If f(x) = 22 – 4x – 5, find the following:
a. f(-2)
b. f (10)
.c. f(0)
Answers
Answer:
a.25
b.-23
c.17
Step-by-step explanation:
Plug each value in for x and solve
Related Questions
Write the following as a percent, decimal and fraction.
43 out of 50
Answers
Percent: 86%
Fraction : 86/100
Decimal: 0.86 or .86
Answer:
Fraction: 43/50
Decimal: 0.86
Percentage: 86%
Step-by-step explanation:
43 out of 50
43/50 = 0.86 = 86%
A 76.00 pound flask of mercury costs $150.50. The density of mercury is 13.534 g/cm3.It takes 4.800 in^3 of mercury to make one manometer. Find the price of the mercury used to make 21 manometers by first calculating the cost of mercury for one manometer.What is the price of mercury used to make one manometer?
Answers
Price of one pound of mercury is derived as follows;
\(\begin{gathered} Price\text{ of 1lb of merc}=\frac{Cost\text{ of flask}}{Pounds\text{ of merc in the flask}} \\ \text{Price of 1 lb}=\frac{150.50}{76} \\ \text{Price of 1 lb}=1.98 \end{gathered}\)This means 1 pound of mercury costs $1.98
1 pound = 453.6 grams
Therefore;
\(\begin{gathered} 1lb=453.6gms \\ 76lb=34,473.6gms \end{gathered}\)The price of 1 gram of mercury would be;
\(\begin{gathered} Price\text{ of 1 gram}=\frac{Price\text{ per pound}}{\text{grams in 1 lb}} \\ \text{Price of 1 gram}=\frac{1.98}{453.6} \\ \text{Price of 1 gram}=0.004365 \end{gathered}\)This means 1 gram of mercury costs $0.004365
Note that you have 13.534 grams per cubic centimeter of mercury. Therefore, the price of 1 cubic centimeter of mercury shall be calculated as follows;
\(\begin{gathered} \text{Price of 1 cubic cm}=grams\text{ per cubic cm x price of 1 gram} \\ \text{price of 1 cubic cm}=13.534\times0.004365 \\ \text{Price of 1 cubic cm}=0.059 \end{gathered}\)This means 1 cubic centimeter of mercury would cost $0.059
Note also that, 1 cubic inch = 16.387 cubic centimeters. Hence,
\(\begin{gathered} Price\text{ of 1 cubic inch}=16.387\text{ cubic cm x }price\text{ of 1 cubic cm} \\ \text{Price of 1 cubic inch}=16.387\times0.059 \\ \text{Price of 1 cubic inch}=0.9668 \end{gathered}\)This means 1 cubic inch costs $0.9668
It takes 4.800 cubic inches to make 1 manometer.
Therefore, the cost of 4.800 cubic inches would be;
\(\begin{gathered} Price\text{ of 4.800 cubic inches}=Price\text{ of 1 cubic inch x 4.800 cubic inches} \\ Price\text{ of 4.800 cubic inches}=0.9668\times4.800 \\ \text{Price of 4.800 cubic inches}=4.64 \end{gathered}\)If it costs 4.800 cubic inches to make 1 manometer, then the cost of 1 manometer would be $4.64
Therefore, to make 21 manometers, we would have;
\(\begin{gathered} 1\text{ manometer}=4.64 \\ 21\text{ manometers}=21\times4.64 \\ 21\text{ manometers}=97.44 \end{gathered}\)ANSWER:
The price of mercury required to make 21 manometers would be $97.44
help me plz...............
Answers
Answer:
2. 7.6
3. .057
4. Nine and three tenths
5. Forty two hundredths
6. Ninety two thousandths
Step-by-step explanation:
Answer:
1. 0.16
2. 7.6
3. 0.057
4. nine and three tenths
5. forty two hundredths
6. ninety two thousandths
I hope this helped
The current population of a small town is 2463 people. It is believed that town's population is tripling every 12 years. Approximate the population of the town 5 years from now.
