a).$ -16.72
b).$75.50
c).$98.28
d).$16.72
e).$ -18.78
Option D
Money earned by Marty is $ 16.72
Solution:
Given that, Marty started a lawn mowing business
He kept track of his expenses and earnings in a table
Lawn Mower = - $49.99
Gasoline = - $8.79
Moyer's yard = $ 40
Griffen's yard = $ 35.50
To find: Money earned by Marty
Total money earned = lawn mower + gasoline + moyers yard + griffens yard
Total money earned = -49.99 - 8.79 + 40 + 35.50
Total money earned = -58.78 + 40 + 35.50
Total money earned = -18.78 + 35.50 = 16.72
Thus money earned by Marty is $ 16.72
What are the zeros of the polynomial function?
f(x) = x^3 + 2x^2 - x - 2
select each correct answer:
-3
-2
-1
0
1
2
3
Answer:
-2, -1 and 1.
Step-by-step explanation:
x^3 + 2x^2 - x - 2 = 0
x^2(x + 2) - 1(x + 2) = 0 Note the common factors (x + 2) so we have
(x^2 - 1)(x + 2) = 0
(x - 1)(x + 1)(x + 2) = 0 (x^2 -1 is the difference of 2 squares).
x = -2, -1 and 1.
A publisher needs to send many books to a local book retailer and will send the books in a combination of small and large boxes. Each small box can hold 20 books and each large box can hold 40 books. A total of 8 boxes were sent which can hold 260 books altogether. Determine the number of small boxes sent and the number of large boxes sent.
Answer:
5 large boxes
3 small boxes
Step-by-step explanation:
Create two equations to represent the problem.
let "a" be the number of small boxes
let "b" be the number of large boxes
20a + 40b = 260 This equation shows the numbers of books
a + b = 8 This equations shows the number of boxes
Solve the system of equations (solve for a and b). We can solve using the substitution method.
Rearrange a + b = 8 to isolate one of the variables.
a = 8 - b New equation that represents "a"
Since we know an equation for "a", we can substitute what "a" equals into the other equation. There will only be one variable in the equation, so we can solve by isolating. Isolate by doing reverse operations.
Substitute "a" for 8 - b
20a + 40b = 260
20(8 - b) + 40b = 260 Distribute 20 over the brackets by multiplying
160 - 20b + 40b = 260 Collect like terms (numbers with same variables)
160 + 20b = 260 Start isolating "b". Subtract 160 from both sides
20b = 260 - 160
20b = 100 Divide both sides by 20
b = 5 Number of large boxes
Substitute "b" for 5 in the simplest equation
a + b = 8
a + 5 = 8 Subtract 5 from both sides to isolate "a"
a = 8 - 5
a = 3 Number of small boxes
Therefore there were 5 large boxes and 3 small boxes sent.
Answer:
s = the number of small boxes
L = the number of large boxes
System of Equations:
25s+40L=250
s+l=7
Step-by-step explanation:
graph the function y=1/7x+2
Answer:
x - 0, 1
y - 2, 15/7
The sum of the digits of a two-digit number is 5. When the digits are reversed, the number increases by 27. Find the original number. The original number is
Answer:
14Step-by-step explanation:
[tex]a-\text{tens digit}\\b-\text{unity digit}\\10a+b-\text{number}\\10b+a-\text{number with reversed digits}\\a+b-\text{sum of digits}\\\\\bold{System\ of\ equations:}\\\\\left\{\begin{array}{ccc}a+b=5\\10b+a=10a+b+27&\text{subtract}\ 10a\ \text{and}\ b\ \text{from both sides}\end{array}\right\\\\\left\{\begin{array}{ccc}a+b=5\\9b-9a=27&\text{divide both sides by 9}\end{array}\right[/tex]
[tex]\underline{+\left\{\begin{array}{ccc}a+b=5\\b-a=3\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad2b=8\qquad\text{divide both sides by 2}\\.\qquad \boxed{b=4}\\\\\text{Put the value of\ b}\ \text{to the first equation}\\\\a+4=5\qquad\text{subtract 4 from both sides}\\\boxed{a=1}[/tex]
The area of one rectangle is 36 square
feet. The area of a second rectangle is
21 square feet. The rectangles have the
same width and the dimensions are
whole numbers. What is the width of
both rectangles?
Answer:
The width of both rectangles are [tex]\frac{36}{l},\frac{21}{L}[/tex].
Step-by-step explanation:
Given : The area of one rectangle is 36 square feet. The area of a second rectangle is 21 square feet. The rectangles have the same width and the dimensions are whole numbers.
To find : What is the width of both rectangles?
Solution :
According to question, the two rectangles have the same widths but they have different lengths.
Let the width of both rectangle be 'w'
Let the length of one rectangle be 'l'
Let the length of second rectangle be 'L'
The area of the rectangle is [tex]\text{Area}=\text{Length}\times \text{Width}[/tex]
The area of one rectangle,
[tex]36=l\times w[/tex]
[tex]w=\frac{36}{l}[/tex]
The area of second rectangle,
[tex]21=L\times w[/tex]
[tex]w=\frac{21}{L}[/tex]
The width of both rectangles are [tex]\frac{36}{l},\frac{21}{L}[/tex].
A country has 32 parks that allow camping and 43 parks that have playgrounds. Of those, 10 parks both allow camping and have playgrounds. The country has a total of 110 parks. What is the probability of randomly selecting a park that neither allows camping nor has a playground? Write your answer as a decimal rounded to the nearest hundredth.
Answer:
25
Step-by-step explanation:
Given:
32 parks allow camping
43 parks allow playgrounds
10 parks both allow camping and playgrounds
110 total parks
First, we need to add 32, 43, and 10
32 + 43 + 10 = 85
Then, we find the difference of 110 and 85
110 - 85 = 25
Since it isn't a decimal, there is no point in rounding.
Using V = lwh, what is an expression for the volume of the following rectangular prism?
The dimensions of a prism are shown. The height is StartFraction 5 Over 2 x + 8 EndFraction. The depth is StartFraction x + 4 Over 4 EndFraction. The length is StartFraction 12 Over x EndFraction.
StartFraction 15 Over 2 x EndFraction
StartFraction 3 x + 12 Over 2 x + 8 EndFraction
StartFraction 15 Over 2 x + 2 EndFraction
Fifteen-eighths
Answer:
Volume of the rectangular prism is given by,
[tex]\frac {15}{2x}[/tex] unit .
Step-by-step explanation:
According to the question,
height of the prism = [tex]\frac {5}{2x + 8}[/tex] unit = h (say)
depth of the prism = [tex]\frac {x + 4}{4}[/tex] unit = w (say)
length of the prism = [tex]\frac {12}{x}[/tex] unit = l (say)
So,
the volume of the rectangular prism,
V = lwh
= [tex]\frac {5}{2x + 8} \times \frac {x + 4}{4} \times \frac {12}{x}[/tex] unit
= [tex]\frac {15}{2x}[/tex] unit
Answer:
A
Step-by-step explanation:
Solve for x: logx3=1/2
Answer:
x= 9
Step-by-step explanation:
Please see attached picture for full solution.
If a candlestick burns at a rate of 0.4 inches per hour, how many hours will it take a 12 inch candle to burn?
Answer: 30 hours
30*0.4 is 12 or 40 percent of 30 is 12
Hope this helps!
The candle burns 12 inch in 30 hour.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into same number of parts.
Given, a candlestick burns at the rate of 0.4 inch per hour.
And 12 inch candle takes time to burn
= division of a 12 with a time taken to burn by ine candle
= 12 / 0.4
= 30 hour
Therefore, the candle burns 12 inch in 30 hour.
To learn more about the division;
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plz help me quick!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Exact Form: 5/2
Decimal Form: 2.5
Mixed Number Form: 2 1/2
Step-by-step explanation:
A spherical shell has inner radius r and an outer radius r+h. Let h=0.1r. Find the volume of the shell in terms of r and then approximate the volume of the shell by 4πr^2h. Does this seem like a reasonable approximation if h is small compared to r?
Step-by-step explanation:
The volume of the shell is the volume of the outer sphere minus the volume of the inner sphere.
V = 4/3 π (r+h)³ − 4/3 π r³
V = 4/3 π (r³ + 3r²h + 3rh² + h³) − 4/3 π r³
V = 4/3 π r³ + 4π r²h + 4π rh² + 4/3 π h³ − 4/3 π r³
V = 4π r²h + 4π rh² + 4/3 π h³
If h = 0.1 r:
V = 4π r² (0.1 r) + 4π r (0.1 r)² + 4/3 π (0.1 r)³
V = 0.4π r³ + 0.04π r³ + 0.00133π r³
V = 0.44133π r³
Using the approximation:
V = 4π r² h
V = 4π r² (0.1 r)
V = 0.4π r³
The approximation is reasonable if h is small compared to r.
Can somebody help
Select the correct solution in the table.
Consider the equation below.
3^(-x) - 3 = 4^x - 1
Select the approximate solution to the equation.
x 3^(-x) -3 4^x - 1
-1.75 3.83 -0.91
-1.5 2.19 -0.88
-1.25 0.95 -0.82
-1 0 -0.75
-0.75 -0.72 -0.65
-0.5 -1.27 -0.50
-0.25 -1.68 -0.29
Answer:
-0.75
Step-by-step explanation:
The table values listed for the left side expression and the right side expression are closest together when the value of x is -0.75.
__
A graphing calculator shows the expressions both have a value near -0.658 when x ≈ - 0.775. The closest table value to x = -0.775 is x = -0.75.
Answer: x = -0.75
-0.72 -0.65
Step-by-step explanation:
Consider the equation below.
3^(-x) - 3 = 4^x - 1
consider the values of x = 1.75, -1.5, -1.25, -1, -0.75,-0.5,-0.25
x 3^(-x) -3 4^x - 1
-1.75 3.83 -0.91
-1.5 2.19 -0.88
-1.25 0.95 -0.82
-1 0 -0.75
-0.75 -0.72 -0.65
-0.5 -1.27 -0.50
-0.25 -1.68 -0.29
The bold values when x = -0.75 gives -0.72 and -0.65 is the approximate solution to the equation
by approximation -0.72 when rounded off = -0.7
and -0.65 when rounded off = -0.7
What is the perimeter of △LMN?
8 units
9 units
6 + StartRoot 10 EndRoot units
8 + StartRoot 10 EndRoot units
Answer:
The perimeter of △LMN is 8 + [tex]\sqrt{10}[/tex]
Step-by-step explanation:
Step 1: Finding the length of LM
Distance formula = [tex]\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}[/tex]
here
[tex]x_1[/tex]= 2
[tex]x_2[/tex]= -2
[tex]y_1[/tex]= 4
[tex]y_2[/tex]=1
LM = [tex]\sqrt{(-2-2)^2 +(1-4)^2}[/tex]
LM = [tex]\sqrt{(-4)^2 +(-3)^2}[/tex]
LM = [tex]\sqrt{16 +9)}[/tex]
LM = [tex]\sqrt{25}[/tex]
LM = 5
Step 2: Finding the length of MN
Distance formula = [tex]\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}[/tex]
here
[tex]x_1[/tex]= -2
[tex]x_2[/tex]= -1
[tex]y_1[/tex]= 1
[tex]y_2[/tex]= 4
LM = [tex]\sqrt{(-1-(-2))^2 +(4 - 1)^2}[/tex]
LM = [tex]\sqrt{(11+2)^2 +(3)^2}[/tex]
LM = [tex]\sqrt{1 +9)}[/tex]
LM = [tex]\sqrt{10}[/tex]
Step 3 : Finding the length of NL
Distance formula = [tex]\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}[/tex]
here
[tex]x_1[/tex]= -1
[tex]x_2[/tex]= 2
[tex]y_1[/tex]= 4
[tex]y_2[/tex]= 4
NL = [tex]\sqrt{(2-(-1))^2 +(4 - 4)^2}[/tex]
NL = [tex]\sqrt{(3)^2 +0}[/tex]
NL = [tex]\sqrt{9 +0}[/tex]
B = [tex]\sqrt{9 }[/tex]
NL = 3
Step 4: Finding the perimeter of the triangle
Perimeter = length of LM + length of MN + length of NL
Perimeter = 5 + [tex]\sqrt{10}[/tex] + 3
Perimeter = 8 + [tex]\sqrt{10}[/tex]
Answer:
its D on edg
Step-by-step explanation:
please help !!
prove abp = dcp
Answer:
∠1≅∠2-------------------------(Given)m∠1=m∠2-------------------(Definition of congruent angles)∠ABP, ∠1 and ∠DCP,∠2 form linear pair---------------Linear pairm∠ABP+m∠1=180° and m∠DCP+m∠2=180°--------definition of linear pair∠ABP≅∠DCP--------------------If equals are subtracted from equals, the remainders are equalAP≅DP----------------------------GivenΔABP≅ΔDCP-------------------AASStep-by-step explanation:
Given, ∠1≅∠2, ∠3≅∠4 and AP≅DP,
We know that,∠1≅∠2(given)
⇒m∠1=m∠2(definition of congruent angles)
∠[tex]ABP+[/tex]m∠1=180° and ∠[tex]DCP[/tex]+m∠2=180° (Linear Pair)180°=180°(Reflexive)
⇒m∠[tex]ABP+[/tex]m∠1=m∠[tex]DCP[/tex]+m∠2
But m∠1 =m∠2 (definition of congruent angles)
⇒m∠[tex]ABP+[/tex]m∠1=m∠[tex]DCP[/tex]+m∠1
m∠[tex]ABP+[/tex]=m∠[tex]DCP[/tex] ( If equals are subtracted from equals, the remainders are equal)
[tex]AP[/tex]=[tex]DP[/tex](GIven)Therefore, Δ[tex]ABP=[/tex]Δ[tex]DCP[/tex] (by AAS criteria)
condition are:
m∠1=m∠2 (Angle)m∠[tex]ABP[/tex]=m∠[tex]DCP[/tex] (Angle)AP=DP (Side)(a - b)(a 2 + ab + b 2)
Please list the steps on how to solve this one.
