Mathematics High School
Answers
Answer 1
Answer:
28y+16
Step-by-step explanation:
8(3y+2)+4y
24y+16+4y
28y+16
Answer 2
The simplification of the given expression is 28y+16.
What is an expression?
Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division. The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol.
We are given an expression as;
8(3y+2)+4y
we need to solve the expression
First open the bracket;
24y+16+4y
Solve the like terms;
28y+16
Therefore, the simplification of the given expression is 28y+16.
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Related Questions
Calculate the length of the sides marked x and y
Answers
Step-by-step explanation:
there is no side marked y.
to get x :
the graphic shows us already the split of the overall object into sub-shapes :
2 right-angled triangles
1 rectangle
x is the sum of the width of the rectangle and the shorter leg of the larger, top right-angled triangle.
to get both we need to use Pythagoras :
c² = a² + b²
with c being the Hypotenuse (the side opposite of the 90° angle), a and b being the legs of the triangle.
let's start with the shorter leg of the larger triangle.
the Hypotenuse is 18, and the longer leg is the same as the length of the "underlying" rectangle : 10.
so, we get
18² = 10² + leg1²
324 = 100 + leg1²
leg1² = 224
leg1 = sqrt(224) = 14.96662955...
now to the width of the rectangle.
it is the same as the longer leg of the smaller triangle on the right side.
its Hypotenuse is 5. its shorter leg is 2.
so, we get
5² = 2² + leg2²
25 = 4 + leg2²
leg2² = 21
leg2 = width rectangle = sqrt(21) = 4.582575695...
x = leg1 + leg2 = 14.96662955... + 4.582575695... =
= 19.54920524...
The width of a human hair is 2 x 10-5 meters. The width of a piece of sand is 1.5 x 10¹ meters.
What is the difference in the widths, in meters, of the human hair and the piece of sand?
Answers
The difference in the widths, in meters, of the human hair and the piece of sand is [tex]1.4998*10^{-1}[/tex] m.
It is given in the question that:-
Width of a human hair = [tex]2*10^{-5}[/tex] m
Width of a piece of sand = [tex]1.5*10^{-1}[/tex]m
We have to find the difference in the widths, in meters, of the human hair and the piece of sand.
We know that,
Difference between the widths = Width of a piece of sand - Width of a human hair
Hence, we can write,
Difference between the widths = [tex]2*10^{-5}[/tex] m - [tex]1.5*10^{-1}[/tex]m
We can write,
[tex]1.5*10^{-1}=15000*10^{-5}[/tex]
Hence,
Difference between the widths =
[tex]15000*10^{-5} - 2*10^{-5}= 14998*10^{-5} = 1.4998*10^{-1}[/tex] m
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18:54:12 simplified
Answers
On simplifying the proportion 18:54:12, we get answer as 3:9:2.
What are the proportional guidelines?
The following are crucial proportional characteristics:
If a: b = c: d, then a + c: b + d. Addendum
A - c: b - d if a: b = c: d. Subtrahendo
Dividendo states that if a: b = c: d, then a- b: b = c- d: d.
If a: b = c: d, then a Plus b: b Equals c+d: d. This is known as combining.
To put it another way, if a: b = c: d, then a: c = b: d.
On simplifying,
18:54:12
Firstly, dividing the all numbers by 3
= 6:18:4
Now dividing by 2
= 3:9:2
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What is 7 7/8 • 2 1/4
Answers
Answer:
Step-by-step explanation:
[tex](7\frac{7}{8} )(2\frac{1}{4} ) = \\\\\frac{567}{32} \\\\OR\\17\frac{23}{32}[/tex]
Gasoline costs $2.20 per gallon. Maddie's mom put 9.5 gallons of gasoline in her car. What was the total cost of the gasoline? Choose the correct answer from the drop-down menu to complete the statement. The total cost of the gasoline can be found by _____ 2.20 and 9.5. The total cost is ______
Answers
Answer:
the multiplication of 2.2.20 and 9.5
Step-by-step explanation:
the total cost is $20.9
what’s the answer to the equation
Answers
Answer:
8x-40=200
Step-by-step explanation:
Rex and Gavin were splitting nachos. Rex ate 5/6 of the nachos
and Gavin ate of the nachos.
1/8
What fraction of the nachos did they eat together?
Answers
Answer: 23/24
Step-by-step explanation:
1) Set up the equation
[tex]\frac{5}{6} + \frac{1}{8}=?[/tex]
2) Set the fractions equal to each other
Find a number that can make both denominators the same.
