Using elimination, what is the solution to the following system?
x+6y=32
-x-3y=-17

Answer:

Answer D

Step-by-step explanation:

The answer here is D since all of the other ones have at least one option that is perpendicular to segment EF.

Center:  ( 6 , 8 )

Radius: 5

Answer:

[tex] x^2 +y^2 = 25 [/tex]

Step-by-step explanation:

Center of the required circle = (0, 0)

Center of the given circle = (6, 8)

Radius of the given circle = 5 units

Distance between the centers of both the circles

[tex] =\sqrt{(6-0)^2 +(8-0)^2} [/tex]

[tex] =\sqrt{(6)^2 +(8)^2} [/tex]

[tex] =\sqrt{36 +64} [/tex]

[tex] =\sqrt{100} [/tex]

[tex] =10\: units [/tex]

Since, required circle is tangent to the given circle with radius 5 units.

Therefore,

Radius of required circle = 10 - 5 = 5 units

Now, Equation of required circle can be obtained as:

[tex] (x - 0)^2 +(y - 0)^2 = 5^2 [/tex]

[tex] (x)^2 +(y)^2 = 25 [/tex]

[tex] x^2 +y^2 = 25 [/tex]

The surface area of the sphere is 113 square cm

The radius is given as:

r = 3 cm

The surface area is calculated as:

[tex]A = 4\pi r^2[/tex]

So, we have:

[tex]A = 4\pi * 3^2[/tex]

Evaluate the product

A = 113

Hence, the surface area of the sphere is 113 square cm

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Answer: 113

Step-by-step explanation: SA formula is = 4*pi*r^2, input our own values into that, and we get 4*3.14*5^2 = 113.04, round down, and you get 113

Answer:

The aswer is buy a rabbit

Step-by-step explanation:

Answer:

1611.372

Step-by-step explanation:

Answer:

The answer is 2.21

Step-by-step explanation:

Answer:

2.21

Step-by-step explanation:

13(.17)

Answer:

A. 3

Step-by-step explanation:

[tex]y = 3x - 8 \\ at \: (6, \: 1) \\ \frac{dy}{dx} = 3 \\ at \: (x, \: y) \\ gradient = \frac{y - 1}{x - 6} \\ 3 = \frac{y - 1}{x - 6} \\ y - 1 = 3(x - 6)[/tex]

Answer:

b) Inductive

Step-by-step explanation:

It is correct to say that this is an example of inductive reasoning, because the reasoning is based on a situational perception and not on actual logic. Sarah based her reasoning on a premise that if she and her brothers have brown hair, then if she had another brother, he would also have brown hair.

Answer: 18

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

The graph shows 180 pages on it, and if you go over and down then it shows chapter 18.

Answer:

no pasa nada

Step-by-step explanation:

espero que eso te ayude:)

Answer:

Cualquier número dividido entre si mismo da como resultado 1

Answer:

8

Step-by-step explanation:

your welcome hope this helps :)

Answer:

It would take 16 years and 64 days until the investment reaches about $ 17323

Step-by-step explanation:

Given that an investment of $ 8500 increases in value by 4.5% every year, to determine how long it would take until the investment reaches about $ 17323, the following calculation must be performed:

8,500 x (1 + 0.045 / 1) ^ X = 17,323

8,500 x 1,045 ^ X = 17,323

1,045 ^ X = 17,323 / 8,500

1.045 ^ X = 2.038

1,045 ^ 16,175 = 2,038

X = 16.175

1 = 365

0.175 = X

0.175 x 365 = X

63.875 = X

Therefore, it would take 16 years and 64 days until the investment reaches about $ 17323

Answer:

C

Step-by-step explanation:

gghiruufkfhfjttyyyyyy

Answer:

the answer is (y-1) (y-5)

Answer:

f(2) = -3

g(-3) = -5

Step-by-step explanation:

----------------------

========================================================

Explanation:

Minor arc QV is 80 degrees because it adds to minor arc VU = 100 to get 80+100 = 180. Note how angle QPU = 180, since it's a straight line and QU is a diameter of the circle.

Add up the minor arcs

to get:  44+100+80 = 224

This means arc TUQ is 224 degrees. Inscribed angle QZT subtends arc TUQ. Use the inscribed angle theorem to say that the inscribed angle is half of the arc it cuts off.

angle QZT = (arc TUQ)/2

angle QZT = 224/2

angle QZT = 112 degrees

Answer:

0,-1, -7-2 is the correct answer

Answer:

[tex]Vertex = (\frac{1}{2},\frac{7}{4})[/tex]

Step-by-step explanation:

Given

[tex]f(x) = x^2 - x +2[/tex]

Required

The vertex

We have:

[tex]f(x) = x^2 - x +2[/tex]

First, we express the equation as:

[tex]f(x) = a(x - h)^2 +k[/tex]

Where

[tex]Vertex = (h,k)[/tex]

