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4 years ago

Estimate the product of the expression below to the nearest whole number.

1 answer:

4 0

Estimate means round
16.77 rounds to 17
3.81 rounds to 4
17X4 = 68

A trick I use for multiplying by 4 is to double the number twice

Example:
17 -> 34 -> 68

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Find the equation of the line that passes through (0, -3) and is parallel to

Tresset [83]

Hey there!

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Answer:

$\green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}}$

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Explanation:

To find the equation of a line, we first have to determine its slope knowing that parallel lines have the same slope.

Let the line that we are trying to determine its equation be $\: \sf{d_1} \:$ and the line that is parallel to $\: \sf{d_1} \:$ be $\: \sf{d_2} \:$ .

$\sf{d_2} \:$ passes through the points (9 , 2) and (3 , -5) which means that we can find its slope using the slope formula:

$\sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{y_2} - \orange{y_1}}{\red{x_2} - \blue{x_1 }}}$

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⇒Subtitute the values :

$\sf{(\overbrace{\blue{9}}^{\blue{x_1}}\: , \: \overbrace{\orange{2}}^{\orange{y_1}}) \: \: and \: \: (\overbrace{\red{3}}^{\red{x_2}} \: , \: \overbrace{\green{-5}}^{\green{y_2}} )}$

$\implies \sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{-5} - \orange{2}}{\red{ \: \: 3} - \blue{9 }} = \dfrac{ - 7}{ - 6} = \boxed{ \bold{\dfrac{7}{6} }}}$

$\sf{\bold{The \: slope \: of \: both \: lines \: is \: \dfrac{7}{6}}}$ .

Assuming that we want to get the equation in Slope-Intercept Form, let's substitute m = 7/6:

Slope-Intercept Form:

$\sf{y = mx + b} \\ \sf{Where \: m \: is \: the \: slope \: of \: the \: line \: and \: b \: is \: the \: y-intercept.}$

$\implies \sf{y = \bold{\dfrac{7}{6}}x + b}$ $\\$

We know that the coordinates of the point (0 , -3) verify the equation since it is on the line $\: \sf{d_1} \:$ . Now, replace y with -3 and x with 0:

$\implies \sf{\overbrace{-3}^{y} = \dfrac{7}{8} \times \overbrace{0}^{x} + b} \\ \\ \implies \sf{-3 = 0 + b} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \sf{\boxed{\bold{b = -3}} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Therefore, the equation of the line $\: \bold{d_1} \:$ is $\green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}}$

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▪️Learn more about finding the equation of a line that is parallel to another one here:

↣brainly.com/question/27497166

8 0

2 years ago

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Suppose that Sin(θ)=5/13 and cos(θ)=-12/13. Find the value of tan(θ), cot (θ), CSC (θ), and sec (θ). Find the value of tan(2θ)

horrorfan [7]

Answer:

Because θ lies in quadrant II, 2θ must lie in quadrant IV. This means the tangent of 2θ is negative.

The adjacent side to θ is 7 because √(25²-24²)=7, so tanθ=7/24.

The double angle formula for tangent is tan 2θ = (2 tan θ) / (1 − tan² θ).

Substituting the value for tanθ in and keeping in mind that this is in quadrant IV, we get tan 2θ = -(2(7/24)/(1-(7/24)²)).

Simplified, this becomes tan 2θ = -336/527.

Therefore, the answer is C. -336/527.

5 0

3 years ago

I will give brainiest to whoever answers correctly !!

Juliette [100K]

Answer:

75.99

Step-by-step explanation:

6 0

3 years ago

Jada bikes 2 miles in 12 minutes.

drek231 [11]

A 1/6 miles per minute

6 0

3 years ago

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Amir stands on a balcony and throws a ball to his dog, who is at ground level. The ball's height (in meters above the ground), x

Y_Kistochka [10]

When the ball hit the ground, the height of the ball will be zero. So using the value of h(x) as zero in the given equation, we can find the time in which the ball will hit the ground.

$0=-(x-2)^{2}+16 \\ \\ 
(x-2)^{2}=16 \\ \\ 
x-2= \sqrt{16} \\ \\ 
x-2=4 \\ \\ 
x=6$

This means the ball will hit the ground 6 seconds after Amir threw it

6 0

3 years ago

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