verbally explain how to obtain the graph of the quadratic function f(x)=-2(x+3)^2-4 from the graph of y=x^2.

If lines A, B and C shows proportional relationships, then the line A has a constant of proportionality between y and x is 5

Given the line A, B and C

The constant of proportionality is the ratio of the y coordinates to the x coordinate

k = y /x

Where k is the constant of proportionality

Consider the line A

One point on the line = (1, 5)

Constant of proportionality K = 5/1

= 5

Consider the line B

One point on the line = (3, 5)

Constant of proportionality k = 5/3

Consider the line C

One point on the line = (7, 5)

Constant of proportionality = 5/7

Therefore, the line A has the constant of proportionality of 5

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The given question is incomplete, the complete question is

Lines A, B, and C show proportional relationships. Which line has a constant of proportionality between y and x of 5?

Using the function rule, the value of g(r +2)  is r-2

Given the function rule g(k) = k-4.

Then g(r + 2)  can be found by replacing k with r+2 in the function g(k):

g(r+2) = r + 2 - 4

           = r - 2

Therefore, g(r+2) gives r - 2 when evaluated using the function rule.

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Answer:

66

Step-by-step explanation:

On a hot summer day, you visit an ice cream shop that offers 15 ice cream flavors, 3 types of cones, and 8 toppings. If you want one ice cream flavor, one cone, and one topping, there are a total of 360 possible combinations you can create.

To find the total number of possible combinations, you simply multiply the number of options for each category. In this case, you have 15 ice cream flavors, 3 types of cones, and 8 toppings.

So, the total combinations would be: 15 (flavors) × 3 (cones) × 8 (toppings) = 360 possible combinations. You can create 360 different ice cream combinations at the shop on a hot summer day.

This is calculated by multiplying the number of ice cream flavors (15) by the number of cone types (3) and the number of toppings (8), which equals 360. So, there are plenty of delicious options to choose from to cool off on a hot summer day.

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To implement the Boolean expression F(x,y,z) = xyz + (y′ + z) using a combinational circuit, we can use two AND gates and one OR gate.

To draw the combinational circuit that directly implements the Boolean expression F(x, y, z) = xyz + (y′ + z), follow these steps:
1. Identify the individual terms in the expression: xyz and (y′ + z).
2. Draw an AND gate for the term xyz:
  - Connect the input lines of the AND gate to x, y, and z.
3. Draw an OR gate for the term (y′ + z):
  - To obtain y′, connect an input line from y to a NOT gate.
  - Connect the output of the NOT gate and an input line from z to the input of the OR gate.
4. Combine the results from steps 2 and 3 with an OR gate:
  - Connect the outputs of the AND gate and the OR gate from steps 2 and 3 to the input lines of a final OR gate.
5. The output of the final OR gate is the function F(x, y, z).
In summary, the combinational circuit consists of 1 AND gate, 2 OR gates, and 1 NOT gate arranged as described above to directly implement the given Boolean expression.

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Answer: 3/5

Step-by-step explanation:

Two parallel lines means that the slope is constant but the y-intercept must vary. In this case, simplifying the equation gives us y = 3/5x + 10, therefore, if the line is requested to be parallel, the slope should be 3/5.

(I think)

im pretty sure its \(m=-\frac{5}{3}\)

Step by step :

Find the negative reciprocal of the slope of the original line.

Answer:

21:15... Simplified is 7:5

Step-by-step explanation:

This is the simplified answer. I hope this helps!

Answer:

D

Step-by-step explanation:

Rolling a die and getting a certain number will not change the chances of you getting the same number a second time. A normal die will always have a 1/2 chance of rolling an even number. However, the other answer choices will make the likelihood of getting the same type of event again slimmer as you remove one of the objects from being chosen again. An example for the first option would be drawing an ace from a deck of 52 cards where you only have 4 aces, so the chance on the first draw would have been 4/52 or a 7.7% chance while the next draw will be a 3/51 or 5.9% chance.

The equations can be solved in the following manner. As shown below.

The equations can be solved in the following manner. As shown below.