________ residents (round to nearest whole number)
Answers
{Answer:
3893 residents.
Step-by-step explanation:
Equation for population growth:
The equation for the size of a population, considering that it doubles every n years, is given by:
\(A(t) = A(0)(3)^{(\frac{t}{n})}\)
In which A(0) is the initial population.
The current population of a small town is 2463 people. It is believed that town's population is tripling every 12 years.
This means that \(A(0) = 2463, n = 12\). So
\(A(t) = A(0)(3)^{(\frac{t}{n})}\)
\(A(t) = 2463(3)^{(\frac{t}{12})}\)
Approximate the population of the town 5 years from now.
This is A(5). So
\(A(t) = 2463(3)^{(\frac{t}{12})}\)
\(A(5) = 2463(3)^{(\frac{5}{12})} = 3892.8\)
Rounding to the nearest whole number, 3893 residents.
Evaluate 3x2 + 3x - 9, when x = 2
Answers
3x2 =6 +3(2)-9
= 3
Answer:
9
Step-by-step explanation:
3x^2 + 3x - 9
Substitute x = 2 into the equation.
3(2)^2 + 3(2) - 9
3(4) + 6 - 9
12 + 6 - 9
18 - 9 =
9
A ship X sailing with a velocity (21 kmh 052⁰) observes a light fron a lighthuse due North. The bearing of the liglhthouse from the ship 20 minutes later is found to be 312. calcuate correct to thre sigificant figures
i) the orignal distance when the lighthoues is due West of the ship from the time when it is due North of the ship.
ii) the time in minutes, when the lighthouse is due West of the ship from the time when it is due North of the ship.
iii) the distance in km of the ship from the lighthoue when the light.hose is due West of the ship
Answers
i) the original distance when the lighthouse is due West of the ship is 7 km
ii) The time in minutes when the lighthouse is due West of the ship is 21 minutes
iii) The distance in km of the ship from the lighthouse when the lighthouse is due West of the ship is 29.97 km
To solve this problem, we'll use the concepts of relative velocity and trigonometry. Let's break down the problem into three parts:
i) Finding the original distance when the lighthouse is due West of the ship:
The ship's velocity is given as 21 km/h at a bearing of 052°. Since the ship observed the lighthouse due North, we know that the angle between the ship's initial heading and the lighthouse is 90°.
To find the distance, we'll consider the ship's velocity in the North direction only. Using trigonometry, we can determine the distance as follows:
Distance = Velocity * Time = 21 km/h * (20 min / 60 min/h) = 7 km (to three significant figures).
ii) Finding the time in minutes when the lighthouse is due West of the ship:
To find the time, we need to consider the change in angle from 052° to 312°. The difference is 260° (312° - 052°), but we need to convert it to radians for calculations. 260° is equal to 260 * π / 180 radians. The ship's velocity in the West direction can be calculated as:
Velocity in West direction = Velocity * cos(angle) = 21 km/h * cos(260 * π / 180) ≈ -19.98 km/h (negative because it's in the opposite direction).
To find the time, we can use the formula:
Time = Distance / Velocity = 7 km / (19.98 km/h) = 0.35 h = 0.35 * 60 min = 21 minutes (to three significant figures).
iii) Finding the distance in km of the ship from the lighthouse when the lighthouse is due West of the ship:
We can use the formula for relative velocity to find the distance:
Relative Velocity = sqrt((Velocity in North direction)² + (Velocity in West direction)²)
Using the values we calculated earlier, we have:
Relative Velocity = sqrt((21 km/h)² + (-19.98 km/h)²) ≈ 29.97 km/h (to three significant figures).
Therefore, the ship is approximately 29.97 km away from the lighthouse when the lighthouse is due West of the ship.
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8. The initial value of an investment is $12,000. If the investment earns an annual interest rate of 2.2%, what is its value in 10 years?
a. $14,917.30
b. $14,640.00
c. $14,627.93
d. $87,655.58
Answers
Answer:
$14,917.30
Step-by-step explanation:Step 1: To calculate your interest rate, you need to know the interest formula I/Pt = r to get your rate. Here,
I = Interest amount paid in a specific time period (month, year etc.)
