The endpoints of JK are J(–25, 10) and K(5, –20). What is the y-coordinate of point L, which divides JK into a 7:3 ratio? a. –16 b.–11 c. –4 d.–1

Answers

Answer 1

let's say the point dividing JK is say point P, so the JK segment gets split into two pieces, JP and PK

[tex]\bf ~~~~~~~~~~~~\textit{internal division of a line segment} \\\\\\ J(-25,10)\qquad K(5,-20)\qquad \qquad \stackrel{\textit{ratio from J to K}}{7:3} \\\\\\ \cfrac{J~~\begin{matrix} P \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} P \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~K} = \cfrac{7}{3}\implies \cfrac{J}{K} = \cfrac{7}{3}\implies3J=7K\implies 3(-25,10)=7(5,-20)\\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf P=\left(\frac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \frac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)\\\\[-0.35em] ~\dotfill\\\\ P=\left(\cfrac{(3\cdot -25)+(7\cdot 5)}{7+3}\quad ,\quad \stackrel{\textit{y-coordinate}}{\cfrac{(3\cdot 10)+(7\cdot -20)}{7+3}}\right) \\\\\\ P=\left( \qquad ,\quad \cfrac{30-140}{10} \right)\implies P=\left(\qquad ,~~\cfrac{-110}{10} \right)\implies P=(\qquad ,\quad -11)[/tex]

Answer 2

Answer:

-11

Step-by-step explanation:

J =(–25, 10)

K=(5, –20)

Point L divides JK into a 7:3 ratio

To find the coordinates of L we will use section formula.

Formula : [tex]x=\frac{mx_2+nx_1}{m+n}[/tex] and [tex]y=\frac{my_2+ny_1}{m+n}[/tex]

m: n = 7: 3

[tex](x_1,y_1)=(-25,10)\\(x_2,y_2)=(5,-20)[/tex]

Substitute the values

[tex]x=\frac{7(5)+3(-25)}{7+3}[/tex] and [tex]y=\frac{7(-20)+3(10)}{7+3}[/tex]

[tex]x=-4[/tex] and [tex]y=-11[/tex]

Hence the y coordinate of L is -11


Related Questions

The graph of y= - 3x^2– 4x + 2 opens downward true or false

Answers

Answer:

True

Step-by-step explanation:

This is a parabola.  The coefficient of the x^2 term is -3

Since it is negative, the parabola opens downward

Answer: False

Step-by-step explanation: A-Pexw

Can someone please help??

Answers

Answer:

24 + 32p = 8(3 + 4p)

Step-by-step explanation:

24 = 8 · 3

32p = 8 · 4p

24 + 32p = 8 · 3 + 8 · 4p = 8 · (3 + 4p)

Ronald spins a spinner that has 10 sections numbered from 1 to 10. What is the probability that the spinner lands on a prime number?

Answers

The probability the spinner lands on a prime number is 4/10 or 40%

Answer:

40%

Step-by-step explanation:

Prime numbers less than 10 are 2, 3, 5, and 7.  Assuming the sections are sized equally, then four out of ten sections is 40%.

Which of the following is the scaling factor a of the function f(x) = 3|x|?
•-1
•-3
• 1
• 3

Answers

Answer:

Last option: 3

Step-by-step explanation:

The following are some transformations for a function f(x):

1) If [tex]a(fx)[/tex] and [tex]|a|>1[/tex], then this function is stretched vertically by a factor of "a".

2) If [tex]a(fx)[/tex] and [tex]0<|a|<1[/tex], then this function is compressed vertically by a factor of "a".

Therefore, given the function [tex]f(x) = 3|x|[/tex], we can observe that the factor "a" is:

[tex]a=3[/tex]

Then:

[tex]a>1[/tex]

This means that  then this function is stretched vertically by a factor of 3.

Therefore, the scaling factor is 3.

The following dot plots shows the number of strokes golf players required at each hole .Each dot represents a different player.Order the holes from least to greatest typical number of strokes per player .

Answers

Answer:

Hole 6,7,5 is the order

Step-by-step explanation:

Final answer:

To order the holes from least to greatest typical number of strokes per player based on the dot plots, count the number of dots for each hole and arrange the holes in increasing order.

Explanation:

To order the holes from least to greatest typical number of strokes per player, we need to look at the dot plots and determine the number of players represented by each dot. We can then count the number of dots for each hole and arrange the holes in increasing order based on the number of players. The hole with the least number of strokes per player would have the fewest dots, while the hole with the greatest number of strokes per player would have the most dots.

Let's say the dot plots show the following:

Hole 1: 2 dotsHole 2: 4 dotsHole 3: 3 dotsHole 4: 1 dotHole 5: 5 dots

Based on the number of dots per hole, the order from least to greatest typical number of strokes per player would be:

Hole 4Hole 1Hole 3Hole 2Hole 5

Evaluate 15cos60°. evaluate.

Answers

Answer:

15/2 or 7.5

Step-by-step explanation:

cos(60)=1/2

so 15(1/2)=15/2 or 7.5

For this case we must evaluate the following expression:

[tex]15 * cos (60)[/tex]

By definition we have that the cosine of 60 degrees is [tex]\frac {1} {2}.[/tex] Then, substituting in the expression we have:

[tex]15 * \frac {1} {2} = \frac {15} {2} = 7.5[/tex]

So, we have:

[tex]15 * cos (60) = 7.5[/tex]

Answer:

[tex]15 * cos (60) = 7.5[/tex]

Monique has $20 available to buy some sweet corn and lima beans to make succotash. If she buys 8 lb of corn, how many pounds of lima beans can she buy

Answers

Answer:

It’s a

Step-by-step explanation:

Answer:

It's A: 4.8 lb

Step-by-step explanation:

Which inequality is shown below ?

Answers

Answer:

b.

Step-by-step explanation:

NEED NOW!!! DONT NEED AN EXPLANATION I HAVE LIKE 5 MIN!!!
Which equation represents a linear function?
y – 2 = –5(x – 2)
x + 7 = –4(x + 8)
y – 3 = y(x + 4)
y + 9 = x(x – 1)

Answers

The first one. x and y only ever appear as first degree terms.

Second one, no y, third one xy isn't linear, fourth one x squared isn't linear.

Answer:

The first one: y - 2 = -5(x - 2)

Step-by-step explanation:

For f(x) = 3x+1 and g(x) = x2 - 6, find
(g/f)(x)

Answers

[tex]\left(\dfrac{g}{f}\right)(x)=\dfrac{x^2-6}{3x+1}[/tex]

Solve for x in the equation 2x2 -5x+ 1 = 3.

Answers

Answer:

[tex]x=\frac{5+\sqrt{41}}{4}[/tex] and [tex]x=\frac{5-\sqrt{41}}{4}[/tex]

Step-by-step explanation:

[tex]2x^2-5x+1=3[/tex]

To solve for x, we make right hand side 0

Subtract 3 from both sides

Given equation becomes

[tex]2x^2-5x-2=0[/tex]

We apply quadratic formula to solve for x

[tex]x=\frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]

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

[tex]x=\frac{5+-\sqrt{5^2-4(2)(-2)}}{2(2)}[/tex]

[tex]x=\frac{5+-\sqrt{41}}{4}[/tex]

[tex]x=\frac{5+\sqrt{41}}{4}[/tex] and [tex]x=\frac{5-\sqrt{41}}{4}[/tex]

Should teens be allowed to play dangerous sports? Why or why not?

Answers

Answer:

I mean if it's there dream then why stop it? Its there life and we can't really stop that cause regardless what you say or do they're gonna find a way to do it. So I would say yes.

I am going to assume this is a poll? For our opinions?

