x is a placeholder for a number. Think of it as a box. Inside the box, we're told that 2 is there.
So we'll replace every x with 2 and use PEMDAS
5*x - 3*x = 5*2 - 3*2 = 10 - 6 = 4
After simplifying, the answer is 4.
Answer:
4
Step-by-step explanation:
5x-3x
We can simplify this expression
2x
Now we can substitute x=2
2(2)
=4
Holly, Maria and Johnny went to a fair over Spring Break. Holly paid $12.50 and went on one ride. Maria paid $15.00 and went on two rides. Johnny paid $20.00 and went on 4 rides. With x being the number of rides and y being the total amount paid, is the situation linear and why?
No. Between Holly and Maria there is an increase of $2.50 and between Maria and Johnny there is an increase of $5.00.
Yes. The y-intercept can be determined to be $10.00.
Yes. There is a constant rate of increase of $2.50 for each ride.
No. We are not given the initial cost if they went on no rides.
Answer:
Yes. There is a constant rate of increase of $2.50 for each ride.
Step-by-step explanation:
Lets write each persons cost and rides in the form y =mx+b
y being the total cost and x is the number of rides
Holly
(1 , 12.50)
Maria
(2,15)
Johnny
(4,20)
Lets calculate the slope
m = (y2-y1)/(x2-x1)
= (20-15)/ (4-2)
= 5/2
We can use the point slope form to determine b
y-y1 = m(x-x1)
y-20 = 5/2 (x-4)
Distribute
y-20 = 5/2x -20/2
Add 20 to each side
y-20+20 = 5/2x -10 +20
y = 5/2x +10
The slope or cost per ride is 2.50 and the y intercept is 10
A 2×2 square is centered at the origin. It is dilated by factor of 3. What are coordinates of the vertices of the square?
The 2x2 square centered at the origin has vertices at (-1,1), (1,1), (-1,-1), and (1,-1). When it is dilated by a factor of 3, the coordinates of the vertices are multiplied by 3, resulting in new vertices at (-3, 3), (3, 3), (-3, -3), and (3, -3).
Explanation:The subject here is Geometry, specifically dealing with transformations such as dilations on a plane. The starting square is 2x2 and centered at the origin means its vertices are at (-1,1), (1,1), (-1,-1), and (1,-1). A dilation by a factor of 3 from the origin means we are going to multiply every coordinate by 3. Doing this, we get the new vertices as (3*-1, 3*1) = (-3, 3), (3*1, 3*1) = (3, 3), (3*-1, 3*-1) = (-3, -3), and (3*1, 3*-1) = (3, -3). Therefore after the dilation, the vertices of the square will be at positions (-3, 3), (3, 3), (-3, -3), and (3, -3).
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If u(x)=-2x²+3 and v(x)=1/x, what is the range of (u ° v)(x)?
[tex]u(x)=-2x^2+3\\\\v(x)=\dfrac{1}{x}\\\\(u\ \circ\ v)(x)=-2\left(\dfrac{1}{x}\right)^2+3=-2\left(\dfrac{1}{x^2}\right)+3=-\dfrac{1}{x^2}+3\\\\\text{The range of}\ y=\dfrac{1}{x^2}\ \text{is all positive real numbers.}\\\\\text{The range of}\ y=-\dfrac{1}{x^2}\ \text{is all negative real numbers.}\\\\\text{The range of }\ (u\ \circ\ v)(x)=-\dfrac{1}{x^2}+3\ is\ (-\infty,\ 3)[/tex]
Answer:
(-∞,3)
Step-by-step explanation:
Imagine functions as little machines that turn one number into another number, the set of numbers that can enter the machine are called domain and the set of numbers that can exit the machine are called range. In this excercise we have to do function composition, which would be like having two machines and take the numbers that exit machine number 2 ([tex]v(x)[/tex]) and enter them into the machine number 1 ([tex]u(x)[/tex]). In math this is done by replacing the [tex]x[/tex] in [tex]u(x)[/tex] with the function [tex]v(x)[/tex] like this:
[tex]u(x)=-2x^{2} +3\\v(x)=\frac{1}{x}\\(u°v)=-2(\frac{2}{x})^{2} +3[/tex]
Now we need the range of the composed function, this will be the numbers that can come out of the machine number 1 when the numbers from the machine number 2 are entered to it.
