Answer:
3x + 5
Step-by-step explanation:
Add like terms together:
8x - 2 - 5x + 7
3x - 2 + 7
3x + 5
How to find the slope of the line between (8,-2) and (-3,9)
Answer:
-x or -1xStep-by-step explanation:
you would find the slope by doing the change in y over the change in x. in your case, the change in y is 11 and the change in x is -11.
Answer:
Slope formula is y2-y1 over x2-x1
Once you find the slope you are going to need to put it into point slope form which is y-y1=m(x-x1)
Step-by-step explanation:
9-(-2) divided by -3-8 is 11 over -11 which your slope is -1 m=-1
Then you use the point slope formula
y-(-2)=-1(x-8)
Then solve algebraically
Y+2=-1x+8
-2. -2
Y=-1x+6 , that is in slope-intercept form your m which is your slope is -1 and your b which is your y intercept is 6
So basically your answer is slope(m) which is -1.. hope this helps!!
Which equation represents a circle with a center at (-3,-5) and a radius of 6 units?
(x – 3)2 + (y – 5)2 = 6
(x – 3)2 + (y-5)2 = 36
(x + 3)2 + (y + 5)2 = 6
(x + 3)2 + (y + 5)2 = 36
va
Answer: (x+3)2 + (y+5)2 =36
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
Simplify an expression for the area of the rectangle.
Answer:
39.6x +26.4
Step-by-step explanation:
The area of a rectangle is given by
A = l*w
A = 13.2 * (3x+2)
Distribute
39.6x +26.4
margot used 1/2 pounds of turkey to make 2/3 liters of turkey chill. If margots recipe is for 1 liter of turkey chill,how many pounds of turkey will she need to make 4 times the recipe
Answer:
2 pounds of turkey?
Step-by-step explanation:
Margot will therefore need 3 pounds of turkey to make 4 liters of her turkey chili.
To find out how many pounds of turkey Margot will need to make 4 times her turkey chili recipe for 1 liter, we first identify the amount needed for 1 liter based on the given ratio, and then multiply that amount by 4.
Margot uses 1/2 pounds of turkey for 2/3 liters of turkey chili. If we need to find out the amount for 1 liter, we can set up a proportion:
1/2 pounds turkey / (2/3 liters) = x pounds turkey / 1 liter
We cross multiply to solve for x:
(1/2) * 1 = x * (2/3)
Now we solve for x:
x = (1/2) * (3/2)
x = 3/4 pounds of turkey for 1 liter of chili
For 4 liters of chili (4 times the recipe), we would multiply:
4 * (3/4 pounds) = 3 pounds of turkey
A car's fuel efficiency is measured by the distance it can drive per a single unit of fuel. A common unit for efficiency is km/1, kilometers per liter of fuel. C(S) models the fuel efficiency of a certain car as a function of the car's speed S (in kilometers per hour). Match each statement with the feature of the graph that most closely corresponds to it.
Answer: Y-intercept: When the car doesn’t move...
Relative max or min: The most efficient...
Increasing or decreasing interval: As the car accelerates...
Step-by-step explanation:
The parameters are matched and shown below..
What is the of [y] - intercept of a graph?The [y] - intercept of a graph is the point where the graph cuts the [y] axis.
We have a curve that models the fuel efficiency of a certain car as a function of the car's speed.
The [y] - intercept of the graph would be at y = 0. This point represents the situation when the car does not have any fuel to move.
The increasing or decreasing value represents as car accelerates towards 55 Km/hr, it gets more efficient.
The relative maximum value represents that the most efficient the car can get is 20 Km/litre.
Therefore, the parameters are matched and shown above.
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What is the value of t?
Explain how to rewrite the equation -2x - 6y = 18 in slope-intercept form.
Answer:
y = -1/3x -3
Step-by-step explanation:
-2x - 6y = 18
We want to solve for y since the slope intercept form is y =mx+b where m is the slope and b is the y intercept
Add 2x to each side
-2x-6y +2x = 2x+18
-6y = 2x+18
Divide each side by -6
-6y/-6 = 2x/-6 + 18/-6
y = -1/3x -3
This is in slope intercept form with the slope -1/3 and the y intercept -3
Answer:
[tex]y = - \frac{x }{ 3} - 3[/tex]
Step-by-step explanation:
-2x - y = 18
Add 2x to both sides.
-6y = 2x + 18
divide both sides by -6.
[tex]y = \frac{2x + 18}{ - 6} [/tex]
divide 2x + 18 by 6
[tex]y = - \frac{x }{ 3} - 3[/tex]
A used car costs $2,200 cash, or $600 down and $100 a month for 20 months. How much money do you save by paying cash?
Answer:
$400
Step-by-step explanation:
Cash = $2200
$600 + ($100*20) = 2600
$2600 - $2200 = 400
The boundary of a field is a right triangle with a straight stream along its hypotenuse and with fences along its other two sides. Find the dimensions of the field with maximum area that can be enclosed with 1000 feet of fencing.(Must show work to back up your answer). A=1/2 bh
Answer:
[tex]500,500\text{ and }500\sqrt{2}[/tex] feet
Step-by-step explanation:
GIVEN: The boundary of a field is a right triangle with a straight stream along its hypotenuse and with fences along its other two sides.
TO FIND: Find the dimensions of the field with maximum area that can be enclosed with [tex]1000[/tex] feet of fencing.
SOLUTION:
Let the other two sides of triangle be [tex]x[/tex] and [tex]y[/tex]
such that, [tex]x+y=1000 \implies x=1000-y[/tex]
Area of triangle [tex]A=\frac{1}{2}\times base\times height=\frac{1}{2}\times x\times y[/tex]
Area of triangle[tex]A=\frac{1}{2}\times(1000-y)\times y=\frac{(1000y-y^2)}{2}[/tex]
to maximize area, put [tex]\frac{d\ A}{d\ y}=0[/tex]
[tex]\implies 500-y=0[/tex]
[tex]\implies y=500\text{ feet}[/tex]
other side [tex]x=1000-y=500\text{ feet}[/tex]
[tex]\text{hypotenuse}^2=x^2+y^2[/tex]
[tex]=500^2+500^2\implies \text{hypotenuse}=500\sqrt{2}[/tex]
dimension of triangle are [tex]500,500\text{ and }500\sqrt{2}[/tex] feet
The problem is solved by using the optimization strategy in mathematics. The maximum area of the field is obtained when the triangular field is an isosceles right triangle with base 500 ft and the hypotenuse side 250 ft each.
Explanation:This problem involves optimization in mathematics. In a right triangle with hypotenuse (h) and other two sides as base (b) and height (h), we know that the hypotenuse is the longest side. The Pythagorean theorem applies which states that h² = b² + h².
Given that the total length of the fences is 1000 ft, we know that b + h + h = 1000. We then solve for h and substitute it into the area formula, A = 1/2 bh. We get a quadratic function upon simplification, and we maximize the function to get the base and the height.
Using the strategy of setting the derivative equal to zero, the dimensions that maximize the area are found to be base b = 500 ft and the two equal sides h = 250 ft each which form the hypotenuse. Therefore, the field will have it's maximum area when it's a isosceles right triangle.
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Two plumbers charge different rates for service. The first plumber charges $100 for every service call plus $25 per hour of service. The second plumber charges $50 for every service call plus $50 per hour of service. After how many hours do the plumbers charge the same amount
After two hours the two plumbers will charge the same amount
Step-by-step explanation:Set up your equations
Plumber 1:
y = 25x + 100
Plumber 2:
y = 50x + 50
Set the two equal to each other and solve
25x + 100 = 50x + 50
-50 -50
25x + 50 = 50x
-25x -25x
50 = 25x
50/25 = 25x/25 <- Divide both sides by 25
x = 2
After two hours the two plumbers will charge the same amount
Ryan mows lawns in the summer. He charges $15 for every 1/2 hour of mowing. This is represented by the equation y = 15x, where y is the total amount Ryan charges and x is the number of 1/2 -hour sessions of mowing. If mr.smith lawn takes 2 hours to mow and mrs.jones lawn 3.5 hours to mow, how much more would Ryan charge mrs Jones then me.smuth
Answer:
$45 more
(but honestly I think I would spend longer mowing their lawns to try and make some more profit)
Step-by-step explanation:
Mr. Smith requires 4 1/2 hours.
Mrs Jones requires 7 1/2 hours.
7 - 4 = 3
3 * 15 = $45
To find the difference in charges between Mrs. Jones and Mr. Smith for mowing lawns, calculate the total amount charged by Ryan for each lawn and subtract the amount charged for Mr. Smith from the amount charged for Mrs. Jones. The difference in charges is $22.50.
Explanation:The question asks how much more Ryan would charge Mrs. Jones than Mr. Smith for mowing lawns.
To find the answer, we need to calculate the total amount charged by Ryan for each lawn and then subtract the amount charged for Mr. Smith from the amount charged for Mrs. Jones.
For Mr. Smith's lawn, the given information is that it takes 2 hours to mow. So, the total amount charged would be y = 15 * 2 = $30.
For Mrs. Jones' lawn, it takes 3.5 hours to mow. So, the total amount charged would be -
y = 15 * 3.5 = $52.50.
To find the difference in charges between Mrs. Jones and Mr. Smith, we subtract $30 from $52.50.
The difference is $22.50.
1. The length of each leg of an isosceles right triangle is 13 cm. What is the length of the hypotenuse?
Answer:
Step-by-step explanation:
For right triangles, we can use the Pythagorean theorem. This means that a2+b2 = c2. In this problem, a and b are the given side lengths of the triangle. This means that a=b=13. To solve this problem, we plug in 13 to the equation above and solve for c.
132 + 132 = c2
169+169 = c2
338 = c2
square root(338) = c
c = 18.38
Answer:18.38
Step-by-step
13^2 +13^2=338
square root 338
=18.38
Carlo rode his bike from his house to his friend Kevin’s house from there he rode to a video game store then he Road 3.2 km from the video game store back to his house that it was in the grid so the path Carlo trouble how many kilometers deCarlo ride his bike
Answer: 13.7
Step-by-step explanation:
The total distance Carlo travelled form his house to Kelvin's house to the game store and back to his house is 13.7 km.
How to calculate distance from the graph?Using the distance formula, we can caulate the distance he rode from his house to Kelvin's house and then to the video game store.
Therefore,
d = √(y₂ - y₁)²+(x₂- x₁)²
Hence,
(0, 0)(2.5, 6)
Distance from his house to Kelvin's house = √(6- 0)²+(2.5 - 0)²
Distance from his house to Kelvin's house = √36 + 6.25 = 6.5 km
Therefore,
(2.5, 6)(2.5, 2)
Distance from Kelvin's house to game store = √(2- 6)²+(2-5 - 2.5)²
Distance from Kelvin's house to game store = √16 = 4 km
Hence,
Total distance travelled = 6.5 + 4 + 3.2 = 13.7 km
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1+1=
2+2=
5x7-2+5=
7000+3+67+90=
Step-by-step explanation:
[tex]1+1=2 \\
2+2=4 \\
57-2+5=60 \\
7000+3+67+90=7160[/tex]
Answer:
7160
Step-by-step explanation:
1+1=2
2+2=4
5x7-2+5=5x7+3
7000+3+67+90+7160
Bank A charger a 4$ service fee and $0.25 for each check written. Bank B charges $5 and $0.20 for each check written . How many checks does a person need to write each month for the two banks to charge the same amounts in fees. Which account would cost less if a person were to write 10 checks in a month?
Answer:
20 checks
Step-by-step explanation:
Penelope invested $32,000 in an account paying an interest rate of 7% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 14 years?
Answer:
85263
Step-by-step explanation:
In Penelope's account $ 85262.6 would be there after 14 years.
What is Compound Interest ?The compound Interest is the interest you earn on Interest .
The formula for calculating the amount when the interest is compounded continuously
P = P₀[tex]\rm e^{rt}[/tex]
Penelope invested $32,000 in an account
interest rate of 7% compounded continuously.
After 14 years the amount will be
P = 32000 * [tex]\rm e^{0.07*14}[/tex]
P = $ 85262.6
Therefore $ 85262.6 would be in the account after 14 years.
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Angle C is inscribed in circle O. AB is a diameter of circle O. What is the radius of circle O?
Answer:
6.5 units
Step-by-step explanation:
In circle with center O, AB is diameter.
[tex] \therefore m\angle ACB = 90°\\[/tex]
(Angle inscribed in a semicircle)
[tex] \therefore \: in\: \triangle ABC, \:AB \: is\: hypotenuse \\[/tex]
By Pythagorean theorem:
[tex]AB = \sqrt{ {12}^{2} + {5}^{2} } \\ = \sqrt{144 + 25} \\ = \sqrt{169} \\ AB \: = 13 \\ r = \frac{13}{2} = 6.5 \: units[/tex]
Nathan needs some paint for his bedroom. He finds two cans of white paint, four cans of green paint and three cans of pink paint in his garage. If he chooses a can of paint without looking at the color, what is the chance that he will paint his bedroom pink
Answer:
3/9 or 33.33%
Step-by-step explanation:
there are 9 total cans and 3 pink cans. So, that'd be 3/9 or 33.33%
hope this helps!
Answer:
1/3
Step-by-step explanation:
A car's fuel efficiency is measured by the distance it can drive per a single unit of fuel. A common unit for efficiency is km/1, kilometers per liter of fuel. C(S) models the fuel efficiency of a certain car as a function of the car's speed S (in kilometers per hour). Match each statement with the feature of the graph that most closely corresponds to it.
The feature of the graph that most closely corresponds to the number of gallons of gasoline necessary to fill an automobile gas tank is the y-axis. The feature of the graph that most closely corresponds to the mass of a textbook is the line or curve representing the fuel efficiency as a function of the car's speed. The feature of the graph that most closely corresponds to the time required to drive from San Francisco to Kansas City at an average speed of 53 mi/h is the distance traveled.
Explanation:The feature of the graph that most closely corresponds to the number of gallons of gasoline necessary to fill an automobile gas tank would be the y-axis. The y-axis represents the fuel consumption or efficiency of the car, which is measured in kilometers per liter (km/1).
The feature of the graph that most closely corresponds to the number of cm in 2 m would be the x-axis. The x-axis represents the speed of the car in kilometers per hour (km/h). It shows the relationship between the car's speed and its fuel efficiency.
The feature of the graph that most closely corresponds to the mass of a textbook would be the line or curve representing the fuel efficiency as a function of the car's speed. This line or curve shows how the car's efficiency changes as its speed varies.
The feature of the graph that most closely corresponds to the time required to drive from San Francisco to Kansas City at an average speed of 53 mi/h would be the distance traveled. The distance traveled is an important factor in determining the car's fuel efficiency.
Find the median, first quartile, third quartile, and the interquartile of the data set.
32,47,49,53,54,66,67,71,72
Answer:
54 = median
48 = 1st quartile
69 = 3rd quartile
21 = interquartile
Hope this helped!! :)
Answer:
54 = median
48 = 1st quartile
69 = 3rd quartile
Step-by-step explanation:
PLZ HELP ASAP 20 POINTS
Step-by-step explanation:
A (the first one)
.............
The upside down U means intersection, which would be the area the two circles overlap.
X’ and y’ would be opposite, so the area not in x or y.
The area would be outside the circles
The answer would be picture b
You are making an open box from a rectangular sheet of cardboard by cutting squares of equal length from each corner and folding up the sides. The dimensions of the sheet of cardboard are 15 inches by 12 inches. Write a polynomial that represents the total volume of the open box.
Answer:
[tex]V(x) = 4x^3 - 54x^2 + 180x[/tex]
Step-by-step explanation:
We are given the following in the question:
A rectangular piece of cardboard of side 15 inches by 12 inches is cut in such that a square is cut from each corner.
Let x be the side of this square cut. When it was folded to make the box.
The height of box =
[tex]x\text{ inches}[/tex]
The length becomes
[tex](15-2x)\text{ inches}[/tex]
The width becomes
[tex](12-2x)\text{ inches}[/tex]
Volume of box =
[tex]V =l\times w\times h[/tex]
Putting values, we get
[tex]V(x) = (15-2x)(12-2x)x\\V(x) = (180-30x-24x+4x^2)(x)\\V(x) = (4x^2 - 54x + 180)(x)\\V(x) = 4x^3 - 54x^2 + 180x[/tex]
is the required polynomial for volume of box formed.
What is the solution to the system of equations 6x+2y=6 7x+3y=5
Answer:
(x,y)=(2,-3)
Step-by-step explanation:
6x+2y=6
7x+3y=5
Multiply both sides by 3
18x+6y=18
7x+3y=5
Multiply both sides by -2
18x+6y=18
-14x-6y=-10
Eliminate one variable by adding the equations
4x=8
x=2
Substitute the value of x to get y
6(2)+2y=6
y=-3
x=2
y=-3
The solution to the system of equations 6x+2y=6 and 7x+3y=5 is x = 2 and y = -3.
The solution to the system of equations 6x+2y=6 and 7x+3y=5 involves finding the values of x and y that satisfy both equations simultaneously.
First, let's multiply:
3(6x + 2y) = 3(6)
=> 18x + 6y = 18
2(7x + 3y) = 2(5)
=> 14x + 6y = 10
Next, we subtract the second equation from the first:
18x + 6y - (14x + 6y) = 18 - 10
4x = 8
x = 2
Now that we have the value of x, we can substitute it back into either of the original equations to find the value of y. For instance, substituting x into the first original equation:
6(2) + 2y = 6
12 + 2y = 6
2y = 6 - 12
2y = -6
y = -3
The solution to the system of equations is x = 2 and y = -3.
Solve -x^2-9x-20=0 with the quadratic formula
plz help!
Answer:
a = -1 b = -9 c = -20
x1 = [--9 +- (sq root -9^2 - 4 * -1 * -20)] / 2 * -1
x1 = 9 +sq root (81 - 80) / -2
x1 = [9 + 1 ] / -2
x1 = -5
x2 = 9 -sq root (81 - 80) / -2
x2 = 8 / -2
x2 = -4
Step-by-step explanation:
The number y of hits a new website receives each month can be modeled by y = 4060ekt, where t represents the number of months the website has been operating. In the website's third month, there were 11,000 hits. Find the value of k. (Round your answer to four decimal places.) k =
Answer: The value of k = 0.9031
Step-by-step explanation: The equation for calculating the number of hits has been given as y = 4060ekt, where y is the number of hits and t is the number of months the website has been operating.
The values for y and t has been determined already as given, (y = 11000 and t = 3) therefore we can substitute for the known values in order to calculate the value of the unknown, k.
y = 4060kt
11000 = 4060 x 3k
11000/(4060 x 3) = k
11000/12180 = k
0.9031198 = k
Rounded to four decimal places,
k = 0.9031
What is 12 divided by 220
Answer:
0.0545454545455
Step-by-step explanation:
How do I solve this math problem you and your friend are selling magazine subscriptions for a fundraiser. After w weeks , you have sold (7w = 6) subsriptions and your friend has sold ( 9w = 2) subscriptions. Whats the diffrence written in simple expression form?
Answer:
The diffrence written in simple expression form is 40/63
Step-by-step explanation:
To solve for the difference normally you have to subtract your own subscription from that of your friends,
Let's perform this operation step wise
Now your subscription is
(7w = 6)
w=6/7
Your friends own is
( 9w = 2)
w=2/9
So the difference in simple form is
6/7-2/9
The LCM is 63 I.E 9*7=63
=54-14/63
=40/63
Evaluate Loga√44+ Log a√275- Log 11a
They all have base 10
Answer:
[tex]log(10a)[/tex]
Step-by-step explanation:
[tex]log(a\sqrt{44})+log(a \sqrt275)-log(11a)[/tex]
We can simplify this using these log laws:
[tex]log(a)+log(b)=log(ab)\\log(a)-log(b)=log(\frac{a}{b})[/tex]
[tex]log(\frac{a^2\sqrt{44} \sqrt{275}}{11a})[/tex]
We also have laws to simplify square roots
[tex]\sqrt{a}*\sqrt{b} = \sqrt{ab}[/tex]
So this becomes
[tex]log(\frac{a^2\sqrt{12100}}{11a})[/tex]
[tex]\sqrt{12100} = 110[/tex]
so this becomes
[tex]log(\frac{110a^2}{11a})=log(10a)[/tex]
Kelly's recipe calls for 13 ounces of chicken. Her scale only measures in grams. Which of the following shows the number of grams of chicken, with the correct significant digits, that Kelly needs to include in her recipe in order to have 13 ounces? (1 ounce = 28.3495 grams)
A) 368.5435
B) 367.9
C) 369
D) 370
Answer:
A
Step-by-step explanation:
13 x 28.3495
Answer:
A
Step-by-step explanation:
1 ounce is 28.3495 grams and Kelly's recipe call for 13 ounces of chicken, so
13 x 28.3495 = 368.5435
Let x^2+17x=-5 What values make an equivalent number sentences after completing the square? (Do not simply your answers)
Answer:
[TeX] (x+\frac{17}{2})^{2}=\frac{269}{4} [/TeX]
Step-by-step explanation:
Given the expression:
[TeX] x^2+17x=-5 [/TeX]
To complete the square,
First Step: Identify the Coefficient of x.
Coefficient of x=17
Second Step: Divide the coefficient of x by 2.
Third Step: Square your result from the second step.
This gives:
[TeX] (\frac{17}{2})^{2}[/TeX]
Fourth Step: Add your result to both sides if the equation.
[TeX] x^2+17x+(\frac{17}{2})^{2}=-5+(\frac{17}{2})^{2} [/TeX]
Fifth Step:Express the left hand side as a square
[TeX] (x+\frac{17}{2})^{2}=-5+(\frac{17}{2})^{2} [/TeX]
Sixth Step:Simplify the Right Hand Side
[TeX] (x+\frac{17}{2})^{2}=\frac{269}{4} [/TeX]
These are the values that make an equivalent number sentence.