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then f(1) = (3(1) + 7)²
= 10²
⇒ f(1) = 100 [OPTION E]
Related Questions
please can you help me!
z-² as a fraction
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Help Please.
1 inch=2.54 centimeters
68 centimeters= ..... inches
(round the answer to two decimal places)
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Show how to multiply 6 x 298 using friendly numbers and then using properties and mental math.Write about which method you like better and why
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Final answer:
To multiply 6 x 298 using friendly numbers, you multiply 6 by 300 and then subtract 12, getting 1788. Using properties and mental math, you break 298 into 200 + 90 + 8, multiply each by 6, and add the results together to get the same answer, 1788. The second method is preferred for its accuracy and reinforcement of the associative property.
Explanation:
To multiply 6 x 298 using friendly numbers, we can adjust 298 to a number that is easier to multiply, such as 300. This method involves approximation for ease of calculation. Here's how it would look:
First, multiply 6 by 300 to get 1800 (since 6 x 3 = 18, and then we add two zeros because we're multiplying by 300).Since we multiplied by 2 more than the original number (298 + 2 = 300), we subtract 2 times 6 from the result (which is 12) to correct for our approximation.Therefore, the final result is 1800 - 12 = 1788.Using properties and mental math, we can use the distributive property to break 298 into more manageable numbers. Here's the step-by-step process:
Break 298 into 200 + 90 + 8.Multiply each part by 6: (6 x 200) + (6 x 90) + (6 x 8).Calculate each multiplication separately: 1200 + 540 + 48.Add the results together: 1200 + 540 + 48 = 1788.I prefer the second method because it guarantees accuracy and still takes advantage of the associative property to simplify calculations without approximations. Additionally, this type of mental math helps to reinforce an understanding of multiplication as a series of simpler, added-together parts.
You have a map where indy and fort wayne are 13 centimeter apart. kokomo and indy are 6.5 cm apart on the map. if you know that indy and fort wayne are actually 120 miles apart, how far apart would indy and kokomo be in real life? express your answer rounded to the nearest tenth of a mile
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The distance between Indy and Kokomo be in real life is given by the proportion A = 60 miles
What is Proportion?The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the proportion be represented as A
Now , the value of A is
Let the distance between Indy and Fort Wayne in map = 13 cm
Let the distance between Indy and Fort Wayne in real = 120 miles
And , let the distance between Kokomo and Indy map = 6.5 cm
So , the proportion is
120 / 13 = A / 6.5
Multiply by 6.5 on both sides , we get
A = 120 / 2
A = 60 miles
Hence , the distance is 60 miles
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A construction crew is lengthening a road. The road started with a length of 54 miles, and the crew is adding 4 miles to the road each day. Let L represent the total length of the road (in miles), and let D represent the number of days the crew has worked. Write an equation relating L to D . Then use this equation to find the total length of the road after the crew has worked 31 days.
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the crew worked for 31 days...so sub in 31 for D
L = 4(31) + 54
L = 124 + 54
L = 178 miles <==
You buy the same number of brushes, rollers, and paint cans. Write and expression in simplest form that represents the toral amount of money you spend for the painting supplies
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X being the amount of supplies
B are the price of the brushes
R is the price of the rollers
C the price of the paint cans
M is the total price
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Three quarters of the batch of twenty cookies burned when you forgot to take them out of the oven how many cookies burned
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A digit thermometer reports a temperature of 32*F as being 32.02*F. Which of the followings true?
A. The thermometer is both accurate and precise.
B. The thermometer is neither accurate nor precise.
C. The thermometer is precise, but not accurate.
D. The thermometer is accurate, but not precise.
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Answer: The thermometer is both accurate and precise
Step-by-step explanation: Hope this helped!!
