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ANSWER

[tex]f(x) = 4 {(x - 7)}^{2} - 19[/tex]

EXPLANATION

The given equation is

[tex]g(x) = 4 {x}^{2} - 16[/tex]

If the equation is shifted 7 units to the right and 3 units down, then the new equation becomes.

[tex]f(x) = g(x - 7) - 3[/tex]

This implies that,

[tex]f(x) = 4 {(x - 7)}^{2} - 16 - 3[/tex]

The required equation is

[tex]f(x) = 4 {(x - 7)}^{2} - 19[/tex]

Answer:

The answer is x + x + x.

Step-by-step explanation:

Tripling something means 3 of that thing. 3 + 3 + 3, which is also 3x.

I hope this helped!

Have a wonderful Wednesday!

~Lola

The expression which is equal to 3x is x+x+x. Therefore, option B is the correct answer.

We need to check which expression from the options is equal to 3x.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

From option B,

In the expression x+x+x, all three terms are same(like terms), by adding them we get

x+x+x=3x

The expression which is equal to 3x is x+x+x. Therefore, option B is the correct answer.

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Answer:

the word is viewpoint

Step-by-step explanation:

Answer:

Step-by-step explanation:

Viewpoint refers to a particular and individual way to see the world. It's the personal perspective in a specific context, it's people's point of view. For example, in a situation like an accident between a motorcycle and a bus, some people would say that the fault is no the bus drives, other would say that it's on the motorcycle driver, but at the end, those just are different viewpoint.

In this case, a writer's opinion or way of seeing an issue, it's referring to a point of view, or viewpoint, because involves an individual opinion about something.

Answer:

92 more miles

Step-by-step explanation:

60 mph is 1 mile per min so in 42 min they traveled 42 miles and 134 miles minus 42 miles is 92 miles

Answer:

20 years

Step-by-step explanation:

Using the formula; A = P(1 + r)^t

We can plug in the known to find t

400 = 220(1.03)^t

then solve for t;

1.818 = 1.03^t

Introducing In

In 1.818 = t × In (1.03)

t = 20.225  

t = 20 years to the nearest year

Answer:

20 years

Step-by-step explanation:

Plato

Answer:

A. 1/5

C. 2/3

Step-by-step explanation:

30x^2 - 26x + 4=0

2(15x^2 - 13x + 2) = 0

2(15x^2 - 10x - 3x  + 2) = 0

2[(5x(3x - 2)  - 1(3x - 2)] = 0

2(5x - 1)(3x - 2) = 0

5x - 1 = 0; x = 1/5

3x - 2 = 0; x = 2/3

Answer:

x = 1/5, x = 2/3.

Step-by-step explanation:

30x^2 - 26x + 4 = 0

15x^2 - 13x +2 = 0

(5x - 1 )(3x  - 2) = 0

5x - 1 = 0  or 3x - 2 = 0

x =  1/5,  2/3.

Answer:

SA = 124 cm²

Step-by-step explanation:

The lateral surface area is the area of all sides besides that base, so 93 cm² is the sum of 3 sides of the tetrahedron.  

93/3 = 31 cm² per side, there are 4 sides, so 31(4) = 123 cm² is the total surface area

The surface area of the tetrahedron is 124 square centimeters.

Let's denote the surface area of one equilateral triangle as A The total surface area of the tetrahedron, which includes all four faces, is then  4A.

 Given that the lateral surface area (which is three faces) is 93 square centimeters, we can write:

 3A = 93

To find the area of one face (A), we divide both sides by 3:

[tex]\[ A = \frac{93}{3} = 31 \][/tex]

Now, to find the total surface area of the tetrahedron, we multiply the area of one face by 4:

[tex]\[ \text{Total Surface Area} = 4A = 4 \times 31 = 124 \][/tex]

Therefore, the surface area of the tetrahedron is 124 square centimeters.

Answer:

The perimeter of rectangle is [tex]18\ cm[/tex]

Step-by-step explanation:

Let

x-----> the length of the rectangle

y----> the width of the rectangle

we know that

[tex]x=y+5[/tex] ----> equation A

[tex]120=xy+2x^{2}+2y^{2}[/tex] ---> equation B (area of the constructed figure)

substitute the equation A in equation B

[tex]120=(y+5)y+2(y+5)^{2}+2y^{2}\\ 120=(y+5)y+2(y+5)^{2}+2y^{2}\\ 120=y^{2}+5y+2(y^{2}+10y+25)+2y^{2}\\ 120=y^{2}+5y+2y^{2}+20y+50+2y^{2}\\120=5y^{2}+25y+50\\5y^{2}+25y-70=0[/tex]

using a graphing calculator -----> solve the quadratic equation

The solution is

[tex]y=2\ cm[/tex]

Find the value of x

[tex]x=y+5 ----> x=2+5=7\ cm[/tex]

Find the perimeter of rectangle

[tex]P=2(x+y)=2(7+2)=18\ cm[/tex]

Answer:

Perimeter of rectangle = 38 cm

Step-by-step explanation:

It is given that, Length of a rectangle is 5 cm longer than the width.

