Question 5 of 10
Which of the following graphs represents a function that has a positive
leading coefficient? Check all that apply.
A. Graph A
B. Graph B
C. Graph C
D. Graph D

The solutions for the quadratic equation:

2x^2 + 12x + 18 = 0

are:

x₋ =  -5.55

x₊  = -0.4

Remember that for a general quadratic equation:

a*x^2 +b*x + c = 0

The solutions are of the form:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]

Here we have the quadratic:

2x^2 + 12x + 18 = 0

Then using the formula for the solutions we will get:

[tex]x = \frac{-12 \pm \sqrt{12^2 - 4*2*18} }{2*2} \\\\x = \frac{-12 \pm 10.2}{4}[/tex]

The two solutions of the quadratic equation are:

x₋ = (-12 - 10.2)/4 =  -5.55

x₊ = (-12 + 10.2)/4 = -0.4

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The 3 in the equation is the starting point

Function given:

h(t) = −4.5t2 + 19.6t + 3

At t =0 we get h(0) = 3. This is called the y-intercept

It is the start point indicating the disc was thrown at 3 feet of height.

Using the common convention in geometry the horizontal axis in a graph in represented by the x-axis and the vertical axis in a graph is represented by the y-axis. The intercepts are the points on the graph at which the graph crosses the two axes. The point where the graph is drawn crosses the horizontal axis is called the x-intercept or the x-axis, and when the graph crosses the vertical axis is called as the y-intercept or the y-axis.

I hope this answer helps.

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Answer: 32130000

Step-by-step explanation:

Multiply all of your numbers

The probability that the price of the used car is less than $65 is 0.55962.

Here it is given that the price of the used car has a mean of $50 and a variance of $100.

Since it follows normal distribution X~N(μ, σ²)

where,

μ = 50

σ = 100

Here we need to find the probability P(X < 65)
To find this we need to convert the distribution to the standard normal form, N~(0, 1)

We know,

P(X < (x - μ)/ σ) = Φ(Z)

Therefore we get

P(X < (65 - 50)/ 100)

Solving this we get the Z value

= Φ(0.15)

From the Z table, we can get our p-value.

= 0.55962

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Answer:

80

Step-by-step explanation:

Coppinger Corp is using Scenario Analysis.

Given, that Coppinger Corp is considering the use of a computer to assign probability distributions to the input variables used in the analysis.

The computer would then randomly select input variables from their distributions and calculate npvs based on those selections

Now, A scenario analysis consists of multiple inputs. For eg. a Company may consider how an increase in available fuel can impact their number of goods sold etc.

Here, also Coppinger Corp is assigning multiple values to the computer and getting outputs.

So, this can be the Scenario Analysis.

Hence, Coppinger Corp is using Scenario Analysis.

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The equation of the parabola that similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5

The equation of the parabola

f(x) = [tex]7x^2[/tex]

The standard vertex form of a parabola is

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

The coordinates of the vertex of a parabola = (3, 5)

Where (h, k)  is the coordinates

From the given function of the parabola f(x) =  [tex]7x^2[/tex]

The value of a = 7

Substitute the values in the vertex form of a parabola

y = [tex]7(x-3)^2[/tex] + 5

Hence, the equation of the parabola that is similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5

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Answer:

74 square yards

Step-by-step explanation:

Area of rectangular garden:

                 l = 20 yds

                 w = 15 yds

     Area of the rectangular garden = l *w

                                                          = 20 * 15

                                                          = 300 square yards.

Area of the outer rectangle (rectangular garden and the sidewalk):

             length = 20 + 1 + 1 = 22 yds

            width   = 15 + 1 + 1  = 17 yds

       Area of outer rectangle = 22 * 17

                                               = 374 square yards

To find the area of the sidewalk, subtract the area of rectangular garden from the outer rectangle.

Area of the sidewalk = area of outer rectangle - area of sidewalk

                                  = 374 - 300

                                  = 74 square yards

The number of days that it will take to sell his box of 35 is 21 days.

Ratio simply demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

In this case, Nigel is selling candy bars for his outdoor club and he is averaging 4 bars every 3 days.

Let the number of days be x.

