what is the y-intercept of the line shown below?

A:3/4
B:2
C:3
D:4​

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Explanation:

Piecewise functions are admittedly a bit confusing at first if you aren't familiar with them.

However, they aren't too bad. Effectively we have two functions going on depending on what the input is.

If the input x is less than 0, then we go for the top row and say [tex]f(x) = x^2[/tex]

OR

If the input x is greater than 0, then we go for the bottom row to say [tex]f(x) = \sqrt[3]{x}[/tex]

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In this case, the input is x = -8. So we go for the first row since this x value satisfies x < 0.

We would then say:

[tex]f(x) = x^2\\\\f(-8) = (-8)^2\\\\f(-8) = 64\\\\[/tex]

Which points us to choice A as the final answer.

Answer:

f(-8) = 64

Step-by-step explanation:

Input -8 into one of the formulas (either will work) and the answer should be 64. therefore, if x is -8, f(-8) would equal 64.

Answer:

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Answer:

D) 1

Step-by-step explanation:

using the distributive property we have ax+a+bx-b-2=0. because the equation is true for all real x, ax=-bx. this means a-b-2=0 and a=-b. a-b-2=0 becomes a=b+2. then we substitute a for -b and get -b=b+2 which becomes 2b=-2 so b=-1. since a=-b, a=1

Answer:

160

Step-by-step explanation:

(3a+4b) = 16

ab = 4

Square (3a+4b)

(3a+4b)(3a+4b) = 16^2

9a^2 + 12ab+12ab+16b^2 = =256

9a^2 +16b^2   +24ab=256

9a^2 +16b^2   +24ab - 24 ab=256 -24ab

9a^2 +16b^2  =256- 24ab

We know ab = 4

9a^2 +16b^2  =256- 24*4

9a^2 +16b^2  =256- 96

9a^2 +16b^2  =160

Step-by-step explanation:

Measure of Angle 1 is 115 due to corresponding angles postulate

Measure of Angle 2 is 65 is linear pair postulate.

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Answer:

  C, D, E

Step-by-step explanation:

Vertical asymptotes are found where the denominator is zero. The denominator will be zero when any of its factors is zero. Then the vertical asymptotes are ...

  x = 0   ⇒   x = 0 . . . . . . choice E

  x -1 = 0   ⇒   x = 1 . . . . . choice C

  x +5 = 0   ⇒   x = -5 . . . choice D

Answer:

c.145.3 to 154.7.

Step-by-step explanation:

We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a p-value of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.645\frac{20}{\sqrt{50}} = 4.7[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 150 - 4.7 = 145.3.

The upper end of the interval is the sample mean added to M. So it is 150 + 4.7 = 154.7.

Thus the correct answer is given by option c.

Answer:

.15

Step-by-step explanation:

Answer:

000023 because if we take three 0's we can get 000023 and 417 million

Answer:

10a²+17a²s-6s²

Step-by-step explanation:

(-2a²+s)(5a²-6s)

= -10a²+12a²s+5a²s-6s²

= -10a²+17a²s-6s²

Answer:

b

Step-by-step explanation:

Answer: D

Step-by-step explanation:

(lines parallel to each other have the same slope)

slope = m = 2

y = mx + b, (5,6)

6 = 2(5) + b

6 = 10 + b

b = -4

y = 2x - 4

y - 6 = 2(x - 5)

y - 6 = 2x - 10

y = 2x -4

Answer:

0.127

Step-by-step explanation:

Given:

The equation of a parabola is:

[tex]y=(x+2)^2-1[/tex]

To find:

The coordinates of the vertex of the given equation.

Solution:

The vertex form of a quadratic function is:

[tex]y=a(x-h)^2+k[/tex]               ...(i)

Where, a is a constant and (h,k) is the vertex.

We have,

[tex]y=(x+2)^2-1[/tex]                 ...(ii)

On comparing (i) and (ii), we get

[tex]a=1[/tex]

[tex]h=-2[/tex]

[tex]k=-1[/tex]

We know that the vertex of the parabola is (h,k).

Therefore, the vertex of the given equation is (-2,-1).

Answer:

[tex]f(3x)=9x^2-3[/tex]

Step-by-step explanation:

One is given the following function:

[tex]f(x)=x^2-3[/tex]

One is asked to evaluate the function for ([tex]f(3x)[/tex]). Substitute ([tex]3x[/tex]) in place of ([tex]x[/tex]) then simplify. Remember that a number raised to an exponent is the same as that number times itself the number of times that the exponent indicates. One can apply this logic here while simplifying,

[tex]f(x)=x^2-3[/tex]

[tex]f(3x)=(3x)^2-3[/tex]

[tex]f(3x)=(3x*3x)-3[/tex]

[tex]f(3x)=(9x^2)-3[/tex]

[tex]f(3x)=9x^2-3[/tex]

Answer:

4% and 5% respectively

Step-by-step explanation:

Let the intrest rate be x in the first account at x% and (x+1)% in the second account.

ATQ, 100=(x)*1500/100+(x+1)*800/100

x=4.

The domain of a set is the possible input values the set can take.

It is true that the domain of ∀x ∃y(x+y≥0) is the set of real numbers

Given that: ∀x ∃y(x+y≥0)

Considering x+y ≥ 0, it means that the values of x + y are at least 0.

Make y the subject in x+y ≥ 0

So, we have:

[tex]\mathbf{y \le -x}[/tex]

There is no restriction as to the possible values of x.

This means that x can take any real number.

Hence, it is true that the domain of ∀x ∃y(x+y≥0) is the set of real numbers.

Read more about domain at:

https://brainly.com/question/15110684

Step-by-step explanation:

How is the graph of y=(x-1)2-3 transformed to produce the graph of y-3(x+4)??

The graph is translated left 5 units, compressed vertically by a factor of 2, and translated up 3 units.

The graph is stretched vertically by a factor of Ź, translated left 5 units, and translated up 3 units.

O The graph is translated left 5 units, compressed horizontally by a factor of 3, and translated down 3 units.

O The graph is stretched horizontally by a factor of Ž, translated left 5 units, and translated down 3 units.

Answer:

B. The graph is stretched vertically by a factor of One-half, translated left 5 units, and translated up 3 units.

Step-by-step explanation:

just did the test

Answer:

8

Step-by-step explanation:

if you have 6 pounds and you use 0.75 pounds per then you can make 6/0.75 dinners = 8

Answer:

n = -10

Step-by-step explanation:

1 / 8^n  = 8^5^2

We know that 1/a^b = a^-b

We also know that a^b^c = a^(b*c)

8^-n = 8^(5*2)

8^-n = 8^(10)

Since the bases are the same, the exponents are the same

-n = 10

n = -10

Answer:

Area of the metal sheet required = 364 square inches

Step-by-step explanation:

Area of the metal sheet required = Surface area of the lateral sides of the vent transition

Since, lateral sides of the vent is in the shape of a trapezoid,

Therefore, surface area of the vent = 4(Surface area of one lateral side)

                                                           = [tex]4[\frac{1}{2}(b_1+b_2)h][/tex]

Here, [tex]b_1[/tex] and [tex]b_2[/tex] are two parallel sides and [tex]h[/tex] is the distance between these parallel sides.

Surface area of the vent = [tex]4[\frac{1}{2}(8+5)14][/tex]

                                         = 364 square inches

Therefore, area of the metal sheet required = 364 square inches

Answer:

-6k = -8 is an expression

A and C are inequalities

D is arithmetic

Answer:

a) 10,025 m = 10km 25m = 10.025 km

b) 1,500 m = 1 km 500 m = 1.5 km

Answer:

a) 10025m = 10km 25m = 10.025km

b) 1500m = 1km 500m = 1.5km

Step-by-step explanation:

Concept:

Here, we need to know the idea of unit conversion.

Unit conversion is the conversion between different units of measurement for the same quantity.

1 km = 1000 m

Solve:

a)

b)

Hope this helps!! :)

Please let me know if you have any questions

Answer:

if we do 9 times a number that will be

9x

Answer:

9x

Step-by-step explanation:

9 times a number (a variable)  = 9x

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Answer:

  g, h, f

Step-by-step explanation:

A graph of two exponential curves will have the one with the least growth rate crossing under the one with the greater growth rate. Here, f(x) is shown crossing under g(x) and is on its way to a point of intersection with h(x). So, f(x) has the least growth rate.

g(x) and h(x) start out at about the same level, but g(x) curves upward faster, indicating it has the higher growth rate.

In order from greatest to least growth rate, the functions are ...

  g(x), h(x), f(x)

We need to find the percent, let's start but making the equation.

The price is 2.69

The tax cost is 0.13

So what percent of 2.69 is = 0.13.

Equation: X/100 x 2.69 = 0.13

Multiply each side by 100 so we can get x alone with the price: 2.69x = 13

Now to get x alone, we must divide both sides by 2.69: x = 4.8

Finally, we just round 4.8 to the nearest whole number, which is 5 (5 or above give it a shove, 4 or below let it go, we have 8 so we give it a shove). This means that the answer will be 5%.

I hope this helps! :)

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Answer:

  (a)  10 cm

Step-by-step explanation:

Since C is the midpoint of AB, the triangle shown is 1/4 of the rectangular area shown. When the tank is sitting horizontally on its 100 cm side, the water height will be 1/4 of the 40 cm height of the tank. It will be 10 cm.

__

More elaborate explanation

Triangle area = 1/2(AD)(AC) = 1/2(AD)(1/2(AB)) = 1/4(AD)(AB)

Whole tank area = (AD)(AB)

So, the triangle area is 1/4 the whole tank area. When the tank is tipped back to horizontal, the water area will still be 1/4 the whole tank area, so will be ...

  water area = (1/4(AD))(AB)

and the height will be 1/4(AD) = 1/4(40 cm) = 10 cm