the cost of a broom is $62.50, and the cost of a mop is x + 15 = 62.5 + 15 = $77.50.
Therefore,
a) 1 mop cost $77.50
b) 1 broom cost $62.50
What is the system of equations?
A system of equations is a set of one or more equations involving a number of variables. The solutions to systems of equations are the variable mappings such that all component equations are satisfied in other words, the locations at which all of these equations intersect.
To find the cost of a mop and a broom, we can set up a system of equations using the information given:
Let x be the cost of a broom
Let y be the cost of a mop (which is $15 more than a broom)
From the problem, we know that:
y = x + 15 (since a mop costs $15 more than a broom)
5x + 7y = 855 (since 5 mops and 7 brooms cost a total of $855)
We can substitute the first equation into the second equation:
5x + 7(x + 15) = 855
5x + 7x + 105 = 855
12x = 750
x = 62.5
Hence, the cost of a broom is $62.50, and the cost of a mop is x + 15 = 62.5 + 15 = $77.50.
Therefore,
a) 1 mop cost $77.50
b) 1 broom cost $62.50
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Please provide an explanation
If [tex]$\mathrm{x} \neq 3$[/tex], the expression [tex]$\frac{2 x^3+7 x^2-3 x-25}{x+3}$[/tex] is equivalent to [tex]$2 x^2+x-6-\frac{7}{x+3}$$[/tex].
What is meant by expression?A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. Any one of the following mathematical operations can be used.
A mathematical sentence with variables, numbers, or both is known as an expression. Operation can also be a part of an expression, although an equal sign is never present in an operation. A mathematical expression that demonstrates the equality of two expressions is called an equation. There is a sign of equality in equations.
An expression in mathematics is made up of a mixture of variables, numbers, and functions (such as addition, subtraction, multiplication or division etc.) In some ways, phrases and expressions are comparable.
Let the equation be
[tex]$\frac{2 x^3+7 x^2-3 x-25}{x+3}[/tex]
simplifying the equation, we get
[tex]$& \text { Divide } \frac{2 x^3+7 x^2-3 x-25}{x+3}=2 x^2+\frac{x^2-3 x-25}{x+3} \\[/tex]
[tex]$& =2 x^2+\frac{x^2-3 x-25}{x+3}[/tex]
[tex]$& \text { Divide } \frac{x^2-3 x-25}{x+3}=x+\frac{-6 x-25}{x+3} \\[/tex]
[tex]$ =2 x^2+x+\frac{-6 x-25}{x+3}[/tex]
Divide [tex]$\frac{-6 x-25}{x+3}=-6+\frac{-7}{x+3}$[/tex]
[tex]$=2 x^2+x-6+\frac{-7}{x+3}$$[/tex]
Simplifying the equation, we get
[tex]$=2 x^2+x-6-\frac{7}{x+3}$$[/tex]
Therefore, the correct answer is option 1) [tex]$2 x^2+x-6-\frac{7}{x+3}$$[/tex].
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A sample of fish from a river showed
that of the fish were less than one
year old. If there are an estimated
8,000 fish in the river, about how
many of them are less than one year
old?
You and 3 friends go out for lunch and the total bill was $36. You decide to split the bill evenly. You also decide to leave a 12% tip on your part. How much are you responsible for paying?
When you and your 3 friends decide to split the bill of $36 evenly and you leaving a 12% tip on your part, you pay a total of $13.32.
Therefore the answer is 13.32 dollars.
When you and your 3 friends decide to split the bill evenly, each person is responsible for paying 1/4 of the total bill. The total bill is $36, so each person is responsible for paying
$36 / 4 = $9
You also decided to leave a 12% tip on your part, so you need to calculate 12% of $36. To do this, you can multiply $9 by 0.12
$36 × 0.12 = $4.32
So, you are responsible for paying $9 + $4.32 = $13.32
So you are responsible for paying $13.32 in total.
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Michael's pumpkin farm sold 75 pumpkins on October 24 that day they made $600. What did Michael charge for each pumpkin?
Answer:
$8.
Step-by-step explanation:
right!!
I need help asap .....
fill in the table using this function rule. y=6x-36
5( x-3 ) + 2x =41
What is x?
Answer:
8
Step-by-step explanation:
5 ( x - 3 ) + 2x = 41
5x - 15 + 2x = 41
5x + 2x - 15 = 41
7x - 15 = 41
7x = 41 + 15
7x = 56
x = 56 / 7
x = 8
Answer:
X=8
Step-by-step explanation:
Combine like terms: 5x + 2x = 7x
-15 + 7x = 41
Solving
-15 + 7x = 41
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '15' to each side of the equation.
-15 + 15 + 7x = 41 + 15
Combine like terms: -15 + 15 = 0
0 + 7x = 41 + 15
7x = 41 + 15
Combine like terms: 41 + 15 = 56
7x = 56
Divide each side by '7'.
x = 8
is y = 1/3x + 4 proportional
Calculate the perimeter of the parallelogram. Round to the nearest tenth, if necessary. Enter the perimeter, in units, using numbers only (decimal point is ok, if needed).
Answer:
28 units
Step-by-step explanation:
Firstly, we can see that the vertical sides are 9 units each.
To get the diagonal sides, we can turn the ends into right triangles, which we can then use with the Pythagorean Theorum.
To make the top side into a triangle, we would draw a horizontal line connecting points (-1, 3) and (3, 3). This creates a right angle which is essential when using the Pythagorean Theorum.
A^2 + B^2 = C^2
We can plug in values for the Pythagorean Theorum because we can see that going across horizontally from point (-1, 3) to (3, 3), there are 4 units in between the two points. This will be our A value. We will do the same but vertically from points (3, 6) to (3, 3). The 3 units between the two points will be our B value. Now, we can plug in our values into the Pythagorean Theorum to find side C, the hypotenuse.
4^2 + 3^2 = C^2
16 + 9 = C^2
25 = C^2
√25 = C
C = 5
Now that we know the diagonal value of the side, we also know the same diagonal value of the bottom side. When you add all four sides together,
9 + 5 + 9 + 5 = 28
you get 28, which is the perimeter of the parallelogram.
John has $4,069 in an account. The interest rate is 12% compounded annually. To the nearest cent, how much interest will he earn in 1 year? Use the formula B=p(1+r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years. $
After solving the equation: the nearest cent, the interest earned is $467.
What is interest?Interest is a mathematical concept used to describe the cost or gain associated with the use of money over a period of time. It is usually expressed as a percentage rate of the principal (the amount borrowed or invested). Interest can be earned or paid, depending on the situation.
Using the formula B=p(1+r)t, John's final balance after 1 year is B = 4069(1+0.12)1 = $4,536.28.
The interest earned in 1 year is the difference between the final balance and the starting amount, which is $4,536.28 - $4,069 = $467.28. To the nearest cent, the interest earned is $467.
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Find two numbers that sum to 27 and their difference is 5
When Tobey was born, his parents invested $2,000 in a fund that paid an annual interest of 6%. How old will Tobey be when the investment is worth at least $5,000?
So, a 72-month loan with a 2 annual simple interest rate is the loan choice that would need her to repay the least amount of money.
What is interest rate ?An interest rate informs you of how much borrowing will cost you and how much saving will pay off. Therefore, the interest rate is the amount you pay for borrowing money and is expressed as a percentage of the entire loan amount if you are a borrower.
According to the information provided, a 72-month loan with a 2 annual simple interest rate is the loan choice that would require her to repay the least amount of money. This is because the amount she would have to pay will be the least compared to other loan options.
[tex]Loan = 72 months (2per cent of $6,000)\\Loan = 120 for 72 months\\Loan =$8,640\\[/tex]
a 72-month loan with a 2 yearly simple interest rate.
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need help with this screenshot
The quadratic equation in vertex form is y = -(x - h)² + k
The parabola passed through points (-1, -3), (0, 0), (1, 1), (2, 0) and so on
How to write the equation of parabola in vertex formFor a vertical parabola, the vertex form of the equation is written as
y = a(x - h)² + k
where:
a = 1/4p
h and k are points of the vertex = v(h, k)
The vertex
v (h, k) = (1, 1)
h = 1
k = 1
y = a(x - 1)² + 1
using point (0, 0)
0 = a(0 - 1)² + 1
-1 = a
hence a = -1
the equation is written as y = -(x - h)² + k
The points the graph passed is read from the graph to be
(-1, -3), (0, 0), (1, 1), (2, 0) and so on
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What word is used to remember the 3 trigonometric ratios?
The word used to remember the 3 trigonometric ratios sine, cosine, and tangent is SOH-CAH-TOA
We know that in right triangle for an angle θ, the trigonmetric ratios are:
sin(θ) = opposite side of θ/ hypotenuse
cos(θ) = adjacent side of θ / hypotenuse
tan(θ) = opposide side of θ / adjacent side of θ
cot(θ) = 1/tan(θ)
sec(θ) = 1/cos(θ)
cosec(θ) = 1/sin(θ)
The word 'SOH-CAH-TOA' is used to remember the sine, cosine, and tangent ratios in a right triangle.
SOH means, Sine = Opposite side / Hypotenuse.
CAH means, Cosine = Adjacent side / Hypotenuse.
TOA means, Tangent = Opposite side / Adjacent side
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The area of a square is given by x?, where x is the length
of one side. Mary's original garden was in the shape of a
square. She has decided to double the area of her
garden.
Part 1 out of 2
Enter an expression that represents the area of Mary's
new garden.
An expression that represents the area is
✓ Check
Next
Answer:
Step-by-step explanation:
If she doubles the area of her lot, it should be 2x^2.
But how do you get that?
The answer is that the sides have now increased to √2x
How did I get that, and why did I choose it?
The formula for a square's area is s^2If you want to double the area, it will be 2 s^2. Now what?Take the square root of 2s^2 which is √(2s^2).What that means is the side is now √2 sPredict the approximate GPA of a student who watches television for 8 hourson average, per day
Answer:
2
Step-by-step explanation:
Han earns 33.00 for babysitting 4 hours at this rate how much will he earn if the babysitter for 7 hours explain your reasoning
Han will make $57.75 for 7 hours of babysitting.
What are equations?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign "=".
Given is that Han earns $33 for babysitting 4 hours.
Han made $33 for 4 hours of work.
Then, he will make $(33/4) in 1 hour of work.
Then, he will make $(33/4 x 7) in 7 hours of work.
$(33/4 x 7)
$(33/4 x 7)
$(231/4)
$57.75
Therefore, Han will make $57.75 for 7 hours of babysitting.
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I have a set of numbers: 7, 3, 9, 5, 2. What number do I have to add to get the mean to be 6?
Answer:
10
Step-by-step explanation:
(7+3+9+5+2+x)/6=6
26+x/6=6
26+x=36
x=10
Answer:
you need to add 10
Step-by-step explanation:
7+3+9+5+2=26
26+10= 36
total 6 numbers so you divide it by 6
36/6= 6
Deon made 4 identical necklaces, each having beads and a pendant. The total cost of the beads and pendants for all 4 necklaces was $21.60. If the beads cost 2.20 for each necklace, how much did each pendant cost?
Answer:by uvyvyvyi
Step-by-step explanation:
Find the measure of angle 3.
A. 15 degrees
B. 45 degrees
C. 30 degrees
D. 60 degrees
Answer:
B. 45
Step-by-step explanation:
If im wrong please let me know
Have a nice day :)
Find the value of x.
Answer:
x = 25
Step-by-step explanation:
The top angle is the supplement of 3x - 10
180 - (3x - 10) = -3x + 190
The sum of the angles in a triangle is 180
(-3x + 190) + (25) + (x + 15) = 180
Combine like terms
-2x + 230 = 180
Subtract 230 from both sides
-2x = -50
Divide both sides by -2
x = 25
Which statement regarding the region of rejection for a 5%
significance level is TRUE?
A z-score higher than 2 is part of the region of rejection
The region of rejection lies between the z-scores -2 and
2.
If a z-score falls within the region of rejection, it indicates
that the alternative hypothesis may be valid.
The region of rejection indicates that the null hypothesis
is true.
The statement regarding the region of rejection for a 5% significance level would be true is the region of rejection lies between the z-scores -2 and 2.Option B is correct.
What is region of rejection?A collection of values for the test statistic for which the null hypothesis is rejected constitutes a critical zone, sometimes referred to as the region of rejection. For example, if the observed test statistic is in the critical range, the null hypothesis is rejected and the alternative hypothesis is accepted.
Further the rejection zone is the area in which we have sufficient data to reject the null hypothesis if our test statistic falls within it. The rejection area, for the right-tailed test, for instance, is any value bigger than the critical value, or c 1 .
Therefore, the interval that causes the null hypothesis H 0 to be rejected in a hypothesis test is known as the region of rejection and is measured in the sampling distribution of the statistic under examination.
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Where would I start when rewriting polynomials in standard form? I have my notes but they’re still unclear to me.
Answer:
Step-by-step explanation:
standard form = combine like therms and degrees drop from left to right
In this there aren’t like therms, so:
6x^3+x^2-9x+5
therms = each therm is seprated by a plus or a minus
in this case there are 4 therms
degree = look at the monomial with the highest degree
in this case is 3
Name = in this case there are four therms so it is a quadrinomial
Standard form denotes to arranging according to degrees or exponents
Standard form
6x³+x²-9x+5Number of terms=4
Degree=3
Name Quadrinomial or Biquadratic
whats the slope and y intercept of y-2x=5
1/3p multiplied by 9q is what?
Answer:
3pq
Step-by-step explanation:
( x - 4 ) + ( 2x - 7 )
- find the Sum or Difference :)
[tex]( x - 4 ) + ( 2x - 7 )[/tex]
Combine Like Terms:
[tex](x+2x)+(-4+-7)[/tex]
[tex](3x)+(-11)[/tex]
[tex]\fbox{3x - 11}[/tex]
Answer:3x-11
Step-by-step explanation:
(x-4)+( 2x-7)
x-4+2x-7
3x-11
What is an irrational number? ????
Answer:
a number that cannot be written as a/b
it's a non-repeating, non-terminating decimal
typically, irrational numbers are square roots of numbers that are not perfect squares; also, π is considered irrational
Step-by-step explanation:
Brian buys bananas from the grocery store each week. Last week he bought 5 pounds of bananas and paid $2.95. If he buys 8 pounds of bananas this week, how much will he pay?
A certain pickup truck gets 14 mpg in the city and 21 mpg on the highway. If the driver drives 220 mi on 12 gal of gas, determine the number of city miles and
highway miles that the truck was driven?
The number of students who picked football and rugby are in the ratio of 4:3 The number of students who picked rugby and tennis are in the ratio of 12:25 150 students picked tennis.Work out how many students picked football.
This question makes no sense, If you mean we are trying to find Rugby, then yes I get that but, Football was only mention once, and once only. I think it's possibly 72 students chose Rugby. The First equation is basically useless unless you are given an Idea of the fact that we need to use the first equation. If that is the case then 12 people chose football. If I didn't help I apologize for that but I was given a question I couldn't make sense of.