This will be:

3/x = 4/35

Cross multiply

4x = 3 × 35

x = (3 × 35)/4

x = 105 / 4

x = 21

It will take 21 days

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Using simplification, the equations that are equivalent to [tex]\frac{(6x+2)}{3} =2-(3x+14)[/tex] are [tex]\frac{(6x+2)}{3 } = -3x-12[/tex] and 6x + 2 = -9x - 36

Two systems of equations are equivalent if they have the same solution(s)

In a simpler term, two equations are equivalent if they have the same solution.

Therefore, let's simplify the equation to find the equivalent solutions.

[tex]\frac{(6x+2)}{3} =2-(3x+14)[/tex]

let's open the brackets of the right side of the equation.

[tex]\frac{(6x+2)}{3}=2-(3x+14)[/tex]

[tex]\frac{(6x+2)}{3} = 2-3x-14[/tex]

[tex]\frac{(6x+2)}{3 } = -3x-12[/tex]

Therefore, let's cross multiply

6x + 2 = 3(-3x - 12)

6x + 2 = -9x - 36

Therefore, the equivalent equation are as follows:

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The minimum amount of fence needed to enclose the lots is 120ft.

Adding areas of both fields, the combined area comes about to be 600sq ft.

The dimensions of the new plot are x length and y breadth. According to the question, there is a fence in the middle with y breadth.

g(x, y, z) = xy - 600

g(x, y, z) = 2x + 3y

∇g = ∇ (xy - 600) = (y, x)

∇f = ∇(2x + 3y) = (2, 3)

Now from the Lagrange method,

∇f = λ∇g

2 = λy

3 = λx

Now to get the value of lambda,

(2/y) = (3/x) = λ

x = 1.5y

Solving now we get,

1.5y² = 600

y = 20

x = 1.5 × 20 = 30

Thus after getting (x,y) we can put the value in the function to get the answer as 120ft.

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Answers:

1st box:  0

2nd box:  67

===============================================

Explanation:

The y intercept always occurs when x = 0. This is when the function curve either crosses or touches the vertical y axis. Therefore, the y intercept is when the student studies 0 hours

Plug x = 0 into the equation

y = 2.7x + 67

y = 2.7*0 + 67

y = 67

Or you can note that the equation is of the form y = mx+b

The y-intercept of 67 tells us that the person studying for 0 hours is estimated to get a score of 67

Answer: [tex]x=7[/tex]

Step-by-step explanation:

[tex]3^x=2187\\\\x=\log_{3} (2187)\\\\x=7[/tex]

The polynomial function which has a leading coefficient 1 is (x-(7+i))(x-(5-i))(x-(7-i))(x-(5+i))

Given that a polynomial function has leading coefficient 1 and roots (7+i) and (5-i) with multiplicity 1.

We want to find the polynomial function.

As we know that the complex conjugate properties of the roots of a polynomial states that if a+bi is a root of a polynomial then their complex conjugate a-bi is also a root.

So, according to this property (7-i) and (5+i) with multiplicity 1 is also a root of polynomial.

Thus, all the roots are x=7+i, x=7-i, x=5+i and x=5-i

So, the polynomial is f(x)=(x-(7+i))(x-(5-i))(x-(7-i))(x-(5+i))

Hence, the polynomial function which has a leading coefficient 1 and roots (7+i) and (5-i) is (x-(7+i))(x-(5-i))(x-(7-i))(x-(5+i)).

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The solution of the equation given as -13x + x = 8x - 20x is infinite many solutions

From the question, the equation is given as

-13x + x = 8x - 20x

To start with, we need to rewrite the expression

So, we have the following representation

x - 13x = 8x - 20x

Solving further, we need to evaluate the like terms

So, we have the following equation

-12x = 8x - 20x

Evaluate the like terms again

So, the equation becomes

-12x = -12x

Both sides of the above equation are the same

i.e. -12x is on both sides of the equation

When we have a solution that all sides of the equation have the same value, then the solution is that the equation has infinite many solutions

Hence, -13x + x = 8x - 20x has infinite solutions

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Ruth must have an initial deposit of $12000 in order to have the same simple interest at the same rate within the same time as Carter

Simple Interest (S.I) is the method of calculating the interest amount for some principal amount of money. Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments.

