The equation to represent the situation is y = 15 + 30x.
The number of hours Sophia used for the guitar training after paying 75 dollars is 2 hours.
How to use equation to represent situations?Sophia takes guitar lessons at home every Sunday. Her instructor charges $15 to cover home visit costs, and $30 per hour of training. One Sunday, Sophia's mother pays the instructor $75 for the guitar lessons.
The equation that can be used to represent the given situation is as follows:
let
x = number of hours used for the training
y = total cost
Therefore,
y = 15 + 30x
Now, Sophia's mother spent 75 dollars for her daughters training. Let's find the hours Sophia used.
Therefore,
75 = 15 + 30x
75 - 15 = 30x
60 = 30x
divide both sides by 30
x = 60 / 30
x = 2
Therefore, she used 2 hours for the training.
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At a candy store, Eva bought 2 pounds of jelly beans and 2 pounds of gummy worms for $26.
Meanwhile, Mimi bought 3 pounds of jelly beans and 2 pounds of gummy worms for $31. How
much does the candy cost per pound?
start with
m: cost per pound for Jelly Beans
n: cost per pound for Gummy Worms
Answer:
cost per pound for Jelly Beans is 5$
cost per pound for Gummy Worms is 8$
The closed right circular cylindrical can of the smallest surface area whose volume is
250 π cm3 has a radius of _____ cm and a height of _____ cm
The closed right circular cylindrical can of the smallest surface area whose volume is 250π cm³ has a radius of 5cm and a height of 10 cm.
Let r and h be the radius and height of the cylinder respectively.
Volume, V= πr²h
Given,
Volume = 250 π
Now, we can solve by:
⇒ 250 π = πr²h
⇒ r²h=250
⇒ h= 250/r²
We know that,
Surface area, A = 2πr²+2πrh
⇒ A = 2πr²+ 2πr(250/r²)
⇒ A = 2πr²+ (500π/r)
Differentiating the above equation,
dA / dr = 4πr+500π(-1/r²)
For A to be maximum or minimum, dA/dr = 0
⇒ 4πr-500(π/r²) = 0
⇒ 4πr - 500π / r² = 0
⇒ 4πr³ -500π/ r² = 0
⇒ π (4r³ -500) = 0
⇒ 4r³ - 500 = 0
⇒ r = ∛125
⇒ r = 5
Putting value of r = 5, we get,
h = 250/(5)² = 10
By second derivative test,
d²A/dr² = 4π-500π(-2/r³)
At r= 5,
d²A/dr² = 4π+1000(π/r³) > 0 .
Therefore, It is a local minimum.
Ans: Radius = 5 and Height = 10
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Is the absolute value of -3 less than, greater than, or equal to -7
The statements are true "3 is less than 7, and the absolute value of 3 is less than the absolute value of 7".
What is absolute value?Absolute value is defined as the magnitude or size of a number, no negatives are allowed.
The distance a number is from 0 on the number line is known as the absolute value of the number.
For example, |5| is 5 because it is 5 units away from 0. Also, |-5| is also 5 because -5 is 5 units from 0.
The absolute value of a number is how distant it is from zero. The standard procedure to represent absolute value is to use a number line to estimate the exact distance the number is from zero.
As per the option, 3 is less than 7 is true.
The absolute value of 3 is less than the absolute value of 7 is true.
Thus, the statements are true "3 is less than 7, and the absolute value of 3 is less than the absolute value of 7".
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The question seems to be incomplete the correct question would be
Which statements about 3 and 7 are true? Choose ALL the correct answers.
3 is less than 7.
3 is greater than 7.
The absolute value of 3 is less than the absolute value of 7.
The absolute value of 3 is equal to the absolute value of 7.
The absolute value of 3 is greater than the absolute value of 7.
A car travels 37 km in 25 minutes.
What is its average speed in km/h?
Give your answer rounded to 1 decimal place.
Answer:
88.8 km/h
Step-by-step explanation:
Giving 50 points!!
Question: Determine whether the dilation from figure K to K’ is an enlargement or a reduction
Answer:
enlargement
Step-by-step explanation:
observe from the figure [tex]OK=x<x+5=7=OK'[/tex]
since [tex]OK<OK'[/tex], then the dilation is an enlargement.
Answer:
Step-by-step explanation:
defsfvbrfdv
What is the slope of the line passing through the points (-1, 0) and (0, - 7)?
Answer:
1/-7
Explanation:
rise/run so up 1 down 7
To get in condition for running on the track team, Paul began by running 2 miles.
mile farther than he ran the day before. How far will Paul run on Day 7?
Every day after that, he ran
4
OA. 6 miles
OB. 6 miles
OC. 7 miles
OD. 8 miles
What is the equation of the line that passes through the point (-2,14) and is perpendicular to the line with the following equation? y= -2/5 x-1
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{2}{5}}x-1\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{-2}{5}} ~\hfill \stackrel{reciprocal}{\cfrac{5}{-2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{5}{-2}\implies \cfrac{5}{2}}}[/tex]
so we're really looking for the equation of a line whose slope is 5/2 and it passes through (-2 , 14)
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{14})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{5}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{14}=\stackrel{m}{ \cfrac{5}{2}}(x-\stackrel{x_1}{(-2)}) \implies y -14= \cfrac{5}{2} (x +2) \\\\\\ y-14=\cfrac{5}{2}x+5\implies {\Large \begin{array}{llll} y=\cfrac{5}{2}x+19 \end{array}}[/tex]
13. Find the measure of
(5x +27)°
(2x + 10)°
(4x + 2)°
Check the picture below.
an oil paint set cost $45 more than an easel . an easel cost $129 what is the total cost of the oil paint set and the easel
ANSWER ASAP A basketball team played six games. In those games, the team won by 8 points, lost by 8, won by 7, won by 10, lost by 2, and won by 9. What was the mean difference in game scores over the six games?
The average difference or mean in game scores across six games is 5.67
MeanThe mean is the average of a data set. The mode is the most common number in a data set. The median is the middle of the set of numbers. The mean is the average or the most common value in a collection of numbers. the mean is one of the measures of b, apart from the mode and median. Mean is nothing but the average of the given set of a data.
To solve this problem, we have to write the wins and loss separate and then find the mean.
Wins = 8 points, 7 points, 20 points, 9 points
Loss = 8 points, 2 points
The sum of win points = 8 + 7 + 20 + 9 = 44 points
The sum of lost points = 8 + 2 = 10 points
The mean difference = (win - loss)/ total number of games
The mean difference = ( 44 - 10) / 6
The mean difference = 34 / 6 =5.67
The mean difference in the game scores over six games is 5.67 points
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pls help me how do I round 9.4725 to the nearest cent with no dollar sign
Rounding off 9.4725 to the nearest cent will give 9.5
Rounding Off NumbersRounding off means a number is made simpler by keeping its value intact but closer to the next number. It is done for whole numbers, and for decimals at various places of hundreds, tens, tenths. When rounding money to the nearest cent, look at the number to the right of the full cents. In this case, that number is 9. If the number is five or more, increase the cents by 1. If the number is four or less, keep the cents the same. Because 9 is more than 5, $3.299 rounds to $3.30.
Applying same principle or concept here, we can round off 9.4725 to the nearest cent to give 9.5.
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The amount of money raised at a fundraiser is directly proportional to the number of attendees. The amount of money raised for 12 attendees is $300. How much money is raised for 75 attendees?.
Answer:
900
Step-by-step explanation:
300/12=25
75*12=900
A store sold towels that cost $5 each at 15% less than the cost. The overhead was 20% of the cost of each towel. What was the selling price of each towel? How much more than $150 did the owner lose if 95 towels were sold?
If the overhead was 20% of the cost of each towel. The selling price of each towel is 5.88.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
The usage of percentages is widespread and diverse. For instance, numerous data in the media, bank interest rates, retail discounts, and inflation rates are all reported as percentages. For comprehending the financial elements of daily life, percentages are crucial.
Suppose the selling price of a towel is x, according to the given condition,
5 = x - 15% of x
5=x-0.15x
5=0.85 x
x=5/0.85
x=5.88
Thus, if the overhead was 20% of the cost of each towel. The selling price of each towel is 5.88.
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The Bartolotti family took out a loan to have a garage built next to their house. The 10-year, 10.4% loan was for $56,188. The monthly payment was $475, but the promissory note stated that there was a balloon payment at the end. what is the sum of all but the last monthly payment?
If the promissory note stated that there was a balloon payment at the end. The sum of all but the last monthly payment is: $56,525, $57,000.
How to find the monthly payment?Total payment = $475 × [(10 years × 12 months) -1]
Total payment = $475 × 119 payment
Total payment = $56,525
Total payment = $475 × [(10 years × 12 months) ]
Total payment = $475 × 120 payment
Total payment = $57,000
Therefore the monthly payment is; $56,525, $57,000.
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Simplify. Express your answer using positive exponents.
(7tuv7)(4t3u4v2)
Answer:
[tex]28t^4u^5v^9[/tex]
Step-by-step explanation:
I will answer this a few different ways depending on whether there are supposed to be exponents in the question.
As written
As written, the product is:
[tex](7tuv7)(4t3u4v2)[/tex]
All of the coefficients can be multiplied together. This is what that looks like:
[tex]4704tuvtuv[/tex]
Now, each variable multiplied by itself gets the exponent of 2.
[tex]4707t^2u^2v^2[/tex]
Assuming exponents and coefficients
Assuming exponents, the product is:
[tex](7tuv^7)(4t^3u^4v^2)[/tex]
Again, the coefficients can be multiplied, and the like variables written next to each other:
[tex]28tt^3uu^4v^7v^2[/tex]
When multiplying like terms with exponents, add the exponents. Variables without an exponent have an exponent of 1.
[tex]28t^4u^5v^9[/tex]
How many Pieces of ribbon .6m long can be cut from 13.2m ribbon?
I think is is 22
because it is asking how many times can .6m go into 13.2m of ribbon? If you start with 20x.6 you will get 12. Then you add on another one and get 12.6. Finally add one more to get 13.2m ribbon which would make the answer 22. You can also divide 13.2m divided by .6m and get 22.
Hopefully this helped you guys. If you guys want more answers please give me those 5 Stars and Give me a thanks to show you appreciation.
Over all the Answer is 22
Have a great day (:
7x+y=5 equations answer
Answer:
[tex]x=\frac{5}{7} -\frac{y}{7}[/tex]
Step-by-step explanation:
You move all terms that dont contain x
to the right side and solve.
Hope this helps! :))
The cost of 4kg of kale and 1.5 kg of beetroot is 12.20
The cost of 5kg of kale and 2kg of beetroots is 15.40 work out the cost of 1kg of beetroot and 1kg of kale
The cost of 1 kg of beetroot and 1 kg of kale are 1.39 units and 2.53 units respectively
How to find the cost of beetroot and Kale?The cost of 4kg of kale and 1.5 kg of beetroot is 12.20. The cost of 5kg of kale and 2kg of beetroots is 15.40.
The cost of 1kg of beetroot and 1kg of kale can be found as follows:
Therefore,
let
x = cost of 1kg of beetroot
y = cost of 1 kg of Kale
Therefore, using equation,
1.5x + 4y = 12.20
2x + 5y = 15.40
x = 12.20 / 1.5 - 4y / 1.5
x = 8.13 - 2.67y
Hence,
5y = 15.40 - 2(8.13 - 2.67y)
5y = 15.40 - 16.26 + 5.34y
5y = -0.86 + 5.34y
5y - 5.34y = -0.86
- 0.34y = - 0.86
y = - 0.86 / - 0.34
y = 2.52941176471
y = 2.53
1.5x = 12.20 - 4(2.53)
1.5x = 12.20 - 10.12
1.5x = 2.08
x = 2.08 / 1.5
x = 1.38666666667
x = 1.39
Therefore,
cost of 1kg of beetroot ≈ 1.39
cost of 1 kg of Kale = 2.53
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Mrs. Sharma is making treats for a tea party later this week, and she has up to 6 eggs to use for this purpose. A batch of scones requires 3 eggs and a batch of miniature tarts requires 2 eggs.
The eggs that will remain after Sharma is making treats for a tea party is 1.
How to calculate the value?From the information, Mrs. Sharma is making treats for a tea party later this week, and she has up to 6 eggs to use for this purpose a batch of scones requires 3 eggs and a batch of miniature tarts requires 2 eggs.
In this case, the eggs remaining will be:
= Total eggs - Eggs used
= 6 - (3 + 2)
= 6 - 5
= 1
There'll be 1 egg remaining.
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Complete question
Mrs. Sharma is making treats for a tea party later this week, and she has up to 6 eggs to use for this purpose. A batch of scones requires 3 eggs and a batch of miniature tarts requires 2 eggs. How many eggs will be left?
your calculations indicate that you will need 20.8 cubic yards of concrete for a slab floor. which of the following quantities would be the best amount to order accounting for waste?
Answer:
Step-by-step explanation:Your calculations indicate that you will need 20.8 cubic yards of concrete for a slab floor. Which of the following quantities would be the best amount to order accounting for waste
PLEASE HELP, I WILL GIVE BRAINLY!!!
Compare the scenarios to determine which represents a greater speed. Explain your choice including a written description of each scenario. Be sure to include the rates in your explanation.
For every 50 y, there is 1 hour
What is the product?
2y 4y-12
y-3 2y+6
O
تان
10
4y
y-3
4y
y+3
The product of the given polynomials is 4y/(y + 3).
We are given two polynomials. A polynomial is a mathematical statement that is composed of the sum of powers in one or more variables multiplied by coefficients. The polynomials are in rational form. A rational number is created by dividing an integer by an integer. The first polynomial is 2y/(y - 3). The second polynomial is (4y - 12)/(2y + 6). We need to find the product of these two polynomials. Let the product be represented by the variable "P".
P = [2y/(y - 3)]×[(4y - 12)/(2y + 6)]
P = [2y/(y - 3)]×[4(y - 3)/2(y + 3)]
P = [2y]×[2/(y + 3)]
P = 4y/(y + 3)
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Solve the equation for y.
2
у - 2/3x= -6
Answer:
[tex]y=1\frac{1}{3}x-3[/tex]
Step-by-step explanation:
Isolate y to find the value of y
2y-2/3x=-6
+2/3x. +2/3x
2y=2/3x-6
/2. /2. /2
y=4/3x-3
Hopes this helps please mark brainliest
A shopkeeper compares the income from sales of a laptop in July and August. August 1/3 Price Number sold 2/5 more than July less than July By what fraction does the income from these sales decrease in August? Answer: Decreases by ....
The fraction that illustrates the decrease in sales is 15.
What is fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this case, August 1/3 and this was 2/5 more than what was sold earlier. Therefore the decrease will be:
= 2/5 - 1/3
= 6/15 - 5/15
= 1/5
The fraction is 1/15.
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at track practice, steve works out doing lunges on a path that is 110 yards long. if steve can cover 22 in with each lunge, how many lunges will it take to cover the path?
Answer:
It will take 5 lunges to cover the path.
Step-by-step explanation:
Path length = 110
1 lunge = 22 yards
110/22 = 5
5 lunges = 22x5 = 110 yards
is 25 3/8 bigger than 25 2/5
best answer = brainliest
Answer:
2/5 is greater than 3/8, so 25 2/5 is greater
Step-by-step explanation:
Find the least common denominator or LCM of the two denominators:
LCM of 5 and 8 is 40
Next, find the equivalent fraction of both fractional numbers with denominator 40
For the 1st fraction, since 5 × 8 = 40,
2/5
=
2 × 8
5 × 8
=
16/40
Likewise, for the 2nd fraction, since 8 × 5 = 40,
3/8
=
3 × 5
8 × 5
=
15/40
Since the denominators are now the same, the fraction with the bigger numerator is the greater fraction
16/40 > 15/ 40 or 2/5 > 3/8
please help i need this quick asap
A matrix is a set of numbers arranges in rows and columns such that it form a rectangular array.
The value of [tex]x_{11}[/tex] is 8
The value of [tex]x_{21}[/tex] is -1
What is a matrix?A matrix is a set of numbers arranges in rows and columns such that it form a rectangular array.
We have,
[tex]\left[\begin{array}{ccc}3&-8\\1&1\\\end{array}\right] X=\left[\begin{array}{ccc}32\\7\\\end{array}\right][/tex] _____(1)
Now,
[tex]X = \left[\begin{array}{ccc}x_{11}\\x_{21}\\\end{array}\right][/tex] ________(2)
Multiplication of matrix.
From (1) and (2) we get,
[tex]3x_{11} - 8x_{21}[/tex] = 32 ____(a)
[tex]x_{11} + x_{21}[/tex] = 7 ______(b)
From (b) we get,
[tex]x_{11}[/tex] = 7 - [tex]x_{21}[/tex] ______(3)
Substitute (3) in (a)
Now,
3 (7 - [tex]x_{21}[/tex]) - 8[tex]x_{21}[/tex] = 32
21 - 3[tex]x_{21}[/tex] - 8[tex]x{21}[/tex] = 32
-11[tex]x_{21}[/tex] = 32 - 21
[tex]x_{21}[/tex] = -1
Now,
[tex]x_{11}[/tex] = 7 - (-1) = 7 + 1 = 8
Thus,
The value of [tex]x_{11}[/tex] is 8
The value of [tex]x_{21}[/tex] is -1
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Barrett works at an ice cream shop. The function f(x) represents the amount of money Barrett earns per gallon of ice cream, where x is the number of gallons of ice cream he makes. The function g(x) represents the number of gallons of ice cream Barrett makes per hour, where x is the number of hours he works. Show all work to find f(g(x)), and explain what f(g(x)) represents.
f(x) = 2x2 + 4
g of x equals the square root of the quantity 3 x cubed
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The value of f(g(x)) is 6x³ + 4.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
3x + 4 = 5 is an equation.
2x + 4x = 4 is an equation.
We have,
The function f(x) represents the amount of money Barrett earns per gallon of ice cream, where x is the number of gallons of ice cream he makes.
The function g(x) represents the number of gallons of ice cream Barrett makes per hour, where x is the number of hours he works.
f(x) = 2x² + 4
g(x) = √(3x³)
Now,
f(g(x)):
= f(√(3x³))
= 2{√(3x³)}² + 4
= 2(3x³) + 4
= 6x³ + 4
Thus,
The value of f(g(x)) is 6x³ + 4.
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What does b represent in the equation of a line in the form y = mx + b?The y-intercept
The value of x when y = 0
The slope
The x-intercept
Answer:
The y intercept
Step-by-step explanation: