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3 years ago

Y= 4x + 1

1 answer:

6 0

Solve one of the equations for x.
y = 4x + 1
y-1 = 4x
(y-1)/4 = x

Next, plug in this expression in the place of “x” in the previous expression
y = 2x - 5
y = 2((y-1)/4) -5
y = 1/2y - 11/2
1/2 y = - 11/2
y = -11

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3. A prop for the theater club’s play is constructed as a cone topped with a half-sphere. What is the volume of the prop? Round

Mariana [72]

The volume of the prop is calculated to be 2,712.96 cubic inches.

<u>Step-by-step explanation:</u>

Step 1:

The prop consists of a cone and a half-sphere on top. We will have to calculate the volumes of the cone and the half-sphere separately and then add them to obtain the total volume.

Step 2:

The volume of a cone is determined by multiplying $\frac{1}{3}$ with π, the square of the radius (r²) and height (h). Here we substitute π as 3.14. The radius is 9 inches and the height is 14 inches.

The volume of the cone : $V=\pi r^{2} \frac{h}{3}$ = $3.14 \times 9^{2} \times \frac{14}{3}$ = 1,186.92 cubic inches.

Step 3:

The area of a half-sphere is half of a full sphere. The volume of a sphere is given by multiplying $\frac{4}{3}$ with π and the cube of the radius (r³).

Here the radius is 9 inches. We take π as 3.14.

The volume of a full sphere = $V=\frac{4}{3} \pi r^{3}$ = $\frac{4}{3} \times 3.14 \times 9^{3}$ = 3,052.08 cubic inches.

The volume of the half-sphere = $\frac{3,052.08}{2}$ = 1,526.04 cubic inches.

Step 4:

The total volume = The volume of the cone + The volume of the half sphere,

The total volume = 1,186.92 + 1,526.04 = 2,712.96 cubic inches.

5 0

3 years ago

Why won’t anyone answer my questions argh! how do you draw starlight line graphs

Oduvanchick [21]

The table tells us that the x coordinate. It also tells us that y is always x + 1.

For #1 you plot the coordinate (0, 1).
0 (the x coordinate) is given to us already.
1 (the y coordinate) is needed to be found by the equation.
You would then need to fill in the equation given with the x coorident.
y = 0 + 1
Then, solve for y.
0 + 1 = 1
The y coordinate is 1
Go to the horizontal line (x) and find 0.
Then go to the veridical line (y) and find 1.
Then match up the the x and y to plot the coordinate.

You would continue with this equation with the rest of the xs.

This is a hard concept to explain in just words, so feel free to comment with any more questions. :D

4 0

3 years ago

The equation of a linear function in point-slope form is y – y1 = m(x – x1). Harold correctly wrote the equation y = 3(x – 7) us

Yanka [14]

Answer:

The point is (7,0).

Step-by-step explanation:

The equation of a linear function in point-slope form is as follows :

$y-y_1=m(x-x_1)$ ...(1)

Where

(x₁,y₁) are the coordinates of the point which the line passes through it and (x,y).

Harold correctly wrote the equation y= 3(x–7)

or we can write it as :

y-0=3(x-7) ...(2)

Comparing equations (1) and (2), we get :

x₁ = 7 and y₁ = 0

So, the point is (7,0).

The correct option is (c).

7 0

3 years ago

What is the 6th term of the geometric sequence where a1 = -4096 and a4 = 64?

Akimi4 [234]

$\bf \begin{array}{llccll}
term&value\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
a_1&-4096\\
a_2&-4096r\\
a_3&-4096rr\\
a_4&-4096rrr\\
&-4096r^3\\
&64
\end{array}\implies -4096r^3=64
\\\\\\
r^3=\cfrac{64}{-4096}\implies r^3=-\cfrac{1}{64}\implies r=\sqrt[3]{-\cfrac{1}{64}}
\\\\\\
r=\cfrac{\sqrt[3]{-1}}{\sqrt[3]{64}}\implies \boxed{r=\cfrac{-1}{4}}\\\\
-------------------------------$

$\bf n^{th}\textit{ term of a geometric sequence}\\\\
a_n=a_1\cdot r^{n-1}\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
----------\\
r=-\frac{1}{4}\\
a_1=-4096\\
n=6
\end{cases}
\\\\\\
a_6=-4096\left( -\frac{1}{4} \right)^{6-1}\implies a_6=-4^6\left( -\frac{1}{4} \right)^5$

4 0

3 years ago

Read 2 more answers

This week laptops are 25 percent off if a laptop cost $340 what is it's sale price

Nata [24]

The sale price is 255 dollars.
To get the answer you find out that ten percent of 340 is 34 dollars. then you double the percentage which brings you to 68 dollars. but you still have 5 percent left over. Half of the ten percent is 17 dollars. finally you add 68 plus 17 which gives you 84 dollars. Lastly subtract 84 dollars from 340 which gives you 255

Hope this helps! :)

3 0

3 years ago

Read 2 more answers