Please help me with this question....

#a

[tex]\\ \rm\Rrightarrow f(-4)[/tex]

[tex]\\ \rm\Rrightarrow 3(-4)+2[/tex]

[tex]\\ \rm\Rrightarrow -12+2[/tex]

[tex]\\ \rm\Rrightarrow -10[/tex]

#b

#1

[tex]\\ \rm\Rrightarrow y=\dfrac{2x-1}{3}[/tex]

[tex]\\ \rm\Rrightarrow x=\dfrac{2y-1}{3}[/tex]

Find y

[tex]\\ \rm\Rrightarrow y=\dfrac{3x+1}{2}[/tex]

Inverse is

[tex]\\ \rm\Rrightarrow g^{-1}(x)=\dfrac{3x+1}{2}[/tex]

#2

[tex]\\ \rm\Rrightarrow gof(x)[/tex]

[tex]\\ \rm\Rrightarrow g(f(x))[/tex]

[tex]\\ \rm\Rrightarrow g(3x+2)[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{2(3x+2)-1}{3}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{6x+4-1}{3}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{6x+3}{3}[/tex]

If we factor out

[tex]\\ \rm\Rrightarrow \dfrac{2x+1}{1}[/tex]

[tex]\\ \rm\Rrightarrow 2x+1[/tex]

#c

[tex]\\ \rm\Rrightarrow f(x)=g(x)[/tex]

[tex]\\ \rm\Rrightarrow 3x+2=\dfrac{2x-1}{3}[/tex]

[tex]\\ \rm\Rrightarrow 3(3x+2)=2x-1[/tex]

[tex]\\ \rm\Rrightarrow 9x+6=2x-1[/tex]

[tex]\\ \rm\Rrightarrow 7x=-7[/tex]

[tex]\\ \rm\Rrightarrow x=-1[/tex]

Answer:

Given functions:

[tex]f(x)=3x+2[/tex]

[tex]g(x)=\left(\dfrac{2x-1}{3}\right)[/tex]

Part (a)

[tex]\begin{aligned}\implies f(-4) & = 3(-4)+2\\& = -12+2\\ & = -10\end{aligned}[/tex]

Part (b)(i)

[tex]\begin{aligned}g(x) & =\left(\dfrac{2x-1}{3}\right)\\\\\textsf{Swap }g(x) \textsf{ for }y : \\\implies y & = \left(\dfrac{2x-1}{3}\right)\\\\\textsf{Make } x \textsf{ the subject}: \\\implies 3y & = 2x-1\\3y+1 & = 2x\\x & = \dfrac{3y+1}{2}\\\\\textsf{Swap }x \textsf{ for }g^{-1}(x) \textsf{ and }y \textsf{ for }x:\\\implies g^{-1}(x) & = \dfrac{3x+1}{2}\end{aligned}[/tex]

Part (b)(ii)

[tex]\begin{aligned}gf(x) & = \dfrac{2[f(x)]-1}{3}\\\\& = \dfrac{2(3x+2)-1}{3}\\\\& = \dfrac{6x+4-1}{3}\\\\& = \dfrac{6x+3}{3}\\\\& = \dfrac{6x}{3}+\dfrac{3}{3}\\\\& = 2x+1\end{aligned}[/tex]

Part (c)

[tex]\begin{aligned}f(x) & = g(x)\\\\\implies 3x+2 & = \dfrac{2x-1}{3}\\\\3(3x+2) & = 2x-1\\\\9x+6 & = 2x-1\\\\7x & = -7\\\\\implies x & = -1\end{aligned}[/tex]

Answer:

38.1971

Step-by-step explanation:

The formula for diameter is circumference/ pi. So 120/3.14... is 38.1971

Considering that 12 is a root of the function, the value of coefficient Q is of 12.

It means that f(x) = 0.

In this problem, the function is given by:

f(x) = x² - 13x + q.

Since 12 is a root, we have that f(12) = 0, hence:

12² - 13 x 12 + q = 0

q - 12 = 0.

q = 12.

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Answer:

4 days

Step-by-step explanation:

8 pints = 1 gallon

2 pints = 1 day

1 gallon = 4 days

Step-by-step explanation:

Susan drinks milk each day = 2 pints

1 gallon = 8 pints

Now, Susan take days to drink 1 gallon of milk

= 8 ÷ 2

= 4 answer

Hence, Susan takes 4 days to drink 1 gallon of milk .

The three side length that describes the triangle in the image attached below are: 5 cm, 12 cm, and 13 cm.

A triangle is a shape that has three sides. The sides can be measured using a ruler.

The sides of the triangle in the image shown have side lengths as measured by the ruler beside each of the sides, which are 5 cm, 12 cm, and 13 cm.

Therefore, the three side lengths of the triangle in the diagram are: 5 cm, 12 cm, and 13 cm.

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The expressions of the number of radians can be expressed in the ways below.

The radius = 1.9 km

The angular speed = 3.1 radians per hour

a. The expression of t from the number of radians

θ = π/2 + 3.1t

x = rcosθ

= 1.9cos(π/2 + 3.1t)km

= rsinθ

= 1.9sin((π/2 + 3.1t)km

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The equation that can be used to find the exponential decay is 3000 = 4599e^k.

The lawn mower is decreasing in value, thus it is the decay constant that would be found.

The formula that can be used to find the value of an asset that decays exponentially is:

Future value = present value x (e^k)

3000 = 4599e^k.

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Answer:

B. -113 inches

Step-by-step explanation:

First you have to find the radius of the two pizzas. The radius is half of the diameter. So, the first pizza would have a radius of 8 inches, since 8 is half of 16. The second pizza would have a radius of 10 inches, since 10 is half of 20. Then you would use the area formula to find the area of the two pizzas. The area formula is A=3.14R^2. The area of the first pizza is 201.06. The area of the second pizza is 314.16. Then you subtract those two numbers to get -113.1. The answer is -113 inches.

Answer:

Hey!

Your Answer Is,

No Triangles: A, C

One Triangle, F, D

Many Triangles: B,E

I hope this helps you!

Step-by-step explanation:

Answer:

So for a quadratic function, the axis of symmetry is the line that divides the curved line in the middle, which is the h value, it can be found by using the formula -b/2a, so for here it would be 4/2(1) = 2, so x =2

Hope that answers your question

Step-by-step explanation:

The rate of change is negative 1.25. The negative of 1.25 represents 1.25 feet is drain every hour. The number 1 represents 1 foot of water that is already present in the pool.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

The Gutierrez family and the Kim family both have pools.

The Gutierrez family is filling their pool, which is modeled by the equation

y = x + 1

The Kim family is draining their pool, which is modeled by the equation

y = -1.25x + 5

In both equations, x represents the time in hours and y represents the depth of the water in the pool in feet.

These two situations can be described by the following system of equations:

Then the rate of change for the Kim family's pool will be

Rate of change = -1.25

The negative of 1.25 represents 1.25 feet is drain every hour.

Looking at the equation for the Gutierrez family's pool.

y = x + 1

The number 1 represents 1 foot of water that is already present in the pool.

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Check the picture below.

Make sure your calculator is in Degree mode.

Answer:

1260 inches

Step-by-step explanation:

Calculator

taking a close look at the graph hmmm we can see that it has roots or solutions at -4 and 5, however, let's notice something, the graph touches the x-axis at -4 and 5 but it doesn't cross it, it simply bounces off of it, which means those roots have an even multiplicity, hmmm let's give it say 2.  Let's also notice the graph has a y-intercept at hmm 100, so the graph passes through (0 , 100).

[tex]\begin{cases} x=-4\implies &x+4=0\\\\ x=5\implies &x-5=0 \end{cases}\implies y=a\stackrel{"2" multiplicity}{(x+4)^2 (x-5)^2} \\\\\\ \textit{we also know} \begin{cases} x=0\\ y=100 \end{cases}\implies 100=a(0+4)^2 (0+5)^2 \\\\\\ 100=a(16)(25)\implies \implies \cfrac{100}{(16)(25)}=a\implies \cfrac{1}{4}=a \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=\cfrac{1}{4}(x+4)^2 (x-5)^2~\hfill[/tex]

Check the picture below.

See below for the proof that ∠1 and ∠14 are supplementary angles

The attached diagram represents the missing information in the question.

The given parameters are:

The next step in the proof is as follows:

∠2 and ∠14 are corresponding angles.

This means that:

∠2 = ∠14

Recall that:

∠1 and ∠2 are supplementary angles

This means that:

∠1 + ∠2 = 180

Substitute ∠2 = ∠14

∠1 + ∠14 = 180

Supplementary angles add up to 180

Hence, ∠1 and ∠14 are supplementary angles

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Answer:

Step-by-step explanation:

the answer is D

The equation is x² + 11x = 12. Here x represents the width of the decorative border and no, it is not reasonable to be 2.5 inches wide.

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

We have an area of border  48 square inches.

Menu dimensions without border =  13-inch by 9-inch

The area of the border can be expressed by the equation:

area of border = area of rectangle with border—area of rectangle without

                            border

48 = (13 + 2x)(9 + 2x) - 13×9

[tex]\rm 48=4x^2+44x[/tex]

After simplification:

[tex]\rm 4x^2+44x-48=0[/tex]

or

x² + 11x = 12

Find the solution of the above quadratic equation:

x = 1 or x = -12(width cannot be negative)

Width should be 1 inches.

We have given x = 2.5 it is not reasonable for the border to be 2.5 inches wide. Due to the cost of printing, the border should have an area of 48 square inches.

Thus, the equation is x² + 11x = 12 here x represents the width of the decorative border and no, it is not reasonable to be 2.5 inches wide.

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Answer:

x=6.18

Step-by-step explanation:

[tex]sin(31) = \frac{opp}{hyp} \\ \frac{0.52}{1} = \frac{x}{12} \\ \\ x = 12(0.52) \\ x = 6.18 [/tex]

Answer: ~96.83°

Step-by-step explanation:

1) It's obvious that the largest angle is the opposite to the largest side.

▪︎ QR = 18 (the largest side)

=> <QPR is the largest angle

2) Cosine Rule:

▪︎ QR^2 = QP^2 + PR^2 - 2*QP*PR*cos(QPR)

▪︎ 18*18 = 13*13 + 11*11 - 2*13*11*cos(QPR)

▪︎ 324 = 169 + 121 - 286*cos(QPR)

▪︎ 34 = -286*cos(QPR)

▪︎ cos(QPR) = -34/286

▪︎ <QPR = arccos(-34/286) = 96.827...°

The value of the digit 5 in the tenths place of 3.545 is 100 times the value of the digit 5 in the thousandths place.

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

We have:

Evan has a bag of apples that weighs 3.545 pounds.

The value of the digit 5 in the tenths place of 3.545 is 0.500

The value of the digit 5 in the thousandths place of 3.545 is  0.005

Take the ratio of both values:

tenths place value/thousandths place value =  0.500/0.005

tenths place value/thousandths place value =  100

tenths place value = 100(thousandths place value)

Thus, the value of the digit 5 in the tenths place of 3.545 is 100 times the value of the digit 5 in the thousandths place.

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Answer:

  5x -4y = 4

Step-by-step explanation:

An equation for the perpendicular line can be found by swapping the x- and y-coefficients, and negating one of them. The constant changes to a value so that the equation is satisfied at the given point.

__

Swapping the coefficients gives us ...

  5x +4y = c . . . . . for some constant c

Negating the y-coefficient (so the x-coefficient remains positive) gives ...

  5x -4y = c

Putting (x, y) = (-4, -6) into the equation gives us the value of c:

  5(-4) -4(-6) = c

  -20 +24 = c = 4

The line perpendicular to the given line and through the point (-4, -6) will have equation ...

  5x -4y = 4

Answer:

250.000$

Step-by-step explanation:

so you multiple 2.000 by 25

Answer:

g= 6.5

Step-by-step explanation:

O.25(g+1.5) = 2

(g+1.5) = 2/0.25 divide both sides with 0.25

g+1.5 = 8

g = 8-1.5

g = 6.5

[tex]~~~~~~\dfrac{3x+15}{6-x} = 0\\\\\implies 3x +15 = 0\\\\\implies 3x = 0-15\\\\\implies 3x = -15\\\\\implies x = -\dfrac{15}3\\\\\implies x = -5[/tex]

Answer:

the answer=  -5

Probability that the mean childhood asthma prevalence for the sample is greater than 2.6% is 0.0357 or 3.57 %.

What is Probability ?

Probability is the measure of likelihood of an event.

For a Normal Distribution ,

the z-score formula is given by

[tex]\rm Z = \dfrac{X - \mu }{\sigma}[/tex]

Here [tex]\rm \mu\\[/tex] is the mean and [tex]\rm \sigma\\[/tex] is the standard deviation .

It is the measure of the deviation of the data from its central tendency.

Each z-score has a probability value.

It is given in the question that

Mean of 2.16% =  [tex]\rm \mu\\[/tex] = 2.16

Standard deviation of 1.36% means that  [tex]\rm \sigma\\[/tex] = 1.36

For Sample of 31 the value of standard deviation is [tex]\rm s = \dfrac{\sigma}{\sqrt{n}}[/tex]

s = 1.36/√31

s = 0.2442

Substituting the values

Z = (2.6 -2.16)/0.2442

Z =1.8

the p value from the graph of z and p , 0.9643

To determine value of probability  more than X is 1 - 0.9643= 0.0357

the

Probability that the mean childhood asthma prevalence for the sample is greater than 2.6% is 0.0357.

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Answer:

Domain = [0 , +∞)

Step-by-step explanation:

since r is the radius of a circle

Then

r must be a positive number.

Then

r ≥ 0

NOTE : if r = 0 ,then the circle reduces to a point .

Answer:

x = 29.44

Step-by-step explanation:

[tex]tan31^{o} =\frac{x}{49}[/tex]

[tex]x=49tan31^{o}[/tex]

[tex]x=29.44[/tex]

Hope this helps

Answer:

[tex]\large\text{$ f(-2.2)=1 $}[/tex]

Step-by-step explanation:

Given function:

[tex]\large\text{$ f(x)=\left\lceil x \right\rceil+3 $}[/tex]

This is a Ceiling Function, denoted by the square brackets [ ] with the bottom part missing.

When graphing a Ceiling Function:

The Ceiling Function gives us the nearest integer up.

So the ceiling of x = -2.2 is -2,  as the greatest integer that is more than (or equal to) -2.2 is -2

Therefore:

[tex]\large\begin{aligned}f(-2.2) & =\left\lceil -2.2 \right\rceil+3\\& = -2+3\\& = 1\end{aligned}[/tex]

This is confirmed when using the graph to solve.

To find f(-2.2), locate x = -2.2 on the graph.  

Trace up vertically until a step is reached. 

The step in this part is not including -3 and including -2, so this confirms that x = -2.2 is in this interval.  

Trace along horizontally to the y-axis to find the corresponding y-value, which is 1.  

Therefore, f(-2.2) = 1

Let's see

[tex]\\ \rm\Rrightarrow f(x)=[x]+3[/tex]

[tex]\\ \rm\Rrightarrow f(-2.2)[/tex]

[tex]\\ \rm\Rrightarrow [-2.2]+3[/tex]

[tex]\\ \rm\Rrightarrow -2+3[/tex]

[tex]\\ \rm\Rrightarrow 1[/tex]

So

Answer:

1.B

2.A

3.B

4.(not sure)

5. C

Step-by-step explanation:

Give brainliest please!

Hope this helped :)

Check the picture below.

so the pyramid is really 4 triangular faces with a base of 6 and a height of 7, and a 6x6 square at the bottom.

[tex]\stackrel{\textit{\LARGE Areas}}{\stackrel{\textit{four triangular faces}}{4\left[\cfrac{1}{2}(\stackrel{b}{6})(\stackrel{h}{7}) \right]}~~ + ~~\stackrel{square}{(6)(6)}}\implies 84~~ + ~~36\implies 120~yd^2[/tex]

Answer:

127.38

Step-by-step explanation:

The surface area formula for a square pyramid is:

A = a^2 + 2a * sqrt[ (a^2 / 4 ) + h^2 ]

So we input the base height as the a value, and the slant as H)

A = 6^2 + 2(6) * sqrt[ (6^2 / 4 ) + 7^2 ]

When using the exponents we get:

A = 36 + 2(6) * sqrt[ (36) / 4 ) + 49 ]

Then multiply/divide:

A = 36 + 12 * sqrt[ (9) + 49 ]

Then add the value in the sqrt.

A = 36 + 12 * sqrt[ 58 ]

Now, if we find the sqrt of 58, we get:     sqrt[ 58 ] ≅ 7.615

A = 36 + 12 * 7.615

When multiplying we get:

A = 36 + 91.38

Finally, after adding, the surface area of the square pyramid is:

A = 127.38