How many solutions does the equation have?

5(n–2)=5n–10

Answer:

1. 4

2. [tex]5\frac{9}{11}[/tex]

3. [tex]7\frac{6}{16} = 7\frac{3}{8}[/tex]

4. [tex]1\frac{8}{7} = 2\frac{1}{7}[/tex]

Answer:

-7x³+ 4x²+x+9

Step-by-step explanation:

Answer:

  (x, y, z) = (1, 1, 0)

Step-by-step explanation:

You want to solve the given system of equations by elimination.

There are a couple of nice choices for variables to eliminate.

The last equation has an x-coefficient that is the opposite of the x-coefficient in the other two equations. Adding that equation to those will eliminate the x-variable:

  (-2x +2y +3z) +(2x +3y +3z) = (0) +(5)   ⇒   5y +6z = 5 . . . . add eqns 1, 3

  (-2x -y +z) +(2x +3y +3z) = (-3) +(5)   ⇒   2y +4z = 2 . . . . add eqns 2, 3

The second of these equations can be divided by 2 to give ...

  y +2z = 1

Three times this equation can be subtracted from the first of the reduced equations to eliminate z:

  (5y +6z) -3(y +2z) = (5) -3(1)   ⇒   2y = 2

  y = 1 . . . . divide by 2

Now, we can substitute this value into the previous equation to find the other variables.

  y +2z = 1 = 1 +2z   ⇒   0 = 2z   ⇒   z = 0

  -2x -y +z = -3 = -2x -(1) +(0)   ⇒   -2 = -2x   ⇒   x = 1

The solution is (x, y, z) = (1, 1, 0).

__

Additional comment

The attachment shows a calculator solution to the system of equations by reducing the augmented matrix to "reduced row-echelon form." In general, that is a process of elimination. Each equation ends up with one variable having a coefficient of 1, so we have x = 1, y = 1, z = 0.

You could also start by eliminating the y-variables. Adding twice the second equation to the first will do that, as will adding 3 times the second equation to the third. The result of these operations is two equations in x and z.

So, from the question statement, we can conclude that the y and x axes are directly proportional. In order to  show it in the equation form, we can write,

Y=kx (directly proportional)

y=k x

The values that are given in the question are

y = 15

and,

x = 10

Now we will put these individual values in the above relation equation of x and y,

y=k x

15=10k

k=15/10

k=1.5

So, we found the unknown factor by putting the values of the available terms. Now in order to find the new value of y, when the new values of x are given and is,

x=22

We will simply modify the relation equation,

y=k x

By putting the known terms in the above equation,

x=22, k=1.5

y=1.5 * 22

y = 33.

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The distance between line k and point F(-4,0) is 3.6 units

The correct answer is an option (G) 3.6 units

We know that for a line l: ax + by + c = 0 and a point P(x1, y1), the distance between the line line 'l' and a point P is:

[tex]d=\frac{|ax_1+by_1+c|}{\sqrt{a^{2} +b^{2} } }[/tex]

In this question we have been given a line k contains points at (4,1) and (-5,-5).

Also, we have been given a point F(-4, 0)

We need to find the distance between line k and point F(-4,0).

First we find the equation of line k.

[tex]\frac{y-1}{-5-1} =\frac{x-4}{-5-4} \\\\\frac{y-1}{-6} =\frac{x-4}{-9} \\\\-9y+9=-6x+24\\\\6x-9y+9-24=0\\\\6x-9y-15=0[/tex]

So, the equation of line k is 6x - 9y - 15 = 0

Now we find the distance between line k and point F(-4, 0).

Using above formula the distance between line k and point F(-4,0) would be,

[tex]d=\frac{|6(-4) - 9(0) - 15|}{\sqrt{6^{2} +(-9)^{2} } } \\\\d=\frac{|-24-0-15|}{\sqrt{36+81} }\\\\ d=\frac{|-39|}{\sqrt{117} } \\\\d=\frac{39}{10.82}\\\\ d=3.6[/tex]

Therefore, the distance between line k and point F(-4,0) is 3.6 units

The correct answer is an option (G) 3.6 units

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Answer:

2000.18

Step-by-step explanation:

Volume=V=(3.14)r^2h=3.14·7^2·13=2000.18.

Hope this helps.

Answer:

The next 50 phones are working? ---> 88.3%

The next 100 phones are working? ---> 93.6%

The next 500 phones are working? ---> 98.6%

Step-by-step explanation:

I hope this helps

Using linear functions, it is found that until $77,000 in sales, Job B pays more, and for more than than, Job A pays more.

A linear function is modeled according to the following rule:

y = mx + b

In which:

For this problem, the earnings are modeled by linear functions, in which:

Hence the earnings for sales of x are given as follows:

Due to the higher intercept, until they are equal, A(x) is greater, and after that B(x) is greater, hence we have to find when they are equal as follows:

A(x) = B(x)

45050 + 0.065x = 46975 + 0.045x

0.025x = 1925ntil $77,000 in sales, Job B pays more, and for more than than, Job A pays more.

x = 1925/0.025

x = 77000.

Hence:

Until $77,000 in sales, Job B pays more, and for more than than, Job A pays more.

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Answer:

3. Line q

4. Point B and Point A

5. Line DC or Line CD

6. Plane G

7. Line n, Line q, Line AB, Line BA, Line BE, Line EB

8. Line N, and Line Q

Step-by-step explanation:

 The vertex, focus and directrix of the parabola y = x²/4 are:

  The parabola is a geometric shape that is formed from the intersection of a vertical plane in a cone.

  The parabola is a quadratic function, it is composed of a vertex, or inflection point, a focus and a directrix.

  In this case we have an expression given by:

x = y²/16

   We must find the canonical equation:

(y - 0)² = 16 (x - 0)

has the form

(y - k)² = 4p(x - h)

  This means that the vertex of this parabola is

v = (h, k)

v = (0,0)

  To know the focus we must know the value of "p".

f = (0 + 4, 0)

f = (4, 0)

d = y = 0 - 4

d = y = -4

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Answer:

after 5 hours: 14.5 inches

after t hours: 2 + 2.5t

Step-by-step explanation:

2 + 2.5t

2 + 2.5(5) = 2 + 12.5 = 14.5

Answer:

84.7

Step-by-step explanation:

first you multiply 3.85 x 25 =96.25 then you need to determin the percent of 12 which is 11.55 the lasly you subtract 96.25-11.55=84.7      btw 84.7 for bannas is a scam for real

Using the midpoint concept, the location of the point directly between the two airplanes is (-500, 1000, 2600).

The midpoint between two points is the halfway point between them, and is found using the mean of the coordinates.

For this problem, the coordinates are given as follows:

Hence the coordinates of the midpoint are given as follows:

The location is (-500, 1000, 2600).

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The product of the two linear functions f(x) = x − 3 and g(x) = −2x + 4 is -2x² + 10x - 12

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the linear functions f(x) = x − 3 and g(x) = −2x + 4, hence:

(f.g)(x) is the product of the two functions:

(f . g)(x) = (x - 3)(-2x + 4)

(f . g)(x) = -2x² + 6x + 4x - 12 = -2x² + 10x - 12

The product of the two linear functions f(x) = x − 3 and g(x) = −2x + 4 is -2x² + 10x - 12

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The value of x is 1.5 units

Given that a quadrilateral RSTU is circumscribed about [tex]\odot J[/tex].

Also given that the perimeter of the quadrilateral is 18 units.

Then the the sides ST, TU, UV and RS are tangents to the circle at points A, B, C and D respectively.

Then we have,

 AT = BT

 BU = UC

 RC = RD

 SD = SA

Given that AT = UC = x and RC = RD = SD = SA = 3 units

Therefore, BT = BU = x

We need to find 'x'.

Perimeter = 18 units

i.e., ST + TU + UV + RS = 18 units

⇒   AT + BT + BU + UC + RC + RD + SD + SA = 18 units

⇒ x + x + x + x + 3 + 3 + 3 + 3 = 18

⇒ 4x + 12 = 18

⇒4x = 6

⇒ x = 6/4 = 3/2

⇒ x = 1.5 units

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Answer: Slope: 3/2

Step-by-step explanation:

Coordinates: (1, -3), (3, 0)

Slope formula: m=(y2-y1)/(x2-x1)

m=(0-(-3))/(3-1)

m=(0+3)/2

m=3/2 ==> Slope: 3/2

Answer:

C

Step-by-step explanation:

[tex]Answer:\ f^{-1}(x)=\sqrt[3]{x} -4[/tex]

Step-by-step explanation:

[tex]f(x)=(x+4)^3[/tex]

Extract the cube root from both parts of the equations:

[tex]\sqrt[3]{f(x)} =x+4\\\sqrt[3]{f(x)}-4=x+4-4\\ \sqrt[3]{f(x)} -4=x[/tex]

Redefine the variables:

[tex]f^{-1}(x)=\sqrt[3]{x} -4[/tex]

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.The ratio of dogs to  in the shelter is 10 to 8. If there are 20 cats, then 25 dogs are in the shelter.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

The ratio of dogs to cats in the shelter is 10 to 8. i.e 10/8

If there are 20 cats then we need to find number of dogs.

Let the number of dogs be x when there are 20 cats.

10/8=x/20

Apply cross Multiplication.

200=8x

Divide both sides by 8.

x=25.

Therefore there are 25 dogs in the shelter if the number of cats are 20.

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Answer:

RM350

Step-by-step explanation:

calculate 30% of RM500

= [tex]\frac{30}{100}[/tex] × 500 = 0.3 × 500 = 150

RM150 is left in the bank

and 500 - 150 = RM350 is the money he has with him

For 10 animals do Jose and Nancy charge the same amount.

For, the given question;

Let there be 'x' number of animals.

Jose charges $15 plus $2 per animal.

15 + 2x

And, Nancy charges $5 plus $3 per animal.

5 + 3x

Then,

For the same amount, equate both equations.

15 + 2x = 5 + 3x

On solving;

x = 10

Thus, for 10 animals, their total charge will be equal.

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No, If y² varies directly with x², it does not that mean y must vary directly with x

Let's say y² =  16 and x² =  4

Now if y²  =  16

Then y = 4 or -4  and same for x = 2 or -2

As the square root can be either negative or positive, if y² varies directly with x², it does not that mean y must vary directly with x .

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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The slope-intercept form is y = 3/2x - 6 for line perpendicular to y = (2/3)x - 1 through (0,6)

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

In an equation, perpendicular lines have the opposite reciprocal slope. In other words, if a line's slope is a positive fraction, its reciprocal slope is negative.

Here given that y = (2/3)x - 1

Here 2/3 is the slope and 1 is the y-intercept

To find a perpendicular line to the following equation, use the opposite reciprocal slope and point, then solve using the point-slope formula.

y - y₁ = m(x - x₁)

We have, m = 3/2, x₁ = 0 and y₁ = 6

y - 6 = 3/2(x - 0)

y - 6 = 3/2x - 0

y = 3/2x - 6

We have the slope-intercept form y = 3/2x - 6 of a line  perpendicular to y = (2/3)x - 1 through (0,6)

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By elimination, the solution of the system of equations, 2r + s = 3 and 4r - s = 9, is (r , s) = (2 , -1).

A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.

There are three methods that can be used to solve system of equations.

1. Elimination

2. Substitution

3. Graphing

Using the elimination method, given two equations in r and s, a variable should be eliminated by adding/subtracting the two equations.

Adding the two equations will eliminate the variable s.

2r + s = 3     (equation 1)

4r  - s = 9     (equation 2)

6r       = 12

r = 2

Substitute the value of r to any of the two equations and solve for s.

2r + s = 3     (equation 1)

2(2) + s = 3

s = 3 - 4

s = -1

Hence, the solution of the system of equations is (r , s) = (2 , -1).

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The range of values for the radius of the explosion circle is found to be 500-600 ft.

A circle is a shape founded by all locus in a plane at a fixed distance from its centre.

Now, according to the stated question;

Evaluate the circumference by the formula;

Formula: 2πr

Radius = 800 feet

Substitute the value in the formula;

C = 2πr

C = 2π800

C = 5026.54825 feet

Therefore, radius of the explosion circle will range from 500 to 600 feet.

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The equation of the circle with radius 10 and center located at (1 , -3) is (x - 1)^2 + (y + 3)^2 = 100.

The general form of the equation of  circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.

Given the radius and center of the circle, substitute these values to the general form of the equation of the circle.

(x - h)^2 + (y - k)^2 = r^2

where (h , k) = (1 , -3)

r = 10

(x - 1)^2 + (y - -3)^2 = 10^2

(x - 1)^2 + (y + 3)^2 = 100

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The formula for nth term of the given sequence is [tex]T_{n+1} = T_{n} - 8[/tex].

According to the given question.

We have a sequence, 21,13,5,-3, .......

Since, the first term of the given sequence is 21.

The second term of the given sequence is 13.

Here we can see that, each term is less than 8 to the previous term. It means the common ratio of the given sequece is -8 and it is an arithmetic sequence.

Therefore, the formula for nth term of the given sequence is given by

[tex]T_{n+1} = T_{n} - 8[/tex]

Where, n is the number of term.

Hence,  the formula for nth term of the given sequence is [tex]T_{n+1} = T_{n} - 8[/tex].

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The correct option is B. 1/11.

The probability of choosing 2 white marbles is 1/11.

A combination is an arithmetical technique for determining the number of different arrangements in a set of items in which the sequence of the selection is irrelevant.

You can choose the objects in any order in combinations. Permutations and combinations are often confused.

Now, as pet the stated question.

The total number of red marble in the bag are 5.

The total number of blue marble in the bag are 2.

The total number of white marble in the bag are 4.

The total number of yellow marble in the bag are 1.

The combination for selecting the 2 white marbles out of 4 are;

⁴C₂ = 4!/(4-2)!2!

⁴C₂ = 6

Ans, the combination for selecting the 2 marbles out of total 12 are;

¹²C₂ = 12!/(12-2)!2!

¹²C₂ = 66

Thus, the combination for selecting the 2 white marbles out of total 12 is;

= ⁴C₂ / ¹²C₂

= 6/66

= 1/11

Therefore, the the probability of outcome of the 2 white marbles out of total 12 marbles is 1/11.

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Answer:

X = 3 and -7

Step-by-step explanation:

area of a triangle is = ½ ×base × height

Answer:

13/15

Step-by-step explanation:

If we give all of these fractions a common denominator, this problem will be much easier. We see that a common denominator can be 15.

We can take 1/3 and multiply both the numerator and denominator by 5, getting 5/15. 7/15 already has a denominator of 15. Now if we multiply the numerator and denominator by 3, we get 9/15. Then we have 11/15.

Now the pattern is 5/15, 7/15, 9/15, 11/15. The numerator increases by 2 each time, so the next fraction should be 13/15.