Use the Pythagorean Theorem to find the length of the sides "d" and "f." Explain your answer.
Answer:
f = 10·√3/3 ≈ 5.774
d = 5·√3/3 ≈ 2.887
Step-by-step explanation:
The given parameters are;
The angles opposite the 90°, right angle, = 60° and 30°
The length of the leg opposite the 60° angle = 5
Therefore, by Pythagorean Theorem, we have;
f² = d² + 5²
However, by trigonometry, we have;
sin(θ) = Opposite/Hypotenuse
For the angle of the triangle, θ = 30°, we have;
sin(30°) = d/f = 0.5
∴ d = f × 0.5 = 0.5·f
Substituting the value of d in the equation given by Pythagorean Theorem, we have;
f² = (0.5·f)² + 5² = 0.25·f² + 5²
f² = 0.25·f² + 5²
f² - 0.25·f² = 5²
0.75·f² = 5²
f² = 5²/0.75 = 100/3
f = 10/√3 = 10·√3/3
f = 10·√3/3
d = f × 0.5 = 10·√3/3 × 0.5 = 5·√3/3
d = 5·√3/3.
A 450 gallon tank full of water is draining at a rate of 20 gallons per minute. We can represent the situation with the equation:
y
=
450
−
20
x
y
=
450
-
20
x
where x is the number of minutes that have passed by, and y is the amount of water in the tank. How long will it take for the tank to have 200 gallons?
A.
12.5 minutes
B.
32.5 minutes
C.
2.15 minutes
D.
20 minutes
Replace y with 200 ( amount of water in the tank) and solve for x:
200 = 450 -20x
Subtract 450 from both sides:
-250 = -20x
Divide both sides by-20:
X = 12.5
The answer is A. 12.5 minutes
Expand the product (x-3)(x+2)
The answer is-
x^2−x−6
Help????? Anyonee?????
Answer:
A
Step-by-step explanation:
Answer:
32.43 increase
Step-by-step explanation:
Please help me!!!! I will mark as brainlist!!
Answer:
117 i think
Step-by-step explanation:
because you need to find the distance from a to b which is 13 units
then you need to find the distance from b to c which is 9 units
and then 9 x 13 is 117
Matea recorded that water levels in one part of the river fell 1.05 millimeters per year for 2.48 years. Describe how you could estimate the total variation in water level.
Answer:
the answer is -13.64 i just took the test and it right promise.
Step-by-step explanation:
mark me as brainliest pls its right
Answer:
The decrease of the decimal rate -1.05 mm/year can be rounded to -1. You don’t need to round 2.48 because you’re multiplying by -1. Since -1.05 is negative and rounded to a greater value, the estimate could be adjusted to a slightly lesser value, maybe -2.5 or -2.6
Twice as many students go to the park than to the theater. Five more students go to the theater than to the museum. If 16 students go to the park, how many students go to the museum?
Answer:
3 students
Step-by-step explanation:
Twice as many students go to the park than to the theater :
Let number who go the theater = t
Number who goes to park = 2t
5 more students go to the theater than to the museum
Number who goes to museum = t - 5
If number of students who goes to park = 16
How many students goes to the museum :
2t = 16
t = 16/2
t = 8
Number who goes to museum = t - 5
t - 5 = 8 - 5 = 3
Hence, number of students who goes to the museum = 3
Factor this polynomial expression.
15x^2- 2x - 8
O A. (5x + 4)(3x - 2)
O B. (5x - 4)(3x+2)
O C. (5x + 2)(3x - 4)
O D. (5x-2)(3x+4)
Answer:
B. (5x - 4)(3x + 2)
Step-by-step explanation:
Factor the following:
[tex] \longrightarrow [/tex] 15x² - 2x - 8
The coefficient of x² is 15 and the constant term is -8. The product of 15 and -8 is -120. The factors of -120 which sum to -2 are 10 and -12.
So,
[tex] \longrightarrow [/tex] 15x² + (10 - 12)x - 8
[tex] \longrightarrow [/tex] 15x² + 10x - 12x - 8
[tex] \longrightarrow [/tex] 5x(3x + 2) - 4(3x + 2)
[tex] \longrightarrow [/tex] (5x - 4)(3x + 2)
it for dreelliot only 2+2 = ?
Answer:
4
Step-by-step explanation:
+
that is as simple as I could put it you literally just need to count the skulls
write the algebraic expression that represents the following
b. Five less than the quotient of nine and a number
c. One half of the sum of six times a number and twenty-two
d. Nine less than twice the difference between a number and seven
e. Eleven less than a number squared
Answer:
9x -5
1/2(6x +22)
2(x-7)-9
x2 -11
HURRY HELP NOW!! Solve for x please !!!!
Answer:
X=9 so D
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
70 and 12x + 2 are same- side interior angles and are supplementary, thus
12x + 2 + 70 = 180 , that is
12x + 72 = 180 ( subtract 72 from both sides )
12x = 108 ( divide both sides by 12 )
x = 9 → D
Suppose a Pony Express rider was paid $168 for 14 weeks of work.
If he was paid the same amount each week, how much was he paid for one week of work?
Which of the following number lines represents the solution to the compound inequality 2x+ 9 <3 or -3x +4<(or equal to) -11 ?
Given: 3x + 2y + 7 = 5x +3y +10
Prove: m = -2
please help im very confused :)
also make sure to include the statements and reasonings as shown in the screenshot!
Answer:
See Below.
Step-by-step explanation:
1) Given:
[tex]3x+2y+7=5x+3y+10[/tex]
2) Subtraction Property of Equality (subtract 2y from both sides):
[tex]3x+7=5x+y+10[/tex]
3) Subtraction Property of Equality (subtract 5x from both sides):
[tex]-2x+7=y+10[/tex]
4) Subtraction Property of Equality (subtract 10 from both sides):
[tex]-2x-3=y[/tex]
5) Symmetric Property:
[tex]y=-2x-3[/tex]
6) Slope-intercept form:
[tex]y=mx+b\text{, where $m$ is slope and $b$ is y-intercept.}[/tex]
7) Substitution:
[tex]m=-2[/tex]
What is the maximum number of intersection points a hyperbola and a parabola could have?
4 intersection points
Find the equation of the line. Use the exact numbers.
Equation: y = _____ x _____
Identify the number of solutions or zeros:
f(3) = 23 – 3.75 +27 – 9
3
1
5
7
Answer:
3
Step-by-step explanation:
PLEASE MARK BRAINLIEST
Answer:
3
Step-by-step explanation:
A biologist uses a rectangular tray that has a width of 1.5 feet and a height of 2 feet. What is the area of the tray in square feet?
Answer: 3ft squared
Step-by-step explanation: to find the area you have to multiply the height by the width. So 2 times 1.5 is equal to 3.
what is 3 1/2 miles -3,520 yards (answer in miles)
Answer:
Step-by-step explanation:
-2mi 0.000000yd
I NEED HELP PLEASE!!!!
Which function represents the sequence in the table?
Answer:
The answer is B
Step-by-step explanation:
So basically the graph starts at 1=-3, 2=-1, 3=1 and so on because of this we now that the graph is going up by two therefore it's B
Evaluate each value expression for the given value of x: 11 + x, x=12
Answer:
The value of 11+x at x=12 will be 23.
Step-by-step explanation:
Given the expression
[tex]11 + x[/tex]As we have to evaluate the expression at x=12
so substitute the value x=12 in the expression
[tex]11 + x[/tex]
[tex]=11+12[/tex]
[tex]=23[/tex]
Therefore, the value of 11+x at x=12 will be 23.
jack is paid £1800 a month. he spends half his money on rent. he spends the rest on food, bills and savings in the ratio 4:3:2 how much does he spend on bills?
Answer:
£300.
Step-by-step explanation:
He has £900 left after paying rent.
The fraction he spends on bills = 3(4+3+2)
= 3/9
= 1/3.
So he spends 900 * 1/3 = £300 on bills.
jsjsjwjwjwjwjqjqjjqkqkakajajajajajjajaj
Answer:
csgrerhhhrsdShuavkilrqadccddvny
Step-by-step explanation:
pls help and it’s not 66
Answer:
15
Step-by-step explanation:
120=8x-10
130=8x
15=x
Answer:
x=15
sorry that should be right now tho
Please help need this before 4:15pm
In which part of the periodic table (top-left, top-middle, top-right, bottom-left, bottom-middle, bottom-right, middle-left, middle-center, middle-right) do we find most of the atoms that make up life?
Answer:
Top right i believe
Step-by-step explanation: the elements that make up life are carbon, hydrogen, oxygen, nitrogen, phosphorus, and sulfur.
escribi los rsultados de cada cálculo como una exprecion decimal.
a)5+1/10+4/100=
b)1+5/10+7/100+5/1.000=
c)3/10+4/1.000=
POR FA NECESITO AYUDA ES PARA HOY
Answer:
a) 257/50 or 5.14
b) 657/100 or 6.57
c) 43/10 or 4.3
Step-by-step explanation:
Espero que esto ayude y que tengas un gran día! :)Solve 6w – 2 ≤ 10 for w.
Answer:
w greater than 2
Step-by-step explanation:
$59.99 DVD box set, 6.5% tax
Answer:
$63.89
Step-by-step explanation:
59.99 * 6.5% = 3.89935. we can round that to $3.90.
59.99 + 3.90 = $63.89 total
Answer:
$3.90
Step-by-step explanation:
6.5% of $59.99 is $3.90.
Feel free to give brainliest.
Have an outstanding day!
what is the answer to (x+3)^2 +(y-6)^2
Answer:
1the answer is 1! hope this helps.
The answer is x^2+ y^2-27
The sum of 2 integers is -1. Their product is -12. What are the integers?
Answer:
-4 and 3
Step-by-step explanation:
-4+3 would equal -1.
Then, -4*3 would be -12.