If p + q = 36, and p -q = 20, then q = ?

Answer:

exactly one

Step-by-step explanation:

1. subtract 2x from the equation 2x + y = 1

2. now you should have y= -2x + 1

3. then on the second equation subtract 4x from 4x + 2y = 2

4. now you should have 2y = -4x + 2

5. divide everything by 2

6. now you should have y = -2x + 1

7. since you got an exact answer on both of them then it is exactly one

Final answer:

To find the dimensions of a rectangle with an area of 24 sq. inches and a perimeter of 50 inches, we set up a system of linear equations and solve for the length and width. The dimensions are found to be either 24 inches by 1 inch or 1 inch by 24 inches.

Explanation:

The question given by a student involves finding the dimensions of a rectangle given its area and perimeter. Given the area (24 sq. inches) and the perimeter (50 in.), we can set up two equations to solve for the length and width:

Area = length imes width = 24 sq. inches

Perimeter = 2 imes (length + width) = 50 inches

We can divide the perimeter by 2 to get the sum of the length and width:

25 = length + width

Since we have two equations, this forms a system of linear equations which we can solve simultaneously. First, assume the length is the larger dimension and let us represent it by 'L' and the width by 'W'. We have:

L imes W = 24

L + W = 25

To solve for L and W, we can use substitution or elimination methods. Let's assume we solve for W in terms of L using the first equation, W = 24/L, and then we substitute it into the second equation:

L + 24/L = 25

Multiplying both sides by L to clear the fraction, we get:

L² + 24 = 25L

Then we rearrange the terms to set the equation to zero:

L² - 25L + 24 = 0

Now we can factor this quadratic equation to find the values of L:

(L - 1)(L - 24) = 0

So, L can be either 1 inch or 24 inches. If L is 24 inches, then W will be 1 inch (since 24 imes 1 = 24), and if L is 1 inch, then W will be 24 inches. Either way, the dimensions that satisfy both the area and perimeter equations are 24 inches by 1 inch.

The dimensions of the rectangle are [tex]\( {24 \text{ inches} \text{ by } 1 \text{ inch}} \)[/tex].

To find the dimensions of the rectangle, let's denote the length by l and the width by w.

Given:

1. The area of the rectangle is 24 square inches:

[tex]\[ l \cdot w = 24 \][/tex]

2. The perimeter of the rectangle is 50 inches, which gives us the equation:

[tex]\[ 2l + 2w = 50 \][/tex]

Let's solve these equations step by step.

From the perimeter equation:

[tex]\[ 2l + 2w = 50 \][/tex]

Divide the entire equation by 2 to simplify:

[tex]\[ l + w = 25 \][/tex]

Now we have two equations:

[tex]\[ l + w = 25 \]\[ l \cdot w = 24 \][/tex]

Let's solve for l and w using substitution or elimination.

From ( l + w = 25 ), we can express l as:

[tex]\[ l = 25 - w \][/tex]

Substitute [tex]\( l = 25 - w \)[/tex] into [tex]\( l \cdot w = 24 \)[/tex]:

[tex]\[ (25 - w) \cdot w = 24 \][/tex]

Expand and rearrange the equation:

[tex]\[ 25w - w^2 = 24 \]\[ w^2 - 25w + 24 = 0 \][/tex]

Now, solve this quadratic equation using the quadratic formula [tex]\( w = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \)[/tex], where ( a = 1 ), ( b = -25 ), and ( c = 24 ):

[tex]\[ w = \frac{{-(-25) \pm \sqrt{{(-25)^2 - 4 \cdot 1 \cdot 24}}}}{{2 \cdot 1}} \]\[ w = \frac{{25 \pm \sqrt{{625 - 96}}}}{2} \]\[ w = \frac{{25 \pm \sqrt{{529}}}}{2} \]\[ w = \frac{{25 \pm 23}}{2} \][/tex]

So, we get two possible values for w:

[tex]\[ w = \frac{{25 + 23}}{2} = 24 \]\[ w = \frac{{25 - 23}}{2} = 1 \][/tex]

Now, find l for each value of w:

1. If ( w = 24 ):

 [tex]\[ l = 25 - 24 = 1 \][/tex]

2. If ( w = 1 ):

[tex]\[ l = 25 - 1 = 24 \][/tex]

Answer:   using t - test value is 1.37<2.08( At 0.05 level of significance)

        The mean of the sample was drawn from the population.

