Combine the like terms to create an equivalent expression. m + 8 + 6n – 3 =​

A zero has the same meaning as the vertex.

The point where two lines meet forming an angle or set of angles is referred to as a vertex. This can also be called a point of origin especially when considering the axis of a Cartesian coordinate.

The vertex can be taken as zero since it is referred to as the point of origin. This is different to the axis of symmetry; as the axis of symmetry is one that splits a given plotted points i.e. a graph into two equal parts.

Thus, a zero has the same meaning as the vertex.

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Using proportions, it is found that the total amount budgeted for entertainment is of $720.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

Researching the problem on the internet, it is found that the day trip amount is 10% of the budget for entertainment, hence:

0.1x = 72

x = 72/0.1

x = 720.

Hence the total amount budgeted for entertainment is of $720.

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Answer:

d

Step-by-step explanation:

Larger samples more closely resemble the population from which they come.

Think of the difference between sampling hundreds of people from a town, perhaps asking them if they've ever ordered fast food.  If you go to McDonald's and ask customers as they come out, you wouldn't expect those answers to represent the entire population of the town, right?

Answer:

X/4=3/6

Start off by cross multiplying the tops and bottoms, so X/4=3/6 turns into 6X=12. Now divide by 6 on both sides.

6X=12      X=2

Answer:

2

Step-by-step explanation:

Cross Multiple and Divide

X. 3

----. = ----

4. 6

So what you want to do is multiply diagonally:

(6)(X) = 6X

(3)(4) = 12

Now that we have our two answers, we put an equal sign between them.

6X = 12

Now to get X alone. Since it's being multiplied by 6, you want to do the opposite and divide.

So remember to divide on both sides to get rid of the 6.

6X divided by 6 is just X.

12 divided by 6 is 2

We got our answers, put the equal sign in-between

X = 2

Answer:

\(6(3x + 1) = 5(2x - 2) \\ 18x + 6 = 10x - 10 \\ 18x - 10x = - 10 - 6 \\ 8x = - 16 \\ x = \frac{ - 16}{8} \\ x = - 2\)

Given equation is {(3x+1)/5} = {(2x-2)/6}

On applying cross multiplication then

⇛6(3x+1) = 5(2x-2)

Multiply the numbers outside the bracket with numbers in bracket.

⇛18x + 6 = 10x - 10

Shift the variable value on LHS and the constant value on RHS.

⇛18x - 10x = -6-10

Subtract the values on LHS and RHS.

⇛8x = -16

Shift the value 8 from LHS to RHS.

⇛x = -16÷8 = -16/8

⇛x = -2

Therefore, x = -2

Answer: Hence, the value of x for the given problem is -2

Please let me know if you have any other questions.

The total number of workers that were studied can be found to be 139,340,000.

The percent of workers unemployed would be 5. 4 %.

Percentage of unemployed men is 5. 6 % and unemployed women is 5. 1%.

Number of employed workers :

= 74,624,000 + 64, 716, 000

= 139,340,000

Percentage unemployed :

= ( 4, 209,000 + 3,314,000 ) / 139,340,000

= 5. 4 %

Percentage of unemployed men :

= 4,209,000 / 74,624,000

= 5.6 %

Percentage of unemployed women:

= 3,314,000 / 64, 716, 000

= 5. 1 %

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The full question is:

a. How many workers were studied?

b. What percent of the workers were unemployed?

c. Compare the percent unemployed for the men and the women.

a) The algebraic fraction \(\frac{{x + 2}}{{(x - 1)^2}}\) is proper. b) The algebraic fraction \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\) can be expressed as \(-\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

Let's solve each part step by step and determine whether the fraction is proper or improper, and then express it accordingly.

a) \(\frac{{x + 2}}{{(x - 1)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 1 (linear term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is less than the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

\(\frac{{x + 2}}{{(x - 1)^2}} = \frac{A}{{x - 1}} + \frac{B}{{(x - 1)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 1)^2)\) to eliminate the denominators:

  (x + 2) = A(x - 1) + B.

Expand the equation and collect like terms:

  x + 2 = Ax - A + B.

Equate the coefficients of like terms:

  Coefficient of x: 1 = A.

  Constant term: 2 = -A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = 1.

Substituting A = 1 into the constant term equation: 2 = -1 + B, we find B = 3.

Therefore, the partial fraction decomposition is:

  \(\frac{{x + 2}}{{(x - 1)^2}} = \frac{1}{{x - 1}} + \frac{3}{{(x - 1)^2}}\).

b) \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 2 (quadratic term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is equal to the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = \frac{A}{{x - 4}} + \frac{B}{{(x - 4)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 4)^2)\) to eliminate the denominators:

  (4x^2 - 31x + 59) = A(x - 4) + B.

Expand the equation and collect like terms:

  4x^2 - 31x + 59 = Ax - 4A + B.

Equate the coefficients of like terms:

Coefficient of \(x^2\): 4 = 0 (No \(x^2\) term on the right side).

Coefficient of x: -31 = A.

Constant term: 59 = -4A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = -31.

Substituting A = -31 into the constant term equation: 59 = 4(31) + B, we find B = -25.

Therefore, the partial fraction decomposition is:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = -\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

The above steps provide the solution for each part, including determining if the fraction is proper or improper and expressing it in partial fractions.

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Answer:

numbers:letters

5:4 (numbers:letters form)

Step-by-step explanation:

There are 5 numbers in the password and 4 letters

Hopefully this helps :)

Answer:

s = 2 1/3 + 1/2

t = 2/3 + 3/2

We have to find the sum of both s and t.

2 1/3 + 1/2 = 2 2/6 + 3/6 = 2 5/6

2/3 + 3/2 = 4/6 +  9/6 = 13/6 = 2 1/6

If we look at the number lines, we can see that c matches with both points.

Answer:

1.A

Step-by-step explanation:

yan po ang Tama po ang sagot..ko

Answer:

The correct answer is: u = 10,500. When the value of the alternative hypothesis is greater than that of the null hypothesis, the power of the test will be increased, so a value of u = 10,500 would yield the greatest power to reject the null hypothesis.

The interpretation of the beam on the wall is that when the function is undefined, the light is not shining completely on the wall and  and the function rate of changes are 55.236, 68.276, 110.473 and 289.221

The given parameter is the graph of the beam

From the graph, we can see that the beam does not shine on all parts of the wall.

It shines on some part and doesn't on other parts

This means that the function is undefined

Hence, the interpretation of the beam on the wall is that when the function is undefined, the light is not shining completely on the wall

To do this, we use the following computations:

[d(0.1) - d(0)]/[0.1 - 0] = [5.5236 - 0]/[0.1 - 0] = 55.236

[d(0.2) - d(0.1)]/[0.2 - 0.1] = [12.3512 - 5.5236]/[0.2 - 0.1] = 68.276

[d(0.3) - d(0.2)]/[0.3 - 0.2] = [23.3985 - 12.3512]/[0.3 - 0.2] = 110.473

[d(0.4) - d(0.3)]/[0.4 - 0.3] = [52.3206 - 23.3985]/[0.4 - 0.3] = 289.221

Hence, the function rate of changes are 55.236, 68.276, 110.473 and 289.221

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Answer: 0.2877

Step-by-step explanation:

Given : The proportion of eggs will be damaged in route to the stores = 15% = 0.15

Sample size = 100

Let p be the probability of her eggs will be damaged.

The probability that less than 13% will be damaged is given by :-

\(P(p<0.13)=P(\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}<\dfrac{0.13-0.15}{\sqrt{\dfrac{0.15\times(1-0.15)}{100}}})\)

\(=P(z<-0.56)\)

\(=1-P(z<0.56)\\\\= 1-0.7123\\\\= 0.2877\)

Hence, the required probability = 0.2877

Answer:

6.8

Step-by-step explanation:

Add the numbers and divide by the amount of numbers and get 6.8

Answer: 6.8.

Step-by-step explanation: When finding the mean of a data set, you need to add all the numbers of the set, and then divide the answer by however many numbers you have on the data set.  The work is done below:

14 + 7 + 2  8 + 3 = 34.

34 / 5 = 6.8, because there are 5 numbers in the data set.

Have a great day! :)

Answer:

B

Step-by-step explanation:

B is the only option between 0, 10 and 12, 1

If the radius is 3 cm, the height of the cylinder is approximately 7.06 cm, which is closest to option B, 7 cm. The correct option is B.

The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height.

We are given that the volume of the cylinder is 637 cm³ and the radius is 3 cm. Substituting these values into the formula, we get:

637 = π(3²)h

Simplifying:

637 = 9πh

h = 637 / (9π)

h ≈ 7.06

Thus, the height of the cylinder is approximately 7.06 cm, which is closest to option B, 7 cm.

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Answer:

undefined

It is undefined because if you put it on a graph you get a line going straight down.

Answer:

The correct answer is: (just took the test)

if a square is a rectangle and if a rectangle is a parallelogram, then a square is a parallelogram

if there is a children’s movie playing at the cinema, Maria’s mother will buy popcorn for Maria

Step-by-step explanation:

For the given answers the answers that follow the law of syllogism is options A and  B.

Given that,
4 statement is given, and we have to pick the statement that follows the low of syllogism.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here
There are only two statements that are following the law of syllogism. ie.

A. If there is a children's movie playing at the cinema, Maria's mother will take her to see it. When Maria's mother takes her to the movie, she buys Maria popcorn. Therefore, if there is a children's movie playing at the cinema, Maria's mother will buy popcorn for Maria.

B. If a square is a rectangle and if a rectangle is a parallelogram, then a square is a parallelogram.

C. and D. are invalid statement because it does not follow the Law of Syllogism.

Thus, for the given answers the answers that follow the law of syllogism is options A and  B.

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Answer:

-----------------------------

Given sequence:

If t(n) = 200, we can try to find the value of n:

There is no integer solution, since 32 < 40 < 64 or 2⁵ < 40 < 2⁶, the value of n should be between 5 and 6.

The sequence should include integer numbers, so there is no solution.

Given function:

Solve for x if f(x) is 200:

Answer:

1.  No

\(\textsf{2.} \quad x=\dfrac{\ln 40}{\ln 2} \approx5.32\;(\sf 2\;d.p.)\)

Step-by-step explanation:

Given sequence:

\(t(n)=5 \cdot 2^n\)

To determine if the sequence has a term with a value of 200, substitute t(n)=200 into the equation and solve for n:

\(\implies 5 \cdot 2^n=200\)

\(\implies 2^n=40\)

\(\implies \ln 2^n=\ln 40\)

\(\implies n\ln 2=\ln 40\)

\(\implies n=\dfrac{\ln 40}{\ln 2}\)

\(\implies n=5.3219280...\)

In a sequence, n is a positive integer.  Therefore, it is not possible for the sequence to have a term with the value of 200, as when t(n)=200, n is not a positive integer.

Given function:

\(f(x)=5 \cdot 2^x\)

To determine if the function has an output of 200, substitute f(x)=200 into the function and solve for x:

\(\implies 5 \cdot 2^x=200\)

\(\implies 2^x=40\)

\(\implies \ln 2^x=\ln 40\)

\(\implies x=\dfrac{\ln 40}{\ln 2}\)

\(\implies x=5.3219280...\)

Therefore, it is possible for the function to have an output of 200 when:

\(x=\dfrac{\ln 40}{\ln 2}\)

The acceleration of the car is 8 m/s^2.

The figure shown in the question is the distance-time graph of a muscle car accelerating from a standstill. The table lists the coordinates of points on the graph.The following observations can be made from the graph and the table: The car is at rest at time t=0 and at distance x=0. It then starts accelerating, and its speed increases uniformly with time. The slope of the distance-time graph is the velocity of the car.

Since the velocity is increasing uniformly, the slope of the graph is a straight line with a positive slope. The area under the graph between two points gives the displacement of the car during that time interval. The displacement can be calculated as the product of the average velocity and the time interval. Using the coordinates in the table, we can calculate the average velocities for each time interval and the displacement during that interval.

(a) The average velocity of the car between t=0 and t=2 is equal to the slope of the graph between the two points (0,0) and (2,32). This can be calculated as the difference in distance divided by the difference in time:Average velocity = (32 - 0) / (2 - 0) = 16 m/sThe displacement during this time interval is given by the area under the graph between the two points:Displacement = (1/2) x 32 x 2 = 32 m

(b) The acceleration of the car is given by the slope of the velocity-time graph. Since the velocity is increasing uniformly with time, the velocity-time graph is also a straight line with a positive slope. The slope of the velocity-time graph is equal to the acceleration. We can calculate the slope of the velocity-time graph between two points using the coordinates in the table. For example, the slope between t=0 and t=2 is given by the difference in velocity divided by the difference in time:Slope = (16 - 0) / (2 - 0) = 8 m/s^2

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Using the ratio of the sides, we have:$x\sqrt{3} = 12\sqrt{3}$ (opposite the $60^{\circ}$ angle is 12$\sqrt{3}$)$x = 2\sqrt{3}\cdot6$ (the hypotenuse is $2x = 12\sqrt{3}$)Simplifying, we have:$x = 12\sqrt{3}$. Therefore $x=y=12\sqrt{3}$, which is our answer

In a 30-60-90 triangle, the sides have the ratio of $1: \sqrt{3}: 2$. Let's apply this to solve for the variables in the given problem.

Instructions: Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your answers as radicals in simplest form. x=y=Let's first find the ratio of the sides in a 30-60-90 triangle.

Since the hypotenuse is always twice as long as the shorter leg, we can let $x$ be the shorter leg and $2x$ be the hypotenuse.

Thus, we have: Shorter leg: $x$Opposite the $60^{\circ}$ angle: $x\sqrt{3}$ Hypotenuse: $2x$

Now, let's apply this ratio to solve for the variables in the given problem. We know that $x = y$ since they are equal in the problem.

Using the ratio of the sides, we have:$x\sqrt{3} = 12\sqrt{3}$ (opposite the $60^{\circ}$ angle is 12$\sqrt{3}$)$x = 2\sqrt{3}\cdot6$ (the hypotenuse is $2x = 12\sqrt{3}$)Simplifying, we have:$x = 12\sqrt{3}$

Therefore, $x=y=12\sqrt{3}$, which is our answer.

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Note that as x gets larger, y gets smaller, but the product xy remains constant at 192.

In mathematics, a function is a relationship between two sets, called the domain and the range, such that each element of the domain corresponds to exactly one element of the range. A function takes an input value (or values) and produces an output value (or values) according to a specific rule or formula. The input values are the domain of the function, and the output values are the range of the function. Functions can be represented using equations, graphs, tables, or verbal descriptions. They are used to model relationships between variables in various fields of mathematics, science, engineering, economics, and many other areas.

Here,

If x and y vary inversely, this means that their product is a constant. We can use this fact to find the constant of proportionality k as follows:

k = xy

If we know that y is 24 when x is 8, we can substitute these values into the equation above to solve for k:

k = xy

= 8(24)

= 192

Now we can use this value of k to write the inverse variation function:

xy = 192

or

y = 192/x

To sketch a graph of this function for x > 0, we can plot a few points and connect them with a smooth curve. Here are some points we can use:

(x, y)

(1, 192)

(2, 96)

(4, 48)

(8, 24)

(16, 12)

(24, 8)

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Check the picture below.

\(\sin( \theta )=\cfrac{\stackrel{opposite}{0.5}}{\underset{hypotenuse}{0.64}} \implies \sin^{-1}(~~\sin( \theta )~~) =\sin^{-1}\left( \cfrac{0.5}{0.64} \right) \\\\\\ \theta =\sin^{-1}\left( \cfrac{0.5}{0.64} \right)\implies \theta \approx 51.4^o\)

Make sure your calculator is in Degree mode.

Answer:

Opinion C

Step-by-step explanation:

hope that will help you

Given

9(y +7)

FInd

Simplify

Explanation

here we use associative law to simplify

a(b+c)=a*c+a*b

so,

Final Answer

the correct option is c.

Answer:

B.

Step-by-step explanation:

Answer:

First one 28

Second one 53

Step-by-step explanation:

Using pythagoras theorem

Sqrt(24^2+7^2)=28

sqrt(45^2+28^2)=53

Answer: y = 40x + 750

Step-by-step explanation:

Linear model;

y = mx + c

y is the total cost of buying granite counter tops for a certain number of square foot as well as the cost to install the counter top.

m is the cost of granite counter tops per square foot which is $40 in this case.

x is the number of square feet required.

c is the base pay for the installation of the counter top which is $750

Linear model will therefore look like this;

y = 40x + 750

To test it. Assume you want enough granite tops for 10 square feet. How much would it cost;

= 40 (10) + 750

= $1,150

Answer:

I think it’s 100 square feet

Step-by-step explanation: