Answer:
x= (2b-2c)/3a
Step-by-step explanation:
3ax+2c=2b
or, 3ax= 2b-2c
Therefore, x= (2b-2c)/3a
Greg saves $15 every week. What expression would represent the amount of money in dollars Greg will save in W weeks?
Answer:
15W
Step-by-step explanation:
$15 is the amount he plans to save every week (constant), the W will represent the number of weeks
Answer:
15w
Step-by-step explanation:
w is the unknown amount and every week greg saves 15. So the equation would be 15w.
You can plug a number to check in for example 5. He would save $75.00 in 5 weeks.
The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $4 and each adult ticket sells for $8. There was a total of $640 in revenue from the sale of 100 total tickets. Graphically solve a system of equations in order to determine the number of student tickets sold, x, and the number of adult tickets sold, y.
Answer:
number of student tickets sold (x) = 40
number of adult tickets sold (y) = 60
Step-by-step explanation:
Let x = number of student tickets sold
Let y = number of adult tickets sold
Given:
total ticket sales = 100⇒ x + y = 100
Given:
student ticket = $4adult ticket = $8total ticket sales = $640⇒ 4x + 8y = 640
Rewrite x + y = 100 to make x the subject:
⇒ x = 100 - y
Substitute x = 100 - y into 4x + 8y = 640 and solve for y:
⇒ 4(100 - y) + 8y = 640
⇒ 400 - 4y + 8y = 640
⇒ 4y = 240
⇒ y = 60
Substitute found value for y into x = 100 - y and solve for x:
⇒ x = 100 - 60
⇒ x = 40
To solve graphically, rewrite both equations to make y the subject:
y = 100 - x
y = 80 - (1/2)x
Plot both lines.
The solution is the point of intersection (40, 60)
If 3 superscript 2 x 1 baseline = 3 superscript x 5, what is the value of x?
The value of x for the considered algebraic equation is 4.
What are some basic properties of exponentiation?If we have [tex]a^b[/tex] then 'a' is called base and 'b' is called power or exponent and we call it "a is raised to the power b" (this statement might change from text to text slightly).
Exponentiation (the process of raising some number to some power) have some basic rules as:
[tex]a^{-b} = \dfrac{1}{a^b}\\\\a^0 = 1 (a \neq 0)\\\\a^1 = a\\\\(a^b)^c = a^{b \times c}\\\\ a^b \times a^c = a^{b+c} \\\\^n\sqrt{a} = a^{1/n} \\\\(ab)^c = a^c \times b^c\\\\a^b = a^c \implies b = c \text{ (if a, b and c are real numbers and } a \neq 1 \: and \: a \neq -1 )[/tex]
For this case, we have got the equation as:
[tex]3^{2x+1} = 3^{x+5}[/tex]
Using the property that: [tex]a^b = a^c \implies b = c \: \:(if \: a \neq 1 \: and \: a \neq -1)[/tex], we get:
[tex]2x + 1 = x + 5\\[/tex]
Solving it further:
[tex]2x + 1 = x + 5\\\\\text{Subtracting 1+x from both the sides}\\\\2x + 1 - (1+x) = x+5 - (1+x)\\x = 4[/tex]
Thus, the value of x for the considered algebraic equation is 4.
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A scouting group eats 64 hot dogs on the first night of their camping trip. As they get tired of eating hot dogs, they eat only half as many as the night before. If the trip lasts 6 days, how many hot dogs do they eat in all?
Answer:
I believe your answer would be 126
Step-by-step explanation:
The math is quite simple, all you must do is divide over and over again. Then add
64/2= 32
32/2=16
16/2=8
8/2=4
4/2=2
Then add these up
64+32+16+8+4+2= 126
Graph the line.
y = −4x + 2
Answer:
it rise over run so put 2y on graph count down 4 and move right 1
Step-by-step explanation:
Find the slope of the line that passes through the points (2,-10) and (-4,2).
Answer:
-0.5
Step-by-step explanation:
Answer:
m = -2
Step-by-step explanation:
Plug the two points in slope formula:
[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}} \\\\\frac{2-(-10)}{-4-2} \\\frac{12}{-6} \\\\m= -2[/tex]
Bruce, Cathy and Dilip paid $7, $10 and $8
respectively for a lotto ticket. The ticket won
a prize of $600. Calculate Bruce's share of
the winnings.
Hey there!
