Let G(x) = -2(3x+4)(x-1)(x-3)^2 be a polynomial function. make a rough sketch of polynomial, label, and name all the x-intercepts and y-intercepts
Answers
The intercepts of the graph are
x-intercepts are -4/3, 1, 3y-intercept is 72How to determine the intercepts of the graphThe polynomial is given as
G(x) = -2(3x+4)(x-1)(x-3)^2
Rewrite as
G(x) = -2(3x+4)(x-1)(x-3)²
The x-intercepts of a polynomial are the points at which the polynomial crosses the x-axis.
To find the x-intercepts, we need to set y = 0 and solve for x.
-2(3x+4)(x-1)(x-3)² = 0
Divide through by -1
(3x+4)(x-1)(x-3)² = 0
Now we can solve for each factor equal to zero:
3x+4 = 0, x = -1.33
x-1 = 0, x = 1
x-3 = 0, x = 3
So the x-intercepts are -4/3, 1, 3
The y-intercept of a polynomial is the point at which the polynomial crosses the y-axis.
For this polynomial, we have
G(0) = -2(30+4)(0-1)(0-3)² = -2(4)(-1)(9) = 72
So the y-intercept is (0, 72)
See attachment for the graph
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Related Questions
Does this graph show a function? Explain how you know. O A. No, the graph fails the vertical line test. OB. No; there are y-values that have more than one xvalue. OC. Yes; the graph passes the vertical line test. OD. Yes; there are no y-values that have more than one x-value.
Answers
The graph satisfies the vertical line test, it may be said that it reflects a function (C) The graph is accurate if it passes the vertical line test.
What is a function in the graph?The collection of all points in the plane with the form (x, f(x)) that make up a function of f's graph. We may alternatively say that the graph of f is the graph of y = f. (x). As a result, the graph of an equation is a particular instance of the graph of a function.Use the vertical line test to establish if a graph reflects a function. The graph is a function if a vertical line drawn across it is moved and only ever touches it at one point. The graph is not a function if the vertical line crosses it at more than one location.First-order variables are present in linear functions, and the graph's placement is determined by two constants. These operations graph into a line in every case. The slope of the line is determined by the constant m. The slope of the line will slope up if it is positive and down if it is negative.
The graph represents a parabola.
The graph can be a function if it passes the vertical line test.
The graph satisfies the vertical line test, it may be said that it reflects a function (C) The graph is accurate if it passes the vertical line test.
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Number 8 is the answer 90*
Answers
Answer:
E
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180°
Consider the triangle on the left
3rd angle = 180° - 60° - 90° = 180° - 150° = 30°
the 3rd angle of the triangle on the left = 30° ( vertically opposite angle ), so
∠ 1 = 180° - 30° - 65° = 180° - 95° = 85°
Which inequality can be used to explain why these three segments cannot be used to construct a triangle?
AC + AB > CB
AC + CB < AB
AC + CB > AB
AC + AB < CB
Answers
The answer choice which explains that the three segments cannot be used to construct a triangle is; AC + CB < AB.
Which inequality explains why the three segments cannot be used to construct a triangle?Since, It follows from the triangle inequalities theorem that sum of the side lengths of any two sides of a triangle is greater than the length of the third side.
Hence, since the sum of sides AC + CB is less than AB, it follows that the required inequality is; AC + CB < AB.
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In London today, twice the high temperature was more than five times the high temperature minus eighty-seven. In interval form, what are the possible temperatures?
Answers
The possible temperatures are represented by (-∝, 29)
How to determine the possible temperatures?Let the high temperature be x
So, the statement can be represented as:
2x > 5x - 87
Subtract 5x from both sides
-3x > -87
Divide both sides by -3
x < 29
In interval form, we have (-∝, 29)
Hence, the possible temperatures are represented by (-∝, 29)
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binary add:
(e) 10110₂ +1010₂ = (?)
Answers
Answer:
278,861,394
Step-by-step explanation:
put in the calculator e but then just square the numbers add it and there is your answer
help me please
What is the midpoint of the horizontal line segment graphed below?
A. (4,3)
B. (8,6)
C. (8,3)
D. (4, 6)
-10
10
(-2,3)
$10
(10, 3)
10
Answers
Answer: A
Step-by-step explanation:
2. Merchandise from the vendor carries an invoice of July 1 and is received on July 4. Terms are 2/10 net 30 EOM, and the invoice is for $5,000. What amount should be remitted if the retailer pays the bill on July 13?
Answers
The retailer would remit $4,900 to the vendor on July 13.
What is invoice date?
The invoice date is the date written on this which is the same as the date the goods were shipped to customer, in this case, invoice date is July 1.
Invoice receipt date?
This is the date the customer received the invoice as well as the goods sent by the vendor, which is July 4 in this case.
2/10 means that a discount of 2% is available if the customer pays within the first 10 days, which starts counting from July 4, not July 1, because the customer actually received the invoice on July 4.
From July 4 to July 13 is a period of 10 days, which means that the 2% cash discount that customer would be entitled if payment is made within the first 10 days is still available
discount=2%*$5000
discount=$100
The retailer would remit the invoice price of $5,000 minus the discount.
amount remitted=$5000-$100
amount remitted=$4,900
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Find each of the following:
pls help me ASAP!!
Answers
Step-by-step explanation:
try this option, answer is marked with red colour.
if x = 2z and y = 3z, find z
Answers
Answer:36
Step-by-step explanation:
Let name the missing angle in the triangle w.
We know that x+z+w=180
We also know that z+w=3z=y.
That means that w=2z.
x=2z, so, 2z+2z+z=180
z=36
Answer:
Z=36 degrees
Step-by-step explanation:
Since angles x and y are supplementary, you know that they add up to 180 degrees.
Since we know that:
=x+y
=2z+3z
=5z
=180 degrees
180/5=36 degrees, so Z=36 degrees
What is 681x239 please help
Answers
681×239 = 162,759
..... ......
162,759 is answer
happy to help
A conduit of circular cross section has 7 cables all same diameter. Inside diameter of conduit is 30cm. What is the cross sectional area of the conduit not part of the 7 cables
Answers
The cross sectional area of the conduit not part of the 7 cables is; 706.5cm²
What is the cross sectional area of the conduit not part of the 7 cables?It follows from the task content that the conduit in discuss has 7 cables all same diameter and has a circular cross section.
Since, the cross sectional area of the conduit not part of the 7 cables is required; it follows that the cross sectional area of the inside cavity can be evaluated as follows;
where radius, r = D/2 = 30/2.
Area = πr² = 3.14 × (30/2)² = 706.5cm²
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Find the measure of a when b=74 and c=165
Answers
Answer:
121°
Step-by-step explanation:
Angles around a point add to 360°.
[tex]a=360-74-165=\boxed{121^{\circ}}[/tex]
What is the standard form equation of an ellipse that has vertices (−2,14) and (−2,−12) and co-vertices (9,1) and (−13,1)?
Answers
Answer:
[tex]\frac{(x+2)^2}{121} + \frac{(y-1)^2}{169} = 1[/tex]
Step-by-step explanation:
First, we identify that the vertices are vertical.
(an image below is attached if you want to see a visualization)
Therefore, the equation is such:
[tex]\frac{(x-h)^2}{b^2} + \frac{(y-k)^2}{a^2} = 1[/tex]
(h,k) is the center of the ellipse, which we could easily calculate by finding the midpoint between any pair of vertices.
This gets us (-2, 1)
Therefore, h = -2, k = 1
Now we want to find a,
we know the length of the major axis is 2a, and in this case, our length of the major axis is 26. So a = 13
Now we want to find b,
We know the length of the minor axis is 2b, and in this case, our length is 22, so b = 11
Now we will just plug in all the values and simplify to get our answer! B)
The weight of each “Golden Dairy’s Probiotic Yogurt with Fruit” cup is normally distributed with a mean of 170 grams and a standard deviation of 12 grams. One package contains six random cups and any package with an average weight per cup lower than 158 grams will be rejected.
Part A: What fraction of packages will be rejected because the average weight is too low?
Part B: In addition to original rejection criteria, suppose any packages that have an average weight per cup higher than 179 grams must be rejected as well. What is the total fraction of packages that will be accepted?
Answers
Using the normal distribution, it is found that:
A. 0.0071 = 0.71% of packages will be rejected because the average weight is too low.
B. 0.96 = 96% of packages that will be accepted.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].For this problem, the parameters are given as follows:
[tex]\mu = 170, \sigma = 12, n = 6, s = \frac{12}{\sqrt{6}} = 4.9[/tex]
Item A:
The proportion is the p-value of Z when X = 158, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{158 - 170}{4.9}[/tex]
Z = -2.45
Z = -2.45 has a p-value of 0.0071.
0.0071 = 0.71% of packages will be rejected because the average weight is too low.
Item B:
The proportion that will be accepted is the p-value of Z when X = 179 subtracted by the p-value of Z when X = 158, hence:
X = 179:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{179 - 170}{4.9}[/tex]
Z = 1.84
Z = 1.84 has a p-value of 0.9671.
X = 158:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{158 - 170}{4.9}[/tex]
Z = -2.45
Z = -2.45 has a p-value of 0.0071.
0.9671 - 0.0071 = 0.96 = 96% of packages that will be accepted.
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A summer camp needed
1,148 popsicles. Boxes of
popsicles were sold with
8 in each. How many
boxes did they have to
buy to have enough
popsicles? How many
were left over?
Answers
Answer:
144 boxes, 4 popsicles left over
Step-by-step explanation:
# of boxes and the remainder: 1148/8 = 143 boxes 4 popsicles left over
Since they need to buy full boxes we add 1 to 143 = 144 boxes
A full box is 8 and they only need 4 more so they have 4 left over.
A certain radioactive material decays in such a way that the mass in kilograms remaining after t years is given by the function
m(t)=120e−0.018t
How much mass remains after 50 years?
Answers
The mass of radioactive material remaining after 50 years would be 48.79 kilograms
How to determine the amountIt is important to note that half - life is the time it takes for the amount of a substance to reduce by half its original size.
Given the radioactive decay formula as
m(t)=120e−0.018t
Where
t= 50 years
m(t) is the remaining amount
Substitute the value of t
[tex]m(t) = 120e^-^0^.^0^1^8^(^5^0^)[/tex]
[tex]m(t) = 120e^-^0^.^9[/tex]
Find the exponential value
m(t) = 48.788399
m(t) = 48.79 kilograms to 2 decimal places
Thus, the mass of radioactive material remaining after 50 years would be 48.79 kilograms
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solve it please as soon as possible with step by step explanation
Answers
By definition of real field and algebra properties we conclude that the product of three positive integers is always equal to a positive integer.
How to make a conjecture
First, we state the conjecture: The product of three positive integers equals a positive integer. Second, we prove if the conjecture is true:
Integers are part of the real field, which mean that the product of two integers is also an element of that field. By algebra we know that the product of two positive integers is equal to another positive integer. Thus, the product of three positive integers is always equal to a positive integer.
Here is an example:
2 × 5 × 7
10 × 7
70
In a nutshell, the conjecture has been proved true.
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What is the simplified form of the expression the quantity x squared minus 4x minus 21 end quantity divided by 4 times the quantity x plus 3 end quantity?
Answers
The simplified form of the given expression [tex]\frac{x^2-4x-21}{4(x+3)}[/tex] is [tex]\frac{x-7}{4}[/tex].
How to simplify a fractional expression?The steps to simplify a fractional expression are:
Factorize the expressions both in the numerator and the denominator using different methodsRemove the common terms in the numerator and denominatorThus, the simplified expression will be obtained.Calculation:The given expression is [tex]\frac{x^2-4x-21}{4(x+3)}[/tex]
Factorizing the numerator:
x² - 4x - 21 = x² - 7x + 3x - 21
= x(x - 7) + 3(x - 7)
= (x - 7)(x + 3)
Then,
[tex]\frac{x^2-4x-21}{4(x+3)}[/tex] = [tex]\frac{(x-7)(x+3)}{4(x+3)}[/tex]
common factor (x + 3) is canceled out from both the numerator and the denominator
So,
[tex]\frac{x^2-4x-21}{4(x+3)}[/tex] = [tex]\frac{x-7}{4}[/tex]
Therefore, the simplified expression is [tex]\frac{x-7}{4}[/tex].
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Answer:x-3/4
Step-by-step explanation:
(x-3)(x+7)/4(x+7)
=x-3/4
HELP PLS!!! I GIVE BRAINLIEST
Answers
Based on the multiplication property of equality, the statement that completes the proof is: C. CD = b(sin A) and CD = a(sin B).
What is the Multiplication Property of Equality?The multiplication property of equality is given as, if a/b = y, then a = yb. Both sides of the equation is multiplied by the same value.
In step 5 where the multiplication property of equality is applied, we would have:
sin(A) = CD/b
Multiply both sides by b
sin(A) × b = CD/b × b
b(sin A) = CD
CD = b(sin A)
This same property is applied to sin B = CD/a to get CD = a(sin B).
Therefore, the missing statement is: C. CD = b(sin A) and CD = a(sin B).
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Alex, Barry, Charles, David, and Eric paint houses for a living. Alone, Alex can paint an entire house in 24 hours, Barry in 26 hours, Charles in 20 hours, David in 21 hours and Eric in 27 hours. If they work together, approximately how long will it take them to paint 3 houses, rounded to the nearest hour?
Answers
It would take 14 hours for all of them to paint the three houses.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let t represent the time it would take them working together, hence:
(1/24 + 1/26 + 1/20 + 1/21 + 1/27)t = 3
t = 14 hours
It would take 14 hours for all of them to paint the three houses.
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15. Solve the following inequality: 38 < 4x + 3 + 7 - 3x.
OA.x < 4
OB.x>4
O C. x < 28
OD. x > 28
Answers
Step-by-step explanation:
38<4x+3+7-3x
4x+3+7>38
4x+3+7<3x
X>7
X<-10
= Ø
Nikos, a 39-year old male, bought a 300,000, 20-year life insurance policy.
What is the total amount he will pay for 20 years of coverage.
13,650
27,300
30,990
61,980
Answers
The total amount he will pay for 20 years of coverage is $61,980. Option D
How to determine the total amount
To find the total amount, we use the expression
First, we multiply the value per $1,000.00 by the number of thousands of face value coverage. This gives an estimate of the annual premium for life insurance policy.
Nikos's premium per year = [tex]\frac{300000}{1000} * 10. 33[/tex]
Niko's premium per year = [tex]300 * 10. 33[/tex]
Niko's premium per year = $3, 099
To find the total amount, we need to multiply by the number of years
= $3,099 x 20
= $61,980
Thus, the total amount he will pay for 20 years of coverage is $61,980. Option D
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PLEASE FAST!!! Explain why, given a large unit A and a small unit B, it is wise to leave the conversion factor in fractional form if the decimal form goes on forever.
Answers
Numbers whose decimals form goes on forever are best represented as fractions because they are non-terminating decimals
How to determine the reasons?The decimal numbers are represented as:
A and B
Where
A > B
Numbers whose decimals form goes on forever are non-terminating numbers, and the complete form cannot be represented using decimals except with the sign .......
Because non-terminating decimals have no end, it is best to represent them as fractions
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A sample of a radioactive isotope had an initial mass of 440 mg in the year 1990 and decays exponentially over time. A measurement in the year 1998 found that the sample's mass had decayed to 40 mg. What would be the expected mass of the sample in the year 2001, to the nearest whole number?
Answers
Using an exponential function, the expected mass of the sample in the year 2001 would be of 16 mg.
What is the exponential function for the amount of a substance?The function is:
[tex]A(t) = A(0)e^{-kt}[/tex].
In which:
A(0) is the initial amount.k is the decay rate.The information given is as follows:
A(0) = 440, A(8) = 40.
Hence:
[tex]A(t) = A(0)e^{-kt}[/tex].
[tex]40 = 440e^{-8k}[/tex].
[tex]e^{-8k} = 0.09090909[/tex]
[tex]\ln{e^{-8k}} = \ln{0.09090909}[/tex]
[tex]-8k = \ln{0.09090909}[/tex]
[tex]k = -\frac{\ln{0.09090909}{8}[/tex]
k = 0.29973691
Then the function is:
[tex]A(t) = 440e^{-0.29973691t}[/tex]
2001 is 11 years after 1990, hence the amount is:
[tex]A(11) = 440e^{-0.29973691 \times 11} = 16[/tex]
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Find the area of the region enclosed by the curves yequals
xsquaredminus2x
and yequals
minusxsquaredplus2
x.
Answers
The area enclosed by the given 2 curves is; 8/3 or 2.67
How to Solve Integration with Limits?We want to find the area enclosed by the curves;
y = x² - 2x
y = -x² + 2x
The point of intersection of the parabola and the line is given by;
x² - 2x = -x² + 2x
2x² - 4x = 0
Solving this gives;
x = 0, 2
Therefore, the area bounded by the parabola and the line between x = 0 and x = 2 is given as;
A = ∫₀² (-x² + 2x - x² + 2x)
A = ∫₀² (-2x² + 4x)
Using online integration calculator here gives;
A = 2.67
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Three quarters of a cake was eaten at a party .how much cake is left?
Answers
Hi! ◈
Answer:
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
1/4 of the cake was left
Step-by-step explanation:
Since the total cake is [tex]\sf{\dfrac{4}{4}}[/tex], all we should do is subtract 3 from 4
[tex]\sf{\dfrac{4-3}{4}}=the \ cake \ that \ was \ left[/tex]
_____________________
[tex]\sf{\dfrac{1}{4} \ of \ the \ cake \ was \ left}[/tex]
Hope this made sense to you !!
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CalligrxphyIM IN A HURRY PLEASE HELP ME QUESTION IS DOWN BELOW WORTH 15 POINTS each
Answers
Answer: x = 6
NS = 8.5
Step-by-step explanation:
JK = KL= KP + LP
26 = 13 + 2x + 1
2x = 12
x = 6
NS = PS
PS = 8.5
NS = 8.5
what is the measure of XYZ?
46°
94°
a. 46°
b. 140°
c. 94°
d. 70°
Answers
Answer:
46+96=140°_÷__^_^^^^=^
For f(x) = 3x+1 and g(x) = x2 - 6, find (F/g)
Answers
Answer: [tex]\frac{3x+1}{x^{2}-6}[/tex]
Step-by-step explanation:
(f/g) represents the division of function f by function g.
A rain gutter is to be made of aluminum sheets that are 16 inches wide by turning up the edges 90. See the illustration.
(a) What depth will provide maximum cross-sectional area and hence allow the most water to flow?
(b) What depths will allow at least 30 square inches of water to flow?
Answers
Based on the width of the aluminum sheets and the angle of the edges, the depth that allows maximum cross-sectional area is 4 inches.
How much can the maximum cross-sectional area?Assuming that the depth is x, the area would be:
= x (16 - 2x)
= 16x - 2x²
The maximum of the parabola is:
x = -b / 2a
= - 16 / (2 x -2)
= -16 / -4
= 4 inches
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