Mathematics College

## Answers

**Answer 1**

In order to evaluate the function, we need to substitute the value -1 into the place of x, that is,

[tex]f(-1)=-4^{2(-1)+3}[/tex]

which gives

[tex]\begin{gathered} f(-1)=-4^{-2+3} \\ f(-1)=-4^1 \end{gathered}[/tex]

Therefore, **the answer is:**

[tex]f(-1)=-4[/tex]

## Related Questions

Rose can choose between two summer jobs. She can work as a checker in a discount store for $8.40 an hour, or she can mow lawns for $12.00 an hour. In order to mow lawns, she must buy a $450 lawnmower. For how many hour must Rose work in order for the mowing to be more profitable than checking?

### Answers

**Explanation: **

**Step 1. **We will define the variable 'x' as the **number of hours worked. **

Since she earns $8.4 per hour working at the store, her earnings from that job would b:

[tex]8.4x[/tex]

we multiply the payment per hour 8.4 by the number of hours worked.

**Step 2. **Her earnings as a lawnmower would be $12.0 per hour multiplied by the number of hours 'x', but since here she needs to buy a $450 lawnmower, this will be deducted from her earnings:

[tex]12x-450[/tex]

**Step 3. **For mowing lawns to be more profitable than working as a checker at the store, her earnings at the two jobs must be equal for a certain value of x:

[tex]12x-450=8.4x[/tex]

**Step 4. **Solving the equation for x:

[tex]\begin{gathered} 12x-8.4x=450 \\ \downarrow \\ 3.6x=450 \end{gathered}[/tex]

Dividing both sides by 3.6

[tex]\begin{gathered} x=450/3.6 \\ \downarrow \\ x=125 \end{gathered}[/tex]

This means that if she works 125 hours, her earnings will be the same as a checker and as a lawnmower, therefore, she just needs to work one more hour -- **126 hours** (or more) for the mowing to be more profitable than checking.

The answer is **at least 126 hours. **

**Answer****: 126 hours**

A line passes through (12,5) and is parallel to the graph of y=2/3x-1. What equation represents the line in slope-intercept?

### Answers

First, we need to find the slope of the equation;

y=2/3x-1

To find the slope, compare the equation with y=mx + b

where m is the slope and b is the intercept

Comparing the two equations, m= 2/3

Slope of parallel equations are equal, hence, the slope of our new equation is 2/3

We will go ahead and find the intercept of the new equation

Substitute m= 2/3 x=12 and y=5 into y=mx + b and solve for b

That is;

y = mx + b

5 = (2/3)(12) + b

5 = 8 + b

subtract 8 from both-side of the equation

5 - 8 = b

- 3 = b

b= -3

To form the new equation

Substritute m = 2/3 and b= -3 into

y=mx + b

y = 2/3 x - 3

It is a fact that the functionhas a limiting value. Use a table ofvalues to estimate the limiting value.Answer:

### Answers

The given function is:

[tex]f(x)\text{ = }\frac{9x^2-3}{3x^2+4}[/tex]

Decide whether the following statement is true or false.Every polynomial function of degree 3 with real coefficients has exactly three real zeros.

### Answers

Consider the next polynomial function,

[tex]\begin{gathered} f(x)=(x+1)(x^2+1) \\ \Rightarrow f(x)=(x+1)(x-i)(x+i) \end{gathered}[/tex]

Notice that f(x) has one real zero and two complex zeros.

However, the expanded form of f(x) is

[tex]f(x)=x^3+x^2+x+1[/tex]

Therefore, f(x) is a polynomial of degree 3 with real coefficients **that has exactly 1 real zero and 2 complex zeros.**

**This is a counterexample of the statement. The answer is False.**

A manufacturing machine has a 8% defect rate.If 8 items are chosen at random, what is the probability that at least one will have a defect?

