5x + 3y = 6
- 5x - 3y = -6

Elimination method step by step

Answer:

x = 3; y = -1

Step-by-step explanation:

2x - 3y = 9

x = 4 + y

Since the second equation is already solved for x, use the substitution method. Substitute 4 + y for x in the first equation and solve for y.

2x - 3y = 9

2(4 + y) - 3y = 9

8 + 2y - 3y = 9

-y = 1

y = -1

Now substitute -1 for y in the second original equation, and solve for x.

x = 4 + y

x = 4 + (-1)

x = 3

Answer: x = 3; y = -1

Check the picture below.

Answer:

[tex]x=64, y=72[/tex]

Step-by-step explanation:

Using the angle sum of a triangle, [tex]x=180-57-59=64[/tex].

Thus, the left hand triangle has angles of 42°, 64° (using vertical angles), and y°. It follows that [tex]y=180-42-64=74[/tex].

For the 5.5% coupon corporate bond, the coupon payment would be $55 per year. For the 6.45% coupon treasury note, the coupon payment would be $64.50 per year.

Calculations using percentages show how much a given number contributes to the total. It is computed by dividing the number by the sum and multiplying by 100. It is denoted by the sign "%." For example, if a basket contains ten apples, three of which are red, the proportion of red apples in the basket is 30% (3/10 x 100). In a wide range of disciplines, including business, statistics, and education, percentage is often utilized. Calculating interest rates, taxes, and other financial activities in the finance industry annually frequently uses percentages. The frequency of events or the likelihood of a certain outcome are both measured using this method in statistics. Calculating grades and evaluating a student's overall performance are both done using this in education.

How to solve?

For the 5.5% coupon corporate bond, the coupon payment would be 5.5% of $1,000 = $55 per year.

For the 6.45% coupon treasury note, the coupon payment would be 6.45% of $1,000 = $64.50 per year.

For the corporate zero-coupon bond maturing in 10 years, there are no coupon payments. The bond will only make a payment of $1,000 at maturity.

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Answer: B

Step-by-step explanation:

For [tex]f(x)=3x-\frac{1}{2}[/tex], comparing it with slope-intercept form yields that the slope is [tex]3[/tex] and the [tex]y[/tex]-intercept is [tex]-1/2[/tex].

For the graphed function, the slope is [tex]\frac{-4-0}{-2-6}=\frac{1}{2}[/tex] and the [tex]y[/tex]-intercept is about [tex]-3[/tex].

Since the absolute value of the slope of the graphed function is less than that of [tex]f(x)[/tex], option B is correct.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

The x-coordinate of the point is 9.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The equation of a line y = (2/3)x - 6 ______(1)

Now,

The line passes through a point (x, 0).

(x, 0) = (x, y) ______(2)

Now,

Putting (2) in (1) we get,

0 = (2/3)x - 6

6 = (2/3)x

x = 6 x 3 / 2

x = 9

Thus,

The x-coordinate of the point is 9.

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The measure of length of side p is 33 ft  .

What is measure of length?

Some of the commonly used units for measuring length are centimeters, millimeters, meters, inches, feet, yards, feet, etc. Some of the units to measure mass are pounds, ounces, kilograms, grams, centigrams, milligrams, etc.

Given as the length of the swimming pool measured by drawing similar triangle :

I.e The smaller Triangle similar to larger Triangle

Let o is the points of meeting of two triangles

And OAB is smaller triangle having sides OA , AB , BO

The measure of side OA = 8 ft

The measure of side AB = 12 ft

Again, OPQ is larger triangle having sides OP , PQ , QO

The measure of side OP = 22 ft

The measure of side PQ = p ft

∵ both Δ OAB    and  ΔOPQ  are similar

The from similarity property  

[tex]\begin{aligned}& \frac{P Q}{A B}=\frac{O P}{O A} \\& \text { l.e } \frac{p}{12}=\frac{22}{8} \\& \text { Or, } \frac{p}{12}=\frac{11}{4} \\& \therefore \mathrm{p}=\frac{11}{4} \times 12 \\& \text { or. } \mathrm{p}=11 \times 3 \\& \text { l.e } \mathrm{p}=33 \mathrm{ft}\end{aligned}[/tex]

Hence, the measure of length of side p is 33 ft  .

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Answer: A linear equation in the form y = mx + b can be determined by examining the values in the table. To find the value of m, we can use the formula for the slope of a line, which is (y2 - y1) / (x2 - x1). Using the first and last values in the table, we can compute the slope as (7 - 15) / (4 - 0) = -1/4.

Therefore, the equation that represents the table is:

y = (-1/4) * x + b

We can use any of the given points to find the value of b. For example, using the point (1, 13), we can solve the equation to find b:

13 = (-1/4) * 1 + b

b = 14 - 1/4 = 13 3/4

Therefore, the final equation that represents the table is:

y = (-1/4) * x + 13 3/4

Let x represent the number of people coming on the trip.

The 3-day ticket rate per person plus the total rental cost is 299 + 872.50 = $<<299+872.50=1171.50>>1171.50.

The total amount paid per person for the trip, assuming Marissa and Mykuria are able to get enough friends to come on the trip so that the vacation rental house will be at maximum capacity, is 361.25. This can be represented as an expression as follows:

(299 + 872.50)/x = 361.25

This equation can be rearranged to solve for the value of x, which represents the number of people coming on the trip.

Answer: no, not in any way

Step-by-step explanation: it does not matter how many times you multiple 12, you will never end up getting 44.

Answer:

-6.5y - 1.1x

Step-by-step explanation:

Rearrange the problem to where like terms are closer together:

11.7y+5.2y + 1.2x + x - 3.3x

Simplify by adding the like terms and your final answer will be -6.5y -1.1x

the name of the line is both XY and YX

By using the concept of reflection, it can be calculated that-

Value of x is 6 and value of y is -7

What is reflection?

Reflection is a mathematical transformation in which a mirror image of an object can be formed with respect to a line called the line of reflection.

The point is (-2, -4)

(-2, 4) is reflected across y-axis

New coordinate after reflection = (2, -4)

By the problem,

(x - 4, y + 3) = (2, -4)

x - 4 = 2

x = 2 + 4

x = 6

y + 3 = -4

y = -4 - 3

y = -7

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Answer:

See Picture

Step-by-step explanation:

Using Venn diagram, The value of x is equal to 15.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

We are given that 50 students study at least one of the subjects geography (G), mathematics (M) and history (H).

Thus, 18 study only mathematics. 19 study two or three of these subjects.

23 study geography.

G + M - (x + 7) = 23 + 18 -(x + 7) = 19

23 + 18 -(x + 7) = 19

41 - x - 7 = 19

x = 15

Therefore,the value of x is 5.

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The function that has the greater initial​ value is function A

From the question, we have the following parameters that can be used in our computation:

Function A: table

Function B: y = 3x + 6

The initial value of a function is when the input value is 0

i.e. when x = 0

From the table, we have

x = 0 when y = 8

From the equation, we have

y = 3(0) + 6

y = 6

8 is greater than 6

Hence. function A has the greater initial value

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Answer:

B

Step-by-step explanation:

The answer is No because one x-value corresponds to two different

y-values.

What is the function?

Each element of X is given exactly one element of Y by a function from a set X to a set Y. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two varying quantities.

Here the given function is,

           x     y

           3     4

           4     4

           5     2

           5     5

From the table we can see that there are 2 values of x having same

y - value.

Hence, the given table does not represents a function.

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Answer:

Not enough context

Step-by-step explanation:

We need the bar graph/information for the amount child and adult tickets cost.

Answer:

No, 9 is not a solution to 12 [tex]\leq[/tex] a

Step-by-step explanation:

 The expression 12 [tex]\leq[/tex] a states " 12 is less or equal to a."  If a were 9, the statement would not be true, since 9 is less than 12.  This contradicts the expression.

The equation of the line that is parallel to y = -1/2x - 3 and passes through the point (4, -1) is y + 1 = -1/2x + 2 written in slope-intercept form.

What is the slope of the equation?

The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).

To find the equation of a line that is parallel to y = -1/2x - 3 and passes through the point (4, -1), we can use the point-slope form:

y - y1 = m(x - x1)

where (x1, y1) is the given point, and m is the slope of the line.

Since the given line is parallel to y = -1/2x - 3, it has the same slope, which is -1/2. Substituting this value for m and the coordinates of the given point into the point-slope form, we get:

y - (-1) = (-1/2)(x - 4)

Combining like terms and multiplying through the parentheses, we get:

y + 1 = -1/2x + 2

Hence, the equation of the line that is parallel to y = -1/2x - 3 and passes through the point (4, -1) is y + 1 = -1/2x + 2 written in slope-intercept form.

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Answer: x = 1.3125

Step-by-step explanation:

−4.75+0.8x=−3.7

First, add 4.75 to both sides

0.8x = 1.05

Then divide by 0.8 on both sides

x = 1.3125

Answer:

x = 1.3125

Step-by-step explanation:

Answer:

y = 2/3x + 3

Step-by-step explanation:

(-1,-1) (3,5)

5+1/3+1

6/4

2/3

y = 2/3x + b

5 = (2/3)(3) + b

5 = 2 + b

b = 3

y = 2/3x + 3

Answer:

The percent decrease is 70%.

Step-by-step explanation:

Answer:

70%

Step-by-step explanation:

Answer

$7

Explaination :

3 bracelet - $5( for 1)

3 necklace - (unknown)

Total amount paid - $40

change - $4

Calculation for all 3 bracelet

$5×3=$15

Calculation for the real amount

$40-$4=$36

Calculation for 3 necklace

$36-$15=$21

Calculation for 1 necklace

$21÷3=$7

There reason I divide it with 3 was because I got the total amount for 3necklace now I only want 1..

