Final answer:
The two numbers are 40 and 13.
Explanation:
We are given that the sum of two numbers is 53, and their difference is 27. Let's denote the two unknown numbers as x and y, where x is the larger number.
The system of equations based on the given information is:
x + y = 53x - y = 27By adding the two equations, the y's cancel out:
(x + y) + (x - y) = 53 + 272x = 80x = 40Now, we can find the value of y by substituting x into the first equation:
40 + y = 53y = 53 - 40y = 13The two numbers are 40 and 13.
how do you find x? really confused
Answer:
[tex]x= 28\°[/tex]
Step-by-step explanation:
We have labelled the given diagram and redrawn again in the attachment.
Also from the labelled diagram given below the given details are;
∠CPQ =[tex](5y-4)\°[/tex]
∠RQF =[tex]3y\°[/tex]
∠BRH =[tex](2x+13)\°[/tex]
∠CPQ = ∠PQF (Alternate Interior Angle)
∠PQF + ∠RQF =180° (Straight angle property)
Now Substituting the values we get;
[tex]5y-4+3y=180\\8y=180+4\\8y=184\\y=\frac{184}{8}=23\°[/tex]
∠RQF =[tex]3y\° = 3\times23 = 69\°[/tex]
∠RQF = ∠BRH (corresponding angles)
[tex]69=2x+13\\2x = 69 -13\\2x=56\\x = \frac{56}{2} = 23\°[/tex]
Hence x = 23°
Which of the following is the inequality −18x + 2y ≥ −13 written in slope-intercept form?
Select one:
A. y ≥ - 6.5x - 9
B. y ≥ 7x - 10
C. y ≥ 9x − 6.5
D. y ≥ 10x - 7
Answer:
C. y ≥ 9x − 6.5Step-by-step explanation:
[tex]-18x+2y\geq-13\qquad\text{add}\ 18x\ \text{to both sides}\\\\-18x+18x+2y\geq18x-13\\\\2y\geq18x-13\qquad\text{divide both sides by 2}\\\\\dfrac{2y}{2}\geq\dfrac{18x}{2}-\dfrac{13}{2}\\\\\boxed{y\geq9x-6.5}[/tex]
P^3×q^2(p^4×q^n×r^3/r^-4)=p^7q^5r^7
What does n=
Answer:
[tex]n = 3[/tex]
Step-by-step explanation:
Given:
The equation given is:
[tex]p^3q^2(p^4q^n\times \frac{r^3}{r^{-4}})=p^7q^5r^7[/tex]
We simplify the given equation using the following law of indices:
[tex]a^m\times a^n=a^{m+n}\\\frac{a^m}{a^n}=a^{m-n}[/tex]
Therefore,
[tex]p^{3+4}q^{n+2}\times r^{3-(-4)})=p^7q^5r^7\\p^7q^{n+2}r^7=p^7q^5r^7\\q^{n+2}=q^5[/tex]
Since the base on both the sides is same, therefore, their exponents must also be same. This gives,
[tex]n+2=5\\n=5-2\\n=3[/tex]
Therefore, the value of 'n' is 3.
Chose the substitution method to solve the system of equations choose the correct ordered pair 3x-y=7 2x-2y2
Answer:
(3, 2)
Step-by-step explanation:
3x-y=7
2x-2y=2
------------
y=3x-7
substitute this equation to 2x-2y=2
first, simplify 2x-2y=2 into x-y=1.
-----------------------------------------------------
x-(3x-7)=1
x-3x+7=1
-2x+7=1
-2x=1-7
-2x=-6
x=-6/-2=3
y=3(3)-7=9-7=2
Answer: x=3, y=2.
Which of the following is NOT a quadrilateral?
Triangle
Rectangle
Square
Trapezoid
Answer:
Triangle
The triangle has 3 sides but the other ones have 4 sides. A quadrilateral has 4 sides.
David drove 135 miles in 3 hours find the unit rate
Answer:
45 mph
The drawing will help
Answer: 45 miles per hour
Step-by-step explanation:
3 hours = 135 miles
divide both sides by 3
1 hour = 45 miles as you can write this as 45 miles per hour
help pls pls Which words or phrases describe parallel lines?
SELECT ALL THAT APPLY!!!!
common points
coinciding
coplanar lines
perpendicular
never intersect
Answer:
Never intersectCoplanar linesYou receive an 11 percent commission on all sales you make if your commission for the month is 512.50 dollars what was your total sales
Total sales were $4659.1
Step-by-step explanation:
Given,
Commission = 11%
Amount of commission = $512.50
Let,
total sales = x
Therefore,
11% of x = 512.50
[tex]\frac{11}{100}x=512.50\\0.11x=512.50[/tex]
Dividing both sides by 0.11
[tex]\frac{0.11x}{0.11}=\frac{512.50}{0.11}\\x= $4659.1[/tex]
Total sales were $4659.1
Keywords: percentage, division
Learn more about division at:
brainly.com/question/13076219brainly.com/question/13096001#LearnwithBrainly
Find the quotient of 2 ÷ 3/ 8. The quotient is 5 and ______
Answer:
1/3
Step-by-step explanation:
2 ÷ 3 /8
To divide by a fraction, multiply by its reciprocal.
2 ( 8 /3 )
Multiply
2
(
8
3
)
.
Tap for more steps...
16
3
The result can be shown in multiple forms.
Exact Form:
16
3
Decimal Form:
5.
¯
3
Mixed Number Form:
5
1 /3
5 is the quotient and 1 is a reminder.
What is the quotient?the result obtained by dividing two numbers is known as the quotient.
dividend / divisor = quotient + reminder
Given problem 2 ÷ 3/8. after simplifying it.
2 ÷ 3/8 = 16 ÷ 3
2 ÷ 3/8 = 5 + 1/3
Therefore the given problem quotient is 5 and the remainder is 1.
Learn more about quotient here:
https://brainly.com/question/27796160
#SPJ3
if 16 candy bars cost $20,how much do 24 candy bars cost.?
To find the cost of 24 candy bars, calculate the cost per candy bar (found by dividing $20 by 16, equaling $1.25) and multiply it by 24. Therefore, 24 candy bars would cost $30.
Explanation:The subject of the question involves unit pricing, a common concept in mathematics. To find the cost of 24 candy bars, first identify the cost per candy bar, then multiply this unit price by the number of candy bars in question.
From the question, we know that 16 candy bars cost $20. So the unit price, or cost per candy bar, is $20 divided by 16, which equals $1.25.
Therefore, the cost of 24 candy bars would be $1.25 (the cost per candy bar) multiplied by 24 (the number of candy bars), which equals $30. Hence, 24 candy bars would cost $30.
Learn more about Unit Pricing here:https://brainly.com/question/32390020
#SPJ2
Solve the equation : n +32=60
1) n= 1.875
2) n= 28
3) n= 38
4) n= 92
N=28
Step-by-step explanation:
Subtract 32 from both sides
i think my answer also n=28
Which graph represents a linear function that has a slope of 0.5 and a y-intercept of 2?
mc008-1.jp
mc008-2.jp
mc008-3.jp
mc008-4.jp
skskskksksksk
D
Answer:
The graph in the attached figure
Step-by-step explanation:
we know that
The equation of the line in slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-intercept
In this problem we have
[tex]m=0.5\\b=2[/tex]
substitute
[tex]y=0.5x+2[/tex]
The easiest way to graph a line is with a pair of points.
Find the intercepts
The y-intercept is given ----> point (0,2)
The x-intercept is the value of x when the value of y is equal to zero
For y=0
[tex]0=0.5x+2[/tex]
[tex]x=-4[/tex]
so
The x-intercept is the point (-4,0)
Plot the intercepts and join the points to graph the line
using a graphing tool
The graph in the attached figure
Anahita drives for 3 hours at 15 miles per hour. How far does she travel?
Answer:
45 Miles
Step-by-step explanation:
3 hours * 15mph= 45 Miles in 3 hours
PLEAASE HELP ASAP!!!!!
language arts!!
1. Decide whether each of the following groups of words is a complete sentence (an independent clause) or an incomplete sentence (a dependent clause). If the sentence is incomplete, capitalize it and do whatever else is necessary to make it complete. If the sentence is complete, capitalize the first word and add the appropriate ending punctuation.
Example: three ships went with Columbus
Three ships went with Columbus.
1.because they found no gold in that country
2. after they went running through
3. he wants to visit the moon
4. the boy who has lots of freckles
5. she turned a page in her book
6. a book that I read
7. before the race began
1. Incomplete/ Because they found no gold in that country...
2. Incomplete/ After, they went running through...
3. Complete/ He wants to visit the Moon.
4. Incomplete/ The boy who has lots of freckles...
5. Incomplete I believe/ She turned a page in her book...
6. Incomplete/ A book that I read...
7. Incomplete/ Before the race began....
Answer:
Incomplete/ Because they found no gold in that country...
2. Incomplete/ After, they went running through...
3. Complete/ He wants to visit the Moon.
4. Incomplete/ The boy who has lots of freckles...
5. Incomplete I believe/ She turned a page in her book...
6. Incomplete/ A book that I read...
7. Incomplete/ Before the race began....
Step-by-step explanation:
11 identical pairs of Air Jordan cost $660.What is the cost of one pair?
Answer:
$60
Step-by-step explanation:
11 identical pairs of Air Jordan cost $660.
To find the cost of one pair, you have simply to divide the total amount paid by the total number of pairs.
Total amount paid = $660
Total number of pairs = 11
The cost of one pair [tex]=\$660 : 11=\$60[/tex]
To find the cost of one pair of Air Jordan sneakers from the total cost of 11 pairs, divide the total cost ($660) by the number of pairs (11), which equals $60 per pair.
Explanation:The question concerns determining the cost of one pair of Air Jordan sneakers given the total cost for 11 pairs. This is a basic division problem that falls under the category of arithmetic in mathematics. To find the cost of one pair, divide the total cost by the number of pairs. Here is how the calculation is done step-by-step:
Determine the total cost of all pairs together, which is given as $660.Count the number of identical pairs, which we know is 11 pairs.Divide the total cost by the number of pairs: $660 ÷ 11 pairs = $60 per pair.Therefore, the cost for one pair of Air Jordan sneakers is $60.
1. Reduce: 21 =
21
Reduce:
28
Answer:
3/4
Step-by-step explanation:
21/28=3/4
Answer:
3/4
Step-by-step explanation:
Perpendicular to 3x-6y=-2 containing points (-3,-8)
Answer:
y = -2x - 14Step-by-step explanation:
[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m\ -\ \text{slope}\\b\ -\ \text{y-intercept}[/tex]
[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\k\ \perp\ l\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\k\ ||\ l\iff m_1=m_2[/tex]
[tex]\text{We have the equation of a line in the standard form.}\\\text{Convert it to the slope intercept from:}\\\\3x-6y=-2\qquad\text{subtract }\ 3x\ \text{from both sides}\\\\-6y=-3x-2\qquad\text{divide both sides by (-6)}\\\\y=\dfrac{-3}{-6}x+\dfrac{-2}{-6}\\\\y=\dfrac{1}{2}x+\dfrac{1}{3}\to m_1=\dfrac{1}{2}[/tex]
[tex]\text{Therefore}\ m_2=-\dfrac{1}{\frac{1}{2}}=-1\cdot\dfrac{2}{1}=-2.\\\\\text{Put the value of a slope and the coordinates of the point (-3, -8)}\\\text{ to the equation of a line:}\\\\-8=-2(-3)+b\\\\-8=6+b\qquad\text{subtract 6 from both sides}\\\\-14=b\to b=-14\\\\\text{Finally:}\\\\y=-2x-14[/tex]
Of the following equations below, which equation represents a direct variation between x and y?
Select one:
A. 2y = 3x −7
B. y −4 = x +6
C. y +3 = x +3
D. 4y +1 = 4x−1
Answer:
C. y +3 = x +3
Step-by-step explanation:
We need to find in below option x has direct variation with y.
We solve for each;
A. [tex]2y = 3x-7[/tex]
From above equation we can state that 2 times y is equal to 7 less than 3 times of x.
Hence it doesn't represent direct variation.
B. [tex]y-4 = x+6[/tex]
Solving above expression we get;
[tex]y-4 = x+6\\y = x+6+4\\y=x+10[/tex]
From above equation we can state that y is equal to 10 more than x.
Hence it doesn't represent direct variation.
C. [tex]y+3 = x+3[/tex]
Solving above expression we get;
[tex]y+3 = x+3\\y = x+3-3\\y=x[/tex]
From above equation we can state that y is equal to x.
Hence it represent direct variation.
D. [tex]4y+1 = 4x-1[/tex]
Solving above expression we get;
[tex]4y+1 = 4x-1\\4y = 4x-1-1\\4y=4x-2[/tex]
From above equation we can state that 4 times y is equal to 2 less than 4 times of x.
Hence it doesn't represent direct variation.
Hence the Answer which represent direct variation of x and y is,
C. [tex]y+3 = x+3[/tex]
it is 6.09 pm the movie starts at 6:30 pm. while standing in the line for the movie, you count 146 people in front of you. nine people buy their tickets in 70 seconds. will you be able to buy your ticket before the movie starts?
Step-by-step explanation:
It is given that [tex]9[/tex] people bought tickets in [tex]70[/tex] seconds.
So,[tex]\frac{9}{70}[/tex] people can buy tickets in a second.
It is given that the current time is [tex]6:09pm[/tex] and movie starts at [tex]6:30pm[/tex].
So there is [tex]30-9=21minutes[/tex] until movie starts.
In [tex]21[/tex] minutes,the number of persons that can buy tickets are [tex]\frac{9}{70}\times 21\times 60=162[/tex].
So,[tex]162[/tex] people can buy tickets in [tex]21[/tex] minutes.
Since there are only [tex]146[/tex] people in front of you,you can buy a ticket.
what value is equivalent to -2 x 3² - 8 ÷ 2 + 6?
Answer:
−18x+2
Step-by-step explanation:
Please help whoever answers get brailnest
Answer:
-2/9
Step-by-step explanation:
using elimination method, simultaneously solve, 6x+2y=20 and 0.5x-0.5y=1
Answer:
x=3, y=1. (3, 1)
Step-by-step explanation:
6x+2y=20
0.5x-0.5y=1
-----------------
6x+2y=20
1/2x-1/2y=1
----------------
6x+2y=20
2(1/2x-1/2y)=2(1)
------------------------
6x+2y=20
x-y=2
-------------------
6x+2y=20
x=y+2
---------------
6(y+2)+2y=20
6y+12+2y=20
8y+12=20
8y=20-12
8y=8
y=8/8
y=1
x=1+2=3
x=3, y=1.
help me plssss last one i need
Answer: y=2x-20
Step-by-step explanation:
y+18=2(x-1)
y+18=2x-2
y=2x-20
3(3p +5) -6p + 3p(5-1)
Answer:
15p+15
Step-by-step explanation:
3(3p+5)-6p+3p(5-1)
9p+15-6p+3p(4)
9p-6p+15+12p
3p+12p+15
15p+15
Suppose g(x) = f(x-2) + 3. Which statement best compares the graph of g(x)
with the graph of f(x)?
Answer:
The graph of g(x) is f(x) translated 3 units up.
Which of the following points is a solution to a system of linear equations
y<3x+5
y>-2/3x-3
_
a.(3,14)
b.(3,9)
c.(3,-14)
d.(3,-9)
Final answer:
The point (3,9) is the solution to the system of linear equations because it satisfies both inequalities y < 3x + 5 and y > -2/3x - 3 when the values of x and y are substituted into them.
Explanation:
To determine which of the given points is a solution to the system of linear equations:
y < 3x + 5
y > -2/3x - 3
We substitute the x and y values of each option into the inequalities to find a match.
For point (3,14): Substitute x = 3 and y = 14 into the inequalities.
14 < 3(3) + 5, which simplifies to 14 < 14; this is false.14 > -2/3(3) - 3, which simplifies to 14 > -5; this is true.So, (3,14) does not satisfy both inequalities.For point (3,9): Substitute x = 3 and y = 9 into the inequalities.9 < 3(3) + 5, which simplifies to 9 < 14; this is true.9 > -2/3(3) - 3, which simplifies to 9 > -5; this is true.Therefore, (3,9) satisfies both inequalities and is the solution.Points (3,-14) and (3,-9) can be quickly dismissed as they give negative values for y, which won't satisfy the first inequality since it requires y to be less than a positive value.
The function f(x) has been transformed to give g(x). Which of the following functions represent g(x)
A. g(x) = (1/2) x^2
B. g(x) = 4x^2
C. g(x) = 1/4 x^2
D. g(x) = 2x^2
f(x) = x2
g(x) = ?
Answer:
Option A is correct.
Step-by-step explanation:
See the two graphs given in the diagram attached.
The first graph shows the function f(x) = x²
Hence, it passes through the points (1,1), (-1,1), (2,4) and (-2,4) points.
Now, from the plotted second graph we see the points (2,2), and (-2,2) are on the curve.
Hence, the y-value corresponding to the same x-value reduces by a factor [tex]\frac{1}{2}[/tex] in the second graph i.e. the graph of y = g(x) compared to the first graph.
So, we can conclude that the transformed graph has the equation [tex]g(x) = \frac{1}{2} x^{2}[/tex].
Hence, option A is correct. (Answer)
Answer:
The answer is g(x) = (1/2) x^2
Step-by-step explanation:
If a dress were 20% off of the marked price of $32.00, how much would it cost?
Answer:
25.6
Step-by-step explanation:
$32.00 / 100 = $0.32
$0.32 x 20 = $6.40
So $32.00 - $6.40 = $25.60
Answer: $25.60
Step-by-step explanation: you just subtract 20% fro 30 on a calculator.
How many 6 1/4-inch pieces of fabric can be cut from a 75-inch roll?
Answer:
12 pieces
Step-by-step explanation:
75 divided by 6 1/4= 12 pieces
x-5y=33
5x-6y=70
solve the system by the addition method
For this case we have the following system of equations:
[tex]x-5y = 33\\5x-6y = 70[/tex]
We multiply the first equation by -5:
[tex]-5x + 25y = -165[/tex]
Thus, we have the equivalent system:
[tex]-5x + 25y = -165\\5x-6y = 70[/tex]
We add the equations:
[tex]-5x + 5x + 25y-6y = -165 + 70\\19y = -95\\y = - \frac {95} {19}\\y = -5[/tex]
We find the value of the variable "x":
[tex]x-5 (-5) = 33\\x + 25 = 33\\x = 33-25\\x = 8[/tex]
Thus, the solution of the system is:
[tex](x, y) :( 8, -5)[/tex]
Answer:
[tex](x, y) :( 8, -5)[/tex]