Mathematics College

please help me with this

Answers

Answer 1

For the given quadratic equation we have:

a) F(-2) = 5

b) F(3) = 40

c) the solutions are:

t = -1

t = -1/3

How to evaluate the quadratic function?

Here we have the following quadratic function:

F(t) = 3t^2 + 4t + 1

a) First, we want to determine the value of F(-2), to do so, we just need to replace the values of the variable, t, by the number -2, we will get:

F(-2) =3*(-2)^2 + 4*(-2) + 1

F(-2) = 3*4 - 8 + 1 = 5

F(-2) = 5

b) Now we want to find the value of the F(3), so this time we evaluate in x = 3.

F(3) =3*3^2 + 4*3 + 1

F(3) = 27 + 12 + 1 = 40

F(3) = 40

c) Last, we want to solve:

F(t) = 0

So we need to solve the quadratic equation:

3t^2 + 4t + 1 = 0

Using the quadratic formula we will get the two solutions:

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

Then the two solutions are:

t = (-4 + 2)/6 = -2/6 = -1/3

t = (-4 - 2)/6 = -1

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Related Questions

Write an equation for (-5,3) and (0,-7)

Answers

The equation of line is y + 2x +7 =0 for the points (-5,3) and (0,-7).

What is equation of line?

A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.

The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.

The given points are (-5, 3) and (0, -7).

To find the equation of line, use formula,

y - y₁ = m(x - x₁) where m = (y₂-y₁)/(x₂-x₁),

y - 3 = (-7 - 3)/(0-(-5)) (x - (-5))

y - 3 = -10 / 5 (x + 5)

y - 3 = -2 (x + 5)

y + 2x +7 =0

The required equation of line is y + 2x +7 =0 .

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The half-life of a drug in the bloodstream is 14 hours. What fraction of the original drug dose remains in 36 hours? in 72 hours?
What fraction of the original drug dose remains in 36 hours?
(Do not round until the final answer. Then round to the nearest hundredth as needed.)

Answers

16.82 % and 2.83% of the original drug dose remain in 36 hours and 72 hours respectively.

What is half-life?

Half-life is a characteristic unit for the exponential decay equation and is constant across the lifespan of an exponentially decaying quantity.

Given, the half-life of a drug(h) = 14 hours

The first condition, time duration (t) = 36 hours

Then, the half-life of the substance can be calculated by:

[tex]A = A_{0} * (1/2)^{\frac{t}{h} }[/tex]

or, [tex]A = A_{0} * (1/2)^{\frac{36}{14} }\\A = A_{0} * (0.1682)\\[/tex]

16.82 % of the original drug dose remains in 36 hours

Hence, 16.82 % of the original drug dose remains in 36 hours

The second condition, time duration (t) = 72 hours

Then, the half-life of the substance can be calculated by:

[tex]A = A_{0} * (1/2)^{\frac{t}{h} }[/tex]

[tex]A = A_{0} * (1/2)^{\frac{72}{14} }\\A = A_{0} * (0.0283)\\[/tex]

2.83 % of the original drug dose remains in 72 hours

Hence, 2.83 % of the original drug dose remains in 72 hours

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The U.S. Postal Service delivers about 212 billion pieces of mail each year. Of this mail, 4/5 is sent by big commercial users. About how many pieces of mail are sent by big commercial users each year? Hint: billion is part of the label “billion pieces of mail”.

Answers

The mail that are sent by big commercial users is 169.60 billion.

How many mails are sent by big commercials users?

A fraction is a non-integer that is made up of a numerator and a denominator. The numerator is the number above and the denominator is the number below. An example of a fraction is 4/5.

In order to determine the pieces of mail that are sent by big commercial users, multiply the fraction by the total number of mails delivered each year.

The mail that are sent by big commercial users = 4/5 x 212 billion = 169.60 billion

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Find x when () = 2. Please explain step by step

Answers

Answer: Ans is 990. First such a number is 5×0 +2=2, then 5×1 +2=7, like that in all 20 numbers are there from 2 to 97 in A.P.with common difference of 5.

