Answer:
d. 64
Step-by-step explanation:
x^1/2 = 8
Square each side
(x^1/2 )^2=( 8)^2
x = 64
Answer:
(d) 64
Step-by-step explanation:
Please write either x^(1/2) or x^0.5 or √x, to reduce the chances of misinterpreting your input.
√x = 8 becomes x = 64 when both sides are squared.
This corresponds to answer (d).
what is the following difference 11 sqrt 45 - 4 sqrt 5
Answer:
29*sqrt(5)
Step-by-step explanation:
Start with sqrt (45). You must reduce it to it's prime factors.
45: 9 * 5 9 is not prime so reduce it.
45: 3 * 3 * 5
When you write √45, you should replace it with √(3*3*5)
The rule is
Rule: when you have a pair of equal prime factors under a root sign, you can take one out and throw one away.
Rule 2: If there are an odd number of equal primes one of them will be left underneath the root sign.
√45 = 3√5
11sqrt(45) - 4 sqrt(5) Substitute for 45
11*3*sqrt(5) - 4sqrt(5) Take out sqrt(5) using the distributive property.
(11*3 - 4)*sqrt(5) Combine 11 * 3
(33- 4) * sqrt(5) Do the subtraction
29 * sqrt(5) Answer
The correct answer is 29[tex]\sqrt{5}[/tex]
The third option.
multiplying mixed numbers and whole numbers 1 1/2 x 2/1 =
Answer: 3
Step-by-step explanation:
1. Convert the mixed number to fraction:
- Multiply the denominator of the fraction by the whole number.
- Add the product obtained and the numerator of the fraction.
- Write the sum obtained as the numerator and rewrite the original denominator of the fraction.
Then:
[tex]1\ 1/2=\frac{(1)(2)+1}{2}=\frac{3}{2}[/tex]
2. Multiply the numerators.
3. Multiply the denominator.
4. Reduce the fraction.
Then:
[tex](\frac{3}{2})(\frac{2}{1})=\frac{6}{2}=3[/tex]
Hayden mixed 6 cups of blue paint with 8 cups of yellow
paint to make green paint. Write an equation that shows the
relationship between the number of cups of blue paint, b,
and the number of cups of yellow paint, y, that are needed to
create the same shade of green paint. The equation should
be in the form b=ky.
Answer:
the answer is probably 6x:8y
Step-by-step explanation:
In each case, determine if the sides form a right triangle. If they do, place in the Yes column. If not, place them in the No column.
The question is asking to determine whether given sets of sides form a right triangle using Pythagorean theorem. The theorem is verified if the square of the length of the longest side equals the sum of the squares of the two other sides. However, some approximations might not perfectly fit the theorem but still form a right triangle.
Explanation:The subject of this question is the Pythagorean Theorem in the field of Mathematics. The theorem is a fundamental principle in Geometry which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as: a² = b² + c².
To determine whether or not a set of sides forms a right triangle, you would need to check if the lengths satisfy the Pythagorean theorem. If they do, then the sides are potentially those of a right triangle. For instance, if you're given sides with lengths 3, 4, and 5, you can check if 5² equals 3² + 4². Since 5² = 25 and 3² + 4² = 9 + 16 = 25, the sides do form a right triangle.
However, checking with the Pythagorean theorem is only conclusive if the lengths already satisfy the theorem. There might be situations where the length measurements are approximations and might not perfectly fit the theorem despite forming a right triangle.
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Using similar triangles to find an unknown value. What is the value of x?
Find the distance between the two points. Round to the nearest tenth if necessary. (6, 11), (0, 3) a. 10 b. 14 c. 15 d. 100
Answer: option a
Step-by-step explanation:
You must apply the formula for calculate the distance between the two points. which is shown below:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Therefore, keeping on mind that the points given in the problem are (6, 11), (0, 3), when you substitute values into the formula shown above, you obtain that the distance between these two points is the following:
[tex]d=\sqrt{(0-6)^2+(3-11)^2}\\d=10[/tex]
Answer:
a. 10
Step-by-step explanation:
We have been given two points (6, 11) and (0, 3). Now we need to find the distance between points (6, 11) and (0, 3) and check which of the following choices are correct:
(6, 11), (0, 3) a. 10 b. 14 c. 15 d. 100
Also we should round to the nearest tenth if necessary.
Apply distance formula :
[tex]distance =\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]
[tex]distance =\sqrt{\left(0-6\right)^2+\left(3-11\right)^2}[/tex]
[tex]distance =\sqrt{\left(-6\right)^2+\left(-8\right)^2}[/tex]
[tex]distance =\sqrt{36+64}[/tex]
[tex]distance =\sqrt{100}[/tex]
[tex]distance =10[/tex]
Hence correct choice is a. 10
2/3miles equal how many feet
Answer: 3,520 feet
Step-by-step explanation:
To solve this exercise you must apply the proccedure shown below.
You know that 1 miles is equal to 5,280 feet.
1 mile=5,280 feet (This is the conversion factor that you should use)
Then, keeping the above on mind, you can convert 2/3 miles to feet as following:
[tex](\frac{2}{3}miles)(\frac{5,280feet}{1mile})=3,520feet[/tex]
If a 13-foot ladder makes a 58 angle with the ground, how many feet up a wall will it reach? Round your answer to the nearest tenth.
Answer:
11.02 = a, rounded to the nearest 10th
Step-by-step explanation:
The length of the ladder (13 ft) forms the hypotenuse of the triangle when leaned against the house. The distance the ladder goes up the wall is the side opposite to the angle we are working with, so we can use the sine function to solve.
Sin X = (opposite side)/(hypotenuse)
Sin 58 = a/13
13(Sin 58) = a
11.02462525 = a
11.02 = a, rounded to the nearest 10th
A 13-foot ladder making a 58-degree angle with the ground will reach approximately 6.9 feet up a wall when we use the cosine function to calculate the height.
To find how many feet up a wall a 13-foot ladder will reach when it makes a 58-degree angle with the ground, we can use trigonometric functions, specifically the cosine function for adjacent and hypotenuse in a right-angled triangle.
The formula we will use is:
cosine(angle) = [tex]\frac{height}{hypotenuse}[/tex]
Re-arranging the equation to solve for the adjacent side, we get:
adjacent side = cosine(angle) * hypotenuse
Now plug in the values:
adjacent side = [tex]cosine(58 ^0) * 13 feet[/tex]
We can calculate the cosine of 58 degrees using a calculator and multiply it by 13, which will give us the height the ladder reaches on the wall. Let's calculate:
adjacent side = 0.5299 * 13 feet
adjacent side = 6.8887 feet
Therefore, a 13-foot ladder at a 58-degree angle with the ground will reach approximately 6.9 feet up a wall.
HELP!
Find the difference: 45.6 - 0.01
A) 35.6
B) 44.59
C) 44.6
D) 45.59
It would be D because 45.60-.01 would mean you subtract the .01 from the .60
Answer:
D)4.193
Step-by-step explanation:
How many solutions does this system have?
The system has Infinite solutions
Justin receives $15 and puts it into his savings account. He adds $0.25 to the account each day for a number of days, d, after that. He writes the expression 15+0.25(d−1) to find the amount of money in his account after d days. Which statement about his expression is true?
a. It is the sum of the initial amount and the additional amount after d days.
b.It is the product of the initial amount and the additional amount after d days.
c.It is the sum of the initial amount and the number of days, d.
d.It is the difference between the initial amount and the additional amount after d days.
Answer:
expression a
Step-by-step explanation:
The given expression is 15+0.25(d−1).
let suppose,
15 = a
0.25(d−1) = b
we get a + b
It clearly indicates the given expression is sum of two entities, we can exclude option b and option d.
Now we are left with option a and c, for that we have to evaluate the term b
b = 0.25(d−1) that is the additional amount after d days
Therefore, expression a is correct.
Answer:
It is the sum of the initial amount and the additional amount after d days.
Step-by-step explanation:
It is the sum of the initial amount and the additional amount after d days. i have ttm
what is 0.01% in decimal value
Answer:
your answer is 0.001
Step-by-step explanation:
you multiply by 100
move the decimal two places to the right
~~→hope this helps← ~~
║bangtanboys7║
Answer:
you get 0.001
Step-by-step explanation:
Convert the percentage to a fraction by placing the expression over 100 . Percentage means 'out of 100 '.
[tex]\frac{0.01}{100}[/tex]
Convert the decimal number to a fraction by shifting the decimal point in both the numerator and denominator. Since there are 2 numbers to the right of the decimal point, move the decimal point 2 places to the right.
[tex]\frac{1}{0000}[/tex]
Convert the fraction to a decimal by dividing the numerator by the denominator. then you get 0.001 as your answer
Hope This Helps
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please answer ASAP
The central angle is described by angle AOC
What is the central angle?
A central angle is an angle formed by two radii (lines from the center of a circle) that intersect at a point on the circle's circumference.
It is called "central" because it originates from the center of the circle.
In this case, the radii are AO and CO
Central angles are essential in geometry
how many eighths of an inch are in 1/4
Answer:
One eighth is one part of eight equal sections. Two eighths is one quarter and four eighths is a half. It's easy to split an object, like a cake, into eighths if you make them into quarters and then divide each quarter in half.
There are two eighths of an inch in a quarter of an inch.
Explanation:The student is asking how many eighths of an inch are in 1/4 of an inch. To get the answer, you have to ask "how many 1/8's fit into 1/4". Since 1/4 is the same as 2/8, there are two eighths in one quarter.The student is asking how many eighths of an inch are in 1/4 of an inch. To get the answer, you have to ask "how many 1/8's fit into 1/4". Since 1/4 is the same as 2/8, there are two eighths in one quarter.The student is asking how many eighths of an inch are in 1/4 of an inch. To get the answer, you have to ask "how many 1/8's fit into 1/4". Since 1/4 is the same as 2/8, there are two eighths in one quarter.
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There are 3.5 times as many cats as there are dogs. If there are 28 dogs, how many cats are there?
Answer:98 I believe
Step-by-step explanation:
Answer:
98.
Step-by-step explanation:
Number of cats = 28 * 3.5
= 98 cats.
That's a zoo!!
if f(x)=-4x^2-6x-1 and g(x)=-x^2-5x+3, fine (f-g)(x)
Answer:
[tex]\large\boxed{(f-g)(x)=-3x^2-x-4}[/tex]
Step-by-step explanation:
[tex](f-g)(x)=f(x)-g(x)[/tex]
[tex]f(x)=-4x^2-6x-1,\ g(x)=-x^2-5x+3\\\\(f-g)(x)=(-4x^2-6x-1)-(-x^2-5x+3)\\\\(f-g)(x)=-4x^2-6x-1-(-x^2)-(-5x)-3\\\\(f-g)(x)=-4x^2-6x-1+x^2+5x-3\qquad\text{combine like terms}\\\\(f-g)(x)=(-4x^2+x^2)+(-6x+5x)+(-1-3)\\\\(f-g)(x)=-3x^2-x-4[/tex]
Determine the binomial probability
Answer:
21. Option d
22. Option b
23. Option b
Step-by-step explanation:
The formula to calculate the binomial probability is represented as follows.
[tex]P(X=x) = \frac{n!}{x!(n-x)!}p^x(1-p)^{n-x}[/tex]
The formula to calculate the binomial probability is represented as follows.
In this formula x represents the number of successes, n represents the number of times the experiment is repeated, p represents the probability of success.
1. First we are asked to calculate the probability of obtaining 3 successes, with n = 6 and p = 0.35.
Then we substitute the values in the formula [tex]P(X=3) = \frac{6!}{3!(6-3)!}(0.35)^3(1-0.35)^{6-3}\\\\P(3) = 0.2354[/tex]
Option d.
2. Second we are asked to calculate the probability of obtaining 5 successes, with n = 20 and p = 60%, p = 0.6.
[tex]P(X=5) = \frac{20!}{5!(20-5)!}(0.6)^5(1-0.6)^{20-5}\\\\P(5) = 0.00129[/tex]
option b
3. Third we are asked to calculate the probability of obtaining 2 successes, with n = 10 and p = 1/2, p = 0.5.
[tex]P(X=2) = \frac{10!}{2!(10-2)!}(0.5)^2(1-0.5)^{10-2}\\\\P(2) = 0.04394[/tex]
option b
one side of a sqaure is 10 units which is greater, the number sqaure units for the area of the sqaure or the number of units for the preimeter explain
The area is greater because you multiply 10 by 10. The perimeter is all the sides added together so that would be 40 units. All sides of the square are the same. Area is length times width
The area of a square with a side of 10 units is 100 square units, which is greater than its perimeter of 40 units, because the area measurement squares the side's length, whereas the perimeter is a sum of side lengths.
To determine which is greater between the area of a square and its perimeter, we start by understanding that the area of a square is calculated by squaring the length of one side. In this case, the square's side is 10 units, so the area is 10 units imes 10 units = 100 square units. The perimeter of a square is the sum of all its sides, which is 4 times the length of one side. Hence, the perimeter is 10 units times 4 = 40 units.
As a result, the area, which is 100 square units, is greater than the perimeter, which is 40 units. This demonstrates that while the perimeter is a measure of the distance around the square, the area represents the entire space enclosed within it, leading to larger numerical values when the sides of the square are squared as opposed to simply multiplied by four.
If a parallelogram is inscribed in a circle, then it must be a? A. Triangle B.rhombus C. Rectangle D. Trapezoid
The answer for your question is:
C: Rectangle
If a parallelogram is inscribed in a circle, then it must be a Rectangle
What is a parallelogram?Any quadrilateral in which opposites sides are parallel is called a parallelogram.
What is a triangle?Any 2 dimensional figure bounded by 3 sides and sum of all the angles is 180° is called a triangle.
What is a rhombus?A parallelogram with four equal sides and sometimes one with no right angles is called a rhombus.
What is a rectangle?A rectangle is a four sided quadrilateral, having all the internal angles equal to 90 degrees and opposite sides are equal.
What is a trapezoid?A trapezoid is a quadrilateral with one pair of opposite sides parallel.
How to know what the parallelogram will be if it is inserted in a circle ?We know that if a quadrilateral is inscribed in a circle then the sum of its opposite sides will be supplementary (180°)We know that all the angles of a rectangle is 90°. So sum of opposite angles will be 180°.This follows the characteristics features of a circle.
So the required parallelogram will be a rectangle.
Option C is correct.
In rhombus and trapezoid the sum of opposite angles are not 180°.A triangle is not a parallelogram.So, options A , B, D are incorrect.
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What is the answer to this please?
Answer:
D
Step-by-step explanation:
The sides of a regular hexagon are congruent
Given that 1 side = 15in, then
perimeter = 6 × 15 = 90 in → D
Farimah and Helio are standing 15 ft. apart from each other and looking up at a kite that is with the flying between them. Farimah is flying the kite on a 57 ft. string at an angle of 68° with the ground. How far is Helio from the kite?
A. 64.1 ft.
B. 56.2 ft
C. 60.0 ft.
D. 53.2 ft.
Answer:
D. 53.2 ft.
Step-by-step explanation:
As you can see in the diagram, Farimah, Helio, and the kite are making a triangle. We know from our problem that the distance from Farimah to Helio is 15 ft, the distance from Farimah to the kite is 57 ft, and the angle of elevation from Farimah to the kite is 68°. From this situation, we can infer that we have two sides of the triangle and the angle between those sides; therefore, we can use the law of cosines to find the third side, which is the distance form Helio to the kite:
[tex]c^2=a^2+b^2-2abcos(C)[/tex]
[tex]c^2=57^2+15^2-2(57)(15)cos(68)[/tex]
[tex]c=\sqrt{57^2+15^2-2(57)(15)cos(68)}[/tex]
[tex]c=53.2[/tex]
We can conclude that Helio is 53.2 ft from the kite.
Answer:
D. 53.2
You can use the Law of Cosines to solve.
Pls help me with number and thanks!
Answer:
the answer would be 3,-5
Step-by-step explanation:
you rotate it in a 90 degree clockwise rotation and you end up with 3,5 and when you reflect it upon the x-axis your point ends up at 3,-5
Answer:
3,-5
Step-by-step explanation:
If you rotate it in a 90 degree rotation in the clock direction you will end in 3.5 and your x-axis will result in 3.5.
Which set of data contains two outliers
Answer:
you need to list the sets of data.
Step-by-step explanation:
can someone help me with these 2?
answer: 1 over 165 step by step: #1 Evaluate the power 5 to the power of 1= 5 because any expression raised to the power of 1 if u asking what's is an expression the expression is five and together is 5 to the power of 1) #2 if a term like five doesn't have a exponent the exponent is 1) #3 remove the parathesis ) #4 subtract 1 and -2 u get 1 over 5 to the power of -4 and 5 to the power of negative four is 1 over 165) the second I don't know
Please help me find DG on the attached diagram. Thanks!
Answer:
Step-by-step explanation:
DG=x+20
DG=2x+17+8+2
x+20=2x+27
20=x+27
-7=x
DG=13
Answer:
DG = 20
Step-by-step explanation:
We are given a straight line DG with point E and F on it and we are to find the length of DG.
We have [tex] D E = 2 x + 7 [/tex], [tex] E F = 8 [/tex], [tex] F G = 2 [/tex] and [tex] D G = x + 20 [/tex].
So we can write it as:
[tex] DG = DE + EF + FG [/tex]
[tex]x+20 = 2x+17+8+2[/tex]
[tex]2x-x=20-17-8-2[/tex]
[tex]x=-7[/tex]
Substituting this value of [tex]x[/tex] to find DG:
DG = [tex]+x+20 = -7+20[/tex] = 13
Which is an equation of a direct proportion?
a.y=1/6x+6 b.y=6/x
c.y=6x-6 d.y=6x
Answer:
Option D. y=6x
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
Verify each case
case a) y=(1/6)x+6
Is a linear equation, but is not a direct variation. The line not passes through the origin
case b) y=6/x
The equation represent an inverse variation
case c) y=6x-6
Is a linear equation, but is not a direct variation. The line not passes through the origin
case d) y=6x
The equation represent a direct variation
Final answer:
Among the options provided, option d. y = 6x is the equation of a direct proportion because it follows the form y = kx where k is the constant of proportionality and there is no added or subtracted constant.
Explanation:
The equation of a direct proportion is one where the dependent variable changes at the same rate as the independent variable. In mathematical terms, if two variables y and x are directly proportional, it implies that y = kx, where k is the constant of proportionality.
Looking at the options provided:
a. y = 1/6x + 6 is not directly proportional because of the addition of the constant 6.
b. y = 6/x is an inverse proportion because y changes inversely with x.
c. y = 6x - 6 is also not directly proportional due to the subtraction of the constant 6.
d. y = 6x perfectly fits the definition of direct proportionality as there is no added or subtracted constant and it follows the form y = kx.
Therefore, the equation of a direct proportion among the options given is d. y = 6x.
Plz help !! Needed to graduate
Answer: [tex]\bold{\dfrac{-5\pm 2\sqrt{10}}{3}}[/tex]
Step-by-step explanation:
[tex]5-10x-3x^2=0\quad \rightarrow \quad a=-3,\ b=-10,\ c=5\\\\\\\text{Quadratic formula is: }x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\\x=\dfrac{-(-10)\pm \sqrt{(-10)^2-4(-3)(5)}}{2(-3)}\\\\\\.\ =\dfrac{10\pm \sqrt{100+60}}{2(-3)}\\\\\\.\ =\dfrac{10\pm \sqrt{160}}{2(-3)}\\\\\\.\ =\dfrac{10\pm 4\sqrt{10}}{2(-3)}\\\\\\.\ =\dfrac{-5\pm 2\sqrt{10}}{3}[/tex]
Find the doubling time of an investment earning 7% interest if interest is compounded continuously
Answer:
The doubling time of this investment would be 9.9 years.
Step-by-step explanation:
The appropriate equation for this compound interest is
A = Pe^(rt), where P is the principal, r is the interest rate as a decimal fraction, and t is the elapsed time in years.
If P doubles, then A = 2P
Thus, 2P = Pe^(0.07t)
Dividing both sides by P results in 2 = e^(0.07t)
Take the natural log of both sides: ln 2 = 0.07t.
Then t = elapsed time = ln 2
--------- = 0.69315/0.07 = 9.9
0.07
The doubling time of this investment would be 9.9 years.
To calculate the doubling time for an investment earning 7% interest compounded continuously, the Rule of 70 is used, which suggests that the investment will double in approximately 10 years.
To find the doubling time of an investment earning 7% interest compounded continuously, we can use the Rule of 70. The Rule of 70 is a quick and useful formula that estimates the number of years it takes for an investment to double given a fixed interest rate, specifically for interest rates below 10%. Here's how you can use it:
Take the number 70 and divide it by your interest rate. In this case, the interest rate is 7%.The formula looks like this: Doubling Time (in years) = 70 / interest rate.Therefore, the doubling time for an investment earning a 7% interest rate is approximately 70 / 7, which equals 10 years.The Rule of 70 assumes continuous compounding. Thus, if an investment has a consistent return of 7% per year, compounded continuously, it will take roughly 10 years to double.
It's also worth noting that the Rule of 72 can be used in a similar way to estimate the doubling time more roughly. In this case, using the Rule of 72, dividing 72 by the interest rate of 7% would provide an estimation of approximately 10.3 years. This is a close approximation and often used due to its simplicity.
Find the circumference of a circle with radius,
r
= 7.5m.
Give your answer rounded to 1 DP.
Answer: C≈47.12m
Step-by-step explanation:
C=2π r=2· π· 7.5≈47.12389m
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a computer store sells computers for 10% more than they pay for them . if the store pays x dollars for a computer , which expression would represent the prince for which the store would sell the computer? a. 0.10x / b. 0.9x / c.1.1x / d. 10x
Answer: C
Explanation:
If a store paid x dollars to buy the computer and they sold it for 10 percent extra, it would be x+.1x. We can use the distributive property to get that x+.1x=x(1+.1) to get 1.1x, or C
Answer: c.1.1x
Step-by-step explanation:
Hi, the correct option is c.1.1x.
Since the price they paid for the computer is 100%, if they sell them for 10% more:
100%+10% =110% (sales percentage)
So, for a price x, to obtain the selling price we have to multiply the price (x) by the sales percentage in decimal form (110/100= 1.1)
The final expression is:
1.1x