solve (4+8x) over 12x

The sum of the numbers on the three chosen slips of paper is either 21 or 23 in both the given cases.

We are given that one of the slips chosen is numbered 7, so the only possible sums of the remaining two slips are:

16 = 7 + 9

14 = 7 + 7

In the statement (1), the sum of two of the numbers chosen is 16, which means that the remaining two slips are 7 and 9. So the sum of the numbers on the three chosen slips of paper is 7 + 9 + 7 = 23.

In the statement (2), the sum of two of the numbers chosen is 14, which means that the remaining two slips are 7 and 7. So the sum of the numbers on the three chosen slips of paper is 7 + 7 + 7 = 21.

Hence, we get that in both cases, the sum of the numbers on the three chosen slips of paper is either 21 or 23.

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If in the party there are 5 different appetizers and 6 different desserts , then the number of different ways the 3 appetizers and 2 desserts can be selected is 150  ways .

the number of different appetizers in dinner party is = 5 ;

the number of different desserts in dinner party is = 6 ;

the number of ways of selecting 3 appetizers from 5 is = ⁵C₃ = 10 ;

number of ways of selecting 2 desserts from 6 is = ⁶C₂ = 15 ;

the number of ways of selecting 3 appetizers and 2 desserts is

= 15 × 10

= 150 ways .

Therefore , 3 appetizers and 2 desserts can be selected in 150 ways .

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The line segment AB has point B(x, y) = (11, - 4) as its other endpoint.

Herein we find the case of a line segment, of which the coordinates of its midpoint and one of its endpoints are known. Midpoint and endpoints are related by following expression:

0.5 · A(x, y) + 0.5 · B(x, y) = M(x, y)

Where:

If we know that A(x, y) = (- 1, 8) and M(x, y) = (5, 2), then the coordinates of the other midpoint are:

0.5 · (- 1, 8) + 0.5 · B(x, y) = (5, 2)

(- 1, 8) + B(x, y) = 2 · (5, 2)

(- 1, 8) + B(x, y) = (10, 4)

B(x, y) = (11, - 4)

The point B(x, y) = (11, - 4) is an endpoint of line segment AB.

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Answer:6/5 or 1 1/5

Step-by-step explanation:

1. Add 2 on each side

2. Then divide 1/5 and 6

Answer:

X = 30

Step-by-step explanation:

Add 2 on both sides, cancelling the -2. Divide 1/5 by 6 (4+2) and you'll get 30

The number of the arrangement for the five sequences will be 6.

Combination and permutation are two different ways in mathematics to divide up a set of elements into subsets. The subset's components can be listed in any order when combined. The components of the subset are listed in a permutation in a particular order.

Given that a sequence is a sequence of positive integers whose terms add up to $5.$ For example, 2, 2, 1 and 2, 1, 2.

The number of the ways will be calculated as:-

3! = 3 x 2

3! = 6

Hence, the number of the different arrangements for the sum of 5 will be 6.

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The logarithmic equation gives the value of n; n = 11/ 6.

This is a form of equation which requires the application of one of the laws of logarithm to solve or determine the value of a variable.

To solve the given logarithmic equation, we have the following steps to follow;

64^(2n - 3) = 4^2

4^3(2n - 3) = 4^2

divide the common terms on both sides to have;

3(2n - 3) = 2

6n - 9 = 2

6n = 2 + 9

6n = 11

n = 11/ 6

Therefore on solving the logarithmic equation, the value of n is 11/ 6.

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The simplified form of the polynomial ( x + 6 )( x² - 3x - 4 ) is x³ + 3x² - 22x - 24

Given the polynomial in the question;

( x + 6 )( x² - 3x - 4 )

Apply distributive property.

x( x² - 3x - 4 ) + 6( x² - 3x - 4 )

x³ - 3x² - 4x + 6x² - 18x - 24

Collect like terms

x³ - 3x² + 6x² - 18x - 4x - 24

Add like terms

x³ - 3x² + 6x² - 18x - 4x - 24

Add -3x² and 6x²

x³ + 3x² - 18x - 4x - 24

Add -18x and -4x

x³ + 3x² - 22x - 24

Therefore, the simplified form is x³ + 3x² - 22x - 24.

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9.43 inches is the measure of the longest segment

We are aware that the diagonal connecting the two opposing corners at the top and bottom will be the longest segment.

We know how to find the diagonal of a right triangular prism using the following formula:

d = [tex]\sqrt{w^2 + l^2+h^2} \\\\[/tex]

where w = width = 1.4

l = length = 4.8

h = height = 8

We would put these values in the formula above

[tex]d = \sqrt{1.4^2 + 4.8^2+8^2} \\\\[/tex]

d = [tex]\sqrt{1.96+23.04+64}[/tex]

d = 9.43

The measure of the longest line segment is given as 9.43 inches

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The child has 14 quarters and 28 dimes if child's bank contains $6.30 in dimes and quarters.

What is Algebraic expression ?

Algebraic expression can be defined as the combination of variables and constants.

With coin problems you need to keep track of the count of the coins and the value.

d = number of dimes

10d = value of the dimes in cents

q = number of quarters

25q = value of the quarters in cents

10d + 25q = 630 cents

d = 2q

substitute

10(2q) + 25q = 630

20q + 25q = 630

45q = 630

q = 14

d = 2q

d = 2*14 = 28

Check the values to be sure this answer is right.

25(14) = 350 cents

10(28) = 280 cents

total = 630 cents

Therefore,  The child has 14 quarters and 28 dimes.

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Answer:

18

Step-by-step explanation:

see attached

1). To eliminate variable x,

we subtract the equation 2 to equation 1

And 2). The solution of the system is x = 16 and y = 20.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given:

Each of 36 students at a school play bought either a cup of orange juice or a sandwich.

A cup of orange juice costs $1 and a sandwich costs $3.

The total amount collected was $76.

Let x represent the number of students who bought a cup of orange juice and y represents the number of students who bought a sandwich.

Then the problem can be represented by this system of equations:

x + 3y = 76   {equation 1}

x + y = 36     {equation 2}

1). To eliminate variable x,

we subtract the equation 2 to equation 1,

2y = 40

y = 20.

And x = 16.

2). The solution of the system is x = 16 and y = 20.

To check the solution, substituting the values to the equation 2,

16 + 20 = 36

36 = 36

Therefore, all the required values are given above.

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The area for the given figure by using distributive property is 5y+35.

What is Area of rectangle?

Area of rectangle can be defined as the product of length and breadth .

From the Given figure,

We have to find the area of rectangle

so,

There is one small rectangle inside that,

So,

total area = area of small rectangle + area of larger rectangle

area = 5*y + 7*5

So by summing up the area of two rectangles

we get,

Total area = 5y+ 35

Therefore, The area for the given figure by using distributive property is 5y+35.

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Step-by-step explanation:

the surface area of a half-cylinder is, surprise, surprise, half of the surface area of a whole cylinder ...

the surface area of a cylinder is

A=2×pi×r×h + 2×pi×r²

r being the radius, h being the height of the cylinder.

the formula simply adds

the sidewall area (which is a rectangle of

circle circumference × height)

+

the top and base circle areas

half of this area calculation for a half-cylinder is

A/2 = pi×r×h + pi×r²

[tex]\textit{midsegment of a trapezoid}\\\\ m=\cfrac{a+b}{2} ~~ \begin{cases} a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ a=11.5\\ m=18.7 \end{cases}\implies 18.7=\cfrac{11.5+b}{2} \\\\\\ 37.4=11.5+b\implies 25.9=b=AB[/tex]

Answer: 2.294524311274043, 4.294524311274043, 6.294524311274043 and 8.294524311274043 radians.

Step-by-step explanation: We can start by isolating the sin function on one side of the equation:

sin (2x-4) = 2/3

Next, we can use the inverse sine function (sin^-1) to find the value of 2x-4:

2x-4 = sin^-1(2/3)

We know that the domain of the inverse sine function is [-1,1], so the value of 2/3 falls in that range. To find the value of x, we can add 4 to both sides and divide both sides by 2:

x = (sin^-1(2/3) + 4) / 2

The value of sin^-1(2/3) is approximately 0.5890486225480862 radians and that's the first solution in the range [0, pi], and we can add multiples of pi to get the other solutions.

x = (0.5890486225480862 + 4) / 2 = 2.294524311274043 radians (in the range [0, pi])

x = (0.5890486225480862 + 4 + pi) / 2 = 4.294524311274043 radians (in the range [pi, 2pi])

x = (0.5890486225480862 + 4 + 2pi) / 2 = 6.294524311274043 radians (in the range [2pi, 3pi])

x = (0.5890486225480862 + 4 + 3pi) / 2 = 8.294524311274043 radians (in the range [3pi, 4*pi])

So there are four solutions to this equation: 2.294524311274043, 4.294524311274043, 6.294524311274043 and 8.294524311274043 radians.

[tex]3\sin(2x-4)=2\implies \sin(2x-4)=\cfrac{2}{3}\implies 2x-4=\sin^{-1}\left( \cfrac{2}{3} \right) \\\\\\ 2x=\sin^{-1}\left( \cfrac{2}{3} \right)+4\implies x=\cfrac{\sin^{-1}\left( \frac{2}{3} \right)+4}{2} \\\\\\ x=\cfrac{\sin^{-1}\left( \frac{2}{3} \right)}{2}+2\implies x\approx\cfrac{0.73}{2}+2\implies \stackrel{II~Quadrant}{x\approx 2.365}\hspace{5em}\stackrel{III~Quadrant}{\stackrel{\frac{\pi -0.73}{2}+2}{x\approx 3.206}}[/tex]

If Alex has an 80% chance of passing a test and Brad has a 60% chance of passing the test ,then the probability that Alex and Broad both fail the test is 0.8 or 8%   .

The percent chance that Alex passes the test is = 80% = 0.8  ;

So , probability that Alex fails the test is = 1 - 0.8 = 0.2 ;

the percent chance that Brad passes the test is = 60% = 0.6 ;

So , the probability that Brad fails the test is - 1 - 0.6 = 0.4 ;

we have to find the probability that Alex and Broad both fail the test ,

the required probability of both failing can be found by using formula :

= (probability Alex fails the test) × (probability Brad fails the test)

= 0.2 × 0.4

= 0.8 .

Therefore , the probability that both fail  the test is 0.8 or 8% .

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Using the laws of exponents to simplify the expression, we have; 5 1/3

When the power of one or more terms of an expression is greater than 1, then the expression is in an exponential form. Thus some laws can be require to simplify an exponential expression.

In the given question,

2^7/ 2^5 + (4^5)^0 + 3^-1

Thus applying the division law of indices to the first term, we have;

2^7/ 2^5 = 2^(7 - 5)

              = 2^2

In the second term, anything to the power of zero is 1. So that;

(4^5)^0 = (1024)^0

            = 1

In the third term, applying the inverse law of indices. We have;

3^-1 = 1/ 3

Therefore,

2^7/ 2^5 + (4^5)^0 + 3^-1 = 2^2 + 1 + 1/3

                                        = 4 + 1 + 1/3

                                        = 5 + 1/3

                                        = 16/ 3

                                        = 5 1/3

The value of the expression is 5 1/3.

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Answer:

89

Step-by-step explanation:

The angles are congruent since they are alternate interior angles of parallel lines cut by a transversal.

30x - 1 = 29x + 2

x = 3

30x - 1 = 30 × 3 - 1 = 89

60 students chose chocolate ice cream If 84 students chose vanilla ice cream.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given, Elmhurst School organized an ice cream social for the incoming sixth graders. At the social, 7 students chose vanilla ice cream for every 5 that chose chocolate ice cream.

Since,

The ratio of students who choose vanilla ice cream to chocolate ice cream is: 7/5

Thus,

for every students choose chocolate ice cream = 5/7 student who chooses vanilla ice cream

If 84 students chose vanilla ice cream

Thus, students choose chocolate ice cream = 5/7 * 84

students choose chocolate ice cream = 12* 5

students choose chocolate ice cream = 60

Therefore, If 84 students chose vanilla ice cream, 60 students chose chocolate ice cream.

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Total amount in Ruby's account after doing one time investment of $6200 for 12 years with rate of interest 4.3% is equal to $10,300 ( nearest hundreds dollars )

Principal 'P' amount in Ruby's account is equal to $6200

Rate of interest 'r' compounded continuously is 4.3%

Time 'N' = 12 years

Let 'A' be the final amount in Ruby's account after 12 years

Amount 'A' = P × ( 1 + (r/100) )ⁿ

Substitute the value in the formula we get,

⇒ A = 6200 × [ 1 + ( 4.3/100) ]¹²

⇒ A = 6200 × [ 1 + 0.043 ]¹²

⇒ A = 6200 × [ 1.043 ]¹²

⇒ A = $10,275.5

⇒ A = $10,300 ( nearest hundreds dollars )

Therefore , the total money in Ruby's account after depositing $6200 with rate of interest 4.3% compounded continuously for 12 years is equal to

$10,300 ( nearest hundreds dollars ).

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Answer: To check if Jose has enough string for his project, we need to add the lengths of the strings he has and compare it to the amount of string he needs for the project.

The length of the first string is 9 1/2 feet, the second string is 3 1/4 feet and the third string is 4.5 feet.

To add these lengths we need to convert them all to the same unit of measurement.

3 1/4 feet can be converted to 3.25 feet

So the total length of the strings Jose has is 9 1/2 + 3.25 + 4.5 = 17.25 feet

Jose needs 20 1/3 feet of string for his project, and he has 17.25 feet of string.

So he doesn't have enough string for his project.

Step-by-step explanation:

Answer:

The answer is side side side (SSS)

Answer:

SSS Similarity

Step-by-step explanation:

121/9 = 8/6 = 16/12

Similar by SSS Similarity

The y-intercept of a line is the point at which the line crosses the y-axis. This means that the x-coordinate of the point is 0.

To find the equation of a line passing through two points, we use the slope-intercept form of the equation of a line: y = mx + b, where m is the slope of the line and b is the y-intercept.

To find the y-intercept of a line passing through two points, we can use the slope-intercept form of the equation of a line and the coordinates of the two points:

(y1, y2) = m(x1, x2) + b

m = (y2-y1)/(x2-x1)

In this case, the two points are (-1,-5) and (6,0)

m = (0-(-5))/(6-(-1)) = 5/7

We can substitute the slope in the slope-intercept form of the equation of a line:

y = mx + b

so we can substitute point (-1,-5) in the equation and solve for b

-5 = (5/7)*(-1) + b

b= -5 + (5/7) = -5 + 0.7142857142857143

So, the y-intercept of the line passing through the two points (-1,-5) and (6,0) is -4.2857142857142865

Answer:

Kinda Hard to explain hope this helps

Step-by-step explanation:

Lets say molly is 6 and parker bought 4 times as many then he bought 24 marbles.Then cole bought 5 fewer then parker so 24-5=19

the equation is 4(6)m=p(24) Cole p(24)-5=Cole

M=6

The correct answer is done by Curran,the equation is an example for Inequality Equations. X = -1\2

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using the inequality symbols.

Examples,

Symbol Name               Symbol                          Example

Not equal                            ≠                                     x ≠ 3

Less than                            (<)                           x + 7 < √2

Greater than                       (>)                        1 + 10x > 2 + 16x

Less than or equal to         (≤)                            y ≤ 4

Greater than or equal to     (≥)                             -3 - √3x ≥ 10

Let's solve your inequality step-by-step.

−4(x−6)<22

Step 1: Simplify both sides of the inequality.

−4x+24<22

Step 2: Subtract 24 from both sides.

−4x+24−24<22−24

−4x<−2

Step 3: Divide both sides by -4.

−4x/4<= -2/-4x

x-1/2

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Answer:

Step-by-step explanation:

x=4
x=-3/2

hope this helps !! :)

Assume the resting position is at y=0, so the function is y = 10sin(π/4 x + π/4).

First one the first point will not be on the midline and will be at the maximum height.

In physics, amplitude refers to the greatest displacement or distance that a point on a vibrating body or wave can move relative to its equilibrium location.

amplitude = 10 = A and y = Asin(Bx - C) + D

Time = 8 seconds

B = 2π/time

B = 2π/8

B = π/4

The sine graph is pushed back by π/2 units since the weight is at its maximum position at x = 0; as a result, C = π/2, D = 0 (the midline is y = 0).

y = 10sin(π/4 x + π/4) is the function.

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The complete question is:

A researcher observes and records the height of a weight moving up and down on the end of a spring. At the beginning of the observation the weight was at its highest point. From its resting position, it takes 12 seconds for the weight to reach its highest position, fall to its lowest position, and return to its resting position. The difference between the lowest and the highest points is 10 in. Assume the resting position is at y = 0. Use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.

A population is the entire group of items of interest in a particular study, and it is not necessarily the same size as the sample. It is not the same as a sample, which is a subset of the population chosen for the study.

A population is the complete set of items of interest in a study. It could be people, animals, plants, objects, or anything else being studied. A population can be large or small, and it is not always the same size as the sample. A sample is a subset of the population that is chosen to represent the entire population. It is important to choose a sample that accurately reflects the population. Sampling techniques, such as random sampling, are used to ensure that the sample is representative of the population. Once the sample is chosen, data is collected from the sample to infer information about the population. This data can then be used to draw conclusions about the population as a whole.

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The difference after the subtraction is: 2a³ +  10a² - 5a - 4

A polynomial is an expression which has one or more of its variables with a power of at least 2 degrees. It can be expressed in form of a term.

Therefore, a polynomial equation is a means of expressing an expression with terms and on variable with a degree of 2 or more.

To find the difference by subtracting the polynomials, we have:

4a³ + 6a² - 11a - 3 - (2a³ - 4a² - 6a + 1) = 4a³ + 6a² - 11a - 3 - 2a³ + 4a² + 6a - 1

collecting like terms,

4a³ - 2a³ +  6a² + 4a²  - 11a + 6a - 3 - 1 = 2a³ +  10a² - 5a - 4

Therefore, the difference by subtracting the two polynomials is:

2a³ +  10a² - 5a - 4

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