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2 years ago

Find intercepts of: 3x-3y+9=0 X-intercept as a ordered pair Y-intercept as a ordered pairr

1 answer:

7 0

3x - 3y + 9 = 0

The y-intercept is the point on the graph where it crosses the y-axis, and has coordinates of (0, b). It is also the value of y when x = 0.

To solve for the y-intercept, set x = 0:

3(0) - 3y + 9 = 0
3(0) - 3y + 9 = 0

Subtract 9 from both sides:
- 3y + 9 - 9 = 0 - 9
- 3y = -9
Divide both sides by -3 to solve for y:

-3y/-3 = -9/-3
y = 3

Therefore, the y-intercept is (0, 3).

The x-intercept is the point on the graph where it crosses the x-axis, and has coordinates of (a, 0). It is also the value of x when y = 0.

To solve for the x-intercept, set y = 0:

3x - 3(0)+ 9 = 0
3x -0 + 9 = 0

Subtract 9 from both sides:
3x + 9 - 9 = 0 - 9
3x = -9

Divide both sides by 3 to solve for x:

3x/3 = -9/3
x = -3

Therefore, the x-intercept is (-3,0).

The correct answers are:
Y-intercept = (0, 3)
X-intercept = (-3, 0)

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In Triangle XYZ, measure of angle X = 49° , XY = 18°, and

marissa [1.9K]

Answer:

There are two choices for angle Y: $Y \approx 54.987^{\circ}$ for $XZ \approx 15.193$ , $Y \approx 27.008^{\circ}$ for $XZ \approx 8.424$ .

Step-by-step explanation:

There are mistakes in the statement, correct form is now described:

<em>In triangle XYZ, measure of angle X = 49°, XY = 18 and YZ = 14. Find the measure of angle Y:</em>

The line segment XY is opposite to angle Z and the line segment YZ is opposite to angle X. We can determine the length of the line segment XZ by the Law of Cosine:

$YZ^{2} = XZ^{2} + XY^{2} -2\cdot XY\cdot XZ \cdot \cos X$ (1)

If we know that $X = 49^{\circ}$ , $XY = 18$ and $YZ = 14$ , then we have the following second order polynomial:

$14^{2} = XZ^{2} + 18^{2} - 2\cdot (18)\cdot XZ\cdot \cos 49^{\circ}$

$XZ^{2}-23.618\cdot XZ +128 = 0$ (2)

By the Quadratic Formula we have the following result:

$XZ \approx 15.193\,\lor\,XZ \approx 8.424$

There are two possible triangles, we can determine the value of angle Y for each by the Law of Cosine again:

$XZ^{2} = XY^{2} + YZ^{2} - 2\cdot XY \cdot YZ \cdot \cos Y$

$\cos Y = \frac{XY^{2}+YZ^{2}-XZ^{2}}{2\cdot XY\cdot YZ}$

$Y = \cos ^{-1}\left(\frac{XY^{2}+YZ^{2}-XZ^{2}}{2\cdot XY\cdot YZ} \right)$

1) $XZ \approx 15.193$

$Y = \cos^{-1}\left[\frac{18^{2}+14^{2}-15.193^{2}}{2\cdot (18)\cdot (14)} \right]$

$Y \approx 54.987^{\circ}$

2) $XZ \approx 8.424$

$Y = \cos^{-1}\left[\frac{18^{2}+14^{2}-8.424^{2}}{2\cdot (18)\cdot (14)} \right]$

$Y \approx 27.008^{\circ}$

There are two choices for angle Y: $Y \approx 54.987^{\circ}$ for $XZ \approx 15.193$ , $Y \approx 27.008^{\circ}$ for $XZ \approx 8.424$ .

6 0

2 years ago

Calculus 3 chapter 16

o-na [289]

Evaluate $\vec F$ at $\vec r$ :

$\vec F(x,y,z) = x\,\vec\imath + y\,\vec\jmath + xy\,\vec k \\\\ \implies \vec F(\vec r(t)) = \vec F(\cos(t), \sin(t), t) = \cos(t)\,\vec\imath + \sin(t)\,\vec\jmath + \sin(t)\cos(t)\,\vec k$

Compute the line element $d\vec r$ :

$d\vec r = \dfrac{d\vec r}{dt} dt = \left(-\sin(t)\,\vec\imath+\cos(t)\,\vec\jmath+\vec k\bigg) \, dt$

Simplifying the integrand, we have

$\vec F\cdot d\vec r = \bigg(-\cos(t)\sin(t) + \sin(t)\cos(t) + \sin(t)\cos(t)\bigg) \, dt \\ ~~~~~~~~= \sin(t)\cos(t) \, dt \\\\ ~~~~~~~~= \dfrac12 \sin(2t) \, dt$

Then the line integral evaluates to

$\displaystyle \int_C \vec F\cdot d\vec r = \int_0^\pi \frac12\sin(2t)\,dt \\\\ ~~~~~~~~ = -\frac14\cos(2t) \bigg|_{t=0}^{t=\pi} \\\\ ~~~~~~~~ = -\frac14(\cos(2\pi)-\cos(0)) = \boxed{0}$

3 0

1 year ago

Math need help asap ty po sa makaka sagot

Hatshy [7]

<h2>Answer:</h2>

please see analysis

<h2>Step-by-step explanation:</h2>

$\left\{\right.{ \triangle}\ RST\cong { \triangle}\ DE$ F

$(SSS\ Congruence\ Postulate)$

$2.\ { \triangle\ CAT\cong { \triangle\ BED\ \left\{\right.Given\left.\ \right\}$

$\bar{AT}\cong\bar{ED}$

$\overline{AT}=20$

$so\ \overline{ED}=20$

$DE=3x-7=20\rightarrow\ x=9$

<em>I hope this helps you:)</em>

4 0

1 year ago

Which phrase best describes the scatterplot below?

Vikentia [17]

Answer:

Strong negative correlation

Step-by-step explanation:

n the scatter plot attached below, as the variable in the x-axis increases, the variable on the y-axis decreases. Thus, if a line of best fit is drawn, it would show a line that slopes downwards to our right. This shows a negative correlation between both variables in the scatter plot.

Also, we also see that the data points represented on the scatter plot are clustered more closely along the slope, showing strong negative correlation.

Therefore, the phrase that best describes the scatter plot is: strong negative correlation.

8 0

2 years ago

Read 2 more answers

Can someone explain how to do this page I wasn't there when my teacher explained it

kodGreya [7K]

Answer:

You have to solve for the letter

Step-by-step explanation:

For example, Q5 is 40 - 5n = -2.

You subtract 40 from -2 and get -42 then you have 5n = -42.

You divide 5 to -42 so $\frac{-42}{5}$ .
The answer is -8.4.

*Use a calculator if necessary.*

~Hope this is helps (.^.)~

5 0

2 years ago