The values of a and b using the factor theorem for the polynomial f(x), we set f(1) and f(-1) equal to zero. Solving the resulting system of equations, we find that a = 12 and b = -1.
To find the values of a and b using the factor theorem, we need to use the given factors (x - 1) and (x + 1) and the fact that they are roots of the polynomial f(x).
The factor theorem states that if (x - c) is a factor of a polynomial, then f(c) = 0. Therefore, we can set x = 1 and x = -1 in the polynomial f(x) to get two equations.
First, let's substitute x = 1 into f(x):
f(1) = (1)^3 + a(1)^2 + b(1) - 12
f(1) = 1 + a + b - 12
Next, let's substitute x = -1 into f(x):
f(-1) = (-1)^3 + a(-1)^2 + b(-1) - 12
f(-1) = -1 + a - b - 12
Since (x - 1) and (x + 1) are factors, f(1) and f(-1) must equal zero. Therefore, we can set the two equations equal to zero and solve for a and b:
1 + a + b - 12 = 0
-1 + a - b - 12 = 0
Rearraning the equations, we have:
a + b = 11
a - b = 13
Now, we can solve this system of equations. Adding the two equations, we get:
2a = 24
a = 12
Substituting the value of a into one of the equations, we find:
12 - b = 13
b = -1
Therefore, the values of a and b are 12 and -1 respectively.
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-8r –9 > -21...............
Answer:
r < 3/2 or r < 1.5
Step-by-step explanation:
-8r - 9 > 21
-8r > -21 +9
-8r > -12
divide both sides by -8
= r < 3/2 or 1.5
WILL GIVE BRAINLIEST
15 POINTS
The area in square feet of a rectangular field is x^2 - 130x + 4000. The width, in feet, is x - 50. What is the length, in feet?
2. There are 225 students at Memorial
Middle School. On Friday, 135 students
wore clothing in the school colors. What
percent of the students wore clothing in
the school colors?
5
The product of twice a number and five is the same as the difference of nine times the number and
3
Find the
number.
Tho numb
Answer: Negative 3
Step-by-step explanation: 2n(5)=9n-3. 10n=9n-3. Subtract 9n from both sides. n= -3
which two intergers have a difference of 24 and a quotient of -7
Answer:
21 and -3
Step-by-step explanation:
Hope this helps!!! :)
72=1/2h(4+5) solve for h
Answer:
h=16
Step-by-step explanation:
1
Simplify —
2
Equation at the end of step
1
:
1
72 - ((— • h) • 9) = 0
2
STEP
2
:
Rewriting the whole as an Equivalent Fraction
2.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 2 as the denominator :
72 72 • 2
72 = —— = ——————
1 2
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
72 • 2 - (9h) 144 - 9h
————————————— = ————————
2 2
STEP
3
:
Pulling out like terms
3.1 Pull out like factors :
144 - 9h = -9 • (h - 16)
Equation at the end of step
3
:
-9 • (h - 16)
————————————— = 0
2
STEP
4
:
When a fraction equals zero
4.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
-9•(h-16)
————————— • 2 = 0 • 2
2
Now, on the left hand side, the 2 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
-9 • (h-16) = 0
Equations which are never true:
4.2 Solve : -9 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation:
4.3 Solve : h-16 = 0
Add 16 to both sides of the equation :
h = 16
if I have three pieces of paper and my friend take a piece of paper from me how many pieces of paper do I have total
Answer: 3
Step-by-step explanation: If he takes one YOU have 2 but in TOTAL you still have 3
Given: <1 - <2
Prove: p || q.
Angles Lines Statements Reasons
21
22
23
р
Statements
Reasons
3
9
2
2
Assemble the proof by dragging tiles to
the Statements and Reasons columns.
Answer:
Step-by-step explanation:
Given that alternate exterior angles ∠1 and ∠2 are equal, line p is parallel to q.
What are alternate exterior angles?Two exterior angles that lie on two different lines cut by a transversal and are placed on the opposite sides of the transversal are called alternate exterior angles.
∠1 = ∠2 (alternate exterior angles)
This implies, p||q.
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17,892÷210 find the quotient
Answer:
85.2
Step-by-step explanation:
17,892 ÷ 210
85.2
Best of Luck!
PLS HELP HELP HELP HELP HELP
Answer:
B 7.5
Step-by-step explanation:
Answer:
B 7.5 because it's a dilation of -5, meaning you divide 15/2 to get the answer.
Step-by-step explanation:
Kareem has 12 ½ yards of material. A cape for a play takes 3 5/6 yards. How many capes can Kareem make with the material? *
Find the surface area of this rectangular prism. Be sure to include the correct unit in your answer.
Answer: 258 [tex]yard^{2}[/tex]
Step-by-step explanation: To find the surface area you add the area of all the sides. And the unit for a surface area is unit (yards) squared.
Front: 5 • 9 = 45
Back: 5 • 9 = 45
Left: 6 • 5 = 30
Right: 6 • 5 = 30
Top: 9 • 6 = 54
Bottom: 9 • 6 = 54
45 + 45 + 30 + 30 + 54 + 54 = 258.
in a typical bag of skittles, the ratio of red to yellow skittles is 3 to 7. If there are 40 skittles altogether, how many red skittles are there?
Answer:
I love Skittles
what's your favorite color?
18. Analyze Information Isabel made the
following graph to show the daily share
price for Company XYZ. What was the
change in the price from Monday to
Friday?
The required change in the price is equal to 0.75 cents.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given that, Isabel made the following graph to show the daily share
price for Company XYZ.
The price on Monday = 0.75
The price on Friday = 1.50
We need to find the change in price from Monday to Friday. It can be calculated as follows;
Change = 0.75 - 1.50
Change = 0.75 cents
therefore, the required change in the price is equal to 0.75 cents.
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Solve the following equation for q. 5q=8p-28+3q
Group of answer choices
q = 4p + 14
q = 4p - 14
q = 4p + 2
q = 4p - 2
A. 7 x 7^4
B. 10^9 divided by 10^7
C.5^8 divided by 5
IN INDEX NOTATION
If $11000 yields $1100 over 5 years, what is the interest rate?
Answer:
1.92449%
Step-by-step explanation:
Simple Interest Rate Formula: A = P(1 + r)ⁿ
Step 1: Define variables
Principle amount P = 11000
Total amount A = 11000 + 1100 = 12100
Years n = 5
Step 2: Substitute and Evaluate for r
12100 = 11000(1 + r)⁵
11/10 = (1 + r)⁵
1.01924 = 1 + r
r = 0.019245
Step 3: Convert to percentage
0.019245 × 100 = 1.92449%
In the diagram below, the lines are parallel. m∠BCD = 52° and m∠EAB = 73°. What is the measure of ∠ABC?
Answer:
235°Step-by-step explanation:
GivenAB ║ CDm∠BCD = 52° m∠EAB = 73°To findm∠ABC = ?SolutionImagine line BF parallel to both AB and CD
Then
m∠ABC = m∠ABF + m∠CBF m∠ABC = (180° - m∠EAB) + (180° - m∠BCD)m∠ABC = (180° - 73°) + (180° - 52°) = 107° + 128° = 235°Answer:
235°Step-by-step explanation:
∠EAB = 73
∠BCD = 52
125
∠ABC = 360 - 125
= 235°
Which number is a factor of 16 but not a multiple of 8???
Answer:
the answer to the question is 4
Step-by-step explanation:
The function g is defined as follows.
g(x)=-4x²+5
If the graph of g is translated vertically downward by 8 units, it becomes the graph of a function h.
Find the expression for h(x).
Answer:
h(x) = 4x^2 - 3
Step-by-step explanation:
4.8 cm
С
A
5.1 cm
00
To the nearest degree, find the measure of angle B.
20°
43
47
70°
The difference between twice a number and
2/3
of the same
number is 68. What is the number?
Answer:
51
Step-by-step explanation:
2x - 2/3x = 68
4/3x = 68
4x = 204
x = 51
The mean distance of the earth from the sun (let's call it d) is 93 million miles. The distance varies as much as 1.6 million miles. Write the equation that describes the possible distances of the earth from the sun, using as distance unit millions of miles.
Answer:
Kindly check explanation
Step-by-step explanation:
Given that :
Mean distance of earth from the sun = 93 million miles
Let mean distance of earth from the sun = d
The variation on the distance is as much as 1. 6 million miles
Possible distances of the earth from the sun can be modeled using :
|d - 93| = ± 1.6
Where d = distance from earth to the sun
d = - 1.6 million + 93 million
d = 91.4 million
d = 1.6 million + 93 million
d = 94.6 million
Hence, possible distance from earth to the sun :
91.4 < d < 94.6
2x² + 10 factorización
Answer:
2(x² + 5)
Step-by-step explanation:
To factor 2x² + 10, we can first factor out the greatest common factor of the terms, which is 2:
2x² + 10 = 2(x² + 5)
We can't factor anymore, so the answer is:
2(x² + 5)
Answer:
2(x² + 5)
Step-by-step explanation:
To factorise this, do the distributive property backwards. In other words:
2x² + 10
2x² ÷ 2 + 10 ÷ 2
x² + 5
2(x² + 5)
∴ 2(x² + 5) is the answer
Which number is a factor of 22 but not a multiple of 2???
Answer:
1 times 22
Step-by-step explanation:
Answer:
11
Step-by-step explanation:
11 x 2 = 22
So 11 is a factor of 22 since 11 multiplied by 2 is 22.
11 is not a multiple of 2 though.
multiples of 2: 2,4,6,8,10,12.....
Hope this helps :)
Which scenario is best represented by the equation y = 8x?
Haddie spent $8 on one hairbrush.
Mike bought books that cost $8 each.
Georgia has as many pennies as Sam.
A cow weights 8 pounds more than a horse.
Answer:
The answer is A.
Step-by-step explanation:
A and B will take the same 10-question examination. Each question will be answered correctly by A with probability .7, independently of her results on other questions. Each question will be answered correctly by B with probability .4, independently both of her results on the other questions and on the performance of A. (a) Find the expected number of questions that are answered correctly by both A and B. (b) Find the variance of the number of questions that are answered correctly by either A or B.
(a) The expected number of questions answered correctly by both A and B is 28.
(b) The variance of the number of questions answered correctly by either A or B is 4.5.
Let's define the following variables:
X = Number of questions answered correctly by A
Y = Number of questions answered correctly by B
(a) Expected number of questions answered correctly by both A and B:
We can use the formula for the expected value of the product of two independent random variables:
E(X × Y) = E(X) × E(Y)
The probability of A answering a question correctly is 0.7, and the probability of B answering a question correctly is 0.4.
Since the questions are independent, we can calculate the expected values for X and Y:
E(X) = 10 (number of questions) × 0.7 (probability of A answering correctly) = 7
E(Y) = 10 (number of questions) × 0.4 (probability of B answering correctly) = 4
Now, the expected number of questions answered correctly by both A and B is:
E(X× Y) = E(X) × E(Y)
= 7×4
= 28
(b) Variance of the number of questions answered correctly by either A or B:
Variance is calculated differently for independent events. Since A and B's performances are independent, we can use the following formula:
Var(X + Y) = Var(X) + Var(Y)
The variance of a binomial distribution with n trials and probability p of success is given by np(1-p).
For A and B:
Var(X) = 10× 0.7 × (1 - 0.7)
= 2.1
Var(Y) = 10 × 0.4× (1 - 0.4)
= 2.4
Now, the variance of the number of questions answered correctly by either A or B is:
Var(X + Y) = Var(X) + Var(Y)
= 2.1 + 2.4
= 4.5
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if you can buy six jars of sun-dried tomatoes for $26.90, then how many can you buy with $53.80?
Answer:
12
Step-by-step explanation: divide 26.9 by six and you get 4.48 which is the price for one then you divide 53.8 by 4.48 and you get 12.0 which is just 12
Quick I need help solving !!!
Answer:
it is 240
Step-by-step explanation:
put in equation and solve
2/3t+10=170
t=240
Jared bought 15 colored pencils for $9. At that rate, how much would it cost to buy 5 colored pencils?
Question 5 options:
$3
$6
$30
$45
Answer:
it would cost him $3
Step-by-step explanation:
$9 divided by the 15 pencils is 0.6 cents
0.6 times 5 equals $3
