If a - b = -5 and ab = 0 then the value of the expression a³-b³ is -125.
In the question ,
it is given that ,
the value of a - b = -5 and ab = 0
we need to find the value of the expression (a³-b³) ,
we know the identity that a³-b³ = (a - b)(a² + b² + ab)
we first need the value of a² + b² .
given that a - b = -5
squaring both the sides , we get
(a - b)² = 25
a² + b² - 2ab = 25
given ab = 0, so a² + b² = 25
Substituting a² + b² = 25 in the identity a³-b³ = (a - b)(a² + b² + ab) ,
we get ,
a³-b³ = (-5)(25 + 0)
a³-b³ = -5 × 25
a³-b³ = -125
the answer is -125 .
Therefore , If a - b = -5 and ab=0 then the value of the expression a³-b³ is -125.
Learn more about Equations here
https://brainly.com/question/29365597
#SPJ9
A line goes through (-5,3), (1,1) and (7,-1)
Step-by-step explanation:
1. Draw x y plane
2. Identify where x = -5, 1, 7 on x plane
3. Identify where y = 3, 1, -1 on y plane
4. Mark the intersection point
5. Draw the line
What is the slope of the line that passes through the points (2, 3) and (0, 11)
Answer:
-4
Step-by-step explanation:
m= y2-y1/x2-x1
m= 11-3/0-2
m= 8/-2
m= -4
Answer: The slope is -4
Step-by-step explanation: The general formula for calculating the slope is [tex]\frac{y2-y1}{x2-x1}[/tex].
x1 = 2, y1 = 3, x2 = 0, y2 = 11
So we have [tex]\frac{11-3}{0-2}[/tex] = [tex]\frac{8}{-2}[/tex] = -4.
Today, the mountain that contains Mount Rushmore is approximately 5,675 feet high. The height of the mountain is 622.5 feet less than 1.1 times its height before construction began.
The equation to find the height of the mountain prior to construction, represented by the variable h, is
1.1h – 622.5 = 5,675
Solve an equation to find the height of the mountain prior to construction, represented by the variable h.
h =
feet
5761.4 feet is the height of the mountain prior to construction
How to solve an equation to find the height of the mountain?
Given: 1.1h – 622.5 = 5,675
This is an algebraic equation, we need to solve for h
1.1h – 622.5 = 5675
collect like terms:
1.1h = 5675 + 622.5
Add like terms:
1.1h = 6337.5
Divide both sides by 1.1:
h = 6337.5/1.1
h = 5761.4 feet
Therefore, the height of the mountain prior to construction is 5761.4 feet
Learn more about algebraic equations on:
https://brainly.com/question/4344214
#SPJ1
Determine the equation of the line that is parallel to the given line, through the given point
y = -5x + 1 ; (-2,3)
The equation of the line that is parallel to the given line, through the given point is y = -5x - 7
Given equation,
y = -5x + 1
Slope = m
= -5
For two lines to be parallel, slope is equal.
Therefore, m = -5 for another line.
Let the equation of the line be y = mx + c
This line passes through A(-2,3)
Therefore, 3 = -5(-2) + c
3 = 10 + c
c = 3 - 10
= -7
Hence, equation of line is y = -5x - 7.
To learn more about equation of the line here:
https://brainly.com/question/21511618
#SPJ1
Pls help due tomorrow!!!!!
Answer:
[tex]\left(m+2\right)\left(n^2+2n+m+1\right)[/tex]
Step-by-step explanation:
Hoooo boy.
This is a long one.
But let's do it!!!!
Apply exponent rule: [tex]\:a^{b+c}=a^ba^c[/tex]
what steps do data analysts take to ensure fairness when collecting data? select all that apply. 1 point clean the data provided use an inclusive sample population understand the social context include data self-reported by individuals
All the steps given are take to ensure fairness when collecting data.
What is data analysts?
A data analyst examines data to find significant customer insights and potential uses for the information. They also advise the company's management and other stakeholders of this information.
You need excellent quantitative and analytical skills to succeed as a data analyst.
To answer problems logically, you must be able to pay attention to detail. Additionally, you must be able to articulate your conclusions clearly to people who will base choices on them.
Therefore, all the steps given are take to ensure fairness when collecting data.
To know more about the data analyst, click on the link
https://brainly.com/question/28465669
#SPJ4
2 ft
2 ft
5 ft
4 ft
4 ft
2 ft
2 ft
Answer:
22ft
Step-by-step explanation:
2+2+5+4+4+2+2= 22
Alexander is working two summer jobs, babysitting and landscaping. He can work a maximum of 14 hours altogether between both jobs in a given week. Write an inequality that would represent the possible values for the number of hours babysitting, b, and the number of hours landscaping, ll, that Alexander can work in a given week.
The inequality that would represent the possible values for the number of hours babysitting and landscaping is b + l ≤ 14.
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal.
Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
In this case, Alexander can work a maximum of 14 hours altogether between both jobs in a given week. This will be illustrated as:
b + l ≤ 14
b = babysitting
l = landscaping
Learn more about inequalities on;
brainly.com/question/25275758
#SPJ1
19. Linej passes through point (2, 0)
and is perpendicular to the graph
of y=x-3. Line k is parallel to
line j and passes through point
(-1, 6). What is the equation in
slope-intercept form of line k?
The equation in slope-intercept form of line k is y = - x + 5.
What is the equation of the line?
A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept.
The equation of a line in slope- intercept form is
y = mx + c
where,
m is the slope and c the y- intercept.
We have,
y = x - 3
∴ It is in the slope intercept form.
with slope m = 1
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular} = -\frac{1}{m} = -\frac{1}{1} = -1[/tex] ,
The partial equation of line j is,
y = - x + c
By substituting (2, 0) into the partial equation we get, c
0 = - 2 + c
c = 0 + 2 = 2
∴ c = 2
The equation of line j is y = - x + 2.
Similarly,
The slopes of parallel lines are the same.
The partial equation of line k is,
∴ y = - x + c
By substituting (- 1, 6) into the partial equation we get, c
6 = 1 + c
c = 6 - 1 = 5
∴ c = 5
The equation of line k is y = - x + 5.
Therefore, the equation in slope-intercept form of line k is y = - x + 5.
To learn more about the equation of the line visit,
https://brainly.com/question/13763238
#SPJ1
how many soluitons does 3x - 13 = 7(x + 2) - 4(x - 7) have?
The equation, 3·x - 13 = 7·(x + 2) - 4·(x - 7), has no solution
What are the types of solutions of an equation?An equation can have no solution, infinitely many solutions or one solution
The equation is; 3·x - 13 = 7·(x + 2) - 4·(x - 7)
Expanding the left and right expressions of the equation, gives;
3·x - 13 = 7·x + 7×2 - 4·x + 4 × 7
Collecting like terms gives;
3·x - 13 = 7·x + 14 - 4·x + 28 = 7·x - 4·x + 14 + 28
3·x - 13 = 7·x - 4·x + 14 + 28 = 3·x + 42
3·x - 13 = 3·x + 42
3·x - 13 + 13 = 3·x + 42 + 13 = 3·x + 55
3·x + 0 = 3·x + 55
3·x = 3·x + 55
3·x - 3·x = 55
3·x - 3·x = 0 = 55 (No solution for x)
Therefore, the value of x in the equation, 3·x - 13 = 7·(x + 2) - 4·(x - 7) has no solution as the left and right expressions are not the same
Learn more about the types of solutions of an equation here:
https://brainly.com/question/21616442
#SPJ1
what is the remainder when P(x)=x3-x2-2x+8 is divided by (x+2)
The remainder when the polynomial P(x)=x3-x2-2x+8 is divided by (x+2) is 0
Remainder Theorem
From the definition of remainder theorem which stated that , if a polynomial f(x) is divided by a binomial (x−a), then the remainder is f(a)
Using the remainder theorem, P(x)=x3-x2-2x+8 is divided by (x+2).
binominal (x-a)
Step 1: We divide p(x) by (x + 2)
P(x)=x3-x2-2x+8 and X = -2
therefore, Remainder = p(-2)
Step 2: Substitute the value of the remainder into p(x)
P(-2) =[tex](-2)^{3}[/tex] -( [tex]-2^{2}[/tex] ) - 2([tex]-2[/tex]) + 8
P(-2) = -8 - 4 + 4 + 8
P(-2) = -12+12
P(-2) =0
Therefore, from the remainder theorem, the remainder when P(x) is divided by (x+2) is 0
Learn more about remainder theorem here: https://brainly.com/question/19030073
#SPJ1
someone please help me.
72/6 = 12
Write a situation for this equation and draw a picture that goes with it.
The picture for the condition is attached below.
What is factors of number?
A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor in mathematics. As an illustration, 3 and 6 are factors of 12 because 12 3 = 4 and 12 6 = 2, respectively. 1, 2, 4, and 12 are the other components that make up 12.
Let, the factors of 72 are
72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24 36, 72.
When we divide 72 by 6 we get 12.
⇒ [tex]\frac{72}{6} = 12[/tex]
To know more about the factors of a number, click on the link
https://brainly.com/question/25829061
#SPJ1
7. The basketball team is selling hats and gloves. They will earn $10 for every hat they sell and $8 for every pair of gloves. They want to sell a total of 40 items. Create two unique equations that model the number of hats, h, and the number of gloves, y, that the team is selling.
Answer:
5h+35y=390$
20h+20y=360$
Step-by-step explanation:
there are many answers possible.
The following are just examples:
5h+35y=390$
20h+20y=360$
What statement about the graph is true?
The true statement about the graph is
It is a function with the domain {-6 < x < 0} and the range {0 ≤ y ≤ 5}.
What is range?The range refers to all possible value in the out put of a graph.
The out put is the y coordinate and the possible values here is within the interval
0 ≤ y ≤ 5
What is domain?The domain refers to all possible value in the input of a graph.
The input is the x coordinate and the possible values here is within the interval
-6 ≤ x ≤ 0
Learn more about domain and range here:
https://brainly.com/question/29403658
#SPJ1
Write the linear equation in standard form. Do not use any spaces in your answer.
2 + (1/2)x = y
By writing both variables in the same side of the linear equation, we will get the standard form:
2y + (-1)*x = 4
How to write the linear equation in standard form?A linear equation between two variables x and y written in standard form is:
a*x + b*y = c
Where the coefficients a, b, and c, are all real numbers.
In this case, we have the linear equation:
2 + (1/2)*x = y
If we multiply both sides by 2, we get:
2*(2 + (1/2)*x) = 2*y
4 + x = 2y
Now we subtract x in both sides to get:
4 + x - x = 2y - x
4 = 2y - x
This is the linear equation in standard form:
2y + (-1)*x = 4
Learn more about linear equations:
https://brainly.com/question/4074386
#SPJ1
m(x) = -2/3x + 8; m(x) = 2
Answer:
Answer is x = 9
In a cookie recipe, 1 2/3 cups of milk makes 16 cookies. How many cups of milk are needed to make 24 cookies?
She uses 32 spacers, plus 7 beads per inch of necklace length. Where is x is the length in inches, of the necklace
If she uses 32 spacers, plus 7 beads per inch of necklace length. The equation to find how many beads Li has" will be,y=32+7x
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable. A linear equation has the form y = mx + b in the slope-intercept format
It is given that, for each necklace, she uses 32 spacers, plus 7 beads per inch of necklace length.
If x is the length in inches, of the necklace. The equation to find how many beads Li has" will be,
y=32+7x
Thus, if she uses 32 spacers, plus 7 beads per inch of necklace length. The equation to find how many beads Li has" will be,y=32+7x.
The question is incomplete. The complete question is"Li is making beaded necklaces. For each necklace, she uses 32 spacers, plus 7 beads per inch of necklace length. Where is x the length in inches, of the necklace? Write an equation to find how many beads Li has"
Learn more about the linear equation here:
brainly.com/question/11897796
#SPJ1
O is the center of the circle, if ∠OPQ = 25° & ∠ORQ = 20°, find ∠PQR and ∠POR
The values of ∠PQR = 45° and ∠POR = 90°.
The circumference of a circle is defined as its linear distance around it. In other words, if a circle is opened to form a straight line, the length of that line equals the circumference of the circle.
The radius of a circle is the distance between the circle's center and any point on its circumference. It is usually denoted by the letters 'R' or 'r'.
Given that
O is the center of the circle, if ∠OPQ = 25° &∠ORQ = 20°
We have to determine the values of ∠PQR and ∠POR
Sol. OP = OQ
⇒∠OQP = ∠OPQ = 25° [Radii of the same circle]
Similarly, ∠OQR = 20°
∠PQR = 25° + 20°
∠PQR = 45°
Furthermore ∠POR = 2 ∠PQR [the angle at the centre is twice the angle at the circumference].
⇒∠POR = 2 × 45°
∠POR = 90°.
Therefore the values of ∠PQR = 45° and ∠POR = 90°.
To learn more about circles visit
https://brainly.com/question/11213974
#SPJ1
Find the length x.
HELPPP PLSSSS
Answer: My answer is 4. You may want another answer.
Step-by-step explanation:
visual studying
solve polynomial equations by factoring
2x³ + 12x² = 0
The value of x is -6 or 0 which is obtained by solving the giving equation using factoring.
What exactly is a polynomial equation? Polynomial equations are those created using exponents, coefficients, and variables. The greater of its possible exponents is referred to as the equation's degree.How can a polynomial equation be solved?Write a polynomial equation in standard form before attempting to solve it. Factor it, then set each variable factor to zero after it has reached zero. Factoring cannot always be used to solve polynomial problems.The original equations' answers are the solutions to the derived equations.Given equation: 2x³ + 12x² = 0
Solving this equation by factoring as follows:
2x³ + 12x² = 0
= 2x²(x+6) = 0
So, x + 6 = 0 or 2x² = 0
x = -6 or x = 0
Therefore, the value of x is -6 or 0 which is obtained by solving the giving equation using factoring.
Learn more about polynomial equation here:
https://brainly.com/question/28947270
#SPJ1
The base of the parallelogram has a length
of 10 cm. What is the height?
10 cm
12cm
14cm
The height is either 10 cm,12 cm,14 cm.
Given:
The base of the parallelogram has a length of 10 cm.
Here area is not given so the height may be anything.
suppose h = 10
area = base * height
= 10 * 10
= 100 cm^2
if h = 12
area = 10 * 12
= 120 cm^2
if h = 14
area = 10 * 14
= 140 cm^2
Therefore the height is either 10 cm,12 cm,14 cm.
Learn more about the parallelogram here:
https://brainly.com/question/19187448
#SPJ1
A vending machine i deigned to dipene a mean of 7. 5 oz of coffee into an 8-oz cup. If the tandard deviation of the amount of coffee dipened i 0. 5 oz and the amount i normally ditributed, find the percent of time the machine will dipene le than 7. 75 oz
The percent of times the machine will dispense less than 7.75 oz. is 69.15%.
In the given question we have to find the percent of time the machine will dispene less than 7.75 oz.
A vending machine we deigned to dipene a mean of 7.5 oz of coffee into an 8-oz cup.
If the standard deviation of the amount of coffee dipened is 0.5 oz and the amount is normally ditributed.
Mean = 7.5 ,
Standard Deviation = 0.5
P(z< 7.5) = P(z<(X-Mean)/Standard Deviation)
P(z< 7.5) = P(z<(7.75-7.5)/0.5)
P(z< 7.5) = P(z<0.25/0.5)
P(z< 7.5) = P(z< 0.5)
P(z< 7.5) = 0.6915
P(z< 7.5) = 69.15%
Hence, the percent of times the machine will dispense less than 7.75 oz. is 69.15%.
To learn more about normally ditribution link is here
brainly.com/question/14919097
#SPJ4
Write a sine function that has an amplitude of 3, a midline of 5 and a period of pie
The sine function is y = 5 sin ([tex]16\pi x[/tex] ) + 3.
What is Sine function?The function y =[tex]sin x[/tex] defines a sine wave as a geometric waveform that oscillates (moves up, down, or side to side) frequently.
It is an s-shaped, smooth wave that oscillates above and below zero, to put it another way.
In its most general form, the sine wave can be described using the function y=[tex]a sin (bx)[/tex]
Given:
Amplitude = 3
midline= 5
As, we know
General sine function: a sin b[tex](x- c)[/tex] + d
and, amplitude = absolute value of a
b = 2π / period
c = phase shift (horizontal shift)
d = vertical shift (i/e., midline is y = d)
So,
a = 5, d = 3, and b = 2π / (1/8) = 16π, c = 0
Substituting the above value in Sine function we get
Thus, y = 5 sin ([tex]16\pi x[/tex]) + 3
Learn more about sine function here:
https://brainly.com/question/27716924
#SPJ1
HEY 55 POINTS!!!!
Complete the sentence.
The greatest amount of sap collected from any one tree is ?
times as great as the least amount of sap collected from
any one tree.
The greatest amount of sap collected from any one tree is ?
times as great as the least amount of sap collected from
any one tree. = 2 times
Solve for y:
-3 + 18iy = x + 9i
A) -3
B) 0.5
C) 2
D) 4
Answer:
Step-by-step explanation:
how to solve and answer:1
1/3(9-6x)=-11
Answer:
x = 2.875
Step-by-step explanation:
1 1/3 (9 - 6x) = -11
12 - 8x = -11
- 8x = -23
x = 2.875
Complete the equation describing how
x and y are related.
X
y
-2 -1 0
1
2 3 4 5
2
3
6 7
y = x + [?]
Enter the answer that belongs in [?].
Step-by-step explanation:
you can see that answer directly at x = 0. because y is then exactly the missing "?".
and that is 4.
so,
? = 4
answer the problems shown
The 65 represents the speed.
97.5 miles covered in 1.5 hours.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given: d= 65t
We know the Formula of Speed- distance
speed= Distance / time
and, distance = speed x time
So, comparing it with given equation
distance =d , time= t and speed= 65
Now, t=1.5 hours
Distance = 1.5 x 65 = 97.5 miles
and, d= 26 miles
t= 26 / 65
t= 0.4
Learn more about Algebra here:
https://brainly.com/question/24875240
#SPJ1
then m = -3,
(2m + 3)² =?
Answer:
9
Step-by-step explanation:
(2(-3)+3)^2
(-6+3)^2
(-3)^2
since the power of 2 is even it will be a positive result (if its a odd number like 3 it will be a negative result)
3^2
=9