### Answers

**Answer**

**Probability that at least one will have a defect = 0.4868**

**Explanation**

**Defect rate = 8% = 0.08**

**Probability that an item will have a defect = 0.08**

**Probability that an item will not have a defect = 1 - 0.08 = 0.92**

So, for **8 items, **

**Probability that at least one will have a defect = 1 - (Probability that none of the items will have a defect)**

**Probability that none of the items will have a defect = (0.92)^8 = 0.5132**

**Probability that at least one will have a defect = 1 - 0.5132 = 0.4868**

**Hope this Helps!!!**

I need help with number 8The answer to number 7 is D

### Answers

**SOLUTION **

(8) The best fit will slope upwards from left to right. This indicates a positive relationship or correlation.

**Hence the answer is option B, there is a positive correlation **

a line has a slope of -2/3 and passes through the point -3,8 how do I get the equation ?

### Answers

**Answer:**

**The equation of the line in slope-intercept form is;**

[tex]y=-\frac{2}{3}x+6[/tex]

**Explanation:**

We want to find the equation of the line with the slope and a point given.

[tex]\begin{gathered} \text{slope m=}\frac{-2}{3} \\ \text{ point (-3,8)} \end{gathered}[/tex]

Recall that the point-slope equation of a straight line is of the form;

[tex]y-y_1=m(x-x_1)[/tex]

substituting the given slope and point into the equation and simplifying;

[tex]\begin{gathered} y-8=-\frac{2}{3}(x-(-3)) \\ y-8=-\frac{2}{3}(x+3) \\ y=-\frac{2}{3}x-\frac{2}{3}(3)+8 \\ y=-\frac{2}{3}x-2+8 \\ y=-\frac{2}{3}x+6 \end{gathered}[/tex]

Therefore, **the equation of the line in slope-intercept form is;**

[tex]y=-\frac{2}{3}x+6[/tex]

Find the slope of the line passing through the given points using the slope formula, Enter the slope as asimplified fraction Describe the slope as positive, negative, zero, or undefined,The graph shows the linear relationship,I

### Answers

Weare asked to find the slope of the line that goes through the points (1, 10) and (3, -5) on the plane

We use the slope formula for that:

slope = (y2 - y1) / (x2 - x1)

in our case:

slope = (-5 - 10 ) / (3 - 1) = -15 / 2

The slope is **negativ**e since we see the line descending from left to right. and also such is confirmed by our calculated slope.

The fraction **- 15/2** cannot be simplified any further, so that is it.

In the box that reads: the line is... look for the word "slanted" for example.

For m enter **-15/2**

Select** "falls from left to right"**

Emma can spend $____ on items.(Round to the nearest cent as needed.)

### Answers

To calculate the total price after applying the sales tax, we just need to apply the sales tax to the final values of the items.

Let *x* be how much she can spent on items.

To apply 5% in *x*, this means we want to calculate the total value plus 5%, that is, 105%.

So, we can multiply *x* by 105%.

However, we need to do this with the percentage in the decimal form:

[tex]105\%=1.05[/tex]

So, the value of *x* after the sales tax will be:

[tex]x\cdot1.05[/tex]

Since she has 80, this final price can be at most 80, so:

[tex]80=x\cdot1.05[/tex]

Now, we just need to solve it.

To do it, let's first switch the sides so the variable *x* is to the left:

[tex]\begin{gathered} 80=x\cdot1.05 \\ x\cdot1.05=80 \end{gathered}[/tex]

Now, we can divide both sides by 1.05 so that we nd up with only *x* on the left side:

[tex]\begin{gathered} x\cdot1.05=80 \\ \frac{x\cdot1.05}{1.05}=\frac{80}{1.05} \\ x=76.19047\ldots \\ x\approx76.19 \end{gathered}[/tex]

So, **she can spend approximately $76.19 on items**.

(0,4) is a solution to 1/2x + <6 is this true or false ?

### Answers

The given expression is

x/2 + y <6

We would substitute x = 0 and y = 4 into the inequality to see if the left hand side would be less than 6.Thus, we have

0/2 + 4 < 6

0 + 4 < 6

4 < 6

4 is actually less than 6

Thus, **it is true**

eighteen decreased by the product of X and 5. A. 5x-18 B. 18÷5+x C. 18-5x

### Answers

Given data:

The expression of eighteen decreased by the product of x and 5 is,

[tex]x5)-18=5x-18[/tex]

Thus, the option **(A) is coorect.**

. The height of a flag is 3 inches more than its length.Write an equation for the area of the rectangle in termsof length, I.Area =√x square inches

### Answers

SOLUTION:

Length = x

Height = x +

I need help figuring out which of these four options is equivalent to[tex](x + 3)(4 {x}^{2} + 5)[/tex]

### Answers

Explanation

The distributive property for the multiplication states that:

[tex]a\cdot(b+c)=a\cdot b+a\cdot c.[/tex]

**(1) **Choosing:

• a = (x + 3),

,

• b = 4x²,

,

• c = 5.

