Answer: Terri brought 10 more centimeters of rope than Gracie.
Step-by-step explanation:
Alan bought two bikes. He sold one to Beth for $300 taking a 25% loss. He also sold one to Greta for $300 making a 25% profit. Did Alan break even? If not, did he have a profit or loss and by how much?
No Alan did not break even
Alan incured a loss of 6.25 %
Solution:
Given that,
Alan bought two bikes
He sold one to Beth for $300 taking a 25% loss
He also sold one to Greta for $300 making a 25% profit
When a person sells two similar items, one at a gain of say x%, and the other at a loss of x%, then the seller always incurs a loss
Which is given as:
[tex]loss\ \% = (\frac{x}{10})^2[/tex]
Here, x = 25
[tex]loss\ \% = (\frac{25}{10})^2\\\\loss\ \% = 2.5^2\\\\loss\ \% = 6.25[/tex]
Thus the loss percentage is 6.25 %
If 32x+1 – 3x+5, what is the value of x?
N
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оооо
o
[tex]\boxed{x=\frac{4}{35}}[/tex]
Explanation:Here we have the following equation:
[tex]32x + 1 = - 3x + 5[/tex]
So let's follows these steps:
Step 1: Add 3x to both sides:
[tex]32x + 1 +3x= - 3x + 5+3x \\ \\[/tex]
Step 2. Combine like terms:
[tex]32x + 3x + 1 = - 3x+3x + 5 \\ \\ 35x+1=5[/tex]
Step 3. Subtract -1 from both sides:
[tex]35x+1-1=5-1 \\ \\ 35x=4[/tex]
Step 4. Divide both sides by 35:
[tex]\frac{35}{35}x=\frac{4}{35} \\ \\ \\ \boxed{x=\frac{4}{35}}[/tex]
Learn more:Solving equations by graph: https://brainly.com/question/10643312
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The system of equations is solved using the linear combination method.
3x+4y=8 = -2(3x+4y=8) — -x-By--16
3x +24y - 12 (3x +24y= 12) ► x+8y=4
00
What does 0 = -12 mean regarding the solution to the system?
There are no solutions to the system because the equations represent parallel lines.
There are no solutions to the system because the equations represent the same line.
There are infinitely many solutions to the system because the equations represent parallel lines.
There are infinitely many solutions to the system because the equations represent the same line.
1
Answer:
There are no solutions to the system because the equations represent parallel lines.
Step-by-step explanation:
The given system is solved using the linear combination method.
By solving we had the result 0=-12.
We need to interpret this result in terms number of solutions.
Since 0 is never equal to -12, it means the system has no solution.
This means that the lines do not intersect
At the beach, Malia measured the footprints of the people who passed by. The line plot displays the length of each footprint. What fraction of the footprints measure more than afoot?
Length of Footprints
Answer:
still need the answer g?
What are the solutions to the system of equations?
y=x2−5x+6y=−4x+6
(−1, 0) and (0, 6)
(0, 6) and (1, 2)
(−1, 0) and (6, 0)
(0, −1) and (6, 0)
Answer:
(0, 6) and (1, 2)
Step-by-step explanation:
hello :
(0, 6) and (1, 2)
put x =0 and y =6 in this system : y=x²−5x+6
y=−4x+6
you have : 6 = 0²-5(0)+6 =6 ...right
6 =-4(0)+6 .... right
same mhethod for:(1, 2)
The solutions are B) (0, 6) and (1, 2).
To find the solutions to the given system of equations:
y = x² − 5x + 6 and y = −4x + 6, we need to set the equations equal to each other and solve for x:
Set x² − 5x + 6 equal to −4x + 6:
x² − 5x + 6 = −4x + 6
Rearrange the equation to get:
x² − x = 0
Factor the equation:
x(x − 1) = 0
Solve for x:
x = 0 or x = 1
Substitute these values back into either original equation to find y:
When x = 0: y = −4(0) + 6 = 6 (so one solution is (0, 6)).
When x = 1: y = −4(1) + 6 = 2 (so another solution is (1, 2)).
Therefore, the solutions to the system of equations are B) (0, 6) and (1, 2)
A pond initially contains 1000000 gal of water and unknown amount of an undesirable chemical. water containing 0.01 g of his chemical per gallon flows into the pond at a rate of 300 gal/h.the mixture flows out at the same rate ,so the amount of water in the pond remains constant .Assume that the chemical is uniformly distributed throughout the pond .How much of the chemical will be in the pond after a very long time ?
