You work as an assistant to a carpenter who designed the tabletop below. He tells you that each shape is a right triangle, and each is the same size. You now need to calculate the area of one triangle so that you can begin building the tabletop. What is the area of each triangle in square inches? 28 1/4" and 20"
Answers
Answer:
A. 200 square inches
Step-by-step explanation:
First, use Pythagorean Theorem to find the base of each triangle.
[tex]a^2+b^2=c^2\\20^2+b^2=(28\frac{1}{4})^2\\400+b^2=798.0625\\b^2=398.0625\\b=\sqrt{398.0625}\\b=19.9515037[/tex]
Finally, use the area of a triangle formula to find the area of each triangle.
[tex]A=\frac{1}{2}bh\\A=\frac{1}{2}(19.9515037)(20)\\A=199.515037[/tex]
Therefore, the area of each triangle is approximately 200 in².
The area of each triangle in square inches is 200 square inches.
What is the area of triangle?The area of triangle is defined as the region enclosed by its perimeter or the three sides of triangle.
Mathematically,
Area of triangle = 1/2(base*height)
Now given that,
Base of the triangle, B = 20''
Hypotenuse of the triangle, H = 28(1/4)'' = 28.25''
So, Height of the triangle, P = [tex]\sqrt{H^2 - B^2}[/tex]
or, Height of the triangle, P = [tex]\sqrt{28.25^2 - 20^2}[/tex]
or, Height of the triangle, P = [tex]\sqrt{398.0625} }[/tex]
or, Height of the triangle, P = 19.95 inches
Finally, use the area of a triangle formula to find the area of each triangle.
Area of triangle = 1/2*(BasexHeight)
⇒Area of triangle = 1/2*(20x19.95)
⇒Area of triangle = 1/2*399
⇒Area of triangle = 199.5 square inches
or, Area of triangle ≈ 200 square inches.
Hence, The area of each triangle in square inches is 200 square inches.
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Related Questions
What ordered pairs are the solutions of the system of equations shown in the graph below?
Answers
The solutions are where the two lines cross over each other.
(0,3) and (4,-5)
Which point on the number line shows the graph of
Answers
Answer:
point E
Step-by-step explanation:
it lies after 1 and before two and 1.6 bar is after 1 and before 2
Please help urgently
Answers
Explanation:
Prove that triangle PQS is congruent to triangle RSQ
PS = QR (given)
PQ = RS (given)
Angle PQS = Angle QSA
Therefore, triangle PQS and triangle QSA is congruent (SAS).
construct a rectangle PQRS, In which AB= 8cm and diagonal AC= 10cm
Answers
A rectangle can be constructed using a straightedge, and a setsquare or compass
Please find attached the drawing of rectangle ABCD
The steps to construct the rectangle ABCD are as follows:
Question:
The missing part of the question is the name of the rectangle = ABCD
The given parameters are;
The length of the side AB = 8 cm
The length of the diagonal of the rectangle ABCD = AC = 10 cm
The steps to construct a rectangle are;
Draw the segment [tex]\overline{AB}[/tex] = 8 cm on a planeDraw perpendicular lines at points A and B with length h given by Pythagoras's theorem as followsh² = [tex]\overline{AC}[/tex]² - [tex]\overline{AB}[/tex]²
∴ h² = 10² - 8² = 36
h = √36 = 6
h = 6 cm = The length of the sides [tex]\mathbf{\overline{AD}}[/tex] and [tex]\mathbf{\overline{CB}}[/tex]
Draw arcs with radius 6 cm from points A and B to intersect the perpendicular lines drawn from points A and B on the same side of the line [tex]\overline{AB}[/tex] at points D and CJoint point C to D with a straight line which is segment [tex]\overline{CD}[/tex] and which completes the rectangle ABCDLearn more about the construction of basic shapes here;
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I need to know the answer ASAP
Answers
Answer:
Step-by-step explanation:
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!
12. The coordinate grid below represents a town.
a. Curtis's house is at (-4, -6) and Jean's house is at (-4, 3). Plot the plots where Curtis's house and Jean's house are located.
b. Each unit on the grid represents 1 mile. If Curtis can ride his bike at a constant rate of 12 miles per hour, how long would it take Curtis to ride from his house to Jean's house?
THIS IS NOT MULTIPLE CHOICE!!!
Answers
We are given:
Coordinates of Curtis's house: (-4, -6)
Coordinates of Jean's house: (-4, 3)
a) Plotting these points:
in the given coordinates, the first number is called the abscissa and denotes the x-coordinate of the point.
the second number is the ordinate. it denotes the y-coordinate of the point
Plotting Curtis's house:
We will start from the origin (0,0). move 4 units to the left because that's where x = -4 is.
Then, we will move 6 units downwards and mark the point.
The point we just marked is (-4, -6), Curtis's house
Plotting Jean's house:
We will go to x = -4 like we just did when plotting curtis's house
then, we will move 3 units upwards and mark the point.
This point is (-4, 3), Jean's house
b) Time taken by Curtis:
Distance between the points:
distance = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex] (distance formula/Pythagoras' Theorem)
where (x₁, y₁) = (-4, -6) and (x₂, y₂) = (-4, 3)
replacing the values in the formula, we get:
distance = [tex]\sqrt{(-4 - (-4))^2 + (3 - (-6))^2}[/tex]
distance = [tex]\sqrt{(0)^2 + (9)^2}[/tex]
distance = [tex]\sqrt{(9)^2}[/tex] = 9 units
since each unit on the grid represents one mile,
distance = 9 miles
speed of Curtis = 12 miles/hour
we know that speed is just (distance covered)/(time taken)
speed = (distance covered)/(time taken)
replacing known values
12 = 9 / time
12 * time = 9 [multiplying both sides by time]
time = 9/12 [dividing both sides by 12]
time = 3/4 hours
time = 0.75 hours OR 45 minutes
9514 1404 393
Answer:
a) see attached
b) 3/4 hour (45 minutes)
Step-by-step explanation:
a) The attached graph shows the points plotted.
__
b) The points lie on the same vertical line. The distance between them is the difference of their y-coordinates: 3 -(-6) = 9 (miles).
The time is related to distance and speed by ...
time = distance/speed
time = (9 mi)/(12 mi/h) = 9/12 h = 3/4 h
It would take Curtis 3/4 hour to ride from his house to Jean's house.
-7/3+1/2w= -9/5
What is w?
Answers
Answer:
w = 124/15 = 8 4/15
Step-by-step explanation:
[tex]-\frac{7}{3}+\frac{1}{2}w=-\frac{9}{5}\\\\\frac{1}{2}w=\frac{62}{15}\\\\w=\frac{124}{15}=8\frac{4}{15}[/tex]
The line perpendicular to y=3/4x+7 containing (3,-4)
Answers
Answer:
y = - [tex]\frac{4}{3}[/tex] x
Step-by-step explanation:
1). [tex]y_{1}[/tex] = [tex]m_{1}[/tex] [tex]x_{1}[/tex] + [tex]b_{1}[/tex]
[tex]y_{2}[/tex] = [tex]m_{2}[/tex] [tex]x_{2}[/tex] + [tex]b_{2}[/tex]
[tex]y_{1}[/tex] ⊥ [tex]y_{2}[/tex] if [tex]m_{2}[/tex] = - [tex]\frac{1}{m_{1} }[/tex]
2). ( [tex]x_{3}[/tex] , [tex]y_{3}[/tex] )
y - [tex]y_{3}[/tex] = m( x - [tex]x_{3}[/tex] )
~~~~~~~~~~~~~~~~~~
y = [tex]\frac{3}{4}[/tex] x + 7
[tex]m_{1}[/tex] = [tex]\frac{3}{4}[/tex]
[tex]m_{2}[/tex] = - [tex]\frac{4}{3}[/tex]
( 3, - 4 )
y - ( - 4) = - [tex]\frac{4}{3}[/tex] ( x - 3 )
y + 4 = - [tex]\frac{4}{3}[/tex] x + 4
y = - [tex]\frac{4}{3}[/tex] x
3x+2y <
11 2x-y<9
Does this graph match this equation?