We have:

[tex](x+3)\cdot(4x^2+5)=a\cdot(b+c).[/tex]

**(2)** Applying the distributive property for the multiplication, we have:

[tex](x+3)\cdot(4x^2+5)=a\cdot(b+c)=a\cdot b+a\cdot c.[/tex]

**(3)** Replacing a = (x + 3), b = 4x² and c = 5, we get:

[tex](x+3)\cdot(4x^2+5)=a\cdot(b+c)=a\cdot b+a\cdot c=(x+3)\cdot(4x^2)+(x+3)\cdot(5).[/tex]Answer

**(A)**

[tex](x+3)\cdot(4x^2)+(x+3)\cdot(5)[/tex]

Assuming that at t = 0 the message in a bottle is at its average height and moves upwards after, what is the equation of the function that could represent the situation?

### Answers

Given that

The period is 24 seconds

The average height is 8 feet.

The distance between the maximum and minimum height is 4 feet.

Cosine function for this model.

At t=0 the function is in average height.

Let y be the height.

Let t be the time of seconds

The general cosine equation is

[tex]y=a\cos (bt)+c[/tex]

Here amplitude |a| represents the half distance between the maximum and minimum height.

[tex]|a|=\frac{4}{2}=2[/tex]

[tex]a=\pm2[/tex]

Substitute a=2 in the general equation, we get

[tex]y=2\cos (bt)+c[/tex][tex]\text{Period =}\frac{2\pi}{|b|}[/tex]

Substitute period =24, we get

[tex]\text{24 =}\frac{2\pi}{|b|}[/tex]

Using the cross product, we get

[tex]24|b|=2\pi[/tex]

Dividing both sides by 24, we get

[tex]|b|=\frac{2\pi}{24}=\frac{\pi}{12}[/tex][tex]b=\pm\frac{\pi}{12}[/tex]

Substitute b=pi/12 in the general equation, we get

[tex]y=2\cos (\frac{\pi t}{12})+c[/tex]

When t=0 the height is 8,

[tex]8=2\cos (\frac{\pi(0)}{12})+c[/tex]

[tex]8=2(1)+c[/tex][tex]c=8-2=6[/tex][tex]c=6[/tex]

Substitute c=6 in the equation, we get

[tex]y=2\cos (\frac{\pi t}{12})+6[/tex]

We get the equation for the average height, it will increase upward and reach the highest height.

Triangle FGH is similar to triangle IJK. Find the measure of side KI. Round your answer to the nearest tenth if necessary.

### Answers

Given data:

The given triagles.

The expression for the ratio of corresponding sides of the similar triangle FGH and IJK is,

[tex]\begin{gathered} \frac{FH}{HG}=\frac{IK}{KJ} \\ \frac{31}{43}=\frac{IK}{8} \\ IK=\frac{248}{43} \\ =5.8 \end{gathered}[/tex]

Thus, the length of **IK is 5.8 units.**

Logarithmsin a research laboratory, biologist studied the growth of a culture of bacteria. From the data collected hourly, they concluded that the culture increases in number according to the formula N(t)=45(1.85)t where N is the number of bacteria present and t is the number of hours since the experiment beganUse the model to calculatea) the number of bacteria at the start of the experiment.b) number of bacteria present after 4 hours, giving your answer to the nearest whole number of bacteria.c) the time it would take for the number of bacteria to reach 1000.

