Answers
The polynomial function that best fits the graph is f(x) = 130(x+3)(x-2)²(x-5).
The given graph exhibits three x-intercepts at x = -3, 2, and 5, and the y-intercept is positioned at (0, 2). The graph passes through the x-axis linearly at x = -3 and x = 5, indicating that the corresponding factors of the polynomial will be linear. However, at x = 2, the graph bounces off the x-axis at the intercept, implying that the corresponding factor of the polynomial will be quadratic. Therefore, the polynomial function can be expressed as follows:
f(x) = a(x+3)(x-2)²(x-5)
To find the stretch factor 'a,' we can use another point on the graph, such as the y-intercept (0, 2). By plugging in the values, we obtain:
f(0) = a(0+3)(0-2)²(0-5)
-2 = a(0+3)(0-2)²(0-5)
-2 = -60a
a = 130
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Related Questions
x^2+7x-9 + 2x-1 what is the polynomial and degree
Answers
Answer:
The given expression is a polynomial:
f(x) = x^2 + 7x - 9 + 2x - 1
Combining like terms, we get:
f(x) = x^2 + 9x - 10
The degree of the polynomial is 2, since the highest power of x is 2.
↑
tructor
Watch the video and then answer the problem given below.
Click here to watch the video.
The circle graph represents a sample of 600 people who were asked which one automobile accessory they would most
prefer to have on a family trip. How many people indicated Bluetooth capability?
people
CEFF
Automobile Accessories for a Family Road Trip
Bluetooth capability 29%
Other 21%
Clear all
Roof rack 8%
Extra cup holders 15%
DVD player 27%
Check answer
Answers
Based on the above, about 174 people out of the sample of 600 people indicated Bluetooth capability.
What is the graph about?To know the number of individuals who shown Bluetooth capability, we have to to begin with calculate the division of individuals who chose this choice from the circle chart.
Note that:
People who Bluetooth capability =29%
Number of people = Percentage × Total sample size
= 0.29 × 600
= 174
So, 174 individuals shows that the Bluetooth capability is their favored option for the family trip.
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Please answer this question, I’ll give brainliest, and no chat gpt
Q7. A 230 kg piano must be lifted onto a stage that is 1.7 m high.
(a) If the piano is lifted straight up by some very strong people, how much force must they apply? [2 marks]
(b) How much work have they done? [2 marks]
(c) If the stage-crew only need to apply a force of 300 N to get the piano onto the stage if they use a 15 m ramp. How much work is done using the ramp? [2 marks]
(d) What is the efficiency of the ramp? [2 marks]
(e) You should notice that the force needed to lift the piano in A is larger than the force needed to lift the piano in C. How is it possible that the piano can be raised with much less force when the incline is used? (In other words, what is the "trade-off" of using an inclined ramp?) [2 marks]
Answers
1. The force they must apply is 2256.3 N
2. The amount of work done = 3835.71 J
3. The work done using the ramp = 4500 J
4. The efficiency of the ramp = 85.24%
5. When the people use inclined ramp, they don't have worry about the gravitational force that is acting on the piano. The trade off with with less force, the ramp is able to cover more distance.
How do we find force applied, work done, and efficiency of ramp?1. To find force applied, used the formula; F = mg
230 x 9.8N
=2256.3N
2. To find the amount of work done, we use the formula;
W = Fd
2256.3 x 1.7 m
= 3835.71J
3. o calculate the work done using the ramp, you use the same formula you used in step 2
300N x 15m
= 4500J
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Use the graph below to answer the question.
Money Spent on Food
dinner
42%
lunch
30%
snacks
10%
breakfast
18%
A shopper spent $100 at the store. How many dollars did the shopper spend on snacks?
A. $10
B. $18
C. $30
D. $42
Answers
if the shopper spent $10 on snacks and 10% of 100 is 10 then the answer is A
4. Find the product
()
Answers
Answer: n^6-25
Step-by-step explanation:
Use the distributive property to obtain: n^6-5n^3+5n^3-25
Simplify: n^6-25
Answer: n^6-25
The product of the given expression [tex](n^{3} + 5) (n^{3} - 5)[/tex] will be the second option [tex]n^{6} - 25[/tex].
This is a simple math problem that can be solved using algebraic identities. Algebraic identities are mathematical formulas that hold true regardless of the value assigned to each of the variables. They can be used to resolve equations and simplify expressions.
In the above question, we have used the following identity:
[tex](a^{2} - b^{2} ) = (a + b) (a - b)[/tex]
In the given question, a = [tex]n^{3}[/tex] and b = 5
So putting values in the identity, we get
[tex][(n^{3})^{2} - 5^{2}] = (n^{3} + 5) (n^{3} - 5)[/tex]
On solving the left side of the equation, we get
[tex]n^{6} - 25[/tex] which is our answer to the given question.
Note: [tex](n^3)^2 = n^6[/tex] because the powers get multiplied.
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2x + y = 7
x + y = 1
Answers
Answer: x = 6 and y = -5.
Step-by-step explanation: Multiply the second equation by -2 to eliminate the y term:
-2(x + y) = -2(1) -> -2x - 2y = -2
Add the resulting equation to the first equation to eliminate the y term:
2x + y = 7
-2x - 2y = -2
0x - y = 5
Solve for y:
-y = 5
y = -5
Substitute y = -5 into either of the original equations and solve for x:
x + y = 1
x + (-5) = 1
x = 6
Therefore, the solution to the system of equations is x = 6 and y = -5.
math complementary angles
Answers
Answer: ∠BDA
Step-by-step explanation:
Complementary: Either of two angles whose sum is 90°.
Starting Angle: ∠BDC
Possible Complement: ∠BDA
Answer: ∠ACD
Step-by-step explanation:
Complementary angles are angles which have a sum of 90 degrees when added together.
Angle ∠ADB is 90°
So ∠BDC and another angle should give you ∠ADB
The angle that when added to ∠BDC give you ∠ADB is ∠ACD
Which number line shows the solution set for |h-3| ≤5?
Answers
Answer:
Second number line
Step-by-step explanation:
(h-3)^2 <= 25
h^2 - 6h + 9 <= 25
h^2 - 6h - 16 <= 0
(h-8)(h+2) <=0
Using the graph of (x-8)(x+2),
-2 <= h <= 8
Hence, the answer is the second one (as it has shaded circles)
Hope this helps and be sure to mark this as brainliest! :)
SAT/ACT An arc has a central angle of
radians and a length of 6. What is the
circumference of the circle?
A 12T
B 15T
30T
D 36л
Answers
Answer: D 36л
Step-by-step explanation:
s = θr
where r is the radius of the circle. given that the arc length is 6, and the central angle is π/3 radians r:
6 = (π/3)r
r = 6/(π/3) = 18/π
the circumference of the circle is given by:
C = 2πr
Substituting r = 18/π, we get:C = 2π(18/π) = 36
A genetic experiment with peas resulted in one sample of offspring that consisted of 427 green peas and 154 yelow peas. a. Construct a 90% confidence interval to estimate of the percentage of yellow peas. b. Based on the confidence interval, do the results of the experiment appear to contradict the expectation that 25%, of the offspring peas would be yellow? a. Construct a 90% confidence interval. Express the percentages in decimal form.
Answers
CI = p ± z*sqrt((p*(1-p))/n)
where:
p = proportion of yellow peas = 154/(427+154) = 0.265
z = z-score for a 90% confidence level = 1.645 (from a standard normal distribution table)
n = sample size = 427+154 = 581
Substituting the values, we get:
CI = 0.265 ± 1.645*sqrt((0.265*(1-0.265))/581)
CI = 0.265 ± 0.042
CI = (0.223, 0.307)
Therefore, we can say with 90% confidence that the true proportion of yellow peas in the population lies between 0.223 and 0.307.
b. The expected proportion of yellow peas is 0.25. Since the confidence interval does not contain 0.25, the results of the experiment appear to contradict the expectation that 25% of the offspring peas would be yellow.
This shows a number line. Which point is located at 90 ?
Answers
Answer:
incomplete question bru
The following residual plot is obtained after a regression equation is determined for a set of data. Does the residual plot indicate that the regression equation is a good model or a bad model of the data? Why or why not?
Answers
The residual plot shows that the regression equation is a good model of the data because it shows a random scatter of points around a horizontal line at zero, with no pattern or trend
What makes a residual plot a good model?A residual plot is a scatter plot of the residuals against the predictor variable(s) or the fitted values. It is used to verify whether the regression equation fits the data well.
In the event that the residual plot shows a random scatter of points around a horizontal line at zero, with no pattern or trend, it shows that the regression equation is a good model of the data.
On the other hand, supposing the residual plot shows a pattern or trend, such as a curve, a U-shape, or a funnel shape, it shows that the regression equation is a bad model of the data.
Therefore, from the graph given, the residual plot shows that the regression equation is a good model of the data.
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A bacteria culture initially contains 2500 bacteria and doubles every half hour.
Find the size of the baterial population after 20 minutes.
Find the size of the baterial population after 4 hours.
Answers
Answer:
After half hour=30 min you have 2×2500=5000 bacteria so you can use this into your equation to write:
and:
Apply the natural logarithm ln to both sides and get:
so in units of
so your equation is now:
1] it t= 50 min substituting you get:
bacteria
2] if t= 8 h = 480 min you get:
bacteria
Step-by-step explanation:
Translate this sentence into an equation.
24 more than Craig's height is 68.
Use the variable c to represent Craig's height.
Answers
We can begin by focusing on c on one side of the equation to help us solve it. Craig's height is 44 as a result.
What is Equation?A mathematical equation is a claim that two expressions are equivalent. It is divided into two sections, the left and the right, by the equal sign (=). Equation's left and right sides each have the potential to include variables, constants, and operators.
Finding the value(s) of the variable(s) necessary to make an equation true is the aim of equation solving. Algebraic techniques like simplification, substitution, and elimination can be used to solve equations.
An equation can be used to represent the following sentence:
c + 24 = 68
Craig's height is represented by c in this equation. The equal sign (=) is used to symbolise the phrase "is 68," while the phrase "is 24 more than Craig's height" is symbolised by c + 24. The formula for the problem can be solved to find the value of c, which corresponds to Craig's height.
We can begin by concentrating c on just one side of the equation in order to solve it:
c + 24 - 24 = 68 - 24
c = 44
Therefore, Craig's height is 44.
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Now, find the solution to the system of equations
Answers
The solution of equation is (2, 3).
We have,
x= 3y -7.........(1)
y= x + 1.........(2)
Solving equation (1) and (2) we get
y = 3y - 7 + 1
y - 3y = -7 + 1
-2y = -6
y = -6/(-2)
y = 3
and, x = 3(3) - 7
x = 9 - 7
x = 2
Thus, the solution of equation is (2, 3).
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18.
Simplify.
y²-6y +11
y-2
Oy-1
Oy³-8y² +23y - 22
none of the answer choices
Oy²-5y +9
O-y²-2y + 10
Answers
Answer:
the answer is none of the answer choices
Answer:
the answer is none of the answer choices
EASY POINTS!
A machine in a factory makes 2 1/4 pounds of nails in 1 1/2 hours. At this rate, in pounds per hour, does the machine make nails? Show your work!
A. 2/3
B. 3/4
C. 1 1/2
D. 3 3/4
Answers
The machine makes 2 1/4 pounds of nails in 1 1/2 hours.
To convert 2 1/4 to an improper fraction, we multiply the whole number (2) by the denominator (4) and add the numerator (1), then write the result over the denominator:
2 1/4 = (2 x 4 + 1)/4 = 9/4
To convert 1 1/2 to an improper fraction, we multiply the whole number (1) by the denominator (2) and add the numerator (1), then write the result over the denominator:
1 1/2 = (1 x 2 + 1)/2 = 3/2
Now we can divide the amount of nails by the time:
(9/4) ÷ (3/2) = (9/4) x (2/3) = 18/12 = 3/2
Therefore, the machine makes nails at a rate of 3/2 pounds per hour. The correct answer is C.
The graph of f(x) and table for g(x)= f(kx) are given.- WORTH 40 BRAINLY POINTS PLEASE ANSWER FAST
The graph shows an upward opening parabola labeled f of x that passes through a point negative 2 comma 8, a point negative 1 comma 2, a vertex 0 comma 0, a point 1 comma 2, and a point 2 comma 8.
x g(x)
−6 8
−3 2
0 0
3 2
6 8
What is the value of k?
k = 3
k is equal to one third
k = 6
k is equal to negative one sixth
Answers
The value of k include the following: B. k is equal to one third.
What is the vertex form of a quadratic equation?In Mathematics, the vertex form of a quadratic function can be modeled by this formula:
y = a(x - h)² + k
Where:
h and k represents the vertex of the graph.a represents the leading coefficient.Based on the information provided about the quadratic function f(x), we can logically deduce that its vertex is at (0, 0);
f(x) = a(x - h)² + k
2 = a(1 - 0)² + 0
2 = a
f(x) = 2(x - 0)² + 0
f(x) = 2x²
For the quadratic function g(x), we have;
g(x) = f(kx)
g(x) = 2(kx)²
g(x) = 2k²x²
By using the point (3, 2) from the table, we have:
2 = 2k²3²
1 = k²9
k² = 1/9
k = √(1/9)
k = 1/3 i.e one third.
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how do I do 75% of 200
Answers
Answer:
150
Step-by-step explanation:
divide the percentage by 100 to make it decimal form,
75/100= .75
The multiple .75 by the total amount to find the 75%,
200 x .75 = 150
Which means 75% of 200 is 150
9. data was collected on houses currently for sale. based on a cubic modeling equation, which prediction about this data is the most reliable? a.
a $70k house would have 1,354 square ft
b. a $70k house would have about 1,460 square ft
c. a $400k house would have 492 square ft
d. a $400k house would have 4,328 square ft
10. suppose a scatterplot is created from the points in the following table. when x=7, what is the second coordinate in a scatterplot of the linearized data? round the answer to the tenth place.
a. 0.8
b. 2.1
c. 54.3
d. 112.8
11. the equation that best models the linearized data for a particular data set is log y= 0.75821x+0.03442. find the approximate value x=4. round your answer to the nearest whole number.
a. 3
b. 25
c. 1,168
d. 62,034
Answers
question 9.
Based on a cubic modeling equation, the prediction about this data that is most reliable is a $70k house would have 1,354 square ft.
Option A is correct.
Question 10.
The second coordinate in a scatterplot of the linearized data and rounding the answer to the tenth place is 0.8
Option A is correct.
Question 11.
The approximate value when x=4 and rounding the answer to the nearest whole number is 1,168
Option C is correct.
How do we calculate?The equation is given as
Log y= 0.75821x+0.03442
We substitute x = 4 into the given equation and solve for y:
log y = 0.75821(4) + 0.03442
log y = 3.07286 + 0.03442
log y = 3.10728
We take the antilogarithm of both sides,
y = 10^(3.10728)
y = 1,168.66
Rounding off, the closest answer is option (c) 1,168.
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Calculating Loan Payments You want to buy a new sports coupe for $69,300, and the finance office at the dealership has quoted you a loan with an APR of 5.6 percent for 48 months to buy the car. What will your monthly payments be? What is the effective annual rate on this loan?
Input area:
Amount borrowed $69,300
APR 5.6%
# of years 4
# of times compounded per year 12
(Output area) Complete the following analysis. Do not hard code values in your calculations. All answers should be positive.
Loan Payment __________
Effective Intrest Rate ____________
Answers
The monthly payments will thus be $1,612.81.
The annual effective rate on this loan is 5.78%.
What is the loan payment formulae?We can use the following loan payment formula to determine the loan payment:
Loan Payment = [tex]\\\frac{p * \frac{r}{n} }{1 - (1 + \frac{r}{n} )^{-n *t} }[/tex]
where P = borrowed amount = $69,300
r = yearly interest rate (decimal) = 0.056
n = number of times compounded per year = 12
t = number of years = 4
When we plug in the values, we get:
Loan Payment = [69300 x (0.056/12)] / [1 - (1 + 0.056/12)^(-12*4)]
= $1,612.81 (to the nearest cent)
The monthly payments will thus be $1,612.81.
We can use the following calculation to obtain the effective annual rate:
Annual Effective Rate =[tex](1 + r/n)^{n-1}[/tex]
When we plug in the values, we get:
Annual Effective Rate =[tex](1 + 0.056/12)^{12 - 1}[/tex]= 0.0578 or 5.78%
As a result, the annual effective rate on this loan is 5.78%.
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I’m unsure where to plot the five points and shade in
Answers
The image is attached of the graph of the inequality y < 4x - 5.
What is the inequality equation?
An inequality equation is a mathematical statement that compares two expressions using an inequality symbol such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).
To graph the inequality y < 4x - 5 using the slope-intercept form, follow these steps:
Rewrite the inequality in slope-intercept form, y = mx + b, where m is the slope of the line and b is the y-intercept.
y = 4x - 5
Plot the y-intercept on the y-axis.
The y-intercept is -5, so plot the point (0, -5).
Use the slope to find a second point on the line.
The slope is 4, so start at the y-intercept and move up 4 units and to the right 1 unit to find the point (1, -1).
Draw a dashed line through the two points.
Since the inequality is y < 4x - 5, use a dashed line to indicate that the line itself is not part of the solution.
Shade the region that satisfies the inequality.
To do this, pick a test point that is not on the line and plug its coordinates into the inequality. If the inequality is true for that point, shade the region that contains the test point. If the inequality is false for that point, shade the region that does not contain the test point.
Let's use the test point (0, 0). Plug its coordinates into the inequality to get:
0 < 4(0) - 5
This simplifies to 5 < 0, which is false. Therefore, we need to shade the region that does not contain the test point.
Since the inequality is y < 4x - 5, we need to shade the region below the dashed line.
Label the shaded region with the inequality symbol.
The inequality is y < 4x - 5, so label the shaded region below the dashed line with the symbol "<".
hence, The image is attached of the graph of the inequality y < 4x - 5.
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A quality control technician at a candle factory tested the eight 16-ounce candles, each 3 inches in diameter. These candles came from the same production run. The table shows the decrease in weight of each candle after burning for 3 hours. Candle makers believe that the rate at which the candles burn is constant.
Write an equation that can be used to model the weight,
of such a candle as a function of
, the number of hours burning. Then, explain how the equation can be used to predict the weight of a candle that has burned for 5 hours.
Enter your equation and your explanation in the box provided.
Answers
Answer:
According to the model. the weight of the candle after S hours of burning would be about 15.05 ounces
Step-by-step explanation:
If the burn rate is believed to be constant, determine the average burn rate for the eight candles as the ratio of weight loss per hour.
ounces lost over three hours
0.5+0.6+0.5÷0.7÷0.7÷0.5÷0.5÷0.6
8
* 0.575
0.575
ounces lost per hour on average
= 0.19
For 0 hours, the weight of each candle is 16 ounces. Therefore, w 16 - 0.19h.
This model can be used to predict the weight of the candle when h, the number of hours of burning, is 5.
W * 16 - 0.19(5)
W = 16 - 0.95
W = 15.05
According to the model. the weight of the candle after S hours of burning would be about 15.05 ounces.
Find the sum of 10x² + 7x + 6 and 6x + 5.
Answer:
Submit Answer
M
DELL
Answers
10x² + 13x + 11 is the sum of linear equation .
What is a linear equation in mathematics?
The algebraic equation y=mx+b is known as a linear equation. All of its terms are constant, first-order linear ones. where m denotes the slope and b the y-intercept.