Answers
Answer:
No.
Step-by-step explanation:
3x+2y<11 doesn't have a y-intercept of 6 and doesn't have a x-intercept of 4.
2x-y<9 is not the same direction as 3x+2y<11.
find the probability of rolling a sum of a three first and then a sum of nine when a pair of dice is rolled twice
Answers
Answer:
Step-by-step explanation:
favorable events for a sum of 3 are 12,21
P(sum 3)=2/36=1/18
favorable events for a sum of 9 are 36,63,45,54
P(sum of 9)=9/36=1/4
Two angles of a triangle have the same measure and the third one is 48 degrees greater than the measure of each of the other two. Find the measure of the LARGEST angle in the triangle.
Answers
Let the two equal angles each be x
Let the third angle be x + 48
Then ATQ
x + x + x + 48 = 180
3x + 48 = 180
3x = 180 - 48 (Angle Sum Property)
3x = 132
x = 132/3
x = 44
Now the two angles are each 44
And the largest angle = 44 + 48
= 92
Answered by Gauthmath must click thanks and mark brainliest
Largest angle in the triangle is [tex]92^{0}[/tex]
What is triangle?"A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry."
What is angle sum property?"Angle sum property of triangle states that the sum of interior angles of a triangle is 180°."
Let us assume the two equal angles be '[tex]x[/tex]'
According to the question,
Two equal angles = [tex]x[/tex]
Third angle = [tex]x+48^{0}[/tex]
We know the angle sum property
[tex]x+x+x+48^{0} =180^{0}[/tex]
⇒[tex]3x+48^{0}=180^{0}[/tex]
⇒[tex]3x=180^{0}-48^{0}[/tex]
⇒[tex]x=\frac{132^{0} }{3}[/tex]
⇒[tex]x=44^{0}[/tex]
Two equal angles [tex]x[/tex] = [tex]44^{0}[/tex]
Largest Angle = [tex]44^{0} +48^{0}[/tex]
∴ Largest Angle = [tex]92^{0}[/tex]
Hence, Largest Angle = [tex]92^{0}[/tex]
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Write the equation in slope-intercept form of a line is parallel to y=2x+5 and has a y-intercept of -7
Answers
Answer:
y = 2x - 7
Step-by-step explanation:
Parallel lines have the same slope so only the y-intercept is different. Therefore nothing is changed between the two equations except the y-intercept is -7.
Help with This question please
Answers
Answer:
A
Step-by-step explanation:
Suppose a shipment of 400 components contains 68 defective and 332 non-defective computer components . From the shipment you take a random sample of 25. When sampling with replacement (so that the p = probability of success does not change), note that a success in this case is selecting a defective part. The standard deviation of this situation is?
Answers
Answer:
The standard deviation for the number of defective parts in the sample is 1.88.
Step-by-step explanation:
The sample is with replacement, which means that the trials are independent, and thus, the binomial probability distribution is used to solve this question.
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
68 defective out of 400:
This means that [tex]p = \frac{68}{400} = 0.17[/tex]
From the shipment you take a random sample of 25.
This means that [tex]n = 25[/tex]
Standard deviation for the number of defective parts in the sample:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{25*0.17*0.83} = 1.88[/tex]
The standard deviation for the number of defective parts in the sample is 1.88.
The standard deviation of the situation is 1.88
The proportion of success is calculated as:
[tex]p = \frac xn[/tex]
So, we have:
[tex]p = \frac {68}{68 + 332}[/tex]
[tex]p = 0.17[/tex]
The standard deviation is then calculated as:
[tex]\sigma= \sqrt{np(1-p)}[/tex]
For a shipment of a random sample of 25, we have:
[tex]\sigma= \sqrt{25 * 0.17 * (1-0.17)}[/tex]
Evaluate the product
[tex]\sigma= \sqrt{3.5275}[/tex]
Evaluate the root
[tex]\sigma= 1.88[/tex]
Hence, the standard deviation of the situation is 1.88
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Knowing that AQPT - AARZ, a congruent angle pair is:
Answers
Answer:
Angle T is congruent to Angle Z
Step-by-step explanation:
Since the 2 triangles are equal, that means that each pair of angles are also congruent. To know which angles are congruent, you check th order of how the triangles are named. Ex. Angle Q is congruent to Angle A, Angle P is congruent to Angle R, and Angle T is congruent to Angle Z.
Aku has less than 3 times as many mangoes as Alaba and half as many mangoes as Amina if alaba has x mangoes the interns of x then how many mangoes do aku alaba and Amina have in combined
Answers
Answer:
I have no clue my bad bro.
A stub function is:__________.
A) A short function
B) A function that has been unit tested
C) A function that acts as a placeholder and returns a simple value so another function can be tested
D) A function that is broken down into smaller steps through step-wise refinement
Answers
Answer: c. A function that acts as a placeholder and returns a simple value so another function can be tested.
Step-by-step explanation:
A stub simply means a function which has an expected signature but has an incomplete implementation. It is put in place in order for codes to be tested before the functions are fully written.
A stub is a function that acts as a placeholder and returns a simple value so another function can be tested. Therefore, the correct option is C.
Help please im new and i need help
Answers
9514 1404 393
Answer:
B) False
Step-by-step explanation:
Triangles are similar when their angles are the same measures. Because the angles sum to 180°, we only need to show that 2 angles of one triangle are equal to 2 angles of the other triangle.
All three of the angles of the first triangle are given: 20°, 40°, 120°.
One of the angles of the second triangle matches: 40°; but the other angle (80°) doesn't match either of 20° or 120°.
The angles aren't the same, so the triangles are not similar.
__
If we want to go to the trouble, we can figure the third angle of the second triangle. It is 180° -40° -80° = 60°.
Then the angles in the two triangles, listed smallest to largest, are ...
20°, 40°, 120°
40°, 60°, 80°
It is clear the angles of these triangles are not the same.
A vending machine dispenses coffee into a twenty-ounce cup. the amount of coffee dispensed into the cup is normally distriubuted with a standard deviation of 0.03 ounce. You can allow the cup to overfill 2% of the time. What amount should you set as the mean amount of coffee to be dispensed?
Answers
Answer:
x=20.938
Step-by-step explanation:
-2.053748911 = (x - 21)/.03
x=20.938
if I have to add 97 oz of algaecide to 10,000 gallons of water how much should I add if I only have 200 gallons of water
Answers
Answer:
1.94 oz
Step-by-step explanation:
x/97 = 200/10000
97*200 = 10,000x
19400 = 10,000x
1.94 oz
You can also do it this way:
200/10000 = 0.02
0.02 * 97 = 1.94
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
find x in the following
Answers
Answer:
i. ans in picture
ii. ans in picture
iii. ans in picture
iv. 19
v. 38
Step-by-step explanation:
i. working in picture
ii. working in picture
iii. working in picture
iv.
180-90=90
90=2x+7+45=2x+52
2x=90-52=38
x=19
v.
angle COD=3x+10
180-3x+10-2x
180+10=2x+3x
190=5x
x=38
Answer:
x = 123- 56=67x= 17x=125x=19x= 20Step-by-step explanation:
Apply the following triangle laws:
The sum of the angles of a triangle will always be 180 degrees.
Eleanor scores 680 on the mathematics part of the SAT. The distribution of SAT math scores in recent years has been Normal with mean 527 and standard deviation 118.
Gerald takes the ACT Assessment mathematics test and scores 27. ACT math scores are Normally distributed with mean 20 and standard deviation 3.
