The polynomial y = (4 / 3) · x³ + (16 / 3) · x² + (4 / 3) · x - 8 is the cubic equation whose zeros are x₁ = -3, x₂ = - 2, x₃ = 1 and intercept is - 8.
How to derive a cubic equation associated with a given set of zeros and a intercept
Herein we must derive a cubic equation such that the zeros are x₁ = -3, x₂ = - 2, x₃ = 1 and its intercept is - 8. Cubic equations are polynomials of the form y = a · x³ + b · x² + c · x + d, where a, b, c, d are real coefficients.
If we know that (x₁, y₁) = (- 3, 0), (x₂, y₂) = (- 2, 0), (x₃, y₃) = (1, 0) and (x₄, y₄) = (0, - 8), then we solve the following system of linear equations to determine all real coeffcients by numerical methods:
- 27 · a + 9 · b - 3 · c + d = 0
- 8 · a + 4 · b - 2 · c + d = 0
a + b + c + d = 0
d = - 8
(a, b, c, d) = (4 / 3, 16 / 3, 4 / 3, - 8)
The cubic equation is y = (4 / 3) · x³ + (16 / 3) · x² + (4 / 3) · x - 8.
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Todd has created the following diagram to prove the Pythagorean theorem. He drew right Δ A B C with leg lengths a and b and hypotenuse length c. Then he drew altitude C Z to the hypotenuse. He determines that c/a=a/x and c/b=b/y. Then he determines that c x=a² and c y=b². What is the next step in proving the theorem?
c²=a²+b²
c x=c y
c x+c y=a²+b²
c(x+y)=a²+b²
cx + cy = a² + b² is the next step to prove the theorem.
Given,
The given Pythagorean theorem was created by Todd.
With leg lengths a and b and a hypotenuse length of c, he drew right
ΔABC. The hypotenuse was then drawn with altitude C Z.
He finds that the equations c/a=a/x and c/b=b/y. He then discovers that c x=a² and c y=b².
We have to find the next step to prove the theorem;
Here,
The next step is to add cx and cy
That is,
cx + cy = a² + b²
Then,
c(x + y) = a² + b²
c² = a² + b²
Therefore,
The next step to prove the theorem is cx + cy = a² + b²
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Naomi's electricity costs depend on the number of kilowatt hours she uses, as shown in the graph below. According to this graph, which expression can be used to calculate her electricity cost after using x kilowatt hours?
A. 0.06x + 40
B. 0.08x + 20
C. 0.1x + 10
D. 0.12x
Answer:
b. 0.08x + 20
Step-by-step explanation:
its B because the price goes up $40 every 500 KW's so
40 divided by 500 = 0.08
The expression used to calculate Naomi's electricity cost after using x kilowatt hours is 0.08x+20. Therefore, option B is the correct answer.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
From the graph we have, (500, 60), (1000, 100), (1500, 140) and (2000, 180).
We know that, slope of a line is Slope=(y2-y1)/(x2-x1)
= (100-60)/500
= 40/500
= 0.08
Substitute m=0.08 and (x, y)=(500, 60) in y=mx+c, we get
60=0.08(500)+c
60=40+c
c=20
Substitute m=0.08 and c=20 in y=mx+c, we get
y=0.08x+20
The expression used to calculate Naomi's electricity cost after using x kilowatt hours is 0.08x+20. Therefore, option B is the correct answer.
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Jacob owns a small business selling bagels. He knows that in the last week 108
customers paid cash, 24 customers used a debit card, and 18 customers used a credit
card.
Based on these results, express the probability that the next customer will pay with a
debit card or a credit card as a decimal to the nearest hundredth.
The probability that the next customer pays with a debit card or a credit card will be 0.28.
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
Jacob claims an independent venture selling bagels. He realizes that somewhat recently 108 clients paid cash, 24 clients utilized a charge debit card, and 18 clients utilized a credit card.
The total number of events is given as,
Total event = 108 + 24 + 18
Total event = 150
The probability that the next customer pays with a debit card or a credit card is written as,
P = (24 / 150) + (18 / 150)
P = 42 / 150
P = 0.28
The likelihood that the following client pays with a check card or a Visa will be 0.28.
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Answer:
Step-by-step explanation:0.28
NO LINKS!! Help me with the 2-Column Proof Part 6aa
Here is the two column proof:
Statement Reason
Diagram Given∠1 and ∠2 are linear pair Shown on the diagram∠1 and ∠2 are supplementary Linear pair postulate ProvedTriangle A and Triangle B are right triangles.
