Triangle ABC is a right triangle. The sides measure AB = 6 and BC = 8. Use the
Pythagorean theorem to find CA.

Answer:

Step-by-step explanation:

This problem can be solved by applying Pythagoras theorem, since the segment AB is tangent to the circle(meaning that the point A is at 90 degree to the circle)

According to Pythagoras theorem "It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides".

given (as seen from the diagram)

x, hypotenuse= ?

opposite= 12

adjacent= 35

Applying Pythagoras theorem

[tex]hyp^2= opp^2+adj^2\\\\hpy=\sqrt{opp^2+adj^2}[/tex]

Substituting our given data and solving for hpy we have

[tex]hyp=\sqrt{12^2+35^2} \\\\hyp=\sqrt{144+1225}\\\\hyp=\sqrt{1369}\\\\hyp= 37[/tex]

hence x= 37

Answer:

y = [tex]\frac{16}{3}x-79[/tex]

Step-by-step explanation:

From the given table,

Two points are (1, 15) and (7, 47)

If the two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are lying on a line then slope 'm' of the line will be,

m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

   = [tex]\frac{47-15}{7-1}[/tex]

   = [tex]\frac{32}{6}[/tex]

   = [tex]\frac{16}{3}[/tex]

Let the equation of a line passing through (h, k) is,

y - h = m(x - k)

If the line passes through (1, 15)

y - 1 = [tex]\frac{16}{3}(x-15)[/tex]

y = [tex]\frac{16}{3}x-\frac{16}{3}(15)+1[/tex]

y = [tex]\frac{16}{3}x-80+1[/tex]

y = [tex]\frac{16}{3}x-79[/tex]

Answer:

Commutative property

Step-by-step explanation:

In the Commutative property,the sequence or the order of factors of product does not change the value of the product.

Example:

in

12*5 = 5*12

also 12 = 3*4

(3*4)5 = (3*5)4

_____________________________

given

(2x)y = (2y)x

here it can be written as

(2*x)*y = (2*y)*x

removing the bracket for LHS we have

2*x*y ,    

applying Commutative property and changing order of x and y

2*x*y = 2*y*x

now again putting the bracket after first two terms

(2x)y = (2y)x

Thus, the expression illustrates Commutative property.

Answer:

[tex]\huge\boxed{14\ \text{and}\ 7}[/tex]

Step-by-step explanation:

[tex]n,\ m-\text{positive integer}\\\\n=2m-\text{a positive integer is twice another}\\\\\dfrac{1}{n}+\dfrac{1}{m}=\dfrac{3}{14}-\text{the sum of the reciprocal of the two positive integer is }\ \dfrac{3}{14}\\\\\text{We have the system of equations:}\\\\\left\{\begin{array}{ccc}n=2m&(1)\\\dfrac{1}{n}+\dfrac{1}{m}=\dfrac{3}{14}&(2)\end{array}\right[/tex]

[tex]\text{Substitute (1) to (2):}\\\\\dfrac{1}{2m}+\dfrac{1}{m}=\dfrac{3}{14}\\\\\dfrac{1}{2m}+\dfrac{1\cdot2}{m\cdot2}=\dfrac{3}{14}\\\\\dfrac{1}{2m}+\dfrac{2}{2m}=\dfrac{3}{14}\\\\\dfrac{1+2}{2m}=\dfrac{3}{14}\\\\\dfrac{3}{2m}=\dfrac{3}{14}\Rightarrow2m=14\qquad\text{divide both sides by 2}\\\\\dfrac{2m}{2}=\dfrac{14}{2}\\\\\boxed{m=7}[/tex]

[tex]\text{Substitute it to (1):}\\\\n=2\cdot7\\\\\boxed{n=14}[/tex]

Answer:

1/5, 0.25, 3/10

Step-by-step explanation:

1/5=2/10= 0.2

3/10= 0.3

hopefully this is helpful

Answer:

0.25,1/5,3/10 is the order from last to greater.

Step-by-step explanation:

Hope it will help you :)

Answer:

The relationship is that the value of the linear correlation coefficient will always have the same sign as the value of the slope of a regression​ line.

Step-by-step explanation:

The slope of regression is simply the covariance between X and Y divided by the variance of X i.e Cov(X, Y)/Var X. Whereas, the correlation is the covariance divided by the product of the standard deviation. Thus, we can say that the correlation is the product of the gradient of the regression line and the ratio of the standard deviations.

Thus, it means when the correlation is positive, the slope is also positive and vice versa.

The sign of the correlation coefficient, r, is always the same as that of the slope of the regression line.

Therefore, the sign of the correlation coefficient, r, is always the same as that of the slope of the regression line.

