Answer:-8,-9
Step-by-step explanation:
Jessica, Kareem, and Lamar served a total of 64 orders Monday at the school cafeteria. Jessica served 8 fewer orders than Lamar. Kareem served 2 times as
many orders as Lamar. How many orders did they each serve?
Answer:
Jessica: 10 orders
Lamar: 18 orders
Kareem: 36 orders
Step-by-step explanation:
Let's first designate each person with a letter.
The number of orders served by Jessica can be designated as [tex]J[/tex]
The number of orders served by Kareem can be designated as [tex]K[/tex]
The number of orders served by Lamar can be designated as [tex]L[/tex]
We know that they all served a total of 64 orders. This can be expressed as the sum of their orders equaling 64.
[tex]J+K+L=64[/tex]
We also know that Jessica served 8 fewer orders than Lamar. This can be expressed as the number of orders served by Jessica, [tex]J[/tex], being equal to Lamar's orders [tex]L[/tex] minus 8.
[tex]J = L-8[/tex]
Fianlly, we know that Kareem served twice as many orders as Lamar. This can be expressed as the number of order's served by Kareem, [tex]K[/tex], being 2 times Lamar's orders [tex]L[/tex].
[tex]K = 2L[/tex]
With these 2 equalities, we can substitute [tex]J[/tex] and [tex]K[/tex] in our original equation,
[tex]J+K+L=64[/tex]
with their values expressed as a subtraction or multiplication of [tex]L[/tex].
[tex]J[/tex] will be substituted with [tex]L-8[/tex], and [tex]K[/tex] will be substituted with [tex]2L[/tex].
[tex]J+K+L=64[/tex]
With substitutions:
[tex](L-8) + 2L + L = 64[/tex]
We can simplify this by combining the L-terms:
[tex]L + 2L + L -8 = 64\\4L - 8 = 64[/tex]
Next, we'll add 8 to both sides.
[tex]4L = 72[/tex]
Divide both sides by 4:
[tex]L = 18[/tex]
Thus, Lamar served 18 orders.
Using our expressions, we can find how many orders the others served.
Jessica:
[tex]J = L-8\\J = 18 -8\\J = 10[/tex]
Jessica served 10 orders.
Kareem:
[tex]K = 2L\\K = 2*18\\K = 36[/tex]
Kareem served 36 orders.
2.) Bill sells cleaning products on commission. He earns 40% commission on his sales. If
he has sales of $983, how much commission does he earn?
Answer:
$393.20
Step-by-step explanation:
There are two easy ways to solve this:
1) Use a setup and cross multiply.
First, set up your problem.
$ x = 40%
$983 100%
$983 is the total amount, so it is equal to 100%. We're trying to find 40% of it, so we can label the amount as $x. Remember, each side has to be in the same type of measurements (i.e. dollars, percentages, inches, etc.).
Then, cross multiply. You should end up with:
100x = 39,320
Then, simplify.
x = 393.2
x = $393.20
2) Convert the percentage to a decimal and multiply.
First, convert the percentage you're looking for into a decimal:
40% × 100 = 0.4
Then, multiply the decimal with the total sales amount:
$983 × 0.4 = 393.2
= $393.20
40% × 100 = 0.4
$983 × 0.4 = $393.20
Bill earns $393.20 commission total.
An app developer projects that he will earn $20.00 for every 8 apps downloaded. Write
an equation to represent the proportional relationship between the number of apps and the total earnings
y = 2.5x
I hope this helps
The required equation is y=2.5x.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
Given that,
Earning of app developer for 8 apps = $20.00
Earning of app developer for 1 app = $2.5
Earning of app developer for x app = $2.5x
Assume, earning of app developer for x app is y
So the equation,
Earning of app developer y=2.5x
The required equation is y=2.5x.
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The remainder after diving x^4+3x^3-8x^2+5x-9 by x+5 is ____.
Use the polynomial remainder theorem. It says that a polynomial [tex]f(x)[/tex] has remainder [tex]f(c)[/tex] upon division by [tex]x-c[/tex].
Here we have
[tex]f(x)=x^4+3x^3-8x^2+5x-9[/tex]
and [tex]c=-5[/tex], so the remainder is
[tex]f(-5)=(-5)^4+3(-5)^3-8(-5)^2+5(-5)-9=\boxed{16}[/tex]
SOMEBODY HELP PLS, WILL GIVE BRAINLIEST TO RIGHT ANSWER
Answer:
a. I, III, II
Step-by-step explanation:
To answer this question, lets take a look at I, II, and III.