Final answer:
To calculate the amount of chemical in the pond after a very long time, multiply the rate at which the chemical flows in per hour by the number of hours that have passed.
Explanation:
To find out how much of the chemical will be in the pond after a very long time, we can first calculate the amount of chemical that flows into the pond per hour. Since 0.01 g of chemical flows in per gallon, and the rate of flow is 300 gallons per hour, the amount of chemical added per hour is 0.01 g/gal * 300 gal/hr = 3 g/hr.
Since the amount of water in the pond remains constant, the concentration of the chemical will also remain constant. Therefore, after a very long time, the amount of chemical in the pond will be the amount added per hour multiplied by the number of hours that have passed. So, if time is represented by 't', then the amount of chemical in the pond after a very long time is given by 3 g/hr * t.
What are the angle measures of triangle ABC?
mA= 30°, m ZB = 60°, m 2C = 90°
mZA= 90°, m ZB = 60°, m 2C = 30°
mZA= 60°, m ZB = 90°, m2C = 30°
mZA= 90°, m ZB = 30°, m2C = 60°
∠A = 90°, ∠B = 60° and ∠C = 30°
Step-by-step explanation:
Step 1: Find whether the triangle is a right angled triangle by using Pythagoras theorem. Given sides are a = 24 (opposite to ∠A), b = 12√3 (opposite to ∠B) and c = 12 (opposite to ∠C).⇒ 12² + (12√3)² = 144 + 432 = 576
⇒ √576 = 24 = a. This shows that the triangle is a right angled triangle.
So ∠A = 90°
Step 2: Use trigonometric equations to determine the other angles.⇒ cos B = AB/BC = 12/24 = 1/2
⇒ ∠B = 60°
Step 3: The sum of the angles in a triangle is 180°. To find ∠C,⇒ ∠C = 180° - (90° + 60°) = 180° - 150°
⇒ ∠C = 30°
The angle measures of triangle ABC is therefore;
mZA= 90°, m ZB = 60°, m ZC = 30°
Angle measures of Right trianglesBy testing for Pythagoras triple;
24² = 12² + (12√3)²576 = 144 + 432576 = 576.Hence, the triangle is a right-angled triangle.
We can then evaluate mZC as follows;
Sin C = 12/24 = 0.5C = Sin-¹(0.5) = 30°And angle B = 180 - 30 -90Angle, B = 60°Read more on angle measures in triangles;
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3x+4y-6=0
Write this in y=mx+b form, show your work
Answer:
y=(-3/4)x+3/2
Step-by-step explanation:
3x+4y-6=0
3x+4y=6
4y=6-3x
4y=-3x+6
y=(-3/4)x+3/2
To convert 3x + 4y - 6 = 0 to y = mx + b form is :[tex]y = -\frac{3}{4}x + 1.5.[/tex]
The equation given is 3x + 4y - 6 = 0. To write it in y = mx + b form, follow these steps:
Add 6 to both sides of the equation: 3x + 4y = 6.Subtract 3x from both sides to isolate the y-term: 4y = -3x + 6.Divide every term by 4 to solve for y:[tex]y = -\frac{3}{4}x + \frac{6}{4}.[/tex]Simplify the constants:[tex]y = -\frac{3}{4}x + 1.5.[/tex]Now, the equation is in slope-intercept form where m (the slope) is[tex]-\frac{3}{4}[/tex] and b (the y-intercept) is 1.5.
family has an annual income of $23 comma 400. Of this, one fourth
is spent for food, one fifth
for housing, one tenth
for clothing, one ninth
for savings, one fourth
for taxes, and the rest for other expenses. How much is spent for each?
$
nothing is spent for food.
Amount spent for food = $5850, housing = $4680, clothing = $2340, savings = $2600, taxes = $5850, expenses = $2080.
Step-by-step explanation:
Step 1:
Given details are Total Income = $23,400
Step 2:
Amount spent for food, F= 1/4th of 23,400 = [tex]1/4 \times 23400[/tex]
= $5850
Step 3:
Amount spent for housing, H = 1/5th of 23,400 = [tex]1/5 \times23400[/tex]
= $4680
Step 4:
Amount spent for clothing, C = 1/10th of 23,400 = [tex]1/10 \times 23400[/tex] = $2340
Step 5:
Amount spent for savings, S = 1/9th of 13,400 = [tex]1/9\times 23400[/tex] = $2600
Step 6:
Amount spent for taxes, T = 1/4th of 23,400 = [tex]1/4 \times 23400[/tex] =$5850
Step 7:
Find amount spent on other expenses by totaling all expenditures and subtracting from the annual income.
