Using substitution, determine whether the given linear expression is a factor of the polynomial. * 2x^3 - 11x^2 + 8x - 15; x - 5 YES OR NO
Answers
Given the ploynomial:
\(\begin{gathered} 2x^3-11x^2+8x-15 \\ \\ \text{ Linear expression: x - 5} \end{gathered}\)A linear expression (x - n) is a factor of a polynomial when x = n is a zero of the polynomial expression. That is when the function f(x) = 0.
Given the linear expression:
x - 5
Equate to zero:
x - 5 = 0
Add 5 to both sides:
x - 5 + 5 = 0 - 5
x = 5
Substitute 5 for x in the polynomial, if the function tends to zero, then the linear expression is a factor of the polynomial.
We have:
\(\begin{gathered} 2(5)^3-11(5)^2+8(5)-15^{} \\ \\ 2(125)-11(25)+8(5)-15 \\ \\ 250-275+40-15 \\ \\ -25+40-15 \\ \\ 15-15=0 \end{gathered}\)Thus:
\(\begin{gathered} f(x)=2x^3-11x^2+8x-15 \\ \\ f(5)=2(5)^3-11(5)^2+8(5)-15^{} \\ \\ f(5)=0 \end{gathered}\)Since the the polynomial function f(x) tends to zero, the linear expression can be said to be a factor of the polynomial
ANSWER:
Yes, the linear expression is a factor of the polynomial
Related Questions
50 Points!!!!!! Triangle ABC is given.
Angle A is labeled two x degrees. Angle B is labeled forty degrees. Angle C is labeled three x degrees.
What is the measure, in degrees, of ∠A?
Enter your answer in the box.
Answers
All 3 angles add up to 180 degrees.
so 40 + 2x + 3x = 180
40 + 5x = 180
5x = 140
x = 28
So angle A = 2x = 2(28) = 56 degrees.
Answer: 56°
Step-by-step explanation:
We know that a triangle's angles add up to 180 degrees. We will create an equation to help us solve for x using this information.
Given:
2x + 3x + 40 = 180
Combine like terms:
5x + 40 = 180
Subtract 40 from both sides of the equation:
5x = 140
Divide both sides of the equation by 5:
x = 28
Next, we will substitute this value of x into the expression for ∠A.
∠A = 2x = 2(28) = 56°
if the cost of 5litre of Petrol is 552.50 find the cost of 1 litre of Petrol
Answers
Answer:
given that the cost of 5 litres of petrol is 552, we have to divide 552 by 5 to find the price of 1 litre of petrol
552÷5= 110.4
Step-by-step explanation:
Answer:
110.5
Step-by-step explanation:
552.5/5= 10.5 which is the cost of 1 liter petrol by unitary method.
Increase 2,400 by 5%
Answers
Increasing 2400 by 5% gives us 2520
we can increase the value by using the formula:
\(initial value+ percentage increase *initial value\) = increased percentage
in the aforementioned question we have
initial value = 2400
percentage increase = 5%
thus we can find out the increased percentage by:
2400 + 2400 X (5/100)
=2400 + 120
=2520
the value by which 2400 is increased is 120
to arrive at the increased value which is 2520
for more questions related to percentage increase :
https://brainly.com/question/6110438
https://brainly.com/question/3502768
Question: "Estimate 8 x 572."
Answers
4580 or 4600 is the best answer I have gotten for this question
Help for Pre Calc please
Answers
The correct statement regarding the inverse function of f(x) = 4x^4 is given as follows:
\(f^{-1}(x) = \pm \left(\frac{x}{4}\right)^{\frac{1}{4}}\); f^(-1)(x) is not a function.
How to obtain the inverse function?The function in this problem is defined as follows:
f(x) = 4x^4.
To obtain the inverse of a function y = f(x), first the variables y and x are exchanged, as follows:
x = 4y^4.
Isolating the variable y, we have that:
y^4 = (x/4).
The inverse operation of the fourth power is the fourth root, hence:
\(y = \pm \sqrt[4]{\frac{x}{4}}\)
\(f^{-1}(x) = \pm \sqrt[4]{\frac{x}{4}}\)
\(f^{-1}(x) = \pm \left(\frac{x}{4}\right)^{\frac{1}{4}}\)
The plus/minus symbol means that for each input of x, the inverse function gives two outputs, meaning that there are multiple outputs mapped to each input, and thus the inverse is not a function.
This means that the second statement is correct.
