Answers
By using a graphing tool, the point of intersection of the two lines is (x, y) = (7, 0).
How to solve a system of linear equations by graphic approach
In this question we have a system of two linear equations with two variables, which can be represented on Cartesian plane. By geometry it is known that a line can be constructed after knowing the location of two distinct points.
First, we find two distinct points from each line:
x + y = 7: (7, 0), (0, 7)
- x + y = - 7: (7, 0), (0, - 7)
Second, set each pair of points and construct the lines on a Cartesian plane.
Third, mark the point of intersection of the two lines. The result is shown in the image attached aside. The point of intersection of the two lines is (x, y) = (7, 0).
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Related Questions
Evaluate the problem
Answers
Answer:
400
Step-by-step explanation:
Change the 16 and the 64 in the numerator to exponents
2^4 x 10^2 x 4^3/2^4 x 4^2
Simplify
10^2 x 4
100 x 4
this question has 2 parts:
Part A
Callie kicks a soccer ball from the ground. The height of the ball, in feet, above the ground t seconds after the ball is kicked can be represented by the expression 38t- 16t². Write the expression in factored form.
Part B
What is the height of the soccer ball 1.25 seconds after Callie kicks it?
______ feet
Answers
Part A The quadratic expression in factored form is 2t(19 - 8t)
Part B The height of the soccer ball 1.25 seconds after Callie kicks it is 22.5 ft
Part A Write the expression in factored form.Since Callie kicks a soccer ball from the ground. The height of the ball, in feet, above the ground t seconds after the ball is kicked can be represented by the expression 38t- 16t².
So, the expression is a quadratic expression, we have that h(t) = 38t- 16t².
To write the expression in factored form, we find the common factors of both terms and factor them out.
So, h(t) = 38t- 16t²
= 2 × 19 × t - 2 × 8 × t × t
Factoring out 2 and t, we have
= 2 × t × (19 - 8 × t)
= 2t(19 - 8t)
So, the quadratic expression in factored form is 2t(19 - 8t)
Part B What is the height of the soccer ball 1.25 seconds after Callie kicks it?Since the quadratic expression h(t) = 38t- 16t² represents the height of the ball above the ground in feet, to find the height of the ball after 1.25 second,we substitute t = 1.25 s into the expression.
So, h(t) = 38t- 16t²
h(1.25) = 38(1.25) - 16(1.25)²
h(1.25) = 47.5 - 16(1.5625)
h(1.25) = 47.5 - 25
h(1.25) = 22.5 ft
So, the height of the soccer ball 1.25 seconds after Callie kicks it is 22.5 ft
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(x-5)/3=21 What is equal to x
Answers
Answer: x=68
Step-by-step explanation:
(x-5)/3=21
(x-5)*3/3=21*3 ==> Multiply both sides by 3 to remove fractions
x-5=21*3
x-5=63
x+5-5=63+5 ==> Add 5 on both sides to isolate the x variable
x=63+5
x=68
Let's solve the problem,
→ (x - 5)/3 = 21
→ x - 5 = 21 × 3
→ x = 63 + 5
→ [ x = 68 ]
Hence, the value is 68.
Mrs. Thomas needs
to set up 5 rows of 3
marsh mellows. She
has 12 marsh C EX
mellows. Does she
have enough marsh
mellows?
A. No, she needs 20 marsh mellows
B. No, she needs 15 marsh mellows
C. Yes, she needs 10 marsh mellows
D. Yes, she needs 8 marsh mellows
Answers
A manufacturer of household items has total revenue given by the function R=16.5x and has total cost given by C=14x+400, where
x is the number of items produced and sold. Use graphical methods to find the number of units at which the manufacturer will break
even for the product.
The number of units that gives break even for the product is
(Simplify your answer.)
Answers
If total revenue given by the function R=16.5x and has total cost given by C=14x+400, where x is the number of items produced and sold then the number of units that gives break even for the product is 160.
What is function?In mathematics, a function is an expression, rule, or law that specifies a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are commonplace in mathematics and are required for expressing physical relationships in the sciences. The present concept of function was proposed by German mathematician Peter Dirichlet in 1837.
If a variable y is so tied to a variable x that there is a rule that determines a unique value of y whenever a numerical value is assigned to x, then y is referred to as a function of the independent variable x.
If the manufacturer will break even for the products then
Revenue = Cost
F(R) = F(C)
14x+400 = 16.5x
On solving the equation
16.5x - 14x = 400
2.5x = 400
x = 400/2.5
x = 160
In the graph the value of x is 160 as well
Thus, to break the product even the number of units =
160
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HELP
The scatterplot for age in months and number of diaper changes per day is shown.
Part A: Estimate and interpret the correlation coefficient. (5 points)
Part B: Create an influential point for this graph that would cause the correlation to decrease. Explain your reasoning.
Answers
Answer:
Here's an answer to part of your question.
Step-by-step explanation:
The older the kids get, the less you have to change their diapers. Therefore, that is why the graph is going down
A company spends $20 million dollars for an office building. Over what period should
the cost be written off?
Answers
Answer:The cost should be 300,000 dollars
Step-by-step explanation:
The sum of two consecutive even integers is 46. Find the integers.
Answers
x + x + 2 = 46
2x + 2 = 46
2x = 44
x = 44/2
x = 22
The even integers are 22 and 24
Answer:
22, 24
Step-by-step explanation:
Hello!
Consecutive integers are integers that come after each other. We want to find two consecutive even integers that when added give us 46.
Let the first consecutive even integer be x. Since even integers come every 2 integers (even, odd, even), the second even integer should be x + 2.
Solve for xx + x + 2 = 462x + 2 = 462x = 44x = 22That means x + 2 should be 24.
The two numbers are 22 and 24.
What is the formula used to arrive at x^2-11x+10
Answers
Answer:
Quadratic Formula
Step-by-step explanation:
x^2-11x+10=
x^2-x-10x+10=
x(x-1)-10(x-1)=(x-10)(x-1)
please help
please hurry
Answers
The turning point of the equation of the graph f(x) = |x - 4| is (4, 0)
How to determine the turning point of the graph?The equation of the graph is given as
f(x) = |x - 4|
The above equation is an absolute value function
An absolute value function is represented as
f(x) = a|x - h| + k
Where the vertex is
Vertex = (h, k)
The vertex also represents the turning point of the absolute value function
From the given equation, we have
(h, k) = (4, 0)
Hence, the turning point of the graph is (4, 0)
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Given the equation y = 3x + 7, which word(s) best describes the 3? Select all that apply.
*
A. slope
B. y-intercept
C. x-intercept
D. coefficient
E. constant
Answers
The slope ( option A) best describes the number 3.
Linear FunctionAn equation can be represented by a linear function. The standard form for the linear equation is: y= ax+b , for example, y=7x+2. Where:
a= the slope. It can be calculated for [tex]\frac{\Delta y}{\Delta x}[/tex].
b= the constant term that represents the y-intercept.
For the given example: a=7 and b=2.
The equation of the question is y=3x+7, when you compare this equation with the standard form for the linear equation is: y= ax+b. You find that a=3, where a represents the slope.
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Need help with this please
Answers
Answer:
HELP WITH WHAT?
Step-by-step explanation:
Adventure Travel has an Adjusted Trial Balance for Year Ended December 31, 20XX with the following account balances:
DEBITS: Cash: 25,000; Accounts Receivable: 15,000; Office Supplies: 4,300; Office Equipment: 29,600
CREDITS: Accumulated depreciation - office equipment: 5,000; Salaries Payable: 2,800; Long-term notes payable: 22,200; Common Stock: 20,000; Retained Earnings: 10,260
DEBIT: Cash Dividends: 1,000
CREDITS: Fees Earned: 75,000
DEBITS: Salaries Expense: 32,800; Rent Expense: 16,800; Depreciation expense - office equipment: 3,960; Advertising expense: 4,000; Office supplies expense: 2,800.
Total Debits = 135,260; Total Credits = 135,260
You have prepared the Income Statement and the Statement of Retained Earnings, now it is time to prepare the Classified Balance Sheet.
What amount do you report for Plant Assets? Specify as a whole number.
Answers
The amount to report for Plant Assets in the Classified Balance Sheet of the company is $24,600
What are plant assets?
Plant assets are long-term fixed assets used to manufacture or sell products and services for Adventure Travel. These assets are of tangible nature and of monetarily benefits to the company for more than one accounting year.
The only plant assets in this case is the office equipment bearing in mind that it has a contra entry, in other words, the $29,600 is the cost of the office equipment , we need to deduct the accumulated depreciation on it so as to determine its current book value
plant assets=$29,600-$5,000
plant assets=$24,600
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A machinist is required to manufacture a circular metal disk with area 600 cm2 . (a) What radius produces such a disk? (b) If the machinist is allowed an error tolerance of ±5cm2 in the area of the disk, how close to the ideal radius in part (a) must the machinist control the radius? (c) In terms of the limit limx→a f(x) = L, what is f(x)? What is a? What is L?
Answers
The required radius and error in radius is 13.8 cm and ± 0.12cm
Given that,
A machinist is required to manufacture a circular metal disk with an area of 600cm².
(a) What radius produces such a disk is to be determined
(b) If the machinist is allowed an error tolerance of ±5cm2 in the area of the disk, how close to the ideal radius in part is to be determined.
The area of a circle is given by the pie times square of the radius.
Area of circle = πr^2
Here,
a) The given area of disk = 600 cm²
πr² = 600
r = √600/3.14
r = 13.8 cm
b) an error tolerance of ± 5 cm² in the area of the disk,
So the percentage of error is 0.84%
Now, 0.84% of radius = 0.84 *13.8/100 = 0.12
The required error in radius will be ±0.12 cm
Similarly,
c) limx→a f(x) = L
Where a is the area of the disk and L is length, and f(x) is function of area.
Thus, the required radius and error in radius is 13.8 cm and ± 0.12cm.
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During a person's commute to school, she spends 12 minutes driving 35 mph and 3 minutes stopped at red lights. What is the person's average
speed during her commute?
Step 1 of 2: First, find the distance of her commute.
Answers
The average speed of person during her commute is 28 miles/ hour.
What do you mean by average speed ?
The entire distance that an object travels in a given amount of time is defined as the average speed for that object.
Total time of driving is 12 minutes.
This can be written as hours which will be :
= 12 / 60
= 1/5 hour
Time of stopping at red lights is 3 minutes and speed is 35 miles per hour.
So , the total distance using the formula will be :
Total distance = Speed × time
Here , the time taken will be equal to :
= [(12 + 3) / 60]
= 15 / 60
= 1/4 hour
So ;
Total distance = 35 × (1/4 hour)
Total distance = 7 miles
And the average speed will be ;
Average speed = Distance / Time
or
Average speed = 7 miles / (1/4) hour
Average speed = 7 × 4 miles/hour
Average speed = 28 miles / hour
Therefore , the average speed of person during her commute is 28 miles/ hour.
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Colton bought some strings of beads. The number of strings was 10 more than the number of beads on each string. There were 119 beads in all. How many strings of beads did Colton buy?
Answers
Answer: 17 strings
Step-by-step explanation:
let the number of strings be a
let the number of beads on each string be b
a − b = 10 (first equation)
a × b = 119 (second equation)
From the first equation:
a = 10 + b
substitute first equation into second equation
b × (10 + b) = 119
10b + b² − 119 = 0
b = 7 or b = -17 reject -17
a − 7 = 10
a = 17
Jenkins Company uses a job order cost system with overhead applied to jobs on the basis of direct labor hours. The direct labor rate is $20 per hour, and the predetermined overhead rate is $15 per direct labor hour. The company worked on three jobs during April. Jobs A and B were in process at the beginning of April. Job A was completed and delivered to the customer. Job B was completed during April, but not sold. Job C was started during April, but not completed. The job cost sheets revealed the following costs for April:
Job A Job B Job C
Cost of Jobs in Process, April 1, Current Year $ 12,000 $ 1,000 $ 0
Direct Materials Used 2,000 8,000 9,000
Direct Labor 10,000 8,000 3,000
Applied Manufacturing Overhead ? ? ?
Required:
If no other jobs were started, completed, or sold, determine the balance in each of the following accounts at the end of April:
work in progress
finished goods
cost of goods sold
Answers
The work in process(Job C) is $14,250
The finished goods(job B) is $23,000
The cost of goods sold(job A) is $31,500
What are work in process, finished goods and cost of goods sold in this case?
The work in process refers to the total costs incurred on Job C, since it was not completed at the end of the month, the finished goods refers to the costs incurred on job B which has been completed but not yet sold and cost of goods sold means the cost incurred on Job A which has been sold since it has been completed.
Job A:
Cost of job in process=$12,000
direct materials used=$2,000
direct labor=$10,000
number of direct labor hours=direct labor cost/ direct labor rate
number of direct labor hours=$10,000/$20=500 hours
Applied Manufacturing Overhead=labor hours*predetermined overhead rate per direct labor hour
Applied Manufacturing Overhead=500*$15=$7,500
cost of goods sold=$12,000+$2,000+$10,000+$7,500
cost of goods sold=$31,500
Job B:
Cost of job in process=$1,000
direct materials used=$8,000
direct labor=$8,000
number of direct labor hours=direct labor cost/ direct labor rate
number of direct labor hours=$8,000/$20=400 hours
Applied Manufacturing Overhead=labor hours*predetermined overhead rate per direct labor hour
Applied Manufacturing Overhead=400*$15=$6,000
finished goods=$1,000+$8,000+$8,000+$6,000
finished goods=$23,000
Job C:
Cost of job in process=$0
direct materials used=$9,000
direct labor=$3,000
number of direct labor hours=direct labor cost/ direct labor rate
number of direct labor hours=$3000/$20=150 hours
Applied Manufacturing Overhead=labor hours*predetermined overhead rate per direct labor hour
Applied Manufacturing Overhead=150*$15=$2,250
work in progress=$0+$9,000+$3,000+$2,250
work in progress=$14,250
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The coldest temperature ever recorded in Mathville was -19°F. This happened on January 30th, 1955. The normal low for that day is 10°F.
How much colder was the record temperature than the normal low temperature?
Answers
Answer:
-29⁰F
Step-by-step explanation:
Because -19-10=-29.
(-4, 12) and (-7, -3) write an equation of the line in slope intercept form that passes through the points.
Answers
Answer:
The equation in slope-intercept form is: [tex]y=5x+32[/tex]
Step-by-step explanation:
To calculate the slope, [tex]m[/tex], we use the formula [tex]\frac{y_{2} -y_{1}}{x_{2}-x_{1} }[/tex] where [tex]y[/tex] are the [tex]y[/tex]-values of the points and [tex]x[/tex] are the [tex]x[/tex]-values.
Pugging our numbers into the formula, we get [tex]\frac{(-3)-12}{-7-(-4)}[/tex]. This simplifies to 5.
To calculate the [tex]y[/tex]-intercept, we first substitute one of our points into the formula. Substituting -4 and 12, we get [tex]12=5(-4)+b[/tex].
Then we can solve for [tex]b[/tex].
[tex]12=5(-4)+b[/tex]
[tex]12=-20+b[/tex]
[tex]32=b[/tex]
So, our slope is 32.
We can then plug these values into the slope-intercept form [tex]y=mx+b[/tex]
Please help what is 8.9 divided
by 0.4
Answers
Answer:
8.9 ÷ 0.4 = 22.25
so the answer is 22.25
hope this helps
Answer:
22.25 is your answer
Step-by-st
Last year, Suzie's salary was $76,000. This year, she is getting a 8% raise. What will her new salary be?
Answers
[tex]76000\times1.08=\boxed{82,080}[/tex]
Answer:
82,080
Step-by-step explanation:
To increase a number by it's percentage, you must first extract what 8% of 76,000 is (6080). Then, you must add the original number to what is 8% of it, to get 82,080, and that, is the final answer.
The sidewalk around a lake is 9/10 mile long. You walk 3 laps Around the lake in the morning and 2 laps in the evening. Your friend walks the same total distance as you on a 1 1/2 mile track. How many laps does your friend walks?
Answers
The total laps your friend runs is 3.
How many laps does your friend run?A fraction is a non-integer that is made up of a numerator and a denominator. The numerator is the number above and the denominator is the number below.
A proper fraction is a fraction where the numerator is less than the denominator. A mixed fraction is a fraction that is made up of a whole number and a proper fraction.
The first step is to determine the total miles you run
Total miles run = length of the side walk x total number of laps
9/10 x (3 + 2)
9/10 x 5 = 45 / 10 = 4.5 miles
The second step is to determine the total number of laps she runs:
4.5 miles / 1 1/2 miles
4.5 / 1.5 = 3 laps
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help me pleaseeeeeeeeee
Answers
Answer:
Step-by-step explanation:
x + x + 16 = 90
2x +16 = 90
2x = 74
x = 37
Computing a percent mixture
A chemist mixes 225 milliliters of a solution that is 39% acid with 25 milliliters of a solution that is 19% acid.
Answer the questions below. Do not do any rounding.
(a) How many milliliters of acid are in the resulting mixture?
milliliters
(b) What percentage of the resulting mixture is acid?
0%
Answers
Part a: Resulting mixture: 92.2 milliliters.
Part b: Percentage of acid in the resulting mixture = 36.88%.
What is defined as the percentage?A percentage is a segment of a whole represented as a number between 0 or even 100 instead of as a fraction. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent. To calculate a percentage, divide the fraction of the total by the total and multiply by 100.Part a: Find the both values from the given percentage;
225 millilitres of a solution contains is 39% acid.