Find the solution to the linear system of differential equations {x′y′==−5x+3y−18x+10y satisfying the initial conditions x(0)=4 and y(0)=11
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[tex]\begin{bmatrix}x\\y\end{bmatrix}'=\begin{bmatrix}-5&3\\-18&10\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}[/tex]
The coefficient matrix has eigenvalues [tex]\lambda=1,4[/tex], with corresponding eigenvectors [tex]\mathbf v=\begin{bmatrix}1\\2\end{bmatrix},\begin{bmatrix}1\\3\end{bmatrix}[/tex]. So the general solution is
[tex]\begin{bmatrix}x\\y\end{bmatrix}=C_1e^t\begin{bmatrix}1\\2\end{bmatrix}+C_2e^{4t}\begin{bmatrix}1\\3\end{bmatrix}[/tex]
Given that [tex]x(0)=4[/tex] and [tex]y(0)=11[/tex], we get
[tex]\begin{cases}4=C_1+C_2\\11=2C_1+3C_2\end{cases}\implies C_1=1,C_2=3[/tex]
so that the particular solution to the system is
[tex]\begin{bmatrix}x\\y\end{bmatrix}=e^t\begin{bmatrix}1\\2\end{bmatrix}+3e^{4t}\begin{bmatrix}1\\3\end{bmatrix}[/tex]
or in equivalent terms,
[tex]\begin{cases}x=e^t+3e^{4t}\\y=2e^t+9e^{4t}\end{cases}[/tex]
The problem given is a linear system of differential equations with initial conditions, but the system is not properly defined and appears to have a typo. Normally, such a system would be in the form x' = ax + by and y' = cx + dy, with initial conditions that would determine the particular solution.
Explanation:This question is about solving a linear system of differential equations with initial conditions, specifically the system {x′y′==−5x+3y−18x+10y with the initial conditions x(0)=4 and y(0)=11. However, there seems to be a typo, as the system is not properly defined and doesn't make sense as written. Under normal conditions, such a system would be in the form x' = ax + by and y' = cx + dy, where a,b,c,d are constants and x' and y' are the derivatives of x and y respectively.
Additionally, the initial conditions x(0)=4 and y(0)=11 would serve to define the particular solution for the system of differential equations. Correcting and resolving such typos would be the first step in progressing towards a solution.
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Under good weather conditions, 80% of flights arrive on time. during bad weather, only 30% of flights arrive on time. tomorrow, the chance of good weather is 60%. what is the probability that your flight will arrive on time?
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The probability that your flight will arrive on time is 0.6, or 60%.
Explanation:To calculate the probability that your flight will arrive on time, we can use the concept of conditional probability. Let A represent the event of good weather and B represent the event of the flight arriving on time. We know P(A) = 0.6, P(B|A) = 0.8, and P(B|A') = 0.3 (where A' represents bad weather). We can use the formula for conditional probability: P(B) = P(A) * P(B|A) + P(A') * P(B|A'). Substituting the given values, we have P(B) = 0.6 * 0.8 + 0.4 * 0.3 = 0.48 + 0.12 = 0.6. Therefore, the probability that your flight will arrive on time is 0.6, or 60%.
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It takes 40 min for a bus to travel the 36 miles from Framingham to Worcester. A car traveling from Worcester to Framingham moves 1.5 times as fast as the bus. If the car and the bus start moving towards each other simultaneously, after how many minutes will they meet?
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The velocity of the bus is:
velocity (bus) = 36 miles / 40 min
velocity (bus) = 0.9 miles / min
Since the car is 1.5 times faster, so the velocity of the car is:
velocity (car) = 1.5 * 0.9 miles / min
velocity (car) = 1.35 miles / min
At the meeting point, the sum of the distance is equal to 36 miles. Therefore:
1.35 t + 0.9 t = 36
2.25 t = 36
t = 16 min
So they will meet after 16 minutes.
Myra borrowed $1,500 at 12.5% interest for three months. How much
does she have to repay under a single-payment plan?
a. $46.88
b. $1,562.50
c. $1,546.88
d. $187.50
**please explain how you got the answer, it's just so that I can understand
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now, 3 months is not even a year, there are 12 months in 1 year, so 3 months is 3/12 years, or 1/4.
[tex]\bf \qquad \textit{Simple Interest Earned}\\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\to& \$1500\\ r=rate\to 12.5\%\to \frac{12.5}{100}\to &0.125\\ t=years\to \frac{3}{12}\to &\frac{1}{4} \end{cases} \\\\\\ I=1500\cdot 0.125\cdot \cfrac{1}{4}\implies 46.875\approx 46.88[/tex]
Twice the difference between a number and 10 is equal to 6 times the number plus 16. What is the number?