Annual Income = F + H + C + S + T + E
Amount spent on other expenses, E = 23400 - (5850 + 4680 + 2340 + 2600 + 5850)
E = 23400 - 21320
E = $2080
Determine the fraction of total interest owed using the rule of 78.
After the six month of a 12 month loan, the numerator is: {(n+11)+(n+10)+(n+9)+(n+8)+(n+7)+(n+6)) =
A.78
B. 57
C.51
The denominator is: ((n)+(n+1)+...+(n+11)} =
A.51
B.78
C.57
Therefore, the fraction is numerator/denominator (to the nearest tenth) =
A.73.1%
B.65.4%
C.136.8%
Answer:
The numerator is 57 ⇒ B
The denominator is 78 ⇒ B
The value of the fraction is 73.1% ⇒ A
Step-by-step explanation:
Let us solve it step by step
∵ The loan is 12 month
∵ The numerator is after 6 month
- Put n = 1 in each bracket
∴ The numerator = {(1 + 11) + (1 + 10) + (1 + 9) + (1 + 8) + (1 + 7) + (1 + 6)}
∴ The numerator = {12 + 11 + 10 + 9 + 8 + 7}
∴ The numerator = {57}
The numerator is 57
∵ The denominator = {(n) + (n + 1) + (n + 2) + .......... + (n + 11)}
- Do the same as the numerator put n = 1
∴ The denominator = {1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12}
∴ The denominator = {78}
The denominator is 78
Now find the value of the fraction
∵ The fraction = [tex]\frac{57}{78}[/tex]
∴ Its value = 0.730769230
- Multiply it by 100%
∴ Its value = 0.730769230 × 100% = 73.0769230%
- Round it to the nearest tenth
∴ Its value = 73.1%
The value of the fraction is 73.1%
The square root of -1 is:
kim's hourly wage is $14. she works 37 hours per week. what is her weekly income? what is her monthly income?kim can pay at most 30% of her income on rent. what is the most she can pay for rent every month?
Answer:
Weekly income = $518
Monthly income = $2072
Rent = $621.6
Step-by-step explanation:
$14 per hour
37 hours per week
37 × 14 = $518
There is about 4 weeks in a month.
$518 × 4 = $2,072
30% of $2,072 = $621.6
Step-by-step explanation:
Kim's weekly income can be found by multiplying her hourly wage to the number of hours she works per week.
So, we have $14 * 37 = $518 weekly income.
Let's assume that Kim gets paid bi-weekly like most jobs, so she'll get paid twice a month usually, ignoring all holidays and other exceptions.
So, we have her weekly income and we are assuming she gets paid bi-weekly per month. So, we need to make her weekly income into a bi-weekly income. We just double her weekly income.
$518 * 2 = $1036 bi-weekly.
Now, we know are assuming she gets paid twice a month, so we need to double her income one more time.
$1036 * 2 = $2072 monthly income.
Now, we have her monthly income, but she can only pay 30% of it towards rent. So, we got to find out what is 30% of $2072.
There are a couple of ways to do this, but the most efficient way is to multiply $2072 by .3
So, $2072 * .3 = $621.60
She can only have $621.60 go towards rent. Hope this helps!
The table of values below represent a function.
Select all of the values of z that will make the relationship a function.
x y
3 3
4 5
5 6
z 5
6 10
A: 0
B: 2
C: 3
D: 5
E: 6
F: 10
Answer:
A) 0
B) 2
F) 10
Step-by-step explanation:
This is because these are not on the chart already and the other choices are. Each input can only have 1 output for it to be a function,
A person paid $60 for a vase at an estate auction. She resold it to an antiques dealer for $40. What was her profit or loss?
Answer:
she lost 20 dollars
Step-by-step explanation:
she paid fpr it for 60.
she sold it for 40.
40 is less than 60.
