Answer: -2 ==> A
Step-by-step explanation:
-23 - 12 - (-33) =
-23 - 12 + 33 = ==> subtracting by a negative number is basically adding by the positive number
-(23 + 12) + 33 =
-35 + 33 =
-(35 - 33)=-2 ==> A
Answer: -2
Step-by-step explanation:
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"
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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
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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.
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On a certain hot summer's day, 559 people used the public swimming pool. The daily prices are $1.25 for children and $2.50 for adults. The receipts for admission totaled $1001.25. How many children and how many adults swam at the public pool that day?
The word problem of swimming pool resulted to a simultaneous equation and the solution is
the number of adults in the pool is 242
the number of children in the pool is 317
How to determine the number of adult or children in the swimming poolThe problem is a simultaneous equation of two unknowns with two equations.
The equations are formed as follows
let the number of adults in the pool be x
let the number of children in the pool be y
559 people used the public swimming pool
559 = x + y
The daily prices are $1.25 for children and $2.50 for adults. The receipts for admission totaled $1001.25
1.25y + 2.50x = 1001.25
Hence:
x + y = 559
1.25y + 2.50x = 1001.25
solving the equation gives
y = 317
x = 242
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a factory makes trash bags using plastic pellets. th plastic pellets are placed in barrels which are then poured into a machine. when the machine is operating the change to a barrel of pellets is 3 kg per minute. Each full barrel contains 18 kg of plastic pellets. are there enough pellets in a full barrel for the machine to make bags for 5 minutes.
Yes, there is enough weight of plastic pellets in a full barrel for the machine to make trash bags for 5 minutes.
It is given that the factory makes trash bags using plastic pellets. The plastic pellets are placed in barrels. The barrels containing the plastic pellets are then poured into a machine. When the machine is operating, the change from a barrel of pellets to the trash bags is 3 kg per minute. Each full barrel contains 18 kg of plastic pellets.
We need to check if there are enough pellets in a full barrel for the machine to make trash bags for 5 minutes. Let the time for which the machine can make the bags from a single barrel of plastic pellets be denoted by the variable "t". The time taken by the machine to fully convert a barrel full of plastic pellets into trash bags is the ratio of the total weight of plastic pellets in the barrel to the rate of conversion of the plastic pellets into trash bags.
t = 18/3
t = 6
Hence, the machine can convert a barrel of plastic pellets into trash bags in a time duration of 6 minutes. So, there are enough pellets in a full barrel for the machine to make bags for 5 minutes.
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Express using exponents and simplify any numerical coefficients: 2 · 2 · y · y · y · y
Answer:
4 x y
Step-by-step explanation:
y x y x y x y = y
2 x 2 = 4
4 x y
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
Let f(x) = 1 + x + x^2. Use the Mean value Theorem to show that there is a real number c,0 < c < 2, such that f(2) - f (0) = f'(c) (2 - 0). Find all such c. Show your work in the space provided.
The value o f c based on The Mean Value Theorem is 1
The Mean Value Theorem stated that if f(x) is a continuous on [a,b] and differentiable on (a,b) then there is a c such that:
f'(c) = [tex]\frac{f(b)-f(a)}{b-a}[/tex] ... (i)
Based on the question, we got equations:
f(x) = 1 + x + x² ... (ii)
By using derivative, we get:
f'(x) = 1 + 2x ... (iii)
From the question, we get:
f(a) = f(0)
f(b) = f(2)
Then we need to find the value of both f(0) and f(2):
f(0) = 1 + (0) + (0)²
f(0) = 1 ... (iv)
f(2) = 1 + (2) + (2)²
f(2) = 7 ... (v)
We also need to find the equation for f'(c) based on equation (iii):
f'(x) = 1 + 2x
f'(c) = 1 + 2c ... (vi)
We will input equations (iv) and (v) into equation (i) to find another equation of f'(c):
f'(c) = [tex]\frac{f(2)-f(0)}{2-0}[/tex]
f'(c) = [tex]\frac{7-1}{2-0}[/tex]
f'(c) = [tex]\frac{6}{2}[/tex]
f'(c) = 3 ... (vii)
Then we will subtitute the equation (vi) with equation (vii) to find the value of c:
f'(c) = 1 + 2c
3 = 1 + 2c
2c = 2
c = 1... (viii)
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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.
Sally earns $37.00 for 4 hours of babysitting. At this rate, how much more would she eam for 9 hours of babysitting? 6.RP.3 Step 1: Find the Unit rate of how much Sally makes per hour?
factorize X² + 2X - 48
Answer:
(X−6)(X+8)
Step-by-step explanation:
can someone please help me?
Using the volume formula, the height of the cylinder is [tex]h = \frac{v}{\pi r^{2} }[/tex]
How to solve for height in a cylinder?A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface.
In other words, a cylinder is a geometric solid with two circular bases joined by a curved surface.
The volume of a cylinder can be represented as follows:
The formula to calculate volume of a cylinder is given by the product of base area and its height
v = πr²hwhere
h = height of the cylinderr = radius of the cylinderTherefore, the question asked us to solve for height, h.
Hence, let's make height the subject of the formula.
v = πr²h
divide both sides by πr²
[tex]\frac{v}{\pi r^{2} }=\frac{\pi r^{2} h}{\pi r^{2} }[/tex]
Therefore,
[tex]h = \frac{v}{\pi r^{2} }[/tex]
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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
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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
To set up a wireless network for internet access at home, you buy a network
router for $75.00. The fee for internet service is $18.00 per month.
a. Write an expression for the amount of money you spend in n months.
b. How much money will you spend in 12 months? Show your work.
a.) Expression for the amount of money is 75+18n
b.) money spend in 12 months is $291
From the question, we have
Buy a network router for $75.00. The fee for internet service is $18.00 per month.
a.) Expression for the amount of money (y) is,
y = 75+18n
b.) money spend in 12 months = 75+18*12
= $291
Addition:
The phrase "the addition" refers to the combining of two or more integers. Three is written as three plus three since the plus sign (+) signifies the sum of two integers. The frequency with which the plus symbol (+) is used is likewise under your control. for example, 3 + 3 + 3 + 3. The teaching of addition in math to children is crucial. In primary school, students learn fundamental addition sums, such as one-digit facts, math addition sums, and double-digit arithmetic addition sums. One of the most fundamental and exciting Math concepts for primary school children is sums in addition. Because math is a fascinating subject, children begin learning basic mathematical concepts like adding numbers in their early years.
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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.
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Find m/ABC and mZCBD if mLABD = 120°.
m/ABC=(5x-6)
m/CBD =2x
If Bisector BD bisects ∠ABC. and ∠ABD= 67°, m∠CBD= 67°then m∠ABC= 134
As given, bisector BD bisects the angle ABC so this means, the angle ABC is divided into two halves. We need to find ∠ABC
So,
angle ABD= angle CBD.
and ∠ABD= (8x + 35)° (i)
∠CBD= (11x + 23)° (ii)
So,
(8x + 35)° = (11x + 23)°
On solving the above equation, we have
3x= 12
x= 4.
Putting x=4 in (i) we have,
∠ABD= 8(4) + 35
∠ABD= 67°
As ∠ABD = ∠CBD, we have
∠CBD= 67°
Now,
∠ABC= ∠ABD + ∠CBD
∠ABC= 67° + 67°
∠ABC= 134°.
Hence, If Bisector BD bisects ∠ABC. and ∠ABD= 67°, m∠CBD= 67° then m∠ABC= 134
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Disclaimer
The question given is incomplete as the diagram is missing, so a similar question has been solved here.
Encuentra todos los ceros X³ +9x²+26x+24 si (x+3) es un factor
The simplified value of the expression (x³ + 9x²+ 26x + 24), when divided by (x + 3), is: the quotient will be x^2 + 6x + 8 and the remainder will be 0. (x + 3) will be a factor of (x³ + 9x²+ 26x + 24).
Let us solve the given algebraic expression by the long division method:
We are given the expression:
(x³ + 9x²+ 26x + 24) and (x + 3)
We need to perform the division of the given algebraic expression:
x + 3 ) x^3 + 9x^2 + 26x + 24 ( x^2 + 6x + 8
x^3 + 3x^2
- -
6x^2 + 26x + 24
6x^2 + 18x
- -
8x + 24
8x + 24
- -
0
So,
quotient = x^2 + 6x + 8
remainder = 0
As the remainder is 0.
So, (x + 3) will be a factor of (x³ + 9x²+ 26x + 24)
Thus, the simplified value of the expression (x³ + 9x²+ 26x + 24), when divided by (x + 3), is: the quotient will be x^2 + 6x + 8 and the remainder will be 0. (x + 3) will be a factor of (x³ + 9x²+ 26x + 24).
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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
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m(x) = -2/3x + 8; m(x) = 2
Answer:
Answer is x = 9
A dressmaker sells a shirt for $75. If she makes a 25% profit, how much did it cost her to make the shirt?
Answer: $56.25
Step-by-step explanation:
x = cost to make the shirt
x + 75(0.25) = 75
x = 75 - 18.25 = 56.25
true or false: the quantity represented by θ is a function of time (i.e., is not constant).
Answer: the answer to this is true
Joy went to a sporting goods store and bought a tennis racket for $78.50. To stick to her budget, she knows she can spend up to $61.50 on new tennis shoes.
Let x represent how much money Joy wants to spend in all. Which inequality describes the problem?
The inequality to represent the problem is x - 78.50 ≤ 61.50.
Joy can sped at most 140 dollars.
How to represent problems with inequality?Joy went to a sporting goods store and bought a tennis racket for $78.50. To stick to her budget, she knows she can spend up to $61.50 on new tennis shoes.
The inequality that can be used to represent the problem is as follows;
Therefore,
x = total money Joy wants to spend in all
Hence, the inequality is x - 78.50 ≤ 61.50
x - 78.50 ≤ 61.50
x ≤ 61.50 + 78.50
x ≤ 140
Therefore, she wants to spend at most 140 dollars.
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You have $300,000 saved for retirement. Your account earns 8% interest.
How much will you be able to pull out each month, if you want to be able to
take withdrawals for 15 years?
Answer:
Step-by-step explanation:
You wire be able to put out
month, for 25 years.
$2307.94 each
Building A is 200 feet shorter than Building B. The total height of the two buildings is 1510 feet. Find the height of each building.
As per given relation about the height of the buildings , the height of building A is 655 feet and height of building B is 855 feet.
As given in the question,
Let us consider height of building A is equal to x feet.
According to given condition height of building A is 200 feet shorter than building B.
Height of building B is equal to ( x + 200 ) feet.
Total height of building A and building B is equal to 1510 feet
Required equation is :
x + x + 200 = 1510
⇒ 2x + 200 = 1510
⇒ 2x = 1510- 200
⇒ 2x = 1310
⇒ x = 655 feet
Height of building B is :
x+ 200 = 655 + 200
= 855 feet
Therefore, for the given relation about the height of the buildings , the height of building A is 655 feet and height of building B is 855 feet.
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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
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
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the volume of a rectangular prism is given by 33x3+71x2+54x+24. the height of the prism is given by 3x+4. find an expression for the area of the base of the prism.
The expression for the rectangular prism's base area is 11x² + 7x + 5.
Given;
The volume of rectangular prism = 33x³ + 43x² + 29x + 10
The height of the prism = 3x + 2
We know that, the area of the prism = length * breadth
where as, volume = length * breadth * height
So, area = volume / height
Using synthetic division, dividing volume by height, we get;
3x+2 ) 33x³ + 43x² + 29x + 10 ( 11x² + 7x + 5
33x3 + 22x2
---------------------------------
21x² + 29x
21x² + 14x
----------------------------------
15x + 10
15x + 10
----------------------------------
x
Quotient is 11x² + 7x + 5 which is equal to expression for the area of the base of the rectangular prism.
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A fast-food restaurant offers delivery service anywhere within a 6-miles radius. What area does the restaurant delivery service cover? Round your answer to the nearest square mile.
The restaurant delivery service cover the area 113.04 miles².
What is Circle?
The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
A fast-food restaurant offers delivery service anywhere within a 6-miles radius.
Now,
The area cover by delivery service = πr²
Here, r = 6 miles
Thus, The area cover by delivery service = πr²
= 3.14 x 6²
= 3.14 x 36
= 113.04 miles²
Therefore, The restaurant delivery service cover the area 113.04 miles².
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pls help. It will make my day even better
Answer:
4th option
Step-by-step explanation:
216p³ + 125q³ ← is a sum of cubes and factors in general as
a³ + b³ = (a + b)(a² - ab + b²)
then
216p³ + 125q³
= (6p)³ + (5q)³ → with a = 6p and b = 5q
= (6p + 5q)((6p)² - 6p(5q) + (5q)² )
= (6p + 5q)(36p² - 30pq + 25q²)