So, we have:

[tex]f(x) = x^2 - x +2[/tex]

--------------------------------------------

Take the coefficient of x: -1

Divide by 2: (-1/2)

Square: (-1/2)^2

Add and subtract this to the equation

--------------------------------------------

[tex]f(x) = x^2 - x +2[/tex]

[tex]f(x) = x^2 - x + (-\frac{1}{2})^2+2 -(-\frac{1}{2})^2[/tex]

[tex]f(x) = x^2 - x + \frac{1}{4}+2 -\frac{1}{4}[/tex]

Expand

[tex]f(x) = x^2 - \frac{1}{2}x- \frac{1}{2}x + \frac{1}{4}+2 -\frac{1}{4}[/tex]

Factorize

[tex]f(x) = x(x - \frac{1}{2})- \frac{1}{2}(x - \frac{1}{2})+2 -\frac{1}{4}[/tex]

Factor out x - 1/2

[tex]f(x) = (x - \frac{1}{2})(x - \frac{1}{2})+2 -\frac{1}{4}[/tex]

[tex]f(x) = (x - \frac{1}{2})^2+2 -\frac{1}{4}[/tex]

[tex]f(x) = (x - \frac{1}{2})^2+ \frac{8 -1 }{4}[/tex]

[tex]f(x) = (x - \frac{1}{2})^2+ \frac{7}{4}[/tex]

Compare to: [tex]f(x) = a(x - h)^2 +k[/tex]

[tex]h = \frac{1}{2}[/tex]

[tex]k = \frac{7}{4}[/tex]

Hence:

[tex]Vertex = (\frac{1}{2},\frac{7}{4})[/tex]

Question: Marsha wants to determine the vertex of the quadratic function f(x) = x2 – x + 2. What is the function’s vertex?

Answer:  A or 1/2 , 7/4

Step-by-step explanation:

did it on an assignment on EDGE

Answer:

By taking the height as x most probably

Step-by-step explanation:

Answer:

p(g) (85 if  3g)

p(g) (135 if 3g)

p(g) (195 if 6g)

lets move p fwd so that 3+3+2 = 8

8 games = 3(85) + 3(135) + 2(195)

               =  255 + 405 + 390

               =  1050 yards

Statement would be something like > more than 1000 or designed around a division as proof to prove average or mean per game  = 1050/8 = 131.25 mean or even the range  405-255 = 150 range whilst the median would be 135

Last question asks '' How many games has James played when he has scored 85 yards? '' The answer would be 1 game can be shown as g or 1g.

Let me know what the statement choices are and I'd be happy to help.

Step-by-step explanation:

Answer:

1.5×10^8

Step-by-step explanation:

Scientific notation can be regarded as

way to express large or too small numbers conveniently written in decimal form.

Given (3.4x10 4) (4.5x10 3).

To write your in scientific notation

3.4x10^4) (4.5x10^3)

This is multiplication

(3.4x10^4) ×(4.5x10^3)

(3.4x10^4)= 34000

(4.5x10^3)= 4500

Then multiply

4500 × 34000

= 153000000

= 1.5×10^8

Answer:

[tex](c)\ \tan B = \sin A[/tex]

Step-by-step explanation:

Given

[tex]\angle A + \angle B = 90[/tex] --- Complement angles

See attachment for complete question

Required

Which is not always true

To do this, we simply test each option

[tex](a)\ \sin A = \cos B[/tex]

The above is always true, if A and B are complements.

Examples are:

[tex]\sin(40) = \cos(50)[/tex]

[tex]\sin(90) = \cos(0)[/tex]

etc

[tex](b)\ \sec A = \csc B[/tex]

The above is always true, if A and B are complements.

The expression can be further simplified as:

[tex]\frac{1}{\cos A} = \frac{1}{\sin B}[/tex]

Cross Multiply

[tex]\sin B = \cos A[/tex]

This is literally the same as (a)

[tex](c)\ \tan B = \sin A[/tex]

The above is not always true, if A and B are complements.

The expression can be further simplified as:

[tex]\frac{\sin B}{\cos B} = \sin A[/tex]

Cross multiply

[tex]\sin B = \sin A * \cos B[/tex]

If A and B are complements. then

[tex]\sin A = \cos B[/tex]

So, we have:

[tex]\sin B = \sin A * \sin A[/tex]

[tex]\sin B = \sin^2 A[/tex]

The above expression is not true, for values of A and B

[tex](d) \cot B = \tan A[/tex]

The above is always true, if A and B are complements.

An example is:

[tex]\cot (55) = \tan (25) = 0.7002[/tex]

etc.

Answer:

3.1 0.6912 = 69.12% probability that one or two out of the next four customers will make a purchase.

3.2 0.9744 = 97.44% probability that at least one out of the next four customers do not make a purchase

Step-by-step explanation:

For each customer, there are only two possible outcomes. Either they make a purchase, or they do not. The probability of a customer making a purchase is independent of any other customer. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

40% of all customers walking into their store will buy at least one item on that occasion.

This means that [tex]p = 0.4[/tex]

4 customers:

This means that [tex]n = 4[/tex]

3.1 What is the probability that one or two out of the next four customers will make a purchase?

This is:

[tex]P(1 \leq X \leq 2) = P(X = 1) + P(X = 2)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 1) = C_{4,1}.(0.4)^{1}.(0.6)^{3} = 0.3456[/tex]

[tex]P(X = 2) = C_{4,2}.(0.4)^{2}.(0.6)^{2} = 0.3456[/tex]

So

[tex]P(1 \leq X \leq 2) = P(X = 1) + P(X = 2) = 0.3456 + 0.3456 = 0.6912[/tex]

0.6912 = 69.12% probability that one or two out of the next four customers will make a purchase.

3.2. What is the probability that at least one out of the next four customers do not make a purchase?​

This is:

[tex]P(X \leq 4) = 1 - P(X = 4)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 4) = C_{4,4}.(0.4)^{4}.(0.6)^{0} = 0.0256[/tex]

[tex]P(X \leq 4) = 1 - P(X = 4) = 1 - 0.0256 = 0.9744[/tex]

0.9744 = 97.44% probability that at least one out of the next four customers do not make a purchase

Answer:

it's B. i individually solved all of them using the pythagorean theorem.

Step-by-step explanation:

"The Pythagorean theorem states that, in a right triangle, the square of the length of the hypotenuse (the side across from the right angle) is equal to the sum of the squares of the other two sides. So if the length of the hypotenuse is c and the lengths of the other two sides are a and b, then c^2 = a^2 + b^2"

sqrt61=6+5

square everything on both sides and ur left with

61=36+25

61=50+11

61=61

boom

The Decreased amount of  £2123 by 8% is approximately; £1953.16

We want to decrease £2123 by 8%.

We can do this by the following formula;

Decreased amount = 2123 * (100% - 8%)

Decreased amount = 2123 * 92%

Decreased amount = £1953.16

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Answer:

A

Step-by-step explanation:

The product of  the expression [tex]\frac{x^2 - 16}{2x + 8} * \frac{x^3 - 2x^2 + x}{x^2 + 3x - 4}[/tex]  is [tex]\frac{x(x- 1)(x - 4)}{x(x + 4)}[/tex]

An expression is an algebraic term used for a mathematical statement that include variables and mathematical operations

Below is how to calculate the product

The product expression is given as:

[tex]\frac{x^2 - 16}{2x + 8} * \frac{x^3 - 2x^2 + x}{x^2 + 3x - 4}[/tex]

Express x^2 - 16 as a difference of two squares

[tex]\frac{(x - 4)(x + 4)}{2x + 8} * \frac{x^3 - 2x^2 + x}{x^2 + 3x - 4}[/tex]

Divide the expression

[tex]\frac{x - 4}{2} * \frac{x^3 - 2x^2 + x}{x^2 + 3x - 4}[/tex]

Factorize the other fraction

[tex]\frac{x - 4}{2} * \frac{x(x^2 - 2x + 1)}{(x -1)(x + 4)}[/tex]

Further factorize

[tex]\frac{x - 4}{2} * \frac{x(x- 1)(x - 1)}{(x -1)(x + 4)}[/tex]

Divide

[tex]\frac{x - 4}{2} * \frac{x(x- 1)}{x + 4}[/tex]

Multiply the fractions

[tex]\frac{x(x- 1)(x - 4)}{x(x + 4)}[/tex]

Hence, the product of  [tex]\frac{x^2 - 16}{2x + 8} * \frac{x^3 - 2x^2 + x}{x^2 + 3x - 4}[/tex]  is [tex]\frac{x(x- 1)(x - 4)}{x(x + 4)}[/tex]

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Answer:

5 students would be expecting to select a gold-wrapped candy from the bag.

Step-by-step explanation:

Since Mrs. Nickel puts a variety of wrapped chocolate candies in a bag, and there are 5 silver-wrapped candies, 1 purple-wrapped candy, 2 striped candies, and 4 gold-wrapped candies, if 15 students select one candy at a time out of the bag, without looking, and replace the candy after each draw, to determine how many students would be expecting to select a gold-wrapped candy from the bag, the following calculation must be performed:

5 + 1 + 2 + 4 = 12

4 gold-wrapped candies out of 12 in total

4/12

15 x 4/12 = X

15 x 0.333 = X

5 = X

Therefore, 5 students would be expecting to select a gold-wrapped candy from the bag.

Answer:

The answer to the question is C

Answer:

It's c

Step-by-step explanation:

[tex] \sqrt{ {15}^{2} + {8}^{2} } = 17 \\ \sin(x) = \frac{8}{17} \\ \cos(x) = \frac{15}{17} [/tex]