Let 'x' be the width then length = x + 5

Area of of rectangle = x(x + 5)

One side of square = ( x+ 5)/4

Area of all squares = [(x +5)/4]² * 4 = (x + 5)²/4

To find the value of x

Total area = 120 cm²

Area of of rectangle + Area of all squares  = 120

x(x + 5) + (x + 5)²/4 = 120

x² + 5x + (x² + 10x + 25)/4 = 120

4x² + 20x + x² + 10x + 25 = 120 * 4

x² + 6x + 5  = 24 * 4

x² + 6x - 96 =0

x = 7

To find the perimeter of rectangle

width = x = 7

Length = x + 5 = 7 + 5 = 12

Perimeter = 2(length + width) = 2(7 + 12) = 38 cm

Answer:

x = -3, x= 0, and x = 1.5

Step-by-step explanation:

The zeros of a function f(x) refers to the x-values for which f(x) = 0.

We simply graph the function and determine the points where the graph crosses the x-axis. Thus, we shall be solving the problem graphically;

From the attachment below, the graph of f(x) crosses the x-axis at;

x = -3, x= 0, and x = 1.5

Step-by-step explanation:

12/3.48= cost of 1 book

cost of 20 books = 12/3.48×20 =68.95

To find the cost of 20 pens when 12 pens cost $3.48, divide $3.48 by 12 to get the cost per pen and then multiply by 20. The cost for 20 pens would be $5.80.

To calculate the cost of 20 pens when 12 pens cost $3.48, first, we need to find the cost of one pen. We do this by dividing the total cost of 12 pens by the number of pens:

$3.48 / 12 pens = $0.29 per pen.

Now that we know the cost of one pen, we can calculate the cost of 20 pens by multiplying the cost per pen by 20:

$0.29 / pen x 20 pens = $5.80.

So, 20 pens would cost $5.80.

Answer:

The theoretical probability of rolling a number smaller than a 3 is __1/3_____because this is what__we expect to happen____ . The experimental probability of rolling a number smaller than a 3 is __1/4____ because this is what___actually happened____

Step-by-step explanation:

The experimental probability is

P (<3) = (  getting a one or 2)/ number of times that he rolled

        He rolled a one or a two 2 times of the 8 times rolled

          = 2/8 = 1/4

Theoretical probability is what we expect  happen

P (<3) = (getting a one or two) / 6

         = 2/6 = 1/3

The theoretical probability of rolling a number smaller than a 3 is __1/3_____because this is what__we expect to happen____ . The experimental probability of rolling a number smaller than a 3 is __1/4____ because this is what___actually happened____

Answer:

25 students in the cooking club

Step-by-step explanation:

Let

x-----> the number of students in art club

y-----> the number of students in drama club

z-----> the number of students in cooking club

step 1

Substitute the value of y in equation A and solve for x

step 2

substitute the value of x in equation B and solve for z

Answer:

C

Step-by-step explanation:

4^5 expanded is 4 * 4 * 4 * 4* 4

Answer:

the first one

Step-by-step explanation:

Your answer is A) 1/2 inch per foot

Multiply the given info by 2 to get the answer.

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➷The answer is: the corresponding angles are both the same.

Explanation: The angles B and F are the same. The same goes for A and E, D and H, and C and G. So the conclusion is that the corresponding angles have both the same measure, or are both congruent.

✽

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

DOGE

Answer:

The answer is C

Step-by-step explanation:

Answer:The answer is actually A

Step-by-step explanation:

1.5 × 10 to the 1 st power

Answer:

0.00002

2*10^-5 = 2*00001 = 0.00002

Answer:

im pretty sure its the second one to the right

Answer:

|7| + |-2| | +|5| + |-8|=

Step-by-step explanation:

We want to find the total number of spaces traveled, it doesn't matter whether they are forward or backward.

We moved 7 spaces right then 2 spaces left then 5 spaces right then 8 spaces left.  The total spaces are just the number of spaces, not whether they were left or right so we take the absolute value

|7| + |-2|  +|5| + |-8|=

Answer:

I am not sure that this is a solvable equation.

x=4

Multiply the reciprocal of 1/24, which is 24, on both sides. You will result in getting x=24/6, or 4

x=4

Answer:

x=4

Step-by-step explanation:

24 divided by 6 = 4

or 6 x 4 = 24

Answer:

Bigger by ¼ of a.

Step-by-step explanation:

Let b be represented by all five slices of the pie, and a by the four yellow slices.

Then a is ⅘ of the pie and it is ⅕ smaller than b.

Now, let's turn the argument around.

The four yellow slices represent a, and all 5 slices represent b.

b is greater than a by one slice compared to four.

In mathematical terms, b is bigger by ¼ of a.

Answer:

Step-by-step explanation:

Answer:

w=3

Step-by-step explanation:

The area of the triangle is given by

A = 1/2 bh

the base is 5 and the height is 3

A = 1/2 (3) * 5 = 15/2  units ^2

The area of a rectangle is

A = l*w

A = 5w

The area of the triangle = 1/2 the area of the rectangle

15/2 = 1/2 *5w

15/2 = 5/2 w

Multiply each side by 2/5 to isolate w

2/5 * 15/2 = 2/5 *5/2 w

3 =w

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Final answer:

The area of the triangle is 7.5 units and the width of the rectangle is 3 units.

Explanation:

The area of a triangle can be calculated using the formula A = (base * height) / 2. In this case, the base of the triangle is given as 5 units and the height is given as 3 units.

So, the area of the triangle is A = (5 * 3) / 2 = 15 / 2 = 7.5 units.

The area of the rectangle is given as 5 units long and units wide. Since the area of the triangle is equal to half of the area of the rectangle, we can set up the equation 7.5 = (5 * width) / 2 and solve for the width.

By multiplying both sides of the equation by 2 and then dividing by 5, we get width = (7.5 * 2) / 5 = 15 / 5 = 3 units. Therefore, the width of the rectangle is 3 units.

x squared and -9 are both square numbers.

the square root of x^2 is x

the square root of -9 is 3. so you just need to write (x+3)(x-3)

you can check by expanding the brackets and the middle x terms should cancel out

Answer:

(x-3)(x+3)

Step-by-step explanation:

Here we have to represent our algebraic expression as difference of square.

In order to do so we have use the formula given under.

[tex](x^2-a^2)=(x-a)(x+a)[/tex]

Hence first we have to guess the square root of the 9 , which is 3 and represent our numeric term in our expression as square of it.

Hence

[tex](x^2-9)\\= (x^2-3^2)[/tex]

Now we apply the formula

[tex](x^2-3^2)=(x-3)(x+3)[/tex]

Hence the above expression is our answer.

Answer:

B. 14 = 125p

Step-by-step explanation:

The correct equation to find what percent 14 is of 125 is 14 = 125p. This equation is solved by dividing both sides by 125. The solution, 0.112 or 11.2%, shows that 14 is 11.2% of 125.

The subject of the question is Mathematics. The question is, 'Which equation can be used to find what percent 14 is of 125?' The correct equation to solve this is: 14 = 125p. The reason for that is because the problem is asking what percent (represented by p) 14 is of 125. So, you want to solve for p. To do so, you would divide both sides of the equation by 125. This would give you p = 0.112, or 11.2%. This means that 14 is 11.2% of 125.

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Answer:

rate change: -8

Equation: y = 232 -8x

After 5 hours: 192

Step-by-step explanation:

8 are destroyed every hour, so there are 8 less every hour, so the rate of change is -8

It starts with 232 and loses 8 per hour, so the formula is

y = 232 - 8x

After 5 hours:

y = 232 - 8(5)

    y = 232 - 40

         y = 192

Answer:

Step-by-step explanation:

The rate of change in this case is -8, since the amount is decreasing.

The equation is:

y=232-8x.

After 5 hours, he will have 192 rews.

The equation of the line below : y= -6x.

Answer:

Step-by-step explanation:

115+10x = y

After 7 trips to the fair, Erin has 185 stamps in her collection according to to the equation y = 115 + 10x.

To find out how many stamps Erin has after 7 trips to to the fair, we can use the given equation:

[tex]\[ y = 115 + 10x \][/tex]

where:

- [tex]\( y \)[/tex] represents the number of stamps in Erin's collection.

- [tex]\( x \)[/tex] represents the number of times Erin has been to to the stamp fair.

Substituting [tex]\( x = 7 \)[/tex] into the equation, we get:

[tex]\[ y = 115 + 10(7) \][/tex]

[tex]\[ y = 115 + 70 \][/tex]

[tex]\[ y = 185 \][/tex]

So, after 7 trips to the fair, Erin has [tex]\( 185 \)[/tex] stamps in her collection.

Answer: The sales tax rate is 5%.

Step-by-step explanation: In order to calculate the sales tax rate you need to divide the amount of sales tax by the amount of the purchase. In this case you divide .20 by $4.00. .2 / 4 = .05 = 5% sales tax rate

The sales tax rate for a pack of cinnamon-scented pencils that sells for $4.00 and totals $4.20 is 5%.

To calculate the sales tax rate for a pack of cinnamon-scented pencils that sells for $4.00 and has a total cost of $4.20 including tax, you first need to find the amount of sales tax paid. The sales tax paid is the difference between the total cost and the sale price, which is

$4.20 - $4.00 = $0.20.

Next, you convert the sales tax amount to the sales tax rate by dividing the tax amount by the original price and then multiplying by 100 to get a percentage. Therefore, the sales tax rate is

($0.20 / $4.00) x 100, which equals 5%. The packed pencils had a 5% sales tax added to the original price.