Answers
Step-by-step explanation:
the area of a trapezoid is
(a + b)/2 × x
a and b being the 2 bases. and x, as requested, is the height.
A
it does not matter which base is which, as long as we keep using them consistently.
so, let's assume a is the first base :
a = x + 5
and then for the second base
b = 2x - 1
now we use that in the main formula :
(x + 5 + 2x - 1)/2 × x = (3x + 4)/2 × x = (3x² + 4x)/2
A = (3/2)x² + (4/2)x = (3/2)x² + 2x ft²
B
now the height is increased by 4 ft.
that means we need to replace x by x + 4.
(3/2)(x+4)² + 2(x+4) = (3/2)(x² + 8x + 16) + 2x + 8 =
= (3/2)x² + (24/2)x + (48/2) + 2x + 8 =
= (3/2)x² + 12x + 24 + 2x + 8 =
= (3/2)x² + 14x + 32 ft²
with x being the original height, of course.
Related Questions
make x the subject of the formula in R = ax-p/q+bx
Answers
R = (ax - p)/(q + bx)
(ax - p) = R(q + bx)
ax - p = Rq + Rbx
ax - Rbx = Rq + p
x(a - Rb) = Rq + p
x = (Rq + p)/(a - Rb)
The angle bisectors of triangle ABC are , , and . They meet at a single point . (In other words, is the incenter of .) Suppose , , , and .
Answers
To solve this we must be knowing each and every concept related to triangle. Therefore, the angle bisector is indeed the ray, line, or fragment that splits a particular angle in two equal pieces.
What is triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The denotes a triangle having vertex A, B, and C. In Euclidean geometry, every three non-collinear points define a unique triangle and, by extension, a unique plane.
In geometry, the angle bisector is indeed the ray, line, or fragment that splits a particular angle in two equal pieces.
Therefore, the angle bisector is indeed the ray, line, or fragment that splits a particular angle in two equal pieces.
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Select each equation that the number 10^3 makes true.
6.01 x
= 601
O 0.305 x
= 305
0.54 x
= 540
O 0.097 x
970
0.97 x
= 97
Answers
All of the equations which the number 10³ makes true include the following:
B. 0.305 × __ = 305
C. 0.54 × __ = 540
How to determine the true equations?In this exercise, you are required to determine the equations which the number 10³ makes true. This ultimately implies that, we would substitute the number 10³ into each of the given equations as follows;
6.01 × 10³ = 601
By expanding the exponent, we have the following equation:
6.01 × 1,000 = 601
6010 = 601 (False).
0.305 × 10³ = 305
By expanding the exponent, we have the following equation:
0.305 × 1,000 = 305
305 = 305 (True).
0.54 × 10³ = 540
By expanding the exponent, we have the following equation:
0.54 × 1,000 = 540
540 = 540 (True).
0.097 × 10³ = 970
By expanding the exponent, we have the following equation:
0.097 × 1,000 = 970
97 = 970 (False).
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x divided by 6 is what
Answers
Answer:x/6
Step-by-step explanation:
Here the value of x is not given and hence the answer to the question is
x/6
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Richard has 11 markers in a backpack. One of them is red and one is purple. What is the probability Richare
will reach into the backpack without looking and grab the red marker and then reach in a second time and
grab the purple marker if:
(a) the first marker is not replaced?
(b) the first marker is replaced?
Express your answers as fractions in simplest form.
Answers
The probability Richard marker is 11.The probability of anything occurring is known as probability.
How are probabilities calculated?The probability of anything occurring is known as probability. To determine probability, divide the total number of possible outcomes by the number of possible ways an event could occur.
The likelihood or chance that a specific event will occur is represented by a probability. Both proportions between 0 and 1 and percentages between 0% and 100% can be used to describe probabilities.
The probability of anything occurring is known as probability. To determine probability, divide the total number of possible outcomes by the number of possible ways an event could occur.
According to question:-
11/1 = 11
11/1 = 11
The probability Richard marker is 11.The probability of anything occurring is known as probability.
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Each other 11 letters of the word mathematics with written on a separate piece of paper and placed in a bowl what is the probability of drawing
Answers
Therefore, the probability of drawing "OBJ" from the bowl is (1/11) * (1/11) * (1/11) = 1/1331
Define Probability.The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Define Statistics.The study of statistics focuses on gathering, organizing, organizing, analyzing, interpreting, and presenting data. It is customary to start with a statistical population or a statistical model to be researched when applying statistics to a scientific, industrial, or social problem.
The word "mathematics" has 11 letters, so there are 11 letters in the bowl. The probability of drawing the letter "O" is 1/11, since there is only 1 "O" in the 11 letters. Similarly, the probability of drawing the letter "B" is 1/11, and the probability of drawing the letter "J" is 1/11 as well.
Since the events of drawing the letter "O", "B", and "J" are independent of each other, the probability of drawing all three letters in order is the product of their individual probabilities.
Therefore, the probability of drawing "OBJ" from the bowl is (1/11) * (1/11) * (1/11) = 1/1331
It is a very low probability, the chances of drawing that sequence are very low.
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Select the correct answer from each drop-down menu. Let d(t) be the total number of miles Joanna has cycled, and let t represent the number of hours after stopping for a break during her ride. So, d(4) = 68 . This means that after a 4 hour break , Joanna cycled 68 miles total .
Answers
The numeric value of the function d(t) = 12t + 20 at t = 4 is given as follows:
d(4) = 48.
The interpretation of this numeric value is that after a time of 4 hours, Joanna has cycled 68 miles.
How to interpret the function?The function for this problem is defined as follows:
d(t) = 12t + 20.
The meaning of each variable is given as follows:
t: time in hours after the break.d(t): distance cycled after t hours.The numeric value at t = 4 is obtained replacing the lone instance of t in the function by 4, as follows:
d(4) = 12(4) + 20
d(4) = 48 + 20
d(4) = 68 miles.
Meaning that after a time of 4 hours, the distance cycled by Joanna was of 68 miles.
Missing InformationThe function for this problem is defined as follows:
d(t) = 12t + 20.
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Let |r| = 6 at an angle of 30° and |s| = 11 at an angle of 225°. Which expression represents |r – s|?
Answers
The resultant of subtraction of both vectors is
|r - s| = √(r² + s² - 2rscos{15})
What are vectors?A vector is an object that has both a magnitude and a direction.
Given is that |r| = 6 at an angle of 30° and |s| = 11 at an angle of 225°.
For the subtraction of vectors, we can write its magnitude as -
|r - s| = √(r² + s² - 2rscos{15})
Therefore, the resultant of subtraction of both vectors is
|r - s| = √(r² + s² - 2rscos{15})
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The relative frequency table below displays the proportion of colors of cars for sale at a dealership.
What proportion of cars are yellow?
0.04
0.1
0.15
0.4
Answers
Proportion of cars which are yellow -
= 1 - (0.24 + 0.20 + 0.15 + 0.12 + 0.15 + 0.10)
= 1 - 0.96
= 0.04
Answer:
A) 0.04
Step-by-step explanation:
edge 2023
Work out
2/3 - 2/5
Give your answer in its simplest form.
Answers
Answer:
4/15
Step-by-step explanation:
find common denominators, which is 15
multiply 2/3 by 5 and and 2/5 by 3
2 x 5 = 10 and
3 x 5 = 15
10/15
2 x 3 = 6 and
5 x 3 = 15
6/15
subtract numerators
10 - 6
15
= 4/15
Describe the error in each problem below. 36÷3+(3²•2)36÷3+9•2 36÷12•2 3•2 6
Answers
Answer:
Step-by-step explanation:
In the last part of the problem, you have to follow PEMDAS.
Instead of you added before dividing. After the step of 36÷3+9x2 you have to divide.
What is x + y when x = 4 and y = -5
Answers
Answer:
x + y = -1
Step-by-step explanation:
4 plus -5 is equivalent (equal to) the equation 4 - 5 which equals -1
Which expression is equivalent to 5-3(x+2)?
A. -3x - 1
B. -3x+10
C. 2x + 4
D. 2x-6
Answers
5-3(x+2)
5-3x-6
-3x+5-6
-3x-1
The table represents a quadratic function C(t).
t C(t)
−2 1
−1 4
0 5
1 4
2 1
What is the equation of C(t)?
C(t) = −(x − 5)2
C(t) = (x − 5)2
C(t) = −x2 + 5
C(t) = x2 + 5
Answers
The equation that presents the table will be C(t) = - t² + 5. Then the correct option is C.
What is the equation of the parabola?Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
The table represents a quadratic function C(t).
t C(t)
−2 1
−1 4
0 5
1 4
2 1
From the table, the coordinate of the vertex will be at (0, 5). Then the equation is given as,
C(t) = a(t - 0)² + 5
C(t) = at² + 5
The equation is passing through the point (1, 4), then we have
4 = a (1²) + 5
4 = a + 5
a = - 1
The equation that presents the table will be C(t) = - t² + 5. Then the correct option is C.
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d. Describe the relationship between the 9s in Ithaca's average annual rainfall?
Answers
Precipitation (inches), 2.08, 1.98, 2.64, 3.29; Snowfall (inches), 17.6, 14.2, 11.7, 3.4; The Ithaca Climate Page.
What is the relationship between the patterns in rainfall and temperature?Increased evaporation as a result of rising average temperatures at the Earth's surface leads to more precipitation overall. As a result, many places might expect more precipitation as a result of a hotter environment.Moving from the equator toward the poles results in less precipitation. Because temperature impacts how much moisture air can contain, precipitation often decreases with increasing latitude, with higher precipitation typically occurring at lower latitudes.There is a larger than 28% chance of rain on any given day during the wetter season, which lasts for 6.4 months from April 2 to October 14.June is the month in Ithaca with the most rainy days, with an average of 11.3 days with at least 0.04 inches of precipitation. From October 14 to April 2, the dry season lasts 5.6 months.Tho learn more about Ithaca climate refer to :
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Multiply: (–4 + i)(2 – 3i)
a. –5 – 10i
b. –8 + 11i
c. –5 + 14i
d. –11 + 14i
Answers
The result of the product of the given complex numbers as required to be determined is; Choice C; -5 + 14i.
What is the product of the given complex numbers?It follows from the task content that the result of the product of the given complex numbers is to be determined.
On this note, since the required product to be evaluated is; (–4 + i) (2 – 3i).
We can therefore multiply as follows;
-8 + 12i + 2i - 3i².
However, it is noteworthy to know that; i² = -1.
Hence, we have that;
-8 + 14i + 3
= -5 + 14i
On this note, it follows that the result of the product of complex numbers as required is; -5 + 14i.
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if june 13 was on monday what day will it be on june 13 math
Answers
Answer:
Monday??????
SteP-by-step explanation:
An architect is designing a circular window to be installed in the
gable of a house. The metal window frame will be 1 foot wide and will be bordered by
the roof above and a wood beam below. The distance from the center of the window to the roof is 3 feet. What will be the circumference of the circular glass pane that will be
needed?
Answers
Answer:
12.57 ft
Step-by-step explanation:
First thing we need to find is the radius of the circular glass pane. We are given the information that the center of the glass plane is directly in the center of the triangle and that the closest distance from the center to the roof is 3 ft, including a metal border with a width of 1 ft.
Since the metal frame is the same width all the way around the window, we can safely conclude that the radius of the circular glass pane is 2 ft, as the 3ft measurement included the radius and the metal frame.
Now that we have our radius we can use the formula:
[tex]C=2\pi r[/tex] (Circumference = 2 x pi x radius)
Using 3.14 for pi we get:
[tex]C=2(3.14)(2)[/tex]
[tex]C=4 \pi[/tex] or 12.57 ft (2.d.p)
Which graph represents a function?
Answers
Answer:
The fourth graph since it passes the vertical line test.
Each input has one output.
Hope this helps :)
Rachel has 13 books and some empty boxes. She can put 4 books in each box. How many boxes can she fill completely?
How many books will be left over?
Answers
Answer:
she can fill 3 boxes completely and one book will be left over
Step-by-step explanation:
if a box can be filled with 4 book then we do 4 multiply 3 and then 12 books will can fill 3 box and there is 13 books so 1 book will be left over
Step-by-step explanation:
- Set up a proportion using the information given. For instance, 4/1 = 13/x.
- Cross multiply. This should give you 4x = 13.
- Divide 4 on both sides to get the x alone. This should give you x = 3.25. But since you can't have 3.25 boxes, you'll have 3 boxes filled completed. If you do the math 4 books x 3 boxes that, would you 12 books meaning 12 books fit in 3 boxes. Therefore, 1 book would be left over.
11-(-2)x4 step by step pls my hm is due tmr
Answers
Answer:
Step-by-step explanation:
11 -(-2) x 4
11 + 2 x 4
11 +8
= 19
Which equation justifies why ten to the one third power equals the cube root of ten?
ten to the one third power all raised to the third power equals ten to the one third plus three power equals ten
ten to the one third power all raised to the third power equals ten to the one third times three power equals ten
ten to the one third power all raised to the third power equals ten to the three minus one third power equals ten
ten to the one third power all raised to the third power equals ten to the one third minus three power equals ten
Answers
The equation that justifies ten to the one third power equals the cube root of ten is ten to the one third power all raised to the third power equals ten to the one third times three power equals ten. Option B
How to justify the powerwe are to find [tex]10^{\frac{1}{3} } = \sqrt[3]{10}[/tex]
The justification has to be done with the use of the properties of powers as well as roots.
[tex]a^\frac{m}{n} = \sqrt[n]{a^m}[/tex]
then we would have:
[tex]\sqrt[3]{10} = \sqrt[3]{10^1} =10^\frac{1}{3}[/tex]
then we would have
[tex](10^\frac{1}{3} )^3\\\\= 10^\frac{3}{3}[/tex]
= 10
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Calculate The Double Integral. ∫∫ 4x 1 + Xy DA, R = [0, 4] × [0, 1]
Answers
Answer:
[tex]20\ln(5)-16\approx16.18876[/tex]
Step-by-step explanation:
[tex]\displaystyle\int\int\limits^{}_R {\frac{4x}{1+xy} } \, dA\\\\\\=\int\limits^4_0\int\limits^1_0 {\frac{4x}{1+xy} } \, dy \, dx\\\\\\=\int\limits^4_0 {\ln(1+xy)\biggr|_0^1} \, dx\\\\\\=\int\limits^4_0 {\ln(1+x)} \, dx\,\,\,\,\,\,\,\,\,\,\,\,\bigr(u=\ln(1+x),\,dv=dx\bigr)\\\\\\=4\biggr(x\ln(1+x)\biggr|_0^4-\int\limits^4_0 \frac{x}{1+x} \,dx\biggr)\\\\=4\biggr(4\ln(5)-\bigr[x-\ln(1+x)\bigr]\biggr|_0^4\biggr)\\\\=4\biggr(4\ln(5)-\bigr[4-\ln(5)\bigr]\biggr)\\\\=4\biggr(5\ln(5)-4]\biggr)\\\\=20\ln(5)-16[/tex]
The morning temperature is -29.8 degrees. The temperature rose 33.2 degrees during the day.
What is the new temperature in degrees?
Answers
Answer:
Step-by-step explanation:use a calculator
Answer:
Step-by-step explanation:
-29.8+33.2=3.4
Round 0.295833333 to the nearest hundredth
Answers
Answer:
The answer is 0.30.
I wish you luck in your assignments.
Answer:
0.3
Step-by-step explanation:
Since 5 rounds up, that would cause the 0.09 to become a 0.1, so it would be 0.3
Can someone solve 18?
Answers
The piecewise function f(x) = 1/2 |x| is equivalent to -
1/2 |x| = {- x/2} {x < 0}
1/2 |x| = {x/2} {x ≥ 0}
What is a piecewise function?A piecewise function is a function that is defined on a sequence of intervals. A common example is the absolute value function. Piecewise functions are implemented in the Wolfram Language as PiecewiseAdditional piecewise functions include the Heaviside step function, rectangle function, and triangle function.Given is the absolute value function -
f(x) = 1/2 |x|
We can write it as a piecewise function as follows. The given function is as follows :
f(x) = 1/2 |x|
The absolute value function is given as -
|x| = - x {x < 0}
|x| = x {x ≥ 0}
So, we can write the piecewise function as -
1/2 |x| = {- x/2} {x < 0}
1/2 |x| = {x/2} {x ≥ 0}
Therefore, the piecewise function f(x) = 1/2 |x| is equivalent to -
1/2 |x| = {- x/2} {x < 0}
1/2 |x| = {x/2} {x ≥ 0}
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A blueprint of a house has a scale in which 1 inch equals 4 1/2 feet. If the living room wall measures 7 1/4 inches on the drawing, what is the actual length of the wall?
The actual length of the wall is ___ feet
Answers
Answer:
Step-by-step explanation:
1 : 4 1/2 :: 8 1/5 : x proportion
x = (4 1/2)(8 1/5) product of means/extremes
x = (9/2)(41/5) change improper fraction
x = 369/10 multiply
x = 36.9 change to decimal
The actual length is 36.9 feet.
Find the midpoint and distance between (-3,10) and (15,-2)
Answers
if 11 is to 22, and 22 to 242, then from 242 to what
Answers
Answer:
it's equal to = 242 =484. I think so that's the right answer please
Canvas Reproductions, Inc has RM4,500 researching a new project. The project requires RM20,000 worth of new machinery which would cost RM3,000 to install. The company would realize RM4,500 in after tax proceeds from the sale of the old machinery. If Canvas’s working capital is unaffected by this project, what is the initial investment amount for this project?
Answers
Hi. This is an informal letter .
The body of letter goes like this
Hi friend hope u are enjoying ur life and luck find u in best state of mind. My exam have been over and wanted to share my experience with my near and dear one so I was planning to come to ur place to enjoy my vacationHi. This is an informal letter .
The body of letter goes like this
Hi friend hope u are enjoying ur life and luck find u in best state of mind. My exam have been over and wanted to share my experience with my near and dear one so I was planning to come to ur place to enjoy my vacationHi. This is an informal letter .
The body of letter goes like this
Hi friend hope u are enjoying ur life and luck find u in best state of mind. My exam have been over and wanted to share my experience with my near and dear one so I was planning to come to ur place to enjoy my vacationHi. This is an informal letter .
The body of letter goes like this
Hi friend hope u are enjoying ur life and luck find u in best state of mind. My exam have been over and wanted to share my experience with my near and dear one so I was planning to come to ur place to enjoy my vacation