if you horizontally stretch the quadratic parent function, f(x)=x^2, by a factor of 3, what is the equation of the new function?

Answer: [tex]x=\±2\sqrt{10}[/tex]

Step-by-step explanation:

To find the solutions of the quadratic equation given in the problem, you can apply the proccedure shown below:

- Subtract 40 from both sides of the equation.

- Multiply both sides of the equation by -1

- Apply square root to both sides of the equation.

Therefore, by applyin the steps above, you obtain:

[tex]40-x^2-40=0-40\\-x^2=-40\\(-1)(-x^2)=(-40)(-1)\\\\x^2=40\\\\\sqrt{x^2}=\±\sqrt{40}\\\\x=\±2\sqrt{10}[/tex]

Answer:

= ±2√10

Step-by-step explanation:

40 − x2 = 0

We could solve this by;

subtracting x² from both sides

we get;

40 = x²

Then we get the square root on both sides;

√x² = √40 ; but the square root of a positive number "a" is +√a or -√a

Therefore;

√x² = ± √40

x = ±√40

√40 = √4√10

       = 2√10

Thus;

x = ±2√10

Answer:

the first number is 5 the second number is 4

Step-by-step explanation:

first number = x

second number = y

X+2y=13 given this isolate x  x = 13-2y

2x+y=14 substitute 13-2y for x

2(13-2y)+y=14

26-4y+y=14

-3y=-12

y=4 taking this number substitute into either equation above

x+2(4)=13

x+8=13

x=5

0.05 ---> 1/18

square root of 0.25 ------> 0.05

1/7------> 0.142857 repeating

0.6 -------> 2/3

Answer:

0.05 ---> 1/18

1/7 ---> 0.142857

0.6 ---> 2/3

0.25 ---> 0.05

Step-by-step explanation:

total distance of 24 laps

29.6km - 0.2km

=29.4km

total distance of each lap

24 laps = 29.4km

1 lap = ?

Use cross-multiple

24 laps × X = 29.4km × 1 lap

X = 29.4km / 24

X = 1.225km

Answer

1.225km

Answer:

1.225km is equal to each laps

Step-by-step explanation:

Since Kristy total distance traveled = 29.6km

And Kristy ran 24 laps and later walk 0.2km. it simply implies that

Total distance traveled = distance covered running + distance covered walking

Since we know that

Total distance traveled = 29.6km

distance covered running = 24 laps

distance covered walking = 0.2km

Distance covered running in km = total distance traveled - distance covered walking

Distance covered running in km = 29.6km - 0.2km = 29.4km.

To now find the distance for each lap.

Since we have:

Distance covered running in km = 29.4km.

Distance covered running in lap = 24 laps

i.e

24 laps = 29.4km

1 lap = x

Use cross-multiple

24 laps * x = 29.4km × 1 lap

x = 29.4km / 24

x = 1.225km

Therefore

1.225km is equal to each laps.

Answer:

D (9,13)

Step-by-step explanation:

Substitute the points into the equation

y =x+4

A (0,0)

0=0+4

0=4  False  This point is not a solution

B (5,54)

54 = 4+4

54=8  False  This point is not a solution

C (7,28)

28 = 7+4

28 = 11  False  This point is not a solution

D (9,13)

13 = 9+4

13=13  True This point is a solution

Answer:

plug in 13 for y you get x = 9  D(9,13)

[tex]1) \: {k}^{2} + 2k - 24 \\ = {k}^{2} + 6k - 4k - 24 \\ = k(k + 6) - 4(k + 6) \\ = (k - 4)(k + 6) \\ \\ 2) \: 4 {k}^{2} - 1 \\ = (2k - 1)(2k + 1) \\ \\ 3) \: 25 {b}^{2} - 30b + 9 \\ = {(5b - 3)}^{2} [/tex]

Answer:57.1

If that helps you

Step-by-step explanation:

Answer:

7 cant go into 40 evenly, it would be 5.7 times if we were just to do 40 divided by 7 . . . .

so i guess (even though its not a even number ) your answer is 5.7

40/7 = 5.71

Alex have 200 cards.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

According to the question

Alex, Gil and Meg shared 740 cards.

Alex had 20 fewer cards than Gil and 120 fewer cards than Meg.

Assuming Alex have x cards

Based on the given condition, write equation

[tex]x+(x+20)+(x+120)=740[/tex]

Solving the equation

[tex]3x =740-20-120[/tex]

[tex]3x=600[/tex]

[tex]x=200[/tex]

Hence, Alex have 200 cards.

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Alex had 193 cards. Meg had 120 more, Gil 20 more than Alex, for a total of 740 shared.

Let x be the number of cards Gil had.

Alex had x - 20 cards.

Meg had x + 120 cards.

The total number of cards is x + (x - 20) + (x + 120) = 740.

Combining like terms, we get 3x + 100 = 740.

Subtracting 100 from both sides, we get 3x = 640.

Dividing both sides by 3, we get x = 213.33.

Since the number of cards must be a whole number, we can round 213.33 down to 213.

Therefore, Alex had 213 - 20 = 193 cards.

So the answer is 193

Answer:

Surface area; Greater; subtract

Step-by-step explanation:

The complete sentence are as follow:

The area is the space occupied by a two-dimensional flat surface. It is expressed in square units. The surface area of a three-dimensional object is the area occupied by its outer surface. It's also expressed in square units.

First, the identical shapes can be recognized using Surface Area because volume is used to measure the capacity.

Now, adding the surface results to the greater surface area.

So, to find the true Surface area it is necessary to subtract the common sides.

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Answer:

3 meters

Step-by-step explanation:

We assume the storage room is a rectangle, like most rooms, no indication it is otherwise.

We know it's a rectangle and not a square because it is longer than wide.

We have the perimeter measurement (16 meters).

So, we can make the following equation:

2x + 2y = 16

x being the width of the room, y being it's length.  A perimeter is the sum of all sides.

We also know the room is 2 meters longer than wide... so:

y = x + 2

If we replace y in the first equation by its value relative to x, we get:

2x + 2(x + 2) = 16 which becomes

2x + 2x + 4 = 16

4x =12

thus x = 3

Width: 3 meters

Length: 5 meters.

Confirms the 16 meters perimeter.

Answer:

Width = 3 meters

Step-by-step explanation:

We are given that for an equipment storage room, it is 2 meters longer than its width and the perimeter of this room is 16 meters.

Given the above information, we are to find the width of the room.

Perimeter = [tex]2l+2w[/tex]

Supposing [tex]x[/tex] to be the width and [tex]x+2[/tex] to the length, we can write it as:

[tex]16=2(x)+2(x+2)[/tex]

[tex]16=2x+2x+4[/tex]

[tex]12=4x[/tex]

[tex]x=\frac{12}{4}[/tex]

x = 3

Therefore, the width = 3 meters.

Using proportional relationships, it is found that:

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

[tex]y = kx[/tex]

k is the constant of proportionality.

In this problem, considering:

Hence, y is a function of x, given by:

[tex]y = 9.6x[/tex]

Also, we can write x as a function of y, as follows:

[tex]x = \frac{y}{9.6}[/tex]

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Yes, y is a function of x as earnings are proportional to hours worked. The equation describing x as a function of y is x = y/9.60, since Lin's sister earns $9.60 per hour.

The problem states that the amount Lin's sister earns at her part-time job is proportional to the number of hours she works, and she earns $9.60 per hour. To answer the question whether y is a function of x, yes, y is indeed a function of x because for each value of x (number of hours worked), there is exactly one value of y (the earnings).

To write the equation describing x as a function of y, we start with the standard form of the equation for a direct proportion: y = kx, where k is the constant of proportionality. In this case, k is $9.60 per hour. So, the equation would normally be written as y = 9.60x. However, the question asks for x as a function of y. Therefore, we need to rearrange the equation to solve for x: x = y/9.60.

Answer:

"multiply the previous value by 3"

Step-by-step explanation:

We can easily see the pattern if we look at the 2nd, 3rd, 4th terms.

Now, we can see 1st and 2nd terms (which wasn't that apparent for some). Does multiplying 1/3 by 3 give us 1? INDEED, it does!

So the rule is "multiplying the previous term by 3".

Answer:

the first one is (cylinder) and second one is (6 units)

The radius of base is, 5 units

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Since, it has a perimeter of 32 units and it is to be rotated about the line, the solid to be created it is a cylinder. As you can see below.

Hence, Let's calculate its radius, based on the information given, i.e. the perimeter as,

2p = 32

Since, We know that;

2p = b + b + h + h

2p = 2 (b + h)

2 (b + h) = 32

b + h = 16

And, bh = 60

This gives solutions,

b = 10 and h = 6

Since, the line of rotation is the center, and the radius is half the line segment of the basis,

Then, The radius is 5.

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Complete question is this,

Rectangle ABCD has a perimeter of 32 units and will

be rotated about line k.

What is the three-dimensional solid created?

cylinder

What is the radius of a base?

10 units

Step-by-step explanation:

Don't see an answer but

You can divide the dollar amount by the kilograms and it should be 4.5, anything that isn't is incorrect.

for example 27/6 is 4.5

28/4 is 7 and therefore not equivalent.

Answer:

Step-by-step explanation:

Using law of indies;

√Xᵃ = Xᵃ/²

√(0.08¹²) = (0.08¹²ˣ¹/²)

                  = 0.08⁶

The correct answer is A; (0.08)⁶

For this case we must simplify the following expression:

[tex](\sqrt {0.08 ^ {12}}[/tex]

By definition of properties of powers and roots we have:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

So, we can rewrite the given expression as:

[tex]0.08 ^ {\frac {12} {2}} =\\(0.08) ^ 6[/tex]

Answer:

[tex](0.08) ^ 6[/tex]

Option A

Answer:

Hence choice A is correct

Step-by-step explanation:

Given equations are [tex]f(x)=\sqrt{x^2-1}[/tex] and [tex]g(x)=\sqrt{x-1}[/tex]

Now we need to find the value of [tex]\left(\frac{f}{g}\right)\left(x\right)[/tex]. Then select correct matching choice from the given choices.

Now let's find  [tex](fof)(3)[/tex]

[tex]\left(\frac{f}{g}\right)\left(x\right)[/tex]

[tex]\left(\frac{f}{g}\right)\left(x\right)=\frac{f\left(x\right)}{g\left(x\right)}[/tex]

[tex]\left(\frac{f}{g}\right)\left(x\right)=\frac{\sqrt{x^2-1}}{\sqrt{x-1}}[/tex]

[tex]\left(\frac{f}{g}\right)\left(x\right)=\frac{\sqrt{\left(x+1\right)\left(x-1\right)}}{\sqrt{x-1}}[/tex]

[tex]\left(\frac{f}{g}\right)\left(x\right)=\sqrt{x+1}[/tex]

Hence choice A is correct

Answer:

a. (f/g)(x) =  √x+1

Step-by-step explanation:

We have given two function.

f(x)  = √x²-1

g(x)  = √x-1

We have to find the quotient of f(x) and g(x).

(f/g)(x) = ?

The formula to find (f/g)(x) is :

(f/g)(x) = f(x) / g(x)

simplifying f(x) , we have

f(x)  = √(x-1)(x+1)

f(x)  = (√x-1)(√x+1)

Putting values in above formula, we have

(f/g)(x) = (√x-1)(√x+1) / √x-1

(f/g)(x) =  √x+1 which is the answer.

[tex] {(4x)}^{2} = 16 \times {x}^{2} [/tex]

There ya go.

The expression can be rewritten as 16x^2.

An expression can be rewritten by opening brackets, completing squares, reducing terms from it, etc.

The given expression is (4x)^2.

We can open the bracket of the given expression.

(4x)^2 = 16x^2

We have rewritten the expression. This expression is in the form of k • x^n.

Therefore, we have rewritten the given expression (4x)^2 as 16x^2.

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75+75=150

180-150=30

your missing angle is 30 degrees

Answer:

125 degrees.

Step-by-step explanation:

m < CBD = m < A + m < C ( by the External Angle of a Triangle theorem).

=  58 + 67 = 125 degrees.

Answer:

Step-by-step explanation:

We know that ∠CBD = ∠ACB + ∠CAB           [ External Angle of a                                                                                         Triangle theorem]

∠CBD = 58° + 67° = 125°

Answer:

C. [tex]g(x)=(x-2)^2[/tex]

Step-by-step explanation:

Remember the rules for function transformations:

- [tex]f(x+a)[/tex] shifts the function, [tex]f(x)[/tex], [tex]a[/tex] units to the left

- [tex]f(x-a)[/tex] shifts the function, [tex]f(x)[/tex], [tex]a[/tex] units to the right

We can infer from the picture that the blue graph is shifted 2 units to the right of the red graph, so we should apply the second rule:

[tex]f(x)=x^2[/tex]

[tex]g(x-2)=(x-2)^2[/tex]

[tex]g(x)=(x-2)^2[/tex]

We can conclude that the correct answer is C. [tex]g(x)=(x-2)^2[/tex]

Answer:

a. 9/10

b. 3/4

c. 1/3

d. 1/15

e. 6/35

f. 1/15

g. 9/32

h. 4/15

Step-by-step explanation:

a. [tex]\frac{3}{10} + \frac{6}{10} = \frac{30+60}{100} = \frac{90}{100} =  \frac{9}{10}[/tex]

b. [tex]\frac{1}{3} + \frac{1}{4}+\frac{1}{6} = \frac{9}{12} =  \frac{3}{4}[/tex]

c. [tex]\frac{5}{6} - \frac{3}{6} = \frac{2}{6} =  \frac{1}{3}[/tex]

d. [tex]\frac{2}{3} - \frac{6}{10} = \frac{20-18}{30} =  \frac{2}{30} = \frac{1}{15}[/tex]

e. [tex]\frac{4}{10}*\frac{3}{7} = \frac{4*3}{10*7} =  \frac{12}{70} = \frac{6}{35}[/tex]

f. [tex]\frac{1}{6}*\frac{6}{15} = \frac{1*6}{6*15} =  \frac{6}{90} = \frac{1}{15}[/tex]

g. [tex]\frac{\frac{1}{8}}{\frac{4}{9} } =\frac{9*1}{8*4} = \frac{9}{32}[/tex]

h. [tex]\frac{\frac{1}{5}}{\frac{3}{4} } =\frac{4*1}{5*3} = \frac{4}{15}[/tex]

Answer:

-1

Step-by-step explanation:

To find the slope of a line, you would need to use the slope formula, and that is [tex]slope=\frac{y2-y1 }{x2-x1}[/tex]

This equation should be used every time you need to find a slope with two given points. If you remember this, you would find questions like this more easy.

First, you would need to plug in your coordinate points into the formula.

You would plug -7 in y2, 2 in y1. And then you will plug in 4 in x2, and -5 in x1.

Your equation should look like this:

[tex]\frac{-7-2}{4-(-5)}[/tex]

Then you solve.

For the top portion of your equation you would get -9. The -5 turns into a positive 5 because when you carry the negative over (distribute it), the negative cancels out and turns into a positive. When you add the 5 and the 4 together, it will get you 9. The bottom portion of the equation will be 9.

Your equation should now look like this:

[tex]\frac{-9}{9}[/tex]

Now, you divide.

When you divide, the two 9's end up as a whole, and you keep the negative since the negative doesn't cancel out in this situation. When you finish dividing, you would get -1.

Your FINAL answer would be -1.

Answer:

-1

Step-by-step explanation:

    Slope formula:

             ↓

 [tex]{\huge\frac{Y_2-Y_1}{X_2-X_1}[/tex]

[tex]\frac{(-7)-2}{4-(-5)}=\frac{-9}{9}=-1[/tex]

Therefore the slope is -1.

-1 is the correct answer.

I hope this helps you, and have a wonderful day!

➷ 1) You have to find the equation of the line first:

y = mx + c

First find the slope

slope = difference in y / difference in x

slope = 6/3

slope = 2

Substitute this into the equation, as well as one of the coordinates

2 = 2(2) + c

Subtract 4 from both sides

c = -2

The equation of the line is y = 2x - 2

I will attach the drawn graph (it won't be in blue but just note that the first graph is the first one)

2) Substitute the values into the equation:

5 = -3(10) + c

c = 35

The equation is y = -3x + 35

I will attach the graph (it will be the second one)

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

d

Step-by-step explanation:

an x without anything in front of it is 1x  you can only mix like terms so 8x+1x+1x=10x - 2y

To express 5 √ 4 using rational exponents, you write it as 5¹ × 4¹⁄₂, as the square root of a number is that number raised to the power of ½.

To write 5 √ 4 using rational exponents, we must express the square root of 4 as a power. From our mathematical rules, we know that a square root can be written as an exponent of ½. Therefore, √4 is equivalent to 4 to the ½ power (4¹⁄₂).

Considering the expression 5 √ 4, we apply the same concept. The 5 is actually 5 to the power of 1 (5¹), and the square root of 4 is 4 to the ½ power. When these are multiplied together, we combine the base of 5 with the exponent expressions, remembering that the 4¹⁄₂ needs to be multiplied by 5¹. Consequently, 5 √ 4 becomes 5¹ × 4¹⁄₂.

The expression 5√4 can be written using rational exponents as 5 * [tex]4^{1/2}[/tex].

To express the given expression 5√4 using rational exponents, we start by understanding what the square root represents in exponential form. The square root of a number x can be written as [tex]x^{1/2}[/tex]. For our given expression, we need to follow these steps:

Therefore, the expression 5√4 can be written as 5 * [tex]4^{1/2}[/tex] using rational exponents.

Answer: Theater A has the greatest percent of seats filled, at 70%

Step-by-step explanation:

To find out which theater has the greatest percent of its seats filled, we need to calculate the percentage of seats filled in each theater. We can use the following formula to calculate percentage:

Percentage = (Part / Whole) x 100

For theater A, we have 112 seats filled out of 160 total seats: Percentage for theater A = (112 / 160) x 100 = 70%

For theater B, we have 84 seats filled out of 140 total seats: Percentage for theater B = (84 / 140) x 100 = 60%

For theater C, we have 117 seats filled out of 180 total seats: Percentage for theater C = (63 / 180) x 100 = 35% (Note that we need to subtract 63 empty seats from the total seats to get the total filled seats in theater C)

Therefore, theater A has the greatest percent of its seats filled, at 70%.

Answer:

At = 21.5 cm2

Step-by-step explanation:

At = Asqr - Acircle

At = A1 - A2

A1 = 10^2  = 100

A2 = Pi*(5)^2 = 78.5

At = 100 - 78.5

At = 21.5 cm2

Best regards

For this case we have that by definition:

The area of a circle is: [tex]A_ {c} = \pi * r ^ 2[/tex]

Where r is the radius of the circle.

The area of a square is: [tex]A_ {s} = l ^ 2[/tex]

Where l is the side of the square.

The area of the shaded region will be:

[tex]A_ {sr} = A {s} -A_ {c}[/tex]

So:

[tex]A_ {s} = 10 * 10\\A_ {s} = 100 \ cm ^ 2[/tex]

On the other hand:

[tex]A_ {c} = \pi * (\frac {10} {2}) ^ 2\\A_ {c} = \pi * 25\\A_ {c} = 78.5375cm ^ 2[/tex]

Finally:

[tex]A_ {sr} = 100-78.5375\\A_ {sr} = 21.4625[/tex]

Rounding out, we have that the area of the shaded region is 21.5 square centimeters.

Answer:

Option D

Answer:

C

Step-by-step explanation:

Simplify everything to get :

-3 - 4i + (?) = -i

From this we know that we need 3i + 3 to get -i.

3y = 3(1 + i)

3y = 3 + 3i

So the answer is C.

The Answer Would be:

C. 3y

Answer:

B. $329

Step-by-step explanation:

Add up the total amount of burgers sold (which is 47) and multiply by $5 to get 235$.

Then add up the amount of hot dogs (which is also 47) and multiply by $2 to get $94.

Then add $235 and $94 to get $329.

Answer:

m2 or inch2 or pulg2

Step-by-step explanation:

Answer: square units

Step-by-step explanation: when you hear of a shape area like 26 square feet or units