The function f(x) = x2 has been translated 9 units up and 4 units to the right to form the function g(x). Which represents g(x)? a. g(x) = (x + 9)2 + 4 b.g(x) = (x + 9)2 − 4 c.g(x) = (x − 4)2 + 9 d.g(x) = (x + 4)2 + 9

The equation is [tex]\sqrt{x-2 \\ \\[/tex] -[tex]\sqrt{2x}[/tex] = [tex]\sqrt{x +2}[/tex]

Solution

Step 1:

Take square on both sides, we get

3x - 2[tex]\sqrt{x-2}[/tex][tex]\sqrt2{x}[/tex] -2 = x +2

Step 2:

Subtract 3x - 2 from both sides, we get

-2[tex]\sqrt{x-2} \sqrt{2x} = -2x + 4[/tex]

Step 3:

Again, square on both sides in order to get rid of the square root from the above equation, we get

[tex]8x^{2}-16x = 4x^{2} -16x +16[/tex]

Now we have to simplify it,

[tex]4x^{2} -16 = 0[/tex]

Step 4:

Now we have to solve this quadratic equation, in order to get the solution.

We get x = 2 and x = -2, When we verifying solution in the original given equation, the solution does not satisfy the equation.

Reason: We get negative number in the square root.

Therefore, it has no Roots.

Answer: b) No roots

N x 7 +3 = 45

N = 6    Hope this helps.

Hi GueenSilia,

Answer: (n x 7) + 3

45 - 3 = 42

42 / 7 = n

n x 7 + 3 = 45

----------------------------

42 / 7 = 6

6 x 7 = 42

42 + 3 = 45

n = 6

Let

n-------> the lesser even number

n+2----> the greater even number

we know that

[tex]3(n+2)=(n-10)[/tex]

Solve for n

[tex]3n+6=n-10[/tex]

Combine like terms

[tex]3n-n=-10-6[/tex]

[tex]2n=-16[/tex]

[tex]n=-8[/tex]

so

[tex]n=-8\\n+2=-8+2=-6[/tex]

therefore

the answer is

the lesser even number is [tex]-8[/tex]

the greater even number is [tex]-6[/tex]

2p² - p - 10 = 0

2 = a

- 1 = b

- 10 = c

To factor, find two numbers that multiply to equal a·c and also that have a sum of b

2p² + 4p - 5p - 10 = 0

2p (p + 2) - 5 (p + 2) = 0

To find the 8th term of the pattern 1, 2, 5, 10, 17, analyze the differences between consecutive terms and find the common difference. Add that common difference to the 7th term to find the 8th term.

To analyze the pattern, we can observe that the difference between consecutive terms is increasing by 1 each time. Let's find the common difference:

From these differences, we can see that the common difference is increasing by 2 each time. So the difference between the 7th term and the 6th term would be 7 + 2 = 9. Using this pattern, we can find the 8th term:

19% turns into 20%

20%*41=8.2

Have a nice day.

Answer:

[tex]y=3[/tex]

Step-by-step explanation:

Given figure is a rectangle.

In a rectangle , opposite sides are equal

to find out y we equate the opposite sides 10 and 2y+4

[tex]10=2y+4[/tex]

Subtract 4 from both sides

[tex]10-4=2y+4-4[/tex]

[tex]6= 2y[/tex]

Divide both sides by 2

[tex]y=3[/tex]

0.09

-hope this helps

False becuase wat you picked is definitley wrong

If the horizontal plan passes through the cone that have horizontal base, the shaped form will be circular.

B AND C I THINK BUT IM NOT SURE

The answer is 83.2%, Hope this helps

The measure of angle A is 61 degrees.

Given that

Angle A and angle B are complementary angles.

If the measure of angle B is 29 degrees.

We have to determine

The measure of angle A?

According to the question

The measure of angle A is determined in the following steps given below.

When adding the two complementary angles the sum of the angle is equal to 90 degrees.

[tex]\rm \angle A + \angle B = 90[/tex]

The measure of angle B is 29 degrees.

Then,

The measure of angle A is,

[tex]\rm \angle A + \angle B = 90\\\\\rm \angle A + 29= 90\\\\\rm \angle A =90-29\\\\\rm \angle A =61[/tex]

Hence, the measure of angle A is 61 degrees.

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Solution 1:

The compound interest formula to be used here is given by:

[tex]A=P(1+r)^{t}[/tex]

Now we are given:

P=$500

r=10% or 0.1

t=5 years

Plugging them in the formula ,

[tex]A=500(1+0.1)^{5}[/tex]

A=$802.255

Answer : After 5 years I will have $802.255 in my account.

Solution 2:

The formula for compound interest here is given by:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Here interest is compounded after every two years, so n=2

r=2% or 0.02

t=6 years

P= $100

Plugging these into the formula:

[tex]A=100(1+\frac{0.02}{2})^{2*6}[/tex]

[tex]A=100(1+0.01)^{12}[/tex]

[tex]A=100(1.01)^{12}[/tex]

A=$112.683

Answer: The balance after 6 years would be $112.683.

Solution 4:

In this situation:

a. Ax+By

Ax represents duration of Podcast A episodes

By represents duration of Podcast B episodes

Ax+By represents total duration of Podcast A and Podcast B songs.

b. A+B

A+B represents total number of episodes of Podcast A and Podcast B.

the answer is b because to find the area of something you have to do Base(b) multiplied by the Height(h) and the area of B was 16

A: 14

B: 16

C: 13.5

D: 14

Answer Is Option(b.) :-To find the greatest area among the given rectangles, calculate the area of each rectangle by multiplying the base by height. The greatest area is of rectangle b.

The subject matter of this question involves finding the area of rectangles. In mathematics, the area of a rectangle is calculated by multiplying its base (b) by its height (h), represented as A = b x h. In this question, you are given four different rectangles (a, b, c, and d) with varying base and height values. You need to calculate the area for each and determine which one is the greatest:

After calculations, you can see that rectangle b has the greatest area.

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Final answer:

The equation of a vertical line passing through the point (5,2) is x = 5. This type of line has an undefined slope and is defined by its x-coordinate, not dependent on the y-coordinate.

Explanation:

The equation of a vertical line that passes through the point (5,2) can be determined by understanding that a vertical line has an undefined slope and does not depend on the y-coordinate for its location on a coordinate plane. Instead, a vertical line's location is solely determined by its x-coordinate. Therefore, the equation of a vertical line that passes through (5,2) will have the same x-coordinate for all its points. This means that the equation for the vertical line through (5,2) is simply x = 5.

This equation is different from the conventional y = mx + b, which defines a straight line with a slope m and y-intercept b. In the case of a vertical line, the slope is undefined, and therefore, the standard linear equation cannot be applied. Instead, the equation is independent of y and is expressed only in terms of the constant x-value of the vertical line.

Multiplying Negatives odd # of negatives means negative answer. even means positive answer.

-4(1.5) Change both to improper fractions

-4/1(6/5) Multiply

-24/5  Simplify

-4 4/5   THE END

To find the product of -4(-1.5) on the number line, start from zero, move 4 units to the left due to the negative sign, and then move 6 units (4 x 1.5) to the right because of the negative multiplied by a negative rule. The result is 6.

To find the product of -4(-1.5) on the number line, you would follow a few steps. First, choose your starting point on the number line. In this case, the starting point would be zero.

Next, because the first number is negative, move 4 units to the left from zero. Since the second number is also negative, it changes the direction. So multiply by 1.5 in the opposite direction, which means moving to the right on the number line.

However, as it's a decimal multiplication you need to move 1.5 times or multiply the distance you moved when you moved 1 unit 4 times. It's like taking 1.5 steps to the right for each of the 4 steps we initially moved to the left. In the end, you will end up 6 units to the right of 0. Thus, the product of -4 and -1.5 is 6.

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That will be 1, since 17 can only be factored by itself and 1

Even though 6 can be factored by 3 and 2, the least common factor between 17 and 6 will be 1.

Hello there,

The correct answer is 2 the (LCM) or Least common factor of 17 and 6 is 2

If my answered helped you understand more greatly please mark me as brainliest thank you and have the best day ever!

Denise needs to buy 25/3 gallons of 85% ethanol and 35/3 gallons of 25% ethanol to have 20 gallons of 50% ethanol.

x | y | 20 gal

use x and y because you don't know how much she needs.

0.85x | 0.25y | 20(0.5)

85% is 85/100 or 0.85, and you need that much of x, same goes for the 25% and 50% mixtures

so now you can make up 2 equations

1) x + y = 20

2) 0.85x + 0.25y= 10 (you get 10 when you multiply 20 by 0.5)

now you can solve for x or y using substitution. first rewrite 1) in terms of x or y:

x+ y= 20 ----> y= 20 - x

now you can substitute 20- x for y in the second equation..

0.85x + 0.25y= 10

0.85x + 0.25(20-x)= 10 distribute here..(0.25 * 20 and 0.25 * (-x) )

0.85x + 5 - 0.25x = 10 combine like terms

0.6x +5 = 10 move the 5 over to the other side

0.6x= 10 -5

0.6x = 5 divide both sides by 0.6

x= 25/3 or 8.3 now you know the amount of x so you can substitue this back into the first equation to find y.

0.85x + 0.25y= 10

0.85(25/3) +0.25y= 10

85/12 + 0.25y= 10

0.25y = 10- 85/12

0.25y= 35/12

y= 35/3 or 11.6

you can check by putting these values into the euations:

1) x+ y= 20

25/3 + 35/3 =20

20= 20 good so far

2) 0.85x + 0.25y= 10

0.85(25/3) + 0.25(35/3)=10

10 = 10 so our values for x and y work

She rode her bike 10.2 mile the final week.

You simply just add all of the numbers together & subtract from 62.9 then get 10.2.

Hopefully this helps! :-)

Answer:  1.  286 different combinations of players are possible.

2.  The probability of selecting a team of 5 girls and 5 boys is [tex]\frac{63}{143}[/tex] and the decimal is 0.4405...

Step-by-step explanation:

1.  Number of girls is 6 and number of boys is 7.

So, the total number of players = 6+7 = 13

A team of 10 players is to be selected from the class.

So, the total possible number of different combinations of players will be:  [tex]^1^3C_{10} = \frac{13!}{10! (13-10)!}=\frac{13*12*11*10!}{10!*3!}= \frac{13*12*11}{6}=286[/tex]

2.   Number of girls is 6 and number of boys is 7.

The possible number of teams by selecting 5 girls and 5 boys will be:  [tex]^6C_{5}\times ^7C_{5} =6\times 21= 126[/tex]

and the number of total possible teams of 10 players [tex]= ^1^3C_{10} =286[/tex]

Thus, the probability of selecting a team of 5 girls and 5 boys [tex]=\frac{126}{286}= \frac{63}{143}[/tex] or [tex]0.4405...[/tex]

change each to improper fractions

21 1/2 = (2*21 +1)/2 = 43/2

2/3 = 2/3

43/2  divided by 2/3    

copy dot flip

43/2 * 3/2

129/4 = 32 1/4

Answer:

Speed of Victoria, [tex]v=32\dfrac{1}{4}\ miles/hour[/tex]

Step-by-step explanation:

It is given that,

Distance covered by Victoria, [tex]d=21\dfrac{1}{2}\ miles=\dfrac{43}{2}\ miles[/tex]

Time taken, [tex]t=\dfrac{2}{3}\ hour[/tex]          

Speed (v) of Victoria is given by total distance divided by total time taken. It is given by :

[tex]v=\dfrac{d}{t}[/tex]

[tex]v=\dfrac{\dfrac{43}{2}\ miles}{\dfrac{2}{3}\ hour}[/tex]

[tex]v=\dfrac{129}{4}\ miles/hour[/tex]

or

[tex]v=32\dfrac{1}{4}\ miles/hour[/tex]

So, the speed of Victoria is [tex]32\dfrac{1}{4}\ miles/hour[/tex]. Hence, this is the required solution.

[tex]Domain:\ x\geq0\\\\5\sqrt[3]{x}+9\sqrt[3]{x}=(5+9)\sqrt[3]{x}=14\sqrt[3]{x}[/tex]

you have to divide 64 and 8

then you get the answer: 8 ounces per cup

laps per minute by:

- Mai- 12/3 = 4 laps

- Lena- 48/6= 8 laps

- Susan- 30/5= 6 laps

thus, the person who drove fastest was Lena, who drove 8 laps per minute.

We are given function f(a) = 1.07a for total amount including sales tax.

g(b) = b+50 total cost including delivery.

We need to write function g(f(a)).

g(f(a)) = g of f(a).

We need to substitute function f(a) in g(b) function for b.

g(f(a)) = g(1.07a) = 1.07a +50.

We are given mattress price a = $1125.

In order to find the total cost including delivery charges, we need to plug a= 1125 in the above function 1.07a +50.

Plugging a= $1125, we get

g(1125) = 1.07a +50 = 1.07*1125 +50 = 1203.75 +50 = 1253.75.

Answer:

g(f(a)) = 1.07a +50.

Total cost including delivery charges is $1253.75.

The equation of the line that is parallel to y = -x + 9 and passes through the point (7, -13) is y = -x - 6.

Now, we want to find the equation of a line that is parallel to this given line and passes through the point (7, -13). Since the new line is parallel, it will have the same slope of -1. Let's denote the equation of the new line as y = mx + b. We know the slope (m = -1), and we have a point (7, -13) that the line passes through. We can use this information to find the value of b.

To find b, we can plug in the coordinates of the point (7, -13) into the equation y = -x + b:

-13 = -1 * 7 + b

Now, solve for b:

b = -13 + 7

b = -6

Therefore, the value of b is -6.

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