we did 4 different substitutions to evaluate the expression in 4 different values of x.
when x = 3 we get 40when x = 5 we get 50when x = -5 we get 0when x = 0 we get 25.How to evaluate an expression?
Here we have a linear expression that depends on the variable x, and can be written as:
(5x + 25)
And we want to evaluate this in some different values of x. This just means that we need to replace the value of x by different numbers.
First, let's use x = 3
This will give:
(5*3 + 25) = 15 + 25 = 40
Then we use x = 5
(5*5 + 25) = 25 + 25 = 50
Then we use x = -5
(5*-5 + 25) = -25 + 25 =0
Finally, we evaluate in x = 0.
(5*0 + 25) = 0 + 25 = 25
So we did 4 different substitutions to evaluate the expression in 4 different values of x.
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in science class, the average score on a lab report is 87 points, with all students scoring within 1.8 points of the average. if x represents a student's score, write an equation that represents the minimum and maximum scores. |x − 87|
The equation representing the minimum and maximum scores |x-87| = 1.8
Given that the average score on a lab report is 87 points. All students score within 1.8 points of the average.
Let 'x' be the score of student. The maximum and minimum score of a student lies within 1.8 points of the average.
Then, maximum score of a student, x = 87+1.8
and minimum score of a student, x = 87-1.8
Combining these two equations, we get, x = 87 ±1.8
Or, more conveniently, |x-87| = 1.8 represents the minimum and maximum scores obtained by a student.
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(4)^2(-7)-(-7)^2
This is all
You want to enlarge a 4 x 5 inch photo to fit into a 1 inch wide frame
that has an outer perimeter of 53 inches.
a. Write and simplify an equation for the outer perimeter of the
picture frame.
b. Determine the factor by which you must enlarge the picture to have it completely fill the inside of the picture frame
The 4•x by 5•x inner dimensions of the 53 inches outer perimeter picture frame, the 1 inch wide frame and the 4 × 5 inch picture to be enlarged, gives;
a. The outer perimeter equation is presented as follows;
18•x + 8 = 53 inches
b. The scale factor required for the enlargement of the picture is 2.5
Which method can be used to write the equation and find the scale factor?The dimensions of the photo = 4 × 5 inch
Width of the frame = 1 inch
Outer perimeter of the frame = 53 inches
The width of the inside of the picture frame = 4•x
The height of the inside of the picture frame = 5•x
a. The equation for the outer perimeter of the picture frame is therefore;
2 × (4•x + 1 + 1) + 2 × (5•x + 1 + 1) = 53
Which gives;
2 × (4•x + 2) + 2 × (5•x + 2) = 53
8•x + 4 + 10•x + 4 = 53
A simplified equation for the outer perimeter of the picture frame is therefore;
18•x + 8 = 53b. Solving the above equation, we have;
18•x + 8 = 53
18•x = 53 - 8 = 45
18•x = 45
Therefore;
x = 45 ÷ 18 = 2.5
x = 2.5
The width and height of the picture frame are therefore;
Width = 4•x = 4 × 2.5 = 10
Height = 5•x = 5 × 2.5 = 12.5
Which gives;
Width = 10 inches
Height = 12.5 inches
The enlargement factor, sf, is given by the ratio of a side of the picture frame to a side of the picture as follows;
sf = 12.5/5 = 2.5
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WILL GIVE BRAINLIEST
To pay for a home improvement project that totals $11,000, Genesis is choosing between taking out a simple interest bank loan at 6% for 3 years or paying with a credit card that compounds monthly at an annual rate of 16% for 6 years. Which plan would give Genesis the lowest monthly payment?%0D%0A%0D%0A The monthly credit card payment would be $396.49, which is lower than the monthly payment on the bank loan.%0D%0A The monthly payment on a bank loan would be $360.56, which is lower than the monthly credit card payment.%0D%0A The monthly credit card payment would be $354.44, which is lower than the monthly payment on the bank loan.%0D%0A The monthly payment on a bank loan would be $323.89, which is lower than the monthly credit card payment.
Using the monthly payment formula, it is found that the best plan is given by:
The monthly credit card payment would be $238.37, which is lower than the monthly payment on the bank loan.
What is the monthly payment formula?It is given by:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which:
P is the initial amount.r is the interest rate.n is the number of payments.For the simple interest payment method, the parameters are given as follows:
r = 0.06, n = 3 x 12 = 36, P = 11000, r/12 = 0.06/12 = 0.005.
Hence:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 11000(0.005)\frac{(1.005)^{36}}{(1.005)^{36} - 1}[/tex]
A = 334.64.
For the credit card payment method, the parameters are given as follows:
r = 0.16, n = 6 x 12 = 72, P = 11000, r/12 = 0.16/12 = 0.0133.
Hence:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 11000(0.0133)\frac{(1.0133)^{72}}{(1.0133)^{72} - 1}[/tex]
A = 238.37.
The monthly credit card payment would be $238.37, which is lower than the monthly payment on the bank loan.
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Solve: 1 1/8 - 3/4
pls answer in fraction!!
Answer:
3/8
change to an improper fraction
1 1/8=9/8
3/4 times 2 equals
6/8
9/8-6/8
3/8
Answer: I think the answer is 3/8 or it can be 5/8.
explanation: I hope this helps.
9. M (2, 1) is the midpoint of segment AB. If the endpoint A has coordinates (5,6), find
the coordinates of endpoint B.
Answer:
(-1, -4)
Step-by-step explanation:
To find the missing endpoint, we can multiply the midpoint coordinates by 2, so we can get 4 and 2. Then we can subtract the coordinates from the endpoint we have, which is A, to those numbers.
4-5 is -1
2-6 is -4
Put them together and we get (-1, -4) as our endpoint B.
Answer:
Step-by-step explanation:
(5+x)/2=2, (6+y)/2=1
for the x value
5+x=4
x=-1
then for the y value
6+y=2
y=-4
then your answer would be (-1,-4)
At a farm market, watermelons are selling 5 for $20. Each watermelon weighs about 8 pounds. What does the unit rate tell you? Responses The number of pounds each watermelon weighs. The number of pounds each watermelon weighs. The number of pounds all of the watermelons weigh. The number of pounds all of the watermelons weigh. The cost of all the watermelons. The cost of all the watermelons. The cost of one watermelon. The cost of one watermelon.
The unit rate of the watermelons would tell us the cost of 1 of the watermelon. The last option is correct.
How to solve for the costThe question tells us that the melons are sold for 5 for $20.
Hence the price of 1 would be at: 20/5
= 4 dollars per watermelon.
The weight of one of the melons is 8 pounds and the unit rate for 1 is 4 dollars. The unit rate is the price per one of the fruits or the cost of the fruit.
Hence we can say that The unit rate of the watermelons would tell us the cost of 1 of the watermelon.
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square root 71 in math
Answer: 8.4261
Step-by-step explanation:
all the numbers from 1 to a 99 are multiplied together.Use a pattern to determine the last digit of the product
The last digit of the product of numbers from 0 to 99 is 0.
What is multiplication?Multiplication is a method of finding the product of two or more numbers.
We have,
1, 2, 3, .............till 99.
We know that any number multiplied by 10 will give us 0 as the last digit.
And there are 10, 20, 30, 40, 50, 60, 70, 80, and 90.
We also know that 5, 15, 25, 35, 45, 65, 75, 85, 95 if multiplied with an even number the last digit is zero.
So if all the numbers from 1 to 99 are multiplied together, the last digit of the product will be a zero.
Thus the last digit of the product of numbers from 0 to 99 is 0.
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the jazz band has b members. to raise money for a tour, each member sold 12 raffle tickets. write an expression that shows the number of raffle tickets sold. submit
The term or expression 12b represents the number of raffle tickets sold by the members of the band.
Expression: An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.
There are b number of members in a jazz band. The jazz band wants to take a tour.
Each of the members sold 12 raffle tickets to raise money for the tour.
Therefore, the number of raffle tickets sold will be the product of the number of jazz members and the number of raffle tickets sold by each member.
So, the expression for the number of raffle tickets sold by the members of the jazz band will be:
= 12 × b
= 12b
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A.10x-5 )=1000 B.10x+5)=1000 C.10x+5=1000 D.10x-5=1000
Probability Question, please help me im stuck!
Answer:
27%
Step-by-step explanation:
3000 + 3500 + 4000 + 4200 = 14700
4000 / 14700 ≈ 0.27
0.27 = 27%
The graph shown corresponds to someone who makes ___
help quick pls
Answer:B $20 an hour
Step-by-step explanation:
if you look at the graph, in one hour he made $20
A manufacturer makes widgets and gadgets. At least 500 widgets and 700 gadgets are
needed to meet minimum daily demands. The machinery can produce no more than 1200
widgets and 1400 gadgets per day. The combined number of widgets and gadgets that the
packaging department can handle is 2300 per day
The combined number of widgets and gadgets that the packaging department can handle is 2300 per day that is x + y =2300
A manufacturer makes widgets and gadgets. At least 500 widgets(x) and 700 gadgets (y) are
[tex]x\geq 500\\\\y\geq 700[/tex]
The machinery can produce no more than 1200 widgets(x) and 1400 gadgets(y) per day
[tex]x\leq 1200\\\\y\leq 1400[/tex]
The combined number of widgets and gadgets that the packaging department can handle is 2300 per day
x+ y =2300
then the possible values of x and y are
( 1000, 1300)
(1100, 1200)
( 1200,1100) etc.
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Which postulate proves the two triangles are congruent
Based on the side-angle-side congruent theorem/postulate, both triangles are congruent. the answers is SAS.
What is the Side-angle-side Congruence Theorem (SAS)?The side-angle-side congruence theorem (SAS) means that two triangles have two pairs of sides that are congruent to each other with a pair of included congruent angles in between the two pairs of congruent sides of both triangles, and thus, both triangles must be congruent to one another.
The diagram shows two triangles that share a common side which is a pair of congruent sides. It also shows a pair of another congruent sides that is marked congruent.
Also, we have a pair of included congruent angles that both triangles have.
Therefore, based on the side-angle-side congruent theorem/postulate, both triangles are congruent. the answers is SAS.
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Simplify
√5 x √12 x √50
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here's the solution ~
[tex]\qquad \sf \dashrightarrow \: \sqrt{5} \times \sqrt{12} \times \sqrt{50} [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{5} \times \sqrt{2 {}^{2} \times 3 } \times \sqrt{2 \times {5}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{5} \times 2 \sqrt{3} \times 5 \sqrt{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: 2 \times 5 \sqrt{5 \times 3 \times 2} [/tex]
[tex]\qquad \sf \dashrightarrow \: 10 \sqrt{30} [/tex]
A boat is currently 63 miles from its destination and is traveling against a river current. The boat travels 10 miles per hour (mph) in still water. The boat's distance from its destination is given by the following formula. D=63-h(10 - c) Given: D = distance in miles, h = number of hours, c = speed of the river's current in mph What is a correct formula for the boat's distance from its destination after 3 hours
The distance of the boat from its destination depends on
Speed of the boatSpeed of the river currentDirection of the river current.So with these factors, the distance of the boat from its distance can be calculated.
The distance of the boat from the destination currently is 63 miles
Speed of the boat is 10 miles / hr
Let c be the speed of the river current and
h be the number of hours to reach a particular destination
So, the formula to find the distance of the boat from destination is given by
D = 63 - h(10 - c)
We need to find the formula for boat's distance from its destination after 3 hours
Thus h = 3 hrs
Let us substitute h in above equation, Then
D = 63 - 3(10 - c)
D = 63 - 30 - 3c
D = 33 - 3c
which is the formula for the boat's distance from its destination after 3 hours.
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when constructing a congruent line segment to cd the ray needed for the construction must be shorter
This statement is false. when constructing a congruent line segment to cd the ray needed for the construction it must be not shorter.