The formula of simple interest is given as

S.I = PRT

We can set up equivalent equations since both interest are equal.

S.I = P(1 + RT)

S.I = 12000(1 + 0.019 * 1)

S.I = 12228

But since they earned the same interest at the same rate within the same period, their principal or initial amount invested must be equal

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The remainder of the long division problem (x + 1)/x is given as follows:

1.

The representation of a long division problem is given as follows:

di(x)/d(x) = q(x) + (r(x)/b(x))

In which the meaning of each symbol is listed as follows:

In the context of this problem, the operation is presented as follows:

(x + 1)/x.

This division can be separated into two divisions that are added, hence:

(x + 1)/x = x/x + 1/x = 1 + 1/x.

Comparing to the standard symbols, we have that:

The expression is:

(x + 1)/x.

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Answer:

B 1

Step-by-step explanation:

36×(35)-1000=1260-1000=260

The histogram that shows a left-skewed distribution is given by:

A. A bar chart plots data points (1, 1), (2, 4), (3, 1), (4, 2), (5, 3), (6, 4) and (7, 3).

An histogram is a graph that shows the number of times each element x was observed on the data-set.

Hence, the meaning of a point (x,y) on the histogram is given as follows:

Observation x was observed y times on the data-set.

The skewness of a distribution can be explained as follows:

Hence in this problem, for the left-skewed histogram, we want an "increasing" histogram, hence option A is correct.

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Answer: 81

Step-by-step explanation:

[tex]v=\sqrt{2gh}\\\\g=32, v=72\\\\\implies 72=\sqrt{2(32)h}\\\\5184=64h\\\\h=81[/tex]

There are 45 yards of cable that will be required.

Since we have given that

Height of cable = 15 yards - 3 yards = 12 yards

Distance from pole = 9 yards

cable is the hypotenuse of the right-angled triangle.

So, it becomes,

[tex]c^{2} = b^{2}+p^{2}[/tex]

[tex]c^{2} = 12^{2}+9^{2}[/tex]

[tex]c^{2} = 144+81[/tex]

[tex]c^{2} = 225[/tex]

[tex]c = \sqrt{225}[/tex]

c=15 yards

Since the number of cables supported = 3

So, the number of yards of cable that will be required would be

= 3  x 15 = 45

Hence, there are 45 yards of cable will be required.

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The solution for x in the equation given as 3/2 (4x – 1) – 3x = 54 –(x + 2) is 13.375

From the question, the algebraic expression is given as

3/2 (4x – 1) – 3x = 54 –(x + 2)

There is no constant to multiply or divide in the expression

3/2 (4x – 1) – 3x = 54 –(x + 2)

Open the brackets

So, we have

6x – 3/2 - 3x = 54  - x - 2

Collect the like term in the above equation

This gives

6x - 3x + x = 54 - 2 + 3/2

Evaluate the like term in the above equation

So, we have the following representation

4x = 53.5

Divide through by 4

x = 13.375

The above equation cannot be solved further

Hence, the solution is x = 13.375

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The equation of line k is y = 1/2x - 1.

The equation y = mx + c is the general equation of any straight line, where m is the gradient of the line and c is the y -intercept.

Given that, the equation for line j can be written as y=1/2x-4. Parallel to line j is line k which passes through the point (-8, -5)

When two lines are parallel their slope are equal, so solving for c,

-5 = 1/2*-8 + c

c = -1

The equation will be,

y = 1/2x - 1

Hence, The equation of line k is y = 1/2x - 1.

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The population growth rate (r) for 2009 in the tiny country of fremont is found as 1.4.

All these elements are taken into account when formulating the population growth formula.

r = [(b + i) - (d + e)]/1000

Put the values in the formula.

r =  [(2,000 + 100) - (500 + 200)]/1000

r = 2100 - 700/ 1000

r = 1.4

Thus, the population growth rate (r) for 2009 in the tiny country of fremont is found as 1.4.

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Answer:

Vertex: (2, -1)

Axis of Symmetry: x=2

Parabola: Downwards

Step-by-step explanation:

The correct statement would be older men tend to have lower muscle density, so the correlation between age and muscle density in older men must be negative.

Increased time studying sets of tea time is associated with higher G. P.A. (Grade point average) This is positive. More time studying G. P. A. Life expectancy increases as body weight decreases. As the weight goes down the life expectancy goes up.

Muscle mass (quantity) is highly correlated with survival in hospitalized patients with advanced cancer, whereas muscle density (quality) is associated with patients’ symptoms, health care use, and survival, according to a group of researchers

In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics it usually refers to the degree to which a pair of variables are linearly related. Familiar examples of dependent phenomena include the correlation between the height of parents and their offspring, and the correlation between the price of a good and the quantity the consumers are willing to purchase, as it is depicted in the so-called demand curve.

Your body shape changes naturally as you age. You cannot avoid some of these changes, but your lifestyle choices may slow or speed the process.

The human body is made up of fat, lean tissue (muscles and organs), bones, and water. After age 30, people tend to lose lean tissue. Your muscles, liver, kidney, and other organs may lose some of their cells. This process of muscle loss is called atrophy. Bones may lose some of their minerals and become less dense (a condition called osteopenia in the early stages and osteoporosis in the later stages). Tissue loss reduces the amount of water in your

The amount of body fat goes up steadily after age 30. Older people may have almost one third more fat compared to when they were younger. Fat tissue builds up toward the center of the body, including around the internal organs. However, the layer of fat under the skin gets smaller.

The tendency to become shorter occurs among all races and both sexes. Height loss is related to aging changes in the bones, muscles, and joints. People typically lose almost one-half inch (about 1 centimeter) every 10 years after age 40. Height loss is even more rapid after age 70. You may lose a total of 1 to 3 inches (2.5 to 7.5 centimeters) in height as you age. You can help prevent height loss by following a healthy diet, staying physically active, and preventing and treating bone loss.

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Answer:

A

Step-by-step explanation:

using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex] , then

[tex]\sqrt{12}[/tex]

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

= [tex]\sqrt{4}[/tex] × [tex]\sqrt{3}[/tex]

= 2[tex]\sqrt{3}[/tex]

Then

[tex]\sqrt{144}[/tex] + 18[tex]\sqrt{12}[/tex] - 5[tex]\sqrt{64}[/tex]

= 12 + 18(2[tex]\sqrt{3}[/tex] ) - 5(8)

= 12 + 36[tex]\sqrt{3}[/tex] - 40

= - 28 + 36[tex]\sqrt{3}[/tex]

Order of greatest y intercept to least y intercept,

1). A linear function has been given as,

   y = [tex]\frac{1}{2}[/tex]x + 4

   Y intercept = 4

2). The graph,

    Y intercept = (2)

3). Graph represented by table

    Y intercept = 1

4). A line passes through two points (-2, -3) and (4, 0)

    Y intercept = -2

It is the total distance from the origin and the intersection of y axis and the formed line. It may be positive, negative or zero.

  From the graph,

    y-intercept = (2)

A line passes through two points (-2, -3) and (4, 0),

Slope of the line = [tex]\frac{y2 - y1}{x2 - x1}[/tex]

                           = [tex]\frac{0-(-3)}{4-(-2)}[/tex]

                           = 1/2

Equation of a line passing through a point (x', y') and slope = m

y - y' = m(x - x')

If the point is (4, 0) and slope = 1/2

y - 0 = 1/2 ( x - 4 )

y = 1/2x - 2

y-intercept of this line = (-2)

A linear function has been given as,

y = [tex]\frac{1}{2}[/tex]x + 4

Comparing it with the slope intercept equation,

y = mx + b

b = y-intercept = 4

From the given table,

For x = 0, f(x) = 1

Therefore, y-intercept = 1

Order of greatest y intercept to least y intercept,

1). A linear function has been given as,

   y = [tex]\frac{1}{2}[/tex]x + 4

Y intercept = 4

2). The graph,

Y intercept = (2)

3). Graph represented by table

Y intercept = 1

4). A line passes through two points (-2, -3) and (4, 0)

Y intercept = -2

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