A rectangular stained glass window is made up of identical triangular parts as pictured below.
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Hence, the area of shaded region is:
72 square inches.
Step-by-step explanation:We have to find the area of the shaded region i.e. we have to find the area of a triangle.
Clearly the shaded triangle is in the shape of a right triangle.
we will firstly find the dimension of the triangle in order to find it's area.
Clearly the base(b) of a triangle is 36/4= 9 inches.
( since the side of the rectangle of length 36 inches is divided into 4 equal parts)
similarly the height(h) of the right triangle is:
48/3=16 inches.
( since the side of rectangle of measure 48 inches is divided into 3 equal parts)
Hence, the area of triangle is calculated as:
[tex]Area=\dfrac{1}{2}\times b\times h\\\\\\Area=\dfrac{1}{2}\times 9\times 16\\\\Area=72\text{square\ inches}[/tex]
Hence, the area of shaded region is:
72 square inches.
Related Questions
Find the number of ways to listen to 4 different cds from a selection of 15 cds.
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Thus, for this type of problem, the appropriate solution would be combination. The equation would be n!/r!(n-r)!. The factorial (!) is solved as follows: for example, 15! would be 15×14×13×12×11×10×9×8×7×6×5×4×3×2×1. Applying this process, we could now determine the answer.
15!/4!(15-4)! = 1,365 ways
Answer:
The First person who answered it was wrong! Its 32,760 I took the test lol!
Step-by-step explanation:
nPr = n!/(n-r)! <-- The equation used for this.
Identify the y-intercept of the function, f(x) = 2x 2 + x - 4. (0,-4) (0,4) (-4,0) (4,0)
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so answer is
y-intercept of the function (0,-4)
Answer:
The y-intercept of the function [tex]f(x)=2x^{2}+x-4[/tex] is [tex](0,-4)[/tex]
Step-by-step explanation:
The y-intercept of a function is the intersection between the graph of the function and the y-axis.This particular point will have a ''0'' in its x-coordinate (because all points over the y-axis have a ''0'' on its x-coordinate).Therefore, we can write the y-intercept as :
[tex]y-intercept=(0,a)[/tex]
We obtain the another coordinate ''a'' replacing ''x'' by a ''0'' in the function.
In this exercise, the function is:
[tex]f(x)=2x^{2}+x-4[/tex]
If x = 0 ⇒
[tex]f(0)=2(0)^{2}+0-4=-4=a[/tex]
We find that ''-4'' is the coordinate ''a'' that we were looking for.
We conclude that the point [tex](0,a)=(0,-4)[/tex]
And [tex](0,-4)[/tex] is the y-intercept of the function.
What is the slope of y-9=-2(x-8)
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Let's write the problem: [tex]y-9=-2\left(x-8\right)[/tex]
We have to isolate for y.
[tex]y-9=-2\left(x-8\right)[/tex]
Apply the distributive property.
[tex]y-9=-2x+16[/tex]
Add 9 to both sides.
[tex]y-9+9=-2x+16+9[/tex]
[tex]y=-2x+25[/tex]
A line equation is on the form of [tex]y=mx+b[/tex]. The [tex]m[/tex] represents the slope. So, our answer would be:
[tex]m=-2[/tex]
Let me know if you have any questions regarding this problem!
Thanks!
-TetraFish
To find the slope, we must first simplify this equation, then turn it into the slope-intercept form :)
So, simplify.
y - 9 = -2x + 16
Remember : Slope-intercept form ~ y = mx+b
Where m = slope, and b = y-intercept
So, now we must add 9 to both sides.
y = -2x + 16 + 9
Simplify.
y = -2x + 25
Since (-2) is in the (m) spot, and m = slope, then -2 is our slope.
Slope = -2
~Hope I helped!~
The tangent of an angle is 3.4. what is the measure of the angle to the nearest tenth? 99.8° 73.6° 68.2° 52.9°
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What is [tex] 3\sqrt{18} [/tex] + [tex] 2\sqrt{50} [/tex] simplified?
F.[tex] 19\sqrt{2} [/tex]
G.[tex] 39\sqrt{2} [/tex]
H.[tex] 77\sqrt{2} [/tex]
I. [tex] 90\sqrt{2} [/tex]
IF THERE IS WORK PLEASE SHOW THANKS:)
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Lisa bought a suit on sale for 459. This price was 15% less than the original price. What was the original price?
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So we have to find 15% more of 459, and to do this, we have to:
Add 100 + 15 = 115
115/100 = 1.15
1.15 x 459 = 527.85
Hope this answers your question
To find the original price of Lisa's suit, convert the discount to a decimal and divide the sale price by one minus the discount rate. The original price is calculated to be $540.
To calculate the original price of Lisa's suit, which she bought on sale for $459 at a discount of 15% less than the original price, we can use the formula:
Original Price = Sale Price / (1 - Discount Percent)
First, we convert the percentage discount to a decimal:
15% = 0.15
Then, we divide the sale price by the complement of the discount rate:
Original Price = $459 / (1 - 0.15)
Original Price = $459 / 0.85
Original Price = $540
Therefore, the original price of the suit was $540.
What type of equation would best model this data
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Find the polynomial f(x) that has the roots of -2, 5 of multiplicity 2. Explain how you would verify the zeros of f(x).
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similarly, if 5 is a root of f, then (x-5) is a factor of f(x).
These roots have multiplicity 2 means that there are 2 of each,
so f(x) is written as (x+2)(x+2)(x-5)(x-5)
[tex]f(x)= (x+2)^{2} (x-5)^{2} [/tex]
[the most general form is f(x)= c*(x+2)^{2} (x-5)^{2}*P(x), where c is a constant and P(x) another polynomial]
To show that -2 and 5 are zeros of f, we must prove that f(-2)=0 and f(5)=0,
Using the function we wrote:
[tex]f(-2)= (-2+2)^{2} (-2-5)^{2}=0* (-7)^{2}=0[/tex]
similarly:
[tex]f(5)= (5+2)^{2} (5-5)^{2}=0 [/tex]
A bag has five red marbles, six blue marbles, and four black marbles. What is the probability of picking a blue marble, replacing it, and then picking another blue marble?
a)1/15
b)8/75
c)4/25
d)1/9
Answers
P(picking blue) = 6/15 ...reduces to 2/5
replacing
P(picking blue) = 6/16...reduces to 2/5
P(both) : 2/5 * 2/5 = 4/25 <==
Answer:
4/15 is 100% the answer *NOT* 1/9 or anything else!
Step-by-step explanation:
Alive the equation 2 k+2= k+1
Answers
2k + 2 = k + 1
Subtract 1k from both sides.
k + 2 = 1
Subtract 2 from both sides.
k = -1
I hope this helps!
What is the simplified form of the quantity of x plus 5, all over the quantity of 9 − the quantity of x plus 4, all over the quantity of x plus 6
Answers
(x+5)/[(9-x+4)/(x+6)]
=(x+5)/[(-x+5)/(x+6)]
=(x+5)*(x+6)/(-x+5)
=[(x+5)(x+6)]/[-x+5]
=(x^2+11x+30)/(-x+5)
the answer is:
(x^2+11x+30)/(-x+5)
Please help!!! (-x/2)+(1/2x)=(-4/x)
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you can't solve that for x because when you multiply both sides by x, 0*x = 0 and [tex]0 \neq 4[/tex]
I think you made a mistake in your typing or something...unless the answer was no solution!
Find the function h(x) = f(x) ∘ g(x) if f(x) = x(2 - x) and g(x) = 3x.
h(x) = 0
h(x) = -32x
h(x) = 2(32x)
h(x) = 3x(2 - 3x)
Answers
Answer: h(x) = 3x(2 - 3x)
Step-by-step explanation:
Here the given functions are,
[tex]f(x) = x(2-x)[/tex]
[tex]g(x) = 3x[/tex]
[tex]h(x) = f(x) \circ g(x) = (f\circ g)(x) = f[g(x)][/tex]
[tex]= f( 3x )[/tex]
[tex]= (3x)[2-(3x)][/tex]
[tex]= 3x(2-3x)[/tex]
Hence,
[tex]h(x) = 3x(2-3x)[/tex]
⇒ Fourth option is correct.
What is the right answer to this?
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The distance between two buildings is 3 inches. This means we have to plug in 13 and multiply by 3.
13(3) = 39.
The distance between the two buildings is 39 miles.
Your answer is B.) 39 miles.
I hope this helps!
A man wishes to construct a pultry house 12 feet long, in which to keep 20 hens. if each hen requires 4 square feet of floor space, how wide should he contruct the poultry house
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Next, we use the formula for the area of a rectangle: A = LW, where L is length and W is width. Substituting all known values,
80 = 12W
W = 80/12
W = 6.67 feet
Thus, the man should construct a farm that is 6.67 feet wide.
order the group of quadratic functions from widest to narrowest graph
y=-7x^2
y=-1/5x^2
y=-1/3x^2
Answers
y=-1/3x^2
y=-7x^2
Answer:
Widest to narrowest
[tex]y=-\frac{1}{5}x^2[/tex] - [tex]y=-\frac{1}{3}x^2[/tex] - [tex]y=-7x^2[/tex]
Step-by-step explanation:
Given : Graph 1 - [tex]y=-7x^2[/tex]
Graph 2- [tex]y=-\frac{1}{5}x^2[/tex]
Graph 3 - [tex]y=-\frac{1}{3}x^2[/tex]
To find : Order the group of quadratic functions from widest to narrowest graph.
Solution :
First we plot the given graph,
Refer the attached figure below.
In the graph, we see that all graph has same vertices (0,0) and
Graph 2 with green in color [tex]y=-\frac{1}{5}x^2[/tex] is the most widest graph among all.
Then graph 3 with purple in color is the widest and then graph 1 with blue in color is the most narrowest graph.
So, The order of the graph from widest to narrowest is
Graph 2 - Graph 3 - Graph 1
[tex]y=-\frac{1}{5}x^2[/tex] - [tex]y=-\frac{1}{3}x^2[/tex] - [tex]y=-7x^2[/tex]
Richard has just been given a 4-question multiple-choice quiz in his history class. each question has four answers, of which only one is correct. since richard has not attended class recently, he doesn't know any of the answers. assuming that richard guesses on all four questions, find the indicated probabilities. (round your answers to three decimal places.) (a) what is the probability that he will answer all questions correctly
Answers
The probability of answering all the question correctly is [tex]\boxed{\bf \dfrac{1}{256}}[/tex]
Further Explanation:
Given:
The total number of question is [tex]4[/tex].
Each question has [tex]4[/tex] options and one is correct.
Concept used:
Probability is defined as the ratio of number of favorable outcomes to number of total outcomes.
[tex]\boxed{\text{Probability}=\dfrac{\text{favorable outcomes}}{\text{total outcomes}}}[/tex]
Calculation:
The probability of getting the correct answer is calculated as follows:
[tex]\begin{aligned}P&=\dfrac{1}{4}\\&=0.25\end{aligned}[/tex]
The probability of getting the incorrect answer is calculated as follows:
[tex]\begin{aligned}P&=1-\dfrac{1}{4}\\&=1-0.25\\&=0.75\end{aligned}[/tex]
The formula for probability of answering all question correctly is as follows:
[tex]\boxed{P'=^nC_{r}P^{r}(1-P)^{n-r}}[/tex]
Here, [tex]n[/tex] is number of question and [tex]r[/tex] is number of correct answer, [tex]P'[/tex] is the probability of answering all question correctly.
Solve the above equation to obtain probability of answer all question correctly.
Substitute [tex]4[/tex] for [tex]n[/tex], [tex]0.25[/tex] for [tex]P[/tex] and [tex]4[/tex] for [tex]r[/tex] in above equation to obtain probability of answering all question correctly.
[tex]\begin{aligned}P'&=^4C_{4}(0.25)^{4}(1-0.25)^{4-4}\\&=\dfrac{4!}{(4-4)!\cdot 4!}\left(\dfrac{25}{100}\right)^{4}(0.75)^{0}\\&=\left(\dfrac{1}{4}\right)^{4}\\&=\dfrac{1}{256}\end{aligned}[/tex]
Therefore, the probability of the correct answer is [tex]0.25[/tex].
The probability of the incorrect answer is [tex]0.75[/tex].
The probability of answering all question correctly is [tex]\dfrac{1}{256}[/tex].
Thus, the probability of answering all question correctly is [tex]\boxed{\dfrac{1}{256}}[/tex].
Learn more:
1. Simplification: https://brainly.com/question/1602237
2. Quadratic equation: https://brainly.com/question/1332667
Answer details:
Grade: High school
Subject: Mathematics
Chapter: Probability
Keywords: Probability, Question, Richard, multiple choice, four answer, class, attend, guesses, correctly answer, favorable outcomes, total outcomes.
The probability that Richard will answer all four questions correctly is 0.004.
Explanation:The probability that Richard will answer all four questions correctly can be determined by multiplying the probability of getting one question correct by itself for each question. Since each question has four answer choices and only one is correct, the probability of guessing the correct answer for one question is 1/4.
Therefore, the probability of Richard answering all four questions correctly is (1/4) * (1/4) * (1/4) * (1/4) = 1/256. Rounded to three decimal places, this probability is approximately 0.004.
Thus, the probability that Richard will answer all questions correctly is 0.004.
Write a compound inequality that represents the situation:
all real numbers at least -6 and at most 3
A) -6 < x ≤ 3
B) -6 ≤ x ≤ 3
C) -6 ≥ x ≥ 3
D) -6 < x < 3
Answers
The keywords at least and at most mean that it has to be less than or equal to/more than or equal to.
There is no value for x that can satisfy the conditions for C
-6 ≤ x ≤ 3
Letter B
Justin wants to use 376 ft of fencing to fence off the greatest possible rectangular area for a garden what dimensions should he use what will be the area of the garden
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the greatest rectangular area is actually a square
so 376/4 = 94 feet.
each side will be 94 feet
area of a square is 94^2
= 94 * 94 = 8836 square feet
Trey went to the batting cages to practice hitting. he rented a helmet for $4 and paid $0.75 for each group of 20 pitches. if he spent a total of $7 at the batting cages, how many groups of pitches did he pay for?
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Find the remaining sides of a 45°-45°-90° triangle if the longest side is 20.
Answers
All 45°-45°-90° triangles have sides that are in a unique ratio. The two legs are the exact same length, and the hypotenuse is that length times the √2.
Let a be the leg then hypotenuse = a√2.
[tex]a \sqrt{2}=20 \ \to a= \frac{20}{ \sqrt{2} } \approx 14.14 \ \text{units}[/tex]
What is the factored form of 2x2 − 7x − 15? (2x + 3)(x − 5) (2x + 5)(x − 3) (2x − 7)(x + 8) (2x + 8)(x − 7)
Answers
(2x + 3)(x - 5) <==
is a factor of (2x+3)(x-5)
Best explained and correct answer gets brainliest.
Answers
3275 = x * (1+0.075/12)^(12*10)
3275 = x * (2.11206463)
x= 3275/2.11206463 = 1550.6154
x=1550.62
she needs to deposit $1,550.62
Quadrilateral $abcd$ is a parallelogram. if the measure of angle $a$ is 62 degrees and the measure of angle $adb$ is 75 degrees, what is the measure of angle $adc$, in degrees?
Answers
In the given parallelogram ABCD, angle $a$ is 62 degrees and angle $adb$ is 75 degrees. Angle $bd$ is calculated to be 105 degrees making angle $adc$ the supplementary to $bd$, and therefore also 75 degrees.
Explanation:In a parallelogram, opposite angles are equal and consecutive angles are supplementary (adding up to 180 degrees). In your given quadrilateral $abcd$, the measure of angle $a$ is 62 degrees and $a$ and $adb$ are consecutive angles. Therefore, knowing that angle $adb$ is 75 degrees, angle $bd$ should be the supplementary to $adb$, which is 180 - 75 = 105 degrees. Finally, since $adc$ is a straight line and $bd$ and $dc$ are parts of it, therefore angle $dc$ = 180 - angle $bd$ = 180 - 105 = 75 degrees. So, the measure of angle $adc$ is 75 degrees.
Learn more about Angles in a Parallelogram here:https://brainly.com/question/16578666
#SPJ12
a factor of the quadratic 6x2-11x-35
Answers
6x^2-11x-35
= (3x+5)(2x-7)
Answer: (3x+5)(2x-7)
6x^2-11x-35
x^2-11x-210
(x-21)(x+10)
(x-(21/6))(x+(10/6))
(x-(7/2))(x+(5/3))
(2x-7)(3x+5)
Final answer: (2x-7)(3x+5)
A plane's airspeed is 400 miles per hour on a heading of 45 degrees south of east (compass: 135 degrees, babylonian 315 degrees). if a wind is blowing from the west with a speed of 50 miles per hour, what is the ground speed and direction of the plane?
Answers
To answer this item, we take the x- and y-components of the speeds.
Airplane:
x-component = (400 mi/hr)(cos 45°) = 282.84 mi/h
y-component = -(400 mi/hr)(sin 45°) = -282.84 mi/h
Wind:
x-component = -(50 mi/hr)(sin 90°) = -50 mi/hr
y-component = 0 mi/hr
Adding up the components:
x-component = 282.84 mi/hr - 50 mi/hr = 232.84 mi/hr
y-component = -282.84 mi/hr
The resultant speed would be,
R = sqrt ((232.84 mi/hr)² + (-282.84 mi/hr)²) = 366.35 mi/h
The direction would be,
tan (∅) = -282.84 mi/hr / 232.84 mi/hr
∅ = 50.53° (south of east)
ANSWER: 366.35 mi/hr, 50.53° South of East
which equation represents the statement thirteen less then a number is forty two
Answers
x is the "variable", you're taking 13 away from that, and the answer is also given, 42.
Answer:
The equation which represents the statement thirteen less then a number is forty two is:
x-13=42
Step-by-step explanation:
Let x be any number
we are given that:
thirteen less then a number is forty two
i.e. x-13=42
Hence, the equation which represents the statement thirteen less then a number is forty two is:
x-13=42
The wildflowers at a national park have been decreasing in numbers. There were 300 wildflowers in the first year that the park started tracking them. Since then, there have been one fourth as many new flowers each year. Create the sigma notation showing the infinite growth of the wildflowers and find the sum, if possible.
I chose C, but can someone check for me? Thanks :)
Answers
Answer: Third option is correct.
Step-by-step explanation:
Since we have given that
Initial wildflowers in the first year = 1200
Every year, the number of wildflower is one fourth of the previous year.
So, it form a geometric series:
1200,300,75............
so, using sigma notation we can express the infinite growth of the wildflowers:
[tex]\sum ^{\infty}_{i=1}1200(\dfrac{1}{4})^{i-1}[/tex]
As we know that sum of infinite terms in case of geometric series is given by
[tex]S_{\infty}=\dfrac{a}{1-r}\\\\S_{\infty}=\dfrac{1200}{1-0.25}\\\\S_{\infty}=\dfrac{1200}{0.75}\\\\S_{\infty}=1600[/tex]
Therefore, there are 1600 wildflowers.
Hence, Third option is correct.
The function f(x) = –x2 + 60x – 116 models the monthly profit, in dollars, a shop makes for repairing windshields, where x is the number of windshields repaired, and f(x) is the amount of profit. Part A: Determine the vertex. What does this calculation mean in the context of the problem? (5 points) Part B: Determine the x-intercepts. What do these values mean in the context of the problem? (5 points)
Answers
Part A:
x = -b / 2 a = - 60 / ( - 2 ) = 30
Then we will charge it into the function:
f ( 30 ) = - 30² + 60 · 30 - 116 = - 900 +1,800 - 116 = 784
The vertex is ( 30, 784 ).
It means that the maximum profit is $784, when 30 windshields are repaired.
Part B:
x 1/2 = ( -60 +/- √(3600 - 464 )/ (- 2 ) = ( -60 +/- 56 ) / ( - 2 )
x 1 = 2, x 2 = 58
It means that a shop has to repair at least 2 windshields and not more than 58 windshields for making a profit.
Answer:
I believe Homer "the genius" math to be incorrect for Part A. (-30)^2+60(30)-116= 900+1800-116=2584; not 784 as he got -900 when squaring -30.
Step-by-step explanation:
What is the solution set of the equation x^2 - 7x - 18 = 0
Answers
x=9 or x=-2
Factoring this trinomial as the product of two binomials,
we have (x - 9)(x + 2) and set that equal to 0.
So we have (x - 9)(x + 2) = 0.
So either x - 9 = 0 or x + 2 = 0.
Solving for x in each equation, we find that our solution is {9, -2}.