Step-by-step explanation:

pls hp me with this question

Answers

Answer:30 1/8

Step-by-step explanation:

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Answers

Answer:

Step-by-step explanation:

0 Assignment is past due
5.PS-20
Question Help
Doug dives from a platform that is 7.5 meters above water. His dive takes him 1.5 meters below the surface of the water. How
far does Doug's dive take him?
Doug's dive takes him meters.

Answers

Answer:

9 meters

Step-by-step explanation:

|7.5|+|-1.5|=9

(the || on either side of each number shows that it's representing how far the number is from 0, so it's essentially 7.5+1.5)

The width of a rectangle is 4 more than the length. If the perimeter is 36 cm, ind the dimensions (length and width) of the rectangle.

Answers

Answer with step-by-step explanation:

Let the width of the rectangle be x.

Given that,

length ⇒ 4

width ⇒ x + 4 ( Because, the rectangle's width is 4 more than the length.)

Perimeter ⇒ 36cm

The formula to find the perimeter of rectangle is:

P = 2 ( l + w )

Now to find the value of x replace P, l & w with 36, 4 & (x + 4) with respectively.

P = 2 ( l + w )

36 = 2 ( 4 + x + 4 )

36 = 2 ( x + 8 )

Solve the brackets.

36 = 2x + 16

Substract 16 from both sides.

36 - 16 = 2x

20 = 2x

Divide both sides by 2.

10 = x

And now let us find the exact dimensions of the rectangle.

Length = 4 cm

Width = x + 4 = 10 + 4 = 14 cm

Solomon invested money in his bank account. He had a principal, P,
of $100 in his account at the beginning of the period, which
increased at a rate, r, of 0.15 per year. At the end of the period, he
had interest, I, of $135 in his account. Use the simple interest
formula 1 Prt, to solve for the time, t, in months that it took to
earn this amount. (1 point)
h
O 9 months
O 108 months
O 233 months
900 months

Answers

The total time required in months is 108 months.

What is simple interest?

Simple interest is defined as the amount of interest paid on a specific principal, an amount at a specific interest rate. It is given by

I = Prt

where, I = simple interest, P = Principal, r = rate of interest, t = time taken

Given, P = $100

I = $135

r = 0.15

t = ?

So, simple interest is given by:

I = Prt

or, 135 = 100*0.15*t

or, 135 = 15*t

or, t = (135/15) = 9 years = 9*12 = 108 months

Hence, the total time required in months is 108 months.

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Answer: 108

Step-by-step explanation:

just took test

CAN SOMEONE HELP WITH THIS QUESTION?✨

Answers

The new equation of graph will be-

y = 5ˣ - 4y = 5ˣ⁻⁵y = 5⁻ˣExplain the term translation?Each point in such a figure is moved the same distances in same direction using a kind of transformation known as translation.A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Each point in an image is thought to reflect other figure when they are all equally spaced apart from one another.

For the stated conditions.

The equation of the graph is given as-

y = 5ˣ

Part a: f(x) is shifted 4 units downward,

y = 5ˣ - 4, is the new image location.

Part b: f(x) is shifted 5 units left,

, y = 5ˣ⁻⁵, change in the y axis with negative sign.

Part c: f(x) is reflected about the y axis.

y = 5⁻ˣ, x coordinates will change, keeping the y axis same.

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Which of the following items is shaped MOST LIKE the Moon?
O An egg
O Asphere
O A cone
O A circle

Answers

Answer:

An egg

Step-by-step explanation:

Hope this helps you

Sphere. A egg is like an oval which the moon isn’t. The moon isn’t a cone. And a circle is 2d.

4. Abby receives a gift card worth $20 to an online retailer that sells digital music and games. Each song
costs $1each, and each game costs $2. She wants to buy at least 15 items with the card. Write a systems
of inequalities and represent the solution on the graph.

