Answer:
7 ft
Step-by-step explanation:
The area of a circle is given by
A = pi r^2
153.86 = 3.14 r^2
Divide each side by 3.14
153.86 / 3.14 = r^2
49 = r^2
Take the square root of each side
sqrt(49) = sqrt(r^2)
7 = r
Square the following numbers: 3 8 10
Answer:
3^2 = 9
8^2 = 64
10^2 = 100
Which is equivalent toStartRoot 10 EndRoot Superscript three-fourths x ?
Answer:
I THINK its the last one (8 root 10 to the power of 3x)
Step-by-step explanation:
A square root is the same thing as raising something to the 1/2. So the expression we have is (10^1/2)^3/4x.
Due to exponent rules we can multiply to get
10^3/8x which is the same thing as 10^3x/8
The 8 goes to the root and the 3x becomes the exponent
In this exercise we have to have knowledge about the properties of powers, so we have to:
Letter D
Recalling some properties of power, we find that:
Multiplication of powers with the same base.Division of powers with the same base.Power of potency.Potency of a product.Quotient power.Are returning to the exercise and using the properties informed, we find that:
[tex](10^{1/2})^{3/4x}\\10^{3/8x} = 10^{3x/8}[/tex]
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The points A, B, C and D lie on a circle. CDE is a straight line. BA=BD, CB=CD, Angle ABD =32 degrees Work out the size of angle ADE. You must give a reason for each stage of working.
Answer:
[tex]\angle ADE =[/tex] [tex]69^\circ[/tex]
Step-by-step explanation:
Given:
[tex]\angle ABD = 32^\circ[/tex]
BA = BD
CB = CD
In [tex]\triangle ABD:[/tex]
BA = BD
We know that in a triangle, angles opposite to equal sides will also be equal.
[tex]\Rightarrow \angle BAD = \angle BDA[/tex]
We know that sum of internal angles of a triangle is equal to [tex]180^\circ[/tex]
[tex]\angle BAD + \angle BDA +\angle ABD=180^\circ\\\Rightarrow \angle BAD + \angle BDA +32=180\\\Rightarrow \angle BAD + \angle BDA = 180 -32\\\Rightarrow \angle BAD + \angle BDA = 148\\\Rightarrow \angle BAD = \angle BDA = \dfrac{148}{2} = 74^\circ[/tex]
Quadrilateral ABCD is cyclic so, sum of opposite angles is equal to [tex]180^\circ[/tex].
[tex]\angle BAD + \angle BCD = 180^\circ\\\Rightarrow 74 + \angle BCD = 180\\\Rightarrow \angle BCD = 180-74 = 106^\circ[/tex]
In [tex]\triangle BCD:[/tex]
BC = CD
We know that in a triangle, angles opposite to equal sides will also be equal.
[tex]\Rightarrow \angle DBC = \angle CDB[/tex]
We know that sum of internal angles of a triangle is equal to [tex]180^\circ[/tex]
[tex]\angle DBC + \angle BCD +\angle CDB=180^\circ\\\Rightarrow \angle DBC + 106 +\angle CDB=180\\\Rightarrow \angle DBC +\angle CDB=180 - 106\\\Rightarrow \angle DBC =\angle CDB=\dfrac{74}{2} = 37^\circ[/tex]
It is given that the line CDE is a straight line, so the sum of angles on one side of point D is [tex]180^\circ[/tex].
[tex]\angle CDB + \angle BDA +\angle ADE = 180^\circ\\\text{Putting values of } \angle CDB \text{ and }\angle BDA:\\\Rightarrow 37 + 74 + \angle ADE = 180\\\Rightarrow \angle ADE = 180 -111\\\Rightarrow \angle ADE = 69^\circ[/tex]
So, the answer is [tex]\angle ADE =[/tex] [tex]69^\circ[/tex]
The size of ∠ADE of the cyclic quadrilateral is;
∠ADE = 53°
We are given;
BA = BD
CB = CD
∠ABD = 32°
Now, ΔABD is an isosceles triangle and since sum of angles in a triangle is 180°, then;
∠ABD + ∠BAD + ∠BDA = 180°
∠BAD + ∠BDA = 180 - 32
∠BAD + ∠BDA = 148°
Since isosceles, then;
∠BAD = ∠BDA = 148/2
∠BAD = ∠BDA = 74°
Now, in cyclic quadrilaterals, opposite angles are supplementary and as such add up to 180°. Quadrilateral ABCD is cyclic and Thus;
∠BAD + ∠BCD = 180°
74 + ∠BCD = 180°
∠BCD = 180 - 74
∠BCD = 106°
ΔBCD is an isosceles triangle and as such;
∠CBD = ∠CDB = 106/2
∠CBD = ∠CDB = 53°
Now, sum of angles on a straight line add up to 180°. Thus;
∠CBD + ∠BDA + ∠ADE = 180°
Plugging in the relevant values gives;
53° + 74° + ∠ADE = 180°
∠ADE = 180 - (53 + 74)
∠ADE = 53°
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The lateral area of a right cylinder having a base diameter of 10 units and height of 10 units is:
Answer:
A = 100π units²
Step-by-step explanation:
To answer this we first find the circumference C = 2πr, and then multiply this C by the height:
C = 2πr, or C = πd. Here, C = π(10 units).
Then the lateral area of the cylinder is A = C*(10 units), or
A = 10π(10) units², or
A = 100π units²
The lateral surface area of the given right cylinder is 314 square units.
What is the lateral surface area of a right cylinder?The lateral surface area of a right cylinder is the product of the circumference of the base and the height of the cylinder.
Given, the base diameter(d) of the cylinder is 10 units.
Therefore, the base radius(r) of the cylinder is
[tex]= \frac{10}{2} units\\= 5 units[/tex]
The height(h) of the cylinder is 10 units.
Therefore, the lateral surface area of the cylinder is
= 2πrh square units
[tex]= 2(3.14)(5)(10)[/tex] square units
[tex]= 314[/tex] square units
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Kyle drops a ball from a height of 15 feet above the ground. The function h = −16t^2 + 15 gives the height h of the ball (in feet) after t seconds. Graph the function. Then determine the approximate time the ball hits the ground.
Answer:
The ball will hit the ground at 0.968 seconds.
Step-by-step explanation:
Please refer to the attached graph in the answer area.
The given equation of height according to input variable time 't' is:
[tex]h = - 16 t^{2} + 15 ...... (1)[/tex]
h is in feet
t is in seconds
Both the values 't' and 'h' will be positive. (Time and height can never be negative)
To determine the time, at which the ball hits the ground, i.e. the height becomes 0.
Putting value of h = 0 in equation (1)
[tex]0 = - 16 t^{2} + 15 \\\Rightarrow t^{2} = \dfrac{15}{16}\\\Rightarrow t = \sqrt{\dfrac{15}{16}}\\\Rightarrow t = 0.968\ sec[/tex]
Hence, the time at which the ball hits the ground is 0.968 seconds.
Remove the bracket a-2(b-3a). *
4 points
a-2b+6a
-2a+7b
7a+2b
-7a-2b
What is the value of arc sin(2√2)?
The sum of three numbers is 54. The third number is 2 times the second. The second number is 10 more than the first. What are the numbers?
Answer:
8, 18 and 36 respectively.
explanationsum=54
1st number=x
2nd number=x+10
3rd number =2(x+10)=2x+20
x+x+10+2x+20=54
put the liketerms together
x+x+2x=54-10-20
4x=24
divide both sides by 4 to get
x=8
Input the other values
If g (x) is the inverse of f(x) and f (x) =4x+12, what is g(x)?
Answer:
y= x/4 - 3
Step-by-step explanation:
In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?
A. 8/21
B. 2/7
C. 1/3
D. 2/3
Answer:
b 2/7
Step-by-step explanation:
Because there is a 6/21 chance and 2/7=6/21
Need help ASAP it’s geometry!!
Answer:
EF = 34, FG = 25
Step-by-step explanation:
EG is the total of the two smaller segments, EF and FG.
Therefore:
8x-14 + 4x+1 = EG
8x-14 + 4x+1 = 59
Now we can solve this equation.
8x-14 + 4x+1 = 59
12x-13 = 59
12x = 72
x = 6
Now, we can plug in the values of x into the expressions for the lengths of EF and FG:
EF
8x-14
8(6)-14
48-14
= 34
FG
4x+1
4(6)+1
24+1
= 25
Help me please people
Answer:
y = 16x +8
Step-by-step explanation:
Per means for every so and so, and a fee is one-time thing, so 16 would be with x and 8 as the y (intercept)
There are 46 children attending the Hefner field trip. Each van will hold 8 children. How many van's will be needed to transport each child to and from the field trip?
