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3 years ago

Write the equation of the line that contains the points (5,7) and (5, -12):

Mathematics

1 answer:

Ainat [17]3 years ago

8 0

Step-by-step explanation:

Well you first have to find the slope, which is y2-y1/x2-x1

Which is -12-7/5-5 and that equals to undefined.

So since you can't find the slope the answer should be undefined.

Hope this helps <3

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From a piece of tin in the shape of a square 6 inches on a side, the largest possible circle is cut out. What is the ratio of th

wel

Answer:

$\sf \dfrac{1}{4} \pi \quad or \quad \dfrac{7}{9}$

Step-by-step explanation:

The width of a square is its side length.

The width of a circle is its diameter.

Therefore, the largest possible circle that can be cut out from a square is a circle whose diameter is equal in length to the side length of the square.

Formulas

$\sf \textsf{Area of a square}=s^2 \quad \textsf{(where s is the side length)}$

$\sf \textsf{Area of a circle}=\pi r^2 \quad \textsf{(where r is the radius)}$

$\sf \textsf{Radius of a circle}=\dfrac{1}{2}d \quad \textsf{(where d is the diameter)}$

If the diameter is equal to the side length of the square, then:
$\implies \sf r=\dfrac{1}{2}s$

Therefore:

$\begin{aligned}\implies \sf Area\:of\:circle & = \sf \pi \left(\dfrac{s}{2}\right)^2\\& = \sf \pi \left(\dfrac{s^2}{4}\right)\\& = \sf \dfrac{1}{4}\pi s^2 \end{aligned}$

So the ratio of the area of the circle to the original square is:

$\begin{aligned}\textsf{area of circle} & :\textsf{area of square}\\\sf \dfrac{1}{4}\pi s^2 & : \sf s^2\\\sf \dfrac{1}{4}\pi & : 1\end{aligned}$

Given:

side length (s) = 6 in
radius (r) = 6 ÷ 2 = 3 in

$\implies \sf \textsf{Area of square}=6^2=36\:in^2$

$\implies \sf \textsf{Area of circle}=\pi \cdot 3^2=28\:in^2\:\:(nearest\:whole\:number)$

Ratio of circle to square:

$\implies \dfrac{28}{36}=\dfrac{7}{9}$

5 0

1 year ago

Use the quadratic formula to findntge roots of the equation 2X2-28X+98=0

JulijaS [17]

The answer to that equation is {7,7}

3 0

3 years ago

Can someone check this out to see if I have this correct? If not can you help me out please? Thank you! The answers are on 2nd p

nataly862011 [7]

Answer:

Answer 1; Angles forming a linear sum to 180°

Answer 2; Substitution

Answer 3; Definition of perpendicular lines

Step-by-step explanation:

The two column proof is presented as follows;

Statement ${}$ Reason

1. ∠SWT ≅ ∠TWU ${}$ Given

2. m∠SWT + m∠TWU = 180° ${}$ Angles forming a linear sum to 180°

3. m∠SWT + m∠SWT = 180° ${}$ Substitution

4. m∠SWT = 90° ${}$ Algebra

5. $\underset{TV}{\leftrightarrow }$ ⊥ $\underset{SU}{\leftrightarrow }$ ${}$ Definition of perpendicular lines

Perpendicular lines are defined as lines that are at right angles (90°) to each other, therefore given that the angle formed by the lines $\underset{TV}{\leftrightarrow }$ and $\underset{SU}{\leftrightarrow }$ m∠SWT = 90°, therefore, the lines $\underset{TV}{\leftrightarrow }$ and $\underset{SU}{\leftrightarrow }$ are perpendicular to each other.

3 0

2 years ago

For which color is the difference between the theorectical probability and experimental probability greatest?

Elan Coil [88]

Answer:

The answer is D. Green; The experimental probability is 22.7%, and the theoretical probability is 15%.

5 0

3 years ago

Factor completely 6x²-4x -2

swat32

$6x^2-4x -2 \\ \\ GCF = 2 \\ \\ 2( \frac{6x^2}{2} + \frac{-4x}{2} - \frac{2}{2} \ / \ factor \ out \ GCF \\ \\ 2(3x^2 - 2x - 1) \ / \ simplify \ terms \\ \\ 2(3x^2 + x - 3x - 1) \ / \ factor \\ \\ 2(x(3x+1) - (3x + 1)) \ / \ factor \ out \ common \ terms \\ \\ 2(3x+1)(x - 1) \ / \ factor \ out \ common \ term \\ \\ Answer: \fbox {2 (3x + 1)(x - 1)}$

7 0

3 years ago

Read 2 more answers