximating to the nearest hundredth gives:

tan 25° = 0.47

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Answer is negative 2

Answer:

[tex]\$20,400[/tex]

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]A=P(1+rt)[/tex]

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

step 1

Find the rate of interest

in this problem we have

[tex]t=4\ years\\ P=\$18,000\\ A=\$21,600\\r=?[/tex]

substitute in the formula above and solve for r

[tex]\$21,600=\$18,000(1+4r)[/tex]

[tex]1.2=(1+4r)[/tex]

[tex]4r=1.2-1[/tex]

[tex]r=0.2/4=0.05[/tex]

The rate of interest is [tex]5\%[/tex]

step 2

Find the sum of  money that will amount to 25,500 in 5 years, at the same rate of interest

in this part we have

[tex]t=5\ years\\ P=?\\ A=\$25,500\\r=0.05[/tex]

substitute in the formula above and solve for P

[tex]\$25,500=P(1+0.05*5)[/tex]

[tex]P=\$25,500/(1.25)=\$20,400[/tex]

Answer:

The scale factor of their side lengths is 4:7.

Step-by-step explanation:

Let the side length of two squares are p and q.

The area of a square is

[tex]A=a^2[/tex]

Using this formula, we get the area of both squares.

[tex]A_1=p^2[/tex]

[tex]A_2=q^2[/tex]

It is given that the areas of two similar squares are 16m and 49m.

[tex]\frac{p^2}{q^2}=\frac{16}{49}[/tex]

[tex](\frac{p}{q})^2=\frac{16}{49}[/tex]

Taking square root both the sides.

[tex]\frac{p}{q}=\sqrt{\frac{16}{49}}[/tex]

[tex]\frac{p}{q}=\frac{4}{7}[/tex]

Therefore the scale factor of their side lengths is 4:7.

To find the scale factor of the side lengths, we can take the square root of the ratio of the areas. In this case, the scale factor is √7/2.

To find the scale factor of the side lengths of the squares, we can take the square root of the ratio of their areas. In this case, the ratio of their areas is 49m:16m, which simplifies to 7:4. Taking the square root of this ratio gives us the scale factor of their side lengths. So, the scale factor is √(7/4) = √7/√4 = √7/2. Therefore, the scale factor of the side lengths is √7/2.

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Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}x-y=4&\text{add}\ y\ \text{to both sides}\\x+2y=-2\end{array}\right\\\\\left\{\begin{array}{ccc}x=4+y&(1)\\x+2y=-2&(2)\end{array}\right\\\\\text{substitute (1) to (2):}\\\\(4+y)+2y=-2\qquad\text{combine like terms}\\\\4+(y+2y)=-2\qquad\text{subtract 4 from both sides}\\\\3y=-6\qquad\text{divide both sides by 3}\\\\y=-2\\\\\text{put the value of}\ y\ \text{to (1):}\\\\x=4+(-2)\\\\x=2[/tex]

Answer:

3 1/3

Step-by-step explanation:

First find the mean which is (2+6+8+12+12)/5=8 then find the distance from the mean and all the numbers in the data set.

For example 2 is 6 away from 8 and so on

Remember it's called the mean absolute deviation so it has to be the absolute value of the distances.

Distances: 6, 2, 0, 4, 4,

Then do 6+2+0+4+4/5 because even though 0 doesn't add anything, it is still a value in the distances. You get 3 1/3

Answer:

[tex]y\geq 0[/tex] or [tex][0, \infty)[/tex]

Step-by-step explanation:

By definition the function

[tex]y = log (x)[/tex] has a domain of [tex]x> 0[/tex].

Since the function is not defined for the values of x negative or equal to zero.

The range of this function is all the real numbers.

Since [tex]y <0[/tex] when [tex]0 <x <1[/tex] and [tex]y\geq0[/tex] when [tex]1\leq x<\infty.[/tex]

In this case we have the function [tex]y = log ^ 2 (x-6)[/tex]

Therefore since the log function is squared then its range is now [tex]y\geq 0[/tex]

Answer:

Ans: All real numbers

Step-by-step explanation:

Answer: DGC

Step-by-step explanation:

Congruent means it's equal, basically the same. In this case the question means to find a triangle that is the same shape as FGA. DGC is FGA flipped backwards, so it's the correct answer

Answer:

DGC

Step-by-step explanation:

Answer:

Sets A and B . choice D

Step-by-step explanation:

A relation from a set X to a set Y is said to be a function if each individual element of X is related to exactly one element in Y. In other words, given an element x contained in X, there is only one element in Y that x is related to.

Going by this definition, Sets A and B are functions since each element in x is related to exactly one element in y.

On the other hand, Set C is not a function since the element x = 2 has two corresponding y elements, 1 and 4

Answer:

sets A and B

Step-by-step explanation:

Answer:

5x-13=7

Step-by-step explanation:

because we have "a number" we substitute that with x.

and the rest you just plug in. hope this helps :) <3

The required number is 4.

Linear equations are equations of the first order. The linear equations are defined for lines in the coordinate system. When the equation has a homogeneous variable of degree 1.

It is given that,

[tex]5x-13=7[/tex]

Now, solve the above equation.

[tex]5x-13=7\\5x=7+13\\5x=20\\x=4[/tex]

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Answer:

The probability of not getting yellow is 2/3 ⇒ 3rd answer

Step-by-step explanation:

* Lets describe the meaning of experimental probability

- Experimental probability is the ratio of the number of times an

  event occurs to the total number of trials

∵ There are 6 blue marbles , 4 yellow marble and 2 red marbles

∴ the total number of marbles = 6 + 4 + 2 = 12 marbles

- The probability of each color is the number of the marbles have the

 same color divided by the total number of the marbles

∴ The probability of blue marbles = 6/12 = 1/2

∴ The probability of yellow marbles = 4/12 = 1/3

∴ The probability of red marbles = 2/12 = 1/6

- To find the probability of not yellow you can add the probability of

  blue and red OR subtract the probability of yellow from 1 because

  the total of probability of all colors is 1

∴ The probability of not yellow = 6/12 + 2/12 = 8/12 = 2/3

OR

∴ The probability of not yellow = 1 - 4/12 = 12/12 - 4/12 = 8/12 = 2/3

* The probability of not getting yellow is 2/3

Answer:

The correct answer is  3rd option

The probability of getting not yellow = 2/3

Step-by-step explanation:

It is given that, there are 6 blue marbles, 4 yellow marbles and 2 red marbles

To find the probability

Total number of marbles = 12 marbles

number of yellow marbles = 4 marbles

probability of getting yellow = 4/12 = 1/3

probability of getting not yellow = 1 - 1/3 = 2/3

Therefore the correct answer is 3rd option

It would be 13.

3x4 = 12

25-12

G= 13

Answer:

13

Step-by-step explanation:

g=25-3r

r=4

3 x 4 = 12

25-12= 13

the answer is 13

Answer:

The solutions are [tex]x=2(+/-)\sqrt{11}[/tex]

Step-by-step explanation:

we have

[tex]x^{2}-4x-7=0[/tex]

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex]x^{2}-4x=7[/tex]

Complete the square. Remember to balance the equation by adding the same constants to each side

[tex]x^{2}-4x+4=7+4[/tex]

[tex]x^{2}-4x+4=11[/tex]

Rewrite as perfect squares

[tex](x-2)^{2}=11[/tex]

Take square root both sides

[tex]x-2=(+/-)\sqrt{11}[/tex]

[tex]x=2(+/-)\sqrt{11}[/tex]

We can solve the problem in two equivalent ways:

if we compute the 45% of the price, we have

[tex]320\cdot \dfrac{45}{100} = 14.4[/tex]

and we subtract the discount from the original price:

[tex]320-144=176[/tex]

Alternatively, we can think as follows: if we discount the 45%, it means that we pay the remaining 55%, i.e. we pay

[tex]320\cdot \dfrac{55}{100} = 176[/tex]

To calculate the sale price, first calculate the discount by multiplying the original price by the discount percentage - 320 * 0.45. Then, subtract the value of the discount from the original price to get the sale price.

The subject of this question is mathematics, specifically percentages. In order to calculate the sale price of the television, we first need to calculate the amount of the discount. The discount can be calculated by multiplying the original price of the TV (£320) by the percentage of the discount (45%). In mathematical terms, this equation can be written as 320 * 0.45. Now, subtract the discount from the original price to find the sale price: 320 - (320 * 0.45).

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Answer:

The figure PEST is a rhombus

Step-by-step explanation:

* Lets talk about the difference between all these shapes

- At first to prove the shape is a parallelogram you must have one

 of these conditions

# Each two opposite sides are parallel OR

# Each two opposite sides are equal in length OR

# Its two diagonals bisect each other

- After that to prove the parallelogram is:

* A rectangle you must have one of these conditions

# Two adjacent sides are perpendicular to each other OR

# Its two diagonals are equal in length

* A rhombus you must have one of these conditions

# Two adjacent sides are equal in length OR

# Its two diagonals perpendicular to each other OR

# Its diagonals bisect its vertices angles

* A square you must have two of these conditions

# Its diagonals are equal and perpendicular OR

# Two adjacent sides are equal and perpendicular

* Now lets solve the problem

∵ The vertices of the quadrilateral PEST are

   P (-1 , -5) , E (8 , 2) , S (11 , 13) , T (2 , 6)

- Lets find the slope from each two points using this rule :

 m = (y2 - y1)/(x2 - x1), where m is the slope and (x1 , y1) , (x2 , y2)

 are two points on the line

- Let (x1 , y1) is (-1 , -5) and (x2 , y2) is (8 , 2)

∴ m of PE = (2 - -5)/(8 - -1) = 7/9

- Let (x1 , y1) is (8 , 2) and (x2 , y2) is (11 , 13)

∴ m of ES = (13 - 2)/(11 - 8) = 11/3  

- Let (x1 , y1) is (11 , 13) and (x2 , y2) is (2 , 6)

∴ m of ST = (6 - 13)/(2 - 11) = -7/-9 = 7/9

- Let (x1 , y1) is (2 , 6) and (x2 , y2) is (-1 , -5)

∴ m of TP = (-5 - 6)/(-1 - 2) = -11/-3 = 11/3

∵ m PE = m ST = 7/9

∴ PE // ST ⇒ opposite sides

∵ m ES = m TP = 11/3

∴ ES // TP ⇒ opposite sides

- Each two opposite sides are parallel

∴ PEST is a parallelogram

- Lets check if the parallelogram can be rectangle or rhombus or

 square by one of the condition above

∵ If two line perpendicular , then the product of their slops = -1

- Lets check the slopes of two adjacent sides (PE an ES)

∵ m PE = 7/9

∵ m ES = 11/3

∵ m PE × m ES = 7/9 × 11/3 = 77/27 ≠ -1

∴ PE and ES are not perpendicular

∴ PEST not a rectangle or a square (the sides of the rectangle and

  the square are perpendicular to each other)

- Now lets check the length of two adjacent side by using the rule

 of distance between two points (x1 , y1) and (x2 , y2)

 d = √[(x2 - x1)² + (y2 - y1)²]

- Let (x1 , y1) is (-1 , -5) and (x2 , y2) is (8 , 2)

∴ PE = √[(8 - -1)² + (2 - -5)²] = √[9² + 7²] = √[81 + 49] = √130 units

- Let (x1 , y1) is (8 , 2) and (x2 , y2) is (11 , 13)

∴ ES = √[(11 - 8)² + (13 - 2)²] = √[3² + 11²] = √[9 + 121] = √130 units

∴ PE = ES ⇒ two adjacent sides in parallelogram

∴ The four sides are equal

* The figure PEST is a rhombus

Answer:

Option D. The given sides and angles can be used to show similarity by both the SSS and SAS similarity theorems.

Step-by-step explanation:

step 1

we know that

The SSS Similarity Theorem , states that If the lengths of the corresponding sides of two triangles are proportional, then the triangles must be similar

In this problem

Verify

substitute the values

---> is true

therefore

The triangles are similar by SSS similarity theorem

step 2

we know that

The SAS Similarity Theorem , states that two triangles are similar if two sides in one triangle are in the same proportion to the corresponding sides in the other, and the included angle are equal

In this problem

Two sides in one triangle are in the same proportion to the corresponding sides in the other, and the included angle are equal

therefore

The triangles are similar by SAS similarity theorem

The true statement is The given sides and angles can be used to show similarity by both the SSS and SAS similarity theorems.

Hence, the correct answer is option (d).

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Answer:

left

Step-by-step explanation:

Answer:

left

Step-by-step explanation:

because it is a negative number you would subtract that from +5

hope this helps :)

Answer:

1/4

Step-by-step explanation:

Answer is

16

8

36

Explanation..multiply each by 4

Answer:

2 < s

Step-by-step explanation:

We need to write expression for 2 less than s

The expression 2 less than s is equal to:

2 < s

The symbol < is used for less than.