Answer:
11
Step-by-step explanation:
2x + x + x + 13 = 57
4x + 13 = 57
4x = 57-13
4x = 44
44/4 = 11
x = 11
The hypotenuse of a 30°-60°-90º triangle is 8 units and one leg is 4 units. What is the length of the other leg?
Answer:
The length of the other leg is [tex]4\sqrt{3}[/tex]
Step-by-step explanation:
There are 2 ways to solve this.
1) Pythagorean theorem (the harder way)
A 30-60-90 triangle is a right triangle, and therefore you can use the pythagorean theorem to calculate the measure of 1 side given the 2 others.
[tex]a^2+b^2=c^2\\a^2+4^2=8^2\\a^2+16=64\\a^2=48\\a=\sqrt{48}\\a=6.9282...[/tex]
That's one solution, but its not a very nice number or the exact answer you probably want. Instead, you can simplify the root.
First, you need to factor 48:
[tex]2*24=48\\2*12=24\\2*6=12\\2*3=6[/tex]
The prime factors of 48 are:
[tex]2*2*2*2*3=48[/tex]
Then, you need to find perfect squares:
[tex](2*2)*(2*2)*3=48\\2^2*2^2*3=48[/tex]
And finally, you can remove those like this:
[tex]\sqrt{48} =\sqrt{2^2*2^2*3} \\\sqrt{48} =2\sqrt{2^2*3} \\\sqrt{48} =2*2\sqrt{3} \\\sqrt{48} =4\sqrt{3}[/tex]
The length of the other leg is [tex]4\sqrt{3}[/tex]
2) 30-60-90 triangle relationships (the easier way)
There are 4 simple rules here:
Short leg × 2 = hypotenuseShort leg × √3 = long legLong leg ÷ √3 = short legHypotenuse ÷ 2 = short legThey're actually pretty easy to remember. You can multiply the short leg by 2 or √3, and 2 is greater than √3 (check a calculator). The hypotenuse of course is also longer than the long leg, so you have to multiply by 2 to get it. Then for the long leg, the only option is to multiply by √3. The same works in reverse for both of those.
Here, we have the short leg. You can check that with the pythagorean theorem again to be sure:
[tex]a^2+4^2=8^2\\a^2+16=64[/tex]
Because 16 is less than half of 64, a has to be the longer leg. Using the rules above, multiply the short leg by √3 to get the answer:
[tex]4 * \sqrt{3} \\4\sqrt{3}[/tex]
Same answer as the previous method.
Please help me out with this Math sheet. Thanks
Answer:
1. acute
2. obtuse
3. right
4. acute
5. straight
6. obtuse
7. acute
8. obtuse
9. straight
10. ∠ EAD , ∠ CED , ∠ BCE , ∠ BEA , ∠EBC
11. ∠CDA , BCD
12. ∠AED ,∠BEC
13. ∠ AEC, ∠ BED
14. ∠ EAU , ∠EUI , ∠IUO , ∠OAE
15. ∠ EUO , ∠IUA
16. ∠AUO , ∠EIO
help plz
find the size of unknown angle in the flowing figures
Answer:
it is 95 degrees because it is a vertically opposite angle
Mr. Haynes wants to expand his rectangular living room to make room for an indoor theater system. He asks the contractor to make the width of the room 5 feet longer and he wants the length of the room to be 5 feet longer than twice the width. When finished the new room will have a perimeter of 140ft around. The new dimensions of the room will be
Step-by-step explanation:
check the image for detailed solution
Please help me :/!!!!
Answer:
(3, 9)
Step-by-step explanation:
Set 3x and 2x+3 equal to each other forming an equation in x.
3x=2x+3
Solve for x.
x=3
Substitute the given value of x into the equation y=3x.
y=3x3
Solve for y.
y=9
(x, y) = (3, 9)
Hope this helps :)
Two functions f and g are defined on the set R, of real numbers by f : x 2x 3 and
x g : x 1 3x . Find the inverse of the function f and the domain of gof.
Answer:8
Step-by-step explanation:
A local hamburger shop sold a combined total of 637 hamburgers and cheeseburgers on Wednesday. There were 63 fewer cheeseburger sold than burgers. How many hamburgers were sold on Wednesday?
¿Qué fuerza media se requiere para que un objeto de 2 Kg aumente su velocidad de 5 m/s a 12 m/s en una distancia de 8 m?
Answer:
14.87
Step-by-step explanation:
Para conocer cual es la fuerza que necesita el cuerpo para aumentar su velocidad de 5 m/s a 12 m/s en 8 m
Necesitamos conocer la aceleración y para conocer la aceleración debemos saber cuanto tiempo tarda en recorrer los 8m
Vf = Vo +a(t)
12 = 5 +a(t) -------> Vamos a despejar el tiempo.
t = 7/a
X= Vo(t) +1/2a(t²)
X= 5(7/a)+1/2a( 7/a )²
8 = 35/a+49/2a
a = 7.43 m/s²
Ahora que conocemos la aceleración podemos calcular la fuerza como:
F = m*a
F = 7.43 * 2 kg.
F = 14.87
brainiest to whoever correct
Answer:
y = 138
Step-by-step explanation:
90 + 4x + 3x + 6 = 180
96 + 7x = 180
7x = 84
x = 12
———
3(12) + 6
36 + 6
42
———
180 - 42 = 138
a scale diagram, 0.125 inch represe
5 feet. How many inches represent
pot?
0.001
0.01
0.1
0.12
Math
Answer:
the scale diagram is 9.12
If each rabbit consumes 10 pounds of rabbit food each year, then how much rabbit food is consumed in 10 years
Answer:
100 pounds in 10 years
Step-by-step explanation:
10 pounds per year for 10 years
We simply multiply 10 pounds to 10 years to get 100 pounds
-Chetan K
How many solutions does this equation have
-4(5-3x)=12x+20
A) no solution
B) one solution
C) two solutions
D) infinitely many solutions
Answer:
A) no solution
Step-by-step explanation:
It’s A Contradiction
Answer:
its one solution
Step-by-step explanation:
-20+12
Simple Arcs and Sectors question attached. First person to answer correctly gets 50 points. ONLY ANSWER 1ST QUESTION Good Luck!! Spam comments will be blocked and accounts reported.
Answer:
θ = 60º
Step-by-step explanation:
s = (θ/180)πr
Solving for θ yields
θ = (180s) / (πr)
--------------------------------
For the 1st one
θ = (180 * 12.56) / (π * 12)
θ = 60º
A shirt cost $24.92 with 10% discount if the sales tax is 6.35% how much will the shirt cost?
5. The coordinate increments from (4, 3) to (9, 7) are :
6. The coordinate increments from (- 6, - 4) to (12, - 9) are:
7. The coordinate increments from (10, - 7) to (14, - 9) are: are:
8. The coordinate increments from (- 47, - 10) to ( 17 , 8) are:
Answer:
the correct answer is 8
Step-by-step explanation:
Answer:
5. Is "+" 6. is "-" 7. is "+" 8. is "-"
Step-by-step explanation:
Dependent Task:
Directions: Write the place value and the value of the underlined digit.
Number PLACE OF VALUE VALUE
1. 0.345 _____________ _____
2. 0.3469 _____________ _____
3. 0.6ó54 _____________ ______
(UNDERLINED DIGIT)
1. 5
2.3
3.4
please
Answer
Use your mind
Nobody wants to help you, especially since you are no help to others.
41/2≤1.2x what is the answer
Answer:
i can help just meassage me
Step-by-step explanation:
ok thak u
Use properties to evaluate 1/3 (-5 ÷ 1/2 ) 1/4?
A. - 5/2
B. 5/8
C. - 5/8
D. 5/2
is 0.667 elastic or inelastic?
Answer:
inelastic is the answer
keep safe
Find the missing value using the given information
(4,p), (p,-3), m=5/3
Answer:
p = 11/8
Step-by-step explanation:
We are trying to find the slope, so use the slope formula
m = ( y2-y1)/(x2-x1)
5/3 = ( -3 -p)/ ( p-4)
Using cross products
5(p-4) = 3(-3-p)
5p-20 = -9-3p
Add 3p to each side
5p+3p -20 = -9-3p+3p
8p-20 = -9
Add 20 to each side
8p-20+20 =-9+20
8p =11
Divide by 8
8p/8 = 11/8
p = 11/8
I need help as soon as possible please!!!!
Answer:
Which grade math is this? I haven't learned it
What is 20% of $1575.00
step:
20% = 20/100
of = ×
20/100 × $1575.00
answer : $315
Step:
20% = 20/100
of = ×
20/100 × $1575.00
Answer : $315
A delivery company has a fleet of vans. The annual operating cost in dollars) per van is C = 0.37m + 2600, where m is the number of miles traveled by a van in a year. What number
of miles will yield an annual operating cost of $13,700?
mi
Answer:
Step-by-step explanation:
put C=13,700 and find m
The number of miles that will yield an annual operating cost of $13,700 is approximately 30,000 miles.
How to determine What number of miles will yield an annual operating cost of $13,700To find the number of miles that will yield an annual operating cost of $13,700, we need to solve the given equation for \(m\):
\[C = 0.37m + 2600\]
Given \(C = 13700\), we can substitute this value into the equation and solve for \(m\):
\[13700 = 0.37m + 2600\]
Subtract 2600 from both sides:
\[11100 = 0.37m\]
Now, divide both sides by 0.37:
\[m = \frac{11100}{0.37}\]
Calculate the value of \(m\):
\[m \approx 30000\]
So, the number of miles that will yield an annual operating cost of $13,700 is approximately 30,000 miles.
Learn more about operating cost at https://brainly.com/question/30566291
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A family buys a studio apartment for $180,000. They pay a down payment of $27,000.
a. Their down payment is what percent of the purchase price?
b. What percent of the purchase price would a $9,000 down payment be
Answer:
down is $153000 while purchase price is $144000
¿Cuál es la pendiente perpendicular a la pendiente m = 3 ?
Answer:
The slope of a line perpendicular to a vertical line is zero.
Step-by-step explanation:
A square field has a side length of 6x10 meters. Which of the following is its area in square meters?
Answer:
60 square meters
Step-by-step explanation:
area is just its length times its width and both numbers are provided here
6 * 10 is 60
The cost of producing higlighters with the company logo printed on them consists of a onetime setup fee of $160.00 plus $0.65 for each higlighter produced. This cost can be calculated using the formula C=160.00+0.65p, where p represents the number of higlighters produced and C is the cost. Use the formula to calculate the cost of producing 2400 higlighters. (Do not inlcude a comma in your answer)
Answer:
7839 ...........
Food A 150 calories in 3/4 of a serving. Food B 250 calories in 2/3 of a serving. Find each unit rate. Which food has fewer calories per serving?
What is the base of 4×4×4×4×4?
Answer:
Step-by-step explanation:
Your base would be the 4
Answer:
4
Step-by-step explanation:
When you have a something raise up to a number this can be represented as:
[tex]b^a = b_1 \cdot b_2 \cdot \cdot \cdot b_a[/tex]
Where [tex]b[/tex] is the base and [tex]a[/tex] the exponent. In this case you have five times four, then you can re-write the expression as:
[tex]4 \times 4 \times 4 \times 4 \times 4 = 4^5[/tex]
Where the [tex]b[/tex] is equal to 4 and [tex]a[/tex] equal to 5
0.7619047619 as a fraction?
which one
1. 1/16
2. 16/21
3. 2
4. 4
Answer:
16/21
Step-by-step explanation: