which equation describes this line? A. y-3=2(x-2) B. y-9=2(x-1) C. y-1=2(x-9) D. y-2=2(x-3)

Answer:

[tex]y = -2x - 8\\OR\\2x+y+8=0[/tex]

Step-by-step explanation:

Given that there are 2 points

[tex]A(-8,8)[/tex] and

[tex]B(1,-10)[/tex]

So, the coordinates are:

[tex]x_2 = 1\\x_1 = -8\\y_2 = -10\\y_1 = 8[/tex]

Equation of a line is given as:

[tex]y =mx+c[/tex]

where 'm' is the slope of the line, formula for 'm' is given as:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex](x,y)[/tex] are the points that satisfy the equation of the line.

[tex]c[/tex] is the [tex]y -[/tex] intercept.

Calculating the value of m using the given coordinates:

[tex]m=\dfrac{-10-8}{1-(-8)}\\\Rightarrow m=\dfrac{-18}{9} = -2[/tex]

So, the equation of line becomes:

[tex]y =-2x+c[/tex]

Now, putting the coordinates of point [tex]A(-8,8)[/tex]

[tex]8 =-2\times (-8)+c\\\Rightarrow 8 = 16+c\\\Rightarrow c = -8[/tex]

Please refer to the graph of given equation of line.

The equation of line is:

[tex]y =-2x+-8\\OR\\2x+y+8=0[/tex]

Answer:

[tex] \sqrt{ {2}^{5} } [/tex]

Step-by-step explanation:

[tex]\huge \bigg( {2}^{ \frac{1}{2} }. {2}^{ \frac{3}{4}} \bigg)^{2} \\ \\ \huge = {2}^{ \frac{1}{2} \times 2 }. {2}^{ \frac{3}{4} \times 2} \\ \\ \huge = 2 \times {2}^{ \frac{3}{2} } \\ \\ \huge = {2}^{ \frac{3}{2} + 1 } \\ \\ \huge = {2}^{ \frac{3 + 2}{2} } \\ \\ \huge = {2}^{ \frac{5}{2} } \\ \\ \huge = \sqrt{ {2}^{5} } [/tex]

Answer:

[tex]\boxed{\sf \ \ \ 3x^2-7x+2 \ \ \ }[/tex]

Step-by-step explanation:

Hello,

There are a lot of polynomials which have 2 and 1/3 as zeroes,

I can show you one below

[tex]3(x-2)(x-\dfrac{1}{3})=(x-2)(3x-1)=3x^2-x-6x+2=3x^2-7x+2[/tex]

hope this helps

Answer:

A.) 2000N

B.) 0

C.) 1414.2 N

Step-by-step explanation:

Given that the force on the rope = 1000N

A.) If the two students pull in the same direction, the resultant force will be addition of the two forces. That is

1000 + 1000 = 2000 N

B.) If the two students pull in the opposite direction, the resultant force will be sum of the two forces equal to zero. That is,

F1 + F2 = 0

F1 = positive 1000N

F2 = negative 1000N

Therefore, 1000 - 1000 = 0

The resultant force of the two forces is zero.

C.) If the two forces are at right angles, south and east to each other, the resultant force R will be achieved by using pythagorean theorem.

R = sqrt( 1000^2 + 1000^2 )

R = sqrt( 2000000 )

R = 1414.2 N

The resultant force of the two forces will be 1414.2N

Answer:

Step-by-step explanation:

Given the following;

cosθ=8/17 and sinθ=−15/17

In trigonometry identity, tanθ = sinθ/cosθ

Substituting the given values in the equation;

tan θ = (−15/17)/(8/17)

tanθ = −15 /17 * 17/8

tanθ = -15/8

Answer:

D. -15/8

Step-by-step Explanation

Answer: No solution

Step-by-step explanation:

This system of equation has no solution because...

-3x+4y=12

1/4x-1/3y=1

[tex]-3x+4y-4y=12-4y[/tex]

[tex]-3x=12-4y[/tex]

[tex]\frac{-3x}{-3}=\frac{12}{-3}-\frac{4y}{-3}[/tex]

[tex]\frac{12}{-3}-\frac{4y}{-3}[/tex]

[tex]x=-\frac{12-4y}{3}[/tex]

substitute

[tex]\frac{1}{4}\left(-\frac{12-4y}{3}\right)-\frac{1}{3}y=1[/tex]

[tex]-1=1[/tex]

-1=1 is false so therefore this system has no solution

Answer:

A

Step-by-step explanation:

vol of a cylinder = pie* r^2×h

r= 5

h= 9

......vol= 9×5^2 pie= 225pie units ^3

Answer:

a b. c=19 it is equal to 19

Answer:

20.3854

Step-by-step explanation:

Answer: 6 cajas de cada tipo de fruta.

Step-by-step explanation:

En cada caja de manzanas, tenemos 13 manzanas.

En cada caja de limones, tenemos 17 limones.

Si el numero total de cajas es C, entonces el numero total de manzanas es:

C*13

y el numero total de limones es: C*17.

Si en total tenemos 180 frutas, entonces tenemos que:

C*13 + C*17 = 180

C*(13 + 17) = 180

C*30 = 180

C = 180/30 = 6

Tenemos 6 cajas de cada tipo de fruta.

Answer:

[tex]\large \boxed{\text{6 boxes of apples and 6 boxes of lemons}}[/tex]

Step-by-step explanation:

     Let m = the number of boxes of apples. Then

        13m = the number of apples

       Let l = the number of boxes of lemons. Then  

          17l = the number of lemons and

13m + 17l = the total number of fruits

You have two conditions:

[tex]\begin{array}{rrclr}(1) & m & = &l\\(2) & 13m + 17l & = & 180\\\end{array}[/tex]

Solve the equations for m and l

[tex]\begin{array}{rrcll}(1) & m & = & l&\\(2) & 13m + 17l & = & 180\\(3)&13m +17m & = & 180 & \text{Substituted (1) into (2)}\\&30m& = &180 &\text{Simplified}\\(4)&m& = &\mathbf{6} &\text{Divided each side by 30}\\& 6& = &l& \text{Substituted (4) into (1)}\\& l& = &\mathbf{6}& \\\end{array}\\\text{You have $\large \boxed{\textbf{6 boxes of apples and 6 boxes of lemons}}$}[/tex]

Check:

[tex]\begin{array}{ccc}6 = 6 & \qquad & 13(6) + 17(6) = 180\\& \qquad & 78 + 102 =180\\& \qquad & 180 = 180\\\end{array}[/tex]

It checks.

Answer:

They are congruent by AAS.

Step-by-step explanation:

Side BD is common to both  triangles and 2 pairs of corresponding angles are congruent.

Answer:

21u-16v+18w

Step-by-step explanation:

(7u-4v+4w) 14u-12v+14w

21u-16v+18w

Answer:

= 21u−16v+18w

Step-by-step explanation:

Let's simplify step-by-step.

7u−4v+4w−2(−7u+6v−7w)

Distribute:

=7u+−4v+4w+(−2)(−7u)+(−2)(6v)+(−2)(−7w)

=7u+−4v+4w+14u+−12v+14w

Combine Like Terms:

=7u+−4v+4w+14u+−12v+14w

=(7u+14u)+(−4v+−12v)+(4w+14w)

=21u+−16v+18w

Answer:

=21u−16v+18w

Answer:

Option (A)

Step-by-step explanation:

Parent function (in red) graph is represented by,

f(x) = x²

If this function is translated by 'a' units to the right, rule to be followed,

f(x) → f(x - a)

If the parent function is shifted by 4 units to the right (blue graph), the new function will be,

g(x) = f(x - 4)

g(x) = (x - 4)²

Therefore, Option (A) will be the correct option.

