The areas of the squares adjacent to two sides of a right triangle are shown below
Answers
Answer:
The area of the square is 85 units^2
Step-by-step explanation:
Okay, here in this question, we are interested in calculating the area of the unknown square.
Kindly note that, since each of the other shapes are squares too, it means that the length of their sides is simply the square root of their areas.
Thus, the length of the squares are ;
√35 units and √50 units respectively
Now to find the area of the larger square, we employ the use of Pythagoras’ theorem which states that the square of the hypotenuse is equal to the sum of the squares of the two other sides
Let’s call the unknown length X
x^2 = (√35)^2 + (√50)^2
x^2 = 35 + 50
x^2 = 85
x = √85 units
Now as we know that the area of a square is simply the length of the side squared,
The area of the biggest square is simply (√85)^2 = 85 units^2
Related Questions
Write each of the following expressions without using absolute value.
|a−7|−|a−9|, if a<7
PLEASE HELP!!!! D:
Answers
=======================================================
If a < 7, then |a-7| = -(a-7) = -a+7 based on how absolute value functions are constructed. We're using the idea that
[tex]|x-k| = \begin{cases}x-k \ \text{ if } \ x \ge k\\ -(x-k) \ \text{ if } \ x < k\end{cases}[/tex]
Also, if a < 7, then |a-9| = -(a-9) = -a+9. This is true whenever 'a' is less than 9 for similar reasoning as above.
---------
So we have,
|a-7| - |a-9| = -a+7 - (-a+9) = -a+7+a-9 = -2
As long as a < 7, the result of |a-7| - |a-9| will always be -2.
---------
As an example, let's say a = 0
|a-7| - |a-9| = |0-7| - |0-9|
|a-7| - |a-9| = |-7| - |-9|
|a-7| - |a-9| = 7 - 9
|a-7| - |a-9| = -2
I recommend you try out other values of 'a' to see if you get -2 or not. Of course only pick values that are smaller than 7.
pls help!!!! it has been a struggle 2 find this answer!
Answers
Answer:
U to V: 5/2
V to U: 2/5
Step-by-step explanation:
Simplify the ratio of the corresponding sides.
20 in to 8 in
25 in to 10 in
30 in to 12 in
PLEASE I NEED HELP ASAP! The function below represents the interest Jessi earns on an investment. Identify the term that represents the amount of money originally invested. f(x) = 1,000(1 + 0.05)x 1,000 1 0.05 1.05
Answers
Answer:
1000
Step-by-step explanation!
The formula for the amount accrued [ƒ(x)] on an investment earning compound interest is f(t) = P(1 + r)^t where:
P = the amount of money invested (the principal)
r = the interest rate per payment period expressed as a decimal fraction
t = the number of periods
Your formula is
f(x) = 1000(1 + 0.05)^x
In comparison, we can see that the term that represents the amount of money originally invested is 1000.
Answer:
(A) 1,000
Step-by-step explanation:
i just took the test
What the answer question now
Answers
Answer:
UW=41
Step-by-step explanation:
the tangent line and the radius always meet at a right angle(90 degrees)
UWV is a right angle triangle, apply the Pythagorean theorem:
a²+b²=c² (a=40, b=9, c=UW)
40²+9²=c²
c=√40²+9²=√1600+81=√1681
c= 41
The area of a circle is 49\pi square units. What is the radius of the circle, in units?
Answers
Answer:
7
Step-by-step explanation:
The formula to find the area of a circle is pi*r^2.
We were given 49pi. This means that 49=r^2.
The square root of 49 is 7.
So our radius is 7.
Hope this helps! <3
Which of these workers is paid less than the minimum hourly wage? Bartender Electrician Hotel Manager Plumber
Answers
Answer:
It's A, the bartender
Step-by-step explanation:
the equation y=2(3^t) shows the number of infected people from an outbreak of the norovirus. the variable y represents the number of infected people and t represents time in weeks.
in how many weeks will the number if infected people reach 1458?
Answers
Answer:
Step-by-step explanation:
We have the equation
[tex] 2(3^t) = 1458[/tex]
Dividing by 2 on both sides we get
[tex] 3^t = 729[/tex]
Taking the natural logarithm on both sides we get
[tex] t \ln(3) = \ln(729)[/tex]
So t = \frac{\ln(729)}{\ln(3)} = 6.
So at 6 weeks we get 1458 infected people.
A driver decends 20 feet in the water from the boat at the surface of the lake. He then rose 12 feet and decends another 18 feet. At this point what is his depth in the water
Answers
Answer:
-26 ft or 26 ft below the surface
Step-by-step explanation:
Starting at the surface
0
Descending 20 ft
0 -20 = -20
Rose 12 ft
-20 +12 = -8
Descends 18 ft
-8 -18= -26 ft
...............................
Answers
Answer:
[tex]2 \sqrt{10} [/tex]Option C is the correct option.
Step-by-step explanation:
√ 8 • √ 5
Calculate the product
[tex] = \sqrt{40} [/tex]
Simplify the radical expression
[tex] = \sqrt{2 \times 2 \times 10} [/tex]
[tex] = 2 \sqrt{10} [/tex]
Hope this helps...
Best regards!!
PLEASE HELP!! A car manufacturer does performance tests on its cars. During one test, a car starts from rest, and accelerates at a constant rate for 20 seconds. another car starts from rest three seconds later, and accelerates at a faster constant rate. The equation that models the distance (d) in metres the first cars equation is d=1.16t^2, where t is time, in seconds, after the car starts. The equation for the second car is: d=1.74(t-3)^2. a) in context, what is a suitable domain for the graph of the system? b) at what time will both cars have driven the same distance? c) how far will they have driven at this time?
Answers
Answer:
0 ≤ t ≤ 2516.348 seconds310.0 metersStep-by-step explanation:
a) Since these are production vehicles, we don't expect their top speed to be more than about 70 m/s, so the distance functions probably lose their validity after t = 25. Of course, t < 0 has no meaning in this case, so the suitable domain is about ...
0 ≤ t ≤ 25
Note that the domain for the second car would be 3 ≤ t ≤ 25.
__
b) The graph of this system shows the cars will both have driven the same distance after 16.348 seconds.
__
c) At that time, the cars will have driven 310.0 meters.
_____
Non-graphical solution
If you like, you can solve the equation for t:
d1 = d2
1.16t^2 = 1.74(t -3)^2
0 = 0.58t^2 -10.44t +15.66
t = (10.44 +√(10.44^2 -4(0.58)(15.66)))/(2(0.58)) = (10.44+8.524)/1.16
t = 16.348 . . . . time in seconds the cars are at the same distance
That distance is found using either equation for distance:
1.16t^2 = 1.16(16.348^2) = 310.036 . . . meters
Which graph shows the solution to the system of linear inequalities? 2x -3y ≤ 12 y < -3
Answers
First solve for y in [tex]2x - 3y \le 12[/tex] to get [tex]y \ge \frac{2}{3}x-4[/tex]. The inequality sign flips because we divided both sides by a negative value.
To graph [tex]y \ge \frac{2}{3}x-4[/tex] we need to graph the boundary line y = (2/3)x - 4. This line has a y intercept of (0,-4) and another point on the line is (6,0).
Draw a solid line through (0,-4) and (6,0). The boundary line is solid because of the "or equal to" part of the inequality sign. The last part is to shade above the boundary line because of the "greater than" sign in [tex]y \ge \frac{2}{3}x-4[/tex].
---------------
As for graphing y < -3, we draw a horizontal dashed line through -3 on the y axis. The line is dashed because there is no "or equal to" here. We do not include boundary points as part of the solution set. Shade below this dashed line due to the "less than" sign.
---------------
After doing both of these things on the same xy grid, you'll get something that looks like choice C. I'm assuming choice C has a dashed line for the red region.
Answer: Choice CThe graph is image 2. (last option)
We first draw the lines 2x - 3y = 12 and y=-3. Image 1.
For 2x - 3y ≤ 12
or, 2x - 12 ≤ 3y
or, 3y ≥ 2x - 12
or, y ≥ (2x - 12)/3
we shade upwards.
For y < - 3 we shade below.
So the graph is image 2.
Learn more: https://brainly.com/question/8806877
Let f(x) = 3x + 5 and g(x) = x2. Find g(x) − f(x).
Answers
Answer:
2x-(3x+5) = -x-5
Step-by-step explanation:
2x + 0
-
3x + 5
-———————-
-x - 5
1. Following is the Receipt and Payment A/c. of a club for the year ended 31-03-2014.
Receipt ₹ Payment ₹
To Balance b/d 75,000 By Salaries 22,000
To Subscription By office expenses 8,000
2012-13 35,000 By Sports equipment
2013-14 9,50,000 (Purchased on 1-10-2013) 6,00,000
2014-15 55,000 10,40,000 By Telephone charges 12,000
To Donation 90,000 By Electricity charges 18,000
To Entrance Fees 60,000 By Travelling Expenses 6,000
To Locker rent 20,000 By 10% Fixed Deposit
To Donation for Building 1,50,000 (made on 1-07-2013) 7,00,000
By balance c/d. 69,000
14,35,000 14,35,000
Additional information:
a) Outstanding subscription for 2013-14 ₹80,000. Outstanding salaries as on 1-04-2013 were ₹2,000 and as on 31-03-2014 were ₹4,000.
b) One third of Entrance fee to be treated as General income.
c) Locker rent rate is ₹2,000 per month.
d) Depreciation on sports equipment 10% p.a.
Prepare Income and Expenditure A/c. for the year ending 31-03-2014.
Answers
Answer:
Excess of income over expenditure is ₹1,185,500.
Step-by-step explanation:
Note: The data in this question are merged together. They are therefore sorted before answering this question. See the attached pdf file for the sorted question.
The question is now answered as follows:
Question: Prepare Income and Expenditure A/c. for the year ending 31-03-2014.
Answer and explanation:
Note: See the attached excel file for the Income and Expenditure A/c. for the year ending 31-03-2014.
Both receipts and payments account and income and expenditure account are prepared by not-for-profit organizations such as charity organizations, human right campaign, clubs, etc.
Receipts and payments account is an account gives a summary of all the cash transitions, cash received and paid, that the organization engaged in during a particular period. It is similar to the cash book prepared by profit making organizations. The receipts and payments account is prepared in or to determine the balance of cash in hand or at bank or bank overdraft at the end of the period.
Income and expenditure account is an account gives a summary of all incomes and expenses of an organization during a particular period. It is similar to the trading and profit and loss account prepared by profit making organizations. The income and expenditure account is prepared in order to determine whether there is a surplus or a deficit balance during the period.
which graph represents exponential decay
Answers
Answer:
1
Step-by-step explanation:
Juanita is cutting a piece of construction paper in the shape of a parallelogram. Two opposite sides of the parallelogram have lengths (5n − 6) cm and (3n − 2) cm. A third side measures (2n + 3) cm. What are the lengths of two adjacent sides of the parallelogram? 2 cm and 2 cm 4 cm and 7 cm 7 cm and 9 cm 13 cm and 19 cm
Answers
=======================================================
Explanation:
For any parallelogram, the opposite sides are the same length. Think of a rectangle, though we could have angles that aren't 90 degrees.
(5n-6) and (3n-2) are the lengths of the opposite sides. Set them equal to one another and solve for n.
5n-6 = 3n-2
5n-3n = -2+6
2n = 4
n = 4/2
n = 2
We can use this to find the length of the opposite sides
5n-6 = 5*2-6 = 10-6 = 4
3n-2 = 3*2-2 = 6-2 = 4
We get 4 each time which helps confirm we have the correct value for n.
The opposite sides are 4 cm each. The other side is
2n+3 = 2*2+3 = 4+3 = 7
Looking at adjacent sides (sides that are next door neighbors), we see 4 cm and 7 cm.
We could easily say "7 cm and 4 cm" as order doesn't matter. Though this isn't listed so we'll go with "4 cm and 7 cm" instead.
How much material would you need to fill the following cylinder? Radius 13 in. and Height 9 in.
39π in3
117π in3
1053π in3
1521π in3
Answers
Answer:
1521 pi in^3
radius x radius x height x pi = volume
13 x 13 x 9 = 1521
We do not multiply by pi because it is already included
Hope this helps
Step-by-step explanation:
1. Robert and Casey added the following values shown below. Who solved
correctly?
ROBERT
CASEY
5 1/8+ 2 1/3 = 7 1/2
-4 1/2+ 6 3/4= 2 1/4
Answers
Answer:
Casey is correct.
Step-by-step explanation:
Robert's 5 1/8 + 2 1/3 = 7 1/2 is wrong because if 5+2 = 7, I would have to change the denominator of both fractions so they are both the same. The denominator would have to be 24. That would make the fractions 3/24 and 8/24. If you added them together, it would not be able to simplify to 1/2.
Casey's -4 1/2 + 6 3/4 = 2 1/4 is correct because —4 - 6 = 2. In order to make the fractions have the same denominator, you would have to multiply -1/2 by 2 on both numerator and denominator wich would equal -2/4. Now add -2/4 and 1/4 and you get 1/4. If my explaining is confusing, I'm sorry!☜(ﾟヮﾟ☜)
Casey is correct and he will get the correct solution.
We have given that,
ROBERT CASEY
5 1/8+ 2 1/3 = 7 1/2 -4 1/2+ 6 3/4= 2 1/4
Robert's 5 1/8 + 2 1/3 = 7 1/2 is wrong because if 5+2 = 7, I would have to change the denominator of both fractions so they are both the same.
What is the equation?A statement that the values of two mathematical expressions are equal.
The denominator would have to be 24.
That would make the fractions 3/24 and 8/24.
If you added them together, it would not be able to simplify to 1/2.
Casey is correct.
-4 1/2 + 6 3/4 = 2 1/4 is correct
because 4 - 6 = 2.
In order to make the fractions have the same denominator, you would have to multiply -1/2 by 2 on both numerator and denominator which would equal -2/4.
Now add -2/4 and 1/4 and you get 1/4.
To learn more about the equation visit:
#SPJ2
The mean height of a Clydesdale horse is 72 inches with a standard deviation of 1.2 inches. What is the probability that a Clydesdale is greater than 75 inches tall?
Answers
Answer:
0.0062
Step-by-step explanation:
Given that:
Mean (μ) = 72 inches, Standard deviation (σ) = 1.2 inches.
The z score is a measure in statistics is used to determine by how many standard deviation the raw score is above or below the mean. If the raw score is above the mean, the z score is positive and if the raw score is below the mean, the z score is negative.
The z score is given as:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
For Clydesdale is greater than 75 inches tall, x = 75 inches, the z score is:
[tex]z=\frac{x-\mu}{\sigma}=\frac{75-72}{1.2} =2.5[/tex]
The probability that a Clydesdale is greater than 75 inches tall = P(X > 75) = P(Z > 2.5) = 1 - P(Z < 2.5) = 1 - 0.9938 = 0.0062 = 0.62%
The probability that a Clydesdale is greater than 75 inches tall is 0.62%
8³=512 indique o expoente
Answers
To make lines m and n parallel, identify the measures of Angle 3 and angle 4.
Answers
Answer:
<3 = 112 degrees
<4 = 68 degrees
Step-by-step explanation:
<3 = 112 degrees (Alternate angles are congruent)
And,
<4+<3 = 180 (Angles on a straight line add up to 180)
=> <4 + 112 = 180
=> <4 = 180-112
=> <4 = 68 degrees
Solve for x. 60 10 20 120
Answers
Answer:
Hey there!
We have the angle is equal to half the measure of the arc of 120 degrees. (Just another rule for circles)
7x-10=0.5(120)
7x-10=60
7x=70
x=10
Hope this helps :)
Answer:
x = 10
Step-by-step explanation:
Tangent Chord Angle = 1/2 Intercepted Arc
7x-10 = 1/2 ( 120)
7x -10 = 60
Add 10 to each side
7x -10+10 = 60+10
7x = 70
Divide by 7
7x/7 = 70/7
x = 10
Find the equation of a line passing through the point A (14,23) and the slope 2.
Answers
Answer:
y=2x-5
Step-by-step explanation:
y=mx+c
mx=slope
In this case, the slope is already given to you which means the m=2.
y=2x+c.
The coordinates are (14, 23) and when you put -5 into c, the line goes through the coordinates (14, 23).
Hope this helps!
The athletic club at school sold raffle tickets to raise money for equipment. The club sold a total of 1050 tickets,515 to teachers and 235 tickets to staff. If the winning ticket was picked at random what is the probability of the teacher or other staff member?
Answers
Answer:
Probability of the teacher or other staff is 0.7143
Step-by-step explanation:
pr(teacher or other staff) = pr(teacher) + pr(other staff) - pr(teacher and other staff)
Total number of tickets = 1050
Number of tickets sold to teachers = 515
Number of tickets sold to other staff = 235
pr(teacher) = [tex]\frac{515}{1050}[/tex]
= 103 [tex]\frac{2}{10}[/tex]
= 0.4905
pr(other staff) = [tex]\frac{235}{1050}[/tex]
= 47 [tex]\frac{2}{10}[/tex]
= 0.2238
Since the picking of the wining ticket is mutually exclusive, then;
pr(teacher and other staff) = 0
Thus,
pr(teacher or other staff) = 0.4905 + 0.2238 - 0
= 0.7143
Gemma wants to draw a triangle with side lengths of 4 inches, 12 inches, and 17 inches. Which statement is true? This triangle exists because the sum of any two side lengths is greater than the length of the third side. This triangle exists because the sum of 4 and 12 is less than 17. This triangle does not exist because the sum of any two side lengths is greater than the length of the third side. This triangle does not exist because the sum of 4 and 12 is less than 17.
Answers
Answer:
The triangle inequality states that the sum of the lengths of the two shortest sides of a triangle must be greater than the length of the largest side. Because 4 + 12 > 17 is not a true statement, the answer is "This triangle does not exist because the sum of 4 and 12 is less than 17."
Answer:
This triangle does not exist due to the fact that the sum of 4 and 12 is less than 17
Step-by-step explanation:
The triangle formaction rule states that the 2 smaller sides must be able to combine and be greater than the greatest side.
Triangle
Sides - 3, 4, 5
3+4=7
Meaning the two smaller sides add up to because greater than 5.
Non-Triangle
Sides - 5, 6, 13
5+6=11
This means that this is not a triangle because the smaller sides ‘5 and 6’ do not add up to become greater than 13.
Gemma’s Triangle
Sides - 4, 12, 17
4+12=16
Hence, Gemma‘s figure is not a triangle because the 2 smaller sides ‘4 and 12’ don‘t add up to be greater than 17.
can someone explain how to use sin cos and tan on right angled triangles
Answers
Round this however you need to
=================================================
Explanation:
The reference angle is 56 degrees. The side 26.5 is adjacent to this angle as it is the leg closest to the angle (in contrast to the opposite leg or opposite side that is furthest from the reference angle)
The hypotenuse is d. The hypotenuse is always the longest side. The longest side is always opposite the largest angle of a triangle.
We will use the cosine ratio as it is the ratio of adjacent over hypotenuse
cos(angle) = adjacent/hypotenuse
cos(56) = 26.5/d
d*cos(56) = 26.5
d = 26.5/cos(56)
d = 47.3897287242421
You use your calculator for the last step shown above. Make sure your calculator is in degree mode. Round that value however you need to.
Here is the formula of sin cos tan :
sin x = opposite/hypotenuse
cos x = adjacent / hypotenuse
tan x = opposite / adjacent
d = hypotenuse
x = the angle known in your pic
like example if in your picture:
adjacent = 26.5
if want to find the d
cos x = adjacent / hypotenuse
cos 56 = 26.5 / d
d = 26.5 : cos(56)
d = 47.390 (3 significant figures)
and if want to find the opposite
tan x = opposite/adjacent
tan 56 = opposite/ 26.5
opposite = 26.5 × tan(56)
opposite = 39.288
-> Sorry if im wrong
On a trip mrs. ahmed drove 188 miles in 4 hours. On the return trip, she took a different route and traveled 197 miles in 4.5 hours. What was the average rate of speed for the trip?
Answers
Answer:
45.29 miles per hour
Step-by-step explanation:
Speed is the distance over time. To find the average rate of speed for a trip, we simply need to take the total distance divided by the total time.
Avg. Speed = (188 miles + 197 miles) / (4 hours + 4.5 hours)
Avg. Speed = 45.29 miles per hour
Hence the average rate of speed for the trip was 45.29 miles per hour.
Cheers.
--------------------------------------------------------
Edit: Thanks to Chegsnut36 for calculation correction
Answer:
≅45.29
Step-by-step explanation:
Hey there!
To find the average rate speed we need to add all the same number.
188 + 197 = 385
4 + 4.5 = 8.5
Now to find the average rate we do,
385 ÷ 8.5 ≅ 45.29
Hope this helps :)
Twenty increased by the product of four and a number is equal to thirty-two. Find the number.
Answers
Answer:
the number would be 3 because you start at 20 and then 4 times something will make 32 so 3 times 4 equals 12 and 20 plus 12 equals 32.
What is the slope intercept form of the equation of the line that passes through the points (7,-5) and (3,-9)?
Answers
Answer:
1
Step-by-step explanation:
y2 - y1 divided by x2 - x1
-9 + 5 = -4
3 - 7 = -4
-4/-4 = 1
Please help I’m being timed!!! System shows there is no profit made until the price reaches $95 per unit, a maximum profit at a price of $140 per unit, and no profit at a price over $185 per unit. Which graph models the function?
Answers
Answer:
4th one
Step-by-step explanation:
Daniel had 80 more stickers than Elle. He gave 1/4 of his stickers to Elle. She then gave 3/5 of her stickers to Daniel. In the end, Daniel had 92 more stickers than Elle. How many stickers did Daniel have at first? (please refrain from using algebra to solve this question as this is a primary 6 question thanks.)
Answers
Answer:
Daniel had 108 stickers at first
Step-by-step explanation:
Number of Daniel's stickers = d
Number of Elle's stickers = e
Since Daniel had 80 more stickers than Elle, d = 80 + e
e = d - 80
Daniel gave 1/4 of his stickers to Elle, Daniel is left with (d - d/4) = 3d/4
Elle now has e + d/4 = d - 80 + d/4 = (5d/4) - 80 = (5d - 320)/4
Elle now gave 3/5 of her remaining stickers to Daniel:
Elle now has:
[tex]e_{new} = \frac{5d -320}{4} - \frac{3}{5} * \frac{5d -320}{4}\\\\e_{new} = \frac{5d -320}{4} - \frac{15d -960}{20}\\\\e_{new} = \frac{25d - 1600 - 15d + 960}{20} \\\\ e_{new} = \frac{10d-640}{20}[/tex]
Daniel now has:
[tex]d_{new} = \frac{3d}{4} + \frac{3}{5} (\frac{5d - 320}{4} )\\d_{new} = \frac{3d}{4} + \frac{15d - 960}{20} \\d_{new} = \frac{30d - 960}{20}[/tex]
Daniel now had 92 more stickers than Elle
[tex]d_{new} = E_{new} + 92[/tex]
[tex]\frac{30d - 960}{20} = \frac{10d - 640}{20} + 92[/tex]
Multiply through by 20
30d - 960 = 10d - 640 + 1840
20d = -640 + 1840 + 960
20 d = 2160
d = 2160/20
d = 108