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shutvik [7]
2 years ago
14

3. Solve for x

Mathematics
1 answer:
padilas [110]2 years ago
4 0
<span>3x + 3 − x + (−7) > 6
2x - 4 > 6
2x > 10
x > 5

answer is </span><span>C. x > 5 </span>
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Write an equation in slope-intercept form for the line that has a slope of -4/5 and passes through (0, 7).
patriot [66]

Answer:

A. y = -\frac{4}{5}x + 7

Step-by-step explanation:

Slope intercept form is y = mx + b where m is the slope and b is the y-intercept

<em>It gives us the slope, so we can plug that in:</em> y = -\frac{4}{5}x + b

<em>Next, it gives us a point, so we can plug in the x and y into our equation and solve for b when (x, y)</em>

y = -\frac{4}{5}x + b

7 =  -\frac{4}{5}(0) + b

7 = b

<em>Last, complete our equation:</em>

y = -\frac{4}{5}x + b

y = -\frac{4}{5}x + 7

4 0
2 years ago
Consider the points A(5, 3t+2, 2), B(1, 3t, 2), and C(1, 4t, 3). Find the angle ∠ABC given that the dot product of the vectors B
Vilka [71]

Answer:

66.42°

Step-by-step explanation:

<u>Given:</u>

A(5, 3t+2, 2)

B(1, 3t, 2)

C(1, 4t, 3)

BA • BC = 4

Step 1: Find t.

First we have to find vectors BA and BC. We do that by subtracting the coordinates of the initial point from the coordinates of the terminal point.

In vector BA B is the initial point and A is the terminal point.

BA = OA - OB = (5-1, 3t+2-3t, 2-2) = (4, 2, 0)

BC = OC - OB = (1-1, 4t-3t, 3-2) = (0, t, 1)

Now we can find t because we know that BA • BC = 4

BA • BC = 4

To find dot product we calculate the sum of the produts of the corresponding components.

BA • BC = (4)(0) + (2)(t) + (0)(1)

4 = (4)(0) + (2)(t) + (0)(1)

4 = 0 + 2t + 0

4 = 2t

2 = t

t = 2

Now we know that:

BA = (4, 2, 0)

BC = (0, 2, 1)

Step 2: Find the angle ∠ABC.

Dot product: a • b = |a| |b| cos(angle)

BA • BC = 4

|BA| |BC| cos(angle) = 4

To get magnitudes we square each compoment of the vector and sum them together. Then square root.

|BA| = \sqrt{4^2 + 2^2 + 0^2} = \sqrt{20} = 2\sqrt{5}

|BC| = \sqrt{0^2 + 2^2 + 1^2} = \sqrt{5}

2\sqrt{5}\sqrt{5}\cos{(m\angle{ABC})} = 4

10\cos{(m\angle{ABC})} = 4

\cos(m\angle{ABC}) = \frac{4}{10}=\frac{2}{5}

m\angle{ABC} = cos^{-1}{(\frac{2}{5})}

m\angle{ABC} = 66.4218^{\circ}

Rounded to two decimal places:

m\angle{ABC} = 66.42^\circ

3 0
2 years ago
Which choice is a correct equation for the graph shown below?
Doss [256]

Answer:

C

Step-by-step explanation:

y = mx +b  The b is where the graph crosses the y axis.  If you look a the graph it is crossing at 5.  The m is the slope.  It is the change in y over the change in x.  If you start at 5 and go up10 and over 1, you will be on the line.  So our slope is 10/1 which is just 10

5 0
2 years ago
Read 2 more answers
What is the chance of rolling a 4 with a single die four times in a row?
BlackZzzverrR [31]

Answer:

16.66

Step-by-step explanation:

5 0
3 years ago
Sabrina rides her bike 2 miles to school each day she leaves her house 7:30 and arrives at 7:50 What is Sabrina's average speed
MakcuM [25]

6 mph.

To find this, create a ratio.

2/20 = x/60

This will allow you to compare here time of twenty minutes to an hour in the same context.

Multiply 2 by 60 and divide by 20 to get the answer of 6 mph.

Thus, Sabrina's average speed in miles per hour is six miles per hour.

Hope this helps!

7 0
3 years ago
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