Answer:

its c.

rotate 90 ccw then mirror from y-axis

Step-by-step explanation:

Answer:

[tex]\frac{1}{9}[/tex]

Step-by-step explanation:

Data provided in the question

There is a total group of 45 students

Art + biology = 5

8 study biology but not Art

Neither subject studied = 9

Based on the above information, the probability of student that studies

art and biology is

Since there is a group of 45 students out of which 5 study both art and biology

So, the ratio is

4: 5

Now divide both sides by 5

So, now the ratio is

9:1

Therefore it means the probability is [tex]\frac{1}{9}[/tex]

Answer:

x=(π+√π)/1-π

or x=(π-√π)/1-π

Step-by-step explanation:

since it is a square all sides are equal

Area of square=x*x=x^2

Area of a circle=πr^2

A=π(x-1)^2

two areas are equal

x^2=π(x^2-2x_1)

x^2=πx^2-2πx-π  

x^2-πx^2-2πx-π=0

x^2(1-π)-2πx-π=0  

using quadratic formula with a=1-π , b=-2π and c=-π

equation of the form ax^2+bx+c=0 by using the quadratic formula:

x=(−b±√b2−4ac)/2a

x=(π+√π)/1-π

or x=(π-√π)/1-π

Answer:

B. [tex]y = 3x^2 -6x -3[/tex]

Step-by-step explanation:

Well, we can use the following formula to find the x coordianate of the vertex  -b / 2a.

So let’s start with a)

-6 / 6

-1

A. is wrong because its vertex starts with -1.

b)

6 / 6

1

now that we have our x coordinate we can plug it into the equation to get our y.

3 - 6 - 3

So the y coordinate is -6.

Hence, the answer choice B. [tex]y = 3x^2 -6x -3[/tex]

look at the image below.

Answer:

15.56%

Step-by-step explanation:

The force applied, F,  to the surface is 90N.

The area, A, of the surface is [tex]20 cm^2[/tex] = [tex]0.002m^2[/tex]

The pressure on the surface is:

P = F / A = 90 / 0.002 = 45000 Nm^2

The force is increased by 5N, the new force is 95N.

The surface area is increased by 5 cm^2 = 0.0005 m^2. The new surface area is 0.0025 m^2.

The pressure is now:

P = 95 / 0.0025 = 38000 Nm^2

The percentage decreased is gotten by dividing the difference in the two values by the old value and then multiplying by 100.

=> Difference = 45000 - 38000 = 7000

% decrease is therefore:

= 7000 / 45000 * 100 = 15.56%

There was a 15.56% decrease.

The ratio of the applied force to the area to which the force is applied,

gives the amount of pressure applied.

The outcome decreases by [tex]\underline{15.\overline 5 \%}[/tex]

Reasons:

[tex]\mathrm{Pressure, P} = \dfrac{Force, \, F}{Area, \, A}[/tex]

The initial force, F₁ = 5 N

The initial area, A₁ = 20 cm²

[tex]\mathrm{ } P_1=\dfrac{F_1}{A_1 }[/tex]

[tex]\mathrm{The \ initial \ pressure \ on \ the \ surface \ is \ } P_1=\dfrac{90 \ N}{0.002 \ m^2} = 45,000 \ Pa[/tex]

The new force, F₂ = F₁ + 5 N = 90 N + 5 N = 95 N

The new area, A₂ = A₁ + 5 cm² = 20 cm² + 5 cm² = 25 cm²

The new pressure after the increase is given by the equation;

[tex]\mathrm{ } P_2=\dfrac{F_2}{A_2 }[/tex]

[tex]\mathrm{The \ surface \ pressure \ after \ the \ increase\ is \ } P_2=\dfrac{95 \ N}{0.0025 \ m^2} = \mathbf{38,000 \ Pa}[/tex]

[tex]Percentage \ change = \dfrac{New \ value - Initial \ value}{Initial \ value} \times 100[/tex]

[tex]Percentage \ change = \dfrac{38,000 - 45,000}{45,000} \times 100 = 15.\overline 5 \%[/tex]

The outcome decreases by 15.[tex]\overline 5 \%[/tex]

Learn more:

https://brainly.com/question/22294092

Answer:

C)you must be no older than 13 to play the game.

Step-by-step explanation:

≤this means equal to or less than which in this case is 13

The situation represented by the inequality g ≤ 13 will be option C. You must be no older than 13 to play the game.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the inequality is g ≤ 13.

The inequality can be represented by the situation you must be no older than 13 to play a game.

To know more about inequality follow

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hello,

the first term is 250 so this is the initial invested amount

[tex](1+\dfrac{0.08}{12})^{12}=(1+\dfrac{8\%}{12})^{12}[/tex]

is to compute 8% annual interest compounded monthly (there are 12 months in a year)

and then multiply by 4 means that it is computed for 4 years so

finally the answer is

$250 is invested at 8% annual interest compounded monthly for 4 years

hope this helps

Answer:

£14.29

Step-by-step explanation:

0.98x=14

x=14.29

Answer:

14.28

Step-by-step explanation:

Answer:

81 students.

Step-by-step explanation:

If 10% of the 90 students were absent, then that means that 9 students were absent. To find the number of students present, simply subtract.

90 - 9 = 81.

- Hope this helped.

Answer:

200

Step-by-step explanation:

Given the first term 39 and the last term 11 then the sum of the 8 layers can be calculated as

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] ( f + l) ← f is the bottom layer anf f the top layer, thus

[tex]S_{8}[/tex] = [tex]\frac{8}{2}[/tex] (39 + 11) = 4 × 50 = 200

Answer:

g=number of girls in the class b=number of boy in the class

g+b=28

g=11+b

solution,

X=5

[tex]y = \frac{x + 9}{x - 3} \\ = \frac{5 + 9}{5 - 3} \\ = \frac{14}{2} \\ = 7[/tex]

hope this helps...

Good luck on your assignment..

Answer:

When x=5

Y=(5+9)÷(5-3)

= 14 ÷2

= 7

Answer:

The equation above represents the total time the play director spent preparing for a play.

Step-by-step explanation:

The time spent by the play director for preparing for a play is, 190 hours.

Of these 190 hours, the director spent varying amounts of time attending 35 rehearsals for the play.

Let the varying amounts of time be denoted by, x.

The director also spent 3/4th of an hour, i.e. 45 minutes, on other responsibilities related to the play.

The equation provided is:

[tex]35x+\frac{3}{4}=190[/tex]

The equation above represents the total time the play director spent preparing for a play.

Answer:

The point-slope form of an equation of the line through the points (-7, 7) and (4,1):

(y - 7) = m(x + 7)

or

(y - 1) = m(x - 4)

with

m = (1 - 7)/(4+7) = -6/11

Answer:

y=-6/11 x +35/11

Step-by-step explanation:

(-7, 7) and (4,1)

m=y2-y1/x2-x1

m=1-7/4-(-7)

m=-6/11

y=mx+b     take one point(4,1) to find b

1=-6/11(4)+b

1=-24/11 +b

b=1+24/11

b=(11+24)/11

b=35/11

y=-6/11 x +35/11

Answer:

0.03 feet

Step-by-step explanation:

d = 0.03r² + r

When d = 0: 0.03r² + r = 0

r(0.03r + 1) = 0

∴ r = 0

When r = 0: d = 0.03 feet

Answer:

120

Step-by-step explanation:

90→75%

X→100%

⇒X=(90×100)÷75=120

Before the price reduction, the cost was 120 dollar.

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

We are given that shop advertises 25% off its prices in a sale a dress is 90% .

Here 90 percent is equivalent to 75%

Let X = 100%

So,X=(90×100)÷75

x =120

The price was 120 dollar.

Learn more about multiplications;

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Answer:

1800 (packages )muffins

Step-by-step explanation:

360  muffins         x muffins

--------                 =    --------

12 min                       60 min

Answer:

1800 maybe

Step-by-step explanation:

in 12 minutes can wrap 360

in 1 hr have 60 minutes

60/12=5

than 360*5 = 1800

Answer:

The answers are options A and E

x² + 4x-9 = 5x + 3

Group like terms

x² + 4x - 5x - 9 - 3 = 0

x² - x - 12 = 0

Using factorization method

(x + 3)( x - 4) = 0

x = - 3 x = 4

Hope this helps