More can be learned about inverse functions at https://brainly.com/question/3831584
#SPJ1
What’s the answer of 7 1/2 divided by 3/4
Answers
Answer:
the answer is 10
Step-by-step explanation:
7 1/2 x 4/3=10
Answer:
5.625
Step-by-step explanation:
6) What is the LEAST COMMON
MULTIPLE of 21 and 60?
Answers
Answer:
420
Step-by-step explanation:
This problem refers to a right triangle ABC with C= 90°. Begin each problem by drawing a picture of the triangle with both the given and asked for information labeled appropriately. Answer to the nearest hundredth of a foot. If B=37.56 and a =49.94ft then b
Answers
The side b is approximately 80.02 feet in length. In a right triangle ABC with angle C equal to 90°, if angle B is 37.56° and side a is 49.94 feet, we can solve for side b using the trigonometric function sine.
First, we can label the triangle as follows:
Side a is opposite angle A,
Side b is opposite angle B,
Side c is the hypotenuse.
Let's label the triangle with the given and asked for information. Angle C is the right angle, angle B is 37.56°, side a is 49.94 feet, and side b is the side we are trying to find.
Using the sine function, we have:
sin(B) = opposite/hypotenuse
sin(37.56°) = a/b
Now we can substitute the known values:
sin(37.56°) = 49.94/b
To solve for b, we rearrange the equation:
b = 49.94 / sin(37.56°)
Using a calculator, we find:
b ≈ 80.02 feet.
For more such questions on Trigonometric function:
https://brainly.com/question/1143565
#SPJ8
Chess is one of the oldest and most popular board games. It is played by two opponents on a checkered board with specially designed pieces of contrasting colors, commonly white and black. White moves first, after which the players alternate turns in accordance with fixed rules, each player attempting to force the opponent’s principal piece, the King, into checkmate—a position where it is unable to avoid capture. In most chess tournaments held since the middle of the 19th century, there has been a very simple scoring system used. Players who scored a win in a game were awarded a point, while those scoring draws were given a half-point. Losing a game, as you might expect, was worth zero points. Five students from AMG chess club participated in a tournament.
a)3 times Mahdi’s score is one and a half. Write an equation that represents the situation, then find Mahdi’s score. Show your work.
Answers
Mahdi's score is,
⇒ 0.5
We have to given that;
3 times Mahdi’s score is one and a half.
Now, Let Mahdi's score = x
Hence, We can formulate;
⇒ 3x = 1 1/2
⇒ 3x = 3/2
⇒ x = 1/2
⇒ x = 0.5
Thus, Mahdi's score is,
⇒ 0.5
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ1
Imagine math Item 994395
Start with the equation 0.2=0 to explain why -4-2 must equal -8.
Drag descriptions and equations to the table to complete the explanation.
Answers
In order to explain why -4 - 2 equals -8, let's start with the equation 0.2 = 0. By analyzing this equation, we can uncover the reason behind this seemingly counterintuitive result.
1. Begin with the equation 0.2 = 0.
2. Subtract 0.2 from both sides of the equation to isolate the variable: 0.2 - 0.2 = 0 - 0.2.
This simplifies to 0 = -0.2.
3. Observe that the right side of the equation, -0.2, is a negative number.
4. Recall that subtracting a negative number is equivalent to adding its positive counterpart. Therefore, -0.2 is the same as +0.2.
5. Rewrite the equation as 0 = +0.2.
6. Notice that 0 on the left side of the equation is equal to 0 + 0, since any number added to zero remains unchanged.
7. Substitute 0 + 0 for 0 in the equation: 0 + 0 = +0.2.
8. Simplify the equation to 0 = +0.2.
9. Finally, recognize that a positive number cannot equal zero. Hence, the equation 0 = +0.2 is false.
10. As a result, the original equation 0.2 = 0 is invalid.
11. Therefore, the logical consequence is that any subsequent deductions based on this invalid equation would also be incorrect.
12. Consequently, -4 - 2 does not equal -8, as per the explanation derived from the flawed equation.
To summarize, by analyzing the equation 0.2 = 0, we can determine that subsequent deductions based on this equation are incorrect. Hence, -4 - 2 does not equal -8.
For more such questions on counterintuitive, click on:
https://brainly.com/question/17004386
#SPJ8
2.
7 in
Н
I
2 in
J
What is the Scale Factor?
21 in
M
6 in
N
Answers
1. A company produces two types of nutritional supplements; Energize and Excel. Energize contains 26 mg of vitamin A, 42 mg of vitamin C and 25 mg of an herbal supplement. Excel contains 68 mg of vitamin A, 61 mg of vitamin C and 15 mg of the herbal supplement. An athlete is told that he needs at least 489 mg of vitamin A, 1130 mg of vitamin C and 348 mg of the herbal supplement for optimal athletic performance. The athlete wants to take the supplements, but at the lowest possible cost. Energize pills cost 40 cents each, while Excel pills cost 100 cents each. Let x = the number of Energize pills to take, and let y = the number of Excel pills to take. Which of the following is the objective function for this situation?
A) Minimize C = 40x + 100y.
B) Maximize C = 40x + 100y.
C) Minimize C = 11300x + 3480y.
D) Maximize C = 100x + 40y.
E) Minimize C = 100x + 40y.
F) None of the above.
2. A company produces two types of bicycles; mountain bikes and racing bikes. It takes 7 hours of assembly time and 5 hours of mechanical tuning to produce a mountain bike. It takes 8 hours of assembly time and 4 hours of mechanical tuning to produce a racing bike. The company has at most 22 hours of mechanical tuning labor per week and at most 190 hours of assembly labor per week. The company's profit is $50 for each mountain bike produced and $130 for each racing bike produced. The company wants to make as much money as possible. Let x = the number of mountain bikes they produce, and let y = the number of racing bikes they produce. What are the constraints for this problem?
a) 7x + 5y ≤ 190, 8x + 4y ≤ 22, x ≥ 0, y ≥ 0.
b) 7x + 8y ≥ 190, 5x + 4y ≤ 22, x ≥ 0, y ≥ 0.
c) 5x + 8y ≤ 190, 7x + 4y ≤ 22, x ≥ 0, y ≥ 0.
d) 7x + 8y ≤ 190, 5x + 4y ≤ 22, x ≥ 0, y ≥ 0.
e) 7x + 8y ≤ 190, 5x + 4y ≥ 22, x ≥ 0, y ≥ 0.
f) none of the above.
3. A certain academic department at a local university will conduct a research project. The department will need to hire graduate research assistants and professional researchers. Each graduate research assistant will need to work 23 hours per week on fieldwork and 17 hours per week at the university's research center. Each professional researcher will need to work 15 hours per week on fieldwork and 25 hours per week at the university's research center. The minimum number of hours needed per week for fieldwork is 154 and the minimum number of hours needed per week at the research center is 140. Each research assistant will be paid $295 per week and each professional researcher will be paid $416 per week. Let xdenote the number of graduate research assistants hired and let y denote the number of professional researcher hired. The department wants to minimize cost. Set up the Linear Programming Problem for this situation.
A) Min C = 416x + 295y; s.t 23x + 17y ≥ 154, 15x + 25y ≥ 140, x ≥ 0, y ≥ 0.
B) Min C = 295x + 416y; s.t 23x + 15y ≥ 154, 17x + 25y ≥ 140, x ≥ 0, y ≥ 0.
C) Min C = 295x + 416y; s.t 23x + 15y ≥ 154, 25x + 17y ≥ 140, x ≥ 0, y ≥ 0.
D) Min C = 295x + 416y; s.t 15x + 23y ≤ 140, 25x + 17y ≤ 154, x ≥ 0, y ≥ 0.
E) Min C = 416x + 295y; s.t 15x + 23y ≥ 154, 25x + 17y ≥ 140, x ≥ 0, y ≥ 0.
F) None of the above.
Answers
Answer:
1)A) Minimize C = 40x + 100y.
2) d) 7x + 8y ≤ 190, 5x + 4y ≤ 22, x ≥ 0, y ≥ 0.
3) B) Min C = 295x + 416y; s.t 23x + 15y ≥ 154, 17x + 25y ≥ 140, x ≥ 0, y ≥ 0.
Step-by-step explanation:
1) Energize pills cost 40 cents each, while Excel pills cost 100 cents each. If x represent the energize pills and y represent the excel pills, the objective function would be:
minimize cost = cost of energize pill + cost of excel pill
Minimize cost = 40x + 100y
2) Let x = the number of mountain bikes they produce, and let y = the number of racing bikes they produce.
7 hours of assemble time to produce a mountain bike and 8 hours of assemble time to produce a racing bike. Since the company has at most 190 hours for assemble time, it can be represented as:
7x + 8y≤ 190
5 hours of mechanical tuning to produce a mountain bike and 4 hours of mechanical tuning to produce a racing bike. Since the company has at most 22 hours for mechanical tuning, it can be represented as:
5x + 4y ≤ 22
Also assemble time and mechanical time must be greater than 0, hence:
x ≥ 0, y ≥ 0
3) The fieldwork constraint can be represented as:
23x + 15y ≥ 154
The time to be spent at university research center can be represented as:
17x + 25y ≥ 140
Both fieldwork time and time spent at university research center mut be greater than 0, hence:
x ≥ 0, y≥ 0
The cost equation is:
Minimize cost = 295x + 416y
A race car traveled for 2 1/2hours with an average speed of 132 5/8 km per hour. Find the total distance it covered.
Answers
Answer: The total distance covered by the car is 331 9/16 km.
Step-by-step explanation:
We know that, speed= distance/time taken
Therefore, distance = speed x time taken
= 132 5/8 x 2 1/2
= 5/2 x 1061/8
= 5305/16
= 331 9/16 km
Therefore, total distance is 331 9/16 km.
Read more about the calculations of Distance,
https://brainly.com/question/51872423
A painter can paint 180 square feet per hour. He charges $0.35 per square foot. Today he paints for 3.5 hours. How much will he charge?
Answers
Answer:
i think it's 1800
Step-by-step explanation:
if it's wrong i'm so sorry :)
The price charged for 630 square feet is $220.5
If a painter can paint 180 square feet per hour, the amount he will paint in 3.5 hours will be 3.5 * 180 = 630 square feet
If the painter charges $0.35 per square foot, the price for 630 square feet will be expressed as 0.35 * 630 = $220.5
Hence the price charge for 630 square feet is $220.5
learn more here: https://brainly.com/question/24191335
In The figure below ABCD is a square points are chosen on each pair of the adjacent sides of ABCD to form four congruent and right angles as shown below each of these has one leg that is twice as long as the other leg what fraction of the area of square ABCD is shaded?
Answers
9514 1404 393
Answer:
5/9
Step-by-step explanation:
The area of one triangle is ...
A = 1/2(x)(2x) = x²
Then the area of the four triangles is ...
unshaded area = 4(x²)
The length of DC is 2x+x = 3x, so the area of ABCD is ...
total area = (3x)² = 9x²
Then the fraction that is shaded is ...
(9x² -4x²)/(9x²) = 5/9
5/9 of the area of ABCD is shaded.
Answer:
5/9 of the area is shaded.
Step-by-step explanation:
Let (-3, 4) be a point on the terminal side of 0. Find the exact values of sin 0, csc 0, and cot 0.
Answers
Therefore, sin θ = 4/5, csc θ = 5/4, and cot θ = -3/4 using trigonometric ratio.
Trigonometric ratio calculation.
We know that the point (-3, 4) is on the terminal side of the angle θ, and we can use the Pythagorean theorem to find the value of the hypotenuse:
r² = x² + y²
r² = (-3)² + 4²
r² = 9 + 16
r² = 25
r = 5
Now we can find the values of sin θ, csc θ, and cot θ:
sin θ = y/r = 4/5
csc θ = r/y = 5/4
cot θ = x/y = -3/4
Therefore, sin θ = 4/5, csc θ = 5/4, and cot θ = -3/4.
Learn more about trigonometric ratio below.
https://brainly.com/question/29529495
#SPJ1
The sum of twice a number, m, and 7 is equal to 15 less than the number,
m. What is the value of m?
Answers
Answer:
2m+7 = m-15
2m-m+7 = -15
1m = -15-7
1m = -22
m = -22
how many turning points will a quartic fumction with four real zeros have?
Answers
upto four roots or zero......
Anne has 5 pints of milk and is planning to make 6 cakes to sell in fundraising. Each cake will require 112 cups of milk. Does she have enough milk to make the 6 cakes? If so, how many cups of milk will be left, and if not, how many extra cups of milk would she need?
Yes she has enough milk; She will have 1 extra cup of milk.
No she does not have enough milk; She will need 1 more cup of milk.
Yes she has enough milk; She will have 112 extra cups of milk.
No she does not have enough milk; She will need 412 extra cups of milk.
Answers
Answer:
Option (1)
Step-by-step explanation:
Each cake requires cups of milk = \(1\frac{1}{2}\) cups ≈ 1.5 cups
6 cakes will require milk = 6 × 1.5
= 9 cups
Anne has milk = 5 pints
∵ 1 pint = 2 cups
∴ 5 pints = 10 cups
Therefore, Anne has milk = 10 cups
Extra amount of milk Anne has = 10 - 9 = 1 cup
Hence, Answer is yes, she has enough milk. She will have 1 extra cup of milk.
Option 1 will be the answer.
ΔQRS is an isosceles triangle. What is the length of RT¯¯¯¯¯
R
T
? Round to the nearest hundredth. Enter your answer in the box.
Answers
\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{11}\\ a=\stackrel{adjacent}{6}\\ o=\stackrel{opposite}{RT} \end{cases} \\\\\\ RT=\sqrt{ 11^2 - 6^2}\implies RT=\sqrt{ 121 - 36 } \implies RT=\sqrt{ 85 }\implies RT\approx 9.22\)
What’s the product of 22 and 49
Answers
Answer:
1078
Step-by-step explanation:
22 x 49 = 1078
Answer:
1,078
Step-by-step explanation:
Anytime that the word "product" is used in math, it means that you are multiplying numbers together to get your answer out of the two numbers being multiplied. For example:
"Factor x Factor = Product."
So we have: "22 x 49 = __"
Now we need to cross-multiply.
22
x 49
198
+ 880
1078
So, the answer is: "22 x 49 = 1,078."
I hope that this helps.
Figure B is a scaled copy of Figure A.
Figure B
44
Figure A
22
20
10
32
40
80
64
What is the scale factor from Figure A to Figure B?
Answers
Answer: Scale factor = 2
=====================================================
Explanation:
Pick on any pair of corresponding sides. I'll pick the right-most sides of each figure. For figure A, that would be the side of 40 units. Figure B has this corresponding side be 80 units long.
The scale factor is 80/40 = 2. This shows that figure B has sides 2 times longer compared to the corresponding sides on figure A.
So in short all you do is divide the corresponding side lengths. We divide in the format (figureB)/(figureA) because of the transition from A to B, and not the other way around.
Determine the slope of the line that has the following coordinates: (2, -1) (7, -1)
Answers
Answer:
Y over X axis pretty sure
So your answer is 2 over -1 if 2 is the Y and 7 over -1 if 7 is the Y
Anyone know the answer to this?
2(8+7)=(_×8)+(_×7)
Use the distributive property to fill in the blanks
Answers
Answer:
Just fill in the blanks with the number 2
Step-by-step explanation:
Since we are using the distributive property, 2(8+7) = (2x8)+(2x7)
Y=5xー2
equals what ? HELPP!!
Answers
Answer:
X=-0.4
Y= - 2
Step-by-step explanation:
First we slove for x intetcept so we put 0 for y.
Y=5X-2
0=5X-2 Now move the variables to
the left side.
5x=-2 Divide both sides by 5
because the coefficient
of your variable is 5.
X=-0.4
Now let's solve for Y intetcept.
Y=5X-2
Y=5(0)-2
Y=-2
To which subset of the real number system does the number LaTeX: 1.\overline{5}1. 5 ¯ belong? Group of answer choices irrational numbers whole numbers natural numbers rational numbers
Answers
Answer:
rational numbers
Step-by-step explanation:
Fill in the missing values below one at a time to find the quotient when x^3 - x^2 - 3x + 2 is divided by x - 2.
Answers
Therefore, the quotient when x³ - x² - 3x + 2 is divided by x - 2 is x² - 2x - 5 with a remainder of -3.
To find the quotient when x³ - x² - 3x + 2 is divided by x - 2, we will use the long division method. Here is the solution:
Step 1: The first term of the quotient is x². Multiply x² by x - 2 to get x³ - 2x². Subtract this product from x³ - x² to get: x² - 3x² = -2x²
Step 2: Bring down the next term of the dividend, which is -3x. The new dividend is -2x² - 3x.
Step 3: The second term of the quotient is -2x. Multiply -2x by x - 2 to get -2x² + 4x. Subtract this product from -2x² - 3x to get -5x.
Step 4: Bring down the last term of the dividend, which is +2. The new dividend is -5x + 2. Step 5: The third term of the quotient is -5. Multiply -5 by x - 2 to get -5x + 10. Subtract this product from -5x + 2 to get -3.
For such more question on Multiply
https://brainly.com/question/29793687
#SPJ8
[(−5+1) ÷ 2]³ − |-7|
Answers
Answer:-15
Step-by-step explanation:
-5+1=-4
-4/2=-2
-2^3=-8
-8-7=-15
Two less than the quotient of a number and 3 is 16. What is the number? Let n be the unknown number
Answers
Answer:
13
Step-by-step explanation:
16/1 -3/1 = 16-3
= 13answer is unknow no.
Need answered ASAP GOT A TIMER!
Answers
Answer:
2
Step-by-step explanation:
To solve this problem you must apply the proccedure shown below:
1. You have the following multiplication given in the problem above:
(x/3)(6/x)
2. Multiply the numerators and the denominators:
(x/3)(6/x) = 6x/3x
3. You can simplify the expression. Then, you have:
6x/3x = 2
Answer:
2
Step-by-step explanation:
1) simplify x
x/x = 1
2) simplify 6 with 3
6/3 = 2
3) multiply the two numbers
2*1 = 2