Solve the equation
3x+1+10x=x+4

Given:

The point [tex]P\left(\dfrac{3}{4},\dfrac{5}{12}\right)[/tex] divides the line segment joining points [tex]A\left(\dfrac{1}{2},\dfrac{3}{2}\right)[/tex] and [tex]B(2,-5)[/tex].

To find:

The ratio in which he point P divides the segment AB.

Solution:

Section formula: If a point divides a segment in m:n, then the coordinates of that point are,

[tex]Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)[/tex]

Let point P divides the segment AB in m:n. Then by using the section formula, we get

[tex]\left(\dfrac{3}{4},\dfrac{5}{12}\right)=\left(\dfrac{m(2)+n(\dfrac{1}{2})}{m+n},\dfrac{m(-5)+n(\dfrac{3}{2})}{m+n}\right)[/tex]

[tex]\left(\dfrac{3}{4},\dfrac{5}{12}\right)=\left(\dfrac{2m+\dfrac{n}{2}}{m+n},\dfrac{-5m+\dfrac{3n}{2}}{m+n}\right)[/tex]

On comparing both sides, we get

[tex]\dfrac{3}{4}=\dfrac{2m+\dfrac{n}{2}}{m+n}[/tex]

[tex]\dfrac{3}{4}(m+n)=\dfrac{4m+n}{2}[/tex]

Multiply both sides by 4.

[tex]3(m+n)=2(4m+n)[/tex]

[tex]3m+3n=8m+2n[/tex]

[tex]3n-2n=8m-3m[/tex]

[tex]n=5m[/tex]

It can be written as

[tex]\dfrac{1}{5}=\dfrac{m}{n}[/tex]

[tex]1:5=m:n[/tex]

Therefore, the point P divides the line segment AB in 1:5.

Answer:

x = 70

Step-by-step explanation:

As the problem states, ∠ABD and ∠DBC are supplementary angles. This means they have a sum of 180°. Since we know this, we can set up an equation to solve for x.

x + 110 = 180

x = 70

Answer: yes

Step-by-step explanation:

Answer:

i'm sure its 16

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

44+32=76

180-76=104

104+36=140

180-140=40

D)40

Answer:

No solution

Step-by-step explanation:

Move all the variables to one side and all the numbers to the other side.

0.5y-2*2/5=1/2y+2.4

-2*2/5=1/2y+2.4-0.5y

-2*2/5-2.4=0

thus there is no solution

Answer:

Area = 30.3 ft²

Step-by-step explanation:

Area = area of a semicircle + area of a rectangle

= (½*πr²) + L*W

Where,

radius (r) = ½ of 4 = 2 ft

Length (L) = 6 ft

Width (W) = 4 ft

Plug in the values

Area = (½*π*2²) + (6*4)

Area = 30.3 ft² (nearest tenth)

Answer:

[tex] \sqrt{32} + 3[/tex]

[tex] - \sqrt{32} + 3[/tex]

Step-by-step explanation:

Use foil method

[tex](y - 3) {}^{2} [/tex]

[tex](y - 3)( y - 3)[/tex]

First multiply y and y

[tex]y \times y = {y}^{2} [/tex]

Next Multiply Outer term y and -3.

[tex]y \times - 3 = - 3y[/tex]

After that ), Multily inner tern -3 and y

[tex] - 3 \times y = - 3y[/tex]

Finally multiply -3 and -3 and you get 9.

Then combine all

[tex] {y}^{2} - 6y + 9 - 32 [/tex]

[tex] {y}^{2} - 6y - 23[/tex]

Now I'm going to complete the square. First get only the y value on the left side so we first set this equal to zero then move add 23 on both sides.

[tex] {y}^{2} - 6y - 23 = 0[/tex]

Add 23

[tex]y {}^{2} - 6y = 23[/tex]

Apply formula

[tex] (\frac{b}{2} ) {}^{2} [/tex]

where b is the coefficient.

plug it in

[tex]( \frac{ - 6}{2}) {}^{2} [/tex]

Which is -3 squared which equal 9.

Then add 9 on both sides

[tex] {y}^{2} - 6y + 9 = 23 + 9[/tex]

23+9=32

Now let factor the left side

the only number that adds to -6 and multiply to 9 is

-3 so we would rewrite the left side as

[tex](x - 3) {}^{2} = 32[/tex]

Now take the sqr root of 32

[tex] \sqrt{(x - 3) {}^{2} } = \sqrt{32} [/tex]

Then add 3 on both sides

[tex]x + - 3 + 3 = \sqrt{32} + 3[/tex]

A sqr root of a number can be positive or negative so

the answer is

[tex] - \sqrt{32} + 3[/tex]

[tex] \sqrt{32} + 3[/tex]

Answer:

18

Step-by-step explanation:

5d/9=10

5d=10*9

5d=90

d=90/5

d=18

Answer:

5000x3.00= total sales  15000 x 16% or.16

= 2400

Step-by-step explanation:

1.Find Gross Sales

2. Get retail sales  3.00 x 5000

3. Total Sales times commission  15000 x .16

Answer:

The inequality that will be used would be

x + 22 <= 55

Answer:

your answer is 4.50. the total of cartons eggs is 3.16+ the total of turkey 27.96+ the jar 4.38= 35.50 now we can do the math 40-35.50= 4.50. I hope it helps!

Step-by-step explanation:

it is

4.50

why os ot because 9 did the math

Answer:

Step-by-step explanation:

(This is technically a personal opinion question) In MY opinion all government run things from libraries to schools to the military come from taxes. If you don't agree with how the government spends the money that you pay in taxes yet enjoy/use government facilities then you have no room to complain and not pay your taxes.

Answer:

I'm not sure but I think u should divide and get 12 kg I am so unsure so pls make sure if it's correct.

Answer:

1/12

Step-by-step explanation:

5/60 divide both sides by 5 is equal to 1/12

Answer:

KM=LN  Given

KM=KL+LM  Segment Addition Postulate

LN=LM+MN  Segment Addition Postulate

KL+LM=LM+MN  Substitution Property of Equality

KL=MN  Subtraction Property of Equality this is the formula :)

Step-by-step explanation:

Answer:

42

Step-by-step explanation:

3/(3+x-6)=5/(5+x)

cross multiply

3(5+x)=5(3+x-6)

15+3x=15+5x-30

15+3x=5x-15

15+15=5x-3x

30=2x

x=15

That means KQ=15 and PK=15-6=9.  Now we have to find PQ, which is the same as JM.  We’ll call that length b.

5/15=6/b

cross multiply

5b=90

b=18

15+9+18=42

Answer:

[tex]cos\ V = \frac{2\sqrt{29}}{29}[/tex]

Step-by-step explanation:

Given

The attached triangle

Required

Find cos V

In trigonometry:

[tex]cos\theta = \frac{Adjacent}{Hypotenuse}[/tex]

In this case:

[tex]cos V= \frac{TV}{UV}[/tex]

Where

[tex]TV = 6[/tex]

and

[tex]UV^2 = TV^2 + TU^2[/tex] -- Pythagoras

[tex]UV^2 = 6^2 + 15^2[/tex]

[tex]UV^2 = 261[/tex]

Take square roots

[tex]UV = \sqrt{261[/tex]

[tex]UV = \sqrt{9*29[/tex]

[tex]UV = \sqrt{9} *\sqrt{29[/tex]

[tex]UV = 3\sqrt{29[/tex]

So:

[tex]cos V= \frac{TV}{UV}[/tex]

[tex]cos\ V = \frac{6}{3\sqrt{29}}[/tex]

[tex]cos\ V = \frac{2}{\sqrt{29}}[/tex]

Rationalize:

[tex]cos\ V = \frac{2}{\sqrt{29}}*\frac{\sqrt{29}}{\sqrt{29}}[/tex]

[tex]cos\ V = \frac{2\sqrt{29}}{29}[/tex]

Answer:

36

Step-by-step explanation:

Its 36 because normally someone would do 18+20=38 but you have to remeber in the problem it says 37! so 2 people didn't want anything, minus that and you get 36.

Answer:

$185 per person

Step-by-step explanation:

22,200/120=185

Answer:

the sine Is 5/13

Step-by-step explanation:

use the trigonometric identity : sin^2+ cos^2 = 1

so the sine Is sqrt(1-(12/13)^2) = 5/13

sqrt means Square root btw

Answer:

x=16

Step-by-step explanation:

so you know that the other side of the right traingle is 15

so x2+18x+81=225+144+x2

18x=288

x=16

Answer:

C on edge 2021

Step-by-step explanation:

Answer:

y⁸/x¹⁰

[tex] \\ [/tex]

Step-by-step explanation:

[tex] \sf{\large{( \frac{ {x}^{ - 4}y }{ {x}^{ - 9} {y}^{5} } ) ^{2} }}[/tex]

[tex] \large{ \sf{= \frac{ {x}^{ - 4 \times 2} {y}^{2} }{ {x}^{ - 9 \times 2} {y}^{5 \times 2} } }}[/tex]

[tex] \large{ \sf{= \frac{ {x}^{ - 8} {y}^{2} }{ {x}^{ - 18} {y}^{10} } }}[/tex]

[tex] \large{ \sf{ = {x}^{ - 8 - ( - 18)} {y}^{2 - 10} }}[/tex]

[tex] \large{ \sf{ = {x}^{ - 8 + 18} {y}^{ - 8} }}[/tex]

[tex] \large{ \sf{ = {x}^{10} {y}^{ - 8} }}[/tex]

[tex] \large{ \sf{ = \frac{ {x}^{10} }{ {y}^{8} } }} [/tex]

[tex] \large{ \sf{ = \frac{ {y}^{8} }{ {x}^{10} } }}[/tex]

Answer:

22 degrees

Step-by-step explanation:

The angle that measures 158 degrees and angle u are supplementary angles, meaning they add up to 180 degrees.

Angle s and angle u are corresponding angles, meaning that they are congruent.

This means that the angle that measures 158 degrees and angle s are supplementary as well. Knowing this, we can construct the following equation:

[tex]180=158+s[/tex]

Subtract both sides by 158

[tex]180-158=158+s-158\\22=s[/tex]

Therefore, angle s has a measure of 22 degrees.

I hope this helps!

Answer:

shed height = 12 feet

shed width = 28 feet

Step-by-step explanation:

3/4"=3'   then 1"=4'

3" tall=4x3"=12'

7" wide=4x7"= 28'

Answer:

Raul traveled 31.25 miles an from 1:50 to 4:20. So, subtract those, you get 2:30. Turn 2:30 into a decimal (2.30) and now divide 31.25 by 2.30. the answer is 13.59 rounded That number turned into a Fraction is about 13 miles an hour.

Step-by-step explanation:

Answer: A

Step-by-step explanation:

the difference between the start time and end time is 2hrs and 30mins

So this means we have to multiply the number and add half of it.

12[tex]\frac{1}{2}[/tex] + 12[tex]\frac{1}{2}[/tex]+ 6[tex]\frac{1}{4}[/tex]= 31[tex]\frac{1}{4}[/tex]

(now can get a brainliest lol)