Consecutive even integers are -8, -6 and -4
Step-by-step explanation:
Let be the first even integer then the next two integers will be: x+2 and x+6
According to given property, we get
[tex]x - 2(x+2) = (x+4)+8\\x-2x-4 = x+4+8\\-x-4 = x+12\\-x-x = 12+4\\-2x = 16[/tex]
Dividing both sides by -2
[tex]\frac{-2x}{-2} = \frac{16}{-2}\\x = -8[/tex]
The two next integers are:
x+2 = -8+2 = -6
x+4 = -8+4 = -4
Verification:
[tex]-8-2(-6) = -4+8\\-8+12 = +4\\4 = 4[/tex]
Hence, Consecutive even integers are -8, -6 and -4
Keywords: Linear equation, Variables
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Which of the following is the correct representation of the polynomial
F(x) = x4 - 2x3 + 2x - 1 as a product of linear factors?
A. F(x) = (x+1)(x - 1)(x - 1)(x+1)
B. F(x) = (x - 1)(x - 1)(x - 1)(x + 1)
C. F(x) = (x-1)(x-1)(x - 1)(x - 1)
D. F(x) = (x + 1)(x + 1)(x+1)(x + 1)
Answer:
Your answer is B: F(x)=(x-1)(x-1)(x-1)(x+1)
What is X +7 equals 14
Answer:
x = 7
Step-by-step explanation:
x + 7 = 14
Subtract 7 from both sides
x = 14 - 7 = 7
Answer: the answer is 7
Step-by-step explanation:
Write an equation In slope intercept form for the line that is parallel to the given line and that passes through the given point
5x - 2y=10 (3 -5)
The equation of the parallel line in slope-intercept form is;
y = [tex]\frac{5}{2}[/tex] x - [tex]\frac{25}{2}[/tex]
Step-by-step explanation:
Let us revise some facts about parallel lines
The equations of two parallel lines have:
Same slopesDifferent y-interceptThe slope-intercept form of the equation of a line is y = m x + b, where m is the slope of the line and b is the y-intercept
The given line has equation 5x - 2y = 10
Put it in the form of y = m x + b to find its slope
∵ 5x - 2y = 10
- Subtract 5x from both sides
∴ -2y = 10 - 5x
- Divide to sides by -2
∴ y = -5 + [tex]\frac{5}{2}[/tex] x
∴ y = [tex]\frac{5}{2}[/tex] x - 5
- The value of m is the coefficient of x
∴ m = [tex]\frac{5}{2}[/tex]
∴ The slope of the given line is [tex]\frac{5}{2}[/tex]
∵ Parallel lines have same slopes
∴ The slope of the parallel line is m = [tex]\frac{5}{2}[/tex]
- Substitute the value of m in the form of the equation
∴ The equation of the parallel line is y = [tex]\frac{5}{2}[/tex] x + b
To find b substitute x and y in the equation by the coordinates of any point lies on the line
∵ The parallel line passes through point (3 , -5)
- Substitute x and y by the coordinates of the point (3 , -5)
∵ x = 3 and y = -5
∴ -5 = [tex]\frac{5}{2}[/tex] (3) + b
∴ -5 = [tex]\frac{15}{2}[/tex] + b
- Subtract [tex]\frac{15}{2}[/tex] from both sides
∴ b = [tex]\frac{-25}{2}[/tex]
∴ The equation of the parallel line is y = [tex]\frac{5}{2}[/tex] x + [tex]\frac{-25}{2}[/tex]
∴ The equation of the parallel line is y = [tex]\frac{5}{2}[/tex] x - [tex]\frac{25}{2}[/tex]
The equation of the parallel line in slope-intercept form is;
y = [tex]\frac{5}{2}[/tex] x - [tex]\frac{25}{2}[/tex]
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F(x)=x^2-8x+12 find the roots by graphing
Answer:
x² - 8x + 12 = 0
(x - 6)(x - 2) = 0
x = 2, 6
f(4) = -4
Plot (0, 12), (2, 0), (4, -4), (6, 0), and (8, 12) on the graph. Then draw a smooth curve that goes through these points.
Help answer this question
Answer:
a = 108° and b = 144°
Step-by-step explanation:
The opposite angles of a rhombus are the same and the sum of all the angles of the rhombus is 360°.
So, from the given diagram of the rhombus we can write
2b + 2× 36 = 360
⇒ 2b = 360 - 72 = 288
⇒ b = 144° (Answer)
Again, the each angles of a pentagon is given to be a.
Hence, we can write 3a + 36 = 360
⇒ 3a = 324
⇒ a = 108° (Answer)
Solve for y. Then find the values of y that correspond
to the given values of x for the linear function.
y + 8x = -2 for x = 0, 1, 2
Write an equation in point slope form line passing through (-4,3), (3,-4)
SHOW WORK
Answer:
[tex]\large\boxed{y-3=-(x+4)}\\or\\\boxed{y+4=-(x-3)}[/tex]
Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - point on a line
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have two points (-4, 3) and (3, -4).
Substitute:
[tex]m=\dfrac{-4-3}{3-(-4)}=\dfrac{-7}{7}=-1[/tex]
Put the value of a slope and the coordiantes of the point (-4, 3) or (3, -4) to the equation of a line:
for (-4, 3)
[tex]y-3=-1(x-(-4))\\\\y-3=-(x+4)[/tex]
for (3, -4)
[tex]y-(-4)=-1(x-3)\\\\y+4=-(x-3)[/tex]
The number of games in the first round of a chess tournament is equal to 2×2×2×2×2×2. Write the number of games using an exponent.
Answer:
2^6
Step-by-step explanation:
2 is being multiplied 6 times meaning it would be 2 to the 6th power.
Multiply. Type your answer in the box. Do not use any spaces.
(–27) x (+8) =
Answer:
-216
Step-by-step explanation:
Negative times positive is negative.
27 * 8 = 216
Answer is negative, so
-27 * 8 = -216
Answer:
-216
Step-by-step explanation:
Write the problem as a mathematical expression. ( − 27 ) ⋅ ( 8 )
multiply -27 by 8
The number 123,456 is divisible by...
Answer:
2
Step-by-step explanation:
Because the # ends in a even number, it can be divisible by 2
Which expression is equal to 4^5x 4^-7 divided by 4^-2
Answer:
4^5x-5
Step-by-step explanation:
4^5x-7/4^-2
=4^5x-5
The expression 4⁵ × 4⁻⁷ divided by 4⁻² simplifies to 1 by using the properties of exponents. First, add the exponents in the numerator, then subtract the exponents for division, resulting in 4⁰, which equals 1.
We need to simplify the expression:
4⁵ times 4⁻₇ ext{ divided by } 4⁻²
To simplify, let's first combine the powers of 4 in the numerator:
Using the property that when multiplying like bases, we add the exponents:= 4⁵ times 4⁻⁷
= 4⁽⁵⁺⁽⁻⁷⁾⁾
= 4⁻²
Next, address the division with a like base, which subtracts the exponents:= 4⁻² ext{ divided by } 4⁻²
= 4⁽⁻²⁻⁽⁻²⁾⁾
= 4⁽⁻²⁺²⁾
= 4⁰
Any number raised to the power of 0 is 1:4⁰ = 1
Therefore, the given expression simplifies to 1.
1. Solve for x.
x + 11 = 3
-11
-11
x=- 8
2. Solve for x.
x + 5 = 11
25-5
*=6)
3. Solve for z.
2-33 = 40
+33 +33
(2
=
–
7
4. Solve for x.
- 8x = 56
Answer:
for #4 x=-7
Step-by-step explanation:
a negative times a negative is a positive and 8 times 7 = 56
Find the points at which the graph of the equation -4y=15-5x crossed the x- axis and the y - axis.
Answer:
see explanation
Step-by-step explanation:
Where the graph crosses the x- axis the y- coordinate is zero.
Let y = 0 in the equation and solve for x
- 4(0) = 15 - 5x, that is
15 - 5x = 0 ( subtract 15 from both sides )
- 5x = - 15 ( divide both sides by - 5 )
x = 3 ← x- intercept ⇒ (3, 0 )
Where the graph crosses the y- axis the x- coordinate is zero.
Let x = 0 in the equation and solve for y
- 4y = 15 - 5(0), that is
- 4y = 15 ( divide both sides by - 4 )
y = - [tex]\frac{15}{4}[/tex] ← y- intercept ⇒ (0, - [tex]\frac{15}{4}[/tex])
The number of students who attended the winter school dance was 20% less than the number of students attending the following if 220 students attend the Fall dance how many fewer students attended the winter day
Answer:
44
Step-by-step explanation:
20 percent less than 220
Answer:
The answer to this question is S=44
Step-by-step explanation:
How old will Bill be in 10 years if he is x + 2 years old now? Which expression represents this? (x + 2) + 10 10(x + 2) (x + 2) - 10
Answer: 10(x+2)
Step-by-step explanation:
Answer:
(x+2) + 10
Step-by-step explanation:
(x+2) is his current age, then you add the 10 years to get your answer.
What is the surface area of a cone that has a radius of 8 feet and a slant height of 12 feet? (Use 3.14 for π.)
301.44 ft 2
502.4 ft 2
200.96 ft 2
803.84 ft 2
Answer:
[tex]SA=502.4\ ft^2[/tex]
Step-by-step explanation:
we know that
The surface area of a cone is equal to
[tex]SA=\pi r^{2}+\pi rl[/tex]
we have
[tex]r=8\ ft\\l=12\ ft\\\pi=3.14[/tex]
substitute the given values
[tex]SA=(3.14)(8^{2})+(3.14)(8)(12)[/tex]
[tex]SA=200.96+301.44=502.4\ ft^2[/tex]
To solve for y in the equation 2 x + y = 5, subtract 2 from both sides of the equation.
True False
Answer:
False.
Step-by-step explanation:
Because we have to isolate y and subtracting 2 will not put y alone on one side.
We have to subtract 2x in order to solve for y.
Answer:
False
Step-by-step explanation:
To solve this equation 2x + y = 5, you need another pair equation with the same variables, or one of the variables (x or y) need to be known to solve this equation.
Or you need to subtract 2x from both side to make y subject of formula.
what is 3² in xpoient
Answer:
9
Step-by-step explanation:
It saying 3 times to the power of 2
or
3 squared
so basically it's saying
3^3=9
The population of Collin County, which follows the exponential growth model, increased from 491,675 in 2000 to 782,341 in 2010. Find the exponential growth rate, k.
Answer:
p=ak^t
p1=491272*k^0
p2=782341*k^10
782341/491272 = k^10
k=1.047629
growth rate is 4.7629%
2012: predicted population is 491272*1.047629^12=858,642 people
1245863=491272*1.047629^t
1.047629^k=2.5363599
ln both sides is k ln 1.0476=ln 2.5363
t=20.000 years.
Rule of 72 would say 72/4.76 or 15.12 years for doubling
14.90 years
2017 predicted is 491272*1.0476^17 or 1083552, or more than actual, so the rate of growth is slowing down.
The required exponential growth rate, k is 4.7629%
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
The exponential function will be as
p=a[tex]k^t[/tex]
p₁=491272*k⁰
p₂=782341*k¹⁰
782341/491272 = k¹⁰
k = 1.047629
So, the growth rate is 4.7629%
2012: the predicted population is 491272 × 1.047629¹² =858,642 people
1245863=491272 × [tex]1.047629^t[/tex]
[tex]1.047629^k[/tex] = 2.5363599
ln both sides is k ln 1.0476 = ln 2.5363
t = 20.000 years.
Rule of 72 would say 72/4.76 or 15.12 years for doubling
14.90 years
2017 predicted is 491272 × 1.0476¹⁷ or 1083552, or greater than the real rate of increase, hence the rate of growth is decreasing.
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A company plans on selling MP3 players for $120. To make the MP3 players, a cost estimator determined it costs the company $1500 per week for overhead and $45 for each MP3 player made. How much profit would the company make if it sold 100 players in one week? Explain.
Answer:
6000
Step-by-step explanation:
Each mp3 sells at $120 per mp3 player multiply that by 100 its $12000
It cost them $45 per mp3 to be made multiply that by 100 its $4500 then add the $1500 for the week and its $6000
$12000-$6000=$6000
They make a profit of $6000 in a week
The company would make a profit of $6,000 from selling 100 MP3 players in one week after subtracting the total costs of $6,000 from a total revenue of $12,000.
The company's profit when selling 100 MP3 players in one week can be calculated by subtracting the total costs from the total revenue. First, we calculate the total revenue by multiplying the selling price of $120 per MP3 player by the number of players sold, which is 100. This results in a total revenue of $12,000 (120 x 100).
Next, we calculate the total costs, which include a fixed overhead of $1,500 per week and a variable cost of $45 per MP3 player. For 100 players, the variable cost sums up to $4,500 (45 x 100). Therefore, the total costs amount to $6,000 ($1,500 + $4,500).
To find the profit, we subtract the total costs from the total revenue:
Total Revenue = 100 x $120 = $12,000
Total Costs = $1,500 (fixed) + 100 x $45 (variable) = $6,000
Profit = Total Revenue - Total Costs = $12,000 - $6,000 = $6,000
Therefore, the company would make a profit of $6,000 if it sold 100 MP3 players in one week.
On five different tests Jake got: 75, 80, 81, 96, and 100. Would the mean of these numbers be greater than the median of these numbers?
Answer:
Yes the mean is greater than the median
Step-by-step explanation:
To find the mean of numbers, you add all of them and divide them by how many there are in total.
75+80+81+96+100= 432
There are five numbers so divide the total by 5.
432÷5= 86.4
That is your mean.
The median is the one in the middle. There are five numbers, so the one in the middle is 81.
The mean is 86.4 and the median is 81.
Answer:
the mean is greater
Step-by-step explanation:
well mean is average so lets do that first
to find the mean, you add all of the percentages up and divide it by the amount of percentage
75 + 80 + 81 + 96 + 100 = 155 + 177 + 100 = 432
and now you divide 432 by 5 to get 86.4
so the mean is 86.4
and the median is the middle:
75 80 81 96 100
↑
81 is the median since its in the middle
86.4 > 81
so the mean is greater than the median
The table shows the cost,c, of buying each number of boxes,b,of cookies. Write an equation that models this situation.
A. b=3c
B. c=3b
C. b=8c
D. c=8b
Answer:
B
Step-by-step explanation:
Each box of cookies is $3 since 4 x 3 =12, 6 x 3 = 18, and 9 x 3 = 27. So we want to multiply the number of boxes, b, by 3 to get the cost, c. The correct equation is c = 3b.
An equation that models this situation is c = 3b. The correct option is B.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given the data is,
b c
4 12
6 16
9 27
c = kb
12 = k x 4
k = 12 / 4 = 3
c = 3b
Therefore, the equation that models this situation is c = 3b. The correct option is B.
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5. Which statement is NOT true?
If x = 1, then x2 = 1.
If x2 = 1, then x = 1.
If x= -1, then x2 = 1.
x2 = 1 if and only if x = 1 or x = -1.
Answer:
[tex]x^{2} =1, then\ x=1[/tex] is NOT true.
Step-by-step explanation:
1.
[tex]If\ x=1, then\ x^{2} =1[/tex] ......True
( 1 )² = 1
2.
If [tex]x^{2} =1, then\ x=1[/tex] ........ NOT True
∴ x =± 1 .........this is correct
3.
[tex]If\ x=-1, then\ x^{2} =1[/tex] ......True
( -1 )² = 1
4.
x2 = 1 if and only if x = 1 or x = -1. .........True
( 1 )² = 1
( -1 )² = 1
simplify
(6 + 3i)(6 − 3i)
Answer:
45
Step-by-step explanation:
(6 + 3i)(6 − 3i) =6 (6 − 3i)+ 3i(6 − 3i)
= 36 -18i +18i-9[tex]i^{2}[/tex]
if [tex]i^{2} =-1[/tex]
36 -18i +18i-9[tex]i^{2}[/tex] = 36-9(-1)
=36+9
=45
=36-9i^2
=6^2 - (3i)^2
Answer:
[tex]\displaystyle 45[/tex]
Step-by-step explanation:
[tex]\displaystyle (6 + 3i)(6 - 3i) = 36 - 9i^2 = 36 - 9[-1] = 36 + 9 = 45[/tex]
Extended Information on the Complex Number System
[tex]\displaystyle \sqrt{-1} = i \\ -1 = i^2 \\ -i = i^3 \\ 1 = 4\:[Any\:multiple\:of\:four][/tex]
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4. During the morning commute
96 cars and 24 trucks passed
through the intersection. What is
the ratio of cars to trucks?
Answer:
Step-by-step explanation:
96:24
96 divide by 24 = 4
so it would be 4 cars to 1 truck
so 4:1
Answer:
4:1 Explanation: because of how when you divide the two its 4 and there's one truck left
the sum of two numbers is 19 and there difference is 7 what are the two numbers
Answer:14 and 5
Step-by-step explanation:
which numbers the additive inverse of -41/4
Answer:
The answer is 41/4.
Step-by-step explanation:
Given:
-41/4 to get the additive inverse.
Now, the additive inverse of any number is a number that, when added to the number the result is zero.
Here, 41/4 is the additive inverse.
Because when it is added to -41/4 the result is 0.
Therefore, the answer is 41/4.
You take out $50,000 for loans during your college career. You must pay it back with 7% APR for 20 years, making monthly payments. Calculate the minimum monthly payment needed to do this.
Answer:
The monthly payment for the loan amount for 20 years is $806.167
Step-by-step explanation:
The principal loan amount= $ 50,000
The rate of interest = 7 %
the time period of loan = 20 years = 20 × 12 = 240 months
let the amount after 20 years = $ A
From Compounded method
Amount = Principal × [tex](1+\dfrac{\textrm rate}{100})^{\textrm Time}[/tex]
or, A = 50,000 × [tex](1+\dfrac{\textrm 7}{100})^{\textrm 20}[/tex]
or, A = 50,000 × [tex](1.07)^{20}[/tex]
Or, A = 50,000 × 3.8696
∴ Amount = $ 193,480
So, The amount after 20 years = $ 193,480
The monthly payment amount = $ [tex]\frac{193480}{240}[/tex] = $ 806.167
Hence The monthly payment for the loan amount for 20 years is $806.167 Answer
unit rate for 8:12 “$8 for 12 cans of pasta sauce”
Ratio:
Unit rate:
Answer:
1.5
Step-by-step explanation:
12 divided by 8 = 1.5
1.5 x 8 = 12
The sine ratio of an angle is the opposite side over the adjacent side.
always
never
sometimes
Answer:
never
Step-by-step explanation:
In a right triangle, every angle has an opposite side and an adjacent side. And there's always a hypotenuse.
The sine of an angle is the ratio of the length of the opposite side divided by the length of the hypotenuse.
The tangent ratio of an angle is the opposite side over adjacent side, it is not the sine ratio of a triangle.
For example, ABC is a right angled triangle having length of the sides are a,b,c.
So
[tex]sine\ C=\frac{a}{c}[/tex]
The sine ratio of an angle sometimes is the opposite side over the adjacent side.
The question pertains to the definition of the sine ratio in trigonometry. The sine ratio of an angle is not defined as the opposite side over the adjacent side; rather, it is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse of a right-angled triangle.
Therefore, the correct statement is the sine ratio of an angle sometimes is the opposite side over the adjacent side, specifically in the case of a 45°-45°-90° triangle where the sides are equal, but this is not generally true for all angles in trigonometry.