Describe the solution of h(x) shown in the graph.

a parabola opening up passing through negative 1 comma zero, zero comma negative 2, and 2 comma zero

A. All solutions that lie on h(x)
B. All real solutions
C. All whole number solutions
D. All positive solutions

Answer:

The domain and range is (as inequalities):

[tex]x\leq 3\text{ and } -\infty < y < \infty[/tex]

Or in interval notation:

[tex]D=(-\infty, 3]\text{ and } R=(-\infty, \infty)[/tex]

Step-by-step explanation:

Recall that the domain is simply the set of all x-values of the function.

From the graph, we can see that the function is defined for all x-values less than or equal to 3.

Therefore, the domain is:

[tex]x\leq 3[/tex]

The range is the set of all y-values of the function.

From the graph, we can see that the range will extend infinitely in both directions.

Therefore, the range is all real numbers. As an inequality:

[tex]-\infty < y < \infty[/tex]

Or in interval notation, the domain is:

[tex](-\infty, 3][/tex]

And the range is:

[tex](-\infty, \infty)[/tex]

Answer:

Step-by-step explanation:

Given functions are,

f(x) = [tex]\sqrt{x} +3[/tex]

g(x) = 4 - [tex]\sqrt{x}[/tex]

22). (f - g)(x) = f(x) - g(x)

                    = [tex]\sqrt{x}+3-(4 - \sqrt{x} )[/tex]

                    = [tex]\sqrt{x} +3-4+\sqrt{x}[/tex]

                    = [tex]2\sqrt{x}-1[/tex]

     Domain of the function will be [0, ∞).

23). (f . g)(x) = f(x) × g(x)

                   = [tex](\sqrt{x}+3)(4-\sqrt{x} )[/tex]

                   = [tex]4(\sqrt{x}+3)-\sqrt{x}(\sqrt{x}+3)[/tex]

                   = [tex]4\sqrt{x} +12-x-3\sqrt{x}[/tex]

                   = [tex]-x+\sqrt{x}+12[/tex]

      Domain of the function will be [0, ∞).

Answer:

-2 0 2 3 this is the domain of the ordered pairs shown in the graph above

Answer:

The vertex form of the quadratic function, f(x) = a·(x - h)² + k

Step-by-step explanation:

The general form of a quadratic function is given as follows;

f(x) = a·x² + b·x + c

The vertex form of the quadratic function is f(x) = a·(x - h)² + k

Where;

(h, k) = The coordinates of the vertex of the parabola

h = -b/2·a, k = f(h)

Answer:

1 and 2.....then 3 is a different question

Answer:

[tex]j = - 0.45[/tex]

Step-by-step explanation:

Combine like terms and apply the rules of algebra.

[tex]2.25 - 11j - 7.75 + 1.5j = 0.5j - 1[/tex]

[tex] - 5.5 - 9.5j = 0.5j - 1[/tex]

[tex] - 9.5j = 0.5j + 4.5[/tex]

[tex] - 10 j= 4.5[/tex]

[tex]j = - 0.45[/tex]

Answer: j = -0.45

Step-by-step explanation:

Step 1: Combine like terms

2.25 - 11j - 7.75 + 1.5j = 0.5j - 1

-5.5 - 9.5j = 0.5j - 1

Step 2: isolate your variable

-5.5 - 9.5j = 0.5j - 1

Subtract 0.5j from both sides

-5.5 - 10j = -1

Add 5.5 to both sides

-10j = 4.5

Divide both sides by -10

j = -0.45

Answer:

2y² - 4y - 24

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

3(2y - 8) - 2y(5 - y)

Step 2: Simplify

Answer:

The population of Fun City after 171 years would be 214563.

Step-by-step explanation:

The statement depicts a case of exponential growth, whose model is described below:

[tex]p(t) = p_{o}\cdot r^{\frac{t}{T} }[/tex] (1)

Where:

[tex]p_{o}[/tex] - Initial population, no unit.

[tex]p(t)[/tex] - Current population, no unit.

[tex]r[/tex] - Growth rate, no unit.

[tex]t[/tex] - Time, in years.

[tex]T[/tex] - Growth period, in years.

If we know that [tex]p_{o} = 21000[/tex], [tex]r = 2[/tex], [tex]t = 171\,yr[/tex] and [tex]T = 51\,yr[/tex], then the population of the city after 171 years is:

[tex]p(t) = 21000\cdot 2^{\frac{171}{51} }[/tex]

[tex]p(t) = 214563[/tex]

The population of Fun City after 171 years would be 214563.

Answer:

6

Step-by-step explanation:

To figure out what needs to be multiplied, we need to find the least common denominator. By finding this, we know that what we multiply the equation with will be a multiple of each denominator, meaning that there will be no fractions left.

We can find the least common denominator by listing multiples of each fraction, and finding which one is the smallest but still in each list.

3: 3, 6, 9, 12...

2: 2, 4, 6, 8...

6: 6, 12, 18, 24...

We can notice that 6 is the lowest number in each list. Therefore, 6 is our least common denominator, and if we multiply by 6, the fractions will be removed.

Answer:

6

Step-by-step explanation:

I took the quiz and got it correct.

Answer:

1)  [tex]T_{(a, \, b)}[/tex] = f(x - a) + b

Coordinate change

(x, y) → (x + a, y + b)

2) RFy(x, y) = f(-x)

Coordinate change

(x, y) → (-x, y)

3) RFx(x, y) = -f(x)

Coordinate change

(x, y) → (-y, x)

4) RCCW90(x, y) = f⁻¹(-x)

Coordinate change

(x, y) → (-y, x)

5) RCCW180(x, y) = -(f(-x))

Coordinate change

(x, y) → (-x, -y)

6) A 270 degrees counterclockwise rotation gives;

RCCW270(x, y) = -(f⁻¹(x))

Coordinate change

(x, y) → (y, -x)

Step-by-step explanation:

1) Horizontal translation a units right = f(x - a)

The vertical translation b units up = f(x) + b

Therefore, we get; [tex]T_{(a, \, b)}[/tex] = f(x - a) + b

The coordinate change

(x, y) → (x + a, y + b)

2) A reflection across the y-axis = RFy(x, y) = f(-x)

The coordinate change

(x, y) → (-x, y)

3) A reflection across the x-axis gives RFx(x, y) → (x, -y)

Therefore, in function notation, we get;

RFx(x, y) = -f(x)

4) A 90 degrees rotation counterclockwise, we get RotCCW90(x, y) → (-y, x)

In function notation RotCCW90(x, y) = INVf(-x) = f⁻¹(-x)

5) A 180 degrees counterclockwise rotation about the origin gives;

(x, y) → (-x, -y)

Therefore, we get;

In function notation RotCCW180(x, y)  = -(f(-x))

6) A 270 degrees counterclockwise rotation gives RotCCW270(x, y) → (y, -x)

In function notation RotCCW270(x, y) = -(f⁻¹(x))

Answer:

7.1

Step-by-step explanation:

We used SOHCAHTOA because it's a right angle triangle

So because we have an angle with an adjacent of 6.3 and hypotenuse of x

We will use

Cos=adjacent /hypotenuse

Hello,

Imagine Algebra does not exist .

Let's suppose all tickets are children's tickets

The sum should be 5$*375=1875$

Not enough, we must have $2153: 2153-1875=278 ($) must be found.

Let's replace a children ticket with an adult one,

we get one dollar more.

We must thus exchange 278 tickets

There are 278 adult tickets and 375-278=97 children tickets

Proof:  278*6+97*5=2153

Answer:

C.) 8 pounds

Hope that can help

Answer:

Step 1 & Step 4 are true statements

Step-by-step explanation:

Explanation in progress! Enjoy your answer first then come back for the explanation once you've done it (●'◡'●)

Answer:

OMG I LOVE LOUIS SO MUCH HE IS SO PERFECT

Step-by-step explanation:

Answer:

<-56, -16>

Step-by-step explanation:

multiply the values by 8 because that's what the question tells you to do

Start by doing the binomial expansion of (x+y)^6 where x represents success. This is

(x^6y^0) + 6(x^5y^1) +15(x^4y^2) +20(x^3y^3) +15(x^2y^4) +6(x^1y^5) +(x^0y^6)

We are interested in the x^3y^3 term which represents exactly 3 sucesses. Since the probalbility of sucess and failure are both .5 we should be able to figure this out just using the coefficients of the terms which is

20/64 = .3125 which is 31.25%

The probability of exactly three successes in six trials of a binomial experiment in which the the probability of is 50% is 31.25%.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

Here,

Probability =(³₆×(50%)³×(1-50%)⁶⁻³

= 20×(1/2)³×(1/2)³

= 20× 1/64

= 20/64

= 5/16

= 0.3125

= 0.3125×100

= 31.25%

Therefore, the probability of exactly three successes in six trials of a binomial experiment in which the the probability of is 50% is 31.25%.

To learn more about the probability visit:

https://brainly.com/question/11234923.

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Answer: Personally I would do option "B" 2 1/3 because it sounds right.

Answer: C. (0, -3)

Step-by-step explanation:

You don't even need to find the function, just mentally graph every point in the options on the graph.

The line is not dotted, showing that the inequality is probably either ≥ or ≤, so points on the line do count as solution.

Answer:

25

Step-by-step explanation:

You need to simplify

.

.

.

.

................... :)

Answer:

D

Step-by-step explanation:

9+24-16+8= 25

Answer:

30 seconds

Step-by-step explanation:

→ Work out how many floors it's going to travel

15 - 3 = 12 floors

→ Work out how many meters 12 floors is

12 × 5 = 60 meters

→ Work out how long that will take

60 ÷ 2 = 30 seconds

Answer:

1/2 + 2/3 + 5/4 = 29/ 12 = 2 5/  12  ≅ 2.4166667

Step-by-step explanation:

Add: 1/ 2  + 2/ 3  = 1 · 3/ 2 · 3  + 2 · 2/ 3 · 2  = 3/ 6  + 4/ 6  = 3 + 4/ 6  = 7/ 6

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(2, 3) = 6. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 3 = 6. In the next intermediate step, the fraction result cannot be further simplified by canceling.

In words - one half plus two thirds = seven sixths.

Add: the result of step No. 1 + 5/ 4  = 7/ 6  + 5/ 4  = 7 · 2/ 6 · 2  + 5 · 3/ 4 · 3  = 14/ 12  + 15/ 12  = 14 + 15/ 12 = 29/ 12

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(6, 4) = 12. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 6 × 4 = 24. In the next intermediate step, the fraction result cannot be further simplified by canceling.

In words - seven sixths plus five quarters = twenty-nine twelfths.

hope it helps...

correct me if I'm wrong...

Answer:

[tex]\angle A=90-72[/tex]

[tex]\angle A=18[/tex]

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

[tex]sin~72=\frac{b}{11}[/tex]

[tex]11\times sin~72=6[/tex]

[tex]b=10.5[/tex]

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

[tex]11\times cos~72=a[/tex]

[tex]a=3.4[/tex]

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

ANSWER:

a=3.4

b=10.5

∠A=18

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

hope it helps...

have a great day!!

Answer:

x = -1, y = -1

Step-by-step explanation:

x = 4y + 3

2x + y = -3

We have the value of x in terms of y, so we substitute that in 2x + y = -3:

2(4y+3)+y = -3

8y+6+y = -3

9y = -9

y = -1

Now we substitute the value of y in x = 4y + 3:

x = 4(-1)+3

x = -1

Answer:

y = -1 & x = -1

Step-by-step explanation:

x = 4y + 3 .... ( 1)

2x + y = -3 ........(2)

substitute the 4y + 3 as x in the second equation

2( 4y + 3) + y = -3

simplify and solve for y

8y + 24 + y = -3

9 y + 24 = -3

9y = -3 -24

9y = -27

y = -27 / 9

y = -1

Now, substitute the value of y -1 in first equation

x = 4y + 3

solve for x

x = 4 ( - 1 ) + 3

x = -4 + 3

x = -1

Answer:

[tex]10^2a^2b[/tex]

Step-by-step explanation:

Exponents are a way of shortening multiplication statements. The exponent represents how many times a term is being multiplied by itself. So, when two terms have the same base it can be written with exponents. For example. 10*10 can be written as [tex]10^2[/tex] because 10 is being multiplied 2 times. Therefore, if we do this with every term you get [tex]10^2a^2b[/tex].

Answer:

[tex]{ \bf {factor : { \tt{x - 1}}}} \\ x - 1 = 0 \\ x = 1 \\ { \tt{f(x) = {x}^{3} - {3x}^{2} + kx - 1}} \\ { \tt{f(1) : {(1)}^{3} - 3 {(1)}^{2} + k(1) - 1 = 0}} \\ { \tt{k - 3 = 0}} \\ { \tt{k = 3}}[/tex]

Answer:

k = 3

Step-by-step explanation:

If x-1 is a factor of x³ - 3x² + kx - 1 then value of x is 1.

f (x ) = x³ - 3x² + Kx - 1 , then

plug 1 as x in the expression.

expand exponents

combine like terms

Add 3 to both side

Answer:

option 4

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

(x + 1)² + (y - 12)² = 25 ← is in standard form

with centre = (- 1, 12 ) and radius = [tex]\sqrt{25}[/tex] = 5

Answer:

C

Step-by-step explanation:

The scale factor is the ratio of corresponding sides, image to original, so

scale factor = [tex]\frac{XY}{AB}[/tex] = [tex]\frac{9}{45}[/tex] = [tex]\frac{1}{5}[/tex] → C

The scale factor will be equal to 1 / 5. the correct option is C.

The scale factor is defined as the proportion of the new image's size to that of the previous image. Dilation is the process of increasing the size of an object while maintaining its shape. Depending on the scale factor, the object's size can be increased or decreased.

In the given image all the angles are the same and the sides are dilated so the scale factor will be calculated as below,

Scale factor = Original size / dilated size

Scale factor = XY / AB

Scale factor = 9 / 45

Scale factor = 1 / 5

Therefore, the scale factor will be equal to 1 / 5. the correct option is C.

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Answer:

[tex]4-6i[/tex]

Step-by-step explanation:

Substitute the value of the variable into the expression and simplify.

the answer is in the picture