What I found is that both numbers can multiply by 24! By multiplying the same number on the denominator and numerator ([tex]\frac{4}{4}[/tex]), the fraction doesn't change.
[tex]\frac{4}{4} * \frac{5}{6} + \frac{1}{8} * \frac{3}{3} =?\\\frac{20}{24} + \frac{3}{24}=?[/tex]
3) Add up the fractions
[tex]\frac{23}{24}}=?[/tex]
if triangles have two corresponding angles and one corresponding side congruent but the side is not between the angles then the triangles are
right,scalene,congruent,obtuse,acute
Answers
Answer: congruent
Step-by-step explanation:
PLEASE HELP DUE IN 3-4 MINUTES THANK YOU!!
Answers
Answer: -28 percent
Step-by-step explanation:
I can’t see tht take another picture
zero point eight times thirty one
Answers
Answer:
24.8
Step-by-step explanation:
hope it help
have a nice day
What is 81  divided by 11016
Answers
The answer to 81 divided by 11016 is 0.00735294
An event tent rental business charges a fee to set up and take down a tent, plus an hourly rate. The equation y = 65x + 150 can be used to find the total fee, y, for renting a tent for x hours.
Part A: What’s the hourly Rate?
Part B: What is the fee to set up and take down the tent?
Answers
The hourly rate is $65 per hour. While the fees to set up the tent is $100 and to take down after t hours is 65t + 100.
As we can see, the relation between the total fees and the hours for renting in hours is related by the equation,
y = 65x + 100
We are assuming that the price is in dollar.
This is an equation of line in slope-intercept form.
In slope intercept form, the coefficient of x is the slope of the line, which is 65 here.
So, the rate at which the fees is changing with time is 65.
So, the hourly rate will be $65 per hours.
The fees when tent is set can be calculated by,
We should put x = 0, because it is the start,
So,
y = 100
So, the fee to set up is $100.
Let us say the tent is removed after t hours, so the fees will be,
y = 65t + 100.
Fees of taking down the tent is $(65t+100)
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Which of the following triangles cannot be solved using the sine law
Answers
1. We can use the sine law since we have two angles and one of the angles had the side opposite it.
2. We can use the sine law because we have two angles, we can find the third angle in the triangle. This means we have all three angles. We now have two angles and one of the angles has the side opposite it.
3. We have a right triangle. We could use the sine law because we have the right angle and the hypotense. We have two sides and one angle.
4. We have two sides and the included angle. We cannot use the sine law. We would have to use the law of cosines to solve this problem.
parabola
described
Write the equation for the
7) A parabola that passes through the point (2, 2) and has a
vertex of (3, -1)
Answers
The most appropriate choice for parabola will be given by-
Equation of parabola that passes through the point (2, 2) and has a
vertex of (3, -1) is
[tex](x - 3)^2 = \frac{y +1}{3}[/tex]
What is parabola?
Parabola is a curve where every point on the curve is equidistant from a fixed point called the focus and a fixed line called the directrix.
Equation of parabola is [tex]y = a(x - h)^2+k[/tex] where (h,k) is the vertex of the parabola
Here,
Equation of the parabola with vertex (3, -1) is
[tex]y = a(x - 3)^2-1[/tex]
The parabola passes through (2, 2)
[tex]2 = a(2-3)^2-1\\2 = a-1\\a=2+1\\a=3[/tex]
Equation of parabola that passes through the point (2, 2) and has a
vertex of (3, -1) is
[tex]y = 3(x-3)^2 - 1\\[/tex]
[tex](x - 3)^2 = \frac{y +1}{3}[/tex]
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Kirsten bought a used car for $3,600. She made a $360 down payment on it. How much more does Kirsten owe on the car?
Answers
Answer:
Kirsten owes $3240 more on the car.
Step-by-step explanation:
$3600 - $360 = $3240
67 - 88 x 90 x 77 + 125 = ?
Answers
i think so is correct
rhe answers is my -609648
how do i create a visual of this
Answers
Answer: Draw a picture of 2 1/2 cups of flour being added to 1 1/2 cups of sugar in a bowl.
Step-by-step explanation: wink wink
-4w = -12 solve for w simplify your answer as much as possible
Answers
Answer:
w = 3
Step-by-step explanation:
-4w = -12
divide both sides by -4:
-4w/-4 = -12/-4
w = 3
Answer:
w=3
Step-by-step explanation:
1. divide -12 by -4
[tex]w = \frac{ - 12}{ - 4} [/tex]
[tex]w = 3[/tex]
BIG IDEAS MATH
#2 i
The table represents a quadratic function. Write an equation of the function in standard form.
x 3 45 6
y 10 7 10 19
y=
Basic
PAUL BENEDICTO
Check
Answers
The equation of the function in the standard form is:
3x + y = 25.
Given, From the table we can get the dy/dx which is the slope (m) ,
Therefore,
dy/dx = (7 - 10 ) / ( 4 - 3 )
dy/dx = -3
f(x) = ax² + bx + c, where a, b, and c are all numbers and an is not equal to 0, is the definition of a quadratic function. A parabola is the shape of a quadratic function's graph. Despite the fact that a parabola's "width" or "steepness" and opening direction can change.
Now,
( y - y₁ ) = m ( x - x₁ )
Putting the value from the table,
( y - 10 ) = -3 ( x -5 )
⇒ y - 10 = -3x + 15
⇒ 3x + y = 25
Hence the equation of the line in standard form is 3x + y = 25.
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-9x+1=-80 what does the x equal
Answers
Answer:
Simplifying
x = 9
Step-by-step explanation:
Simplifying
9x + -1 = 80
Reorder the terms:
-1 + 9x = 80
Solving
-1 + 9x = 80
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '1' to each side of the equation.
-1 + 1 + 9x = 80 + 1
Combine like terms: -1 + 1 = 0
0 + 9x = 80 + 1
9x = 80 + 1
Combine like terms: 80 + 1 = 81
9x = 81
Divide each side by '9'.
x = 9
What are the coordinates of the point on the direct line segment from (-5, -10) to (2, 4) that partitions the segment into a ratio of 2 to 5?
Answers
Now the given coordinates are,
(-4,10) and (2,-10)
Thus, we have,
x₁ = -4
y₁ = 10
x₂ = 2
y₂ = -10
Given ratio, m₁ : m₂ = 1 : 3
⇒ m₁ = 1; m₂ = 3
Let (x,y) be the coordinates of the point on the directed line segment from (-4,10) to (2,-10) that partitions the segment into a ratio of 1 to 3.
Since the section formula is given as,
So, x = (m₁x₁ + m₂x₂) / (m₁ + m₂)
y = (m₁y₁ + m₂y₂) / (m₁ + m₂)
Put the values,
x = [1(-4) + 3*2)] / (1 + 3) = (-4+6) / 4 = 2/4
⇒ x = 1/2
Similarly y = [1(10) + 3*(-10)] / (1 + 3) = (10-30) / 4 = -20/4
⇒ y = -5
So, the required coordinates are (1/2, -5)
Thus, the coordinates of the point on the directed line segment that partitions the segment into a ratio of 1 to 3 is (1/2, -5).
Answer:(-3,-6)
Step-by-step explanation:
a farmer decides to enclose a rectangular garden, using the side of a barn as one side of the rectangle. what is the maximum area that the farmer can enclose with 48 ft of fence? what should the dimensions of the garden be to give this area? question content area bottom part 1 the maximum area that the farmer can enclose with 48 ft of fence is
Answers
The maximum area that the farmer can enclose for the rectangular garden is 488 sq ft and the dimensions of the rectangular garden are 24ft and 12 ft respectively.
It is given that a farmer decided to enclose a rectangular garden with one side using the barn of a tree and other 3 sides with 48 ft of fencing.
Let the length of the rectangle be y and the breadth of the rectangle be u.
So perimeter of the fencing needed = y + 2u (as one side is barn)
∴ y + 2u = 48
⇒ y = 48 - 2u (equation 1)
Area = yu (equation 2)
Putting the value of variable y from equation 1 in equation 2 we have,
Area = (48-2u)u
∴ Area = 48u - 2[tex]u^{2}[/tex]
⇒ Area = -2[tex]u^{2}[/tex] + 48u
⇒ Area = -2([tex]u^{2}[/tex] - 24u)
⇒ Area = -2([tex]u^{2}[/tex] - 24u + 144) + 288 (using completing the square method)
⇒ Area = -2[tex](u-12)^{2}[/tex] + 288
So the maximum area is 288 sq units as for any value of u the area value will decrease as seen from the above equation.
So if Area = 288
Then yu = 288
⇒ u = 288/y equation 3
Putting this value in Perimeter equation 1 we have,
y = 48 - 2u
⇒ y = 48 - 2 x [tex]\frac{288}{y}[/tex]
⇒ [tex]y^{2} = 48y - 576[/tex]
⇒ [tex]y^{2} - 48y + 576 = 0[/tex]
⇒ [tex](y-24)^{2}[/tex] = 0
Solving we get y = 24 ft
Hence the value of u is calculated as follows:
⇒ u = 288 / y
⇒ u = 288/ 24 = 12 ft
The maximum area that the farmer can enclose is 488 sq ft and the dimensions of the rectangle are 24ft and 12 ft respectively.
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the radius of a spherical balloon is increasing at a rate of 4 centimeters per minute. how fast is the volume changing when the radius is 10 centimeters? (round your answer to four decimal places. be sure to choose the correct units.)
Answers
The air is filled inside the balloon at the rate of 1600π cm³/sec.
What is termed as the rate of change?The momentum of a variable is represented by the rate of change, which is used to arithmetically define the percentage change in value over a specified period of time.The amount of air blown through will be evaluated in volume per unit of time. That is the rate at which volume changes with respect to time.
The rate during which air is blown into the balloon is identical to the rate that the volume of a balloon grows.
Volume of the spherical balloon;
V = (4/3)πr³
Given is dr/dt = 4 cm/sec.
To calculate the volume change with respect to time.
dV/dt when r = 10 cm.
Differentiate V = (4/3)πr³ with respect to t.
d(V)/dt = (d/dt)(4/3)πr³
dV/dt = (4/3)π. 3r² dr/dt
dV/dt = 4πr² dr/dt
Put the values.
dV/dt = 4π(10)² .(4)
dV/dt = 1600π cm³/sec
Thus, air is filled inside the balloon at the rate of 1600π cm³/sec.
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Please help
Quick thank you :)
Answers
Answer:
Ray
Step-by-step explanation:
A ray has a starting point and then continues in one direction.
Please help with this i will give lots of points
Answers
The equations of the line will be expressed as y = 4 and y = -2x + 11 respectively.
Slope of a line may be defined as the steepness of a curve on graph. Slope is denoted by 'm'. If we are given two points (x₁, y₁) and (x₂, y₂) then the slope of line can be given by m = (y₂ - y₁)/(x₂ - x₁). Now, we have a line y = 6 and this line is parallel to x-axis, so the slope of this line is zero. Since, we have to find the equation of line parallel to given line so the slope of the line parallel to line y = 6 will also be equal to zero. Now, equation of line from points (3, 4) and slope zero is given by
(y - 4) = 0×(x - 3)
=> y - 4 = 0
=> y = 4 which is the required equation.
Now, for the second part we have need to find the equation of line parallel to line y = -2x - 1 and from point (4, 3). The slope of new line is -2 which will be same as the given line as they both are parallel. Now, equation of line will be
(y - 3) = -2(x - 4)
(y - 3) = -2x + 8
y = -2x + 8 + 3
=> y = -2x + 11 which is the required equation.
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Simplify the expression. Show your work
Answers
Answer:
simplify(cube_root(27⋅x⋅exp(6)⋅y⋅exp(4)))
Step-by-step explanation:
derivative(cube_root(27⋅x⋅exp(6)⋅y⋅exp(4)))
limit(cube_root(27⋅x⋅exp(6)⋅y⋅exp(4)))
taylor_series_expansion(cube_root(27⋅x⋅exp(6)⋅y⋅exp(4)))
antiderivative(cube_root(27⋅x⋅exp(6)⋅y⋅exp(4)))
integral(cube_root(27⋅x⋅exp(6)⋅y⋅exp(4)))
equation_solver(cube_root(27⋅x⋅exp(6)⋅y⋅exp(4))=0)
simplify(cube_root(27⋅x⋅exp(6)⋅y⋅exp(4)))
Solve V³ = 40
…………….
Answers
[tex]2 \sqrt[3]{5} [/tex]
2(3^√5
Daniel has read 40% of a book. He has 42 more pages to finish. How many pages are there in the book?
Answers
Answer:
70 pages
Step-by-step explanation:
42=60% so 42/6=10% or 7, 7x4=40% or 28+42=70 pgs
y = 3x + 7
y = -2x - 8
Answers
Answer: the answer for y=3x+7 is x=y-7/3
the answer for y = -2x - 8 x=-8-y/2
Step-by-step explanation:
if the probability that an event will occur is changed as a result of the occurrence of a previous event, the events are said to be \ \ \ \ \ \ \ \ \ .
Answers
If the probability that an event will occur is changed as a result of the occurrence of a previous event, the events are said to be dependent events.
There, are two types of events- dependent and independent. Independent ones are those wherein the occurrence of one event has no effect on the probability of occurrence of another one. For example- you and your classmate passing a test are both independent events.
On the other hand, dependent events are those events that are affected by a change in any one of the events probability changing. For example- studying for a test and passing the test are both dependent events.
Thus, if the probability that an event will occur is changed as a result of the occurrence of a previous event, the events are said to be dependent events.
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