Add the total of Bruce, Cathy and Dilip
=> 7 + 10 + 15
=> 25
Then, Divide it by 600
=> 600 ÷ 25
=> 24
To find how much Bruce's share
we multiply 24 times the $10 he contributed
=> 24 × 10
=> 240
Therefore, Bruce's share would be $240
Wien Remainders
There are 76 ounces of fluid in container A. This is about 8 times the amount of fluid in container B.
About how many ounces of fluid are there in container B?
Hank has picked 1.3 pounds of berries and picks about 75 pounds per minute. Tom has picked
2.5 pounds of berries and picks about 5 pounds per minute. In how many minutes will Hank have
picked at least as many pounds of berries as Tom?
Answer:
x=4.6
Step-by-step explanation:
take the numbers and add them all together then divide them by 3
PLS HELP ASAP THANKS ILL GIVE BRAINLKEST PLS THANKS PLS
Answer:
(-2, 10)
step-by-step explanation:
original vertex A: (4, -10)
If translated horizontally, there will be change in x axis
new coordinates: (4-6, -10) → ( -2 , -10)Then reflected over x axis, so use the formula: (x, y) → ( x, -y)
new coordinates: (-2, 10)Rewrite the expression in a to the power of n form
Answer:
[tex]a^{-7}[/tex]
Step-by-step explanation:
using the rule of exponents
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex] , then
[tex]\frac{a^{-13} }{a^{-6} }[/tex]
= [tex]a^{(-13-(-6))}[/tex]
= [tex]a^{(-13+6)}[/tex]
= [tex]a^{-7}[/tex]
Answer:
[tex]a^-7[/tex]
Step-by-step explanation:
[tex]\frac{a^m}{a^n}=a^{(m-n)}, then[/tex]
[tex]\frac{a^{-13} }{a^{-6} }[/tex]
[tex]=a^{(-13-(-6))}[/tex]
[tex]=a^{(-13+6)}[/tex]
[tex]=a^{-7}[/tex]
Claire is planning on becoming a member at the gym down the street from her house. They charge a $60 sign-up fee and an additional $8 per month. Write a linear equation y=mx+b to represent this situation, using x to respresent the number of months and y to represent the total cost of her membership.
Answer:
The linear equation is y = 8x + 60
Step-by-step explanation:
the slope-intercept form of the linear equation is
y = m x + b, where
m is the slope of the line (the rate)b is the y-intercept (the fixed amount)∵ Claire charge a $60 sign-up fee
→ This means it is a fixed amount for a sign-up
∴ b = 60
∵ There is an additional $8 per month
→ This means it is the rate
∴ m = 8
∵ y represents the total cost of her membership in x months
→ Represent this situation by the form of the linear equation above
∴ y = 8x + 60
∴ The linear equation is y = 8x + 60
If one angle of a parallelogram measures 80° what are the measures of the other three angles in a parallelogram
In a parallelogram the 4 angles need to sum to 360 degrees. There are two sets of identical angles, so one of the other angles would also be 80 degrees.
Now find the other two angles:
360 - 80 - 80 = 200 degrees
200 degrees / 21 = 100 degrees each.
The other 3 angles are: 80, 100 and 100
Pls, help me solve this. Show your work
Answer:
y = 2x + 1/3
Step-by-step explanation:
Since the line is parallel to y = 2x - 5, its slope is also 2x, as parallel lines have the same slope, leaving you with y = 2x.
Since it intercepts the y-axis at 1/3, and y = 2x intercepts the y-axis at 0, you will now need to add a 1/3 to the end of the equation for it to intersect the y-axis at the right place.
Therefore, the equation is: y = 2x + 1/3
There are 16 boys in an English class of 28 students. The ratio of boys to the total number of students in this class is typical of the whole school. There are 476 students in the school. About how many are boys?
Proportions In Word Problems
—In the picture, when I wrote at the top: “B” is for the boys in the equation and the “S” is for the students in the English class, if anyone was wondering what that meant—
Gabriel must practice piano at least 15 hours a week. This week he has practiced 6 hours so far. Piano lessons are part of Gabriel’s practice time. His teacher gives 2-hour lessons. what inequality can be used to find x, the number of lessons Gabriel must attend this week?
Answer:
9
Step-by-step explanation:
Answer:
lessons he must complete: 15= 2x-6
Step-by-step explanation:
On the left side of the equation you have 15 hours which is what he must fulfill. X represents number of lessons he must complete. You convert the lessons to hours by multiplying by two because that is how long each lesson is. Im not sure if your teacher wants u to put 2x-6=15 or 2x= 11. Most likely the first answer
Nicole ordered a volleyball for $9.75, a net for $29.99, and knee pads for $15.00. Nicoles mother said that she would pay for the order on her credit card if Nicole gave her the money. Nicole gave her mother $40.00. Her mother also applied the money that she owed Nicole for babysitting. Nicoles mother then gave her back $5.26. How much did Nicoles mother owe Her for babysitting?
