Solve the simultaneous equation
-4x+3y=1
6x-y=2

Answer: 14

Step-by-step explanation:

First. take the prime factorization of all three numbers:

42: 21*2 ==> 3*7*2

70: 35*2 ==> 5*7*2

84: 42*2 ==> 21*2*2 ==> 3*7*2*2

Notice any common factors? That's the GCF.

GCF: 7*2=14

GCF: 14

Answer:

14

Step-by-step explanation:

The greatest number that divides 42, 70, and 84 exactly is their greatest common factor.

Factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42

Factors of 70 = 1, 2, 5, 7, 10, 14, 35, 70

Factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

The GCF of 42, 70, and 84 is 14.

The greatest number that divides 42, 70, and 84 is 14.

What is GCF?

The biggest positive integer that divides evenly into all the numbers with no remainder is the greatest common factor (GCF, GCD, or HCF) of a set of whole numbers. For instance, the GCF is equal to 6 for the set of numbers 18, 30, and 42.

How do I get the GCF of something?

The greatest common factor among numbers can be discovered in a number of ways.

Factoring:

List each number's factors in order to calculate the GCF by factoring. The factors that evenly divide into the number with no remainder are known as whole numbers. The GCF is the largest number that appears on each list of common factors for each number.

Example: Find the GCF of 18 and 27

The factors of 18 are 1, 2, 3, 6, 9, 18.

The factors of 27 are 1, 3, 9, 27.

The common factors of 18 and 27 are 1, 3 and 9.

The greatest common factor of 18 and 27 is 9.

Prime Factorization:

List all of each number's prime factors to determine the GCF by prime factorization. List the prime factors that each of the original numbers has in common. Include the most instances of each prime factor that each original number has in common. To find the GCF, multiply these by one another.

You'll observe that the prime factorization approach may be simpler than straight factoring as numbers grow larger.

Example: Find the GCF (18, 27)

The prime factorization of 18 is 2 x 3 x 3 = 18.

The prime factorization of 27 is 3 x 3 x 3 = 27.

The occurrences of common prime factors of 18 and 27 are 3 and 3.

So the greatest common factor of 18 and 27 is 3 x 3 = 9.

There is another method but it focuses on more complex numbers.

Hope this helps!

Answer:

Area of Desert 1 = 12,000,000     Area of Desert 2 = 3,000,000

Step-by-step explanation:

x+y=15,000,000

x=4y

4y+y=15,000,000

5y=15,000,000

y=3,000,000

The two points on the y axis that are 25 units from (-24,3) will be (0, 10) and (0, - 4).

We are given a point:

( - 24 , 3 )

We need to find a point on the y - axis, that is 25 units away from the axis.

The coordinate of the point will be:

(0, y)

So, by using the distance formula, we get that:

D = √ ( y₂ - y₁)² + ( x₂ - x₁)²

25 = √ ( y + 3)² + (0 + 24)²

625 = y² + 9 - 6 y + 576

625 = y² - 6 y + 585

y² - 6 y - 40 = 0

y² - 10 y + 4 y - 40 = 0

y ( y - 10 ) + 4 ( y - 10 ) = 0

(y - 10)(y + 4) = 0

y = - 4 or y = 10.

So, the two points will be:

(0, 10) and (0, - 4)

Therefore, we get that, the two points on the y axis that are 25 units from (-24,3) will be (0, 10) and (0, - 4).

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Answer:

x = 1/2

Step-by-step explanation:

4x -3 = 2x - 2  There are many ways to approach this problem.  I am going to start by subtracting 2x from both sides of the equation.

2x -3 = -2  I am going to add 3 to both sides of the equation

2x = 1  Divide both sides of the equation by 2

x = 1/2

The acres of vacant land that the county have now will be 144 acres.

Since 36% has been used, the remaining percentage will be:

= 1 - 36%

= 64%

Therefore, the acres of vacant land that the county have now will be:

= 64% × 225

= 64/100 × 225

= 0.64 × 225

= 144

Therefore, the acres of vacant land that the county have now will be 144 acres.

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Answer:

Yes

Step-by-step explanation:

If you have a graphing calculator or something similar, that could really help because all you would have to do is plug in the equation and look up the table and it would show that coordinate in there.

Answer:

a)

sin30=high of steps/175

sin30=1/2

so

high of steps= 175/2

high of steps=87.5cm

b)

cos30=wide/175

cos30=3^1/2÷2

wide=175*3^1/2÷2

3^1/2=1.73

so

wide=175*1.73/2

wide=151.37

Answer:

See below to complete

Step-by-step explanation:

ABC = 37 +21 °

LMN = 85 +23 °

Answer:

Image 2: a segment from -4 to 4 with the endpoints excluded (with empty circles).

Step-by-step explanation:

|x| < 4 means "the distance from x to 0 is less than 4". That means that any number bigger than -4 and smaller than 4 matches the inequality from the question.

Side note: Please start analyzing the absolute values as "distance from 0" and you'll be able to solve those questions yourself with less effort.

Height is h = 8 and base  = 19 inch in triangle .

What Does a Triangle's Area Mean?

Area of a triangle whose base is b and height is h is =1/2 * b * h

Let the height of given triangle be h inch and as base of a triangle is 3 inch greater than the height, base is ( 2h + 3)

b = 2h + 3

Hence, its area is 1/2 × h ×  (2h + 3 ) = 76 inch²

So,   1/2 × h × (2h + 3)  = 76

       2h² + 3h  = 76 × 2

       2h² + 3h - 152 = 0

       2h² + 19h - 16h - 152 = 0

       h( 2h + 19 ) -8 (2h + 19) = 0

        (h-8) ( 2h - 19)

 now   h = 8    and  h = -19/2  but height of triangle cannot be negative.

Hence height is h = 8 and base = 2 * 8 + 3 = 19 inch

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A line has no thickness, but it does have direction and infinite length.

A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions.

Given the variety of geometries in modern mathematics, the idea of a line is directly related to how the geometry is described. For instance, a line in the plane is frequently defined in analytic geometry as the collection of points whose coordinates satisfy a given linear equation, but in a more abstract context, such as incidence geometry, a line may be an independent object, distinct from the collection of points that lie on it.

In cartesian plane the general equation of a line is given by :

y=mx+c where the slope is denoted by m and the y-intercept by c.

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keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of TU

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{-8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-8}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{-2}-\underset{x_1}{1}}} \implies \cfrac{-13}{-3}\implies \cfrac{13}{3}[/tex]

hmmmm, well, if that's so, then the slope of VW will be the negative reciprocal of that only if both are really perpendicular, so

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{13}{3}} ~\hfill \stackrel{reciprocal}{\cfrac{3}{13}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{3}{13}}}[/tex]

since now we know the slope if VW, let's use it

[tex](\stackrel{x_1}{7}~,~\stackrel{y_1}{-9})\qquad (\stackrel{x_2}{-6}~,~\stackrel{y_2}{y}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{y}-\stackrel{y1}{(-9)}}}{\underset{run} {\underset{x_2}{-6}-\underset{x_1}{7}}} \implies \cfrac{y +9}{-13}~~ = ~~\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{3}{13}}\implies y+9=\cfrac{3(-13)}{-13} \\\\\\ y+9=3\implies {\LARGE \begin{array}{llll} y = -6 \end{array}}[/tex]

Answer:

Step-by-step explanation:

z=9(x+2)

z=9x+18

Subtract 18 from both sides

z-18=9x+18-18

z-18=9x

Divide both sides by 9

z-18/9 =x

Therefore

X= z-18/9

The expression that uses an additive inverse and represents his net calorie intake 200 + (- 200) = 0.

In mathematics, the additive inverse of a number a is the number that, when added to a, yields zero. This number is also known as the opposite (number), sign change, and negation.

Now it is given that,

Calories burned by Greg = -200

Calorie taken from protien shake = + 200

Thus, Net calorie intake =  Calorie taken + Calories burned

⇒ Net calorie intake = 200 + (-200) = 0

Thus, the expression that uses an additive inverse and represents his net calorie intake 200 + (- 200) = 0.

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7+(-1) = -3

Steps of adding 7+(-10) using number line are as following:

1) Draw a number line by ranging from -10 to +10.

2) Point out 7 on the number line.

3) Because -10 is added to 7 on the number line, please move 10 numbers left to 7 on the number line. We always go left in addition of a negative number on the number line.

4) The number we reach -3 on left side would be our final sum.

5) From the number we can clearly see that moving 10 number on left to 7, we get -3.

Note: We are moving left because of negative sign in front of 10.

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Answer:$976

Step-by-step explanation:

Answer:

45%

Step-by-step explanation:

1,450 - 1,000 = 450

the 450 becomes 0.45

to make 0.45 a percent, we multiply it by 100

0.45 x 100 = 45

45%

Answer:

$16.60

Step-by-step explanation:

Setup the formula to calculate the cost of each pound of salmon and swordfish for the 2.5 pounds of salmon (x) and 1.25 pounds of swordfish (y) which is equal to $31.25

2.5x + 1.25y = 31.25

Setup a formula to figure out how much a single pound of swordfish (y) is. The problem states it cost $0.20 less than a pound of salmon (x).

y = x - .20

Plug the y = x - .20 into the first equation.

2.5x + 1.25(x - .20) = 31.25

Distribute the 1.25 by multiplying it with x and -.20

2.5x + 1.25x - .25 = 31.25

Combine like terms, x on the left side

3.75x - .25 = 31.25

Add .25 to both sides to get x on one side

3.75x = 31.50

Divide both sides by 3.75 to get x by itself

x = 8.4

So, each pound of salmon, x, cost $8.40 per pound

Use y = x - .20 and plug in x = 8.4 to figure out how much a pound of swordfish cost.

y = 8.4 - .20

So, a pound of swordfish cost $8.20 per pound

The question wants to know the combined cost, z, of 1 pound of salmon, x, and 1 pound of swordfish, y.

x + y = z

8.4 + 8.2 = 16.6

The combined cost of 1 pound of salmon and 1 pound of swordfish is $16.60

The approximate side length of a square on the quilt = 6.32 inch

In this question,

Taynia makes a quilt using fabric squares.

We have been given the side length of each fabric square is the square root of the area.

Here, the area of each fabric square is 40 square inches.

We need to find the approximate side length of a square on the quilt.

Let A be the area.

A = 40 square inches

To find the side length, we need to take the square root of 40.

Let s be the side length.

⇒ s = √A

⇒ s = √40

⇒ s = 6.32 inch

Therefore, the approximate side length of a square on the quilt = 6.32 inch

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The mean of the data is 30 and the median of the data is 27.5.

Mean is defined as the ratio of the sum of the number of the data sets to the total number of the data. The mean of the data will be calculated by adding all the numbers and dividing it by the quantity of the numbers.

The median of the data generally refers to the middle most value of the series. The median of the data is calculated by arranging the numbers in increasing order and getting the middle value of the numbers.

Given data is 26, 29, 27, 28, 29, 27, 27, 53, 25, 29 arrange all the numbers in increasing order.

25,26,27,27,27,28,29,29,29,53

Mean = Sum of all the numbers / Total numbers

Mean =  (25 + 26 + 27 + 27 + 27 + 28 + 29 + 29 + 29 + 53 ) / 10

Mean = 300 / 10

Mean = 30

Median = ( 27 + 28 ) / 2 = 27.5

Therefore, the mean of the data is 30 and the median of the data is 27.5.

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The numeric values for the functions are given as follows:

6 - a) f(-2) = -13.

6 - b) g(4) = 11.

To find the numeric value of a function, we replace each instance of the variable by the desired value.

At item 6a, the function is given by:

f(x) = 5x - 3.

The numeric value at x = -2 is:

f(-2) = 5(-2) - 3 = -10 -3 = -13.

Hence f(-2) = -13.

At item 6b, the function is given by:

g(x) = 0.5x² + 3.

The numeric value at x = 4 is:

g(4) = 0.5(4)² + 3 = 8 + 3 = 11.

Hence g(4) = 11.

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In a physical bus topology, both ends of the medium must be terminated in order to prevent "single bounce."

Bus topology, also recognized as line topology, is a network topology in which all network devices are connected by a single RJ-45 network cable and coaxial cable.

The bus, backbone, or trunk is the single cable through which all data is transmitted among devices.

Some pros of bus topology are-

Some cons of bus topology are-

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Answer:

x² + (y + 3)² = 25

Step-by-step explanation:

the centre (C) of the circle is at the midpoint of the diameter.

using the midpoint formula

midpoint = ( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

with (x₁, y₁ ) = P (3, 1 ) and (x₂, y₂ ) = Q (- 3, - 7 )

C = ( [tex]\frac{3-3}{2}[/tex] , [tex]\frac{1-7}{2}[/tex] ) = ( [tex]\frac{0}{2}[/tex] , [tex]\frac{-6}{2}[/tex] ) = (0, - 3 )

the radius r is the distance from the centre to either P or Q

using the distance formula

r = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = C (0, - 3 ) and (x₂, y₂ ) = P (3, 1 )

r = [tex]\sqrt{(3-0)^2+(1-(-3)^2}[/tex]  

 = [tex]\sqrt{3^2+(1+3)^2}[/tex]

 = [tex]\sqrt{3^2+4^2}[/tex]

 = [tex]\sqrt{9+16}[/tex]

 = [tex]\sqrt{25}[/tex]

 = 5

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (0, - 3 ) and r = 5 , then

(x - 0 )² + (y - (- 3) )² = 5² , that is

x² + (y + 3)² = 25

Answer:

6

Step-by-step explanation:

6 x 6 = 36