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3 years ago

Please help! Which line would be perpendicular?

Mathematics

1 answer:

givi [52]3 years ago

8 0

Answer:

D. -2x + 2y = 1

Step-by-step explanation:

When the line is given in standard form:

ax + by = c, it has slope of -a/b

Given line:

4x + 4y = 3

It has a slope:

m = -4/4 = -1

A line perpendicular to the given should have a slope m = 1 as negative reciprocal to the given

Let's see which line has the slope of 1:

1. m = -(-1)/6 = 1/6 - NO
2. m = -4/4 = -1 - NO
3. m = -2/4 = -1/2 - NO
4. m = -(-2)/2 = 1 - YES

Correct option is D

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Find the first five terms of the sequence in which a1 = –10 and an = 4an – 1 + 7, if n ≥ 2.

Naddika [18.5K]

Answer:

-10, -33, -125, -493, -1965

Step-by-step explanation:

a1 is -10, meaning the first term is -10. therefore the first term of the sequence has to be -10

7 0

4 years ago

How do I solve a given right triangle to find Cos, Sin, and Tan. How do I solve for a missing adjacent side? (For Example: Imagi

Sphinxa [80]

The steps to find cos, sin, and tan and missing adjacent side of a given right angle triangle is explained.

Solution:

Given, a right triangle with A, B, and C.

Opposite side = 70 inches

Hypotenuse = 12 feet = 12 $\times$ 12 inches = 144 inches

Adjacent side = "x" inches.

We are not given angle, so we have to use the hypotenuse theorem

Hypotenuse theorem means square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.

$\text { hypotenuse }^{2}=(\text { opposite side })^{2}+(\text { adjacent side })^{2}$

Substituting the values we get,

$\begin{array}{l}{\rightarrow 144^{2}=70^{2}+x^{2}} \\\\ {\rightarrow x^{2}=20736-4900} \\\\ {\rightarrow x^{2}=15836} \\\\ {\rightarrow x=\sqrt{15836}} \\\\ {\rightarrow x=125.841}\end{array}$

So, the adjacent side value is 125.8 inches approximately.

Hence the steps to find adjacent side is shown above

Now let us find cos, sin and tan

$\begin{aligned} \sin \theta &=\frac{\text {opposite side}}{\text {hypotenuse}} \\\\ \cos \theta &=\frac{\text {adjacent side}}{\text {hypotenuse}} \\\\ \tan \theta &=\frac{\text {opposite side}}{\text {adjacent side}} \end{aligned}$

By substituting the required values, we can find cos, sin and tan

$\begin{array}{l}{\sin \theta=\frac{70}{144}=\frac{35}{122}} \\\\ {\cos \theta=\frac{125.8}{144}=\frac{62.9}{122}} \\\\ {\tan \theta=\frac{70}{125.8}=\frac{35}{62.9}}\end{array}$

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3 years ago

What is the probability that a point chosen inside the large rectangle is not in the shaded region?

Maurinko [17]

The shaded region has an area of 12 while the whole thing is 50 mutiply both by 2 to get the area of the shaded region and the whole thing by 100 After that subtract 24 from 100 and you get a 76 percent chance that you will randomly select an area in that box that isn't shaded.

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3 years ago

Which of these systems of equations shows the solution for the graph?

Semmy [17]

Answer:

Step-by-step explanation:

Solution of the equation is given by the intersecting point which is (2 , -1)

Find the equation of the line:

(0,4) ; (2 , -1)

$Slope = \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\dfrac{-1-4}{2-0}\\\\m =\dfrac{-5}{2}$

m = -5/2 ; (0 , 4)

Equation: y - y1 =m(x -x1)

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3 years ago

Describe how trigonometric equations differ from trigonometric identities.

vovikov84 [41]

Answer:

Trigonometric identities describe equalities between related trigonometric expres- sions while trigonometric equations ask us to determine the specific values of the variables that make two expressions equal.

7 0

2 years ago