Answer:
[tex]\frac{m - 4}{m + 4} / (m + 2)[/tex] is equivalent to [tex]\frac{(m - 4)}{(m + 4)(m + 2)}[/tex]
Step-by-step explanation:
Given Parameters;
(m-4)/(m+4) and (m+2)
Required:
To divide and write out the equivalent expression.
Two or more expressions are said to equivalent if and only if they give the same result.
Solving (m-4)/(m+4) divided by (m+2)
We have
[tex]\frac{m - 4}{m + 4}[/tex] divided by [tex]m + 2[/tex]
[tex]= \frac{m - 4}{m + 4} / (m + 2)[/tex]
Convert division to multiplication
[tex]= \frac{m - 4}{m + 4} *\frac{1}{(m + 2)}[/tex]
= [tex]\frac{(m - 4) * 1}{(m + 4) * (m + 2)}[/tex]
[tex]= \frac{(m - 4)}{(m + 4)(m + 2)}[/tex]
We can't simplify any further;
Hence, [tex]\frac{m - 4}{m + 4} / (m + 2)[/tex] is equivalent to [tex]\frac{(m - 4)}{(m + 4)(m + 2)}[/tex]
To check if this is true
Let m = 1
[tex]\frac{m - 4}{m + 4} / (m + 2)[/tex] becomes
[tex]\frac{1 - 4}{1 + 4} / (1 + 2)[/tex]
[tex]\frac{-3}{5} / (3)[/tex]
[tex]\frac{-3}{5} * \frac{1}{3}[/tex]
[tex]\frac{-1}{5}[/tex]
And
[tex]\frac{(m - 4)}{(m + 4)(m + 2)}[/tex] becomes
[tex]\frac{(1 - 4)}{(1 + 4)(1 + 2)}[/tex]
[tex]\frac{(-3)}{(5)(3)}[/tex]
[tex]\frac{-1}{5}[/tex]
Hence, [tex]\frac{m - 4}{m + 4} / (m + 2)[/tex] is equivalent to [tex]\frac{(m - 4)}{(m + 4)(m + 2)}[/tex]
Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2 and the profit on every wrap is $3. Sal made a profit of $1,470 from lunch specials last month. The equation 2x + 3y = 1,470 represents Sal's profits last month, where x is the number of sandwich lunch specials sold and y is the number of wrap lunch specials sold. Change the equation to slope-intercept form. Identify the slope and y-intercept of the equation. Be sure to show all your work. Describe how you would graph this line using the slope-intercept method. Be sure to write using complete sentences. Write the equation in function notation. Explain what the graph of the function represents. Be sure to use complete sentences. Graph the function. On the graph, make sure to label the intercepts. You may graph your equation by hand on a piece of paper and scan your work or you may use graphing technology. Suppose Sal's total profit on lunch specials for the next month is $1,593. The profit amounts are the same: $2 for each sandwich and $3 for each wrap. In a paragraph of at least three complete sentences, explain how the graphs of the functions for the two months are similar and how they are different. Below is a graph that represents the total profits for a third month. Write the equation of the line that represents this graph. Show your work or explain how you determined the equations. graph of line going through ordered pairs (0, 300) and (450, 0)
Sarah only knows the diameter of a circle. What should she do to find the radius?
Multiply the diameter by 2.
Divide the diameter by 2.
Multiply the diameter by pi
Divide the diameter by pi
Answer:
Therefore. The correct option is B. Divide the diameter by 2.
Step-by-step explanation:
Diameter of the circle : It is defined a line segment joining two points on the circumference of circles provided the segment passes through the center of the circle.
Radius of the circle : It is defined as a line segment joining any point on the circle to the center of the circle.
So, it can be illustrated that the radius is half of the diameter of the circle.
If we are given the diameter of the circle and we need to find the radius of the circle.
So, we will divide the given diameter of the circle by 2 to obtain the required radius of the circle.
Therefore. The correct option is B. Divide the diameter by 2.
A number is one seventh of another number the difference of the number is 18 assume u are subtracting the smaller number from the other number
The perimeter of parallelogram WXYZ is 50 millimeters. What is WZ?
Write two numbers, neither of which is 8, whose GCF is 8.
To find two numbers whose GCF is 8 but neither is 8, choose multiples of 8 that are not equal to 8 itself.
Explanation:To find two numbers whose GCF is 8 and neither of which is 8, we need to find two numbers that have 8 as their largest common factor.
The easiest way to do this is to select a number that is a multiple of 8, such as 16, and then choose another number that is also a multiple of 8, but not equal to 8 itself, such as 24.
So, the two numbers whose GCF is 8 and neither of which is 8 are 16 and 24.
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The wall at the front entrance to the rock and roll hall of fame and museum in cleveland, ohio, is an isosceles triangle. the triangle has a vertex angle of 102 degrees. what is the measure of the base angles? answer
The measure of the base angles is 39° respectively.
An Isosceles triangle is a triangle that has two equal sides.
Note: The base angle of an isosceles triangle is equal.
From the question,
The sum of the angle in a triangle is 180°.
⇒ a+b+c = 180°............... Equation 1
Given:a = 102°b = c = x = base angle of the isosceles triangle.Substitute these values into the equation.
102+x+x = 180102+2x=180Solve for x.
2x = 180-1022x = 78x = 78/2x = 39°Hence, the measure of the base angles is 39° respectively.
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5c + 2a − b; a = 5, b = 11, and c = 3
The value of the expression 5c + 2a − b at a = 5, b = 11, and c = 3 will be 14.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
⇒ 5c + 2a − b
The value of the expression 5c + 2a − b at a = 5, b = 11, and c = 3 will be given as,
⇒ 5c + 2a − b
⇒ 5 x 3 + 2 x 5 − 11
Simplify the expression, then we have
⇒ 5 x 3 + 2 x 5 − 11
⇒ 15 + 10 − 11
⇒ 25 − 11
⇒ 14
The worth of the articulation 5c + 2a − b at a = 5, b = 11, and c = 3 will be 14.
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An incompressible steady flow pattern is given by u=x^3+2z^2 and w=y^3-2yz. what is the most general form of the third component v(x,y,z) which satisfies continuity?
Final answer:
For an incompressible steady flow with u and w components as [tex]x^{3} +2z^{2}[/tex] and [tex]y^{3}-2yz[/tex], respectively, the v component of the velocity that satisfies continuity is of the form [tex]v(x,y,z)=y^{2}-3x^{2y}+f(x,z)[/tex], where f(x, z) is an arbitrary function of x and z.
Explanation:
The question is asking for the most general form of the third component v(x, y, z) of a velocity vector field that satisfies the continuity equation for an incompressible steady flow. Given that the u and w components of the velocity are
u = [tex]x^{3} +2z^{2}[/tex] and
w = [tex]y^{3}-2yz[/tex],
respectively, we can use the continuity equation for incompressible flow, which is
∇ ⋅ β = 0,
or written out,
∂u/∂x + ∂v/∂y + ∂w/∂z = 0.
By substituting the given components into the continuity equation, and taking the respective partial derivatives, we get:
∂u/∂x = [tex]3x^{2}[/tex],
∂w/∂z = -2y,
So, the continuity equation becomes: [tex]3x^{2}[/tex] + ∂v/∂y - 2y = 0.
Rearranging terms we get: ∂v/∂y = 2y - [tex]3x^{2}[/tex]
Integrating with respect to y, we find that v must generally be of the form: [tex]v(x,y,z)=y^{2}-3x^{2y}+f(x,z)[/tex], where f(x, z) is an arbitrary function of x and z since the partial derivative with respect to y of any function that does not contain y will be zero, preserving the continuity.
a car cost $25000 plus $675 for tax, title, and license fees. Ari finances the car by putting down $2,500 in cash and taking out a 3-year, 4% loan. what will his monthly payments be (if figured across all 3 years rather than annually)?
Elly buys 75 shares of stock in a mutual fund for a total investment of $450. She sells 50 shares of her stock for total proceeds of $400. Determine if Elly made a profit or loss, and how much per share.
Answer:
She made a profit of $ 2 on each share of stock
Step-by-step explanation:
Elly buys 75 shares of stock in a mutual fund for a total investment of $450.
cost of 1 share of stock= $ 450/75
= $ 6
She sells 50 shares of her stock for total proceeds of $400.
selling price of 1 share of stock=$ 400/50
= $ 8
Hence, She made a profit of $ 2 on each share of stock ($8-$6=$2)
Eleven years ago, you deposited $3,200 into an account. seven years ago, you added an additional $1,000 to this account. you earned 9.2 percent, compounded annually, for the first 4 years and 5.5 percent, compounded annually, for the last 7 years. how much money do you have in your account today? $8,666.67 $7,411.90 $7,717.29 $8,073.91 $8,708.15
Dipping your spoon into the bowl 4 times, what is the probability that you randomly select at least 1 heart
Probability randomly select at least 1 heart is 5 / 14
Probability based questions:Given question is incomplete, complete question is as follows;
Number of hearts = 5
Number of clover = 3
Number of stars = 4
Number of moons = 2
Find:
Probability randomly select at least 1 heart
Computation:
Total item = 5 + 3 + 4 + 2
Total item = 14
Probability randomly select at least 1 heart = 5 / 14
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Carla and Ross competed in the long-jump at a track meet. Carla jumped 3.5 meters. Ross jumped 99 inches. Who jumped farther and by approximately how many feet? Use 1 m = 3.27 ft. Explain how you solved this problem.
solve the equation.
| 2z - 3| = 4z - 1
The solution to the given inequality expression is -1 and 2/3.
Solving inequality expressionTo solve the equation |2z - 3| = 4z - 1, we need to consider two cases: one where the expression inside the absolute value is positive and another where it is negative. Remember that the absolute value of a number is always non-negative.
Case 1: (2z - 3) is non-negative (greater than or equal to zero).
In this case, |2z - 3| = 2z - 3. So we have:
2z - 3 = 4z - 1
Now, let's solve for 'z':
2z - 4z = -1 + 3
-2z = 2
z = 2 / -2
z = -1
Case 2: (2z - 3) is negative (less than zero).
In this case, |2z - 3| = -(2z - 3) = -2z + 3. So we have:
-2z + 3 = 4z - 1
Now, let's solve for 'z':
-2z - 4z = -1 - 3
-6z = -4
z = -4/-6
z = 2/3
Therefore, we have two possible solutions: z = -1 and z = 2/3.
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Which of these r-value represent the strongest correlation-0.7, -0.6, -0.5, -0.8
Why is simple interest useful for planning parts of your financial future?
Simple interest is useful for planning parts of your financial future because it helps you calculate how much interest you will earn or owe on a loan or investment.
Explanation:Simple interest is useful for planning parts of your financial future because it helps you calculate how much interest you will earn or owe on a loan or investment. It is a straightforward calculation that only takes into account the principal amount and the interest rate. By using simple interest, you can make informed decisions about saving, borrowing, or investing money.
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thomas earned $80 plus 10% of his sales for a net of $132. How much were his sales?
subtract base pay ( $80) from total pay
132-80 = 52
divide 52 by 10% for total sales = 52/0.1 = 520
his sales were $520
Answer:
Sales amount is $520 .
Step-by-step explanation:
Let us assume that the sales amount be x .
As given
Thomas earned $80 plus 10% of his sales for a net of $132.
10% is written in the decimal form
[tex]= \frac{10}{100}[/tex]
= 0.10
Thus
Total Earned amount = Earned amount + 0.10 × Sales amount
Put all the values in the above
132 = 80 + 0.10 × x
132 - 80 = 0.10x
52 = 0.10x
[tex]x = \frac{52}{0.10}[/tex]
x = $520
Therefore the sales amount is $520 .
Solve for c: 6/13=3/c
Can you show me the formula for this?
Solve |a| = -6
{-6}
{-6, 6}
Ø
Mathematically, the absolute value of a number is always non-negative, which means it can never be equal to a negative number. Hence, there's no possible value for 'a' in the equation |a| = -6, making the correct answer Ø.
Explanation:To solve |a| = -6, it’s important to understand the concept of absolute values. The absolute value of a number is its distance from zero on the number line. Therefore, it's always non-negative, because distances cannot be negative. Thus, there are no values of 'a' that would make |a| = -6, because absolute values cannot be negative.
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The velocity of an object fired directly upwards given v=96-48t, where t is in seconds. When will the velocity be between 48 and 80 feet per second
what do you think the sum of the probabilities for all the possible outcomes must be for any situation. explain
What is the volume in cubic meters of a greenhouse that is 30 feet long, 15 feet wide, and 8 feet high
The volume of the greenhouse is approximately 101.952 cubic meters.
To calculate the volume of the greenhouse in cubic meters, we first need to convert the measurements from feet to meters.
1 foot is approximately equal to 0.3048 meters.
Given measurements:
Length = 30 feet
Width = 15 feet
Height = 8 feet
Converting to meters:
Length = 30 feet * 0.3048 meters/foot ≈ 9.144 meters
Width = 15 feet * 0.3048 meters/foot ≈ 4.572 meters
Height = 8 feet * 0.3048 meters/foot ≈ 2.4384 meters
Now, we can calculate the volume in cubic meters:
Volume = Length * Width * Height
Volume ≈ 9.144 meters * 4.572 meters * 2.4384 meters ≈ 101.952 cubic meters
The volume of the greenhouse is approximately 101.952 cubic meters.
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Pleasssssseeeee hellppppppppppppppppppppppppppppp
There is an average of 3.5 x 10^−2 kilograms of dissolved salt in each liter of seawater. The South China Sea contains approximately 9.88 x 10^18 liters of seawater. About how many kilograms of dissolved salt are in south china sea Enter your answer, in scientific notation, in the boxes. __×10__ kg
Answer:
[tex]3.458\times10^{17}[/tex] kg
Step-by-step explanation:
It has been given that in 1 liter of seawater, the amount of dissolved salt is [tex]3.5\times10^{-2}[/tex]kg
Let x kg of salt is dissolved in [tex]9.88\times10^{18}[/tex] liters of seawater.
Thus, we have
[tex]\frac{1}{3.5\times10^{-2}}=\frac{9.88\times10^{18}}{x}[/tex]
On cross multiplying, we get
[tex]x=3.5\times10^{-2}\times9.88\times10^{18}\\\\x=34.58\times10^{16}[/tex]
In scientific notation,
[tex]x=3.458\times10^{17}[/tex]
Thus, [tex]3.458\times10^{17}[/tex] kg of salt is dissolved.
what is the vertex of the quadratic function: y=-3(x+5)^2-4
What number is 30% of 150
The percentages can also be represented in decimal or fraction form. In academics the marks obtained in any subject are calculated in terms of the percentage. Here 30% of 150 is 45.
What is percentage?In mathematics, the percentage is defined as a number or ratio which can be expressed as a fraction of 100. If we have to calculate the percentage of a number, divide the number by the whole and it should be multiplied by 100.
So percentage means a part per hundred. The word percent means per 100. It is represented by the symbol %. For example 10% is equal to 1/10 fraction. Percentage have no dimension.
The formula used to calculate the percentage is:
Percentage = Value / Total value × 100
30% of 150 is:
150 × 30 /100 = 45
Thus 30% of 150 is 45.
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Cassie has 1/2 pound of sugar in her cabinet. Her cake recipe calls for 2/10 of a pound of sugar. How many cakes can she make?
Elle wanted to order candy online. Company A is offering 2 1/2 pounds of chocolate for $32.50, while Company B is offering 2 3/4 pounds of the same chocolate for $35.00. Which company is offering the lowest price per pound. Justify your answer.
Based on the price offered per company, we can infer that the cheaper company is Company B.
The cheaper company is the one that is selling a pound of chocolate for a lower price than the other company.
First convert the mixed fractions to decimals for easier calculation:
Company A = 2 ¹/₂ = 2.5 pounds
Company B = 2 ³/₄ = 2 + (3/4) = 2.75 pounds
The cost per pound is:
= Cost of chocolate / Number of pounds
Company A: Company B:
= 32.50 / 2.5 = 35 / 2.75
= $13 per pound = $12.73
In conclusion, Company B is cheaper for selling at $12.73.
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The mean of the scores obtained by a class of students on a physics test is 42. The standard deviation is 8%. Students have to score at least 50 to pass the test. Assuming that the data is normally distributed, % of the students passed the test.
identify the function rule shown in the table.
n 3 4 5 6
y 2 1 0 -1
a. y = 2 + n
b. y = 5n
c. y = 5 -n
d. not enough information
3+2 = 5
4+1 = 5
5+0 = 5
6-1 =5
so answer would be C. y=5-n
check:
5-3 = 2
5-4 =1
5-5 =0
5-6 = -1