one leg of a right triangle is 42 inches longer than the other leg, and the hypotenuse is 78 inches. find the lengths of the legs of the triangle
Answers
Answer:
use phythagoras formula of calculating right angles
a^2=b^2+c^2
42^2=b^2+78^2 (substitution + transposement)
b^2=72^2-42^2
b^2=3420 (introduce a square root both sides)
what you do on the left .you also do it on the right
b is the unknown side of the triangle
b=58.48 inched
The lengths of the legs of the right angle triangle is 30 inches and 72 inches.
What is a triangle?A triangle is a closed plane figure formed by joining three noncolinear points.
We know Pythagoras's theorem which states the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.
Given one leg of a right-angle triangle is 42 inches longer than the other leg.
Assuming the smallest leg to be x inches.
∴ The other leg is (x + 42) inches also given hypotenuse is 78 inches.
∴ (x + 42)² + x² = 78².
x² + 84x + 1764 + x² = 6084.
2x² + 84x - 4320 = 0.
x² + 42x - 2160 = 0.
As length can not be negative value of x = 30 inches.
∴ The smaller leg is 30 inches and the larger leg is (30 + 42) = 72 inches.
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Related Questions
Round 23,839 to the nearest thousand
Answers
Answer:
24, 000[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
Answer:
24000
Step-by-step explanation:
instead of 20000 you've got to round the no before it then you'll know your answer as 24000
Can someone please help me?
Answers
a) Since division by zero is undefined, we have that
[tex]13-x\neq0\Leftrightarrow x\neq13[/tex]
In interval notation
[tex]D=( -\infty ,13) \cup ( 13,\infty )[/tex]
b) Since a square root of a negative number is undefined over the Reals, we have that
[tex]9+x\geqslant 0\Leftrightarrow x\geqslant -9[/tex]
In interval notation
[tex]D=[-9,\infty )[/tex]
c)Since division by zero is undefined, we have that
[tex]2x+1\neq 0\Leftrightarrow 2x\neq -1\Leftrightarrow x\neq -\frac{1}{2}[/tex]
In interval notation
[tex]D=\left( -\infty ,-\frac{1}{2}\right) \cup \left( -\frac{1}{2} ,\infty \right)[/tex]
d) Since a square root of a negative number is undefined over the Reals, we have that
[tex]4x-3\geqslant 0\Leftrightarrow 4x\geqslant 3\Leftrightarrow x\geqslant \frac{3}{4}[/tex]
In interval notation
[tex]D=\left[\frac{3}{4} ,\infty \right)[/tex]
At the beginning of the day, a water tank contained 526.8 gallons of water. During the day, some of the water was used to water a garden. At the end of the day, the water tank contained 318.05 gallons of water.
What was the total amount of water used that day?
a. 202.75 gallons
b. 208.75 gallons
c. 208.85 gallons
d. 210.80 gallons
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!!!
Answers
Answer:
B. 208.75 gallonsStep-by-step explanation:
Let the volume of used water is x.
We have:
526.8 - x = 318.05x = 526.8 - 318.05x = 208.75Correct choice is B
please help me this is for tomorrow and i have to sleep
Answers
Answer:
The answer is C
Step-by-step explanation:
The line graph shows the line going right so it greater than or >. The circle is not colored in so there is no line under the greater than sign > so answer is C
A football team lost 9 yards on each of two consecutive plays. represent the total change as a product of sun numbers and then find the total loss.
Answers
Do the total list is -18 yards
Do the following graphs represent a mathematical function? If not, explain why.
Answers
Answer:
1 = YES
2 = NO
Both graphs pass the vertical line test, because for every x-value, there is at most one y-value.
There is no vertical “overlap” in either graph.
3/8 of a scholarship fund was 1500 find the full amount of the scholarship fund
Answers
Answer:
The full scholarship fund will be 4000
Step-by-step explanation:
When doing these types of problems I like to do this.
