Joe worked for 14 hours at Job A and for 16 hours at Job B.
What are simultaneous equation?In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
Now it is given that,
Joe works two part-time jobs for a total of 30 hours a week.
Let x be the number hours that Joe worked at job A in a week.
and y be the number hours that Joe worked at job B in a week.
⇒ x + y = 30 ...(i)
Now Job A pays $5.90 per hour,
Therefore,
Amount receive from Job A = 5.9x
And Job B pays $7.20 per hour
Therefore,
Amount receive from Job B = 7.20y
Also it is given that, he work at each job the week that he made $197.80
Therefore,
5.90x + 7.20y = 197.8 ....(ii)
Now multiplying equation (i) by 5.9 we get,
5.90x + 5.90y = 177 ....(iii)
Subtracting equation (ii) and equation (iii) we get,
1.3y = 20.8
Dividing both the side by 1.3 we get,
1.3y/1.3 = 20.8/1.3
Solving we get,
y = 16
Putting the value of y in equation (i) we get,
x + 16 = 30
Subtracting both the side by 16 we get,
x + 16 - 16 = 30 - 16
Solving we get,
x = 14
Thus, we get
x = 14
y = 16
Hence,
Number hours that Joe worked at job A in a week = 14 hours
and,
Number hours that Joe worked at job B in a week = 16 hours
Thus, Joe worked for 14 hours at Job A and for 16 hours at Job B.
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4. What is the equation of the line that passes
through the point (6, 0) and has a slope of -3?
1) y = −3x + 6
2) y=-3x - 18
3) y=-3x - 6
4) y = −3x + 18
Answer: the fourth choice, or y=-3x+18
Step-by-step explanation:
using the point-slope form, we can plug in the values:
y-0= -3(x-6)
distributing the right side we get
y-0=-3x+18
putting it into y=mx+b form we get y=-3x+18
a car is traveling at a rate of 90 miles per hour. what is the car's rate in feet per second?
Answer:
132 feet per second
Step-by-step explanation:
Mary deposits $30,000 into an account that pays 4% interest per year, compounded annually. Josh deposits $30,000 into an account that also pays 4% per year. But it is simple interest.
Find the interest Mary and Josh earn during each of the first three years. Then decide who earns more interest
Interest earned by Mary is $ 3,745.92 which is more than the interest than Josh earned that is $ 3,600.
For Mary:
Principal = $ 30,000
Interest rate = 4 %
Compounded annually
t = 3 years
Amount = $ 30,000 ( 1 + 4 / 100 )³
A = 30,000 ( 1.04)³
A = 30,000 ( 1.124864 )
A = $ 33,745.92
Interest = A - P = 33,745.92 - 30,000 = $ 3745.92
For Josh:
Principal = $ 30,000
Simple interest
t = 3 years
Interest = 30,000 × 3 × 4 / 100
Interest = $ 3600
Therefore, interest earned by Mary is $ 3,745.92 which is more than the interest than Josh earned that is $ 3,600.
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Write the following in terms of cos0 only? Csc0
Answer:on the given cushion. We want to represent cost like 30 in terms of cost. Rita. Now by the identity sector tragical toe one by scientists. Now we know that science can't theta plus Costco Arteta is equal to one. So they get signed. Tetteh is equal to plus minus quite a tough one. Minus cause squared theta. So this will be a photo one by plus minus square wrote off one minus y squared theta.
Step-by-step explanation:
In the diagram below, AD || EH, m/ABF
m/CGH = 80°. Find m/I.
Step
1
2
try
Angle
m/ABF = 138°
m/CGH 80°
m/
-
D
H
O
80°
G
I
C
= 138° and
Select a Reason
F
Reason
Given
Given
B
138⁰
E
Answer:
Step-by-step explanation:for the triangle GIF, angle g = 80
angle f = 42 since angle FBA = 138
so angle i = 180 - 42 - 80
= 58
A fraction is a number which can be written in the form a/b, where a, b are _____numbers and b ≠ 0
Answer:
Step-by-step explanation:
a and b are integers
A number that can be written in the form a/b where a and b are integers. However, b cannot equal zero. Therefore a rational number
solve the following equation for d. 4hd=3f-g3
Step-by-step explanation:
Divide by 4h, d=3f-g3/4h
Which expression is represented by the following area model?
