What is the intersection of the sets A= {2,3,4,7} and B= {2,5,7,13}

x + y = 12

Equation 2: Difference:

x - y = 4

Solution:

x + y = 12

x - y = 4

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

Add the two equations together:

2x = 16

Divide both sides by 2:

x = 8

Solve for y:

Use equation 1 substituting for x:

x + y = 12

8 + y = 12

Subtract 8 from both sides:

y = 4

Answer:

one number is 8 and the other number is 4.

8 + 4 = 12

8 - 4 = 4

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The numbers are 8 and 4.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Let the two numbers be M and N.

Now,

The sum is 12 and their difference is 4.

This can be written as,

M + N = 12 _____(1)

M - N = 4 _______(2)

From (1) we get,

M = 12 - N ______(3)

Putting (3) in (2) we get,

M - N = 4

12 - N - N = 4

12 - 2N = 4

Add 2N on both sides.

12 = 4 + 2N

Subtract 4 on both sides.

12 - 4 = 2N

8 = 2N

Divide 2 on both sides.

N = 8/2

N = 4

Now,

Put N = 4 on (3).

M = 12 - 4

M = 8

We can cross-check.

M + N = 12

8 + 4 = 12

12 = 12

M - N = 4

8 - 4 = 4

4 = 4

Proved.

Thus,

The numbers are 8 and 4.

Learn more about expressions here:

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Answer:309.799

Step-by-step explanation:293.08

14.00 =309.799

+ 2.719

Answer:

1) The simplified radical form is  [tex]\sqrt{36x^2}=6x[/tex]

2) The simplified radical form is  [tex]\sqrt{72x^3}=6x\sqrt{2x}[/tex]

3) The simplified radical form is  [tex]\sqrt{15x^8}=\sqrt{15}x^4[/tex]

4) The simplified radical form is  [tex]\sqrt{36x^7}=6x^3\sqrt{x}[/tex]

Step-by-step explanation:

1) Given expression is [tex]\sqrt{36x^2}[/tex]

To find the simplified radical form of the given expression :

[tex]\sqrt{36x^2}[/tex]

[tex]=\sqrt{36\times x^2}[/tex]

[tex]=\sqrt{36}\times \sqrt{x^2}[/tex]

[tex]=\sqrt{6\times 6}\times \sqrt{x\times x}[/tex]

[tex]=6\times x[/tex]

[tex]\sqrt{36x^2}=6x[/tex]

Therefore the simplified radical form is  [tex]\sqrt{36x^2}=6x[/tex]

2)Given expression is [tex]\sqrt{72x^3}[/tex]

To find the simplified radical form of the given expression :

[tex]\sqrt{72x^3}[/tex]

[tex]=\sqrt{72\times x^3}[/tex]

[tex]=\sqrt{72}\times \sqrt{x^3}[/tex]

[tex]=\sqrt{9\times 8}\times \sqrt{x\times x\times x}[/tex]

[tex]=\sqrt{9}\times \sqrt{8}\times x\sqrt{x}[/tex]

[tex]=3\times 2\sqrt{2}\times x\sqrt{x}[/tex]

[tex]\sqrt{72x^3}=6x\sqrt{2x}[/tex]

Therefore the simplified radical form is  [tex]\sqrt{72x^3}=6x\sqrt{2x}[/tex]

3) Given expression is [tex]\sqrt{15x^8}[/tex]

To find the simplified radical form of the given expression :

[tex]\sqrt{15x^8}[/tex]

[tex]=\sqrt{15\times x^8}[/tex]

[tex]=\sqrt{15}\times \sqrt{x^8}[/tex]

[tex]=\sqrt{5\times 3}\times \sqrt{x^4\times x^4}[/tex]

[tex]=\sqrt{15}\times x^4[/tex]

[tex]\sqrt{15x^8}=\sqrt{15}x^4[/tex]

Therefore the simplified radical form is  [tex]\sqrt{15x^8}=\sqrt{15}x^4[/tex]

4) Given expression is [tex]\sqrt{36x^7}[/tex]

To find the simplified radical form of the given expression :

[tex]\sqrt{36x^7}[/tex]

[tex]=\sqrt{36\times x^7}[/tex]

[tex]=\sqrt{36}\times \sqrt{x^7}[/tex]

[tex]=\sqrt{6\times 6}\times \sqrt{x^3\times x^3\times x}[/tex]

[tex]=6\times x^3\sqrt{x}[/tex]

[tex]\sqrt{36x^7}=6x^3\sqrt{x}[/tex]

Therefore the simplified radical form is  [tex]\sqrt{36x^7}=6x^3\sqrt{x}[/tex]

We are given a painter can paint 350 square feet in 1.25 hours.

