According to the synthetic division below, which of the following statements
are true?
Check all that apply.
3)2 -2 -12
6 12
2 4 0
A. (x+3) is a factor of 2x² - 2x-12.
B. The number -3 is a root of F(x) = 2x² - 2x-12.
c. (2x²-2x-12) + (x-3) = (2x + 4)
D. The number 3 is a root of F(x) = 2x2 - 2x-12.
E. (x-3) is a factor of 2x² - 2x-12.
O (2x2-2x-12) + (x+3) = (2x + 4)
Answers
The true statements about the synthetic division are
c. (2x²-2x-12) + (x-3) = (2x + 4)d. The number 3 is a root of F(x) = 2x^2 - 2x-12.e. (x-3) is a factor of 2x² - 2x-12.How to determine the true statements?The synthetic division is given as:
3)2 -2 -12
6 12
2 4 0
In the above representation of the synthetic division, we have:
Quotient = 2x + 4Dividend = 2x^2 - 2x - 12Divisor = x- 3Remainder = 0Because the remainder is 0, then
(2x^2 - 2x - 12) ÷ (x - 3) = (2x + 4) --- option C
Set the divisor to 0
x - 3 = 0
Solve for x
x = 3
This means that 3 is a root of 2x^2 - 2x - 12 --- option (D) and x - 3 is a factor of 2x^2 - 2x - 12 --- option (E)
Hence, the true statements are (C), (D) and (E)
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Related Questions
These questions are in Spanish, someone who knows Spanish, the topic is mathematics, please.
(That solves it in Spanish)
Answers
The interest that Marcos will get is 50000.
How to calculate the interest?The following can be deduced from the information given:
Principal = 50000
Interest rate = 12.5%
Time = 8 years
The simple interest will be:
= (PRT/100)
= (50000 × 12.5 × 8)/100
= 50000
The amount that will be obtained after 8 years will be:
= Principal + Interest
= 50000 + 50000
= 10000
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Answer:
The interest that Marcos will get is 50000.
Distinguish arithmetic vs geometric sequences
Answers
Answer:
Arithmetic sequence
Step-by-step explanation:
The given sequence is arithmetic because it is increases gradually by 5
so the answer is "an arithmetic" and "difference" is equal to "5"
If P(x + 2) = x² + 3x + 1, then find P(x-1)?
A) x²+3x+1
B) x²-3x+1
C) x-2
D) X-3
Answers
Observe that
[tex]x^2 + 3x + 1 = (x^2 + 4x + 4) - x - 3 \\\\ ~~~~~~~~ = (x + 2)^2 - x - 3 \\\\ ~~~~~~~~ = (x + 2)^2 - (x + 2) - 1[/tex]
so that
[tex]P(x+2) = (x+2)^2 - (x+2) - 1 \implies P(x) = x^2 - x - 1[/tex]
Then
[tex]P(x - 1) = (x-1)^2 - (x-1) - 1 \\\\ ~~~~~~~~ = (x^2 - 2x + 1) - (x - 1) - 1 \\\\ ~~~~~~~~ = \boxed{x^2 - 3x + 1}[/tex]
Alternatively, we can avoid find [tex]P(x)[/tex] altogether and instead first write [tex]x-1[/tex] in terms of [tex]x+2[/tex] :
[tex]x - 1 = (x - 1) + 2 - 2 = (x + 2) - 1 - 2 = (x + 2) - 3[/tex]
Then
[tex]P(x - 1) = P((x + 2) - 3) \\\\ ~~~~~~~~ = (x - 3)^2 + 3 (x - 3) + 1 \\\\ ~~~~~~~~ = x^2 - 3x + 1[/tex]
Geometry question I’m confused with this help
Answers
Answer:
<PQR is 130 degrees
Step-by-step explanation:
When it says the line bisects the angle, that means the two smaller angles are equal to each other.
Therefore 3x+5 = 2x+25
Now rearrange to get x.
3x-2x=25-5
x=20
Now plug the x back into both phrases and them together to get the final answer for <PQR.
20 * 3 + 5 = 65
20 * 2 + 25 = 65
65*2 = 130
Find the measure of side c if a is 5 cm and b is 9 cm in a right triangle
Answers
The measure of side c if a is 5 cm and b is 9 cm in a right triangle is √106 cms.
The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The size of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides, according to this rule.
