By setting up an equation with x as the cost of Tanya's items, we find that each of Tanya's items cost $9.00. Tony's items, being $2.25 cheaper, cost $6.75 each. The solution is checked by ensuring both Tanya's and Tony's total expenditure was equal.
The question asks us to find the individual cost of items purchased by Tanya and Tony at a store, given that Tony's items each cost $2.25 less than Tanya's but both spent the same amount overall.
Equation Setup
Let x represent the cost of one of Tanya's items. Since Tanya bought 3 items, she spent 3x dollars. Tony's items each cost $2.25 less, so they cost (x - $2.25) each. Tony bought 4 items, spending 4(x - $2.25). Since both spent the same amount:
3x = 4(x - $2.25)
Solving the Equation
To solve for x:
Distribute the 4 on the right side of the equation to get 3x = 4x - $9.00.Subtract 4x from both sides to get -x = -$9.00.Divide both sides by -1 to get x = $9.00.So, each of Tanya's items cost $9.00.
Checking the Solution
To verify:
Tanya's total is 3($9.00) = $27.00.Tony's total is 4($9.00 - $2.25) = 4($6.75) = $27.00.Both totals match, confirming that the solution is correct.
Tanya's items each cost $9.00, while Tony's items, costing $2.25 less, each cost $6.75.
Rob measures his go-cart’s speed to be 250 inches per second. What is the go-cart’s speed in miles per hour (to the nearest tenth) ?
A) 7.1 mph
B) 14.2 mph
C) 28.4 mph
D) 35.2 mph
Answer:
b.14.2 mph
Step-by-step explanation:
Answer:
The cart’s speed in miles per hour is 14.2 miles per hour .
Option (B) is correct .
Step-by-step explanation:
As given
Rob measures his go-cart’s speed to be 250 inches per second.
As
[tex]1\ inch = \frac{1}{63360}\ miles[/tex]
[tex]1\ second = \frac{1}{3600}\ hours[/tex]
Now convert 250 inches per second into miles per hour .
[tex]250 inches\ per\ second = \frac{250\times \frac{1}{63360}}{\frac{1}{3600}}\ miles\ per\ hour[/tex]
[tex]250 inches\ per\ second = \frac{\frac{250}{63360}}{\frac{1}{3600}}\ miles\ per\ hour[/tex]
[tex]250 inches\ per\ second = \frac{250\times 3600}{63360}\ miles\ per\ hour[/tex]
[tex]250 inches\ per\ second = \frac{900000}{63360}\ miles\ per\ hour[/tex]
250 inches per second = 14.2(Approx) miles per hour.
Therefore the cart’s speed in miles per hour is 14.2 miles per hour .
Option (B) is correct .
Factor.
12x^2-44x+7 and 35x^2-27x-18
12x^2-44x+7 = (6x - 1)(2x - 7)
35x^2-27x-18 = (7x - 9)(5x +2)
Multiply. Express your answer in simplest form. 5/8 x 4/7
Answer 5/14
Step-by-step explanation:
The simplest form of the given expression [tex]\frac{5}{8} \times \frac{4}{7}[/tex] is [tex]\frac{5}{14}[/tex].
An expression is a combination of numbers, variables, operations, functions, and often symbols that are combined according to particular rules to represent a mathematical computation or relation.
Expressions can be both simple as a single number or variable and complex by involving multiple variables and operations.
Some examples of Expressions are x, 4, x² + 6y + 2xy +6, [tex]\frac{x}{y}[/tex], [tex]\frac{x}{y} \times \frac{p}{q} \div e^7[/tex] etcectra.
The given expression is
[tex]\frac{5}{8} \times \frac{4}{7}[/tex] [tex]= \frac{5}{2}\times \frac{1}{7}[/tex]
[tex]= \frac{5\times1}{2\times7}\\ = \frac{5}{14}[/tex].
Hence the given expression [tex]\frac{5}{8} \times \frac{4}{7}[/tex] can be simplified as [tex]\frac{5}{14}[/tex].
