Sole by substitution.
-3x+2y=16
X-2y=-12

Answer:

use photomath

Step-by-step explanation:

Answer:

The maximum value of P is 34 and the minimum value of P is 0

Step-by-step explanation:

we have the following constraints

[tex]x+y \leq 6[/tex] ----> constraint A

[tex]2x+3y \leq 16[/tex] ----> constraint B

[tex]x\geq 0[/tex] ----> constraint C

[tex]y\geq 0[/tex] ----> constraint D

Solve the feasible region by graphing

Using a graphing tool

The vertices of the feasible region are

(0,0),(0,5.33),(2,4),(6,0)

see the  attached figure

To find out the maximum and minimum value of the objective function P, substitute the value of x and the value of y for each of the vertices in the objective function P, and then compare the results

we have

[tex]P=5x+6y[/tex]

For (0,0) ----> [tex]P=5(0)+6(0)=0[/tex]

For (0,5.33) ----> [tex]P=5(0)+6(5.33)=31.98[/tex]

For (2,4) ----> [tex]P=5(2)+6(4)=34[/tex]

For (6,0) ----> [tex]P=5(6)+6(0)=30[/tex]

therefore

The maximum value of P is 34 and the minimum value of P is 0

Answer:

A. h(x)= -5.86x^2 + 23.37x + 34

Step-by-step explanation:

If the scientist uses the same amount of pesticide on the two farms then the x's of the functions are the same.

Then, the combined yield [tex]h(x)[/tex] of the two farms is just the yield of the first farm plus the yield of the second farm:

[tex]h(x)=f(x)+g(x)[/tex].

Now, since

[tex]f(x)= -2.43x^2+10.37x+9[/tex]

and

[tex]g(x)= -3.43x^2+13x+25[/tex],

then

[tex]h(x)= (-2.43x^2+10.37x+9)+(-3.43x^2+13x+25)[/tex]

we add the coefficients of the  corresponding terms to get:

[tex]h(x)= (-2.43x^2-3.43x^2)+(10.37x+13x)+(9+25)[/tex]

[tex]\boxed {h(x)=-5.86 x^2 + 23.37 x + 34.}[/tex]

Which is choice A.

Answer:

1) The slope for the given points (6,7) and (-10,4) is [tex]m=\frac{3}{16}[/tex]

2) The slope for the given points (17,4) and (13,20) is [tex]m=-4[/tex]

3) The slope for the given points (12,19) and (14,18) is [tex]m=-\frac{1}{2}[/tex]

4) The slope for the given points (-11,0) and (18,13) is [tex]m=\frac{13}{29}[/tex]

5) The slope for the given points (3,6) and (-8,20) is [tex]m=-\frac{14}{11}[/tex]

6) The slope for the given points (-16,-20) and (12,5)  is [tex]m=\frac{25}{28}[/tex]

7) The slope for the given points (13,20) and (14,-14)  is [tex]m=-34[/tex]

8) The slope for the given points (18,15) and (3,0) is [tex]m=1[/tex]

Step-by-step explanation:

To find the slope of the line through each pair of points:

1) Given points are (6,7) and (-10,4)

The slope formula is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the given points (6,7) and (-10,4) respectively

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m=\frac{4-7}{-10-6}[/tex]

[tex]m=\frac{-3}{-16}[/tex]

[tex]m=\frac{3}{16}[/tex]

Therefore the slope for the given points (6,7) and (-10,4) is [tex]m=\frac{3}{16}[/tex]

2) Given points are (17,4) and (13,20)

The slope formula is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the given points (17,4) and (13,20) respectively

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m=\frac{20-4}{13-17}[/tex]

[tex]m=\frac{16}{-4}[/tex]

[tex]m=-4[/tex]

Therefore the slope for the given points (17,4) and (13,20) is [tex]m=-4[/tex]

3) Given points are (12,19) and (14,18)

The slope formula is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the given points (12,19) and (14,18) respectively

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m=\frac{18-19}{14-12}[/tex]

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

Therefore the slope for the given points (12,19) and (14,18) is [tex]m=-\frac{1}{2}[/tex]

4) Given points are (-11,0) and (18,13)

The slope formula is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the given points (-11,0) and (18,13) respectively

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m=\frac{13-0}{18-(-11)}[/tex]

[tex]m=\frac{13}{29}[/tex]

Therefore the slope for the given points (-11,0) and (18,13) is [tex]m=\frac{13}{29}[/tex]

5) Given points are (3,6) and (-8,20)

The slope formula is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the given points (3,6) and (-8,20) respectively

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m=\frac{20-6}{-8-3}[/tex]

[tex]m=\frac{14}{-11}[/tex]

[tex]m=-\frac{14}{11}[/tex]

Therefore the slope for the given points (3,6) and (-8,20) is [tex]m=-\frac{14}{11}[/tex]

6) Given points are (-16,-20) and (12,5)

The slope formula is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the given points (-16,-20) and (12,5) respectively

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m=\frac{5-(-20)}{12-(-16)}[/tex]

[tex]m=\frac{5+20}{12+16}[/tex]

[tex]m=\frac{25}{28}[/tex]

Therefore the slope for the given points (-16,-20) and (12,5)  is [tex]m=frac{25}{28}[/tex]

7) Given points are (13,20) and (14,-14)

The slope formula is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the given points (13,20) and (14,-14) respectively

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m=\frac{-14-20)}{14-13}[/tex]

[tex]m=\frac{-34}{1}[/tex]

[tex]m=-34[/tex]

Therefore the slope for the given points (13,20) and (14,-14)  is [tex]m=-34[/tex]

8) Given points are (18,15) and (3,0)

The slope formula is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the given points  (18,15) and (3,0) respectively

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m=\frac{0-15}{3-18}[/tex]

[tex]m=\frac{-15}{-15}[/tex]

[tex]m=1[/tex]

Therefore the slope for the given points  (18,15) and (3,0) is [tex]m=1[/tex]

Answer:

B.  Exponential.

Step-by-step explanation:

Each year you can find the estimated population for the following year by multiplying by  1 + 1.7%  = 1.017.

The population estimate in  x years time =  78,918 (1.017)^x.

Answer: The answer is B

Step-by-step explanation:

Answer:

1. The option of spinning the chamber to make it random again gives you a probability of surviving of 67% (1 - Probability of having a bullet in the chamber). The option of taking the gun as it is for a second attempt gives you a probability of surviving of 60% (1- Probability of having a bullet in the chamber after a first non-bullet attempt). Therefore, spinning the chamber to make it random again gives you a better chance of surviving.

2. The option of spinning the chamber to make it random again gives you a probability of surviving of 83% (1 - Probability of having a bullet in the chamber). The option of taking the gun as it is for a second attempt gives you a probability of surviving of 80% (1- Probability of having a bullet in the chamber after a first non-bullet attempt). Therefore, spinning the chamber to make it random again also gives you a better chance of surviving with only one bullet.

Step-by-step explanation:

1. Which option gives you a better chance of surviving?

Let's assume the gun has six chambers, so the probabilities are:

Number of bullets remaining/Number of chambers

For the first attempt, probabilities are = 2/6 or 33%

For the second attempt of shooting the gun, the probability of having a bullet in the chamber would be = 2/5 or 40%

On the other hand, if you spin the chamber to make it random again, the probability of having a bullet in the chamber would be = 2/6 or 33%

The option of spinning the chamber to make it random again gives you a probability of surviving of 67% (1 - Probability of having a bullet in the chamber). The option of taking the gun as it is for a second attempt gives you a probability of surviving of 60% (1- Probability of having a bullet in the chamber after a first non-bullet attempt). Therefore, spinning the chamber to make it random again gives you a better chance of surviving.

2. What would the answer be if there was only 1 bullet instead?​

Number of bullets remaining/Number of chambers

For the first attempt, probabilities are = 1/6 or 17%

For the second attempt of shooting the gun, the probability of having a bullet in the chamber would be = 1/5 or 20%

On the other hand, if you spin the chamber to make it random again, the probability of having a bullet in the chamber would be = 1/6 or 17%

The option of spinning the chamber to make it random again gives you a probability of surviving of 83% (1 - Probability of having a bullet in the chamber). The option of taking the gun as it is for a second attempt gives you a probability of surviving of 80% (1- Probability of having a bullet in the chamber after a first non-bullet attempt). Therefore, spinning the chamber to make it random again also gives you a better chance of surviving with only one bullet.

Answer:

Step-by-step explanation:

Since the sale price is always less than the original, we take the original and subtract from it the percent off to give us the sale price.  Putting that into equation form:

s = r - .10r

which says, in words, that the sale price is equal to the regular price minus 10% of the regular price.

Hey Kim! :)

Glad to see you on Brainly.

Look below and watch how we solve this problem.

Ask any questions if you need it! I'll respond when you need it!

[tex]Remove \\parentheses. \\7+30-2=7 * 3\\\\7 + 30 - 2 = 161\\37 - 2 = 161\\\\35 = 161\\ \\ No solution.[/tex]

Answer:

y = 1x + 2

please mark me as brainliest, thank you and have a good day!

Answer:

y = 5/8x + 9/4

but it can be

y=5/8x+6

or

y=5/8x+1

Explaination:

but there can be other solutions

First let's find the slope (5/8(

(-2,1) and (6,6)

let plug those numbers in

[tex]\frac{6-1}{6-(-2)}[/tex]

which becomes

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

that's your slope, plug that into the slop-intercept equation

y = mx + b tp y = 5/8x + b

b can be either y-values (1 or 6) but 9/4 is also an answer

Answer:

39.95 × 3 = $119.85

Estimated at $40 each

3 pairs total $120

18 km

Step-by-step explanation:

The vector appears as shown in the attached illustration. This is tantamount to finding the ? side of the right-angled triangle. The formulae is;

a² + b² = c²

24² + x² = 30²

x² = 30² – 24²

= 900 - 576

x² = 324

x = 18

Learn More:

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Final answer:

By using the Pythagorean theorem on the right triangle formed by the paths of the two airplanes, it is determined that the eastbound airplane has traveled 18 kilometers.

Explanation:

The question involves a geometrical problem that can be solved using the Pythagorean theorem. We are given that two airplanes leave the same airport, one heading north and the other heading east. After a certain time, the northbound airplane has traveled 24 kilometers. We are asked to find out how far the eastbound airplane has traveled, given that the two airplanes are now 30 kilometers apart.

To solve this, we can consider the path of the two airplanes as two sides of a right triangle, with the distance between the two airplanes being the hypotenuse. Using the Pythagorean theorem which states that in a right triangle the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b), or a2 + b2 = c2, we have:

Let x be the distance traveled by the eastbound airplane.

242 + x2 = 302

x2 = 302 - 242

x2 = 900 - 576

x2 = 324

x = √324

x = 18 kilometers

The eastbound airplane has traveled 18 kilometers.

Answer: First option.

Step-by-step explanation:

You can idenfity in the figure that [tex]\angle FCE[/tex] is formed by two secants that intersect outside of the given circle.

It is important to remember that, by definition:

 [tex]Angle\ formed\ by\ two\ Secants=\frac{1}{2}( Difference\ of\ intercepted\ Arcs)[/tex]

Knowing this, you can set up the following equation:

[tex]m\angle FCE=\frac{1}{2}(BD-FE)[/tex]

Therefore, you must substitute values into the equation and then evaluate, in order to find the measure of the angle [tex]\angle FCE[/tex].

This is:

[tex]m\angle FCE=\frac{1}{2}(112\°-38\°)\\\\m\angle FCE=37\°[/tex]

Option B

7569 number of people are going to vote for the other candidate

Solution:

Given that candidate took a phone poll of 110 people

Of the 110 people polled, 87 said they would vote for the other person

There are 9570 people in the district

You can set up this problem like a proportion

Let "x" be the number of people who would vote for the other candidate

[tex]\frac{87}{110} = \frac{x}{9570}[/tex]

To solve proportions, you cross-multiply. This means you multiply the numerator by the other denominator, and the denominator by the other numerator

[tex]87 \times 9570 = 110 \times x[/tex]

832590 = 110x

x = 7569

Thus 7569 number of people are going to vote for the other candidate

Answer:

Your answer is B. 7569 people hopefully this helps!

Answer:

6.855

Step-by-step explanation:

I don't know how to explain that, you can use a calculator.

Youssef lives 15 blocks away from his work

Solution:

Given that Youssef can either way from his home to his workplace or ride his bicycle

Let "x" be number of blocks away from work Youssef works

Case 1: walking

He walks at a pace of 1 block per min

Therefore,

1 block = 1 minute

Thus to cross "x" blocks he takes "x" minutes

Case 2: Bicycle

He can travel 1 block in 20 sec on his bicycle

We know that,

To convert seconds to minute, divide the time value by 60

[tex]\rightarrow 20 seconds = \frac{20}{60} minutes = \frac{1}{3} minutes[/tex]

Thus he takes 1/3 minutes for 1 block

So to cross "x" blocks he will take [tex]\frac{x}{3}[/tex] minutes

Given that it takes youssef 10 min longer to walk to work than to ride his bike

This means difference between time taken to cross "x" blocks by walking and ride by bicycle is 10 minutes

[tex]\rightarrow x - \frac{x}{3} = 10\\\\\rightarrow \frac{3x - x}{3} = 10\\\\\rightarrow \frac{2x}{3} = 10\\\\\rightarrow x = \frac{30}{2}\\\\\rightarrow x = 15[/tex]

Thus he lives 15 blocks away from his work

Final answer:

Youssef lives 15 blocks away from his workplace, which is determined by solving the equation x = x/3 + 10 after converting his biking speed to 3 blocks per minute.

Explanation:

To solve for how many blocks away Youssef lives from his workplace, we'll set up an equation using the information given. First, let's convert Youssef's bicycling speed to blocks per minute. Since he can travel 1 block in 20 seconds, and there are 3 sets of 20 seconds in a minute, he travels at a speed of 3 blocks per minute on his bicycle.

Let's denote the number of blocks to Youssef's workplace as 'x'. According to the question, walking there takes Youssef 10 minutes longer than biking. If he walks at the pace of 1 block per minute, walking to work takes 'x' minutes. Biking, at 3 blocks per minute, would take 'x/3' minutes. The relationship between the walking time and biking time is therefore 'x = x/3 + 10'.

We can solve the equation by multiplying each term by 3 to get rid of the fraction: '3x = x + 30'. Solving for 'x' gives us '2x = 30', and thus 'x = 15'. Youssef lives 15 blocks away from his workplace.

the variable qould b and aStep-by-step explanation:

Good evening ,

Answer :

A.

x = ±20

Step-by-step explanation:

x² − 1 = 399 ⇔ x²= 400 ⇌ x² = 20² ⇌ x² − 20² = 0 ⇌ (x-20)(x+20) = 0

⇌ x = 20 or x = -20.

:)

X=20 and x=-20 are the solutions to the equation [tex]x^{2} -1 = 399[/tex]

A quadratic equation exists as an algebraic equation of the second degree in x. The quadratic equation in its standard form exists [tex]ax^{2} + bx + c = 0[/tex], where a and b exist as the coefficients, x is the variable, and c stands as the constant term.

Given,

[tex]x^{2} -1 = 399[/tex]

To find,

The solutions to the equation.

Step 1

[tex]x^{2} -1 = 399[/tex]

Move terms to the left side

[tex]&x^{2}-1=399 \\[/tex]

[tex]&x^{2}-1-399=0[/tex]

Subtract the numbers

[tex]&x^{2}-1-399=0 \\[/tex]

[tex]&x^{2}-400=0[/tex]

Use the quadratic formula

[tex]$$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$$[/tex]

Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic equation.

[tex]&x^{2}-400=0 \\[/tex]

a=1

b=0

c=-400

[tex]&x=\frac{-0 \pm \sqrt{0^{2}-4 \cdot 1(-400)}}{2 \cdot 1}[/tex]

[tex]&x=\frac{-0 \pm \sqrt{(0^{}-1600)}}{2 }[/tex]

[tex]$x=\frac{\pm 40}{2}$[/tex]

[tex]$x=\frac{40}{2}$[/tex]

[tex]$x=\frac{-40}{2}$[/tex]

Hence,

[tex]$x=20$[/tex]

[tex]$x=-20$[/tex]

Thus, Option A. X=20 and x=-20 are the solutions to the equation [tex]x^{2} -1 = 399[/tex]

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Answer:

4.

a)  [tex]4x^4-4x^3-16x^2+16x[/tex]

b)  [tex]4x^4-4x^3-16x^2+16x[/tex]

5. Yes

Step-by-step explanation:

The distributive property is:

[tex](a+b)(c+d)=ac+ad+bc+bd[/tex]

It can be extended to a lot of terms as well.

We will use this to multiply both of the probelms shown.

4 a)

[tex](4x^2-4x)(x^2-4)=(4x^2)(x^2)-(4)(4x^2)-(4x)(x^2)+(4x)(4)=4x^4-16x^2-4x^3+16x=4x^4-4x^3-16x^2+16x[/tex]

The answer is [tex]4x^4-4x^3-16x^2+16x[/tex]

4 b)

[tex](x^2+x-2)(4x^2-8x)=(x^2)(4x^2)-(8x)(x^2)+(x)(4x^2)-(8x)(x)-(2)(4x^2)+(2)(8x)=4x^4-8x^3+4x^3-8x^2-8x^2+16x=4x^4-4x^3-16x^2+16x[/tex]

The answer is  [tex]4x^4-4x^3-16x^2+16x[/tex]

5. Yes

Answer: B, D, E

Step-by-step explanation:

Using function concepts, it is found that the correct options are:

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

A similar problem is given at https://brainly.com/question/13421430

Answer:

Explanation:

1. Cost of each liter of yellow paint:

Yellow paint is sold in 5 litre tins and ach tin costs £26, thus the cost of one liter is £26 / 5 liters = £5.2 per liter.

2. Cost of each liter of blue paint:

Blue paint is sold in 10 litre tins and each tin costs £48, thus the cost of one liter of blue paint is £48 / 10 liters = £4.8 per liter

3. Cost of each liter of green paint.

Green paint is made by mixing yellow paint and blue paint in the ratio 2:3

Thus, 5 liters of green paint will cost:

2 liters yellow paint: 2 liter × £5.2 / liter = £10.4

3 liters blue paint:     3 liter × £4.8 / liter = £14.4

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

5 liters green paint:   5 liter                        £24.8

Cost of one liter of gree paint: £24.8 / 5 liter = £4.96 / liter

4. Profit

Price of each liter of green paint: £66.96 / 10 liters = £6.696 / liter = £6.70 / liter

Profit per liter = price per liter - cost per liter = £6.70/liter - £4.96 / liter = £1.74 / liter

Percentage profit = profit per liter / cost per liter × 100

Percentage profit = (£1.74 / liter) / (£4.96/liter) × 100 =  35.08% = 35%

Answer: OPTION A.

Step-by-step explanation:

Let be "e" the number of tickets that the radio station gave away to employees and "l" the number of tickets that the radio station gave away to listeners.

Based on the data given in the exercise, you can set up the following System of equations:

[tex]\left \{ {{e+l=192 } \atop {l=5e}} \right.[/tex]

Finally you must apply the Substitution Method to solve the System of equations.

To apply it, you must substitute the second equation into the first one and then you must for the variable "e".

Through this precedure you get the following value of "e":

[tex]e+l=192\\\\e+(5e)=192\\\\6e=192\\\\e=\frac{192}{6}\\\\e=32[/tex]

Answer:

-4x^9-12x^4+2x^3-7x+8

Answer:

=−4x9−12x4+2x3−7x+8

Step-by-step explanation:

Distribute the Negative Sign:

=2−4x9+3x3+−1(7x+x3−6+12x4)

=2+−4x9+3x3+−1(7x)+−1x3+(−1)(−6)+−1(12x4)

=2+−4x9+3x3+−7x+−x3+6+−12x4

Combine Like Terms:

=2+−4x9+3x3+−7x+−x3+6+−12x4

=(−4x9)+(−12x4)+(3x3+−x3)+(−7x)+(2+6)

=−4x9+−12x4+2x3+−7x+8

Answer:

Step-by-step explanation:

7 + 3 + 5 + 15 = 30

Answer:

Step-by-step explaination:

I would try to help u but im not big brain and i really need the points

Answer:

A)  The equation has no solution

B ) The equation has one solution

C ) The solution of equation is 1

D ) The solution of equation is 20

E ) The solution of inequality is  x [tex]<[/tex] 8

Step-by-step explanation:

Given as :

A ) The equation is written as

5 ( x - 9 ) = 5 x

So, solving the equation

i. e  5 x - 5 × 9 = 5 x

or, , (5 x - 5 x) - 45 = 0

or, (0) - 45 = 0

∵ The equation do not have any variable terms

So, the equation has no solution

B) The equation is written as

- 2 ( x - 1 ) = 2 x - 2

So, solving the equation

i.e - 2 x + 2 = 2 x - 2

or, ( - 2 x - 2 x ) = - 2 - 2

or, - 4 x = - 4

∴ x = [tex]\dfrac{-4}{-4}[/tex]

I.e x = 1

So, The equation has one solution

C) The equation is written as

3 x + 6 = 9

So, solving the equation

I.e 3 x = 9 - 6

or, 3 x = 3

∴ x = [tex]\dfrac{3}{3}[/tex]

I.e x = 1

So, The solution of equation is 1

D) The equation is written as

[tex]\dfrac{x}{4}[/tex] - 1 = 4

Or, [tex]\dfrac{x}{4}[/tex] = 1 + 4

or, [tex]\dfrac{x}{4}[/tex] = 5

∴ x = 5 × 4

I.e x = 20

So, The solution of equation is 20

E) The equation of inequality is written as

9 x [tex]<[/tex] 72

Or, x [tex]<[/tex] [tex]\dfrac{72}{9}[/tex]

∴  x [tex]<[/tex] 8

So, The solution of inequality is  x [tex]<[/tex] 8

Hence , A)  The equation has no solution

B ) The equation has one solution

C ) The solution of equation is 1

D ) The solution of equation is 20

E ) The solution of inequality is  x [tex]<[/tex] 8

Answer

Answer:

Smaller t = 2

Larger t = 5

Step-by-step explanation:

Given:

The given function is.

[tex]f(t)=-(t-2)(t-5)[/tex]

Find the zeros of the function.

Solution:

[tex]f(t)=-(t-2)(t-5)[/tex]

Simplify the equation above equation.

[tex]f(t)=-(t^{2}-5t-2t+10)[/tex]

[tex]f(t)=-(t^{2}-7t+10)[/tex]

[tex]f(t)=-t^{2}+7t-10[/tex]

Now, we first find the root of the above equation.

Use quadratic formula with [tex]a=-1, b=7, c=-10[/tex].

[tex]t=\frac{-b\pm \sqrt{(b)^{2}-4ac}}{2a}[/tex]

Put a, b and c value in above equation.

[tex]t=\frac{-7\pm \sqrt{(7)^{2}-4(-1)(-10)}}{2(-1)}[/tex]

[tex]t=\frac{-7\pm \sqrt{49-4\times 10}}{-2}[/tex]

[tex]t=\frac{-7\pm \sqrt{49-40}}{-2}[/tex]

[tex]t=\frac{-7\pm \sqrt{9}}{-2}[/tex]

[tex]t=\frac{-7\pm 3}{-2}[/tex]

For positive sign

[tex]t=\frac{-7 + 3}{-2}[/tex]

[tex]t=\frac{-4}{-2}[/tex]

t = 2

For negative sign

[tex]t=\frac{-7 - 3}{-2}[/tex]

[tex]t=\frac{-10}{-2}[/tex]

t = 5

Put t = 2 in given function.

[tex]f(t)=-(2-2)(2-5)=0[/tex]

Put t = 5 in given function.

[tex]f(t)=-(5-2)(5-5)=0[/tex]

So, the zeros of the function is t = 2 or 5

Therefore, the smaller value of t = 2 and larger value of t = 5.

Answer:

p=40

w=l-8

40=w+l

40=2(l-8)+2l

40=2l-16+2l

40=4l-16

56=4l

14=l

length=14

w=14-8=6

l=14

w=6

Main equation:

2L + 2w = 40

We know that

w = L - 8

Substitute in known value

2L + 2(L - 8) = 40

Solve

2L + 2L - 16 = 40

4L = 24

L = 6

Length = 6 inches

Width =  14 inches

Hope this helps :)

Answer:

The value of the expression is [tex]\frac{9}{20}[/tex]

Step-by-step explanation:

In order to sum or subtract these fractions we need to find their LCM.

The overall LCM is 20.

Thus:

The we get:

= -16/20+25/20

Which gives:

=9/20

Answer:

The number of adults tickets sold is 165

The number of students tickets sold is 35

Step-by-step explanation:

Given as :

The total people that concert venue hold = 200 people

The price of adults tickets = $50

The price of students tickets = 50% less than adults tickets

I.e The price of students tickets = $50 - 50% of $50

Or, The price of students tickets = $25

The total revenue earn = $9125

Let The number of adults tickets sold = A

The number of students tickets sold = S

Now, According to question

The total people that concert venue hold = 200

Or, A + S = 200        ...........1

The total revenue earn = The number of adults tickets sold × The price of adults tickets +  The number of students tickets sold × The price of students tickets

Or, A × $50 + S × $25 = $9125

Or, 50 A + 25 S = 9125           ..........2

Solving both equations

(50 A + 25 S) - 25 × (A +S) = 9125 - 25 × 200

Or, (50 A - 25 A) + (25 S - 25 S) = 9125 - 5000

Or, 25 A + 0 = 4125

∴ A = [tex]\dfrac{4125}{25}[/tex]

I.e A = 165

So, The number of adults tickets sold = A = 165

Put the vale of A in eq 1

I.e A + S = 200

So, S = 200 - A

∴ S = 200 - 165

I.e S = 35

So. The number of students tickets sold = S = 35

Hence The number of adults tickets sold is 165 and

The number of students tickets sold is 35   Answer

Answer:

4 1/2

Step-by-step explanation:

Answer:

4 1/2

Step-by-step explanation:

He made the recipe 3 times. 1 1/2*3=4 1/2

Answer:

Step-by-step explanation:

Incomplete question.