simplest form of equation V= 60
Simplifying a fraction means reducing a fraction to its simplest form. A fraction is in its simplest form if its numerator and denominator have no common factors other than 1.
A 'Simplest Form Calculator' is a free online tool that reduces a fraction to its simplest form. In this calculator, you can enter value and find its simplest form within a few seconds.
V=S3
S = 20
Give your answer in simplest form.
V = S3
V = S× 3
S = 20
Therefor
V = 20 × 3
V= 60
simplest form V= 60
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This is algebra 2, please help.
The vertex and axis of symmetry of the graph is shown in image.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The function is,
⇒ f (x) = 1/4 (x + 6)² - 5
Now,
Since, The function is,
⇒ f (x) = 1/4 (x + 6)² - 5
Hence, The points corresponds to x = - 2 and - 4 are;
For x = - 2;
⇒ f (x) = 1/4 (x + 6)² - 5
⇒ f (x) = 1/4 (-2 + 6)² - 5
⇒ f (x) = 1/4 (4)² - 5
⇒ f (x) = 4 - 5
⇒ f (x) = - 1
For x = - 4;
⇒ f (x) = 1/4 (x + 6)² - 5
⇒ f (x) = 1/4 (-4 + 6)² - 5
⇒ f (x) = 1/4 (2)² - 5
⇒ f (x) = 1 - 5
⇒ f (x) = - 4
Thus, The points are;
⇒ (- 2, - 1) , (- 4, - 4)
And, The vertex of the function is,
⇒ ( - 6, - 5 )
And, The axis of symmetry of the graph is,
⇒ x = - 6
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a pair of sneakers in on sale as shown the sale price is $51. This is 75% of the original price. what was the original price of the shoes?
work pls/ explain
Answer:
$68
Step-by-step explanation:
So, we will start off by putting our original price as a variable, x. Now, we will need an equation to show the relationship between the current price and three-fourths of the original price. The equation will look like this:
[tex]\frac{3}{4} x = 51[/tex]
Then, we will multiply both sides by 4 to get rid of the fraction, giving us:
3x = 204
Finally, we will divide by 3 to find the original price of the sneakers:
x = 68
So the pair of shoes originally cost $68.
Hope this helped!
Find the largest prime number that divides the quantity 0! + (1!) x 1 + (2!) x 2 + (3!) x 3 + ... + (50!) x 50
The largest prime number that divides the quantity is the largest prime number less than 5.5e+22.
A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. A prime number that divides a quantity is a prime number that is a factor of that quantity.
We can start by computing the values of the factorials, and then use the property of modular arithmetic to find the prime divisors of the quantity.
0! = 1
1! = 1
2! = 2
3! = 6
...
50! = 30414093201713378043612608166064768844377641568960512000000000000
Now we can write the expression as
(0! + 1x1!) + (2x2!) + (3x3!) + ... + (50x50!)
We can notice that the number is very large, and it's impractical to factorize it using traditional methods.
We can use the property that if n is not divisible by a prime number p, then n! is not divisible by p^2. So we can eliminate all the powers of 2 and 5 from the expression, since 2 and 5 are the only prime factors of the factorials.
The next step would be to check if the remaining number is divisible by any prime numbers.
Since it's impractical to check for all the prime numbers, we can use the fact that the largest prime number is less than the square root of the number in question. Therefore, we can check for all primes less than √(50!) = √(30414093201713378043612608166064768844377641568960512000000000000)
Which is approximately 5.5e+22.
Therefore, the largest prime number that divides the quantity is the largest prime number less than 5.5e+22.
It's important to note that this is a very large number and checking for all prime numbers less than it would take a long time. And thus, answer cannot be given.
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The diagram shows two proportional right triangles.
What is the perimeter of the larger triangle?
The perimeter of the possible larger triangle with possible side lengths of 24, 32 and 40 is 96 units
What is the perimeter of a plane figure?The perimeter of a figure is the length of the boundary surrounding the figure.
Two triangles that have proportional dimensions are similar triangles
The dimensions (arranged in the order of corresponding sides) of the possible similar right triangles in the question, obtained from a related question, having two similar right triangles, posted online are;
First (larger) triangle side lengths; 24, 32, and xSecond (smaller) triangle side lengths; 9, 12, and 15The similarity of the triangles (proportional corresponding sides, indicates that we get;
[tex]\dfrac{24}{9} = \dfrac{32}{12} = \dfrac{x}{15}[/tex]
Therefore, by cross multiplication, we get;
32 × 15 = 12 × x
x = 32 × 15 ÷ 12 = 40
The perimeter of the larger triangle is; 24 + 32 + 40 = 96
The perimeter of the larger triangle is 96 units.Please find attached the possible diagram of proportional right triangles, created with MS Word, obtained from a question with regards to proportional right triangles online.
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How do you solve 7x 5y?
We can solve the given linear equation 7x = 5y by plotting the graph of x and y on the coordinate plane.
An equation is known to be a linear equation in two variables if it is written in the form of ax + by + c = 0, where a, b and c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.
First, solve for x
7x = 5y
Divide both sides by 7
7/7 x = 5/7 y
Dividing by 7 undergoes the multiplication by 7
x = 5/7 y
Similarly, solve for y
7x = 5y
Divide both sides by 5
7/5 x = 5/5 y
Dividing by 5 undergoes the multiplication by 5
y = 7/5 x
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If ABCD is dilated by a factor of the
coordinate of D' would be:
4-3
12
3
N
18
T
2
3
4
5
O
9 10
D'=([?]))
Enter
When ABCD is dilated by a factor of the coordinate of D' and the size of the coordinate point is, A"s coordinate would be (-6, -2) (-3, -1) .
what is coordinates ?When locating points or other geometrical objects precisely on a manifold, such as Euclidean space, a coordinate system is a technique that uses one or more integers or coordinates. Locating a point or item on a two-dimensional plane requires the use of coordinates, which are pairs of integers. Two numbers called the x and y coordinates are used to describe a point's location on a 2D plane. a collection of integers that represent specific locations. The figure often has two numbers. The first number denotes the front-to-back measurement, while the second number denotes the top-to-bottom measurement. For example, in (12.5), there are 12 units below and 5 above.
given
The coordinate point's size is specified as (-3, -1).
The coordinate A' will be supplied as follows if the coordinate A is dilatable by a factor of two: A' = (2(-3), 2(-1)) = (-6, -2)
Consequently, A"s coordinate would be (-6, -2)
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How do you tell if a log graph is growth or decay?
To tell if a log graph is a growth or decaying, look at the slope of the line. If the slope is positive, then it is growth; if the slope is negative, then it is decay.
A positive slope indicates that the value is increasing over time, while a negative slope indicates that the value is decreasing over time. To find the slope, take two points on the line and calculate the change in the y-value divided by the change in the x-value.
If the answer is positive, the graph is growth; if the answer is negative, the graph is decay. Additionally, you can look at the y-intercept of the graph, which is the value where the line meets the y-axis. If the y-intercept is positive, the graph is growth; if the y-intercept is negative, the graph is decay.
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Circle C is inscribed with 5 lines. Point C is at the center of the circle. 3 lines come out of point C and make points D, A, and B on the edge of the circle. Another line comes out of point C and goes past the edge to point E. Another line connects points D and A.
Which geometric figures are drawn on the diagram? Check all that apply.
Line segment C A
Ray A C
∠ABC
∠BCE is drawn, line segment CA is drawn, Ray CA is drawn, For Circle C is drawn, Ray BE is not drawn.
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
Given that Circle C is inscribed with 5 lines
Point C is at the center of the circle
3 lines come out of point C and make points D, A, and B on the edge of the circle.
Another line comes out of point C and goes past the edge to point E.
For ∠ABC
The geometric figure is not drawn.
For ∠BCE
The geometric figure is drawn.
For line segment CA
The geometric figure is drawn.
For Ray CA
The geometric figure is drawn.
For Circle C
The geometric figure is drawn.
For Ray BE
The geometric figure is not drawn.
For Line segment AE
The geometric figure is not drawn.
Hence, ∠BCE is drawn, line segment CA is drawn, Ray CA is drawn, For Circle C is drawn, Ray BE is not drawn.
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Find the interet and total amount due on 1200 after 1 year 5 month at a rate
of interet of 4% p. A
Total interest earned = 68
Total amount collected = 1268
What is simple Interest ?Simple interest is a way to figure out how much interest will be paid on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the following year's principal to compute interest, the principal amount under simple interest remains constant.
Simple interest is a quick and simple approach to figure out how much money has accrued interest. Interest is always applied to the initial principle amount and is calculated at the same rate for each period of time. Any bank where we deposit money will pay us interest on that amount. Simple interest is one of several forms of interest that banks charge. Now, let's first clarify what a loan is before delving further into the idea of simple interest.
Since nothiong mentioned the interest is considered simple
Total amount = 1200 (principal)
Time = 1 year 5 month = [tex]1\frac{5}{12} = \frac{17}{12}[/tex]
rate = 4 %
Total interest earned = [tex]\frac{1200 * 4 * \frac{17}{12} }{100}[/tex] = 68
Total amount generated = 1200 + 68 = 1268.
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hree hundred books sell for 40 dollars each, resulting in a revenue of 12,000 dollars. For each $5 increase in the price, 25 fewer books are sold. Write the revenue R as a function of the number x of $ 5 increases.
A total of 12,000 dollars is made from the sale of 300 books at a price of $40 each. 25 fewer books are sold for every $5 increase in price. R(x)=(40+5x)(300−25x) R ( x ) = ( 40 + 5 x ) ( 300 − 25 x )
What is the revenue R as a function of number x ?Assumed in this instance is , At a price of 40 dollars apiece, [tex]$(300)(40 \$)=12,000 \$$[/tex] books generate $300 in revenue. The result is that 25 fewer books are sold if we raise the price of each book by $5. That's [tex]$(300-25 x)$[/tex]. Due to the fact that the price always rises by five times more than the number of books, the cost is [tex]$(40+5 x)$[/tex].
[tex]$R=(300-25 x) \cdot(40+5 x)$[/tex]
[tex]$R=12000+6000 x-1000 x-125 x^2$\\$R=-125 x^2+5000 x+12000$\\$R=125 x^2-5000 x-12000$[/tex]
The revenue R is expressed as a function of the number x as it approaches 5. R(x)=(40+5x)(30025x) is the necessary revenue function. R(x) = (40 + 5 x)(300 25 x) is the necessary revenue function.
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2 The test statistic in a two-tailed test is z=-2. 75 use a 0. 05 significance level to find the P value and state the conclusion about the null hypothesis
The p-value of the test statistic is p-value = 0.006. The null hypothesis will be rejected at 5% level of significance.
What Is Two-Tailed Test?A two-tailed test in statistics determines if a sample is more than or less than a specific range of values by using a two-sided critical area of a distribution. It is employed in testing the null hypothesis and determining statistical significance. The alternative hypothesis is accepted in place of the null hypothesis if either of the critical areas apply to the sample under test.
A two-tailed test in statistics determines if a sample is greater or less than a range of values by using a two-sided critical area of a distribution.
It is employed in testing the null hypothesis and determining statistical significance.
The alternative hypothesis is accepted in place of the null hypothesis if either of the crucial areas apply to the sample under test.
Conventionally, two-tailed tests with a 2.5% cutoff on each side of the distribution are employed to evaluate significance at the 5% level.
How to calculate the p-value?
Determine the level of relevance, sometimes referred to as the level, in step one. Assume 0.05 if it isn't specified. Step 2: Evaluate the level of significance in relation to the p-value. Make the conclusion that supports the possible change and reject the null hypothesis if the p-value is lower.
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Can anyone help please for e and f
Therefore ,this maxima of the preceding problem is 2 ≥ 0 , which leads to x²+90=> f(x) ≥ 9 , indicating that there is no maxima.
Describe maxima.The maxima & minima of the a function are its maximum and minimum points within or across a given range, and these points are collectively referred to as extrema in mathematical analysis. The highest value of the variable. The maximum amount, level, etc. The variable can only take a maximum of 2. Maximum refers to a peak (plural maxima). The lowest position is referred to as minimal (multiple minimum). Extremum is a phrase for the largest or least of anything (multi-extremum). Peaks (or minima) are used if there are better (or worse) sites available elsewhere but they are not nearby.
Here,
Given :
=> f(x) = x²+9 20
=> x²+9>0 and
=> f(x) 9,
maxima are not possible.
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HELP!! Find the inverse of the matrix…
Answer:
the answer is b
Is 2x 3 a linear function?
Answer:
yes
Step-by-step explanation:
The word linear is used for a straight line. A linear function is a function of a straight line, which means that the degree of a linear function must be 0 or 1 . In this case, The degree of f(x)=2x−3 f ( x ) = 2 x - 3 is 1 , which makes the function a linear function.
Select all of the expressions that are equivalent to 109+ 29m − 49n.
2(5 + m − 2n)
9(10 + 2m + 4n)
29(5 + m − 2n)
2(−2n + m + 5)
9(−4n + 2m + 10)
−29(2n − m − 5)
The equivalent expressions of 10/9 + 2/9m − 4/9n are 2/9(5 + m - 2n) and -2/9(2n − m − 5)
How to determine the equivalent expressionsFrom the question, we have the following parameters that can be used in our computation:
109+ 29m − 49n
Express the expression properly
So, we have the following representation
10/9 + 2/9m − 4/9n
Factor out 2/9
So, we have
2/9(5 + m - 2n)
Factor out -1 from the expression
So, we have the following representation
-2/9(2n − m − 5)
Hence, the equivalent expression is -2/9(2n − m − 5)
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Eating at the all-you-can-eat buffet at your favorite restaurant currently costs $18.50, and in cost by 6% each year
1.write a function that correctly depicts this scenario
2. How much will this cost 10 years from now ( round your answer to the nearest cent)
3 how much did this cost 15 years ago ( round your answer to the nearest cent
Answer:
The function that correctly depicts the scenario is:
cost(n) = 18.50 * 1.06^n
This function takes the number of years n as input and returns the cost of eating at the all-you-can-eat buffet after n years.
The cost of eating at the all-you-can-eat buffet 10 years from now can be calculated as follows:
cost(10) = 18.50 * 1.06^10 ≈ $30.59
The cost of eating at the all-you-can-eat buffet 15 years ago can be calculated as follows:
cost(-15) = 18.50 * 1.06^(-15) ≈ $8.01
Step-by-step explanation:
Notice the number of edge tiles (column 3) is equal to two less than the number of tiles on one side (column 1) multiplied by four. Knowing this relationship, if we built a 10 by 10 square mirror, write a numerical expression that would help us calculate the number of edge tiles we would need.
A numerical equation using addition as the only operator, for instance, is 2 + 17.
What is meant by numerical expression?An expression that uses only numbers and one or more operation symbols is referred to as a numerical expression. Operations like addition, subtraction, multiplication, and division are represented by symbols. Additionally, the square root sign or the absolute value symbol can be used to represent it. A numerical equation using addition as the only operator, for instance, is 2 + 17. An equation with three operators, 11 + 43 x (-4), starts with addition and moves through multiplication and subtraction. Operations are applied to numbers in numerical expressions. Numerical expressions include things like 2(3 + 8). At least one variable and one operation are included in algebraic expressions (addition, subtraction, multiplication, division). An algebraic expression is, for instance, 2(x + 8y).To learn more about numerical expression, refer to:
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What is y=-6x+2 in standard form
What is the value of (-1-¹) ÷ (-4)?
A. -1/
T
B. -21
C.
D. 1/1/12
Answer:
D. 1 5/16
Step-by-step explanation:
mark brainliest
1) state whether the dilation with the given scale factor would be a reduction or an enlargement
k=4
k=1/2
k= .75
k=5/2
Reducing the object's size by dilation is a change. The items are enlarged or shrunk through dilation.
How do you know if a dilation is an enlargement or reduction?Resizing an object is accomplished through a change called dilation. The objects can be enlarged or shrunk via dilation.
A diminution in the image occurs when the scale factor is between 0 and 1. An enlarged version of the image is shown if the scale factor is larger than 1.
An enlargement (imagine stretching) is a dilation that makes a larger image, whereas a reduction (think shrinking) is a dilation that creates a smaller image. A diminution in the image occurs when the scale factor is between 0 and 1. An enlarged version of the image is shown if the scale factor is larger than 1.
A transformation called a dilation (similarity transformation) alters the size of a figure. A center point and a scaling factor, k, are necessary. Which kind of dilation it is—an enlargement or a reduction—depends on the value of k. An enlargement results from a dilatation if |k|>1.
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Radicals help please
The simplified form of radical √18 . 3√5 = 9√10
What is radical?In mathematics, a radical expression is defined as any expression containing a radical (√) symbol. Many times it is used to determine the square root of a number. However, it can also be used to describe a cube root, a fourth root, or higher. When the radical symbol is used to denote any root other than a square root, there will be a superscript number in the 'V'-shaped part of the symbol.
For example, ³√(8) means to find the cube root of 8. If there is no superscript number, the radical expression is calling for the square root.
The term underneath the radical symbol is called the radicand.
Given radical
√18 . 3√5
⇒ √(9 × 2) . 3√5
⇒ 3√2 . 3√5
⇒ 9(√2.5)
⇒ 9√10
⇒ 28.46
Hence, The radical √18 . 3√5 can be simplified to 9√10 having value = 28.46
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simplify square root of 3y^2 if y<0
Note that the resultant expression after simplifying simplify square root of 3y² if y<0 is: y√3
What is the rationale for the above result?Note that we need to take a factor out of the square root: √(3y²) , where y<0.
The given expression is √(3y²)
Recall that to take out a factor out of the square root that factor must have a degree in multiple of 2 such as x², x⁴, (x-2)⁴, thus,
√(3y²) = √3y²
⇒ √3 √y²
⇒ √3 (y²)[tex]^\frac{1}{2}[/tex]
⇒ √3 (y)[tex]^\frac{2}{2}[/tex]
= y √3
Thus, having simplified the expression √(3y²), the result is: y √3.
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Suppose that you have 8 cards. 5 are green and 3 are yellow. The 5 green cards are numbered 1, 2, 3, 4, and 5. The 3 yellow cards are numbered 1, 2, and 3. The cards are well shuffled. You randomly draw one card. G
The necessary probabilities are 3/8, 1/3, 9/64, and 37/64.
What is probability?The field of mathematics concerned with probability is known as probability theory. Although there are various distinct interpretations of probability, probability theory approaches the idea rigorously mathematically by articulating it through a set of axioms. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.
Here,
S = { G1, G2, G3, Y1, Y2, Y3, Y4, Y5 }
G = { G1, G2, G3 }
P(G) = 3/8
E = { G2, Y2, Y4 }
P(G|E) = 1/3
P(G and E) = P(G)*P(E) = (3/8)*(3/8) = 9/64
P(G or E) = P(G) + P(E) - P(G and E) = (3/8) + (3/8) - (9/64) = (6/8) - (9/64) = (48/64) - (9/64) = 37/64
The required probability is 3/8, 1/3, 9/64 and 37/64.
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Are the following statements true or false? Justify your answers. Complete parts (a) through (c) below. (This is a reading assessment question. Be certain of your answer because you only get one attempt on this question.) (a) In statistics, results are always reported with 100 % certainty. Choose the correct answer below A. False. In statistics, results are always reported with 100 % certainty only when discrete variables are measured. Results cannot be reported with 100 % certainty when continuous variables are measured. B. True. Statistics is the science of collecting, organizing, summarizing, and analyzing information to draw conclusions or answer questions. Since it is a science, results are always reported with 100 % certainty. C. True. Statistics would not be useful if they were not presented with 100 % certainty . Statistics is a form of mathematics, which means that as long as correct procedures are used, all results must be correct. D. False. In statistics, results are not reported with 100% certainty. Because statistical studies draw on samples, and because there is variation within groups, results cannot be reported with 100 % certainty.
The correct option that tests the given claim on statistics is; D. False. In statistics, results are not reported with 100% certainty. Because statistical studies draw on samples, and because there is variation within groups, results cannot be reported with 100 % certainty.
How to interpret the conclusion of a statistics research?Statistical research is defined as the rigorous development of improved or new statistical methods grounded in probability and statistical theory.
Statistical data analysis is basically a procedure that is used to perform various statistical operations.
Now, from the question, the claim is that In statistics, results are always reported with 100 % certainty.
Now, this claim needs to be examined because there is no perfect human being and as such since statistics is drawn from a lot of samples and groups, there is guaranteed to be some form of variability in responses or results as the case may be.
Therefore, we can say that is option D.
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How many solutions does 3x 2y 6 have?
The linear equation 3x – 2y = 6 has one real solution. To find it, you can solve the equation for one of the variables (either x or y) and then substitute the result into the equation to find the other variable.
For example, you can solve for y to get y = (6 + 3x)/2, and then substitute this into the equation to get 3x – 2((6 + 3x)/2) = 6, which you can then solve for x. Doing this will give you x = 3, which means that the solution is (3, 3).
The linear equation 3x – 2y = 6 has infinitely many solutions. To find them, you can solve the equation for one of the variables (either x or y) and then substitute the result into the equation to find the other variable
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The um of three number i 50 the firt number i twice the econd number the third number i half the firt number
If the sum of three numbers is 50, it forms a linear equation that is x + y + z = 50. By solving this equation we can get the value of x, y and z.
The Equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. There are different types of equations like linear, quadratic, cubic, etc. There are numerous ways in which one may define an equation. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. The most basic and simple algebraic equations consist of one or more variables in math.
The sum of three number is 50 the first number is twice the second number the third number is half the first number.
x + y + z = 50
x = 2y
z = x / 2
Here we form a linear equation. A linear equation may have more than one variable. A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. By solving this linear equation we can get the value of x, y and z.
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What is 3 and 2/3 as a mixed number?
3 and 2/3 as a mixed number will be 11/3.
Define integers.Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The set of integers is frequently represented in mathematical notation by the boldface Z or blackboard bold Z.
What is a mixed number?A mixed number is a combination of a whole number and a fraction. It represents a number that is greater than zero but less than the next whole number. A mixed number is written with the whole number followed by a space and then the fraction.
[tex]=3+2/3[/tex]
[tex]=(3*3+2)/3[/tex]
[tex]=(9+2)/3[/tex]
[tex]=11/3[/tex]
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Eve has been keeping an eye on an emerald ring she likes. Its original price was $1,730. After
being marked down for a clearance sale, it is now $1,038. By what percent has the price of the
ring gone down?
40 percent price of the ring gone down due to a clearance sale
What is percent value?
In mathematics, percent implies a relative value of any quantity. Generally, percent value expresses the hundredth parts of any given quantity. Sometimes, operator % is used to indicate a percent value.
From a given percent value we can determine the real value and percent value is calculated from the original data.
What is the percent value of the ring that gone down?
given, the original price of the emerald ring = $1730
after a clearance sale, the price of ring became = $1038
difference in price = $(1730-1038) = $ 692
hence, the price of the ring that gone down = $692
now, percent value of the price gone down = $692/$1730 × 100
= 40%
hence, forty percent of the ring price gone down.
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2n+4=22
gimme the answer
Answer: n=9
Step-by-step explanation:
I'm assuming you want to solve for n, as that's the only possible question I can think of.
To solve for n, we want to isolate n by using inverse operations.
2n+4=22 [subtract both sides by 4]
2n=18 [divide both sides by 2]
n=9
Therefore, n=9 Is the answer.
If it takes 10 hours to travel from North Carolina to Florida driving an
average speed of 60 mph, how long will it take to travel from North
Carolina to Florida driving an average speed of 70 mph?
Is it direct variation or indirect variation?
Answer:
8.5 hrs? direct variation
Step-by-step explanation:
60 per hour is 600 for 10 hours so 70 per hour to go 600 miles is 8.57142857143 in the calculator
600/60 =10
600/70 = 8.5
and its direct variation because on a graph 8.5 8.5 squares up for ever 1 square going over every time and the graph does curve but I haven't learned this stuff in years so I'm not 100% sure