Answer:y=-24
Step-by-step explanation:
Move all terms not containing
y
to the right side of the equation.
Is -8-2(3+2n) + 7n equivalent to -30-13n? Explain why or why not.
1|4)
4x + 3y = 4 4 (3.2) +
2X- $y = -28
20:0)
6x=
The solution to the system of equations is x = -2 and y = 4
How to solve the equation
To solve this system of equations using Cramer's rule, we need to first express the equations in standard form: Ax + By = C
According to the problem, we have the equations
4x + 3y - 4 = 0
6x = 8 - 5y.
This is the same as
4x + 3y = 4
6x + 5y = 8
The determinants required for Cramer's rule:
Coefficient matrix (D)
[tex]\[D = \begin{vmatrix} 4 & 3 \\ 6 & 5 \end{vmatrix} = (4 \times 5) - (3 \times 6) = 20 - 18 = 2\][/tex]
For Dₓ
[tex]\[D_x = \begin{vmatrix} 4 & 3 \\ 8 & 5 \end{vmatrix} = (4 \times 5) - (3 \times 8) = 20 - 24 = -4\][/tex]
For D y
[tex]\[D_y = \begin{vmatrix} 4 & 4 \\ 6 & 8 \end{vmatrix} = (4 \times 8) - (4 \times 6) = 32 - 24 = 8\][/tex]
Using Cramer's rule:
[tex]\[x = \frac{D_x}{D} = \frac{-4}{2} = -2\][/tex]
[tex]\[y = \frac{D_y}{D} = \frac{8}{2} = 4\][/tex]
complete question
Solve the following simultaneous equations using Cramer's rule.
4x + 3y - 4 = 0
6x = 8 - 5y
Suppose the two line segments in a coordinate plane one with a length of 120 units and other with a length of 240 units were both rotated 90 degrees about the origin and then translated 50 units up one of the resulting segments could have a length of...units.
In the image, the length of the segment will be 120 units.
Step-by-step explanation:
Whatever may be transformation, either rotation, reflection or translation, the length the line segment will not change.
Here one segment with 120 units and other segment with 240 units is rotated 90 degrees about the origin and then it is translated 50 units up, we will get the image of the segment with the same size.
In the image, the length of the segment will be 120 units.
Can you please explain how to do this
ANSWER ASAP!!!!!!!!!
x = 0,1
y = 0,-5
hope this helped ___~ ~___
0
\
Write an algebraic expression half the quantity of X plus Y?
Final answer:
The algebraic expression for half the quantity of X plus Y is (1/2) × (X + Y) or (X + Y) / 2.
Explanation:
To write an algebraic expression for half the quantity of X plus Y, you start by adding X and Y together. This can be represented as (X + Y). To find half of this quantity, you multiply the sum by 1/2 or divide by 2. Therefore, the algebraic expression that represents half the quantity of X plus Y is (1/2) × (X + Y) or (X + Y) / 2.
April worked 1 1/8 times longer on her math project than Carl, he worked 5 3/4, how many more hours did April work? Please show how to get answer. Thank you
Answer:
[tex]\frac{23}{32}\ hours[/tex]
Step-by-step explanation:
step 1
Find out the number of hours worked by April on her math project
Multiply 1 1/8 by 5 3/4
so
[tex]1\frac{1}{8} (5\frac{3}{4})[/tex]
Convert mixed number to an improper fraction
[tex]1\frac{1}{8}=1+\frac{1}{8}=\frac{1*8+1}{8}=\frac{9}{8}[/tex]
[tex]5\frac{3}{4}=5+\frac{3}{4}=\frac{5*4+3}{4}=\frac{23}{4}[/tex]
substitute
[tex]\frac{9}{8} (\frac{23}{4})=\frac{207}{32}\ hours[/tex]
Convert to mixed number
[tex]\frac{207}{32}=\frac{192}{32} +\frac{15}{32} =6\frac{15}{32}\ hours[/tex]
step 2
How many more hours did April work?
Subtract the hours worked by Carl from the hours worked by April
[tex]\frac{207}{32}-\frac{23}{4}=\frac{207-8*23}{32}=\frac{23}{32}\ h[/tex]
Write a phrase $3 more than four times the cost of a pretzel as an algebraic expession
Answer:
[tex]4x+3[/tex]
Step-by-step explanation:
Let
x ----> the cost of a pretzel
we know that
The phrase" $3 more than four times the cost of a pretzel" is equal to multiply the cost of a pretzel x by 4 and adds the number 3
so
The algebraic expression is
[tex]4x+3[/tex]
Answer:
4p + $3
Step-by-step explanation:
more than= + (plus sign)
four times the cost of a pretzel= 4p
Remember 4 times cost of pretzel
times= multiplication sign
p=cost of pretzel
So: 4p + $3
Which of the following is equal to one million three hundred thousand?
A 1.3×106
B 1.3×109
C 1.03×106
D 1.03×109
1 million is 1*10^6
300 thousand is 3*10^5
Since 300,000 is one power of ten below 1 million, it's either A or B.
The correct choice is A, however, because of 1 million being 10^6. We choose the biggest value we get.
Hope this helped!
A survey of all beings on planet Pib found 20% preferred umpt juice to all other juices. if 6 brings preferred umpt juice, how many beings were surveyed altogether?
Answer:
30 people.
Step-by-step explanation:
In a survey it is found that 20% of the people preferred umpt juice to all other juices.
Now, if 6 of the surveyed people are being preferred umpt juice, then we have to find the total number of people that were surveyed altogether.
So, 20% of the people being surveyed is equal to 6 people.
Therefore, 100% of the people is equal to [tex]6 \times \frac{100}{20} = 30[/tex] people. (Answer)
Sgt. Merritt has bought a house now that his tour of duty is up. He wants to stain the wood floors of the living room, which measure 18x14. The stain costs $120 per square yard. How much will it cost to stain floor of the entire room?
It costs $ 30240 to stain floor of the entire room
Solution:
Given that,
Sgt. Merritt has bought a house now that his tour of duty is up
He wants to stain the wood floors of the living room, which measure 18 x 14
Therefore,
length = 18 yards
Width = 14 yards
Find the area:[tex]Area = length \times width\\\\Area = 18 \times 14\\\\Area = 252[/tex]
Thus area of wood floors is 252 square yards
How much will it cost to stain floor of the entire room?The stain costs $120 per square yard
[tex]Cost = 252 \times 120\\\\Cost = 30240[/tex]
Thus it costs $ 30240 to stain floor of the entire room
To stain Sgt. Merritt's living room floors, which measure 18x14 feet, first calculate the area in square feet, convert to square yards, and then multiply by the cost per square yard. The total cost will be $3,360.
To determine the cost to stain the wood floors in the living room, first we need to calculate the total area in square yards since the stain is sold by square yard. The room measures 18 feet by 14 feet.
Step 1: Calculate Square Footage
Multiply the length and width in feet to get the square footage:
18 feet × 14 feet = 252 square feet
Step 2: Convert Square Feet to Square Yards
There are 9 square feet in 1 square yard. Therefore, we divide the total square footage by 9 to convert to square yards:
252 square feet / 9 square feet per square yard = 28 square yards
Step 3: Calculate the Cost
The cost to stain one square yard is $120. So, we multiply the total square yards by $120 to get the total cost:
28 square yards × $120 per square yard = $3,360
Therefore, the cost to stain the entire living room floor will be $3,360.
7 + (5 – 9)2 + 3(16 ÷ 8).
Answer:
5
Step-by-step explanation:
7 + (5 - 9)2 +3(16/8)
7 + (-4)2 +3(2)
7+(-8) +6
7 -8 +6
7 -2
5
A garden supply store sells two types of lawn mowers. The smaller mower costs $249.99 and the larger mower costs $329.99. If 30 total mowers were sold and the total sales for a given year was $8379.70, find how many of each type were sold.
19 small mowers and 11 large mowers are sold
Solution:
Let "a" be the number of small mowers sold
Let "b" be the number of large mowers sold
Cost of each small mower = $ 249.99
Cost of each large mower = $ 329.99
30 total mowers were sold
Therefore,
a + b = 30
a = 30 - b ------------- eqn 1
The total sales for a given year was $8379.70
Thus we frame a equation as:
number of small mowers sold x Cost of each small mower + number of large mowers sold x Cost of each large mower = 8379.70
[tex]a \times 249.99 + b \times 329.99 = 8379.70[/tex]
249.99a + 329.99b = 8379.70 ---------- eqn 2
Let us solve eqn 1 and eqn 2
Substitute eqn 1 in eqn 2
249.99(30 - b) + 329.99b = 8379.70
7499.7 - 249.99b + 329.99b = 8379.70
80b = 8379.70 - 7499.7
80b = 880
Divide both sides by 80
b = 11
Substitute b = 11 in eqn 1
a = 30 - 11
a = 19
Thus 19 small mowers and 11 large mowers are sold
A bag contains 6 gray tiles and 3 blue tiles. Jenny reached into the bag and picked a tile
randomly, and then without replacing it, picked a second tile.
What is the probability that she
picked a gray tile with her second pick given that she picked a blue tile with her first pick?
Answer:
The probability that Jenny picked a gray tile with her second pick given that she picked a blue tile with her first pick = 0.25
Step-by-step explanation:
i.) there are 6 gray tiles and 3 blue tiles
ii) the probability that Jenny picked a blue tile first is given by
[tex]\frac{number\hspace{0.1cm} of \hspace{0.1cm} blue\hspace{0.1cm} tiles }{total \hspace{0.1cm}number\hspace{0.1cm} of \hspace{0.1cm}tiles\hspace{0.1cm} } = \frac{3}{9} = \frac{1}{3}[/tex]
iii) the probability that Jenny picked a gray tile with her second pick without replacing the first tile[tex]\frac{number\hspace{0.1cm} of \hspace{0.1cm} blue\hspace{0.1cm} tiles }{total \hspace{0.1cm}number\hspace{0.1cm} of \hspace{0.1cm}tiles\hspace{0.1cm} } \times \frac{number\hspace{0.1cm} of \hspace{0.1cm} gray\hspace{0.1cm} tiles }{total \hspace{0.1cm}number\hspace{0.1cm } of \hspace{0.1cm}tiles\hspace{0.1cm} - 1 } = \frac{3}{9} \times \frac{6}{8} = \frac{1}{3} \times \frac{3}{4} = \frac{1}{4} = 0.25[/tex]
The probability that Jenny picked a gray tile with her second pick given that she picked a blue tile with her first pick = 0.25
in the equation 3/4(x+8)=9 ,what does x equal
Answer:
x=4
Step-by-step explanation:
The given equation, the value of x is :
Solving the equation
[tex]3/4(x+8)=9\\0.75(x+8)=9\\0.75x+6.00=9\\0.75x=3\\x=3/0.75\\x=4[/tex]
The value of x is 4 .
The sum of two numbers is 30 and their difference is 12 find the 2 numbers
Answer:
The two numbers are 21 and 9
Step-by-step explanation
(15+6) minus (15-6) gives a difference of 12
21- 9 = 12
Write an equivalent expression for 20(x-5)
Answer:
40(x-10)
Step-by-step explanation:
The area of a rectangular field is 7050m^2. If the width of the field is 75m, what is its length?
Answer:
Step-by-step explanation: Area =length × width
7050m^2 = X× 75m
7050 =75X
Divide both sides by 75
7050÷75 =75÷75
74m= X
3(4x-5)+4(2x+6) simplify
Answer:
20+9
Step-by-step explanation:
Answer: 20x+9 (I THINK that’s the answer but I’m not completely sure so...)
Step-by-step explanation: (12x-15) + (8x+24)
12x+8x= 20x
-15+24 (or 24-15)= 9
20x+9
Please show work for both problems
Answer:
3) x = 15; 95 and 85 4) x = 12; 98 for both angles
Step-by-step explanation:
2x + 65 + 3x + 40 = 180 Set the equations equal to 180
5x + 105 = 180 Combine like terms
- 105 - 105 Subtract 105 from both sides
5x = 75 Divide both sides by 5
x = 15
Plug 15 into both equations
2(15) + 65 = 95
3(15) + 40 = 85
4) 5x + 38 = 9x - 10 Set the equations equal to each other
- 5x - 5x Subtract 5x from both sides
38 = 4x - 10
+ 10 + 10 Add 10 to both sides
48 = 4x Divide both sides by 4
12 = x
Plug 12 into both equations
5(12) + 38 = 98
9(12) - 10 = 98
The slide at the playground has a height of 6 feet.The base of the slide measured on the ground is 8 feet.what is the length of the slide
Answer: 10ft
Step-by-step explanation:
Using the Pythagorean theorem (a² + b² = c²) you would end up with an equation like this: 36 + 64 = 100. You would then square root 100 and the answer would be 10 ft
What is 4,095 divisible by
Answer:
5
Step-by-step explanation:
the answer would be 819
Answer: 5
Step-by-step explanation:
Black bears lose 1/5 of the body weight during hibernation. A black bear weighs 265 poundBlack bears lose 1/5 of their body weight during hibernation. A blackK Bear weighs 260 pounds. How much weight did it lose while hibernating
Answer:
52lbs
Step-by-step explanation:
To find out how much weight the black bear lost during hibernation, subtract the weight after hibernation from the weight before hibernation: 265 - 260 = 5 pounds.
Explanation:To find out how much weight the black bear lost during hibernation, we can use the information that black bears lose 1/5 of their body weight during hibernation. We know that the black bear weighed 265 pounds before hibernation and weighs 260 pounds after hibernation. To calculate the weight loss, we subtract the weight after hibernation from the weight before hibernation: 265 - 260 = 5 pounds. Therefore, the black bear lost 5 pounds while hibernating.
Learn more about Weight loss during hibernation here:https://brainly.com/question/28772240
#SPJ12
A runner increased her distance from 9 miles to 12.5 miles a week. Find the percent increase in mileage.
A. 28%
B. 39%
C. 58%
D. 42%
Answer:
39 percent is increase in mileage.
Thus, the correct option is B. 39%.
Step-by-step explanation:
Given:
A runner increased her distance from 9 miles to 12.5 miles a week.
Now, to find percent increase in mileage.
Previous mileage = 9 miles.
Present mileage = 12.5 miles.
Mileage increase = 12.5 - 9 = 3.5 miles.
Now, to get the percent increase in mileage:
[tex]\frac{Mileage\ increased}{previous\ mileage} \times 100[/tex]
[tex]=\frac{3.5}{9} \times 100[/tex]
[tex]=\frac{350}{9}[/tex]
[tex]=38.88\%.[/tex]
Approximately the percent increase = 39%.
Therefore, 39% is increase in mileage.
Thus, the correct option is B. 39%.
100 POINTS!!!!
Which number should each side of the equation 2/3x=10 be multiplied by to produce the equivalent equation of x = 1/5?
−2/3
1/3
3/2
3
Answer:
2/3x = 10.....multiply both sides by 3/2 giving u :
x = 10 * 3/2
x = 30/2 which equals 15
Step-by-step explanation:
So your answer is 3/2 or 32
The perimeter of a rectangular garden is 110ft. The length is 5 ft greater than the width. Find the length and width.
P = perimeter
L = length
W = width
Formula for the perimeter of a rectangle = L + L + W + W or P = 2L + 2W
You know:
P = 110ft
L = W + 5 [length is 5ft greater than the width]
So plug this into the formula:
P = 2L + 2W Substitute/plug in (W + 5) for L
110 = 2(W + 5) + 2W Distribute/multiply 2 into (W + 5)
110 = (2)W + (2)5 + 2W
110 = 2W + 10 + 2W Combine like terms (2W + 2W)
110 = 4W + 10 Subtract 10 on both sides
110 - 10 = 4W + 10 - 10
100 = 4W Divide 4 on both sides to get "W" by itself
[tex]\frac{100}{4}=\frac{4W}{4}[/tex]
25 = W Now that you know the width, plug it into the equation for length
L = W + 5 Plug in 25 for W
L = 25 + 5
L = 30
L = 30 ft
W = 25 ft
PROOF
P = 2L + 2W
110 = 2(30) + 2(25)
110 = 60 + 50
110 = 110
URGENT!!
These triangles are similar looking at the angles.
True or false
Answer:
False
Step-by-step explanation:
Answer:
False
Step-by-step explanation:
Plz, I'm desperate for 5 answers. help me ASAP on the attachments I'll give everything I can, Brainly award, high ratings, thanks, everything, I need help! Please I need help!
Answer:
[tex]1.\ 8n+4\\\\2.\ 5x+13\\\\3.\ x+3\\\\4.\ x-6\\\\5.\ 4x+1[/tex]
Step-by-step explanation:
1.
[tex]Sum=2n+6+6n-2\\\\Sum=2n+6n+6-2\ \ \ \ \ \ \ \ (using\ commutative\ property\ of\ addition\ a+b=b+a)\\\\Sum=8n+4[/tex]
2.
[tex]Sum=3x+9+2x+4\\\\Sum=3x+2x+9+4\ \ \ \ \ \ \ \ (using\ commutative\ property\ of\ addition\ a+b=b+a)\\\\Sum=5x+13[/tex]
3.
[tex]Difference=(3x+5)-(2x+2)\\\\Difference=3x+5-2x-2\ \ \ \ \ \ \ [using\ distributive\ property\ -(a+b)=-a-b]\\\\Difference=3x-2x+5-2\ \ \ [commutative\ property]\\\\Difference=x+3[/tex]
4.
[tex]Difference=(4x+3)-(3x+9)\\\\Difference=4x+3-3x-9\ \ \ \ \ \ \ [using\ distributive\ property\ -(a+b)=-a-b]\\\\Difference=4x-3x+3-9\ \ \ [commutative\ property]\\\\Difference=x-6[/tex]
5.
[tex]Difference=(6x+2)-(2x+1)\\\\Difference=6x+2-2x-1\ \ \ \ \ \ \ [using\ distributive\ property\ -(a+b)=-a-b]\\\\Difference=6x-2x+2-1\ \ \ [commutative\ property]\\\\Difference=4x+1[/tex]
what is the wavelength of an electromagnetic wave with a frequency of 135,000 Hz?
The wavelength of an electromagnetic wave with a frequency of 135,000 Hz is approximately 2,222 meters. This can be calculated using the equation λ = c / f, with c being the speed of light and f the frequency of the wave.
Explanation:The wavelength of an electromagnetic wave can be calculated from the frequency when we understand their relationship through the wave's speed. In the case of an electromagnetic wave, this speed is the speed of light (denoted by c), which is approximately 3.00 x 108 m/s. This relationship is expressed by the equation c = fλ, where f is the frequency and λ is the wavelength.
To calculate the wavelength (λ) from the frequency (f), we rearrange the equation to λ = c / f. Substituting 3.00 x 108 m/s for c and 135,000 Hz for f, gives λ = 3.00 x 108 m/s / 135,000 Hz. After performing the calculation, we find the wavelength to be approximately 2,222 meters.
Learn more about Wavelength of an Electromagnetic Wave here:https://brainly.com/question/14316836
#SPJ12
The wavelength of an electromagnetic wave with a frequency of 135,000 Hz is approximately 2,222 meters, based on the relationship provided by the equation c = fλ.
Explanation:The wavelength of an electromagnetic wave is directly related to its frequency by the equation c = fλ, where 'c' is the speed of light in vacuum, 'f' is the frequency and 'λ' is the wavelength. In this equation, the speed of light 'c' is typically 3.00 × 108 m/s. Therefore, if we want to figure out the wavelength of an electromagnetic wave with a frequency of 135,000 Hz, we can rearrange the equation to solve for the wavelength: λ = c/f. Substituting the given values, we have λ = (3.00 × 108 m/s)/(135,000 s-1), which simplifies to λ = 2,222 m.
Learn more about Wavelength of Electromagnetic Wave here:https://brainly.com/question/14316836
#SPJ12
How many times greater is the 5 in
458,039 than the 5 in 271,145?
A. 10
B. 100
C. 1,000
D. 10,000
Answer:
D.
Step-by-step explanation:
The 5 in 458,039 is 100 times greater than the 5 in 271,145 because it represents 50,000 while the 5 in 271,145 represents 500. This can be determined by understanding place values, as each digit's value depends on its position in the number.
Explanation:The 5 in 458,039 is in the ten thousands place, meaning it represents 50,000. The 5 in 271,145 is in the hundreds place, meaning it represents 500. To understand how many times greater one is than the other, we would divide 50,000 by 500. The result is 100, therefore, the 5 in 458,039 is 100 times greater than the 5 in 271,145. So, the answer is B. 100.
This problem involves place values in numbers, where each digit in a number has a different value depending on its position.
Learn more about Place Values here:https://brainly.com/question/35447631
#SPJ11
Friday, a store sold 10 blue shirts and 20 white shirts. what percentage of the shirts sold were blue? give answer to the ones place
Answer:
10+20=30
10 is what percent of 30?
10 is 1/3 of 30
Step-by-step explanation:
10 is 33.33% of 30
so 33% of the shirts sold were blue
33.33% of the shirts sold were blue.
Given that, Friday, a store sold 10 blue shirts and 20 white shirts.
We need to find out what percentage of the shirts sold were blue.
What is the percentage?The percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Now, 10+20=30
We need to calculate 10 is what per cent of 30.
Let the percentage be x.
So, x% of 30=10
⇒x/100 × 30=10
⇒3x/10=10
⇒3x=100
⇒x=33.33%
Therefore, 33.33% of the shirts sold were blue.
To learn more about the percentage visit:
https://brainly.com/question/15308590.
#SPJ2