The simplified form of 18^1/2 is 3√2
Radical expressions and indicesGiven the exponential expression
18^1/2
According to power law of Indices:
a½ = \sqrt{a}
Applying this law to the given expression;
This can also be written as:
[tex]18^{1/2} =\sqrt{18}[/tex]
Simplify the radical to have:
[tex]\sqrt{18} = \sqrt{9 \times 2} \\\sqrt{18} = 3\sqrt{2}[/tex]
Hence the simplified form of 18^1/2 is 3√2
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whats the answer to -6= -2+w
Answer:
im so handsome
Step-by-step explanation:
jesus created me
Answer:
The answer is w= -4.
-2+-4=-6
<3 Please mark as brainliest! Thx :)
Step-by-step explanation:
Earth has a diameter of about 2292 leagues long. What is the total surface area of earth? Rounded to the nearest whole number.
Answer: 16,503,616 leagues²
Step-by-step explanation:
Assume that the Earth is a sphere. Then, you need to use the formula for calculate the surface area of a sphere:
[tex]SA=4\pi r^2[/tex]
Where r is the radius.
Divide the diameter by 2 to calculate the radius of the Earth:
[tex]r=\frac{2,292\ leagues}{2}\\r=1,146\ leagues[/tex]
Substituting values into the formula [tex]SA=4\pi r^2[/tex], you get that the total surface of the Earth to the nearest whole number is:
[tex]SA=4\pi (1,146\ leagues)^2=16,503,616\ leagues^2[/tex]
The correct answer is that the total surface area of Earth is approximately 510 million square kilometers.
To calculate the total surface area of Earth, we can use the formula for the surface area of a sphere, which is [tex]\( A = 4\pi r^2 \)[/tex], where r is the radius of the sphere. Since the diameter of Earth is given as 2292 leagues, we first need to convert leagues to kilometers. Historically, one league was approximately 5.556 kilometers.
Using this conversion, the radius of Earth in kilometers is:
[tex]\[ r = \frac{2292 \text{ leagues} \times 5.556 \text{ km/league}}{2} \] \[ r = \frac{2292 \times 5.556}{2} \] \[ r = 1146 \times 5.556 \] \[ r \approx 6337.536 \text{ km} \][/tex]
Now, we can calculate the surface area using the radius:
[tex]\[ A = 4\pi r^2 \] \[ A = 4\pi (6337.536 \text{ km})^2 \] \[ A = 4\pi (404,089,630.24 \text{ km}^2) \] \[ A \approx 4\pi (4.04 \times 10^9 \text{ km}^2) \] \[ A \approx 4 \times 3.14159 \times 4.04 \times 10^9 \text{ km}^2 \] \[ A \approx 50.26548 \times 10^9 \text{ km}^2 \] \[ A \approx 5.026548 \times 10^{10} \text{ km}^2 \][/tex]
Rounding to the nearest whole number, the total surface area of Earth is approximately 510 million square kilometers.
(15 points)
Find the perimeter of each polygon. Assume that lines which appear to be tangent are tangent.
Thats exactly what i wanted to answer
What is the first step in evaluating the expression shown below?
12÷(7.4−3.6)+8−2
A. Subtract 7.4−3.6.
B. Divide 12÷7.4.
C. Add 3.6+8.
D. Subtract 8−2.
Answer:
the answer is A
Step-by-step explanation: because the way you work out problems with parenthesis is Parenthesis Exponents Multiplication Division Adding Subtraction and what ever id in the parenthesis comes first
A is the correct answer as you should always do the expression that’s in parentheses first
A company policy requires that, for every 40 employees, there must be 3 supervisors. If the are 285 supervisors at the company how many employees does the company have?
Answer:
11,400.0
Step-by-step explanation:
There needs to be 40 employees per every 3 supervisors, so this means multiplication, or division, but I went with the multiplication route.
285 x 40 = 11,400.
11,400 / 40 = 285.
The reason I multiplied 285 by 40 is because the supervisors was the main piece to the puzzle, and was much easier than if it gave you employees first, and that's when you'd divide by 3.
If there's 285 supervisors, you have the full amount of supervisors, now you need employees, so you are free to multiply by 40, since thats how many supervisors are available every 40 employees. I hope this helps.
To solve this problem, we'll first establish the ratio of employees to supervisors as given by the company policy. The policy states that for every 40 employees, there must be 3 supervisors.
To find the number of employees that can be supervised by a single supervisor, we'll divide the number of employees by the number of supervisors in that ratio.
So, for every 3 supervisors, there are 40 employees. We want to know how many employees would be there per 1 supervisor. Thus, we divide 40 (the number of employees) by 3 (the number of supervisors):
Number of employees per supervisor = \( \frac{40 \text{ employees}}{3 \text{ supervisors}} \)
Now, if there are 285 supervisors at the company, we can find out the total number of employees by multiplying the number of supervisors by the number of employees per supervisor.
Therefore, the total number of employees \( E \) is:
\( E = 285 \text{ supervisors} \times \frac{40 \text{ employees}}{3 \text{ supervisors}} \)
The "supervisors" unit cancels out, and we are left with only the "employees" unit.
Now let's do the multiplication. We divide 40 by 3 and then multiply the result by 285:
\( E = 285 \times \frac{40}{3} \)
Calculating that results in:
\( E = 95 \times 40 \)
\( E = 3800 \)
Thus, the company has 3,800 employees.
The perimeter of this isosceles triangle is 22 cm. If one side is 6 cm, what are the possible lengths of the other two sides?
Final answer:
In an isosceles triangle with a perimeter of 22 cm and one side of 6 cm, the other two sides must be equal in length and must be 8 cm each to satisfy the perimeter condition.
Explanation:
The question asks for the possible lengths of the other two sides of an isosceles triangle with a perimeter of 22 cm, where one side is already known to be 6 cm. In an isosceles triangle, the two other sides must be of equal length because an isosceles triangle has two sides that are the same.
Let's denote the length of these two equal sides as 'x'. The perimeter of a triangle is the sum of the lengths of all three sides:
6 cm + x + x = 22 cm
2x + 6 cm = 22 cm
2x = 22 cm - 6 cm
2x = 16 cm
x = 8 cm
Therefore, the other two sides of the triangle must each be 8 cm long.
It's important to note that all three sides of a triangle must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, the other two sides cannot both be less than 6 cm, otherwise, they will not form a triangle with the third side of 6 cm. The solution provided meets this requirement.
find the product.(x+ut)(9x-8ut)
Final answer:
To find the product of the binomials (x + ut)(9x - 8ut), we use the FOIL method and combine like terms, resulting in the expression 9x² + uxt - 8u²t².
Explanation:
To find the product of the binomials (x + ut)(9x - 8ut), we will use the distributive property (also known as the FOIL method in this case), which involves multiplying each term in the first binomial by each term in the second binomial:
First, multiply the first terms: x and 9x, which gives 9x².Outer, multiply the outer terms: x and -8ut, which gives -8uxt.Inner, multiply the inner terms: ut and 9x, which gives 9uxt.Last, multiply the last terms: ut and -8ut, which gives -8u²t².Combining like terms, the final product is:
9x² + 9uxt - 8uxt - 8u²t²
Since 9uxt and -8uxt are like terms, we can simplify further:
9x² + uxt - 8u²t²
Which equation has solutions of 6 and -6?
A. x^2-12x+36=0
B. x^2 + 12x – 36 = 0
C. x^2 + 36 = 0
D. x^2 – 36 = 0
Answer is D
use the factor method to get the answer
x^2-36=0
x^2-6^2=0
(x-6)(x+6)=0
x=6 or -6
Solve the system of equations by substitution. 2x + y = 3z x + y = 6z What is the value for y from the first equation, that could be substituted into the second equation?
