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2 years ago

These lines are parallel. Is this statement true or false? y = - 2 3 x + 8 y = 2 3 x − 5 A. true B. false

Mathematics

1 answer:

Alecsey [184]2 years ago

6 0

Answer:

This statement would be false.

Step-by-step explanation:

The given equations have slopes that are positive and negative. Therefore, we know that they will intersect at some point because the slopes are not the same. In fact, they intersect at the point (9 3/4, 1 1/2).

I have attached an image of the graph of these two equations for your reference.

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Can you please answer this question

tamaranim1 [39]

$3tan^{2} \theta +7sec\theta=3$
First I converted the equation terms into sine and cosine.
$tan^{2}\theta = \frac{sin^{2}\theta}{cos^{2}\theta}$ and $sec\theta= \frac{1}{cos\theta}$
Substitution:
$\frac{3sin^2\theta}{cos^2\theta} + \frac{7}{cos\theta} =3$
Common Denominator Created:
$\frac{3sin^2\theta}{cos^2\theta} + \frac{7cos\theta}{cos^2\theta} =3$
Multiply each term by the LCD:
$3sin^2\theta+7cos\theta=3cos^2\theta$
Substitution: Recall ⇒ $sin^2\theta =1-cos^2\theta$
$3(1-cos^2\theta)+7cos\theta=3cos^2\theta$
Distribute and collect all terms on one side:
$6cos^2\theta-7cos\theta-3=0$
Factor and set each factor equal to 0:
$(2cos\theta-3)(3cos\theta+1)=0$
$2cos\theta-3=0$ ⇒ $theta=cos^{-1} \frac{3}{2}$
$3cos\theta+1=0$ ⇒ $theta=cos^{-1} \frac{-1}{3}$
The 2nd factor provides only possible answer 109.5 degrees

4 0

2 years ago

Please help and please say the formula!!

Damm [24]

Answer:

Step-by-step explanation:

Formula: 4*((15*7)/2) + 15^2

This is the area of the four triangles combined (210 cm^2) plus the area of the square (225 cm^2)

8 0

2 years ago

Need help asap!!!!!!!

kherson [118]

Answer:

Multiplication

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Show how to solve the following; answer must be with fractions and pi

Bess [88]

Answer:

3pi/4 and -pi/4

Step-by-step explanation:

We can simplify -6/6 to -1.

Therefore, this function can be simplified to arctan(-1).

Recall that the meaning of arctan is to find a value that will get the value inside the parenthesis when taken the tangent of it. In other words, tan(x) = -1.

Recall that tan(x) = sin(x)/cos(x). Now recall that sin(pi/4) and cos(pi/4) are both sqrt(2)/2, meaning that tan(pi/4) is 1. To make it -1, we can either make sin(x) -1 while keeping cos(x) 1, or the other way around.

If x is -pi/4, cos(x) will still be 1, but sin(x) will be -1, so tan(-pi/4) will be -1.

If x is 3pi/4, cos(x) will be -1, but sin(x) will still be 1, so tan(3pi/4) will be -1.

Side note: there are still infinite more answers. You can attain them by adding or subtracting 2pi as many times as you want from 3pi/4 or -pi/4 and still get an arctan of -1.

3 0

2 years ago

URGENT!!!!<br> Please add workings out

Artist 52 [7]

Answer: 26.457 cm

Explanation:

First, the height of an equilateral triangle of side length a is:

$h = \frac{\sqrt{3} }{2}*a$

In this case, the side-length of the triangles is a = 10cm, then the height will be:

$h = \frac{\sqrt{3} }{2}*10cm = 8.66cm$

Now we can think on a triangle rectangle such that:

Point A and point F are vertexes of the triangle.

The line we want to find, the line from A to F, is the hypotenuse.

One cathetus is a the height of the triangle, that comes down from point A, the length of this cathetus is 8.66cm

The other cathetus is equal to half the side length of the triangles (5cm) plus the segments BD and DF (of 10cm each)

Then the length of this cathetus is 10cm + 10cm + 5cm = 25cm

Now, we can remember the Pythagorean theorem.

If H is the hypotenuse, and A and B are the catheti, then we have:

A^2 + B^2 = H^2

In this case, we know the length of both cathetus, and want to know the length of the hypotenuse, then:

(25cm)^2 + (8.66cm)^2 = H^2

√( (25cm)^2 + (8.66cm)^2) = H = 26.457 cm

Then the line from A to F is 26.457 cm

6 0

2 years ago