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The coordinate of E will be (1, -3) if the coordinates of E if E divides CH three -fourths of the way from C to H

Midpoint of a line is a point that divides a line into two equal parts.

If the line is divided in the ratio a:b, then the midpoint formula will be expressed as:

[tex]M(X,Y) =(\frac{ax_1+bx_2}{a+b}, \frac{ay_1+by_2}{a+b})\\[/tex]

Given the coordinate points, C(2, 1) and H(-2, 15) divided in the ratio of 3:4

[tex]X = \frac{3(2)+1(-2)}{3+1}\\X= \frac{6-2}{4}\\X=\frac{4}{4}\\X = 1[/tex]

Get the coordinates Y:

[tex]Y = \frac{3(1)+1(-15)}{3+1}\\Y= \frac{3-15}{7}\\Y=\frac{-12}{4}\\Y= -3[/tex]

This shows that the coordinate of E will be (1, -3)

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Answer:

It is y = x - 5

Step-by-step explanation:

General equation of a line:

[tex]{ \bf{y = mx + c}}[/tex]

m is the gradient, and c is y-intercept.

For gradient:

[tex]slope = \frac{y_{2} - y_{1} }{x _{2} - x_{1}} [/tex]

substitute:

[tex]slope = \frac{1 - ( - 2)}{6 - 3} \\ \\ = \frac{3}{3} \\ slope \: = 1[/tex]

m = 1

for y-intercept:

consider point (6, 1):

[tex]y = mx + c \\ 1 = (6 \times 1) + c \\ 1 = 6 + c \\ c = 1 - 6 = - 5[/tex]

therefore:

[tex]{ \sf{equation \: is \: \{y = x - 5 \}}}[/tex]

Answer:

C. 164

Step-by-step explanation:

its self explanitory

Answer:

they would each get 6 and there would be 2 left over

Step-by-step explanation:

3x6=18

20-18=2

=2 leftovers

Answer:

Each of the friends will get 6 with 2 small prizes remaing

Step-by-step explanation:

20 ÷ 6 = 18 remainder of 2

Ignore the 2 because you cannot split 2 evenly from 3 people.

So each friend gets 6, while there is a 2 remainder

To check our work just do 6 × 3 = 18 and 20 - 18 = 2

So, in conclusion, each friend get 6 while there are 2 small prizes left

Answer:

Ruby = 18+6=24

Isaac = 18

Svetlana = 4*18=72

24+18+72=114

Step-by-step explanation:

Ruby= x+6

Isaac= x

Svetlana = 4x

x+6+x+4x = 114

6x = 114 - 6

x = 108/6

X = 18

Answer:

45

Step-by-step explanation:

....................

Hey there! I'm happy to help!

We see that the cupcakes are $2, but for every 8 you buy you get 1 free.

So, if we buy 8 cupcakes, we will be paying $16, but we will actually be receiving 9 donuts, so that means that for every $16 we pay, we get 9 donuts.

Let's see how many times $16 goes into $80.

80/16=5

So, this means that our $16 that gives us 9 donuts was done 5 times, which totals up to 80 dollars. Let's multiply our donuts now.

9*5=45

So, Fatimah will get 45 donuts during the promotion.

Have a wonderful day and keep on learning! :D

Answer:

[tex]x=5[/tex]

Step-by-step explanation:

1. Approach

The most logical steps to solve the given equation are to distribute and simplify the left side of the equation. Then use inverse operations to bring all of the terms to the left side of the equation. After doing so, one can factor the equation again, then use the zero-product property to solve it.

