Answer:
A=[tex]\frac{a+b}{2} (h)[/tex]
Step-by-step explanation:
Option first, option second, and option fourth are correct this expression is equivalent to the formula for a trapezoid.
What is a trapezoid?It is defined as the quadrilateral having four sides in which two sides are parallel to each other, it is a 2-dimensional geometry.
The options are:
h=2A/(b1+b2)b1=2A/h - b2b2= 2A/b1 - hb2= 2A/h - b1b1= 2A//b2 - hWe have a formula for finding the area of the trapezoid:
[tex]\rm A= \dfrac{1}{2}h(b_1+b_2)[/tex]
Make a subject h and solve for h:
[tex]\rm \dfrac{2A}{(b_1+b_2)}= h[/tex]
or
[tex]\rm h = \dfrac{2A}{(b_1+b_2)}[/tex]
[tex]\rm b_2 = \dfrac{2A}{h}- b_1[/tex]
[tex]\rm b_1 = \dfrac{2A}{h}- b_2[/tex]
Thus, option first, option second, and option fourth are correct this expression is equivalent to the formula for a trapezoid.
Learn more about the trapezoid here:
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What are the restrictions of the domain of f(g(x))?
a) x is not equal to -5
b) x is not equal to -3
c) x is not equal to 2
d) There are no restrictions.
Find the tangent of each specified angle. Write each ratio as a fraction and as a decimal rounded to the
nearest hundredth.
Answer:
<Q= 15/36=0.42
<R= 36/15=2.4
Step-by-step explanation:
When doing trig you have to remember, "SOH CAH TOA"
Since you're looking for the tangent for angles Q and R, it would be the opposite over adjacent which is what "TOA" stands for. So, opposite of Q is 15 and adjacent to Q is 36, so you get 15/36. Opposite of R is 36 and adjacent is 15 so you get 36/15.
Solve the simultaneous equations. You must show all your working to find x and y. 1/2x -3y = 9 5x y + y = 28
Answer:
[tex]\huge\boxed{x = 6 , y = -2}[/tex]
Step-by-step explanation:
[tex]\sf \frac{1}{2} x - 3y = 9-----------(1)\\5x + y = 28 ----------(2)[/tex]
Taking equation (1)
[tex]\sf \frac{1}{2} x -3 y=9[/tex]
Multiplying both sides by 2
[tex]\sf x-6y = 18[/tex]
Adding 6y to both sides
[tex]\sf x = 18+6y[/tex]
Putting this in (2)
5(18+6y) + y = 28
5(18+6y) + y = 28
90 + 30y+y = 28
31y+90-28 = 0
31 y + 62 = 0
31y = -62
Dividing both sides by 31
y = -2
Now,
x = 18 + 6y
x = 18+6(-2)
x = 18-12
x = 6
An exponential function f(x)= ab^x passes through the points (0,10) and (3,1250). What are the values of a and b?
a = I know it’s 10
b = ?
Answer:
a = 10 and b = 5
Step-by-step explanation:
We write out f(x)= ab^x for x = 0 and x = 3 to create two equations in a and b that must be solved simultaneously:
(0, 10): 10 = a*b^0
This tells us that 10 = a*1, or a = 10.
(3, 1250): 1250 = a*b^3 => 10*b^3, or
1250 = 10*b^3, or
125 = b^3. Taking the cube root of both sides, we obtain b = 5.
a = 10 and b = 5
- The water rate for Columbus Ohio
is $1.98 per 750 gallons of water.
What is the water bill for a resident
who used 27,000 gallons?
Divide total amount used by the amount in the rate:
27,000 / 750 = 36
Multiply that number by the rate:
36 x 1.98 = 71.28
The bill is $71.28
What is the volume of the square pyramid shown to the nearest tenth? The figure is not drawn to scale. width of 16 and a length of 17 A. 1,280.0 ft^3 B. 85.3 ft^3 C. 1,920.0 ft^3 D. 3,840.0 ft^3
The volume of the pyramid is 1,280 cubic feet. Thus, the correct option is A.