Answer:
y = 3z - 2x
Step-by-step explanation:
Systems of equations can be solved by a number of know techniques, such as substitution, elimination or graphical approach.
We are required to solve the system of equations given via substitution;
2x + y = 3z
x + y = 6z
The question requires us to determine the value for y from the first equation, that could be substituted into the second equation.
We simply need to make y the subject of the formula from the first equation;
2x + y = 3z
To do this we subtract 2x on both sides of the equation;
2x + y -2x = 3z - 2x
y = 3z - 2x
This is the value of y from the first equation, that can be substituted into the second equation.
How does your sine graph change when including the c-value?
Answer:
Changing value of "c" changes the phase shift of the sine graph.
Step-by-step explanation:
Question says to find about how does the c value affect your sine graph.
General equation of sine function can be given as:
[tex]y=a\cdot\sin\left(bx-c)\right)+d[/tex]
In that formula, value of "c/b" gives phase shift.
So changing value of "c" changes the phase shift of the sine graph.
How to work out the missing sides?
Answer:
5[tex]\sqrt{2}[/tex]
Step-by-step explanation:
The triangle has 2 equal legs, name them x so
Using Pythagoras' identity
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
x² + x² = 10²
2x² = 100 ( divide both sides by 2 )
x² = 50 ( take the square root of both sides )
x = [tex]\sqrt{50}[/tex] = [tex]\sqrt{25(2)}[/tex] = 5[tex]\sqrt{2}[/tex]
Find the surface area of a melon with circumference of 18 in. Round your answer to the nearest square inch.
that is, the length down the middle of the melon is 18.
[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\ \cline{1-1} C=18 \end{cases}\implies 18=2\pi r\implies \cfrac{18}{2\pi }=r\implies \cfrac{9}{\pi }=\boxed{r} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \textit{surface area of an sphere}\\\\ A=4\pi r^2~~ \begin{cases} r=radius\\ \cline{1-1} \boxed{r}=\frac{9}{\pi } \end{cases}\implies A=4\pi \left( \cfrac{9}{\pi } \right)^2\implies A=4\pi \cdot \cfrac{81}{\pi ^2} \\\\\\ A=4\cdot \cfrac{81}{\pi }\implies A=\cfrac{324}{\pi }\implies A\approx 103.13\implies \stackrel{\textit{rounded up}}{A=103}[/tex]
PLEASE HELP ME with THIS please explain to Thank You and please
Step-by-step explanation: (for #1)
Area of a square= lw
A = 2 x 2
A = 4
Area of a triangle= 1/2bh
A = 1/2 1 x 2
A = 1
4 + 1 = 5in.
Step-by-step explanation: (for #2)
A = lw
A = 3 x 2
A = 6
Area = lw
A = lw
A = 1 x 1
A = 1
6 + 1 = 7cm
Here are the first five terms of a sequence:
4,11,22,37 and 56
Find an expression, in terms of n, for the nth term of this sequence.
Help ASAP please
Answer:
2n² + n + 1
Step-by-step explanation:
4, 11, 22, 37
Difference between: 7, 11, 15
7,11,15 are all 4 apart. You divide the 4 by 2 to get 2n² (it is squared because you needed a second level to find the difference)
And then I knew you needed to put the original 2n² with the sequence we are trying to work out.
2, 8, 18, 32
4, 11, 22, 37
difference between the 2 sequences 2, 3 ,4 ,5 (which all has a difference of 1) which means 1n or just n.
So that's 2n² + n
I
The sequence is quadratic as the second difference is constant. The nth term expression can be established as 2n² for which the coefficient 2 is half of the second difference. Further, by matching the sequence to the nth term, we adjust the expression to 2n² + n + 1.
Explanation:A key step to finding an expression for the nth term of this sequence is finding the difference between consecutive terms. For this particular sequence, you can see that the difference isn’t constant, thus, it's a quadratic sequence. However, if the second difference is constant, the nth term of the sequence is a quadratic:
4, 11, 22, 37, 56The first differences are: 7(11-4), 11(22-11), 15(37-22), 19(56-37).
The second differences are 4(11-7), 4(15-11), 4(19-15).
Since the second difference is constant and equals to 4. We divide this by 2 to get 2. This is the coefficient of the n² term in our sequence. Thus, the first part of the nth term is 2n².
The next step is to write out the sequence of 2n², subtract this sequence from the original sequence, and identify the differences:
Original sequence = 4, 11, 22, 37, 56Sequence of 2n² = 2, 8, 18, 32, 50Difference = 2, 3, 4, 5, 6The difference above is clearly linear (increases by 1 each time) and thus the format for nth term has improved from 2n² to 2n²+n. So far this match has worked for the first 5 terms, but we need to look at the nth term to see if it works:
Original sequence: 4, 11, 22, 37, 56
Sequence of 2n²+n: 3, 10, 21, 36, 55
To match the original sequence, add 1 to each term in our sequence. The nth term is therefore 2n² + n + 1.
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An architect is designing a scale model that is similar to an actual building in the shape of a triangular prism. If the ratio of the height of her scale model to the height of the actual building is 1:98, what is the ratio of the volume of the scale model to the volume of the building?
Answer:
The ratio of the volume of the scale model to the volume of the building is [tex]\frac{1}{941,192}[/tex]
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube, and the ratio of its corresponding sides is equal to the scale factor
so
Let
z-----> the scale factor
x----> the volume of the scale
y----> the volume of the building
[tex]z^{3}=\frac{x}{y}[/tex]
In this problem we have
[tex]z=\frac{1}{98}[/tex]
substitute
[tex](\frac{1}{98})^{3}=\frac{x}{y}[/tex]
[tex](\frac{1}{941,192})=\frac{x}{y}[/tex]
rewrite
[tex]\frac{x}{y}=\frac{1}{941,192}[/tex]
What is the value of x? Round to the nearest hundredth.
Answer:
Step-by-step explanation:
You need to use trigonometry (SOHCAHTOA)
As from the focus angle -thetre- (65^o) you have the adjecent (x) and hypotenuse (the side opposite the right angle - 81.9m):
cos(θ) = adjacent/hypotenuse
cos (65) = x/81.9
as the opposite of dividing is mulitplying, you multiple both sides by 81.9
81.9*cos(65) = x
using calculator - in degree mode-
x = 34.6124
Thus it is the first choice, x = 34.61.
Answer:
The correct answer is first option
X = 34.61
Step-by-step explanation:
Points to remember
Trigonometric ratios
Sin θ = Opposite side/Hypotenuse
Cos θ = Adjacent side/Hypotenuse
Tan θ = Opposite side/Adjacent side
From the figure we can see that a right angled triangle with base x and hypotenuse = 81.9.
One angle = 65°
To find the value of x
We have Cos θ = Adjacent side/Hypotenuse
Cos 65 = X/81.9
X = 81.9 * Cos 65
= 81.9 * 0.4226
= 34.61
Therefore X = 34.61
The correct answer is first option
The variables A, B, and C represent polynomials where A = x2, B = 3x + 2, and C = x – 3. What is AB – C2 in simplest form? 3x3 + 2x2 – x + 3 3x3 + 2x2 – x – 3 3x3 + x2 – 6x + 9 3x3 + x2 + 6x – 9
Answer:
AB - C² = 3x³ + x² + 6x - 9 ⇒ last answer
Step-by-step explanation:
* Lets study the problem to solve it
- The variables are:
# A = x²
# B = 3x + 2
# C = x - 3
* At first lets find AB
∵ A = x² and B = 3x + 2
∴ AB = x²(3x + 2)
∵ x² × 3x = 3x³ ⇒ same base so we added the power
∵ x² × 2 = 2x² ⇒ coefficient of x² is 1 multiplied by 2
∴ AB = 3x³ + 2x²
* At second find C²
∵ C = x - 3
∴ C² = (x - 3)²
- To solve bracket to the power of 2 use this rule:
# square the first term + 1st term × 2nd term × 2 + square the 2nd term
∴ (x - 3)² = (x²) + (x) (-3) (2) + (-3)² = x² - 6x + 9
∴ C² = x² - 6x + 9
* Now lets find AB - C²
∵ AB - C² = 3x³ + 2x² - (x² - 6x + 9) ⇒ multiply the bracket by -ve sign
∵ -ve × -ve = +ve
∵ -ve × +ve = -ve
∴ AB - C² = 3x³ + 2x² - x² + 6x - 9 ⇒ Add the like terms
∴ AB - C² = 3x³ + x² + 6x - 9
* AB - C² = 3x³ + x² + 6x - 9
Answer:
d for edge2020
Step-by-step explanation:
The area of a rectangle is 63 ft2. If the rectangle is 9 feet long. What is it’s width
Divide the area with the length ( 9 feet long)
Area: 63/9
= 7 feet long
7*9=63 ft 2
Answer: 7 feet long
7 feet.
The area of a rectangle is equal to its length times its height.
In this case, the area can be represented by 63 = 9 * w.
Divide both sides of the equation by 9 to get 7 = w.
This means the width is 7 feet.
doris tiene en su cartera billetes de $10 y de $20.si en total tienen 25 billetes y $330 ¿cuantos billetes tiene cada uno?
Answer:
8 billetes de 20
17 billetes de 10
Step-by-step explanation:
Answer:
17 $10s y 8 $20s
Step-by-step explanation:
if the mean of a set of 12 number is 13 then the sum of the number is?
The sum of the numbers is 156.
Explanation:The sum of a set of numbers can be calculated by multiplying the mean by the total number of elements in the set. In this case, the mean is 13 and the total number of elements is 12. Therefore, the sum of the numbers is 13 multiplied by 12, which is 156.
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To find the sum of 12 numbers with a mean of 13, we multiply the mean by the number of numbers, resulting in a sum of 156.
If the mean of a set of 12 numbers is 13, we can find the sum of the numbers using the formula for the mean.
The formula for the mean is : Mean = Sum of Numbers / Number of Numbers
Given:
Mean = 13
Number of Numbers = 12
We need to find the sum of the numbers:
Sum = Mean x Number of Numbers
Substitute the given values:
Sum = 13 x 12
Sum = 156
This means the sum of the 12 numbers is 156.
Round your answer to two decimal places
Answer:
B. 0.56.
Step-by-step explanation:
That would be the number of sophomore / total number of people
= 77 / 137
= 0.56.
The probability that the randomly chosen person from this group is a sophomore is B. 0.56.
What is Probability?Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.
The value of probability will be always in the range from 0 to 1.
Given that,
Total number of people attended in the school event = 137
Number of sophomores in the group = 77
To find the probability, we have to divide the number of desired outcomes by the total number of outcomes.
Here total number of outcomes is 137 and the number of sophomores is 77.
Probability = 77 / 137 = 0.562 ≈ 0.56
Hence the probability is 0.56.
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5(2y - 1) = 3(y - 4)
How would I do this question/what is the answer?
Answer:
Step-by-step explanation:
=10y - 5 = 3y - 12
=7y - 5 = -12
=7y = -7
y = 1
Answer:
y = -1
Step-by-step explanation:
to solve this equation, you would solve for y by isolating y on one side of the equation
5(2y - 1) = 3(y - 4) < distribute 5 into 2y - 1 and 3 into y - 4
5(2y - 1)
5 x 2y = 10y
5 x - 1 = -5
= 10y - 5
3(y - 4)
3 x y = 3y
3 x -4 = -12
= 3y - 12
we get the new equation:
10y - 5 = 3y - 12 < add 12 to both sides to eliminate -12 from the right side
+ 12 + 12
10y + 7 = 3y < subtract 10y from both sides
-10y -10y
7 = -7y < divide both sides by -7 to isolate y
7/-7 = -1
-7y/-7 = y
-1 = y
our solution to the equation is y = -1. we can see if this is an answer by plugging it in and seeing if both sides are equal, but its not necessary. i will show the check anyway:
CHECK
5(2y - 1) = 3(y - 4) when y = -1
5(2(-1) - 1) = 3((-1)- 4)
5(-2 - 1) = 3( -1 - 4)
5(-3) = 3(-5)
-15 = -15
both sides check out so y = -1 is a solution to the equation
what is the answer to this??
Answer:
∠1 = 23°
Step-by-step explanation:
∠WXZ = ∠WXY + ∠YXZ
Note that ∠2 = 4∠1 ( angle 2 is 4 times angle 1 )
Hence
4∠1 + ∠1 = 115
5∠1 = 115 ( divide both sides by 5 )
∠1 = 23°
Part 3 out of 3 How much will Alice pay for carpet that costs $2.50 per square foot? Alice will pay $ for the carpet.
Answer:
How big is the carpet though.
Step-by-step explanation:
You will just times the square foot by $2.50 to get an answer.
If it is 4 square feet then just go 4 times $2.50 = $10
Please help me with this question and my next one!
Answer:
Step-by-step explanation:
If the price is linear, then the slope between each pair of points must be the same.
m = Δy/Δx
m = (150 - 70) / (5 - 1) = 20
m = (450 - 150) / (20 - 5) = 20
m = (1050 - 450) / (50 - 20) = 20
So the equation is indeed linear. It has a slope of 20 and y-intercept of 50.
p = 20n + 50
A tutor gives John 5 assignments and asks him to complete 5. How many possible combinations? Pls answer ASAP
Answer:
There is 1 possible combination
Step-by-step explanation:
There are 5 assignments and they must be completed. 5. We want to find the number of combinations, then we use the formula of combinations.
[tex]nCr =\frac{n!}{r!(n-r)!}[/tex]
Where n is the total number of objects and you choose r from them
Then
[tex]n= 5\\\\r = 5[/tex]
[tex]5C5 =\frac{5!}{5!(5-5)!}[/tex]
[tex]5C5 =\frac{5!}{5!(0)!}[/tex]
[tex]5C5 =\frac{5!}{5!}[/tex]
[tex]5C5 =1[/tex]
Amanda saves $5 each week for 16 weeks. She spent 80% of her savings on a present for her mom. How much did her mom’s present cost?
Answer:
$64
Step-by-step explanation:
5 x 16 = $80
80% of $80 = $64
A manatee surfaced for air 3 times in 120 seconds. How many seconds went by before the manatee surfaced the first time if it held its breath for the same rate?
Answer:40
Divide 120 by 3
so lets simplify this equation to do it mentally
turn 120=12
now 12÷ 3=4
the zero from 120 will be added to 4
because of the tens place it becomes 40
hope this helps! if so please leave a brainliest.
What similarity statement can you write relating the three triangles in the diagram?
Answer:
Option A
Step-by-step explanation:
Suppose ∠I = 30° in ΔHIF,
∴ ∠F = 60°
Now consider the ΔGFH,
∠G = 90° and ∠F = 60°
∴ ∠GHF = 30°
Also in ΔGHI,
∠G = 90° and ∠I = 30°
∴∠GHI = 60°
∴ ΔGFH ≈ ΔGIH ≈ ΔHIF
Answer:
a
Step-by-step explanation:
3.
(07.04A)
If y = 5x − 4, which of the following sets represents possible inputs and outputs of the function represented as ordered pairs? (4 points)
{(0, −4), (2, 6), (4, 20)}
{(0, −4), (2, 6), (4, 16)}
{(0, 4), (2, 6), (4, 16)}
{(0, 4), (2, −6), (4, 20)}
Answer:
the answer is B {(0,-4),(2,6)(,4,16)
happy to help
Answer:
B {(0,-4),(2,6)(,4,16)
Step-by-step explanation: