How do you find the equation of a line of a triangle when given the area and one set of coordinates?

Given:

y is directly proportional to x.

[tex]y=30[/tex] when [tex]x=5[/tex]

To find:

The equation that connects y with x.

Solution:

It is given that, y is directly proportional to x. So,

[tex]y\propto x[/tex]

[tex]y=kx[/tex]                     ...(i)

Where, k is the constant of proportionality.

We have, [tex]y=30[/tex] when [tex]x=5[/tex]. Substituting these values in (i), we get

[tex]30=k(5)[/tex]

Divide both sides by 5.

[tex]\dfrac{30}{5}=k[/tex]

[tex]6=k[/tex]

Substituting [tex]k=6[/tex] in (i), we get

[tex]y=6x[/tex]  

Therefore, the required equation is [tex]y=6x[/tex].

Answer:The expression that can be used to convert 100 USD to Japanese Yen is 100 USD = 100/Y Japanese Yen.

Step-by-step explanation:

Answer:

L = 31.5 w = (4/7)31.5 = 18 p = 2 * 31.5 + 2 * 18 A = 31.5 * 18

Step-by-step explanation:

Answer: [tex]167.5\ in.^3[/tex]

Step-by-step explanation:

Given

Height of paper cone [tex]h=10\ in.[/tex]

Radius of cone [tex]r=4\ in.[/tex]

The volume of the cone is given by

[tex]\Rightarrow V=\dfrac{1}{3}\pi r^2h[/tex]

Insert the values

[tex]\Rightarrow V=\dfrac{1}{3}\times 3.14\times 4^2\times 10\\\\\Rightarrow V=167.5\ in.^3[/tex]

Thus, the volume of the cone is [tex]167.5\ in.^3[/tex]

Answer:

hi, the answer is Nu5000

250×20=5000

Step-by-step explanation:

(4/3)–1 = 3/4 and (1/4)–1 = 4/1

now we have,

(3/4 - 4)–1 = (-13/4)–1

= -4/13

Answer:

If i recall Maria collected 34 cicadas

Answer:

17 Cicadas

Step-by-step explanation:

62 - 28 divided by two will give us the amount Maria collected.

62 - 28 = 34

34/2 = 17

Maria had 17 cicadas.

How to verify:

17 + 28 + 17 Should equal 62

34 + 28 = 62

Answer:

The goal to reduce the amount of energy used to provide products and services; saving the earth vibes.

Answer:

1499

Step-by-step explanation:

Given that :

New discounted price = 1274

Let original price = p

Reduction in original price = 225

Original price is the sum of the reduction and the new discounted price

The Original price = Reduction in original price + new discounted price

P = 225 + 1274

P = 1499

Answer:

(0,0), (0,9), (9,0)

Step-by-step explanation:

The matrix corresponding vertices are:

(0,0)

(0,3)

(3,0)

Rosa scales by 3T, so we need to multiply each point by 3.

(3*0, 3*0)

(0*3, 3*3)

(3*3, 0*3)

=

(0,0)

(0,9)

(9,0)

last answer choice is right.

pls mark me brainly

The vertices of the scaled triangle, 3T is, (0, 0), (0, 9), (9, 0).

The scale factor defines a variable in a ratio of two different measurements.

Sometimes drawings of large models are represented in a scale factor of a smaller unit.

Given, A matrix [tex]T=\begin{bmatrix}0 & 0 & 3\\0 & 3 & 0\end{bmatrix}[/tex] represents the vertices of a triangle.

Let, ABC be the triangle,

So, A(0, 0), B(0, 3), C(3, 0).

Now, If [tex]T=\begin{bmatrix}0 & 0 & 3\\0 & 3 & 0\end{bmatrix}[/tex], Then [tex]3T=3\begin{bmatrix}0 & 0 & 3\\0 & 3 & 0\end{bmatrix}[/tex].

Therefore, [tex]3T=\begin{bmatrix}0 & 0 & 9\\0 & 9 & 0\end{bmatrix}[/tex].

Hence, The new vertices are, (0, 0), (0, 9), (9, 0).

learn more about matrices here :

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Answer:

The answer is E.

Step-by-step explanation:

A quadrilateral that has only one pair of parallel sides is called a Trapezoid.

Answer:

3 marbles

Step-by-step explanation:

and they have died inside too

Answer:

31 batches

Step-by-step explanation:

Find how many batches of orange punch smoothies he can make by dividing 560 by 18:

560/18

= 31.11

Since we can only have a whole number answer, round down.

So, he can make 31 batches of orange punch smoothies.

fig 3 would take 18 triangle

fig 4 would take 30 small triangles

if its wrong i am sorry

Answer:

Answer:

S = {(0, 5), (0, - 5), (3, 4), (3, -4), (-3, 4), (-3, -4), (4, 3), (4, -3), (-4, 3), (-4, -3), (5,0), (-5, 0) }

Step-by-step explanation:

Remember that the distance between two points (a, b) and (c, d) is given by:

[tex]distance = \sqrt{(a - c)^2 + (b - d)^2}[/tex]

So, here we have that the distance between the point (x, y) and the origin, (0, 0) must have a magnitude of 5 units, then we want to solve:

[tex]5 = \sqrt{(x - 0)^2 + (y - 0)^2} \\5 = \sqrt{x^2 + y^2}[/tex]

If we square both sides, we get

[tex]5^2 = (\sqrt{x^2 + y^2} )^2\\25 = x^2 + y^2[/tex]

Now we want to find all the points (x, y) that meet this condition, suc that:

x ∈ Z

y ∈ Z

So both x and y must be integers.

So here we can just play with different values of x and y.

For example, if we define:

x = 0 we get:

25 = 0^2 + y^2

25 = y^2

√25 = y

Then we can have y = 5 or  y = -5

from this we got two points:

(0, 5) and (0, - 5)

if x = 1 we have:

25 = 1^2 + y^2

25 - 1 = y^2

24 = y^2

There is no integer such that its square is equal to 24, so we can stop here.

if x = 2 or - 2, we have:

25 = 2^2 + y^2

25 = 4 + y^2

25 -4 = 21 = y^2

Again, there is no integer such that its square is equal to 21, so we can stop here.

if x = +3 or -3, we have:

25 = 3^2 + y^2

25 = 9 + y^2

25 - 9 = 16 = y^2

√16 = y

then we can have y = 4 or y = -4

from this we got four points:

(3, 4)

(-3, 4)

(3, -4)

(-3, -4)

And for symmetry, if x = 4 or -4 we have the points:

(-4, 3)

(4, 3)

(-4, -3)

(4, -3)

finally, again for symmetry, if we take x = 5 or x = -5 we have the points:

(5,0)

(-5, 0)

Concluding, the set of all possible values (x, y) is:

S = {(0, 5), (0, - 5), (3, 4), (3, -4), (-3, 4), (-3, -4), (4, 3), (4, -3), (-4, 3), (-4, -3), (5,0), (-5, 0) }

Step-by-step explanation:

[tex]\longmapsto \rm \dfrac{5x}{7} - \dfrac{x}{14} = \dfrac{9}{7} \\ [/tex]

[tex]\longmapsto \rm \dfrac{10x + x}{14} = \dfrac{9}{7} \\ [/tex]

[tex]\longmapsto \rm \dfrac{11x}{14} = \dfrac{9}{7} \\ [/tex]

→ 11x(7) = 14(9)

→ 77x = 126

→ x = 126 ÷ 77

→ x = 1.63

Answer:

True is the correct answer

Answer:

I believe the answer is true

Answer:

$375.32

Step-by-step explanation:

100% - 40% = 80%

80/100 = 0.8 (multiplier)

521.28 x 0.8 = 417.024

417.024 to 417.02 (2 d.p.)

100 - 10 = (ans)/100 = 0.9

417.02 x 0.9 = 375.318

$375.32

Step 1: Find the sales price

The surfboard was marked down 40% of its original price, $521.28.

0.40(521.28) = 208.512

521.28 - 208.512 = 312.768

Step 2: Find the final price

We add the tax on the sales price, not the original price. The tax is 10% in this case.

0.10(312.768) = 31.2768

312.768 + 31.2768 = 344.0448

Final price = $344.04

---I did not round until the end in this case, but rounding at every step leads to an answer of $344.05

Hope this helps!

Answer: hello your question is vague hence i will provide a more general answer

Area of a right angled triangle = 1/2 * b * h

Step-by-step explanation:

For a right- angled triangle; the sum of squares of the opposite and adjacent sides = square of the longest side ( i.e. hypothenuse )

hence the Area of a right angled triangle = 1/2 * b * h

where : b = adjacent , h = opposite side

Answer:

second option

Step-by-step explanation:

y + y + 38 = 180 degree ( sum of interior angle of a triangle is 180 degree)

2y = 180 - 38

y = 142/2

y = 71 degree

Answer:

71 degrees

Step-by-step explanation:

Hi there!

All the interior angles of a triangle add up to 180 degrees.

Knowing this, we can construct the following equation:

[tex]180=y+y+38\\180=2y+38[/tex]

Subtract 38 from both sides

[tex]180-38=2y+38-38\\142=2y\\71=y[/tex]

I hope this helps!

Answer:

5%

Step-by-step explanation:

Percent error = (actual - estimated) / actual x 100

(240 - 228) / 240 x 100 = 5%

Answer:

20

Step-by-step explanation:

One pattern is that we are adding one row and one column for each step.

The first step has 1 row and 2 columns,

the second one has 2 rows and 3 columns,

and the third has 3 rows and 4 columns.

Thus, it would make sense for the fourth step to have 4 rows and 5 columns. This makes a rectangle with a length and a width, with the area of the rectangle being length * width. 4 * 5 = 20 as our number of dots

Answer:

The answer is D I think :)))

Answer:

2nd option

Step-by-step explanation:

The discriminant b² - 4ac tells us about the nature of the roots

• If b² - 4ac > 0 then 2 real and distinct roots

• If b² - 4ac = 0 then 2 real and equal roots

• If b² - 4ac < 0 then the roots are not real

Here b² - 4ac = 15 > 0

Then there are 2 real and distinct roots

x = 2 and x = - 3 are possible solutions to the equation

Answer:

option b) x = 2 and x = -3

Step-by-step explanation:

If discriminant is greater than zero, then the quadratic equation will have two solutions.

If discriminant is equal to zero, then the quadratic equation will have only one solution.

If discriminant is less than zero no solution

Here the discriminant is 15 , which is greater than zero.

Therefore we will have to solutions.

There is only one option with two solutions for x.

So option b is the answer.

Answer:

-80

Step-by-step explanation:

So basically what we need to do is find the value of x that satisfies the equation.

When I mean satisfy, I basically mean a value of x that makes one side of the equals sign equal to the other side of the equals sign.

So in this case, we need -6 = -6.

To find this lets solve the equaion step by step:

-6=x/8+4

So first off, you always want to get the variable on one side, and the number on the other.

This means you want to subtract the 4 from both sides, leaving x/8:

-6=x/8+4

-4       -4

-10=x/8

Whenever x is not 1x, you have to divide or multiply to get it equal to 1x.

If this is a bit confusing, here is an example:

100=10x

We need 1x, but above is 10x. The reason why we want 1x is because it is the lowest ratio, and most accurate x value.

You can think of it like a 1 dollar bill. Its easier and better to use than per say a 3 dollar bill.

So in the example above you would divide by 10, since 10x/10 would equal 1x.

Remember the rule however, that what you do on one side you must do on the other. This emans you would divide both sides by 10:

100/10 =10x/10

=

10=1x

We have in our equation:

-10=x/8

Our x is lower than 1. It x/8. Whenever we have a value of x greater than 1, we divide, like we did in the example. However here, it is below x. So we multiply.

In this case we multiply by 8, since its x/8:

-10 * 8 = x/8 * 8

=

-80=x

So x is equal to -80.

I hope you understand it better now :D

Answer:

[tex] \sqrt{x + 2} [/tex]

If you horizontally shift the square root parent function f(x)=√x left two units the equation of the new function is: g(x) = √(x + 2).

A horizontal shift is a function transformation that shifts a graph to the left or right without changing its shape.

If we want to shift the square root parent function f(x) = √x two units to the left, we must replace the argument x with (x + 2), because a positive value of x + 2 gives us the same x value two units to the left.

So the equation of the new function is:

g(x) = √(x + 2)

This new function is the square root function shifted two units to the left. For any given input value of x, we add 2 to it before taking the square root. This causes the graph to shift horizontally to the left by two units.

Thus, g(x) = √(x + 2) will be the new function.

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Answer:

no thanks i dont feel like doing all that work to help u. i apologize my dear friend bahahahahahahahahahahhahaha

Step-by-step explanation:

Answer:

x = 46°

Step-by-step explanation:

64° + 70° + x = 180°

x = 180° - 64° - 70°

x = 46°

Answer: A , 4x - 5y = 5

Step-by-step explanation:

i just did it , duhhh

Answer:

a

Step-by-step explanation: