Which graph represents the function f(x) = –|x + 3|?

Answer:

v = 4

Step-by-step explanation:

[tex]collect \: like \: terms \: \\ 7v - 4v - v + 4v = 7 + 7 + 10\\ 3v - v + 4v = 14 + 10\\ \\ 2v + 4v = 24 \\ 6v = 24 \\ v = 4[/tex]

The correct option regarding the area of the figure is given as follows:

14+16.25π units².

The figure, given with no scale at the end of the answer, is composed by:

The sides of the right-triangle are given as follows:

The area of a right triangle is given by half the multiplication of the sides, hence:

At = 0.5 x 7 x 4 = 14 units.

The radius of the semicircle is half the hypotenuse of the right triangle, hence, applying the Pythagorean Theorem:

h² = 7² + 4²

h = sqrt(7² + 4²)

r = 0.5sqrt(7² + 4²)

r = 4.03 inches.

The area of a semicircle of radius r is:

As = πr².

Hence:

As = π(4.03)² = 16.25 π.

The total area is obtained as the sum of the areas of each separate part, hence:

A = At + As = 14+16.25π units².

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Answer:

Step-by-step explanation:

14+8.125

C

Answer:

[tex] \sqrt[2]{15} = 7.5[/tex]

The time taken to reaches its maximum height is 3s.

In the question,

It is given that,

Height, h(t) = [tex]96t - 16t^{2}[/tex]

The maximum value of the function is obtained if the first derivative of the function h (t) = 0.

[tex]\frac{dh(t)}{dt} = 96 - 32t = 0[/tex]

⇒ [tex]t = 3[/tex]

So, time taken to reach its max height is 3 seconds.

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Answer:

Step-by-step explanation:

a. 1 hectare = 2.471 acres 

6 hectares x (2.471 acres / 1 hectare)

=14.826 acres

b. prices per acre: 150,000/14.826

=10,117.36 per acre

The inequality that can be used to determine the maximum number of hours h the frozen yogurt machine can be used if the rental cost for the day will not exceed $300 is 150+25h ≤300.

According to the question,

We have the following information:

The cost to rent a frozen yogurt machine is $150 per day plus $25 per hour of use.

And h represents the number of hours.

So, we have the following expression to find the total cost:

150+25h

Now, it is given that the total rental cost should not exceed $300.

So, we have the following inequality:

150+25h ≤300

Hence, the correct option is C.

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Answer: 5q-5r               -5q+5r

Answer: [tex]\frac{4\sqrt{x} }{t^2}[/tex]

Step-by-step explanation:

You can start by either applying the exponent to both the numerator and denominator (exponent rule), or make things simpler by dividing first. Doing the latter allows me to show both properties. Since the terms in the fraction are being multiplied, we can divide common terms which will leave us with [tex]\frac{16x}{t^4}[/tex] on the inside. Now that it is simplified, we can apply the exponent. We will end up with 4x^1/2 in the numerator and t^2 in the denominator. If the exponent seems daunting, it is also helpful to know that raising something to the exponent of 1/2 is basically taking the square root of it.

The acceleration when the car comes to a full stop is 20.76 meters per square second.

Here we have the velocity function:

v(t) = -3t^2 + 18t + 9

To find the acceleration we need to differentiate with respect to the variable t, so we will get the acceleration:

a(t) = 2*(-3)*t + 1*18

a(t) = - 6*t + 18

Now, the car will come to a stop when the velocity is equal to zero, so we need to solve:

-3t^2 + 18t + 9 = 0

Dividing all by -3 we get:

(-3t^2 + 18t + 9)/-3 = 0

t^2 - 6t - 3 = 0

The solutions are:

[tex]t = \frac{6 \pm \sqrt{(-6)^2 - 4*1*-3} }{2*1} \\\\t = \frac{6 \pm 6.92}{2}[/tex]

We only care for the positive solution:

t = (6 + 6.92)/2 = 6.46

The acceleration at that time is:

a(6.46) =  - 6*6.46 + 18 = -20.76

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The amount invested in the account that yields 10% simple interest is $1,000.

The amount invested in the account that yields 7% simple interest is $9,000.

The first step is to form a system of equations using the information provided in the question:

a + b = $10,000 equation 1

0.1a + 0.07b = 730 equation 2

Where:

a = amount invested in the account that yields 10% simple interest

b =  amount invested in the account that yields 7% simple interest

The elimination method would be used to solve the equations

Multiply equation 1 by 0.1

0.1a + 0.1b = 1000 equation 3

Subtract equation 2 from equation 3

0.03b = $270

Divide both sides of the equation by 0.03

b = $270 / 0.03

b = 9,000

Substitute for b in equation 1

a + 9,000 = 10,000

a = 10,000 - 9,000

a = 1000

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The linear equation in the table is written as:

y = (1/4)*x + 6

The linear equation in slope-intercept form is written as:

y = m*x+ b

Where m is the slope and b is the y-intercept.

We know that if a line passes through two points (x₁, y₁) and (x₂, y₂), then the slope is:

m = (y₂ -  y₁)/(x₂ - x₁)

Here we can use the first two points on the table:

(-4, 5) and (0, 6), so the slope is:

m = (6 - 5)/(0 + 4) = 1/4

And because of the point (0, 6) we know that the y-intercept is 6, then the line is:

y = (1/4)*x + 6

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The exact value of sin(θ) given that cos(θ) = -2√5/5 is √5/5

The given trigonometry ratio is

cos(θ) = -2√5/5

By the trigonometry ratio, we have

sin²(θ) + cos²(θ) = 1

Substitute cos(θ) = -2√5/5 into the above equation

So, we have the following representation

sin²(θ) + (-2√5/5)² = 1

Evaluate the exponent

sin²(θ) + 4/5 = 1

Subtract 4/5 from both sides

This gives

sin²(θ) = 1/5

Take the square root of both sides

√sin²(θ) = √1/5

Evaluate the square root

sin(θ) = ±1/√5

Sin is positive in quadrant II

So, we have

sin(θ) = 1/√5

Rationalize

sin(θ) = 1/√5 * √5/√5

This gives

sin(θ) = √5/5

This gives the value of sin(θ)

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The average rate of change = 1.59 ≈ 2

The average rate of change can be calculated by

1) The first one = [tex]\frac{3 + 0}{2}[/tex] = 1.5

2 ) the second can also be solved by ; 8 + 2/ 2 = 5

3 ) the third one will be 20 + 6 / 2 = 13

4) 8.5

5) 12.5

To calculate the average rate of change

we will first add all the distance

Adding all the distance we will get the sum = 3 + 8 + 20 + 10 + 10 = 51

The total time = 2 + 6 + 9 +15 = 32

Thus the average rate of change = 51 / 32 = 1.59

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Answer:

Step 1:subtract 5 from both sides

step 2: divide both sides by two

final answer: c= p-5/2

Answer:

Step 1: Subtract 5 from both sides.

Step 2: Divide 2 from both sides.

Final answer: C= p-5 / 2

Step-by-step explanation:

The degree and number of unique zeros of f(x) = (x – 5)(x + 3)(x – 1)² is:

Degree: 4; number of unique zeros: 3.

The end behavior of the polynomial is:

As x → –∞, f(x) → ∞ and as x → ∞, f(x) → ∞.

The degree of the polynomial function is given by the sum of the multiplicities of the roots.

These roots are given as follows:

Hence the degree is:

1 + 1 + 2 = 4.

The unique zeros are the roots, hence there are three unique zeros, which is the same number of linear factors of the function.

The end behavior is the limit of the function as x goes to negative infinity and to positive infinite, hence:

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The acceleration of the car three seconds before it comes to a stop is  -2.76 m/s² (Letter B).

Derivative indicates the rate of change of a function with respect to a variable. Thus, when you derivate the position function, you find the velocity function. And, when you derivate the velocity function, you find the acceleration function.

In other words, the velocity function represents the first derivative of the position, meanwhile, the acceleration function represents the second derivative of the position.

For derivating an equation, you should apply the rule: [tex](\frac{d}{dx} ) (x^n ) = nx^{n-1}[/tex]. Example: x²= 2x

The car stops when the velocity is equal to zero. Thus, v(t) = -3t² + 18t + 9 =0. Therefore, you  should solve this quadratic function:

Δ=b²-4ac=[tex]18^2-4\left(-3\right)\cdot \:9=324+12*9=324+108=432[/tex]

[tex]t_{1,\:2}=\frac{-18\pm \sqrt{432}}{2\left(-3\right)}\\ \\ t_{1,\:2}=\frac{-18\pm \sqrt{432}}{-6}[/tex]

[tex]t_1=\frac{-18+12\sqrt{3}}{-6}=3-2\sqrt{3}[/tex]

[tex]t_2=\frac{-18-12\sqrt{3}}{-6}=3+2\sqrt{3}[/tex]

Like t is a positive number, you should use [tex]t_2[/tex]. Thus, the value of t that you should apply to find the acceleration of the car three seconds before it comes to a stop is [tex]2\sqrt{3}[/tex].

The acceleration can be found from the derivative of the velocity function. See below.

a(t)= -6t+18 , for t=[tex]2\sqrt{3}[/tex]

a(t)= -6*[tex]2\sqrt{3}[/tex]t+18

a(t)= [tex]-12\sqrt{3}[/tex]t+18

a(t)=-2.76

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The inequality that represents the number and type of shots the player needs to win the title is -

x + 2y ≥ 28

What is Equation Modelling?

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have A basketball player in a game who makes [x] free throws worth 1 point and [y] free throws worth 2 point baskets. The player needs to score at least 28 points to win the scoring title.

The inequality that represents the number and type of shots the player needs to win the title is -

x + 2y ≥ 28

Therefore, the inequality that represents the number and type of shots the player needs to win the title is -

x + 2y ≥ 28

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Step-by-step explanation:

81 3/8 ÷ 9 2/5

81*8+3 = 651

651/8

9 2/5 = 9*5+2=47

47/5

651/8 ÷ 47/5 =

651/8 * 5/47 = 3255/376 =

8.65691489362

The angle x will be 34°.

From the properties of circles we get to know that the angle at the center and the angle between two tangents are always supplementary.

Supplementary angles are those which always sum to to 180°.

For example ∠HJK is supplementary to ∠HIK the their sum will come out to be 180°.

similarly ∠ROP + ∠RQP = 180°

∠RQP = 180° - ∠ROP

∠ROP is given to us 146°

After putting it in the equation above we get ∠RQP = 34°

Therefore x comes out to be 34°.

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The given statement "In a geometric sequence, the difference between each pair of consecutive terms must be the same" is false.

Number sequence is a progression or an ordered list of numbers governed by a pattern or rule. For example -

3, 6, 9, 12, 15

x, x + 2, x + 4, x + 6

Given is the following statement -

"In a geometric sequence, the difference between each pair of consecutive terms must be the same"

The given statement is false as the statement mentioned above is the definition of a arithmetic sequence. In geometric sequence, the ratio of each pair of consecutive terms must be the same. Mathematically -

a[n + 1]/a[n] = r {constant}

Therefore, the given statement "In a geometric sequence, the difference between each pair of consecutive terms must be the same" is false.

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By graphing, the solution of the system of equations is: (-4, 1).

The solution to the system of equations can be solved by graphing both lines of each equation on a coordinate plane, then find the coordinates of the point where both lines intersect each other.

Given the following equations:

y = 1/4x + 2

y = -2x - 7

The graph for y = 1/4x + 2 will intercept the y-axis at 2 and also has a slope of 2. The line for this equation is the red line.

The graph of y = -2x - 7 will also have a slope of -2. Its y-intercept would be -7. The line of the equation is the blue line.

The graph below shows the lines of both equations which intersect at (-4, 1), The solution is, (-4, 1).

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The probability of rolling a 3 first time and a number greater than 4 thre second time is 1/18

Probability is the likelihood that an event will happen. This can range from an event being impossible to some likelihood to being absolutely certain. In math terms, probability is on a scale from 0 to 1. Zero means the event is impossible, like rolling a seven on a die that only has digits from 1 to 6. One is an event that will happen, it is certain. An example of a certain event is tomorrow being Friday if today is Thursday. This is definitely going to happen.

The possible outcomes of a fair die are : 1, 2, 3, 4, 5, 6. which is 6 in all

the required outcome for obtaining a 3 = 3 which is 1 outcome

the required outcome for obtaining a number greater than 4 : 5, 6. which is 2 outcomes.

probability of getting 3 first time = 1/6

probability of getting a number greater than 4 = 2/6 ( lowest term = 1/3)

Probability of rolling a 3 first time and a number greater than 4 second time is  = 1/6 x 1/3 = 1/18

In conclusion, probability of obtaining a 3 and a number greater than 4 is 1/18.

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Answer:

Step-by-step explanation:

there is no question?

y = -4x²+24x-30 is the standard form of parabola whose equation is  y = -4(x - 3)² + 6

Parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.

The given equation is y = -4(x - 3)² + 6.

We need to write this equation as standard form of parabola.

the equation of a parabola in  standard form is.

y=ax² +bx+c

The given equation should be expanded y = -4(x - 3)² + 6.

y = -4(x²+9-6x)+6

Now apply distributive property

y = -4x²-36+24x+6

y = -4x²+24x+6-36

y = -4x²+24x-30

Hence y = -4x²+24x-30 is the standard form of parabola whose equation is  y = -4(x - 3)² + 6

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Answer:

x > -5

Make a number line.  Put a circle on the number line at -5 and then darken an arrow on the number line going to the right of -5

Step-by-step explanation:

-8-8(2x-4) > -5(4x -5) -21  Distribute the -8 and -5

-8 - 16x + 32 > -20x +25 -21  Combine like terms

-16x + 24 > -20x +4  Add 20x to both sides

4x + 24 > 4  Subtract 24 from both sides

4x > -20  Divide both sides by 4

x > -5