Given the parent function f(x)=x2, what is the new equation if the function is translated 4 units to the right and 3 units down

let y = x^2

4y^2 -21y + 20 = 0

solve for y

then substitute back in to get x

Answer:

4y^2 - 21y + 20 = 0

Step-by-step explanation:

As (4x^4 - 21x^2 + 20=0) being a biquadratic equation, meaning it is a 4-degree equation without the terms of degree 1 and 3.

To solve this particular case you only need to replace the variables of degree 4 and 2 for a new variable of degree 2 and 1 and solve it as regular quadratic equation and then undo the change.

* Using a new variable we can rewrite the equation:

Let y be the new variable;

y= x^2, then y^2= x^4

Then we have;

4y^2- 21y+20=0

Solve for y and then find X which will be the roots for the biquadratic equation.

Because there are 2 minus signs next to each other, we can replace both of them with a single plus sign.

This changes the equation to -7 + 3

Adding to a negative number makes the number appear smaller, so 3 + -7 = -4.

Remove parenthesis

-7=3

Calculate the sum

-4

The equation is: 7 + (x + 5)

The expression for '7 plus the sum of a number x and 5' is written as '7 + (x + 5)'.

The phrase '7 plus the sum of a number x and 5' can be written as an algebraic expression. This involves taking the sum of the variable x and the number 5, and then adding 7 to this sum. In mathematical terms, this is expressed as 7 + (x + 5).

Let's break it down step by step:

First, identify the sum: x + 5.

Next, add 7 to the result of this sum.

So, if we were to evaluate this expression for x = 4, we would calculate it as follows:

7 + (4 + 5) = 7 + 9 = 16

We are given that

y-scale is a distance in miles

x-scale is a time in hours

and we are given

The graph of the distance a car travels at a constant speed passes through the points (0,0) and (2,136)

so, points would be

(0,0)

x1=0 , y2=0

(2,136)

x2=2 , y2=136

so, slope would be speed

because speed = distance / time

we can use slope formula

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

now, we can plug values

[tex]m=\frac{136-0}{2-0}[/tex]

[tex]m=68[/tex] miles per hour

so, option-B..........Answer

Answer:

B

Step-by-step explanation:

A. distributive property

i hope this helps

A is your answer because 4×1=4 so it means that it is thedistributive property

I don't know if you accidentally put down the wrong variable, but the answer for h would be h=4. First things first, you have to subtract 100 from both sides, and this would become -15h=-60. After that, divide -15 on both sides, thus it leaves you with h by itself and it's value is 4. h=4

Hope this was helpful:)

80 = 3y + 2y + 4 +1

80 = 5y + 5

80 - 5 = 5y

75 = 5y

75 = 5y/5y

75/5 = y

15 = y

Answer:

answer is 9.

Step-by-step explanation:

A I think

it could be wrong though

Answer:

We have

k^2 - 25f^2 + 5kf - 25f^2 =

k^2 - (5f)^2 + 5f( k - 5f) =

( k - 5f )( k + 5f ) + 5f( k - 5f ) =

( k - 5f )( k + 5f + 5f ) =

( k - 5f )( k + 10f );

Step-by-step explanation:

Answer:  The required factored form of the given expression is [tex](k-5f)(k+10f).[/tex]

Step-by-step explanation:  We are given to factor the following quadratic expression :

[tex]E=k^2+5kf-50f^2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To factor the given expression, we need two integers with sum 5 and product -50 and those two integers are 10 and -5.

The factorization of expression (i) is as follows :

[tex]E\\\\=k^2+5kf-50f^2\\\\=k^2+10kf-5kf-50f^2\\\\=k(k+10f)-5f(k+10f)\\\\=(k-5f)(k+10f).[/tex]

Thus, the required factored form of the given expression is [tex](k-5f)(k+10f).[/tex]

Answer:

Option C is correct

Step-by-step explanation:

In similar triangles corresponding sides are in same ratio.

Notice that  sides b and q are corresponding ( they are opposite equal angles)  and so are a and p

The correct equation from the option is b/q = a/p. Hence, option C is correct.

To make a proportional relationship from the two triangles ABC and PQR given ;

Express corresponding sides as ratios ;

Using the given sides , the possible proportions are ;

a/p = b/q

b/q = c/r

a/p = c/r

Comparing the ratios with the options given, Only option B gives a correct proportional relationship.

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Answer:

1/6

Step-by-step explanation:

First, you want the denominators to be the same so you can subtract them.

1/3=2/6

2/6-1/6=1/6

Hope this helped!

it depends on how much the turtle and the dog treats are use that like 5 dolor each so im going to say 8 maybe

Answer: The answer to this problem is: no solution

Step-by-step explanation: The trick to solving this problem is listing out 38's factors:

1, 2, 19, 38. As you can see, none of these pairs add up to 15, so there is no solution (unless you are talking about fraction factors)

The expression 6a − 3b = 5b after solving for a:b is 4:3 after using arithmetic operation.

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

It is given that:

The expression is:

6a − 3b = 5b

To solve the above expression:

6a = 5b + 3b

6a = 8b

a/b = 8/6

As we know,

The expression can be defined as the combination of constants and variables with mathematical operators.

a:b = 8: 6

a:b = 4: 3

If in the linear expression, one variable is present, then the expression is known as the linear expression in one variabe.

Thus, the expression 6a − 3b = 5b after solving for a:b is 4:3 after using arithmetic operation.

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Jayden's stack of superhero cards, which is 0.41 meters high, is taller than Brett's stack of superhero cards, which is 0.405 meters high. The number sentence to compare them is 0.41 > 0.405.

The student is asking to write a number sentence that compares Jayden's stack of cards to Brett's stack of cards.

Jayden's stack was 0.41 meter high, and Brett's stack was 0.405 meter high. To compare these two stacks, we look at the decimal values given for the heights. Since 0.41 is greater than 0.405, the number sentence that compares the two stacks is:

Jayden's stack > Brett's stack

Or in terms of the specific values:

0.41 > 0.405

This shows that Jayden's stack of cards is taller than Brett's stack of cards.

You can use the given distance to amount of gasoline used relationship to find how much gasoline is needed for 1 km of traveling. Then use that data to find the amount of gasoline needed to travel 500 km.

The amount of gasoline needed to travel 500 km is 40 L

We can equate the 150 km figure to 12 L use of gasoline on the basis of usage.

Thus,

[tex]\rm 150 \: km = 12 \: L\\\\\\\text{Dividing both quantities in 150 parts}\\\\\\dfrac{150}{150} \: km = \dfrac{12}{150} \: L\\\\1 \: km = 0.08 \: L[/tex]

Thus, there will be use of 0.08 L gasoline for travelling 1 km by that same car.

Using that above derived relationship, we can find the amount of gasoline needed to travel 500 km by that same car.

[tex]1 \rm \: km = 0.08 \: L\\\\\text{Multiplying 500 on both the sides}\\\\500 \: km = 40 \: L[/tex]

Thus,

The amount of gasoline needed to travel 500 km is 40 L

Learn more about division here:

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Given the speed is 200 km /hr

use 1 km  = 1000 meter

1 hr = 3600 seconds

so

[tex]200 km/hr = \frac{200*1000}{1*3600}   m/s[/tex]

simplifies to

[tex]\frac{5000}{9} m/s[/tex]

[tex]55.6 m/s[/tex]

so option C

Answer:  C) 55.6 m/s  

Step-by-step explanation:  200km/1hr x 1000m/1km x 1hr/60min x 1min/60s = 55.6 m/s

If the conversion factors are properly set up and all numbers are correct, the unwanted units cancel out leaving the units of the final answer.

Answer:

2

--

6

Step-by-step explanation:

2 over 6

Answer:

the answer is 11/36

Step-by-step explanation:

Answer:

288

Step-by-step explanation:

Maya swims 0.75 kilometers each day because to convert 750 meters to kilometers, we divide by 1,000.

The student wishes to know how many kilometers Maya swims each day if she swims 750 meters. To convert meters to kilometers, we use the fact that 1 kilometer is equivalent to 1,000 meters. So, to find out how many kilometers 750 meters is, we divide the number of meters by 1,000.

750 meters \/ 1,000 = 0.75 kilometers

Therefore, Maya swims 0.75 kilometers each day.

A should be your answer no 100 %

[tex]Solution, solve\:for\:x,\:x^2-8x+7=0\quad :\quad x=7,\:x=1[/tex]

Steps:

[tex]Solve\:with\:the\:quadratic\:formula, \mathrm{For\:}\quad a=1,\:b=-8,\:c=7:\quad x_{1,\:2}=\frac{-\left(-8\right)\pm \sqrt{\left(-8\right)^2-4\cdot \:1\cdot \:7}}{2\cdot \:1},\\[/tex]

[tex]x=\frac{-\left(-8\right)+\sqrt{\left(-8\right)^2-4\cdot \:1\cdot \:7}}{2\cdot \:1}:\quad 7[/tex]

[tex]x=\frac{-\left(-8\right)-\sqrt{\left(-8\right)^2-4\cdot \:1\cdot \:7}}{2\cdot \:1}:\quad 1[/tex][tex]\mathrm{The\:final\:solutions\:to\:the\:quadratic\:equation\:are:} x=7,\:x=1[/tex]

The correct answer is B.

1 ≤ s -8

1+8 ≤ s

9. ≤ s

The value of the variable s is greater than or equal to 9.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.

The inequality is given below.

1 ≤ s - 8

Simplify the inequality, then the value of the variable s will be

1 ≤ s - 8

1 + 8 ≤ s

9 ≤ s

Thus, the value of the variable s is greater than or equal to 9.

More about the inequality link is given below.

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Convert all statistics into percentages:

CA: 3/25=0.12 -> 12%

NY: 3/50=0.06 -> 6%

TX: 2/25=0.08->8%

(A) Out of the three states, California has the largest population

(B) Out of the three states, NY has the smallest population

(C) USA=100%, CA+NY+TX=26%, therefore 74% of USA do not live on those three states.  

Answer:

NO the Earth to Sun distance is 9.3 x 10^7 miles.

Earth to Noon distance is 2.4 x 10^5 miles

9.3 x 10^7 is 387.5 times larger than 2.4 x 10 ^ 5

Step-by-step explanation:

Answer:

31 times bigger is the distance from earth to the sun than the distance from earth to the moon.

Step-by-step explanation:

Given : The distance from the earth to the sun is 9.3×10 to the 6(power) miles. The distance from earth the moon is 3×10 to the 5th(power) miles.

To find : How many times bigger is the distance from earth to the sun than the distance from earth to the moon?

Solution :          

The distance from the earth to the sun is [tex]9.3\times 10^{6}[/tex] miles.

The distance from the earth to the moon is [tex]3\times 10^{5}[/tex] miles.

To know, times bigger is the distance from earth to the sun than the distance from earth to the moon is given by,

[tex]n=\frac{9.3\times 10^{6}}{3\times 10^{5}}[/tex]

[tex]n=3.1\times 10^{6-5}[/tex]

[tex]n=3.1\times 10[/tex]

[tex]n=31[/tex]

Therefore, 31 times bigger is the distance from earth to the sun than the distance from earth to the moon.

Answer:

true

Step-by-step explanation: