Answers
Part A
Slope:
m = (y2-y1)/(x2-x1)
m = (9-5)/(4-2)
m = 4/2
m = 2
Use this slope to find the y intercept b
y = mx+b
5 = 2(2)+b
5 = 4+b
b = 1
Therefore the equation is y = 2x+1
-------------------
Part B
Slope:
m = (y2-y1)/(x2-x1)
m = (20-10)/(4-2)
m = 10/2
m = 5
Use this slope to find the y intercept b
y = mx+b
10 = 5*2+b
b = 0
Therefore the equation is y = 5x
===============================================
Problem 7
A) The coefficients are 7, 25, and -2. These are the values in front of the variables
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B) The variables are m, y, and y^3. Basically any term with a letter in it.
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C) The constant is 44. This is the term without any variables (letters) attached.
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D) There are four terms and the four terms are: 7m, 25y, 44 and -2y^3
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E) 25y and 2y^3 are NOT like terms. We cannot combine unlike terms. It's like trying to add 25a and 2b. We could think of it as having 25 apples and 2 bananas. We can't combine them to get 27a (there aren't 27 apples, only 25). Likewise we can't add them to get 27b (there aren't 27 bananas, only 2). Saying 27ab is also incorrect.
===============================================
Problem 8
Plug in n = 1
2^2*(n+3)
2^2*(1+3)
4*(1+3)
4*4
16
So the output is 16
-------------------
Plug in n = 3
2^2*(n+3)
2^2*(3+3)
4*(3+3)
4*6
24
So the output is 24
-------------------
Plug in n = 4
2^2*(n+3)
2^2*(4+3)
4*(4+3)
4*7
28
So the output is 28
-------------------
Plug in n = 6
2^2*(n+3)
2^2*(6+3)
4*(6+3)
4*9
36
So the output is 36
See the image attachment for the completed table.
===============================================
Problem 9
Plug in d = 6 and evaluate
C = 40 + 8(d-3)
C = 40 + 8*(d-3)
C = 40 + 8*(6-3) ... Replace d with 6
C = 40 + 8*(3)
C = 40 + 24
C = 64
It will cost 64 dollars.
Related Questions
What is the number in standard form?
3.23×1012
Answers
Please help me with this problem.
I've never really been good with this...
Answers
Proton + electrons = ?
3+ (-3)=0
0 is neutral, meaning not negative or positive so that means your lithium atom has neutral charge.
If you had a number line and you put your finger on 3 you would move 3 spaces left towards the negative numbers because 3 is negative and it would land you at 0.
Which number is a factor of 24 but not a multiple of 6
Answers
Answer:8
Step-by-step explanation:
can someone help me please
Answers
the answer is A
see attached picture:
Write a number with the digit 8 in the tens place
Answers
9,785,754,990,110,180
80
hope this helps
Find the average rate of change of f on the interval [50, 70].
Answers
Final answer:
The average rate of change of a function on an interval is calculated by finding the difference in the function's values at the endpoints of the interval, and then dividing that difference by the length of the interval. In this case, the interval is [50, 70], so the average rate of change of the function is (f(70) - f(50)) / (70 - 50).
Explanation:
The average rate of change of a function on an interval is calculated by finding the difference in the function's values at the endpoints of the interval, and then dividing that difference by the length of the interval.
In this case, the interval is [50, 70], so the average rate of change of the function is (f(70) - f(50)) / (70 - 50).
For example, if the function is f(x) = 2x + 3, then the average rate of change on the interval [50, 70] would be (f(70) - f(50)) / (70 - 50) = (2(70) + 3) - (2(50) + 3) / 20 = (143 - 103) / 20 = 40 / 20 = 2.
Allen’s score in a video game was changed by -75 points because he missed some targets. He got -15 points for each missed target. How many targets did he miss?
Answers
Answer:
he missed 5 targets. -75 ÷ -15
Mary's making curtains out of some fabric for five Windows the two larger windows are the same size and the three smaller windows are the same size the one larger window requires 3 3/4 of fabric and one smaller window needs one and one third yard of fabric how many yards of material will Mary need
Answers
2(3 3/4) + 3(1 1/3) =
2(15/4) + 3(4/3) =
30/4 + 12/3 =
7 1/2 + 4 =
11 1/2 (or 11.5) yds of fabric are needed <==
Marys need a total of 23/2 yard of fabric for his all windows.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Summation = addition of two or more numbers or variable
For example = 2 + 8 + 9
Subtraction = Minus of any two or more numbers with each other called subtraction.
For example = 4 - 8
Division = divide any two numbers or variable called division.
For example 4/8
Multiplication = to multiply any two or more numbers or variables called multiplication.
For example 5 × 7.
Given,
Fabric required in 1 larger window = 3 3/4
⇒ [(4×3)+3] /4 = 15/4
Fabric required in 1 smaller window = 1 1/3
⇒ (3+1)/3 = 4/3
Now,
Mary has 2 larger windows and 3 smaller
So,
Total fabric = 2 Larger + 3 smaller
Total fabric = 2(15/4) + 3(4/3)
Total fabric = 15/2 + 4
Total fabric = 23/2
Hence "Marys need a total of 23/2 yard of fabric for his all windows".
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I need help deriving : (7x)/(3+x^2), I keep on deriving it wrong and I am not sure as to why
Answers
The derivative of [tex]\( f(x) = \frac{7x}{3 + x^2} \)[/tex] is [tex]\( f'(x) = \frac{-7x^2 + 21}{(3 + x^2)^2} \)[/tex].
To find the derivative of the function [tex]\( f(x) = \frac{7x}{3 + x^2} \)[/tex] , we can use the quotient rule. The quotient rule states that if you have a function [tex]\( g(x) = \frac{u(x)}{v(x)} \)[/tex] , then the derivative [tex]\( g'(x) \)[/tex] is given by:
[tex]\[ g'(x) = \frac{u'(x)v(x) - u(x)v'(x)}{[v(x)]^2} \][/tex]
In this case, let u(x) = 7x and v(x) = 3 +[tex]x^2[/tex] . Now, find the derivatives u'(x) and v'(x):
u'(x) = 7
v'(x) = 2x
Now, apply the quotient rule:
[tex]\[ f'(x) = \frac{(7)(3 + x^2) - (7x)(2x)}{(3 + x^2)^2} \][/tex]
Simplify the expression:
[tex]\[ f'(x) = \frac{21 + 7x^2 - 14x^2}{(3 + x^2)^2} \][/tex]
Combine like terms:
[tex]\[ f'(x) = \frac{-7x^2 + 21}{(3 + x^2)^2} \][/tex]
So, the derivative of [tex]\( f(x) = \frac{7x}{3 + x^2} \)[/tex] is [tex]\( f'(x) = \frac{-7x^2 + 21}{(3 + x^2)^2} \)[/tex].
Complete Question: What is the derivation of (7x)/(3+[tex]x^2[/tex]).
*HELP* I've been stuck for mins. The graph shows the number of birdhouses Penn and his father can build if they have enough time to build no more than 10 birdhouses. What is the domain of this graph?
Answers
The answer to the question would be, All whole numbers from 0 to 10
If the graph shows the number of birdhouses Penn and his father can build if they have enough time to build no more than 10 birdhouses, the domain of the graph is given as [0, 10).
From the graph given, we are to find the domain of the graph. From the graph, we can see that;
The number of birdhouses is along the horizontal x-axisThe amount of time worked is along the vertical y-axisWe are to find the domain of the given graph. The domain of the graph is the input values for which the graph exists.
The domain of the graph is the values along the x-axis of the graph. Hence the domain of the graph is given as [0, 10).
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Help, I'm bad at math!
A bouncing ball reaches a height of 27 feet at its first peak, 18 feet at its second peak, and 12 feet at its third peak. Describe how a sequence can be used to determine the height of the ball when it reaches its fourth peak.
Answers
so, let's take a peek, 27, 18, 12
now, to get the common factor from a geometric sequence, since it's just a multiplier, if you divide any of the terms by the term before it, the quotient is then the common factor, let's do so with hmm say 12 and 18, 12/18 = 2/3 <---- the common factor, you can check if you so wish with 18/27.
and the first term is of course, 27.
[tex]\bf n^{th}\textit{ term of a geometric sequence}\\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ a_1=27\\ r=\frac{2}{3} \end{cases}\implies a_n=27\left( \frac{2}{3} \right)^{n-1}[/tex]
To determine the height of the bouncing ball at the fourth peak, we recognize a geometric sequence, where each peak's height is two-thirds of the previous peak. Applying this pattern, the height of the fourth peak is found to be 8 feet.
A sequence can be used to determine the height of a bouncing ball when it reaches its fourth peak. You can observe that the heights of the ball at each peak form a sequence, which in this case appears to be decreasing. By analyzing the pattern in the sequence, you can predict the height of the ball at its fourth peak.
A bouncing ball reaches various heights at different peaks which suggests a pattern. To determine the height of the fourth peak, we look at the sequence formed by the heights of the previous peaks. Noticing the pattern, each peak's height is [tex]\frac{2}{3}[/tex] of the previous one.
First peak: 27 feet
Second peak: 18 feet( [tex]27*\frac{2}{3}[/tex])
Third peak: 12 feet ([tex]18*\frac{2}{3}[/tex] )
To find the fourth peak, we continue the pattern:
Fourth peak: 12 feet *[tex]\frac{2}{3}[/tex] = 8 feet
Therefore, the fourth peak would be 8 feet high. By understanding the geometric sequence, we're able to predict future behavior.