Learn more about correlation coefficient on:

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Answer:

24 inches

Step-by-step explanation:

The perimeter of the shape is 36 inches since the other sides are given as 12 and 3, 6 will be left for the x

12 + 12 + 3 + 3 + x = 36 and x = 6

Susie then drew a square using part of this shape and one side of the square is x inches if one side is x then all fours sides will be x inches

so the perimeter of the square is 4 × x = 24 because we already know x = 6

Answer:

The probability that a randomly selected passenger car gets more than 37.3 mpg is 0.1587.

Step-by-step explanation:

Let the random variable X represent the miles-per-gallon rating of passenger cars.

It is provided that [tex]X\sim N(\mu=33.8,\ \sigma^{2}=3.5^{2})[/tex].

Compute the probability that a randomly selected passenger car gets more than 37.3 mpg as follows:

[tex]P(X>37.3)=P(\frac{X-\mu}{\sigma}>\frac{37.3-33.8}{3.5})[/tex]

                   [tex]=P(Z>1)\\\\=1-P(Z<1)\\\\=1-0.84134\\\\=0.15866\\\\\approx 0.1587[/tex]

Thus, the probability that a randomly selected passenger car gets more than 37.3 mpg is 0.1587.

Answer:

72

32 x

________

 144

2160  +

________

2304

Step-by-step explanation:

Answer: $384

Step-by-step explanation:

1000- 1000=0

900-500=400

20-36=-16

400+-16=384

Answer:

18 millimeters

Step-by-step explanation:

The perimeter of any shape is the sum of the sides.  A trapezoid has four sides, so the perimeter is found by adding the four side lengths together.

The trapezoid in this problem has side lengths of 5 mm, 2 mm, 5 mm, and 6 mm.

Add the sides together.

5 mm + 2 mm + 5 mm + 6 mm

7 mm + 5 mm + 6mm

12 mm + 6 mm

18 mm

The perimeter of the trapezoid is 18 millimeters.

Answer:

(1) 0.75

(2) 30

(3) 56

Step-by-step explanation:

Let X represent the time for service call.

It is provided that: [tex]X\sim Uni(20, 60)[/tex]

The probability density function of X is:

[tex]f_{X}(x)=\frac{1}{b-a};\ a<X<b[/tex]

(1)

Compute the probability that the service call takes longer than 30 minutes as follows:

[tex]P(X>30)=\int\limits^{60}_{30} {\frac{1}{60-20}} \, dx[/tex]

                 [tex]=\frac{1}{40}\times |x|^{60}_{30}\\\\=\frac{60-30}{40}\\\\=\frac{3}{4}\\\\=0.75[/tex]

Thus, the probability that the service call takes longer than 30 minutes is 0.75.

(2)

The Inter quartile range is the difference between the 75th and 25th percentile.

From part (1), we know that P (X > 30) = 0.75.

⇒ 1 - P (X > 30) = 0.75

⇒ P (X < 30) = 0.25

The 25th percentile is 30.

Compute the 75th percentile as follows:

[tex]P(X<x)=0.75\\\\\int\limits^{x}_{20} {\frac{1}{60-20}} \, dx=0.75\\\\\frac{1}{40}\times |x|^{x}_{20}=0.75\\\\x-20=40\times 0.75\\\\x=30+20\\\\x=50[/tex]

The 75th percentile is 50.

Then the inter quartile range is:

[tex]IQR=P_{75}-P_{25}[/tex]

        [tex]=50-20\\=30[/tex]

Thus, the inter quartile range is 30.

(3)

Compute the 90th percentile as follows:

[tex]P(X<x)=0.90\\\\\int\limits^{x}_{20} {\frac{1}{60-20}} \, dx=0.90\\\\\frac{1}{40}\times |x|^{x}_{20}=0.90\\\\x-20=40\times 0.90\\\\x=36+20\\\\x=56[/tex]

The 90th percentile is 56.

Answer:

addition and multiplication

Step-by-step explanation:

The only operations that can use the commutative and associative properties are addition and multiplication.

Answer:

Step-by-step explanation:

Addition and Multiplication on edg.

Answer:

B. 16

Step-by-step explanation:

F(3) means we must plug the number "3" into the equation for each x.

(3)^2 + 3(3) -2

9 + 9 - 2

16

Answer:

16

Step-by-step explanation:

F(x) = x² + 3x - 2

Let x=3

F(3)= 3^2 +3*3 -2

     = 9+9-2

    = 18-2

     =16

Answer:

(-1/4, -5 3/4) or (-0.25, -5.75)

Step-by-step explanation:

Answer:

the answer is 2

Step-by-step explanation:

you subtract 10 by 8 and get 2, so w would be 2

Answer:

2

Step-by-step explanation:

w+8=10

Subtract 8 on both sides

w+8=10

   -8   -8

    w=2

Answer:

She must sell $60,000

Step-by-step explanation:

4 percent of 60,000 is 2,400 and you add the $400 that she automatically makes every month and you get $2800 as the total amount she makes.

Answer:

0.982 * [tex]\pi[/tex]  = 3.085 cubic units

Step-by-step explanation:

To find the volume of the solid generated by a region that is bounded by lines where x = 0 , x (b) = 2 we apply the formula given in the attachment below  

the required region boundaries are

y = e^-x2 , y = 0 ,  x = 0,  x = b ( b >0)

attached below is a detailed solution of the problem

Answer:

39

Step-by-step explanation:

difference=28

other number=11

so:

11+28=39

39 is your other number

Answer:

Just simply add the given two numbers and you ll get the answer 39 now to check whether its right or wrong subtract 11 from 39 and you ll get 28 which proves that its correct

Step-by-step explanation:

Answer:

x= 1/2

Step-by-step explanation:

Solving

Checking

Answer:

dy/dx = 8x + 1

Step-by-step explanation:

dy/dx = 2(2x+1)*2 - 3

dy/dx = 4(2x + 1) - 3

dy/dx = 8x + 4 - 3

dy/dx = 8x + 1

Answer:

A. <6

Step-by-step explanation:

Exterior angle of this geometric shape is 6

The exterior angle in the given figure is ∠6.

Option A is the correct answer.

The angles between two lines are the angles formed by two intersecting lines, measured in degrees or radians.

Several different types of angles can be formed between two lines, including acute angles, right angles, and obtuse angles.

We have,

From the diagram,

We see that the exterior angle is ∠6.

Now,

The exterior angle is the sum of its two nonadjacent interior angles.

So,

∠6 = ∠1 + ∠3

Thus,

The exterior angle is ∠6.

Learn more about angles here:

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Given that :-

To Find :-

Solution :-

→ Perimeter = 2( Length + breadth)

→ 26 = 2 ( Length+ 4 )

→ 26/2 = Length + 4

→ 13 = Length + 4

→ Length = 13 -4

→ Length = 9 meters.

So the Length of Lisa's garden is 9 meters .

Answer:

9

Step-by-step explanation:

Answer:

a) true

Step-by-step explanation:

Empirical hypothesis is the type of hypothesis used to try and explain a  phenomenon which leads to a theory been developed and put to the test, using observation and experiment.

Radium was discovered due to a discrepancy in pitchblende's radiation. It was noted by the Curies that Polonium alone could not suffice for that amount of radiation, leading to the theory that another element could be present. After further testing, Radium was discovered as the culprit element.

Also, the presence pf another planet, later discovered to be Neptune was theorized to explain the phenomenon that could cause the irregularities in the motion pattern of the planet Uranus. After much experimentation, observations and calculations, Neptune was discovered.

Let's first find the greatest common factor of 66 and 30.

To do this, start by dividing 66 by every natural

number you can until you hit repeat factors.

Also note, we need factors that are natural numbers! No decimals!

66 ÷ 1 = 66

66 ÷ 2 = 33

66 ÷ 3 = 22

66 ÷ 6 = 11

We can stop here because if we continue dividing, we hit repeat factors.

So the factors of 66 are 1, 2, 3, 6, 11, 22, 33, and 66.

Now do the same for 30.

30 ÷ 1 = 30

30 ÷ 2 = 15

30 ÷ 3  = 10

30 ÷ 5 = 6

The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.

Now look for the largest number shared by the two lists.

In this case, we have 6 as our gcf for the numbers.

Now let's do the variables.

To qualify for the Greatest Common Factor,

the variable must appear in every monomial.

Since the y doesn't appear in every monomial, it does not qualify.

If the variable does appear in every monomial, the Greatest

Common Factor will use the smallest power on that variable.

In this case, the smallest power between x and x² is x.

So our answer is 6x.

Answer:

Mark Me as Brainlieist

Step-by-step explanation:

6x

Answer:

4y - y^2 = 10

Step-by-step explanation:

Let x and y be the two numbers

x+y = 4

xy = 10

Taking the first equation and solving for x

x = 4-y

Substituting this into the second equation

(4-y) *y = 10

4y - y^2 = 10

Answer:

Step-by-step explanation:

no. of black balls = 5

no. of white balls = 6

total no. of balls = 5 + 6 = 11

The probability of picking a white ball = 6/11

no. of red balls = 15

no. of black balls = 25

total no. of balls = 15 + 25 = 40

The probability of selecting a black ball = 25/40

by simplifying,

25/40 = 5/8

hope this helps

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