60-40=20
Answer: She losses 20$ for want she sold
Find the slope of the line below
Answer:
(5,1) (8,5)
(5-1)/(8-5)= 4/3 is the slope
can someone please help been trying to figure this out for 2 days -.-
Answer:
PC=40 units
Step-by-step explanation:
we know that
The circumcenter is the center of the triangle's circumcircle (the circle that passes through all three of the triangle's vertices)
That means
PC=RC=QC----> is the radius of the circumcircle
step 1
Find the value of x
equate PC and RC
[tex]3x+7=5x-15[/tex]
solve for x
[tex]5x-3x=7+15\\2x=22\\x=11[/tex]
Verify
substitute the value of x
[tex]PC=3x+7=3(11)+7=40\ units[/tex]
[tex]RC=5x-15=5(11)-15=40\ units[/tex]
[tex]QC=51-x=51-11=40\ units[/tex]
so
[tex]PC=RC=QC[/tex] ----> is ok
Which expression is equivalent to the following complex fraction?
2 minus StartFraction 1 Over y EndFraction divided by 3 + StartFraction 1 Over y EndFraction
StartFraction 3 y + 1 Over 2 y minus 1 EndFraction
StartFraction (2 y minus 1) (3 y + 1) Over y squared EndFraction
StartFraction y squared Over (2 y minus 1) (3 y + 1) EndFraction
StartFraction 2 y minus 1 Over 3 y + 1 EndFraction
i hope this will help :)
Answer:
2y-1/ 3y+1
Step-by-step explanation:
I WILL GIVE BRAINLIEST TO FIRST CORRECT ANSWER
Every month, Midtown Grocery Store donates 8-ounce cans of vegetables to a food bank. The food bank's volunteers fill bags with these cans and deliver the bags to families in need.
There is a proportional relationship between the number of bags the food bank's volunteers can fill, x, and the total number of cans they deliver, y.
x (bags) y (cans)
5 50
7 70
8 80
9 90
What is the constant of proportionality? Write your answer as a whole number or decimal.
cans per bag
Answer:8 80
Step-by-step explanation:
Answer:
9
Step-by-step explanation:
Lee earns $1,075 each month. How much does he earns in 6 months?
Answer:
6450
Step-by-step explanation:
1075*6=6450
Answer:
$6450.00
Step-by-step explanation:
1075 x 6 = 6450
add the .00 because the unit is dollars
Juliet paid $3.84 in sales tax on an item that cost $48.00 before tax. At that rate, how much would she pay in sales tax for an item that costs $55.00 before tax?
Answer:
Step-by-step explanation:
3.84 is what percent of 48
(3.84 / 48) * 100 = 0.08 * 100 = 8% tax rate
for an item that is $ 55
8% of 55 = 0.08 * 55 = $ 4.40 <=== sales tax
What kind of solution is x(5 - 2) = 4x - x
Answer:
x=x or it cancels out, it's one of those.
A shipping container is in the shape of a right rectangular prism with a length of 8 feet, a width of 3.5 feet, and a height of 14.5 feet. The container is completely filled with contents that weigh, on average, 0.65 pound per cubic foot. What is the weight of the contents in the container, to the nearest pound?
Answer:
Volume = 8 * 3.5 * 14.5 =
406 cubic feet
.65 pounds / cubic foot * 406 =
263.9 pounds
Step-by-step explanation:
Answer:
264 pound if you had to round it
Step-by-step explanation:
Give the 46th term of the following sequence: -2, -5,-8, -11, -14, ...
[A] -137
[B] 44
[C] -134
[D] -138
Answer:
d
Step-by-step explanation:
it the 46 one in the pattern
Find the missing number:
QUICKLY PLEASE
Answer:
10
Step-by-step explanation:
r(x)=2[tex]\sqrt{x}[/tex] s(x)=[tex]\sqrt{x} \\[/tex]
Step-by-step explanation:
We have,
[tex]r(x)=2\sqrt{x}[/tex] and [tex]s(x)=\sqrt{x}[/tex]
and [tex](rs)(4)=8[/tex]
To find, the value of [tex](\dfrac{r}{s})(3) =?[/tex]
∴ [tex]r(x)s(x)=2\sqrt{x} \sqrt{x}[/tex]
[tex](rs)(x)=2x[/tex]
Also,
[tex](\dfrac{r}{s})(x) =\dfrac{2\sqrt{x} }{\sqrt{x} }[/tex]
[tex]=2[/tex]
∴ The value of [tex](\dfrac{r}{s})(3)[/tex] = 2
Thus, the value of [tex](\dfrac{r}{s})(3)[/tex] is equal to 2.
You refer:
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over a month the weight of a turkey increases from 20kg to 24kg calculate the increase as a percentage
Answer:
%120
Step-by-step explanation:
Step 1: Divide the new weight by the original weight.
24/20 = 1.2
Step 2: Change 1.2 into percent
To make a percent, multiply the number by 100
1.2 * 100 = %120
Answer: %120
I Suck at maths
Put the following in order from smallest to largest.
Answer:
0.027, [tex]\frac{1}{6}[/tex], 23%, 0.29, [tex]\frac{3}{5}[/tex]
Step-by-step explanation:
Here we have to convert the fractions and percents to decimal form, then we have to arrange them from smallest to largest.
[tex]\frac{1}{6} = 0.167[/tex]
23% = [tex]\frac{23}{100} = 0.23[/tex]
[tex]\frac{3}{5} = 0.6[/tex]
0.29
0.027
Now we have to arrange from smallest to largest.
0.027 < 0.167 < 0.23 < 0.29<0.6
From smallest to largest
0.027, [tex]\frac{1}{6}[/tex], 23%, 0.29,[tex]\frac{3}{5}[/tex]
Is it undefined? I'm not sure.
Answer:
no
Step-by-step explanation:
the line has a value which is y=7
Answer: Zero slope
Step-by-step explanation: A common mistake made by many students is to confuse what no slope is and what zero slope.
If a line has a slope of zero, it means that the line is flat or horizontal.
No slope is a vertical line or straight up and down. No slope means that we cannot describe its slope using a number because its line is vertical and it's slope is undefined. This has to do with dividing a number by 0. When you do this, you should get an error message or it should say undefined.
So, this line would have zero slope because it's flat.
Meiko is hanging a picture collage on her wall. The dimensions of the collage are shown in the diagram. She plans to cover
the collage with smaller pictures that have the same shape as the collage. If the base of each small picture is 4.5 inches and
the height is 3.5 inches, how many small pictures will fit within the collage?
Answer: [tex]\frac{A_{collage}}{15.75\ in^2}[/tex]
Step-by-step explanation:
Since you did not attach the diagram and I don't know the dimensions of the collage, I will give you a general explanation of the procedure you need to use in order to solve the exercise:
1. You need to use the formula for calculate the area of a rectangle:
[tex]A=lw[/tex]
Where "l" is the length and "w" is the width.
2. Using the formula, you must calculate the area of an small picture.
You know that its length is 4.5 inches and its width is 3.5 inches. Therefore, its area is:
[tex]A_{picture}=(4.5\ in)(3.5\ in)\\\\A_{picture}=15.75\ in^2[/tex]
3. Calculate the area of the collage using the formula:
[tex]A_{collage}=(l_{collage})(w_{collage})[/tex]
4. Finally, divide the area of the collage by the area of an small picture in order to find the number of small pictures that will fit within the collage:
[tex]\frac{A_{collage}}{15.75\ in^2}[/tex]
Answer:
C is the answer
Step-by-step explanation: I took a test
Solve: 746 ÷ 11
Show the remainder as a fraction.
The correct answer is [tex]67\frac{9}{11}[/tex]
Write the problem in long division format,
Divide 74 by 11 to get 6,
Multiply the quotient digit (6) by the divisor 11,
Subtract 66 from 74,
Bring down the next number of the dividend,
Divide 86 by 11 to get 7,
Multiply the quotient (7) by the divisor 11,
subtract 77 from 86.
[tex]\(746 \div 11\)[/tex] equals 67 with a remainder of 9. The remainder expressed as a fraction is [tex]68\frac{2}{11}\).[/tex]
To solve the division problem 746 ÷ 11 and express the remainder as a fraction, we can perform the long division as follows:
Step 1: Divide 7 by 11, which is 0 with a remainder of 7. So, the first digit of the quotient is 0, and we bring down the next digit, which is 4, to form the dividend 74.
Step 2: Now, divide 74 by 11. The largest multiple of 11 that does not exceed 74 is 6 times 11, which is 66. The remainder is 74 - 66 = 8.
Step 3: Bring down the next digit, which is 6, to form the new dividend 86.
Step 4: Divide 86 by 11. The largest multiple of 11 that does not exceed 86 is 7 times 11, which is 77. The remainder is 86 - 77 = 9.
Step 5: Finally, bring down the last digit, which is 0, to form the new dividend 90.
Step 6: Divide 90 by 11. The largest multiple of 11 that does not exceed 90 is 8 times 11, which is 88. The remainder is 90 - 88 = 2.
Now, we have completed the long division. The quotient is 68, and the remainder is 2. To express the remainder as a fraction, we can write it as [tex]\(\frac{2}{11}\).[/tex]
So, [tex]\(746 \div 11 = 68\frac{2}{11}\).[/tex]
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