t = mr^2/3
Divide both sides by r^2/3
m = t / r^2/3
Answer:
[tex]\large\boxed{m=\dfrac{3t}{r^2}}[/tex]
Step-by-step explanation:
[tex]\dfrac{mr^2}{3}=t\qquad\text{multiply both sides by 3}\\\\mr^2=3t\qquad\text{divide both sides by}\ r^2\\\\m=\dfrac{3t}{r^2}[/tex]
What is the answer to 8x^3+125 by factoring the perfect cube?
Answer:
[tex]\large\boxed{8x^3+125=(2x+5)(4x^2-10x+25)}[/tex]
Step-by-step explanation:
[tex]8x^3+125=2^3x^3+5^3=(2x)^3+5^3\\\\\text{use}\ a^3+b^3=(a+b)(a^2-ab+b^2)\\\\=(2x+5)((2x)^2-(2x)(5)+5^2)\\\\=(2x+5)(4x^2-10x+25)[/tex]
What is 10 minutes before 9
➷ To figure this out, you need to understand that there are 60 minutes in an hour
Subtract 10 from this value:
60 - 50
As it isn't 60 minutes, it wouldn't be 9 anymore
9-1 = 8
The correct answer would be: 8:50
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How many cubes are needed to fill the rectangular prism PLZ HUUURRRRRYYYYYY
Which of the following equations will make a V-shaped graph?
y = |x|
y = 2x
x 2 + 5 = y
y = 1/3x
Y=|x|. An absolute value has a V shape.
Final answer:
The equation that will make a V-shaped graph is y = |x|, as it plots the absolute value of x, creating a V shape by reflecting points on the positive side of the y-axis for both positive and negative values of x.
Explanation:
The student asked which of the following equations will make a V-shaped graph. The answer is y = |x|. This is because the absolute value function produces a graph that is V-shaped, reflecting the positive distance from zero for both positive and negative values of x. The other options presented, such as y = 2x, would produce a straight line; x² + 5 = y (correctly read as y = x² + 5) would produce a parabola; and y = 1/3x would also result in a straight line, just with a different slope. Only the graph of y = |x| has the distinct V shape as it plots the absolute value of x, meaning it reflects the points on the positive side of the y-axis for both positive and negative values of x.
Evaluate the exponential function f(x)=8^x+1 Which value completes the table?
A.0
B.3
C.9
D.25
The value of exponential function, which completes the table for variable x at 1/3 is 3. The option B is correct.
Exponential function is the function in which the function growth or decay with the power of the independent variable.
The curve of the exponential function depends on the value of its variable.
The exponential function with dependent variable y and independent variable x can be written as,
[tex]y=a^x[/tex]
Here, [tex]x[/tex] is the variable in the power of a number.
Given information-
The given exponential function in the problem is,
[tex]f(x)=8^x+1[/tex]
The value of function at the value of variable x as 1/3 has to be find to complete the table. Put 1/3 in the above equation on the place of x as,
[tex]f(x)=8^{\frac{1}{3}}+1[/tex]
The number 8 can be written as the [tex]2^3[/tex]. Thus,
[tex]f(x)=(2^3)^{\frac{1}{3}}+1\\f(x)=(2)^{\dfrac{3\times1}{3}}+1\\f(x)=(2)^1+1\\f(x)=2+1\\f(x)=3[/tex]
Thus the value of exponential function, which completes the table for variable x at 1/3 is 3. The option B is correct.
Learn more about the exponential function here;
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harold deposits $30 a week into a savings account. hid balance in his savings account grows by a constant rate. true or false
an online retailer sells cans of tennis balls look at the first rule to find the unit rate then use the unit rate to complete the table to show the cost of ordering 100 and 250 cans.
please help as soon as possible.
To find the unit rate, divide total cost by number of cans bought.
$30 / 12 cans = $2.50 per can.
Now multiply the unit cost by the number of cans you want to buy:
2.50 x 100 = $250.00
2.50 x 250 = $625
How did the absent minded professor burn his ear?
He was ironing when the phone rang.
The absent-minded professor burned his ear due to the lens effect caused by sunlight reflecting off a concave mirror. The mirror focused the sunlight onto his ear, causing it to burn.
Explanation:The absent-minded professor burned his ear due to the lens effect caused by sunlight reflecting off a concave mirror. When the professor held the mirror close to his ear and exposed it to sunlight, the mirror focused the sunlight onto his ear, causing it to burn.
The concave mirror has a curve that causes the light rays to converge at a specific point called the focal point. This concentrated light energy resulted in the burning sensation on the professor's ear.
This phenomenon is similar to using a magnifying glass to focus sunlight onto an object and create heat. The concave mirror acted as a magnifying glass, amplifying the intensity of the sunlight and leading to the ear burn.