So first which numbers will come out of machine number 2([tex]v(x)[/tex])? All but 0 because we there is no number that we can divide 1 by it that will give us the value 0 (not even zero itself because it is and indeterminate form).
We have now which numbers will enter machine number 1 (we dont have any restrictions in [tex]u(x)[/tex] to enter numbers)
The range of the composed function will be then the range of [tex]u(x)[/tex] less the value that we woud obtain by replacing [tex]x[/tex] with 0.
The range of [tex]u(x)[/tex] is (-∞,3] according to the attached graph and the value that we woud obtain by replacing [tex]x[/tex] with 0 is 3 so we would have (-∞,3).
Which type of triangle, if any, can be formed with sides measuring 8 inches, 8 inches, and 3 inches
Please help with 25
I need this plz
Can someone give me the answer for this
Answer:
perpendicular
You are paid $15.60/hr. Your deductions are FICA (7.65%), federal tax withholding (11.15%), and state tax withholding (6.5%). You work 15 hr/wk and save 10% each week. How much do you save each month?
a) $76.61
b) $79.29
c) $69.92
d) $71.04
Option C is the answer.
Explanation:
Amount paid per hour = $ 15.60
Total working hours in a week = 15
Hence, total earnings in a week are = 15.60 x 15 = $234
Deductions are =
7.65 % of 234 = [tex]\frac{7.65}{100}*234= 17.90[/tex]
11.15 % of 234 = $26.09
6.5% of 234 = $15.21
So totaling all deductions we get $59.20
Hence, earnings per week after deductions become = 234-59.20 = $174.80
As each week, 10% is saved, so amount saved each week is = 174.80 x 0.10 = $ 17.48
So, savings per month (4 weeks in a month) becomes = 17.48 x 4 = $69.92
Hence, option c) $69.92 is the answer.
write the equation of the line in slope intercept form with the given conditions (slope = 3 and passes through (1,-3))
Answer:
Because we have a point and slope, we can use at the beginning the point-slope form: y-y1=m(x-x1)
Step-by-step explanation:
m=3 , x1=1 , y=-3
y-(-3)=3(x-1)
y+3=3x-3 subtract 3 from both sides
y=3x-6 the answer in the slope-intercept form y=mx+b
Simplify the square root of 5 times 3 square root of 5
Answer:
15
Step-by-step explanation:
The square root of 5 times 3 square root of 5 is 5√3
How to simplify?[tex] \sqrt{5 \times 3} \sqrt{5} [/tex]
[tex] = \sqrt{15} \times \sqrt{5} [/tex]
[tex] = \sqrt{75} [/tex]
[tex] = \sqrt{25 \times 3} [/tex]
[tex] = 5 \sqrt{3} [/tex]
The simplification of the square root of 5 times 3 square root of 5 is 5√3
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NEED HELP ASAP Determine if each function is linear or nonlinear.
Drag each function into a box to correctly classify it.
Answer
=====================
The length of a rectangle is 3yd longer than its width. If the perimeter of the rectangle is 50yd, find it’s length and width
Answer:
3(15)
Step-by-step explanation:
We found that the width is 11 yards and the length is 14 yards.
We are given that the length of a rectangle is 3 yards longer than its width and that the perimeter of the rectangle is 50 yards. To find the length and width, we can set up a system of equations based on the information provided.
Let the width of the rectangle be w yards. Then the length would be w + 3 yards. Because the perimeter of a rectangle is the sum of all its sides, we can express the perimeter P as:
P = 2 * ( L + B)
Substituting the given values:
50 = 2(w + 3) + 2w
Now, let's solve the equation:
50 = 2w + 6 + 2w
50 = 4w + 6
44 = 4w
11 = w
Thus, the width is 11 yards. The length is 14 yards (because it is 3 yards longer than the width).
Given the two expressions shown below: square root of 3 plus square root of 2 square root of 5 plus square root of 6 Which statement best describes the two expressions? Both are rational. Both are irrational. A is rational, but B is irrational. A is irrational, but B is rational.
Answer:
they are both irrational
Step-by-step explanation:
if you add them, then they turn out to be decimals that go on and have no pattern
Answer:
Both will be irrational
Carrie is looking for a job cutting hair. One option is self-employment at The Belmont Salon, where she would pay $438 per month to rent a station and keep all her earnings. Another option is to work at a franchise, where she just have to pay $2 for every haircut. if she performed a certain number of haircuts every month, the amount paid to either salon would be the same. how much would Carrie pay? how many haircuts would that be? ( Can you also show the steps please?)
Answer:
She would have to do 219 haircuts in a month for the costs to be the same, which would be $428.
Step-by-step explanation:
To find this we take the costs of the first place.
$438
Next we can look at the costs of the second place using x as the number of haircuts she'd do.
2x
Now we can set the two equal to each other to find the number of cuts.
438 = 2x
219 = x
what is the value of x in the diagram below ? A. 9 B. 6 C. 7 D. 8
Answer:
9
Step-by-step explanation:
In the larger triangle you divided 12 by 2 which gave you the length of its corresponding side. So if you do 12/6 to get 2, you divide 54 by 6 and get 9.
Two times the sum of three consecutive odd integers is fifteen more than three times the largest of the integers. Find the integers?
Answer: 5, 7, 9
Step-by-step explanation:
1st#: 2k+1
2nd#: 2k+3
3rd#: 2k+5
2(2k+1 + 2k+3 + 2k+5) = 3(2k+5) + 15
2(6k + 9) = 6k + 15 + 15
12k + 18 = 6k + 30
6k = 12
k = 2
1st#: 2k+1 = 2(2) + 1 = 5
2nd#: 2k+3 = 2(2) + 3 = 7
3rd#: 2k+5 = 2(2) + 5 = 9
Explain how to represent functions as graphs. Give an example.
Answer:
In order to represent functions as graphs, first we need to make a table of x and y values and plot those x,y values on the graph
Step-by-step explanation:
Suppose we have a statement as below:-
The cost of carrot is $2.50/lb
We can convert this statement into a function as
total cost = price per lb * weight of carrot bought
Let y be the total cost and x be weight of carrot bought
So,
y = 2.50 * x
where x is the independent variable and y is the dependent variable
A function represents an equation that shows the relationship between the input x and the output y.
The input x is also known as the Domain
The output y is also known as the Range
1) We can represent this function as a graph. In order to make a graph we need to begin by making a table containing inputs and their corresponding outputs.
Input, x (lb) Output, y ($)
0 0
1 2.50
2 5.00
3 7.50
The above table is generated by plugging in the values of x as 0, 1, 2, 3 into the function y=2.50*x and calculating the corresponding value of y
2) Now, we just need to plot the above pair of x,y values on the graph as shown in the attached figure.
Can someone help me on number 24?
Answer:
x must be less than or equal to 5 hours
Step-by-step explanation:
24. C= 2(x-2) +3
C must be less than 10
10> 2(x-2) +3
Distribute the 2
10> 2x-4+3
Combine like terms
10> 2x-1
Add 1 to each side
10+1> 2x-1+1
11> 2x
Divide each side by 2
11/2 >2x/2
5.5 >x
We can only have whole hours
x must be less than or equal to 5 hours
The amount Bryce earns babysitting in a month is represented by the equation a=10.5h. In the equation, a represents the total amount Bryce earns. The number of hours he babysits is represented by h. What is the constant of proportionality (unit rate) of a to h? A. 10.50/hr B.10.00/hr C.9.50/hr D.5.10/hr
Answer:
A. 10.5h
Step-by-step explanation:
a new car is sold for its sticker value of $19,400. three years later the customer returns to the car dealership to trade the car in. she is told that her car now has a value of $12,105. what is the rate of decline in the value of the car? In your final answer, include all of your calculations.