First, lets take a look at I. It states that the m∠SQT = 180 by the definition of a straight angle. We can get that the m∠SQT = 180 just by looking at the image and by knowing our second given. So I just has to be below the second given.
Now, lets take a look at II. It states that m∠SQV + m∠VQT = 180 by the Substitution Property of Equality. We can find that m∠SQV + m∠VQT = 180 just by looking at the image along. But knowing that it is found by the Substitution Property of Equality, we can find that m∠SQV + m∠VQT = 180 was derived from the fact that m∠SQT = 180 and that m∠SQV + m∠VQT = m∠SQT, or I and III. So II was derived from I and III, and II should come after I and III.
Now lets look at III. It states that m∠SQV + m∠VQT = m∠SQT by the Angle Addition Postulate. Since III is found by the Angle Addition Postulate, we can find that III was derived from I, and III should come after I.
So knowing that II should come after III and I, and that III should come after I, we can find that the order should be I, III, II.
I hope you find my answer and explanation to be helpful. Happy studying.
what is the area of the figure?
Answer:
24
Step-by-step explanation:
Answer:
24
Step-by-step explanation:
you can split it into two parts. One with 4 x 3 = 12 and the other with 2 x 6 = 12. then add them together and you get 24.
find the area of each shaded region
In a quadratic equation a^2+ bx + c = 0, why is it that the value of a cannot be equal to zero?
Answer:
Someone please help me because i have this question on my test someone please help us
Step-by-step explanation:
Test 4,580 for divisibility by 2, 3, 5, 9, and 10.
By 2 = 2290
By 3 = about 1526.6667 or you can just write 4580/3
By 5 = 916
By 9 = about 508.8889
By 10 = 458
what’s 4 2/3 divided by 3 1/2 ?
Answer:
the answer to this problemis 1 1/3
Find the value of x so that f(x)=7.
Answer:
slope: 0
y intercept: (0, 7)
Step-by-step explanation:
-5m - 2m = 21 what is m
Answer:
m=-3
Step-by-step explanation:
Answer:
m = -3
Step-by-step explanation:
Simplify -5m - 2m to -7m
-7m = 21
Divide both sides by -7
m = 21/-7
Simplify 21/-7 to -3
m = -3
Hope this helps!
-Jerc
Use the information given to answer the question
An artist prints T shirts to sell at a fair for $14 each
• The artist has some initial T shirts ready to sell and works for h hours more, printing a constant number of T-shirts every
hour
• The expression 14(12h + 30) represents the amount, in dollars, the artist will earn selling all the T-shirts.
Part A
How many T shirts did the artist have initially?
A rectangle is twice as long as it is wide. If it has an area of 84.5 square inches, what are its dimensions?
Enter them below, separated by a comma.
Answer:
The rectangle is 18 square inches
Step-by-step explanation:
A rectangle has Length that is twice its Width.
The Width = 3.
What is the area of the rectangle?
First, we know that L, the length, is 6 (twice as long as its width).
Remember that the area of a rectangle is Length times Width:
A = L W
and so
A = 6 × 3 = 18
The rectangle is 18 square inches
Find the width of a rectangular wall if the perimeter is 148 feet and the width is two more than seven times the length.
Answer:
Step-by-step explanation:
Perimeter of a rectangular wall P = 2L+2W
L is the length of the wall
W is the width
Given
P = 148feet
If the width is two more than seven times the length, this is represented as
W = 7L+2
Substitute W = 7L+2 into the formula above
P = 2L + 2(7L+2)
P = 2L +14L+4
P == 16L+4
148 = 16L+4
16L = 148-4
16L = 144
L = 144/16
L = 9
To get the width
W = 7L+2
W = 7(9)+2
W = 63+2
W = 65feet
Hence the width of the rectangular wall is 65feet
Javier has a basket of oranges and apples. The number of oranges is 2 more than twice the number of apples in the basket. The difference of half the number of oranges and half the number of apples is 4.
An equation created to find the number of apples Javier has in the basket will have
Number of oranges is (2a + 2)
Half the number of oranges is 1/2(2a + 2)
Half the number of apples is 1/2a
The difference between half the number of oranges and half the number of apples equals 4 looks like this:
1/2(2a + 2) - 1/2a = 4
Now solve.
1/2(2a + 2) - 1/2a = 4 (multiply 1/2 by what's inside the parenthesis)
1a + 1 - 1/2a = 4
1a + 1 -1 - 1/2a = 4 - 1
1a - 1/2a = 3
1/2a = 3
1/2a ÷ 1/2 = 3 ÷ 1/2
a = 6
He has 6 apples.
Substitute 6 into the equation for the number of oranges.
2a + 2
2(6) + 2 = 14
He has 14 oranges.
Check your work.
The difference between half the number of oranges (7) and half the number of apples (3) does indeed equal 4.
Therefore, the equation has one solution.
Answer:
it is one solutionStep-by-step explanation:
Three times a number decreased by 5 equals 10. Write the equation and find the number.
Answer:
3x - 5 = 10
Step-by-step explanation:
3 questions on percentage ❤️
Answer:
Question 1: 131.25 Question 2: 83.33 Question 3. 133.33
Step-by-step explanation:
1. 131.25% x 150
2. Trial and error
3. 60 ÷ 45%
What TWO requirements does a graph need to meet to be considered proportional?
Answer:
straight line and it needs to go through the origin
solve the polynomial equation:
x^3-7x^2-x+7=0
show your steps please
Answer:
x = {-1, 1, 7}Step-by-step explanation:
Solving for x
x^3 - 7x^2 - x + 7 = 0(x^3 - x) - (7x^2 - 7) = 0x(x^2 - 1) - 7(x^2 - 1) = 0(x - 7)(x^2 - 1) = 0(x - 7) (x + 1) (x - 1) = 0x - 7 = 0 ⇒ x = 7x + 1 = 0 ⇒ x = -1x - 1 = 0 ⇒ x = 1The solutions to the polynomial equation [tex]x^3 - 7x^2 - x + 7 = 0[/tex]are[tex]x = 1, x = 7,[/tex] and [tex]x = -1.[/tex]
The given polynomial is [tex]x^3 - 7x^2 - x + 7 = 0[/tex]
We can observe that the polynomial has a common factor of (x - 1).
By dividing the polynomial by (x - 1), we can simplify the equation:
[tex](x - 1)(x^2 - 6x - 7) = 0[/tex]
Now we have factored the polynomial equation as a product of two factors, [tex](x - 1)[/tex] and [tex](x^2 - 6x - 7).[/tex]
To find the solutions, we set each factor equal to zero and solve for x.
Setting [tex](x - 1) = 0[/tex], we get [tex]x = 1.[/tex]
Now, let's solve the quadratic factor [tex](x^2 - 6x - 7) = 0[/tex]
Using factoring or the quadratic formula, we find the roots of the quadratic equation:
[tex]x^2 - 6x - 7 = 0[/tex]
[tex](x - 7)(x + 1) = 0[/tex]
Setting each factor equal to zero:
[tex]x=7[/tex] and [tex]x=-1[/tex]
Therefore, the solutions to the polynomial equation [tex]x^3 - 7x^2 - x + 7 = 0[/tex]are[tex]x = 1, x = 7,[/tex] and [tex]x = -1.[/tex]
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solve the inequality 2(4+2x) is less than or equal to 5x+5
a. x is Less than or equal to -2
b. x is greater than or equal to -2
c. x is less than or equal to 3
d. x is greater than or equal to 3
Answer:
the answer is d, anything lower than 3 would make the solution incorrect
A person invested $6,000 in an account growing at a rate allowing the money to
double every 11 years. How much money would be in the account after 19 years, to the
nearest dollar?
Answer:
P(19)=$19,852
To the nearest dollar.
Step-by-step explanation:
Exponential Growth
The natural growth of some magnitudes can be modeled by the equation:
[tex]P(t)=P_o(1+r)^t[/tex]
Where P is the actual amount of the magnitude, Po is its initial amount, r is the growth rate and t is the time.
We are given the condition that an investment of Po=$6,000 in an account doubles every 11 years. The final value of the investment in t=11 is P(11)=$12,000.