The measure of side c if a is 5 cm and b is 9 cm in a right triangle will be,
c² = 5² + 9²
c = √106 cms
Hence, the measure of side c if a is 5 cm and b is 9 cm in a right triangle is √106 cms.
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How many grapes?
Help me please! Thanks
Answers
Using proportions, considering the given ratio, it is found that 9090 grapes were there.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The ratio of bananas to grapes of 3:101 means that out of 104 fruits, 3 are bananas and 101 are grapes. Hence the rule of three is given as follows:
3 bananas - 101 grapes
270 bananas - n grapes.
Applying cross multiplication:
3n = 101 x 270
n = 101 x 270/3
n = 9090.
9090 grapes were there.
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can someone explain what to do
Answers
Answer:
8
Step-by-step explanation:
The equation of the parabola can be represented as
[tex]y = a(x + 1)(x - 5)[/tex]
for some constant a.
Since the coefficient of x² is 2, a = 2, so
[tex]y = 2(x + 1)(x - 5) \\ \\ y = 2( {x}^{2} - 4x + 5) \\ \\ y = 2 {x}^{2} - 8x + 10[/tex]
So, the answer is 8.
A place kicker in pro football has a 77% probability of making a field goal over 40 yards, and each attempted field goal is independent. If the kicker made his first two but missed his third attempt and is now trying for his fourth field goal of the game to win in overtime, what is the probability that his team will win the game
Answers
The probability that the team will win the sport is 77%.
Given that an area kicker in pro football incorporates a 77% probability of creating a field goal over 40 yards and every attempt field goal is independent.
Probability is how something is likely to happen. The probability of a happening is calculated by the probability formula by simply dividing the favorable number of outcomes by the overall number of possible outcomes.
So, his team will win the sport if he makes a goal otherwise loses.
Therefore, the Probability that his team will win the sport P[E] =P[making a field goal]
P[E]=77%
Hence, the probability that the team will win the sport when making a field goal is 77%.
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Please help.
The function of t(n) has an input variable of n and an output variable of t. t(n) = 8·n+3/2. What is the equation for the inverse function n(t)?
A. n(t) = 4t+12
B. n(t)= t/4-3
C. n(t)= 8t-24
D. n(t)= 2t-3/8
I know the answer is B, I just don't know how to get to that answer. Please explain how to solve an inverse like this.
Answers
The equation of the inverse function is given as n(t) = (t+3)/4
Inverse of a functionGiven the function that is represented as;
[tex]t(n)=8\cdot\frac{n+3}{2}[/tex]
This is further simplified to have:
t(n) = 4(n + 3)
Replace t with t(n)
t = 4n - 3
Make n the subject of the formula
4n = t+3
n = (t+3)/4
Hence the equation of the inverse function is given as n(t) = (t+3)/4
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4) Fred, Bob and Gladys took a maths test. The test was out of 200. Fred scored 50%, Bob scored 25% and Gladys scored 10%. How much did each person score?
if you can please answer
Answers
Answer:
Fred scored 100
Bob scored 50
Gladys scored 20
Step-by-step explanation:
Fred = 50% * 200
= 50/100 * 200
= 0.5 * 200
= 100
Bob = 25% * 200
= 25/100 * 200
= 0.25 * 200
= 50
Gladys = 10% * 200
= 10/100 * 200
= 0.1 * 200
= 20
calculate the values of 2. f * x ^ 2 + y ^ 2 = 5/8 * and * 4/3 * xy = 1/4 (a) (x + y) (b) (x-y) (c) (x^2-y^2)
Answers
Answer:
(a) 1
(b) 1/2
(c) 1/2
Step-by-step explanation:
[tex]x^2 + y^2 = 5/8 (1)\\\frac{4}{3}xy = \frac{1}{4} (2)\\\\\textrm {From (2) by multiplying both sides by 3/4 we get}\\\\xy = \frac{3}{16} (3)\\\textrm{We know that } (x + y)^2 = x^2 + 2xy + y^2 \\\textrm{Adding 2xy to the LHS and RHS of equation 1 gisues us }\\x^2 + y^2 + 2xy = \frac{5}{8} + 2 * \frac{3}{16} = \frac{5}{8} + \frac{3}{8} = \frac{8}{8} = 1[/tex]
[tex](x + y)^2 = 1 == > x+y = \sqrt{1} = 1\\\\(x - y)^2 = x^2 -2xy + y^2\\\\\textrm{Subtracting 2xy from both sides of Equation 1}\\x^2 + y^2 - 2xy = \frac{5}{8} - 2*\frac{3}{16} = \frac{5}{8} - \frac{3}{8} = \frac{2}{8} = \frac{1}{4} \\x-y = \sqrt{\frac{1}{4}} = \frac{1}{2}\\\\x^2 - y^2 = (x+y)(x-y) = 1 . \frac{1}{2} = \frac{1}{2}[/tex]
the perimeters of a square and rectangle are equal. one side of a rectangle is 11cm and the area of the square is 4cm^2 more than the area of the rectangle. find the side of the square.
Answers
Answer:
The side of the square can be 13 or 9
Step-by-step explanation:
Let x equal the unknown side of the rectangle and y equal the side of the square. The given information is that the area of the square is 4cm^2 larger than that of the rectangle. Mathematically this can be represented as
[tex]11x+4=y^2[/tex]
The second known is that their perimeters are equal so,
[tex]22+2x=4y[/tex]
Solve the first equation in terms of x and substitute it into the second and you get the quadratic
[tex]y^2-22y+117=0[/tex]
[tex](y-13)(y-9)=0[/tex]
Therefore your side length for the square can be either of those.
Cindy works at Jurassic Park and has been tasked to design a container in the shape of a rectangular prism for the incoming baby dinosaurs. The scaled model of the container has dimensions 2m by 4m by 6m. Cindy has decided to increase each dimension of the scaled model by the same amount in order to produce a container with a volume of 84 times the volume of the scale model. By what amount should Cindy increase each dimension of the scaled model?
Answers
The amount Cindy should increase in each dimension of the scaled model is 12 m.
What is a rectangular prism?It is defined as the six-faced shape, a type of hexahedron in geometry.
It is a three-dimensional shape. It is also called a cuboid.
We have:
The scaled model of the container has dimensions 2m by 4m by 6m.
Volume of the scaled model = 2×4×6 = 48 cubic m
Let x be the amount by which each dimension is increased.
(2 + x)(4 + x)(6 + x) = 84(48)
[tex]\rm 48+44x+12x^2+x^3=4032[/tex]
[tex]\rm x^3+12x^2+44x-3984=0[/tex]
[tex]\rm x-12=0\quad \mathrm{or}\quad \:x^2+24x+332=0[/tex]
The quadratic equation has no real solution so,
x = 12 m
Thus, the amount Cindy should increase in each dimension of the scaled model is 12 m.
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You enter a room. 2 dogs, 4 horses, one giraffe, and a duck are laying on a bed. 3 chicken are flying over a chair. How many legs are on the ground?.
Answers
Answer:
28 legs are on the ground
Seriously help I’m about to submit this: A researcher wishes to estimate the percentage of adults who support abolishing the penny what size sample should be obtained if he wishes the estimate to be within three percentage points with a 95% confidence if he:
A: uses a previous estimate of 26%?
B: he does not use any prior estimates?
Answers
Using the z-distribution, the sample sizes are given as follows:
a) 822.
b) 1068.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.The margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
Item a:
The estimate is of [tex]\pi = 0.26[/tex], hence we solve for n when M = 0.03.
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.96\sqrt{\frac{0.26(0.74)}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.96\sqrt{0.26(0.74)}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.26(0.74)}}{0.03}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.26(0.74)}}{0.03}\right)^2[/tex]
n = 821.2
Rounding up, a sample of 822 is needed.
Item b:
No prior estimate, hence [tex]\pi = 0.5[/tex].
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.96\sqrt{0.5(0.5)}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.5(0.5)}}{0.03}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.5(0.5)}}{0.03}\right)^2[/tex]
n = 1067.11
Rounding up, a sample of 1068 is needed.
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a company sold it's bond to interested members of the public and paid them an interest rate of 15percent per annum. how much will Mr Rogers receive if he bought a bond worth k 200 000.00
Answers
The amount that Mr Rogers would receive per annum is K 30,000.
How much would Mr Rogers receive per annum?
The amount of money that Mr Rogers would receive per annum is a function of the worth of the bond bought and the interest rate.