Final answer - $7#

Hope this helped :)

Answer:

----------------------------

Each bracelet cost $5 and necklace costs x.

The total for 3 of each is:

Set equation and solve for x:

The difference between the two is only 0.01 %. The first size is a better purchase for Unit Price even though both might be rounded off to $0.3/oz.

Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.

Create a square on paper by using a pencil. Two dimensions make it up. A shape's area on paper is the space it takes up.

Imagine that your square is made up of smaller unit squares.

The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.

To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.

According to our question-

A shampoo's unit price is its cost per ounce. It is a straightforward division problem that may be solved with a simple calculator or pen and paper.

The first size weighs 14.2 ounces and costs $3.98.

This shampoo's unit price is ($3.98/14.2 oz) = $0.28/oz ( rounded off to nearest cent)

The second size weighs 33.9 ounces and costs $9.98.

The second shampoo's unit price is ($9.98/33.9 oz) = $0.29/oz (also rounded off to nearest cent)

Hence, There is just a 0.01% difference between the two. Even though both sizes may be rounded to $0.3/oz, the first size is the preferable choice in terms of unit price.

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Complete Question-

A certain shampoo is available in two sizes. A 13.5 ounce bottle costs $2.19, A 29.2 ounce bottle costs $5.37. Find the unit price for each size. then state which size is the better buy based on the unit price. Round your answers to the nearest cent.?

The value of the unknowns are w = 5 , x = 12 , y = 1 and z = 15

What is a Matrix?

In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object

A+B = B+A  Commutative Law of Addition.

A+B+C = A +(B+C) = (A+B)+C  Associative law of addition.

ABC = A(BC) = (AB)C  Associative law of multiplication.

A(B+C) = AB + AC  Distributive law of matrix algebra.

R(A+B) = RA + RB

Given data ,

Let the Matrix be A

Now , the given matrices are

[tex]2\left[\begin{array}{ccc}w&2\\5&z\\\end{array}\right] + 3\left[\begin{array}{ccc}2&x\\-2&-6\\\end{array}\right] =4\left[\begin{array}{ccc}4&7\\y&3\\\end{array}\right][/tex]

On simplifying the matrices , we get

[tex]\left[\begin{array}{ccc}2w&4\\10&2z\\\end{array}\right] + \left[\begin{array}{ccc}6&2x\\-6&-18\\\end{array}\right] =\left[\begin{array}{ccc}16&28\\4y&12\\\end{array}\right][/tex]

Now , from the distributive law of matrices ,

2w + 6 = 16   be equation (1)

4 + 2x = 28   be equation (2)

10 - 6 = 4y     be equation (3)

2z - 18 = 12    be equation (4)

So on simplifying the equation , we get

2w + 6 = 16   be equation (1)

Subtracting 6 on both sides , we get

2w = 10

Divide by 2 on both sides , we get

w = 5

So on simplifying the equation , we get

4 + 2x = 28   be equation (2)

Subtracting 4 on both sides , we get

2x = 24

Divide by 2 on both sides , we get

x = 12

So on simplifying the equation , we get

10 - 6 = 4y     be equation (3)

4y = 4

Divide by 4 on both sides , we get

y = 1

So on simplifying the equation , we get

2z - 18 = 12    be equation (4)

Adding 18 on both sides , we get

2z = 30

Divide by 2 on both sides , we get

z = 15

Therefore , the values are w = 5 , x = 12 , y = 1 and z = 15

Hence , The value of the unknowns are w = 5 , x = 12 , y = 1 and z = 15

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The required possible lengths of the parking lot is 300.

The  perimeter of a shape is characterized as the complete length of its limit. The border of a not entirely set in stone by adding the length of the relative multitude of sides and edges encasing the shape.

The area of a shape is the "space encased inside the border or the limit" of the given shape. We compute the region for various shapes utilizing math equations.

Perimeter = 520 feet, area = 12000 feet

We know that,

Perimeter = 2(L + B)

2(L + B) = 520

(L + B) = 260--------(1)

And

Area = L×B = 12000

From equation(1),we get

L(L - 260) = 12000

L^2 - 260L = 12000

L^2 - 260L - 12000 = 0

On solving above quadratic equation

L = 300 or L = -40

Thus, possible value of length is 300.

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If the volume of a cube decreases at a rate of 10 m/sec, then the  rate at which the side of the cube changes when the side of the cube is 2 m is -0.83 meter per second

The rate of  volume of the the cube decreasing = 10 meter per second

Consider the side of the cube is x

The volume of the cube = x^3

The rate of change of volume with respect to time

dV / dt = 3x^2 dx/dt

dV / dt = -10 meter per second

The dx / dt = (dV / dt) / 3x^2

We haver to find the rate at which side of the cube changes when the side of the cube is 2 meter

Then x = 2

dx / dt = -10 / (3 × 2^2)

= -10 / 12

= -0.83 meter per second

Therefore, the rate at which side of the cube changes when the side of the cubes is 2 meter is -0.83 meter per second

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