MATH HELP

Which statement is true of the function f(x) = -3 squared root x

grigory [225]

Using translation concepts, it is found that the function $f(x) = -3\sqrt{x}$ is the function $g(x) = \sqrt{x}$ reflected over the x-axis and vertically stretched by a factor of 3.

<h3>What is a translation?</h3>

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, from $g(x) = \sqrt{3}$ to $f(x) = -3\sqrt{x}$ , g(x) was multiplied by -3, that is, it was reflected over the x-axis(due to the multiplication by the negative number) and vertically stretched by a factor of 3.

More can be learned about translation concepts at brainly.com/question/27948675

#SPJ1

6 0

2 years ago

Please assist me with these problems

Alex73 [517]

Answer:

1) $350

2) 55°

3) $300

Step-by-step explanation:

1) The total cost is the cost of the appointment plus the cost of the repair work. The appointment costs $50. The repair work costs $120 per 2 hours. So the total cost is:

C = 50 + (120/2) t

C = 50 + 60t

For 5 hours of work, the cost is:

C = 50 + 60(5)

C = 350

It costs $350.

2) The temperature starts at 70°. It drops 10° in 4 hours. So the temperature after t hours is:

T = 70 + (-10/4) t

T = 70 − 2.5t

After 6 hours:

T = 70 − 2.5(6)

T = 55

The temperature is 55°.

3) Jennie's total pay is her weekly pay plus her commissions. If her commission is x% of her sales, then her pay is:

P = 250 + (x/100) S

When her sales is $1000, her pay is $275.

275 = 250 + (x/100) 1000

275 = 250 + 10x

25 = 10x

x = 2.5

So her pay is:

P = 250 + (2.5/100) S

When S = $2000:

P = 250 + (2.5/100) 2000

P = 250 + 50

P = 300

Her total pay is $300.

8 0

3 years ago

20 points! Please draw this out on a number line so I have a direct answer, thank you! :D

mario62 [17]

Answer:

see attached

hope it helps!

5 0

3 years ago

Find the least common multiple (LCM) of 8y^6+ 144y^5+ 640y^4 and 2y^4 + 40y^3 + 200y^2.

Mice21 [21]

Answer:

LCM = $8y^{4}(y+ 10)^{2}(y + 8)$

Step-by-step explanation:

Making factors of $8y^{6}+ 144y^{5}+ 640y^{4}$

Taking $8y^{4}$ common:

$\Rightarrow 8y^{4} (y^{2}+ 18y+ 80)$

Using factorization method:

$\Rightarrow 8y^{4} (y^{2}+ 10y + 8y + 80)\\\Rightarrow 8y^{4} (y (y+ 10) + 8(y + 10))\\\Rightarrow 8y^{4} (y+ 10)(y + 8))\\\Rightarrow \underline{2y^{2}} \times 4y^{2} \underline{(y+ 10)}(y + 8)) ..... (1)$

Now, Making factors of $2y^{4} + 40y^{3} + 200y^{2}$

Taking $2y^{2}$ common:

$\Rightarrow 2y^{2} (y^{2}+ 20y+ 100)$

Using factorization method:

$\Rightarrow 2y^{2} (y^{2}+ 10y+ 10y+ 100)\\\Rightarrow 2y^{2} (y (y+ 10) + 10(y + 10))\\\Rightarrow \underline {2y^{2} (y+ 10)}(y + 10) ............ (2)$

The underlined parts show the Highest Common Factor(HCF).

i.e. HCF is $2y^{2} (y+ 10)$ .

We know the relation between LCM, HCF of the two numbers 'p' , 'q' and the numbers themselves as:

$HCF \times LCM = p \times q$

Using equations (1) and (2): $\Rightarrow 2y^{2} (y+ 10) \times LCM = 2y^{2} \times 4y^{2}(y+ 10)(y + 8) \times 2y^{2} (y+ 10)(y + 10)\\\Rightarrow LCM = 2y^{2} \times 4y^{2}(y+ 10)(y + 8) \times (y + 10)\\\Rightarrow LCM = 8y^{4}(y+ 10)^{2}(y + 8)$

Hence, LCM = $8y^{4}(y+ 10)^{2}(y + 8)$

5 0

3 years ago

How many table spoons of vanilla will she use? Plss provide how you got the answer

Ksivusya [100]

Hi!
In one batch she uses 3/4 teaspoon of vanilla
therefore in 5 batch she uses 5*3/4=15/4 teaspoons of vanilla.
as it is given that 3 teaspoons=1 tablespoon
the amount of vanilla used for 5 batches =(15/4)/3=(15/4)*1/3=5/4==1.25 tablespoons.

All the best.

4 0

3 years ago