Solve each system by elimination or substitution.
y = 3x+1 , 2x - y = 8

A constant is a value or number that is consistently the same regardless of how it is expressed.

In the mathematical expression 3x + 5y + 3 the constant is 3.

Therefore, in the mathematical expression 3x + 5y + 3 the constant is 3.

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Answer: y - 6 = -(1/2)(x+1)

Step-by-step explanation:

1. First step is to remember point slope form (a common way of expressing the equation for a line).

y - y1 = m(x - x1)

2. Next fill in the data we are given.

y - 6 = m(x -(-1)) ----> y - 6 = m(x + 1)

3. Next step is to find the value of the slope (m) using slope formula.

m = (y2 - y1) / (x2 - x1)

4. Fill in the data

m = (5 - 6) / (1 +1) = - 1 /2

5. Add the calculated slope to the point slope form.

y - 6 = -(1/2)(x+1)

Answer:

0=-6 (No solution)

Step-by-step explanation:

2(7x-7)=14x-20 - Distribute the 2 to 7x-7

14x -14 = 14x -20 - Subtract +14 from both sides
    + 14          +14

14x = 14x -6

-14x    -14x

0=-6

Step-by-step explanation: I hope this helps.

Answer: 7.07 units

The first number (a) is - 5 and the second number (b) is 4.

let the first number be a

let the second number be b

given,

On adding 3 times the first number and 4 times the second number we get 1

=> 3 a + 4 b = 1                -      eq 1

On adding 2 times the first number and 3 times the second number we get 2

=> 2 a + 3 b = 2              -      eq 2

To solve the obtained equations using elimination method

Multiplying eq 1 with 3 and eq 2 with 4, we get

9 a + 12 b = 3                 -    eq 3

8 a + 12 b = 8                -     eq 4

Subtract eq 4 from eq 3

=> a = - 5

On Substituting the value of a in either eq 1 or eq 2, we get

b = 16

Therefore, using the elimination method, we get the first number as - 5 and the second number as 4.

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By substitution, the solution of the system of equations, r + s = -12 and 4r - 6s = 12, is (-6 , -6).

A system of linear 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 both equations.

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

1. Elimination

2. Substitution

3. Graphing

Using substitution method, given two linear equations in r and s,

r + s = -12     (equation 1)

4r - 6s = 12     (equation 2)

Using the first equation, find the value of one variable, lets say r, in terms of the other.

r + s = -12     (equation 1)

r = -12 - s

Substitute the value of r to the second equation.

4r - 6s = 12     (equation 2)

4(-12 - s) - 6s = 12

-48 - 4s - 6s = 12

Combining all terms containing the variable s on one side and the constants on the other side of the equality, and solving for s.

-48 - 4s - 6s = 12

-4s - 6s = 12 + 48

-10s = 60

s = -6

Substitute the value of s in the equation of r and solve for r.

r = -12 - s

r = -12 - (-6)

r = -12 + 6

r = -6

Hence, the solution of the given system of equations is (-6 , -6).

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Answer:

i had this question before and the correct answer was "subtract 12r from both sides of the equation" im sorry if im wrong that was my correct answer when i had this question

Step-by-step explanation:

On simplifying the expression 13.8+ (-11.5) , we get 2.3 . And additions

13.8 + (-11.5) and (-13.8) +  11.5 are numbers will same value and opposite sign.

For adding a negative and a positive number, use the sign of the larger number and subtract.

For example: (–8) + 2 = -6

Given that we have to solve 13.8 + (-11.5) = 13.8-11.5 (we subtract smaller no from larger and will use the sign of lager number that is + here)

13.8+(-11.5) = 13.8-11.5 =2.3

13.8+(-11.5) simply means that 13.8 -11.5 which is subtraction of 11.5 from 13.8

but (-13.8) +  11.5 = -13.8 +11.5  =  -( 13.8 -11.5) [taking -1  common from the expression]

Therefore , -13.8 + 11.5 has same value as 13.8- 11.5 but opposite  in sign.

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Answer:

[tex]{ \tt{area = \pi {r}^{2} }} \\ \\ { \tt{ = 3.14 \times {6}^{2} }} \\ \\ = 113.04 \: mm {}^{2} [/tex]

Answer:

A = 113.1 mm²

Step-by-step explanation:

Area of circle = πr²

A = 22/7(6mm)²

A = 22/7(36mm²)

A = 792mm²/7

A = 113.1 mm²

Therefore the area of the circle is 113.1mm².

Answer: $744.25

Step-by-step explanation:

6 * 114.95 = 689.7

689.7 + 54.55 = 744.25

Answer:

2) (1/3)x + 15 = 45

Step-by-step explanation:

Given that,

→ Katelynn's commute takes 15 minutes more than 1/3 as many min as Petra's.

→ It takes Katelynn 45 minutes.

Then the equation will be,

→ (1/3) times + 15 = 45

→ (1/3)x + 15 = 45

Hence, option (2) is correct.

If we find the decimal values of 1/9,2/9 and so on then we will get 1/9=0.11,2/9=0.22,3/9=0.33,4/9=0.44,5/9=0.55,6/9=0.66,7/9=0.77,

8/9=0.88,9/9=1.

Given some values in which the denominator is 12 and we are required to find the values of numbers whose denominator is 9.

Decimal expansion is basically representation of a non-negative real number r is its expression as a sequence of symbols consisting of decimal digits traditionally written with a single separator.

1/9=0.11

2/9=0.22

3/9=0.33

4/9=0.44

5/9=0.55

6/9=0.66

7/9=0.77

8/9=0.88

9/9=1

Hence if we find the values of 1/9,2/9 and so on then we will get decimals of 1/9=0.11,2/9=0.22,3/9=0.33, 4/9=0.44,5/9=0.55,6/9=0.66, 7/9=0.77, 8/9=0.88,9/9=1.

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Answer:

at least two solution so c

Answer:

4.92 ft

Step-by-step explanation:

The ladder is the hypotenuse of a right triangle

adjacent  leg / hypotenuse =  cos 75

cos 75 = adjacent leg / 19

19 cos 75 ° = adjacent leg = 4.92 ft

Answer: C. 7/9

Step-by-step explanation:

When the thermometer reads 6 degrees the temperature drops 15 degrees overnight, the temperature at 9:00pm will be 16°.

From the information, the thermometer reads 6 degrees the temperature drops 15 degrees overnight the it rises 25 degrees at 9:00am.

Therefore, the temperature at 9:00pm will be:

=6° - 15° + 25°

= 16°

Therefore, the temperature at 9:00pm will be 16°.

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Answer:

Step-by-step explanation:

8-3k-6 = 2-3k   (distribute -3 to (k+2))

-3k+2 = 2-3k  (8-6 is 2)

2 = 2   (subtract 3k from both sides)

2 = 2 means all real numbers

Answer:

0

Step-by-step explanation:

Distribute

8-3(k+2)=2-3k

8-3k+2=2-3k

subtract

8-6=2

2-3k+2=3k

rearrange

-3k+2=3k

I dont feel like typing the rest, watch khan academy

(ill take your email if you want to review on the weekend)

The required slope of the line through the points (0, 15), (9, 0)

is -5 / 3.

Given that,
To determine the slope of the line passing through the pair of points (0, 15), (9, 0).

The slope of the line is a tangent angle made by line with horizontal. i.e. m = tanx where x in degrees.

Here,
Slope of line ( m ) = [ y₂ - y₁ ]  /   [x₂ - x₁]
We have points (0, 15), (9, 0).
y₂ = 0  y₁ = 15  x₂ = 9  x₁ = 9
now,
m = 0 - 15 / 9 - 0
m = -15 / 9
m = -5 / 3

Thus, the required slope of the line is -5 / 3.

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 A parabola having vertex at the origin and focus at (2,0) is expressed by the following equation:

x = y²/8

  A parabolic function is one that has a quadratic variable, its shape is defined by the intersection of an inclined plane whose angle of inclination with respect to the axis of revolution of the cone is equal to that presented by its generatrix.

Since the vertex and the focal axis are on the same axis, we analyze that:

(y - 0)² = 4p(x - 0)

Focus

0 + p = 2

p = 0 + 2

p= 2

(y - 0)² = 4*2(x - 0)

(Y)² = 8(X)

x = y²/8

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The expression "quantity negative three and one third times n plus one sixth end quantity plus quantity one and three sixths times n minus three twelfths end quantity" or (-3 1/3n + 1/6) + (1 3/6n - 3/12) is equivalent to "negative eleven sixths times n minus one twelfth" or -11/6n - 1/12.

An algebraic expression is a number, variable, or the combination of both and operational symbols.

To determine the equivalent of the expression "quantity negative three and one third times n plus one sixth end quantity plus quantity one and three sixths times n minus three twelfths end quantity" or simply (-3 1/3n + 1/6) + (1 3/6n - 3/12), combine all like terms and perform necessary operations.

(-3 1/3n + 1/6) + (1 3/6n - 3/12)

⇒ -3 1/3n + 1 3/6n + 1/6 - 3/12

⇒ (-3 1/3 + 1 3/6)n + 1/6 - 3/12

⇒ (-10/3 + 9/6)n + 2/12 - 3/12

⇒ (-20/6 + 9/6)n - 1/12

⇒ -11/6n - 1/12

Hence, the equivalent expression is negative eleven sixths times n minus one twelfth" or -11/6n - 1/12.

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The tangent ratio for the ΔABC is tanФ = 1.

Some of the trigonometric ratios are-

For the given right angles triangle ABC.

The sides AC = CB = 15

As, the angle ACB is the right angle i.e, ∠ACB = 90°, so, AB is the hypotenuses of the triangle.

For finding the value of tangent ratio;

tan = perpendicular/base

tan B = AB/ CB

tan B = 15/15

tan B = 1/1

tan B = 1

Thus, the value of tangent ratio = 1.

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Answer:

1 5/6 or 11/6

Step-by-step explanation:

2/3+3/4+5/12 = 11/6

Answer:

22/12

Step-by-step explanation:

Add all 2/3 + 3/4 +5/12

=take LCM of 3 , 4, 12

=

12/8 +9 + 5

= 22/12

For equation (1), we get the Slope as 3 / 4 and y intercept as - 9 and for equation (2), we get the Slope as 3 / 4 and y intercept as - 4.

We are given 2 equations:

y = 3 / 4 x - 9 ...(1)

and y = 3 / 4 x - 4 ... (2)

Slope for equation (1) will be

slope = m1 = 3 / 4

Slope for equation (2) will be

Slope = m2 = 3 / 4

Y intercept for equation (1) will be:

= - 9

Y intercept for equation (2) will be:

= - 4

Also, since the Slope of equation are equal, so, it has no solutions as they are parallel to each other.

Therefore, for equation (1), we get the Slope as 3 / 4 and y intercept as - 9 and for equation (2), we get the Slope as 3 / 4 and y intercept as - 4.

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Answer:

Perimeter: 2(7+12), 2*7+2*12, 7+12+7+12

Area: 7*12, 7*10 + 7*2

neither: 7+12

Step-by-step explanation:

perimeter is like if you want a fence all the way around your property and your yard is 7x12 feet. In that case you could use the first option because you have to count the sides and add them up. If it’s a rectangle then there are 2 12’s and 2 7’s so the first one would work. The fourth one also uses distribution. The Fourth and first one are pretty much the same and have the same answer so the fourth one would work for perimeter.

Another way to do perimeter is to instead of multiplying, is to add the sides. 7+12+7+12 is basically 7 times 2 plus 12 times 2 (the fourth ne) and the answer is still correct so this one works too,

For area you times one of the dimensions by the other so 7*12 would work for area.
7*10 + 7*2 would also work because that uses the distributive property and that’s 70 + 14 which is 84 which is still the same answer.


The only one that falls under neither is the fifth one. 7+12 is half of the perimeter because it only adds two of the sides together and has n multiplying so it’s not area either.

The expression to represent the number of cousins that Anna has is c + 5.

We are given a statement that says:

Number of cousins that Simon has is equal to = c

Now, it is also given that Anna has 5 more cousins than Simon.

So, we have to write an expression to show the number of cousins that Anna has.

An expression is a combination of constants and variables to express something or a statement.

So, the expression will be made by adding 5 to c

So, we get the expression as:

The number of cousins that Anna has = c + 5

Therefore, we get that, the expression to represent the number of cousins that Anna has is c + 5.

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After a translation 4 units left, a reflection across the x-axis, and a translation 2 units down, the coordinates of the image are (-1, 2).

In mathematics, a translation is the movement of a shape to the left or right, and/or up or down. The translated shapes appear to be the same size as the original shape, implying that the shapes are congruent.

They have simply been moved in one or more directions. There is no change in the shape because it is simply moving from one location to another.

According to transformation rule in graph, when moving it to the right, you add the x value And when moving to the left, you subtract the x value,

Value of x = 3

Here the reflection of x has translated 4 units left, which implies

3 - 4 = -1

And, when moving up you add to the y value and when moving down you  subtract to the y value,

Value of y = 4

Here the reflection of y has translated 2 units down, which implies

4 - 2 = 2

Thus, the coordinates of the image formed by the reflection are (-1, 2)

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Based on the calculation below, we have:

The tuition per year is $36,000; and

The amount of increase in the tuition each year is $1,000.

The tuition per year and the amount of increase in the tuition each year can be calculated as follows:

Number of semesters in a year = 2

Tuition per semester = $18,000

Amount of increase in the tuition each semester = $500

Therefore, we have:

Tuition per year = Number of semesters in a year * Tuition per semester = 2 * $18,000 = $36,000

Amount of increase in the tuition each year =  Number of semesters in a year * Amount of increase in the tuition each semester = 2 * $500 = $1,000

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In horse racing, a trifecta, which is a bet that the first three finishers in a race are​ selected, and they are selected in the correct order, involves selection done in permutation.

Permutation is the method of selecting or arranging objects or numbers in order. It is used when the order or sequence of the elements selected is important. The number of permutations of n objects taken r at a time is determined by the following formula: P(n , r) = n!

On the other hand, combination is the method of selecting or arranging objects or numbers from a group of objects or numbers where order does not matter. The number of combinations of n objects taken r at a time is determined by the following formula: C(n , r) = n!/[r!(n - r)!]

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Answer:

Step-by-step explanation:

Because the order of the first three finishers does not make a​ difference, the trifecta involves permutations