You can find the prime factorization of 360 by dividing it by 2. Then you get 2 * 180. 180 can be simplified to 2 * 90. 90 can be simplified to 2 * 45. 45 can simplified to 3 * 15. 15 can be simplified to 3 * 5.
The prime factorization of 360 is 2^3 * 3^2 * 5.
You can check that answer. 2^3 = 8 → 3^2 = 9 → 8 * 9 * 5 = 360
The length of a chord is equal to its distance to the center of the circle. A second chord in the same circle is twice as long as the first one. How far is the second chord from the center?
Answer:
The distance from the center of the circle to the longer chord is twice smaller than the distance from the center to the shorter chord.
Step-by-step explanation:
The length of the chord AB is the same as the distance OC from the center to the cord. Let OC=2x, then CA=x. By the Pythagorean theorem, the radius r of the circle is
[tex]r^2=OC^2+AC^2,\\ \\r^2=(2x)^2+x^2=5x^2,\\ \\r=\sqrt{5}x.[/tex]
The length of the arc ED is 4x.
Consider right triangle EFO. In this triangle, EF=2x, EO=r, then the distance OF is
[tex]OF^2=OE^2-EF^2,\\ \\OF^2=5x^2-(2x)^2=x^2,\\ \\OF=x.[/tex]
The distance from the center of the circle to the longer chord is twice smaller than the distance from the center to the shorter chord.
The distance between the second chord from the center of the circle is 'a' (half the length of the first chord).
What is a chord?A circle chord is a straight line segment with both endpoints on a circular arc.
As the length of a chord is equal to its distance to the center of the circle, therefore, the length of the chord and the distance to the center of the circle is 2a. Thus, In ΔAOB the length of the third side of the triangle can be written as,
[tex]OA^2= OB^2+AB^2\\\\OA^2 =(2a)^2+a^2\\\\OA^2=5a^2\\\\OA = a\sqrt5[/tex]
Now, OA and OQ are the radii of the circle and the length of the radius of the circle is a√5 units.
Now, the length of the second chord in the same circle is twice as long as the first one, therefore, the length of the half chord is 2a. Therefore, in ΔAOB the length of the perpendicular side of the triangle can be written as,
[tex]OQ^2=OP^2+PQ^2\\\\(a\sqrt5)^2= OP^2+(2a)^2\\\\5a^2-4a^2=OP^2\\\\OP = a[/tex]
Hence, the distance between the second chord from the center of the circle is 'a' (half the length of the first chord).
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please help me with this
Answer:
s - 8
Step-by-step explanation:
TO find the function rule, substitute (s-2) in place of v. Then simplify.
h(v) = v - 6
h(s - 2) = (s - 2) - 6
h(s - 2) = s - 8
A car servicing station is running a special offer. The breakdown of the cost for different services is given below.
Membership Fee: $50 (one-time cost)
Air Freshener Cost: $4 per car per month
Washing Cost: $10 per car per month
Tire Replacement Cost: $400 per car
Tire Pressure Check Cost: $15 per month
The total cost for 12 months of this service for n cars is given by the expression below.
568n + 230
Answer:
Option C
Step-by-step explanation:
There are several types of costs in this problem:
* Unique costs
* Costs that depend on the number of cars
* Costs that depend on the number of months
* Costs that depend on the number of months and the number of cars.
The costs that depend on the number of cars represent the coefficient of the variable n.
The costs that do not depend on the number of cars represent the constant value of the equation.
Then, to solve this problem you must identify the costs that do not depend on the number of cars.
These costs are:
* Membership Fee: $ 50 (one-time cost)
* Pull Pressure Check Cost: $ 15 per month
[tex]\$50 + \$15(12\ month) = \$230[/tex]
Then the answer is option C
Graph the solution for the following linear inequality system. Click on the graph until the final result is displayed. x + y ≤ 6 x ≤ 4
Answer: The graph is attached.
Step-by-step explanation:
The region is limited by two lines:
[tex]x+y=6[/tex] and [tex]x=4[/tex]
You can write the first inequlity [tex]x+y\leq6[/tex] in the following form:
[tex]y\leq-x+6[/tex]
This region are all the values for which the y-axis is less than the line f(x)=x+6 (all the values under the line).
The other inequality x ≤ 4 are all the values for which the x-axis is less than the line x=4 (all the values to the left of the line).
Observe the graphs attached.
Answer:
its this one
Step-by-step explanation:
what number is 4.0003 x 10^7 in scientific notation
4.0003 x 10^7 is already in scientific notation. If you mean in regular notation/as a regular number, it is 40003000. Since it is 10 to the power of positive 7, you move the decimal place 7 to the right.
Answer:
40,003,000
Step-by-step explanation:
The given number is :
[tex]4.0003\times 10^{7}[/tex]
As we can see that [tex]4.0003\times 10^{7}[/tex] is already in scientific notation.
Scientific notation means writing numbers in powers of 10.
Hence, we can write this notation in regular way as:
40,003,000
What is the volume of a cylinder with a radius of 7 feet and a height of 12 feet? Use 3.14 for pi. Round your answer to the nearest hundredth. (4 points)
1,846.32 cubic feet
1,950.25 cubic feet
1,999.21 cubic feet
2,000.31 cubic feet
Answer:1846.32
Step-by-step explanation:
3.14 times 7 squared times 12 equals 1846.32
The answer should be 1846.32 ft³
write the equation 2/3 of c subtracted from 2
Hello.
You would write the equation like this: [tex]\frac{2}{3} c - 2[/tex]
Let me know if that was what you were looking for.
Plz help !! Needed to graduate
Answer: 3x
Step-by-step explanation:
[tex]\dfrac{\sqrt[3]{54x^5}}{\sqrt[3]{2x^2}}=\dfrac{\sqrt[3]{3\cdot 3\cdot 3\cdot 2\cdot x\cdot x\cdot x\cdot x^2}}{\sqrt[3]{2x^2}}=\dfrac{3x\sqrt[3]{2x^2}}{\sqrt[3]{2x^2} }=\boxed{3x}[/tex]
what is the answer to this problem? simplify 3^5*3^4
Answer:
3^9
Step-by-step explanation:
We we multiply exponents with the same base, we can add the exponents
a^b * a*c = a^(b+c)
3^5 * 3^4
3^(5+4)
3^9
You have $20.43 in your wallet. You find $5.12 in your pocket before washing your clothes. How much money do you have?
20.43+5.12=25.55 so ur answer is 25.55
Answer:
$25.55
Step-by-step explanation:
43+ 12 =55
20+5=25
The answer is $25.55.
Identify the figure formed by the net
Answer:
cylinder
Step-by-step explanation:
The description below represents Function A and the table represents Function B: Function A The function is 2 more than 5 times x. Function B x y −1 2 0 5 1 8 Which statement is correct about the slope and intercept of the two functions?
Answer:
The slope of Function A is greater than the slope of function B while the y-intercept of Function B is greater than the y-intercept of function A.
Step-by-step explanation:
Function A is f(x) = 5x + 2
The slope is 5 and the y-intercept is (0, 2).
Function B. The slope is (5-2) / (0- -1) = 3.
also (8-5) / (1 - 0) = 3
The slope is 3.
The y-intercept is at (0, 5) because one point on the graph is (0, 5).
Answer:
Their slopes are equal but y-intercepts are not equal.
Step-by-step explanation:
Its simple arithmatics
How can you calculate realative frequencies as percents?
Answer:
1. Count the total number of items. In this chart the total is
2. Divide the count (the frequency) by the total number.
3. Then, convert it to a percent.
Answer ASAP
Which two expressions are equivalent to 6 * V * W * 1/2
A. 1 * 3 * v * w + 0
B. 3(v + w)
C. 3 * v * w
D. w * v * 1/2 * 6 + 1
E. 2 * v * w
* = multiplication
The answer is C. Hope this helps!
Which pair of expressions has equivalent values?
Answer:
first one
Step-by-step explanation:
first one
1^13 = 1
1^15 = 1
P.S.
1 to the exponent of any number is equal 1
Answer:
1¹³ and 1¹⁵
Step-by-step explanation:
The answer does not change however we add or reduce the exponents. This is the uniqueness of the integer 1. When the others are tried, 6¹=6 and 9¹=9
7⁸=5764801 and 8⁷=2097152
9²=81 and 4³=64
Therefore the integer 1 is the only number that is not affected by exponents.
Given the graph of a circle and a line, how many solutions to the system of equations exist?
-no solutions
-one
-two
-three
Answer:
First Option
Step-by-step explanation:
The number of solutions is given by the values in which the equation of the circumference is equal to the equation of the line.
In other passwords the number of solutions is equal to the number of times the line intersects or touches the circumference.
Notice in the graph that the line does not touch the circumference.
Therefore for this case there are no solution
Answer:
The answer is A (no solution)
Step-by-step explanation:
which shows a perfect square trinomial?
Answer:
THE THIRD ONE I THINK :D
21....................
Answer:
The answer is (b) ⇒[tex]\frac{d^{5} }{2\sqrt{c} }[/tex]
Step-by-step explanation:
∵ [tex]\frac{\sqrt{c^{2}d^{6}}}{\sqrt{4c^{3}d^{-4}}}[/tex]
∵ √x² = x ⇒ that means to cancel the square root divide
the power by 2
∴ [tex]\sqrt{c^{2}d^{6}}=cd^{3}[/tex]
∵ √4 = 2 ⇒ √2×2 = √2² = 2
∵ √c³ = [tex]c^{\frac{3}{2}}[/tex]
∴ [tex]\sqrt{4c^{3}d^{-4}}=2c^{\frac{3}{2}}d^{-2}[/tex]
∴ [tex]\frac{cd^{3}}{2c^{\frac{3}{2}}d^{-2}}[/tex]
∵ In the same base with multiplication we add the power,
in same base with division we subtract the power
∴ [tex]\frac{1}{2}c^{1-\frac{3}{2}}d^{3-(-2)}=\frac{1}{2}c^{\frac{-1}{2}}d^{5}=[/tex]
[tex]\frac{d^{5}}{2c^{\frac{1}{2}}}=\frac{d^{5}}{2\sqrt{c}}[/tex] ⇒ [tex]c^{\frac{1}{2}}=\sqrt{c}[/tex]
∴ The answer is (b) ⇒ [tex]\frac{d^{5}}{2\sqrt{c}}[/tex]
Answer:
b. [tex]\frac{d^{5}}{2\sqrt{c} }[/tex]
Step-by-step explanation:
The given expression is
[tex]\frac{\sqrt{c^2d^6} }{\sqrt{4c^3d^{-4}} }[/tex]
We simplify the radicand using the property; [tex]\frac{a^m}{a^n} =a^{m-n}[/tex]
[tex]\frac{\sqrt{d^{6--4}} }{\sqrt{4c^{3-2}} }[/tex]
[tex]\frac{\sqrt{d^{10}} }{\sqrt{4c^{1}} }[/tex]
[tex]\frac{d^{5}}{2\sqrt{c} }[/tex]
How can x + 3 = −2x + 5 be set up as a system of equations?
Answer:
y = x+3; y = -2x +5
Step-by-step explanation:
x + 3 = -2x + 5
Let y = x + 3 = -2x + 5
If a = b = c then a=b and a=c
we can write the equation as
y = x + 3 and y = -2x + 5
Thus, this is the system of equations
y = x + 3
y = -2x + 5
Answer:
y = x + 3 and y = -2x + 5
Step-by-step explanation:
If we consider one set of equation as:
[tex] y = x + 3 [/tex]
and the other set of equation as:
[tex] y = - 2 x + 5 [/tex]
Since the left hand side for both these equations is same, therefore we can equate the right hand side and write it as:
[tex] x + 3 = - 2 x + 5 [/tex]
The current in a simple electric circuit varies inversely as the resistance. If the current is 20amps when the resistance is 5 ohms, find the current when the resistance is 8 ohms
Answer:
0.5amps
Step-by-step explanation:
I is inversely proportional to resistance
I = k/R
k = I/ R
k = 20/5
k = 4
This means that, I = 4/R
So, when R = 8ohms,
I = 4/8
=0.5amps
Using Ohm's law, the inverse relationship between current and resistance in a simple circuit allows calculation of the new current as 12.5 amps when the resistance changes from 5 ohms to 8 ohms.
Explanation:The student's question involves an application of Ohm's law, which is a fundamental principle in Physics that relates electric current (I), resistance (R), and voltage (V). According to Ohm's law, in a simple circuit, the current is inversely proportional to the resistance when the voltage is held constant. Given that the current is 20 amps when the resistance is 5 ohms, we can write the relationship as I1 * R1 = I2 * R2 where I1 and R1 are the initial current and resistance, and I2 and R2 are the final current and resistance we wish to find.
Plugging in the given values, we have:
20 amps * 5 ohms = current when resistance is 8 ohms * 8 ohms
Solving for the current when the resistance is 8 ohms:
20 amps * 5 ohms = I2 * 8 ohms
100 = I2 * 8
I2 = 100 / 8
I2 = 12.5 amps
Therefore, the current when the resistance is 8 ohms is 12.5 amps.
A swimming pool had 2.5 million liters of water in it. Some water evaporated, and then the pool only had 2 million liters in it.
Answer:
The swimming pool lost 500,000 liters
Step-by-step explanation:
Now it only has .5 million liters now
1. What is the solution to the system of equations?
3x + 4y = 12
x + 2y = 10
(a) Show how to solve the system of equations using the linear combination or elimination method.
(b) Show that you can get the same answer by using the substitution method.
Please help worth 93 points
Answer:
Step-by-step explanation:
(a) In order to use the elimination method, multiply the second equation by 2.
It becomes 2x + 4y = 20.
Subtract that from the first equation: 3x + 4y = 12
3x + 4y - 2x - 4y = 12 - 20
x = -8
Put that back in the second equation: -8 + 2y = 10
2y = 18
y = 9
(b) In order to use the substitution method, subtract 2y from the second equation.
It becomes x + 2y - 2y = 10 - 2y
x = 10 - 2y
Substitute that into the first equation:
3(10 - 2y) + 4y = 12
30 - 6y + 4y = 12
30 - 2y = 12
2y = 18
y = 9
Put back into the equation for x:
x = 10 - 2(9)
= 10 - 18
= -8
Answer:
Step-by-step explanation:
(1) 3x + 4y = 12
(2) x + 2y = 10
(2)*3: 3x+6y=30
by elimination (2)*3 - (1)
6y-4y=30-12
2y=18
y=9
x+2(9)=10
x=-8
rearrange (2): x=10-2y
substitute in (1): 3(10-2y)+4y=12
30-6y+4y=12
2y=30-12
y=9
x=10-2(9)
=-8
same ans either way
g^2 +23 when. g=6 please help
Answer:
59
Step-by-step explanation:
Substitute.
6 ^ 2 = 36
36 + 23 = 59
help please! which choice represents the fraction below as a single exponential expression?
Answer:
B
Step-by-step explanation:
use the exponent rule of division: you just subtract the exponents if the base is the same, so 4-8=-4
The fraction with a numerator of 3.74 x 10⁻¹⁶ and a denominator of 10⁻³⁰ represented as a single exponential expression is 3.74 x 10¹⁴, obtained by dividing the digit terms and subtracting the exponents.
Explanation:To represent the fraction as a single exponential expression, you follow the division of exponentials rule, which involves dividing the digit terms and subtracting the exponents of the exponential terms. Given the fraction with a numerator of 3.74 x 10-16 and a denominator of 10-30, you would divide 3.74 (the digit term of the numerator) by 1 (the implied digit term of the denominator) which is just 3.74, and subtract the exponents (-16 - (-30)) which equals 14. Therefore, the fraction as a single exponential expression is 3.74 x 1014.
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Complete the factorization of 3x2 – 10x + 8.
3x2 – 10x + 8 = (x –
)(
x – 4)
Answer:
We shall use the method of splitting the middle term
To factorize
3x² - 10 x + 8
We need two numbers which add to give -10 and multiply to give 3 × 8 = 24
The numbers are -6 & -4
(-6)+(-4) = -10
(-6)(-4) = 24
So we shall split -10x as -6x - 4x
We get
3x² -10x + 8
= 3x² -6x -4x+8
Taking out 3x common from first two terms & -4 from the lest two terms we get
= 3x(x-2)-4(x-2)
Taking out (x-2) common we get
= (x-2)(3x-4)
So
3x² - 10x + 8 = (x-2)(3x-4)
Answer:
2 and 3
Step-by-step explanation:
on EDGE 2021
111 = 14g what is g??
Answer:
the answer to this is 7.9 or 7 13/14
Step-by-step explanation:
1. Divide both sides by 14
111/14 = 14g/14
2. Simplify
g = 7 13/14
Final answer:
The variable 'g' in the equation 111 = 14g is found by dividing 111 by 14, resulting in approximately 7.929 (rounded to 4 significant figures).
Explanation:
The equation given is 111 = 14g, which seems to be a simple algebra equation where you are solving for the variable g. To find g, you would divide both sides of the equation by 14 to isolate g.
This calculation yields: g = 111 / 14, which equals 7.92857142857. However, this number might need to be rounded depending on the context or instructions for significant figures. If the problem instructions mentioned 4 sig figs, the answer would be rounded to 7.929.
a laptop was originally sold for $975. The laptop is now on sale for $828.75. What is the percent markdown?
so the difference is 975 - 828.75 = 146.25.
now, if we take 975 to be the 100%, what is 146.25 off of it in percentage?
[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 975&100\\ 146.25&x \end{array}\implies \cfrac{975}{146.25}=\cfrac{100}{x}\implies 975x=14625 \\\\\\ x=\cfrac{14625}{975}\implies x=15[/tex]
A local grocer cut his marketing budget by 57% last year. He spent only $650 on marketing this year and is happy with his decision. How much did the grocer spend on marketing last year?
I know that the answer is $1511.63, I just need to know the math of how we get that answer.
To find out how much the grocer spent on marketing last year, we need to set up an equation with x as the original budget. By solving the equation, we find that the grocer spent approximately $1511.63 on marketing last year.
Explanation:To find out how much the grocer spent on marketing last year, we first need to determine the original marketing budget. Since the grocer cut their marketing budget by 57%, this means they spent only 43% of their original budget this year. Let's represent the original budget as 'x'.
Set up an equation: 43% of x = $650Convert 43% to decimal form by dividing by 100: 0.43x = $650Solve for x by dividing both sides of the equation by 0.43: x = $650 / 0.43Calculate the value of x using a calculator or long division: x ≈ $1511.63Therefore, the grocer spent approximately $1511.63 on marketing last year.
What is the distance between points D and H? Round to the nearest tenth of a unit. D(1,3) H(9,8)
Answer:
9.4 units
Step-by-step explanation:
To find the distance between two points D ( 1, 3 ) and H ( 9, 8 ), we can use the distance formula:
d = √(( x₂ - x₁ )² + ( y₂ - y₁ )² )
Substituting the coordinates, we have:
d = √( ( 9 - 1 )² + ( 8 - 3 )²)
Simplifying,
d = √( 8² + 5² )
d = √( 64 + 25 )
d = √89
d ≈ 9.4 units
The distance between point D and H to the nearest tenth is 9.4 units
What is distance between two points?The distance between two points is the length of the line segment joining them. Since the length of the line segment cannot be negative, the distance between two points is always positive.
The distance between two points is expressed as
S = √ X -x)² + (Y -y)²
= √ 9-1)² + 8-3)²
= √ 8² + 5²
= √ 64 +25
= √89
= 9.4 ( nearest tenth)
Therefore the distance between point D and H to the nearest tenth is 9.4 units
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What is the result of 3÷3/5
A.1/9
B.1/5
C.5
D.9
I WILL MARK BRAINLIEST AND GIVE ALL STARS with 30 points!
Answer:
C
Step-by-step explanation:
To divide 3 by 3/5
Leave the 3, change division to multiplication and turn the fraction upside down, that is
3 ÷ [tex]\frac{3}{5}[/tex]
= 3 × [tex]\frac{5}{3}[/tex]
= [tex]\frac{3(5)}{3}[/tex] = [tex]\frac{15}{3}[/tex] = 5 → C