Answers

Answer:

card worth $20

the link to the graph down in the below

Step-by-step explanation:

The radius of a circular play ground is 77 m. Calculate the distance covered by a runner in 5 complete rounds around the ground.

Answers

Answer:

Step-by-step explanation:

77*5=385

Think About the Process You have 30 quarters. You find 20% more quarters in your room. Then you go shopping and spend 50% of the total number of quarters. Write an expression to represent the total number of quarters you take with you shopping. Calculate, in dollars, the amount of money you have left.

Answers

Answer: $4.5 left.

Step-by-step explanation:

You have 30 quarters, and find 20% more. To convert percentages to decimals for calculations, simply move the decimal two spaces to the left.

20% is 20. ---> 2.0 ---> .20

30 * 0.2 = 6. Now add 6 (found) to 30 (original) to get the total.

30+6 = 36 total quarters.

You spend 50% of the quarters, 36 * 0.5 = 18.

This means you have 18 quarters left (or you spent 18).

18 quarters, each quarter is worth 0.25 dollars, so multiply the number left by how much each is worth.

18 * 0.25 = $4.5.

$4.50 is the amount left

Mike had 6 1/4 pounds of potatoes to share with his friends. He gave them 3 4/5 pounds. How many pounds of potatoes does Mike have left?

Answers

Answer: 2 9/20

Step-by-step explanation:

First, rewriting our equation with parts separated

=6+14−3−45

Solving the whole number parts

6−3=3

Solving the fraction parts

14−45=?

Find the LCD of 1/4 and 4/5 and rewrite to solve with the equivalent fractions.

LCD = 20

520−1620=−1120

Combining the whole and fraction parts

3−1120=2920

Solution by Formulas

First:

Convert any mixed numbers to fractions.

Then your initial equation becomes:

254−195

Applying the fractions formula for subtraction,

=(25×5)−(19×4)4×5

=125−7620

=4920

Simplifying 49/20, the answer is

=2 9/20

A bowling alley charges a flat fee to rent shoes. There is an additional fee for each game played. The function y = 4x + 3.5 represents the cost y of bowling x games. Interpret the parameters of the function.
What represents the price per game?
What represents the shoe rental charge?

Answers

Answer: the price per game is 4 per game and the shoe rental is the additional fee to bowl

Step-by-step explanation:

Scott whose eye level is 1.5m above the ground, stands 30m from a tree. The angle of elevation of a bird at the top of the tree is 36 degrees. How far above the ground is the bird?
A. 21.8 m
B. 23.3 m
C. 41.3 m

Answers

Using trigonometric ratio, the distance of the bird is 21.8m

Angle of Elevation

The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.

To solve this problem, we have to use trigonometric ratio of SOHCAHTOA

Let's define the variables given;

Using Tangent of an angle;

tanθ = opposite / adjacent

tan 36 = x / 30

Cross multiply both sides and solve for x

30 tan36 = x

21.8 = x

The distance above the ground from the bird is 21.8 meter.

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Plot four lines to connect the points in adjacent
quadrants. One is done for you.
Line
# 1 y= -2 (x-6)+1
10
# 2?
#3?
#4?

Answers

Answer:

[tex]\textsf{Line \#2}: \quad y=x-5[/tex]

[tex]\textsf{Line \#3}: \quad y=\dfrac{1}{4}(x-1)-4[/tex]

[tex]\textsf{Line \#4}: \quad y=-8x-29[/tex]

Step-by-step explanation:

Given points:

(-4, 3)(6, 1)(1, -4)(-3, -5)

To find the equations for each of the lines:

Find the slope of the line by substituting two points on the line into the slope formula.Substitute the found slope and one of the points on the line into the point-slope formula and simplify.

