The graph of h(x) = x2 – 3 is a translation of the
graph of f(x)
by
units.

Answer:

a) C) The system has no solutions only when h=3 and k is any real number.

b) D) The system has a unique solution when [tex]h=(-\infty,3)U(3,\infty)[/tex] and k is any real number.

c) The system has may solutions when h=3 and k=15

Step-by-step explanation:

a) In order to determine when the system will have no solution, we can start by solving the equation by substitution. We can solve the first equation for x1:

[tex]x_{1}+hx_{2}=3[/tex]

so

[tex]x_{1}=3-hx_{2}[/tex]

Next we can substitute this into the second equation so we get:

[tex]5(3-hx_{2})+15x_{2}=k[/tex]

We distribute the 5 into the first parenthesis so we get:

[tex]15-5hx_{2}+15x_{2}=k[/tex]

and group like terms:

[tex]-5hx_{2}+15x_{2}=k-15[/tex]

we factor x2 so we get:

[tex]x_{2}(-5h+15)=k-15[/tex]

and solve for x2:

[tex]x_{2}=\frac{k-15}{-5h+15}[/tex]

this final answer is important because it tells us what value the system of equations is not valid for. That answer will not ve vallid if the denominator is zero, so we can set the denominator equal to zero and solve for h, so we get:

[tex]-5h+15= 0[/tex]

and solve for h:

[tex]-5h= -15[/tex]

[tex]h=\frac{-15}{-5}[/tex]

[tex]h= 3[/tex]

so it doesn't really matter what value k gets since all that matters is that the denominator of the answer isn't zero.

b)

For part b we need to know when the system of equations will have infinitely many answers. Generally, this will happen when both equations are basically the same, so we need to make sure to simplify the second equation so it looks like the first equation, compare them and determine the respective coefficients.

So we take the second equation and factor it:

[tex]5x_{1}+15x_{2}=k[/tex]

we start by factoring a 5 from the left side of the equation so we get:

[tex]5(x_{1}+3x_{2})=k[/tex]

Next, we divide both sides of the equation into 5 so we get:

[tex]x_{1}+3x_{2}=\frac{k}{5}[/tex]

we now compare it to the first equation:

[tex]x_{1}+hx_{2}=3[/tex]

[tex]x_{1}+3x_{2}=\frac{k}{5}[/tex]

In this case, every coefficient of the two equations must be the same for us to get infinitely many answers, so we can see that h=3 and [tex]\frac{k}{5}=3[/tex]

when taking the second condition and solving for k we get that:

[tex]k=3(5)[/tex]

so

k=15

Anything else than the specific combination h=3 and k=15 will give us unique solutions, so for b, the answer is:

D) The system has a unique solution when and k is any real number.

c)

We have already solved part c on the previous part of the problem, so the answer is:

The system has many solutions when h=3 and k=15

Answer: omg I- I tried but got nothing I’m sorry

Step-by-step explanation:

Answer:

83 fifth grade students

Step-by-step explanation:

the total amount was 1,245

they each bought 15

equation is 1,245/15=?

answer is 83

Answer:

3 students went to the book fair

Step-by-step explanation

Doing inverse operations so you do 1245 divided by 15 and that would be your answer.

Answer:

its rotation

because it just rotate one time

Answer:

7 orange and black fish

Step-by-step explanation:

a fifth of the remaining fish is 7 because you are doing 35*1/5. 35 is the remaining number of fish because already half of the other fish is 35 and they are orange

Answer:

good for alex

Step-by-step explanation:

Answer:

-207

Step-by-step explanation:

Using r= -3, we can substitute r in the whole equation as (-3) which gives you: ((-3)-3)^3 +(-3)^2. Now you can calculate these values in a step by step manner. (-6)^3 +9 then to -216 +9 which brings you to the answer of -207.

Answer:

225

Step-by-step explanation:

(r - 3)³ + r² if r = -3 and s = -4

(-3 - 3)^3 + (-3)^2

(-6)^3 + (9)

(-6 x -6 x -6) + 9

-216 + 9

-207

Answer: 6

Step 1: Subtract 8.

32 - 8 = 24

Step 2: Divide by 4, since the question is asking for 4 times the number.

