Please help!

Which line is parallel to the line<br> shown below?

Travka [436]

<h3>Answer: Choice D</h3>

4x - 3y = 15

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Explanation:

The two points (-1,-1) and (2,3) are marked on the line

Let's find the slope of the line through those two points.

$(x_1,y_1) = (-1,-1) \text{ and } (x_2,y_2) = (2,3)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{3 - (-1)}{2 - (-1)}\\\\m = \frac{3 + 1}{2 + 1}\\\\m = \frac{4}{3}\\\\$

The slope is 4/3 meaning we go up 4 and to the right 3.

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Parallel lines have equal slopes, but different y intercepts. We'll need to see which of the four answer choices have a slope of 4/3.

Solve the equation in choice A for y. The goal is to get it into y = mx+b form so we can determine the slope m.

$3x + 4y = -4\\\\4y = -3x-4\\\\y = -\frac{3}{4}x-\frac{4}{4}\\\\y = -\frac{3}{4}x-1$

Equation A has a slope of -3/4 and not 4/3 like we want.

Therefore, this answer choice is crossed off the list.

Follow similar steps for choices B through D. I'll show the slopes of each so you can check your work.

slope of equation B is 3/4
slope of equation C is -4/3
slope of equation D is 4/3

We have a match with equation D. Therefore, the equation 4x-3y = 15 is parallel to the given line shown in the graph.

You can use graphing tools like Desmos or GeoGebra to confirm the answer.

4 0

1 year ago

Filipo is building a rectangular sandbox . The length of the sandbox is 1 foot longer than twice the width of the sandbox .the p

Alla [95]

Answer:

Part A : D.) $2w + 2(2w+ 1) = 29$

Part B : Length of the sandbox is 10 feet.

Step-by-step explanation:

Given,

Perimeter = 29 ft

We need to find the equation for the perimeter and also the length of the sandbox.

Solution,

Let the width of the sandbox be 'w'.

Now as per question said;

The length of the sandbox is 1 foot longer than twice the width of the sandbox.

So we can say that;

Length = $2w+1$

Now we know that the perimeter is equal to the sum of twice of length and width.

framing in equation form, we get;

Perimeter = $2(2w+1)+2w$

we have given the perimeter, so on substituting the value, we get;

$29=2(2w+1)+2w$

Hence The equation used to find the width is $29=2(2w+1)+2w$ .

Now we solve for 'w'.

Applying distributive property, we get;

$4w+2+2w=29\\\\6w+2=29$

Subtracting both side by '2' we get

$6w+2-2=29-2\\\\6w=27$

Dividing both side by 6 we get;

$\frac{6w}{6}=\frac{27}{6}\\\\w=4.5\ ft$

Width of the sandbox = 4.5 ft

Length of the sandbox = $2w+1=2\times4.5 +1 = 9+1=10\ ft$

Hence Length of the sandbox is 10 feet.

3 0

3 years ago

Helpppppppp plssssssss!

tester [92]

Answer:Taco Bell

Step-by-step explanation:

It’s always right g

5 0

3 years ago

$$ \sqrt{6\frac{1}{4}} $$

ratelena [41]

Chu gf fr uvv V dhh gg jb cub

6 0

3 years ago

A 5-gallon jug of cleaning solution contains 6% bleach. How much pure water should be added to it to dilute to 4% bleach?

mihalych1998 [28]

Let's bear in mind that 5 gallons with a solution of 6% bleach, contains some water plus some bleach, how much bleach? well, is just 6% of 5 gallons or namely (6/100) * 5 gallons, or 0.30 gallons.

if we use "x" gallons of water, well pure water has no bleach, so is 0% bleach, and it has a (0/100) * x or 0x gallons of bleach.

the mixture will be say "y" gallons, and is 4% bleach, so (4/100) * y is 0.04y gallons in the mixture of bleach.

$\bf \begin{array}{lcccl}
&\stackrel{gallons}{quantity}&\stackrel{\textit{\% of bleach}}{amount}&\stackrel{\textit{gallons of bleach}}{amount}\\
&------&------&------\\
\textit{pure water}&x&0.00&0x\\
\textit{6\% solution}&5&0.06&0.3\\
-----&------&------&------\\
mixture&y&0.04&0.04y
\end{array}
\\\\\\
\begin{cases}
x+5=\boxed{y}\\
0x+0.3=0.04y\\
---------\\
0.3=0.04\left( \boxed{x+5} \right)
\end{cases}
\\\\\\
0.3=0.04x+0.2\implies 0.1=0.04x\implies \cfrac{0.1}{0.04}=x\implies 2.5=x$

3 0

3 years ago