Help me. Two numbers have a sum of 30. Half of their difference is 7. Find the numbers.
Answers
Answer:
the answer is x equals 22 and y equals 8
Step-by-step explanation:
first equation is x+y=30
Second equation is x-y/2=7 that simplify's to x-y=14
then you add then so they will cancel out and you are left with 2x=44 so divide two by both sides which gives x=22
then you subsitute the 22 in the first equation. It will be 22+y=30 then you subtract 22 from the 30 that gives you y=8
so the two numbers are 22 and 8
Hope this helps!!!!
The numbers satisfying the given conditions are 22 and 8.
What is the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
The equation of a straight line can be also written as -
Ax + By + C = 0
By = - Ax - C
y = (- A/B)x - (C/A)
We have the following problem -
Two numbers have a sum of 30. Half of their difference is 7.
We can write the equations as -
x + y = 30
1/2(x - y) = 7
Rearranging, we get -
y = - x + 30
y = x - 14
Plot the graph, the point of intersection is the solution. The number will be 22 and 8.
Alternativelyy = - x + 30
y = x - 14
Equating both, we get -
- x + 30 = x - 14
30 + 14 = 2x
2x = 44
x = 22
and
y = 22 - 14
y = 8
Therefore, the numbers satisfying the given conditions are 22 and 8.
To solve more questions on straight lines, visit the link below-
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Related Questions
what is the product of 2/3 multiplied by 3
Answers
Answer:
The answer is 2
Step-by-step explanation:
HOpe this helps
Answer:
4/3
Step-by-step explanation:
Is figure B and scale copy of figure A?
Answers
Answer:
Yes it is
Step-by-step explanation:
A house sold for $275,100.00. The buyer's real estate agent earned a commission of $11,004.00, and the seller's real estate agent earned a commission of $6,877.50. What was the commission rate of each agent?
Answers
Answer:
Buyer's real estate agent's commission rate = 4%
Seller's real estate agent's commission rate = 2.5%
Step-by-step explanation:
Given that:
Amount for which the house was sold = $275,100.00
Earnings by buyer's Real Estate Agent = $11004.00
Earnings by seller's Real Estate Agent = $6,877.50
To find:
The commission rate of each agent = ?
Solution:
Commission rate can be calculated by finding the percentage for both the real estate agents with the amount for which the house was sold.
i.e.
[tex]\text{Rate of Buyer's agent } = \dfrac{\text{Earnings of Buyer's agent}}{\text{Amount for which the house was sold}}[/tex]
[tex]\Rightarrow \dfrac{\$11004.00}{\$275,100.00}\times 100 = 4\%[/tex]
[tex]\text{Rate of Seller's agent } = \dfrac{\text{Earnings of Seller's agent}}{\text{Amount for which the house was sold}}[/tex]
[tex]\Rightarrow \dfrac{\$6,877.50}{\$275,100.00}\times 100 = 2.5\%[/tex]
Therefore, the answer is:
Buyer's real estate agent's commission rate = 4%
Seller's real estate agent's commission rate = 2.5%
Determine the type of triangle that is drawn below. ASAP PLZZ!!!!!
Answers
Answer:
Isosceles right
Step-by-step explanation:
two same side and there's a right angle
A rock show is being televised. The lead singer, who is 75 inches tall, is 15 inches tall on a TV monitor. The image of the bass player is 13 inches tall on the monitor. How tall is the bass player?
Answers
Answer:
The bass player is 65 inches tall.
Step-by-step explanation:
15 inches is 20% of 75, so the monitor reduces their height by 20%. 13 is 20% of 65, so the bass player must be 65 inches tall.
A sketch artist sells on demand portraits and name doodles at the state fair. The artist has a personal maximum of 40 creations per day. With his current paper supply the artist is equipped to create up to 30 portraits and up to 20 name doodles. If the artists profit is $10 on each portrait and $20 on each name doodle, how many of each item should he aim to sell to maximize his profit?
Answers
Answer:
profit will be maximized by making 20 doodles and 20 paintings = ($10 x 20) + ($20 x 20) = $600
Step-by-step explanation:
we have to maximize the following equation:
$10P + $20D
where:
P = number of portraits
D = number of doodles
the constraints are:
P + D ≤ 40
P ≤ 30
D ≤ 20
we do not need to use solver or any other type of linear programming tool to solve this, since profit will be maximized by making 20 doodles and 20 paintings = ($10 x 20) + ($20 x 20) = $600
hello i need help.....
Answers
Hope this helps :)
did I get all of these right? feedback from experts please!
Answers
Answer:
ucf8riucfuvigruvufgv
Step-by-step explanation:
u7dfi8t57dch
Carolina is making punch for a party. She made 6 bowls of punch. Each bowl holds 2 1/2 gallons of punch. 1 gallon is equal to 4 quarts. She thinks each person will drink about 1 quart of punch. How many people will the 6 bowls of punch serve?
Answers
Answer:
60 people
Step-by-step explanation:
Bowls of Punch = 6
Each bowl holds 2 1/2 gallons of punch
6 bowls = 2 1/2 gallons × 6
= 5/2 × 6 gallons
= 30/2
= 15 gallons
6 bowls of Punch = 15 gallons of Punch
1 gallon = 4 quarts
15 gallons = 4 × 15 quarts
= 60 quarts
6 bowls of Punch = 15 gallons of Punch = 60 quarts of punch
She thinks each person will drink about 1 quart of punch.
How many people will the 6 bowls of punch serve?
6 bowls of Punch = 15 gallons of Punch = 60 quarts of punch
60 quarts of punch / 1 person
= 60 people
The 6 bowls of punch will serve 60 people
-3mn+4m-3 when m=2 and n=-4
Answers
Answer:
29
Step-by-step explanation:
m = 2 and n = -4
-3mn + 4m - 3
-3(2)(-4) + 4(2) - 3
-6(-4) + 8 - 3
24 + 8 - 3
32 - 3 = 29
[tex]\huge\boxed{29}[/tex]
Solution Steps:______________________________
1.) Fill in the variables with the information given:[tex]-3(2)(-4)+4(2)-3[/tex]
- M = 2
- N = -4
2.) Multiply:[tex]-3[/tex] × [tex]2=-6[/tex][tex]4[/tex] × [tex]2=8[/tex]- The reason we multiply first is due to Order of Operations or PEMDAS: Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction.
- When we see y(x) this just means whatever number or variable is before the parenthesis, you multiply it by that.
Equation at the end of Step 2:
[tex]-6(-4)+8-3[/tex]3.) Multiply again:[tex]-6[/tex] × [tex]-4=-24[/tex]- We do this once more because we had one last parenthesis.
Equation at the end of step 3:
[tex]24+8-3[/tex]4.) Add:[tex]24+8=32[/tex]Equation at the end of Step 4:
[tex]32-3[/tex]5.) Subtract: [tex]32-3=29[/tex]______________________________
What is the expression for "the sum of 8 times a number and two"?
Answers
Or I could be backwards as well
Hope this helps
What method can be used to write the equation of a line in slope-intercept form given two points?
A: Find the slope using the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction, and then substitute one point and the slope into the equation y = m x + b to find the y-intercept.
B: Find the slope using the formula m = StartFraction x 2 minus x 1 Over y 2 minus y 1 EndFraction, and then substitute one point and the slope into the equation y = m x + b to find the y-intercept.
C: Find the y-intercept using the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction, and then substitute one point and the y-intercept into the equation y = m x + b to find the slope.
D: Find the y-intercept using the formula m = StartFraction x 2 minus x 1 Over y 2 minus y 1 EndFraction, and then substitute one point and the y-intercept into the equation y = m x + b to find the slope.
Answers
Answer: A: Find the slope using the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction, and then substitute one point and the slope into the equation y = m x + b to find the y-intercept.
Answer:
Answer: A: Find the slope using the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction, and then substitute one point and the slope into the equation y = m x + b to find the y-intercept.
