The student council sold long sleeve shirts for $12.50 and short sleeve shirts for $10.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the cost of long sleeve and y represent the cost of short sleeve, hence:
24x + 18y = 480 (1)
Also:
34x + 25y = 675 (2)
From both equations:
x = 12.5, y = 10
The cost of long sleeve shirts was $12.50 while short sleeve was $10 each.
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Good people I critically need an assistance with great pleasure!!
Answer:
(y + 3)² - 8
Step-by-step explanation:
y² + 6y +1
Step 1: Divide the co efficient of y by 2
6 ÷2 = 3
Step2: Now find the square of 3
3² = 9
Step3: Add and subtract 9
y² + 6y + 9 - 9 + 1 = y² +6y + 9 - 8
= y² + 2*y*3 + 3² - 8
Compare y² +2 * y*3 + 3² with a² +2ab + b²
= (y + 3)² - 8
If the length of a rectangle is 4 more than the width and if the perimeter of the rectangle is 52, what is the width of the rectangle? O 11 O 12 O 15 0 24
Answer:
11
Step-by-step explanation:
Perimeter is figured out by adding all 4 sides.
Width of 11 + width 11 + length 15 + length 15 = 52
And the length of 15 is 4 more than the width of 11
12x + 3y = 9 solve for y
Answer:
[tex]\Longrightarrow: \boxed{\sf{y=3-4x}}[/tex]
Step-by-step explanation:
To solve for y, you have to isolate it on one side of the equation.
12x+3y=9First, you have to subtract by 12x from both sides.
[tex]\Longrightarrow:\sf{12x+3y-12x=9-12x}[/tex]
Solve.
[tex]\Longrightarrow:\sf{3y=9-12x}[/tex]
Then, you divide by 3 from both sides.
[tex]\Longrightarrow:\sf{\dfrac{3y}{3}=\dfrac{9}{3}-\dfrac{12x}{3}}[/tex]
Solve.
[tex]\sf{\dfrac{9}{3}-\dfrac{12x}{3}}[/tex]
[tex]\sf{\dfrac{9-12x}{3}}[/tex]
Use the distributive property.
[tex]\underline{\text{DISTRIBUTIVE PROPERTY:}}[/tex]
⇒A(B+C)=AB+AC9-12x=3(3-4x)
[tex]\sf{\dfrac{3\left(3-4x\right)}{3}}[/tex]
Divide the numbers from left to right.
3/3=1
3-4x
Then, rewrite the problem down.
[tex]\Longrightarrow: \boxed{\sf{y=3-4x}}[/tex]
Therefore, the correct answer is y=3-4x.I hope this helps! Let me know if you have any questions.
Answer:
y = (3) - (4x)
Step-by-step explanation:
Note: Since there is only one equation given, the value of "y" will not be a fixed value.
Given equation:
12x + 3y = 9Our main goal to solve for "y" is to have the y-variable on one side, and a specific value or variable on the other side (e.g., y = 3 or y = 4x) . Start out by subtracting both sides by 12x. This will isolate the y-variable and it's cooeficient (3).
⇒ 12x + 3y = 9⇒ 12x + 3y - 12x = 9 - 12x⇒ 3y = 9 - 12xOnce the y-variable and the cooeificent of the variable have been isolated, we can divide both sides by the cooeficient to isolate the variable.
⇒ 3y/3 = (9 - 12x)/3⇒ y = (9 - 12x)/3⇒ y = (9 ÷ 3) - (12x ÷ 3)⇒ y = (3) - (4x)Therefore, the value of "y" is 3 - 4x.
Miranda is standing at the corner of a
70 m by 110 m soccer field. She needs
to go to the corner diagonally opposite
from where she is standing. How
much shorter is it if she cuts across the
diagonal instead of walking around
the perimeter of the field? Round your
answer to the nearest tenth.
The distance between the diagonal and the the perimeter of the field is given by D = 229.2 m
What is the diagonal of a rectangle?The diagonal of a rectangle is calculated by the formula
From the Pythagoras Theorem , The hypotenuse² = base² + height² , and
Diagonal of a Rectangle = √ ( Length )² + ( Width )²
Given data ,
Miranda is standing at the corner of a 70 m by 110 m soccer field.
Let the dimensions of the rectangle be 70m x 100m
Now , the length of the diagonal is D
And , from the Pythagoras theorem ,
Diagonal of a Rectangle = √ ( Length )² + ( Width )²
D = √ ( 70 )² + ( 110 )²
D = 130.8 m
Now , the perimeter of the rectangle is P = 2 ( 70 + 110 ) = 360 m
And , walking around the perimeter of the field
Now , by cutting across the diagonal instead of walking around the perimeter of the field, Miranda can save approximately 360 m - 130.8 m ≈ 229.2 m.
Hence , the diagonal of the rectangle is 130.8 m
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please help, i’ll give 20 points
Express the number 68,708 in word form and expanded form.
Word form ?
Expanded form ?
What is the most important question jamir needs to consider before he agrees to a lease? will he enjoy driving his new car? will he be able to stay under the 15,000 miles per year limit? will he be able to afford his $432 payment? will he be able to come up with the $2,500 down payment?
Answer:
Answer is B. Will he be able to stay under the 15,000 miles per year limit?
Step-by-step explanation:
Just took the tes
Answer:
B. Will he be able to stay under the 15,000 miles per year limit?
Step-by-step explanation:
Manuel labore earns $19. 50/hr. And works an average of 38 hours a week. He is considering renting a house for $1,700/ month. His real estate friend recommends he spend no more than 28% of his monthly income on housing.
Answer:
Given:
Wage = $19.50 per hourWeekly hours worked = 38⇒ Weekly income = 38 × $19.50 = $741
⇒ Monthly income = ($741 × 52.14) ÷ 12 = $3219.65
28% of monthly income
= 0.28 × $3219.65 = $901.50
As $1700 > $901.50 Manuel should not rent the house for $1700 per month since it is more than 28% of his income.
The cost of rent at $1700 per month is actually 52.8% of his monthly income:
(1700 / 3219.65) x 100 = 52.8%
Select the correct answer from each drop-down menu. observe the functions below. complete the following sentences to compare the two functions. over the interval , the average rate of change of g is greater than the average rate of change of f. as the value of x increases, the average rates of change of f and g , respectively. when the value of x is equal to 8, the value of . it can be further generalized that a quantity increasing exponentially will exceed a quantity increasing linearly.
The answers will be:
(4, 5)remain constant and increaseg(x) exceeds the value of f(x)What is Slope and curve?a) The slope of the curve g(x) roughly matches that of f(x) at about x=4. Above that point, the curve g(x) is steeper than f(x), so its average rate of change will exceed that of f(x). An appropriate choice of interval is (4, 5).
b) As x increases, the slope of f(x) remains constant (equal to 4). The slope of g(x) keeps increasing as x increases. An appropriate choice of rate of change descriptors is (remain constant and increase).
c) The curves are not shown in the problem statement for x = 8. The graph below shows that g(x) has already exceeded f(x) by x=7. It remains higher than f(x) for all values of x more than that. We can also evaluate the functions to see which is greater:
f(8) = 4·8 +3 = 35
g(8) = (5/3)^8 ≈ 59.54 . . . . this is greater than 35
g(8) > f(8)
d) Realizing that an exponential function with a base greater than 1 will have increasing slope throughout its domain, it seems reasonable to speculate that it will always eventually exceed any linear function (or any polynomial function, for that matter).
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1. (4,5)
2. remain constant and increase
3. g(x) exceeds the value of f(x)
4. eventually
Step-by-step explanation:
10.) It costs $5 to enter the arcade and $0.75 for every game you play once inside.
You have
$20 to spend. How many games can you play?
Write
an equation using g to stand for the games. Solve your equation for g.
Answer:
y=0.75x+5
Step-by-step explanation:
x=20
y=20
20-5=15
15/0.75=20
20 games
Write
8
38
in lowest terms.
Answer:
4/19
Step-by-step explanation:
Both the numerator and denominator can be divided by 2, giving 4/19
Find the equation of the line that goes through the points (2, 2) and (6, 6).
y = 6x + 2
y = -x
y = 2x + 6
y = x
Answer:
D
Step-by-step explanation:
y=6x+2
2=12+2
NO
y=-x
2=-2
NO
y=2x+6
2=4+10
NO
y=x
2=2
6=6
Answer:
[tex]y=x[/tex]
Step-by-step explanation:
We will use slope-intercept form:
[tex]y=mx+b[/tex]
Where [tex]m=[/tex]slope and [tex]b =[/tex]y-intercept
To find the slope we use the slope formula:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
We plug in the coordinates getting:
[tex]\frac{6-2}{6-2} =\frac{4}{4} = 1[/tex]
So we have a slope of 1:
[tex]y=(1)x+b[/tex]
If we look at the answer choice we see that only one of them has a slope of 1 so the equation is:
[tex]y =x[/tex]
Solve the following system mathematically. Place the solution in the ordered pair set provided below
y = 4x - 11
- 4x - y = -5
Answer:
ok real answer 2,-3
Step-by-step explanation:
3. A line passes through (9. -9) and (10,-5).
a. Write an equation for the line in point-slope form.
b. Rewrite the equation in standard form using integers.
y-9= 4(x-9); -4x + y = 45
y+9= 4(x-9); -4x+y = -45
y-9= 4(x +9); -4x+y = 45
y+9= 4(x +9); -4x+y = -45
Step-by-step explanation:
a. y-y1/y2-y1=x-x1/x2-x1
y+9/-5+9=x-9/10-9
y+9/4=x-9/1
y+9/4=x-9
b. y+9=4(x-9)
y+9=4x-45
y-4x=-45-9
y-4x=-54
WILL GIVE BRAINLIEST
Write 2/7x(1.4x^2-3.5y) as a polynomial
The expression (2/7)x (1.4x² - 3.5y) can be written in the form of a polynomial as 0.4x³ - xy.
What is polynomial?Polynomial is an algebraic expression that consists of variables and coefficients. Variables are called unknown. We can apply arithmetic operations such as addition, subtraction, etc. But not divisible by variable.
The expression is given below
[tex]\rm \dfrac{2x}{7} \times (1.4x^2-3.5y)[/tex]
The expression can be written in the form of the polynomial
[tex]\rightarrow \rm \dfrac{2x}{7} \times (1.4x^2-3.5y)\\\\\\\rightarrow \rm \dfrac{2x \times 1.4x^2}{7} - \dfrac{3.5y\times 2x}{7 }\\\\\\\rightarrow \dfrac{2.8x^3}{7} - \dfrac{7xy}{7 }\\\\\\\rightarrow 0.4x^3 - xy[/tex]
The expression in the form of a polynomial is given as
[tex]\rm \rightarrow 0.4x^3 - xy[/tex]
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Please help!! A red block and a block are on a scale right. The red block weighs 9 ounces. The total weight of both blocks is 16 ounces. Which inequality best represents b, the possible weight of the blue block in ounces?
Answer:
b ≤ 7
Step-by-step explanation:
Given that:
A red block and a blue block are on a scale. The red block weights 9 ounces. The total weight of both blocks is 16 ounces.
To Find:
Which inequality best represents b, the possible weight of the blue block in ounces?
Knowing that;
< ⇒ less than
> ⇒ Greater than
≤ ⇒ less than or equal to
≥ ⇒ greater than or equal to
Solve:
Since the total blocks is 16 ounces that means it can't be pass 16 also known as can't be greater than. As well as, it given us that the red block weight 9 ounces that means
16 - 9 = 7
which given us that it must be equal to 7 or less than 7 to make it true.
Thus,
b ≤ 7
Kavinsky
URGENT PLEASE IM BEING TIMED!!!
What are the solutions to the system of equations graphed below?
(-5, -4) and (2, 0)
(0, 4) and (2, 0)
(-5, -4) and (0, -1)
(0, 4) and (0, -1)
Answer:
(2,0)
(-5,-4)
Step-by-step explanation:
you first have to determine where the two graphs intersect, then easily you should write the (x,y) of the point in which there is an intersection
all possible 4 digit patterns with 2,4,5,6,7,8,9
Answer:
7^4 = 2401
Step-by-step explanation:
___, ___, ___, ___
all blank spaces can be filled with all 7 numbers each.. so 7*7*7*7 is total number of paterns you can get if repititions is allowed
State the center and radius of each circle. then write the equation of the circle in standard form.
See attached:
Answer:
Step-by-step explanation:
Center: (h, k) (the coordinate of the middle point)r(radius): d(diameter)/2 (can be found by counting the number of units vertically or horizontally)Standard form of a circle: (x - h)² + (y - k)² = r²1.
Center: (-2, 3)
Radius: 10/2 = 5
Standard form/ equation: (x + 2)² + (y - 3)² = 25
Standard form:
(x - (-2))² + (y - 3)² = 5²
(x + 2)² + (y - 3)² = 25
2.
Center: (1, 1)
Radius: 6/2 = 3
Standard form/ equation: (x - 1)² + (y - 1)² = 9
Standard form:
(x - 1)² + (y - 1)² = 3²
(x - 1)² + (y - 1)² = 9
Hope this helps!
#1
Centre(-2,3)Radius=5=rEquation:-
(x-h)²+(y-k)²=r²(x+2)²+(y-3)²=5²(x+2)²+(y-3)²=25★More simply.
x²+4x+4+y²-6y+9=25x²+y²+4x-6y=12#2
Centre(1,1)Radius=3Equation
(x-1)²+(y-1)²=3²(x-1)²+(y-1)²=9★HELP
Marine had a cable that was 875 feet long. He cut the cable into 23 equal pieces.
Which measurement is closest to the length of each of these pieces of cable?
A. 38 feet
B. 35 feet
C. 31 feet
D. 30 feet
Answer:
its answer a :)
Step-by-step explanation:
875/23 = 38.04, round down to get 38
Wendy drives a car 110 kilometers per hour. What is this rate, in miles per hour, to the nearest tenth?
Answer:
68.3 miles per hour
Step-by-step explanation:
One kilometer is 0.62 miles.
110 times 0.62 is 68.3
Wendy's rate of 110 kilometers per hour is 68.3 miles per hour.
To convert kilometers per hour to miles per hour, we need to use the conversion factor of 1 kilometer = 0.621371 miles.
Given that Wendy drives at a rate of 110 kilometers per hour.
we can multiply this value by the conversion factor to obtain the equivalent rate in miles per hour.
110 kilometers per hour × 0.621371 miles per kilometer
= 68.34381 miles per hour
We get 68.3 miles per hour.
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The set of ordered pairs below represents a linear function
((-2,-3), (0,-2), (2, -1), (x, y)}
What is another pair of coordinates that could be the missing ordered pair, (x,y),
in this set?