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A bouncing ball reaches a height of 27 feet at its first peak, 18 feet at its second peak, and 12 feet at its third peak. Describe how a sequence can be used to determine the height of the ball when it reaches its fourth peak.
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18-12 = 6
12- n = 3
-n = 3-12
-n = -9 ( cancel the negative sign by simple divide both sides with -1 )
n = 9
Therefore the height of the ball is 9 feet when it reaches fourth peak .
Answer:
so on the fourth bounce the ball will reach a height of 8 feet
Step-by-step explanation:
There is a common ratio of 2/3 between the height of the ball at each bounce so the bounce height from a geometric sequence 27,18,12 two-thirds of 12 is 8 so on the fourth bounce the ball will reach a height of 8 feet
which is the longer length 29ft or 9 yards
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9 yards, or 27 feet, is shorter than 29 feet.
29 feet is longer than 27 feet.
To compare 29 feet and 9 yards, convert 9 yards to feet, which equals 27 feet. Since 29 feet is greater than 27 feet, 29 feet is longer.
To determine which length is longer between 29 feet and 9 yards, we need to convert one of the measurements to the same unit. We know that 1 yard is equal to 3 feet. Therefore, to convert 9 yards to feet:
9 yards x 3 feet/yard = 27 feetComparing the two lengths, 29 feet is longer than 27 feet.
Thus, 29 feet is the longer length.
What are the solutions of the following system?
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2x + y = -5.....y = -2x - 5
x^2 + (-2x - 5)^2 = 25
x^2 + (-2x - 5)(-2x - 5) = 25
x^2 + (4x^2 + 20x + 25) = 25
5x^2 + 20x + 25 = 25
5x^2 + 20x = 0
5x(x + 4) = 0
5x = 0 2(0) + y = -5
x = 0 y = -5
x + 4 = 0 2(-4) + y = -5
x = -4 -8 + y = -5
y = 3
solutions are : x = 0, y = -5.....and x = -4, y = 3
To solve the system of equations, set the demand and supply equation equal to each other and solve for the unknown. Substitute Qd with Qs and solve for P.
Explanation:We now have a system of three equations and three unknowns (Qd, Qs, and P), which we can solve with algebra. Since Qd = Qs, we can set the demand and supply equation equal to each other:
By substituting Qd with Qs, we get:
16 - 2P = 2 + 5P
From here, we can solve for P to find the value of the unknown.
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Josh is twenty-five years older than his son Carlos. In ten years Josh will be twice as old as Carlos. How old is Carlos now?
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Given that the points (-1, 6), (3, 6), (3, 1), and (-1, 1) are vertices of a rectangle, how much shorter is the width than the length?
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Answer:
1 unit shorter
Step-by-step explanation:
By plotting the given points in the coordinate plane,
We get a rectangle ABCD having vertices,
A(-1,6), B (3,6), C (3,1), D (-1,1)
By the distance formula,
Shorter side or width of the rectangle,
[tex]AB=\sqrt{(3-(-1))^2+(6-6)^2}=\sqrt{4^2+0}=4\text{ unit}[/tex]
Longer side or length of the rectangle,
[tex]BC=\sqrt{(3-3)^2+(1-6)^2}=\sqrt{5^2}=5\text{ unit}[/tex]
The difference between length and width,
[tex]BC - AB = 5 - 4 = 1\text{ unit}[/tex]
Hence, the width of rectangle is 1 unit less than the length.
Recycling Center A processes aluminum at a rate of 100 pounds per hour, while Recycling Center B processes aluminum at a rate of 2 tons per week. Assuming that both centers operate all day every day, which center processes aluminum faster, and why?
A:Recycling Center A processes aluminum faster; Recycling Center B’s rate is about 12 pounds per hour.
B:Recycling Center A processes aluminum faster; Recycling Center B’s rate is about 24 pounds per hour.
C:Recycling Center B processes aluminum faster; its rate is about 120 pounds per hour.
D:Recycling Center B processes aluminum faster; its rate is about 240 pounds per hour.
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The first thing to be done is to convert the 2 tons into pounds.
1 pound is equal to 0.0005 tons (US). So, 2 tons divided by 0.0005 will give us the aluminium pounds per week that are processed by the Recycling Centre B.
[tex] \frac{2}{0.0005} [/tex]=4000
Recycling Centre B processes 4000 pounds/week. In order to compare to Recycling Centre A, we need to find the rate in pounds per hour. To do so divide the 4000 pounds by 168 (24×7 = number of hours in a week).
[tex] \frac{4000}{168} [/tex]≈23.8
The Recycling Centre B processes about 23.8 pounds/hour whereas the Recycling Centre A processes 100pounds/hour.
which statements are true about the regular polygon? check all that apply.
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its 1, 3, and 5 I think
Answer:
1) False
2) True
3) True
4) False
5) True
Step-by-step explanation:
We are given the following information in the question:
1) False
The sum of measures of interior angle is given by:
[tex](n-2)\times 180^\circ\\\text{where n is the number of sides in regular polygon}[/tex]
Putting n = 5
Sum of interior\r angle = [tex](5-2)\times 180 = 3\times 180 = 540^\circ[/tex]
2) True
Each interior angle measure =
[tex]\displaystyle\frac{\text{Sum of interior angles}}{\text{Number of sides}} = \frac{540}{5} = 108^\circ[/tex]
3) True
All the angles in a regular polygon are equal.
4) False
The polygon is a regular pentagon.
5) True
The sum of measures of interior angle is given by:
[tex]180^\circ(5-2)[/tex]
Jay is cutting a roll of biscuit dough into slices that are 3/8 inch thick. If the roll is 10 1/2 inches long, how many slices
can he cut?
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21/2 * 8/3 =
84 / 3 =
28 <== he can cut 28 slices
The number of slices that Jay could make is equal to 28
What is a mixed fraction?A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, and 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.
Given here: Dimension of the roll= 10¹/₂ inches and length of each slice=3/8 inch
Thus the number of slices that Jay could make is = 10+ 1/2 /3/8
=21/2 × 8/3
=28
Hence The number of slices that Jay could make is equal to 28
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How do I solve for x?
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5 6
---- = ---------
14 6 + x
Then 30 + 5x = 84, and 5x = 54, and so x = 54/5, or 10.8, or 10 4/5.
Evaluate the line integral ∫cf⋅dr∫cf⋅dr, where f(x,y,z)=−5xi+yj+zkf(x,y,z)=−5xi+yj+zk and c is given by the vector function r(t)=⟨sint,cost,t⟩, 0≤t≤3π/2.
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[tex]=\displaystyle\int_0^{3\pi/2}(-6\sin t\cos t+t)\,\mathrm dt=\frac{9\pi^2}8-3[/tex]
one pumpkin vine produce 5pumpkins I harvest 30 how many vines do I have
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Reuben bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $150 more than the desktop. He paid for the computers using two different financing plans. For the desktop the interest rate was 7% per year, and for the laptop it was 9.5% per year. The total finance charges for one year were $303 . How much did each computer cost before finance charges?
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a = price for the desktop
b = price for the laptop
we know the laptop is 150 bucks more than the desktop, b = a + 150.
how much is 7% of a? (7/100) * a, 0.07a.
how much is 9.5% of b? (9.5/100) * b, 0.095b.
total interests for the financing add up to 303, 0.07a + 0.095b = 303.
[tex]\bf \begin{cases} \boxed{b}=a+150\\ 0.07a+0.095b=303\\ ----------\\ 0.07a+0.095\left(\boxed{a+150} \right)=303 \end{cases} \\\\\\ 0.07a+0.095a+14.25=303\implies 0.165a=288.75 \\\\\\ a=\cfrac{288.75}{0.165}\implies a=1750[/tex]
how much was it for the laptop? well b = a + 150.
Kwan's parents bought a home for $50,000 in 1997 just as real estate values in the area started to rise quickly. Each year, their house was worth more until they sold the home for $309,587. Model the growth of the home's value from 1997 to 2007 with both linear and an exponential equation. Graph the two models below.
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A. First let us start with the linear model.