1. What is Elanor's standardized score?
Round to 2 decimal places.
3. What is Gerald's standardized score?
Round to 2 decimal places.
4. Assuming that both tests measure the same kind of ability, who has the higher score?
i. Gerald.
ii. Elanor.
iii. They both did equally well.
Answers
Answer:
1. Elanor's standardized score is 1.19
2. Gerald's standardized score is 0.72
3. Elanor has higher score.
Step-by-step explanation:
To compare Elanor's and Gerald's math scores, we need to standardize them and calculate their z-scores.
z score can be calculated using the formula
z=X-M over 8 where
X is the student's score
M is the mean score of the exam
s is the standard deviation of the exam
Elanor's standardized score is:
z(e) =680-554 over 106 ≈ 1.19
Gerald's standardized score is:
z(g)= 27 - 24.7 over 3.2 ≈ 0.72
Since z(e) > z(g), Elanor has higher score
Given the sequence 4, 8, 16, 32, 64, ..., find the explicit formula.
Answers
128Answer:
128
Step-by-step explanation:
vì 4+4=8
8+8=16
16+16=32
32+32=64
64+64=128
If the statement is true, type true in the space provided. If it is false, replace the underlined
word(s) with the word(s) that will make the statement true.
* The associative (associative is underlined) property is used on the following expression: 2 + 3 = 3 + 2.
Answers
Simplify the exponential expression -8 squared
Answers
Example: 4 squared= 4x4 which is 16
Answer:
-64
Step-by-step explanation:
-8^2
-8( -8)
=-64
Margaret drives 188 miles
with 8 gallons of gas. Find the unit rate
Answers
The unit rate will be "23.5 miles/gallon". In the below segment, a further solution to the given question is provided.
Given values in the question are:
Total distance,
= 188 miles
Total gas used,
= 8
Now,
⇒ The rate of gas consumption will be:
= [tex]\frac{Total \ distance}{Total \ gas \ used}[/tex]
By putting the given values in the above formula, we get
= [tex]\frac{188}{8}[/tex]
= [tex]23.5 \ miles/gallon[/tex]
Thus the above is the appropriate solution.
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find the value of the trigonometric ratio. make sure to simplify the fraction if needed
Answers
Answer:
12/5
Step-by-step explanation:
since we are dealing with the angle at Z, we consider Z also to be the center of a circle.
then 10 is the radius of this circle.
24 is tan Z in this circle with radius 10.
tan Z in the standard circle with radius 1 is simply 1/10 of the tan Z in the circle with radius 10.
so, tan Z = 24/10 = 12/5
n eight-sided die, which may or may not be a fair die, has four colors on it; you have been tossing the die for an hour and have recorded the color rolled for each toss. What is the probability you will roll a blue on your next toss of the die
Answers
Answer:
The answer is "21%".
Step-by-step explanation:
[tex]\to 26 + 20 + 29 + 49 = 124\\\\=\frac{26\ \text{brown times}}{124 \ \text{total times}} \\\\= \frac{26}{ 124} \\\\ = 0.209677 \\\\[/tex]
Calculating the percentage:
[tex]= 20.9677 \times 100\\\\=20.9677\% \approx 21\%[/tex]
There are 25 peanut candies in a bowl. 4 red, 3 orange, 4 yellow, 5 green, 6 blue and 3 brown. what is the probability of randomly choosing a blue candy from the bowl?
Answers
Answer:
6/25 or 24%
Step-by-step explanation:
Answer:
6/25, 0.24, or 24% chance
Step-by-step explanation:
Hi there!
We're given that:
⇒ There are 25 peanut candies in total
⇒ 6 out of the 25 candies are blue
To find the probability of randomly choosing a blue candy from the bowl, divide 6 by 25:
6/25 = 0.24 = 24%
I hope this helps!
Translate into an algebraic expression:
n-1 increased by 110%
Answers
Answer:
Step-by-step explanation:
(n-1)1.1