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the length of a rectangle is 4 units shorter than on-fourth of the width, x. Write an expression that represents the perimeter of the rectangle (Use one variable and a fraction) (MUST SHOW WORK PLEASE)
ASNSWER
[tex]Perimeter=\frac{5x-16}{2}[/tex]
EXPLANATION
Let [tex]w=x[/tex] represent the width of the rectangle.
One-fourth of the width will be,
[tex]\frac{1}{4}x[/tex]
Let [tex]l[/tex] represent the length of the rectangle.
Then, subtracting 4 units from one-fourth the width gives us the length
[tex]\Rightarrow l=\frac{1}{4}x-4[/tex]
Perimeter[tex]=2x+2l[/tex]
[tex]\Rightarrow Perimeter=2x+2(\frac{1}{4}x-4)[/tex]
We expand to obtain;
[tex]Perimeter=2x+\frac{x}{2}-8[/tex]
[tex]Perimeter=\frac{x+4x-16}{2}[/tex]
[tex]Perimeter=\frac{5x-16}{2}[/tex]
2(x+3) great her that or equal to -10 - 4x
2(x + 3) ≥ -10 - 4x
2x + 6 ≥ -10 - 4x
+4x +4x
6x + 6 ≥ -10
-6 -6
6x ≥ -16
[tex]\frac{6x}{6} \geq \frac{-16}{6}[/tex]
[tex]x \geq -\frac{8}{3}[/tex] reduced fraction
2(x+3) greater than or equal to -10 - 4x
So
2(x+3) >= -10 - 4x
2x + 6 >= -10 - 4x
2x + 4x >= -10 - 6
6x >= - 16
x >= - 16/6
x >= - 8/3
What is the graph of the function?
F(x) = 1/2x^2
F(x) = 1/2x^2 is a variation of the basic graph y = x^2 (the squaring function).
The graph of the squaring function has the shape of a parabola that opens up. Its vertex is at (0,0).
The graph of F(x) = (1/2)x^2 has the same shape, but is compressed vertically by a factor of (1/2). The vertex of F(x) = (1/2)x^2 is still (0,0). That eliminates the first 2 possible answers. Note that F(1) = (1/2)(1)^2 = 1/2. The point (1, 1/2) is on the third graph, but not on the fourth. Thus, the third graph is correct.
Only the third graph (option C) represents the graph of [tex]F(x) = \frac{1}{2} x^2[/tex]
The given function is:
[tex]F(x) = \frac{1}{2} x^2[/tex]
This graph is of the form [tex]y = ax^2[/tex] and it takes the shape of a parabola with center at (0, 0)
Only two of the graphs shown among the options have the center at the origin (0, 0), but only one is scaled by 0.5
Therefore, the graph of the function [tex]F(x) = \frac{1}{2} x^2[/tex] is plotted below
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Ishi makes $8.50 an hour rolling sushi at kyoto japanese restaraunt his paycheck shows that he worked 20.88 hours over the past two weeks how muck did ishi earn
Which of the following points are solutions to the equation
y=3x+5
(7,16)
(-2,1)
(2,11)
(-7,16)
select two
I only get one (2, 11)
to find the points which are solutions, substitute the x-coordinate into the equation and if the value obtained equals the y-coordinate of the point then it is a solution
(7, 16) : y = (3 × 7 ) + 5 = 21 + 5 = 26 ≠ 16
( - 2, 1): y = (3 × - 2) + 5 = - 6 + 5 = - 1 ≠ 1
(2, 11) : y = (2 × 3) + 5 = 6 + 5 = 11
( - 7,16 ): y = (3 × - 7) + 5 = - 21 + 5 = - 16 ≠ 16
the only point from the given list that is a solution is (2 , 11)
By substituting the x and y values of the given points into the equation 'y = 3x + 5', we can determine that the only solution from the given points is (2,11).
Explanation:The given equation is y = 3x + 5. We can find out which of the points are solutions to the equation by substituting the x-coordinate and y-coordinate of each point into the equation. If the equation holds true, then the point is a solution.
For the point (7, 16), the equation becomes 16 = 3*7 + 5. This simplifies to 16 = 21 + 5. This is not true, so (7, 16) is not a solution. For the point (-2,1), the equation becomes 1 = 3*(-2) + 5. This simplifies to 1 = -6 + 5. This is also not true, so (-2,1) is not a solution. For the point (2, 11), the equation becomes 11 = 3*2 + 5. This simplifies to 11 = 6 + 5, which is true, so (2,11) is a solution. For the point (-7,16), the equation becomes 16 = 3*(-7) + 5. This simplifies to 16 = -21 + 5. This is not true, so (-7,16) is not a solution.
So, the points that are solutions to the equation y = 3x + 5 are (2,11).
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What is the vertex of this function f(x)=x^2+12x
Answer:
(-6, 36)
Step-by-step explanation:
The standard form: ax^2 + bx + c
In this case:
a is 1
b is 12
c is 0
Calculate -b / 2a. This is the x-coordinate of the vertex.
To find the y-coordinate of the vertex, simply plug the value of -b / 2a into the equation for x and solve for y. This is the y-coordinate of the vertex.
-12 / ( 2 x 1 )
-12 / 2
-6
You log -6 in the function
f(x) = x^2 + 12x
f(-6) = (-6)^2 + 12(-6)
= 36 + (-72)
= 36 - 72
= 36
I hope this
Answer: A (-6, -36)
Step-by-step explanation:
Dennis traveled at an average speed of 60 mph on his vacation trip. How far did he travel in the first 4.5 hours
Answer: 280 Miles.
Step-by-step explanation: 60 x 4 = 240 + 40 = 280 Miles.
Shawn’s rectangular mobile home is 7.2 meters wide and 19.5 meters long what is the area
Answer: The area of the mobile is 140.4 m².
Step-by-step explanation:
Hi to solve this problem we have to analyze the information given:
Width : 7.2 meters (a)
Length : 19.5 meters (b)
The mobile is rectangular. So, we have to apply the area of a rectangle formula.
Area = width x length A = 7.2 x 19.5 = 140.4 m²The area of the mobile is 140.4 m².
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Clara and Toby are telemarketers. Yesterday, Clara reached 4 people in 10 phone calls, while Toby reached 3 people in 8 phone calls. If they continue at those rates, who will reach more people in 40 phone calls?
toby will reach more people in 40 phone calls
The way to solve this problem is to turn both denominators into 40
4 * 4 16
_ = --- so Clara will reach 16 people in 40 phone calls
10 * 4 40
3 * 5 15
_ = ---- so Toby will reach 15 people in 40 phone calls
8 * 5 40
Therefore Clara will reach more people in 40 phone calls than Toby.
The question of the week! (Please show your work!)
Sarah's craft project uses pieces of yarn that are 1/8 yard long. She has a piece of yarn that is 3 yards long. How many 1/8 yard pieces can she cut and still have 1 1/4 yards left?
please help on this one?
If you have 2 squares with the same side lengths are they still considerd scaled copies of each other?
Describe how to find the number of seats on the middle and lower levels of the stadium when solving for the variable only gives the number of seats on the upper level.
Use the value for the variable to solve for the other unknowns. Substitute the value for the variable into the expression for the number of seats on the middle level. Substitute the value for the variable into the expression for the number of seats on the lower level.
Use the value for the variable to solve for the other unknowns. Substitute the value for the variable into the expression for the number of seats on the middle level.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Use the value for the variable to solve for the other unknowns. Substitute the value for the variable into the expression for the number of seats on the middle level. Substitute the value for the variable into the expression for the number of seats on the lower level.
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What should be the next number in the following series? 3 6 4 7 5 8
The next number would be 6.
The pattern is add 3, then subtract two.
The next number in the series 3 6 4 7 5 8 is 6.
Explanation:The next number in the series 3 6 4 7 5 8 is 6.
This is an alternating pattern where the first number increases by 1, the second number stays the same, and the third number increases by 1. So, starting with 3, the next number after 8 should be 9. However, since 9 is not given in the options, we can look for the closest number that follows the pattern, which is 6.
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Which graph represents the solution to the system of inequalities?
y ≥ x – 5
y < –x + 4
A. hope this helps. Mark as Brainliest.
Jordan bought 9/16 of a pound of sunflower seeds and divided them evenly into 9 snack bags for his lunch what is the weight of sunflower seeds in each snack bag?
A)1/16 of a pound
B)1/9 of a pound
C)16/81 of a pound
D)81/16 of a pound
A.1/16 of a pound. Hope i helped
Answer:
A
Step-by-step explanation:
Based on your knowledge of taxes you estimate the net pay will be 65%of your gross pay you think you will need 250 per week after taxes to get by. What annual gross will you need?
Answer:
You need annual gross pay of 20000.
Step-by-step explanation:
Suppose, your annual gross pay is [tex]x[/tex]
You estimate that the net pay will be 65% of your gross pay. So, the annual net pay will be: [tex]x*65\% = 0.65x[/tex]
As there are 52 weeks in 1 year, so your weekly net pay will be: [tex]\frac{0.65x}{52}[/tex]
Given that, you will need 250 per week after taxes to get by. So, the equation will be......
[tex]\frac{0.65x}{52}=250\\ \\ 0.65x= 52*250=13000\\ \\ x=\frac{13000}{0.65}=20000[/tex]
So, you need annual gross pay of 20000.
Which ordered pair (m, n) is a solution to the given system of linear equations?
6m-5n= 14
2m+2n= -10
a) (-4,-1)
b) (-31/11,-24/110
c) (-1,-4)
d) (11,-16)
ANSWER: NOT B
Answer:
Option C
Step-by-step explanation:
given two equations
6m-5n= 14 ... i
2m+2n= -10 ...ii
We can solve this by elimination.
For elimination consider the coefficients of m.
They are 6 and 2, with LCD 6
You multiply 2nd equation by 3 to have
6m+6n =-30 ... iii and
6m-5n = 14 ... i
Subtract i from iii
11n = -44
Divide by 11 to get n
n = -4
Substitute in I equation
6m-5(-4) =14
6m +20 = 14
subtract 20
6m =14-20 =-6
divide by 6
m =-1
Hence answer is m=-1 and n=-4
(-1,-4)
Option C is the answer.
if f(x)=3x+5 and g(x)=-2x^2-5x+3, find (f+g) (x)
[tex]f(x)=3x+5,\ g(x)=-2x^2-5x+3\\\\(f+g)(x)=f(x)+g(x)=(3x+5)+(-2x^2-5x+3)\\\\=3x+5-2x^2-5x+3=-2x^2+(3x-5x)+(5+3)=-2x^2-2x+8\to\boxed{C.}[/tex]
In general, employment applications require all of the following except:
A.references.
B.your employment history.
C.your GPA.
D.your highest level of education.
Answer:
C.your GPA
Step-by-step explanation:
In general, employment applications require all of the following except:
C.your GPA
The GPA is not as important as the references, ones employment history and the highest level of education.
These information gives an overview about your history like if you are a fresher or an experienced person. And what education have you got, or who referred you to this particular company.
The GPA's are not considered at the first place. When a person progresses in an interview, then GPA might be considered to gather information like the person is how much efficient in that particular subject.
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Solve x2 + 4x − 4 = 0.
x equals the quantity of negative 2 plus or minus square root 16 all over 2
x equals negative 4 plus or minus square root 2
x equals negative 2 plus or minus 2 square root 2
x equals the quantity of 4 plus or minus square root 18 all over 2
ANSWER
[tex]x=-2\pm 2\sqrt{2}[/tex]
EXPLANATION
Given:
[tex]x^2+4x-4=0[/tex]
We complete the square as follows;
Add 4 to both sides of the equation:
[tex]x^2+4x=4[/tex]
Add half the coefficient of [tex]x[/tex] to both sides of the equation.
