Describe the shape, orientation, and vertex of
each parabola relative to the graph of y=x².
Sketch each graph.
a) y=-0.5x² + 2
c) y = -0.1x² - 6
e) y=-3x²-5
g)y=8x²+4
b) y = 2x²
d)y=x²+4
f) y=0,1x² +2
h) y=-0.7x²-3

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

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

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;

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:

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

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

Step-by-step explanation:

Given

While sailing a boat offshore, Bobby sees a lighthouse and calculates that

the angle of elevation to the top of the lighthouse is 3°.

When she sails her boat 700 m closer to the lighthouse, she finds that the angle of elevation is now 5°.

To find:

How tall, to the nearest tenth of a meter, is the lighthouse?

Explanation:

It is given that,

While sailing a boat offshore, Bobby sees a lighthouse and calculates that

the angle of elevation to the top of the lighthouse is 3°.

When she sails her boat 700 m closer to the lighthouse, she finds that the angle of elevation is now 5°.

That implies,

Also,

Therefore,

Then,

Hence, the height of the light house is, 91.5m.

Solution

a + b = (-2, -1)

Using Parallelogram method

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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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

BD= 12

BC=7

Is this from a graded quiz?

The mean absolute deviation is 2.5.

The average distance between each data value and the mean is known as the mean absolute deviation (MAD) of a data collection. A measure of variance in a data collection is the mean absolute deviation. We may determine how "spread out" the values in a data collection are by looking at the mean absolute deviation.

How to calculate the mean deviation from the mean:

Given data:1, 1, 3, 5, 5, 6, 8, 11

So, mean of the data is

= 1+ 1 +3 +5 +5+ 6+ 8 +11 / 8

= 40 /8=

5

Now, Mean absolute deviation is

= | 1-5| + |1-5| + |3-5 | + |5-5| + |5-5| + |6-5| + |8-5| + |11-5|/ 8

= 4 + 4 + 2+ 0 + 0+ 1 + 3 +6 /8

= 20/8

=2.5

Hence, the mean absolute deviation is is 2.5.

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Answer:

4x>13

Step-by-step explanation:

4 × X=4x

>=more than symbol

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

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.

a) Perimeter =  17.4 cm

b) Perimeter   =210.6 cm

How are the perimeters calculated?

a) The perimeter of an irregular polygon = Sum of all the sides of the polygon.

Converting value of all sides to centimetres.

Perimeter = 3.4 +3.2 +4.3 +3.7+2.8

                 = 17.4 cm

b) The perimeter of an irregular polygon = Sum of all the sides of the polygon.

Converting value of all sides to centimetres.

Perimeter = 29.1+25.3+30+28.6+32.6+36.5+28.5

                 =210.6 cm

What is the perimeter of a polygon?

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Hello there. To solve this question, we have to remember some properties about conversion of values.

1. How many 2-liter bottles of soda will you need to fill ten 500 mililiter containers?

First, multiply the number of containers by its capacity, that is

Notice that 1000 mililiters is equivalent to 1 liter, hence

To fill these containers with 2-liter bottles of soda, you'll need at least 3 bottles.

The answer to the first question is 3.

2. How many mililiter are 1/5 liter?

Considering 1 liter = 1000 mililiters, we have that

Hence the answer to this question is 2. 200

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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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:

Step-by-step explanation:

You have to assume each roll is independent. The probability of rolling a fair die is 1/6. When you roll the die, you only care about 2,4,5, and 6 since you do not want to get 1 or 3. So the probability is of getting a 2,4,5 and 6 is 4/6.

You could of also see it as the probability of NOT getting a 1 or 3 is:

[tex]1-\frac{2}{6} =\frac{4}{6}=\frac{2}{3}[/tex]

Now you roll the die 4 times with each success being 2/3

[tex]\frac{2}{3} \cdot \frac{2}{3} \cdot \frac{2}{3} \cdot \frac{2}{3} =(\frac{2}{3})^4=.197530864[/tex]

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

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

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:

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

A non-zero matrix A with A² = 0 is A = [tex]\left[\begin{array}{cc}0&1\\0&0\end{array}\right][/tex].

We need to find a 2 x 2 non- zero matrix with A² = [tex]\left[\begin{array}{cc}0&0\\0&0\end{array}\right][/tex]

A² = A x A

If A = [tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right][/tex], then A x A =  [tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right][/tex] x  [tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right][/tex]

                                          = [tex]\left[\begin{array}{cc}a^2+bc&ab+bd\\ac+dc&bc+d^2\end{array}\right][/tex]

This is called matrix multiplication.

Now consider the matrixes of the form A = [tex]\left[\begin{array}{cc}0&x\\0&0\end{array}\right][/tex]

Then A² =   [tex]\left[\begin{array}{cc}0&x\\0&0\end{array}\right][/tex]  x  [tex]\left[\begin{array}{cc}0&x\\0&0\end{array}\right][/tex]

              =  [tex]\left[\begin{array}{cc}0&0\\0&0\end{array}\right][/tex]

Also Consider a matrix A = [tex]\left[\begin{array}{cc}0&0\\x&0\end{array}\right][/tex]

Then A² =    [tex]\left[\begin{array}{cc}0&0\\x&0\end{array}\right][/tex] x  [tex]\left[\begin{array}{cc}0&0\\x&0\end{array}\right][/tex]

              =  [tex]\left[\begin{array}{cc}0&0\\0&0\end{array}\right][/tex]

So any matrix of the form  [tex]\left[\begin{array}{cc}0&x\\0&0\end{array}\right][/tex] and   [tex]\left[\begin{array}{cc}0&0\\x&0\end{array}\right][/tex] with x any number, will give A² = 0

In particular, A =  [tex]\left[\begin{array}{cc}0&1\\0&0\end{array}\right][/tex] is a non-zero matrix with A² = 0.

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Answer:

346 + 360k

You can get coterminal angles by adding intervals of 360 degrees

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

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:

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.