Triangle A has a height of 8 meters and a base of 6 meters.
Triangle B has a height that is one unit greater than triangle A and a base that is one unit less.
Part A
What is the measure of the hypotenuse of triangle A? Show your work.
Part B
Determine if the hypotenuse of triangle B has the same hypotenuse as triangle A. Justify your solution.
what is 6 + 3 to the 4th power
Answer:
the answer is 87!
Answer: 6561
Step-by-step explanation: 6+3=9
9^4 = 9*9*9*9 = 81 * 81 = 6561
1.
Which inequality represents the expression 9 is less than or equal
to b?
Answer:
Step-by-step explanation:
9 ≤ b
( I think unless it faces the other side...if wrong then I'm sorry)
Find the measure of x
Answer: x = 7
Step-by-step explanation:
15(x+2) = R because they are equal angles.
set 135 = 15(x=2) because they are opposite each other so they equal each other
[tex]\frac{135}{15} =\frac{15(x+2)}{15} \\9 = x+2\\x=7[/tex]
Add the equations.
2 x-3 y=-1
+3 x+3 y=26
A. 5 x=25
B. 5 x=27
C. 5 x-6 y=-27
D. 6 y=25
Answer: 5x= 25
Step-by-step explanation:
Answer: The correct answer is A. 5x = 25
Step-by-step explanation:
Add the equations:
2x - 3y = -1
3x + 3y = 26
Add the like terms:
2x + 3x = 5x
3y + -3y = 0
26 + -1 = 25
The resulting equation:
5x = 25
The Royal Fruit Company produces two types of fruit drinks. The first type is 40% pure fruit juice, and the second type is 90%
pure fruit juice. The company is attempting to produce a fruit drink that contains 45% pure fruit juice. How many pints of each
of the two existing types of drink must be used to make 170 pints of a mixture that is 45% pure fruit juice?
Answer: 131.36363 pints of the first type of drink, and 38.63636 pints of the second type of drink.
Step-by-step explanation:
We can use the principle of linear equations. Let's say that the first type of drink is represented by x, and the second type is represented by y. We can then set up the following system of equations:
x + y = 170 (1)
0.4x + 0.9y = 0.45 * 170 (2)
We can solve for x and y using the methods of linear algebra. To do this, we can multiply equation (1) by 0.9, and equation (2) by 0.4, and then subtract the two equations to get the following equation:
0.9x - 0.4y = 0.45 * 170 - 0.4x - 0.9y
0.5x = 0.45 * 170 - 0.9y
x = (0.45 * 170 - 0.9y) / 0.5
We can substitute this expression for x into equation (1) and solve for y:
y = 170 - x
y = 170 - (0.45 * 170 - 0.9y) / 0.5
2.2y = 170 - 0.45 * 170
y = (170 - 0.45 * 170) / 2.2
y = 85 / 2.2
We can then substitute this value for y back into equation (1) to solve for x:
x = 170 - y
x = 170 - (85 / 2.2)
x = 170 - 38.63636
x = 131.36363
Therefore, the Royal Fruit Company needs to use 131.36363 pints of the first type of drink, and 38.63636 pints of the second type of drink, in order to produce 170 pints of a mixture that is 45% pure fruit juice.
Many members of a certain workforce died from cancer supposedly resulting from exposure to radioactive
fallout Suppose that among the 215 members of the workforce, 91 developed cancer. For that time period
and for the age of the cohort, the incidence of cancer was about 40%. Use the randomization procedure
and a 0.05 significance level to test the claim that the sample of this workforce is from a population in which
the rate of cancer is greater than 40%. The accompanying set of 500 sample proportions (rounded to four
decimal places) was obtained by resampling using technology as part of the randomization procedure; use
P-value=
(Round to three decimal places as needed.)
ample Get more help -
Clear all
Check answer
The p-value of the test hypothesis is given as follows:
0.2420.
What are the hypothesis tested?At the null hypothesis, it is tested if the proportion is not greater than 40%, that is:
[tex]H_0: p \leq 0.4[/tex]
At the alternative hypothesis, it is tested if the proportion is greater than 40%, that is:
[tex]H_1: p > 0.4[/tex]
What are the test statistic and the p-value?The test statistic is given by the equation presented as follows:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which the parameters are defined as follows:
[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.The values of these parameters for this problem are given as follows:
[tex]p = 0.4, n = 215, \overline{p} = \frac{91}{215} = 0.4233[/tex]
Hence the test statistic is given as follows:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.4233 - 0.4}{\sqrt{\frac{0.4(0.6)}{215}}}[/tex]
z = 0.7.
Using a z-distribution calculator, with a right-tailed test, as we are testing if the proportion is greater than a value, the p-value is of:
0.2420.
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What is the solution to this system of equations?
{3x-4y=-10
{4x+2y=-6
A. (2, 4)
B. (-1, -1)
C. (-2, 1)
D. (1, -5)
The correct option is C (-2, 1)
According to the question,
3x -4y = -10 --------equation 1
3x = 10 + 4y
[tex]x = \frac{ - 10 + 4y}{3} [/tex]
Also,
4x + 2y = -6 --------equation 2
Put the value of x in the equation,
4((−10+4y)÷3)+2y=−6
[tex] - \frac{40}{3} + \frac{16y}{3} + 2y = - 6[/tex]
[tex] \frac{ - 40 + 16y + 6y}{3} = - 6[/tex]
-40 + 22y = -6*3
-40 + 22y = -18
22y = 40-18
22y=22
y=1
Solving equation 1 for x by putting values if y
3x-4=-10
3x=-6
x=-2
Hence the values of x is -2 and y is 1
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When naming a segment , wy is the same as yw
True or False ?
Answer:
Yes it is true.............
What is the solution to the system of two equations shown?
{y=4x+16y=−2x−2
y=4x+16 y=-2x-2
The solution of the given system of equation is x = -3 and y = 4 respectively.
What is a system of linear equations?A system of linear equations can be defined as a number of equations needed to solve the equations. For n number of variables n number of equations are required.
The given system of equations is as,
y = 4x + 16 (1)
y = −2x − 2 (2)
In order to solve them, substitute equation (2) into (1) as follows,
4x + 16 = −2x − 2
=> 4x + 2x = -2 - 16
=> 6x = -18
=> x = -3
Then, y = -2 × -3 - 2 = 4
Hence, the solution of the given system of equation is x = -3 and y = 4.
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It is the vector physical quantity that measures the intensity of the interaction between two or more objects.
The vectorial physical quantity that measures the intensity of the interaction between two or more objects is called force.
¿What is force?The force is a vector quantity, it is completely defined with:
A numeric valueOne directionA senseA unitIn physics, it is established that physics is any factor capable of generating a deformation or change of state, in the movement, of a body. From Newton's second law, a force can be calculated as:
F = m aWhere:
F = forceM = mass A = accelerationForce is the vector quantity with which we can express, for example, the intensity of interaction between two or more bodies.
¡Hope this helped!
Find the measure of ∠ 1
a 180°
b 30°
c 60°
d 120°
Answer:
120 degrees
Step-by-step explanation:
sum of all three angles of any triangle is 180
X+30+30=180
x+60=180
-60. -60
x=120
Hopes this helps
Help please me find the answer need help as soon as possible
∠COD=72°
what is angle?
When two lines meet at a point, an angle is created. An "angle" is the measurement of the "opening" between these two rays. It is symbolised by the character. The circularity or rotation of an angle is often measured in degrees and radians. Angles are a common occurrence in daily life. Angles are used by engineers and architects to create highways, structures, and sports venues.
Given:
Let, ∠AOB=a=42°
∠EOF=b=66°
∠AOF=c
∠COD=d
by angle sum property,
a+b+c=180°
42°+66°+c=180°
c=72°
c=d because alternate angles are same
therefore d=72°
hence proved.
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During bowling practice, Marley rolled 28 strikes out of 70 attempts. What percent of Marley's
attempts were strikes?
40 percent of Marley's attempts were strikes, when Marley rolled 28 strikes out of 70 attempts.
Define percentage.Rather than being expressed as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the whole by the whole and multiply the result by 100 to get the percentage. A % is a number that indicates how many out of 100 it is, and it can also be expressed as a decimal or a fraction. Put the percentage value in the numerator and 100 in the denominator to convert a percentage to a fraction.
Given,
28 strikes rolled by Marley
Total attempts = 70
For percentage,
28/ 70 × 100%
0.4 × 100%
40%
40 percent of Marley's attempts were strikes, when Marley rolled 28 strikes out of 70 attempts.
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5 to the power of 2 plus 0.7 to the power of 2
Answer: 25.49
Because the internet has a good calculator
The line passing through -1, 4 and 1, 7
Answer:
6
Step-by-step explanation:
Graph the function. Identify whether or not the graph is a function
Answer:
No
Step-by-step explanation:
Because a vertical line can intersect the curve more than once, the graph does not represent a function.
a rectangle is 14 inches long and 16 inches wide what’s its area
Multiply the width by the length:
14 • 16 = 224
Its area is 224.
I need help with this question pls someone fast I’ll give brainliest and good amount of points
Answer:
Below
Step-by-step explanation:
180° rotation (clockwise OR counterclockwise)
Reflection across y axis would put the diagram in Q IV
90 degree rotation CCW would also be in Q IV
Translation R and up would be more centered around the origin
which expression is equivalent to (3/2)^-4
Answer:18/61 0r decimal form 0.20
Step-by-step explanation:
R
What is the approximate distance between points A and B7 (5 points)
+
-5-4-3-2-10
2
34
-2
B
-3
-5
0723 45
IN
5
Answer:
7.62 units C
the sum of a number (n) and 23 is 33. which equation shows this relationship?
n+23=33 - This equation shows this relationship.
Let, one number be = n
another number is =23
The sum of two numbers is = 33
The sum is the result of adding two or more numbers in mathematics. It is an essential and valuable concept in mathematics. The numbers which are to be added are called addends.
In short, some can be defined as a way by which all things can be put together. We can show an equation of a sum horizontally or vertically.
Horizontal Addition :
59+37=96
Vertical addition:
59
+37
= 96
Therefore, the equation is: n+23 =33
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The radius of a moon is 798 miles. Use the formula for the radius r of a
A
4t
sphere given its surface area A, r =
moon.
to find the surface area of the
The surface area A of the moon is
(Round to the nearest whole number as needed.)
The total surface area of the moon is A = 79,98,258[tex]miles^{2}[/tex]
or A = 2.07153931 × [tex]10^{13} m^{2}[/tex]
as per given in the question,
the radius of the moon ( r) is 798 miles
to find the area of the total surface area of the cylinder
Area (A) = [tex]4\pi r^{2}[/tex] where r is radius of the sphere,
by substituting the radius in total surface area formula area,
A = [tex]4\pi (798) ^{2}[/tex]
( let [tex]\pi =3.14[/tex])
A = [tex]4\times3.14\times798\times798[/tex]
A = [tex]12.56\times63684[/tex]
A = 79,98,258.24
( by rounding to the nearest whole number we get )
A = 79,98,258[tex]miles^{2}[/tex]
or we can write in
A = 2.07153931 × [tex]10^{13} m^{2}[/tex]
( in terms of meters)
the total surface are of the sphere is A = 79,98,258[tex]miles^{2}[/tex]
A = 2.07153931 × [tex]10^{13} m^{2}[/tex]
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Is 2x^x a power function? Explain why or why not.
[tex]2x^{x}[/tex] is not a power function because variable exponent should be constant.
What is Power function?A power function is a function with a single term that is the product of a real number, a coefficient, and a variable raised to a fixed real number.
The function is [tex]2x^{x}[/tex] is not a power function because a power function requires the exponent to be a constant value.
In the given function the variable x as power x which is variable.
The variable exponent should be constant.
When x is zero it is undefined. Another issue is the table indicates for negative values the output alternates between being positive and negative. So it is also not an exponential function either.
Hence, [tex]2x^{x}[/tex] is not a power function because variable exponent should be constant.
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Annie bought 149 5-oz bags of peanuts.
What's the total weight of the peanuts in pounds? Round answer to the hundredths place.
PLEASE HELP!
Answer:
46.5625 lbsStep-by-step explanation:
First of all, WHO IN THEIR RIGHT MIND NEEDS THAT MANY PEANUTS
Second:
1lb=16oz
5oz≈1/3lb
149×5=745 ((I have no idea where this is going))
745oz=46.5625 ((You can do the rounding my head hurts.))
what the dog doing ?
The dog is playing with his chew toy!
Answer:
Explanation
Step-by-step explanation:
In general, dogs can run 15-20 mph
humans can run 6-8 mph
You are significantly slower than the dog,
the fastest human is around 27 miles per hour, unfortunately, even if you were this fast
the fastest dog can run 40 miles per hour as an estimate
even house cats can run at 30 mph maximum if they really wanted,
You have no chance of outrunning this dog, and barely a chance of outsmarting it if that option was available, in conclusion, the dog is chasing you at a speed of around 30 mph about 6-7x more than your own speed with no chance of outrunning it(the dog).