Answer:
6
Step-by-step explanation:
There are 46 children attending the field trip.
Each van needs to transport 8 children.
To find the number of vans they need, we will divide the number of children by the number of children per van:
46 / 8 = 5.75 ≅ 6 vans
They need 6 vans.
Write the equation in both factored and standard form?
Answer:
Factored Form: x = y/2 + 7
Standard Form: 2x - y = 14
Step-by-step explanation:
Use the grouping method to factor x3 + x2 + 3x + 3.
A.(x + 1)(x2 + 3)
B.(x + 1)(x + 3)
C.x(x + 3)(x + 1)
D. (x + 1)(x+3)
Answer:
(x+1) (x^2+3)
Step-by-step explanation:
x^3 + x^2 + 3x + 3
x^3 + x^2 + 3x + 3
Factor out x^2 from the first group and 3 from the second group
x^2(x+1) +3(x+1)
Then factor out (x+1)
(x+1) (x^2+3)
Answer:
[tex](x + 1)( {x}^{2} +3 )[/tex]
Answer A is correct
Step-by-step explanation:
[tex] {x}^{3} + {x}^{2} + 3x + 3 \\ {x}^{2} (x + 1) + 3(x + 1) \\ = ( {x}^{2} + 3)(x + 1)[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
The GCF of the numbers in the expression (32 + 16) is
Answer:
GCF= 16
Step-by-step explanation:
factors of 32= 32, 16, 8, 4, 2, 1
factors of 16= 16, 8, 4, 2, 1
16 is the largest factor both numbers have in common
Answer: 16
Step-by-step explanation:
Select the correct answer.
Which of these numbers are 11 units from 0 on the number line?
A:0
B: +11
C: -11
A. A and B
B: A and C
C: B and C
D: C only
the 11 units from 0 is c only
Find the value of x
4x - 13 = 3x +7
Step-by-step explanation:
4x - 13 = 3x + 7
4x - 3x = 7 + 13
x = 20
Therefore x = 20
Can somebody help me figure out what 2x+3=2(x+3) equals? Thank you :)
[tex]\text{Solve:}\\\\2x+3=2(x+3)\\\\\text{Use the distributive property:}\\\\2x+3=2x+6\\\\\text{Subtract 2x from both sides}\\\\3=6\\\\\text{Since 3 doesn't equal 6, this equation is not true}\\\text{Therefore, there are no solutions}\\\\\boxed{\text{No solutions}}[/tex]
[x^2+2y]^3
expand it
[tex](a + b) {}^{3} = a {}^{3} + 3a {}^{2} b + 3ab {}^{2} + b {}^{3} \\ \\ x {}^{6} + 6x {}^{4} y + 12x {}^{2} y {}^{2} + 8y {}^{3} [/tex]
Answer:
x^6 + 6x^4 y + 12x^2 y^2 + 8y^3.
Step-by-step explanation:
Using the Binomial Theorem:
(x^2 + 2y)^3 = (x^2)^3 + 3C1 (x^2)^2 (2y) + 3C2 x^2 (2y)^2 + (2y)^3
= x^6 + 3*x^4*2y + 3*x^2*4y^2 + 8y^3
= x^6 + 6x^4 y + 12x^2 y^2 + 8y^3.
Danielle says that her set of numbers are integers. Left-brace negative 253, negative 45, negative 0.9, 0, 26 Right-brace Danielle is wrong. Which explanation of why she is wrong is correct? Danielle has included negative numbers. Negative numbers are not integers. Danielle has included a decimal. Decimals are not integers. Danielle included zero. Zero is not an integer. Danielle included a positive number. Positive numbers are not integers.
Hey!Here is ur answer:
Danielle is wrong cause 'she has included a decimal'.
U might doubt that zero is might not be an integer but it is a neutral integer.
HOPE IT MAKES UR DAY BETTER!!
Danielle says that her set of numbers are integers the statement is wrong as the set contain decimal number because decimal numbers are not integers, so option C is correct.
What are integers?All whole numbers and negative numbers are considered integers. This means that if we combine negative numbers with whole numbers, a collection of integers results.
Given:
Danielle says that her set of numbers are integers. Left-brace negative 253, negative 45, negative 0.9, 0, 26 Right-brace,
Write the above phrase in the mathematical form as shown below,
(-253, -45, -0.9, 0, 26)
As we know that integers are whole numbers, they can't be a decimal numbers or a fraction,
Thus, the set of numbers are integers is wrong because it contains decimal numbers.
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help me please! I NEED TO HAND IT IN NOW
Answer:
4n + 4
Step-by-step explanation:
Azhar - n years old now.
Last year he was (n-1).
His mother was 4(n -1) last year.
Now his mother 4(n-1) + 1.
7 years later she will be 4(n - 1) + 1 + 7 = 4n - 4 + 8 = 4n + 4
the number 301 can be written as?
Answer:
three hundred and one
Step-by-step explanation:
This wasn't very clear..
Answer: the number 301 can be written as three hundred one.
Step-by-step explanation: the number 301 can be written as three hundred one. To find a, take the number and move a decimal place to the right one position. Now, to find b, count how many places to the right of the decimal. There are 2 places to the right of the decimal place.
A number cube is rolled. What is the likelihood that a number less than or equal to three is rolled?
The probability that a number less than or equal to three is rolled is 1/2.
Given that, a number cube is rolled, we need to find that what is the probability that a number less than or equal to three is rolled,
So, the probability = favorable outcomes / total outcomes
Here, the favorable outcome = 1, 2, 3 = 3
The total outcomes = 1, 2, 3, 4, 5, 6 = 6
So, the probability = 3/6 = 1/2
Hence, the probability that a number less than or equal to three is rolled is 1/2.
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I’m really stuck on this ☹️
Answer:
2 adults and 2 senior citizens.
Step-by-step explanation:
There are 8 children, which means we need to take the number that represents the children from the graph which is 4 and multiply it by the 8 children going.
1. 4x8=32
So we have found the total for the 8 children, however there are 4 spots left
We take the total from the #1 and add 2 adults and 2 senior citizens.
32+6+6+3+3=50
We then come to the conclusion of 2 adults and 2 seniors.
can someone please help???
Answer:
2/3
Step-by-step explanation:
.that's the answer
Which of the following lists of ordered pairs is a function?
A) (1,1), (2,2), (3,1), (3,2)
B) (-2,3), (2,4), (-3,6), (3,7)
C) (0,3), (-1,4), (1,6), (-1,7)
D) (2,5), (3,-4), (4,7), (2,2)
Answer:
B
Step-by-step explanation:
its B because the input for every pair has the same output, if the input had different outputs it would be considered not a function. Imagine it like a vending machine, if you were to press 3 on the vending machine you would get whatever 3 was, but if you pressed 3 and you get something else besides whatever 3 is it would be broken. I hope this was helpful, I struggled learning this stuff but now I got it down lol.
Create your own ratio. Be sure to describe the ratio in words first and then write the ratio as a fraction
[tex]7:3[/tex]
The ratio of 7 to 3.
The ratio as a fraction would be:
[tex]\frac{7}{3}[/tex]
Factorise
3x square +6x
Hey!!
Solution,
3x^2+6x
take the common,
3x(X+2)
hope it helps
Good luck on your assignment
Three out of seven students in the cafeteria line are chosen to answer survey questions. How many different combinations of three students are possible? 7 C 3 = StartFraction 7 factorial Over (7 minus 3) factorial 3 factorial 7 35 70 210
Answer:
The number of different combinations of three students that are possible is 35.
Step-by-step explanation:
Given that three out of seven students in the cafeteria line are chosen to answer a survey question.
The number of different combinations of three students that are possible is given as:
7C3 (read as 7 Combination 3)
xCy (x Combination y) is defines as
x!/(x-y)!y!
Where x! is read as x - factorial or factorial-x, and is defined as
x(x-1)(x-2)(x-3)...2×1.
Now,
7C3 = 7!/(7 - 3)!3!
= 7!/4!3!
= (7×6×5×4×3×2×1)/(4×3×2×1)(3×2×1)
= (7×6×5)/(3×2×1)
= 7×5
= 35
Therefore, the number of different combinations of three students that are possible is 35.
There are 35 different combinations to chose 3 students from the 7 students
How to determine the number of combinations?The given parameters are:
Students, n = 7
Selected , r = 3
The number of different combinations is calculated using:
Combination = nCr
This gives
Combination = 7C3
Using the combination formula, we have:
Combination = 35
Hence, there are 35 different combinations to chose 3 students from the 7 students
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