Write an equation in slope-intercept form given the information about each line.
10. slope = 4, goes through the point (3, 10)

Answer:

Step-by-step explanation:

The equation of a line which passes through (x₁, y₁) and with slope of m in point-slope form:

                                y - y₁ = m(x - x₁)

m = -¹/₃

(1, 2)    ⇒   x₁ = 1,  y₁ = 2

Therefore,  the equation of the line which passes through (1, 2) and with slope of −1/3 in point-slope form:

y - 2 = -¹/₃(x - 1)

y - 2 = -¹/₃x + ¹/₃                     {add ¹/₃x to both sides}

¹/₃x + y - 2 = ¹/₃                     {add 2 to both sides}

¹/₃x + y = 2¹/₃                       {multiply both sides by 3}

x + 3y = 7            

Answer: terminating decimal

Step-by-step explanation:    :)

Answer:

x =10

Step-by-step explanation:

Using the pythagoras theorem om one of the right triangle;

(√74)² = (x/2)²+7²

74 = (x/2)²+49

(x/2)² = 74 - 49

(x/2)² = 25

Square root both sides

√ (x/2)² = ±√25

x/2 = ±5

x = 2 * ±5

x = ±10

Hence the value of x is 10

Answer:

Don Abel debe construir un cuadrado con lados de 25 metros de longitud.

Step-by-step explanation:

Geométricamente hablando, el área y el perímetro del rectángulo rodeado por el cerco son representadas por las siguientes fórmulas:

[tex]A = w\cdot l[/tex] (1)

[tex]p = 2\cdot (w+l)[/tex] (2)

Donde:

[tex]A[/tex] - Área, en metros cuadrados.

[tex]p[/tex] - Perímetro, en metros.

[tex]w[/tex] - Ancho, en metros.

[tex]l[/tex] - Longitud, en metros.

Puesto que el área a cercar debe ser la máxima posible y la longitud disponible de malla es de 100 metros, cabe despejar el ancho en (2):

[tex]w = \frac{p}{2}-l[/tex]

Ahora, aplicamos esta expresión en (1) y expandimos la expresión resultante:

[tex]A = \left(\frac{p}{2}-l\right) \cdot l[/tex]

[tex]A = \frac{p\cdot l}{2} -l^{2}[/tex] (3)

A continuación, obtenemos la primera y segunda derivada de (3):

[tex]A' = \frac{p}{2}-2\cdot l[/tex] (4)

[tex]A'' = -2[/tex] (5)

Igualando (4) a cero, tenemos que el valor crítico de la longitud del rectángulo es:

[tex]\frac{p}{2}-2\cdot l = 0[/tex]

[tex]2\cdot l = \frac{p}{2}[/tex]

[tex]l = \frac{p}{4}[/tex]

Por (5), sabemos que ese valor crítico está asociado al área máxima.

Si sabemos que [tex]p = 100\,m[/tex], entonces la longitud del rectángulo es:

[tex]l = 25\,m[/tex]

Ahora, tenemos el ancho de la figura por (2):

[tex]w = \frac{p}{2}-l[/tex]

[tex]w = 25\,m[/tex]

En consecuencia, don Abel debe construir un cuadrado con lados de 25 metros de longitud.

Answer:

13

Step-by-step explanation:

8/2=16/4

=4

x-3=2.5*4

x=10+3

x=13

Answer: 100

Step-by-step explanation:

2 x 102 = 204 and 1 x 104 = 104.

204 — 104 = 100.

Answer:

6715

Step-by-step explanation:

I hope this helps, :)

9514 1404 393

Answer:

  1. 3(0.96059601^t) = 15; t = -40.03

  2. 4.121204(1.01^t) = 8; t = 66.66

Step-by-step explanation:

The applicable rules of exponents are ...

  (a^b)^c = a^(bc)

  (a^b)(a^c) = a^(b+c)

The solution for an exponential problem using logarithms is ...

  a·b^x = c   ⇒   log(c/a)/log(b) = x

_____

1. Rewrite: (3)(0.99^4)^t = 15  ⇒  3(0.96059601^t) = 15

Solution: t = log(15/3)/log(0.96059601) ≈ -40.03

__

2. Rewrite: 4(1.01^3)(1.01^t) = 8  ⇒  4.121204(1.01^t) = 8

Solution: t = log(8/4.121204)/log(1.01) ≈ 66.66

Answer:

Use 1.75 cups of blue and 1 cup of yellow

Step-by-step explanation:

The given problem can be placed in the category of ratios and proportions. There is a ratio of color mixing which contains the proportion of two colors i.e blue and yellow. When we use 2 cups of yellow with 3.5 cups of yellow then we get green color so if we mix half of their amounts then we can get less or simply half amount of color too. Hence adding 1 cup of yellow and 1.75 cup of blue will give us small amount in result.

Answer:

[tex]Area = 287\ in^2[/tex]

Step-by-step explanation:

Given

[tex]Length = 20.5[/tex]

[tex]Space = 4.25[/tex]

[tex]Panels = 3[/tex]

See attachment

Required

The area of one panel

From the attachment, the total width is 50.5in.

i.e.

[tex]Total\ Width = 50.5[/tex]

Given that there are 2 spaces between the 3 panels and each space has a length of 4.25 in.

The reduced width is:

[tex]Reduced\ Width = 50.5 - 2 * 4.25[/tex]

[tex]Reduced\ Width = 42[/tex]

At this point, we can calculate the width of one panel by dividing the reduced width by the number of panels (3).

[tex]Width = \frac{42}{3}[/tex]

[tex]Width = 14[/tex]

The area of one is:

[tex]Area = Length * Width[/tex]

[tex]Area = 20.5 * 14[/tex]

[tex]Area = 287\ in^2[/tex]

Answer:18

Step-by-step explanation:

Given

The school has 200 boys and 300 girls

The ratio of boys and girls is 2:3

If 45 seventh grade students are selected then the ratio of boys and girls remain the same

suppose there are 2x boys and 3x girls, such that ratio is 2:3

[tex]\Rightarrow 2x+3x=45\\\Rightarrow 5x=45\\\Rightarrow x=9[/tex]

No of the boys are [tex]2x=2\times 9=18[/tex]

Answer:

18

Step-by-step explanation:

what the another person said

Answer:

3x = -6у + 3 and   2y = -x+1 are the same

i dont know what the question is but this should help. they are the same line on  a graph

Step-by-step explanation:

3x = -6y + 3

2y = -x + 1 adding x on both sides and subtracting 2y on both sides

x = -2y + 1 multiply by 3

3x = -6y + 3

Answer:

Look below.

Step-by-step explanation:

We can use the information provided to plug it into a...

Fomula to find a volume of a cylinder:

V=πr^2h

V=π(10)^2(15)

V≈4712.39ft

Answer:

I can't see it

Step-by-step explanation:

Answer:C

Step-by-step explanation: it’s 3/15, meaning, for example, taking 3 chocolate bars from a bunch of 15

Answer:

hello as I think the answer is X= 6

Answer:

6

Step-by-step explanation:

Given

- 2(3x + 2) > - 8x + 6 ← distribute parenthesis on left side

- 6x - 4 > - 8x + 6 ( add 8x to both sides )

2x - 4 > 6 ( add 4 to both sides )

2x > 10 ( divide both sides by 2 )

x > 5

The only value on the list greater than 5 is 6

Then 6 is in the solution set

Answer:

3y-5 would be your equation

Step-by-step explanation:

Answer:

H-u-H?!

Step-by-step explanation:

Answer:168

Step-by-step explanation:

Answer:

1. +25

2. +14

3. -10

4. -3

5. +2

Step-by-step explanation:

I hope these help , please tell me if i got any incorrect or misunderstood!

Answer:

The horizontal value in a pair of coordinates: how far along the point is. The X Coordinate is always written first in an ordered pair of coordinates (x,y), such as (12,5). In this example, the value "12" is the X Coordinate. Also called "Abscissa" See: Coordinates.

Answer:

Y=4/6X ( or u can write it as Y=1.5X) .

Hope it was helpful for you .

Answer:

y=4

Step-by-step explanation:

2(6 + 2y) = 28

(6 x 2 + 2y x 2) = 28

(12 + 4y) = 28

12 + 4y = 28

 12 + -12 + 4y = 28 + -12

 12 + -12 = 0

0 + 4y = 28 + -12

4y = 28 + -12

 28 + -12 = 16

4y = 16

16\4

 y = 4

Answer:

$1.91 per bottle :)

Step-by-step explanation:

Answer:

perpendicualr

Step-by-step explanation:

Answer:

I will explain it to you in a jiffy ok? Can you wait a sec

Answer:

175+(25*∞d)

Step-by-step explanation:

So d will represent the days which we don't know yet

100 + 50 + 25 + 25d

175+25d

and in this case it will be infinite the amount of days so

175+(25*∞d)

The total amount given by Ram to his son starting from the first day, if he lives forever is 200 nairas.

Given,

Ram gives his son 100 nairas on one day, 50 nairas on the second day, 25 nairas on the third day, and so on.

We need to find what will be the total amount given by Ram to his son starting from the first day if he lives forever.

It is a sequence where each term after the first term is found by multiplying the previous terms by a common ratio.

Example:

2, 4, 8, 16, 32

Common ratio = 4/2 = 8/4 = 16/8 = 2

The sum of the nth term of a geometric sequence is given by:

S = a [ [tex]r^{n}[/tex]- 1 ) / ( r - 1 ) ] if r > 1 ______(1)

S = a [ 1 - [tex]r^{n}[/tex] ) / ( 1 - r ) ] if r < 1 _______(2)

We see that,

Ram gives his son 100 nairas on one day, 50 nairas on the second day, 25 nairas on the third day, and so on.

This is a geometric sequence.

Find the sequence.

100, 50, 25, ,,,,,,, ∞

Here,

The common ratio is:

r = 50 / 100 = 25/50 = 1/2

i.e r < 1

Find the sum of at ∞.

Now,

a = 100

r = 1/2

n = ∞

From (2)

S = a [ 1 - [tex]r^{n}[/tex] ) / ( 1 - r ) ]

S = 100 [ 1 - 0 ] / (1 - 0.5 ) ]

S = 100 [ 1 / 0.5 ]

S = 100 / 0.5

S = 200

Thus the total amount given by Ram to his son starting from the first day, if he lives forever is 200 nairas.

Learn more about geometric sequences here:

https://brainly.com/question/11266123

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