The sum of a number and 12 is 20. What is the number?
Answers
The number is 8.
We verify:
x + 12 = 20
x = 20 - 12
x = 8
Regards !
I hope it helps you :)
"The sum of a number and 12..." The word sum is the keyword of what operation we are doing. We are doing addition. When we continue the phrase we know we are adding a number (an unknown) and 12.
So, on the left-hand side we have x + 12.
"... is 20" In mathematics, the word 'is' can mean equal. So, the left-hand side will equal the number 20.
Now we have the equation x + 12 = 20.
Solve for x.
x + 12 = 20
x = 8 <-- Subtract each side by 12
So, x is equal to 8.
is this proportion true 12/15=47/50
16/36=12/27
15/20=24/26
or 4/16=2/14
Answers
For 16/36 and 12/27, we'll notice that 36 and 27 are both multiples of 9, so we need to get that as the denominator! Multiply 16/36 by (1/4)/(1/4) because 9 goes into 36 4 times and 12/27 by (1/3)/(1/3) due to that 27 goes into 9 3 times, we get 4/9=4/9 - these are equal!
I challenge you to get the rest of them on your own using my techniques!
Final answer:
To determine if a proportion is true, we must verify that the cross-products of the ratios are equal. Only two of the given proportions, 16/36 = 12/27 and 15/20 = 24/32, are true when applying this method.
Explanation:
To determine if a proportion is true, we check whether the cross-products are equal. In other words, for a proportion in the form a/b = c/d, if a * d equals b * c, the proportion is true.
Let's apply this to the provided proportions:
12/15 = 47/50 is not true because 12*50 does not equal 15*47.
16/36 = 12/27 is true because 16*27 equals 36*12.
15/20 = 24/32 is true because 15*32 equals 20*24.
4/16 = 2/14 is not true because 4*14 does not equal 16*2.
Proportions can be a useful tool in many areas of mathematics, such as solving for unknown variables and comparing relative frequencies. Remember, if you encounter large numbers or fractions, simplifying before checking the cross-product can often make the process easier.
What is 0.947 founded to the nearest tenth
Answers
the sum of twice a number and 15 is -42
Answers
sum of twice the number and 15 means that you will first multiply the number by 2 then add 15.
the equation us:
2n + 15 = -42
2n = -42-15
2n = -57
n = -28.5
2(number)+15-15=-42-15
2(number)=-57
2(number)÷2=-57÷2
number=-28.5
Debra found that 6 of the 24 students in her class own a cell phone what is th ratio of students that own a cell phone to students that do not
Answers
6 own a cell, the rest does not, 24 - 6 is 18, so 18 do not.
[tex]\bf 6:18\implies \cfrac{6}{18}\implies \cfrac{1}{3}[/tex]
Juanita is making necklaces to give as presents. She plans to put 15 beads on each necklace. Beads are sold in packages of 20. What is the least number of packages she can buy to make necklaces and have no beads left over
Answers
4 * 20 = 80
4 * 15 = 60
Remember we still have 20 beads left over now. Add it to 60 and bam! You're done!
Use your calculator to evaluate e^-2. Round your answer to three decimal places.
Answers
Which statement about the equation is true?
x + 2 = x + 4
a)The equation has no solution.
b)The equation has one solution.
c)The equation has infinitely many solutions.
Answers
Yes, the equation has no answer, I took this and there was no solution. hope this helped
You purchased 8 pounds 10 ounces of candy from a candy shop. You want to split it equally among 3 classrooms at a local school.
Answers
3 classrooms = 138 ounces
1 classroom = 138/3
= 46 ounces
= 2 pounds 14 ounces
Each classroom should receive 2 pounds and 14 ounces of candy.
Answer:
Each classroom will receive 2 pounds and 14 ounces of candy .
Step-by-step explanation:
Given that
Purchased candy= 8 pounds and 10 ounces
First we convert pound into ounces
1 Pound=16 ounces
8 pound = [tex]16\times 8[/tex]
8 pounds= 128 ounces
Now, purchased candy in ounces= 128+10=138 ounces
If we want to distribute purchased candy into three calssroom equally
Therefore, we divide purchased candy by 3
Each classroom receive candy= [tex]\frac{138}{3}[/tex]
Each classroom receive candy=46 ounces
Each classroom receive candy in pounds
16 ounces=1 pound
1 ounces=[tex]\frac{1}{16}[/tex] pounds
46 ounces=2 pounds and 14 ounces
Each classroom receive candy=2 pounds and 14 ounces
Hence, each classroom receive candy =2 pounds and 14 ounces.If θ is in Quadrant III and sinθ = -3/5, then cosθ = _____.
Answers
Solving for x: x = plus or minus 4. Since we are in QIII, let x = -4.
Then cos omega is opp / hyp, or -4/5.
Answer:
-4/5
Step-by-step explanation:
plug into equation: sin squared + cos squared = 1 and solve
negative bc cos negative in quad III
15/16 is 1 sixteenth groups of what size?
Answers
15/ 16 = 1/16 x (X)
multiplying both sides with 16 we get, 15 = X
so 15 is the answer.
there is another way to find the answer if we divide 15 / 16 with 1/ 16, we get the answer which is 15 from this method also.
To determine the number which, when divided into 1/16 groups, gives 15/16, we should multiply 15/16 by 16. Therefore, 15/16 is 1 sixteenth of a group of 15.
Explanation:The question is essentially asking for a number which, when divided into 1/16 groups, would give 15/16.To find 1 sixteenth of a number, divide the number by 16. In this case, we want to find 1 sixteenth of what number is equal to 15/16. So, 15/16 is equal to 1/16 of what number. To find this number, we can simply invert the operation. Instead of dividing by 1/16, we should multiply 15/16 by 16. This gives us:
15/16 * 16 = 15.
Therefore, 15/16 is 1 sixteenth of 15.
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Half of the class plays the saxophone and 2⁄5 of the class plays the trumpet. How much of the class plays either the saxophone or the trumpet?
Answers
9/10
suppose 255,113 people live in a city is it reasonable to say that about 300,00 live in the city? use the number line to help you solve the problem .
Answers
the length of a each edge of a cube is x centimeters. if x is an integer, why can't the volume of the cube equal 15cm3
Answers
The volume of the cube can't equal 15cm ³ because 15 has no cube roots, the volume of the cube equals 15 cm squared.
What is the volume of the cube?The volume of a cube is equal to the product of the length, width, and height of a cube.
The volume of a cube is given by the formula as
The volume of a cube = length × breadth× height
What is a cube root?The cube root of a number is the component that we multiply by itself three times to produce that number.
The cube root is denoted by the'∛ ' symbol.
Example: ∛216 = ∛(6 × 6 × 6) = 6.
Here the length of each edge of a cube is x centimeters.
If we write the cube of a number
1³ = 1
2³ = 8
3³ = 27
Now we have a volume of 15 that contains no cube root.
A cube root is also contained in the volume of the cube.
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Name the rule and find the next two numbers in the pattern 10,70,490
Answers
Answer:
Next numbers: 3430, 24010
Step-by-step explanation:
AS you can see you just need to discover the pattern by dividing the subsequent numbers by the direct number before that:
490/70=7
70/10=7
So both numbers indicate the patter on multiply by 7.
So to calculate the next number we first have to multiply 490*7= 3430
Now we just have to multiply the 3430 by 7 and that would be 24010.
So the next numbers would be 3430 and 24010,
When markups are based on the selling price, the selling price is
A. cost – markup.
B. the portion.
C. 100% + cost percent.
D. 100%.
Answers
Markup is the amount added to the total cost of product to cover the total overheads and profit.
In markup based on selling price method, the selling price is considered as the endpoint that companies wanted to achieve, (100%) and the markup will be adjusted to cater into thaat equation.
When markups are based on the selling price, the selling price is seen as 100% since markup is a percentage of the selling price. The cost and markup together make up 100% of the selling price.
Explanation:When markups are based on the selling price, the selling price can be seen as 100%.
This is because the markup is calculated as a percentage of the selling price rather than the cost of the item.
Assuming that the entire selling price is 100%, the markup portion and the cost portion together make up this 100%.
The cost and markup are represented as percentages of the selling price, so if you know the cost and markup percentages, you can calculate the selling price.
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jake studied r hours for a big test . julie studied twice as long . write an algebraic expression for how long julie studied
Answers
If a honeybee beats its wings 250 times per second, how many times can it beat its wing in 1 hour?
Answers
Remember that there are 3600 seconds in an hour.
So, 3600 * 250 = x where x equals the total amount of beats.
3600 * 250 = 900,000
A honeybee beats its wings 900,000 times every hour.
250 x 60 = 15000
15000 x 60 = 900000
A honeybee beats its wings 900000 in an hour c: (wow)
Megan sent 12 postcards last week. This week she sent 4 postcards. How many more postcards didn't she sent last week?
Answers
Answer:
She sent 8 more postcards last week.
Step-by-step explanation:
Consider the provided information.
Megan sent 12 postcards last week. This week she sent 4 postcards.
We need to find How many more postcards did she sent last week?
To find this simply subtract the numbers as shown:
12-4 = 8
Hence, she sent 8 more postcards last week.