Answer:
12√2
7√3
Step-by-step explanation:
The length of the hypotenuse of a 45°-45°-90° triangle with a leg of 12 is 12√2 and the length of longer leg is 7√3 for 30°-60°-90° triangle.
What is Right Angled Triangle?Right angled triangle are those triangle for which one of the angle is 90 degrees.
Ratio of the sides of a 45°-45°-90° triangle is 1 : 1 : √2.
That is,
If sides opposite to 45° = x, then the side opposite to 90° = √2 x
That is, length of the hypotenuse = √2 x
Given length of a leg = 12
Length of the hypotenuse = √2 × 12 = 12√2.
Ratio of the length of sides of 30°-60°-90° triangle is 1 : √3 : 2.
That is,
Length of side opposite to 30° = x
Length of side opposite to 60° = √3 x
Length of side opposite to 90° = 2x (Hypotenuse)
We have to find the longer leg, that is √3 x.
Length of hypotenuse = 14
2x = 14 ⇒ x = 7
Length of longer leg = 7√3
Hence the lengths are 12√2 and 7√3.
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You put $1000 in a savings account. The account earns 5% simple interest per year. How many years will the money need to remain in the savings account in order to earn $200 in interest?
Answer:
Im not sure but i think it is 30.
Step-by-step explanation:
Over the last three evenings, Ivanna received a total of 116 phone calls at the call center. The third evening, she received 4 times as many calls as the first
evening. The second evening, she received 10 fewer calls than the first evening. How many phone calls did she receive each evening?
Answer:
first evening = 21 phone calls
second evening = 11 phone calls
third evening = 84 phone calls
Step-by-step explanation:
Total phone calls = 116
Let
Number of calls in the first evening = x
The second evening = x - 10
The third evening = 4x
Total phone calls = first evening + second evening + third evening
116 = x + (x - 10) + 4x
116 = x + x - 10 + 4x
116 + 10 = 6x
126 = 6x
x = 126 / 6
x = 21 phone calls
Number of calls in the first evening = x
= 21 phone calls
The second evening = x - 10
= 21 - 10
= 11 phone calls
The third evening = 4x
= 4(21)
= 84 phone calls
a) Work out angle x.
x
55°
b) Write down the value of angle y, giving a reason for your answer.
y =
67°
Answer:
math is hard for me but yeah a good place to find answers is here or ggl maybe search on gg and the at the end put answer key i do that a lot hope my
Step-by-step explanation:
explanation helps
Each square is one square unit. Sienna uses the same square units to draw a 6 x 2 rectangle and says that it has the same area as the 3 x 4 rectangle. Is she correct?
Answer:
Yes, Sienna is correct because 6 times 2 is 12 and 3 times 4 is 12.
What is the slope in th
y=x + 3
Answer:
1
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
The slope is 1 which is times to the variable x. When there is x by itself then remember that there is a 1 times to the x.
Hope this helps, thank you !!
6 over square root 3
The side of a box has length x feet, and another side has length (x-7) feet. What value of a would produce an area of 18 square feet?
Answer:
x=9
Step-by-step explanation:
(9-7) = 2
9 times 2 = 18 square feet
Value of x is 9 , -2
Given that;
Length of box = x feet
Width of box = (x - 7) feet
Area of box = 18 square feet
Find:
Value of x
Computation:
Area of rectangle = Length × Width
Area of rectangular box = x × (x - 7)
x² - 7x = 18
x² - 7x - 18 = 0
Using factorisation;
x² - 7x - 18 = 0
x² - (9 - 2)x - 18 = 0
x² - 9x + 2x - 18 = 0
x(x - 9) + 2(x - 9) = 0
(x - 9)(x + 2) = 0
So,
x = 9, x = -2
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The solution to a system of linear equations is (0,4) one of linear equations in the system is y=8x+4
Answer:
(-1/2, 4)
Step-by-step explanation:
Get the x intercept. The x intercept occurs at when y = 0
0 = 8x + 4
-8x = 4
x = 4/-8
x = -1/2
Get the y intercept
y intercept occurs at x = 0
y = 8(0) + 4
y = 0+4
y = 4
Hence the required solution is (-1/2, 4)
!!!Please Help!!! Urgent!!! -Geometry 1
FIND THE QUADRANTS OF POINT P of triangle PST, a 45°-45°-90° triangle with vertices S(3, −5) and T(−4, 2) and mangleS = 90°. P is in Quadrant I.
Answer in simplest radical form.
Please help it would be very much appreciated (:
Answer:
Coordinates of P: (10,2)
Step-by-step explanation:
Slope of ST = (2-(-5))/(-4-3) = -1
angle S = 90° so Slope of SP = 1
P(10,2)
Ella takes hours to complete a painting. Holly takes of the time that Ella takes. How long will Holly take to complete 5 paintings
Answer:
6 hours
Step-by-step explanation:
Ella takes 1 3/5 hours to complete a painting. Holly takes 3/4 of the time that Ella takes. How long will Holly take to complete 5 paintings?
Ella =1 3/5 hours = 8/5 hours
Holly = 3/4 of 8/5 hours
= 3/4 × 8/5
= (3*8)/(4*5)
= 24/20
= 6/5 hours
Number of hours : number of painting = 6/5 hours : 1 painting
How long will Holly take to complete 5 paintings
Let x = number of hours
Number of hours : number of painting = x hours : 5 painting
6/5 hours : 1 painting = x hours : 5 painting
6/5 ÷ 1 = x ÷ 5
6/5 × 1/1 = x / 5
6/5 = x / 5
Cross product
6 * 5 = 5 * x
30 = 5x
x = 30/5
x = 6 hours
It will take Holly 6 hours to complete 5 paintings
Find the missing sides of the triangle. Leave your answers in simplest radical form. Please help!
PLEASE HELP :)))
triangle similarity theorem
Answer:
x= 24 if this right there
michelle says that 4,902 x 0.001 is the same as 4,902 ÷ 10³
Answer:
Michelle is correct.
Step-by-step explanation:
The statement Michelle said is valid and correct since 10 to the power of 3 in the denominator is equivalent to 0.001 in the numerator.
Dividing by 1,000 is the same as multiplying by 0.001.
how do I explain this?
Answer:
Step-by-step explanation:
To do this, we have to prove that ∠1=∠5. We can do this using the corresponding angles theorem, which states that these two angles are congruent. Since ∠G=∠1, we can say ∠G=∠1=∠5, and as this, ∠G=∠5
What is the length of segment AB?
Answer:
Option 1
Step-by-step explanation:
Use Pythagorean theorem,
AB² = base² + altitude²
= 7² + 6²
= 49 + 36
= 85
AB =√85
Answer:
option a.
6²+7²=ab²(by Pythagoras theorem)
36+49=ab²
85=ab²
square root 85=ab
The temperature at 6 AM what is -12°F the temperature increased by 1/2°F each hour for six hours what is the temperature in degrees Fahrenheit at noon
1/2 degree x 6 hours = 3 degree increase.
-12 + 3 = -9
The temperature at noon was -9 degrees.
Thomas decides on a destination for his vacation. If he takes the train there, it will take 5 1/8 hours to get there. If he takes the plane, it will take him 2 2/3 hours
Answer: 2 11/24
Step-by-step explanation:
How many hours does the plane save?
Time taken for the train = 5 1/8
Time taken for the plane = 2 2/3
The number of hours saved will then be:
= 5 1/8 - 2 2/3
Let the lowest common multiple be 24
= 5 3/24 - 2 16/24
= 2 11/24
The number of hours saved by the plane will be 2 11/24
Solve the equation for y. Type out your steps to solve this problem as you are showing your work:
4y – 4 = 2y + 8
A shirt increased by 1/4 after the increase it was priced at £65 what was the original price of the T-shirt
Answer:
Step-by-step explanation:
A shirt increased by 1/4 after the increase it was priced at £65 what was the original price of the T-shirt
Find the slope of (0,4), (-5,2)
Answer:
-4/5
Step-by-step explanation:
A person earns $17,300 one year and gets a 5% raise in salary. Calculate the new yearly salary using a percent greater than 100.
Answer: $18,375
Step-by-step explanation:
The person was earning $17,300 and got a 5% raise.
The $17,300 represents 100% of itself. If it were to increase by 5% therefore, the new salary would be: 100 + 5 = 105%
The new salary would be 105% of $17,300.
= 17,300 * 105%
= 17,500 * 105/100
= $18,375
Consider the equation showing the distributive property.
84 +93 = 3 (28+ D)
Enter the unknown value that would make the equation true.
t
X
1
2
3
4
5
7
8
9
0
Answer:
D = 31
Step-by-step explanation:
Consider the equation showing the distributive property.
84 +93 = 3 (28+ D)
The unknown value we are asked to find is D
Hence:
84 + 93 = 84 + 3D
Collect like terms
84 - 84 + 93 = 3D
93 = 3D
D = 93/3
D = 31
Therefore, the unknown value that would make the equation true is 31
you and your want to go rock climbing. How far is the top?
Answer:
the top is far up
Step-by-step explanation: if u fall u will die
PLEASE HURRY PLEASE HURRY ILL MARK BRANLIEST
Answer:
Option 2 and option 4
Step-by-step explanation:
Andrew owns a lawn-mowing business which contracts with 43 customers each week. Last week the business earned $870.75. How many weeks will it take to earn $6095.25?
Answer:
2
Step-by-step explanation:
What is the value of the expression 44?
Please help I only have an hour! I will give brainliest!
Answer:
256
Step-by-step explanation:
The value is 256 because 4^4 is 4*4*4*4 which equals 256 :))
Hope this helps:)) Plz mark Brainliest :))
Choose the correct algebraic equation to represent: the amount decreased by $9 is $42.
Giving brainlist please help!
9 - m
9 – m = 42
m - 9
m – 9 = 42
m - 9 = 42
42 is our final answer so that should be by itself.
If something is being decreased by 9, that means that we are taking away 9 from something so it should be m - 9.
Answer:
m-9=42
Step-by-step explanation:
I'm pretty sure that m-9=42 is the correct answer because m or the amount is being decreased by 9 as 9 is being subtracted from it.
please help me i need help
Answer:
21/8 cups of vegetables per cup of cheese
round 0.0564 correct to the 1 significant figure
Answer:
0.06
Step-by-step explanation:
What is the distance between (-6,4) and (-8,6)? Choose 1 answer:
A. 2
B.3
C
[tex] \sqrt{4} [/tex]
D
[tex] \sqrt{8} [/tex]
Answer:
D
Step-by-step explanation:
We want to find the distance between (-6, 4) and (-8, 6).
We can use the distance formula given by:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]
Let (-6, 4) be (x₁, y₁) and let (-8, 6) be (x₂, y₂).
Substitute:
[tex]d=\sqrt{(-8-(-6))^2+(6-4)^2[/tex]
Evaluate:
[tex]d=\sqrt{(-2)^2+(2)^2[/tex]
Evaluate:
[tex]d=\sqrt{4+4}=\sqrt{8}[/tex]
Hence, our answer is D.