A. 3/5(2/5 + 1/3)
B. 3/5 x 2/5 + 1/3
C. 3/5 + 2/5 + 1/3
D. 3/5 x 2/5 x 1/3
From the fig the Area model is, = 3/5(2/5 + 1/3)
Area is defined as the total space taken up by a flat (2-D) surface or shape of an object. Take a pencil and draw a square on a piece of paper. It is a 2-D figure. The space the shape takes up on the paper is called its Area. Now, imagine your square is made up of smaller unit squares.
Area of rectangle = l x b
given that, lets consider the fig as rectangle with one side 2/5+1/3 as breadth and another side 3/5
As we know , Area of rectangle = l x b
l=3/5
b=2/5+1/3
Area model= 3/5(2/5 + 1/3)
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Answer:
The Area model for the fig. is, = 3/5(2/5 + 1/3).
Step-by-step explanation:
Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies. Consider your square as being composed of smaller unit squares.
Rectangle area = l x b
Given that, let's imagine the fig as a rectangle with a width of 2/5+1/3 and a length of 3/5.
As we know , Area of rectangle = l x b
l=3/5
b=2/5+1/3
Area model= 3/5(2/5 + 1/3)
53/14
As mixed fraction
Answer:3 11/14
Step-by-step explanation:im right
A pretzel factory has daily fixed costs of $1200. In addition, it costs 40 cents to produce each bag of pretzels. A bag of pretzels sells for $1.80. (a) Find the rule for the cost function c(x) that gives the total daily cost of producing x bags of pretzels. c(x)= enter your response here (Simplify your answer.) Part 2 (b) Find the rule of the revenue function r(x) that gives the daily revenue from selling x bags of pretzels. r(x)= enter your response here (Simplify your answer.) Part 3 (c) Find the rule of the profit function p(x) that gives the daily profit from x bags of pretzels. p(x)= enter your response here (Simplify your answer.)
The rule for the cost function c(x) that gives the total daily cost of producing x bags of pretzels will be 1200 + 0.4x
b. The revenue function will be 1.80x.
c. The profit function p(x) is 1.4x - 1200.
How to illustrate the information?It should be noted that fixed cost = 1200
Also, it costs 40 cents to produce each bag of pretzels. Therefore, the cost function will be:
= 1200 + 0.4(x)
= 1200 + 0.4x
The revenue function will be:
= Price × Quantity
= 1.80 × x
= 1.8x
c. The profit function p(x) will be:
= Revenue - Cost
= 1.8x - 1200 + 0.4x
= 1.4x - 1200
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help Katherine has a new job and earns salary of $55,000. max has a new job and earns a salary of $64,000. Katherine will receive a salary increase of $2,500 per year and Max will receive a salary increase of $1,500 per year.
Which equation ca be used to find x, the number of years it will take Katherine to earn the same salary as Max?
A. 55,000x+2,500x=64,000+1500x
B. 55,000+2500x=64,000+15000x
C. 55,000+64000x+1.500
D. 55,000x+2500=64,000+1,500
The equation that represent the same salary is 55,000x+2,500x=64,000+1500x
What is Algebra?Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols.
Given:
Katherine has a new job and earns salary of $55,000. Katherine will receive a salary increase of $2,500 per year .
max has a new job and earns a salary of $64,000. Max will receive a salary increase of $1,500 per year.
So, in the case they would have the same salary for some x years the expression can be
Katherine salary along with increment= 55000+ 2500x
Max salary along with increment= 64000+ 1500x
Hence, equation ca be used to find x, the number of years it will take Katherine to earn the same salary as Max is 55,000x+2,500x=64,000+1500x.
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16) Working alone, it takes LeeAnn 30 minutes to clean the backyard. Mandy can clean the
backyard in 25 minutes. If they worked together, how long would it take them to clean the yard?
Round to the nearest minute.
Answer:
Step-by-step explanation:
Work done is transfer of energy...... but without complicating things a little further let's just consider the amount of work done while cleaning the backyard is the same regardless of who the doer is/ how many in number are the doers. So
So power is the time rate change of work done:
[tex]P=w/t\\[/tex]
let's say power of LeeAnn =L, Mandy=M
[tex]L=w/30 minutes\\M=w/25 minutes\\[/tex]
And if they worked together their power will add up to L+M
[tex]L+M=w/T\\[/tex], while T is the amount of time needed when they clean together.
[tex]L+M=w/T\\w/30min + w/25min =w/T\\1/30min+1/25min=1/T, w\neq 0\\1+(6/5)=30/T\\11/5=30/T\\11T=150\\T=150/11 min\\T=13.6 min[/tex]
Which expression is equivalent to one sixth times the quantity 4 times x plus 18 end quantity minus 13 over 18 times x?
a) negative one eighteenth times x minus three
b) negative one eighteenth times x plus 3
c) one eighteenth times x minus 3
d) one and seven eighteenths times x plus three
The expression is negative one eighteenth times x plus 18.
How to find equivalent expression?The expression says "one sixth times the quantity 4 times x plus 18 end quantity minus 13 over 18 times x".
Therefore, the statement can be expressed as follows;
1 / 6 × 4 × x + 18 - 13 / 18 × x
Therefore, let's simplify it
1 / 6 × 4 × x + 18 - 13 / 18 × x
4x / 6 + 18 - 13 / 18 × x
4x / 6 + 18 - 13 / 18 x
combine like terms
4x / 6 + 18 - 13 / 18 x
4x / 6 - 13 / 18 x + 18
12x - 13x / 18 + 18
Therefore,
- 1 / 18 x + 18
Therefore, the expression is negative one eighteenth times x plus 18.
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Answer: b) negative one eighteenth times x plus 3
Step-by-step explanation: :)
Find the distance between B(4,1) and C (4,8)
Answer:7
Step-by-step explanation: the answer is 7
if a coin is flipped 3 times what is the probability it will show all heads
Answer:
1/8
Step-by-step explanation:
Surface Area of Square Pyramids
Find the surface area of a square pyramid with side length 4 ft and slant height 3 ft.
The surface area of square pyramid is 64 ft²
What is square pyramid?
In terms of geometry, a square pyramid is a pyramid with a square base and four lateral faces. A pyramid is a type of polyhedron with three or more triangular faces that meet above its base (the apex). A square pyramid is a pentahedron, a three-dimensional shape with a total of five faces. The Great Pyramid of Giza is a well-known example of a real-life pyramid. When we learn about pyramids, we must also learn other concepts that are related to them, such as the volume and area of the pyramid. In this article, we will learn what a square pyramid is, its types, characteristics, surface area formulas, and volume formulas with numerous examples and solutions.
For a square pyramid, the surface area is given by the following equation:
SA = a^2 + 4(a)(h)
where a is the side length of the base and h is the slant height.
In this case, a = 4 and h = 3. Therefore,
SA = 4^2 + 4(4)(3)
SA = 16 + 48
SA = 64 ft^2
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What is 9 to the power of 3/2
please help
please hurry
Γ(n+2) = (n+1)!
Prove it using Γ(n+1)=n Γ(n)
PLEASE HELP 30 POINTS!!
help me pls asap ill give u 21 points'
Answer:
I think the answer is A
Step-by-step explanation:
I'm not sure if it's correct or not but I chose the option because the atoms in substance are not chemically combined
Given matrix A = 2-143 and B = -11-2-4
Find the product of matrices A and B
The product of matrices A and B is the elements 0 and 6 in the first row and -10 and -8 in the second row.
Matrices, the form of a matrix, area unit the arrangements of numbers, variables, symbols, or expressions during a rectangular table that contains numerous numbers of rows and columns.They're rectangular-shaped arrays, that completely different operations like addition, multiplication, and transposition area unit outlined. The numbers or entries within the matrix area unit referred to as its components. Horizontal entries of matrices area unit referred to as rows and vertical entries area unit referred to as columns.Given that the matrix A = 2 - 143 and B = -11-2-4.
Assume that the order of the matrix of A and B is 2x2.
The elements of matrix A are as below:a₁₁ = 2, a₁₂ = -1, a₂₁ = 4, a₂₂ = 3
The elements of matrix B are as below:b₁₁ = -1, b₁₂ = 1, b₂₁ = -2, b₂₂ = -4
We need to find the product of matrices A and B.
Let C denote the product of matrices A and B.
Then the order of the matrix C is 2x2 and its elements are calculated as follows : c₁₁ = a₁₁·b₁₁ + a₁₂·b₂₁ ⇒ c₁₁ = 2(-1) + (-1)(-2)⇒ c₁₁ = -2 + 2⇒ c₁₁ = 0 c₁₂ = a₁₁·b₁₂ + a₁₂·b₂₂⇒ c₁₂ = 2.1 + (-1)(-4)⇒ c₁₂ = 2 + 4⇒ c₁₂ = 6c₂₁ = a₂₁b₁₁ + a₂₂b₂₁⇒ c₂₁ = 4(-1) + 3(-2)⇒ c₂₁ = -4 -6⇒ c₂₁ = -10c₂₂ = a₂₁b₁₂ + a₂₂b₂₂⇒ c₂₂ = 4(1) + 3(-4)⇒ c₂₂ = 4 - 12⇒ c₂₂ = -8
Therefore the required matrix has the elements 0 and 6 in the first row and -10 and -8 in the second row.
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The matrix format was not clear from the question.So, assumptions were made to answer this question.
Ali bought three pieces of fruit with the following weights, 8.712 grams, 14.125 grams, and 21.926 grams. What is the best estimate for the total weight of the fruit?
Find square root of 456 and 5678 up to 2 decimal place by using division method.
Answer:
Hope this helps
Step-by-step explanation:
full explanation in the given picture
x - √x + 3 = 0; [-1, 5]
Solve the equation graphically with the given interval . Rounded to two decimals
The graph is made and attached.
Given, the equation is x ₋ √x₊3 = 0
substitute values for x from the interval ₋1 to 5 and then graph the points.
for x = ₋1:
₋1 ₋ √₋1 ₊ 3 = 0
₋1 ₋ 1.42 = 0
₋2.42
for x = 0
0 ₋ √0₊3 = 0
₋1.74
for x=1
1 ₋ √1₊3 = 0
1 ₋ √4 = 0
1 ₋ 2 = 0
₋1
for x = 2
2 ₋ √2₊3 = 0
2 ₋ √5 = 0
2 ₋ 2.24 = 0
0.24
for x = 3
3 ₋ √3₊3 = 0
0.55
for x = 4
4 ₋ √4₊3 = 0
4 ₋ √7 = 0
1.25
for x = 5
5 ₋ √5₊3 = 0
2.17
hence we have the points (₋1,₋2.42) (0,₋1.74)(1,₋1)(2,0.24)(3,0.55)(4,1.25) and(5,2.17)
plot the above points on the graph.
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Solve the system of equations.
y=9x+14
y=6x+35
x=
y=
The solution of the system of equations are x = 7 and y = 77
Given data
y = 9x + 14
y = 6x + 35
How to solve the system of equationssolving using substitution method to solve the simultaneous equation we have
y = 9x + 14 equation 1
y = 6x + 35 equation 2
equating the both equations will give
9x + 14 = 6x + 35
9x - 6x = 35 - 14
3x = 21
x = 7
plugging x = 7 into equation 1
y = 9x + 14
y = 9 * 7 + 14
y = 63 + 14
y = 77
The solution of the system of equations are x = 7 and y = 77
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Given that line CD is a perpendicular bisector of triangle ABC, if side AB has a length of 11 and side AC has a length of 14 what is the length of side CD? Write your answer to the
nearest hundredth
Answer:
12.87
Step-by-step explanation:
Since we know that line CD is a perpendicular bisector, triangle ACD is a right triangle, and thus we can apply the Pythagorean theorem to determine the length of side CD. Since the Pythagorean theorem states that a^2 + b^2 = c^2, where c is the hypotenuse and a and b are the adjacent sides, we can plug in the values of side AD and AC.
As side CD is the bisector of side AB, sides AD and DB are both half the length of side AB, so:
AD = 11/2
AD = 5.5
We now know two values of our equation, and thus we can solve for the missing third value.
5.5^2 + b^2 = 14^2
14^2 - 5.5^2 = b^2
196 - 30.25 = b^2
165.75 = b^2
[tex]\sqrt{165.75} = b[/tex]
b = 12.87
A sample of 30 students at a local college were given a test consisting of 10 questions about current news events. The distribution of the number of correct answers given is recorded in the frequency column of the table below. Questions that were not answered were marked incorrect. The frequency represents how many of the 30 students who took the test got a certain number of answers correct. For example, three students answered five questions correctly.
Number correct Frequency
0 3
1 2
2 6
3 1
4 1
5 3
6 2
7 4
8 4
9 2
10 2
What is the mean test score?
Round to one decimal place.
Answer:
Step-by-step explanation:
meow meow its 99
Using it's concept, the mean test score is of 4.9.
What is the mean?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.
From the frequency table, the sum of the 30 observations is given by:
0 x 3 + 1 x 2 + 2 x 6 + 3 x 1 + 4 x 1 + 5 x 3 + 6 x 2 + 7 x 4 + 8 x 4 + 9 x 2 + 10 x 2 = 146.
Hence the mean test score is given as follows:
M = 146/30 = 4.9.
The mean test score is of 4.9.
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Solve for y.
6x - 4y = 11
The solution of the given equation is y = (6x - 11)/4.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
We have been given that equation as
⇒ 6x - 4y = 11
We have to determine the solution for y.
⇒ 6x - 4y = 11
Rearrange the terms of the above equation and solve for y,
⇒ 4y = 6x - 11
Divided by 4 on both the side of the equation, we get
⇒ y = (6x - 11)/4
Hence, the solution of the given equation is y = (6x - 11)/4.
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what are the factor pairs of 34
Answer:
2 and 17
Step-by-step explanation:
2 x 17= 34
hope it helps
Two fizgigs and three whatsits weigh 22 noozwhats.
Four fizgigs and two whatsits weigh 28 noozwhats.
Use a graphing calculator to determine which
solution matrix gives the weight of a fizgig and the
weight of a whatsit.
Using a system of equations, the solution matrix that gives the weight of a fizgig and the weight of a whatsit is:
[x y] = [5 4]
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For this problem, the variables are given as follows:
Variable x: weight of a fizgig.Variable y: weight of a whatsit.Two fizgigs and three whatsits weigh 22 noozwhats, henec:
2x + 3y = 22.
Four fizgigs and two whatsits weigh 28 noozwhats, hence:
4x + 2y = 28.
Simplifying by 2:
2x + y = 14
y = 14 - 2x.
Replacing in the first equation:
2x + 3(14 - 2x) = 22
2x + 42 - 6x = 22
4x = 20
x = 20/4
x = 5 noozwhats.
y = 14 - 2(5) = 4 noozwhats.
Hence the solution matrix that gives the weight of a fizgig and the weight of a whatsit is:
[x y] = [5 4]
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