This table gives a few (x,y) pairs of a line in the coordinate plane.
x y
48 -30
61 -45
74 -60
What is the x-intercept of the line?
Answers
Answer:
22
Step-by-step explanation:
First, find the equation of the line in slope-intercept form, y = mx + b.
Using the coordinates of these two pairs, (48, -30) and (61, -45), the slope (m) can be calculated as follows:
[tex] m = \frac{y_2 - y_2}{x_2 - x_1} = \frac{-45 -(-30)}{61 - 48} = \frac{-15}{13} [/tex]
[tex] slope (m) = -\frac{15}{13} [/tex]
Find the y-intercept (b) by substituting x = 48, y = -30, and [tex] m = -\frac{15}{13} [/tex] into y = mx + b:
[tex] -30 = -\frac{15}{13}(48) + b [/tex]
Solve for b.
[tex] -30 = -\frac{720}{13} + b [/tex]
Add [tex] -\frac{720}{13} [/tex] to both sides
[tex] -30 + \frac{720}{13} = b [/tex]
[tex] \frac{-390 + 720}{13} = b [/tex]
[tex] \frac{330}{13} = b [/tex]
[tex] b = \frac{330}{13} [/tex]
Substitute [tex] m = -\frac{15}{13} [/tex] and [tex] b = \frac{330}{13} [/tex] into y = mx + b
[tex] y = -\frac{15}{13}x + \frac{330}{13} [/tex]
The x-intercept of the line with the above equation, would be the value of x when y = 0. This is the value of x where the line cuts across the x-axis. To calculate this, substitute y = 0 into [tex] y = -\frac{15}{13}x + \frac{330}{13} [/tex].
[tex] 0 = -\frac{15}{13}x + \frac{330}{13} [/tex]
Subtract [tex] \frac{330}{13} [/tex] from both sides
[tex] -\frac{330}{13} = -\frac{15}{13}x [/tex]
Divide both sides by [tex] -\frac{13}{15}x [/tex]
[tex] \frac{-\frac{330}{13}}{-\frac{13}{15}} = x [/tex]
[tex] -\frac{330}{13}*-\frac{13}{15} = x [/tex]
[tex] -\frac{330}{1}*-\frac{1}{15} = x [/tex]
[tex] \frac{330}{15} = x [/tex]
[tex] 22 = x [/tex]
The x-intercept = 22
Answer:
(22,0)
Step-by-step explanation:
Related Questions
TIME REMAINING
54:32
Tom would like to take out a secured loan to help pay for a vacation this summer. He has offered his car as collateral.
His car is worth $3,500. His bank can offer loans for 80% of collateral value. The vacation he has planned will cost
$4,750. Approximately how much additional collateral will Tom need to offer in order to borrow enough to go on his
vacation as planned?
$1,000.00
b. $1,362.50
c. $2,437.50
d. $2,800.00
a.
Please select the best answer from the choices provided
A
B.
ОООО
D
Answers
Tom will need to offer additional collateral of C. $2,437.50 to borrow enough for his planned vacation.
What is collateral?Collateral refers to a valued property or financial security offered by the borrower to the lender to guarantee repayment of a loan.
Lenders sell collaterals when the borrowers fail to comply with their loan terms.
How is the additional collateral determined?Car's value = $3,500
Collateral value in percentage = 80%
Car's collateral value = $2,800 ($3,500 x 80%)
Planned cost of vacation = $4,750
Additional cost to meet vacation cost = $1,950 ($4,750 - $2,800)
Additional collateral value to meet target = $2,437.50 ($1,950/80%)
Total collateral that Tom needs to offer = $5,937.50 ($3,500 + $2,437.50)
80% of $5,937.50 = $4,750
Another way is to work with the planned cost and the collateral percentage offered by Tom's bank:
Planned cost of vacation = $4,750
Collateral value in percentage = 80%
Total collateral to be offered by Tom = $5,937.50 ($4,750/80%)
Car's collateral value = $3,500
Additional collateral value = $2,437.50 ($5,937.50 - $3,500)
Thus, Tom needs additional collateral of C. $2,437.50.
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can someone help me plz
Answers
28 PLEASE GIVE BRAINLIEST
which equation matches this graph?
Answers
Slope: y2 - y1
-———
X2 - X1
Y = MX + B
Y - Y1 = m ( X - X1)
M=slope
B=y-intercept
X=input
Y=output
F(x)= y
If ( y+6=3/4(x+4) ) is your equation then A is your answer
Help me please 50 points .