24 ÷ 4 = 6

Answer = 6

03 = 1000

8. 10-5 = 1/100,000 = 0.00001

9. 109 = 1,000,000,000

10. 1 X 10-2 = 1/100Answer:

1. 100 = 102

2. 10,000,000 = 107

3. 1 / 10,000 = 10-4

4. one million = 106

5. 1 / 10,000,000 = 10-7

6. one ten millionth = 10-7

7. 1 = 0.01

Step-by-step explanation:

Answer: 45

Step-by-step explanation: The 3rd partner has 45% of the store. Which is also $315,000.

Answer: the third partner owns 45% or $315,000 of the business.

Step-by-step explanation:

30 percent of 700,000=210,00

25 percent of 700,000=175,000

175,000+210,000=385,000

700,000-385,000= 315,000

the third partner owns 315,000 and 315,000=45%

Answer:

true

Step-by-step explanation:

Trust me

Answer:

True

Step-by-step explanation:

2(12)+3(12)=60

24+36=60

Answer:

5 hours; Home Decor

Step-by-step explanation:

First thing you want to do is make an equation of the two to find when they'll be the same price. So it'll look something like this:

500+35x=600+15x

Get like terms together

100=20x

divide

x=5

After 5 hours, they'll be the same price.

For the second half, plug in the number 3 instead of 5 into the original equation

500+105     600+45

605             645

So he'd go with the first company

Answer:

sure

Step-by-step explanation:

I will do that okay

Answer: 3 Multiply

Step-by-step explanation: u would Multiply 4x7

Answer:

Step-by-step explanation:

ADE=DHG

FEH=IHE

ADE=DHE

ADC=EHI

BEF=IHE <This would be the correct answer if segment CDEF is parallel to segment GHI.

Answer:400

Step-by-step explanation:10×40=400

Answer:400

Step-by-step explanation:

Answer:

could I have a picture of the line

Answer: The cost per bag is $27

Step-by-step explanation:

Divide 135 by 5 = 27

Unit ratio means that if you know the rate per unit, you can calculate the cost by multiplying the constant rate by the number of units. In this question, the rate is $27 and the unit is the bag.

The ratio looks like

1:27 as 2:54 as 3:81 as 4:108 as 5:135

They are all equivalent to 1/27

y = 27x is another way of writing an equation for this ratio.

Answer:

x = 11

Step-by-step explanation:

f(x) = -x + 7

f(x) = -4

Using substitution, -x + 7 = -4

Then you can solve from there

-x + 7 = -4

-x = -11

x = 11

Hope this helps!

(I apologize if I'm incorrect)

Answer:

a

Step-by-step explanation:

Answer:

.1

Step-by-step explanation:

Answer:

Point Q is represented by the ordered pair (-2,9)

Answer:

10 feet.

Step-by-step explanation:

First time: 160/2=80.

Second time: 80/2=40.

Third time: 40/2=20.

Fourth time: 20/2=10.

Boom.

Answer:

answer is 142

Step-by-step explanation:

Answer:

Answer the three consecutive integers are 85, 86 and 87. Taxicab number 1729 is the smallest integer that can be expressed as a sum of two positive integer cubes in 2 distinct ways.

Answer:

85, 86, and 87

Step-by-step explanation:

85 + 86 + 87 = 258

Brainliest Please???

153 miles x 5280 feet per mile = 807,840 feet per hour.

1 hour = 3600 seconds.

The speed is 807,840 feet / 3600 = 224.4 feet per second.

Distance in 15 seconds = 224.4 x 15 = 3,366 feet.

The height of the rocket after t seconds is given by the equation h(t) = -16t² + 42t

An equation is an expression that shows the relationship between two or more variables and number.

1 mile = 5280 feet, 1 hour = 3600 seconds

153 miles per hour = (153 * 5280) / (3600) ft/s = 224.4 ft/s

After 15 seconds, height = 224.4 ft/s * 15 s = 3366 ft

The speed of the parachute is 224.4 ft/s, while after 15 seconds the distance fell was 3366 ft.

Find out more on equation at: https://brainly.com/question/2972832

#SPJ2

Answer:

A. 2

Step-by-step explanation:

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

Use any two points given in the table of values. Let's use (1, 5), (3, 9)

Let,

[tex] (1, 5) = (x_1, y_1) [/tex]

[tex] (3, 9) = (x_2, y_2) [/tex]

Plug these values into the slope formula:

[tex] slope (m) = \frac{9 - 5}{3 - 1} [/tex]

[tex] slope (m) = \frac{4}{2} [/tex]

[tex] slope (m) = 2 [/tex]

Answer:

I believe it is 5 because when simplified they all simplify to 1/5