what is this expression in simplified form?

Check the picture below.

Make sure your calculator is in Degree mode.

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 .

#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:

1260 inches

Step-by-step explanation:

Calculator

∠IKL and ∠IKC and ∠DLH and ∠JLD are pairs by the Transitive Property of Congruency.

This states that, if a pair of lines or angles or triangles are said to be congruent to a third line or angle, therefore, the first line or angle or triangle is said to be congruent to the third line or angle.

∠IKL and ∠IKC and ∠DLH and ∠JLD are pairs by the Transitive Property of Congruency. because the two angles and the other side of the angle/triangle are said to be equal to two angles and other side of the other triangle.

∠IKC ≅ ∠JLD, so m∠IKC = m∠JLD  and as such angle is Applying the  Transitive Property of Congruency because  if A =b, and b = c then A = c and therefore, the above is true.

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Answer:

38.1971

Step-by-step explanation:

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

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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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:

[tex]x > - 1 \\ the \: answer \: is \: {d}[/tex]

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

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:

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:B

Step-by-step explanation:

"the quantity of can be ignored".

(x+4)/3=2

(x+4)=6

x=2

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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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

The sum of supplementary angles is 180 degrees. The measure of angle 7 is 48 degrees

The sum of supplementary angles is 180 degrees.

Let the supplement of the angle be "x", so that;

x + 132 = 180

Subtract 132 from both sides

x + 132 - 132 = 180 - 132
x =. 180 - 132
x = 48 degrees

Hence the measure of angle 7 is 48 degrees

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The conclusion drawn is not valid. This is as a result of the fact that the sample is inappropriate.

We are told that a restaurant is analyzing its customer satisfaction level. Now, the conclusion drawn was that most of the customers are satisfied with the service they receive.

Now, we can say that the conclusion drawn is not valid. This is as a result of the fact that the sample is inappropriate as it does not deal with the actual response from the customers but only observational.

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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:

The first option.  See attachment.

Step-by-step explanation:

Explained on attached image.

The total volume of the wedding cake would be 620 in³.

A rectangular prism is a three-dimensional shape. It also known as a cuboid.

Volume = length x width x height

The volume of the cake is the sum of the volume of the three layers.

Volume of the first layer = 2 1/2 x 12 x 10

5/2 x 12 x 10 = 300 in³

Volume of the second layer = 2 1/2 x 10 x 8

5/2 x 10 x 8 = 200 in³

Volume of the third layer = 2 1/2 x 8 x 6

= 5/2 x 8 x 6 = 120 in³

Total volume = 300 + 200 + 120 = 620 in³

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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.

[tex] \begin{gathered}\\ \large\dashrightarrow\mathsf { \: \: 5 < b = 6 \: \: \: or \: \: \: b - 5 = 6 } \\ \end{gathered}[/tex]

[tex] \begin{gathered}\\ \large\dashrightarrow\mathsf { \: \: b - 5 = 6 } \\ \end{gathered}[/tex]

[tex] \begin{gathered}\\ \large\dashrightarrow\mathsf { \: \: b = 6 + 5 } \\ \end{gathered}[/tex]

[tex] \begin{gathered}\\ \large\dashrightarrow \: \: \underline{ \boxed{\mathbf \red{ \: \: b = 11 \: \: }}} \\ \end{gathered}[/tex]

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

[tex]\begin{gathered}\begin{gathered}\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \small \color{blue}{ \underline{\boxed{ \begin{array}{cc} \small \underline{\underline{\bf{ \color{red}{{ \orange \bigstar \: MᴏʀE \: IᴅᴇɴᴛɪᴛɪᴇS \: \orange \bigstar}}}}} \\ \\ \: \frak{ {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} }\:\\ \\ \: \frak{ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} }\:\\ \\ \: \frak{ {x}^{2} - {y}^{2} = (x + y)(x - y)}\:\\ \\ \: \frak{ {(x + y)}^{2} - {(x - y)}^{2} = 4xy}\:\\ \\ \: \frak{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}\:\\ \\ \: \frak{ {(x + y)}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y)}\:\\ \\ \: \frak{ {(x - y)}^{3} = {x}^{3} - {y}^{3} - 3xy(x - y) }\:\\ \\ \: \frak{ {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )}\: \\ \: \end{array} }}}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered} \: \: [/tex]

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

^०^

Answer:

Step-by-step explanation:

We'll look for a line with the form of y = mx + b, where m is the slope and b is the y-intercept (the value of y when x = 0).

A parallel line will have the same slope as the reference line,  For y=3x-8, the slope is 3.  We can write:

y =3x + b for the new line.  We need a value of b that will cause the line to include point (6,-4).  To find a b that will work, simple use the given point in the above equation and solve for b:

y =3x + b

-4 =3(6) + b  for (6,-4)

-4 =18 + b

b = -22

The parallel line that goes through point (6,-4) is y = 3x - 22

See the attached graph.

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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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 translated vertices are:

The vertices of the original figure are:

Now we want to apply a translation of four units to the right and 2 units down, then each point (x, y) becomes (x + 4, y - 2).

This means that the translated vertices are:

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