Step-by-step explanation:
Hope i could help
Keith rented a truck for one day. There was a base fee of $17.99, and there was an additional charge of 97 cents for each mile driven. Keith had to pay $137.30 when he returned the truck. For how many miles did he drive the truck? miles
Answers
Answer:
216 miles
Step-by-step
ex15.95+.73x=173.63
.73x=173.63-15.95
.73x=157.68
x=157.68/.73
x=216 miles driven.
PROOF;
15.95+.73*216=173.63
15.95+157.68=173.63
173.63=173.63
Answer: Keith drove the truck for 123 miles
Step-by-step explanation:
17.99+0.97m=137.30
Subtract 17.99 on both sides:
17.99-17.99+0.97m=137.30-17.99
0.97m=119.31
Divide 0.97 on both sides:
0.97m/0.97=119.31/0.97
m=123 miles
Which expression is equivalent to 75 + 24?
3 (25+8)
25 (3 + 24)
5 (70 + 24)
3(75 +8)
Answers
Answer:
The expression that is equivalent to 75 + 24 is 3(25+8)
Step-by-step explanation:
When you add 75 and 24
you get 99.
The equivalent expression:
First you do what's in the paranthese. Add 25 and 8 is get 33. After you get that simply multiple 33 and 3 to get 99.
Find the slope of the line.
Help pleasee!!
Answers
Answer:
4/4
Step-by-step explanation:
y=4 x+1
4 hope that helps!!
don´t forget to thank and Brainliest.
6th grade math i mark as brainliest
Answers
Answer:
8
Step-by-step explanation:
I have to write 20 words but the answer is 8 :)
The marked price of a machine is $1200. How much will it cost if there is a discount of 20%? *
Answers
Answer:
discount amount=20%of mp
=240
now sp=mp-discount=1200-240=960
Complete the steps to solve for x.
4
1
-X = 11
07
4
II
x = 11
20
II
(11)
20
Answers
i hope it helps u:)))))actually I'm pretty sure about it because
11/20x=11
x=11×20/11
(11 gets cancelled and 20 is left)
therefore x=20
and this proves my answer
Find the slope of the line between the points (0, -4) and (2, 8).
Answers
Answer: The slope is 6.
is -5.5645 repeating irrational
Answers
Answer:
This number is neither repeating or irrational.
Step-by-step explanation:
An irrational number is a number with a never-ending decimal that does NOT repeat. This number would be considered rational.
4x3 what is 4x3 I really want to know
Answers
Answer:
The answer to 4x3 is 12
same as adding 4 thee times!
4 plus 4 plus 4 equals 12
Answer:
4X3=12
Step-by-step explanation:
It's like adding 4 3 times
sarah drives at an averadge speed of 58 mph for 4 hours. How many miles does Sarah drive?
Answers
Answer:
232 miles
Step-by-step explanation:
Multiply 58 by 4 equals 232
Can i have brainliest pls?
Answer:
The answer is 232
Step-by-step explanation:
Because what you would do is You would multiply 58 times 4 because you want to know how many miles she drove.
A surf shop charges $6 to rent a wetsuit and $12 per hour to rent a surfboard. Write a function to model the cost, c, to rent a wetsuit and surfboard for h hours. Enter the correct function in the box.
Answers
C = 6 + [tex]12^{x}[/tex]
The required function to model the cost is given as c = 6h + 12h.
Given that,
A surf shop charges $6 to rent a wetsuit and $12 per hour to rent a surfboard. To write a function to model the cost, c, to rent a wetsuit and surfboard for h hours.
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
here,
According to the question,
Rent on a wetsuit for h hours = 6h
Rent on a surfboard for h hours = 12h
Total rent, c = 6h + 12h
Thus, the required function to model the cost is given as c = 6h + 12h.
Learn more about function here:
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iff (x) = 4x3 + 3x2 - 5x + 20 and g(x) = 9x3 - 4x2 + 10x - 55, what is (g- f)(x)?