If so then yes, I think that kids should be allowed to play dangerous sports..Football fatalities remain rare, but the game can be dangerous. That doesn't mean kids shouldn't play, same with hockey and any other

The figure shows the function p(x)=[x]. Which statement about the function is not true?

A) p(0)=0
B) p(-4)=4
C) p(4)=-4
D) The domain of p(x) is all real numbers

Answers

Answer:

The option that's not true is:

C) p(4) = -4

Because if you look at that graph, you can tell, p(4) = 4 not -4.

The domain of the function p(x) = [x] is not all real numbers; it excludes integer values of x where the function is discontinuous. Statement D is not true.

The function p(x) = [x], where [x] represents the greatest integer less than or equal to x (the floor function). Let's evaluate each statement:

A) p(0) = [0] = 0. This is true.

B) p(-4) = [-4] = -4. This is true.

C) p(4) = [4] = 4. This is true.

D) The domain of p(x) is all real numbers. This statement is not true. The domain of p(x) is actually all real numbers except the points where x is an integer. At those points, there are discontinuities, and the function is undefined because the floor function jumps from one integer value to the next.

So, the statement that is not true is D) The domain of p(x) is all real numbers. The correct statement is that the domain of p(x) is all real numbers except at integer values of x.

For more such questions on domain:

https://brainly.com/question/30096754

#SPJ2

Solve w = t(11 + r) for t.

Answers

Answer:

t = w/(11+r)

Step-by-step explanation:

To solve for t, we need to divide anything that t is multiplied to to get it on the other side of the equal sign.

w = t(11+r)

w/(11+r) = t

Answer:

t = w/(r + 11)

Step-by-step explanation:

Solve for t:

w = t (r + 11)

w = (r + 11) t is equivalent to (r + 11) t = w:

t (r + 11) = w

Divide both sides by r + 11:

Answer: t = w/(r + 11)

Help me please! BRAINLIEST

Answers

Answer:

1. 53 by 58 , 222 ft

2. 321000

3.1080

4.  3.5

Step-by-step explanation:

1. 23+15+15 = 53

28+15+15= 58

53+53+58+58= 222

If f(x) = 5x + 40, what is f(x) when x = –5?

Answers

First note that f(x) means the same thing as y. To solve for f(x) or y you need to plug in -5 for x and solve using the rules of PEMDAS

5(-5) + 40

-25 + 40

15

When x is -5 then y is 15

Hope this helped!

~Just a girl in love with Shawn Mendes

The library is located 1.8 miles west of Callie’s house. The grocery store is located 2.4 miles south of the library. What is the length of a straight line between Callie’s house and the grocery store? Enter your answer in the box.

Answers

Check the picture below.

By using a right triangle rectangle, we will see that the distance is equal to 3 miles.

How to find the distance?

You can think of the distance as the hypotenuse of a right triangle with legs that measure 1.8 miles and 2.4 miles.

Then, using the Pythagorean theorem we can write:

H^2 = (1.8 mi)^2 + (2.4 mi)^2

H = √((1.8 mi)^2 + (2.4 mi)^2) = 3mi

So the distance between Callie's house and the grocery store is 3 miles.

If you want to learn more about right triangles, you can read:

https://brainly.com/question/2217700

The following two-way table shows the data for the students of two different grades in a school:

Member of Science Club Not Member of Science Club Total
Grade 7 20 2 22
Grade 8 20 8 28
Total 40 10 50

Based on the relative row frequency, the students of which grade are more likely to be members of the science club?


Grade 7

Grade 8

The students of both grades are equally likely to be members of the science club

No conclusion can be drawn about the chances of a student being a member of the science club

Answers

Answer: grade 7

Step-by-step explanation:

Grade 7: 20/22 students in club

Grade 8: 20/28 students in club

Grade 7 has higher % of students in science club

Answer:

Grade 7

Step-by-step explanation:

The relative row frequency of members of the Science Club is: Member of Science Club / Total

in Grade 7: 20/22 = 0.91.

And in Grade 8 is: 20/28 = 0.71.

Then, students of Grade 7 are more likely to be members of the science club.

what is the difference between the mean of each set?

a) 4
b) 5
c) 7
d) 9

Answers

Mean is the average

So the first mean is 11
The second one is 14.7 so round to 15

15-11 is 4. Hope that is correct
The difference is 4

Which describes the correlation shown in the scatterplot?

Answers

Answer:

None

Step-by-step explanation:

For there to be a correlation it  needs to either be in  a line or have equal stuff on both sides

Answer:

Option c is right

Step-by-step explanation:

Given is a scatter plot with points scattered.

We have to find from the shape the correlation coefficient

The points on the scatter plot do not support a linear correlation between the two variables.

There does not seem to be a line of fit which has minimum deviations from the line.

Hence there is no correlation is the correct answer.

From the given graph, we can say that option c is right.

The sum of 26 and twice a number is 312. Find the number.

Answers

Answer:

Step-by-step explanation: 26+2c=312

Now we solve for c.

Subtract 26 on both sides giving 2c=286

So c=143

This is the equation in numbers translated (n is a number)

26 + 2n = 312

We have to find what the number (n) is. This means we must isolate n. To do this you must subtract 26 to both sides

26 - 26 + 2n = 312 - 26

0 + 2n = 286

2n = 286

To further isolate n you must divide 2 to both sides

2n/2 =286/2

n = 143

Check:

26 + 143*2 = 312

26 + 286 = 312

312 = 312

The number is 143

Hope this helped!

~Just a girl in love with Shawn Mendes

in order to graph a linear equation in slope-interceot form, what do you need to know? what does the equation look like when the y-intercept of the line is equal to 0? what does the equation look like when it also has a slope equal to 1?

Answers

Answer:

(a) Slope and y-intercept; (b) y = mx; (c) y = x + b

Step-by-step explanation:

1. Need to know

Slope and y-intercept.

You use these numbers to calculate one other point. Then you draw a straight line between the y-intercept and the other point to get the graph.

2. y-Intercept = 0

The form of the equation is y = mx + b, where b is the y-intercept.

If the intercept is zero, b = 0, and the equation has the form

y = mx

The graph is a straight line passing through the origin.

3. Slope = 1

m represents the slope. If m = 1, the equation has the form

y = x + b

If the axes are scaled equally, the graph is a straight line that crosses the y-intercept at an angle of 45°.  

If h(x) is the inverse of f(x), what is the value of h(f(x))?
OO
0 1
f(x)

Answers

Answer:

x.

Step-by-step explanation:

h(f(x) = x.

For example the inverse of  f(x) = 2x  is g(x) = x/2

f((gx)) 2 (x/2)

= 2x / 2

= x.

Answer:

If h(x) is the inverse of f(x), then  the value of h(f(x)) is:

                                   x

Step-by-step explanation:

Inverse of a function-

The inverse of  a given function is a function which reverses the action of the other function.

Also, the composition of a function and it's inverse no matter in which order they are applied always gives us the identity function.

( Identity function-- Identity function is a function which when applied to some other function always retains that function )

i.e.   If h(x) is the inverse of f(x) ; then we have:

                  [tex]h(f(x))=f(h(x))=x[/tex]

3. Solve the system of equations. Show your work. y = x^2-3x+4 x + y = 4

Answers

Answer:  x = 2, y = 2

Step-by-step explanation:

[tex]y=x^2-3x+4\\x + y = 4\quad \implies y=4-x\\\\\underline{\text{Substitute y (in the first equation) with 4 - x:}}\\4-x=(4-x)^2-3(4-x)+4\\\\\underline{\text{Expand and distribute right-hand side:}}\\4-x=16-8x+x^2-12+3x+4\\\\\underline{\text{Simplify right-hand side:}}\\4-x=8-5x+x^2\\\\\underline{\text{Set left-hand side equal to zero (subtract 4 and add x):}}\\0=4-4x+x^2\quad \implies 0=x^2-4x+4\\\\\underline{\text{Factor and solve for x:}}\\0=(x-2)(x-2)\\0=x-2\\2=x[/tex]

Replace x with 2 in the second equation to solve for y:

x + y = 4

2 + y = 4

     y = 2

The diagonal of a square is x units. What is the area of the square in terms of x? square units square units 2x square units square units

Answers

For this case we have that by definition, if we draw the diagonal of a square two rectangular triangles are formed. If the diagonal measures "x", then the Pythagorean theorem is fulfilled:

[tex]l ^ 2 + l ^ 2 = x ^ 2[/tex]

Where:

l: It's the side of the square.

[tex]2l ^ 2 = x ^ 2\\l ^ 2 = \frac {x ^ 2} {2}[/tex]

We know that the area of a square is given by:

[tex]A = l ^ 2[/tex]

So, the area is:

[tex]A = \frac {x ^ 2} {2}[/tex]

Answer:

[tex]A = \frac {x ^ 2} {2}[/tex]

Answer:

Option A: 1/2 x^2

Step-by-step explanation:

f(x) = x2 + 5x - 1 is shifted 3 units left. The result is g(x). What is g(x)?

Answers

Answer:

g(x) = (x + 3)^2 + 5(x + 3) - 1

Step-by-step explanation:

Please use " ^ " to denote exponentiation:  f(x) = x^2 + 5x - 1.

Shifting the graph of this function 3 units left results in

g(x) = (x + 3)^2 + 5(x + 3) - 1

What is the following sum? Assume.. (look at picture)

Answers

ANSWER

The correct answer is B

EXPLANATION

The given sum is

[tex] \sqrt{ {x}^{2} {y}^{3} } + 2 \sqrt{ {x}^{3} {y}^{4} } + xy \sqrt{y} [/tex]

We need to remove the perfect squares.

[tex]\sqrt{ {x}^{2} \times {y}^{2} \times y } + 2 \sqrt{ {x}^{2} \times ( {y}^{2})^{2} \times x } + xy \sqrt{y} [/tex]

Let us split the radical sign for the factors to get;

[tex]\sqrt{ {x}^{2}} \times \sqrt{ {y}^{2}} \times \sqrt{y} + 2 \sqrt{ {x}^{2} } \times \sqrt{( {y}^{2})^{2}} \times \sqrt{x} + xy \sqrt{y} [/tex]

This simplifies to

[tex]xy \sqrt{y} + 2x {y}^{2} \sqrt{x} + xy \sqrt{y} [/tex]

Group similar terms to get:

[tex]xy\sqrt{y} + xy \sqrt{y} + 2x {y}^{2} \sqrt{x} [/tex]

Combine the similar terms to get:

[tex]2xy\sqrt{y} + 2x {y}^{2} \sqrt{x} [/tex]

The correct answer is B.

please helpppppp me

Answers

Answer:

B. [tex] 4 \times 10^{12} [/tex]

Step-by-step explanation:

[tex] (6 \times 10^{8}) \div (1.5 \times 10^{-4}) = [/tex]

[tex] = \dfrac{6 \times 10^{8}}{1.5 \times 10^{-4}} [/tex]

[tex] = \dfrac{6}{1.5} \times \dfrac{10^{8}}{10^{-4}} [/tex]

[tex] = 4 \times 10^{8 - (-4)} [/tex]

[tex] = 4 \times 10^{12} [/tex]

Solve for x. (x - 8)(x - 8) = 0

Answers

The answer is x equals 8

Answer: x=8

Step-by-step explanation:

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

Set the first factor equal to 0 and solve.

x−8=0

x−8=0

the table represents a function​

Answers

Answer:

-8

Step-by-step explanation:

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