Line #2

Points:

Let (x₁, y₁) = (6, 1)Let (x₂, y₂) = (1, -4)

Find the slope:

[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-4-1}{1-6}=\dfrac{-5}{-5}=1[/tex]

Substitute the found slope and one of the points into the point-slope formula:

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

[tex]\implies y-1=1(x-6)[/tex]

[tex]\implies y=(x-6)+1[/tex]

[tex]\implies y=x-5[/tex]

Line #3

Points:

Let (x₁, y₁) = (1, -4)Let (x₂, y₂) = (-3, -5)

Find the slope:

[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-5-(-4)}{-3-1}=\dfrac{-1}{-4}=\dfrac{1}{4}[/tex]

Substitute the found slope and one of the points into the point-slope formula:

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

[tex]\implies y-(-4)=\dfrac{1}{4}(x-1)[/tex]

[tex]\implies y+4=\dfrac{1}{4}(x-1)[/tex]

[tex]\implies y=\dfrac{1}{4}(x-1)-4[/tex]

Line #4

Points:

Let (x₁, y₁) = (-3, -5)Let (x₂, y₂) = (-4, 3)

Find the slope:

[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{3-(-5)}{-4-(-3)}=\dfrac{8}{-1}=-8[/tex]

Substitute the found slope and one of the points into the point-slope formula:

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

[tex]\implies y-(-5)=-8(x-(-3))[/tex]

[tex]\implies y+5=-8(x+3)[/tex]

[tex]\implies y=-8(x+3)-5[/tex]

[tex]\implies y=-8x-24-5[/tex]

[tex]\implies y=-8x-29[/tex]

Please help with this question

[tex]10 \sqrt{2} [/tex]

Answers

10 root to 2= 14.142

Answer:

The answer is approximately equal to 14.14214

Two ocean beaches are being affected by erosion. The table shows the width, in feet, of each beach at high tide measured where 1995 is represented by year 0.

Year number Western Beach width (in feet) Dunes Beach width (in feet)
0 100 20
5 90 45
10 80 70
11 78 75
12 76 80
15 70 95

Describe the patterns shown by the erosion data measurements shown for each of the beaches in the table.
Between which years will the beaches have approximately the same width?
Assuming these rates remain constant, what can you do to get a better approximation of when the two beaches will have the same width?

Answers

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Given f(x) = 2x and g(x) = f(x − 4) + 5, write the new function rule (equation) for function and

describe

Answers

The new function rule is g(x) = 2x -3

What is a function?

A technical definition of a function is: a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

This means that if the object x is in the set of inputs (called the domain) then a function f will map the object x to exactly one object f(x) in the set of possible outputs (called the codomain).

if f(x) = 2x, then f(x-4) = 2(x-4)

g(x) = f(x-4) + 5

substitute f(x-4) into g(x)

g(x) = 2(x-4) + 5

g(x) = 2x -8 + 5

g(x) = 2x - 3

In conclusion, the function rule g(x) is 2x - 3

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Crumbs Cookies was interested in seeing if there was an association between cookie flavor and whether or not there was frosting. Given are the results of the last week's orders. Frosting No Frosting Total Sugar Cookie 56 Chocolate Chip 70 136 Red Velvet 50 Total 180 400 Which category has the greatest joint frequency? Sugar cookies Cookies with no frosting Chocolate chip cookies with frosting Sugar cookies with no frosting

Answers

The category which has the greatest joint frequency is sugar cookies with a frequency of frosting and no frosting as 56 and 120 and a joint frequency of 176

Which category has the highest joint frequency?

Frosting No frosting Total

sugar cookies 56 120 176

Chocolate cookie 66 70 136

Red velvet 38 50 88

Total 160 240 400

Chocolate cookies with frosting = Total chocolate cookies - chocolate cookies with no frosting

= 136 - 70

= 66

Red velvet cookies with frosting = Total cookies with frosting - (Chocolate cookies with frosting + sugar cookies with frosting)

= 160 - (56 + 66)

= 160 - 122

= 38

Total red velvet cookies = Red velvet cookies with frosting + Red velvet cookies with no frosting

= 50 + 38

= 88

Total cookies with no frosting = Total cookies - Total cookies with frosting

= 400 - 160

= 240

Total sugar cookies with no frosting = Total cookies with no frosting - (chocolate cookies with no frosting + Red velvet cookies with no frosting)

= 240 - (70 + 50)

= 240 - 120

= 120

Total sugar cookies = Total sugar cookies with no frosting + Total sugar cookies with frosting

= 120 + 56

= 176

In conclusion, the highest joint frequency is sugar cookies.

Answers

Answer:

20 flowers at sides and 4 flowers at the corner then

total flowers are 24

cost of 2 flowers is 6 then of one flower will be 3

total cost of the flowers will be 24×3=72

Step-by-step explanation:

1. Julia used square tiles to make
a design. She laid the tiles in a
square, 8 tiles wide by 8 tiles
long. Each tile has an area of 1
square inch. What is the area of
Julia's tile design?

Answers

If each tile has an area of 1, then all we have to do is multiply 8 tiles by 8 tiles, and we get 64. So, the area of Julia’s design is 64.

A 12 ft ladder reaches 9 ft up a wall.
What is the angle formed between the
ladder and the ground?

Answers

Answer:

Step-by-step explanation:

Does the graph below represent a function

A. Yes
B. No
C. Sometimes
D. Not enough information

Answers

Answer:

Step-by-step explanation:

Yes, it is a function.

The reason for this is because it passes what is called the Vertical Line Test, notice how if you draw a completely straight line down, it will only make contact with the graph one time. It is hard to tell, but even though it looks like the graph stops at x=±3, the graph is actually approaching the values ever so slightly, therefore maintaining the conditions for the vertical line test.

The answer is A. Yes.

A

Yes the graph represents a function

In Silvergrove, the library is due south of the courthouse and due west of the community swimming pool. If the distance between the library and the courthouse is 9 kilometers and the distance between the courthouse and the city pool is 10 kilometers, how far is the library from the community pool? If necessary, round to the nearest tenth.

Answers

The distance of the library from the community pool is given as 4.4 km

How to solve for the distance

We have to solve this problem with the use of the Pythagoras theorem.

The formula is given as

a² = b² + c²

The total distance flown would be represented by a = 10 kilometer

the distance for the courthouse would be given as 9 kilometers

When we put these values in the formula we would have

10² = a² + 9²

100 = a² + 81

a² = 100 - 81

a² = 19

a = √19

a = 4.4 km

Hence the calculated distance is given a 4.4 km from the library to pool.

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d) please help me with question d)

Answers

Thank me later ………………………….

Each lap of the pool is 1/10 of a mile. You need to swim 25 laps. How many miles did you swim?

Answers

Answer:5/2 miles or 4 and half mile

Step-by-step explanation:

1/10 times 25

25/10

5/2

Answer:

Step-by-step explanation:

the answer is 2 1/2 miles

a. How many cubes with an edge length of b. What is the volume, in cubic inches, of inch are needed to build a cube with one cube with an edge length of inch? an edge length of 1 inch?

Answers

The number of cubes of edge length 1/3 is 27 and the volume of the cube is 1 cubic inches

How to determine the number of cubes

From the question, we have the following parameters that can be used in our computation:

Edge length of cube 1 = 1/3 inchEdge length of cube 2 = 1 inch

The volume of a cube is the cube of its edge length

This means that the volumes are

Volume = Edge length³

So, we have

Volume of cube 1 = (1/3 inch)³ = 1/27 cubic inches

Volume of cube 2 = (1 inch)³ = 1 cubic inch

The number of cubes is then calculated as

Number of cubes = Volume of cube 2/Volume of cube 1

This gives

Number of cubes = 1/(1/27)

Number of cubes = 27

The volume of the cubes

Here, we have

Edge length of cube = 1 inch

The volume of a cube is the cube of its edge length

This means that the volumes are

Volume = Edge length³

So, we have

Volume of cube = (1 inch)³ = 1 cubic inch