P = Principle amount (the money before interest)
t = Time period involved
r = Interest rate in decimal
Step 2: Once you put all the values required to calculate your interest rate, you will get your interest rate in decimal. Now, you need to convert the interest rate you got by multiplying it by 100. For example, a decimal like .11 will not help much while figuring out your interest rate. So, if you want to find your interest rate for .11, you have to multiply .11 with 100 (.11 x 100).
Amount get after 10 year is $14,640
Given information:
Initial amount invested = $12,000
Annual interest rate = 2.2%
Number of year = 10 year
Find:
Amount get after 10 year
Computation:
Amount of interest = Initial amount invested × Annual interest rate × Number of year
Amount of interest = 12,000 × 2.2% × 10
Amount of interest = $2,640
Amount get after 10 year = Initial amount invested + Amount of interest
Amount get after 10 year = 12,000 + 2,640
Amount get after 10 year = $14,640
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M(6, 6) is the midpoint of RS. The coordiantes of S are (9, 5). wHAT ARE THE COORDINATES OF r?
Answers
The point R has its coordinates to be (3, 12)
How to determine the coordinate of point R?From the question, the given parameters are:
Midpoint, M = (6, 6)
Endpoint S = (9, 5)
The midpoint of a line or points is then calculated using the following midpoint formula
Midpoint (x, y) = 1/2 * (x₂ + x₁, y₂ + y₁)
Where x and y are the coordinates of M and S
Substitute the known values in the above equation
So, we have the following equation
(6, 6) = 1/2 * (9 + x, 5 + y)
Multiply through by 2
So, we have
(12, 12) = (9 + x, 5 + y)
By comparison, we have
x + 9 = 12
y + 5 = 12
Evaluate the solutions of x and y
So, we have
x = 3 and y = 12
Rewrite as
(x, y_ = (3, 12)
This means that
R = (3, 12)
Hence, the coordinates of point R are (3, 12)
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Convert 5613, base 10 to
base 8
Answers
Answer:
12755 base-8
Step-by-step explanation:
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Ivan started the week on page 35 of his book and read 20 pages each night. What page will Ivan be on if he reads for 8 nights?
Answers
Answer: he should be on page 195
Step-by-step explanation:
Which value of c is in the domain of f(x)
Answers
The value of c in the domain of f(x) depends on the specific function f(x) and its domain.
In order to determine which value of c is in the domain of f(x), we need to know the function f(x) and its domain. A domain is the set of all possible input values of a function.
If a value of c is in the domain of f(x), then we can plug it into the function and get a valid output.
In general, a function f(x) can have a restricted domain due to certain conditions or limitations. For example, a square root function cannot have negative values under the radical because that would result in an imaginary number.
Thus, the domain of a square root function is restricted to non-negative values.
In order to find the domain of a function, we need to consider any restrictions on the input values. For example, if we have the function f(x) = 1/x, we cannot plug in x = 0 because that would result in division by zero, which is undefined.
Therefore, the domain of f(x) is all real numbers except 0. We can write this as D(f) = {x : x ≠ 0}.Once we know the domain of f(x), we can check which value of c is in the domain by seeing if it satisfies the condition.
For example, if the domain of f(x) is D(f) = {x : x > 2}, then c = 3 is in the domain because 3 is greater than 2. On the other hand, c = 1 is not in the domain because 1 is less than 2.
Therefore, the value of c in the domain of f(x) depends on the specific function f(x) and its domain.
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What is the intermediate step in the form
(x+a)^2=b as a result of completing the square for the following question
Answers
The intermediate step in completing the square is\($x^2 + 2ax + (a^2) = b - a^2 + (a^2)$\)
To complete the square for the equation \($(x+a)^2=b$\), we can follow these steps:
1. Expand the left side of the equation: \($(x+a)^2 = (x+a)(x+a) = x^2 + 2ax + a^2$\).
2. Rewrite the equation by isolating the squared term and the linear term: \($x^2 + 2ax = b - a^2$\).
3. To complete the square, take half of the coefficient of the linear term, square it, and add it to both sides of the equation:
\($x^2 + 2ax + (a^2) = b - a^2 + (a^2)$\).