Substituting into the general equation:
[tex]12,000=6,000(1+r)^{11}[/tex]
Dividing by 6,000 and swapping sides:
[tex](1+r)^{11}=2[/tex]
Taking the 11th root:
[tex]1+r=\sqrt[11]{2}[/tex]
[tex]1+r=1.065[/tex]
Substituting into the formula:
[tex]P(t)=6,000(1.065)^t[/tex]
Now we need to find the money in the account after t=19 years:
[tex]P(19)=$6,000(1.065)^{19}[/tex]
P(19)=$19,852
To the nearest dollar.
rewrite the function and isolate Y
the square with a side length (x + 3) and an equilateral triangle with side lengths (3x-1) have the same perimeter what is the value of x?
Help please
Answer:
x = 3
Step-by-step explanation:
Side lenght of square = (x + 3)
Side length of equilateral triangle = (3x - 1)
It is Given that:
Perimeter of square = Perimeter of equilateral triangle
4 times side length of square = 3 times side length of equilateral triangle.
[tex] \therefore \: 4(x + 3) = 3(3x - 1) \\ \\ \therefore \: 4x + 12 = 9x - 3 \\ \\ \therefore \:12 + 3 = 9x - 4x \\ \\ \therefore \:15 = 5x \\ \\ \therefore \:x = \frac{15}{5} \\ \\ \huge \red{ \boxed{\therefore \:x = 3}}[/tex]
Write an equation for the line graphed.
A) y = 2
B) y = 2x
C) y = -2x
D) y = 2x + 1
Answer:
the answer is "d" because the x region is negative 2 and the y region is a positive1
How is dividing and multiplying with an area model similar and How is it different?
Answer:
In multiplication the numbers you multiply are called factors; the answer is called the product. In division the number being divided is the dividend, the number that divides it is the divisor, and the answer is the quotient.
Henry is filling up his fish tank with water at a constant rate.
At 2 minutes the water level is 16 cm. At 8 minutes the water level is at 34 cm.
Explain how you figured out the water level at 0 minutes.
Answer:
It would have started to be filled at 10 cm
Step-by-step explanation:
FInd teh difference between 8 and 2 which is 6
Find the difference between 34 and 16 which is 18
Divide 18 by 6 which is 3
Subtract 2(3) = 6 by 16 which is 10
Using the linear system to solve the problem. Then the water level at 0 minutes is 10 cm.
What is the linear system?It is a system of an equation in which the highest power of the variable is always 1. It is a combination of infinite points side by side.
Given
Henry is filling up his fish tank with water at a constant rate.
At 2 minutes the water level is 16 cm.
At 8 minutes the water level is at 34 cm.
We know that the linear equation
[tex]\rm y = mx +c[/tex]
Where
m be the rate of filling water in the tank.
c be the initial water in the tank.
y be the water level of the tank in cm.
x be the time in minutes.
At 2 minutes the water level is 16 cm. Then
[tex]\rm 16 = 2m + c[/tex] ...1
At 8 minutes the water level is at 34 cm. then
[tex]\rm 34 = 8m +c[/tex] ...2
From equations 1 and 2, we have
m = 3, and c = 10
Then the equation will be
[tex]\rm y = 3x + 10[/tex]
For x = 0, then y = 10
Thus, the water level at 0 minutes is 10 cm.
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Baron, Gab, and Oliver can paint a room together in 2 hours, 1f Gab does the job alone. he can paint the same room in 5 hours. If Baron works alone, he can paint the room in hours. If Oliver works alone, how long would it take him to paint the room?
Answer:
11 hours
Step-by-step explanation:
I hope this help!
What value of x is in the solution set of 2(3x-1) 24x 6? a-10 b-5 c-3 d 1
Answer:
-1
Step-by-step explanation:
Step 1: Write inequality
2(3x - 1) ≥ 4x - 6
Step 2: Solve for x
Distribute 2: 6x - 2 ≥ 4x - 6Subtract 4x on both sides: 2x - 2 ≥ -6Add 2 to both sides: 2x ≥ -4Divide both sides by 2: x ≥ -2Step 3: Find
-10 ≥ -2? No
-5 ≥ -2? No
-3 ≥ -2? No
-1 ≥ -2? Yes
The equation 2(4x + 1) = 4(2x + 5) has no solutions. Which of the following best explains why?
Answer:
See below
Step-by-step explanation:
[tex]2(4x + 1) = 4(2x + 5)[/tex]
[tex]8x + 2 =8x + 20[/tex]
[tex]\nexists x \in \mathbb{R} \text{ That makes the equality true}[/tex]
The equation has no solution because no matter what the value we plug for [tex]x[/tex] in the equation, it will not be true and will lead to a contradiction. This is the meaning of not having a solution.