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A rhombus has one diagonal that is 14 centimeters long and one diagonal that is 12. What is the area of the rhombus?
Answer:
168
14 times 12
Point O is the center of the circle. What is the value of X?
Answer options: 24, 15, 27, 20
Answer: FIRST OPTION
Step-by-step explanation:
To solve this problem you must apply the Intersecting Secant-Tangent Theorem. By definition, when a secant line and a tangent lline and a secant segment are drawn to a circle from an exterior point:
[tex](Tangent\ line)^2=(Secant\ line)(External\ Secant\ line)[/tex]
The total measure of the secant shown is:
[tex]18+Diameter[/tex]
If the radius is 7, then the diameter is:
[tex]D=7*2=14[/tex]
Therefore:
[tex]Secant\ line=18+14=32[/tex]
You also know that:
[tex]External\ Secant\ line=18\\Tangent\ line=x[/tex]
Keeping the above on mind, you can substitute values and solve for x:
[tex]x^{2}=32*18[/tex]
[tex]x=\sqrt{576}\\x=24[/tex]
The measure of the side length of the tangent line PQ to the circle O is 25 units
What is the measure of side length x?From the image, Line segment PQ is a tangent line because it touches the curve at point Q.
Therefore, triangle PQO forms a right triangle.
Leg 1 of the right triangle = OQ = 7
Leg 2 of the right triangle = PQ = x
Hypotenuse = PO = 18 + 7 = 25
Now, to solve for the measure of side length x, we use the Pythagoras theorem:
PQ = √( PO² - OQ² )
Plug in the values:
x = √( 25² - 7² )
x = √( 625 - 49 )
x = √576
x = 24
Therefore, the value of x is 24.
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Which expression is equivalent to
Answer:
[tex]\dfrac{7.7.7.7.7}{7.7}[/tex]
Step-by-step explanation:
Finding the expression of the value [tex]\dfrac{7^{5} }{7^{2}}[/tex] is just like taking the spread out value of the two variables raised to their exponents.
[tex]\dfrac{7^{5}}{7^{}}=\dfrac{7.7.7.7.7}{7.7}[/tex]
So if we multiply all the values together we get:
=[tex]\dfrac{16807}{49}[/tex]
=343
This method is just one of the methods that can be used to finding the quotient of a variable raised to an exponent.
Write an expression that, when simplified is equivalent to 15x +7
Answer:
2(7.5x+3.5)
Step-by-step explanation:
I can't remember what these equations are actually called, however in order to solve this you simply multiply 7.5 by 2, and then 3.5 by 2.
find the area of equilateral triangle of side 4 cm.
Answer:6.928
Step-by-step explanation: formula A=√ 3*(side^2/4)
The area would be 7 cm
Step-by-step explanation:See the image
The graph of an equation representing a direct variation passes through the point (6, 10). Give another point with integral coordinates that is also on the graph of this equation.
[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (\stackrel{x}{6},\stackrel{y}{10})\qquad \textit{we know that } \begin{cases} x=6\\ y=10 \end{cases}\implies 10=k6\implies \cfrac{10}{6}=k\implies \cfrac{5}{3}=k \\\\\\ therefore\qquad \boxed{y=\cfrac{5}{3}x}[/tex]
to get another point, we simply can pick a random independent variable, namely "x", say hmmmm x = 9, thus
[tex]\bf y=\cfrac{5}{3}(\stackrel{\stackrel{x}{\downarrow }}{9})\implies y=5\cdot \cfrac{9}{3}\implies y=10~\hspace{7em}\boxed{(9, 10)}[/tex]
To find another point with integral coordinates on the graph of the equation representing a direct variation, we can use the given point (6, 10) and the fact that the equation represents a direct variation. By finding the value of the constant of variation, we can substitute an integral x-value to find the corresponding y-value for another point on the graph.
Explanation:To find another point with integral coordinates on the graph of the equation representing a direct variation, we need to use the given point (6, 10) and the fact that the equation represents a direct variation. A direct variation equation has the form y = kx, where k is the constant of variation. In this case, we can use the given point to find the value of k. When x = 6 and y = 10 in the equation y = kx, we can substitute these values to solve for k: 10 = k * 6. Solving for k, we get k = 10/6 = 5/3.
Now that we know the value of k, we can find another point with integral coordinates. Let's try x = 3. Using the equation y = kx, we can substitute x = 3 and k = 5/3 to find y: y = (5/3) * 3 = 5.
So, another point with integral coordinates on the graph of the equation representing a direct variation is (3, 5).
the volume of a gold bar is 100cm cubed, the density of gold is 19.3g/cm cubed so what is the mass of the gold bar
➷ Use this formula:
density = mass / volume
Rearrange it for mass:
mass = density x volume
Substitute the values in:
mass = 100 x 19.3
Solve:
mass = 1930g
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4x+5=2x+6 (what is x?)
Answer:
x = 1/2
Step-by-step explanation:
Subtract 2x from both sides
4x + 5x - 2x = 6
Combine 4x and -2x to get 2x.
2x + 5 = 6
Subtract 5 from both sides.
2x = 6 - 5
Subtract 5 from 6 to get 1.
2x=1
Divide both sides by 2.
x = 1/2
Which of the following is the graph of f(x) = x2 − 4x − 5?
A. graph of a quadratic function with a minimum at 2, negative 9 and x intercepts at negative 1 and 5
B. graph of a quadratic function with a minimum at 3, negative 4 and x intercepts at 1 and 5
C. graph of a quadratic function with a minimum at 2.5, negative 2.4 and x intercepts at 1 and 4
D. graph of a quadratic function with a minimum at negative 1.5, negative 6.2 and x intercepts at 1 and negative 4
The answer is A because completing the square gives a minimum of 2,-9 and factorising gives roots of 5 and -1 :)
Answer:
Minimum at (2,-9) and intercepts are (-1,5)
Step-by-step explanation:
f(x) = [tex]x^2 -4x-5[/tex]
completing square method adding and subtracting the square of half of coefficient of 4 ,we get
f(x) = [tex]x^2 -4x+4 -4 -5[/tex]
f(x) =[tex](x-2)^2 -9[/tex]
on comparing it with standard vertex form [tex](x-h)^{2} +k[/tex]
where k is suppose to be the minimum value
on comparing it we get k = -9
which is minimum value of f(x)
at x =2
and if we find the zeros of
[tex]x^2 -4x-5[/tex] ,we get
[tex]x^2 -5x+x -5[/tex]
[tex]x^2 -4x-5[/tex]
x(x-5)+1(x-5)
(x+1)(x-5)
on setting it equals zero ,we get
x+1 =0 and x=5
x =-1 and x=5
therefore option A is answer
Minimum at (2,-9) and intercepts are (-1,5)
1. Does the data in the table below represent exponential growth or exponential decay?
Hint: Are the values in the bottom row increasing or decreasing?
A
exponential growth
B
exponential decay
Exponential decay because it is decreasing
Solve -9.4 > 1.7x + 4.2. I need this ASAP
Hello.
We are solving -9.4 > 1.7x + 4.2.
First we need to swap sides:
[tex]1.7x + 4.2 = -9.4[/tex]
Now we need to subtract 4.2 from both sides.
1.7x + 4.2 = -9.4
-4.2 . -4.2
Now let's combine -4.2 + 4.2 which is 0.
We get 1.7x < -9.4 - 4.2
Now let's divide both sides by 1.7
1.7x | -13.6
1.7 1.7
x < -13.6
1.7
So we just divided to get x < -8.
Answer:
[tex]\boxed{\bold{x<-8}}[/tex]
Step By Step Explanation:
Switch Sides[tex]\bold{1.7x+4.2<-9.4}[/tex]
Multiply Both Sides by 10[tex]\bold{1.7x\cdot \:10+4.2\cdot \:10<-9.4\cdot \:10}[/tex]
Refine[tex]\bold{17x+42<-94}[/tex]
Subtract 42 From Both Sides[tex]\bold{17x+42-42<-94-42}[/tex]
Simplify[tex]\bold{17x<-136}[/tex]
Divide Both Sides By 17[tex]\bold{\frac{17x}{17}<\frac{-136}{17}}[/tex]
Simplify[tex]\bold{x<-8}[/tex]
Louis found two bakeries to provide bagels for his sub shop. The first bakery offers 350 bagels for $168.00 and the second bakery offers 475 bagels for $209. How much will Louis pay for 800 bagels if he buys from the bakery with the lower price?
Answer:
$352Step-by-step explanation:
Find out the price of one bagel by dividing the price by the number of bagels:
350 Bagels = $168
1 Bagel = $0.48
475 Bagels = $209
1 Bagel = $0.44
0.48 > 0.44
This means the second bakery has the lower price.
Louis wants 800 bagels, so multiply the price by 800.
0.44 * 800 = $352
You can check it's lower by comparing it with the first bakery.
0.48 * 800 = $384
384 > 352
Start with the standard formula for the area of a triangle, and rewrite it to solve for the base, b.
Answer:
2A/h = b
Step-by-step explanation:
The formula for area of a triangle is
A = 1/2 bh
Multiply each side by 2
2A = 2*1/2 bh
2A = bh
Divide each side by h
2A/h = bh/h
2A/h = b
Answer:
b=2A/h
Step-by-step explanation:
The formula for area of a triangle is
A = 1/2 bh
Multiply each side by 2
2*1/2 bh = 2A
bh = 2A
Divide each side by h
bh/h = 2A/h
b = 2A/h
Simplify -3 over 5 divided by 7 over 6.
A = -7 over 10
B = -18 over 35
C = 18 over 35
D = 7 over 10
Answer:
Simplify:
-3/5 ÷ 7/6
Step-by-step explanation:
1. To solve you have to switch the ÷ to x, but once you do that 7/6 would be switched too:
-3/5 x 6/7
2. Simplify,
-18/35
So, the answer to this is B.
Hope this Helped!!!!!
~Shane
Help, please!
Show how the GCF of the numbers 10 and 15 can be used to reduce the fractions [tex]\frac{10}{15}[/tex]
Answer: [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
The greatest GCF is 5 because 5 goes into 15, and 10. Therefor, the answer would be 2/3.
* Hopefully this helps:) Mark me the brainliest:)!!!
Answer:
⅔
Step-by-step explanation:
Find all the factors of 10 and 15.
Factors of 10: 1, 2, 5, 10
Factors of 15: 1, 2, 3, 5, 15
The highest factor that is in both 10 and 15 is 5.
To reduce the fraction 10/15, divide both the numerator and denominator
by 5.
10/15 = (10 ÷ 5)/(15 ÷ 5) = ⅔
The sum of four and the product of three and a number x.
Answer:
4 + 3xStep-by-step explanation:
The product of three and a number x: 3 · x = 3x
The sum of four and the product of three and a number x:
4 + 3x
there are 5 teen age boys in the slack family. the boys drink 1 and 2 thirds of milk each day. at this rate, how many gallons of milk will the boys drink in a week?
A. 4 and 1 thirds
B. 11 and 2 thirds
C. 5 twentieth
D. 4 and 1 5th
sharon is 3 years old less than twice her younger brother's age. Let (s) repressent sharons age and (b) repressent her brother's age. which equation could be used to show sharons age?
A: s = 3-2b
B: b = 2x-3
C: s = 2b-3
D: b = 3 -2x
E: s = 3b-2
If Sharon is 3 years younger, then it's s = 3-b. However, it's twice her brothers age, which makes the formula our final answer, A, or [tex]s = 3 - 2b[/tex]
The correct option is A
Write the ratio 14:56
In its simplest form
Answer:
14/14 = 1 and 56/14 = 4
Thus, 14:56 ratio simplified is 1:4
hope this helps:)sorry if it doesnt
brainliest plz
When making a telephone call using a calling card, a call lasting 5 minutes cost $0.95. A call lasting 13 minutes cost $1.75. Let y be the cost of making a call lasting x minutes using a calling card. Write a linear equation that models the cost of making a call lasting x minutes.
A. y = 10x - 981/20
B. y = -0.1x + 1.45
C. y = 0.1x + 0.45
The linear equation that models the cost of making a call lasting x minutes using a calling card is y = -0.1x + 1.45.
Explanation:To write a linear equation that models the cost of making a call lasting x minutes using a calling card, we can use the given information about two calls. If a 5-minute call costs $0.95 and a 13-minute call costs $1.75, we can set up two equations:
0.95 = 5m + b
1.75 = 13m + b
Solving these equations, we find that m = -0.1 and b = 1.45. Therefore, the linear equation that models the cost of making a call lasting x minutes is y = -0.1x + 1.45.
A rectangle is 2/5 inches long and 1/3 inches wide. WORTH 20 POINTS!!!!!
What is the area of the rectangle?
Enter your answer in the box as a fraction in simplest form.
Answer:
2/15 inches squaredStep-by-step explanation:
Area = L * W
2/5 * 1/3 =
2 * 1 = 2
5 * 3 = 15
= 2/15 inches squared
What we do is find area
Area of rectangle=(l*w)
length=2/5
width=1/3
Area=2/5*1/3
Answer=2/15
Answer=2/15
Emma has 5 3/8 punds of potato salad and 2 7/8 pounds of egg salad for a picnic. How many more pounds of potato salad than egg salad does Emma have? A - 3 pounds B- 2 3/4 pounds C - 2 1/2 pounds D - 2 1/4 pounds
Answer:
The correct answer option is C. [tex]2\frac{1}{2}[/tex] pounds
Step-by-step explanation:
We are given that Emma has [tex]5\frac{3}{8}[/tex] pounds of potato salad and [tex]5\frac{3}{8}[/tex] pounds of egg salad for a picnic.
We are to find out how much more pounds Emma has of potato salad than the egg salad.
To find this, we simple need to subtract the pounds of egg salad from the pounds of potato salad.
[tex]5\frac{3}{8} - 5\frac{3}{8}[/tex] [tex]=\frac{43}{8} -\frac{23}{8} =\frac{43-23}{8} = 2\frac{1}{2}[/tex] pounds