Answer:
(x - 1)(3x + 2)
Step-by-step explanation:
By the Remainder theorem
Given expression is divisible by x - 1 then f(1) = 0
when divided by (x + 1) then f(- 1) = 2
when divided by x - 2 then f(2) = 8
Substitute x = 1, x = - 1, x = 2 into the expression , that is
a + b + c = 0 → (1)
a - b + c = 2 → (2)
4a + 2b + c = 8 → (3)
Subtract (1) from (2) to eliminate a and c
- 2b = 2 ( divide both sides by - 2 )
b = - 1
Subtract (1) from (3) to eliminate c
3a + b = 8 ← substitute b = - 1
3a - 1 = 8 ( add 1 to both sides )
3a = 9 ( divide both sides by 3 )
a = 3
Substitute a = 3, b = - 1 into (1) and evaluate for c
3 - 1 + c = 0
2 + c = 0 ( subtract 2 from both sides )
c = - 2
Then a = 3, b = - 1, c = - 2
Thus
ax² + bx + c
= 3x² - x - 2
= (x - 1)(3x + 2) ← in factored form
A soccer tournament was designed with 512 teams where an eighth of the teams were eliminated after each round. Write a function, f(x), that models the number of teams still in the number of teams still in the tournament after x rounds have been played.
Answer:
f
Step-by-step explanation:
fsdsdsdwdd
The sum of two numbers is 58. The difference between the same two numbers is 6. Find the two
numbers, and then find the PRODUCT of the two numbers.
The product of the two numbers is 32
The product of the two numbers is 58
The product of the two numbers is 832
The product of the two numbers is 64
Answer:
The product of the two numbers is 832
Step-by-step explanation:
x+y= 58
x-y=6
2x = 64
x = 32
y = 26
32*26=832
How do I complete the square for 4x^2+ 8x-5= 0?
Answer:
man I have no idea dude I don't really know squares if you're talking about square root I really don't know
Answer:
x = [tex]\frac{1}{2}[/tex], - [tex]\frac{5}{2}[/tex]
Step-by-step explanation:
This is not so fun!
[tex]4x^{2} + 8x - 5 = 0\\[/tex]
Step 1: Move the 5 to the right side
[tex]4x^{2} +8x = 5[/tex]
Step 2: Divide thru by 4
[tex]x^{2} + 2x = \frac{5}{4}[/tex]
Step 3: Divide 2 (from 2x) by 2 and square the result and add that to both sides of the equation.
2/2 = 1 1 squared = 1
[tex]x^{2} + 2x + 1 = \frac{5}{4} +1 = \frac{9}{4}[/tex]
Step 4: Factor the left side
[tex](x + 1)^{2} = \frac{9}{4}[/tex]
Step 5: Take the square root of both sides
x + 1 = ±[tex]\sqrt{\frac{9}{4} }[/tex] = ± [tex]\frac{3}{2}[/tex]
Step 6: Move the 1 to the right side and add the results
x = -1 ± [tex]\frac{3}{2}[/tex] = -1 + [tex]\frac{3}{2}[/tex] or -1 - [tex]\frac{3}{2}[/tex]
= [tex]\frac{1}{2}[/tex] or - [tex]\frac{5}{2}[/tex]
And bingo, you have the solutions by completing the square. Lot of fun, huh.
The number 160 is increased by 50%. The result is then decreased by 25%. What is the final number?
The final number is what?
Answer:
60
Step-by-step explanation:
50%=.50
160×.50=80
160+80=240
25%=.25
240×.25=60
60 is the final number
Is 18/5 and 7/2 proportional
Answer:
no its not
Step-by-step explanation:
Put the following equation of a line into slope-intercept form, simplifying all fractions. 3y - 40 = 9
Answer:
3y=49
Step-by-step explanation:
yeppp I'm pretty sure
5. help me i’ll give you brainliest if u get this right
Answer: D.) 2
Step-by-step explanation:
In a rhombus, all sides are congruent; they have the same lengths (like a square). This means that if this parallelogram was a rhombus, 14 - x and 2x + 8 will have to be equal.
14 - x = 2x + 8
Subtract 2x from both sides
14 - 3x = 8
Subtract 14 from both sides
-3x = -6
Divide both sides by -3
x = 2
What is the solution of the system of equations shown in the graph below?
Answer:
The point on the plane (4, 2)
That is x = 4 and y = 2
Step-by-step explanation:
Look for the point where the two lines given by the system of linear equations intersect. That point is (4, 2)
x = 4 and y = 2
bag contains 150 jelly beans. Toros reached into the bag 20 times and randomly selected one jelly bean. Each time, he recorded the color of the jelly bean, placed it back in the bag, and then mixed the jelly beans.