1.  Multiplication Property of Equality

10a + 35b = 0, 21a - 35b = 217            

2.  Addition Property of Equality

31a = 217

3.  Division Property of Equality

a = 7

4.  Substitution Property of Equality

2(7) +7b = 0

5.  Simplify

14 + 7b = 0

6.  Subtraction Property of Equality

7b=-14

7.Division Property of Equality

b= -2

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Answer:

B. Exactly one solution

Step-by-step explanation:

Answer:

20 inches

Step-by-step explanation:

Step 1: Subtract the total from what was left

\(95 - 15 = 80\)

Step 2: Divide the result into the 4 pieces

\(80 \div 4\)

\(=\frac{80}{4}\)

\(= 20\)

Each of the four pieces Lily cut was 20 inches.

Answer:

x=18

Step-by-step explanation:

Being that the angles are corresponding they are going to equal the same thing.

(7x+7)=133

Now just follow the laws of PEMDAS

7x+7=133

-7 -7

7x=126

÷7 ÷7

x=18

The cost of the tabletop is $251.10. Option C

The formula for calculating the area of a rectangle is expressed as;

Area = lw

Such that the parameters are;

From the diagram shown, we have;

The width = 6 3/4 feet = 27/4 feet

The length = 3 feet

Substitute the values

Area = 27/4 × 3

Multiply

Area = 20. 25 square feet

But;

1 square foot = $12.40

Then  20. 25 square feet = x

x = $251. 10

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Answer:

∠ C

Step-by-step explanation:

sin C = 14 / 50 = 7 / 25

Answer:

<C

Step-by-step explanation:

7/25 = 14/50

sin X = opp/hyp = 14/50

opp = 14

The angle whose opposite leg is 14 is <C.

Answer: <C

The dimensions of the can that minimize the cost of the material are approximately:

Radius (r) ≈ 6.324 cm

Height (h) ≈ 3.984 cm

To determine the dimensions of the can that minimize the cost of the material, we need to find the dimensions that minimize the surface area of the can.

Let's assume the can has a height of h and a radius of r.

The volume of a cylinder is given by:

V = πr²h

Given that the can should hold 500 cubic centimeters of liquid, we have:

500 = πr²h

We want to minimize the cost, which depends on the surface area of the can.

The surface area of the can is the sum of the areas of the top, bottom, and side surfaces.

The cost of the top and bottom surfaces is twice as expensive per square centimeter as the sides.

Let's assume the cost per square centimeter of the sides is c, so the cost per square centimeter of the top and bottom surfaces is 2c.

The surface area of the sides of the cylinder is given by:

A_sides = 2πrh

The surface area of the top and bottom surfaces (each) is given by:

A_top_bottom = 2πr²

The total surface area (cost) is given by:

Cost = 2(2c)A_top_bottom + cA_sides

= 4cπr² + 2c(2πrh)

= 4cπr² + 4cπrh

To minimize the cost, we need to minimize the surface area. To do this, we can express the surface area in terms of a single variable, such as the radius (r) or the height (h).

From the volume equation, we have:

h = 500 / (πr²)

Substituting this value of h into the surface area equation, we get:

Cost = 4cπr² + 4cπr(500 / (πr²))

= 4cπr² + 2000c/r

Now, we can take the derivative of the cost function with respect to r, set it equal to zero, and solve for r to find the critical points:

dCost/dr = 8cπr - 2000c/r² = 0

8cπr = 2000c/r²

8πr³ = 2000

r³ = 250 / π

r ≈ 6.324

Now, we can substitute this value of r back into the equation for h:

h = 500 / (π(6.324)²)

≈ 3.984

So, the dimensions of the can that minimize the cost of the material are approximately:

Radius (r) ≈ 6.324 cm

Height (h) ≈ 3.984 cm

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Answer:

Step-by-step explanation:c because I’m in college and Ik trust me

Answer:

A1 = 18

A(n) = A (n-1) -2

Step-by-step explanation:

N represents the number in a sequence and the difference in the sequence is -2 since each time the number is listed in the sequence it is divide by 2.

The rate of change of the functions are: I. -3 II. -1/4.

Therefore, C. Both functions are decreasing and have different rates of change.

The rate of change of any function can be calculated as = change in y / change in x.

