what is the distance between the points (5,7)and (-3,4) on the coordinate plane

Hey there! :)

Answer:

6x³ + 14x² + 6x - 12.

Step-by-step explanation:

Given:

(2x² + 6x + 6)(3x - 2)

Multiply each term in the first polynomial by both terms in the second:

3x( 2x² + 6x + 6) - 2(2x² + 6x + 6) =

6x³ + 18x² + 18x - 4x² - 12x -12 =

Combine like-terms:

6x³ + 14x² + 6x - 12.

Answer:

g(-5)=-25

Step-by-step explanation:

Answer:

190 Baseballs

Step-by-step explanation:

Since he put 304 baseballs into 8 trash cans with an equal amt. in each,

--> we do 304/8 to find how much baseballs we put in each

=> 304/8 = 38

Now, we takes 5 of these 38 trash cans filled with balls to the field

--> we would do 5 x 38 => 5 x 38 = 190

and Thus, we have our answer of 190 baseballs

Hope this helps!

Answer:

T ≥ 8x

50 ≥ 8x .......1

x ≤ 6

Liam can buy lunch for 6 people.

Step-by-step explanation:

Let x represent the number of people Liam can buy lunch for.

Given;

Lunch cost per person r = $8 per person

The total amount he has T = $50

The cost of buying lunch for c people is;

C = $8 × x

C = 8x

Therefore, to be able to buy lunch for them, the total cost C must be less than the total amount he has.

T ≥ C

Substituting C, we have;

T ≥ 8x

50 ≥ 8x ,.......1

Solving the inequalities;

8x ≤ 50

x ≤ 50/8

x ≤ 6.25

To the nearest whole number;

x ≤ 6

Liam can buy lunch for 6 people.

Answer:

-4

Step-by-step explanation:

y = -4x + 6 is the equation and -4 is the slope

Answer:

m∠x = 65°

m∠y = 81°

m∠z = 34°

Step-by-step explanation:

Since we have 2 transversals and a pair of parallel lines, we can see that at ∠A it equals 65°. If we use the Corresponding Angles Theorem, the m∠A = m∠x. Therefore, x = 65°

To find y, we know that a line is 180°. So, 180 - (65 + 34) = 81°

To find z, we know that all angles in a triangle add up to 180°. So, 180 - (81 + 65) = 34°. Alternatively to find z, we could use Alternate Interior Angles Theorem.

Answer:

He will have 13 packages containing 3 pairs of headphones and 1 music player each.

Step-by-step explanation:

He has 39 pairs of headphones and 13 music players.

He wants to sell both set of items in identical packages.

To do this he has to divide them in such a way that the same number of both set of objects are in every box.

Let us find the ratio of the pairs of headphones to music players:

39 : 13 = 3 : 1

Therefore, dividing the pairs of headphones into 3 parts and the music players into 1 part, he can have identical packages.

So, he will have 13 packages containing 3 pairs of headphones and 1 music player each.

Answer:

a. 24

b. 864

Step-by-step explanation:

a. The demand function is:

P = 60 - 2Q

When P = 12:

12 = 60 - 2Q

2Q = 60 - 12

2Q = 48

Q = 48/2 = 24

b. Consumer surplus is given as the integral of Demand function:

[tex]CS = \int\limits {[P(Q) - (p)(Q)] \ dQ\\[/tex]

This implies that:

[tex]CS = \int\limits {60 - 2Q} \, dQ\\\\CS = 60Q - Q^2\\\\CS = (60 * 24) - 24^2\\\\CS = 1440 - 576\\\\CS = 864[/tex]

Answer:

The mean of the following set of data would be 807.5

Step-by-step explanation:

mean: 806 + 809 = 1,615 ÷ 2 = 807.5

Basically, you just have to add the two numbers in the set of data or the listed numbers...

Then you have to divide it with the total amount of numbers there are in the set of data.  In this problem it would be 2 since there are only 2 numbers in the set of data.

Step-by-step explanation:

mean is total÷no.

806+809=1615, the total, the no. is 2

1615÷2=807.5

The simplest way

Answer:

  -63

Step-by-step explanation:

Compare ...

  f(x) = x^2 -3x +18

to the standard form ...

  f(x) = ax^2 +bx +c

and you will see that ...

  a = 1, b = -3, c = 18.

__

The value of the discriminant is ...

  d = b^2 -4ac

  d = (-3)^2 -4(1)(18) = 9 -72 = -63

The discriminant is -63.

Answer: 48

Step-by-step explanation:

The share of sand in the mixture is 3/7

To make 112 kgs. of concrete, he will need

3/7 x 112 = 48 units of sand

Answer:

solution,

Ratio of cement:sand:aggregate

=1:3:3

Total of ratios=1+3+3

=7

Total concrete=112 kg

Amount of sand required:

[tex] \frac{ratio \: of \: sand}{total \: ratio} \times amount \: of \: concrete \\ = \frac{3}{7} \times 112 \\ = 48 \: kg[/tex]

Hope this helps...