2. Simplify

Distribute the terms on the left side, multiply everything in the first parenthesis by everything in the second,

[tex](x+1)(x-11)=-36[/tex]

[tex](x)(x)+(1)(x)+(-11)(x)+(1)(-11)=-36[/tex]

Simplify this expression by performing the multiplication and then combining like terms,

[tex](x)(x)+(1)(x)+(-11)(x)+(1)(-11)=-36[/tex]

[tex]x^2+x-11x-11=-36[/tex]

[tex]x^2-10x-11=-36[/tex]

Inverse operations,

[tex]x^2-10x-11=-36[/tex]

[tex]x^2-10x+25=0[/tex]

3. Factor and solve,

Now that has the simplified version of the equation, one should factor it. Rewrite the quadratic expression as a product of two linear expressions,

[tex]x^2-10x+25=0[/tex]

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

Use the zero product property to solve this expression. The zero product property states that any number times zero equals zero. Since ([tex](x-5)^2[/tex]) is just ([tex]x-5[/tex]) multiplied by itself, thus, when solving, one can ignore the square part of the equation:

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

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

Inverse operations,

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

[tex]x=5[/tex]

Answer:

44 sq. ft

Step-by-step explanation:

5(2^2) = 20

4(3x2) = 24

20+24 = 44

Answer:

1/5, 1/3, 0.4, 1/2

Step-by-step explanation:

1/5 = 0.2

1/3 = 0.33

1/2 = 0.5

Answer:

$2.20

Step-by-step explanation:

The tip is 10% of $22, or 0.1 * 22 = 2.2

So $2.20 (we can add a hidden 0 on the end)

Answer:

18√2

Step-by-step explanation:

2√3 x 3√6

2 x 3 x (√6 x √3)

=> 6√18

=> 6√(3x3x2)

=> 6 x 3√2

=> 18√2

Answer:

30 is the nearest tenth of 26

Answer:

yes it is true

Step-by-step explanation:

write the first five elements then write their cubes then write the cubes in the same form

for eg:

4³=16= 3×5+1= 3n+1

7³=49=3×16 +1= 3n + 1

and so on till the fifth element...

Answer:

done the first 3

Step-by-step explanation:

5×-3=-15

2×4=8

3×-5=-15

(-15+8)²+-15

(-7)²+-15

-49-15

=-74

(2×-3×-6)²-5(4)

(36)²-20

1296-20

=1276

(-3×4×-5)+3(4)³

60+192

=252

Answers;

1. {(5x + 2y)}^{2} + 3z \\ {(5( - 3) + 2(4))}^{2} + 3( - 5) \\ {( - 15 + 8)}^{2} - 15 \\ {( - 7)}^{2} - 15 \\ 49 - 15 \\ 34 \\ \\ 2. \: 2 {(xz)}^{2} - 5y \\ 2 ({( - 3)( - 5)})^{2} - 5(4) \\ 2 {(15)}^{2} - 20 \\ 2(225) - 20 \\ 450 - 20 \\ 430

Answer:

9,-9

Step-by-step explanation:

Because your opponent is in the positive while you are in the negative

Answer:

She makes $2,250/day

Step-by-step explanation:

$75 x 6 = $450 (amount of patients seen)

$450 x 6 = $2,700 (amount of hours she works)

$2,700 - $450 = $2,250 (the cost of the building, reception desk, & insurance)

We are given that the doctor charges $75 for each patient

In each she sees an average of 6 patients so,

Charge each hr = $75(6) = $450

For each hr she receives $450

So, for 6 hrs she receives = $450(6) = $2700

She pays for all the stuff = $200 + $200 + $50 = $450

Profit = Selling Price - Cost Price

Profit = $2700 - $450

Profit = $2250

Hi ;-)

Equation 1°

[tex]2(x+1)=-8x+8(x-2)\\\\2x+2=-8x+8x-16\\\\2x+8x-8x=-16-2\\\\2x=-18 \ \ /:2\\\\\huge\boxed{x=-9}[/tex]

Equation 2°

[tex]4(7+2x)=-2(x+4)+4x\\\\28+8x=-2x-8+4x\\\\8x+2x-4x=-8-28\\\\6x=-36 \ \ /:6\\\\\huge\boxed{x=-6}[/tex]

3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609433057270365759591953092186117381932611793105118548074462379962749567351885752724891227938183011949129833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901224953430146549585371050792279689258923542019956112129021960864034418159813629774771309960518707211349999998372978049951059731732816096318595024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303598253490428755468731159562863882353787593751957781857780532171226806613001927876611195909216420198938095257201065485863278865936153381827968230301952035301852968995773622599413891249721775283479131515574857242454150695950829533116861727855889075098381754637464939319255060400927701671139009848824012858361603563707660104710181942955596198946767837449448255379774726847104047534646208046684259069491293313677028989152104752162056966024058038150193511253382430035587640247496473263914199272604269922796782354781636009341721641219924586315030286182974555706749838505494588586926995690927210797509302955321165344987202755960236480665499119881834797753566369807426542527862551818417574672890977772793800081647060016145249192173217214772350141441973568548161361157352552133475741849468438523323907394143334547762416862518983569485562099219222184272550254256887671790494601653466804988627232791786085784383827967976681454100953883786360950680064225125205117392984896084128488626945604241965285022210661186306744278622039194945047123713786960956364371917287467764657573962413890865832645995813390478027590099465764078951269468398352595709825822620522489407726719478268482601

Answer:

-33/80

Step-by-step explanation:

3/20 - 9/16

(4)(3/20) - (9/16)(5)

12/80 - 45/80

= -33/80

Answer:

RT = 25.5

Step-by-step explanation:

RT = RS + ST = 17 + 8.5 = 25.5

Answer:

a. hundreds

55,600

b. thousandths

55,553.65500

Answer:

13:9 with 9 being unshaded

Step-by-step explanation:

i drew a similar grid, shaded them in in the way you specified, then counted the squares on either side. the i put the numbers in a fraction and simplified

[tex]\\ \qquad\quad\sf\longmapsto 4x+9y-3=0[/tex]

[tex]\\ \qquad\quad\sf\longmapsto 4(-m)+9(3)-3=0[/tex]

[tex]\\ \qquad\quad\sf\longmapsto -4m+27-3=0[/tex]

[tex]\\ \qquad\quad\sf\longmapsto -4m+24=0[/tex]

[tex]\\ \qquad\quad\sf\longmapsto -4m=-24[/tex]

[tex]\\ \qquad\quad\sf\longmapsto m=\dfrac{-24}{-4}[/tex]

[tex]\\ \qquad\quad\sf\longmapsto m=6[/tex]

Step-by-step explanation:

[tex] \frac{10}{6} \\ \frac{15}{9} \\ \frac{20}{12} [/tex]

Answer:

C

Step-by-step explanation:

We want to solve the inequality:

[tex]\displaystyle 5.1(3 + 2.2x) > -14.25 - 6(1.7x+4)[/tex]

Distribute:

[tex](15.3+11.22x) > -14.25 + (-10.2x-24)[/tex]

Combine like terms:

[tex]15.3 + 11.22x > -10.2x-38.25[/tex]

We can add 10.2x to both sides:

[tex]15.3 + 21.42x > -38.25[/tex]

Subtract 15.3 from both sides:

[tex]21.42x > -53.55[/tex]

And divide both sides by 21.42. Hence:

[tex]\displaystyle x > -2.5[/tex]

This means all values greater than -2.5. Hence, in interval notation:

[tex](-2.5, \infty)[/tex]

In conclusion, our answer is C.

Answer:

960

Step-by-step explanation:

x=0.6x+384

0.4x=384

960

Answer:

960

Step-by-step explanation:

x = 0.6x + 384

Subtract 0.6x in both sides:

0.4x = 384

Divide both sides by 0.4:

x = 384/0.4

x = 960

Answer:

Sinθ = Opposite/hypotenuse

[tex] \sin(21) = \frac{x}{22} \\ 0.358 = \frac{x}{22} \\ x = 22 \times 0.358 \\ x = 7.88[/tex]

I hope I helped you^_^