If the rate of change is a negative number, the function is decreasing. If it is a positive number, the function is decreasing:

Rate of change of the line that passes through (3, 3) and (4, 0):

Rate of change = (0 - 3) / (4 - 3)

= -3/1

= -3 [this means the function is decreasing].

Rate of change of the function represented by the table, using two pairs of the table values, (0, -1) and (-4, 0):

Rate of change = (0 -(-1)) / (-4 - 0)

= 1/-4

= -1/4 [this shows the function is decreasing]

Therefore, the answer is: C. Both functions are decreasing and have different rates of change.

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Answer:

1/9

Step-by-step explanation:

4/12 x 4/12 = 1/9

Answer: 1/9

Step-by-step explanation: CORRECT ON EDMENTUM

If the approximate areas of Colorado and Hawaii are listed as Colorado: 2.7 x 105 square kilometers. The amount  larger is Colorado is: 2.417 x 10^5.

The first step is to divide the area of Hawaii by the area of Colorado and before we do that we must ensure that both of these figures have the same exponent.

So,

2.7 x 10^5 square km - 2.83 x 10^4 square km

2.83 x 10^4 = 0.283 x 10^5

Hence,

2.7 x 10^5 - 0.283 x 10^5

= 2.417 x 10^5

Therefore  Colorado is 2.417 x 10^5 square kilometers larger than Hawaii.

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Answer:

it’s -93

Step-by-step explanation:

The measure of center that is the most appropriate for this data set is option (A) mean.

Measure of center.

Measure of center refers a summary measure that attempts to describe a whole set of data with a single value that represents the middle or center of its distribution.

Given,

Here we have the data set and we need to find the measure of the center of the data.

Here we know that the given data are

=> 20, 6, 42, 13, 15, 10, 9, 12, 12

Now, we have to arrange the numbers from least to greatest, then we get the sequence as,

=> 6, 9, 10, 12, 12, 13, 15, 20, 42

While we looking into the given data, we have identified that the mean of this data set is 15.44 and the median is 12 and the mode is 12

Therefore, the given data is normally distributed, the correct measure of center is the mean.

So, the correct option is (A)

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The standard method for solving an equation like 3x + 5 = 26 is to use the Subtraction Property of Equality and then the Division Property of Equality.

Typically, the Subtraction Property of Equality is used first, followed by the Division Property of Equality, to solve equations like 3x + 5 = 26. According to the Subtraction Property of Equality, we can take away the same amount from each side of an equation without changing the answer. In this instance, we may get 3x = 21 by taking 5 off of both sides of the equation. The Division Property of Equality asserts that we can divide both sides of an equation by the same non-zero quantity without changing the result, which is the next strategy we can employ.

To obtain x = 7 in this situation, divide both sides by 3. Hence, x = 7 is the answer to the equation 3x + 5 = 26. This method is widely used because it is straightforward and easy to remember.

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The dimensions that maximize the area are, 96cm and 84cm.

What is area?

The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Let the height of poster be h and breadth be b,

bh = 15630cm square........(1)

Height of the printed area=h-10-10 = h - 20

(decrement of 10 from top and bottom)

the breadth of the printed area b-6-6 = b-12

(decrement of 9 from both sides)

for maximum printed area:

A=(h-20)(b-12) should be maximum

\(A = (h - 20)(\frac{15360 }{h}-12)\)

From equation (1)  

\(A = 15360-12h-\frac{307200}{h} +240\)

A = 15600 - 12h - (307200/h)

differentiate with respect to h (it should be=0)

\(\frac{dA}{dh}= 0-12 + \frac{307200}{h^2}\)

\(12 = \frac{307200}{h} \\h = 160 cm\)

from equation (1),

\(bh = 15630cm^2\\b = 96cm\)

dimension of printed area,

= h - 20

= 160 - 20

= 140 cm

= b - 12

= 96 - 12

= 84 cm

Therefore, the dimensions that maximize the area are, 96cm and 84cm.

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Answer:

4

Step-by-step explanation:

25/100 x 80/1 = 20/1

80 - 20 = 60

30/100 x 80/1 = 24/1

80 - 24 = 56

60-56=4

Answer: they are both absolute value numbers

Step-by-step explanation:

|76| = 76

|43| = 43

the difference between them is 33