Answer:
The length of EF is 5.29
Step-by-step explanation:
If BC = 12 then;
FB = 12 × sin65 = 10.876
BA = FB/(sin50) = 10.876/(sin50) = 14.2
BD = AB (Sides of isosceles triangle) = 14.2
∴ DF = BD + FB = 10.876 + 14.2 = 25.07
∠F C D = tan⁻¹(D F/F C) = tan⁻¹(25.07/(12×cos65)) = 78.6
∠F A D = tan⁻¹(D F/A F) = tan⁻¹(25.07/(14.2×cos50)) = 70
∴ ∠D = 180 - (78.6° + 70°) = 31.4°
AE = AD × sin31.4° = 2×AB×cos(70° - 50°) × sin31.4
∴ AE = 2×14.2×cos(20°) × sin31.4 = 13.92
EC = AC × cos78.6° = (AB×cos50 + BC×cos65)×cos78.6° = 2.815
Therefore, from cosine rule, a² = b² + c² - 2·b·c × cos(A)
Hence, we have;
EF² = EC² + FC² - 2 × EC × FC ×cos∠FCD (Cosine rule)
That is, EF² = 2.815² + (12×cos65)² - 2 × 2.815× (12×cos65) ×cos78.6°
EF² = 27.98
∴EF = √27.98 = 5.29.
Answer:
The length of EF is 5.29
Step-by-step explanation:
Please Find attached
Answer:
Using distance formula :
AB² = (5+1)² + (3-6)²
AB² = 36 + 9
AB² = 45
AB = 6.71 units
1. Solve for x
X - 10 = 15
Pedro is playing a game where he has to roll a fair number cube with faces labeled from 1 to 6. What is the probability that he will roll either a 2, 3, or a 4 on his next roll?
Answer:
50%
Step-by-step explanation:
Hope it helps
Find the solution to x^2=64
Answer:
[tex] \boxed{x = 8} [/tex]
Step-by-step explanation:
[tex] = > {x}^{2} = 64 \\ \\ = > {x}^{ \cancel{2}} = {8}^{ \cancel{2}} \\ \\ = > x = 8[/tex]
If A( 6, -1) , B( 1,3) and C( k, 8) are three points such that AB = BC, find the value of k
Answer:
De value of k is 9
Step-by-step explanation:
6,-1
b(1,3)
(k,8)
am using bodmas
a6-1×1=6a
b1×3=3b
abc=8
6a+3b+8=17-8
=9
Solve fraction 2/3x -1/2=1/6x-1/9
Answer:
Exact Form: x=7/9 Decimal Form: 0.7 (repeating)
Step-by-step explanation:
Hope this helps!! :)
The diameter of a basketball is 9.39 inches. Which is closest to the number of square inches of material used in constructing a basketball?
Answer:
Area, [tex]A=69.21\ \text{inches}^2[/tex]
Step-by-step explanation:
We have,
The diameter of a basketball is 9.39 inches.
It is required to find the number of square inches of material used in constructing a basketball. It means we need to find the area of basketball. It is given by :
[tex]A=\pi r^2[/tex]
r is radius of basketball, r = 4.695 inches
So,
[tex]A=3.14\times (4.695)^2\\\\A=69.21\ \text{inches}^2[/tex]
So, the area of the basketball is [tex]69.21\ \text{inches}^2[/tex].
Which expression is equivalent to -3 1/8 minus 2 1/2
Answer:
-5 5/8
Step-by-step explanation:
A negative minus a positive is essentially a negative plus a negative! The two values will add on top of each other to create a larger negative number.
I'd recommend turning the mixed numbers into improper fractions: 25/8 and 5/2. Then, make sure their denominators are equal by multiplying 5/2 by a "big one" or 4/4. This should get you 20/8.
Now, solve for -25/8 - 20/8 to get -45/8. Turn that number into a mixed number, and you have your answer!
what is the length of a leg in a 45-45-90 triangle is the hypotenuse is 8
Answer:
The legs are both of length 4√2
Step-by-step explanation:
Let the length of one of the two equal legs be x. Then, by the Pythagorean Theorem, x^2 + x^2 = 8^2, or
2x^2 = 64, or x^2 = 32 = 2(16)
Solving for x, x = 4√2. The legs are both of length 4√2.
what is 4 raised to the third power
Answer:
4³=64
Step-by-step explanation:
A number raised to a power implies the repeated multiplication of that number by itself to the value of its power.
Hence, four raised to the third power means multiplication of 4 by itself 3 times( 3 being the value of its exponent).
》 4×4×4=64
Go to link for the question thx!!
solve: 9^8-x= 27^x-3
Answer:
x = 4.25
Step-by-step explanation:
First, alter the equation until both exponents have the same base. We know that 9^3 is 27. Therefore, we can change 27^(x-3) into 9^3(x-3).
Now, the equation can be written as 9^(8-x) = 9^(3x-9)
Now that the bases are the same, we can cancel them out and just solve for the exponents. This will look like:
8-x = 3x-9.
8 = 4x - 9
17 = 4x
x = 4.25
When Wyatt commutes to work, the amount of time it takes him to arrive is normally
distributed with a mean of 45 minutes and a standard deviation of 3 minutes. Using
the empirical rule, what percentage of his commrtes will be between 36 and 54
minutes?
Answer:
Step-by-step explanation:
Using the Empirical Rule, it is found that 99.7% of his commutes will be between 36 and 54 minutes.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, considering a mean of 45 minutes and a standard deviation of 3 minutes, we have that:
36 = 45- 3 x 3
54 = 45 + 3 x 3
Within 3 standard deviations of the mean, hence, 99.7% of his commutes will be between 36 and 54 minutes.
More can be learned about the Empirical Rule at brainly.com/question/24537145
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Please help asap!!!!!!!!!!!!!!!!
Answer: ok what do you need help with
Step-by-step explanation:
The lengths of two sides of a right triangle are given. Find the length of the third side. Round to the nearest tenth if necessary.
leg: 29 m; hypotenuse: 46 m
54.4 m
35.7 m
40.9 m
50.5 m
The length of the third side of a right triangle is 35.7 m
What is a right triangle?"It is a triangle whose one of the angle measures 90° "
What is hypotenuse?"It is the longest side of the right triangle."
What is Pythagoras theorem?"For a right triangle, [tex]x^{2} + y^{2}= z^{2}[/tex]
where z is the hypotenuse and x, y are other two sides of the right triangle."
For given question,
We have been given the two sides of a right triangle.
leg = 29 m; hypotenuse = 46 m
Let 'a' be the other leg of the right triangle.
Using Pythagoras theorem,
[tex]\Rightarrow a^{2} + 29^{2}= 46^{2}\\\\\Rightarrow a^{2}=46^{2}- 29^{2} \\\\\Rightarrow a^{2}=2116-841\\\\\Rightarrow a^{2} = 1275\\\\\Rightarrow a=\sqrt{1275}\\\\\Rightarrow a=35.7[/tex]
Therefore, the length of the third side of a right triangle is 35.7 m
Learn more about the Pythagoras theorem here:
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What is the order of the numbers form least to greatest?
Answer:
B < A < C < D
Step-by-step explanation:
We can easily order the numbers by using a shortcut. To do this, you just look at the exponents. The more negative the exponent, the lower the number is. The more positive the exponent is, the greater the number is.
Answer:
The answer is option 2.
Step-by-step explanation:
In a faster way to see this you can just look at the power :
A = -4
B = -6
C = 4
D = 5
B < A
A < C
C < D
So the order is B, A, C and D.
An 11 ft flag pole is mounted on top of a school building. If the top of the flagpole forms a 60° angle with the ground 50 ft from the base of the building, about how tall is the school building?
Answer:
39 feet
Step-by-step explanation:
plz give me brainliest >.<
Factor the monomial for 27n^2o
Nat says that a square is a rectangle because it has four right angles. Amy says that a square is a rhombus because it has 4 equal sides. Who is correct? Explain *
Answer:
They are both correct in special cases of a rectangle and rhombuses
Step-by-step explanation:
A square is quadrilateral, with four equal sides and four equal interior angles of 90°
A rectangle is a quadrilateral, with four equal angles which are all 90°. Therefore, a square is a special case of a rectangle with all the sides equal
A rhombus is also a equilateral quadrilateral with having equal opposite angle.
Therefore, when any of the interior angles is equal to 90°, the rhombus becomes known as a square, hence, a square is a special form of rhombus.
Question 1 (1 point)
Identify the slope and y-intercept.
y = -4x - 2
m = -2, b = -4
b
m = 4, b = 2
m = -4. b = 2
m= -4, b= -2
Answer:
m = - 4, b = - 2
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + b ( m is the slope and b the y- intercept )
y = - 4x - 2 ← is in slope- intercept form
with m = - 4 and b = - 2
Can you put the digits 1 to 11 in the circles so that every line has the same total?
Put the 1 in the middle, and then put on two opposite circles two numbers that sum to 11:
1, 10
2, 9
3, 8
4, 7
5, 6
Yes, you put the digits 1 to 11 in the circles so that every line has the same total.
What are the digits?A number is a count or measurement that is really an idea in our minds.
The digits 1 to 11 in the circles so that every line has the same total.
The given digits are as follows;
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11.
The sum of the first number and last number is;
1 + 11 = 12
Similarly, the sum of the second number and second last element is;
2 + 10 = 12
The sum of the third number and third last element is;
3 + 9 = 12
The sum of the fourth number and fourth last element is;
4 + 8 = 12
The sum of the fifth number and fifth last element is;
5 + 7 = 12
The sum of the sixth number and sixth last element is;
6 + 6 = 12
The sum of the seventh number and seventh last element is;
7 + 5 = 12
The sum of the eighth number and eighth last element is;
8 + 4 =12
The sum of the ninth number and ninth last element is;
9 + 3 = 12
The sum of the tenth number and tenth last element is;
10 + 2 = 12
The sum of the eleventh number and eleventh last element is;
11 + 1 = 12
Hence, yes you put the digits 1 to 11 in the circles so that every line has the same total.
Learn more about digits here;
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20+20+20+20+20+20+20+9893-2839283+93749-93+8366754439=???
Answer:
=8,364,018,845
Step-by-step explanation:
Mark me brainiiest.
Answer:
8364018845
Step-by-step explanation:
20+20+20+20+20+20+20 = 140
140+20893-2839283+93749-93+8366754439
Can someone explain this and help me with the answer?
Answer:
Distributive Property, Subtraction Property of Equality, Subtraction Property of Equality, Division Property of Equality
Step-by-step explanation:
First, you need to distribute. Next, you subtract on both sides. Then, you subtract again. Finally, you divide.
Draw a tree diagram for three fair coins tossed together once.
a) Derive the sample space.
b) Find the probability of getting:
i) at least one head
ii) at most one tail
iii) exactly three heads.
Answer:
I have attached a picture with the work to your question.
Please see the attachment below.
I hope this helps.
10. Susan went out and bought 2 packs of toilet paper and 4 containers of Clorox wipes for $46. She told her friend where she found them and her friend went out and bought 1 pack of toilet paper and 3 containers of Clorox wipes for $27. How much did a pack of Clorox wipes cost? *
Answer:
$9
Step-by-step explanation:
Let's make the price of toilet paper x, and the clorox wipes y. We can then use the given information to create a system of equations.
Our equations are 2x+4y=36 (because 2 packs of toilet paper and 4 containers of Clorox wipes cost $46) and x+3y=27 (because 1 pack of toilet paper and 3 containers of Clorox wipes cost $27). Now, let's solve!
2x+4y=36 (1)
x+3y=27 (2)
2x+6y=54 (3) (i just mutiplied (2) by 2 so that i could eliminate x)
2y=18 (3)-(1)
y= $9/pack
What is the slope of the line y = 20x?
Answer:the slope is 20
Step-by-step explanation:
Answer:
m=20
Step-by-step explanation:
The line is in point slope form, or
y=mx+b
where m is the slope and b is the y-intercept
For the equation
y=20x
20 and x are being multiplied. The number being multiplied by x is the slope, therefore the slope is 20
Three coins are flipped.
a)
How many possible outcomes are there?
b)
What is the possibility of getting no heads?
c)
What is the probability of getting at least 2 tails?
I'm kinda stuck. plz help
Answer:
ooooh Mthswath again. a=8 b=1/8 c=4/8 or 1/2
Step-by-step explanation:
a= there are 8 outcomes you can multiply the outcomes. 2×2×2=8
b= (i don't want to insert a picture again, as I already did for the last one you asked) So it is 1/8
c= Again, list out all the possibilities and you will find there are 4 with at least 2 tails or simplify it, 1/2
what’s the value of x ?
AYUDAAA porfavorrrr primera urna 6 bolas verdes y 3 rojas segunda urna 3 verdes, 3 blancas y 3 rojas tercera urna 6 verdes, 1 blanca y 2 rojas a) si sacan una bola de la primera urna que color es más probable de que se obtenga b) calculen las probabilidades de sacar una bola verde, una roja y una blanca de cada urna c) si quieren tomar una bola verde que urna elegirian d) supongan que sacan una bola verde de la tercera urna y no la regresan, lo que se conoce como extraccion sin reemplazo ¿que probabilidad tiene cada bola de salir en la siguiente extraccion?
We have the following information:
first urn: 6 green balls and 3 red ones
total: 6 + 3 = 9
second urn: 3 green, 3 white and 3 red
total: 3 + 3 + 3 = 9
third urn: 6 green, 1 white and 2 red
total: 6 + 1 + 2 = 9
a) A green ball is more likely to be obtained, since there are more green balls than red balls, which makes the probability higher.
b) probability of drawing a green, red and white ball.
first urn:
green = 6/9 = 66.66%
red = 3/9 = 33.33%
white = 0/9 = 0%
second urn:
green = 3/9 = 33.33%
red = 3/9 = 33.33%
white = 3/9 = 33.33%
third urn:
green = 6/9 = 66.66%
red = 2/9 = 22.22%
white = 1/9 = 11.11%
c) it would be chosen where the probability of drawing green would be the highest, which means that it would be possible both in the first and in the third ballot box, the probability is equal 66.66%
d) without a green ball, the third ballot box would look like this:
5 green balls, 2 red balls and 1 white ball, with a total of 8.
The probability of drawing would be:
green = 5/8 = 62.5%
red = 2/8 = 25%
white = 1/8 = 12.5%
What is the volume of a cone with diameter of 30 ft and height of 60 feet use 3.14 for pi enter your answer in the Box
Area of the top:
3.14 x 15^2 = 706.5 square feet.
Volume = area of top x height:
Volume = 706.5 x 60 = 42,390 cubic feet