find the area of the circle whose equation is x2+y2=6x-8y​

Answer:

A computer parts company wants to make a rectangular memory board that has a perimeter of 28 centimeters and a diagonal length of 10 centimeters. Find the dimensions of the board. Consider the length to be the longer side.: Call the two sides L & W: the perimeter 2L + 2W = 28 Simplify, divide by 2 L + W = 14 L = (14-W); use this form for substitution

Step-by-step explanation:

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

Explanation:

x = width

y = length

both x and y are positive real numbers, and the units of which are in cm.

The perimeter of any rectangle is found by saying

P = 2*(length+width)

P = 2*(x+y)

Plugging in P = 14 leads us to

P = 2*(x+y)

14 = 2*(x+y)

14/2 = x+y

7 = x+y

Solve for one of the variables. Let's say we solve for y. That should get us y = 7-x which we'll use a bit later.

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

Notice how the diagonal forms two identical right triangles. The legs of which are x and y as defined earlier. The hypotenuse is 5, which is the diagonal length.

Use the pythagorean theorem to help solve for x

a^2 + b^2 = c^2

x^2 + y^2 = 5^2

x^2 + (7-x)^2 = 25 ... plug in y = 7-x

x^2 + 49 - 14x + x^2 = 25 ... use FOIL rule

2x^2-14x+49 = 25

2x^2-14x+49-25 = 0

2x^2-14x+24 = 0

2(x^2-7x+12) = 0

x^2-7x+12 = 0

(x-3)(x-4) = 0

x-3 = 0 or x-4 = 0

x = 3 or x = 4

If x = 3, then y = 7-x = 7-3 = 4

If x = 4, then y = 7-x = 7-4 = 3

We have this symmetry going on. If x is one of 3 or 4, then y is the other of those values. Because x = 3 and y = 4, or vice versa, this means we have a 3-4-5 right triangle (well to be fair we have two identical copies of such a triangle to form the rectangle).

Therefore, the dimensions of the rectangular board is 3 cm by 4 cm. The order doesn't matter so you could easily say "4 cm by 3 cm" to mean the same thing.

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

Check:

P = perimeter

P = 2*(length+width)

P = 2*(x+y)

P = 2*(3+4)

P = 2*7

P = 14

That helps confirm the answer.

A shape of a trapezoid has exactly one line of symmetry. The correct option is B.

An open, flat object with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium.

A balanced and proportionate likeness between an object's two halves is referred to as symmetry in geometry. It implies that one half is the other's mirror image.

A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel. The parallel sides may be vertical, horizontal, or angled.

Therefore, the shape of a trapezoid has exactly one line of symmetry. The correct option is B.

To know more about Trapezoids follow

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Answer:

1500000

Step-by-step explanation:

1 metre = 100 cm

15000metre =15000*100

=1500000

Answer:

team a and team c scored 74 points which is 48 points more than team b, scoring 26 points.

Step-by-step explanation:

the center is at the origin of a coordinate system and the foci are on the y-axis, then the foci are symmetric about the origin.

The hyperbola focus F1 is 46 feet above the vertex of the parabola and the hyperbola focus F2 is 6 ft above the parabola's vertex. Then the distance F1F2 is 46-6=40 ft.

In terms of hyperbola, F1F2=2c, c=20.

The vertex of the hyperba is 2 ft below focus F1, then in terms of hyperbola c-a=2 and a=c-2=18 ft.

Use formula c^2=a^2+b^2c

2

=a

2

+b

2

to find b:

\begin{gathered} (20)^2=(18)^2+b^2,\\ b^2=400-324=76 \end{gathered}

(20)

2

=(18)

2

+b

2

,

b

2

=400−324=76

.

The branches of hyperbola go in y-direction, so the equation of hyperbola is

\dfrac{y^2}{b^2}- \dfrac{x^2}{a^2}=1

b

2

y

2

−

a

2

x

2

=1 .

Substitute a and b:

\dfrac{y^2}{76}- \dfrac{x^2}{324}=1

76

y

2

−

324

x

2

=1 .

Answer:

The right answer is:

(a) 0.1456

(b) 18.125, 69.1202, 8.3139

Step-by-step explanation:

Given:

N = 24

n = 5

r = 7

The improperly drilled gearboxes "X".

then,

⇒ [tex]P(X) = \frac{\binom{7}{x} \binom {17}{5-x}}{\binom{24}{5}}[/tex]

(a)

P (all gearboxes fit properly) = [tex]P(x=0)[/tex]

                                               = [tex]\frac{\binom{7}{0} \binom{17}{5}}{\binom{24}{5}}[/tex]

                                               = [tex]0.1456[/tex]

(b)

According to the question,

[tex]X = 91+5[/tex]

Mean will be:

⇒ [tex]\mu = E(x)[/tex]

       [tex]=E(91+5)[/tex]

       [tex]=9E(1)+5[/tex]

       [tex]=9.\frac{nr}{N}+5[/tex]

       [tex]=9.\frac{5.7}{24} +5[/tex]

       [tex]=18.125[/tex]

Variance will be:

⇒ [tex]\sigma^2=Var(X)[/tex]

         [tex]=V(9Y+5)[/tex]

         [tex]=81.V(Y)[/tex]

         [tex]=81.n.\frac{r}{N}.\frac{N-r}{N}.\frac{N-n}{N-1}[/tex]

         [tex]=81.5.\frac{7}{24}.\frac{24-7}{24}.\frac{24-5}{24-1}[/tex]

         [tex]=69.1202[/tex]

Standard deviation will be:

⇒ [tex]\sigma = \sqrt{69.1202}[/tex]

       [tex]=8.3139[/tex]      

Answer:

a) 75

b) 4.33

c) 0.75

d) [tex]3.2 \times 10^{-13}[/tex] probability that no one in a simple random sample of 100 young adults owns a landline

e) [tex]6.2 \times 10^{-61}[/tex] probability that everyone in a simple random sample of 100 young adults owns a landline.

f) Binomial, with [tex]n = 100, p = 0.75[/tex]

g) [tex]4.5 \times 10^{-8}[/tex] probability that exactly half the young adults in a simple random sample of 100 do not own a landline.

Step-by-step explanation:

For each young adult, there are only two possible outcomes. Either they do not own a landline, or they do. The probability of an young adult not having a landline is independent of any other adult, which 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.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

75% of all young adults between the ages of 18-35 do not have a landline in their homes and only use a cell phone at home.

This means that [tex]p = 0.75[/tex]

(a) On average, how many young adults do not own a landline in a random sample of 100?

Sample of 100, so [tex]n = 100[/tex]

[tex]E(X) = np = 100(0.75) = 75[/tex]

(b) What is the standard deviation of probability of young adults who do not own a landline in a simple random sample of 100?

[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100(0.75)(0.25)} = 4.33[/tex]

(c) What is the proportion of young adults who do not own a landline?

The estimation, of 75% = 0.75.

(d) What is the probability that no one in a simple random sample of 100 young adults owns a landline?

This is P(X = 100), that is, all do not own. So

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

[tex]P(X = 100) = C_{100,100}.(0.75)^{100}.(0.25)^{0} = 3.2 \times 10^{-13}[/tex]

[tex]3.2 \times 10^{-13}[/tex] probability that no one in a simple random sample of 100 young adults owns a landline.

(e) What is the probability that everyone in a simple random sample of 100 young adults owns a landline?

This is P(X = 0), that is, all own. So

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

[tex]P(X = 0) = C_{100,0}.(0.75)^{0}.(0.25)^{100} = 6.2 \times 10^{-61}[/tex]

[tex]6.2 \times 10^{-61}[/tex] probability that everyone in a simple random sample of 100 young adults owns a landline.

(f) What is the distribution of the number of young adults in a sample of 100 who do not own a landline?

Binomial, with [tex]n = 100, p = 0.75[/tex]

(g) What is the probability that exactly half the young adults in a simple random sample of 100 do not own a landline?

This is P(X = 50). So

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

[tex]P(X = 50) = C_{100,50}.(0.75)^{50}.(0.25)^{50} = 4.5 \times 10^{-8}[/tex]

[tex]4.5 \times 10^{-8}[/tex] probability that exactly half the young adults in a simple random sample of 100 do not own a landline.

Answer:

[tex]x = y^3+5y[/tex]

Step-by-step explanation:

Complete question

[tex]\frac{x - 5y}{y^3} - 1=0\\[/tex]

Required

Solve for x

We have:

[tex]\frac{x - 5y}{y^3} - 1=0[/tex]

Collect like terms

[tex]\frac{x - 5y}{y^3} = 1[/tex]

Multiply through by [tex]y^3[/tex]

[tex]x - 5y = y^3[/tex]

Make x the subject

[tex]x = y^3+5y[/tex]

Answer:

Just to recap, an equation has no solution when it results in an incorrect "equation".

For  example:

Equation: x+3 = x+4

Subtract x: 3 = 4???

But clearly, 3 is not equal to 4, so this equation has NO SOLUTION.

Now onto our problem:

13y+2-2y = 10y+3-y

11y+2 = 9y+3

2y=1

y=1/2

9(3y+7)-2 = 3(-9y+9)

27y+61 = -27y+27

54y = -34

y = -34/54

32.1y+3.1+2.4y-8.2=34.5y-5.1

34.5-5.1=34.5y-5.1

5.1=5.1

infinite solutions

5(2.2y+3.4) = 5(y-2)+6y

11y+17 = 11y-10

17 = -10??

That's not true, so the option "5(2.2y+3.4) = 5(y-2)+6y" has no solution.

Let me know if this helps

Answer: 3

happy learning

Answer:

B.

Step-by-step explanation:

From the point (-1,0) the next point on the graph is up 3, right 1, making the slope a positive 3.

Answer:

No

Step-by-step explanation: Bye

Answer:

The AP is 1, 11/2, 10, 29/2, 19, ....

Step-by-step explanation:

Let the first term be a and d be the common difference of the arithmetic progression.

ATQ, a+2d+a+6d=38, 2a+8d=38 and a+8d=37. Solving this, we will get a=1 and d=9/2. The AP is 1, 11/2, 10, 29/2, 19, ....

Answer:

Let the number of courses that are worth 3 credits each be x and those worth 4 credits be y. With the given information, you can write the following equations:  

x + y = 48

3x + 4y = 155

You can solve the above equations by method of elimination/substitution

x + y = 48 ⇒ x = 48 - y (Now, substitution this equation into 3x + 4y = 155)

3(48 - y) + 4y = 155

144 -3y + 4y = 155

y + 144 = 155

y = 11

Now plug this solution back into x = 48 - y  

x = 48 - 11 = 37  

Check work (by plugging the solutions back into the 3x + 4y and see if it's equal to 155):

3(37) + 4(11) = 155

Answer: There are 37 of the 3-credit course and 11 of the 4-credit course

Answer:

h = 6[tex]\sqrt{3}[/tex]

Step-by-step explanation:

The given is the special right triangle with angle measures : 90-60-30

and the side lengths for the given angles are represented by :

2a-a[tex]\sqrt{3}[/tex]-a

the side length that sees 60 degrees is represented by a[tex]\sqrt{3}[/tex] (h in this case)

the area of a triangle is calculated by multiplying height and base and that is divided by 2

a[tex]\sqrt{3}[/tex]*a/2 = 18[tex]\sqrt{3}[/tex] multiply both sides by 2

a^2[tex]\sqrt{3}[/tex] = 36[tex]\sqrt{3}[/tex] divide both sides by [tex]\sqrt{3}[/tex]

a^2 = 36 find the roots for both sides

a = 6

since h sees angle measure 60 and is represented by a[tex]\sqrt{3}[/tex]

h = 6[tex]\sqrt{3}[/tex]

Answer:

[tex]x=2[/tex]

Step-by-step explanation:

[tex]\frac{3x-2}{7}-\frac{5x-8}{4}=\frac{1}{14}[/tex]

In order to factor an integer, we need to divide it by the ascending sequence of primes 2, 3, 5.

The number of times that each prime divides the original integer becomes its exponent in the final result.

In here,  Prime number 2 to the power of 2 equals 4.

[tex]\frac{3x-2}{7}-\frac{5x-8}{2^{2} }=\frac{1}{14}[/tex]

First, We need to add fractions-

Rule:-

[tex]\frac{A}{B} +\frac{C}{D} =\frac{\frac{LCD}{B}+\frac{LCD}{D}C }{LCD}[/tex]

LCD = [tex]7 \cdot 2^{2}[/tex]

[tex]\frac{4(3x-2)+7(-(5x-8))}{7*2^{2} } =\frac{1}{14}[/tex]

[tex]x=2[/tex]

OAmalOHopeO

9514 1404 393

Answer:

  C. EGD

Step-by-step explanation:

A major arc is typically named using the end points and a point on the arc. Here, the end points are E and D, and points on the major arc include C, G, and F. The major arc ED could be named any of

Of course, the reverse of any of these names could also be used: DCE, DGE, DFE.

Answer:

x = -4/3

Step-by-step explanation:

6x + 11 = -6x - 5

12x = -16

x = -4/3

Answer:

x = -4/3

Step-by-step explanation:

6x + 11= - (6x + 5)

Distribute the minus sign

6x+11 = -6x-5

Add 6x to each side

6x+11 +6x = -6x-5+6x

12x+11 = -5

Subtract 11 from each side

12x+11-11 = -5-11

12x = -16

Divide by 12

12x/12 = -16/12

x = -4/3

Answer:

182/3,3 8/3, 152/3

Step-by-step explanation:

a+b+c=124

a trừ c=  10

4b=c

Answer:

a=29,b=79,c=19

Step-by-step explanation:

a=c+10

b=4c

=> a+b+c=c+10+4c+c=124

=> c=19

=> a= 29, b=79

Water drunk by Bobby in 10 hours = 5 units

So, water drink by Bobby in 1 hour

= 5/10 units

= 1/2 units

= 0.5 units

Answer:

1/2 water

Step-by-step explanation:

We can use a ratio to solve

5 waters        x waters

-----------   = ------------

10 hours             1 hours

Using cross products

5*1 = 10 *x

5 = 10x

Divide by 10

5/10 = x

1/2 waters =x

Answer:

Step-by-step explanation:

9514 1404 393

Answer:

  7.92 years

Step-by-step explanation:

We want to find t such that ...

  3 = 2^(t/5)

where 2^(t/5) is the annual multiplier when doubling time is 5 years.

Taking logs, we have ...

  log(3) = (t/5)log(2)

  t = 5·log(3)/log(2) ≈ 7.92 . . . years

It will take about 7.92 years for the population to triple.

Answer:

1st option

Step-by-step explanation:

Evaluate f(- 5) then substitute the value obtained into g(x)

f(- 5) = - 2(- 5) - 7 = 10 - 7 = 3 , then

g(3) = - 4(3) + 6 = - 12 + 6 = - 6

Answer:

y > -1

Step-by-step explanation:

the line is going across the y axis and is everything above -1

Answer:

Probability-Between    .8574 = 85.74%

Step-by-step explanation:

Z1=-2.14 Z2=1.14

*x-1 35

*x-2  58

*µ 50

*σ 7

Answer:

640

Step-by-step explanation:

muntiply all the number length width height

Let missing side be x

Using basic proportionality theorem

[tex]\\ \sf\longmapsto \dfrac{18}{14}=\dfrac{27}{x}[/tex]

[tex]\\ \sf\longmapsto \dfrac{9}{7}=\dfrac{27}{x}[/tex]

[tex]\\ \sf\longmapsto 9x=7(27)[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{7(27)}{9}[/tex]

[tex]\\ \sf\longmapsto x=21[/tex]

Answer:

$465.6 should be budgeted.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Normally distributed with mean $440 and standard deviation $20.

This means that [tex]\mu = 440, \sigma = 20[/tex]

How much should be budgeted for weekly repairs and maintenance so that the probability the budgeted amount will be exceeded in a given week is only 0.1?

The 100 - 10 = 90th percentile should be budgeted, which is X when Z has a p-value of 0.9, so X when Z = 1.28. Then

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.28 = \frac{X - 440}{20}[/tex]

[tex]X - 440 = 1.28*20[/tex]

[tex]X = 465.6[/tex]

$465.6 should be budgeted.

Answer:

[tex]C. \ \ \ 86[/tex]°

Step-by-step explanation:

1. Approach

In order to solve this problem, one must first find a relationship between arc (a) and arc (c). This can be done using the congruent arcs cut congruent segments theorem. After doing so, one can then use the secants interior angle to find the precise measurement of arc (a).

2. Arc (a) and arc (c)

A secant is a line or line segment that intersects a circle in two places. The congruent segments cut congruent arcs theorem states that when two secants are congruent, meaning the part of the secant that is within the circle is congruent to another part of a secant that is within that same circle, the arcs surrounding the congruent secants are congruent. Applying this theorem to the given situation, one can state the following:

[tex]a = c[/tex]

3. Finding the degree measure of arc (a),

The secants interior angle theorem states that when two secants intersect inside of a circle, the measure of any of the angles formed is equal to half of the sum of the arcs surrounding the angles. One can apply this here by stating the following:

[tex]86=\frac{a+c}{2}[/tex]

Substitute,

[tex]86=\frac{a+c}{2}[/tex]

[tex]86=\frac{a+a}{2}[/tex]

Simplify,

[tex]86=\frac{a+a}{2}[/tex]

[tex]86=\frac{2a}{2}[/tex]

[tex]86=a[/tex]

Answer:

16 once is the better one.

Answer: 12-ounce bag is better by $0.02 per ounce

Concept:

When coming across questions that ask for a comparison between prices, we should make the final unit [price per object].

In finding [price per object], simply do [Total price / number of objects].

Solve:

A 12-ounce bag of rice costs $4.08

Total price / number of objects = 4.08 / 12 = $0.34 per ounce

A 16-ounce bag of rice costs $5.76

Total price / number of objects = 5.76 / 16 = $0.36 per ounce

$0.36 - $0.34 = $0.02

$0.34 < $0.36, therefore, 12-ounce bag is better by $0.02 per ounce.

Hope this helps!! :)

Please let me know if you have any questions