6 times a number is 7 less than the square of that number. Find the positive solution.

Answer:

AP = 18, PL = 9

Step-by-step explanation:

assuming AL, is a median of the triangle

then AP = [tex]\frac{2}{3}[/tex] AL = [tex]\frac{2}{3}[/tex] × 27 = 18

PL = [tex]\frac{1}{3}[/tex] AL = [tex]\frac{1}{3}[/tex] × 27 = 9

The smaller tap take 25 hours to fill the tank and the larger tap take 10 hours to fill the tank.

How to calculate time taken to fill the tank for each tap?

Given,

Time taken for two tap together to fill the tank = [tex]9\frac{3}{8}[/tex] hours = [tex]\frac{75}{8}[/tex] hours

Time taken for smaller tap to fill the tank = x hours

Time taken for larger tap to fill the tank = x - 10 hours

So,

Tank filled by two tap together in 1 hour = [tex]\frac{8}{75}[/tex]

Tank filled by smaller tap in 1 hour = [tex]\frac{1}{x}[/tex]

Tank filled by larger tap in 1 hour = [tex]\frac{1}{x-10}[/tex]

Then, tank filled by two tap together is equal to tank filled by smaller tap and larger tap. So,

[tex]\frac{8}{75} = \frac{1}{x} + \frac{1}{x-10}[/tex]

[tex]\frac{8}{75} = \frac{x-10+x}{x(x-10)}[/tex]

[tex]\frac{8}{75} = \frac{2x-10}{x^{2}-10x}[/tex]

[tex]8x^{2}-80x = 150x - 750[/tex]

= [tex]8x^{2} - 230x + 750[/tex]

= [tex]2(4x^2 - 115x + 375)[/tex]

= [tex]4x^2 - 100x - 15x + 375[/tex]

= [tex](4x - 15) (x - 25)[/tex]

If, x = [tex]\frac{15}{4}[/tex] then x - 10 for larger tap equal to [tex]\frac{15}{4}[/tex] - 10 = [tex]- \frac{25}{4}[/tex] < 0 hours, so it is impossible.

Then, x must be 25. So, for larger thank is 25 - 10 = 15.

Smaller tap take 25 hours to fill the tank

Larger tap take 15 hours to fill the tank.

Thus, the smaller tap take 25 hours to fill the tank and the larger tap take 10 hours to fill the tank.

Your question is not complete, but most probably your full questions is (image attached)

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Answer:

it is c

Step-by-step explanation:

you do 9x2 6+1 = 7 + 18 =25

Answer:

y = 2 ; y = -7

Step-by-step explanation:

sum of two numbers = 5

product of two numbers = -14

the two numbers are 7 and -2

(y-2)(y+7) = 0

y = 2

y = -7

For the given matrix A = [tex]\left[\begin{array}{ccc}8&-4\\-7&0\\\end{array}\right][/tex] and B = [tex]\left[\begin{array}{ccc}2&5\\2&0\\\end{array}\right][/tex] then value of matrix X which satisfy the given equation 3X = -3A + 4B is equal to [tex]X = \frac{1}{3} \left[\begin{array}{ccc}-16&32\\29&0\\\end{array}\right][/tex].

As given in the question,

Given matrix are equal to :

A = [tex]\left[\begin{array}{ccc}8&-4\\-7&0\\\end{array}\right][/tex]

B = [tex]\left[\begin{array}{ccc}2&5\\2&0\\\end{array}\right][/tex]

Simplify the equation which satisfy the equation 3X = -3A + 4B is given by :

Substitute the value of matrix A and matrix B in the given equation we get:

3X  =  [tex]-3\left[\begin{array}{ccc}8&-4\\-7&0\\\end{array}\right] + 4\left[\begin{array}{ccc}2&5\\2&0\\\end{array}\right][/tex]

⇒ 3X =  [tex]\left[\begin{array}{ccc}-24&12\\21&0\\\end{array}\right] + \left[\begin{array}{ccc}8&20\\8&0\\\end{array}\right][/tex]

⇒ 3X = [tex]\left[\begin{array}{ccc}-16&32\\29&0\\\end{array}\right][/tex]

To get the value of X divide both the side by 3 we have,

⇒ X   = [tex]\frac{1}{3} \left[\begin{array}{ccc}-16&32\\29&0\\\end{array}\right][/tex]

Therefore, for the given matrix A = [tex]\left[\begin{array}{ccc}8&-4\\-7&0\\\end{array}\right][/tex] and B = [tex]\left[\begin{array}{ccc}2&5\\2&0\\\end{array}\right][/tex] then value of matrix X which satisfy the given equation 3X = -3A + 4B is equal to [tex]X = \frac{1}{3} \left[\begin{array}{ccc}-16&32\\29&0\\\end{array}\right][/tex].

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[tex]b = \frac{96-3m}{4}[/tex] and [tex]m = \frac{96-4b}{3}[/tex]  for the equation that models.

Jada sells b books and m magazine subscriptions to raise money for a choir trip. She earns $4 for each book and $3 for each magazine subscription she sells, and she earns a total of $96 toward the cost of her choir trip.

Given that

1. Jada sells b books and m magazines

2. She earns $4 for each book and $3 for each magazine

3. Total amount she earned is $96

Given equation is

4b + 3m = 96

Solve 4b + 3m = 96 for b

Subtract 3m from both sides

4b + 3m - 3m = 96 - 3m

4b = 96 - 3m

Now divide both sides by 4

= [tex]b = \frac{96-3m}{4}[/tex]

So, the answer for b is [tex]\frac{96-3m}{4}[/tex]

Now, solve 4b + 3m = 96 for m

Subtract 4b from both sides

4b + 3m - 4b = 96 - 4b

= 3m = 96 - 4b

Now divide both sides by 3

= [tex]m = \frac{96-4b}{3}[/tex]

So, the answer for m is [tex]\frac{96-4b}{3}[/tex]

Hence the answer is [tex]b = \frac{96-3m}{4}[/tex] and [tex]m = \frac{96-4b}{3}[/tex] for the equation that models.

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Answer:960000000

Step-by-step explanation:

Answer: 960000000

Step-by-step explanation:

960 times 1.0 times 10^6 look it up !!

A coefficient is an integer that is written along with a variable or it is multiplied by the variable. In other words, a coefficient is the numerical factor of a term containing constant and variables. For example, in the term 2x, 2 is the coefficient.

Given that Mr. Townsend needs to make 13 pairs of butterfly wings for costumes for a play. Each pair of wings is made with 3/4 yards of fabric. The fabric costs $8 per yard. The total cost of the fabric is $78.

The total cost formula is used to get a total by combining the variable and fixed expenses of delivering commodities.

The step-by-step is given as follows:

1) Total cost  (TC) = 3/4 (P) x 13

2) 1 pair of wings = 3/4 yard fabric

Recall that the price of 1 yard of fabric = $8

3) 1 pair of wings = $8 x 3/4 = $6

4) Therefore total cost = $6 x 13 = $78

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The probability that the spinner lands on yellow and the coin toss is tails is 9/10.

What is probability?

Probability shows the likelihood of an event happening.  it can be calculated by dividing the number of outcomes of an event by the total number of possible outcomes or sample space. Probability is equal to '1' when the event is certain to occur. i.e P =1. It is less than '1' when it is not likely to occur. i.e P< 1

Probability P=no. outcomes/total no. of the possible outcomes

From the question;

No of blue=1

No of yellow=9

No. of total possible outcome=10

Therefore the probability that the spinner lands on yellow and the coin toss is tails P= 9/10.

           P= 9/10                            

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Answer:

1

Step-by-step explanation:

1.5/2.5= 0.6

0.6 nearest tenth is 1

0.0-0.5 --0

0.6-0.9 --1

The range of the given graph is [5, ∞).

Range.

Range refers the set of possible output values, and if we have the graph, then the set of all possible y values on the graph is defined as the range.

Given,

Here we have the graph.

Through the given graph we have to find the range of the line.

As per the definition of range, we have identified that the range take the value of y axis.

While we lookin into the given graph, we have identified that the starting point of the line is

=> (0, 5)

In this point 0 refers the x coordinate and 5 refers the y coordinate. So, the starting range is 5.

And the end of the line is not pointed.

So, we can consider that this line goes infinitely.

So, the range of the graph is  [5, ∞).

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The angle measures are ∠1 = 66°, ∠2 = 114°.

Given that m<1 = (x+81)° and m<2=2x°.

Here ∠ 1 and ∠ 2 are adjacent angles and are supplementary ( sum to 180°), then

2x + x + 81 = 180 , that is

3x + 81 = 180 ( now subtract the number 81 from both the sides )

3x = 99 ( now divide both the sides by the number 3 )

So that, x = 33

Thus, putting the value of x in the below equations:

∠ 1 = 2x = 2 × 33 = 66°

∠ 2 = x + 81 = 33 + 81 = 114°

Hence the answer is the angle measures = ∠1 = 66°, ∠2 = 114°.

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Answer:

2.9 × 1025

(scientific notation)

= 2.9e25

(scientific e notation)

Step-by-step explanation:

hope this helped

Answer:

Step-by-step explanation:

The equation of the line that passes through the point and slope (-2, -7) m = 4/5

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

The line contains the following point and slope. (-2, -7) m = 4/5

y - y1 = m(x - x1)

y + 7 = 4/5(x + 2)

y = 4x/5 + 8/5 - 7

y = 4x/5 - 27/5

Thus, the equation of the line that passes through the point and slope (-2, -7) m = 4/5

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The two equations that can be formed by adding or subtracting is

4x−4y = 16 and  2x − 6y = -8 .

the two equations are : x + y = 12 and 3x − 5y = 4

Adding we get :

x + y = 12

3x − 5y = 4

4x -4y = 16

Subtracting we get:

x + y = 12

3x − 5y = 4

-2x + 6y = 8 or 2x - 6y = -8

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the unknown parameters variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign.

It will be regarded as a phrase. In the following section of this article, you will discover the distinction between an equation and an expression.

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We have elaborate below a real-world problem that involves a decimal divided by a decimal.

Since we are given a problem that says that Jake owns a bakery  amd he makes 8.5 boxes of cupcakes in 15.5 hours,  the question is how many cupcakes he makes in 1 hour .So the time taken is 15.5 and the number of cupcakes made in the  15.5 hours is 8.5. So 15 .5hours=8.5 cupcakes, now dividing both sides by 15.5, we get: 1 hour=8.5/15.5 =0.54 = 1 cupcake, therfore, it needs 1 hour  to make 1 cupcake. Here we had two quantities in form of decimals, so there division of expression of decimal dividing a decimal.

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A bicycle rider rides 24 km riding at a rate greater than 8 km/ h.

Given that, a bicycle rider is riding at a rate of 15 km/h for 4/9 of his ride.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

Let total number of km be x.

Distance1 =4/9 x

Distance2 =2/9 x

Remaining distance = x-(4x/9 + 2x/9)

= x-6x/9

=(9x-6x)/9

= 3x/9

Now, time =1 hour

8 = 3x/9 ÷ 1

⇒ 8×9=3x

⇒ x=24 km

Hence, a bicycle rider rides 24 km riding at a rate greater than 8 km/ h.

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I believe that f(2) would be 10 and f(-2) would be -5.

Answer:

Step-by-step explanation:

Since the two vector have opposite directions, their sum will be the difference of magnitudes:

And the direction is the same with the vector with greater magnitude, so it is south.

Answer:

Magnitude = 39 km

Direction = South

Step-by-step explanation:

Formula we use,

→ r + s

Now the required answer will be,

→ r + s

→ 164 + (-125)

→ 164 - 125

→ 39 km

Thus, answer is 39 km due south.

As the sample size (n) increases, the number of degrees of freedom increases, and the t-distribution approaches a normal distribution.

What is degrees of freedom ?

The variety of degrees of freedom is the amount of values within the final calculation of a datum that are liberal to vary. Estimates of applied math parameters are often primarily based upon totally different amounts information|of knowledge or data.

Main Body:

Degrees of freedom typically equals the quantity of observations (or items of information) minus the quantity of parameters calculable. once you perform regression, a parameter is calculable for each term within the model, and and every one consumes a degree of freedom. Therefore, as well as excessive terms during a multivariate analysis model reduces the degrees of freedom on the market to estimate the parameters' variability.

Hence the number of degrees of freedom increases,as the sample size (n) increases.

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The equation that shows the relationship between the nights and the length knitted is y = 22x.

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Let the nights = x

Let the length knitted = y

The appropriate equation will be:

y = (22 × x)

y = 22x

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Answer:

1. -3

2. 6

3.less than

Step-by-step explanation:

The point that represent the origin in the number line is Point W

A number line is a horizontal representation of numbers in parts with equal intervals

The numbers in a number line is arranged to be increasing from left to right , hence drawing a number line will have the smaller values to the left of the bigger values at right

number line on -5 to 5 will have the origin at the center and te center here is zero which is similar to p

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Y-intercept(b)= 10

equation wasnt written in the correct order so b is 10

Using a linear equation to solve this problem, the charge for a 3.5 hour job is 85.45 dollar.

To find how much was the bill, we need to write an equation or linear equation for this.

For every linear equation, it takes the form of y = mx + c.

Where m and c are the slope and intercepts of the straight line.

In this case, our linear equation can be written as

y = 18.70x + 20

where x = number of hours worked.

If the job took three and a half hour which is 3.5 hours, we can substitute this into the equation and solve.

y = 18.70(3.5) + 20

y = 85.45

The charge is 85.45 dollar.

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Answer:

a^2 - 5ab

Step-by-step explanation:

[3a * (a-b)] - [2a * (a+b)]

[3a(a) - 3a(b)] - [2a(a) + 2a(b)]

3a^2 - 3ab - (2a^2) - (2ab)

3a^2 - 2a^2 - 3ab - 2ab

a^2 - 5ab