### Answers

Growth of Culture of bacteria increases in number according to the formula :

[tex]N(t)=45(1.85)^t[/tex]

N = Number of bacteria present

t = number of hours from the initial state.

a) *number of bacteria at the start of the experiment.*

In the begining when the expreiment start, the time is zero

t = 0

Substitute t = 0 in the growth expression of bacteria

[tex]\begin{gathered} N(t)=45(1.85)^t \\ N(0)=45(1.85)^0 \\ as\colon a^0=1 \\ N(0)=45(1) \\ N(0)=45 \end{gathered}[/tex]

**When the experiment start, number of bacteria is 45**

*b) number of bacteria present after 4 hours, giving your answer to the nearest whole number of bacteria.*

After fours hours, i.e. t = 4

Substitute t = 4 in the growth expression of bacteria

[tex]\begin{gathered} N(t)=45(1.85)^t \\ N(4)=45(1.85)^4 \\ N(4)=45\times11.7135 \\ N(4)=527.1077 \\ N(4)=527 \end{gathered}[/tex]

**Number of bacteria after 4 hours are 527**

*c) the time it would take for the number of bacteria to reach 1000.*

Here, we have number of bacteria 1000 i.e. N = 1000

Substitute the value and solve for t:

[tex]\begin{gathered} N(t)=45(1.85)^t \\ 1000=45(1.85)^t \\ \frac{1000}{45}=1.85^t \\ 1.85^t=\frac{200}{9} \\ 1.85^t=22.22 \\ \text{Taking log on both side: } \\ t\ln (1.85)=\ln (22.22) \\ t=\frac{\ln (22.22)}{\ln (1.85)} \\ t=5.0409 \\ t=5 \end{gathered}[/tex]

**It will take 5 years to reach upto 1000 bacteria**

**Answer: **

**a) Number of bacteria at the start of experiment 45**

**b) Number of bacteria after 4 hours 527**

**c) It would take 5 years to reach upto 1000 bacteria**

The price of a technology stock has business and $9.67 today. Yesterdays price was $9.54. Find a percentage increase. Round answer to the nearest 10th of a percent

### Answers

we know that

Yesterday's price was $9.54 ----------> represents the 100% percentage

Applying proportion

Find out how much percentage represents the difference (9.67-9.54)

so

[tex]\begin{gathered} \frac{100\%}{9.54}=\frac{x}{\left(9.67-9.54\right)} \\ \\ x=\frac{100\operatorname{\%}}{9.54}*(9.67-9.54) \\ \\ x=1.4\% \end{gathered}[/tex]The answer is 1.4%

1.What type of number is the product of 5 and sqrt(5)?A.integerB.rationalC.irrationalD.transcendental

### Answers

Given

Product means multiplication

[tex]5\times\sqrt[]{5}[/tex]

Let's explain all the options first

1.** An integer** is a number with no decimal or fractional part, from the set of negative and positive numbers, including zero.

2. A Rational Number can be made by dividing an integer by an integer.

3. An Irrational Number is a real number that cannot be written as a simple fraction

4. A transcendental number is a (possibly complex) number that is not the root of any integer polynomial, meaning that it is not an algebraic number.

**The final answer **

[tex]5\times\sqrt[]{5}\text{ =11.18033989}\ldots[/tex]

**is irrational **

Part of a city map is shown.16У1 st Ave42nd AveNх-674 -24.62Central Ave4Main RoadD Street-6A city planner wants to build a road parallel to 2nd Ave. What is the slope of the new road?

### Answers

If the city planner wants to build a new road that is **parallel to 2nd Ave**, the slope of this road will be the same as the slope of 2nd Ave.

In the xy-plane, 2nd Ave has a slope of 0 (y=0x+1), as it does not change with the variations of x.

Then, **the new road will also have a slope of 0.**

Subtract these polynomials.(3x²+2x+4) - (x²+2x+1)=A. 2x² + 3B. 2x² +5C. 2x² + 4x+5D. 2x² + 4x + 3

### Answers

**Answer:**

**B. 2x² + 3**

**Explanation:**

The given expression is

(3x² + 2x + 4) - (x² + 2x + 1)

To subtract the polynomials we need to write the expression without the parenthesis as

3x² + 2x + 4 - x² - 2x - 1

Now, we need to add the like terms

(3x² - x²) + (2x - 2x) + (4 - 1)

2x² + 0 + 3

2x² + 3

Therefore, the answer is

B. 2x² + 3

ActivitySelma uses a jogging trail that runs through a park near her home. The trail is a loop that is of a mile long. On Monday, Selma ran the loop in 3of an hour. What is Selma's unit rate in miles per hour for Monday's run?In this activity, you will use the common denominator method to calculate a unit rate that involves fractions. Answer the questions that follow tocalculate Selma's unit rate in miles per hour.Part AAccording to the question, the unit rate is to be expressed in which units?

### Answers

The trail is a loop that is 3/4 of a mile long

Selma ran the loop 1/6 of a hour

so, the unit rate = distance/time = (3/4 miles) / (1/6 hour) =

so, the unit rate = 4.5 miles/hour

express as fraction = (9/2) miles/hour

Can you please help

### Answers

Lets first find the derivative of f:

[tex]\frac{d}{dx}(e^{2x}+e^{-x})=e^{-x}(2e^{3x}-1)[/tex]

Now lets set the derivative equal to zero to find the minimum value:

[tex]e^{-x}(2e^{3x}-1)=0[/tex][tex](2e^{3x}-1)=0[/tex][tex]x=\frac{-ln(2)}{3}[/tex]

And replacing that value of x, we have:

[tex]e^{2(\frac{-\ln(2)}{3})}+e^{-(\frac{-\ln(2)}{3})}[/tex][tex]e^{\frac{-2\ln (2)}{3}}+e^{(\frac{\ln (2)}{3})}[/tex][tex]\frac{3\sqrt[3]{2}}{2}[/tex]

The local minimum of f is at:

[tex](\frac{-ln(2)}{3},\frac{3\sqrt[3]{2}}{2})[/tex]

Find the area bounded by the graphs of y = x - 1 , y = 0 and the lines x = 1 and x =4. Use the limit definition.

### Answers

The **area bounded** by the **graphs** of y = x - 1, y = 0, x = 1 and x =4 is 4.5 unit square.

The** area bounded** by **curves** is given by finding the intersection point or the limits of the integral and finding the **integral** of the **function** and putting the **limits**.

[tex]A=\int\limits^a_b {f(x)} \, dx[/tex]

Where a and b are the limits and f(x) is the function of graph.

The **graph** of the lines y = x - 1 , y = 0 , x = 1 and x =4 is attached below,

As seen from the graph, the upper limit is 4 and the lower limit is 1.

So, the **area **under the line is given by **integral,**

[tex]A=\int\limits^4_1 {x-1} \, dx \\A=[\frac{x^{2} }{2} -x]\limits^4_1\\[/tex]

Now, putting the **limits**,

[tex]A=[\frac{4^{2} }{2} -4-(\frac{1}{2}-1) ]\\\\\\A=8-4-\frac{1}{2} +1\\\\A=4.5[/tex]

Hence, the **area bounded **by the graphs is 4.5 unit square.

To learn more about the **Area under curve** visit here:

https://brainly.com/question/20733870

**#SPJ9**

OPRobert made a design on his wall with the similar pentagon tiles shownR9 cm9 cmKMQs15 cm10 cm10 cm15 cmUT10 cmP15 cmNnot drawn to scaleWhat is the length of side RS?3 cm

### Answers

Since they are simmilar we will then have the following relationships.

[tex]\frac{15}{10}=\frac{9}{x}[/tex]

Now, we solve for x, as follows:

[tex]x=\frac{9\cdot10}{15}\Rightarrow x=6[/tex]

The expression goes along the lines of. 15 is to 10 what 9 is to x, with this as was done we solve for x and determine it's value, that since they keep proportionality.

16 in12 inOriginal3 in20 in5 inHow do the perimeters of the similarshapes above compare?

### Answers

The original has dimensions 16 in, 12 in and 20 in.

The image has dimensions 3 in, 4 in and 5 in.

We need to **find the perimeter of both triangles and then compare them**.

The perimeter of a triangle is given as:

**P = a + b + c**

where a, b, c are the three sides of the triangle

Therefore, the perimeter of the original is:

P = 16 + 12 + 20 = **48 in**

The perimeter of the image is:

p = 3 + 4 + 5 = **12 in**

By comparing these two perimeters, we can see that **the perimeter of the original is 4 times that of the image.**

So **the image's perimeter is 1/4 that of the original**. (Option B)

What is the volume of this sphere? Use i 3.14 and round your answer to the nearest hundredth. 3 cm cubic centimeters

### Answers

In order to find the volume of the sphere, use the following formula:

**V = 4/3 · π r³**

where π = 3.14 and r = 3 cm. Replace these values into the previous formula for V:

V = 4/3 · (3.14)(3 cm)³

V = 43 · (3.14)(27 cm³)

**V = 113.04 cm³**

**Hence, the volume of the given sphere is 113.04 cm³**

Solve the following system using substitution -3x + 2y = 16 2x + y = 1

### Answers

We have the system of equations:

[tex]\begin{gathered} -3x+2y=16 \\ 2x+y=1 \end{gathered}[/tex]

We have to solve by substitution. We will clear y from the second equation and replace it in the first equation. Then solve for x:

[tex]\begin{gathered} 2x+y=1 \\ y=1-2x \end{gathered}[/tex][tex]\begin{gathered} -3x+2y=16 \\ -3x+2(1-2x)=16 \\ -3x+2-4x=16 \\ -7x+2=16 \\ -7x=16-2 \\ -7x=14 \\ x=\frac{14}{-7} \\ x=-2 \end{gathered}[/tex]

Now we can solve for y as:

[tex]y=1-2x=1-2(-2)=1-(-4)=1+4=5[/tex]

**Answer: x=-2 and y=5**

Your kite stuck in a tree that is 39 feet tall the angle you’re string makes with the ground is 73° rather than worrying about the kite you decide to calculate how much string you have let out assuming the string is held tight and makes a straight line to the ground how much string have you let out￼

### Answers

**ANSWER:**

40.78 feet

**STEP-BY-STEP EXPLANATION:**

We make a sketch of the situation of the statement in order to better understand the question.

We can determine the requested distance that is x, using the trigonometric function sine, which relates the opposite side to the hypotenuse of the triangle, like this:

[tex]\begin{gathered} \sin \theta=\frac{\text{ opposite}}{\text{ hypotenuse}} \\ \text{opposite = 39} \\ \theta=73\text{\degree} \\ \text{ hypotenuse = x} \\ \text{ replacing} \\ \sin 73=\frac{39}{x} \\ x=\frac{39}{\sin 73} \\ x=40.78\text{ ft} \end{gathered}[/tex]

The amount of string is 40.78 feet

Use the formula for compound amount to find the interest amount:$12,000 at 8% compounded annually for 4 years

### Answers

The formula to be using is as follows:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

But A is the total amount, that is, the initial amount plus the interest amount. If we want just theinterest, I, we need to substract the initial amount:

[tex]\begin{gathered} I=A-P \\ I=P(1+\frac{r}{n})^{nt}-P \end{gathered}[/tex]

The given information are:

[tex]\begin{gathered} P=12000 \\ r=0.08 \\ n=1 \\ t=4 \end{gathered}[/tex]

Where r was converted from percentage to decimal and n is 1 because it is compounded only once per year.

So, substituting these values, we have:

[tex]\begin{gathered} I=P(1+\frac{r}{n})^{nt}-P \\ I=12000(1+\frac{0.08}{1})^{1\cdot4}-12000 \\ I=12000(1+0.08)^4-12000 \\ I=12000(1.08)^4-12000 \\ I=12000\cdot1.36048\ldots-12000 \\ I=16325.867\ldots-12000 \\ I=4325.867\ldots\approx4325.87 \end{gathered}[/tex]

So, the interest amount is **approximately $4,325.87**.

The hurricane has brought a huge storm to Reidsville. If it rains 3 inches an hour for 5hours, which function could be used to describe the total amount of rain, T, comparedto the number of hours, h, it has been raining?

### Answers

Total amount of rain = T

Number of hours it has been raining =h

It rains 3 inches an hour, for 5 hours.

So, it rains 3 inches per hour.

So, the total amount of rain (T) is equal to the amount of rain per hour (3) multiplied by the number of hours h.

T = 3h