The aforementioned is occasionally referred to as a "linear equation in two variables" where y and x are variables. One or more variables may be present in a linear equation. The term "bivariate linear equation" refers to a linear equation with two variables.
two equations are 10x² + 7x + 6 and 6x + 5.
now add both equations
= (10x² + 7x + 6 )+ (6x + 5)
= 10x² + 7x + 6 + 6x + 5
= 10x² + 13x + 11
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What is the perimeter of the parallelogram?
units
Answers
Answer:
Step-by-step explanation:
URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
Answers
Answer:
Step-by-step explanation:
1 -E (102/234) *100 =43.6%
2- F
3-C
4-A
4. Mackenzie's dog can jump 2 1/2 feet off the ground. Jordyn's dog can
jump 1/2 foot off the ground. What is the difference in inches between
2how high Mackenzie's dog can jump and how high Jordyn's dog can
jump? Circle what to do to solve this problem.
Answers
The difference in the length of dogs jump is 24 inches.
Given that, Mackenzie's dog can jump [tex]2\frac{1}{2}[/tex] =5/2 feet off the ground. Jordyn's dog can jump 1/2 foot off the ground.
We know that, 1 feet = 12 inches
Here, 5/2 feet = 5/2 ×12
= 30 inches
1/2 foot = 1/2 ×12
= 6 inches
Now, difference = 30-6 = 24 inches
Therefore, the difference in the length of dogs jump is 24 inches.
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As seen in the diagram below, Dalvin is building a walkway with a width of x x feet to go around a swimming pool that measures 7 feet by 9 feet. If the total area of the pool and the walkway will be 143 square feet, how wide should the walkway be?
Answers
Answer: 2
Step-by-step explanation:
(7+2x)(9+2x)= 143 (area= length x width)
63+14x+18x+4x^2=143
4x^2+32x−80=0
x^2+8x−20=0
(x−2)(x+10)=0
x = 2 or -10
Since the length of the walkway can't be negative, the answer is 2.
What is the area of this figure?
20 mi
3 mi
11 mi
7 mi
3 mi
4 mi
3 mil
Write your answer using decimals, if necessary.
square miles
3 mi
Answers
The area of the figure composed of two rectangles is 99 mi²
How to solve an equation?An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.
The area of a figure is the amount of space it occupies in its two dimensional state.
For the first rectangle:
Area = 11 mile * 5 mile = 55 mi²
For the second rectangle:
Area = 11 mile * 4 mile = 44 mi²
The area of figure = 55 mi² + 44 mi² = 99 mi²
The area of the figure is 99 mi²
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A sample of n = 64 scores has a mean of M = 68. Assuming that the population mean is μ = 60, find the z-score for this sample:
If it was obtained from a population with σ = 16
z =
If it was obtained from a population with σ = 32
z =
If it was obtained from a population with σ = 48
z =
Answers
c) Population [tex]\sigma = 48[/tex]
Z = [tex]\frac{68-60 }{\frac{48 }{\sqrt{64}}}[/tex]
Z-score= 1.3333
How to solveAccording to the question , sample size n=64 , mean M = 68 , population mean [tex]\mu= 60[/tex]
Z = [tex]\frac{M-\mu }{\frac{\sigma }{\sqrt{n}}}[/tex]
where M = Sample Mean
[tex]\mu[/tex] = Population Mean
[tex]\sigma[/tex] = Population Standard Deviation
n = Sample Size
a) Population [tex]\sigma[/tex] = 16
Z = [tex]\frac{68-60 }{\frac{16 }{\sqrt{64}}}[/tex]
Z-score = 4
b) Population [tex]\sigma[/tex] = 32
Z = [tex]\frac{68-60 }{\frac{32 }{\sqrt{64}}}[/tex]
Z-score = 2
c) Population [tex]\sigma[/tex]= 48
Z = [tex]\frac{68-60 }{\frac{48 }{\sqrt{64}}}[/tex]
Z-score= 1.3333
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