Answer:
1. b = 2A/h
2. h = 2A/b
Step-by-step explanation:
All you have to do is isolate the variable.
1.
Isolate b:
A = 1/2 x b x h
Multiply each side by 2
2A = b x h
Isolate b by dividing both sides by h
b = 2A/h
2.
Isolate h:
A = 1/2 x b x h
Multiply each side by 2
2A = b x h
Isolate h by dividing both sides by b
h = 2A/b
Marissa buys a rare gem priced at $82.00. The sales tax rate is 7.9%.
What is the tax amount to the nearest cent?
label required
The tax amount to the nearest cent:$6.478
What is Tax?
Tax is the sum of money that citizens hand up to the government in exchange for goods and services. A taxpayer and a tax collector are both partners in any tax transaction. An entity that pays taxes to the government is referred to as a taxpayer. Any middleman that collects taxes on the government's behalf, including the government, is a tax collector.
Given,
The price of Rare gem = $82.00
The sales tax = 7.9%
Converting percent into decimal
7.9 / 100 = 0.079
The amount of sales tax = 82 x 0.079
= $6.478
The Total amount of the gem before the sales tax:
82 - 6.478 = $75.522
Hence, The tax amount to the nearest cent is $6.478
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the number of cars produced when x x dollars is spent on labor and y y dollars is spent on capital invested by a manufacturer can be modeled by the equation 45 x 1 3 y 2 3
The formula in terms of x and y for dy/dx is y/ -2x
The value of dy/dx at the point (1,1) is -0.5
The question is incomplete, the full question is given below:
200 cars can produced when x dollars is spent on labor and y dollars is spent on capital. the equation that relates x and y is 45 x^1/3 y^2/3= 200
a. Find a formula in terms of x and y for dy/dx
b. Find the value of dy/dx at the point (1,1). Round your answer to 4 decimal places
Part a
A formula in terms of x and y for dy/dx
We differentiate equation that relates x and y with respect to x by implicit differentiation:
=d/dx(45 x^1/3 y^2/3) =d/dx( 200)
=> 45 *(1/3) x^-2/3 y^2/3 + 45 x^1/3 2/3 y^ -1/3 dy/dx=0
=> x^-2/3y^2/3+ 2 x^1/3 y^-1/3 dy/dx=0
=> y/x= -2dy/dx
=> log y = -2 log x +log c
=> y= x^ -2 +c
putting x=y=1
c=0
then y= 1/x^2
b) y/x= -2dy/dx
put x=y=1 we get
-1/2 = dy/dx
dy/dx =-0.5
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1) [tex]\frac{2x-3}{3} +\frac{x-1}{5}[/tex]
Answer:
4_62
Step-by-step explanation:
its is just leave me
Physical Science: A ball was dropped from a height of 100 meters. Its height above the ground
in meters at different times after its release is given in the table. Do these ordered pairs satisfy a
linear function? Explain.
Time (s)
Height (m)
0
1
2
100 90.2 60.8
3
11.8
Answer: Yes they do.
Karyn proofreads 15 pages in 2 hours for $40. What is her proofreading rate in pages per hour? How much does she earn per hour?
The proofreading rate will be ( 7.5 pages/ hour) and the cost per hour will be $20.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Karyn proofreads 15 pages in 2 hours for $40. The rate will be calculated as:-
Rate of reading = ( 15 / 2 )
Rate of reading = ( 7.5 ) pages per hour
The cost will be calculated as:-
For 2 hours = $40
For 1 hour = ( 40 / 2 )
For 1 hour = $20
Therefore, the proofreading rate will be ( 7.5 pages/ hour) and the cost per hour will be $20.
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The figure shows rectangle RSTW. Which of the following conditions satisfies the criteria for rectangles?
a. m∠SRZ = 40°
b. m∠STZ = 40°
c. m∠SRW = 80°
c. m∠TWR = 80°
For the given rectangle RSTW, the condition satisfies the criteria of rectangles is equal to m ∠SRZ = 40°.