Which expression is equivalent to 8a3 + c3?
I'm assuming we factor...
The answer is (2a + c)(4a^2 - 2ac + c^2.)
⭐ Please consider brainliest! ⭐
✉️ If any further questions, inbox me! ✉️
(The question that got me to Ace rank!)
Answer:
(2a + c)(4a² - 2ac + c²)
Step-by-step explanation:
8a³ + c³ ← is a sum of cubes and factors in general as
a³ + b³ = (a + b)(a² - ab + b²)
Given
8a³ + c³
= (2a)³ + c³
= (2a + c)((2a)² - 2ac + c²), that is
= (2a + c)(4a² - 2ac + c²)
Liz runs 8 feet per second. Katie runs 350 feet in 31 seconds. Katie runs 350 feet in 31 seconds. Stephanie runs 1 mile in 388 seconds. Stephanie runs 1 mile in 388 seconds. Noah runs 541 feet in 1 minute. Noah runs 541 feet in 1 minute.
Answer: Stephanie is the fastest
Step-by-step explanation:
Here we have to find who runs faster:
Liz:
[tex]8 ft/s[/tex]
Katie:
[tex]\frac{350 ft}{31 s}=11.29 ft/s[/tex]
Stephanie:
[tex]\frac{1 mile}{388 s}. \frac{5280 ft}{1 mile}=\frac{5280 ft}{388 s}=13.60 ft/s[/tex]
Noah:
[tex]\frac{541 ft}{1 min}. \frac{1 min}{60 s}=9.01 ft/s[/tex]
As we can see after comparing, Stephanie is the fastest, since she travels more distance in less time.
A line goes through the point (-3,2) and has a slope of 1. Write the equation of this line in standard form .
Answer:
y - 2 = x + 3
y = x + 5
-x + y = 5 standard form
Solve for h.
3(h +1) = 18
Answer: h =5
Step-by-step explanation:
3(h+1) = 18
Expand the L.H.S to give
3h + 3 = 18
subtract 3 from both sides
3h = 15
divide through by 3
h = 15/3
h = 5
Step-by-step explanation:
Divide both sides by 3
H+1=6
Move the constant to the right
H=6-1
Subtract the numbers
3.1 in standard form
3.1 is already in standard form.
Abby bought two slices of pizza and three bottles of water for $7.25 Cameron bought four slices of pizza and one bottle of water for $8.25 what is the solution
The solution is price of 1 slice of pizza is $ 1.75 and price of 1 bottle of water is $ 1.25
Solution:
Let "p" be the price of 1 slice of pizza
Let "b" be the price of 1 bottle of water
Given that Abby bought two slices of pizza and three bottles of water for $7.25
So we can frame a equation as:
two slices of pizza x price of 1 slice of pizza + three bottles of water x price of 1 bottle of water = $ 7.25
[tex]2 \times p + 3 \times b = 7.25[/tex]
2p + 3b = 7.25 ------- eqn 1
Cameron bought four slices of pizza and one bottle of water for $8.25
So we can frame a equation as:
four slices of pizza x price of 1 slice of pizza + one bottles of water x price of 1 bottle of water = $ 8.25
[tex]4 \times p + 1 \times b = 8.25[/tex]
4p + 1b = 8.25 ----- eqn 2
Let us solve eqn 1 and eqn 2 to find values of "p" and "b"
Multiply eqn 1 by 2
4p + 6b = 14.5 ----- eqn 3
Subtract eqn 2 from eqn 3
4p + 6b = 14.5
4p + 1b = 8.25
( - ) ------------------
5b = 6.25
b = 1.25
Substitute b = 1.25 in eqn 1
2p + 3b = 7.25
2p + 3(1.25) = 7.25
2p + 3.75 = 7.25
2p = 3.5
p = 1.75
Summarizing the results:
price of 1 slice of pizza = $ 1.75
price of 1 bottle of water = $ 1.25
Is x=4 and y=5 perpendicular
True!
Explanation:The Cartesian coordinate system is formed by two perpendicular axes, which are the x-axis and y-axis. In this problem, we are given two lines:
[tex]x=4 \ and \ y=5[/tex]
The line [tex]x=4[/tex] is parallel to the y-axis and has an undefined slope.The line [tex]y=5[/tex] is parallel to the x-axis and has a slope of zero.Since the x and y-axes are perpendicular, then the lines [tex]x=4 \ and \ y=5[/tex] are also perpendicular.
Learn more:Cartesian coordinate system: https://brainly.com/question/2141683
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22. What is the percent of increase for a population
that changed from 438,000 to 561,000?
Answer: 28.08%
Step-by-step explanation: To find the percent increase, we divide the amount of change by the original number.
The amount of change is the difference between the two numbers which in this case is 561,000 - 438,000 and the original number is 438,000.
561,000 - 438,000 is 123,000 so we are left with 123,000 divided by 438,000 which is 0.2808. Finally, since our problem is asking us for a percent, we write 0.2808 as a percent by moving the decimal point two places to the right to get 28.08%.
So when the population changes from 438,000 to 561,000, it has increased by 28.08%.
How do you find the slope of a line? Answer it in your OWN OPINION.
You divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points.
Best of Luck to you.
Write equation 7x -5y = -18 in y=mx +b
Slope intercept and y intercept
Answer:
Step-by-step explanation:
7x -5y = -18
Making y as subject
-5y = -7x - 18
Dividing through by -5
y = -7/-5x - 18/-5
y = 7/5x + 18/5
Slope m = 7/5
Intercept b = 18/5
Every winter, the math club sells cookie dough to raise money. Last year, they sold 2,080 pounds of cookie dough to 520 people. This year, they predict that they will sell cookie dough to between 630 and 670 people. About how many pounds of cookie dough will they need?
Final answer:
After calculating that each person bought an average of 4 pounds of cookie dough last year, and using the average predicted sales of 650 people for this year, the math club should prepare approximately 2600 pounds of cookie dough.
Explanation:
The question is asking for an estimation of how many pounds of cookie dough the math club will need to sell this year, given that they predict selling to more people than last year. To calculate this, we need to find the average amount of cookie dough sold per person last year and then multiply that by the predicted number of people for this year.
Last year, the math club sold 2,080 pounds of cookie dough to 520 people. Thus, each person bought an average of
2080 pounds ÷ 520 people = 4 pounds per person.
This year, they are predicting sales to between 630 and 670 people. We will use the average of these two numbers for a better estimation, which is (630 + 670) ÷ 2 = 650 people.
Now, we multiply the average amount of dough per person by the estimated number of people:
4 pounds per person × 650 people = 2600 pounds.
Therefore, the math club should prepare approximately 2600 pounds of cookie dough for this year's fundraiser.
Given f(x)=4x-6 and g(x)=8x+4 findthe value of x for which f(x)=g(x)
The value of "x" is [tex]\frac{-5}{2}[/tex]
Solution:
Given f(x) = 4x - 6
g(x) = 8x + 4
To find: value of x when f(x) = g(x)
We can equate f(x) and g(x) as per given statement and solve for x
f(x) = g(x)
Substituting the values of f(x) and g(x) in above expression,
4x - 6 = 8x + 4
4x - 8x = 4 + 6
-4x = 10
On solving,
[tex]x = \frac{10}{-4}\\\\x = \frac{-5}{2}[/tex]
Thus value of "x" is [tex]\frac{-5}{2}[/tex]
Three oblique pyramids have the same regular square base. Which one has a volume of 15 cubic units if the area of the bases are all 15 square units?
Answer:
The one which has a height of 3 units. H=3
Step-by-step explanation:
Well, the volume of pyramid is equal to the area of base multiply by the height of pyramid and divide by 3. Writing as a formula it can be expressed as V=(A*H)/3 where V is volume of pyramid, A is area of base and H is the height of pyramid. If V=15 cubic units and A=15 square units, H should be equal to 3 (to be cancelled out by 3. Please look at formula above) in order to make V=15.
Answer:
b
Step-by-step explanation:
HEEEEELLLPPPP!!! I really need this to be answered im soo confused!!
Answer:
C
Step-by-step explanation:
∠ AFD = ∠ AFC + ∠ CFD
Given ∠ CFA = 90° and
∠ CFD = 90° - ∠ EFD, that is
∠ CFD = 90° - 62° = 28°, thus
∠ AFD = 90° + 28° = 118° → C
Answer:
answer is c. 118
angle AFC+ angleCFD = angle AFD..
[ANGLE AFD =AFC + CFD][ANGLE CFD = 90 -62 ]