Answers
Answer:
D. $80
Step-by-step explanation:
kayla equation: 30x+20=y
Sara equation: 35x+10=y
30x+20=35x+10
10=5x
2=x
30(2)+20=$80
35(2)+10=$80
Answer: $80
Step-by-step explanation:
Kayla:
Lesson fee ($30) + first-time fee ($20) = 50
Another lesson fee will make is $80
Sara:
Lesson fee ($35) + first-time fee ($10) = 45
Another lesson fee will make $80
Answer = 80
A farmer is looking at his tractor at the other end of his field. Assume the field is mapped onto the coordinate plane as shown in the graph. What is the exact distance from the farmer to his tractor?
Question 5 options:
A)
units
B)
units
C)
units
D)
units
Answers
The distance of the farmer to the tractor would be gotten by subtracting the coordinate of the farmer from that of the point of the tractor.
What is distance?The definition of distance in mathematics is the shortest space that lies between two different points.
Given that the points that the farmer and the tractor are standing on are unspecified, the distance would be point of farmer subtracted from that of the tractor.
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Determine the values of m, a, p, q and r.
Answers
Answer:
m= 68 degrees
a= 68 degrees
p= 68 degrees
q= 112 degrees
r= 68 degrees
Step-by-step explanation:
Hope this helps, if so mark me brainliest???
x-3=1/2x
find x
please help
Answers
Answer:
x=6
Step-by-step explanation:
2x-6=x
2x-x=6
x(2-1)=6
x=6
Answer: x=6
Step-by-step explanation:
simplify 1 over 2x to x over 2. multiply both sides by 2. subtract 2x from both sides. simplify x minus 2x to negative x. multiply both sides by -1. switch sides.
factor 49x^2-7^2
and please explain how
Answers
Answer:
[tex]49x^2-7^2=49(x-1)(x+1)[/tex]
Step-by-step explanation:
Factoring
We need to recall this property of binomials:
[tex](a-b)(a+b)= a^2-b^2[/tex]
It allows us to factor the difference between two squares as follows.
[tex]a^2-b^2=(a-b)(a+b)[/tex]
The given expression is
[tex]49x^2-7^2[/tex]
Comparing with the above expression:
[tex]a^2=49x^2[/tex]
Taking square root:
[tex]a = 7x[/tex]
[tex]b^2=7^2[/tex]
Taking square root:
b=7
Factoring:
[tex]49x^2-7^2=(7x-7)(7x+7)[/tex]
Now we can see each factor can be taken out the common factor 7:
[tex]49x^2-7^2=7(x-1)*7(x+1)[/tex]
Multiplying:
[tex]\boxed{49x^2-7^2=49(x-1)(x+1)}[/tex]
Please help y < 5 inequality
Answers
Answer:
Step-by-step explanation:
17. The sum of three consecutive integers is three times the second integer.
Show that this is true for the three consecutive integers 7, 8, and 9.
I
twork being lat
Set up an equation that models this statement.
Show, by solving the equation, that this equation will always be true for any three consecutive integers.
Answers
Answer:
By using Carl Gauss's clever formula, (n / 2)(first number + last number) = sum, where n is the number of integers, we learned how to add consecutive numbers quickly. We now know that the sum of the pairs in consecutive numbers starting with the first and last numbers is equal.
Step-by-step explanation:
Answer:
Step-by-step explanation:
7+8+9=24.
8 is the second integer and 8*3=24.
A company plans to sell a new type of vacuum cleaner for $280 each. The company’s financial planner estimates that the cost, y, of manufacturing the vacuum cleaners is a quadratic function with a y-intercept of 11,000 and a vertex of (500, 24,000). Which system of equations can be used to determine how many vacuums must be sold for the company to make a profit?
StartLayout Enlarged Left-Brace 1st Row y = 280 x 2nd Row y = negative 0.052 (x minus 500) squared + 24,000 EndLayout
StartLayout Enlarged Left-Brace 1st Row y = 280 x 2nd Row y = 0.052 x squared + 11,000 EndLayout
StartLayout Enlarged Left-Brace 1st Row y = 280 x 2nd Row y = 0.052 (x minus 500) squared + 24,000 EndLayout
StartLayout Enlarged Left-Brace 1st Row y = 280 x 2nd Row y = negative 0.052 (x minus 500) squared + 11,000 EndLayout
Answers
Answer:
StartLayout Enlarged Left-Brace 1st Row y = 280 x 2nd Row y = negative 0.052 (x minus 500) squared + 24,000 EndLayout
Step-by-step explanation:
Given that:
Cost per cleaner = $280
The cost of x vacuum cleaners will be :
Cost per cleaner * number of cleaners
$280 * x
= $280x
The general vertex firm equation :
y-k = a(x-h)^2
Vertex = (500, 24000) ; Vertex = (h, k)
h = 500 ; k =24000 y= 11000, x = 0
y intercept = 11000
Plugging the values :
11000 - 24000 = a(0 - 500)^2
- 13000 = a(-500)^2
-13000 = a * 250000
a = - 13000 / 250000
a = - 0.052
Hence,
y - 24000 = a(0 - 500)^2
y = - 0.052(0 - 500)^2 + 24000
Answer:
A on edge
Step-by-step explanation:
i took the test
How many oz. of mixed nuts that contain
30% peanuts must Abhasra add to 6.9 oz.
of mixed nuts that contain 20% peanuts to
make a mixture with 27% peanuts?
Answers
Answer:
77
Step-by-step explanation:
what energy is made when you do a backflip?
Answers
Answer:
kinetic energy is possessed
A personnel manager has found that, historically, the scores on aptitude tests given to applicants for entry-level positions follow a normal distribution with standard deviation 21.73 points. A random sample of 14 test scores from the current group of applicants had a mean score of 74.57 points. Based on these sample results, a statistician found for the population mean a confidence interval extending from 65.7425 to 83.3975 points. Find the confidence level of this interval. Round off your answer to two decimal places.
Answers
Answer:
The value is [tex]C = 85\%[/tex]
Step-by-step explanation:
From the question we are told that
The standard deviation is [tex]\sigma = 21.73[/tex]
The sample size is n = 14
The mean score is [tex]\= x = 74.57[/tex]
The confidence interval is 65.7425 to 83.3975
Generally the degree of freedom is mathematically represented as
[tex]df = n -1[/tex]
=> [tex]df = 14 -1[/tex]
=> [tex]df = 13[/tex]
Generally the margin of error is mathematically evaluated as
[tex]E = \frac{83.3975 -65.7425 }{2}[/tex]
=> [tex]E = 8.828[/tex]
Generally this margin of error is mathematically represented as
[tex]E = t_{\frac{\alpha }{2} , df} * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]8.828 = t_{\frac{\alpha }{2} , df} * \frac{21.73 }{\sqrt{14} }[/tex]
=> [tex]t_{\frac{\alpha }{2} , df} = 1.520[/tex]
From the t distribution table the probability of [tex]( t> 1.520 )[/tex] at a degree of freedom of 13 is
[tex]\frac{\alpha }{2} = P( t > 1.52 ) = 0.076[/tex]
=> [tex]\alpha = 2 * 0.076[/tex]
=> [tex]\alpha = 1.52[/tex]
So the confidence level is evaluated as
[tex]C = 1- \alpha[/tex]
=> [tex]C = 1- 0.152[/tex]
=> [tex]C = 0.85[/tex]
Converting to percentage
=> [tex]C = 0.85 * 100[/tex]
=> [tex]C = 85\%[/tex]
7.53333333333 as a fraction
Answers
Answer:
Step-by-step explanation:
Step by step
Step 1 of 2: Convert decimal to fraction.
Convert decimal to fraction
Step 2 of 2: Reduce fraction to lowest terms.
Reduce fraction to lowest terms
1 is the greatest common divisor of 753 and 100. The result can't be further reduced.
Step 2 of 2: Convert improper fraction to mixed number.
Convert improper fraction to mixed number
753 ÷ 100 = 7 remainder 53
Point A is rotated 90 degrees counterclockwise around point C to form the image A'. Select three true statements based on the given information.
Answers
Answer:
When we rotate a point A, around point C, the distance between the points is invariant.
This means that if A' es the image of the rotated point, then A' must lie in a circle centered in C with radius AC.
Then the correct statements are:
A' lies on a circle centered at point C with radius AC
This is by definition.
m∠ACA' = 90°
This is because A is rotated 90° around C to form the image A', then the measure must be 90°.
AC = A'C
As we already defined, the distance between the rotated point and the center of rotation is invariant, then the distance between A and C must be the same as the distance between A' and C.
Answer:
AC = A'C
A' lies on a circle centered at point C with radius AC
m∠ACA' = 90°
Step-by-step explanation:
When we rotate a point A, around point C, the distance between the points is invariant.
This means that if A' es the image of the rotated point, then A' must lie in a circle centered in C with radius AC.
As we already defined, the distance between the rotated point and the center of rotation is invariant, then the distance between A and C must be the same as the distance between A' and C.
Ben goes to buy some school supplies at a store. He has $30.
COST OF SCHOOL SUPPLIES
Cost per Item
Items
(in dollars)
Notebook
12.50
Pen
0.75
Pencil box
2.25
Stapler
7.00
Calculator
17.00
Answers
Answer:
it’s a Stapler, to pencil boxes and two pens
Step-by-step explanation:
are you have to do is add a calculator stapler stapler to pencil boxes and two pens altogether and you get exactly 30/// So technically you add 17+7+4.5+1.5
solve for x SOMEONE PLS!
71+49+7x+11=180
Answers
71+49+7x=169
71+7x=120
7x=49
x=7
Who started with the greatest initial value of Halloween candy? Jeremy, Josh, Rachel, or Lydia?
Answers
Answer: Rachael Ray.
Step-by-step explanation: Have a blessed day hopefully this helped!