The following table represents the number of times Toros chose each color of jelly bean.
Based on these results, what is the probability that the next jelly bean Toros draws out of the bag will be yellow?
5.3 lesson 14 problem set answer
the table shows running speeds of 10 randomly selected lions.
speed (miles per hour) 48, 45, 50, 44, 46, 45, 42, 47, 45, 48. based on the data
select the most reasonable prediction about the speed of the lion
A. the top speed of a lion is 48 miles per hour.
B. the typical lion runs at a speed of about 46 miles per hour.
C. the typical lion runs at a speed of about 40 miles per hour.
D. the typical lion runs at speeds greater than 50 miles per hour.
Answer:
I think B
Step-by-step explanation:
Find the average
Answer:
B
how i know: i took the test
When 0.5(20x – 50y + 36) – 0.25(–100x + 40y – 12) is simplified, what is the resulting expression?
10x-25y+18-25x+10y-3
-15x-15y+15
-10x+25y+18+25x-10y+3
35x-35y+21
Answer:
35x-35y+21
Step-by-step explanation:
You would have to combine the like terms together to get 35x-35y+21.
By applying algebra properties we notice that the algebraic expression 0.5 · (20 · x - 50 · y + 36) - 0.25 · (- 100 · x + 40 · y - 12) is equivalent to 35 · x - 35 · y + 21. (Correct choice: D) #SPJ5
How to simplify an algebraic expressionIn this question we must simplify an algebraic expression by applying the following list of properties:
Commutative propertyAssociative propertyModulative propertyDistributive propertyExistence of additive inverseExistence of multiplicative inverseNow we proceed to simplify the expression given in the statement:
0.5 · (20 · x - 50 · y + 36) - 0.25 · (- 100 · x + 40 · y - 12) Given
10 · x - 25 · y + 18 + 25 · x - 10 · y + 3 Distributive and associative properties/Definition of multiplication
35 · x - 35 · y + 21 Result
By applying algebra properties we notice that the algebraic expression 0.5 · (20 · x - 50 · y + 36) - 0.25 · (- 100 · x + 40 · y - 12) is equivalent to 35 · x - 35 · y + 21. (Correct choice: D) #SPJ5
To learn more on polynomials, we kindly invite to check this verified question: https://brainly.com/question/11536910 #SPJ5
Taryn buys 8 identical glasses. Her total is $48 before tax. How much did Taryn pay for each pair of glasses?
Answer:
$12 per pair of glass.
$6 per glass.
Step-by-step explanation:
48/8 = 6
A pair is 2, so I multiplied 6 by 2.
6 x 2 = 12
So, Taryn paired $12 per glass.
--
ANSWER: $12 per pair
EXPLANATION: $48 divided by 8 pairs of glasses equals $6 per glasses. So then you multiply 6 by 2 to get the amount per pair.
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Suppose $5,000 is divided into two bank accounts. One account pays 5% simple interest per year and the other pays 7% per year. If after one year there is a total of $310 in interest between the two accounts, $3,000 was invested at 5%
Answer:
What is the question?
Step-by-step explanation:
A long-distance delivery truck averages 8 miles per gallon when the truck is full. The
miles per gallon improves by 20% when the truck is empty. If the truck travels 160 miles
full to deliver its goods, and then travels back 160 miles empty, approximately how many
gallons will the truck use in all?
The gas used by truck is 36.66 mpg.
What is linear equation?When graphed, a linear equation always produces a straight line because it is an algebraic equation with each term having an exponent of 1. It is referred to as a "linear equation" for this reason.
One-variable linear equations and two-variable linear equations exist.
Given
A long-distance delivery truck averages 8 miles per gallon when the truck is full.
The miles per gallon improve by 20% when the truck is empty.
The distance delivery truck averages 8 miles per gallon when full, and the amount of gasoline used (g) is expressed in terms of the number of miles driven ([tex]m_{f}[/tex]).
When the truck is full, the amount of gasoline is shown as,
[tex]m_{f}[/tex] = d/8
given distance is 160 miles
[tex]m_{f}[/tex] = 160/8 = 20 mpg
Then,
The miles per gallon improve by 20% when the truck is empty.
The number of miles driven when empty is represented as,
[tex]m_{e}[/tex] = d/(8 + 1.6)
[tex]m_{e}[/tex] = d/9.6
[tex]m_{e}[/tex] = 160/9.6
[tex]m_{e}[/tex] = 16.66 mpg
total gasoline required = [tex]m_{e}[/tex] + [tex]m_{f}[/tex] = 20 + 16.66 = 36.66 mpg
Hence the total gas used is 36.66 mpg.
