Answers
to find the hypotenuse on the given triangle
divide the given height ( 3sqrt(2) ) by the sin of the given angle (45)
3sqrt(2) / sin 45 = 6
answer is B. 6
The sides of a right-angle triangle are equal when the angle = 45°
[tex] a^2 = b^2 + c^2 \\ a^2 = (3 \sqrt{ 2 })^2 + (3 \sqrt{ 2 })^2 \\ a^2 = 9 \times 2 + 9 \times 2 \\ a^2 = 36 \\ a = \sqrt {36} = 6 [/tex]
Method 2:
(Optional)
Using TOA CAH SOH method
Where:
TOA is Tan θ = Opposite/Adjasent
CAH is Cos θ = Adjasent/Hypotenuse
SOH is Sin θ = Opposite/Hypotenuse
You have an angle of 45° and OPPOSITE the angle is a known length.
These are the 2 information we know.
We need to find the third information, which is the HYPOTENUSE.
Notice the capatialised words start with the letter O ans H?
Find in the TOA CAH SOH the corresponding letters, in this case SOH.
SOH is sin θ = opposite/hypotenuse
Simply substitude in the values and find the hypotenuse!
sin 45° = (3√2)/ hypotenuse
hypotenuse = (3√2) / sin 45° = 6
Answer is B.
And there you go! Both methods can be used and gives the same answer.
However the limitations to method 2 are:
1. It must be a right-angle triangle
2. An angle and a side must be given.
If you think method 2 is too confusing, stick to method 1.
Good luck!
Related Questions
During the 2005 football season, Team Tackle beat Team Sack by 5 points. If their combined scores totaled 89, find the individual team scores.
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A bakery makes donuts at the rate of 225 per hour. How long will it take the bakery to fill an order of 500 donuts?
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I hope you found this helpful! C:
It will take them ~2.22 hours to make 500 donuts.
Doris put $4000 in a 2-year CD paying 6% interest, compounded monthly. After 2 years, she withdrew all her money. What was the amount of the withdrawal?
a. 4000.00
B. $4214.41
C. $4508.64
D. $4448.13
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What is the length of the hypotenuse of an isosceles right triangle with an area of 32?
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factor the trinomial x^2 - 16x +63
Answers
x^2 - 16 x + 63
The factors of 63 that sum to -16 are -7 and -9. So, x^2 - 16 x + 63 = (x - 7) (x - 9):
Answer: (x - 7) (x - 9)
Karen's penny bank is 1/3 full. After she removes 240 pennies, it is 1/9 full. How many pennies can Karen's bank hold?
Answers
2/9 of the capacity if 240 pennies
2/9 * x=240
x=240*(9/2)=1080
the penny bank can hold 1080 pennies
The difference between the bank being 1/3 and 1/9 full equals 240 pennies, so 1/9 of the bank's capacity equals 120 pennies. So, Karen's bank can hold a total of 1080 pennies.
Explanation:This is a mathematics problem dealing with fractions and subtraction. From the problem, we understand that after Karen removes 240 pennies, the bank is 1/9 full from previously being 1/3 full. So, the difference between 1/3 and 1/9, which is 2/9, accounts for the 240 pennies that were removed.
To find out the total capacity of the penny bank, you need to consider that 1/9 (the fraction representing the bank's fill level after removal of the 240 pennies) is equivalent to 120 pennies (half of 240, as 2/9 of the capacity is 240 pennies). This means that the total capacity of the bank (comparable to 9/9 of the fraction) is 120 pennies times 9, which equals to 1080 pennies.
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Solve the equation the square root of the quantity x minus 6 plus 2 equals 6 for the variable. Show each step please. Remember the X - 6 is under a square root sign
Answers
sqrt(x-6) = 4
sqrt(x-6) squared = 4 squared
x-6 = 16
x = 10
How to find slope when there is the y intercept and x-intercept?
Answers
[tex] \frac{rise}{run} = \frac{y2 - y1}{x2 - x1} [/tex]
that's the equation used to find your slope
Example:
(4,2) (8,6) let's say those are the points you pick from the line
so then you subtract 6-2=4 (6 is your y2 and 2 is your y1)
then subtracts 8-4=4 (8is your x2 and 4 is your x1)
then your left with
[tex] \frac{2}{4} [/tex]
if you can reduce the reduce in this case you can which leaves you with
[tex] \frac{1}{2} [/tex]
and that's how you find the slope
A triangle has three different integer side lengths and a perimeter of 20 units. What is the max length of any one side?
Answers
Final answer:
Using the Triangle Inequality Theorem and given a perimeter of 20 units for a triangle with integer side lengths, the maximum length of one side is found to be 15 units.
Explanation:
To determine the maximum length of one side of a triangle with integer side lengths and a perimeter of 20 units, we must apply the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Given a perimeter of 20 units, if we denote the longest side as x, and the other two sides as y and z, we must satisfy two conditions:
x + y + z = 20 (perimeter condition)
x < y + z (Triangle Inequality Theorem)
Since the triangle has different integer side lengths, the largest x can be is when y and z are consecutive integers because this allows for the largest possible x. If we try the smallest integers, 1 and 2, for y and z, their sum is 3. To satisfy the triangle inequality, the largest possible integer for x would be 20 - 1 - 2 = 17. However, this does not satisfy the inequality x < y + z, because 17 is not less than 3.
Next, we increase y and z to 2 and 3, respectively, which sums up to 5. Thus, for x, we have 20 - 2 - 3 = 15. Since 15 is less than 2 + 3, it satisfies the condition required by the Triangle Inequality Theorem. Therefore, the maximum length of any one side of the triangle is 15 units.
Which inequality represents this sentence? Ten minus three is greater than one plus two.
Answers
One plus two ⇒ 1 + 2
Greater than use the symbol >
Ten minus three greater than one plus two
10 - 3 > 1 + 2
7 > 3
How to find the distance between two lines in 3d?
Answers
Answer:
Step-by-step explanation:
Which graph represents the inequality y<−1+2x?
Answers
N a contest, a total of $12,000 was divided among the first, second, and third-place winners in the ratio of 3 to 2 to 1, respectively. how much did the first-place winner receive
Answers
The first Winner
3/6 × 12,000 = $6,000
The Second Winner
2/6 × 12,000 = $ 4,000
The Third Winner
1/6 × 12,000 = $2,000
How to solve nonlinear equations using iteration method?
Answers
A pizza parlor sold 38mc005-1.jpg pizzas during a dinner hour. If each pizza contained 8 slices, how many slices of pizza were sold?
The options are
Answers
38 pizzas times 8 slices each =
38 *8 = 304 slices total
Which point is an x-intercept of the quadratic function
f(x) = (x – 8)(x + 9)?
Answers
x-intercept means f(x) = 0
(x-8)(x+9) = 0 ⇒ x = 8 or x = - 9
There are two points which are x-intercepts. They are (8,0) and (-9,0).
What is the maximum length possible for her blanket?
Answers
It looks like you are missing some information
Answer: c: 60
Step-by-step explanation:
i did the test
Astronauts use a tool in space that weigh 5 ounces on Earth. How many grams does the tool weigh? Round your answer to the nearest hundredth.
Answers
the key here would be
1 oz. = 28.35g or 1 oz. = 28 g
Answer: 141.75
Step-by-step explanation: Yw future edge users
Emma read the statement “the quotient of six and a number, x, is the same as negative two times the difference of x and 4.5.” She translated it as shown below.
Answers
Emma should have used division to represent the quotient of six and x, and she should have used parentheses to show that -2 is multiplied by (4.5 - x). Hence the correct options are 1 and 5.
Emma made two errors in translating the statement "the quotient of six and a number, x, is the same as negative two times the difference of x and 4.5." First, instead of representing the quotient of six and x, she incorrectly wrote 6x, which implies multiplication rather than division. The correct representation should be 6/x.
Second, Emma failed to use parentheses to show that -2 is multiplied by the difference of x and 4.5. The correct expression should be -2(x - 4.5) to ensure proper order of operations. These errors impact the accuracy of the translated equation, and correcting them would yield a more faithful representation of the original statement. Hence the correct options are 1 and 5.
Complete question:
Emma read the statement "the quotient of six and a number, x, is the same as negative two times the difference of x and 4.5." She translated it as shown below 6x=-2x-4.5 What errors did Emma make? Select two options
She should have used division to represent the quotient of six and x.
She should not have included an equal sign.
She should have used parentheses to show that -2 is multiplied by (x-4.5).
She should have subtracted the difference (x-4.5) from -2.
She should have used parentheses to show that -2 is multiplied by (4.5-x).
Emma made the following errors in her translation:
E. She should have used parentheses to show that -2 is multiplied by (x-4.5). Emma’s equation, 6x = -2x - 4.5, lacks parentheses around the expression (x-4.5). To correctly represent the difference of x and 4.5 being multiplied by -2, she should have written -2(x-4.5).
D. She should have subtracted the difference (x-4.5) from -2. Emma’s equation does not correctly account for the subtraction of the difference (x-4.5) from -2. The correct equation should be 6x = -2(x-4.5).
The other options are not relevant to Emma’s specific errors in translating the statement.
Emma made the following errors in her translation:
E. She should have used parentheses to show that -2 is multiplied by (x-4.5). Emma’s equation,
6x = -2x - 4.5, lacks parentheses around the expression
(x-4.5). To correctly represent the difference of x and 4.5 being multiplied by -2
, she should have written
-2(x-4.5)
.D. She should have subtracted the difference(x-4.5) from -2
. Emma’s equation does not correctly account for the subtraction of the difference
(x-4.5)
from
-2
The correct equation should be
6x = -2(x-4.5)
Complete question:
Emma read the statement "the quotient of six and a number, x, is the same as negative two times the difference of x and 4.5." She translated it as shown below 6x=-2x-4.5 What errors did Emma make? Select two options
A. She should have used division to represent the quotient of six and x.
B. She should not have included an equal sign.
C. She should have used parentheses to show that -2 is multiplied by (x-4.5).
D. She should have subtracted the difference (x-4.5) from -2.
E. She should have used parentheses to show that -2 is multiplied by (4.5-x).
The admission fee at an amusement park is $2.00 for children and $5.60 for adults. On a certain day, 352 people entered the park, and the admission fees collected totaled 1280 dollars. How many children and how many adults were admitted?
Answers
What would '6 meters to 60 meters' be in a ratio
Answers
Explain how to write and evaluate an algebraic expression that represents the situation. The blueberries were divided equally into six bowls. Evaluate when b = 210.
Answers
The variable is the number of blueberries, the operation is division, and the constant is 6. Write the division expression as the fraction, b/6 . To evaluate, substitute 210 in for the variable, b, and simplify. 210 divided by 6 is 35. So each bowl has 35 blueberries.
The algebraic expression can be written in terms of the variable b and and evaluated as b/6 = 210/6 = 35
According to the question;
The blueberries were divided equally into six bowls;Hence, the algebraic expressions is;
b/6where, b = total number of blueberries
Hence, when b= 210
The number of blueberries in each bowl is; 210/6 = 35
Read more on Algebraic expressions;
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Vectors...
Let u = <-3, -5>, v = <-3, 1>. Find u + v.
Answers
-5 + 1 = -4
vector = < 0,-4 >
Answer:
u + v = <-3 + -3, -5 + 1> = <-6 , -4>
u + v = <-6 , -4>
Step-by-step explanation:
I hope this helped you.
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A rectangle has length x+9 and width 2x-1 what are the areas of the rectangle
Answers
a=(x+9)(2x-1) <--- Use FOIL
a=2x²-x+18x-9
a=2x²+17x-9
Hope I helped :)
Complete the equation of the line through (4,-8) and (8,5).
Use exact numbers.
y=_______ Topic:
Slope-intercept from two points.
Answers
y = mx + b
b= y - mx
b = -8 - (13/4) (4)
b = -8 -13
b = -21
equation
y = 13/4x - 21
The equation of the line that passes through (4, -8) and (8, 5) in slope intercept form is y = 13 / 4 x - 21
Slope intercept form of a lineThe slope intercept form of a line is represented as follows;
y = mx + b
where
m = slopeb = y-interceptTherefore,
(4, -8) and (8, 5)
m = 5 + 8 / 8 - 4
m = 13 / 4
Therefore, using (8, 5)
5 = 13 / 4(8) + b
5 = 26 + b
b = 5 - 26
b = -21
Hence, the equation is as follows:
y = 13 / 4 x - 21
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The function f(x) is graphed on the coordinate plane. What is f(−4) ?
Answers
y = 4 where x = -4.
That's the same as saying: "what is the y-value when x = -4?)
f(-4) = y = 4
Consider the equation below. log4 (x+3)=log2 (2x). Which system of equations can represent the equation?
Answers
[tex]log_{4} (x+3) = \frac{log_{2} (x+3)}{log_{2}4} [/tex]
Therefore, given
log₄(x+3) = log₂(2x), obtain
[tex] \frac{log_{2}(x+3)}{log_{2}4}=log_{2} (2x) \\ log_{2}(x+3) = log_{2}4 log_{2}(2x) \\ x+3 = (2x)^{log_{2}4} [/tex]
Because
log₂4 = log₂ 2² = 2 log₂ 2 = 2, therefore
x + 3 = (2x)² = 4x²
4x² - x - 3 = 0
This factorizes into
(4x + 3)(x - 1) = 0
Answer:
4x² - x - 3 = 0
or
4x + 3 = 0, and
x - 1 = 0
Which ordered pairs lie on the graph of the exponential function f(x)=4(5)2x?
Select each correct answer.
(−1,4/25)
(0,0)
(1,4)
(2,2500)
Answers
Please help me asap
It's due tomorrow
Answers
-15 < 3n <= 6
-5 < n <= 2
n is an integers and must be greater than -5 and can be as great as 2.
n can be -4, -3, -2, -1, 0, 1, 2
After 6 years, what is the total amount of a compound interest investment of $35,000 at 4% interest, compound quarterly?
Round to the nearest cent.
Answers
1.06 is the mutiplier.
A=35000(1+1/100)^4×6
A=$44440.7127
A=$44441