Solve for the given variables

Answer:

346 + 360k

You can get coterminal angles by adding intervals of 360 degrees

The age of Maggie is 9 years and her brother whose age 3 years less than four times Maggie's age is 33 years old.

What is age?

Age is the difference in days, months, and years between the day, month, and year of birth and the day, month, and year of the event, expressed in the largest completed unit of solar time, such as years for adults and children and months, weeks, days, hours, or minutes of life, as appropriate, for infants under one year of age (Gregorian calendar).

Let the ages of Maggie and her brother be X and Y.

There are two condition given in the question through which we can form a system of equation containing two equations.

First condition: The sum of their ages is 42.

Therefore,

X + Y = 42

Second Condition: Maggie's brother is 3 years younger than four times her age.

Therefore,

4X - 3 = Y

We get the system of equation:

X + Y = 42

4X - 3 = Y

Solving this system of equation

4X - 3 = Y

4X - 3 = 42 - X

X = 45/5

X = 9

Putting the value of X in one of the equation:

Y = 42 - X

Y = 42 - 9

Y = 33

Therefore, age of Maggie is 9 years and age of her brother is 33 years.

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Side of cube = 8 ft

Volume of cube = Side x Side x Side

Volume of cube = 8 x 8 x 8

Volume of cube = 512 feet^3

A cylinder with diameter 8feet is cute form the cube

Height of cylinder = Side of cube

Height of cylinder = 8 feet

Diameter of cylinder = 8 feet

Radius of cylinder = 4feet

The volume of resulting shape = Volume of cube - Volume of cylinder

Volume of resulting shape = 512 - 401.92

Volume of resulting shape = 110.08 ft^3

Answer: 110.08 ft^3

Answer:

0.26599

Step-by-step explanation:

We will assume a normal distribution for the salaries

We have the following information

Mean μ = 64000

Standard deviation σ = 6400

And we are asked to find P(X < 60000)

First find the z score corresponding to X = 60000

The z score is given by (X - μ) / σ

z score for 60000 with μ = 64000 and σ = 6400 is

z = (60000 - 64000)/6400
z = -40000/6400 = -0.625

We can either look up the P value from the z-tables or simply use a calculator

P(X < 60000)  and this works out to 0.26599

Let 'a' represent the unknown side of the triangle.

To solve for the unknown side, we will apply the Pythagoras theorem.

Let solve for cscθ

Let us solve for cosθ

Let us solve for tanθ

Remember the following transformations of a function:

This transformation stretches the function over the vertical axis if c>1 and shrinks it if 0

If c is positive, the orientation is mantained, and if c is negative, the function is also flipped over (it shrinks if -1

This transformation moves the function vertically c units. It goes up if c>0 and down if c<0.

Therefore, starting with the absolute value function:

Multiply the function by 2:

Since 2>1, then this is a vertical stretching by a factor of 2.

Next, add 1:

This will translate the stretched absolute value function one unit upwards.

Therefore, the complete description of the transfromation would be:

Is a vertical stretching of the absolute value function by a factor of 2, translated 1 unit upwards.

f(x) = 5x - 7

g(x) = -2x + 9

g(f(x)) = -2(5x -7) + 9 = -10x + 14 + 9 = -10x + 23

g(f(x)) = -10x + 23

Answer:

Option A: -10x + 23

Answer:

-1, 0

Step-by-step explanation:

Hello!

We can test each solution for by substituting the value for x, and see if the inequality is true.

This inequality is true.

This inequality is not true because 12/7 is greater than 1.

This is inequality is true.

This inequality is not true because 27/12 is greater than 1.

The solutions that work are -1 and 0.

Answer: A

Step-by-step explanation:

Following the instructions provided, we shall use a graphing calculator (Desmos) to determine the equation of the circle shown by the "colorful people."

The first step is to determine the radius which we can observe from the circle itself, whose diameter spans from 0 units to 10 units along the x-axis. The radius therefore is 5 units (half of the diameter).

Observe also that the center has now moved away from the origin (0, 0), and if we move the slider very carefully for h, that would be 5 units away from the origin towards the right (along the x-axis), andk would be 7 units away from the origin) towards the bottom (along the y-axis).

