Answer:
d
Step-by-step explanation:
In trapezoid PQRS, PQ is parallel to SR. What is the area of PQRS in simplest radical form?
The area of the considered trapezoid PQRS in simplest radical form is given by: Option c: 256 + 128√3 (in sq. units)
How to find the area of a trapezoid?The area of a trapezoid is the half of the product of sum of its parallel sides to the height of that trapezoid (the distance between those parallel sides).
Thus, if we have:
Length of its parallel sides = 'a' and 'b' units respectively
Perpendicular distance between its parallel sides = 'h' units,
Then, we get:
[tex]A = \dfrac{1}{2}\times(a+b) \times h \: \rm unit^2[/tex]
Consider the figure attached below, which is a bit more labeled figure of the given trapezoid.
We constructed PA perpendicular to the level of SR, and therefore, as SR is parallel to PQ, we have PA perpendicular to PQ too.
Similarly, QB is constructed perpendicular to both PQ and SR.
Thus, for PQBA, all pair of adjacent sides are perpendicular to each other, therefore its a rectangle.
Sum of parallel sides = Length of PQ + Length of SR
= 24 + |SR| = 24 + |SB| + |BR| = 24 + |AS| - |AS| + |SB| |+ |BR|
= 24 + |AS| + |SB| + |BR| - |AS| = 24 + |AB| + |BR| - |AS|
Due to PABQ being a rectangle (its four sides are such that adjacent sides are perpendicular to each other), we have |PQ| = |AB| = 24 units.
Thus, we get:
Sum of parallel sides = 24 + |AB| + |BR| - |AS| = 48 + |BR| - |AS|
Perpendicular distance between its parallel sides = |PA| = |QB|
Thus, we need to find the values of 3 line segments, which are:
|BR|, |AS|, and |PA| (instead of |PA|, we can find |QB| too, since both are of same length).
Case 1: Finding the length of BR:From the perpective of angle R(interior) in right triangle RBQ, we know the side RQ's length (32 units), and want length of BR.
Thus, its hypotenuse and base from the perspective of angle R (interior).
Thus, we can use cosine ratio or secant ratio. Let we use cosine ratio.
Then, we get:
[tex]\cos(30^\circ) = \dfrac{|BR|}{|RQ|} \\\\|BR| = 32 \times \cos(30^\circ) = 32 \times \dfrac{\sqrt{3}}{2} = 16\sqrt{3}\: \rm units[/tex]
For the same triangle as in case 1 (ie RBQ), but now taking the sine ratio, we get:
[tex]\sin(30^\circ) = \dfrac{|BQ|}{|RQ|} \\\\|BQ| = 32 \times \sin(30^\circ) = 16 \: \rm units[/tex]
This is same as |PA| because of PQBA being a rectangle.
Case 3: Finding the length of AS:The angle PSA is supplement of angle PSR as both joined make a straight line ASR. Thus, we get:
[tex]m\angle PSA + m\angle PSR = 180^\circ\\m\angle PSA = 180^\circ-135^\circ = 45^\circ[/tex]
Thus, for the triangle PSA, similar to the first case or second case, but now using tangent ratio as we've got |PA| = |QB| = 16 units, we get:
[tex]\tan(m\angle PSA) = \dfrac{|PA|}{|AS|}\\\tan(45^\circ) = \dfrac{|PA|}{|AS|} \\\\|AS| = 1 \times 16 = 16 \: \rm units[/tex]
Thus, we get:
Sum of parallel sides = 48 + |BR| - |AS| = 48 + 16√3 - 16 = 32 + 16√3 units
Perpendicular distance between its parallel sides = |PA| = |QB| = 16 units.
Thus, Area of the trapezoid PQRS is evaluated as:
[tex]A = \dfrac{1}{2} \times \text{Sum of parallel sides} \times \text{Distance between those sides}\\A =\dfrac{1}{2} \times (32 + 16\sqrt{3}) \times 16 \\\\A = 256 + 128\sqrt{3} \: \rm unit^2[/tex]
Thus, the area of the considered trapezoid PQRS in simplest radical form is given by: Option c: 256 + 128√3 (in sq. units)
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helpppppppppp 85 points
Area of vertical rectangle
LB16(4)64cm²Area of horizontal rectangle
6(11-4)6(7)42cm²Total:-
42+64106cm²What is the answer for x?
Step-by-step explanation:
[tex]180 = 70 + 90 + y \\ y = 20 \\ (x + y + 18) + 44 + 90 = 180 \\ y = 8[/tex]
Which expression represents the volume, in cubic units, of the composite figure? One-third(8)(6)(6) (8)(6)(4) One-third(8)(6)(10) (8)(6)(4) (8)(6)(4) – (One-third)(8)(6)(6) (8)(6)(4) – (One-third)(8)(6)(10).
The expression of Volume in cubic meter [tex]\frac{1}{3}[/tex] (8)(6)(6)+(8)(6)(4)
The correct option is (1)
What is Volume?Volume can also be defined as the amount of space occupied by a 3-dimensional object. The volume of a solid like a cube or a cuboid is measured by counting the number of unit cubes it contains.
Volume will be,
V= Volume of rectangular pyramid + Volume of cuboid
Volume of rectangular pyramid= [tex]\frac{1}{3}[/tex] * base area* height
= [tex]\frac{1}{3}[/tex] * 6*8*(10-4)
=[tex]\frac{1}{3}[/tex] * 6*8*6
Volume of cuboid= l*b*h
= 4*6*8
So, Volume =[tex]\frac{1}{3}[/tex] * 6*8*6 + 4*6*8
= [tex]\frac{1}{3}[/tex] (8)(6)(6)+(8)(6)(4)
So, The expression of Volume in cubic meter [tex]\frac{1}{3}[/tex] (8)(6)(6)+(8)(6)(4).
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State the. expression (10+16)x49
help
Answer:
the sum of 10+16 multiplied by 49
Step-by-step explanation:
Mara ran 3 km north and then 4 km east. she will finish her run by running directly home. what was the total distance of her run? a right triangle with side lengths 8 kilometers and 4 kilometers. a point at intersection of the side with length 3 kilometers and the hypotenuse is labeled mara's house. 5 km 7 km 12 km 14 km
Based on the calculations, the total distance of Mara's run is equal to: C. 12 km.
How to determine the total distance of Mara's run.In order to determine the total distance of Mara's run, we would solve for the length of the hypotenuse by applying Pythagorean's theorem and then add it to the other distances.
Mathematically, Pythagorean's theorem is given by this formula:
c² = a² + b²
Where:
c is the hypotenuse.a is the adjacent side.b is the opposite side.Substituting the given parameters into the formula, we have;
c² = 3² + 4²
c² = 9 + 16
c = √25
c = 5 km.
Now, we can determine the total distance of Mara's run:
Total distance = 3 + 4 + 5
Total distance = 12 km.
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Answer:
c 12
Step-by-step explanation:
for problems 8-9 find the area to the nearest hundredth use 3.14 for pi
please answer questions
8 and 9
Combine these radicals - square root 5 - 3 square root 5
Answer:
-1√5-3√5=(√5)(-1-3)=(√5)(-4)=-4√5
Step-by-step explanation:
if you combine the radicals, you will receive the answer that is shown above.
Answer:
[tex]-4\sqrt{5}[/tex]
Step-by-step explanation:
Given expression: (square root 5) - (3 square root 5)
⇒ [tex]-\sqrt{5} - 3\sqrt{5}[/tex]Since we have √5 common in both terms, let's factor √5.
⇒ [tex]\sqrt{5} - 3\sqrt{5}[/tex]⇒ [tex]\sqrt{5} \times (-1 - 3)[/tex]Finally, we can simplify;
⇒ [tex]\sqrt{5} \times (-4)[/tex]⇒ [tex]-4\sqrt{5}[/tex]Therefore, the combined radical of (square root 5) - (3 square root 5) is [tex]-4\sqrt{5}[/tex]
What is The Volume? Show Your Work Please
The volume of the given figure is 434 ft³. The volume of the figure is obtained in the two parts.
What is volume?The term “volume” refers to the amount of three-dimensional space taken up by an item or a closed surface. It is denoted by V and its SI unit is in cubic cm.
The volume of the given figure is;
[tex]\rm V = l_1 \times b_1 \times h_1 + l_2 \times b_2 \times h_2 \\\\ V= 7 \times 13 \times 4 + 2\times 5 \times 7 \\\\ V= 434 \ fT^3[/tex]
Hence, the volume of the given figure is 434 ft³.
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Wesley has started to collect sports cards. The graph
shows how many sports cards he has collected.
8
6
Number of
Sports Cards
0 2 4 6 8 10 X
Weeks
Which table shows the information in the graph?
Weeks (x) 2 4 6 8
Weeks (x) 2 4 6 8
Number of
Number of
1 2 3 4
2 4 5
A Sports Cards (y)
(y
B Sports Cards ) 2 3 4 5
2 4 6 8
2 4 6 8
Weeks (x)
Number of
C Sports Cards ()
Weeks (x)
Number of
D Sports Cards (y)
2 4 6 8
3 5 7 9
Answer:
B
Step-by-step explanation:
It goes up by one, to the right by 2. Or flip that, Im dyslexic
Answer:
B!!
Step-by-step explanation:
Hope nthis helps!!!!!
Here is information about two savings account. Savemore compound interest 1. 25%each year. Highbrook compound interest 2. 1% for first year 0. 95%for each extra year. Abi is going to invest £5000 in one of these saving accounts for 3years. She wants to have as much money as possible in the account at the end of 3years. Which saving account should Abi choose
The Highbrook account which offers 25% compound interest each year is a better place to save as much money as possible.
What is interest?The term interest is the amount that is obtained as the return for money invested or the amount paid on top of a loan.
We can clearly see that the Highbrook account which offers 25% compound interest each year is a better place to save as much money as possible.
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What is the solution of x+8=13
Answer:
x = 5.Step-by-step explanation:
x + 8 = 135 + 8 = 13x = 5Nothing else to say lol.
Answer:
x=5
Step-by-step explanation:
x+8= 13
x=13-8
x= 5
hope it helpsss
The functions f and g are defined by f: x = 4 - x and g: x = hx² + k. If the composite function gf is given by gf: x + 2x² - 16x + 26, find
(a) the value of h and of k,
Answer:
Step-by-step explanation:
f(x) = 4-x
g(x) = h[tex]x^{2}[/tex]+k
g(f(x)) = 2[tex]x^{2}[/tex]-16x+26
so put f(x) in g(x)
h[tex](4-x)^{2}[/tex]+k
h((4-x)(4-x) + k
h([tex]x^{2}[/tex]-8x+16)+k
if h = 2 , then
2[tex]x^{2}[/tex]-16x+32 + k
and we want 26 instead of 32 so subtract 6 so K = (-6)
2[tex]x^{2}[/tex]-16x+32 + (-6)
2[tex]x^{2}[/tex]-16x+32 - 6
2[tex]x^{2}[/tex]-16x+26
h=2
k=(-6)
Need help on how to solve
Answer:
b
Step-by-step explanation:
64 = 2x^2
32 = x^2
x = 4√2
ans is b
1. Ned shows that V16 =162. Part of his work is shown below. Which expression or equation
can be placed in the blank to correctly complete Ned's work?
116 = 4 = 4' = 4
- 162
11
1
1
A. (42)
B. 4 + 4
C.4ż . 4ż = (4 • 4),
464
D. 42 • 4Ż = (4. 4)+
1
1
.
4 1/2 ⋅ 4 1/2=(4 x 4)^1/2
could i get help? it would be great!
Answer:
B. supplementary angles
Step-by-step explanation:
7x+8=-5x+32 can someone tell me what (x) is pls
[tex]7x + 8 = ( - 5x) + 32 \\ 7x + 5x = 32 - 8 \\ 12x = 24 \\ x = \frac{ \cancel{24} {}^{ \: \: \: 2} }{ \cancel{12}}\\x=2 [/tex]
[tex] \Large{\boxed{\sf x = 2}} [/tex]
[tex] \\ [/tex]
Explanation:Given equation:
[tex] \sf 7x + 8 = -5x + 32 [/tex]
[tex] \\ [/tex]
Substract 8 from each side :
[tex] \sf 7x + 8 - 8 = -5x + 32 - 8 \\ \\ \sf 7x = -5x + 24 [/tex]
[tex] \\ [/tex]
Add 5x to both sides :
[tex] \sf 7x + 5x = -5x + 24 + 5x \\ \\ \sf 12x = 24 [/tex]
[tex] \\ [/tex]
Divide both sides by 12 :
[tex] \sf \dfrac{12x}{12} = \dfrac{24}{12} \\ \\ \\ \boxed{\boxed{\sf x = 2}} [/tex]
[tex] \\ \\ [/tex]
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Which graph correctly represents the relationship between arc length and the measure of the corresponding central angle on a circle with radius r?
Any smooth curve connecting two points is called an arc. The correct option is c.
What is the Length of an Arc?Any smooth curve connecting two points is called an arc. The arc length is the measurement of how long an arc is. The length of an arc is given by the formula,
[tex]\rm{ Length\ of\ an\ Arc = 2\times \pi \times(radius)\times\dfrac{\theta}{360} = 2\pi r \times \dfrac{\theta}{2\pi}[/tex]
where
θ is the angle, that arc creates at the centre of the circle in degree.
If the central angle has a measure of π/2(90°), then the length of the arc will be one-fourth of the total, while if the measure of the angle is π(180°), then the length of the arc will be half of the total.
Similarly, if the measure of the angle is 3π/4, then the length of the arc will be three-fourth of the total, while if the measure of the angle is 2π(360°), then the length of the arc will be 2πr.
Hence, the correct option is c.
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Given f(x) = x4 – 3x3 + x – 3. What is Limit of f (x) as x approaches negative 2? –45 –13 3 35
Answer:
35
Step-by-step explanation:
Directly plug in the limit and evaluate
[tex]\displaystyle \lim_{x\rightarrow-2}x^4-3x^3+x-3=(-2)^4-3(-2)^3+(-2)-3=35[/tex]
Write a verbal expression for:
20+6
what is the result of the addition of 20 and 6
[tex]\boxed{\sf twenty~plus~six }\boxed[/tex]
I have no idea how to do this also explain
Answer: w =1 L=6
Step-by-step explanation:
What is Perimeter = 2 L + 2W
2L + 2B =14
L = 2W + 4
2(2W + 4) + 2W = 14
4W +8 +2W =14
6W=14-8
W=1
L=2W +4= 6
In a certain Algebra 2 class of 21 students, 10 of them play basketball and 9 of them
play baseball. There are 8 students who play neither sport. What is the probability
that a student chosen randomly from the class plays both basketball and baseball?
Step-by-step explanation:
out of the 21 students, 8 do not play neither basketball nor baseball.
so, 13 students play at least one of these games.
10 play basketball, and 9 play baseball. that would be 19 together. but we have only 13 players.
that means 6 students (19 - 13) must play both games.
remember, a probability is always
desired cases / possible cases
so, when we are looking for the students, who play both games, we have 6 desired cases out of a total of 21.
and the probability to pick one of them is therefore
6/21 = 2/7 = 0.285714286...
A 12 inch line segment is divided into two parts. Which
of the following lengths result in a ratio closest to the
golden ratio, ?
2
1+v5
O A. 6 inches and 6 inches
O B. 7 inches and 5 inches
C. 7.5 inches and 4.5 inches
O D. 7.75 inches and 4.25 inches
The length which result in a ratio closest to the golden ratio is equal to 7.5 inches and 4.5 inches. Option C is correct.
What is the length of line segment?The line segment is made with two end points. Length of a line segment is the distance of both the ends of it.
A 12 inch line segment is divided into two parts. Suppose the line segment is AC which is divided into AB and BC parts. Thus,
AB+BC=AC
AB+BC=12 ....1
The value of golden ratio is equal to 1.618. It can also be given as (1+√5)/2. The ratio of both segment is equal to golden ratio. Thus
[tex]\dfrac{AB}{BC}=\dfrac{AC}{AB}=\dfrac{1+\sqrt{5}}{2}\\\dfrac{12}{AB}=1.618\\AB=7.4166 \rm\; in[/tex]
Put this value in equation one as,
AB+7.4166=12
AB=4.5834
The length which result in a ratio closest to the golden ratio is equal to 7.5 inches and 4.5 inches. Option C is correct.
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Contestants in a game show are each given three pairs of numbers (for example, 2 and 3, 5 and 6, and 6 and 1). a person in the audience is randomly picked and asked to roll two dice, one white and one red. the white die gives the first number in the pair, and the red die gives the second number. the probability that each player has of winning is .
The game is an illustration of probability, and the probability that each player wins is 1/12
How to determine the probability of winning?From the question, we have the following parameters:
Number of a pair of numbers = 3
A die has 6 possible outcomes.
So, the probability of getting the first pair is:
P1 = 1/6
The probability of getting the second pair is:
P2 = 1/6
The probability of getting the first and the second pairs is
P = 1/6 * 1/6
Evaluate
P = 1/36
There are three pairs of numbers in total.
So, the probability of winning is:
P(Win) = 3 * 1/36
Evaluate
P(Win) = 1/12
Hence, the probability that each player wins is 1/12
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Answer:
1/12.
Step-by-step explanation:
The probability that each player has of winning is 1/12.
how do i solve this equation
Answer:5.4
Step-by-step explanation:
so first you cross multiply and then you solve for x from there. You shold get 5.385164807. But you need to round that so I rounded to the nearest tenth, which would be 5.4
Factorise x³+3x²y+3xy²+y²-125
Answer: Heyaa!
Your Answer Is x+y = 5
Step-by-step explanation:
(x+y)^3 = 125
x+y = 5
Hopefully this helps you
- Matthew :)
what is -1/2 - 2/3?
A ___________ models the behavior of data displayed in a scatter plot.
A.)positive association
B.)negative association
C.)scatter plot
D.)trend line
Answer:
D
Step-by-step explanation:
Please help me on this!
I am stuck on this one lol. Coleman pays $12.99 for 3 hamburgers. How much would Coleman pay for 10 hamburgers? Enter your answer in the box.
Answer:
$43.30
Step-by-step explanation:
What we know,
3 hamburgers = $12.99
Coleman wants to know how much would he have to pay for 10 hamburgers,
In order to find out how much 10 hamburgers cost, you need to find out how much 1 hamburger costs,
To find how much 1 hamburger costs divide 12.99 by 3,
12.99/3
= 4.33
Now we know that 1 hamburger cost $4.33,
Now time to find out how much 10 hamburgers cost,
Multiply 4.33 by 10,
4.33 × 10
= 43.30
Therefore it cost $43.30 for 10 hamburgers.
