Use the pythagorean theorem to find the distance between x(7,11) and y(-1,5)..

Answers

Answer 1

so, if the legs are a and b and the hypothuse is c then
a²+b²=c²

the distance bewteen the points is the hyptohuse

the legs are the distances between th x and y values

so
(7,11) and (-1,5)
distances between the x values are 1 leg
that is from 7 and -1, a distance of 8 units

distances betweeen the y values are the other leg
that is from 11 to 5
that is 6 units

a²+b²=c²
8²+6²=c²
64+36=c²
100=c²
sqrt both sides
10=c
the distance between them is 10 units

Related Questions

Compare 9 ⋅ 104 to 3 ⋅ 102.

9 ⋅ 104 is 3 times larger than 3 ⋅ 102.
9 ⋅ 104 is 30 times larger than 3 ⋅ 102.
9 ⋅ 104 is 300 times larger than 3 ⋅ 102.
9 ⋅ 104 is 3,000 times larger than 3 ⋅ 102.

Answers

9×10⁴ is 300 times greater than 3×10²
as, (9×10⁴)/(3×10²)=3× 10²
and the proper of writting powers in computer form is a×10^b

Answer:

9×10⁴ is 300 times greater than 3×10²

Step-by-step explanation:

guy above me's work. thanks to him we get this answer :)

In the above figure, AE = 2, CE = 3, and DE = 4. What is the length of BE?

Answers

BE= 6. I had this question not too long ago. Hope this helps. :)

Answer:

its 6 i think

Explanation:

if you have the choices 6, 8, 12, 5.. then 6 is ur answer. why?

well u do CE x DE = AE x BE

(3)(4)= (2)(BE)

12=2x

12÷2= 6

Which person in the high rise building is closest to the street level?Moira is in her doctor’s office on the fourth floor.Geoffrey is in the elevator between the second and third floors.Sandy is in the laundry room on the –2 basement floor.Hasim is leaving the parking garage and is currently between –1 and –2 levels.

Answers

Arranging in value from top to bottom. The chart is Moira (4), Geoffrey (2.5) Ground Floor (0), Hasim (-1.5) and Sandy (-2). The closest number to 0 is -1.5, so that means that Hasim is the closest to the ground floor.

Answer

Hasim is the closest... I just took the test

The length of a rectangle is twice its width. if the area of the rectangle is 162 cm2 , find its perimeter.

Answers

Let the width of the rectangle be x
Then, the length of the rectangle will be 2x
The area of the rectangle will be
2x(x)=2x^2
Since the area of the rectangle is 162cm2
2x^2=162
x^2=81
x=9
Width of the rectangle=9
Length of the rectangle=9x2=18
Perimeter of a rectangle
=2(width) + 2(length)
=2(9)+2(18)
=54cm

The line through the midpoint of and perpendicular to the segment joining points (1, 0) and (5, -2). The answe is x_ _= something

Answers

First, you have to find the midpoint of the segment. Using the midpoint theorem, (which is (x1+x2)/2, (y1+y2)/2 ) the midpoint of that segment in (3,-1)

Next find the slope of the segment 1,0 and 5,-2 using rise over run or deltax / deltay which is a fancy way of saying change in x over change in y.

The slope is 4/2 or 2
When a line is perpendicular to another the slope is the negative reciprocal so the slope of our new line will be -1/2

Now plug in the coordinate (3, -1) to find the y-intercept and the equation of that line will be complete

so -1 = -1/2 (3) +b
-1= -1.5 +b
0.5 = b

The final equation will be -1/2x + 0.5 =y

hope this helps:)

State two reasons why including the p-value is prudent when you are reporting the results of a hypothesis test.

Answers

In general as we know when we perform a hypothesis test in statistics then p value help us to determine the significance of our result.
Hypothesis test are generally used to test a validity of claim that is made about a population.This claim that's on trial in essence is called as a Null Hypothesis.

The p - values is a number between 0 to 1 and interpreted in following way:

A small p - value (<= 0.05) indicates the strong evidence against a null hypothesis , so you reject a null hypothesis.

A large p - value (>0.05) indicates weak evidence against a null hypothesis , so you fail to reject the null hypothesis.

The reason which include the p - value is prudent when you are reporting the result of a hypothesis test are given below:

1. It allows us for evaluating the strength of the evidence against the null hypothesis.

2. Allow us for assessing significance at any desired level . The null hypothesis can be rejected at any significance level larger than or equal to p - value and it can not be rejected at any significance level smaller than the p - value.

Find the value of X.

Answers

RS + ST = RT

3x + 1 + 2x - 2 = 64
5x - 1 = 64
5x = 64 + 1
5x = 65
x = 65/5
x = 13 <==

(14 + 13) + 2 = 29 Choose an equivalent addition sentence that shows the associative property of addition. 29 = (14 + 13) + 2 (14 + 13) + 2 = 29 14 + (13 + 2) = 29 14 + 13 + 2 = 29

Answers

Final answer:

An equivalent addition sentence showing the associative property of addition in the given example is 14 + (13 + 2) = 29, where the grouping changes but the sum remains the same, rooted in the commutative property of addition.

Explanation:

The question is about the associative property of addition which essentially states that when you add three or more numbers, the way in which you group them doesn't affect the sum. To illustrate with the given example $(14 + 13) + 2 = 29$, an equivalent sentence that demonstrates the associative property would be 14 + (13 + 2) = 29. Here, the grouping has changed, but the resulting sum remains the same. The reason this works is due to the commutative property of addition which tells us that changing the order of the numbers we're adding doesn't change the sum, expressed as A + B = B + A. This universality is showcased by the idea that regardless of 'real-world context' or 'complexity of calculation', the same rules apply.

help please

Given the vertices of ∆ABC are A (2,5), B (4,6) and C (3,1), find the vertices following each of the transformations FROM THE ORIGINAL vertices:
a. Rx-axis
b. Ry = 3
c. T<-2,5>
d. T<3,-6>
e. r(90◦, o)

Answers

Given the vertices of a triangle as A(2, 5), B(4, 6) and C(3, 1).

a.) A transformation, R_x-axis means that the vertices of the rectangle were reflected across the x-axis.
When a point on the coordinate axis is refrected across the x-axis, the sign of the y-coordinate of the point changes.
Therefore, the vertices of the triangle A'B'C' resulting from the transformation of triangle with vertices A(2, 5), B(4, 6) and C(3, 1) with the rule R_x-axis are A'(2, -5), B'(4, -6), C'(3, -1)

b.) A transformation, R_y = 3 means that the vertices of the rectangle were reflected across the line y = 3.
When a point on the coordinate axis is refrected across the a horizontal line, the distance of the point from the line is equal to the distance of the image of the point from the line.
Therefore, the vertices of the triangle A'B'C' resulting from the transformation of triangle with vertices A(2, 5), B(4, 6) and C(3, 1) with the rule are A'(2, 1), B'(4, 0), C'(3, 5)

c.) A transformation, T<-2, 5> means that the vertices of the rectangle were shifted 2 units to the left and 5 units up.
Therefore, the vertices of the triangle A'B'C' resulting from the transformation of triangle with vertices A(2, 5), B(4, 6) and C(3, 1) with the rule T<-2, 5> are A'(0, 10), B'(2, 11), C'(1, 6).

d.) A transformation, T<3, -6> means that the vertices of the rectangle were shifted 3 units to the right and 6 units down.
Therefore, the vertices of the triangle A'B'C' resulting from the transformation of triangle with vertices A(2, 5), B(4, 6) and C(3, 1) with the rule T<3, -6> are A'(5, -1), B'(7, 0), C'(6, -5).

e.) A transformation, r(90°, o) means that the vertices of the rectangle were rotated 90° to the right about the origin.
When a point on the coordinate axis is rotated about the origin b 90°, the quadrant of the point changes to the right with the x-value and the y-value of the point interchanging.
Therefore, the vertices of the triangle A'B'C' resulting from the transformation of triangle with vertices A(2, 5), B(4, 6) and C(3, 1) with the rule r(90°, o) are A'(5, -2), B'(6, -4), C'(1, -3)

Answer with explanation:

Vertices of ∆ABC are A (2,5), B (4,6) and C (3,1).

Plotting the points on coordinate plane

a.→ [tex]R_{x}[/tex]

We have to find vertices of image , that is ΔA'B'C' when ∆ABC is reflected across x axis.

The Distance from each of the vertices of ∆ABC from X axis will be same as Perpendicular distance from each of vertices of ∆A'B'C' from X axis.

Result is shown in the image 1.

b.→[tex]R_{y}=3[/tex]

We have to find the image of vertices of triangle through line, y=3.

The Distance from each of the vertices of ∆ABC from line,y=3 will be same as Perpendicular distance from each of vertices of ∆A'B'C' from line, y=3.

Result is shown in the image 2.

c. →T(-2,5)

Translation of vertices of triangle ABC by 2 units left and 5 units up.

[tex]A(2,5)_{-2,5} \rightarrow (2-2,5+5)\rightarrow (0,10)\\\\B(4,6)_{-2,5} \rightarrow (4-2,6+5)\rightarrow (2,11),\\\\C(3,1)_{-2,5} \rightarrow (3-2,1+5)\rightarrow (1,6)[/tex]

d.→T(3,-6)

Translation of vertices of triangle ABC by 3 units right and 6 units left.

[tex]A(2,5)_{3,-6} \rightarrow (2+3,5-6)\rightarrow (5,-1)\\\\B(4,6)_{3,-6} \rightarrow (4+3,6-6)\rightarrow (7,0),\\\\C(3,1)_{3,-6} \rightarrow (3+3,1-6)\rightarrow (6,-5)[/tex]

e.→Rotation by 90° with respect to Origin

When rotated in clockwise direction ,vertices of ΔABC changes by the rule ,that is (x,y)→(y,-x) and in anticlockwise direction ,(x,y)→(-y,x).

In clockwise direction

A(2,5)→A"(5,-2)

B(4,6)→B"(6,-4)

C(3,1)→C"(1,-3)

In Anti clockwise direction

A(2,5)→A'(-5,2)

B(4,6)→B'(-6,4)

C(3,1)→C'(-1,3)

Image is depicted below.

Solve by taking square roots: x^2 - 40 = 9

Answers

To solve for x^2 - 40 = 9, take the square roots of both sides and solve.
The answer is x = 7, -7.

[tex] x^{2} -40= 9[/tex]

[tex] x^{2} = 49[/tex]

[tex] \sqrt{ x^{2} } = \sqrt{49} [/tex]

x = +7 or -7

What would be the point of discontinuity in the following function f(x)=x^2+5x+6/x+3

Answers

The point of discontinuity can be easily detected when you see the face of the graph. If it contains any breaks, there are points of discontinuity. You can determine this analytically if when you substitute x to the equation, the answer would be undefined. Undefined numbers are ∞-∞, 0/0, 0×∞, 0^0, 1^∞ or any number divided by zero.

For the expression f(x)=x^2+5x+6/x+3, you see that there is a term 6/x. Therefore, the expression can be continuous when x=0 because 6/0 or any number divided by zero is undefined. To verify this, let's see the graph by assigning values of x and plotting them against their values of y. As you can see, the curves only approach zero but never touches zero. These are called asymptotes.

Which law would you use to simplify the expression (p/q)^3

Answers

Answer:

B. Power of quotient.

Step-by-step explanation:

We have been given an expression [tex](\frac{p}{q} )^3[/tex] and we are asked to choose the correct rule to simplify our given expression.

Since our given expression is a fraction raised to 3rd power. Power of a quotient rule states when a quotient is raised to an exponent, then the exponent is distributed to both numerator and denominator of the quotient.

Using power of a quotient rule, we will get,

[tex](\frac{p}{q} )^3=\frac{p^3}{q^3}[/tex]

Therefore, we can simplify our given expression using power of a quotient and option B is the correct choice.

The power of quotients is the law that would be used to simplify the expression.

What is the power of quotients?

This is a mathematical rule that states that the power of a quotient is the same thing as the quotient that is gotten.

Given that the numerator p and the denominator q are raised to to the power expressed in the question separately.

The division is calculated after this has done

Read more on the power of quotient here:

https://brainly.com/question/2141690

A carpet cleaning business has 100 customers when they charge $125 for a cleaning. Research shows that every $5 reduction in price attracts another 20 customers. What price should the business implement to maximize its revenue?
a $75
b $100
c $120
d $90

Answers

Since a $5 decrease in price increases customers by 20 we can say that we have two points:

(125,100) and (120,120), from these we can find the slope or rate of change of customers as a function of price...

m=20/-5

m=-4

m=-4

c(p)=-4p+b, now we can use (125,100) to solve for b

100=-4(125)+b

100=-500+b

600=b, so our number of customers as a function of price is:

c(p)=600-4p

Revenue will simply be the number of customers times the price charged per customer...or p*c(p):

r(p)=600p-4p^2

We can find price that creates maximum revenue by finding when the derivative is equal to zero...

dr/dp=600-8p

dr/dp=0 only when

0=600-8p

8p=600

p=75

So the price that maximizes revenue is $75.

The linear relationship is c(p) = -4p + b. Then the price that maximizes revenue is $75.

What is the linear system?

It is a system of an equation in which the highest power of the variable is always 1.

A carpet cleaning business has 100 customers when they charge $125 for cleaning.

Research shows that every $5 reduction in price attracts another 20 customers.

Since a $5 decrease in price increases customers by 20, we can say that we have two options.

(120, 100) and (120, 120) from these we can find the slope or rate of change of customers as a function of price.

[tex]\rm m = \dfrac{20}{-5}\\\\ m = -4[/tex]

Then we have

[tex]\rm c(p ) = -4 p +b[/tex]

Now, we can use (125, 100) to solve for b

100 = -4(125) + b

b = 600

So our number of customers as a function of price is

[tex]\rm c(p) = 600 - 4p[/tex]

Revenue will simply be the number of customers times the price charged per customer will be

[tex]\rm r(p) = 600 p -4p^2[/tex]

We can find a price that creates maximum revenue by finding when the derivative is equal to zero.

[tex]\rm \dfrac{dr}{dp} = 600 - 8p\\\\[/tex]

WE know that for maximum,

[tex]\rm \dfrac{dr}{dp} = 0\\\\0 = 600 - 8p\\\\p = 75[/tex]

So, the price that maximizes revenue is $75.

More about the linear system link is given below.

Choose the correct simplification of (6x4y2z3)(3x4y3z5).
18x16y6z15
18x8y5z8
9x8y5z8
9x16y6z15

Answers

6x4 * 3x4 = 18x^8

y2*y3 = y5
z3 * z5 = z8

answer is 18x8y5z8

B

Answer:

18 x 8y 5z 8 witch is answer choice B

Step-by-step explanation:

the minute hand of a clock is 9.5cm long, How far does the tip of the hand travel in one day?

Answers

The tip of the hand travels the circumference of a circle with radius (r) 9.5 cm every hour;
The formula for circumference of a circle (c) is:
c = πd = 2πr
So, for a circle with radius 9.5, the circumference is:
c = 2π(9.5)
= 19π cm
The tip travels 19π cm every hour, so in a day of 24 hours it will travel:
24 * 19π = 456π cm
(= 1432.566... ⇒ 1432.6 cm)

Solve the system using elimination. y – x = 13 7y + x = 11

Answers

y – x = 13
7y + x = 11
---------------------add
8y = 24
y = 3

y – x = 13
3 – x = 13
-x = 10
x = -10

answer
x = -10 and y = 3

What is the remainder of (x3 - 6x2 - 9x + 3) ÷ (x - 3) A. -25 B. -52 C. -51 D. -17

Answers

D is the correct answer.

BRAINLIEST PLS!!!

the correct answer in C. -51 hope this helps you

What are the possible values of x in x2 + 3x + 3 = 0?

Answers

I'm assuming that that is a quadratic equation:
[tex] x^{2} +3x+3=0[/tex]
The only way to solve this is to use the quadratic formula. When you do that you get a negative number under the square root sign which we all know is illegal, UNLESS you factor out the imaginary "i". So your roots would be this:
[tex]x= \frac{-3+ \sqrt{3}i }{2} ,x= \frac{-3- \sqrt{3}i }{2} [/tex]

Which number line represents the solution set for the inequality 2x – 6 ≥ 6(x – 2) + 8?

what way do you shade in

Answers

2x - 6 > = 6(x - 2) + 8...distribute thru the parenthesis
2x - 6 > = 6x - 12 + 8...simplify
2x - 6 > = 6x - 4...subtract 6x from both sides
2x - 6x - 6 > = 6x - 6x - 4...simplify
-4x - 6 > = -4 ...add 6 to both sides
-4x - 6 + 6 > = -4 + 6...simplify
-4x > = 2...divide both sides by -4, change the inequality sign
x < = -2/4
x < = -1/2 or -0.5

so u would have a solid circle (because of ur equal sign) on -1/2...and the shading would go to the left (because less then goes to the left)

** the reason the inequality sign was changed is because when multiplying/dividing by a negative, u have to flip the sign...but dont forget to keep the = sign in there

Answer:

x < = -1/2 or -0.5

Step-by-step explanation:

that's the answer

The legs of a right triangle have lengths of 3 and 4. What is the length, to the nearest tenth, of the altitude to the hypotenuse?

Answers

a² + b² = c²
9 + 16 = c²
25 = c²
5 = c
The lenght of the hypotenuse is 5

Write an inequality for the situation.

all real numbers y that are less than –3 or greater than 18

A) y < –3 or y < 18
B) y < 18 or y > –3
C) –3 < y < 18
D) y < –3 or y > 18

Answers

The answer is D. The numbers for y have to be less than -3, which is shown using the less than sign, and they also have to be greater than 18, which is shown with the greater than sign.

All real numbers y that are less than -3 means that the values of y need to be less than -3 so;
y<-3.
Next, it is greater than 18 which means the value of y is greater than 18;
y>18
Also, this is known as the compound inequality which you could write as: 1818. In conclusion, D is the only correct answer. Have a nice day!

Maureen is taking an antibiotic. The table below shows the amount of antibiotic f(t), in mg, that was present in her body after time t:

t (hours) 1 2 3 4 5
f(t) (mg) 150 90 54 32.4 19.4

Ken was administered 200 mg of the same antibiotic. The amount of antibiotic f(t) in his body after time t is shown by the equation below:

f(t) = 200(0.976)t

Which statement best describes the rate at which Maureen's and Ken's bodies eliminated the antibiotic?
Maureen's body eliminated the antibiotic faster than Ken's body.
Maureen's body eliminated the antibiotic at the same rate as Ken's body.
Maureen's body eliminated the antibiotic at half of the rate at which Ken's body eliminated the antibiotic.
Maureen's body eliminated the antibiotic at one-fourth of the rate at which Ken's body eliminated the antibiotic.

Answers

One way to test this is by using the equation for Ken on Maureen. Let's say in the first hour,

f(t) = 200(0.976)^1 = 195.2 mg

In the second hour,

f(t) = 200(0.976)^2 = 190.52 mg

In the third hour,

f(t) = 200(0.976)^3 = 186 mg

If you compare this with Maureen's data which is 150, 90 and 54 for the first, second and third hour, respectively, you will see that Maureen's rate is much faster. However, you cannot tell by what factor because the function is exponential, not a multiple. There is no constant difference between their rates. Therefore, we only know that Maureen's rate is much faster.

The answer is Maureen's body eliminated the antibiotic faster than Ken's body.

Answer:

(A)Maureen's body eliminated the antibiotic faster than Kens body

Step-by-step explanation:

We already have the table for Maureen, so lets figure out the table for Ken. We've been given the formula 200(0.976)^t.

we already know our starting point is 0, 200

first we substitute 1 into t, which would look like this 200(0.976)^1

So we would solve the power of 0.976 to the power of 1, which is just 0.976. so now we do 200 x 0.976 which results in 195.2. on the chart, the point would be (1, 195.2). now lets solve for the rest doing the same steps.

(2, 1905.5)

(3, 181.4)

(4, 135.5)

(5, 01.9)

*WILL GIVE BRAINLIEST* (08.03)Consider the following set of equations:

Equation C: y = 2x + 8
Equation D: y = 2x + 2

Which of the following best describes the solution to the given set of equations?
No solution
One solution
Two solutions
Infinite solutions

Answers

Answer:

No solution

Step-by-step explanation:

This is because either way you do it it still doesnt make any sense and doesent line up correctly. THis is high school workand im doing it in 8th grade

Answer:

no solution

Step-by-step explanation:

because it just is

Tony is four years younger than his brother josh, and two years older than his sister cindy. tony also has a twin brother, evan. all the ages of the children totaled together is 66. how old is tony?

Answers

To solve this problem, let us assign the variables. Let us say that:

x = age of Tony = which also the age of his twin brother Evan

x + 4 = age of Josh (since tony is 4 years younger, then josh must be 4 years older)

x – 2 = age of Cindy (since tony is 2 years older, then cindy must be 2 years younger)

There are a total of 4 children, therefore:

x + x + x + 4 + x – 2 = 66

4 x + 2 = 66

4 x = 64

x = 16

Therefore Tony is 16 years old.

Final answer:

To find Tony's age, we can set up an equation using the information given and solve for x. After solving the equation, we find that Tony is 16 years old.

Explanation:

To solve this problem, we can assign variables to each person's age. Let's say Tony is x years old. Since Tony is four years younger than Josh, Josh's age can be represented as x + 4. Since Tony is two years older than Cindy, Cindy's age can be represented as x - 2. Since Tony has a twin brother, Evan, we can assign Evan's age as x as well.

According to the information provided, the sum of all their ages is 66, so we can set up the equation: x + (x + 4) + (x - 2) + x = 66. Simplifying the equation, we get 4x + 2 = 66. By subtracting 2 from both sides and dividing by 4, we find that x = 16.

Therefore, Tony is 16 years old.

To make bread dough, a baker mixes flour, eggs, yeast and salt by weight in pounds in the ratio of 11:9:3:2, respectively. how many pounds of yeast are required to make 20 pounds of bread dough?

Answers

In a standard batch, you have 11 pounds of flour, 9 pounds of eggs, 3 pounds of yeast and 2 of salt. This means the bread dough will weigh 11+9+3+2=25 pounds. The ratio of yeast to dough is then 3:25. To get 20 pounds of dough, we need x amount of yeast. Since its a ratio, 3/25 = x/20. We then solve for x, so x = 20*(3/25) = 12/5 = 2.4 pounds of yeast.

The graph shows the functions f(x), p(x), and g(x): Graph of function g of x is y is equal to 1 plus the quantity 1.5 raised to the power of x. The straight line f of x joins ordered pairs 4, 1 and 2, negative 3 and is extended on both sides. The straight line p of x joins the ordered pairs 0, 2 and 1, negative 5 and is extended on both sides. Courtesy of Texas Instruments Part A: What is the solution to the pair of equations represented by p(x) and f(x)? (3 points) Part B: Write any two solutions for f(x). (3 points) Part C: What is the solution to the equation p(x) = g(x)? Justify your answer. (4 points)

Answers

Part A: Intersection at [tex]$(-13/4, -83/4)$[/tex].

Part B: Two solutions for [tex]$ f(x) $: (0, -11) and (5, 14).[/tex]

Part C: Solve [tex]$ p(x) = g(x) $[/tex] graphically for the Point of intersection

Part A: Solution to the Pair of Equations (p(x) and f(x)):

The solution to the pair of equations represented by [tex]$ p(x) $ and $ f(x) $[/tex]is the point of intersection. From the information provided, it seems that the intersection point is [tex]$(-13/4, -83/4)$.[/tex]

Part B: Two Solutions for [tex]$ f(x) $[/tex]:

1. [tex]$ (0, -11) $[/tex]

2. [tex]$ (5, 14) $[/tex]

Part C: Solution to [tex]$ p(x) = g(x) $[/tex]:

To find the solution to [tex]$ p(x) = g(x) $, set $ p(x) = 7x + 2 $[/tex] equal to [tex]$ g(x) = 1 + 1.5^x $. Solve for $ x $[/tex] to determine the point of intersection between [tex]$ p(x) $ and $ g(x) $[/tex]. The solution to this equation provides the [tex]$ x $[/tex] coordinate, and substituting it into either [tex]$ p(x) $ or $ g(x) $[/tex] gives the [tex]$ y $[/tex] coordinate. The justification lies in the graphical intersection of the functions.

Note: It's essential to examine the graph for precise details, as visual inspection can help confirm the solutions.

For such more questions on point of intersection

https://brainly.com/question/29185601

#SPJ6

What is the equation in point-slope form of the line passing through (0, 5) and (−2, 11)? y − 5 = −3(x + 2) y − 5 = 3(x + 2) y − 11 = −3(x − 2) y − 11 = −3(x + 2)

Answers

hello :

Hello : let A(0,5) B(-2,11)
the slope is : (YB - YA)/(XB -XA)
(11-5)/(-2-0) = 6/(-2)
the slope is : -3

the equation in point-slope form of the line is : y-11 = -3(x+2)

Answer: [tex]y-11=-3(x+2)[/tex]

Step-by-step explanation:

Given points : (0, 5) and (−2, 11)

Slope of the line passing through given points .

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{11-5}{-2-0}=\frac{6}{-2}=-3[/tex]

Thus, slope of line passing through given points m=-3

We know that the equation of a line passing through points [tex](x_0,y_0)[/tex] with slope 'm' is [tex](y-y_0)=m(x-x_0)[/tex]

Thus, equation of a line passing through (−2, 11) with slope m=-3 will be

[tex](y-11)=(-3)(x-(-2))\\\Rightarrow\ y-11=-3(x+2)[/tex]

Hence, the equation of line is [tex]y-11=-3(x+2)[/tex]

2, -4, 8, -16, . . . find the next two numbers in the pattern and describe the pattern.

Answers

the next numbers are 32 and -64 the pattern multiplies by -2

The sum of two numbers is 47 and the difference is 25 . what are the numbers?

Answers

The numbers are: 36 and 11 .
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Explanation:
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Let us represent the TWO (2) numbers with the variables;
         "x" and "y" .
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     x + y = 47 .

     y − x = 25.
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Since: " y − x = 25 " ;

Solve for "y" in terms of "x" ;

y − x = 25 ;

Add "x" to each side of the equation:
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   y − x + x = 25 + x ;

to get:

   y = 25 + x .

Now, since:

x + y = 47 ;

Plug in "(25 + x)" as a substitution for "y"; to solve for "x" :

x + (25 + x) = 47 ;

x + 25 + x + 47 ;

2x + 25 = 47 ;

Subtract "25" from each side of the equation:

2x + 25 − 25 = 47 − 25 ;

2x = 22 ;

Divide EACH SIDE of the equation by "2" ;
to isolate "x" on one side of the equation; and to solve for "x" ;

2x / 2 = 22 / 2 ;

    x = 11 ;
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x + y = 47 ;

Plug in "11" for "x" into the equation ; to solve for "y" ;

11 + y = 47 ;

Subtract "11" from EACH SIDE of the equation;
to isolate "y" on one side of the equation; and to solve for "y" ;

11 + y − 11 = 47 − 11 ;

            y = 36 .
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So: x = 11 , y = 36 ;
___________________________________________
Let us check our work:

y − x = 25 ;

36 − 11 =? 25 ? Yes!

x + y = 47 ;

36 + 11 =? 47 ? Yes!
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The numbers are: 36 and 11 .
______________________________________________

points (0,0) and (3,3) lie on line k what is the slope of the line that is perpendicular to k

Answers

slope equation: y2-y1 over x2-x1
3-0 over 3-0 = 1
to get the perpendicular slope of a line, you must use the negative reciprocal therefore, the slope of a line that is perpendicular to k is equal to -1

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