Tell whether the given number is a solution of each question. ( Must show work for credit)


1. 9 = 2a + 3; 3


2. 5n - (-30) = 5; 7


3. 4.4r - 2.8 = 1.6; 1​

Answer:

21, 7

Step-by-step explanation:

1st number = x, 2nd number = y

Given x + 3y = 42    (1)

find maximum value of xy.

Multiply by x on (1), get

x^2 + 3xy = 42x

3xy = -x^2 + 42x = -(x^2 - 42x)

Make a perfect square,

3xy = -(x^2 - 42x + 21^2) + 21^2

3xy = 21^2 - (x - 21)^2

Note (x - 21)^2 is non-negative, so when x = 21, the right hand side has a maximum value of 21^2, so xy is a maximum.

Use (1) and x = 21, we get 21 + 3y = 42, 3y = 21, y = 7

Hence, the two positive real numbers are 21 and 7

Given that x is equal to 1 and S is the centroid of the triangle NLQ, NS will have a length of 4 units.

The centroid of a flat figure or solid figure, also known as the geometric center or center of figure, in mathematics and physics, is the arithmetic mean position of all the points on the figure's surface. Any n-dimensional Euclidean object is included by the same definition. The centroid of a triangle is the location where the triangle's three medians connect. It may alternatively be described as the location where the three medians come together. A line connecting a side's midpoint and the triangle's opposite vertex is called the median.

Here,

We may infer from the centroid's features that it divides each median in a ratio of 2:1.

NS=2SR

7x-3=2(5x-3)

7x-3=10x-6

3x=3

x=1

NS=7x-3

=7*1-3

=4 units

The length of NS will be 4 units as the value of x is 1 and S is the centroid of triangle NLQ.

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The vertical value in a pair of coordinates. How far up or down the point is. The Y Coordinate is always written second in an ordered pair of coordinates (x,y) such as (12,5). In this example, the value "5" is the Y Coordinate.

Answer:

They are perpendicular

Step-by-step explanation:

If 2 slopes are negative reciprocals of each other, it means they are perpendicular

Answer:

The lines are perpendicular because they have opposite reciprocal slopes.

Step-by-step explanation:

The mortar shell will strike the target in 0.02 seconds

The duration to strike the target is solved using the formula for velocity which is

= distance / time

The problem gives the distance to be 3 feet and velocity is 150ft/s

therefore

150 = 3 / time

time = 3 / 150

time = 0.02 seconds

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Answer:

48-19=29

$29 is the answer

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

From 7 to 10 AM is THREE hours (if the times are all on the same day)

Answer:

18.84 square inches

Step-by-step explanation:

Distance across = diameter. The area formula for circles is A= πr. r in here means radius which is 6 inches (half of diameter). π is generally 3.14 or 22/7 depending on the question. multiply the value of π and 6, then you get the answer.

Answer:

y = mx + b

m = (-5-1)/(3-1)

m = -3

1=(-3)1 + b

b= 4

y= -3x + 4

A linear equation is an algebraic equation of the form \(y=mx+b.\) involving  where m is the slope and b is the y-intercept

Company A charges is represented by equation, \(A=55+0.5x\)

Company B charges is represented by equation , \(B=0.6x\)

Let number of miles is represented by  x .

\(1 cent= \frac{1}{100}dollar\\\\50cents=\frac{50}{100}=0.5dollar\\\\60 cents=\frac{60}{100}=0.6dollar\)

Since, Company A charges an initial fee of $55 and an additional 50 cents for every mile driven.

So, equation is,  \(A=55+0.5x\)

Since, Company B has no initial fee but charges 60 cents for every mile driven.

So, equation is,  \(B=0.6x\)

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Answer: $ 251.93

Step-by-step explanation:

For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

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Answer:

no it is not. the line crosses the x in 20, and crosses the y in 40

Answer:

2 * x^2

Step-by-step explanation:

in word form: two times the square of x

"a number" can be any variable; i used x

Answer:

x² × 2

Step-by-step explanation:

Notice vocabulary:

Put this information together.

"Twice the square of a number"

Since it says of a number, this number comes first → \(x\)

"Twice the square of a number"

The square of a number means that the variable will be squared → \(x^2\)

"Twice the square of a number"

Multiply the variable by a factor of two → \(x^2*2\)

:Done

Thus, the scale factor from circle A to circle B is found to be 2.

The ratio between comparable measurements of just an element and a portrayal of that element is known as a scale factor in mathematics. The copy will be larger if the scaling factor is a whole number. A fractional scaling factor means that the duplicate will be smaller.

You must first choose which direction we are scaling in order to determine the scale factor:

The radius of circle A = 2 units

The radius of circle B = 4 units.

So, there is a dilation with the scale factor of 2 units as 2*2 = 4 units.

Thus, the scale factor from circle A to circle B is found to be 2.

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Answer:r=2 cos^4(theta)

Step-by-step explanation:To find the values of theta where the maximum r-values occur on the graph of the polar equation r = 2 cos^4(theta), we need to find where the derivative of r with respect to theta is equal to zero, since the maximum r-values occur at these points.

First, we can simplify the equation by using the identity cos(2theta) = 2cos^2(theta) - 1 and substituting cos^2(theta) = (1 + cos(2theta))/2. This gives:

r = 2 cos^4(theta) = 2(1/2 + 1/2 cos(2theta))^2 = 1 + cos(2theta) + cos^2(2theta)/2.

Next, we can take the derivative of r with respect to theta, using the chain rule:

dr/dtheta = -sin(2theta) - 2cos(2theta)sin(2theta).

Setting this equal to zero and factoring out sin(2theta), we get:

sin(2theta)(-1 - 2cos(2theta)) = 0.

This equation is satisfied when sin(2theta) = 0 or cos(2theta) = -1/2.

When sin(2theta) = 0, we have 2theta = k*pi for some integer k. Therefore, theta = k*pi/2.

When cos(2theta) = -1/2, we have 2theta = 2*pi/3 + 2*k*pi or 2theta = 4*pi/3 + 2*k*pi for some integer k. Therefore, theta = pi/3 + k*pi or theta = 2*pi/3 + k*pi.

These are the values of theta where the maximum r-values occur on the graph of the polar equation r = 2 cos^4(theta).

The slope of the equations is equal. Then the lines are parallel to each other.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The linear equation is given below.

y = 2x + 1        ....1

2x - y = 3

y = 2x - 3         ....2

The slope of both equations is 2.

The slope of the equations is equal. Then the lines are parallel to each other.

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there are 3 cups of lemonade in each cup

Answer:

Segment ED has the same length as EA

The line segment which is equal to EA is ED. Therefore, option B is the correct answer.

In the given diagram, a line perpendicular to line AB passes through point C.

A tangent to a circle is a line which intersects the circle at only one point. The common point between the tangent and the circle is called the point of contact.

The length of two tangents drawn from an external point to a circle is equal.

From the given figure we can see there are three circles, two large circles and one small circle.

Line segment EA is tangent to a small circle.

The line segment which is equal to EA is ED because ED is another tangent to a small circle from the same external point.

The line segment which is equal to EA is ED. Therefore, option B is the correct answer.

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Answer:

Average time per day = 1.2 hours per day
Average time per day = 72 minutes per day

Step-by-step explanation:

To find Clarence's average time per day, we need to divide the total time he takes to walk the 15.5 miles by the number of days he walks, which is five.

Let's calculate his average time per day:

Average time per day = Total time / Number of days

Since Clarence takes a total of 6 hours to walk the 15.5 miles, we'll divide 6 by 5 to find his average time per day:

Average time per day = 6 hours / 5

Average time per day = 1.2 hours per day

To convert hours to minutes, we'll multiply the average time per day by 60:

Average time per day = 1.2 hours * 60 minutes

Average time per day = 72 minutes per day

Therefore, Clarence's average time per day is 72 minutes.

Answer:

Step-by-step explanation:

To calculate the probability of winning any amount of money, we need to sum up the probabilities of winning each individual prize.

Given the probabilities stated on the game card:

Probability of winning $10 prize = 0.2

Probability of winning $5 prize = 0.1

Probability of winning $0 prize = 0.7

To find the probability of winning any amount of money, we add these probabilities together:

0.2 + 0.1 + 0.7 = 1

The sum of the probabilities is 1, which indicates that the total probability of winning any amount of money is 1 or 100%.

Therefore, the probability of winning any amount of money in this game is 100%.

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Answer:

\(\frac{3}{4}(m+n)-\frac{1}{4}(m-n) = \frac{14}{24}\)

Step-by-step explanation:

Given

\(\frac{3}{4}(m+n)-\frac{1}{4}(m-n);m=\frac{1}{2},n=\frac{1}{3}\)

Required

Solve

To do this, we simply substitute values of m and n in the given expression

\(\frac{3}{4}(\frac{1}{2}+\frac{1}{3})-\frac{1}{4}(\frac{1}{2}-\frac{1}{3})\)

Evaluate the brackets

\(\frac{3}{4}(\frac{3 + 2}{6})-\frac{1}{4}(\frac{3-2}{6})\)

\(\frac{3}{4}(\frac{5}{6})-\frac{1}{4}(\frac{1}{6})\)

Open Brackets

\(\frac{15}{24} - \frac{1}{24}\)

Take LCM

\(\frac{15 - 1}{24}\)

\(\frac{14}{24}\)

Hence:

\(\frac{3}{4}(m+n)-\frac{1}{4}(m-n) = \frac{14}{24}\)

The equation will be  \(y=40000+16000*x\)

Solve one of the equations for a particular variable. After that, insert that into the other equation and find the variable there. To find the value for the other variable, enter that value into either equation.

Equations come in two varieties: identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true. Two expressions joined by the equals symbol ("=") form an equation.

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There is no real Value of k that will satisfy the equation 2x² - x + 8k = 0 if a and 1/a are the roots of the polynomial.

(i) Zeroes of the polynomial:

In the graph, we have two points where the curve intersects the x-axis: one is at (-1,0), and the other is at (2,0).The corresponding values of x are -1 and 2, and they are the zeros of the polynomial. Therefore, the zeros of the polynomial are -1 and 2.(ii) Forming the quadratic polynomial:

From the graph, we can observe that the curve intersects the y-axis at the point (0,5), implying that the constant term of the polynomial is 5.

We can use the formula to find the quadratic polynomial if we have two zeros and one constant term. Thus, the quadratic polynomial is given by:(x + 1)(x - 2) = x² - x - 2x + 2 = x² - 3x + 2. Therefore, the quadratic polynomial is x² - 3x + 2.(iii) Value of k if a, 1/a are the zeroes of the polynomial 2x² - x + 8k:

We know that a and 1/a are the zeroes of the polynomial 2x² - x + 8k. Therefore, we can find the sum and product of the roots and use them to determine the value of k.

The sum of the roots is a + 1/a, and their product is a(1/a) = 1. Using the sum and product of the roots, we can write: a + 1/a = 1/2 (1/2 is the coefficient of x)Substituting a with 1/a in the above equation, we get: 1/a + a = 1/2Multiplying both sides of the equation by 2a, we get: 2 + 2a² = a

Simplifying the equation, we get: 2a² - a + 2 = 0Multiplying both sides by 2,

we get: 4a² - 2a + 4 = 0Dividing both sides by 2, we get: 2a² - a + 2 = 0

Using the quadratic formula, we get: a = [1 ± √(1 - 4(2)(2))]/(2(2))

Simplifying, we get: a = [1 ± √(-31)]/4Since the discriminant of the quadratic formula is negative, the roots are imaginary. Therefore, there is no real value of k that will satisfy the equation 2x² - x + 8k = 0 if a and 1/a are the roots of the polynomial.

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Answer:

6.8

Explanation:

Locate and underline the tenth place 7, and look to the right 8.

Like this. 6.789

Then, the digit to the right 8 is 5 or above. So, we add 1 to the tenth place 7. The digits at the right 8 becomes 0, thus we get 6.8 as the answer.

The rate of change of the simple index over one day is approximately 12.78%.

To calculate the rate of change of the simple index over one day, we need to determine the percent change in the total value of the index between Monday's opening and Tuesday's opening.

On Monday, Stock A has 5000 shares at $2.75 per share, so its total value is:

Total value of Stock A on Monday = 5000 * $2.75 = $13,750

Similarly, on Monday, Stock B has 3000 shares at $4.30 per share, so its total value is:

Total value of Stock B on Monday = 3000 * $4.30 = $12,900

The total value of the index on Monday is the sum of the values of Stock A and Stock B:

Total value of the index on Monday = $13,750 + $12,900 = $26,650

On Tuesday, Stock A opens at $3.10 per share, and Stock B opens at $4.85 per share. Both stocks still have the same number of shares as on Monday.

The total value of Stock A on Tuesday is:

Total value of Stock A on Tuesday = 5000 * $3.10 = $15,500

The total value of Stock B on Tuesday is:

Total value of Stock B on Tuesday = 3000 * $4.85 = $14,550

The total value of the index on Tuesday is the sum of the values of Stock A and Stock B:

Total value of the index on Tuesday = $15,500 + $14,550 = $30,050

To calculate the percent change in the index, we use the formula:

Percent Change = ((New Value - Old Value) / Old Value) * 100

Percent Change = (($30,050 - $26,650) / $26,650) * 100 ≈ 12.78%

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Answer:

W = 4

Step-by-step explanation:

4/6 = 6/9

2/3 = 2/3  

Answer:

Rounded to the nearest tenth, $.0.11 per fish stick

Step-by-step explanation:

I divided the cost of the fish sticks, $1.95, and how many in each pack, 18, so the answer was 0.10833333333... and that rounded would be $0.11

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a) The mean of the data-set is of 2.

b) The range of the data-set is of 4 units, which is of around 4.3 MADs.

The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations in the data-set, which is also called the cardinality of the data-set.

The dot plot shows how often each observation appears in the data-set, hence the mean of the data-set is obtained as follows:

Mean = (1 x 0 + 5 x 1 + 3 x 2 + 5 x 3 + 1 x 4)/(1 + 5 + 3 + 5 + 1)

Mean = 2.

The range is the difference between the largest observation and the smallest, hence:

4 - 0 = 4.

4/0.93 = 4.3 MADs.

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