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3 years ago

I need help with this what’s the answer

Mathematics

2 answers:

Lostsunrise [7]3 years ago

7 0

Answer:

x+4

Step-by-step explanation:

To solve this question we must look at the examples :

x=2 and y=6

6-2=4

x=2 and y=7

7-3=4

so the aswer is : y = x + 4

matrenka [14]3 years ago

3 0

Answer:

If we look at the table we notice that 2 + 4 = 6, 3 + 4 = 7, 4 + 4 = 8 and so on so the equation is y = x + 4.

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Determine the slope of the line given the points (2,1) and (4,0)

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The slope is the change in Y over the change in X.

Slope = (0 - 1) / 4-2)

= -1/2

The slope is -1/2

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3 years ago

Find the domain and range. state whether each set of ordered pairs is a function or not.

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Answer:

Set A is a function

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3 years ago

Find the area of the triangle with the given vertices. Use the fact that the area of the triangle having u and v as adjacent sid

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Answer:

The area of the triangle is $A=\sqrt{\frac{4027}{2}}$

Step-by-step explanation:

Using the fact that the area of the triangle having u and v as adjacent sides is given by

$A=\frac{1}{2}||{\bf u} \times {\bf v} ||$

We know that we want to take a cross product to compute the area of the triangle, but we need to be careful because it doesn't make sense if we take the cross product of points.

The first step is to build some vectors that describe this triangle.

According with the graph we can build the vectors:

${\bf AB}$ and ${\bf AC}$

The vector ${\bf AB}$ is the difference of point B minus point A

${\bf AB}=(5-3,5-5,0-9)=(2,0,-9)$

and the vector ${\bf AC}$ is the difference of point C minus point A

${\bf AC}=(-4-3,0-5,2-9)=(-7,-5,-7)$

Next we need to find the cross product of this vectors.

${\bf AB} \times {\bf AC}=\begin{pmatrix}2&0&-9\end{pmatrix}\times \begin{pmatrix}-7&-5&-7\end{pmatrix}$

This is the definition of cross product of two vectors in space:

Let ${\bf u} = u_1{\bf i}+u_2{\bf j}+u_3{\bf k}$ and ${\bf v} = v_1{\bf i}+v_2{\bf j}+v_3{\bf k}$ be vectors in space. The cross product of ${\bf u}$ and ${\bf v}$ is the vector

${\bf u} \times {\bf v}=(u_2v_3-u_3v_2){\bf i}-(u_1v_3-u_3v_1){\bf j}+(u_1v_2-u_2v_1){\bf k}$

Applying this definition we get

${\bf AB} \times {\bf AC}=\begin{pmatrix}2&0&-9\end{pmatrix}\times \begin{pmatrix}-7&-5&-7\end{pmatrix}$

$\begin{pmatrix}0\cdot \left(-7\right)-\left(-9\left(-5\right)\right)&-9\left(-7\right)-2\left(-7\right)&2\left(-5\right)-0\cdot \left(-7\right)\end{pmatrix}\\\\\begin{pmatrix}-45&77&-10\end{pmatrix}$

$||{\bf AB} \times {\bf AC}||=\sqrt{(-45)^2+(77)^2+(-10)^2} \\\\||{\bf AB} \times {\bf AC}||=\sqrt{2025+5929+100}\\\\||{\bf AB} \times {\bf AC}||=\sqrt{8054}$

The area of the triangle is

$A=\frac{1}{2}||{\bf AB} \times {\bf AC} ||=\frac{1}{2}\sqrt{8054}=\sqrt{\frac{4027}{2}}$

7 0

4 years ago

An environmental scientist estimated the number of drops of water in two different jugs. He estimated that the smaller jug conta

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Answer:

The difference the number of drops of water in the larger jug and the number of drops of water in the smaller jug is <u>1,472,000.0000000005</u>.

Step-by-step explanation:

Given:

An environmental scientist estimated the number of drops of water in two different jugs. He estimated that the smaller jug contains 808,000 drops of water and the larger jug contains 2,280,000.0000000005 drops of water.

Now, to find the difference between the number of drops of water in the larger jug and the number of drops of water in the smaller jug.

The drops of water larger jug contains = 2,280,000.0000000005.

The drops of water smaller jug contains = 808,000.

Now, to get the difference between the number of drops of water in the larger jug and the number of drops of water in the smaller jug we subtract:

$2,280,000.0000000005-808,000\\\\=1,472,000.0000000005.$

Therefore, the difference the number of drops of water in the larger jug and the number of drops of water in the smaller jug is 1,472,000.0000000005.

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3 years ago

Frances can complete 91 oil changes in 7 days.

SOVA2 [1]

Answer:

143 oil changes

Step-by-step explanation:

We first find the unit rate.

(91 oil changes)/(7 days) = 13 oil changes/day

Since we want to know the number of oil changes in 11 days, we multiply the unit rate by 11 days.

13 oil changes/day * 11 days = 143 oil changes

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3 years ago