1500 ÷ 3 = 500 (We do this because you want to find out what 1/8 is)
Since 500 is 1/8 of the part, all you have to do is multiply 500 by 8
500 × 8 = 4000
Check all that apply.
x² - 4=0
A. X = -4
U
B. X = 2
DC. X = -2
]
D. X = -1
O E. x = 4
O F. X = 1
A
Answers
Answer:
x=2 (option B)
Explanation
x²-4=0
x²=4
x=2
Struggling with this one really need help on this one!!
Answers
Hi
P(C) is first B then C
so P ( B) = 0.4
event C is 0.2 also P( C) = 0.4 x 0.2 = 0.08
Which of the following would be the slope of the line parallel to the following:
3x+4y=8
a. 4/3
b. 3/4
c. -4/3
d. -3/4
Answers
Answer:
-3/4
Step-by-step explanation:
slope of given line:
4y=-3x+8
y=-3/4 *x+8
m=-3/4
parallel lines have equal slopes so required slope is -3/4
Dean's balcony is 3 feet wide and 9 feet long. Dean paid $2.00 per square foot to have the balcony stained. How much did he pay?
plz hurry!
Answers
Answer:
$54.00
Step-by-step explanation:
area of balcony= length * width
area= 3*9
area= 27 sq.feet
cost of 1 sq.feet=$2.00
cost of 27 sq.feet= $2.00*27
cost of 27 sq.feet= $54.00
6. Sam is buying tickets to a movie
online. The price of one ticket is $8.50.
An equation showing the total cost is
C = 8.50t +3.50 where t is the
number of tickets and $3.50 is a
convenience fee. What is the total cost
if he buys 4 tickets?
What’s the answer to this problem?
Answers
Answer: C = $37.5
Step-by-step explanation:
Given information
Price of one ticket = $8.50
Convenience fee = $3.50
Number of tickets = 4
Given expression
C = 8.50t + 3.50
Substitute the value of the ticket into the expression
C = 8.50 (4) + 3.50
Simplify by multiplication
C = 34 + 3.5
Simplify by addition
C = $37.5
Hope this helps!! :)
Please let me know if you have any questions
How does the graph change between point A and point B? On a coordinate plane, a graph increases from (0, 0) to point A and then continues to increase through B. The graph increases. The graph decreases. The graph remains constant. The graph increases, then decreases.
Answers
9514 1404 393
Answer:
the graph increases
Step-by-step explanation:
If you read your problem statement, you find it tells you the answer:
"... point A and then continues to increase through B"
That is, between points A and B, ...
the graph increases
Answer:
It's option A hope this helps
A point estimate is defined as:
a. a single value that is the best estimate of the upper range of a population parameter
b. a single value that is the best estimate of an unknown sample statistic
c. the average of the sample values
d. the average of the population values
e. a single value that is the best estimate of an unknown population parameter
pls describe:)
Answers
E
Step-by-step explanation:
cause it the best estimate of a value of an unknown parameter and E describes it best
Select all the equivalent ratios of 8:12... 7:21 20:30 5:15 2:3 16:24 and 1:3
Answers
8:12 is 2/3 and so is 16:24, 2:3, and 20:30
Step-by-step explanation:
For example (includes simplified problem solving),
8 ÷ 4 = 2
12 ÷ 4 =3
You would want to divide the numerator and denominator by the greatest common factor (GCF)
The ratio 8:12 can be reduced to its lowest terms by dividing both terms by the GCF
Therefore 8:12 is 2:3
4(x-1) =2(x+9)
2 11
Show ur work
Answers
Answer:
[tex]thank \: you[/tex]
Answer: x = 11
Step-by-step explanation:
Given
4 (x - 1) = 2 (x + 9)
Expand parentheses and apply the distributive property
4x - 4 = 2x + 18
Subtract 2x on both sides
4x - 4 - 2x = 2x + 18 - 2x
2x - 4 = 18
Add 4 on both sides
2x - 4 + 4 = 18 + 4
2x = 22
Divide 2 on both sides
2x / 2 = 22 / 2
[tex]\boxed {x=11}[/tex]Hope this helps!! :)
Please let me know if you have any questions
Please help! I'm stuck on this big ideas math problem and I can't figure it out. Need to learn this and solve ASAP! :)
Answers
Answer:
a) greater than 20
b) 20 is the estimate (round all the three other numbers and add, then subtract from 80 because 20, the average, times the four meetings is 80)
c) You can check your estimate by adding all of the numbers and subtracting the answer by 80. 18 + 17 + 21 = 56. 80 - 56 = 24
24 is closer to 20 than 30, so our estimate is correct.
Step-by-step explanation:
Tom owns a landscaping business. He charges $40 for a yard cleanup, $50 to mow a lawn, and $75 to mulch a yard. On average, it takes Tom 25 minutes for a yard cleanup, 40 minutes to mow a lawn, and 2 hours to mulch a yard. Tom's clients are Mr. Hansen, Ms. Martinez, and Mrs. Johnson. . Mr. Hansen paid $125 for lawn services this week. . Tom spent more than an hour at Ms. Martinez' house this week. • Mrs. Johnson wrote Tom a check for $165 for the week. Tom made $405 from his three clients this week.
Answers
Answer:
Ms. Martinez = Tom received $115, $75 to mulch the yard and $40 for a yard cleanup.
Step-by-step explanation:
Tom made $405 for the week from his three clients
Mr. Hansen paid Tom $125
Mrs. Johnson paid Tom $165
405-165-125=115
Ms. Martinez paid Tom $115, which meant that he would have cleaned the yard ($40) and mulch the yard ($75)
The unit amount and time for each service offered by Tom can be represented as equations. The conclusion from the given parameters are:
Mr. Hansen paid $125 to mow a lawn and to mulch a yard.Mrs. Johnson paid $165 for the three servicesMs. Martinez paid $115 for a yard cleanup and to mulch a yard.Given that:
Cost
[tex]\$40 \to[/tex] Yard cleanup
[tex]\$50 \to[/tex] Mowing a lawn
[tex]\$75 \to[/tex] Mulching a yard
Time
[tex]2\ hrs \to[/tex] Yard cleanup
[tex]40\ mins \to[/tex] Mow a lawn
[tex]2\ hrs \to[/tex] Mulching a yard
[tex]Total\ Earnings = \$405[/tex]
From the question, we understand that:
[tex]Mr.\ Hansen = \$125[/tex]
Recall that:
[tex]\$50 \to[/tex] Mowing a lawn
[tex]\$75 \to[/tex] Mulching a yard
Add up:
[tex]\$50 + \$75 = 125[/tex]
This means that Mr. Hansen paid $125 to mow a lawn and to mulch a yard.
[tex]Mrs.\ Johnson= \$165[/tex]
Recall that:
[tex]\$40 \to[/tex] Yard cleanup
[tex]\$50 \to[/tex] Mowing a lawn
[tex]\$75 \to[/tex] Mulching a yard
Add up:
[tex]\$40 + \$50 + \$75 =\$165[/tex]
This means that Mrs. Johnson paid $165 for the three services
The amount paid by Ms. Martinez is calculated as follows:
[tex]Mr.\ Hansen + Mrs.\ Johnson + Ms.\ Martinez = Total\ Earnings[/tex]
Substitute known values
[tex]\$125 + \$165 + Ms.\ Martinez = \$405[/tex]
[tex]\$290 + Ms.\ Martinez = \$405[/tex]
Collect like terms
[tex]Ms.\ Martinez = \$405 - \$290[/tex]
[tex]Ms.\ Martinez = \$115[/tex]
This means that Ms. Martinez paid $115
Recall that:
[tex]\$40 \to[/tex] Yard cleanup
[tex]\$75 \to[/tex] Mulching a yard
Add up
[tex]\$40 +\$75 = \$115[/tex]
This means that Ms. Martinez paid $115 for a yard cleanup and to mulch a yard.
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In Ted's class, students were asked to name their favorite sport. Football was the response of 1/8 of them. If 3 students said football, how many students are in Ted's class?
Answers
24 Students
If 1/8 of the total is 3, then the total is 3 multiplied by 8 = 24
Another way:
1/8= 12.5%
12..5%_____3
100%_____x
Cross multiplication
12.5x =3x100(300)
X=24
12.5% of 24 = 3
There are 24 students in Ted's class.
Given that;
In Ted's class, students were asked to name their favourite sport.
And, Football was the response of 1/8 of them.
Let's assume the total number of students in the class is represented by "x".
According to the information given, 1/8 of the class said football, which means (1/8) × x students named football.
We also know that 3 students said football.
So, we can set up the equation:
(1/8) × x = 3
To solve for x, we can multiply both sides of the equation by 8:
x = 3 × 8
x = 24
Therefore, there are 24 students in Ted's class.
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Anyone help me to solve this probability question in details. I have problems with probabilities. I will be giving the brainliest
Answers
Answer:
Step-by-step explanation:
The probability of breakdown
Concrete mixer is 1/4, dumper 1/6, and hoist 1/8.
1. All machines breakdown.
1/4 +1/6 + 1/8 = 13/24
2. 2 machines break down
CM and D 1/4 + 1/6 = 5/12
CM and H 3/8
D and H 7/24
Find the common ratio for the following sequence.
1/2, -1/4, 1/8, -1/16
1. -2
2. 1/2
3. 2
4. -1/2
Answers
Answer:
-1/2
Step-by-step explanation:
(-1/4)/(1/2)=-1/2
Convert to decimal form/ 3.1 x 10^6
Answers
Answer:
0.000036 i think it the answer
The Sunshine Cleaning service can vacuum 8 square yards of flooring every 4 minutes. Which graph includes ordered pairs that represent this relationship?
Answers
Answer:
It's the second graph, I circled it in blue
there are 5 boys to every 6 girls. if there are 385 students how many are boys?
Answers
5:6
So if we do that for 385 students the ratio would show 462 girls
Pls give me a brainliest if this helped thx
pls help with this problem
Answers
====================================================
Explanation:
Refer to the diagram below. The rectangle MATH has the diagonal MT that cuts the rectangle into two identical right triangles.
We then use the pythagorean theorem to find the length of the hypotenuse MT.
a^2 + b^2 = c^2
10^2 + 24^2 = c^2
100 + 576 = c^2
676 = c^2
c^2 = 676
c = sqrt(676)
c = 26
Segment MT is 26 cm long.
This applies to the other diagonal AH as well.
If a dilation produces a congruent figure, then the scale factor was equal to
Answers
Answer:
the answer is 1
Step-by-step explanation:
because I said so
State the domain and range of the following function.
{(1, 3), (2,7), (- 3,4), (- 2, 3), (5,4)}
Answers
Answer:
okay
Step-by-step explanation:
Range is {3, 4, 7}
The measure of L in triangle LMN is 40°. The measure of M is 78°. What is the measure of N?
Answers
Answer: 62°
Step-by-step explanation:
Total angle in a triangle = 180°
40° + 78° + < N = 180°
118° + <N =180
<N = 180 -118
<N=62°
Which equation should be used to answer “24 is 40% of what number?”
Answers
Answer:
24=40/100×x
Step-by-step explanation:
i think the equation is
24=40/100×x
24 is equal to 40 percent of a number which I have represented by x
I hope this helps
Here it is
40% of x= 24
0,4x=24
x=24/0,4
x=60
A Shape Question 5 options: 13 yd.² 314 yd.² 251 yd.² 503 yd.²
Answers
Answer:
What is question? surface area of upright part of cylinder is approx 314 sq yd. Surface area of entire cylinder is approx 471 sq yd, which isn't a choice.
Step-by-step explanation:
Assuming you're looking for surface area of cylinder (since answers are in sq units), you would need to find the area of the top and bottom circles, and the rectangle made by flattening out the upright part of cylinder.
Area of a circle is πr^2 so area of bottom is 25π and of both circles is 50π which equals approx 157.08 sq yd.
The rectangle formed from the upright part would have a width of 10 yds and a length equal to circumference of the circle. Since C = πd, C is approx 31.4yd. A = l x w so A = 31.4 x 10 or approx 314 sq yd.