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Algebraically find the slope and the y-intercept of 3y - 8 = 2x.

thank you!!

Answer:

Step-by-step explanation:

Answer:

Where the line is going

Step-by-step explanation:

Put attention next time

Ps. Just check if its on x or on the y

The slope of line that passes through the points (1, -6) and (-2, –8) is 2/3.

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

y = mx + b

In which the coefficients are described as follows:

• The coefficient m is the slope of the function, representing the rate of change of the function.

• The coefficient b is the y-intercept of the function, representing the value of y when the function crosses the y-axis(x = 0).

Here the points are(1, -6) and (-2, –8) :

and it is to find the equation of line passing through these points :

Now using slope formula to find the slope of line m :

m = (y₂-y₁)/ (x₂-x₁)

m = (-8+6)/(-2-1)

m = -2/-3

m = 2/3

Therefore, the slope of line that passes through the points (1, -6) and (-2, –8) is 2/3.

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Answer:

y = 120°

Step-by-step explanation:

If AC ≅ AD and BC ≅ BD then the shape of the figure is a kite.

Therefore, ∠D ≅ ∠C

Sum of interior angles in a kite = 360°

⇒ ∠A + ∠B + ∠C + ∠D = 360°

⇒ 120° + ∠B + 100° + 100° = 360°

⇒ ∠B = 40°

Sum of interior angles of a triangle = 180°

⇒ ∠B + ∠BDY + ∠y = 180°

⇒ 40° + 20° + ∠y = 180°

⇒ ∠y = 120°

5 feet is the greatest distance that a person could be from the lamp and be detected.

A circle is defined as round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center).

Since we have given that

The equation is :

[tex](x+15)^2+(y-12)^2=25[/tex]

It is the equation of circle in which center is (h,k) i.e. ( 15,12)

The general equation of circle is given by

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Here, the radius 'r' is given by

[tex]r^2=25[/tex]

[tex]r=\sqrt{25[/tex]

[tex]r=5[/tex]

Here, the greatest distance a person could be from the lamp and be detected is represented by radius i.e. r = 5 feet.

Hence, 5 feet is the greatest distance that a person could be from the lamp and be detected.

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Answer:

B

Step-by-step explanation:

$20-$11.29= 8.71 change he wil get back

Answer:

Choice C

Step-by-step explanation:

This is like a matching question. Here's what I mean by this. We know Triangle BCA and Triange JKL are congruent. So, what we have to do is match the side lengths together.

So the first side of BCA matches with JKL, the second side of BCA matches with JKL, the third side of BCA matches with JKL.

So first side:

BC is congruent  to JK

So second side:

CA is congruent  to KL

So third side:

JL is congruent  to BA

The third side is one of our answer choices.

That answer choice is C.

Answer:

c

Step-by-step explanation:

Step-by-step explanation:

Adjacent sides of a square and a rectangle are always perpendicular to each other. Sides of the right-angled triangle enclosing the right angle are perpendicular to each other.

Answer:

[tex]328units^2[/tex]

Step-by-step explanation:

First off,  I do want to say that you could word this more easily.

98 is the perimeter. length is 41. width is 8.

the area is length*width for rectangles.

98-41=57

57-41=16

16/2=8

8*41=328 units^2

Answer:

the shirt should be $20 and the pants $30

Answer:

Equations: 40-7=33 and 33÷11=3

Step-by-step explanation:

40-7=33

Since there are 3 sides,(q) then you do 33 divided by 3=11.

Equations: 40-7=33

And

33÷11=3

Answer:

∠Z ≅ ∠G and XZ ≅ FG or ∠Z ≅ ∠G and XY ≅ FE  are the additional information could be used to prove that ΔXYZ ≅ ΔFEG using ASA or AAS.

The additional information to prove that ΔXYZ ≅ ΔFEG using ASA or AAS

is ∠Z ≅ ∠G and XY ≅ FE

Option E is the correct answer.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

ΔXYZ ≅ ΔFEG

We see that,

∠X and ∠F are equal

To prove that ΔXYZ ≅ ΔFEG using ASA or AAS.

We need one more congruent angle and one corresponding side.

∠Z ≅ ∠G and XY ≅ FE can be used to prove this.

Now,

∠X = ∠F (angle)  (given)

∠Z ≅ ∠G (angle)

XY ≅ FE (side)

ΔXYZ ≅ ΔFEG

Thus,

The additional information is:

∠Z ≅ ∠G and XY ≅ FE

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[tex]y=sin(x)\implies \cfrac{dy}{dx}=\boxed{cos(x)} \\\\[-0.35em] ~\dotfill\\\\ ycot(x)\implies \stackrel{y}{~~\begin{matrix} sin(x) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }\cfrac{cos(x)}{~~\begin{matrix} sin(x) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }\implies \boxed{cos(x)}[/tex]

Answer to first four-

first one- 2f+2f=60

4f=60

f=15

second one-18+2d=38

2d=20

d=10

(short side is 9)

third one-2a+a+5+a+5=26

4a+10=26

a=4

long side is 9

short side is 8

fourth one-3xy+3xy+xy=63

7xy=63

xy=9

long side is 27

Answer:

The answer would be 2x+4+3x+4, 5x+8, and 2(2x+4) +x

Step-by-step explanation:

Step 1. Simplify 2x+4+3x+4 into 5x (combine the x's) +8 (combine the 2 4's)
Step 2. Simplify 2(2x+4)= x into 4x + 8 + x (<-- distribute the 2 to the 2x and 4) and 4x+x would equal 5x meaning 5x + 8.
I hope that this helps! :)

[tex]\text{Given that,}~ f(x) =2x-3\\\\\dfrac{f(a+h) - f(a)}{h}\\\\=\dfrac{(2(a+h)-3)-(2a-3)}{h}\\\\=\dfrac{2a+2h-3-2a+3}h}\\\\=\dfrac{2h}{h}\\\\=2[/tex]

Answer:

17+y

Step-by-step explanation:

Answer:

2/9

Step-by-step explanation:

The sum of two numbers is 5/9 can be expressed as:

[tex]\displaystyle \large{x+y=\dfrac{5}{9}}[/tex]

One of the numbers is 1/3. Find the other - this means that either x or y is 1/3 but that doesn’t matter as we can either let x = 1/3 or y = 1/3 via property:

[tex]\displaystyle \large{x+y = y+x}[/tex]

Hence, let x = 1/3:

[tex]\displaystyle \large{\dfrac{1}{3}+y=\dfrac{5}{9}}[/tex]

Solve for y - subtract both sides by 1/3:

[tex]\displaystyle \large{\dfrac{1}{3}-\dfrac{1}{3}+y=\dfrac{5}{9}-\dfrac{1}{3}}\\\displaystyle \large{y=\dfrac{5}{9}-\dfrac{1}{3}}[/tex]

We know that we can only evaluate the fractions if both have same denominator so what we have to do is to multiply 1/3 by 3 for both top and bottom:

[tex]\displaystyle \large{y=\dfrac{5}{9}-\dfrac{1\cdot 3}{3\cdot 3}}\\\displaystyle \large{y=\dfrac{5}{9}-\dfrac{3}{9}}\\\displaystyle \large{y=\dfrac{2}{9}}[/tex]

Therefore, the other number is 2/9

Answer:

The other number is 2/9

Step-by-step explanation:

"a" is the other number

The equation:

[tex]a+\frac{1}{3} =\frac{5}{9}[/tex]

Then

[tex]a=\frac{5}{9} -\frac{1}{3} =\frac{15-9}{27} =\frac{6}{27}[/tex]

simplifying the fraction:

[tex]a = \frac{2}{9}[/tex]

Hope this helps

Answer:

75%

Step-by-step explanation:

75% of 200 is 150

Answer:

75% since [tex]50 + 50 + 50 = 150[/tex] which is [tex]3[/tex] quarters of [tex]200[/tex]

Please mark brainliest.

Answer:

(x + 42)(x - 42)

Step-by-step explanation:

Keep this in mind :

In this case,

So, by factorizing,

★a²-b²=(a+b)(a-b)

So

a=x ,b=42

Done!

Answer:

284*20

Step-by-step explanation:

since there are 284 boxes of each 20 books, 1box = 20 books then 284 boxes = (284*20) books

If factor delivered 284 boxes of books to stores and 20 books in each box then the total number of books deliver by factor are 5680.

Two or more expressions with an Equal sign is called as Equation.

Given that a factor delivered 284 boxes of books to stores.

There are 20 books in each box.

We have to find the number of books the factor deliver

To find this we have to multiply the number of boxes with the number of books in a box

Number of books deliver = 284×20

Two hundred eighty four times of twenty

Number of books deliver =5680

Hence, if factor delivered 284 boxes of books to stores and 20 books in each box then the total number of books deliver by factor are 5680.

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Answer:

r=4.998

Step-by-step explanation:

The equation for volume of a sphere is [tex]V = \frac{4}{3} \pi r^3[/tex].

We can subsatute 523 in for V and then solve for r by multiplying both sides by 3 and then dividing both sides by 4pi.  Then, take the cube root of each side and you will get r.

Answer:

-2.1

Step-by-step explanation:

its a 0.1 step.

hope you understand

Answer:

7:63

Step-by-step explanation:

It's a 1 to 9 ratio, which means the second number is 9 times bigger.

To make it equivalent, you need to make 7 9 times bigger as well.

7x9=63

Answer: 7:63

[tex]\text{Given that,} \sin x = \dfrac{\sqrt 5}3,~~ \text{and}~~~ \sin y =\dfrac{\sqrt 2}2\\\\\\~~~~~~~\sin x = \dfrac{\sqrt 5}3\\\\\implies \sin^2 x = \dfrac 59\\\\\implies 1- \cos^2 x = \dfrac 59\\\\\implies \cos^2 x =1- \dfrac59 \\\\\implies \cos^2 x = \dfrac 49\\\\\implies \cos x = \dfrac 23~~~~~~~;[\text{In quadrant I, all ratios are positive.}]\\\\\\\\[/tex]

[tex]~~~~~~\sin y =\dfrac{\sqrt{2}}2\\ \\\implies \sin y = \dfrac 1{\sqrt 2}\\\\\implies \sin^2 y = \dfrac 12\\\\\implies 1-\cos^2 y = \dfrac 12\\\\\implies \cos^2 y = 1-\dfrac 12=\dfrac 12\\\\\implies \cos y = \dfrac 1{\sqrt 2}\\\\\\[/tex]

[tex]\text{Now,}\\\\\cos(x+y) = \cos x \cos y - \sin x \sin y\\\\\\~~~~~~~~~~~~~~=\dfrac 23 \cdot \dfrac 1{\sqrt 2}- \dfrac{\sqrt 5}3 \cdot \dfrac 1{\sqrt 2}\\\\\\~~~~~~~~~~~~~~=\dfrac{2- \sqrt 5}{3\sqrt 2}\\\\\\~~~~~~~~~~~~~~=\dfrac{\sqrt2\left(2 -\sqrt 5 \right)}6[/tex]

By using the formula for the area of a cone, we will get:

First, let's find the area of the original cone. Remember that for a cone of radius R and height H, the surface area is:

A  = pi*R^2 + pi*R*H

Then for the original cone where:

R = 10cm

H = 20cm

The area is:

A = 3.14*(10cm)^2 + 3.14*10cm*20cm = 942 cm^2

Now, we remove a smaller cone at 6 cm from the vertex, so we are removing a cone with height of 6 cm, and the radius of this cone is given by:

R' = R*(H'/H) = 10cm*(6cm/20cm) = 3cm

So the area of the removed cone is:

A' = 3.14*( (3cm)^2 + 3cm*6cm) = 84.78cm^2

The final area of the mute will be equal to the difference between the area of the original cone and the area of the removed cone, plus the area of the top cross-section (a circle of radius of 3cm)

A'' = 942 cm^2 - 84.78cm^2 + 3.14*(3cm)^2 = 885.48cm^2

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The milk can is in the shape of a cylinder.

The surface area of cylinder is defined as the sum of curved surface and the two circular bases of the cylinder;

‎ㅤ‎ㅤ‎ㅤ➙ (curved surface ) + 2(base area )

‎ㅤ‎ㅤ‎ㅤ➙ 2πrh + 2πr²

‎ㅤ‎ㅤ‎ㅤ➙ 2πr( h + r )

Here, in this question we have;

Therefore, Surface Area ( S.A ) :

➝ S.A = 2πr( r + h )

➝ S.A = 2 × π × 1 ( 1 + 6 )

➝ S.A = 2π ( 7 )

➝ S.A = 2 × 3.14 × 7

➝ S.A = 14 × 3.14

➝ S.A = 43.96cm²

Answer:

Surface area of cylindrical milk can is 43.96cm²

Step-by-step explanation:

Given :-

To find:-

Solution:-

formula for surface area cylindrical milk can :-

2πr(h+r)

putting the known values ,

2 × 3.14 × 1 (6+1) cm²

Surface area :- 43.96 cm²