MATHEMATICS COLLEGE

What is the equation of the line

Answers

Answer 1

Answer: find the equation of a line given that you know points it passes through

Answer 2

Answer:

Answer:

picture?

Step-by-step explanation:

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The formula for the length of the hypotenuse in a right triangle is squared a^2+b^2 where a and b are the lengths

Answers

Answer:

the hypotenuse in a right triangle formula is c= sqrt(a^2+b^2)

Step-by-step explanation:

The original Pythagorean's theorem equation is a^2+b^2=c^2 which we can take the square root of to isolate and solve for the equation for just the hypotenuse length. This of course is assuming that a and b are the legs of the triangle. Let me know if this wasn't what you were asking or if you need more clarification and I'll amend my answer

How much wrapping paper would you need to cover a rectangularbox that is 19 inches by 12 inches by 3 inches if you need 10% more
wrapping paper than the surface area of the box? Give your answer
to the nearest square inch.

PLEASE HELP T-T

Answers

Step-by-step explanation:

a box (like a "deformed" die) has 6 sides.

and in case of such a rectangular box there are 3 pairs of equal sides.

the area of each side is a rectangle.

top and bottom : 19×12 times 2

front and back : 19×3 times 2

left and right : 12×3 times 2

so, we get

19×12×2 + 19×3×2 + 12×3×2 = 642 in²

and now, we need 10% more.

10% = 642/10 = 64.2 in²

the total is then

642 + 64.2 = 706.2 ≈ 706 in²

A 46- inch piece of steel is cut into three pieces so that the second piece is twice as long ad the first piece , and the third piece is one inch more than six times the length of the first piece. Find the lengths of the pieces.

Answers

Hope this helps you.

Final answer:

The first piece is 5 inches long, the second piece is 10 inches long, and the third piece is 31 inches long.

Explanation:

The problem involves a piece of steel that is 46 inches long and it is cut into three pieces. The wording of the problem gives us equations we can use to solve for lengths of the pieces. We're told:

The second piece is twice as long as the first piece.
The third piece is one inch more than six times the length of the first piece.

We can let x represent the length of the first piece. Then the length of the second piece is 2x, and the length of the third piece is 6x+1.

Because the three pieces together form the original 46-inch piece, we can set up this equation: x + 2x + 6x + 1 = 46, which simplify to 9x +1 = 46. Solving for x gives x = 5. Therefore, the lengths of the pieces are 5 inches, 10 inches (2 * 5), and 31 inches (6 * 5 + 1).

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Find the exact values of the six trigonometric functions of given the point (-4, 5) on the terminal side of in standard position.

Answers

Answer:

$\sin(\theta)=5√(41)/41\text{ and } \csc(\theta)=√(41)/5\n\cos(\theta)=-4√(41)/41\text{ and } \sec(\theta)=-√(41)/4\n\tan(\theta)=-5/4\text{ and } \cot(\theta)=-4/5$

Step-by-step explanation:

Please refer to the attached figure.

So, we can see that our angle θ is in QII.

Recall All Students Take Calculus. Since this is QII, we use the Students. In other words, only sine (and cosecant) is positive. So, cosine and tangent are negative.

Now, we also know that a point is (-4,5). Referring to our figure, this means that our adjacent side is 4 (technically -4, but we can ignore this) and our opposite side is 5. So, to find the other ratios, let's find the hypotenuse.

Use the Pythagorean Theorem:

$a^2+b^2=c^2$

Substitute 4 for a and b for 5. Solve for c. So:

$4^2+5^2=c^2$

Square:

$16+25=c^2$

Add:

$c^2=41$

Take the square root:

$c=√(41)$

So, our side lengths are: Opposite=5; Adjacent=4; and Hypotenuse=√41.

Now, we can find our side lengths.

Sine and Cosecant:

$\sin(\theta)=opp/hyp$

Substitute 5 for Opp and √41 for Hyp. So:

$\sin(\theta)=5/√(41)$

Rationalize:

$\sin(\theta)=5√(41)/41$

Since our angle is in QII, sine stays positive.

Cosecant is the reciprocal of sine. So:

$\csc(\theta)=√(41)/5$

Cosine and Secant:

$\cos(\theta)=adj/hyp$

Substitute 4 for Adj and √41 for Hyp:

$\cos(\theta)=4/√(41)$

Rationalize:

$\cos(\theta)=4√(41)/41$

Since our angle is in QII, cosine is negative. So:

$\cos(\theta)=-4√(41)/41$

Secant is the reciprocal of cosine. So:

$\sec(\theta)=-√(41)/4$

Tangent and Cotangent:

$\tan(\theta)=opp/adj$

Substitute 5 for Opp and 4 for Adj. So:

$\tan(\theta)=5/4$

Since our angle is in QII, tangent is negative. So:

$\tan(\theta)=-5/4$

Cotangent is the reciprocal of tangent:

$\cot(\theta)=-4/5$

And we are finished!

Final answer:

Using the given point (-4,5) in standard position, first calculate the radius using the Pythagorean theorem. Then, calculate each of the six trigonometric functions using the coordinates and the calculated radius.

Explanation:

The given point is (-4,5). In the standard position, the x-coordinate represents the cosine of the angle, while the y-coordinate represents the sin of the angle. However, we need to find the radius (r), which can be found using Pythagorean theorem:

r = sqrt(x

+ y

)

meaning, r = sqrt((-4)

+ 5

) = sqrt(41).

Now, each of the six trigonometric functions can be calculated as follows:

Sine (Sin θ = y/r): Sin θ = 5/sqrt(41),
Cosine (Cos θ = x/r): Cos θ = -4/sqrt(41),
Tangent (Tan θ = y/x): Tan θ = -5/4,
Cosecant (Csc θ = r/y): Csc θ = sqrt(41)/5,
Secant (Sec θ = r/x): Sec θ = -sqrt(41)/4,
Cotangent (Cot θ = x/y): Cot θ = 4/5.

Learn more about Trigonometric Functions here:

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Polygon ABCDEFGH will be dilated by a scale factor of 3.4 with the origin as the center of dilation to produce polygon A′B′C′D′E′F′G′H′. What will the length of `bar(A'H')` be? A. 1.7 units B. 2 units C. 3.4 units D.

Answers

Answer:

Given: Polygon AB C D E F G H

it is not given whether polygon is regular,So we will consider it as non regular convex polygon.

Polygon AB C D E F G H is dilated by a scale factor of 3.4 to get the polygon A′B′C′D′E′F′G′H.

As the length of each side will increase by a factor of 3.4 with origin as center of dilation.

So , A'H'= Length of side AH × Scale factor of dilation

A'H'=3.4 AH

Given the expression 2x(y + z)2, which is TRUE? A) The factor 2x depends on (y + z)2. B) The factor (y + z)2 depends on 2x. C) The factors 2x and (y + z)2 are dependent of each other. D) The factors 2x and (y + z)2 are independent of each other.

Answers

If we assume that x, y, and z are independent variables, then the appropriate choice is ...
D) The factors 2x and (y + z)² are independent of each other.

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There are 13 apples in a basket. 4 of these apples are green. The rest are red. what is the ratio?

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Help please! I’ll give brainliest!