13x3 - x2 + 5x - 35
5x3 + x2 + 5x + 35
ОА
OB
- 5x3 + 7x2 - 15x + 75
5x3 - 7x2 + 15x - 75
Answers
Answer:
(g-f)(x) = 9x³ - 4x² + 10x - 55 - [ 4x³ +3x² - 5x + 20]
Step-by-step explanation:
what is the reciprocal of 4 3/7?
Answers
Answer:
0.22580645161?
Step-by-step explanation:
The slope intercept of y=10x-5
Answers
Answer:
The slope is 10
The y-intercept is -5
Answer:
Since y=10x-5 is already written in slope-intercept form, I am assuming you want the slope and y-intercept. Slope is 10, and the y-intercept is (0,-5)
Step-by-step explanation:
The position of an open-water swimmer is shown in the graph. The shortest route to the shoreline is one that is perpendicular to the shoreline. Write an
equation that represents this path.
Answers
*attachment contains the omitted graph
Answer:
[tex] y = -\frac{4}{3}x + 9 [/tex]
Step-by-step explanation:
The equation that represents the path of the swimmer to the shoreline can be represented in the slope-intercept form, given as [tex] y = mx + b [/tex].
Where,
Slope (m) = the negative reciprocal of the slope of the shoreline, since it is perpendicular to it = ??
y-intercept (b) = ??
Find the slope of the shoreline using, (0, 1) and (4, 4):
[tex] m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 1}{4 - 0} = \frac{3}{4} [/tex].
Since the slope of the shoreline is ¾. The slope of the path of the swimmer would be the negative reciprocal of ¾.
The negative reciprocal of ¾ = -⁴/3.
The slope of the swimmer's path = -⁴/3.
Using the coordinate of the point of the swimmer (6, 1), and the slope of the path, we can find b, the y-intercept of the path.
Substitute x = 6, y = 1 and m = -⁴/3 into y = mx + b, to find b.
Thus:
1 = (-⁴/3)(6) + b
1 = -8 + b
Add 8 to both sides
1 + 8 = b
9 = b
b = 9
Substitute m = -⁴/3 and b = 9 into y = mx + b.
✅The equation that represents the path would be:
[tex] y = -\frac{4}{3}x + 9 [/tex]
Section 1 - Question 9
Frankie argues that the fraction 20 is a rational number because the square root of 20 is 10. Frankie believes that because 10 is a whole number, it is rational
Alejandro disagrees. He believes that 20 is a rational number because the square root falls between 4 and 5, and the decimal terminates.
Which statement BEST describes who is correct?
А
Frankie is correct because the 20 is 10 which is a rational number.
B
Alejandro is correct because the 20 falls between 4 and 5 and the decimal terminates
С
Both students are correct because 20 is a rational number.
D
Neither student is correct because 20 is an irrational number
©2020 Illuminate Education,
Answers
Alejandro is correct because the 20 falls between 4 and 5 and the decimal terminates. Option B is correct.
Given that,
Frankie argues that the fraction 20 is a rational number because the square root of 20 is 10. Frankie believes that because 10 is a whole number, it is rational. Alejandro disagrees. He believes that 20 is a rational number because the square root falls between 4 and 5, and the decimal terminates.
Rational numbers are numbers that can be structured in the form of the fraction of integers. Eg- 5/6, 2/3 etc.
Here,
20 is a rational number but its square root is not 10 so, Frankie is not correct.
The square root of 20 falls between 4 and 5 the decimal terminates. its true and Alejandro is correct.
Thus, Alejandro is correct because the 20 falls between 4 and 5 and the decimal terminates. Option B is correct.
Learn more about Rational numbers here: https://brainly.com/question/17450097
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Lowest common denominator in 2/3 and 1/2
Answers
LCD = 6
Equivalent Fractions with the LCD
2/3 = 4/6
1/2 = 3/6
Simplifying 84 - (16 - 8) + 5
Answers
Answer:
81
Step-by-step explanation:
use pemdas
Answer:
84-(16-8)+5
= 81
Step-by-step explanation: