Which equation is the equation of the line, in point-slope form, that has a slope of 12 and passes through the point (-1, 14) ?
Oy+14=12 (2-1)
Oy-14=12(x+1)
Oy-14=12 (2+1)
Oy-14=12 (x-1)

The solution of system of equations is (1,-1).

Given that the system of equations is x+5y=-4, x+6y=-5.

The system of equations can be written in matrix form as

x+5y=-4

x+6y=-5

[tex]\left[\begin{array}{ll}1&5\\ 1&6\end{array}\right]=\left[\begin{array}{l}-4\\ -5\end{array}\right][/tex]

Write the matrix on the left as the product of coefficients and variables.

[tex]\left[\begin{array}{ll}1&5\\ 1&6\end{array}\right]\left[\begin{array}{l}x\\ y\end{array}\right]=\left[\begin{array}{l}-4\\ -5\end{array}\right][/tex]

Firstly, find the inverse of the coefficient matrix.  

The inverse of [tex]\left[\begin{array}{ll}1&5\\ 1&6\end{array}\right][/tex] is

[tex]\begin{aligned}\left[\begin{array}{ll}1& 5\\ 1&6\end{array}\right]&=\frac{1}{6(1)-5(1)}\left[\begin{array}{ll}6&-5\\ -1&1\end{array}\right] \\ &=\left[\begin{array}{ll}6&-5\\ -1&1\end{array}\right]\end{aligned}[/tex]

Next, multiply each side of the matrix equation by the inverse matrix .  Since matrix multiplication is not commutative, the inverse matrix should be at the left on each side of the matrix equation.

[tex]\begin{aligned}\left[\begin{array}{ll}6&-5\\ -1& 1\end{array}\right]\left[\begin{array}{ll}1&5\\ 1&6\end{array}\right]\left[\begin{array}{l}x\\ y\end{array}\right]&=\left[\begin{array}{ll}6&-5\\ -1& 1\end{array}\right]\left[\begin{array}{l}-4\\ -5\end{array}\right]\\ \left[\begin{array}{ll}1&0\\ 0&1\end{array}\right]\left[\begin{array}{l}x\\ y\end{array}\right]&=\left[\begin{array}{l}1\\ -1\end{array}\right]\end{aligned}[/tex]

The identity matrix on the left verifies that the inverse matrix was calculated correctly.

[tex]\left[\begin{array}{l}x\\ y\end{array}\right]=\left[\begin{array}{l}1\\ -1\end{array}\right][/tex]

The solution is (1,-1).

Hence, the solution of the system of equtions using matrix is x+5y=-4, x+6y=-5 is (1,-1).

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The radius of the new parking area is 82 meters

The radius of the old parking area is given as

Radius, R = 123 meters

From the question, we understand that:

The parking area must be temporarily reduced to 1/3 of its original area

This means that

New Radius = Old radius - Old radius * 1/3

So, we have

New Radius = 123 meters - 123 meters * 1/3

Evaluate the product

So, we have

New Radius = 123 meters - 41 meters

Evaluate the difference

New Radius = 82 meters

Hence, the radius of the new parking area is 82 meters

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After evaluating the logarithm log ₇ 49, we get the result as 2.

The common logarithm is also known as the base 10 logarithm. It is represented by log10 or simply log.

For example, the common logarithm of 1000 is written as log(1000). The common logarithm defines how many times we need to multiply by 10 to get the required output.  The natural logarithm is called the logarithm of base e. The natural logarithm is represented by ln or loge. Here, "e" stands for Euler's constant which is approximately equal to 2.71828.

We need to evaluate log ₇ 49

x = log₇ 49

We can also write it as:

7ˣ = 49

7ˣ = 7²

Comparing the bases, we get that:

x = 2

Therefore, after evaluating the logarithm log ₇ 49, we get the result as 2.

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1.

[tex] 2x {}^{2} + 17x + 35 \\ = 2x {}^{2} + 10x + 7x + 35 \\ = 2x(x + 5) + 7(x + 5) \\ = (2x + 7)(x + 5)[/tex]

2.

[tex]2y {}^{2} - 5y - 3 \\ = 2y {}^{2} -6y + y - 3 \\ = 2y(y - 3) + 1(y - 3) \\ = (2y + 1)(y - 3)[/tex]

3.

[tex]3x {}^{2} - 8x + 4 \\ = 3x {}^{2} - 6x - 2x + 4 \\ = 3x(x - 2)( - 2)(x - 2) \\ = (3x - 2)(x - 2)[/tex]

The property with each of Tyrone's steps for solving the equation is;

4x = 2 - 4(2 - 3x)

4x = 2 - 8 + 12x

4x = - 6 + 12x

4x - 12x = -6

-8x = - 6

x = -6 / - 8

x = 3/4

Therefore, the solution to Tyrone's equation for x is 3/4

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Answer:

3 i  √7

Step-by-step explanation:

sqrt (-63)  = sqrt ( -1 * 3 * 7 *3) =  sqrt (-1) * 3 * sqrt 7 =  3 i sqrt 7  

The total amount did he earn this month is $3125.

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

Dave earns his salary by making a 12.5% commission.

sales= $25000 this month.

According to given question we have

The basic formula is

Sales × Commission Percent/100 = Commission

$25000  ×12.5/100= Commission

Commission=$3125

Therefore, the total amount did he earn this month is $3125.

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The amount of change that Melvin would receive from a $20 bill is equal to: C. $11.78.

In order to determine the amount of change that Melvin would receive from a $20 bill, we would first of all calculate the total cost before tax.

For the cinnamon roll, we have:

Cinnamon roll's cost = $2.59.

For three (3) doughnuts, we have:

Doughnut's cost = 0.95 × 3

Doughnut's cost = $2.85.

For two (2) dozen doughnut holes, we have:

Doughnut hole's cost = 1.75 × 2

Doughnut hole's cost = $3.5.

Total cost = $2.59 + $2.85 + $3.5

Total cost = $8.94

Next, we would determine the new cost after applying sales tax:

New cost = 8.94 - 0.72

New cost = $8.22.

Now, we can determine Melvin's change:

Change = Dollar bill - New cost

Change = $20 - $8.22.

Change = $11.78.

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Answer:

4 C$11.78

Step-by-step explanation:

The value of the expression (4x^6) * 3y^5/6x^3y^3 is 2x^3y^2

The expression is given as

(4x^6) * 3y^5/6x^3y^3

Divide 3 and 6 by 3

So, we have

(4x^6) * 3y^5/6x^3y^3 = (4x^6) * y^5/2x^3y^3

Apply the law of indices to the exponents

(4x^6) * 3y^5/6x^3y^3 = (4x^6) * y^2/2x^3

Remove the bracket

(4x^6) * 3y^5/6x^3y^3 = 4x^6 * y^2/2x^3

Divide 4 and 2 by 2

So, we have

(4x^6) * 3y^5/6x^3y^3 = 2x^6 * y^2/x^3

Apply the law of indices to the exponents

(4x^6) * 3y^5/6x^3y^3 = 2x^3y^2

Hence, the value of the expression (4x^6) * 3y^5/6x^3y^3 is 2x^3y^2

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Answer:

-41.1 feet

Step-by-step explanation:

-32.5-8.6=-41.1

1/2=0.5

3/5=6/10=0.6

After solving the given equation 3²x=6561, the value of x=729.

So,

Then,

Therefore, after solving the given equation 3²x=6561, the value of x=729.

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Shape Y has a volume of 3200 cm3.

Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed mathematically using imperial or SI-derived units. The volume of a container is typically thought of as its capacity, not as the amount of space it takes up. In other words, the volume is the amount of fluid (liquid or gas) that the container may hold.

A solid object's surface area is a measurement of the overall space that the object's surface takes up.

Scale Factor Formula

Scale up (Smaller to larger) =  (lager figure measurement)/(smaller figure measurement)

Scale down (Larger to smaller) = (smaller figure measurement)/(larger figure measurement)

A ratio greater than 1 is the scale factor for scaling up. A ratio of less than 1 is the scale factor for scaling down.

Given data:

The total surface area of shape X is 450 cm².

The total surface area of shape Y is 800 cm².

The volume of shape X is 1350 cm³.

Scale Factor for Area = (Surface area of shape x)/(surface area of shape y)

=450/800

=16/9

Scale factor for Length = [tex]\frac{\sqrt{16}}{\sqrt{9} }[/tex]

= 4/3

Scale factor for volume =4³/3³

= 64/27

Volume of shape y = volume of shape x*scale factor for volume

=1350×(64/27)

=450×(64/9)

=50×64

=3200 cm³.

Therefore, the volume of shape Y is 3200 cm³.

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Answer:

0.1 or 1/10

Step-by-step explanation:

-2/5 + 1/2 is also - 4/10 + 5/10 which is 1/10

Step-by-step explanation:

-2x2/5x2+1x5/2x5

-4/10+5/10

1/10

Answer:

Q= (1, -1), R = (7,-1), S = (7,-10), P =. (1,-10)

Step-by-step explanation:

Look at the coordinate grind then look at the coordinates (x) vertically, then look at the coordinates(y) horizontally.

then plot it as (x, y)

Answer:

Eighth Grade ( [tex]\frac78[/tex] )

Step-by-step explanation:

The larger the denominator is, the smaller one "piece" of it is.
If we imagine a cake, for instance, then one piece of a cake that is split into 8 pieces would be smaller than a piece of a cake that is split into 7 pieces.

Therefore, if the piece is smaller, the closer the fraction is to being equal to 1, meaning, [tex]\frac78 > \frac67[/tex]

The the equation of a line that passes through the point (2, −10) and is parallel to 14x+2y=6 is 7x + y + 8 = 0.

A straight line is just a line with no curves. So, a line that extends to both sides till infinity and has no curves is called a straight line.

The equation of a line parallel to a given line will have the same slope as the given.

The equation of a line having a slope m and passing through the point (x', y') is written as

y - y' = m (x - x').

This is called point - slope equation of a straight line.

In the given equation,

14x+2y=6

⇒ 2y = -14x + 6

⇒ y = -7x + 3

Comparing it with standard equation of a straight line; y = m x + c, the slope m of the given line = -7

Therefore equation of the line parallel to the given line and passing through point (x', y') = (2, -10) would be:

y - (-10) = -7x + 2

⇒ y + 10 = -7x + 2

⇒ 7x + y + 8 = 0

Hence the required equation of line 7x + y + 8 = 0

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Answer:

x=0

Step-by-step explanation:

12 = -4(-6x-3)

12 = 24x+12

-12         -12

0 = 24x

/       /

24   24

0 = x

Check

12 = -4(-6(0)-3)

12 = -4(0-3)

12 = 0 + 12

12 = 12

The wave will take 5.23 seconds to cover the area of the pond and the diameter of the lake is 167.52 feet when the area of the lake is given as 22000 feet.

We are given that the area of the pond = 22,000 square feet

Area = 22,000 feet²

π r² = 22,000

22 / 7 r² = 22,000

r² = 22000 × 7 / 22

r² = 7000

r = √ 7000

r = 10 √70

r = 83.76 feet

Also, since the wave travels 16 feet per second,

Time taken to cover the entire area = 83.76 / 16 = 5.23 seconds

The diameter of the lake = 83.76 + 83.76

d = 167.52 feet

Therefore, we get that the wave will take 5.23 seconds to cover the area of the pond and the diameter of the lake is 167.52 feet when the area of the lake is given as 22000 feet.

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In a figure we can see that 0.7 and0.70 are equivalent, we have shade in the figure.

Given that,

To illustrate that 0.7 and 0.70 are equivalent, shade the models.

We have 0.7

We can say 7/10

For example, take a square and divide it by 10 part in column and shade 7 column.

Draw horizontal lines connecting the model's dots using a ruler.

Now divide it into 100 equal pieces.

So,

70/100

Shade the 7 rows and column.

Shaded at 70 or 0.70.

Therefore, in a figure we can see that 0.7 and0.70 are equivalent.

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200+10=210 this is the answer

please like it if it is correct

The estimated value of 197 + 10.3 is 210.

Although the term "rounding" is a general one, we typically use the terms "round up" or "round down" to indicate whether the number has gone up or down after being rounded. The supplied number is said to be rounded up when the rounded number is increased, and it is said to be rounded down when the rounded number is dropped.

Given:

197 + 10.3

Now, rounding off nearest 10

197---> 200

and, 10.3 ----> 10

So, 197+ 10.3 = 200+ 10 = 210

Hence, the estimated value is 210.

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Relation r is not a function and Inverse function because a single

input gives several outputs.

1. Identity Relation: In an identity relation, every element is related to itself. Its notation is I = (a, a), A.

2. Empty relation: In an empty relation, there will be no connection between the set's components. This is a subset of.

3. Reflexive relation: Each element is mapped to itself in a reflexive relation. If (a, a) R for all aR, a relation R in a set A is automatic.

4. An irreflexive relation exists when two elements are not related to one another.

5. Inverse relation: An inverse relation exists when a set contains elements that are inverse pairs of those in another set. For instance, R-1 = (q,p), (s,r) if A = (p,q), (r,s), etc.

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1st - 3

2nd-1

3rd-4

5th-2

Answer:times  5 and 5 =25  7 and 7=49 add answers 74

Step-by-step explanation:

The inequalities that model the given situation are 0.5x+y<20, y≥2x and x>0.

Let Jackie wants to make x necklace and y bracelets.

Now, Since it take her half an hour to make a necklace and one hour to make a bracelet.

Also since she has fewer than 20 h total to work on the jewelry. So we have

0.5x + 1y < 20

=> 0.5x + y < 20

and she want at least twice as many bracelets as necklace, so we have

y ≥ 2x

also the number of necklace should be greater than 0. So x > 0

So the required inequalities are:

0.5x + 1y < 20

y ≥ 2x

and x > 0

Hence, The inequalities that model the given situation are 0.5x+y<20, y≥2x and x>0.

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Answer:70

Step-by-step explanation:

70 divided by 5 equals 14

The solution of the given equation by rounding off it to the nearest ten-thousandth is 55.5000.

What is a round-off of the digit?

In mathematics, a round-off is defined as an approximation of the given number to a fewer number of significant digits by taking into consideration some rules.

For eg: 13.58 ~ 13.6

Solving the given equation: 8 x = 444

We are given that 8 x = 444            —- 1

x = 444 / 8

= 55.5

Hence, the solution of the given equation rounded off to the nearest ten-thousandth is 55.5000.

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