[tex]x^2+4x+(2)^2=4+(2)^2[/tex]
The Left Hand Side of the equation is now a perfect square.
[tex](x+2)^2=4+4[/tex]
[tex](x+2)^2=8[/tex]
Take the square root of both sides
[tex]x+2=\pm \sqrt{8}[/tex]
[tex]x=-2\pm 2\sqrt{2}[/tex]
Hence the correct answer is option C
Given equation is [tex]x^2+4x-4=0[/tex]
compare with [tex]ax^2+bx+c=0[/tex]
we get: a=1, b=4, c=-4
plug these values into quadratic formula:
[tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{-4 \pm \sqrt{4^2-4(1)(-4)}}{2(1)}[/tex]
[tex]x=\frac{-4 \pm \sqrt{16-4(-4)}}{2}[/tex]
[tex]x=\frac{-4 \pm \sqrt{16+16}}{2}[/tex]
[tex]x=\frac{-4 \pm \sqrt{32}}{2}[/tex]
[tex]x=\frac{-4 \pm 4\sqrt{2}}{2}[/tex]
[tex]x=-2 \pm 2\sqrt{2}[/tex]
Hence finall answer is:
[tex]x=-2+2\sqrt{2}[/tex] and [tex]x=-2-2\sqrt{2}[/tex]
Paul invested three times as much money in the account paying 5% interest then he did in an account paying 4% of the total interest paid was $475 how much did he invest in each
Given
Paul invested three times as much money in the account paying 5% interest then he did in an account paying 4%.
Total interest paid was $475
Find out he invest in each.
To proof
Let us assume that Paul invested in an account paying 4% be = x
As given in the question
Paul invested three times as much money in the account paying 5% interest then he did in an account paying 4%.
Let us assume that Paul invested in an account paying 5% be = 3x
Total interest paid = $475
First convert 4% in the decimal form
[tex]=\frac{4}{100}[/tex]
= 0.04
First convert 5% in the decimal form
[tex]=\frac{5}{100}[/tex]
= 0.05
Than the equation become in the form
0.04x + 0.05 × 3x = 475
0.04x + 0.15x = 475
0.19x = 475
x = $2500
Paul invested in an account paying 4% be = $2500
Paul invested in an account paying 5% be = $7500
Hence proved
Simplify. Remove all perfect squares from inside the square root. 63
[tex]\sqrt{63} = \sqrt{9*7} = \sqrt{3*3*7} = 3\sqrt{7}[/tex]
The simplified form of √(63) after removing all perfect squares from inside the square root is 3√(7).
To simplify the square root of 63 and remove perfect squares, we start by finding the prime factorization of 63. The prime factorization of 63 can be obtained by dividing the number by its smallest prime factor, which is 3, and then continuing the process for each quotient until we get a prime number. The prime factorization of 63 is:
63 = 3 * 3 * 7.
Now, we look for any perfect square factors within the square root of 63. In this case, the perfect square factor is 3 * 3 (3 squared). We can remove this perfect square from the square root, leaving us with:
√(63) = √(3 * 3 * 7).
Since we removed one pair of 3's (3 * 3), the simplified square root of 63 becomes:
√(63) = 3√(7).
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-6/5x+2=21/25 anyone?
x=-64/35
-6/5x+2= 21/25
Do fraction cross multiply
(-6*25=(5x+2)21
Then swap the sides (5x+2) *21 = (-6)*25
multiply(5x+2)21= -150/21
simplify
5x+2=- 50/7
subtact 2
5x+2-2=- 50/7-2
silmplify 5x=-64/7
divide by 5
5x/5=-64/7/5
simplify
x= -64/35
Solve:
-6/5x + 2 = 21/25
Steps:
Solution -6/5x + 2 = 21/25 =======> 29/30, Decimal =====> x = 0.96667
Subtract 2 from both sides:
-6/5x + 2 - 2 = 21/25 - 2
Simplify:
-6/5x = -29/25
Multiply both sides by -25:
(-6/5x )(-5) = (-29/25 )(-5)
Simplify:
6x = 29/5
Divide both sides by 6:
6x/6 = 29/5/6
Simplify:
Answer x = 29/30 Decimal: 0.96667....
Hope that helps!!!! : )
Which function is a horizontal compression of its parent function f(x)=x^7 by a factor of 4
Answer:
[tex]r(x)=(4x)^7[/tex]
Step-by-step explanation:
For a horizontal compression, we multiply whole numbers greater than 1 in front of [tex]x[/tex] of the given function.For horizontal expansion, we multiply by the reciprocal of the number for horizontal compression, in front of [tex]x[/tex] of the function.For example,
If we wanted to horizontally compress [tex]y=x^2[/tex], we would multiply by 4 to get [tex]y=(4x)^2[/tex], and
if we wante to horizontally expand [tex]y=x^2[/tex], we would multiply by [tex]\frac{1}{4}[/tex] to get [tex]y=(\frac{1}{4}x)^2[/tex]
Since this question asks for horizontal compression, we multiply the [tex]x[/tex] of the function by 4. So the function we need is [tex]f(x)=(4x)^7[/tex]. The second choice is correct.
Divide. Write the answer in simplest form. 7 1/5 divided by 1/8
First we have to change 7 1/5 into an improper fraction. 7 1/5 converted to an improper fraction is 36/5. Now, to divide this by 1/8, we need to multiply it by 8 (multiplying by the reciprocal). 36/5 * 8/1 = 288/5. In simplest form, this is 57 3/5.
The division problem 7 1/5 divided by 1/8 is solved by converting the mixed number to an improper fraction, converting the division problem to a multiplication problem by multiplying by the reciprocal, and then simplifying the resulting fraction. The final answer is 57.6.
To solve the problem 7 1/5 divided by 1/8, we first need to convert the mixed number 7 1/5 into an improper fraction. We do this by multiplying the whole number 7 by the denominator of the fraction 5 and then adding the numerator 1. So, 7 * 5 + 1 = 36.
So, 7 1/5 becomes 36/5. Now, we have 36/5 divided by 1/8.
When we are dividing by a fraction, we need to multiply by its reciprocal. The reciprocal of 1/8 is 8/1. So the problem becomes 36/5 multiplied by 8/1.
When multiplying fractions, we simply multiply the numerators and the denominators together. So, 36 * 8 = 288 and
5 * 1 = 5. Therefore, our answer is 288/5. Lastly, when we simplify this, it becomes 57.6.
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An onsite oil change service charges a flat rate of $40.00 per service call and an additional $2.25 per mile fee for travel outside a certain radius. Josh budgets $200 per year for oil changes on his vehicle. He lives 7 miles outside the radius. What is the greatest number of oil changes (c) that he can schedule and keep on budget for the year?
Answer:
c = 3 oil changes
Step-by-step explanation:
The fixed rate for oil change is $ 40
The surplus rate for miles outside the radius is $ 2.25
Josh lives 7 miles of the radius
Therefore an equation for c: The largest number of oil changes that can be scheduled and maintained within the budget for the year is:
[tex]\\40c + 2.25 * 7c = 200\\c (40 + 2.25 * 7) = 200\\c =\frac{200}{40 + 2.25 * 7}\\c = 3,578\\c = 3[/tex] oil changes
Therefore, with the budget set Josh can make a maximum of 3 oil changes per year
Answer:
The answer is 3
Step-by-step explanation
mileage fee for each oil change: 7(2.25) = $15.75
service call + mileage fee = total for each oil change
$40 + $15.75 = $55.75
c = number of oil changes
55.75c = total amount for all oil changes
55.75c ≤ 200
c ≤ 3.59
Therefore, the greatest number of oil changes that Josh can schedule without exceeding his budget is 3.