Good luck on your assignment...

Answer:

Uncle is 34. Nephew is 10.

Step-by-step explanation:

Let u equal the age of the uncle, and n equal the age of the nephew.

First, two years ago, the sum of their ages was 40. We can represent this by subtracting 2 from each variable. Thus:

[tex](u-2)+(n-2)=40[/tex]

[tex]u+n-4=40[/tex]

[tex]u+n=44[/tex]

Next, in two years time, the uncle will be three times as old as his nephew. We can represent this by adding 2. Thus:

[tex]u+2=3(n+2)[/tex]

We now have a system of equations and can solve accordingly.

First, from the first equation, we can determine that:

[tex]u=44-n[/tex]

We can substitute this into the second equation.

[tex](44-n)+2=3(n+2)[/tex]

[tex]46-n=3n+6[/tex]

[tex]40=4n[/tex]

[tex]n=10[/tex]

Thus, the nephew's age is 10.

And the uncle's age is 44-10 or 34.

Answer:

x=0

Step-by-step explanation:

3(7x – 12) + 26 = 3x – 10

Distribute

21x -36 +26 = 3x-10

21x -10 = 3x-10

Add 10 on each side

21x-10+10 = 3x-10+10

21x = 3x

Subtract 3x from each side

21x-3x = 0

18x =0

x=0

Answer:

x=0

Step-by-step explanation:

3(7x – 12) + 26 = 3x – 10

21x-36+26-3x+10=0

18x-10+10=0

18x+0=0

18x=0

x=0

check : 3(7(0)-12)+26=3(0)-10

          : -36+26=-10

          -10=-10 it is correct

Answer: A

Step-by-step explanation:

2x²-2x-9=0

this is a quadratic equation so we will use the quadratic formula .

 Δ= b²-4*a*c

let's calculate Δ to khow how many solutions this equations have .

 Δ= (-2)²-4*2*(-9)

    = 76

 we notice that 76>0

so this equation has two solutions :  (-b-√76)/4 and (-b+√76)/4

the trick here is to notice that :

[tex]\sqrt{76}[/tex] = [tex]\sqrt{19*4}[/tex]

      = [tex]\sqrt{19} *\sqrt{4}[/tex]

      = 2[tex]\sqrt{19}[/tex]

Now we will simplify Δ by factoring by 2

so the answer is a .

Answer:

zero residual equals zero mean

A line of best fit is a straight line that shows the appropriate correlation among scatter plots of a given data. It is majorly used when the plotted points are not linear, it can be used to express the relationship between dependent and independent variables.

The sum of the residuals should be close to zero because it shows that the line of best fit is accurately drawn. Thus, it implies that there is a linear relationship between the two variables. Since he residual is close to zero, the graph could be said to be a linear graph.

Answer:

y ≥ -2/3x +3

Step-by-step explanation:

incline is -2/3

and intercept with y-axis is 3

so the equation of the line is

y = -2/3x +3

Since the intended area in the graph I above the line, we now know enough to find the right one question:

y ≥ -2/3x +3

Answer: y>-2/3x+3 because the line is dotted its >

Answer:

C, D, and F

Step-by-step explanation:

The roots of the cubic polynomial are 1, (5+√17)/2, and (5-√17)/2 options (C), (D), and (F) are correct.

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

We have a cubic or third-degree polynomial:

F(x) = x³ - 6x² + 7x - 2

To find the all possible roots of the cubic polynomial

By using the trial and error method:

Plug x = 1

F(1) = 1 - 6 + 7 - 2

F(1) = 8 - 8

F(1) =0

x = 1 is one of the roots of the polynomial.

We can write the cubic polynomial in the factored form:

F(x) = (x - 1)(x² -5x + 2)

We have a quadratic polynomial:

= x² -5x + 2

To find the roots of the quadratic polynomial use the quadratic formula:

a= 1, b = -5, and c =2

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

[tex]\rm x = \dfrac{-(-5) \pm\sqrt{(-5)^2-4(1)(2)}}{2(1)}[/tex]

After solving:

x = (5+√17)/2

x = (5-√17)/2

Thus, the roots of the cubic polynomial are 1, (5+√17)/2, and (5-√17)/2 options (C), (D), and (F) are correct.

Learn more about Polynomial here:

brainly.com/question/17822016

#SPJ5

Answer:

Step-by-step explanation:

graph attached

Answer:

graph y

Step-by-step explanation:

The question is not typed properly! Complete question along with answer and step by step explanation is provided below.

Question:

Scores on the Critical Reading part of the SAT exam in a recent year were roughly Normal with mean 495 and standard deviation 118 .

You choose an SRS of 100 students and average their SAT Critical Reading scores. If you do this many times, the standard deviation of the average scores you get will be close to

a. 118

b. 118/100=1.18

c. 118/√100= 11.8

d. cannot be determined

Answer:

The standard deviation of the sample would be  

[tex]s = \frac{\sigma}{\sqrt{n}} \\\\s = \frac{118}{\sqrt{100}} \\\\s = 11.8[/tex]

The correct option is (c)

Therefore, the standard deviation of the average scores you get will be close to 11.8

Step-by-step explanation:

From the given information,  

The population mean SAT critical reading score is

[tex]\mu = 495[/tex]

The population standard deviation is

[tex]\sigma = 118[/tex]

You choose an SRS of 100 students and average their SAT Critical Reading score.

[tex]n = 100[/tex]

Since the sample size is quite large then according to the central limit theorem,

The mean sample will be the same as the population mean  SAT critical reading score.

[tex]\bar{x} = \mu = 495[/tex]

The standard deviation of the sample would be  

[tex]s = \frac{\sigma}{\sqrt{n}} \\\\s = \frac{118}{\sqrt{100}} \\\\s = 11.8[/tex]

The correct option is (c)

Therefore, the standard deviation of the average scores you get will be close to 11.8

Answer:

Pascal's triangle is a triangular array of the binomial coefficients. It is used to find combinations.

Answer:

In mathematics, Pascal's triangle is a triangular array of the binomial coefficients.

Step-by-step explanation:

Answer:

[tex]\large \boxed{\sf \ \ \ x-y=-2\sqrt{7} \ \ \ }[/tex]

Step-by-step explanation:

Hello,

it took me some time to understand the correct equations, I believe that you mean

[tex]x+y=4\\\\x^2+y^2=22\\\\x^4=y^4-176\sqrt{7}[/tex]

So let's play with these equations

[tex]x^4=y^4-176\sqrt{7}\\\\<=>y^4-x^4=176\sqrt{7}\\\\<=>y^4-x^4=(y^2)^2-(x^2)^2=(y^2-x^2)(y^2+x^2)=(y-x)(y+x)(x^2+y^2)\\\\=176\sqrt{7}[/tex]

So

[tex]x-y=-\dfrac{176\sqrt{7}}{(x+y)(x^2+y^2)}=-\dfrac{176\sqrt{7}}{4*22}=-2\sqrt{7}=-5.291503...[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

No it was not

why... well he spent 25% time.

Step-by-step explanation:

Answer:

The answer is option D.

g(x) = (1/3x)²

Hope this helps you

Answer:

Total number of flash = 50 flash

Step-by-step explanation:

Given:

Time taken of a flash = 3/5 minute = 3/5 × 30 = 36 sec

Total time = 30 minute = 30 × 60= 1800 sec

Find:

Total number of flash in 30 minutes

Computation:

⇒ Total number of flash = Total time / Time taken of a flash

⇒ Total number of flash = 1800 / 36

⇒ Total number of flash = 50 flash

Answer:

Step-by-step explanation:

[tex]y = 1/2x +3\\m =1/2\\m_1m_2 = -1\\1/2m_2 =-1\\m_2= -2\\(10 ,-5)\\x = 10\\y = -5\\y = mx+b \\-5 = -2(10) + b\\-5=-20+b\\-5+20 =b\\b = 15\\m = -2\\Substitute -given -values- into- slope -intercept-form\\y = mx+b\\y = -2x+15[/tex]

Answer:

15

Step-by-step explanation:

q-v

             substitute values for q and v

28-13

15 is your answer. Hope this helps.

Answer:

C

Step-by-step explanation:

Use the sine ratio in the left, right triangle to find the common side to both triangles and the exact values

sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] , thus

sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{opp}{7\sqrt{3} }[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

2 × opp = 21 ( divide both sides by 2 )

opp = [tex]\frac{21}{2}[/tex]

Now consider the right triangle on the right, using the cosine ratio

cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{\frac{21}{2} }{x}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )

x = [tex]\frac{21}{2}[/tex] × [tex]\sqrt{2}[/tex] = [tex]\frac{21\sqrt{2} }{2}[/tex] → C

Answer: the answer is A

Step-by-step explanation:

Answer:

JL = 32

Step-by-step explanation:

We are told in the above question that:

In triangle △JKL, ∠JKL is right angle, and KM is an altitude. JK=24 and JM=18, find JL.

From the attached diagram, we can see that

JL : JK = JK: JM

Therefore,

JL/ JK = JK /JM

Where JL = Unknown

JK = 24

JM = 18

JL/ 24 = 24/18

Cross Multiply

24 × 24 = JL × 18

Divide both sides by 18

JL = (24 × 24) /18

JL = 576/18

JL = 32

Answer:

16/64 i think

Step-by-step explanation:

Answer:

[tex]\frac{1}{4}[/tex]

Step-by-step explanation:

Total Marks = 64

Correct = 48

Incorrect = 64-48

=> 16

Fraction of Incorrect Answers:

=> [tex]\frac{16}{64}[/tex]

In simplest form:

=> [tex]\frac{1}{4}[/tex]