Why configured line segment to CD the ray never can be shorter?Because when constituting a configured line segment to CD the ray never can be shorter. The reason is when we constitute a configured it's Ray line is always increase that mean it's go up Hight and it's must be longer . That's why this statement is false.
What is a congruent line segment?Congruent line segments are geometrical figures in one dimension with identical dimensions. In terms of congruent lines, the word "congruent" refers to the equality of the two line segments. When two lines are the same length, they are said to be congruent. Superimposable figures that entirely enclose each other when stacked one atop the other are congruent segments. The congruent segments continue to be congruent even after being turned, flipped, or rotated.
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Rafael wants to find the average time it takes Central High School students to run a lap around the track. So he will consider 55 students to find the average
time.
Answer the questions below.
(a) Which unit(s) could be used for the unit of measurement? Check all that apply.
seconds Omilligrams 0 minutes
kilograms
grams
(b) Which of the procedures below would be the best way to find the average time?
O Randomly pick 55 students to run a lap around the track and measure their times.
O Randomly pick 55 students to run a lap around the track and have them state their own times.
O Ask for 55 volunteers to run a lap around the track and have them state their own times.
O Measure the times of 55 volunteers who run a lap around the track.
Answer:
Seconds and Minutes
Step-by-step explanation:
Randomly pick 55 students to run a lap around the track and measure their time.
This is the only option that avoids any type of bias.
Keisha has $585.43 in her checking account. She must maintain a balance of $300 to avoid a fee. She wrote a check for $302.05 today. Write an inequality, using x for the variable, that would be used for the least amount of money she needs to deposit to avoid a fee.
The inequality that would be used for the least amount of money she needs to deposit to avoid a fee will be 585.43 + x - 302.05 ≥ 300.
How to calculate the value?From the information, it was stated that Keisha has $585.43 in her checking account and that she must maintain a balance of $300 to avoid a fee and then she wrote a check for $302.05 today.
The inequality that would be used for the least amount of money she needs to deposit to avoid a fee will be:
585.43 + x - 302.05 ≥ 300
Collect like terms
x ≥ 300 - 585.43 + 302.05
x ≥ $16.62
She's needs to deposit at least $16.62.
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suppose a survey of 979 business owners found that more than % bought . which part of the survey represents the descriptive branch of statistics? make an inference based on the results of the survey.
In this problem, descriptive statistics is used because the survey percentage is used to make inference for all business owners.
What is descriptive statistics?
Descriptive statistics is used when data from a sample, which is a sub-set of a population, is used to make inferences about the entire population.
In this problem, the data 979 business owners sampled is used to make inference about the population, which is composed by all business owners, hence descriptive statistics is used.
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What is the area??? Please help!!!
Answer:
169 squared I think,hope this helps
two years ago, paul was 7 times as old as matt was. two year from now, paul will be five times as old as matt will be. find the present age of each
The present age of Paul is 52 years and the present age of Matt is 10 years.
We are given that two years ago, Paul = 7 times as Matt
Let the current age of Matt be x and of Paul be y
2 years ago, we will have that:
Age of Matt = x - 2
So, we get the equation as:
Age of Paul = 7 ( x - 2) = 7 x - 14
y - 2 = 7 x - 14
y = 7 x - 14 + 2
y = 7 x - 12
Also, we are given that to year from now, Paul = five times Matt
We get that:
y + 2 = 5 ( x + 2)
y + 2 = 5 x + 10
y = 5 x + 10 - 2
y = 5 x + 8
So, we get:
7 x - 12 = 5 x + 8
7 x - 5 x = 8 + 12
2 x = 20
x = 20 / 2
x = 10
y = 5 (10) + 2
y = 50 + 2
y = 52
Therefore, the present age of Paul is 52 years and the present age of Matt is 10 years.
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whitney makes $60000 in salary eight percent commission in may whitney had $13000 in sales how much did whitney make in may including her salary and commission
The total earning of Whitney in may including her salary and commission is $70,400.
What is sales commission?A sales commission is money given to an employee for completing a task, typically selling a specific amount of products or services.
Sales commissions are sometimes used as incentives by employers to increase work efficiency. A commission can be paid in regards to or in place of a salary.Now, as per the given question;
The monthly salary of Whitney is $60000.
The sales he did in the month of the may is $13000.
He got 8% commission on his total sales.
8% of $13000 = 10,400.
Thus, the total earning of the may will be-
Total earning = Salary + commission
Total earning = $60000 + 10,400
Total earning = $70,400
Therefore, the total earning done by Whitney in the May is $70,400.
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Solve the following equation for q
7p-5q=-35
Answer:
q = [tex]\frac{7}{5}[/tex]p + 7
Step-by-step explanation:
7p -5q = -35 Subtract 7p from both sides of the equation
-5q = -7p - 35 /Dive all the way through by -5
q = [tex]\frac{7}{5}[/tex]p + 7
What is the slope of a line parallel to the line whose equation is 18x + 15y = 90. Fully simplify your answer.
Answer:
6/5
Step-by-step explanation:
Rise
_____
Run
The slope of parallel line is -6/5
What is slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx
where, m is the slope
given:
Equation: 18x + 15y = 90.
Now, writing the given equation in slope intercept form
15y= 90- 18x
y= 90/15 - 18/15 x
y= 6 - 6/5x
So, the slope of given line is -6/5
Now, the slope of parallel and given is same.
Thus, the slope of parallel line is -6/5
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prove 2/sqrt3cosx+sinx=sec(pi/6-x)
Thus L.H.S = R.H.S that is [tex]\frac{2}{\sqrt{3} cosx + sinx }[/tex] = [tex]sec(\frac{\pi }{6-x} )[/tex] is proved
According to the question we have been given that
[tex]\frac{2}{\sqrt{3} cosx + sinx }[/tex] = [tex]sec(\frac{\pi }{6-x} )[/tex]
And we need to prove that left hand side is equal to the right hand side.
To prove this we will solve the right-hand side of the equation first with the help of trigonometry identity. The right hand side of the equation is :
R.H.S = [tex]sec(\frac{\pi }{6-x} )[/tex]
= [tex]\frac{1}{cos(\frac{\pi }{6-x} )}[/tex]
[As secƟ = 1/cosƟ)
= [tex]\frac{1}{\frac{cos\pi }{6cosx} + \frac{sin\pi }{6sinx} }[/tex]
[As cos (X-Y) = cosXcosY + sinXsinY , which is a trigonometry identity where X = Π/6 and Y = x]
[tex]=\frac{1}{\frac{\sqrt{3} }{2}cosx + \frac{1}{2}sinx } \\= \frac{1}{\frac{\sqrt{3}cosx + sinx }{2} }\\=\frac{2}{\sqrt{3}cosx + sinx}[/tex]
R.H.S = L.H.S
or L.H.S = R.H.S
Hence [tex]\frac{2}{\sqrt{3} cosx + sinx } = sec(\frac{\pi }{6-x})[/tex] is proved
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Add. Write your answer in scientific notation. (1.38×104)+(8×103) 9.38×1049 point 3 8 times 10 to the 4th power 2.18×1042 point 1 8 times 10 to the 4th power 9.38×1079 point 3 8 times 10 to the 7th power 2.18×107
The addition of the expression (1.38×10⁴) + (8×10³) written in scientific notation is "9 point 3 8 times 10 to the 7th power". option C
Scientific notation(1.38×10⁴) + (8×10³)
= (1.38 + 8) × 10^(4 + 3)
= 9.38 × 10^7
Options:
9 point 3 8 times 10 to the 4th power9.38×10⁴
2 point 1 8 times 10 to the 4th power2.18×10⁴
9 point 3 8 times 10 to the 7th power9.38×10^7
2.18×10^7Therefore, the addition of the expression (1.38×10⁴) + (8×10³) written in scientific notation is "9 point 3 8 times 10 to the 7th power".
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PLEASE help with this problem in math!!
b. Name three points coplanar with point B.
FO
OE
G
D
A
B
l
m
P