Answers
Answer:
[tex]x=16.4\ y=13.7[/tex]
Step-by-step explanation:
[tex][Kindly\ refer\ the\ attachment.]\\We\ are\ given\ that,\\\triangle ABC\ is\ a\ right-triangle\ and\ has\ it's\ legs\ x\ and\ z.\\It's\ altitude\ CD\ separates\ it\ into\ two\ triangles:\\\triangle BCD\ and\ \triangle ADC,\ both\ of\ which\ are\ right-triangles.\\Now,\\The\ Pythagoras\ Theorem\ tells\ us\ that:\\'The\ sum\ of\ squares\ of\ both\ the\ legs\ is\ equal\ to\ the\ square\ of\ the\\ hypotenuse'.\\Here,\\Lets\ consider\ three\ triangles\ separately.\\[/tex]
[tex]In\ \triangle ADC\ right\ angle\ is\ at\ \angle ADC.\\Hence,\\AC\ is\ the\ hypotenuse, and\ AD\ and\ DC\ are\ it's\ legs.\\Hence,\\AD^2+DC^2=AC^2\\Or,\\9^2+y^2=x^2\\\\Lets\ take\ the\ above\ equation\ as\ E_1.[/tex]
[tex]In\ \triangle BDC\ right\ angle\ is\ at\ \angle BDC.\\Hence,\\BC\ is\ the\ hypotenuse, and\ DC\ and\ DB\ are\ it's\ legs.\\Hence,\\DC^2+DB^2=BC^2\\Or,\\21^2+y^2=z^2\\Lets\ take\ the\ above\ equation\ as\ E_2.[/tex]
[tex]Now,\\In\ whole\ \triangle ACB\ right\ angle\ is\ at\ \angle ACB.\\Hence,\\AB\ is\ the\ hypotenuse, and\ AC\ and\ BC\ are\ it's\ legs.\\Hence,\\AC^2+BC^2=AB^2\\Or,\\x^2+z^2=(21+9)^2=30^2\\Lets\ take\ the\ above\ equation\ as\ E_3.[/tex]
[tex]Lets\ now\ gather\ the\ three\ equations:\\9^2+y^2=x^2\\21^2+y^2=z^2\\x^2+z^2=30^2\\Now,\\Lets\ pair\ and\ add\ E_1\ and\ E_2.\\Hence,\\(9^2+y^2)+(21^2+y^2)=(x^2)+(z^2)\\Hence,\\81+y^2+441+y^2=x^2+z^2\\Hence,\\2y^2+522=x^2+z^2\\Considering\ E_3,\\We\ already\ know\ that,\\x^2+z^2=30^2\\Hence,\\2y^2+522=30^2\\Hence,\\2y^2+522=900\\2y^2=900-522=378\\Hence,\\y^2=\frac{378}{2}=189\\Hence,\\y=\sqrt{189}=13.7\\[/tex]
[tex]Plugging\ in\ y=13.7\ in\ E_1,\\9^2+(13.7)^2=x^2\\81+189=x^2\\x^2=270\\x=\sqrt{270}=16.4[/tex]
Related Questions
help plz!! i’ll give brainliest
Answers
Answer:
answer choice a! (16)
Step-by-step explanation:
Write a small statement to convince others of the importance of food safety
Answers
Answer:
Food is what fuels our bodies. Food is what keeps us alive, but when food is not kept fresh and safe, it can cause us to get sick or even die from food poisoning.
You spin a spinner numbered from 1 to 8 twice. Find the probability of getting a 1 on the first spin and a 2 on the second spin.
Answers
Answer:
[tex]Probability = \frac{1}{64}[/tex]
Step-by-step explanation:
The sample space of the spinner is:
[tex]Sample\ Space = \{1,2,3,4,5,6,7,8\}[/tex]
So:
[tex]n(S)= 8[/tex]
All of which have the same probability.
Required
Determine the probability of 1, then 2 when spin twice
The probability of the first being 1 is:
[tex]P(1)= n(1)/n(S)[/tex]
[tex]P(1)= 1/8[/tex]
The probability of the second being 2 is:
[tex]P(2)= n(2)/n(S)[/tex]
[tex]P(2)= 1/8[/tex]
So, the required probability is:
[tex]Probability = P(1) * P(2)[/tex]
[tex]Probability =1/8* 1/8[/tex]
[tex]Probability = \frac{1}{64}[/tex]
These two more geometric figures that are identical in shape but not in size what is it?
Answers
Answer: Congruent
Step-by-step explanation:
Two figures are congruent if they have the same shape and size. Two angles are congruent if they have the same measure. Two figures are similar if they have the same shape but not necessarily the same size.
HELP ME WITH THIS ASAP PLEASE I WILL PUT FIRST ANSWER AS BRAINLIEST!!!
Answers
Answer:
A
Step-by-step explanation:
You only need one admission ticket, so there is no need to have a variable with it. She golfed multiple rounds, so you need a variable by $6.25. You are adding the charges together so you need an addition symbol.
Hope this helps!
You will be redoing the moulding around the windows and the door of your bedroom. You have 2 windows that measure 110 cm x 65 cm, and the door measures 76 cm x 198 cm. You do not install moulding along the base of the door. Moulding costs $0.98 per foot. What will be the total cost of the moulding for this project?
Answers
Answer:
$31.26 if you could buy the exact amount necessary
Step-by-step explanation:
2[2(110)+2(65)]=windows
700 = windows
76+2(98)=door
272=door
total=972 cm=31.9 feet (you might have to buy 32 feet though)
31.9x0.98=$31.26
Solve for x: x/7 - 3 ≥ 8.
Answers
Answer:
x is more than or equal to 77
Step-by-step explanation:
Which function matches the graph?
-2
a. f(x) = -2(x - 3)2 + 1
b. f(x) - 2(x+3)2 - 1
c. f(x) = (x+3)²+2
d.
A(x) = 1/(x - 3)² - 1
Answers
Answer:
Its a or c sorry if im wrong
(hope this helps :D hehe)
Step-by-step explanation:
Answer:
Please insert a graph.
Step-by-step explanation:
If you submit a picture of the graph on here, I will see how how I can help.
1 . A birdwatcher wishes to model the number of birds arriving at a particular barn per hour.
a) State two conditions needed for a Poisson distribution to be a suitable model.
b) The expected number of birds arriving per hour is 7. Assuming the conditions for a Poisson model are met, find the probability that, in a randomly chosen hour during the day, the number of birds arriving at the barn is:
(i) fewer than 4
(ii) at least 7
(iii) exactly 9
Answers
Answer:
b I guess
what is that at the bottom?
Mr. Brown purchased tires for his car. The tires were $75 each, including tax, plus $10 for installation. Mr. Brown paid $160 for the tires and installation. Which equation can be used to find the number of tires, t, that Mr. Brown purchased?
A. t = 160 + 75(10)
B. 75 + t(10) = 160
C. 75t + 10 =160
D. 160t - 75 = 10
Could you show your work? Thanks!
Answers
Answer:
Step-by-step explanation:
The answer is C because t = 2 so 75x2=150 and 150 + 10= 160.
A chemist needs to mix 6 parts acid to 7 parts base for a reaction. If they need a total of 52mL (milliliters) of reaction, how many mL
of acid and base are needed?
Answers
Answer:
24 millilitres acid
28 millilitres base
Step-by-step explanation:
First, we need to know how many parts there are in total. We do this by adding the number of parts of acid (6) and base (7). 6+7=13
Then, divide 52 by 13 to find out how many millilitres makes up a part.
52/13=4
Then you multiply this by the number of parts for each substance.
4x6=24 millilitres acid
4x7=28 millitres base
If two tangents are inclined at 60° are drawn to a circle of radius 3cm then find length of each tangent.
Answers
5.19cm
Step-by-step explanation:
draw perpendicular from the center of the circle to produce a right angle triangle which will have 3cm and an angle of 30 degrees. use tan to find the adjacent line which is the length of the tangent.
You might need: Calculator
Raj wants to take yoga classes. There are two yoga studios that have different membership plans.
The first studio charges a fixed amount of $70 per month, and you can take as many classes as you want
for no additional charge.
The second studio charges a smaller initial fee plus an additional fee for each class taken. The monthly price
(in dollars) of the second studio as a function of the number of classes taken is given by the following table
of values:
Classes
Price (dollars)
1
35
3
45
5
55
Which studio charges more for each additional class?
Answers
Answer:
Which studio charges more for each additional charge? B
Raj wants to take 8 classes each month. Which studio is cheaper for him? A
Step-by-step explanation:
Studio one has no additional charge.
Studio two 8 classes would be 100 dollars more than the 70dollar flat fee of studio one.
anyone can help me ?
Answers
Answer:
the 4th one
Step-by-step explanation:
it shows that k is greater than 11
Simplify the expression using the distributive property:
-30x+24
—————— =
-6
Answers
Answer:
-30x+24= -6
-30(1)+24= -6
Which equation represents a proportional relationship?
y = 5x + 1
y=−5(x+1)
y=
1
5x
y=−x
Answers
Which expression is equivalent n + n - 0.24n?
Answers
Answer:
Without seeing the expressions that you can choose from, I can't tell you which one is correct, but I can tell you that n + n - 0.24n is equal to 1.76n
Jan walks 2 miles at a constant rate of 3 miles per hour and then runs 1 mile at a constant rate of 8 miles per hour.
(a) What is Jan’s average speed for the entire trip?
(b) Is the average speed in part (a) equal to the average of Jan’s two speeds?
Answers
Answer:
(a).4.36 mph
(b) No
Step-by-step explanation:
We are given that
Jan covered distance,s1 =2 miles
Speed of Jan, a=3 mph
s2=1 mile
b=8mph
a.
We have to find the Jan' s average speed for the entire trip.
Average speed =[tex]\frac{2ab}{a+b}[/tex]
Using the formula
Average speed=[tex]\frac{2(3)(8)}{3+8}=4.36mph[/tex]
b.
Average speed with two speed
Average of Jan’s two speeds
[tex]=\frac{a+b}{2}[/tex]
=[tex]\frac{3+8}{2}=5.5 mph[/tex]
[tex]4.36\neq 5.5[/tex]
Hence, the average speed in part (a) is not equal to the average of Jan’s two speeds.
Cynthia Besch wants to buy a rug for a room that is 19 ft wide and 25 ft long. She wants to leave a uniform strip of floor around the rug. She can
afford to buy 315 square feet of carpeting What dimensions should the rug have?
Answers
Answer:
13 x 158
Step-by-step explanation:
L= 2W
A= 315 sq ft^2
A= L*W
315= 2W* W
315/2= 158 = w^2
W^2= 158
W=[tex]\sqrt{158}[/tex]
W= 13
The rug should have a dimension of 15 ft wide and 21 ft long.
What is a rectangle?A Rectangle is a four sided-polygon, having all the internal angles equal to 90 degrees. The two sides at each corner or vertex, meet at right angles.
Let the length of the room be l and h be the width.
So, given that,
l = 19 ft
h = 25 ft
Let w be the width of rug,
Since Cynthia can afford to buy 315 square feet of carpeting
So, area of the rug should be given as,
l*h = 315
Now to carpet the room along its dimension, each side of the width is
w + w = 2w.
So, l =25 - 2w
h = 19 - 2w
Now, ∵ l*h = 315
Put the values we get,
(25 - 2w)*(19 - 2w) = 315
expanding we get,
4w² - 88w + 475 = 315
or, 4w² - 88w + 160 = 0
or, w² - 22w + 40 = 0
using the quadratic equation we get two solutions:
w = 2
w = 20
Since, w = 20 is greater than one of the width of the room i.e 19ft
So,we take the solution w = 2
Thus, dimensions of rug is given as,
l = 25 - 2*2 = 21 ft
h = 19 - 2*2 = 15 ft
Thus, the rug should have a dimension of 15 ft wide and 21 ft long.
To learn more about rectangle :
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The temperature outside changed from 98°F to 42°F over a period of eight days. If the temperature changed by the same amount each day, what was the daily temperature change?
Answers
Answer:
ummmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm
Step-by-step explanation:
Answer:
7° each day
Step-by-step explanation:
98-42=56. 56 is the amount that dropped within those 8 days. Divide 56 by 8 and you get 7
13 points so please help meee with a and b!
Answers
Answer:
(a)
$24.10,
$18.20,
$15.25,
$9.35,
$0.50,
(b)
b=30-2.95g
Step-by-step explanation:
Answer: a) 2:24.10 4:18.20 5:15.25 7:9.35 10:.50
b) b=30-2.95g
What are the scale factor and center of the dialtion?
Will mark brainliest
Answers
Answer:
.
Step-by-step explanation:
Scale factor ⅓
help pls I will give brainliest to whoever answers best
Answers
Step-by-step explanation:
its 60
Please help i will give brainly FIRST PERSON TO GET IT RIGHT EVERY TIME I POST A QUESTION YOU WILL ALWAYS GET BRAINLY
Answers
Hope this helped
5x-9y=-26 and -2x+3y=11 combing the equations
Answers
5x - 2x = 3x
-9y + 3y = -6y
-26 + 11 = -15
helppp! doing test!!
Answers
Answer:
Can you show more of the question?
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Basically, division. divide 85.60 by 4 in order to get each hour.
Stephanie is saving money to buy a bike that costs $189. She has saved $99 so far. She plans on saving $10 each week. How many weeks will it take for her to save enough money for the bike? Write an equation. Use x to represent the number of weeks
Answers
Answer:
189=99+10x, it will take her 9 weeks to save up enough
Step-by-step explanation:
Answer:
189 = 99 + 10x
Step-by-step explanation:
189 = 99 + 10x
-99 -99
90 = 10x
/10
9 = x
The difference quotient is used to determine the average rate of change of g(x) = 5x2 + 6x on the interval from x = 1 to x = 5. Which statement describes the process correctly?
Answers
Answer:
C. The difference quotient is 10x+5h +6, so the average rate of change is 10(1)+ 5(4) + 6 = 36
Step-by-step explanation:
The statement is the difference quotient is 10x+5h +6.
What is average rate of change of function?It is a measure of how much the function changed per unit, on average, over that interval. It is derived from the slope of the straight line connecting the interval's endpoints on the function's graph.
Given function:
g(x) = 5x² + 6x
interval is x= 1 to x=5
so, the average rate of change is
=10(1)+ 5(4) + 6
= 36
Learn more about average rate of change here:
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i need help asapp i’ll be giving a brainliest to the person with the correct answer
Answers
Are they correct? Is that the question? Well, the first one is correct because Slope (m) = -6/1 =-6
Equation of the line:
y = -6x + 15
When x=0, y = 15
When y=0, x = 2.5
and the other one:
Is incorrect and the correct answer is A because y= 7.5x -2. 7.5 is positive, the slope, and -2 is the y-intercept. Its negative.
Triangle A is the pre-image in a translation, and triangle B is the image, as shown below.
On a coordinate plane, triangle A is shifted 6 units to the right to form triangle B.
How was triangle A translated?
four units left
four units right
six units left
six units right
Answers
Answer: D is correct
Step-by-step explanation: Got a 100% on my test
The translation of triangle A is (d) six units right
The translation from triangle A to BTranslation involves changing the position of a shape
From the question, we understand that:
Triangle A represents the pre-imageTriangle A is shifted to the right by 6 unitsThis means that, triangle A was translated by 6 units to the right
Hence, the true statement is (d)
Read more about translation at:
https://brainly.com/question/4289712