After following these steps, we can replicate the circle given in the question and if we now substitute the values of h, k and r into the equation of a circle, we would end up with;

The arrows indicate that the graph of the function continues beyond what can be seen in the image.

Notice that the graph does not appear to have asymptotes; then, the domain of the function is:

And the range is:

Since the graph seems to continue towards the +y-direction and the -y-direction

Finally, notice that for each value of x, the graph has only one value of y. This is the key characteristic of a function; the graph is a function.

Answer:

when rounding the answer it shouldn't be the exact answer so add or multiply then once you find your product round it off and add a decimal

SIMPLIFY  THE EQUALITY FIRST

[tex]3x \leqslant - 2 + 5 \\ 3x \leqslant 3 \\ \frac{3x}{3} \leqslant \frac{3}{3} \\ x \leqslant 1[/tex]

X CAN BE ALL THE NUMBERS LESS OR EQUAL TO 1

IN THE PICTURE THE ONLY OPTION THAT CONTRAST THE INEQUALITY IS OPTION B BECAUSE IT IS GREATER THAN 1.

HOPE THIS HELPS

Answer:

option B

Step-by-step explanation:

3x - 5 ≤ -2

add 5 to both sides

3x - 5 + 5 ≤ -2 + 5

3x ≤ 3

divided both sided by 3 to get x alone

3x/3 ≤ 3/3

x ≤ 1

option B is the only choice that is above 1.01 making it not a solution

Answer:

0

Step-by-step explanation:

2(3x -1)  + 2(4x + 5) = 8  Distribute the 2's

2(3x) + 2(-1) + 2(4x) + 2(5) = 8

6x - 2 + 8x +10 = 8  Combine like terms

14x + 8 = 8    Subtract 8 from both sides of the equaion

14x = 0  Divide both sides by 14

x = 0

Part b.

If we want to dilate a figure we simply multiply each x- and y-coordinate with the scale factor we want to dilate with. Therefore:

Factor of 3

Multiply:

Answer:

Answer: .25x + 75.00 = C(x)

Step-by-step explanation:

First, find the slope of the line using the slope formula:

Provided two points (a,A) and (b,B) on a line, its slope is given by:

For the points (-6,7) and (4,-2), we have:

The equation of a line in slope-intercept form, of a line with slope m and y-intercept b is:

Substitute m=-9/10 and the coordinates of one point to find the y-intercept. Use, for instance, the point (-6,7):

Substitute b=8/5 and m=-9/10 to find the equation of line Q:

Given that the illuminator 100 plus bulb movies onto larger screen farther away as shown in the diagram attached then;

Illuminator 100 plus bulb

It movies onto screens ;

108 ft wide

180 ft away from the projector

Illuminator 100 bulb

81 ft wide

? : from the projector

Here apply the idea of similarity ratios where;

The ratio

The required sample size of the given estimate is 3030.65.

Given that,
The population standard deviation is approximately σ = 50.2. You would like to be 90% confident that your estimate is within 1.5 of the true population mean.

Statistics is the study of mathematics that deals with relations between comprehensive data.

Here,
For the 90% confidence the value of the z = 1.645
Now the sample size is given as,
n = [z × σ/1.5]²
Substitute values in the above equation,
n = [1.645×50.2/1.5]²
n = 3030.65

Thus, the required sample size of the given estimate is 3030.65.

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Answer:

  ∡BOA ≅ ∡DOC

Step-by-step explanation:

Given a circle O with congruent chords BA and DC, you want the relation between angles BOA and DOC.

All of the radii of circle O are congruent. That means BO≅AO≅DO≅CO. The chords BA and DC are marked as congruent. This means ∆BOA and ∆DOC are congruent by the SSS postulate.

Corresponding parts of congruent triangles are congruent, so ...

  ∡BOA ≅ ∡DOC

Given:

Frank knows that his first four test grades were 74, 76, 77, and 84

We will find Frank's grade on the fifth test if his test average is 80.6.

So, let the fifth grade = x,

The average is the sum of the grades over the number of the grades

So,

Solve the expression to find x:

So, the answer will be: the fifth grade = 92

The given expression is

Since sec is the opposite of cosine, then

Since the value of cos(3pi/2) is 0, then

Since 1/0 is an undefined value, then

The answer is undefined

Answer:

(x,y)->(x+4,y-5)

Step-by-step explanation:

Find a set of common points first, for example, A and A', or B and B'
Then, find the coordinates of the two points. I'm choosing B and B'.
B: (1,8) x = 1, y = 8
B':(5,3) x = 5, y = 3
from B to B', we see that the x increases by 4 and the y decreases by 5. So, the third option, (x,y)->(x+4,y-5) is correct

In order to calculate the area of carpet needed to cover the entire floor, we just need to calculate the area of the room.

The area of a rectagle is calculated by the product of its dimensions, so we have:

So the area of carpet needed is 132 square feet.

Given:-

To find the volume of cone.

So the volume formula for cone is,

Substituting we get,

So the required solution is 190.76

The quotient of 7.7 x 10^8 and 5.5 x 10^2 expressed in scientific notation is 1.4x10^6.

What is quotient?

A quotient in mathematics is the amount created by dividing two numbers. The term "quotient" is used frequently in mathematics and is used to describe the integer component of a division (when Euclidean division), as well as a fraction or a ratio (when proper division). A quotient in the second sense is only the proportion of a dividend to its divisor.

Lets calculate the quotient for the value given in question:

[tex]7.7 \times 10^8[/tex]

[tex]5.5 \times 10^2[/tex]

Now we divide the 7.7 by 5.5

[tex]\frac{7.7}{5.5} = 1.4[/tex]

we get value 1.4.

on dividing  [tex]\frac{10^8}{10^2}[/tex] we get, [tex]10^6[/tex]

Combining both the value, we get

quotient = [tex]1.4 \times 10^6[/tex]

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Answer:

y = 24x + 17 20

Step-by-step explanation:

Firstly, let's say that 153 and 17 are both the y-intercepts of their respective equations, while 22 and 24 are the slope. With this we can create the following set of equations:

y = 24x + 17

y = 22x + 153

So your answer would be y = 24x + 17

Now let's find the sales answer!

Since we know that Ida made 4 more sales than Wade this week, we could say:

y = 24(x+4) + 17

y = 22x + 153

Now since we know that they earned the same amount we can do the following:

24(x+4) + 17 = 22x + 153

Simplify...

24x + 96 + 17 = 22x + 153

Simplify again:

24x + 113 = 22x + 153

subtract 22x and 113 from both sides...

2x = 40

Then:

x = 20

So this means that Wade made 20 sales this week!

So let's check if we are right:

Now that we know that x = 20, we need to plug it into Wade's equation!

y = 22(20) + 153

y = 440 + 153

y = 593

Wade made $593 this week!

To check if we are right, let's plug it into Ida's equation:

y = 24x + 113

y = 24(20) + 113

y = 480 +113

y = 593

Ida also made $593 this week!

MEANING we are right!

I hope I helped :P

We a figure is being reflected over the y-axis, the y-coordinates of its point will not change. However, the x-coordinates will be multiplied by -1.

Given points of the figure:

Point A: -5,-2

Point B: -4,-4

Point C: -6,-4

Let's now determine the new points of the figure once reflected over the y-axis.

Point A: -5,-2 ➜ Point A': (-5)(-1),-2 = 5,-2

Point B: -4,-4 ➜ Point B': (-4)(-1),-4 = 4,-2

Point C: -6,-4 ➜ Point C': (-6)(-1),-4 = 7,-4

Looking at the

BD= 12

BC=7

Is this from a graded quiz?

The correct inequality sign for the first number expression is > and for the second number, the expression is <.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

The mixed fractions are:

-19 5/6 = -119/6 = -19.83

-20 1/6 = -121/6 = -20.166

-19 5/6 > -20 1/6

|-19 5/6| = |-119/6| = 19.83

|-20 1/6| = |-121/6| = 20.166

|-19 5/6| < |-20 1/6|

Thus, the correct inequality sign for the first number expression is > and for the second number, the expression is <.

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