Answer:
use synthetic division
Step-by-step explanation:
use synthetic division to solve [tex]\frac{x^{3}-x^{2} -17x-15}{x-5}[/tex].
if solved correctly, you should get [tex]x^{2} +4x+3[/tex] with no remainder.
because there is no remainder, x-5 is a factor of the polynomial given.
[tex](x-5)[/tex] is a factor of the given polynomial because the value of the polynomial is [tex]0[/tex] at [tex]x=5[/tex].
Given:
The given polynomial is [tex]x^3-x^2-17x-15[/tex].
Explanation:
We know that, [tex](x-c)[/tex] is a factor of [tex]P(x)[/tex] if and only if [tex]f(c)=0[/tex].
We have,
[tex]P(x)=x^3-x^2-17x-15[/tex]
Substituting [tex]x=5[/tex] in the above polynomial, we get
[tex]P(5)=(5)^3-(5)^2-17(5)-15[/tex]
[tex]P(5)=125-25-85-15[/tex]
[tex]P(5)=0[/tex]
Since [tex]P(5)=0[/tex], therefore [tex](x-5)[/tex] is a factor of the given polynomial.
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A_________is the2 points at which line segments are connected on a polygon.
Answer:
Vertex
Step-by-step explanation:
I think
Find the distance between the pair of points. (2,-5) and (7,7)
Answer:
5,12
Step-by-step explanation:
because 7-2 is 5 and it would take 12 to get to 7
Which is a solution to the quadratic equation 1/4x^2 - x - 8 = 0?
Answer:
its -x-15/2
I'm not sure this is correct but I think that's the answer
The quantity demanded x of a certain brand of DVD player is 3000/week when the unit price p is $485. For each decrease in unit price of $20 below $485, the quantity demanded increases by 250 units. The suppliers will not market any DVD players if the unit price is $350 or lower. But at a unit price of $525, they are willing to make available 2500 units in the market. The supply equation is also known to be linear. (a) Find the demand equation. p(x) = (b) Find the supply equation. p(x) = (c) Find the equilibrium quantity and the equilibrium price. PLEASE help I am totally lost on this
Answer:
a) Demand equation :[tex]y=-\frac{2}{25}x+725[/tex]
b) Supply equation : [tex]y=\frac{7}{100}x+350[/tex]
C) The equilibrium quantity and the equilibrium price are 2500 and $ 525 respectively
Step-by-step explanation:
We are given that For each decrease in unit price of $20 below $485, the quantity demanded increases by 250 units.
Since decrease in unit price of $20 increase demand by 250 units
So, Slope =[tex]\frac{-20}{250}=\frac{-2}{25}[/tex]
We are given that The quantity demanded x of a certain brand of DVD player is 3000/week when the unit price p is $485.
Now for demand equation:
Use point slope form : [tex]y-y_1=m(x-x_1)[/tex]
So, [tex]y-485=\frac{-2}{25}(x-3000)\\y=-\frac{2}{25}x+725[/tex]
a)So, Demand equation : [tex]y=-\frac{2}{25}x+725[/tex]
Now to find supply equation
We have two points (0,350) and (2500,525)
[tex](x_1,y_1)=(0,350)\\(x_2,y_2)=(2500,525)\\y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\y-350=\frac{525-350}{2500-0}(x-0)\\y-350=\frac{7}{100}x\\y=\frac{7}{100}x+350[/tex]
b) So, Supply equation : [tex]y=\frac{7}{100}x+350[/tex]
Now to find equilibrium quantity and price equate demand and supply equation
[tex]-\frac{2}{25}x+725=\frac{7}{100}x+350\\725-350=\frac{7}{100}x+\frac{2}{25}x\\x=2500[/tex]
So, equilibrium quantity = 2500
To find equilibrium price substitute equilibrium quantity in any equation
[tex]y=\frac{7}{100}x+350\\y=\frac{7}{100}(2500)+350\\y=525[/tex]
C) The equilibrium quantity and the equilibrium price are 2500 and $ 525 respectively
Write a percent between 25% and 50%.
Then write it as a decimal and as a fraction in simplest form.
Percent - 24%
Decimal - 0.24
Fraction - 24/100=6/25
8+a=21 plssssssssssssszzzz
Answer:
13
Step-by-step explanation:
because a is the missing number. Well, 21 minus or - 8 is equal to 13.
solve by factoring
k2 +6k =16
Answer:
k=2 k=-8
Step-by-step explanation:
what place value is the 9 out of 874.15239
Answer:
100 thousandths
Step-by-step explanation:
Hope this helps:)
The Andersons rented 5 rectangular tables for $35 and 30 chairs for $60. Which quotients can be used to calculate the unit cost for tables and the unit cost for chairs? Check all that apply.
