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3 years ago

Problem 1

Mathematics

1 answer:

Aleksandr [31]3 years ago

6 0

Answer:

A and C

Step-by-step explanation:

Calculate the concentrations for each mixture.

Mixture A:

(4 teaspoons salt) / (2 cups water) = 2 teaspoons/cup

(0.25 cup sugar) / (2 cups water) = 0.125 cup/cup

Mixture B:

(3 teaspoons salt) / (1.5 cups water) = 2 teaspoons/cup

(0.2 cup sugar) / (1.5 cups water) = 0.133 cup/cup

Mixture C:

(2 teaspoons salt) / (1 cups water) = 2 teaspoons/cup

(0.125 cup sugar) / (1 cups water) = 0.125 cup/cup

Mixtures A and C have the same concentration.

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Find the equation of the line that passes through (0, -3) and is parallel to

Tresset [83]

Hey there!

$\\$

Answer:

$\green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}}$

$\\$

Explanation:

To find the equation of a line, we first have to determine its slope knowing that parallel lines have the same slope.

Let the line that we are trying to determine its equation be $\: \sf{d_1} \:$ and the line that is parallel to $\: \sf{d_1} \:$ be $\: \sf{d_2} \:$ .

$\sf{d_2} \:$ passes through the points (9 , 2) and (3 , -5) which means that we can find its slope using the slope formula:

$\sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{y_2} - \orange{y_1}}{\red{x_2} - \blue{x_1 }}}$

$\\$

⇒Subtitute the values :

$\sf{(\overbrace{\blue{9}}^{\blue{x_1}}\: , \: \overbrace{\orange{2}}^{\orange{y_1}}) \: \: and \: \: (\overbrace{\red{3}}^{\red{x_2}} \: , \: \overbrace{\green{-5}}^{\green{y_2}} )}$

$\implies \sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{-5} - \orange{2}}{\red{ \: \: 3} - \blue{9 }} = \dfrac{ - 7}{ - 6} = \boxed{ \bold{\dfrac{7}{6} }}}$

$\sf{\bold{The \: slope \: of \: both \: lines \: is \: \dfrac{7}{6}}}$ .

Assuming that we want to get the equation in Slope-Intercept Form, let's substitute m = 7/6:

Slope-Intercept Form:

$\sf{y = mx + b} \\ \sf{Where \: m \: is \: the \: slope \: of \: the \: line \: and \: b \: is \: the \: y-intercept.}$

$\implies \sf{y = \bold{\dfrac{7}{6}}x + b}$ $\\$

We know that the coordinates of the point (0 , -3) verify the equation since it is on the line $\: \sf{d_1} \:$ . Now, replace y with -3 and x with 0:

$\implies \sf{\overbrace{-3}^{y} = \dfrac{7}{8} \times \overbrace{0}^{x} + b} \\ \\ \implies \sf{-3 = 0 + b} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \sf{\boxed{\bold{b = -3}} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Therefore, the equation of the line $\: \bold{d_1} \:$ is $\green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}}$

$\\$

▪️Learn more about finding the equation of a line that is parallel to another one here:

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1 year ago

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When jack went to the movie he paid $8 for his popcorn and $4 for each additional order of popcorn. if i represents the total co

melamori03 [73]

I = 8 + 4x

XD That's expensive popcorn!

8 0

3 years ago

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Find the slope of the line passing through the points (-4, -2) and (6, -2).

Tems11 [23]

Answer: (-4, -2) and (6, -2)'s slope is 0, (2,9) and (2, -5)'s is undefined

Step-by-step explanation:

bro its not that hard, y1-y2 divided by x1-x2

4 0

2 years ago

3) Using J =

MrRa [10]

Answer:

Diameter = 49

radius = 49/2

circumference of circle is = 2π r

=. 2*22/7*49/2

= 154 cm

hope it helps

3 0

3 years ago

Find the x-intercepts of the parabola with vertex (1, -9) and y intercept at (0, -6).

Sergio [31]

Hello,

Equation is y=k(x-1)²-9
and when x=0,y=-6==>-6=k*1²-9==>k=3

y=3(x-1)²-9
when y=0, 3(x-1)²-9=0
==>(x-1-√3)(x-1+√3)=0
x-intercepts are (1+√3,0) and (1-√3,0)

Answer B.

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3 years ago