We want to figure out the painting rate in square feet per hour. “Per hour” means for every 1 hour.

To find this, an equation like 350 = 1.25h (h for hours) can be set up. To solve, the only thing we need to do is divide by 1.25 to get h alone:

350/1.25 = 1.25h/1.25 or 280 = h

The painter can paint 280 square feet per 1 hour.

Answer:

A   =  90,312.5 square feet is the maximum area.

Step-by-step explanation:

Here, the shape of the enclosure  = Rectangle

Now, 3 sides of the rectangle needs to be fenced.

Total length of the fencing wire  = 1000 ft

Let us assume the length of the enclosure = L

The width of the enclose = W

According to question:

The length to fenced = Perimeter of the rectangle - 1 side of Enclosure

⇒ 1000  =  2 (L + W) - L

or, 1000 = L +  2 W

or, L  = 1000 - 2 W  .... (1)

Now, as we need to MAXIMIZE the area of the enclosure:

Area of the enclosure  = L x W    =  (1000 - 2 W) x  W

Now simplifying the area expression, we get:

[tex]A(w) = 1000 w - 2w^2[/tex]

This is a parabola that opens downward so there is a maximum point.

The vertex of the parabola is (h,k) where h is the "maximizing number" and k is the maximum area.

Use the fact that h   =   -b/2 a

h   =    -850/(2*[-2])

h  =   -850/(-4)

h   =   212.5 would be the length of all four sides if it were not for the barn

Therefore you have an extra 212.5 feet

Add the 212.5 feet to the opposite side(length) to get 425 feet.

You have a rectangle that is 212.5 feet by 425 feet by 212.5 feet by "the barn".

The width is 212.5 feet which maximizes the area.

A  =   l w

A  =  425*212.5

A   =  90,312.5 square feet is the maximum area.

For this case we must simplify the following expression:

[tex]\frac {3- \frac {2} {a}} {5+ \frac {3} {a}}[/tex]

So, we have:

[tex]\frac {\frac {3a-2} {a}} {\frac {5a + 3} {a}} =[/tex]

We apply double C:

[tex]\frac {a (3a-2)} {a (5a + 3)} =[/tex]

We simplify:

[tex]\frac {3a-2} {5a + 3}[/tex]

Answer:

The simplified expression is:

[tex]\frac {3a-2} {5a + 3}[/tex]

Answer:

number of sodas sold = 105

number of hot dogs sold = 61

Step-by-step explanation:

i) Let the number of sodas sold be = x

ii) Let the number of hot dogs sold be = y

iii) It is given that the total number of hot dogs and sodas sold = 166

Therefore we can say that x + y = 166

iv) It also given that the number of sodas sold was 44 more than the number of hot dogs sold

Therefore we can say that x = y + 44

v) Substituting the value of x from iv) in the equation in iii) we get

    (y + 44) + y  = 166 ⇒    2y + 44 = 166    ⇒   2y = 122  ∴ y = 61

   Therefore the number of hot dogs sold = 61

vi) Substituting the value of y from v) in iv) we get

            x = y + 44    ⇒    x = 61 + 44   ∴ x = 105

     Therefore the number of sodas sold = 105

Answer:

Step-by-step explanation:

so John (lol...who names a snake John)....ok...so at 5 months he was 4 ft...and at 6 months, he was 4'2....means he is growing at a rate of 2 inches per month. So if he continues to grow at 2 inches per month, then this is linear...but if he doesn't, its not linear.

So from 6 months to 1 year, is a period of 6 months...and if he grows at 2 inches per month, in 6 months he should have grown (6 * 2) = 12 inches.

4'2" + 12 inches = 4 ft 14 inches = 5 ft 2 inches......but he is not 5'2" at age 1, he is only 5 ft.....so NO, this is NOT linear.

Answer:

It has 2 solutions

Step-by-step explanation:

Solution 1

-17(y - 2) = -17y + 64 - 17(y - 2)

Solution 2

-17y + 64 - 17(y - 2) = -17y + 64

-17(y - 2) = -17y + 64

-17y  + 34 = -17y + 64

-17y + 17y = 64 - 34

0 = 30 (incorrect)

this system has NO SOLUTIONS

Answer:

37.41

Step-by-step explanation:

multiply 4.30 by 10 to get 43

then make it a decimal =0.43

after that multiply it by 13

0.43 times 13 = 5.59

subtract 5.59 from 43

Answer:

701 revolutions

Step-by-step explanation:

Given: Length= 2.5 m

            Radius= 1.5 m

            Area covered by roller= 16500 m²

Now, finding the Lateral surface area of cylinder to know area covered by roller in one revolution of cylindrical roller.

Remember; Lateral surface area of an object is the measurement of the area of all sides excluding area of base and its top.

Formula; Lateral surface area of cylinder= [tex]2\pi rh[/tex]

Considering, π= 3.14

⇒ lateral surface area of cylinder= [tex]2\times 3.14\times 1.5\times 2.5[/tex]

⇒ lateral surface area of cylinder= [tex]23.55 \ m^{2}[/tex]

∴ Area covered by cylindrical roller in one revolution is 23.55 m²

Next finding total number of revolution to cover 16500 m² area.

Total number of revolution= [tex]\frac{16500}{23.55} = 700.6369 \approx 701[/tex]

Hence, Cyindrical roller make 701 revolution to cover 16500 m² area.

The number of revolutions a cylindrical roller makes can be determined by first finding the area it covers in one revolution (using the formula for the surface area of a cylinder) and then dividing the total area covered by this. The formula to calculate the surface area of a cylinder is 2πrh, where r is the radius and h is the length of the cylinder.

First, we need to find the surface area of the roller. The surface area of a cylinder can be calculated using the formula: 2πrh, where r is the radius and h is the height (or in this case, the length of the roller). Here, r = 1.5m and h = 2.5m, so the surface area that the roller covers in one revolution is 2π(1.5m)(2.5m) = 11.25π m².

The roller covers an area of 16500 m², so to find out how many revolutions it makes, we divide the total area by the area covered in one revolution. That is, 16500m² / 11.25π m². After carrying out the division, we get the number of revolutions the roller makes. This will give us the desired answer.

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Answer:

X = 0.75

Step-by-step explanation:

0.25[2.5x + 1.5(X-4)]= -X

0.25[2.5x + 1.5x - 6] = -x

0.25[4x -6] = -x

1x + x = 1.5

2x = 1.5

x = 1.5/2

x = 0.75

Answer: 0.766 = x/12

Final answer:

The correct equation for the triangle is determined by the context provided, which may involve setting up proportions or using trigonometric ratios such as the tangent. Without specific information from a diagram or narrative of the triangle, the correct equation cannot be identified.

Explanation:

The correct equation based on the triangle shown is determined by setting up a mathematical relationship (proportion or equation) that represents the situation described in the diagram or narrative associated with the triangle. Without the specific diagram or narrative details, it is impossible to determine the correct equation. However, generally, if you are given the lengths of sides in different units (for example, feet and inches), you would set up a proportion like

1 foot/12 inches = x feet/y inches

and then cross-multiply to solve for x or y.

If you are dealing with trigonometric functions and are given an angle, you may use a function like sine, cosine, or tangent to find a relationship between the sides. The correct equation could include the tangent ratio if the triangle is right-angled and you have the lengths of the opposite and adjacent sides to the given angle:

tan(theta) = opposite/adjacent

Answer:

The ratio of AC to CB is 1.677 to  5.03

Step-by-step explanation:

Step 1: Finding the distance of AC

By using distance formula

[tex]AC = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}[/tex]

Substituting the values

[tex]AC = \sqrt{(1.5 -0)^2 + (0.75 -0)^2}[/tex]

[tex]AC = \sqrt{(1.5 )^2 + (0.75)^2}[/tex]

[tex]AC = \sqrt{2.25 +0.5625 }[/tex]

[tex]AC = \sqrt{2.8125 }[/tex]

AC= 1.677

Step 2: Finding the distance of CB

[tex]CB = \sqrt{(6 - 1.5)^2 + (3 - 0.75)^2}[/tex]

Substituting the values

[tex]CB = \sqrt{(4.5)^2 + (2.25)^2}[/tex]

[tex]CB = \sqrt{(20.25) + (5.0625)}[/tex]

[tex]CB = \sqrt{25.3125}[/tex]

CB = 5.03

The Ratio is   1.677 to  5.03

Answer:

Therefore the coordinates of C is

C(4,9).

Step-by-step explanation:

Given:

Point A , B , and C are Collinear.

i.e A-B-C is a Straight Line

AB : BC = 1 : 1

i.e B is the Mid Point of AC.

And Point A , B and C lie on the Same Line

point A( x₁ , y₁) ≡ ( 0 ,-9)

point B( x , y) ≡ (2 , 0)

To Find:

point C( x₂ , y₂) ≡ ?

Solution:

B is the Mid Point of AC. Hence by Mid point Formula,

[tex]Mid\ point(AC)=(\dfrac{x_{1}+x_{2} }{2}, \dfrac{y_{1}+y_{2} }{2})[/tex]

Substituting the values we get

[tex]B(2,0)=(\dfrac{0+x_{2} }{2}, \dfrac{-9+y_{2} }{2})[/tex]

Substituting x and y value we get

[tex]2=\dfrac{0+x_{2} }{2}\\and\\0=\dfrac{-9+y_{2} }{2}[/tex]

[tex]x_{2}=4\\and\\y_{2}=9[/tex]

Therefore the coordinates of C is

C(4,9).

Answer:

DC = 4.5

Step-by-step explanation:

Since DC is on AC it is a segment bisector.

This divides AC exactly in half.

AC = 9 / 2  = 4.5

DC = 4.5

x + 5y = -9

8x - 10y = 28

Set y equal

-2y - 10y = 18

8x - 10y = 28

Subtract from one another

-10x = -10

Divide

x = 1

Plug x in one of the equations and solve

x + 5y = -9

1 + 5y = -9

5y = -10

y = -2

Answer

(1,-2)

Hope this helps! ;)

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}x+5y=-9\\8x-10y=28&\text{divide both sides by 2}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}x+5y=-9\\4x-5y=14\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad5x=5\qquad\text{divide both sides by 5}\\.\qquad\boxed{x=1}\\\\\text{Put it to the first equation}\\\\1+5y=-9\qquad\text{subtract 1 from both sides}\\5y=-10\qquad\text{divide both sides by 5}\\\boxed{y=-2}[/tex]

Each month for 9 months, Jordan buys 2 sports books. How many more sports books does he need to buy before has bought 25 sports books?

Jordan needs to but 7 more sports book

From given,

Each month for 9 months, Jordan buys 2 sports books

Thus for one month he buys 2 sports books

For, 9 months, number of books is bought is given as:

[tex]\text{Number of books bought in 9 months } = 9 \times 2 = 18[/tex]

Thus, in 9 months he has bought 18 books

He needs to buy 25 sports books

Therefore, remaining books to be bought = 25 - 18 = 7

Thus he needs to buy 7 more books to have 25 of them

Answer:

78,732

Step-by-step explanation:

a_1 = 4

a_2 = 12

a_2/a_1 = 12/4 = 3

a_1 = 4

a_2 = 4 * 3 = 4 * 3^1 = 12

a_3 = 4 * 3 * 3 = 4 * 3^2 = 36

a_n = 4 * 3^(n - 1)

For n = 10:

a_10 = 4 * 3^(10 - 1) = 4 * 3^9 = 4 * 19,683 = 78,732

Final answer:

The formula for the nth term of a geometric sequence is a(n) = [tex]\[ a_n = a_1 \times r^{(n-1)} \][/tex], where a(n) is the nth term, a(1) is the first term, and r is the common ratio. In this case, the first term is 4 and the second term is 12. By using the formula, the calculated tenth term is 78,732. Therefore, the correct answer is C.

Explanation:

The formula for the nth term of a geometric sequence is given by:

[tex]\[ a_n = a_1 \times r^{(n-1)} \][/tex]

where:

- [tex]\( a_n \)[/tex] is the nth term,

- [tex]\( a_1 \)[/tex] is the first term,

- [tex]\( r \)[/tex] is the common ratio,

- [tex]\( n \)[/tex] is the term number.

In this case, the first two terms are given as 4 (which is [tex]\( a_1 \)[/tex]) and 12 (which is [tex]\( a_2 \)[/tex]).

The common ratio ([tex]\( r \)[/tex]) can be found by dividing the second term by the first term:

[tex]\[ r = \frac{a_2}{a_1} = \frac{12}{4} = 3 \][/tex]

Now, you can use this common ratio in the formula to find the 10th term [tex](\( a_{10} \))[/tex]):

[tex]\[ a_{10} = 4 \times 3^{(10-1)} \][/tex]

[tex]\[ a_{10} = 4 \times 3^9 \][/tex]

[tex]\[ a_{10} = 4 \times 19683 \][/tex]

[tex]\[ a_{10} = 78,732 \][/tex]

So, the correct answer is: C) 78,732

Answer:

Step-by-step explanation:

8. The volume of the rocket = the volume of the cone + the volume of the cylinder.

The volume of the cone is = [tex]\frac{1}{3} \pi \times radius^{2} (height) = \frac{1}{3} \pi \times 3^{2} \times5 = 15\pi[/tex] [tex]inch^{3}[/tex].

The volume of the cylinder is [tex]\pi \times radius^{2} \times height = \pi \times 3^{2} \times 10 = 90\pi[/tex] [tex]inch^{3}[/tex].

The total volume is [tex]15\pi + 90\pi = 105\pi inch^{3}[/tex].

9. Matt made the error in calculating the volume.

The diameter of the spherical ball is given by 15 centimeter.

The volume of a spherical ball is calculated by the formula [tex]\frac{4}{3} \pi \times radius^{3}[/tex].

Matt put the diameter of the spherical ball instead of its radius.

Answer:

y=3x+-7

Step-by-step explanation:

the standard form is y=mx+b

m being the slope and b being the y intercept

Answer:

$722.40

Step-by-step explanation:

2.8% x 4300 = 120.4

120.4 x 6 = 722.40

Step-by-step explanation:

9/8 × (-7/3) =

9 × -7 = -63

8 × 3 = 24

-63/24 simplify

-21/8

[tex]4NO+6H_{2} O\Leftrightarrow4 NH _{3}+5O_{2}[/tex]

Step-by-step explanation:

[tex]NO+H_{2} O\rightarrow NH _{3}+O_{2}[/tex]

[tex]4NO+6H_{2} O\Leftrightarrow4 NH _{3}+5O_{2}[/tex]

Answer:

x=6

Step-by-step explanation:

2x+(4x+3)=39

2x+4x+3=39

6x+3=39

6x=39-3

6x=36

x=36÷6

x=6

Solving the system of equations y = 4x + 3 and 2x + y = 39, we first substitute y from the first equation into the second. Simplifying, we find x = 6. Substituting x = 6 into the first equation, we find y = 27. Therefore, the solution is x = 6, y = 27.

To find the answer to this system of linear equations using substitution method, we first need to make y the subject of the first equation. From y = 4x + 3, we then substitute y in the second equation, thereby getting 2x + 4x + 3 = 39.

After simplifying, the combined equation becomes 6x + 3 = 39. We then isolate x by subtracting 3 from both sides, giving 6x = 36, and therefore x = 6.

To find y, substitute x = 6 into the first equation, y = 4x + 3. Thus, y = 4*6 + 3, which gives y = 27.

So, for the equations y = 4x + 3 and 2x + y = 39, the solution is x = 6, y = 27.

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Answer: x = -9, x = 115

Step-by-step explanation:

when x = -9 :

5(-9) + 40

-45 + 40

= -5

when x = 15

5(15) + 40

75 + 40

= 115

Answer:

X = -5, 40, 115

Step-by-step explanation:

when x = 0-9

5(0-9) + 40

-45 + 40

= -5

when x = 0T =0

5(0) + 40

0 + 40

= 40

when x = 015=15

5(15) + 40

75 + 40

= 115

The expression for the number of words Craig types in m minutes is 20 words/minute × m minutes. This equation can be used to calculate how many words Craig can type in any given number of minutes.

If Craig types at a speed of 20 words per minute, to find the expression for the number of words he types in m minutes, you would use the simple formula of rate times time. The rate is the number of words per minute, and the time is how many minutes he is typing. Therefore, the expression would be:

20 words/minute × m minutes = number of words Craig can type in m minutes.

To find out if Craig can type more than 200 words, you can set m to a value greater than 10, since 20 words/minute for 10 minutes would result in 200 words exactly (20 × 10 = 200).