39% of 225 = (39×225)/100 = 87.75 millilitres.
Now, 25 milliliters of a solution contains is 19% acid.
19% of 25 = (19×25)/100 = 4.75 millilitres.
Mixture solution = 87.75 + 4.75
Mixture solution = 92.2 milliliters of acid.
Part b: percentage of the resulting mixture is acid.
92.2 milliliters of the total 250 milliliters is acid.
= 92.2/250 × 100
= 36.88 %
Thus, 36.88% of the the resulting mixture contains acid.
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what is the parent function f(x)=2x^2+3x-4
Answers
Answer:
x^2
Step-by-step explanation:
it's a quadratic equation so the parent function is x^2.
PLS ANSWER 50 POINTS Simplify 6-3/6-4
Answers
The expression 6-3/6-4 after simplification will look like 1.5.
Given that the expression is 6-3/6-4.
We are required to find the value after simplification.
Simplification or simplify fractions basically means to simplify a complicated mathematical expression to get a single or direct answer.
We have to use BODMAS rule for the simplification. The full form of BODMAS is Brackets, Open, Division, Multiplication,Addition and Subtraction. Simplication is nothing but to reduce the expression.
The expression is 6-3/6-4.
We have to do division first.
6-3/6-4 =6-0.5-4
Now we have to do subtraction now.
6-0.5-4=5.5-4=1.5
Hence the expression 6-3/6-4 after simplification will look like 1.5.
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Which of the following represents an INEFFICIENT point of production?
a. Point A
b. Point B
c. Point D
d. None
e. Point C
Answers
The INEFFICIENT point of production in the given graph is represented by Point A , the correct option is option (a).
The given graph is for skateboards vs Bikes .
We need to find the point representing the Inefficient Point of Production.
The Production Possibility Curve points are said to be Inefficient when the resources are not utilized to the fullest.
In the given Production Possibility Curve between Skateboards and Bikers the point A is the inefficient point of production .
Therefore , the Inefficient point of production in the given curve is represented by Point A , the correct option is option (a)
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A small plant is 212 inches tall. How tall will it be in 3 weeks if it grows 34 inch each week? Which method will NOT give the correct number of inches?
Answers
The small will grow 19/4 inch in 3 weeks and the method which will not give the correct inches will be the first option which is
multiply [tex]2\frac{1}{2} * 3[/tex] and then add 3/4.
According to the question we have been given that
The height of the small plant = [tex]2\frac{1}{2}[/tex] inch
In 1 week the plant grows = [tex]\frac{3}{4}[/tex] inch
We need to find the height of the small plant after 3 weeks.
For that we will first find how much tall it will be in 3 weeks using unitary method that is,
1 week = [tex]\frac{3}{4}[/tex] inch
3 week = [tex]\frac{3}{4}[/tex] * 3 inch
= 9/4 inch
Therefore the height of the small plant after 3 weeks will be
[tex]=2\frac{1}{2} + \frac{9}{4} \\= \frac{5}{2} + \frac{9}{4}\\= \frac{10+9}{4} \\= \frac{19}{4}[/tex]
hence the height is 19/4 inch
And the method which will not give the correct number of inches is the first option which is
multiply [tex]2\frac{1}{2} * 3[/tex] and then add 3/4.
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There are 6 black marbles and 4 red marbles in a jar. If you add 4 red marbles to the jar, how many black marbles do you need to add to keep the ratio of black marbles to red marbles the same?
Answers
You need to add 6 red marbles for the ratio to stay the same
How many black marbles do you need to add?The given parameters are:
Black = 6
Red = 4
Represent as ratio
Ratio = Red : Black
This gives
Red : Black = 4 : 6
When you add 4 red marbles, we have:
4 + 4 : 6 + x = 4 : 6
Where x represents the additional number of black marbles
This gives
8 : 6 + x = 4 : 6
Multiply 4 : 6 by 2
So, we have:
8 : 6 + x = 8 : 12
By comparing both sides, we have
6 + x = 12
This gives
x = 6
Hence, you need to add 6 red marbles for the ratio to stay the same
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How much money do you save by purchasing the vanilla cupcakes in a dozen Pak versus buying 12 individual cupcakes? $11.53 for dozen pack and twelve individual cupcakes is $2.15
Answers
Answer:
You save $ 14.27
Step-by-step explanation:
12 dozen = 11.53
2.15 x 12 = 25.80
25.80 - 11.53 = 14.27