Which line is parallel to the line y = 2x + 7 and passes through the point (1, 4)? *
2 points
(y - 4) = 2(x - 1)
(y - 4) = 7(x - 1)
(y + 4) = 2(x + 1)
(y + 4) = 7(x + 1)
Answers
Answer:y-4=2(x-1)
Step-by-step explanation:
It has the same slope as the y=2x+7, making it parallel, and crosses the point (1,4)
----% of 50 shirts is 35 shirts
Answers
Answer:
70%
Step-by-step explanation:
50/10 is 5 (which is 10%). 5 x 7 is 35 (or 70%)
For this type of problem we can use a ratio. Using a ratio allows us to to find how much needs to be multiplied by 50 to get 35 (or our percentage needed).
To write the ratio we can say “for every 50 shirts there are 35 once multiplied by a certain percentage”. The ratio would be written out as 35:50. We need to find a way to get 50 to 35 by multiplying (by the percentage). To find the percentage we need to divide 35 by 50. 35/50=0.7.
When working with percentages, decimals will be multiplied by 100 and transferred to a percentage (0.7*100=70 which is then 70%. Multiplying 50 by 0.7 (or 70%) will then give you 35.
Math is hard.
Whats 9 + 10 = ????
Answers
Answer:
19
Step-by-step explanation:
im jumping off a bridge
Answer:
the answer in 19
Step-by-step explanation:
use Ur brain
The heights of women aged 20 to 29 are approximately Normal with mean 64.3 inches and standard deviation 2.7 inches. Men the same age have mean height 69.9 inches with a standard deviation 3.1 inches. Describe in lay terms what information the z scores give that the original nonstandardized heights do not.
Answers
Answer:
In a lay term; The z-score gives us information concerning how many percentages of data lie between the given data interval. The z-score gives us an overview of the distance from the mean a data point is. In addition to that, it measures the degree of standard deviations below or above the population mean a raw score. We can place a z-score on a normal distribution curve.
Step-by-step explanation:
Given that:
Height of woman between age 20 -29 are approximately normal with:
population mean = 64.3 inches &;
standard deviation = 2.7
For men:
population mean = 69.9 inches
Standard deviation = 3.1 inches
In a lay term; The z-score gives us information concerning how many percentages of data lie between the given data interval. The z-score gives us an overview of the distance from the mean a data point is. In addition to that, it measures the degree of standard deviations below or above the population mean a raw score. We can place a z-score on a normal distribution curve.
This is hard I’d love help
Answers
1/8
Katie Perry is standing 30 feet away from the entrance to a store. She sees Taylor Swift walk out of the store, and Katie keeps walking away from her at speed of 4 feet each second. Write an equation that represents Katie's distance from the store's entrance.
PLEASE HELP MEMEMEMEME
Answers
Answer:
y=4x+30
Step-by-step explanation:
y is distance, x is time
After knee surgery, your trainer tells you to return to your jogging program slowly. He suggests jogging for 12 minutes each day for the first week. Each week thereafter, he suggests that you increase that time by 6 minutes per day. How many weeks will it be before you are up to jogging 60 minutes per day?
Answers
Answer:
8 weeks
Step-by-step explanation:
1. Write out the equation
12+6x=60
2. Subtract 12 from both sides
6x = 48
isolate the variable (divide 6 on both sides)
x= 8
Which decimal is the best best estimate of the fraction 29/40
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Answers
Answer:
C
Step-by-step explanation:
I hope this helps!!!!
The best estimate of the fraction 29/40 would be; 0.7
How can we interpret the division?When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get. Division can be interpreted as equally dividing the number that is being divided into total x parts, where x is the number of parts the given number is divided.
We need to find the decimal that best best estimate of the fraction 29/40
A negative divided by a negative is positive, then;
29/40 = 0.72
Therefore, The best estimate of the fraction 29/40 would be; 0.7
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The length of a rectangle is 4 inches more than its width, and its perimeter is 34 inches. Find the length and width of the rectangle. Find the width of the rectangle. Type a numerical answer in the space provided.
Answers
Answer:
w mean widh
Step-by-step explanation:
p=2l+2w
given w+4 2+w p= 34
34 =2w+4 + 2 w
w=24
26
_ 6.5
4
L w+4 =6.5 +4 =10.5
How can you solve an equation with a variable on both sides? Complete the explanation.
You can solve the equation by using ____ operations to get the variable terms on one side of the equal sign and the constant terms on the ____ side. Then ____ both sides by the
coefficient of the resulting variable term.
Answers
Answer:
order of operations, right?, divide
Step-by-step explanation:
sorry if this is wrong :)
3(4x - 6) - 2x + 1 = 3 - (3x - 6)?
Answers
10x - 17 = -3x + 9
13x = 26
x = 2
I hope this helps
