Can someone explain why we have to cross multiply in this equation

Answer:

-1/4 Abs(x+12) + 10

Step-by-step explanation:

The vertex form of an absolute function is of the form
y = a|x -h| + k   here |x-h| is the absolute value
where (h, k) are the coordinates (x, y) of the vertex

The vertex is given as (-12, 10)

So h = -12, k = 10

Plugging these in we get the vertex form as

y = a|x - (-12)| + 10

y = a|x + 12| + 10

All it remains is to find a

Given point (4, 6) as a point on the graph, plug these values
y = 6 = a|4 + 12| + 10

6 = a|16| + 10

6 = 16a + 10      since absolute value of a positive number is the number

Switch sides
16a + 10  = 6

Subtract 10 from both sides:
16a + 10 - 10 = 6 - 10
16a = -4
a = -1/4

So the equation of the function is
y = -1/4|x + 12| + 10

The second point is not needed to derive the function equation but let's use it to verify our calculated equation

Point (-8, 9)
Plug x = -8,  into y = -1/4|x + 12| + 10

=> y = -1/4|-8+12| + 10
=> y = -(1/4)·4 + 10

=> y = -1 + 10

= y = 9 which matches with the y -coordinate of the second point

So everything looks cool

Final Solution
-1/4 Abs(x+12) + 10

For  - 1/4 if it does not accept fractions, enter -0.25

I have also provided a screenshot which shows what should go into each box to help you out

Hope that helps and feel free to ask any clarifications

Answer:

20 inches

Step-by-step explanation:

7x2=14

3x2=6

14+6=20

The unknow angles are as follows:

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, vertically opposite angles etc.

Therefore,

m∠4 = 72 degrees

Hence,

m∠1 + m∠4 = 180 (angle on a straight line)

m∠1 = 180 - 72

m∠1 = 108 degrees

m∠2 = m∠4 (vertically opposite angles)

Vertical angles are the angles formed when two lines intersect each other. Vertical angles are congruent.

Therefore,

m∠2 = 72 degrees

m∠5 = m∠1 (corresponding angles)

Corresponding angles are angles that occur on the same side of the transversal line and are equal in size.

m∠5 = 108 degrees.

m∠7 = m∠5(vertically opposite angles)

m∠7 = 108 degrees

m∠8 = m∠2 (alternate exterior angles)

Alternate exterior angles are congruent.

m∠8 = 72 degrees

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Answer:

width=x

length=5x

area= 300ft2

area=lxb

300=5x(x)

300=5x^2

x^2=60

x=7.74

7.74(5)=38.7

dimensions are 38.7ft by 7.74 ft

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Step-by-step explanation:

the area of a rectangle is

length × width = 300 ft²

length = width + 5

(width + 5) × width = 300

width² + 5×width = 300

width² + 5×width - 300 = 0

the general solution to such a quadratic equation is

width = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = 5

c = -300

width = (-5 ± sqrt(5² - 4×1×-300))/(2×1) =

= (-5 ± sqrt(25 + 1200))/2 =

= (-5 ± sqrt(1225))/2 = (-5 ± 35)/2

width1 = (-5 + 35)/2 = 30/2 = 15 ft

width2 = (-5 - 35)/2 = -40/2 = -20 ft

negative lengths for an actual object don't make sense, so width = 15 ft is our solution.

length = width + 5 = 15 + 5 = 20 ft

well, the tell-tale part in the points will be the coordinates, hmmm now, the x-coordinate for both points is the same, well, that simply means is a vertical line.  Check the picture below.

Answer: A. Cubic

Step-by-step explanation:

When the student needs to select a statistical question to research for a project, the question that he should select is D. How many students in my class were absent last Wednesday?

Any question that may be answered statistically is one for which data collection is possible and for which there will be some degree of data variability. Because there is no variability in the data used to answer the question, questions that can only be answered with a single data point are not statistical questions.

To do research for a project, a student must choose a statistical question. In this case, it should be noted that it's important to select a question that's specific. This was illustrated by option D.

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Answer: y = -3x + 6

Step-by-step explanation:

If it is perpendicular to the line -3x + 2, then it's slope should also be -3.

The standard form of a line is y = mx + b. As our slope is -3, we have that our line is y = -3x+b. Now, let's put the given point into the line. x = 3 and y = -3, so -3 = -3*3 + b. Hence, b = -3+9 = 6. The equation of the line is y = -3x + 6.

The mean of the sample means of the given data is 40

The provided sample size is 100, with a standard deviation 20and mean of the as 25.

Mean of the population, μ = 25

The standard deviation of the population, σ = 20.

Size of the sample, n = 100

Let X be the mean of the sample means,

The formula for the sample mean is

X = μ

where μ, as we know is the mean of the population

By substituting the value in the above equation, we get

X = 40

Therefore, we get the mean of the sample means is 40

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The conversion of the fraction -30 ¹⁹/₄₀ to decimal is expressed as; -30.475

Fractions usually have a numerator and denominator. Now, fractions can also be expressed as mixed fraction, improper fraction and proper fraction.

Now, we are given the fraction in mixed fraction. This is expressed as;

-30 ¹⁹/₄₀ = -30 - ¹⁹/₄₀

Now, the proper fraction part of the mixed fraction can be expressed as;

¹⁹/₄₀ = 0.475

Thus, our fraction is now;

-30 - 0.475 = -30.475

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Answer:

The second bag (4.75)

Step-by-step explanation:

Answer:

percentage of boys:

6/20x100

=30%

percentage of girls:

14/20x100

=70%

Answer:

Step-by-step explanation:

70%

Answer:

8.277

Step-by-step explanation:

Pretty simple, just add up the values but convert the word form into decimals.

[tex]6+2.2+0.033+0.044=8.277[/tex]

Also, your question said 33 thousandths, so it is what I answered.

Answer:

8.277

Step-by-step explanation:

Answer: 9.52

Step-by-step explanation: I looked it up but you would do 17 divided by 56 and get a decimal and then move the decimal point over 2 spaces to the right and then you have your answer.

Hope it helped

The number of pennies that Ari has is 14.

The number of nickels that Ari has is 8.

The linear equations that represent this question are:

0.01p + 0.05n = $0.54 equation 1

p + n = 22 equation 2

Where:

In order to determine the number of nickels, multiply equation 2 by 0.01

0.01p + 0.01n = 0.22 equation 3

Subtract equation 3 from equation 1:

0.04n = 0.32

Divide both sides by 0.04

n = 0.32 / 0.04

n = 8

Substitute for n in equation 2:

8 + p = 22

p = 22 - 8

p = 14

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Answer:

2x+20≥84

2x≥64

x≥32

Step-by-step explanation:

Graph A, and graph C could not possibly be density curves for a continuous random variable if they were provided with the right scale.

A symbol (often a letter) used in algebra to represent an unknowable numerical value in an equation. Variables can have a wide range of values, which is why they are called variables. Thus, a variable can be thought of as a quantity that can take on different values depending on the circumstances of a given issue. As the program executes, we may store, modify, and access this data thanks to variables. All types of information can be stored in variables.

Four graphs of different nature as options.

We are required to find a graph that is not a continuous variable.

In mathematics, a continuous function is a function such that a continuous variation of the argument induces a continuous variation of the value of the function.

Continuous lines are those lines that when decreased, decrease with continuity and when increased, increase with continuity.

Given that,

When we observe graph A, graph C. In these graphs, the value of the function keeps increasing and decreasing a lot and is not in continuity.

Hence, graph A, and graph C could not possibly be density curves for a continuous random variable if they were provided with the right scale.

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Answer:

geometric sequence

Step-by-step explanation:

an arithmetic sequence has a common difference d between consecutive terms.

40 - 200 = - 160

8 - 40 = - 32

no common difference thus not arithmetic

a geometric sequence has a common ratio r between consecutive terms

[tex]\frac{40}{200}[/tex] = [tex]\frac{4}{20}[/tex] = [tex]\frac{1}{5}[/tex]

[tex]\frac{8}{40}[/tex] = [tex]\frac{1}{5}[/tex]

thus there is a common ratio so sequence is geometric

Answer:

The equations is t = 1/4n + 40

The slope is 1/4 and the y-intercept is 40

t is the temperature.

n is the number of chirps per minute.

Step-by-step explanation:

The transformation that takes place on the parent function ( f (x) = log (x) ) to achieve the graph of g(x)=log(-3x+9)+4  can be described as a reflection across the y-axis. Then you horizontally shrink a factor of three; shift three units to the right, and shift four units upwards.

Step 1: The parent graph is to be translated 3 units to the right side to achieve: y = log (x-3)

2. Shrink the graph by a factor of three by multiplying x by three:

⇒ y = log 3(x-3)

3. Reflect the function y = log 3(x-3) across line -3 = x to achieve:
y = -3(x-3)

4. Translate the function y = log 1-3(x-3) four units upwards to achieve

y = log (-3 + 9) +4

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By the Law of Sines,

[tex]\frac{\sin B}{b}=\frac{\sin A}{a} \\ \\ \sin B=\frac{b \sin A}{a} \\ \\ =\frac{244\sin 37.8^{\circ}}{229} \\ \\ B \approx 37.42^{\circ}, 142.58^{\circ}[/tex]

Of these, only 37.42° is a possible value of B (sum of angles of a triangle is 180°).

So, we have that:

[tex] a=229, b=244, A=37.8^{\circ}, B=\arcsin \left(\frac{244\sin 37.8^{\circ}}{229} \right)[/tex]

Angles of a triangle add to 180°, so:

[tex]C=180^{\circ}-A-B=142.2^{\circ}-\arcsin \left(\frac{244\sin 37.8^{\circ}}{229} \right)

[/tex]

Using the Law of Sines again,

[tex]\frac{c}{\sin C}=\frac{a}{\sin A} \\ \\ c=\frac{a \sin C}{\sin A} \\ \\ =\frac{244\sin \left(142^{\circ}-\arcsin \left(\frac{244 \sin 37.8^{\circ}}{229} \right) \right)}{\sin 37.8^{\circ}}[/tex]

So, there is one possible triangle, where:

[tex]a=229 \\ \\ b=244 \\ \\ c=\frac{244\sin \left(142^{\circ}-\arcsin \left(\frac{244 \sin 37.8^{\circ}}{229} \right) \right)}{\sin 37.8^{\circ}} \\ \\ A=37.8^{\circ} \\ \\ B=\arcsin \left(\frac{244\sin 37.8^{\circ}}{229} \right) \\ \\ C=142.2^{\circ}-\arcsin \left(\frac{244\sin 37.8^{\circ}}{229} \right)[/tex]

Answer:

267,168 inches

Step-by-step explanation:

If your box is a rectangular prism or a cube, the only information you need is the box's length, width, and height. You can then multiply them together to get volume. This formula is often abbreviated as V = l x w x h.

Volume = L × W × H

Where,

Volume = 22 inches × 12 inches × 1012 inches

Volume = 267,168 inches

So, her cooler can hold 267,168 inches of ice

Answer:

30%

Step-by-step explanation:

6/20 = .3

.3 x 100 = 30

Based on the commission percentage that William makes when he sells goods at the electronics store, the amount that William made in commission from the computer is $ 45. 84.

Commission made on goods and services are a percentage that is paid to sales people when they make a certain number of sales. The commission is based on the amount that the good or service in question is sold for.

The commission to William here can be found by the formula:

= Percentage made for commission on everything sold x Amount that the computer sold for

Solving for the commission to William gives:

= 6 % x 764

= 0. 06 x 764

= $ 45.84

In conclusion, the commission that William made from the sale of the computer which was valued at $ 764 is $ 45.84.

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Answer:

45. 84

Step-by-step explanation:

Based on the commission percentage that William makes when he sells goods at the electronics store, the amount that William made in commission from the computer is $ 45. 84.How to find the money made from commission?Commission made on goods and services are a percentage that is paid to sales people when they make a certain number of sales. The commission is based on the amount that the good or service in question is sold for. The commission to William here can be found by the formula:= Percentage made for commission on everything sold x Amount that the computer sold for Solving for the commission to William gives:= 6 % x 764 = 0. 06 x 764= $ 45.84

Answer:

1/3

Step-by-step explanation:

the is slope of this graph is 1_3

Answer:

1/3

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Step-by-step explanation:

To find the slope of a graph you need to look for 2 pairs of accurate xand y values

First value which is accurate is:

x = 1 and y= 4

Second pair which is accurate is :

x = 7 and y = 6

Gradient = rise/run = y2-y1/x2-x1

im taking y2 as 6, x2 as 7, y1 as 4 and x1 as1

6-4/7-1

=2/6

=1/3

The value of 600 as the product of prime factors will be 2³ × 3 × 5².

It should be noted that a prime number simply means the number that can be multiplied by itself and 1.

Therefore, it should be noted that 600 will be expressed thus:

600 = 2 × 2 × 2 × 3 × 5 × 5

600 = 2³ × 3 × 5².

Therefore, the value is 2³ × 3 × 5².

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Answer:

0.900.........

Step-by-step explanation:

thats it

0.898 rounded to nearest hundred will be 0.90 .

Given,

Number = 0.898

Here,

Now when we round numbers, anything greater than 5 gets rounded up, and anything less than 5 gets rounded down.

So 9 is greater than 5 thus the number will be rounded off to 0.90 .

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The Additive inverse of f(x) is 70x – 10x² and the multiplicative inverse of f(x) is   [tex](x^{2} -7x)[/tex] x [tex](1/10)[/tex]

The value of tan33° is 11/20.

A triangle with an angle measure of 90° is called a right triangle.

Given that, tan(x) = (length of the opposite side)/ (length of an adjacent side)

Therefore, for the given triangle, it follows:

tan33° = 11/20

Hence, the value of tan33° is 11/20.

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