Given points $A(2,3)$, $B(-1,4)$, and $C(-2,-2)$, determine point $D$ so that the slope from $A$ to $B$ equals the slope from $C$ to $D$, and the slope from $A$ to $D$ equals the slope from $B$ to $C$.

Answers

Answer 1

Answer:

D is approximately (-2, -1)

Step-by-step explanation:

[tex]{ \tt{slope \:AB = slope \: CD }} \\ \\ { \tt{ \frac{(4 - 3)}{( - 1 - 2)} = \frac{(y - ( - 2))}{(x - ( - 2))} }} \\ \\ { \tt{ \frac{1}{ - 3} = \frac{y + 2}{x + 2} }} \\ \\ { \tt{x + 2 = - 3y - 6}} \\ { \underline{ \tt{ \green{ \: \: 3y + x = - 8 \: \: }}}}[/tex]

[tex]{ \tt{slope \: AD= slope \: BC}} \\ \\ { \tt{ \frac{y - 3}{x - 2} = \frac{ - 2 - 4}{ - 2 - 1} }} \\ \\ { \tt{ \frac{y - 3}{x - 2} = \frac{6}{3} }} \\ \\ { \tt{ \frac{y - 3}{x - 2} = 2}} \\ \\ { \tt{y - 3 = 2(x - 2)}} \\ { \tt{y - 3 = 2x - 4}} \\ { \underline{ \tt{ \blue{ \: \: y - 2x = - 1 \: \: }}}}[/tex]

Solve the green equation and blue equation simultaneously:

[tex]{ \boxed{ \tt{ \red{ \: y \approx - 2 \: \: }}and \: \: { \red{x \approx - 1}}}}[/tex]

Answer 2

Let the co-ordinates of D be (a,b)

Slope of AB =Slope of CD

[tex]\\ \tt\hookrightarrow \dfrac{4-3}{-1-2}=\dfrac{b+2}{a+2}[/tex]

[tex]\\ \tt\hookrightarrow \dfrac{-1}{2}=\dfrac{b+2}{a+2}[/tex]

[tex]\\ \tt\hookrightarrow -a-2=2b+4[/tex]

[tex]\\ \tt\hookrightarrow a+2b+6=0\dots(1)[/tex]

Slope of AD=Slope of BC

[tex]\\ \tt\hookrightarrow \dfrac{b-3}{a-2}=\dfrac{-2-4}{-2+1}[/tex]

[tex]\\ \tt\hookrightarrow \dfrac{b-3}{a-2}=6[/tex]

[tex]\\ \tt\hookrightarrow 6a-12=b-3[/tex]

[tex]\\ \tt\hookrightarrow 6a-b-9=0\dots(2)[/tex]

Multiplying 2 with eq(2)

[tex]\\ \tt\hookrightarrow 12a-2b-18=0\dots(3)[/tex]

Add eq(1) and (3)

[tex]\\ \tt\hookrightarrow 13a-12=0[/tex]

[tex]\\ \tt\hookrightarrow a=12/13=0.9\to 1[/tex]

Put in eq(1)

[tex]\\ \tt\hookrightarrow 12/13+2b+6=0[/tex]

[tex]\\ \tt\hookrightarrow 90/13=-2b[/tex]

[tex]\\ \tt\hookrightarrow b=-90/26=-3 4\to 3[/tex]


Related Questions

You spent $14.80 at a restaurant and want to leave a 15% tip. How much do you leave as a tip?

Answers

Answer:

You leave $2.22

Step-by-step explanation:

convert 15% to 0.15

multiply $14.80*0.15

14.80*0.15=2.22

tip:$2.22

Answer:

Step-by-step explanation: in a calculator type in 15%14.80 and it will be 2.22

so ur answer is $2.22

The polynomial −2x3 − x2 + 13x in the last line is the result of

Answers

-x(2x^2 + x -13)

Hope this helps!! :D

Answer:

The Second Option as of 2022

Step-by-step explanation:

subtracting 3x4 + 9x3 + 3x2 from the

dividend and bringing down 13x .

3 over 4 of 4 over 5 ?

Answers

Answer:

what's the question? it could be both

A quadrilateral has two angles that measure 135º and 85º. The other two angles are in a
ratio of 2:5. What are the measures of those two angles?

Answers

Answer:

40, 100

Step-by-step explanation:

the sum of a quadrilateral is 360, 360 - 135 - 85 =140

140 ÷ 7 × 2 = 40, 140 ÷ 7 × 5 = 100.

whats is the solution to this system?

Answers

Answer:

(3, -2)

Step-by-step explanation:

The solution to a system of equations is the point where the two lines intersect. In the graph, you can see the the two lines intersect at the point (3, -2). Thus, the solution to the system is (3, -2).

Have a lovely rest of your day/night, and good luck with your assignments! ♡


Please Hurry and Answer this

Answers

Answer:

5x + 20 = 5(x+4)

5(2x+8) = 10x + 40

5(x+8) =5 + 5 x 8

Step-by-step explanation:

Red beads come in packages of 10. Blue beads come in packages of 12. Lee wants to buy an equal number of red and blue beads. He thinks he has to buy 10 packages of blue beads and 12 packages of red beads to have the least equal number of each. Is lee correct?
(Needs answer asap)

Answers

No, the lowest should be 6 package of red beads (60) and 5 packages of blue beads (60).

123,456.78901 to ten – thousandths
-

Answers

Answer:

123,456.789

Step-by-step explanation:

The ten thousandth place is less than 5.

Answer:

123,456.789

Explanation:

Given: 123,456.789..........the last 3 digit after decimal place is thousands and 1 digit after decimal place is tenths.

NASA scientists discovered a planet in December of 2004. After observation, they have come to a conclusion that the population doubles in January of every third year and due to calamities the population decreases to one-sixth in March of every 6th year. If the population in December of 2022 is 512 , then what was the population when the planet was discovered?


correct answer gets brainliest

Answers

Step-by-step explanation:

so, there is a population in that planet. right ?

that means they discovered a populated planet.

anyway,

18 years

p0 is the start population.

p0 × 2 after 3 years

p0 × 2 × 2 = p0 × 4 after 6 years

p0 × 4 / 6 after 6 years

(p0 × 4 / 6) × 2 after 9 years

(p0 × 4 / 6) × 4 after 12 years = p0 × 8/3 after 12 years

(p0 × 8/3) / 6 after 12 years = p0 × 8/18 = p0 × 4/9

p0 × 4/9 × 2 after 15 years

p0 × 4/9 × 4 after 18 years

p0 × 4/9 × 4 / 6 after 18 years = p0×16/54 = p0 × 8/27 = 512

p0 = 512×27/8 = 1728

p(n) = p0 × (2/3)^(n/6)

with n being years.

because

the population changes by a factor 2 every 3 years = 2^(n/3)

and by a factor 1/6 every 6 years = (1/6)^(n/6).

so,

p(n) = p0 × 2^(n/3) × (1/6)^(n/6)

2^(n/3) = 2^(2n/6) = 2²^(n/6) = 4^(n/6)

therefore,

p(n) = p0 × 4^(n/6) × (1/6)^(n/6) =

= p0 × (4/6)^(n/6) = p0 × (2/3)^(n/6)

Seven decreased by 13

Answers

Answer:

13-7

=6

hope it helps you

make me brainliest plz

Answer:

it will be 6

Step-by-step explanation:

decreases by means - soo

13-7=6

Please I need help thanks

Answers

Answer:

  12

Step-by-step explanation:

The slope of function 1 can be found using the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (-14.5 -(-9.25))/(6 -3) = -5.25/3 = -1.75

The y-intercept is given by ...

  b = y1 -m(x1)

  b = -9.25 -(-1.75)(3) = -9.25 +5.25 = -4

The y-intercept of Function 1 is -4.

__

The slope of Function 2 can be found by looking for points where the graph crosses intersections of the grid lines. One of those is the x-intercept, (-4, 0). Another is over 1 and up 2 from that, (-3, 2). The slope of function 2 is then ...

  m = rise/run = 2/1 = 2

We can use the formula for the y-intercept with point (-4, 0):

  b = y1 -m(x1)

  b = 0 -(2)(-4) = 8

The y-intercept of Function 2 i s 8.

The difference between the y-intercepts is (8 -(-4)) = 12.

Today only, a sofa is being sold at a 33% discount. The sales price is $603 what was the sales price yesterday

Answers

Answer: 801.99

Step-by-step explanation:

603 + Percentage increase =

603 + (33% × 603) =

603 + 33% × 603 =

(1 + 33%) × 603 =

(100% + 33%) × 603 =

133% × 603 =

133 ÷ 100 × 603 =

133 × 603 ÷ 100 =

80,199 ÷ 100 =

801.99

Answer:

$801.99

Step-by-step explanation:

You first make 33% into a decimal which makes .33

Then multiply .33 by $603 which equals $198.99

Lastly add $198.99 to $603 and you get $801.99

Which expression is equivalent to the given expression?

7x−3


7x−3x

3−7x

4x−3+3x

3−6+3x

Answers

Answer:

4x–3+3x

Step–by–step explanation:

Look at each term as positive or negative. I will use brackets for the sake of clarity, but that is not necessary. Here, that would look like:

[+4x] [–3] [+3x]

Rearrange the terms.

[+4x] [+3x] [–3]

Remove the brackets.

4x +3x –3

Simplify.

7x – 3

Answer:

Option C

Step-by-step explanation:

Let's verify all the options.

Option A:

7x - 3x = 7x - 3=> 4x = 7x - 3 (False)

Option B:

3 − 7x = 7x - 3=> 3 + 3 = 14x (False)

Option C:

4x − 3 + 3x = 7x - 3=> 7x - 3 = 7x - 3 (True)

Option D:

3 − 6 + 3x = 7x - 3=> 3x - 3 = 7x - 3=> 3x = 7x (False)

We can conclude that option C is correct.

-18 subtracted from - 7

Answers

the answer is 11 my friend :)

Answer:

[tex]-7-(-18)\\-7+18\\11[/tex]

Step-by-step explanation:

Grace was out at a restaurant for dinner when the bill came. Her dinner came
to $33. After adding in a tip, before tax, she paid $38.61. Find the percent tip.

Answers

Answer:

Based on the given conditions, formulate: (38.6-33)÷33

Calculate the sum or difference:5.61/33

Convert decimal to fraction:5.61/100/33

Divide a fraction by multiplying its reciprocal:561/100 × 1/33

Cross out the common factor:17/100

Rewrite a fraction with denominator equals 100 to a percentage:17%

Answer: 17%

The difference of the squares of two numbers is 15. The difference of twice the square of the first number and the square of the second number is 30. Find the numbers

Answers

Step-by-step explanation:

Let x represent the first number, and y be the second number.

The first statement can be modeled as

[tex] {x}^{2} - {y}^{2} = 15[/tex]

The second statement can modeled as

[tex]2 {x}^{2} - {y}^{2} = 30[/tex]

If we multiply 2 both sides of the first equation,

[tex]2( {x}^{2} - {y}^{2} ) = 15 \times 2[/tex]

[tex]2 {x}^{2} - 2 {y}^{2} = 30[/tex]

Subsitue this for 30 in second equation,

[tex]2 {x}^{2} - {y}^{2} = 2 {x}^{2} - {2y}^{2} [/tex]

[tex] {y}^{2} = 0[/tex]

[tex]y = 0[/tex]

Subsitue this for y in either equation,

[tex] {x}^{2} = 15[/tex]So our answer is

plus or minus sqr root of 15, 0).

[tex](± \sqrt{15} ,0)[/tex]

[tex]x = \sqrt{15} [/tex]

or

[tex]x = - \sqrt{15} [/tex]

a decimal in between 0.25 and 0.125

Answers

0.2 is a decimal between 0.25 and 0.125

Plz help I can’t figure this out

Answers

Answer:

57

Step-by-step explanation:

[tex]9+6 (2^2 +4)\\9+6 (4 +4)\\9+6 *8\\9+48\\57[/tex]

Your answer is 57.

Hope this helps! Brainliest would be much appreciated! Have a great day! :)

Answer:

The answer is 57.

Step-by-step explanation:

[tex]{\tt{\underline{\underline{\pink{SOLUTION:}}}}}[/tex]

To solve the above equation we will follow the BODMAS rule.

[tex]\blue\star[/tex] BODMAS is an order of mathematic operations.[tex]\blue\star[/tex] BODMAS rule is to be followed while solving expressions in mathematics.

It stands for :

[tex]\purple\star[/tex] B = bracket[tex]\purple\star[/tex] O = order of power[tex]\purple\star[/tex] D = division[tex]\purple\star[/tex] M = multiplication[tex]\purple\star[/tex] A = addition[tex]\purple\star[/tex] S = subtraction

Solving this question by bodmas rule :

[tex]\begin{gathered}\qquad{\sf{ = 9 + 6( {2}^{2} + 4)}}\\\\\qquad{\sf{ = 9 + 6(2 \times 2 + 4)}}\\\\\qquad{\sf{ = 9 + 6(4 + 4)}}\\\\\qquad{\sf{ = 9 + 6(8)}}\\\\\qquad{\sf{ = 9 + 6 \times 8}}\\\\\qquad{\sf{ = 9 + 48}}\\\\\qquad{\sf{ = 57}}\end{gathered}[/tex]

Hence, the answer is 57.

[tex]\rule{300}{2.5}[/tex]

I need help answering this question

Answers

Answer:

The 2nd option is the correct answer.

since you split 12 pieces with 3 people there is 4 pieces per person.

what is the simplification of 1.1​

Answers

Answer:

1 1/10

Step-by-step explanation:

I hope it's what you wanted

The Wing Station wants the average price of the lunch meal deals to be $8.


Lunch Meal Deal Prices
Item
Price ($)
Deluxe hamburger
$9
Reuben sandwich
$7
Chicken wings
Chicken stir fry
$9
Cobb salad
$6
Make your own sandwich
$10

What does the price of the chicken wings need to be for this to happen?

Answers

Answer:

$7step-by-step

Step-by-step explanation:

7is the answer

Answer:

7 the person above me is right

Step-by-step explanation:

help pls ill mark brainliest!!!!!!!!!!!!!!!!!

Answers

Any points that are less than 6. So 5, 4, 3, 2, etc.

Answer:

He could've sent 5, 4, 3, or 2 postcards

Step-by-step explanation:

Solve for x.
[tex] \rm \longrightarrow \dfrac{x}{ \sqrt{ {x}^{2} + 1} } = {x}^{4} - x[/tex]
Best answer will be rewarded. ​

Answers

Factorize both sides of the equation:

[tex]\dfrac x{\sqrt{x^2+1}} = x^4 - x[/tex]

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

[tex]\dfrac x{\sqrt{x^2+1}} - x(x^3-1) = 0[/tex]

[tex]x \left(\dfrac1{\sqrt{x^2+1}} - (x^3 - 1)\right) = 0[/tex]

One immediate solution is then x = 0. This leaves us with

[tex]\dfrac1{\sqrt{x^2+1}} - (x^3 - 1) = 0[/tex]

or as we had earlier,

[tex]\dfrac1{\sqrt{x^2+1}} = x^3 - 1[/tex]

Take the square of both sides:

[tex]\dfrac1{x^2+1} = \left(x^3-1\right)^2[/tex]

[tex]\dfrac1{x^2+1} = x^6 - 2x^3 + 1[/tex]

Turn this into a polynomial equation:

[tex]1 = \left(x^2+1\right) \left(x^6-2x^3+1\right)[/tex]

Expand the right side and make it equal to zero:

[tex]1 = x^8 + x^6 - 2x^5 - 2x^3 + x^2 + 1[/tex]

[tex]0 = x^8 + x^6 - 2x^5 - 2x^3 + x^2[/tex]

Each term in the polynomial has a common factor of x². Factoring this out just gives x = 0 again as a solution.

[tex]0 = x^2 \left(x^6 + x^4 - 2x^3 - 2x + 1\right)[/tex]

[tex]0 = x^6 + x^4 - 2x^3 - 2x + 1[/tex]

You'll need a computer to solve the remain se.xtic equation. Solving over reals, you would find two solutions, x ≈ 0.438 and x ≈ 1.18, but only x ≈ 1.18 is valid.

Answer:

x = 0 and x = 1.181

Step-by-step explanation:

Another solution is graphical.

Take either side as a function and find the intersection of the graphs.

Use graphing software to make it much easier.

See below

Find the equation of the exponential function represented by the table below

Answers

Answer:

[tex]y=4(4)^x[/tex]

Step-by-step explanation:

Exponential functions are represented in the form [tex]y=a(b)^x[/tex], where a is the initial value and b is the multiplier.

Here, we see that when x = 0, y = 4. This means that 4 is our initial value, or a. You can look at the a variable almost being like the y-intercept of a graph.

Next, we must solve for b. We can do 16 ÷ 4 to find the slope, or multiplier of this function, because 16 is 1 input x-value up from 0. 16 ÷ 4 = 4.

So, we now have all the needed variables, so we plug them into the formula

[tex]y=a(b)^x[/tex]

use words to write this number: 40302010

Answers

40,302,010

forty million, three hundred two thousand, ten

Portfolio Option 1: Sports Graph

This portfolio problem will have you write. You will turn in a “mathematical paper” of about 1 page of writing. You can use this handout to write rough draft ideas first.

Brainstorm: Which of the above sports do you think the graph could represent? Why?

Brainstorm: What vocabulary and properties of graphs and functions do you see represented in the graph? How did any of those affect your choice for the sport?

Use your brainstorms above to write a 1 page paper that talks about this graph, what sport you believe it could represent, and what properties of functions and graphs support your answer. You can add diagrams as well.

Answers

Answer:The graph represent skydiving, Because when you jump out of the plane you have a bunch of speed and when you pull your parachute the speed will drop exceedingly.

Step-by-step explanation:

A number decreased by 5 is less than 33.

Answers

Step-by-step explanation:

ket the number be x

Decreased by 5 means x-5

Less than 33 means x - 5 < 33

x < 33 + 5

x < 38

1. Services performed but unbilled and uncollected at July 31 were $1,730.
2. Depreciation on equipment for the month was $180.
3. One-twelfth of the insurance expired.
4. A count shows $330 of cleaning supplies on hand at July 31.
5. Accrued but unpaid employee salaries were $410.

Answers

The appropriate journal entries for the transactions are: Debit Accounts receivable $1,730; Credit Sales revenue$1,730.

Journal entries

July 31

Debit Accounts receivable $1,730

Credit Sales revenue  $1,730

July 31

Debit Depreciation expenses $180

Credit Accumulated depreciation $180

July 31

Debit Insurance expenses xx(1/12)

Credit repaid insurance xx(1/12)

July 31

Debit Supplies expenses $330

Credit Supplies $330

July 31

Debit Salaries wages and expense $410

Credit Salaries and wages payable $410

Inconclusion the appropriate journal entries for the transactions are: Debit Accounts receivable $1,730; Credit Sales revenue$1,730.

Learn more about journal entries here:https://brainly.com/question/14279491

[tex]n = 20[/tex] , ∑[tex]x = 1570[/tex] , ∑[tex]x^2 = 125696[/tex] , minimum = 60, maximum = 100

Find s. Round your answer to one decimal place.

Estimate s by using the range rule-of-thumb. (If you can explain the range rule of thumb it'll be greatly appreciated).

Answers

Answer:

s=10

Step-by-step explanation:

Basically, the range rule-of-thumb is that the range is generally about four times the standard deviation.

First, we find the range:

Range=Maximum-Minimum

Range=100-60

Range=40

Next, divide the range by 4 to get the standard deviation

Range=4(Standard Deviation)

40=4(Standard Deviation)

10=Standard Deviation

Therefore, s=10, which is the standard deviation

Mean:-

[tex]\\ \tt\hookrightarrow \overline{x}=\dfrac{\sum x}{n}=\dfrac{1570}{20}=78.5[/tex]

Standard deviation:-

Two ways are available ,Let's do in both.

WAY-1(apply common formula)

[tex]\\ \tt\hookrightarrow \sigma=\sqrt{\dfrac{\sum x^2}{n}-(\overline{x})^2}[/tex]

[tex]\\ \tt\hookrightarrow \sigma=\sqrt{\dfrac{125696}{20}-(78.5)^2}[/tex]

[tex]\\ \tt\hookrightarrow \sigma=\sqrt{6284.8-6162.25}[/tex]

[tex]\\ \tt\hookrightarrow \sigma=\sqrt{122.55}[/tex]

[tex]\\ \tt\hookrightarrow \sigma=11.07=11.1[/tex]

Way-2(Apply range-rule of thumb):-

So the rule basically defines that range is approximately equal to four times of standard deviation.

[tex]\\ \tt\hookrightarrow Range=max-min=100-60=40[/tex]

NOW

[tex]\\ \tt\hookrightarrow \sigma \approx \dfrac{Range}{4}[/tex]

[tex]\\ \tt\hookrightarrow \sigma\approx \dfrac{40}{4}[/tex]

[tex]\\ \tt\hookrightarrow \sigma\approx 10[/tex]

Make sure to use approx sign instead of equal to as range -rule of thumb doesn't give accurate standard deviation.

The value of 22 to the nearest hundred

Answers

Answer:

0

Step-by-step explanation:

Since the tens place is below 5 you would round down to zero. 5 and above round up, four and below round down.

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