Two ramps are placed back to back as shown. What is the length of the ramp labeled x?

Answer:

(x-8)(x+3)

Step-by-step explanation:

Final answer:

To factor the quadratic expression x² - 5x - 24, we find the factors that multiply to -24 and add to -5, which are -8 and 3. Therefore, the factored form of the expression is (x - 8)(x + 3).

Explanation:

To factor the quadratic expression x² - 5x - 24 completely, we need to find two numbers that multiply to -24 (the constant term) and add to -5 (the coefficient of the x term). The numbers that fit this criteria are -8 and 3. So, our expression factors into:

(x - 8)(x + 3)

We can check our factoring by expanding these factors to see if we get the original expression:

(x - 8)(x + 3)
= x² + 3x - 8x - 24
= x² - 5x - 24

Thus, the original expression is correctly factored as (x - 8)(x + 3).

There were about 6001 bacteria X bring introduced into the egg salad. The number of bacteria in the food 4 hours after contamination is 63000.

To find the initial number of bacteria X introduced into the egg salad, divide the final number by (1 + growth rate)^time. For estimating the number of bacteria in the food 4 hours after contamination, multiply the initial number by (1 + growth rate)^time.

To find the initial number of bacteria X introduced into the egg salad, we can use the formula:

Initial Number = Final Number / (1 + Growth Rate)^Time

Plugging in the given values, we have:

Initial Number = 35,000 / (1 + 180%)^3 = 35,000 / (1 + 1.8)^3 = 35,000 / 3.027 = 11,542.52

To estimate the number of bacteria in the food 4 hours after contamination, we can use the same formula:

Number after 4 hours = Initial Number * (1 + Growth Rate)^Time

Plugging in the values, we have:

Number after 4 hours = 11,542.52 * (1 + 180%)^4 = 11,542.52 * (1 + 1.8)^4 = 11,542.52 * 10.4044 = 120,108.83

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Answer:

4 possible outcomes

Step-by-step explanation:

we know that

The probability of an event is the ratio of the size of the event space to the size of the sample space.  

The size of the sample space is the total number of possible outcomes  

The event space is the number of outcomes in the event you are interested in.  

so  

Let

x------> size of the event space

y-----> size of the sample space  

so

[tex]P=\frac{x}{y}[/tex]  

In this problem

The probability of choose a blue card is

[tex]x=7[/tex]

[tex]y=7+4+6+8=25[/tex]

substitute

[tex]P=\frac{7}{25}[/tex]

The probability of choose a green card is

[tex]x=4[/tex]

[tex]y=7+4+6+8=25[/tex]

substitute

[tex]P=\frac{4}{25}[/tex]

The probability of choose a red card is

[tex]x=6[/tex]

[tex]y=7+4+6+8=25[/tex]

substitute

[tex]P=\frac{6}{25}[/tex]

The probability of choose a yellow card is

[tex]x=8[/tex]

[tex]y=7+4+6+8=25[/tex]

substitute

[tex]P=\frac{8}{25}[/tex]

The sum of the probabilities of the 4 possible outcomes  is equal to

[tex]\frac{7}{25}+\frac{4}{25}+\frac{6}{25}+\frac{8}{25}=\frac{25}{25}[/tex] ----> represent the 100%

Explanation:

When looking at x on number lines, x is represented by the bold line. The x value can be anything on the bold line and therefore the line must respect the restrictions of x.

This question says -2 ≥ x which means "-2 is greater than or equal to x". Inversely, this also means that x is less than or equal to -2 because the original question can also be written as x ≤ -2. So, we are looking on the number line for the bold line that starts at -2 and continues to the left of -2, where the numbers that are less than -2 will be found.

The correct answer would be B.

Hope this helps!

Answer:

Explanation given below.

Step-by-step explanation:

The first step is to put the parabola in the form  [tex]ax^2+bx+c[/tex] , which is the standard form of a parabola

Note: a is the coefficient before x^2 term, b is the coefficient before x term, and c is the independent constant term

The axis of symmetry divides the parabola symmetrically. The axis of symmetry has the equation  [tex]x=-\frac{b}{2a}[/tex]

Where a and b are the respective values shown above

So, that is how you get the axis of symmetry of any parabola.

Answer:

The equation of the axis of symmetry of the parabola is x = h,

 where h is the x-coordinate of the vertex point

Step-by-step explanation:

* The axis of symmetry is the line which divides the

 shape into two congruent parts

* The general form of the quadratic equation is:

 ax² + bx + c = 0

* The quadratic equation is represented graphically by parabola

∵ The parabola has minimum point or maximum point

∴ The axis of symmetry of the parabola is passing through this point

   This point is called the vertex point or the turning point

- Lets find this point:

* the x-coordinate of this point calculated from the equation

 x- coordinate of the vertex point h = -b/2a

- where b is the coefficient of x and a is the coefficient of x²

∴  The equation of the axis of symmetry of the parabola is x = -b/2a

EX:

- If ⇒ x² - 4x + 4 = 0

∵ a = 1 , b = -4

∴ h = -(-4)/2(1) = 2

∴ The equation of the axis of symmetry of the parabola is x = 2

The graph show you the axis of symmetry

Answer:

9.42 square meters i think

Step-by-step explanation:

Answer:

the answer is 28.26

Answer:

Step-by-step explanation:

55-20 is less than or equal to (d)

i think...

Answer:

The solution would be d ≥ 75

Step-by-step explanation:

To find this we know that we have at least 55, which can be modeled as:

d ≥ 55

And then we need to add 20

d ≥ 55 + 20

d ≥ 75

The answer to this is the last one as it shows that not is not larger than 9 but it can equal to it. This makes the original statement true

Answer:  The correct option is

(D) [tex]n\leq 9.[/tex]

Step-by-step explanation:  We are given that the greatest value of n is 9.

We are to select the inequality that best shows all the possible values of n.

Since the greatest value of n is 9, it means that the value of n is less than or equal to 9.

But the values of n cannot be greater than 9.

So, we will be using the sign of less than or equal to in the inequality.

Therefore, the required inequality that best shows all the possible values of n is given by

[tex]n\leq 9.[/tex]

Thus, (D) is the correct option.

Find the spread for both by subtracting the hlowest number from the highest number:

Basketball: 85-67 = 18

Baseball: 76 - 64 = 12

Now subtract the two to find their difference:

18-12 = 6

The answer would be C. The spread of data for basketball players is 6 inches greater than baseball players.

Answer:

a

Step-by-step explanation:

Answer:

H

Step-by-step explanation:

Let a represent Ann's height, and let j represent Jay's height

Break up the sentence into the key parts.

"The difference between Ann's and Jay's heights" "is" "half of Jay's height"

"The difference between Ann's and Jay's heights" becomes the expression:

         a - j

"is" is math means an equal sign '='

"half of Jay's height" becomes the expression: (1/2)j

Put the 3 parts together and get the equation:

a - j = (1/2)j,

Since all the equations in the answer choices are in terms of a, solve the above equation for a...

a = (1/2)j + j, which is answer H

a. Angles ABC and CBD are supplementary, so you know that [tex]m\angle ABC=180^\circ-24^\circ=156^\circ[/tex]

The interior angles of any triangle sum to 180 degrees in measure, so that [tex]m\angle ACB=180^\circ-156^\circ-16^\circ=8^\circ[/tex].

By the law of sines, we then have

[tex]\dfrac{\sin8^\circ}{7600\,\mathrm{ft}}=\dfrac{\sin16^\circ}{BC}\implies BC=\dfrac{(7600\,\mathrm{ft})\sin16^\circ}{\sin156^\circ}\approx15052\,\mathrm{ft}[/tex]

b. In triangle BCD, we have

[tex]\sin24^\circ=\dfrac{CD}{BC}[/tex]

and so

[tex]CD=\sin24^\circ\dfrac{(7600\,\mathrm{ft})\sin16^\circ}{\sin8^\circ}\approx6122\,\mathrm{ft}[/tex]

• They're 180°

• Short, thin, or thick

• Could be curved, zig-zag, straight, bent etc.

• Perpendicular

A line is characterized by its length exceeding its width and the path it takes. Its qualities can express emotions and control the viewer's attention, with variations such as curved or angular, smooth or staccato, and different thicknesses. Lines play a crucial role in defining shapes and in expressive forms of writing such as calligraphy.

The characteristics of a line in design are defined by its length being greater than its width and by the paths it takes. A line is essentially a point in motion and is characterized by how it is used in art to determine motion, direction, and energy. When speaking of the qualities of a line, we refer to its character which can animate a surface. Lines can be curved or angular, and can progress smoothly or with a staccato rhythm, and they can be thick or thin, pale or bold.<\/p>

Lines have an emotional and expressive content that is understood both rationally and emotionally; they can control the viewer's attention and direction. Different types of lines like outline or contour line define shapes. Moreover, lines are integral to objects and writing symbols, where they denote meaning and can be expressive in themselves, illustrating their significance in calligraphy and other forms of art.<\/p>

Gestures are also related to lines, where a line produced by the artist's movement can be interpreted in various ways, like conveying calm with evenly drawn horizontal lines or rigidity with straight lines, which can be impactful depending on the context.<\/p>

A multiple of a number is a number multiplied by another number.

Considering this definition, the first three multiples of 6 are 6, 12, and 18 because it is six multiplied by 1, 2, and 3.

Similarly, the multiples of 11 are 11, 21, and 33 and the multiples of 14 are 14, 28, and 42.

The first three multiples of 6 are 6, 12, and 18, the first three multiples of 11 are 11, 22, and 33, and the first three multiples of 14 are 14, 28, and 42.

The first three multiples of a number are obtained by multiplying that number by 1, 2, and 3, respectively. For the given numbers:

These calculations are made by simply multiplying the original number by 1, then 2, then 3. It's foundational multiplication, a key concept in Mathematics.

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Answer:

[tex]\large\boxed{d=\sqrt{29}}[/tex]

Step-by-step explanation:

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We have the points (2, 4) and (7, 2). substitute:

[tex]d=\sqrt{(7-2)^2+(2-4)^2}=\sqrt{5^2+(-2)^2}=\sqrt{25+4}=\sqrt{29}[/tex]

Answer: The meadian of a data set is the number in between all of the numbers.

Step-by-step explanation: For example, you havent put any numbers so ill just use 1-10. so you first list all the numbers in order, grom smallest to biggest. then find the muddle number

Final answer:

To determine the median of a data set, arrange the data in ascending order and find the middle value for an odd number of data, or the average of the two middle numbers for an even number of data. The median is resistant to outliers and splits the data set into two equal halves.

Explanation:

To determine the median of a data set, you need to arrange the data in ascending order first. If the number of data values is odd, the median is the middle value. For example, in a set of 11 data values, the 6th number would be the median. If the number of data values is even, the median is the average of the two middle values. For instance, if a data set has 14 values, you would take the average of the 7th and 8th values after arranging the data.

To find the median in a data set with even number of values, such as 14, add the two middle values, 6.8 and 7.2, together and then divide by two, yielding a median of 7.0. It's important to note that the median separates the data into two equal halves, where half the values are same or smaller than the median, and the other half are same or larger.

When a data set contains extreme values or outliers, the median can be particularly useful as it is not influenced by these extreme values, unlike the mean.

Answer:

57 inches

Step-by-step explanation:

divide 121/2 = 60.5 .. make the 3 1/2 inches into a decimal: 3.5 and then subtract 60.5 - 3.5 = 57 inches.. hope this helps

Her hair would be 57 inches after the haircut.

Hope this helps!

Answer:

yes

Step-by-step explanation:

sum:

• `x+y=6`

• `y=6-x`

Difference:

• `y-x=6`

• `y=x+6`

Answer:

yes 12-6 has a difference of 6 and a sum of 6

Step-by-step explanation:

Answer:

2. y = 25 km

Step-by-step explanation:

To find the dimensions, write a proportion. A proportion is an equation of ratios.

[tex]\frac{scale}{factor} = \frac{Actual}{Model}[/tex]

Then solve for the unknown value by cross multiplying.

2. [tex]\frac{2}{5} = \frac{10}{y}[/tex]

2y = 5*10

2y = 50

y = 25

Answer:

24 and 144

Step-by-step explanation:

a = 4

t4 = 864

864 = 4*r^(4 - 1) divide by 4

216 = r^3            Take the cube root of 216

6 = r

Note you can find the cube root of any number by using your calculator.

t2 = a * r^(2 - 1)

t2 = 4 * 6^1

t2 = 24

=================

t3 = a*r^(3 -1)

t3 = 4 * 6^2

t3 = 4 * 36

t3 = 144

Answer

24 and 144

The right option is (D) 5

−2x²+wx−4−(x²+5x+6)=−3x²−10

Add 3x^2 to both sides.

wx−3x²−5x−10+3x²=−3x²−10+3x²

wx−5x−10=−10

Add 5x to both sides.

wx−5x−10+5x=−10+5x

wx−10=5x−10

Add 10 to both sides.

wx−10+10=5x−10+10

wx=5x

Divide both sides by x.

wx /x = 5x/x

w=5

Area = Base x Width ÷ 2

Area = 32cm^2

Base = 8cm

32 ÷ 8 = 4

4 × 2 = 8

Answer = 8

To check our answer:

8 x 8 = 64

64 ÷ 2 = 32

:)

To find the height of a triangle with an area of 32 square centimeters and a base of 8 centimeters, we use the formula A = 1/2 × base × height. The height is calculated to be 8 centimeters.

The student has asked about finding the width of a triangle, given its area in square centimeters and the length of its base. There seems to be a confusion with the terminology; the width of a rectangle is being referred to instead of the triangle's height. However, to provide assistance with the appropriate concept, we will focus on finding the height of a triangle.

The area of a triangle is calculated by the formula A = 1/2 ×base× height. When we know the area and the base length, we can rearrange the formula to solve for the height. For a triangle with a base of 8 centimeters and an area of 32 square centimeters, the calculation would be as follows:

Area = 1/2 × base × height
32 = 1/2 × 8 × height
32 = 4 × height
height = 32 / 4
height = 8 centimeters

Therefore, the height of the triangle would be 8 centimeters.

Answer:the answer is -7

Step-by-step explanation:

156=2b+5(-8-6b)

2b+5(-8-6b)

expand 2b+5(-8-6b) ---> -28b-40

-28b-40=156

add 40 to both sides

-28b-40+40=156+40

simplify

-28b=196

divide both sides by -28

(-28b/-28b) = (196/-28b)

simplify

b=-7

Answer:

8

Step-by-step explanation:

6 / .75(3/4)

When repetition is allowed, there can be 64 different 3-letter words made from the letters 'FGHI'. When repetition is not allowed, there can be 24 different 3-letter words made from those letters.

In this question, we are asked to find the number of 3-letter words that can be made from the letters 'FGHI' with and without repetition. When repetition is allowed, each letter can be chosen independently for each position, so we have 4 choices for each position. Therefore, the total number of words is 4*4*4 = 64. When repetition is not allowed, each letter can only be used once, so we have 4 choices for the first position, then 3 choices for the second position, and finally 2 choices for the third position. Therefore, the total number of words is 4*3*2 = 24.

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Answer:   [tex]\bold{\dfrac{-2\pm \sqrt{22}}{3}}[/tex]

Step-by-step explanation:

[tex]3x^2+4x-6=0\quad \rightarrow \quad a=3,\ b=4,\ c=-6\\\\\\\text{Quadratic formula is: }x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\\x=\dfrac{-(4)\pm \sqrt{(4)^2-4(3)(-6)}}{2(3)}\\\\\\.\ =\dfrac{-4\pm \sqrt{16+72}}{2(3)}\\\\\\\\.\ =\dfrac{-4\pm \sqrt{88}}{2(3)}\\\\\\\\.\ =\dfrac{-4\pm 2\sqrt{22}}{2(3)}\\\\\\\\.\ =\dfrac{-2\pm \sqrt{22}}{3}[/tex]

they’re the same shape and size

Answer:

They are going to have a congruent match of sides and angles

Step-by-step explanation:

This is because congruent parts of congruent triangles are congruent.

Please mark Brainliest

The only label that could replace "A" in the diagram is Rational Numbers only.

The correct answer is A. Rational Numbers only.

Here's a breakdown of the diagram and the reasoning behind the answer:

The diagram shows that "A" is a subset of real numbers but not a subset of whole numbers.

This means that "A" must include some numbers that are not whole numbers.

Of the given options, only rational numbers fit this description. Integers are a subset of whole numbers, and irrational numbers are not a subset of real numbers.

Complete Question:

Which label or labels could replace "A" in the diagram below?

A. Rational Numbers only

B. Rational Numbers or Integers

C. Integers only

D. Irrational Numbers

Answer:

Vf = 118.365 m3

Step-by-step explanation:

Vcil = Pi*[(20)^2]*(100=

Vcil = 125.600 m3

Vesf = (4/3)*Pi*(12)^3

Vesf = 7235 m3

Then

Vf = Vci - Vesf

Vf = 125.600 - 7235

Vf = 118365 m3

Best regards

The image would be (-1, 5)

Answer:

Zero property

Step-by-step explanation:

We are making a equation equal 0