StartFraction 5 Over 35 EndFraction
StartFraction 35 Over 5 EndFraction
StartFraction 60 Over 30 EndFraction
StartFraction 30 Over 60 EndFraction
Answer:
35/5 and 60/30
Step-by-step explaning
i got it right on enginuity
Answer:
35/5 and 60/30
Whats the product of 6/9 and 3/8 in simplest form
If 8 tennis balls cost $24, how much do 12 tennis balls cost?
Answer:
36
Step-by-step explanation:
half of 8 is 4 so half of 24 is 12 and 12 plus 24 is 36
Answer:
$36
Step-by-step explanation:
First divide the $24 to find how much each tennis ball costs.
24 / 8 = 3
Then multiply 3 (the cost per tennis ball) by 12 (the amount of tennis balls)
3 x 12 = 36
36 is your answer
PQ=2x+1 and QR=5x-44; Find PR
Answer:
x=15
Step-by-step explanation:
subtract 1 from both sides so you are left with 2x=5x-45
then subtract 5x from both sides and you have -3x=-45
then finally divide -3 from -45 to get x=15
I have a picture I really need help with math please someone
Step-by-step explanation:
6 goes in ones or the green
3 goes in tenths or the yellow
2 goes in hundreths or the purple
4 goes in thousands or the orange
Answer: 6 goes in the ones then the 3 goes tenths 2 in hundredths and 4 in the thousands
eight hundredths six tens three ones decimal one tenths four hundredths one thousand
Step-by-step explanation:
I need some help with this question.
Answer:
it is stq utv
Step-by-step explanation:
Answer:
its top right option
Step-by-step explanation:
Evaluate using the order of operation, please help me
Answer:
[tex]\frac{7}{9}[/tex]Step-by-step explanation:
[tex]1-\frac{4}{2\cdot \:7+4}\\\\\frac{4}{2\cdot \:7+4} = \frac{2}{9} \\\\=1-\frac{2}{9}\\\\\mathrm{Convert\:element\:to\:fraction}:\quad \:1=\frac{1\cdot\:9}{9}\\\\=\frac{1\cdot \:9}{9}-\frac{2}{9}\\\\Since\:the\:denominators\:are\:equal,\\\:combine\:the\:fractions}:\\\\\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\\\=\frac{1\cdot \:9-2}{9}\\\\1\cdot \:9-2 =7\\\\=\frac{7}{9}[/tex]
what s 1 times 1 is it 2?
Answer:
1 x 1 = 1
Step-by-step explanation:
Anything that is multiplied by 1, is going to stay the same
Example would be 1 x 5
that would equal 5
Hope this helped<3
Answer:
it is one, no matter what
Step-by-step explanation: if u take on and make it bigger (multiply it) one time, u still only get one!!
Brainliest please!! Have a great day!!
If you draw a tree to show the number of ways to spin a spinner with five regions twice, how many possibilitdies would there be? There would be possibilities.
There are 5 spaces and 2 slots, so there are 5*5 = 25 different outcomes.
Think of a table that has 5 rows and 5 columns. There would be 25 cells in this table. Each cell is a different outcome.
The probability tree would have 5 branches on the upper level. Then for each upper branch, there are 5 lower sub-branches. Add up all the possible paths and you should find 25 total paths (each path representing a different outcome).
(2x + 3) (x² + x - 2)
Answer:
(2x + 3) • (x + 2) • (x - 1)
Step-by-step explanation:
7th grade math help me plzzz
Answer:
a. -10 + 8
b. -20 +10
c. -20 + 20
d. -20 +5
Step-by-step explanation:
can u give me brainliest please?? :>
Simplify (3p^2)5
Please i need the answer asap
Answer:
15p^2. Hope this helps
Step-by-step explanation:
Write the sentence as an inequality. A number n plus 7 is less than or equal to 9.
Answer:
[tex] n + 7 \le 9 [/tex]
Step-by-step explanation:
[tex] n + 7 \le 9 [/tex]
Graph two lines whose solution is (1,4)
Answer:
(1,4) and (0,-1)
Plzzzzzz help right answer gets brainly
Write an
equivalent unit rate
to selling 15
cookies in 1/8 of an
hour.
Answer:
y=1/8x + 15
Step-by-step explanation:
y=1/8x+15 because 1/8 hours and add 15
Find the equation of the line shown
Answer:
-4 times, multiply, divide, subtract or add by 1
-4 is on the x line and (x) comes first in the equation. so x + y. Or whatever way your finding the answer.
Please need help thank you
Answer:
People drank 75 cups, First find the amount of juice that Mrs. Jackson bought .Then subtract the 3 cups of juice that were left over
5 x 16=80
80-3= 77
Determine by inspection whether the vectors are linearly independent. Justify your answer. [ 8 [ 12 -6 -9 4] 6]A. The set of vectors is linearly independent because nothing times the first vector is equal to the second vector. (Type an integer or a simplified fraction.) B. The set of vectors is linearly dependent because nothing times the first vector is equal to the third vector. (Type an integer or a simplified fraction.) C. The set of vectors is linearly dependent because one of the vectors is the zero vector. D. The set of vectors is linearly independent because none of the vectors are multiples of the other vectors.
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Option C is correct, the set of vectors is linearly dependent because one of the vectors is the zero vector.
What is Matrix?A matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns.
To determine if the set of vectors is linearly independent, we need to check if any of the vectors can be expressed as a linear combination of the others.
Let's consider the first vector [8 -6 4].
If we try to express this vector as a linear combination of the other vectors, we get:
[8 -6 4] = a[12 -9 6] + b[0 0 0]
where a and b are constants.
We can immediately see that this equation has infinite solutions, because the third component of the second vector is zero, which means we can choose any value for b and still satisfy the equation.
Therefore, the set of vectors is linearly dependent.
Hence, Option C is correct, the set of vectors is linearly dependent because one of the vectors is the zero vector.
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Determine by inspection whether the vectors are linearly independent. Justify your answer.
[8 -6 4][12 -9 6]
A. The set of vectors is linearly independent because nothing times the first vector is equal to the second vector. (Type an integer or a simplified fraction.)
B. The set of vectors is linearly dependent because nothing times the first vector is equal to the third vector. (Type an integer or a simplified fraction.)
C. The set of vectors is linearly dependent because one of the vectors is the zero vector.
D. The set of vectors is linearly independent because none of the vectors are multiples of the other vectors.
Work out an equation of the straight line with gradient 3 that passes through the point with coordinates (2, 4).
Answer:
The answer is
[tex] \huge \boxed{y = 3x - 10}[/tex]
Step-by-step explanation:
To find an equation of a line given the slope and a point we use the formula
[tex]y - y_1 = m(x - x_1)[/tex]
where
m is the slope
( x1 , y1) is the point
From the question the point is (2, 4) and the slope is 3
The equation of the line is
[tex]y - 4 = 3(x - 2) \\ y + 4 = 3x - 6 \\ y = 3x - 6 - 4[/tex]
We have the final answer as
[tex]y = 3x - 10[/tex]
Hope this helps you
HELP GIVING BRAINLIEST AND A BUNCH OF POINTS
Answer:
my name is keff 4
Step-by-step explanation:
The line shown represents the amount of money left on a gift card, y, after Mina buys lattes. After buying 2 lattes, she has $2 left. What is an equation of the line in point- slope form?
Answer:
[tex] y - 2 = -3(x - 2) [/tex]
Step-by-step explanation:
Given that after she buys 2 lattes, she has $2 left, this represents a point on the line in the graph, which is (2, 2).
Point-slope form of equation for a line is given as [tex] y - b = m(x - a) [/tex]. Where,
(a, b) = a point on the line
m = slope
The equation of the line in point-slope form is given by the formula, [tex] y - b = m(x - a) [/tex], where,
(a, b) = coordinates of a point on the line.
[tex] m = slope = \frac{y_2 - y_1}{x_2 - x_1} [/tex]
We already have values for (a, b) = (2, 2), let's find the slope (m).
Using (2, 2) and any point on the line, such as (0, 8), we can find the slope as follows:
[tex] m = slope = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8 - 2}{0 - 2} [/tex]
[tex] = \frac{6}{-2} [/tex]
[tex] m = -3 [/tex]
Now we know that a = 2, b = 2 , and m = -3. Let's plug in this values into the point-slope equation as shown below:
[tex] y - b = m(x - a) [/tex]
[tex] y - 2 = -3(x - 2) [/tex]