As given in the question,
In the given figure of rectangle RSTW,
Conditions satisfies the criteria of the rectangles are as follow:
a. m ∠SRZ = 40°
Line segment SR is parallel to TW. TR is the transversal.
m ∠SRT = m ∠WTR ( Alternate interior angles)
T -Z - R
m ∠SRZ = m ∠WTZ = 40°
Given criteria is satisfies the criteria of rectangles.
b. m ∠STZ = 40°
All the interior angles of rectangle are of measure 90°
m ∠STW = 90°
m ∠WTZ = 40° (given)
m ∠STZ + m ∠WTZ = 90°
⇒ m ∠STZ = 50°
Given option does not satisfies the criteria of rectangles.
c. m ∠SRW = 80°
All the interior angles of rectangle are of measure 90°
Given option does not satisfies the criteria of rectangles.
d. m ∠TWR = 80°
All the interior angles of rectangle are of measure 90°
Given option does not satisfies the criteria of rectangles.
Therefore, for the given rectangle RSTW, the condition satisfies the criteria of rectangles is equal to m ∠SRZ = 40°.
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rewrite this expression as an addition equation -4 3/8 - (-1 1/4)=
Given the equation:
[tex]\text{ - 4 }\frac{3}{8}\text{ - (-1 }\frac{1}{4})[/tex]help me please can you solve this for meh
Answer: 6w^3-3+18u^2
Step-by-step explanation:
JP Computers produces both laptop
and desktop computers. Laptop
computers take up 2 cubic feet of
space and desktop computers take up
5 cubic feet of space. The maximum
capacity on the delivery truck is 800
cubic feet. Due to demand, they need
to load at least 300 laptop computers.
They profit $225 on each laptop and
$280 on each desktop computer. How
many of each should they load on the
truck to maximize profit?
The load each should get to maximize the profit is $67,500, $78,700 and $90,000
What Is Profit?
In accounting, a profit is an income that is given to the owner throughout a successful market producing process. Profitability, which is the owner's primary interest in the income-formation process of market production, is measured by profit. There are various profit metrics that are frequently used.
Let x represent the total number of laptops and y represent the total number of desktop computers.
A laptop computer occupies 2 cubic feet, hence x laptops each use 2x cubic feet. Desktop computers take up 5 cubic feet of space, hence 5y cubic feet of room is required for 5y desktop computers.
They require 2x + 5y cubic feet in total.
Since the delivery truck's maximum capacity is 800 cubic feet,
2x + 5y <= 800.
They must load at least 300 laptops because of the demand,
hence, x >= 300
They make $225 on each laptop, which translates to $225 times as many computers. They make a profit of $280 on each desktop computer, or $280y on y desktops.
Total profit is:
P=$(225x + 280y)
Draw the inequality system (see attached diagram)
2x + 5y <= 800.
x >= 300
One of the common region's three vertices will have the most profit:
P(300,0) = 225(300) + 280(0) = $67,500
P(300,40) = 225(300) + 280(40) = $78,700
P(400,0) = 225(400) + 280(0) = $90,000
Hence, each should load $67,500, $78,700 and $90,000 on the truck to maximize profit
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If A=B and B=C, which property let's us say A=C?
Answer:
By using commutative property, if a = b and b = c, then a = c.
Step-by-step explanation:
Answer:
translative property
Step-by-step explanation:
I need help with this math problem. Find the distance between points J and M
Answer:
0.75
Step-by-step explanation:
in the pic
goodluck
How many units is 523 from 0?
Using proportions, it is found that the number 523 is 523 units from zero.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the context of the problem using arithmetic operations such as multiplication and division with the unit rates of the measures.
One example of application is for the digit values of a number, as:
Each unit is worth 1.Each tenth is worth 10.Each hundredth is worth 100.Each thousandth is worth 1000.And so on...
For the number 523 given in this problem, since each unit is worth one, the number of units that it is away from zero is given by:
523/1 = 523 units.
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A monthly produce box is
delivered to Ms. Jones'
door. There is an initial set
up fee of $25.00 plus
$30.00 each week. If Ms.
Jones spent $265, then
how many weeks did she
receive the produce
box?
Ahmed says eight weeks
because
25+ 30x = 265.
Amy says nine weeks
because
30+ 25x = 265.
Answer: 8 weeks
Step-by-step explanation:
PLS HELP
Yan is climbing down a ladder. Each time he descends 4 rungs on the ladder, he stops to see how much farther he has to go. If Yan made 8 stops with no extra steps, which expression best shows another way to write the product of the number of ladder rungs that Yan climbed?
4 + 4 + 4 + 4
8 + 8 + 8 + 8
(Negative 1) (4 + 4 + 4 + 4)
(Negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4)
The expression shows the product of the number of ladder rungs that Yan climbed is D. (Negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4)
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.
We have been given that each time Yan descends 4 rungs on the ladder.
SInce, each time the number of ladder rungs that Yan climbed is negative 4, where negative sign represent descends.
Yan made eight stops with no extra steps.
-4 x 8 = -32
It can also written as; (-4) + (-4)+(-4)+(-4)+(-4)+(-4)+(-4)+(-4)
The correct answer is D. (Negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4)
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Qué número sumado igual da 60 que no sea 20
Answer: 30
Step-by-step explanation:
8. Give the slope of y + 2 = 3(x-7) and a point on the line.
a. The slope is 3 and (-7, 2) is on the line.
b. The slope is 3 and (7, -2) is on the line.
c. The slope is 2 and (7, 3) is on the line.
d. The slope is 7 and (3, 2) is on the line.
9. What is the point-slope equation of the line containing the points (3, 3) and
(6,5)?
a. y - 3=(x-3)
b. y 3 = (x + 3)
c. y + 3 =(x-3)
d. y + 3 = 3(x - 2)
10. The slope of a given line is 3. The line that is parallel to it has a slope of:
a. -3
b. ½
C. -1
d. 3
11. The slope of a given line is 4. The line that is perpendicular to it has a slope of:
a. -4
b. -
C. 4
Answer: b c
Step-by-step explanation:
4) Krysta is attending a school orchestra concert. She sees her math teacher seated 12 meters ahead of her and her science teacher seated 9 meters to her right. How far apart are the two teachers? Submit meters Work it out Not feeling ready yet? These can help: Pythagorean theorem: find the missing leg or hypoten... (80) Distance/direction to starting point
Pythagoras's theorem - The two teachers are both seated at a distance of 15 meters from each other.
What is Pythagoras' theorem?
The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic Euclidean geometry relationship between a right triangle's three sides. According to this rule, the area of the square with the hypotenuse (the side across from the right angle) is equal to the sum of the areas of the squares with the other two sides. The Pythagorean equation, which generally refers to the relationship between the lengths of the legs a, b, and the hypotenuse c, can be used to represent this theorem.
We are given,
the distance between Krysta and her math teacher to be 12 meters, and the distance between Krysta and her science teacher to be 9 meters
for simplicity, we'll let
the distance between Krysta and her math teacher to be KM =12 meters
and the distance between krysta and her science teacher to be KS =9 meters we need to find the distance between the maths teacher and the science teacher, i.e. MS.
all three people's sitting arrangement makes a triangle, with them sitting on the vertex of it.
Using Pythagoras' theorem,
(KM)² + (KS)² = (MS)²
(12)² + (9)² = (MS)²
144 + 81 = (MS)²
225 = (MS)²
√225 = (MS)
thus, MS = 15 meters
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Renz wishes to make an open box froma square piece of cardboard with a sidethat measures 15 inches by cuttingequal squares from the four cornersand folding the sides. what will be thevolume of the box if he cuts a squarewith 2 inch sides?
2.5 inches will be the volume of the box if he cuts a square with 2 inch sides.
What is volume ?
Every three-dimensional item takes up space in some way. The volume of this area is what is being measured. The area contained by an object's limits in three-dimensional space is referred to as its volume. It is sometimes referred to as the object's capacity.Let each side of he square that's cut-off from each corner be represented by x.
This means that the base of the box will be of dimension of the side 15−2x while the height of the box will be x.
Thus;
Volume of box is:
V = (15 − 2x)(15 − 2x)x
V = (15 − 2x)²x
V = (4x² - 60x + 225)x
V = 4x³ - 60x² + 225x
Let's differentiate with respect to x to get;
dV/dx = 12x² - 120x + 225
Maximum value of x is at dV/dx = 0
12x² - 120x + 225 = 0
Using quadratic formula, we arrive at;
x = 2.5 or 7.5
Now, let's find the second derivative of the volume;
d²V/dx² = 24x - 120
Putting x = 2.5 gives;
d²V/dx² = 24(2.5) - 120
d²V/dx² = -60Thus, V is maximum at x = 2.5, since d²V/dx² is negative
At x = 7.5;
d²V/dx² = 24(7.5) - 120
d²V/dx² = 60
Thus, V is minimum at x = 7.5, since d²V/dx² is negative
Thus,we will use x = 2.5
Maximum volume; V = (15 − 2(2.5))(15 − 2(2.5))(2.5)
V = 10 × 10 × 2.5
V = 250 Sq.inches
Dimensions are;
(15 − 2x) = 15 - 2(2.5) = 10 inches
(15 − 2x) = 15 - 2(2.5) = 10 inches
x = 2.5 inches
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Ava is trying to add together 3/5 and 2/9
Her first step is to rewrite the fractions using their lowest common denominator.
What denominator should she use?
Explanation:
The LCM of 5 and 9 is 5*9 = 45
This is the LCD of the two fractions.
3/5 = 27/45 after multiplying top and bottom by 92/9 = 10/45 after multiplying top and bottom by 5So,
3/5 + 2/9 = 27/45 + 10/45 = 37/45
Maria paid $240 for a table set after a discount of 40%. What was the original price? Use scratch paper to create a model to help solve the problem (e.g., tape diagram, table, double number line diagram, 10×10 grid).
The original price was $
Answer:
$400
Step-by-step explanation:
We see that the discount price is (100-40) = 60% of the original price
If 60% corresponds to $240, than 10% corresponds to 240/6 = $40
Since the original price is 100% = 10*10%, the original price is 10* $40 = 400.
I can't make something with scratch paper right now, i hope you will be able yourself to put the above information is a table :-)
Good luck with it!
Which measuring cups do you use to measure out 1 3/4 cups if you don't have a 3/4 cup measuring cup?
1 cup, 1 cup
1 cup, 1/2 cup
1/4 cup, 1/3 cup, 1/2 cup
1 cup, 1/2 cup, 1/4 cup
Answer:
d
Step-by-step explanation:
1 = 1 cup
1/2 can be 2/4
2/4+1/4=3/4
1+3/4 = 1 3/4
Consider the first 2 terms of the sequence 28, 14, ...
Determine whether the sequence is arithmetic or geometric. Explain your reasoning.
please help me with 1 and 2
1. The given sequence 28, 14 ..... will be either arithmetic or geometric sequence.
2. The common difference of the sequence 28, 14 ..... will be;
d = - 14
And, Next three terms of the arithmetic sequence are;
0, -14, -28
What is Geometric sequence?
An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.
Given that;
The first two terms of the sequence,
28, 14 .....
Now,
Let the sequence is in arithmetic sequence, then;
28, 14 ......
The common difference of the sequence is;
d = 14 - 28
d = - 14
And, Let the sequence is in geometric sequence, then;
28, 14 ......
The common difference of the sequence is;
d = 14/28
d = 1/2
Thus, The given sequence 28, 14 ..... will be either arithmetic or geometric sequence.
2. If the given sequence is in arithmetic sequence, then;
28, 14 ......
The common difference of the sequence is;
d = 14 - 28
d = - 14
And, The nth term of the arithmetic sequence is;
⇒ [tex]a_{n} = a + (n - 1)d[/tex]
Where, 'a' is the first term and 'd' is the common difference of the sequence.
So, The 3rd term of the arithmetic sequence is,
⇒ [tex]a_{n} = a + (n - 1)d[/tex]
[tex]a_{3} = 28 + (3-1)(-14)\\ \\a_{3} = 28 - 2 * 14\\\\a_{3} = 28 - 28\\\\a_{3} = 0[/tex]
And, The 4th term of the arithmetic sequence is,
[tex]a_{4} = 28 + (4-1)(-14)\\ \\a_{4} = 28 - 3 * 14\\\\a_{4} = 28 - 42\\\\a_{4} = -14[/tex]
And, The 5th term of the arithmetic sequence is,
[tex]a_{5} = 28 + (5-1)(-14)\\ \\a_{5} = 28 - 4 * 14\\\\a_{4} = 28 - 56\\\\a_{5} = -28[/tex]
Therefore, Next three terms of the arithmetic sequence are;
⇒ 0, -14, -28
Thus,
1. The given sequence 28, 14 ..... will be either arithmetic or geometric sequence.
2. The common difference of the sequence 28, 14 ..... will be;
d = - 14
And, Next three terms of the arithmetic sequence are;
0, -14, -28
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Click on the graph to choose the correct answer to the equation. y ≥ 2 x + 1
The graph of the linear inequality can be seen in the image at the end.
How to identify the graph of the inequality?
Here we have the linear inequality:
y ≥ 2x + 1
To graph this, we first need to graph the line.
y = 2x + 1
With a solid line, because we have the symbol ≥, which means that the points on the line are solutions.
Once we graphed that line, we look at our inequality:
y ≥ 2x + 1
It says that y is larger than or equal to the values on the line, so once the line is graphed we need to shade all the region above that line.
The shaded region (and the line itself) represent all the solutions of the linear inequality.
And the graph can be seen below.
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HELP IS DUE AT 10pm AND IM IN THE LAST QUESTION SOMEBODY PLEASE SOS
how dose parallelogram work
Answer:
Parallelograms are shapes with 2 pairs of parallel sides, like a square or a rhombus. Parallel means lines on a shape that never touches.
Step-by-step explanation:
Hope this helps!
P.S, brainliest? Thanks!
May you guys/girls please help me I have to submit this before midnight and I do not fail because my parents will get me , so may y'all please help me out!?
Answer:
Answer down below!
Step-by-step explanation:
Let's try and find a point that we can easily start on (a point that lands perfectly on the graph)
The point that we will use is (2,2)
So, starting from there we use rise/run to get our answer
We go up 1 and over -2
So, our slope will be (since we cannot simply it...)
-1/2
Hello!
To find the slope:
==> need to pick two points on the line
(x₁, y₁): (0,3)
(x₂,y₂): (4,1)
[tex]Slope = \dfrac{y_2-y_1}{x_2-x_1} =\dfrac{1-3}{4-0} =\dfrac{-2}{4} =-\dfrac{1}{2}[/tex] <== Answer
Hope that helps!
Julie says that the constant of proportionality in the equation below is 0.45. Is Julie correct?
P = 0.45n
The constant of proportionality in the equation:
P = 0.45*n
Is k = 0.45, so we can conclude that Julie is correct.
What is the constant of proportionality?A proportional relationship between two variables x and y is written as:
y = k*x
Where k is the constant of proportionality.
In this case, we have the variables P and n, and the proportional relationship is:
P = 0.45*n
So we can see that the value of the constant of proportionality is k = 0.45, so yes, Julie is correct.
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work out the length of x
Answer:Tes icahd
Step-by-step explanation:
Boris received a $20.50 gift card for a photo center. He used it to buy prints that cost 6 cents each. The remaining balance, B
(in dollars), on the card after buying x prints is given by the following function.
B(x)=20.50-0.06.x
What is the remaining balance on the card if Boris bought 15 prints?
Answer:
$19.6
Step-by-step explanation:
B=20.50-0.06.x
B=20.50-0.06*15
B=20.50-0.9
B=19.6
Need help please : Given the equation 6x + 18 = 72: Part A: Write a short word problem about a purchase made to illustrate the equation. Part B: Solve the equation showing all work. Part C: Explain what the value of the variable represents.
A. A short word problem about a purchase made to illustrate the equation is that John bought six pens and bought books for $18. The total amount is $72. Find the cost of each pen.
B. The cost of each pen is $9
C. The variable is x.
How to illustrate the equation?A. The problem is that John bought six pens and bought books for $18. The
B. The equation to illustrate this will be:
6x + 18 = 72
Collect like terms
6x = 72 - 18
6x = 54
Divide
x = 54 / 6.
x = $9
The cost of each pen is $9.
C. The variable is x = 9. This is the cost of the pen.
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