Interest= bond value x interest rate
0.15 x 200,000 = $30,000
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You can work a total of no more than 40 hours each week at your two jobs. Housecleaning pays $8 per hour and your sales job pays $119 per hour. You need to earn at least $323 each week to pay your bills. Write a system of inequalities that shows the various numbers of hours you can work at each job.
A) h+ s ≥ 40 and 8h + 11s ≥ 323
B) h+ s < 40 and 8h + 11s ≤ 323
C) h + s ≤ 40 and 8h + 11s ≥ 323
D) h + s ≤ 40 and 8h + 11s < 323
Answers
Answer:
C
Step-by-step explanation:
you can only work 40 or less hours per week but you must earn greater then or equal to $323.
Find the missing side of the triangle.
Answers
Answer:
1
Step-by-step explanation:
1 is ans p²=h²-b²
solved
can anybody help me with order of operations
Answers
Answer:
The order of operations is Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction.
Step-by-step explanation:
The order of operations is PEMDAS.
P: Parenthesis
E: Exponents
M: Multiplication
D: Division
A: Addition
S: Subtraction
An easy way to remember PEMDAS is, please excuse my dear aunt sally.
Hope this helps!
If not, I am sorry.
PLEASE HELP, ASAP (PLEASE, I MEAN THAT AS NICE AS POSSIBLE) GEOMTRY BTW
Answers
The value of angle x is 127 degrees.
How to find angles?The angle x can be found as follows:
Angle on a straight line is 180 degrees.
Therefore, the sum of 53 degrees and x degrees is 180 degrees.
Therefore,
53 + x = 180°(sum of angles on a straight line)
subtract 53 from both sides of the equation
53 - 53 + x = 180 - 53
x = 127°
Therefore, the angle of x is 127 degrees.
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HELP ME PLEADE I NEED THIS ( PLATOOOOOO)
Answers
Answer: f(x+3), f(x+2), f(x), f(x-1/2), f(x-4), f(x-7)
Step-by-step explanation:
For y=f(x-a), the vertex is shifted a units to the right.
So, to order from left to right, we need to order them so that the value of a increases from the least to the most.
GET BRAINLY! please help me figure this out
Answers
Answer: x > -1, see attached.
Step-by-step explanation:
To solve the inequality, we will isolate the x-variable.
Given:
3x - 19 > -22
Add 19 to both sides:
3x > -3
Divide both sides by 3:
x > -1
To graph, we will use an open circle since it is only greater than and not equal to. Then, we will place this circle on -1. Lastly, we will shade to the right of -1, since it is greater than -1.
Suppose the correlation coefficient between a baby’s weight and the price of a smartphone is 0.87. Which statement must be true?
Answers
The true statement that explains the correlation coefficient is: C. As the baby gains weight, the prices of smartphone tend to increase.
What is Correlation Coefficient?The value of the correlation coefficient shows a relationship between two variables. A positive value suggests a positive relationship, meaning as one variable increases, the other also increases.
A correlation coefficient of 0.87 suggests a positive relationship between baby's weight and the price of smartphone, therefore, the true statement is:
C. As the baby gains weight, the prices of smartphone tend to increase.
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find the slope of the line passing through the points (-5, 3) and (7, 9)
Answers
[tex] \sf{\red{Answer}}[/tex]
[tex]\sf{m = \frac{1}{2} }[/tex]
[tex] \sf{\purple{Explanation}}[/tex]
[tex] \sf{m = \frac{y_{2}- y_{1}}{m_{2} - m_{1}} }[/tex]
[tex] \sf{m = \frac{9- 3}{7- ( - 5)} }[/tex]
[tex]\sf{m = \frac{6}{7 + 5} }[/tex]
[tex]\sf{m = \frac{6}{12} }[/tex]
[tex]\sf{m = \frac{1}{2} }[/tex]
Manda converted the following repeating decimal a fraction. Her work is shown below.
Answers
In analyzing Manda’s work, she made a mistake instep 3, she did not subtract one x from the left side.
What is the fraction about?Fractions are known to be the parts of a complete or whole numbers of objects. It is known to have a numerator and a denominator and when solving for it, the rule of BODMAS must be obeyed.
In step 3 we see that (image attached) she did not subtract one x from the left side. The right thing to do is to use x to cancel out on the both side and that will make the answer to be correct but she did not.
So her error is seen in step 3 and as such, option C is correct.
See full question in the image attached.
Options are
Analyze Manda’s work. Is she correct? If not, what was her mistake?
A. Yes, she is correct.
B. In step 2, she needed to multiply both sides by 10.
C. In step 3, she did not subtract one x from the left side.
D. In step 4, she did not simplify her fraction.
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Explain why the value of the sine ratio for an acute angle of a right triangle must always be a positive value less than 1
Answers
The sine is defined as the ratio of the length of the opposite leg and the hypotenuse. Since the hypotenuse is the longest side, the numerator will be less than the denominator, and thus the fraction will be less than 1.
Answer:
The sine is defined as the ratio of the length of the opposite leg and the hypotenuse. Since the hypotenuse is the longest side, the numerator will be less than the denominator, and thus the fraction will be less than 1.
Step-by-step explanation:
A store pays $140 for a cell phone. The store sells the cell phone for $315. Your classmate says that the markup is 125% because $175$140=1.25. Is your classmate correct? (brainliest for correct answer)
Answers
The store bought the phone for $140 and sells the cell phone for $315 at a markup of 125%.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let x represent the markup, since the store sells the cell phone for $315, hence:
(315 - 140)/140 * 100% = x
x = 125%
The store bought the phone for $140 and sells the cell phone for $315 at a markup of 125%.
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A characteristic of a simple random sample is that all samples of the same _______ have an equal chance to be selected.
Answers
A characteristic of a simple random sample is that all samples of the same population have an equal chance to be selected.
What is a simple random sampling?A subset of a statistical population called a simple random sample is one in which each member has the same chance of being picked or selected.
A subset of participants is chosen at random by the researcher using this sampling approach from a population.
To make sure that the sample represents the population, simple random sampling is often performed and this technique helps to sample bigger populations more frequently than smaller subpopulations.
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At the carnival, we found a bean bag toss booth. There's a 0.64 probability of throwing the bean bag into the outer ring, a 0.11 probability of throwing it into the middle ring, and the remaining probability throwing it into the center of the target. Tickets are awarded depending on which ring the bean bag lands in. We get 1 ticket for the outer ring, 2 tickets for the middle ring, and 3 tickets for the center. What is the expected value (number of tickets) we will get if we play the game 10 times
Answers
The expected value after 10 game at a carnival is 16.1 tickets.
Given the probabilities that bag lands into the outer ring, middle ring, center are 0.64, 0.11 and remaining. 1 ticket awarded for the outer, 2 for middle and 3 for middle.
We have to find the expected value we will get if we play the game 10 times.
Probability is the chance of happening an event among all the events possible. Value of probability lies between 0 and 1. The formula of probability is as under:
Probability=number of items/ total items in consideration.
Probability that bag lands in center is 1-0.64-0.11=0.25.
Expected value when game is played 1 time=1*0.64+2*0.11+3*0.25
=0.64+0.22+0.75
=1.61
Expected value when the game is played 10 times=10*1.61
=16.1 tickets.
Hence the expected value when game is played 10 times is 16.1 tickets.
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A right triangle is plotted in an x y plane. The vertices of the triangle are as follows: (0, 0); (x sub 1, y sub 1) in the second quadrant; and (x sub 2, y sub 2) in the first quadrant. Right angle is at the origin.
What is the area of the triangle in the diagram?
A.
B.
C.
D.
Answers
Based on the calculations, the area of this triangle is equal to: A. Area = 1/2 × [√(x₂² + y₂²) × √(x₁² + x₁²)].
How to calculate the area of a triangle?Mathematically, the area of a triangle can be calculated by using this formula:
Area = 1/2 × b × h
Where:
b is the base area.h is the height.Next, we would find the distance between points A and B:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
AB = √[(x₂ - 0)² + (y₂ - 0)²]
AB = √(x₂² + y₂²)
Also, we would find the distance between points A and C:
Distance = √[(x₁ - x₂)² + (y₁ - y₂)²]
AC = √[(x₁ - 0)² + (y₁ - y0)²]
AC = √(x₁² + x₁²).
Now, we can find the area of this triangle:
Area = 1/2 × b × h
Area = 1/2 × AB × AC
Area = 1/2 × [√(x₂² + y₂²) × √(x₁² + x₁²)]
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Answer: B. 1/2√(x2^2 - x1^2) ( y2^2 - y1^2
Step-by-step explanation: Edmentum