Learn more about linear equation;
https://brainly.com/question/29739212
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will mark brainlest if correct! pls help
Answer:
See below.
Step-by-step explanation:
[tex] y_2 = 4x^2 [/tex]
[tex] x = 1 [/tex]
[tex] y_2 = 4(1)^2 = 4 = a [/tex]
a = 4
[tex] y_3 = 4^x [/tex]
[tex] x = 1 [/tex]
[tex] y_3 = 4^1 = 4 = b [/tex]
b = 4
[tex] y_1 = 4x [/tex]
[tex] x = 2 [/tex]
[tex] y_1 = 4(2) = 8 = c [/tex]
c = 8
[tex] y_3 = 4^x [/tex]
[tex] x = 2 [/tex]
[tex] y_3 = 4^2 = 16 = d [/tex]
d = 16
[tex] y_1 = 4x [/tex]
[tex] x = 3 [/tex]
[tex] y_1 = 4(3) = 12 = e [/tex]
e = 12
[tex] y_2 = 4x^2 [/tex]
[tex] x = 3 [/tex]
[tex] y_2 = 4(3)^2 = 36 = f [/tex]
f = 36
[tex] y_3 = 4^x [/tex]
[tex] x = 3 [/tex]
[tex] y_3 = 4^3 = 64 = g [/tex]
g = 64
simplify 2 to the power of 4 times 2 to the power of 6
Answer:
1/4
Step-by-step explanation:
=2^4×2^-6
=2^-2
=1/4
Answer:
you add the exponents so youd do 4+6 which is 10. and then 2 to the power of 10 is 1024
A school store has 1200 pencils and sells 25 per day the manager reorders when the number of pencils in stock is 650
Answer:
He reorders after 22 days
Answer:
(1200÷25) ÷ans= days
Step-by-step explanation:
Determine the value of the variable that makes each equation true.
Answer:
-9
-11
-4
Step-by-step explanation:
100 points and a Brainliest
just answer this question
what is dabi real name off of my hero academia
Answer: Toya Todoroki
Step-by-step explanation:
Answer:
Touya Todoroki
Step-by-step explanation:
i used to watch the show
37=-3+5(x+6), Please provide explanation.
Answer:
x=2
Step-by-step explanation:
youd distribute the 5 first so the equation is now
37=-3+5x+30
then group the common terms (-3 and 30 in this case)
37=5x+27
now subtract 27 from both sides to start to isolate 5x
10=5x
divide by 5 to find x
2=x
hope i helped :)
The diameter of a circle is 5 cm. Find its area to the nearest tenth.
Please help I have 30 mins
Answer: 0.6 in 10 % ; 0.4 in 15 %
Step-by-step explanation:
1. (x*10%) + (y*15%)/ x+y=12%
2. x+y = 1 x= 1-y
(0.1x + 0.15y/ x+y= 12/100) * 100
(10x + 15y/x+y = 12)*(x+y)
10x+15y= 12x + 12y
-2x=-3y
2x = 3y 2(1 - y)= 3y
2-2y=3y 2= 5y
y= 0.4
x= 0.6
help me pleaseeeeeeeeeeeeeeeee
Step-by-step explanation:
-d=0.8-1.5
-d=-0.7
d=0.7
Answer:
d=0.7
Step-by-step explanation:
1.5=d+0.8
d=1.5-0.8
d=0.7
how many times does the divisor 4 divides into 324
Answer:
81 times
Step-by-step explanation:
4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4
Find the 92nd term of the arithmetic sequence -29, -22, -15, ...
Answer:
608
Step-by-step explanation:
The appropriate general formula here is a(n) = a(1) + (n -1)d, where d is the common difference. Here, d = +7. Thus:
a(92) = -29 + (92-1)(7) = 608
Lance is drawing a triangle. He draws one side that is 8 inches long and another side that is 5 inches
long. Which one of the following could be the third side?
Answer:
6 inches
Step-by-step explanation:
(8-5)>x>(5+8)
Which would be an estimate for 36,004 ÷ 853
Answer:
42.21
Step-by-step explanation:
Answer:
42.2086752638
Step-by-step explanation:
calculator
Q:
What is 9.687-3.699?
Answer:
5.988
Step-by-step explanation:
_9.687
3.699
=5.988
find the value of d.
1/2d - 5 -1/4d = 10