There are 4 white and 8 red roses in a bouquet. Find the ratios.
the ratio of the number of all roses to the number of red roses

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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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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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

Answer:70

Step-by-step explanation:

70 divided by 5 equals 14

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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Answer:

-41.1 feet

Step-by-step explanation:

-32.5-8.6=-41.1

1/2=0.5

3/5=6/10=0.6

The image of the triangle at point L is L' = (-8, 4)

The vertices of the triangle are given as:

L(4, 8), M(4, 3), and N(8, 8)

The transformation rule is given as

270 degrees rotation

The rule of 270 degrees rotation is

(x,y) = (-y , x)

When the above rule is applied to the vertices of the triangle, we have:

L' = (-8, 4)

Hence, the image of the triangle at point L is L' = (-8, 4)

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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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your ans

Step-by-step explanation:

the value of x is 6

The value of x will be 6 for the given triangle.

Pythagorean theorem states that in the right angle triangle, the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Given that in the right-angle triangle, the hypotenuse is 10, the base is 8 and the perpendicular is x.

The value of x will be calculated as:-

x² = 10² - 8²

x² = 100  - 64

x² = 64

x = √36

x = 6

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1st - 3

2nd-1

3rd-4

5th-2

Answer:

True

Step-by-step explanation:

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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Answer:

the third option I think it says (-1,4)

Step-by-step explanation:

So the directions are basically asking to turn in the paper 3 times ending up in the 1st quadrant. Because 90*3 equals 270 degrees. There would be only one point in the negative and there are 2 options. So, we would immediately know that the first option or the last option is wrong. I don't really know how to explain this without drawing so if you could try turning your paper 3 times then you'll see what I mean. Comment if you need any more help. Or if you have any questions. My explanation is pretty bad I apologize.

APR include: Interest on the loan

What does APR mean?

The APR which means annual percentage rate, is the interest rate on the loan, it is expressed in annual terms which is normally compounded monthly, by monthly compounding I mean the interest is computed on monthly basis.

APR has does not have anything to do with the principle and term of the loan since the principle is the loan amount and the term is the number of periods that the borrower is allowed to make repayments until the loan is fully repaid

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

Step-by-step explanation:

Answer: 110 degrees

Step-by-step explanation:

We know that all the angles of a triangle add to 180 degrees. Notice how there are already 60 and 50 degrees on the triangle. In order to find the last angle, we subtract 110 (60+5) from 180 to get 70.

Now, we know that the angle of a straight line is 180.

So, in order to find <BCD, take 70 and subtract it from 180.

Doing this, we find that m<BCD is 110 degrees

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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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)

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:

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]

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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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 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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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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