Another pair of coordinates that could be the missing ordered pair, (x,y) in this set is (1, 0)
Linear functionsLinear functions are functions that have a leading degree of one,
Given the coordinate points ((-2,-3), (0,-2), (2, -1), (x, y)}, we need to determine the missing coordinate points
Since the x-coordinates has a difference of 2, hence the missing x-coordinate is given as:
x = -1 + 2
x = 1
For the y-coordinate
y = -1 + 1
y = 0
Hence another pair of coordinates that could be the missing ordered pair, (x,y) in this set is (1, 0)
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Find the length of the missing side please help
Step-by-step explanation:
7. Since they are similar triangles we have:
[tex] \frac{10}{8} = \frac{x}{12} \\ \\ x = 15[/tex]
So DF is 15
8. They are also similar. So:
[tex] \frac{14}{7} = \frac{x}{5} \\ x = 10[/tex]
So PR is 10
(Pls need help ASAP) Willing to give 10 points for 1 question)
Answer:
D. {(1,2) , (2,3) , (3,4) , (4,5)}
Step-by-step explanation:
Functions are relations with one output for any unique input. Relations that pass the vertical line test have one output for each input. In this case, D was the only set that met the criteria.
hey please i need this really quick
Answer:
the answer of that question is 45
Karl earns $8.50 per hour at his part-time job. Last week he worked 18 hours. This week he worked 14 hours. What is the total amount of money that Karl earned for working these two weeks?
Determine the total annual fica tax for an annual salary of $38,480. a. $294.37 b. $717.96 c. $2,385.76 d. $2,943.72
The total annual fica tax for an annual salary of $38,480 is: d. $2,943.72.
Total annual FICA taxFICA tax comprises of:
Social security= 6.2%
Medicare=1.45%
Hence:
Social Security=$38,480 x 0.062
Social security =$2,385.76
Medicare= $38,480 x 0.0145
Medicare=$557.96
FICA tax=$2,385.76+$557.96
FICA tax=$2,943.72
Therefore the total annual fica tax for an annual salary of $38,480 is: d. $2,943.72.
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Answer:
D
Step-by-step explanation:
I hate asking for help, but maths GCSE edexcel people or anyone who can do this please help! Need explanation
Basically to find solutions of the equation. Find the x intercept points.
Equation: x² - 4x + 2
when solved using quadratic formula:
[tex]\dashrightarrow \sf x_{1,2}= \dfrac{-\left(-4\right)\pm \sqrt{\left(-4\right)^2-4\cdot \:1\cdot \:2}}{2\cdot \:1}[/tex]
[tex]\dashrightarrow \sf x_1 \dfrac{-\left(-4\right)+2\sqrt{2}}{2\cdot \:1},\:x_2=\dfrac{-\left(-4\right)-2\sqrt{2}}{2\cdot \:1}[/tex]
[tex]\dashrightarrow \sf x=2+\sqrt{2}, \ 2-\sqrt{2}[/tex]
[tex]\dashrightarrow \sf x=3.414, \ 0.586[/tex]
These are the solutions to the quadratic equation.
Answer:
x ≈ 0.6 , x ≈ 3.4
Step-by-step explanation:
the solutions to the quadratic equation from the graph are where the graph crosses the x- axis.
these are at approximately x = 0.6 and x = 3.4
help I have to turn this is tomorrow and I don’t know how to do it
Step-by-step explanation:
The area of the triangular base is: 19
square units
How to calculate the base area
The given parameters are:
Volume = 27.36 cubic units
Height = 2.88 unit
The volume of a triangular prism is:
V = 0.5 * B *h
Where B represents the base area.
So, we have:
27.36 = 0.5 * B * 2.88
27.36 B * 1.44 -
Solve for B
B = 19
Hence, the area of the triangular base is: 19 square units
Based on her past experiences, a homeowner estimates that appliances lose 25% of their resale value each year. If her estimate is accurate, how much will an appliance currently valued at $1,500 be worth in 8 years?
Using an exponential function, it is found that an appliance currently valued at $1,500 will be worth $150.17 in 8 years.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.In this problem, we have that:
The appliance is currently valued at $1,500, hence A(0) = 1500.It loses 25% of their resale value each year, hence r = 0.25.Thus, the equation is given by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
[tex]A(t) = 1500(1 - 0.25)^t[/tex]
[tex]A(t) = 1500(0.75)^t[/tex]
In 8 years, the value will be given by:
[tex]A(8) = 1500(0.75)^8 = 150.17[/tex]
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