Answers
Given:
The figure of a right angle triangle with hypotenuse 10 and two angles [tex]45^\circ, 90^\circ[/tex]
To find:
The lengths of the legs.
Solution:
Two angles are given. By using the angle sum property, the third angle is:
Third angle = [tex]180^\circ-45^\circ- 90^\circ[/tex]
= [tex]45^\circ[/tex]
Base angles are equal it means the given triangle is an isosceles right triangle. So, the lengths of both legs are equal.
Let x be the lengths of both legs. Then by using Pythagoras theorem, we get
[tex]Hypotenuse^2=leg_1^2+leg_2^2[/tex]
[tex](10)^2=x^2+x^2[/tex]
[tex]100=2x^2[/tex]
[tex]\dfrac{100}{2}=x^2[/tex]
[tex]50=x^2[/tex]
Taking square root on both sides, we get
[tex]\pm \sqrt{50}=x[/tex]
[tex]\pm 5\sqrt{2}=x[/tex]
[tex]\pm 5\sqrt{2}=x[/tex]
The side length cannot be negative. So, the only value of x is [tex]5\sqrt{2}[/tex].
Therefore, the length of the both legs is [tex]5\sqrt{2}[/tex] units.
Related Questions
Figure J is similar to Figure M.
D
8
M
A
F
w
Which equation is true? (Picture is shown)
Answers
Answer:
what are the equations?
Step-by-step explanation:
Help me who here is a master at math I need your help !!
Answers
Answer:
88.4ft²
Step-by-step explanation:
oh lordy, why, why, nobody's garden is actually like this, and even if it was, you don't need to know the area, hold onto your hats:
So, we're going to assume that we can split the 10.4 evenly into the triangles and the trapezoid, so let's start with that:
10.4 ÷ 2 = 5.2 (if this is what get the whole thing wrong, I'm so sorry)
So, now we're going to do the triangle to the left of the trapezoid (remember that the formula for a triangle is base x height ÷ 2):
6 x 5.2 ÷ 2 = 15.6
So the area is 15.6ft
Now let's do the triangles under the trapezoid:
So the entire length of the under thing is 18 feet, and we take off 6 from the previous triangle, so:
18 - 6 = 12
and we're going to assume that both the triangles are equal:
12 ÷ 2 = 6
6 x 5.2 = 15.6 (at this point I realize that all the triangles are equal, welp, we just did that for nothing, anyways) now we need two of them
15.6 x 2 = 31.2
So the area of the triangles under the trapezoid is 31.2ft
Now, the trapezoid:
so we know that the top base is 4 feet, and we know that the bottom one is 12 from the triangles above us, (the formula for a trapezoid is (base + base)height ÷ 2) so:
4 + 12 = 16
16 x 5.2 = 83.2
83.2 ÷ 2 = 41.6
So the trapezoid is 41.6ft
Now we add all of our disgustingness together:
15.6 + 31.2 + 41.6 = 88.4
So, the area of the entire garden is 88.4ft²
hope this helps:)
Which of the following is false about the figure?
a. m CUD = m VUM
b. M AUV + m DUA = 180
c. m MUC - m MUD = mzCUD
d. m PUD + m VUP = m PUM + m_CUA
Answers
Answer:
d.
Step-by-step explanation:
Let's examine each statement:
Option A: m<CUD = m<VUM (CORRECT)
Rationale: vertical angles are congruent to each other.
Option B: m<AUV + m<DUA = 180 (CORRECT)
Rationale: angles on a straight line
Option C: m<MUC - m<MUD = m<CUD (CORRECT)
Rationale:
m<MUC = m<MUD + m<CUD
Subtract m<MUD from each side
m<MUC - m<MUD = m<CUD
Option D is FALSE
Rationale:
m<PUD + m <VUP = 180° (angles on a straight line)
m<PUM + m<CUA ≠ 180°
Therefore,
m<PUD + m<VUP = m<PUM + m<CUA IS FALSE.
can you guys help me pls
Answers
Answer:
D. (4 1/2, 2 1/2)
Step-by-step explanation:
Look for each point on the coordinate graph.
3 Ms. Sosa's principal gave her $350 to spend on school supplies at the beginning of the year. She bought 10 packs of dry erase markers for $9.98 each and 15 packs of pre-sharpened pencils that cost \$12.99 each . How much does she have left to spend?
A $302.03
B $644.65
C $55.35
D $295.65
Answers
Answer:The answer is D
Step-by-step explanation: Mark me brainliest please
For f(x) = -5x + 4, what is the value of x for which f(x) = 20
Answers
Answer:
- 3.2
Step-by-step explanation:
- 5x + 4 = 20
- 5x = 20 - 4
- 5x = 16
x = 16 / - 5
x = - 3.2
what is the domain of the function given below f(x)= log(x+5)-2
Answers
Answer:
Domain:
(
5
,
∞
)
,
{
x
|
x
>
5
}
Range:
(
−
∞
,
∞
)
,
{
y
|
y
∈
R
}
Step-by-step explanation:
what is 5 cm in mm. i need a simple answer. NO LINKS
Answers
50 millimeters
keystrokes
Round to one billion place. Drop the zeros.
28,436,297,825
30,943,267,101
45,831,246,935
Answers
Answer:
28,436,297,825
30,943,267,101
45,000,000,000
Step-by-step explanation:
ur welcome
A consumer group wants to know if an automobile insurance company with thousands of customers has an average insurance payout for all their customers that is greater than $500 per insurance claim. They know that most customers have zero payouts and a few have substantial payouts. The consumer group collects a random sample of 18 customers and computes a mean payout per claim of $579.80 with a standard deviation of $751.30.
Is it appropriate for the consumer group to perform a hypothesis test for the mean payout of all customers?
A. Yes, it is appropriate because the population standard deviation is unknown.
B. Yes, it is appropriate because the sample size is large enough, so the condition that the sampling distribution of the sample mean be approximately normal is satisfied.
C. No, it is not appropriate because the sample is more than 10 percent of the population, so a condition for independence is not satisfied.
D. No, it is not appropriate because the standard deviation is greater than the mean payout, so the condition that the sampling distribution of the sample mean be approximately normal is not satisfied.
E. No, it is not appropriate because the distribution of the population is skewed and the sample size is not large enough to satisfy the condition that the sampling distribution of the sample mean be approximately normal.
Answers
Answer:
E. No, it is not appropriate because the distribution of the population is skewed and the sample size is not large enough to satisfy the condition that the sampling distribution of the sample mean be approximately normal.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question:
Standard deviation larger than the sample mean means that the distribution is skewed.
By the Central Limit Theorem, when the distribution is skewed, normality is assumed for samples sizes of 30 or higher. In this question, the sample is of 18, which is less than 30, so the hypothesis test is not appropriated, and the correct answer is given by option E.
Select all expressions equivalent to 6x + 12 – 4x – 3 + 3x.
1. 2x+3x+15
2. 2x+3x+9
3. 5x+15
4. 5x+9
Select all expressions equivalent to 7x + (x + 2) + 4x.
1. 12x+2
2. 8x+2+4x
3. 11x+2
4. 7x+2+4x
Answers
Answer:
First task: 2., 5.
Second task: 1., 2.
Sheila had one gallon of milk. She used gallon of milk to make ice cream. She used another gallon of milk to make cookie dough. How much of a gallon of milk does Sheila have left?
Answers
Answer:
Step-by-step explanation:
we know that
1) Sheila had 1 gallon of milk
2) she used 1/4 of a gallon of milk ------> 1-1/4-----> 3/4 gallon left
3) she used 1/6 of a gallon of milk------> 3/4-1/6---> (6*3-4*1)/24---> 14/24
14/24-----> 7/12 gallon
4. Complete the number sentence below: *
x 102 = 2,500
Help me please !!!
Answers
10 POINTS FOR THE CORRECT ANSWER PLEASE HELP ME
Answers
Answer:
10.3
Step-by-step explanation:
6²+b²=9²
36+b²=81
b²=81-36
b²=45
b=√45
b=6.7
So CE is 6.7.
6²+b²=7²
36+b²=49
b²=49-36
b²=13
b=√13
b=3.6
so EA is 3.6
AC = CE+EA = 6.7+3.6 = 10.3
Find the surface area plz
Answers
Answer:
Step-by-step explanation:
4 triangles
Each of the 3 from the vertical ones has area
A = bh/2 = 10.12/2 = 60ft^2
The latter surface pointing down
A = bh/2 = 10.8.7/2 = 43.5 ft^2
SO summation of all
60+43.5 = 103.5 ft^2
area of circle if circumference is 132m
Answers
Answer:
1386 cm²
Step-by-step explanation:
Here's your answer!
Hope it helps :)
Answer:
1386.56m²
Step-by-step explanation:
A=C2
4π
Circumference^2/4(3.14)
What is
7(2b + 3) - 2b
Pls I need help fast
Answers
Answer:
b= = - 7/4 or -1.75
Step-by-step explanation:
14b +21 -2b=0
12b +21=0
12b= -21
b= -21/12
b= - 7/4 or -1.75
Answer:
i dont know what you neccesarily want but here are two answers b=-7/4 or -1 3/4 other answer is 12b+21
Step-by-step explanation:
first, you have to set this question equal to 0.
7(2b+3)-2b=0
now you have to distribute the 7 to everything inside the parentheses.
14b+21-2b=0
combine like terms
12b+21=0
you can stop here and take this answer if this is the one you want
now subtract each side by 21
12b=-21
divide each side by 12
b=-21/12
simplify
b=-7/4
hope this helps! have a nice day :)
What’s the volume and surface area
Answers
Surface area and volume are calculated for any three-dimensional geometrical shape. The surface area of any given object is the area or region occupied by the surface of the object. Whereas volume is the amount of space available in an object.
An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 6.5 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 26 engines and the mean pressure was 6.6 pounds/square inch with a standard deviation of 1.0. A level of significance of 0.01 will be used. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.
Answers
Answer:
The calculated value t = 0.510 < 2.7874 at 0.01 level of significance
The null hypothesis is accepted at 0.01 level of significance
The engineer designed the valve such that it would produce a mean pressure of 6.5 pounds/square inch
Step-by-step explanation:
Step:-1
Given that mean of the population (μ) = 6.5 pounds/ square inch
Given that the sample size 'n' = 26
Given that mean of the sample ( x⁻) = 6.6 pounds/ square inch
Given that the standard deviation of the sample (σ) = 1.0
t₀.₀₁ = 2.7874
Step:-2
Null hypothesis:H₀: μ = 6.5
Alternative Hypothesis:H₁: μ ≠6.5
Test statistic
[tex]t = \frac{x^{-}-mean }{\frac{S}{\sqrt{n} } }[/tex]
[tex]t = \frac{6.6-6.5}{\frac{1.0}{\sqrt{26} } }[/tex]
t = 0.510
The calculated value t = 0.510 < 2.7874 at 0.01 level of significance
Final answer:-
The calculated value t = 0.510 < 2.7874 at 0.01 level of significance
The null hypothesis is accepted at 0.01 level of significance
The engineer designed the valve such that it would produce a mean pressure of 6.5 pounds/square inch
Tyler has 2 1/3 cups of yogurt to make smoothies. Each smoothie uses 1/3 cup of yogurt. How many smoothies can Tyler make with the yogurt?
Answers
Answer:
7 smoothies
Step-by-step explanation:
change 2 1/3 into improper fraction => 7/3
divide 7/3 by 1/3:
=> 7/3 × 3
=> 7
Answer:
2 1/3
Step-by-step explanation:
Rewrite as an exponential equation.
In7 = y
Answers
Please help!!!!!!!!!
Answers
10+6+9+13+7= 45
and divide it by 5
the answer is 9
the answer is 2.74, this is easy to figure out if you want to you can look up a claculator for it
The window above Matt's front door is shaped like a triangle.
How many equal-length sides does the window have?
Enter the correct answer in the box.
PLEASE HELP
Answers
Answer:
It has 2 equal side lengths
2- Describe the cross section
Answers
The cross-section cut by the plane yields a quadrilateral with length and width equal to the length and width of the face that is parallel to the plane.
Solve for angle x help plz
Answers
Answer:
123 degrees
Step-by-step explanation:
Answer:
123°
Step-by-step explanation:
360 - 114 - 43 - 80 = 123
Two stacks of quarters are shown. Both stacks have the same amount of quarters.
The statement below uses the Cavlieri's principle to explain why the volumes of these two stacks of
quarters are equal.
the sections made by planes
from their respective bases are always equal, then the
volumes of the two solids are equal.
Which of the following pair of statements can be use to fill in the empty boxes above?
Answers
Answer:
in geometry nation its in two solids of equal altitude, parallel to and at the same distance.
Step-by-step explanation:
just got it wrong :(
Answer:
D
Step-by-step explanation:
What is the measure of the central angle that goes with the given arc measure shown below
Answers
Since the arc is equal to 90 the central angle is also equal 90
$61.60 for parts and labor rate is $30.00 per hour total cost 136.60 how many hours will.the job take
Answers
Answer: 5
Step-by-step explanation:
The area of a triangle is 92 square inches. The base is 23 inches. What is the height in inches? Do not include units in your answer.
Answers
Answer:
34,5 ?? I am not good at this but I did 92-23 that's 69 ÷ 2 = 34.5 ?
Answer:
Step-by-step explanation:
We can use the formula for the area of a triangle, to help us find the height:
Area=12⋅b⋅h
Using the formula for area, we can solve for the height by plugging in the information we have about the area and the base:
92=12⋅23⋅h
Isolate h by multiplying both sides by 2 and dividing both sides by 23.
hh=2⋅9223=8
The height is 8 inches.
10.) Find values of x and y for which ABCD must
be a parallelogram.
A x=2 y=4
B x=2 y=6
C x=2 y=16
D x=6 y=2
Answers
Answer:
B x=2 y=6
Step-by-step explanation:
For ABCD to be parallelogram, following conditions should be satisfied:
2x - 0 = x + 2 & 4y - 8 = y + 10
2x - 0 = x + 2
2x - x = 2
x = 2
4y - 8 = y + 10
4y - y = 10 + 8
3y = 18
y = 18/3
y = 6