Step-by-step explanation:

Here sample size n=22

Given sample mean =530

Given population mean   =500

[tex]t=\frac{sample mean-µ}{\frac{S}{\sqrt{n-1} } }[/tex]

given sample standard deviation s=100

a) null hypothesis:-  The mean of the sample was drawn from the population   µ =500

Alternative hypothesis:-

The most powerful test you can use is t - distribution.

The test statistic is  

[tex]t=\frac{sample mean- µ}{\frac{S}{\sqrt{n-1} } }  

here S is the standard deviation of the sample

b)  The value of the test statistic

           [tex]t=\frac{sample mean- µ}{\frac{S}{\sqrt{n-1} } }  

substitute given values sample size n=22

sample mean =530

sample standard deviation s =100

mean of the population µ =500

the calculated value of t =[tex]\frac{530-500}{\frac{100}{\sqrt{22} } }[/tex]

                      the calculated value=1.3748

c) The degrees of freedom =n-1 = 22-1 = 21

     The table value of t are 0.05 level of significance with 21 degrees of freedom is 2.08

       The calculated value 1.37<2.08

∴ we accept null hypothesis at 0.05 level of significance

conclusion:-

The mean of the sample was drawn from the  population.

A t-test is the most powerful test for this hypothesis. The test statistic value is calculated using t = (X - µ) / (s / √n). Based on a significance level of 0.05, we can conclude by comparing the calculated t-value with the critical t-value from t-distribution table.

The subjects of this question are hypothesis testing and statistics.

To answer your question: a) The most powerful test to use to test your hypothesis is the t-test for single mean. This is because you have one sample mean, one hypothesized population mean, and the population standard deviation is not known.

b) The value of the test statistic can be calculated using the formula: t = (X - µ) / (s / √n), where X is the sample mean, µ is the population mean, s is the sample standard deviation, and n is the sample size. Plugging in your values, the formula becomes t = (530 - 500) / (113/ √22).

c) With a = 0.05, we conclude by comparing the calculated t-value with t-distribution table (df = 22-1 = 21). If the calculated t-value exceeds the critical t-value from the t-distribution table, we reject the null hypothesis.

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Answer:

x=2

Step-by-step explanation:

so if the bigger one is 16 and the other one is 4 that means you need to multiply 4 by 4 to get 16 so to find x you need to divide the 8 by 4 to find your answer

Answer:

x = 2

Step-by-step explanation:

Since the triangles are similar then the ratios of corresponding sides are equal, that is

[tex]\frac{x}{8}[/tex] = [tex]\frac{4}{16}[/tex] ( cross- multiply )

16x = 32 ( divide both sides by 16 )

x = 2

Answer:

[tex]\theta=205.298^o[/tex]

Step-by-step explanation:

We know

[tex]cos\theta=-.9041[/tex]

in the third quadrant [tex]180^o<\theta<270^o[/tex]

We use a scientific calculator to find the inverse cosine of -0.9041 to find

[tex]\theta=154.702^o[/tex]

Since this angle is not in the required quadrant we must find the other angle who has the same cosine. The required angle is equidistant from the found value from the 180 degrees angle, so our solution is

[tex]\theta=180^o+(180^o-154.702)=205.298^o[/tex]

Answer:

Area of ΔDEF is [tex]45\ cm^2[/tex].

Step-by-step explanation:

Given;

ΔABC and  ΔDEF is similar and ∠B ≅ ∠E.

Length of AB = [tex]2\ cm[/tex] and

Length of DE = [tex]6\ cm[/tex]

Area of ΔABC = [tex]5\ cm^2[/tex]

Solution,

Since, ΔABC and  ΔDEF is similar and ∠B ≅ ∠E.

Therefore,

[tex]\frac{Area\ of\ triangle\ 1}{Area\ of\ triangle\ 2} =\frac{AB^2}{DE^2}[/tex]

Where triangle 1 and triangle 2 is  ΔABC and  ΔDEF respectively.

If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.

[tex]\frac{5}{Area\ of\ triangle\ 2} =\frac{2^2}{6^2}\\ \frac{5}{Area\ of\ triangle\ 2}=\frac{4}{36}\\ Area\ of\ triangle\ 2=\frac{5\times36}{4} =5\times9=45\ cm^2[/tex]

Thus the area of  ΔDEF is [tex]45\ cm^2[/tex].

The ratio 6 to 2 is equivalent to the ratio 3 to 1, obtained by dividing both the numerator and denominator of the ratio by their greatest common divisor, which is 2.

To find a ratio equivalent to 6 to 2, you simplify the ratio by dividing both numbers by their greatest common factor. In this case, the greatest common factor is 2, so 6 ÷ 2 = 3 and 2 ÷ 2 = 1. Therefore, the equivalent ratio is 3 to 1.

The ratio 6 to 2 can be simplified by dividing both numbers by their greatest common divisor, which is 2. Therefore, 6 divided by 2 is 3, and 2 divided by 2 is 1. This simplification shows that the ratio 6 to 2 is equivalent to 3 to 1. Ratios compare two quantities and can be expressed in several forms such as fractions, with a colon, or using the word "to". An equivalent ratio maintains the same proportional relationship between its components, just like how 6:2 has the same proportional relationship as 3:1.

===============================================

Explanation:

The x intercept is (-2,0) which is where the graph crosses the x axis.

The y intercept is (0,-6) which is where the graph crosses the y axis.

-----

Find the slope of the line through those two points

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

m = (-6-0)/(0-(-2))

m = (-6-0)/(0+2)

m = -6/2

m = -3

-----

The y intercept (0,-6) leads to b = -6

Both m = -3 and b = -6 plug into y = mx+b to get

y = mx+b

y = -3x+(-6)

y = -3x-6

-----

Now add 3x to both sides

y = -3x-6

y+3x = -3x-6+3x

3x+y = -6

-----

Lastly, multiply both sides by -2 so that the "-6" on the right hand side turns into "12" (each answer choice has 12 on the right hand side)

3x+y = -6

-2(3x+y) = -2(-6)

-2(3x)-2(y) = 12

-6x-2y = 12

which is what choice B shows.

Answer:

22 people with red shirts and 10 people with yellow shirts

Answer:

The value of g(x) at x  = -3 is 18.

Step-by-step explanation:

Here, the given function is:

g(x) = - 5 x + 3

Now, for the value of x = -3 ,

g (-3) : Substitute the value of x  = -3 in g(x) , we get

g (-3)  =  -5 (-3) + 3

          =  15 + 3 = 18

or, g ( -3) = 18

Hence, the value of g(x) at x  = -3 is 18.

Answer:

C = 8 + 3x

The rate of change in the above equation is 3 dollars per game and it interpret the cost per game.

The initial value in the above equation is 8 dollars, which interpret the entry fee that every one person has to pay to enter the fair.

Step-by-step explanation:

Let the admission cost of the fair is $x and each game is $3.

Now, Steven went to the state fair, played  4 games and spent a total of $20 on  admission and games.

So, we can write 20 = x + 4 × 3 {As the relation is linear}

⇒ x = $8

Therefore, the admission cost in the fair is $8.

Therefore, the equation that models the situation is  

C = 8 + 3x ............ (1)

Where C is the total cost and x is the number of games played.

So, the rate of change in equation (1) is 3 dollars per game and it interprets the cost per game.

Again, the initial value in equation (1) is 8 dollars, which interprets the entry fee that each person has to pay to enter the fair. (Answer)

The right answer is Option D.

Step-by-step explanation:

Given equations are;

2x+4y=3    Eqn 1

x+3y=13    Eqn 2

When we use subtraction-addition method, we make one of the variables same with opposite signs so that only one variable remains after addition or subtraction.

In the given problem, we will multiply Eqn 2 with "-2" so that the x variables become equal and then we can add both the equations and solve for y.

Therefore,

The first step will be to multiply the second equation by -2 to solve the linear system of equations.

The right answer is Option D.

Keywords: linear equations, subtraction

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Answer:

It's D.

Step-by-step explanation:

It was correct on my unit test review.

First choice: m^32n^16

Hope this helps!

Answer:

The correct answer would be m^32n^16.

Step-by-step explanation:

This is because when you have a power inside parenthesis multiplied by a power outside the parenthesis, you are simply going to multiply the numbers like so:

8 • 4 = 32

4 • 4 = 16

m^32n^16

Hope this helps,

♥A.W.E.S.W.A.N.♥

Answer:

Step-by-step explanation:

Let's first find the rate of increase for each period which is 3 months here.

According to the table at month [tex]x=0[/tex] value is [tex]2000[/tex]dollars and at month [tex]x=3[/tex] value is [tex]2012[/tex]dollars.

∴[tex]2012=2000(1+\frac{r}{100} )^1[/tex]

⇒[tex]1+\frac{r}{100} =\frac{2012}{2000}=1.006[/tex]

⇒[tex]r=0.006*100[/tex]

⇒[tex]r=0.6[/tex]%

Now the question is to find how long it will take for the investment value to increase 10 percent.

[tex]y=2000(1+0.006)^\frac{x}{3}[/tex]

[tex]2000(1+0.1)=2000(1.006)^\frac{x}{3}[/tex]

⇒[tex](1.006)^\frac{x}{3} =1.1[/tex]

⇒[tex]\frac{x}{3}=\frac{log(1.1)}{log(1.006)}[/tex]

⇒[tex]x=3(\frac{log(1.1)}{log(1.006)} )[/tex]

⇒[tex]x=47.7979126....[/tex]

∴at [tex]x=48[/tex] the value will slightly cross 10 percent increase.

Answer:

[tex]a_n=-3*\left ( -\frac{2}{3} \right )^n \ n>=0[/tex]

Step-by-step explanation:

Succession can be understood as a sorted collection of values that respond to a general term or rule. We need to find if these numbers are in arithmetic progression or geometric progression.

In an arithmetic progression, every number is obtained as the previous number plus or minus a constant value called common difference. In a geometric progression, we get the next numbers as the previous one multiplied or divided by a constant value, called the common ratio.  

If we try to find a possible common difference between first and second terms we get:

[tex]2-(-3)=5[/tex]

If it was an arithmetic progression, third term should be

[tex]2+5=7[/tex]

Which is obviously not true. Now let's try to find a possible common ratio by dividing second by first term

[tex]r=\frac{2}{-3}=-\frac{2}{3}[/tex]

Testing our value to find the third term we get

[tex]a_3=2*(-\frac{2}{3})=-\frac{4}{3}[/tex]

Since we have more terms to test:

[tex]a_3=(-\frac{4}{3})*(-\frac{2}{3})=\frac{8}{9}[/tex]

The given value is just as predicted

The fourth term can be accurately predicted also:

[tex]a_4=(\frac{8}{9})*(-\frac{2}{3})=\frac{16}{27}[/tex]

Now we are sure it's a geometric progression, it can easily be stated the general term of the progression is

[tex]a_n=a_1*r^n \ n>=0[/tex]

[tex]a_n=-3*\left ( -\frac{2}{3} \right )^n \ n>=0[/tex]

Answer:

[tex]-0.4(3x-2)+\frac{2x+4}{3}=0\ \textrm{for}\ x=4[/tex]

Step-by-step explanation:

Given:

The expression to evaluate is given as:

[tex]-0.4(3x-2)+\frac{2x+4}{3}[/tex]

The value of 'x' is 4.

Plug in 4 for 'x' in the above expression and simplify. This gives,

[tex]=-0.4(3(4)-2)+\frac{2(4)+4}{3}\\=-0.4(12-2)+\frac{8+4}{3}\\=-0.4(10)+\frac{12}{3}\\=-4+4\\=0[/tex]

Therefore, the value of the given expression for 'x' equal to 4 is 0.

The required value of the given expression is 0 when substituting the value of x = 4 into the expression.

The expression is given as follows:

-0.4(3x - 2) + (2x + 4) / 3

Let's evaluate the given expression for x = 4:

Expression = -0.4(3x - 2) + (2x + 4) / 3

Substitute x = 4 into the given expression:

Expression = -0.4(3 × 4 - 2) + (2 × 4 + 4) / 3

Expression = -0.4(12 - 2) + (8 + 4) / 3

Expression = -0.4(10) + 12 / 3

Expression = -4 + 12 / 3

Expression = -4 + 4

Expression = 0

Therefore, when x = 4, the value of the expression is 0.

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Answer:

see the explanation

Step-by-step explanation:

we know that

The rule of the reflection of a point across the y-axis is equal to

(x,y) -----> (-x,y)

The rule of the reflection of a point across the x-axis is equal to

(x,y) -----> (x,-y)

so

Verify each statement

1) Point (3,2) to (3,-2) is a reflection over the y-axis.

The statement is false

Because, is a reflection over the x-axis

A reflection over the y-axis will be

(3,2) -----> (-3,2)

2) A(1,3) to A'(-1,3) is a reflection over the y-axis

The statement is true

Answer:

Step-by-step explanation:

(0^209 + 1(209)/(209))^0 + 208

Answer:

a^2 -6

Step-by-step explanation:

use ur basic knowing of equations

Answer:

6 units long.

Step-by-step explanation:

Given:

A polygon drawn on a graph.

In order to determine the distance of the horizontal line at the top, we find the coordinates of the end points and then use distance formula to find the exact distance.

Let us label the polygon as ABCD as shown below. AB is the length of the horizontal line.

Coordinates of A are [tex](x_1,y_1)=(-3, 4)[/tex] as seen in the graph.

Coordinates of B are [tex](x_2,y_2)=( 3, 4)[/tex] as seen in the graph.

Now, distance formula  for two points [tex](x_1,y_1)\ and\ (x_2,y_2)[/tex] is:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\d_{AB}=\sqrt{(3-(-3))^2+(4-4)^2}\\d_{AB}=\sqrt{(3+3)^2+0}\\d_{AB}=\sqrt{36}=6\ units[/tex]

Therefore, the horizontal line at the top is 6 units long.

Answer:

6 units long

Step-by-step explanation:

brainly patrol what is wrong with that

Answer:

[tex] \frac{5}{2} \\ [/tex]

Step-by-step explanation:

[tex] \frac{ - 5 - 5}{ - 8 - - 4} [/tex]

Y - Y divided by X - X, the Y is 5 and the X is 2 (Rise over Run)

Answer:

[tex]\displaystyle 2\frac{1}{2} = m[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \\ \frac{-5 - 5}{4 - 8} = \frac{-10}{-4} = 2\frac{1}{2}[/tex]

I am joyous to assist you anytime.

Answer:

place

Step-by-step explanation:

Answer:

The answer is " Place value"

Step-by-step explanation:

The place value determines the value of the digit in a number, based on its position.

A standard form number is divided into groups of three digits using commad. Each of these groups is called a period.

Answer:

2 years ago :/

Step-by-step explanation:

Answer:

Y- intercept is 5!

There are 27 purple marbles

Step-by-step explanation:

Let p be the purple marbles

and

w be the white marbles

Then according to given statements

[tex]p+w = 34\ \ \ Eqn\ 1\\p = 4w-1\ \ \ Eqn 2[/tex]

Putting p = 4w-1 in equation 1

[tex]4w-1 +w = 34[/tex]

Adding one on both sides

[tex]5w-1+1 = 34+1\\5w = 35[/tex]

Dividing both sides by 5

[tex]\frac{5w}{5} = \frac{35}{5}\\w = 7[/tex]

Putting w = 7 in equation 2

[tex]p = 4(7)-1\\p = 28-1\\p = 27[/tex]

Hence,

There are 27 purple marbles

Keywords: Linear equation

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Answer: 838% to the nearest percent

Step-by-step explanation:

225 - 24 =201

=201/24 * 100

= 838% to the nearest percent

Answer:

903 1/8

Step-by-step explanation:

Just divide 7225 by 8. :) I put it in fraction form but decimal form is just 903.125. I hope this helps you out. :)

Answer:

its 903 with 1 left over

Answer:

Step-by-step explanation:

B :because 11 pound in Ounces is 176

The total number of college students was 17.94 million.

Step-by-step explanation:

Percentage of part time students = 34%

Number of part time students = 6.1 million

Let,

x be the total number of students

According to statement,

34% of x = 6.1 million

[tex]\frac{34}{100}x=6.1\ million\\0.34x=6.1[/tex]

Dividing both sides by 0.34

[tex]\frac{0.34x}{0.34}=\frac{6.1}{0.34}\\x=17.94\ million[/tex]

The total number of college students was 17.94 million.

Keywords: percentage, division

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