What is the volume of the pyramid?Let h be the height of the pyramid, l be the slant height, and A be the base area of the pyramid. Then the volume of the pyramid will be given as,
Volume = (1/3) × A × h
The slant height is given as,
l² = (half of the side)² + h²
Given that:
Slant height, l = 17 ft
Side length, a = 16 ft
The height of the pyramid is calculated as,
17² = (16/2)² + h²
h = 15
The volume of the pyramid is calculated as,
V = 1/3 x 16 x 16 x 15
V = 256 x 5
V = 1,280 cubic feet
Thus, the correct option is A.
More about the volume of the pyramid link is given below.
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Math Question (10 Points):
Answer:
Step-by-step explanation:
We need the two numbers to tell us where the point is on the coordinate plane. The first number tells us where it is on the x-axis, and the second number tells us where it is on the y-axis. The very middle of the coordinate plane is the point (0, 0)
Based on this the answer is horizontol plane and x coordinate
the graph of y=f(x) is shown below. find all the values of x where f(x)=8
Answer:
x = 4
Step-by-step explanation:
Find 8 on the y-axis. Draw a horizontal line through y =8. Determine the x value for which the graph intersects this horizontal line y = 8. It is x = 4
The value of x when f(x) = 8 according to the graph is; 4.
According to the graph;
To determine the value of x when f(x) = 8.We must plot a line of the equation; y = 8.
This line of y = 8 results in an horizontal line.The point at which the horizontal line, y = 8 intersects the given graph has an x coordinate.Ultimately, the x coordinates of this point is 4 and hence, the value of x when f(x) = 8 is 4.
Read more;
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What is the determinant of A = -3 6 1 -6
Step-by-step explanation:
ydudhdhdjjdbdjdmdjdkdjd
Find the value of m∠ACD. A. 30º B. 15º C. 60º D. 90º
Answer:
A. 30 degrees
Step-by-step explanation:
Set the two angles equal to each other:
3x-15 = 45-x
Solve for x:
4x -15 = 45
4x = 60
x = 15
Finally, plug in the x to one of the equations (preferably 45 - x since it's easier to solve) and solve for x.
45 - 15 = 30
Answer:
A 30 degrees
Step-by-step explanation:
In 2021, Ryan Management collected rent revenue for 2022 tenant occupancy. For financial reporting, the rent is recorded as deferred revenue and then recognized as revenue in the period tenants occupy rental property. For tax reporting, the rent is taxed when collected in 2021. The deferred portion of the rent collected in 2021 was $66 million. Taxable income is $260 million in 2021. No temporary differences existed at the beginning of the year, and the tax rate is 25%. Prepare the appropriate journal entry to record income taxes in 2021. (If no entry is required for a transaction/event, select "No journal entry required" in the first account field. Enter your answers in millions rounded to 1 decimal place (i.e., 5,500,000 should be entered as 5.5).)
Answer:
Answer and Explanation:
The Journal entry is shown below:-
1. Income Tax Expense Dr, $336 million
Deferred Tax Assets Dr, $29 million
($116 million × 25%)
To Income Tax Payable $365 million
($1,460 × 25%)
(Being income tax and deferred tax is recorded)
2. Income Tax Expense Dr, $400 million
To Income Tax Payable $340 million
($1,360 × 25%)
To Deferred Tax Assets $60 million
(($354.0 million - $116 million) × 25%)
(Being income tax and deferred tax is recorded)
Step-by-step explanation:
*PLEASE ANSWER TY* What is the density of a 50-gram pyramid with rectangular base 4 cm x 8 cm and height 10 cm?
Answer:
[tex]\frac{0.47 g}{cm^{3} }[/tex]
Step-by-step explanation:
→ First work out volume of pyramid using the formula [tex]\frac{lwh}{3}[/tex] where 'l' is the length, 'w' is the width and 'h' is the height
[tex]\frac{lwh}{3}[/tex] ⇔ [tex]\frac{4*8*10}{3}[/tex] ⇔ [tex]\frac{320}{3}[/tex] ⇔ 320 ÷ 3 = 106.666666667
→ Volume of pyramid = 106.666666667. Substitute this value into the density formula
Density = Mass ÷ Volume
Density = 50 ÷ 106.666666667
Density = 0.46875 to 1 decimal place is 0.47
helpyffhvjvjnvhdfuguig
Answer:
x = 0, x = 4
Step-by-step explanation:
12x - 21 = 5x + 7(x - 3)
First, foil out the right side --> 5x² - 15x + 7x - 21, which simplifies down to 5x² - 8x - 21.
Move the 12x - 21 to the right side by subtracting --> 0 = 5x² - 20x.
Factor out a 5x --> 0 = 5x(x - 4)
If you want to solve for x, set 5x = 0 and x - 4 = 0.
For 5x = 0, divide both sides by 5 to isolate the x --> x = 0/5, which simplifies down to x = 0.
For x - 4 = 0, add 4 to both sides to isolate the x --> x = 0 + 4, which simplifies down to x = 4.
Plug the values back into the original equation to check if it works
12(0) -21 = 5(0) + 7((0) - 3) --> -21 = -21
12(4) - 21 = 5(4) + 7((4) -3) --> 27 = 27
Hope this helps!
Which equation represents the graphed function?
a)–3x + 2 = y
b) –2/3 x + 2 = y
c) 3/2 x – 3 = y
d) 2x – 3 = y
Answer: C is your answer.
Step-by-step explanation:
X/2 - 1/5 = x/3 + 1/4 linear equation
Answer:
x/2 - x/3 = 1/4 + 1/5
(3x-2x)/6 = (5+4)/20
3x-2x = (9/20)*6
x = 54/20
x = 2.7
Answer:
x = 2.7 or 27/10.
Step-by-step explanation:
x/2 - 1/5 = x/3 + 1/4
Multiply through by the LCD of 2, 5, 3 and 4 which is 60:
30x - 12 = 20x + 15
10x = 27
x = 2.7
help me plz i dont get this
Answer:
56 [tex]in^2[/tex]
Step-by-step explanation:
We can first break this down into 2 smaller rectangles.
1x2x4 rectangle
4x3x4 rectangle.
Then we can find out the area of each, and we get 8+48 = 56.
You also could find this out by subtracting the area that is missing.
Answer:
The volume of the container is 56 in^3
Step-by-step explanation:
To solve, I split this figure vertically at the corner between the two steps. We know that the formula for volume of a container is V= l*w*h. The first, smaller portion of the container has a length of 4, a width of 1, and a height of 2. 4*1*2= 8 in^3
The second, larger portion of this container has a length of 4, (look at the side of the first portion), a width of 3, (4-1=3), and a height of 4. 4*3*4= 48 in^3.
Finally, add together the volumes of the two portions and that is the volume of the whole figure. V= 56 in^3
Find the volume. Show work plz
Answer:
196π or 615.75 m^3 to the nearest hundredth.
Step-by-step explanation:
This is a cone, so:
Volume = 1/3 π r^2 h
= 1/3 * π * 14^2 * 3
= 196π m^3.
Simplify the expression where possible. (r^-3 s^2 t)^4
Answer:
[tex]\frac{(s^8t^4)}{r^{12}}[/tex]
Step-by-step explanation:
Assuming that you tried to write:
[tex](r^{-3} s^2 t)^4,[/tex]
we can multiply the 4 on the outside of the parenthesis to all the terms. Multiplying, we get
[tex](r^{-12}s^8t^4)[/tex]
Because you don't want any negative powers in the top, we can move it down to get:
[tex]\frac{(s^8t^4)}{r^{12}}[/tex]
Answer:
there is no sign in between the two terms in the parenthese, maybe a google search on the properties of exponents would help because that's what this seems like
Step-by-step explanation:
Sam's Lawn Service uses the equation, y = 15x + 25 to calculate the cost, y, to work on a
customer's lawn for x number of hours.
Ron's Lawn Service uses the table below to calculate the cost to work on a customer's
lawn.
Answer:
Rons costs less by 4 dollars
Step-by-step explanation:
Sams
y = 15x+25
x=3
y = 15*3+25
= 45+25
=70
Rons
Using averaging
for 3 hours Add 2 and 4 hours and divide by 2
(49+ 83) / 2 = 132/2= 66
Rons costs less by
70-66 =4
Open-Ended Write three equations with variables on both sides of the equal sign with one having no solution, one having exactly one solution, and one being an identity. please help guys
Answer:
Summary. If the equation ends with a false statement (ex: 0=3) then you know that there's no solution. If the equation ends with a true statement (ex: 2=2) then you know that there's infinitely many solutions or all real numbers
Step-by-step explanation:
Answer: answer in the attachment
Step-by-step explanation:
Hope this might have helped you
Given the following three points, find by hand the quadratic function they represent.
(0,6), (2,16), (3, 33)
(1 point)
f(x) = 4x2 – 3x + 6
f(x) = -4x2 – 3x + 6
Of(x) = -4x2 + 21x + 6
Of(x) = 4x2 + 3x + 6
Given the following three points, find by hand the quadratic function they represent.
(-1,-8), (0, -1),(1,2)
(1 point)
O f(x) = -3x2 + 4x - 1
O f(x) = -2x2 + 5x - 1
Of(x) = -5x2 + 8x - 1
O f(x) = -3x2 + 10x - 1
Find the equation of a parabola that has a vertex
(3,5) and passes through the point
(1,13). (1 point)
Oy=2(x – 3)' + 5
Oy= -2(x – 3)' + 5
Oy= -3(x – 3)' +5
Oy= 2(x + 3)" - 5
Determine if the following set of ordered pairs represents a quadratic function. Explain.
(5, 7), (7, 11), (9, 14), (11, 18)
(1 point)
The y-values go up by the square of the x-value (22 = 4). Therefore, the ordered pairs represent a quadratic equation.
The y-values go up by the square of the x-value (22 = 4). Therefore, the ordered pairs do not represent a quadratic equation.
Since the differences between the differences of the y-values is not consistent, the ordered pairs do not represent a quadratic equation.
Since the differences between the x-values is 2 and the differences between the y-values is 4, that means that the differences between the differences
of the y-values are all zero. Therefore, the ordered pairs represent a quadratic equation.
Determine if the following table represents a quadratic function. Explain.
х
1
2
3
4.
5
y 13 22 37 58 85
(1 point)
O The differences between the differences of the y-values is a constant 6, so the ordered pairs do not represent a quadratic equation.
The differences between the y-values is a constant 9, so the ordered pairs represent a quadratic equation.
The differences between the differences of the y-values is a constant 6, so the ordered pairs represelo a quadratic equation.
The differences between the y-values is a constant 9, so the ordered pairs do not represent a quadratic equation.
i’m in a rush :( pls help
Answer:
A B A C C are the correct answers~_~
Step-by-step explanation:
what is the first step to solving this problem: 3x-10=2(x+3)
Answer:
x = 16
Step-by-step explanation:
3x - 10 = 2(x+3)
First step is solve this:
2(x+3) = 2*x + 2*3 = 2x + 6
then:
3x - 10 = 2x + 6
3x - 2x = 6 + 10
x = 16
Check:
3*16 - 10 = 2(16+3)
48 - 10 = 2*19 = 38
Answer:
x = 16
Step-by-step explanation:
you start off by isolating the variable
Find the median of the data in the dot plot below.
Answer:
40
Step-by-step explanation:
The median is the middle value of the data arranged in ascending order. If there is no exact value in the middle then it is the average of the values either side of the middle.
The data is arranged in ascending order within the dot plot
There are 10 values in the data set
Thus the median is between the fifth and sixth values.
Counting from the left (35)
The fifth value = 39 and the sixth value = 41, thus
median = [tex]\frac{39+41}{2}[/tex] = [tex]\frac{80}{2}[/tex] = 40
Answer:
Step-by-step explanation:
Data:
35 , 38, 38 , 39 , 39, 41, 42 , 43, 43, 44
Total number of data = 10
Number of data is even. so, median is the average of (n/2)th term & ([tex]\frac{n}{2}+1[/tex] ) middle term,
Median = average of 5th and 6th term
= (39 + 41)/2 = 80/2 = 40
Slim Johnson was usually the best free-throw shooter on his basketball team. Early in the
season, however, he had made only 9 of 20 shots. By the end of the season, he had made all
the additional shots he had taken, thereby ending with a season record of 3:4. How many
additional shots had he taken?
Answer:
24
Step-by-step explanation:
(9 + x)/(20 + x) = 0.75
Solve that for x, the number of additional free throws taken.
9 + x = 15 + 0.75 x
0.25 x = 6
x=24
The required number of additional shots that were shot is 24.
Given that,
He had made only 9 of 20 shots. By the end of the season, he had made all the additional shots he had taken, thereby ending with a season record of 3:4.
The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.
Here,
Let the extra shots be x,
Now, according to the question,
Number of shots will be 9 + x and 20 + x,
And their ratio is 3:4
9 + x / 20 + x = 3 / 4
[9 + x] × 4 = 3 [20 + x]
36 + 4x = 60 + 3x
x = 60 - 36
x = 24
Thus, the required number of additional shots that were shot is 24.
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12
121 °
9
can it make a triangle if so what the area ?
Answer:
no it can not
Step-by-step explanation:
Triangle is always 180° in total.
The vertex formation of a parabola is x = 8(y- 1)2-76.
What is the standard form of the equation?
Answer:
[tex]\boxed{x=8y^2-16y-68}[/tex]
Step-by-step explanation:
Hello, please consider the following.
[tex]x=8(y- 1)^2-76\\\\x=8(y^2-2y+1)-76\\\\x=8y^2-16y+8-76\\\\\boxed{x=8y^2-16y-68}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
The quotient of 32 and 4 divided by the sum of 1 and 3
Answer:
2
Step-by-step explanation:
32 divided by 4 = 8 (quotient)
1 + 3 = 4 (sum)
8 divided by 4 = 2
Answer:
88
Step-by-step explanation:
You move down 3 units and up 3 units. You end at (-3, 4). Where did you start?
Answer: You started at (-3, 4)
Step-by-step explanation:
If you started at (-3, 4) and moved down 3 units, you would be at (-6, 4). If you moved back up 3 units, you would be at your original starting point (-3, 4).
Answer:
Step-by-step explanation:
All motion here is up and down, so the x-coordinate does not change.
Work backwards to answer this question:
(-3, 4), and down three units, and then up three, puts you where you started, at (-3, 4).
can somewon help me plz i want help
Answer:
5 * 10^10.
Step-by-step explanation:
(9 * 10^10) - (4 * 10^10) = (9 - 4) * 10^10 = 5 * 10^10.
Hope this helps!
Answer:
5*10^10
Step-by-step explanation:
9 times ten is 9^10, and 4 Times 10^10 is 4^10 so 9^10 minus 4^10 is 50000000000 which is also called 5^10 which is also 5 x 10^10 I think. pls correct me if im wrong
Factor 3x^2 – 12x – 36.
Answer:
The answer is 3( x - 2)(x + 6)Step-by-step explanation:
3x² - 12x - 36
To factorize the expression first factor 3 out of the expression
That's
3( x² - 4x - 12)
Factorize the terms in the bracket
To do so write - 4x as a difference
That's
3( x² + 6x - 2x - 12)
Factor out x from the expression
3[ x( x + 6) - 2 ( x + 6) ]
Next factor x + 2 out
We have the final answer as
3( x - 2)(x + 6)Hope this helps you
