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3 years ago

Indicate the equation of the given line in standard form. The line through (2, -1) and parallel to a line with slope of 3/4

1 answer:

7 0

Well, for a line with a slope of 3/4, any other parallel line to it, will also have the same slope of 3/4

so if the line through (2, -1) is parallel to it, it has a slope of 3/4 as well

$\bf \begin{array}{lllll}
&x_1&y_1\\
% (a,b)
&({{ 2}}\quad ,&{{ -1}})\quad 

\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{3}{4}
\\\\\\
% point-slope intercept
y-{{ y_1}}={{ m}}(x-{{ x_1}})\qquad 
\begin{array}{llll}
\textit{plug in the values for }
\begin{cases}
y_1=-1\\
x_1=2\\
m=\frac{3}{4}
\end{cases}\\
\textit{and move everything}\\
\textit{to the left-hand-side}
\end{array}\\

\left. \qquad \right. \uparrow\\
\textit{point-slope form}$

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The area of triangle formed by points of intersection of parabola y=a(x+5)(x−1) with the coordinate axes is 12. Find a if it is

Pie

We know that the points at which the parabola intersects the x axis are

(-5,0) and (1,0)

So the extent between these two points would be the base of the triangle

lets find the length of the base using the distance formula

$\sqrt{[(-5-1)^{2}+(0-0)^{2} ]}$

the base b=6

We will get the height of the triangle when we put x=0 in the equation

y=a(0+5)(0-1)

y=-5a

so height = -5a (we take +5a since it is the height)

We know that the area of the triangle =

$\frac{1}{2}$ × 6 × (5a) = 12

15a=12

a= $\frac{4}{5}$

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3 years ago

Olive reads 4 books every month for school. How many books does she read in 8 months?

Novosadov [1.4K]

Answer:

32 books.

Step-by-step explanation:

What do we know?

As Olive continues this pattern, this will involve multiplication.

4 books per month and 8 months.

4*8=32 books.

So, Olive will read 32 books within 8 months.

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3 years ago

What is the value of sin-1(1)? negative startfraction pi over 2 endfraction 0 startfraction pi over 2 endfraction π

mariarad [96]

The value of sin-1(1) is negative startfraction pi over 2 endfraction, startfraction -pi over 2 endfraction.

<h3>What is the value of sin (π/2)?</h3>

The value of sin (π/2) is equal to the number 1. The value of the sin-1(1) has to be find out.

Suppose the value of this function is <em>x</em>. Thus,

$x=\sin^{-1}(1)$

Solve it further,

$\sin(x)=(1)$ ......1

The value of sin (π/2) and -sin (-π/2) is equal to 1 such that,

$\sin\dfrac{\pi}{2}=-\sin\left(-\dfrac{\pi}{2}\right)=1$

Put this value in the equation 1,

$\sin(x)=\sin\left(\dfrac{\pi}{2}\right)=-\sin\left(-\dfrac{\pi}{2}\right)$

Thus, the range will be,

$\left(\dfrac{\pi}{2},-\dfrac{\pi}{2}\right)$

Thus, the value of sin-1(1) is negative startfraction pi over 2 endfraction, startfraction -pi over 2 endfraction.

Learn more about the sine values here;

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3 years ago

Write an equation in slope-intercept form which has a slope of 1/4 and crosses the Ÿ-axis at (0,7)

12345 [234]

Answer:

y= 1/4 x +7

Step-by-step explanation:

The slope intercept form of a line is

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

the slope is 1/4 and the y intercept is 7

y= 1/4 x +7

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3 years ago

Solve the inequality. Graph the solution on a number line. 7 ≥ t/-2

Elodia [21]

$t\geq -14$

The graph is shown in the figure attached.

Step-by-step explanation:

We need to solve the inequality $7\geq \frac{t}{-2}$ and graph the solution.

Solving the inequality: $7\geq \frac{t}{-2}$

Switch sides and reverse the inequality:

$\frac{t}{-2}\leq 7$

Multiplying both sides by -2 and reverse the inequality

$-2\frac{t}{-2}\geq 7*-2$

$t\geq -14$

The graph is shown in the figure attached.

Keywords: Graph the inequality

Learn more about Graph the inequality at:

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3 years ago