4. Simplify the right side of the equation: \($x^2 + 2ax + (a^2) = b$\).
This step can be represented as: \(\[x^2 + 2ax + (a^2) = b - a^2 + (a^2)\]\)
This intermediate step helps us rewrite the equation in a form that allows us to factor it into a perfect square.
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Solve for x(need help)
Answers
Answer:
x = 18
Step-by-step explanation:
I the given triangle, it appears that M and N are the midpoints of the segments BG and BD respectively. If it so, then let us solve it.
By mid segment theorem:
2MN = GD
2(6x - 51) = 114
12x - 102 = 114
12x = 114 + 102
12x = 216
x = 216/12
x = 18
____ + g − g = k
help
Answers
Answer: umm it k
Step-by-step explanation: k+g-g=k
g-g=0
k=k
ABC is a right angled triangle. if B = 90°, AC = 96 cm, C = 30°.
Answers
The length of side AB in right angled triangle ABC will be 48 cm.
What is a right angled triangle?Every triangle with one 90° angle is said to have a right angle. The triangle with a right angle is known as a right triangle because a right angle is 90 degrees.The longest side of a right angle is known as the hypotenuse, and it is opposite the right angle.
Given,
∠B= 90°, AC = 96 cm, ∠C = 30°
Now, we know, Trignometric ratio sin θ in triangle can be given by-:
sin θ = \(\frac{perpendicular}{hypotenuse}\)
From given figure,
Perpendicular= AB= ?
and Hypotenuse= AC = 96
and θ= 30°
Hence,
sin 30° =\(\frac{perpendicular}{hypotenuse}\)= \(\frac{AB}{96}\)
\(\frac{1}{2} = \frac{AB}{96}\) (∵ sin 30°= 1/2)
\(AB=\frac{96}{2}\)
\(AB= 48 cm\)
Thus, AB= 48 cm
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Correct Question:ABC is a right angled triangle. if B = 90°, AC = 96 cm, C = 30°. Find AB = ?
Find two integers whose sum is 11 and whose product is 30.
Answers
5 x 6 = 30
0.45 is the result of finding the product of 3 and 12 minus a number. What is the number?
7/20
19/60
−1/60
−1/20
Answers
Answer:
The answer is 7/20
Step-by-step explanation:
This is for k-12!!
Currently taking the quiz just want to help others:)
Answer:
The answer is indeed 7/20 !!
Step-by-step explanation:
For the k12 5.17 Quiz: Model with Multistep Equations
Good luck on the rest of your quiz !!!
You would like to have $20,000 to use a down payment for a home in five years by making regular, end-of-month deposits into an annuity that pays 6% interest compounded monthly.
How much should you deposit each month?
Round your answer to the nearest cent. Do not include the dollar sign in the answer box below.
Answers
The amount that should be deposited monthly is $286.66.
What is a monthly deposit?The monthly deposit is the periodic payment into an investment account that earns interest at a compound rate.
The monthly deposit can be determined using an online finance calculator.
N (# of periods) = 60 months (5 years x 12)
I/Y (Interest per year) = 6%
PV (Present Value) = $0
FV (Future Value) = $20,000
Results:
Monthly Deposit = $286.66
Sum of all periodic deposits = $17,199.36
Total Interest = $2,800.64
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Find the unknown 9,006-7,474?
Answers
pls help me with this math question i beg
Answers
Answer:
All angles in a quadrilateral = 360°
b =?
b = 360 - (128 + 61 + 57)
b = 360 - 246
b = 114°
(PLEASE ANSWER ASAP)
Answers
Answer:
alternate interior angles are congruent
WILL MARK BRAINLIEST!
Given: parallelogram ABCD, calculate the length of AD
Answers
Answer:
15
Step-by-step explanation:
Due to it being a parallelogram 6x-10=3x+5 which makes it 3x-10=5 when you subtract both sides by 3x then you add 10 to both sides to make 3x = 15 which gets you x = 5 finally you put this into 4x-5 which is 4*5-5, 20-5=15 so the answer is 15
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Determine the value of x in the figure.
Question 20 options:
A)
x = 9
B)
x = 3
C)
x = 6
D)
x = 4.5
Answers
A football club is the only one in its region and is therefore able to behave like a monopolist. It sells tickets to Adults (a) and Juniors (j), whose demand curves are given by:
Pa = 200 − Qa
Pj = 160 − Qj
Additionally, the club’s total costs are given by = 20Qi
The club hires an economist to consider its pricing strategy and receives the advice that it should charge different prices to each type of supporter. Find the prices it sets in both markets, the sales (output) in each and its overall level of profit and illustrate profit maximising outputs and prices of each consumer type on a graph (one graph for each type of consumer). Calculate consumer surplus in this case.
Answers
Answer:
Adult market
price: 110sales: 9900profit: 8100consumer surplus: 9000Junior market
price: 90sales: 6300profit: 4900consumer surplus: 5600Total profit: 13000
Total consumer surplus: 14600
Step-by-step explanation:
Given Adult (a) and Junior (j) demand equations Pa = 200 -Qa and Pj = 160 -Qj, and cost equation C = 20Q, you want to find the price in each market that maximizes profit, the sales in each market, and the consumer surplus, and a graph of profit-maximizing sales and prices.
RevenueEach demand equation is of the form P = Pmax -Q, where P is the price that will result in sales of Q tickets. The revenue (R) in each case is the product of numbers of tickets sold (Q) and the price at which they are sold (P).
R = QP = Q(Pmax -Q)
ProfitThe profit is the difference between revenue and cost.
Profit = R - C = Q(Pmax -Q) -20Q
Profit = Q(Pmax -20 -Q)
Writing the demand equation in terms of P, we find ...
Q = Pmax -P
Substituting this into the Profit equation gives ...
Profit = (Pmax -P)(Pmax -20 -(Pmax -P))
Profit = (Pmax -P)(P -20)
The profit function describes a downward-opening parabolic curve with zeros at P=Pmax and P=20. The maximum profit is on the line of symmetry of this curve, halfway between these values of P:
Price for maximum profit = (Pmax +20)/2 = Pmax/2 +10
PricesIn the adult market, Pmax = 200, so the profit-maximizing ticket price is ...
Pa = 200/2 +10 = 110 . . . . price for maximum profit in Adult market
In the Junior market, Pmax = 160, so the profit-maximizing ticket price is ...
Pj = 160/2 +10 = 90 . . . . price for maximum profit in Junior market
SalesUsing the revenue equation, we find the sales in each market to be ...
Qa = 200 -Pa = 200 -110 = 90
Ra = Qa·Pa = 90(110) = 9900 . . . . sales in Adult market
Qj = 160 -Pj = 160 -90 = 70
Rj = Qj·Pj = 70(90) = 6300 . . . . sales in Junior market
Overall ProfitThe profit in each market is ...
Adult market profit = 90(110 -20) = 8100
Junior market profit = 70(90 -20) = 4900
The overall profit will be the sum of the profits in each market:
Overall profit = 8100 +4900 = 13000
Consumer surplusThe consumer surplus in each market is the area below the demand curve and above the price point. It is half the product of the maximum price and the quantity actually sold.
CSa = (1/2)(200)Qa = 100(90) = 9000
CSj = (1/2)(160)(Qj) = 80(70) = 5600
The total consumer surplus is ...
CS = CSa +CSj = 9000 +5600 = 14,600 . . . . total consumer surplus
Graph
The first attachment shows the sales (output) in each market (red=Adult, purple=Junior) as a function of ticket price. It also shows the corresponding profit (orange=Adult, blue=Junior). The profit-maximizing price point is marked on each curve. You will note that it is different from the output-maximizing price point.
The second attachment illustrates the consumer surplus in each market. That graph has price on the vertical axis, and quantity on the horizontal axis. The colors correspond to the colors on the graph in the first attachment.
Find the area and the circumference of a circle with diameter 3 ft.
Use the value 3.14 for it, and do not round your answers. Be sure to include the correct units in your answers.
ft
3 ft
Area: 1
Circumference:
Х
Answers
Step-by-step explanation:
circumference of a circle :
2×pi×r
area of a circle
pi×r²
r(radius) is diameter/2. = 1.5ft
we shall assume 3.14 to be pi.
so,
circumference is
2 × 3.14 × 1.5 = 3.14 × 3 = 9.42 ft
area is
3.14 × 1.5² = 3.14 × 2.25 = 7.065 ft²
Olivia measures the heights of two trees and the lengths of their shadows. She notices that the height of each tree and the length of its shadow are directly proportional. One of the trees has a height of 15 m and a 10 m long shadow. The other tree has a 14.4 m long shadow. Calculate its height, in metres (m). Give any decimal answers to 1 d.p. 15 m 10 m ? m 14.4 m
Answers
Step-by-step explanation:
directly proportional means
y = kx
with k being a constant factor for all values of x.
we get k by using the given data point (10, 15).
15 = k×10
k = 15/10 = 1.5
so, now for the other tree we know k and x and calculate y
y = 1.5×14.4 = 21.6 m
it is 21.6 m tall (its height is 21.6 m).
Look for factors that will help you determine what type of economy exists in Country A.
Based on the clues in this passage, what type of economy does Country A have?
developed
developing
transitioning
command
Answers
developing:
a low GDP
an economy based on agriculture
Based on the limited information provided, it is not possible to definitively determine the type of economy in Country A. More specific details and factors would be necessary to make a conclusive determination.
Determine the value of x.
A) 2√3 B) 6√3 C) 12 D) 12√3
Answers
The required measure of the value of x is given as 2√3. Option A is correct.
What are trigonometric equations?
These are the equation that contains trigonometric operators such as sin, cos.. etc. In algebraic operations.
here,
Consider the given triangle,
perpendicular = 6
base = x
Applying trigonometric operation,
tan30 = perpendicular/base
tan30 = 6/ x
x = 6/√3
x = 2√3
Thus, the required measure of the value of x is given as 2√3. Option A is correct.
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PLEASE I NEED HELP the question is,
In the diagram of triangle LAC and triangle DNC below, LA = DN, CA = CN, and DAC is perpendicular to LCN.
a) Prove that triangle LAC = triangle DNC.
b) Describe a sequence of rigid motions that will map triangle LAC onto triangle DNC.
Answers
Answer:
1244 DCD
Step-by-step explanation:
In a large population, 69 % of the people have been vaccinated. If 3 people are randomly selected, what is the probability that AT LEAST ONE of them has been vaccinated?
Give your answer as a decimal (to at least 3 places) or fraction.
Answers
The required probability is 0.970 (approx.) or 97/100 (in fraction).
Given that 69% of people in a large population have been vaccinated. We are required to determine the probability of at least one person being vaccinated if three people are randomly selected. Let's solve it using the complement rule.
The complement rule states that the probability of an event occurring is equal to 1 minus the probability of that event not occurring. That is, if A is an event, then P(A) = 1 - P(A').
We can solve the given problem using the complement rule as follows: Let P(A) be the probability of at least one person being vaccinated.
Then, the probability of no one being vaccinated is P(A') = (100 - 69) = 31%.
To find the probability of at least one person being vaccinated, we can subtract the probability of none of them being vaccinated from 1. That is, P(A) = 1 - P(A') = 1 - 0.31 × 0.31 × 0.31 = 1 - 0.029791 = 0.97021.
Hence, the probability of at least one person being vaccinated if three people are randomly selected is 0.97021 (rounded to 3 decimal places).
Therefore, the required probability is 0.970 (approx.) or 97/100 (in fraction).
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