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Elena L [17]
3 years ago
10

Please help me with this.what are the x-intercepts of the graph of this equation?

Mathematics
1 answer:
aleksandr82 [10.1K]3 years ago
8 0

Hello!

To find the x-intercept given the equation of a line, we substitute y for 0 and solve for x.

0=4x²-9

We add 9 to both sides.

9=4x²

We find the square root of both sides.

3=4x

We divide both sides by 4.

x=3/4

Therefore, our x-intercept is 3/4.

I hope this helps!

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Answer:

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Step-by-step explanation:

You divide all the dimensions of the larger triangle by 4 to get the dimensions of the smaller triangle.

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If the altitude of an equilateral triangle is 9 what is the perimeter
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aalyn [17]

Answer:

a)  81π  in³

b)  27  in³

c)  divide the volume of the slice of cake by the volume of the whole cake

d)  10.6%

e)  see explanation

Step-by-step explanation:

<h3><u>Part (a)</u></h3>

The cake can be modeled as a <u>cylinder </u>with:

  • diameter = 9 in
  • height = 4 in

\sf Radius=\dfrac{1}{2}diameter \implies r=4.5\:in

\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}

\begin{aligned}\sf \implies \textsf{Volume of the cake} & =\pi (4.5)^2(4)\\ & = \sf \pi (20.25)(4)\\ & = \sf81 \pi \:\: in^3\end{aligned}

<h3><u>Part (b)</u></h3>

\begin{aligned}\textsf{Circumference of the cake} & = \sf \pi d\\& = \sf 9 \pi \:\:in\end{aligned}

If each slice of cake has an arc length of 3 in, then the volume of each slice is 3/9π of the entire volume of the cake.

\begin{aligned}\implies \textsf{Volume of slice of cake} & = \sf \dfrac{3}{9 \pi} \times \textsf{volume of cake}\\\\& = \sf \dfrac{3}{9 \pi} \times 81 \pi\\\\& = \sf \dfrac{243 \pi}{9 \pi}\\\\& = \sf 27\:\:in^3\end{aligned}

<h3><u>Part (c)</u></h3>

The volume of each slice of cake is 27 in³.

The volume of the whole cake is 81π in³.

To calculate the probability that the first slice of cake will have the marble, divide the volume of a slice by the volume of the whole cake:

\begin{aligned}\implies \sf Probability & = \sf \dfrac{27}{81 \pi}\\\\& = \sf 0.1061032954...\\\\ & = \sf 10.6\% \:\:(1\:d.p.)\end{aligned}

<h3><u>Part (d)</u></h3>

Probability is approximately 10.6%  (see above for calculation)

<h3><u>Part (e)</u></h3>

If the four slices of cake are cut and passed out <em>before </em>anyone eats or looks for the marble, the probability of getting the marble is the same for everyone. If one slice of cake is cut and checked for the marble before the next slice is cut, the probability will increase as the volume of the entire cake decreases, <u>until the marble is found</u>.  So it depends upon how the cake is cut and distributed as to whether Hattie's strategy makes sense.

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Answer:

The reason for the columns adding up to 1 is that each individual consumes a proportion or a fraction of the total quantity produced under each product category and every product is consumed.  There is no leftover.

When the proportions of all the individuals are added up, the sum is always 1 under each product category because each individual can only consume a part of the whole.

Step-by-step explanation:

a) Data and Calculations:

                        Food   Clothes  Housing  Energy  High Quality 100

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Farmer             0.25      0.15       0.25        0.18            0.20                    

Tailor                0.15      0.28       0.18         0.17            0.05

Carpenter        0.22      0.19       0.22        0.22           0.10

Coal Miner       0.20      0.15       0.20        0.28           0.15

Slacker Bob     0.18      0.23        0.15        0.15            0.50

Total                 1.00      1.00        1.00         1.00            1.00

6 0
3 years ago
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