The equation is in the form of y = m x + b
Calculating for the slope m:
m = (309,587 – 50,000) / (2007 – 1997)
m = 25,958.7
Subsituting:
y = 25,958.7 x + b
Taking x = 1997, y = 50,000. Solve for b:
50,000 = 25,958.7 (1997) + b
b = -51,789,523.9
The complete equation is therefore:
y = 25,958.7 x - 51,789,523.9
B. The exponential model has the following form:
y = a b^x
where a and b are constants
Taking x1= 1997, y1 = 50,000; x2 = 2007, y2 = 309,587
50,000 = a b^1997
309,587 = a b^2007
Combining in terms of a:
50,000 / b^1997 = 309,587 / b^2007
b^2007 / b^1997 = 309,587 / 50,000
b^10 = 6.19174
b = 1.2
Substituting:
y = a 1.2^x
Solving for a:
50,000 = a 1.2^1997
a = 3.75 x 10^-154
The complete equation is:
y = 3.75 x 10^-154 * 1.2^x
A baseball team has a goal of hitting more than 84 home runs this season. They average 7 home runs each game and have already hit 35 home runs so far. How many more games, x, will it take the baseball team to reach its home run hitting goal if they continue to average 7 home runs per game?
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Final answer:
The baseball team needs to play 7 more games to exceed its goal of 84 home runs, based on their current average of 7 home runs per game.
Explanation:
The baseball team has hit 35 home runs and wants to hit more than 84. To find how many more games it will take, we first calculate the total number of home runs needed to surpass 84, which is 84 - 35 = 49 home runs. Since the team averages 7 home runs per game, we divide the remaining home runs needed by the average per game to find x, the number of games needed: 49 home runs / 7 home runs per game = 7 games.
Therefore, the baseball team needs to play 7 more games to reach its goal, assuming the average stays constant.
Arleen has a gift card for a local lawn and garden store. She uses the gift card to rent a tiller for 4 days. It cost $35 per day to rent the tiller. She also buys a rake for $9.
A. Find the change to the value on the gift card. (Question #1)
B. The original amount on the gift card was $200. Does Arleen have enough to buy a Wheelbarrow for $50? (Question #2)
Answers
200 - 149 = 51 left on gift card. Yes she has enough to buy the wheelbarrow.
Answer:
Step-by-step explanation:
Arleen has a gift card of the amount = $200
The total cost to rent the tiller for 4 days and a rake for $9
= ($35 × 4) + $9
= 140 + 9 = $149
A. Now the balance on the gift card = $200 - $149
= $51
B. Arleen have $51 in her gift card so she has enough to buy a wheelbarrow for $50.00.
Evaluate the upper and lower sums for f(x) = 1 + x2, −1 ≤ x ≤ 1, with n = 3 and 4.
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Answer:
92/27 and 58/27 for n=3 and 13/4 and 9/4 for n=4
Step-by-step explanation:
n = 3: First let’s find ∆x:
∆x = (b − a)/n = 1 − (−1)3 = 2/3
We will have three intervals: −1 ≤ x ≤ −1/3, −1/3 ≤ x ≤1/3, 1/3 ≤ x ≤ 1.
Upper sum: On the first interval, the highest point occurs at f(−1) = 2. On the second interval, the highest point occurs at f(1/3) = f(−1/3) = 1 + ( 1/3)^2=1 + 1/9 = 10/9
On the third interval, the highest point occurs at f(1) = 2. So A ≈ A upper = 3Σ i=1 f(xi)∆x = [f(−1) + f (1/3)+ f(1)]∆x = (2 +10/9+ 2)*2/3 = 92/27
Lower sum: On the first interval, the lowest point occurs at f(−1/3) = 10/9
On the second interval, the lowest point occurs at f(0) = 1. On the third interval, the lowest point occurs at f(1/3) = 10/9. SoA ≈ A lower =3Σ i=1 f(xi)∆x = f(−1/3) + f(0) + f(1/3) . ∆x = (10/9+ 1 +10/9)· 2/3= 58/27
Apply the same technique for n=4
Find the second of two consecutive integers if the second is 13 less than twice the first.
Answers
Hope this helps!
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