Find A∩​B, given A={−6,−2,0,2,6} and B={−4,0,1,2,5,6}.

Answer:

  (A, B, C) = (8, 17, 23) inches

Step-by-step explanation:

We can let A, B, and C represent the corresponding side lengths. Then we are given ...

  A + B + C = 48 . . . . . . the perimeter is 48 inches

  B = A + 9 . . . . . . . . . . . B is 9 inches longer than A

  C = 2A +7 . . . . . . . . . . the base (remaining side) is 7 inches more than ...

Substituting for B and C in the first equation, we have ...

  A + (A+9) +(2A+7) = 48

  4A = 32 . . . . . . . . . . . . . . collect terms, subtract 16

  A = 8

  B = A+9 = 17

  C = 2A +7 = 23

Side A is 8 inches, side B is 17 inches, and side C is 23 inches.

Answer:

B {6, 6, 7}

Step-by-step explanation:

Which set of numbers may represent the lengths of the sides of a triangle? (A) {2,5,9} (B) {6,6,7} (C) {6,4,2} (D) {7,8,1}

For a given triangle with 3 sides, the sun of the length of any two sides must be greater Than the third side. This can be expressed mathematically as;

Let the side be ;

x, y and z

Then:

x > (y + z) or

y > (x + z) or

z > (x + y)

For A{2,5,9}

(2 + 5) < 9 (does not meet criteria)

For B {6,6,7}

(6 +6) > 7

(7 +6) > 6

Meets all criteria

For C {6,4,2}

(4 +2) is not greater Than 6 (does not meet criteria)

For D {7,8,1}

(7 +1) is not greater Than 8 ( does not meet criteria)

Answer:

Hey there!

There are actually multiple answers.

7 and 14 have a GCF (greatest common factor) of 7, and so do 7 and 7.

Let me know if this helps :)

Answer:

answers are:

7 and 14

The factors of 7 is:  1, 7

The factors of 14 is:  1, 2, 7, 14

28 and 7

Factors of 28:  1, 2, 4, 7, 14, 28

Facotrs of 7:  1, 7

Step-by-step explanation:

others:  

21, 3 is GCF is 3

The factors of 3 are: 1, 3

The factors of 21 are: 1, 3, 7, 21

7, 1 is GCF is 1

The factors of 1 are: 1

The factors of 7 are: 1, 7

Answer:

153:108

1.42

1 [tex]\frac{5}{12}[/tex]

1.42 is the approximate value of the ratio [tex]\frac{153}{108}[/tex].

The ratio is the number of times one value contains or is contained within the other in a quantitative relationship between two numbers.

The ratio of 153:108 is given.

Other forms of the ratio are

[tex]\frac{153}{108}=\frac{17}{12}[/tex]

[tex]=1.41666...\approx 1.42[/tex] (rounded to the hundredth place.

Learn more about ratios in- https://brainly.com/question/13419413?referrer=searchResults

#SPJ2

Answer:

2 works

-3 is extraneous

Step-by-step explanation:

sqrt(x + 7) - 1 = x                      Add 1 to both sides

sqrt(x + 7) = x + 1                     Square both sides

(x + 7) = (x + 1 )^2

x + 7 = x^2 + 2x + 1                Subtract x from both sides

0 = x^2 + x + 1 -7                    

0 = x^2 + x - 6                        This will factor

(x + 3)(x - 2)  = 0                      Find the values for x

x + 3 = 0

x = - 3

x - 2 = 0

x = 2

Now you must check this to see if both values work

sqrt(-3 + 7)  - 1 = -3

sqrt(4) - 1 = -3

2 - 1 =? - 3

1 does not equal - 3. Therefore - 3 is extraneous. Try x = 2

sqrt(2 + 7) - 1 = 2

sqrt(9) - 1 = 2

3 - 1 = 2

2 = 2

Answer:

t = 0.7 h

The time he rode at a slower speed is 1.2 h

Step-by-step explanation:

-The question involves algebra, to find the time the distance formula is used involving the values ​​of distance, time and speed.

- distance = speed 1 * time 1 + speed 2 * time 2

If Oscar traveled for t minutes at 9mph and it took him 15 minutes longer than when he traveled at 16mph it means that:

speed 1 * time 1 + 30 minutes.

But 30 minutes converted to hours is 0.5 hours

22 miles = 9 * (t + 0.5) + 16 * t

22 = 9t + 4.5 + 16t

17.5 = 25t

17.5 / 25 = t

The answer is: t = 0.7

Checking the value in the equation:

22 miles = 9 * (t + 0.5) + 16 * t

22 = 9 * (0.7 + 0.5) + 16 * 0.7

22 = 9 * 1.2 + 11.2

22 = 10.8 + 11.2

22 = 22

Answer:

50

Step-by-step explanation:

8 + 10a - 3 + 5a   when a=3

8+10(3)-3+5(3)=

8+30-3+15=

38+15-3=50

Answer: 11 9/35

Step-by-step explanation: just add the whole number to the fraction.

Answer & Step-by-step explanation:

[tex]11+\frac{9}{35}[/tex]

Add the whole number to the fraction:

[tex]11 \frac{9}{35}[/tex]

:Done

Answer:

-8 degrees

Step-by-step explanation:

4-12 = -8

It dropped 12 degrees in 7 hours.

Answer: -8°

Step-by-step explanation:

4 - 12

One example is the idea of two parts of a book that open up. Each flat part is a plane and the two planes intersect along the spine of the book.

Another example would be a wall intersecting with the floor. Both are flat surfaces.

A third example would be a laptop's screen as one plane and the keyboard as the other plane. They intersect at the hinge of the laptop.

For each example, the surface has a finite amount of area and it doesn't extend forever in all four directions. Theoretically, a plane is where the flat surface extends in all four directions infinitely. Though of course, real life has limitations but the idea is still applicable in a way.

Note how for each example, the two planes intersect to form a line. Also, each plane must be flat without bending or curving in any way.

Answer:

D. 327.25

Step-by-step explanation:

You start out with a gross pay of $415.00. When you have a deduction from your gross pay, it means it gets subtracted. So subtract the deductions of 48, 31.25, and 8.50 from 415 and it leaves you with 327.25.

415 48-31.25-8.50 = 327.25

Answer:

10

Step-by-step explanation:

Mathematical Formula: [tex]\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]

Therefore: [tex]\sqrt{\left(6-0\right)^2+\left(8-0\right)^2}[/tex]

Which = 10

Answer:

  a = 3x^2 +9x

Step-by-step explanation:

Put the given dimensions in the formula and simplify. The distributive property is useful.

  a = (1/2)bh

  a = (1/2)(6x)(x+3) = 3x(x +3)

  a = 3x^2 +9x

Answer:

x = 45°, y = 53°, z = 82°

Step-by-step explanation:

x is the first angle, y is the second, and z is the third.

The sum of the second and third, which is denoted by y + z, is 3 times the measure of the first, which is just x. So, we have:

y + z = 3 * x

Additionally, the third angle, z, is 29 more than the second, y, so:

z = 29 + y

We also know that the sum of the three is 180, so:

x + y + z = 180

Let's substitute y + z in the last equation with 3 * x:

x + y + z = 180

x + 3x = 180

4x = 180

x = 45

Now, we know that y + z = 3 * 45 = 135. We also know that z = 29 + y, so substitute 29 + y in for z in y + z = 135:

y + z = 135

y + (29 + y) = 135

2y + 29 = 135

2y = 106

y = 53

Finally, use this value of y to solve for z:

z = 29 + y

z = 29 + 53 = 82

Thus, the angles are x = 45°, y = 53°, and z = 82°.

~ an aesthetics lover

Answer:

D

Step-by-step explanation:

I answer this already.  XD

Answer:

D

Step-by-step explanation:

sorry i needed these points XD

Answer:

not equal

Step-by-step explanation:

Answer:

4/5 is not equal to 5/4.

4/5 x 4 = 16/20

5/4 x 5 = 25/20

25/20 > 16/20

Answer: Pick anyone that suits you

Step-by-step explanation:

Answer:

[tex]\large \boxed{\mathrm{Eight \ subtracted \ from \ the \ product \ of \ three \ and \ a \ number.}}[/tex]

Step-by-step explanation:

[tex]\sf 3n-8[/tex]

n is a number.

8 is subtracted from the product of 3 and a number.

The verbal expression would be :

Eight subtracted from the product of three and a number.

Answer:

[tex]\mathbf{S =6 \sqrt{1 + \dfrac{\pi^2}{9} }+ \dfrac{18}{\pi} In (\dfrac{\pi}{3}+ \sqrt{1+ \dfrac{\pi^2}{9}})}[/tex]

Step-by-step explanation:

Given that

curve [tex]y = \dfrac{\pi x}{3}, 0 \leq x \leq 3[/tex]

The objective is to find the area of the surface obtained by rotating the above curve about the x-axis.

Suppose f is positive and posses a continuous derivative,

the surface is gotten by the rotating the curve about the x-axis is:

[tex]S = \int ^b_a 2 \pi f (x) \sqrt {1 + (f' (x))^2 } \ dx[/tex]

The derivative of the function [tex]y' = \dfrac{\pi}{3} cos \dfrac{\pi x}{3}[/tex]

As such, the surface area is:

[tex]S = \int ^3_0 2 \pi sin \dfrac{\pi x}{3} \sqrt {1 +(\dfrac{\pi}{3}cos \dfrac{\pi x}{3})^2 } \ dx[/tex]

Suppose ;

[tex]u = \dfrac{\pi}{3}cos \dfrac{\pi x}{3}[/tex]

[tex]du = -( \dfrac{\pi}{3})^2 sin \dfrac{\pi x}{3} \ dx[/tex]

If x = 0 , then [tex]u = \dfrac{\pi}{3}cos \dfrac{\pi (0)}{3} = \dfrac{\pi}{3}[/tex]

If x = 3 , then [tex]u = \dfrac{\pi}{3}cos \dfrac{\pi (3)}{3}[/tex]

[tex]u = \dfrac{\pi}{3}(-1)[/tex]

[tex]u = -\dfrac{\pi}{3}[/tex]

The equation for S can now be rewritten as:

[tex]S = \int^3_0 2 \pi sin \dfrac{\pi x}{3} \sqrt{1+(\dfrac{\pi}{3} cos \dfrac{\pi x}{3})^2 }\ dx[/tex]

[tex]S = 2 \pi \int ^{-\frac{\pi}{3} }_{\frac{\pi}{3}}(-\dfrac{9 \ du }{\pi^2} ) \sqrt{1+u^2}[/tex]

[tex]S = 18 \pi * \dfrac{1}{\pi ^2 } \int ^{-\frac{\pi}{3}}_{\frac{\pi}{3}} \sqrt{1+u^2} \ du[/tex]

[tex]S = \dfrac{18} {\pi} \int ^{-\frac{\pi}{3}}_{\frac{\pi}{3}} \sqrt{1+u^2} \ du[/tex]

[tex]S = \dfrac{18} {\pi} (2 \int ^{-\frac{\pi}{3}}_{0} \sqrt{1+u^2} \ du)[/tex]

since [tex](\int ^a_{-a} fdx = 2\int^a_0 fdx , f= \sqrt{1+u^2} \ is \ even )[/tex]

Applying the formula:

[tex]\int {\sqrt{1+x^2}} \ d x= \dfrac{x}{2} \sqrt{1+x^2}+ \dfrac{1}{2} In ( x + \sqrt{1+x^2})[/tex]

[tex]S = \dfrac{36}{x}[ \dfrac{u}{2} \sqrt{1+u^2}+ \dfrac{1}{2} \ In (u+ \sqrt{1+u^2}) ] ^{\frac{\pi}{3}}_{0}[/tex]

[tex]S = \dfrac{36}{x}[ \dfrac{\dfrac{\pi}{3}}{2} \sqrt{1+\dfrac{\pi^2}{9}}+ \dfrac{1}{2} \ In (\dfrac{\pi}{3}+ \sqrt{1+\dfrac{\pi^2}{9}})-0 ][/tex]

[tex]S =6 \sqrt{1 + \dfrac{\pi^2}{9} }+ \dfrac{18}{\pi} In (\dfrac{\pi}{3}+ \sqrt{1+ \dfrac{\pi^2}{9}})[/tex]

Therefore, the exact area of the surface is [tex]\mathbf{S =6 \sqrt{1 + \dfrac{\pi^2}{9} }+ \dfrac{18}{\pi} In (\dfrac{\pi}{3}+ \sqrt{1+ \dfrac{\pi^2}{9}})}[/tex]

The area of the surface is,[tex]S = 6\sqrt{1+\dfrac{\pi ^2}{3}} + \dfrac{18}{3}\ ln (\dfrac{\pi }{3}+\sqrt{1+\dfrac{\pi ^2} {9}})[/tex].

Given that,

The exact area of the surface obtained by rotating the curve about the x-axis. y = sin πx\3 , 0 ≤ x ≤ 3.

We have to determine,

Area of the surface obtained by rotating the curve.

According to the question,

Suppose f is positive and posses a continuous derivative,

The surface is gotten by the rotating the curve about the x-axis is:

Area of the surface is given by,

[tex]S = \int\limits^b_a {2\pi f(x) .\sqrt{1+ (f'(x))} } \, dx[/tex]

The given curve is x-axis,

[tex]y = \dfrac{sin\pi x}{3}[/tex]

The derivative of the function is,

[tex]\dfrac{dy}{dx} =\dfrac{\pi }{3} \dfrac{ cos\pi x}{3}[/tex]

The surface area is,

[tex]S = \int\limits^b_a {2\pi f(x) .\sqrt{1+(\dfrac{\pi }{3} \dfrac{ cos\pi x}{3})^2} }}} \, dx[/tex]

Substitute the value of f(x),

[tex]S = \int\limits^3_0{2\pi\dfrac{sin\pi x}{3} .\sqrt{1+(\dfrac{\pi }{3} \dfrac{ cos\pi x}{3})^2} }}} \, dx[/tex]

Suppose;

[tex]u = \dfrac{\pi }{3}cos\dfrac{\pi x}{3}dx\\\\\du =( \dfrac{-\pi }{3})^2 sin\dfrac{\pi x}{3}dx\\\\if \ x = 0, \ then \ u = \dfrac{\pi }{3}cos\dfrac{\pi (0)}{3} = \dfrac{\pi }{3}\\\\if \ x = 3, \ then \ u = \dfrac{\pi }{3}cos\dfrac{\pi (3)}{3} = \dfrac{\pi }{3}(-1)= \dfrac{-\pi }{3}[/tex]

Then,

[tex]S = \int\limits^3_0{2\pi\dfrac{sin\pi x}{3} .\sqrt{1+(\dfrac{\pi }{3} \dfrac{ cos\pi x}{3})^2} }}} \, dx\\\\S = 2\pi \int\limits^{\frac{-\pi}{3}}_ \frac{\pi }{3} (\dfrac{-9du}{\pi ^2})\sqrt{1+u^2} \ du\\\\S = 18\pi \times \dfrac{1}{\pi ^2}\int\limits^{\frac{-\pi}{3}}_ \frac{\pi }{3} \sqrt{1+u^2} \ du\\\\S = \dfrac{18}{\pi}\int\limits^{\frac{-\pi}{3}}_ {0} 2\sqrt{1+u^2} \ du\\\\\\[/tex]

Since,

[tex](\int\limits^a_{-a}{f} \, dx = 2\int\limits^a_0 {f} \, dx , \ f = \sqrt{1+u^2}\ is \ even)[/tex]

By applying the formula to solve the given integration,

[tex]\int {\sqrt{1+x^2} } \, dx = \dfrac{x}{2}\sqrt{1+x^2} + \dfrac{1}{2} \ ln(x+\sqrt{1+x^2})\\\\S = \dfrac{36}{2} [ \dfrac{u}{2} \sqrt{1+u^2} + \dfrac{1}{2} \ ln(u+\sqrt{1+u^2})}]^{\frac{\pi }{3}}_0\\\\[/tex]

[tex]S = \dfrac{36}{2} [ \dfrac{\dfrac{\pi }{3}}{2} \sqrt{1+\dfrac{\pi^2 }{9}} + \dfrac{1}{2} \ ln(\dfrac{\pi }{3}+\sqrt{1+\dfrac{\pi ^2} {9}}-0)]\\\\S = 6\sqrt{1+\dfrac{\pi ^2}{3}} + \dfrac{18}{3}\ ln (\dfrac{\pi }{3}+\sqrt{1+\dfrac{\pi ^2} {9}})[/tex]

Hence, The area of the surface is,[tex]S = 6\sqrt{1+\dfrac{\pi ^2}{3}} + \dfrac{18}{3}\ ln (\dfrac{\pi }{3}+\sqrt{1+\dfrac{\pi ^2} {9}})[/tex]

To know more about Integration click the link given below.

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Answer: 11 stamps per page

Step-by-step explanation: 132 divided by 12

Answer:

A. 18

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Write out expression

12(20 - 18) - 3(6)

Step 2: Multiply parenthesis

12(20 - 18) - 18

Step 3: Parenthesis

12(3) - 18

Step 4: Multiply

36 - 18

Step 5: Subtract

18

Answer:

approximately 26.7 million

Step-by-step explanation:

Let x be the number of cruise passengers in 2017.

6.7% increase of x gives us 28.5 m cruise passengers in 2018.

Thus, 106.7 % of x = 28.5

[tex] \frac{106.7}{100} * x = 28.5 [/tex]

[tex] \frac{106.7x}{100} = 28.5 [/tex]

Multiply both sides by 100

[tex] \frac{106.7x}{100} * 100 = 28.5*100 [/tex]

[tex] 106.7x = 2850 [/tex]

Divide both sides by 106.7

[tex] \frac{106.7x}{106.7} = \frac{2850}{106.7} [/tex]

[tex] x = 26.7 [/tex] (approximated)

Number of passengers in 2017 must have been approximately 26.7 million

Answer:

[tex]0 \leq x \leq 100[/tex]

0, 40, and 80 are the values that work for this compound inequality.

Step-by-step explanation:

To create a compound inequality, we have to examine the conditions for [tex]x[/tex] to work.

Since [tex]x[/tex] can not be below 0° C, that means that [tex]x[/tex] must be greater than or equal to 0.

Which is represented as [tex]x\geq 0[/tex], or [tex]0\leq x[/tex].

Since [tex]x[/tex] can not be above 100° C, that means [tex]x[/tex] must be less than 100.

Which is represented as [tex]x \leq 100[/tex].

We can combine both inequalities into one, where [tex]x[/tex] is shared between the two. This creates [tex]0\leq x \leq 100[/tex].

Let's test each value of [tex]x[/tex] .

0 is equal to 0 and less than 100, so it works.

40 is greater  than 0 and less than 100, so it works.

80 is greater  than 0 and less than 100, so it works.

120 is greater  than 0 and greater than 100, so it doesn't work.

160 is greater  than 0 and greater than 100, so it doesn't work.

Hope this helped!

Answer:

x = -34 , y = 31

Step-by-step explanation suing Gaussian elimination:

Solve the following system:

{2 x + 3 y = 25

3 x + 4 y = 22

Express the system in matrix form:

(2 | 3

3 | 4)(x

y) = (25

22)

Write the system in augmented matrix form and use Gaussian elimination:

(2 | 3 | 25

3 | 4 | 22)

Swap row 1 with row 2:

(3 | 4 | 22

2 | 3 | 25)

Subtract 2/3 × (row 1) from row 2:

(3 | 4 | 22

0 | 1/3 | 31/3)

Multiply row 2 by 3:

(3 | 4 | 22

0 | 1 | 31)

Subtract 4 × (row 2) from row 1:

(3 | 0 | -102

0 | 1 | 31)

Divide row 1 by 3:

(1 | 0 | -34

0 | 1 | 31)

Collect results:

Answer: {x = -34 , y = 31

Answer:

Cosec θ = – 25/24

Step-by-step explanation:

From the question given, we obtained the following information:

Tan θ = – 24/7

Cosec θ =?

Tan θ is negative in the forth quadrant.

Please see attached photo.

Tan θ = Opposite /Adjacent

Opposite = – 24

Adjacent = 7

Hypothenus = x

Thus, we can obtain the value of x by using the pythagoras theory as illustrated below:

x² = (–24)² + 7²

x² = 576 + 49

x² = 625

Take the square root of both side

x = √625

x = 25

Next, we shall determine Sine θ. This can be obtained as follow:

Opposite = – 24

Hypothenus = 25

Sine θ = ?

Sine θ = Opposite /Hypothenus

Sine θ = –24/25

Finally, we shall determine the Cosec θ. This can be obtained as follow:

Cosec θ = 1 /Sine θ

Sine θ = –24/25

Cosec θ = 1 ÷ –24/25

Cosec θ = 1 × – 25/24

Cosec θ = – 25/24

Answer:

[tex]\sqrt{4}, \ \sqrt{9} \text{ are rational numbers.}[/tex]

Step-by-step explanation:

Hello,

[tex]\sqrt{n^2}=n \ for \ n\geq 0\\\\\text{For instance}\\\\\sqrt{2^2}=2=\sqrt{4}\\\\\sqrt{3^2}=3=\sqrt{9}[/tex]

Answer:

B

Good luck in Geometry my guy!

Answer:

Options (B) and (C)

Step-by-step explanation:

We have to form a function which has following characteristics,

1). Its range is all real numbers

 Which means graph of the given function starts from negative side of the y-axis (-∞) and goes towards positive direction of the y-axis (+∞).

It's a typical characteristic of odd degree polynomial/function.

2). The graph has exactly two x-intercepts.

  Which means when we put f(x) = 0, we get exactly two values of x.

Therefore, function will be, f(x) = x³ + x²

Range of the function → (-∞, ∞) Or a set of all real numbers.

x-intercepts → f(x) = x³ + x² = 0

                             x²(x + 1) = 0

                             x = -1, 0

Therefore, Options (B) and (C) will be the answer.