Answer:
100/19400*12105=62.3969072165 100-62.3969072165 = 37.60% (rounded)
Step-by-step explanation:
100% = 19'400 divide and multiply with the current value, this will give you the % deductions. Simply deduct the result from 100.
Answer:
copy paste version
Step-by-step explanation:
we know that the formula to calculate the depreciated value is equal to:
D = P(1-r)^t
where
D is the depreciated value
P is the original value
r is the rate of depreciation in decimal
t is Number of Time Periods
In this problem we have:
P = $19,400
D = $12,105
t = 3 years
substitute in the formula above and solve for r:
$12,105 = $19,400(1-r)^3
Simplify:
(12,105/19,400) = (1-r)^3
(1-r) = 3√(12,105/19,400)
r = 1 - 3√(12,105/19,400)
r = 0.1455
Convert to percentage:
r = 14.55%
420=2(r+10) what is the total value of r
Answer:
(420/2)-10=r
r=200
Step-by-step explanation:
Answer:
r = 200
Step-by-step explanation:
divide both sides by 2
210 = r + 10 ( subtract 10 from both sides )
200 = r ⇒ r = 200
Find the quotient 744 divided by 3.1
Answer:
240
Step-by-step explanation:
Once you divide, using a calculator if possible, you get the exact solution.
Answer:
240
Step-by-step explanation:
1st you gotta turn 3.1 into a whole number by moving the decimal 1 space to the right then add a 0 to 744, next you divide normally
How can you determine the domain and range of function.
Answer:
The domain of a function is the complete set of possible values of the independent variable.
In plain English, this definition means:
The domain is the set of all possible x-values which will make the function "work", and will output real y-values.
When finding the domain, remember:
The denominator (bottom) of a fraction cannot be zero
The number under a square root sign must be positive in this section
Step-by-step explanation:
Answer and explanation:
The set of all possible values of x that will make the function work, giving an output of real y values is said to be the domain of a function.
The domain of a function is determined by looking for the values of the independent variable (which is usually x) that are allowed to use.
While the complete set of all possible output values of the dependent variable (usually y), when we substitute the x values is called the range.
Range can be determined by the spread of the possible y-values (minimum y-value to maximum y-value).
A rectangle has an area of 40 square units. The length is 6 units greater than the width
Answer:
The width is 4 units, and the length is 10 units.
Step-by-step explanation:
area of rectangle = length * width
Let L = length; let W = width.
"The length is 6 units greater than the width.": L = W + 6
area = LW = 40
Since L = W + 6, we substitute L with W + 6.
(W + 6)W = 40
W^2 + 6W = 40
W^2 + 6W - 40 = 0
(W - 4)(W + 10) = 0
W - 4 = 0 or W + 10 = 0
W = 4 or W = -10
A width cannot be a negative number, so we discard the solution W = -10.
W = 4
L = W + 6 = 4 + 6 = 10
The width is 4 units, and the length is 10 units.
Answer:
10 by 4 or B
Step-by-step explanation:
took test on edge
find the area of a circle with a circumference of 11pi feet
Answer:
Step-by-step explanation:
did this on my hw got a 100
The area of the circle has a circumference of 11pie is 94.98 ft sq.
What is the area of the circle?The area of the circle is the region enclosed by a circle of radius r.
The area of the circle = [tex]\pi r^{2}[/tex]
It is given that
The circumference of a circle = [tex]2\pi r[/tex] = 11π
[tex]2\pi r[/tex] = 11π
r = 11/2
The area of the circle = [tex]\pi r^{2}[/tex]
= [tex]\pi \times (11/2)^{2}[/tex]
= [tex]3.14 \times 121/4\\[/tex]
= 94.98 ft sq
Thus, The area of the circle has a circumference of 11pie is 94.98 ft sq.
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what is the answer to this math question 4×(-9+12)÷(2×3) I keep getting 14
Answer:
2
Step-by-step explanation:
Answer:
2. Hope this helps.
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Can I get brainliest?
please help asap ‼️
which of these sets of points lie within plane w?
a. C and G
b. H and E
c. C and E
d. A and D
Answer:
Im pretty sure its a. C and G
Step-by-step explanation:
Answer: The answer is (C) C and E.
Step-by-step explanation: We are given a figure including a plane 'w' and a number of points A, B, C, D, E and F around the plane. We are to select the pair of points from the given options that lie within the plane 'w'.
We can see in the figure that the points A and F lie above the plane 'w'; the points B and D lie below the plane 'w'; the points C and E lie on or within the plane 'w'.
Since we are to find the set of points lying within the plane 'w', so option (C) is the correct option.
which is more 4feet or 48inches
Answer:
4 feet = 48 inches
Step-by-step explanation:
In one foot there are 12 inches and since we have 4 of them we multiply to find how many total inces there are:
4x12=48
If you wanted to check the other side of it you would divide 48 inches by 12 inches to find out how many feet you have:
48÷12=4
Answer:
They are equal.
Step-by-step explanation:
A foot is made up of 12 inches
4 feet= 12*4 inches
4 feet= 48 inches
There you go!
The two are equal to each other
Mark and Melissa went to the garden center together to buy plants. Mark bought six ferns and one azalea for $80. Melissa bought five ferns and three azaleas for $84. how much was a single fern
Answer:
Price of single fern is $12
Price of single azalea is $8
Step-by-step explanation:
Let's assume
price of each fern is x
price of each azalea is y
Mark bought six ferns and one azalea for $80
so, we got first equation as
[tex]6x+y=80[/tex]
Melissa bought five ferns and three azaleas for $84
so, we got second equation as
[tex]5x+3y=84[/tex]
now, we can solve it
Firstly, we can solve for y from first equation and then plug that in second equation
[tex]6x+y=80[/tex]
[tex]y=80-6x[/tex]
now, we can plug that into second equation
[tex]5x+3(80-6x)=84[/tex]
[tex]-13x+240=84[/tex]
[tex]-13x=-156[/tex]
[tex]x=12[/tex]
now, we can solve for y
[tex]y=80-6\times 12[/tex]
[tex]y=8[/tex]
ms jefferson spent $15 to buy 12.8 ounces of smoked trout what was the cost per pound
Answer:
Step-by-step explanation:
Pounds to Ounces: 1 ounce = 0.625 pounds
12.8 ounces = 0.8 pounds
15/0.8 = 18.75 dollars
18.75 dollars
HW #35: similar polygons
Answer:
Q 9:
Because the two polygons are similar so AB ≈ PQ = SR
Scale factor is 25/20 = 1.25
Perimeter of ABCD = 14+20+14+20 = 68
We can find the length of SP by multiplying the scale factor with the AD so
SP = 14 * 1.24= 17.5
Perimeter of PQRS = 17.5+25+17.5+25 = 85
-----------------------------------------------------------------------------------
Q 10:
Because the two polygons are similar so AD ≈. EH
Scale factor is 7/14 = 0.5
Perimeter of ABCD = 12+14+13+26 = 65
Because the two polygons are similar so DC ≈ HG
and our scale factor is 0.5 so HG = 13/2 = 6.5
Perimeter of EFHG = 6 + 7 + 6.5 + 13 = 32.5
----------------------------------------------------------------------------------
Q 11:
The Geometric Mean is a special type of average where we multiply the numbers together and then take a square root (for two numbers). And the formula for finding the Geometric mean of two numbers a and b is
[tex]\sqrt{a*b}[/tex]
So geometric mean of the 8 and 10 can be found as
[tex]\sqrt{8*2} = \sqrt{16} = 4[/tex]
-----------------------------------------------------------------------------------
Q 12:
Similarly we can using the above formula of finding the geometric mean of 5 and 45 as
[tex]\sqrt{5*45} = \sqrt{225} = 15[/tex]
-------------------------------------------------------------------------------
Q 13:
and we can find the geometric mean of 6 and 30 by using the same formula
[tex]\sqrt{6*30} = \sqrt{180} = 13.41[/tex]