Answer:
$9.48Step-by-step explanation:
The total amount for the order is
$9.75+$29.99+ $15.00=$54.74
let the money her mother owes her be x
so summing all the amount plus the balance given to her must equal $54.74
so x+40+5.26=54.74
solving fo x we have
x+45.26=54.74
make x subject of formula we habe
x=54.74-45.26
x=9.48
Nicoles mother owe Her $9.48for babysitting
god bless u Step-by-step explanation:
An adult male blue whale weighs about 160 tons (1 ton = 1,000 kg). Show that the weight of an adult blue whale is equal to 1.6 × 105 kg.
Answer:
Step-by-step explanation:
1.6x10^5=160,000; 160x1000=160,000
What is the length of line segment AB? The diagonal of rectangle ABCD measures 2 inches in length.
1 inch 60
[tex] \: \sqrt{3} inches \\[/tex]
4 inches
[tex] 4 \: \sqrt[]{3} [/tex]
Answer:
√3
Step-by-step explanation:
Triangle ABC is a special right triangle with angle measures of 30° 60° 90° and side length x 2x x√3
7/1 x 1/4=?
thanks for the help!!!
Answer:
1.75
Step-by-step explanation:
Answer:
7/4 or 1¾ or 1.75
Step-by-step explanation:
7/1 × 1/4
7 × 1 = 7
1 × 4 = 4
Can anyone HELP ME WITH THIS QUESTION ON VOLUME ILL GIVE BRANNIEST
The diameter of a cylinder is 1 yd. The height is 12 yd.
Find the volume of the cylinder.
Answer: V≈9.42 yd^3
the formula to use for a cylinder is V=πr^2h. The radius is 0.5 since the diameter is 1. The height is 12. Plug them in and you get that answer.
Hope it helps!
A football is punted from a height of 3. 5 feet about the ground with an initial velocity of 45 feet per second. This situation can be represented by the function −16t2 + 45t + 3. 5 , where t is the number of seconds elapsed since the football was kicked. If the football is caught at a height of 5. 5ft on the ball’s descent, when was the football in the air at that height?
Answer:
h= -5.6444444444 ft
Step-by-step explanation:
h= 5.5
5.5= -16^2 + 45 t +3.5
5.5 = 256 +45t +3.5
2= 256+45t
-254= 45t
t=- 5.6444444444
I hope that's right formula for you. Thanks.
(8x-14)° (5y+16)° (5x+34)° Write the equation to solve for x
Answer:
The equation to solve for x is 8x - 14 = 5x + 34
The value of x is 16
Step-by-step explanation:
Let us use the angles between the parallel lines to find x
∵ Lines l and m are parallel
∴ ∠(8x - 14)° and ∠(5x + 34)° are alternate exterior angles
∵ The alternate exterior angles are congruent
∴ ∠(8x - 14)° ≅ ∠(5x + 34)°
→ Equate them
∴ 8x - 14 = 5x + 34
∴ The equation to solve for x is 8x - 14 = 5x + 34
Let us solve it to find x
∵ 8x - 14 = 5x + 34
→ Subtract 5x from both sides
∵ 8x - 5x - 14 = 5x - 5x + 34
∴ 3x - 14 = 34
→ Add 14 to both sides
∴ 3x - 14 + 14 = 34 + 14
∴ 3x = 48
→ Divide both sides by 3 to find x
∴ [tex]\frac{3x}{3}=\frac{48}{3}[/tex]
∴ x = 16
∴ The value of x is 16
Find the slope and the y intercept for the equation below 2x+y=7
Answer:
the slope is 2
y- intercept is 7
Step-by-step explanation:
Answer:
Step-by-step explanation:
1) Isolate y:
y=-2x+7
2) Identify the slope (it is the coefficient of x after isolating y):
slope=-2
3) Replace x=0 to find the y intercept:
y=-2(0)+7=7.
How much will Molly’s monthly payment be using the Bankrate calculator?.
Molly’s monthly payment by using the Bankrate calculator is $286 per month.
It is given that
The downpayment Molly has = $2500.
Interest rate APR = 1.9%
Cash allowance by dealer = $500
Selling price = $25,495
Loan tenure N= 7 years
Amount of loan needed = 25495-2500-500 = $22495
What is Equated monthly payment(EMI)?An equated monthly installment (EMI) is a set monthly payment provided by a borrower to a creditor on a set day, each month.
The EMI or monthly payment will be calculated by the following formula,
[tex]EMI = \frac{P.\frac{APR}{12} .(1+\frac{APR}{12})^N }{(1+\frac{APR}{12})^N-1 }[/tex]
Put APR =0.019(decimal value of APR)
N = 7
EMI = $286 per month.
Therefore, Molly’s monthly payment by using the Bankrate calculator is $286 per month.
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Teddy is preparing to sell some wooden blocks at a garage sale. Before pricing individual bags of blocks, he decides to determine the approximate number of blocks per pound by researching the weights of different sets of blocks. The graph shows his data. A graph shows weight of set (pounds) labeled 0. 5 to 5 on the horizontal axis and number of blocks on the vertical axis. A line increases from 0 to 5. 5. About how many blocks are there per pound? Round to the nearest block. 10 20 30 40.
Slope is also known as the gradient of a line. The number of blocks that Teddy is weighing is 20 blocks per pound.
What is the Slope of a line?
A slope is also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line. It also tells us the rate between the two given quantities.
As the graph is given to us and we need to find the number of blocks teddy is putting per pound, therefore, we need to calculate the rate of the graph also known as the slope of the graph, therefore, using any of the two points to calculate the slope of the graph,
[tex]{\rm Point1} : (x_1, y_1) = (0, 0)\\\\{\rm Point2} : (x_2, y_2) = (5, 100)[/tex]
We know that the slope of the line is given as,
[tex]\text{Slope of the line} = \dfrac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values,
[tex]\text{Slope of the line} = \dfrac{100-0}{5-0} = \dfrac{100}{5}=20[/tex]
Hence, the number of blocks that Teddy is weighing is 20 blocks per pound.
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Kenny pays $50.00 for a total of 12 books. If each book cost the same, how much was each book?
Answer:
x= 4 1/6
Step-by-step explanation:
1. Create equation
12x=50
2. Solve
12x/12=50/12
x=4 1/6
3. Check
12x4 1/6=50
12x50/12=50
50=50
Correct!
4. Answer
x= 4 1/6
An object is moving at a speed of 5 kilometers every 4.5 hours. Express this speed miles per minute. Round your answer to the nearest hundredth. Someone please help me I’m struggling with this one
Answer:
speed is 0.01 miles per minute
Step-by-step explanation:
We know speed = distance/time
since we need speed in miles per minute we need to convert KM into miles
and hours in minutes
--------------------------------------------------------
distance = 5 km
1 km = 0.621371 miles
5KM = 5*0.621371 miles = 3.10686 miles = 3.12 miles(rounded to nearest hundredth)
1 hour = 60 minutes
4.5 hours = 4.5*60 minutes = 270 minutes
speed = distance in KM/time in minutes = 3.12 miles/270 minutes
speed = 0.012 miles per minute
rounding the answer to the nearest hundredth
speed is 0.01 miles per minute
The radius is cm.
The circumference in terms of his vt cm
Using 3.14 for a, the approximate circumference of the
v cm.
circle is
d = 2 cm
Answer:
The radius is 1.75 cm, 1 3/4 cm, or 7/4 cm (all the same, just in different forms)
The circumference in terms of π is 7/2(π) cm, 3.5(π), or 3 1/2(π) cm (all the same, just in different forms)
The approximate circumference of the circle is 10.99 or 11 cm. (don't know if it's supposed to be rounded)
Step-by-step explanation:
Radius = 1/2 of the diameter, so 1/2 of 7/2 is 1.75, 1 3/4, or 7/4 cm.
Circumference in terms of pi means to not approximate pi. Circumference of circle is πd, so the exact circumference would be 7/2 pi cm, 3.5 pi cm, or 3 1/2 pi cm.
3.5 x 3.14 = 10.99. 10.99 cm ≈ 11 cm.
Solve −x+4y−28=0 for y .
Answer:
y= -x/4 +7
Step-by-step explanation:
x+4y−28=0
Subtract x from both sides. Anything subtracted from zero gives its negation.
4y−28=−x
Add 28 to both sides.
4y=−x+28
The equation is in standard form.
4y=28−x
Divide both sides by 4.
4y/4 = 28−x/4
Dividing by 4 undoes the multiplication by 4.
y= 28-x/4
Divide −x+28 by 4.
y= -x/4 +7
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