11. Graph the system of equations, then estimate
the solution.
Y= 1.5 41
ya-1.51 + 55

A system of equations is a set of two or more equations with two or more variables. The number of solutions to a system of equations depends on the number of equations and the number of variables.

It's important to note that the number of solutions is not determined by the number of equations, but by the relationship between the equations and the variables.

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For a specific distance between two places, a grid scale factor is determined and referred to as a "line scale factor."

The ratio of the two equivalent side lengths of comparable figures is known as the scale factor, sometimes known as the linear scale factor. The shapes of similar figurines are the same, yet they come in various sizes. Geometrical problems are solved using the scale factor. To determine a figure's missing side lengths, apply the scale factor.

The ratio of one object's scale to that of a new object, which has its representation but is larger, is known as a scale factor (bigger or smaller). By multiplying each side by a certain number, say 2, we can increase the size of a rectangle with sides of 2 cm and 4 cm.

A mathematical phrase known as an equation demonstrates the connection between two or more variables and numbers.

A figure's size may enlarge or contract by dilation.

The diagram shows:

scaling factor of BA = AC/CA' = 4/(4 + 16)=1/5

Line segment BA's elongation is scaled by a factor of 1/5.

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The triangle ΔSTW is similar to the triangle ΔUVW. Then the value of the variable 'x' is 12.5 meters.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

In triangles ΔSTW and ΔUVW, we have

∠T = ∠V      (Given)

∠W = ∠W    (Common angle)

Then the triangles ΔSTW and ΔUVW will be similar to each other. Then the ratio of the corresponding sides will be constant. Then the equation is given as,

ST / UV = VW / TW

ST / UV = VW / (TV + VW)

5 / x = 6 / (9 + 6)

x = 5 (9 + 6) / 6

x = 5(15) / 6

x = 75 / 6

x = 12.5

The triangle ΔSTW is similar to the triangle ΔUVW. Then the value of the variable 'x' is 12.5 meters.

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By applying the distributive property to open the parentheses and then combining like terms, the answers above are gotten when each expressions are simplified.

To simplify an expression that as parentheses, we can apply the distributive property to get the answer.

Given the expression, 2(4 + 3(x - 5)), to get the answer in simple form. apply the distributive property to open the parentheses:

2(4 + 3x - 15)

Combine like terms:

2(3x - 11)

Apply the distributive property:

6x - 22

Also, follow the same process to simplify -3(9 - 2(k + 3) + 5k):

-3(9 - 2(k + 3) + 5k)

Apply the distributive property:

-3(9 - 2k - 6 + 5k)

Combine like terms:

-3(3k + 3)

Apply the distributive property:

-9k - 9

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By evaluating the system of inequalities we will see that the point (0, 1) is not a solution.

Here we know that a student says that (0, 1) is a solution to the system of inequalities below:

y > x

y > 2x + 1

A point (x, y) is a solution of the system of eqations if, when we replace both values, both inequalties are true.

Replacing the values of the point (0, 1) we will get:

1 > 0

1 > 2*0 + 1  → 1 > 1

The second inequality is false, then the point (0, 1) is not a solution of the system.

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Answer:

s >= 18 and s <= -18

Step-by-step explanation:

-|s| <= -18

|s| >= 18

The value inside the module can be either positive or negative:

positive:

s >= 18

negative:

-s >= 18

s ≤ -18

The value of 'n' in the equation 3n + 7 = 25 is equal to 6.

In the equation 3n + 7 = 25, 'n' is a variable representing an unknown value. To find the value of 'n', we need to isolate it on one side of the equation.

The first step is to remove the constant term 7 from the equation. This can be done by subtracting 7 from both sides of the equation, which gives:

3n = 18

The next step is to get 'n' alone on one side of the equation. This can be done by dividing both sides of the equation by 3, which gives:

n = 18/3

n = 6

So the value of 'n' in this equation is 6.

--The question is not readable, answering to the question below--

"What is the value of an in 3n + 7 is equal to 25?"

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[tex] = \frac{3}{5} - \frac{1}{10} \\ [/tex]

[tex] = \frac{3}{5} \times \frac{2}{2} - \frac{1}{10} \\ [/tex]

[tex] = \frac{6}{10} - \frac{1}{10} \\ [/tex]

[tex] = \frac{6 - 1}{10} \\ [/tex]

[tex] = \frac{5}{10} \\ [/tex]

Change in lowest term

answer [tex] = \frac{1}{2} \\ [/tex]

The theoretical probability of getting a blue color is 1/4.

The experimental probability of landing a blue color is 35%.

Option A is the correct answer.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Number of times the blue color is recorded = 7

The total number of times each color is recorded = 20

Now,

Number of sections = 4

Number of blue sections = 1

So,

The theoretical probability of getting a blue color.

= 1/4

Now,

Experimental probability of landing a blue color.

= 7/20

= 7/20 x 100

= 35%

Thus,

Theoretical probability of getting a blue color is 1/4.

Experimental probability of landing a blue color is 35%.

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Answer:

(2,-5)

Step-by-step explanation:

find the coordinates which forms rectangle with othe given points

The coordinates of the fourth vertex of the rectangle are (2, -5).

A rectangle is defined as a four-sided shape with opposite sides that are equal in length and parallel to each other.

We have to determine the fourth vertex of the rectangle.

As we know that the opposite sides of a rectangle are equal.

The x-coordinate of the second vertex (2,4) is equal to the x-coordinate of the fourth vertex.

So, the x-coordinate of the fourth vertex = 2

The y-coordinate of the third vertex (-2,-5) is equal to the y-coordinate of the fourth vertex.

So, the y-coordinate of the fourth vertex = -5

Therefore, the coordinates of the fourth vertex of the rectangle are (2, -5).

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Coupon 1 is the better deal, as it offers a 40percentage discount on one of the two items.

Coupon 1:

Cost of 1 item: 18

Discount of 1 item: 40% (7.2)

Total cost with coupon 1: 10.8

Coupon 2:

Cost of 2 items: 36

Discount of 2 items: 25% (9)

Total cost with coupon 2: 27

Coupon 1 is the better deal for Brittni's purchase. It offers her a 40% discount on one of the two items, which means she would save 7.2 on the item. The total cost with coupon 1 would be 10.8. On the other hand, coupon 2 offers a 25% discount on the entire purchase, which would amount to 9 in savings. However, the total cost with coupon 2 would still be higher at 27. Thus, coupon 1 is the better deal for Brittni's purchase.

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The cosine of a right-angled triangle is defined by the trigonometric word “cos” meaning.The neighboring base-to-hypotenuse ratio is known as the cos function in a right-angled triangle.

It aids in determining the triangle's side lengths regardless of the provided angle. If the angle between the neighboring side and the hypotenuse of a right triangle is, we can write this using the cos function.

In a right triangle, the ratio between an angle's adjacent side and the hypotenuse is known as the cosine of the angle. It is written as:

Cos = Base of the right-angled triangle/ Hypotenuse of the right-angled triangle.

The cosine function takes up different values depending upon the value of

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The slope of y=-10x is -10.

The slope of a linear equation in the form of y = mx + b is represented by the coefficient of x, which is also known as the "slope" or "rate of change." In this case, the coefficient of x is -10.

This means that for every unit increase in x, there is a corresponding decrease of 10 units in y. In other words, the line represented by this equation has a negative slope, meaning it slopes downwards as it goes from left to right.

A linear equation is an equation that can be written in the form of y = mx + b, where m is the slope (or rate of change) and b is the y-intercept (the point where the line crosses the y-axis). Linear equations represent straight lines on a graph, and their slope and y-intercept can be used to determine the characteristics of the line, such as its direction and position.

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The dependent and independent variables ,C is 3 + 1(X) (X)

where, C is the price of gift-wrapping, X is the quantity of wrapped goods.

The number of goods that were wrapped is the independent variable for this function, and the price paid to wrap the presents is the dependent variable.

The number of goods that were wrapped is the independent variable for this function, and the price paid to wrap the presents is the dependent variable.

As opposed to the dependent variable, which is the function's output, the independent variable refers to the function's input. The function in this instance is written as follows:

C = 3 + 1(X) (X)

where,

C is the price of gift-wrapping.

X is the quantity of wrapped goods.

The complete question is,

An order will cost $3 plus $1 for each item that will be wrapped as a present. What are the dependent and independent variables?

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M = A + |B| is the function's highest possible value. When sin or cos x equals 1, this maximum value is reached. m = A |B| is the function's lowest possible value. If either cos x or sin x is equal to 1, this minimum will be reached.

Example :

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With a $250 original cost and a 30% discount, The cost after discount is $175.00. $75.00 was saved by you.

Think about the pre-sale price. Multiply the initial cost by 30, then divide it by 100. Subtract the old number from this new one. Your discounted value is the new figure. With a $250 original cost and a 30% discount, The cost after discount is $175.00. $75.00 was saved by you.

The simplest method for figuring out a discount is to multiply the original cost by the percentage rate in decimal notation. Any item's selling price is determined by deducting the discount from the purchase price. Value-based rebates or discounts are described by Discount Rules at the product (SKU) or order level. They can be described in terms of proportions or absolute values (net price). A discount rule only applies to the product to which it refers.

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The profit percent for the pencils is equal to 10%.

If C is the cost and P is the price, then the formula for the profit percent is:

p = 100%*(P - C)/C

Here we know that the selling price of 10 pencils is equal to the cost price of 11 pencils, then we can write the eqation:

10*P = 11*C

We can solve this for P.

P = (11/10)*C = 1.1*C

Replacing that in the given formula we will get:

p = 100%*(1.1*C - C)/C

p = 100%*(1.1 - 1)*C/C

P = 10%

The profit percent is 10%.

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If two numbers A and B are given, then the formula of the commutative property of numbers for addition is given as: A + B = B + A

The commutative property deals with the arithmetic operations of addition and multiplication. It means that changing the order or position of two numbers while adding or multiplying them does not change the end result.

For example, 4 + 5 gives 9, and 5 + 4 also gives 9. The order of two numbers being added does not affect the sum.

As a result, the commutative property is concerned with moving the numbers about. So, if altering the order of the operands has no effect on the result of the arithmetic operation, that arithmetic operation is commutative.

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The correct way to write greater than 3 is A > 3 where it tells that A having greater value than 3.

In mathematics,

→The greater than symbol (>) is used to indicate that one value is larger than another. For example, if we say "A > B," this means that the value of A is greater than the value of B.

→The less than symbol (<) is the opposite, it indicates that one value is smaller than another. For example, if we say "A < B," this means that the value of A is less than the value of B.

→The greater than or equal to symbol (≥) indicate that one value is larger than or equal to another. For example, if we say "A ≥ B," this means that the value of A is greater than or equal to the value of B.

→The less than or equal to symbol (≤) indicate that one value is smaller than or equal to another. For example, if we say "A ≤ B," this means that the value of A is less than or equal to the value of B.

These symbols are commonly used in mathematical expressions, equations, and inequalities.

To write "greater than 3" in mathematical notation, you would use the greater than symbol (>) followed by the letter 3. For example:

A > 3

This means that A is greater than 3.

Therefore, the correct way to write greater than 3 is A > 3 where it tells that A having greater value than 3.

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The formula of distributive property is the following, a(b+c) = ab + ac , where a,b,c are real numbers.

The distribution property of multiplication over addition applies when values are multiplied by sums. The expression for the distribution characteristic is expressed as: a × (b + c) = (a × b) + (a × c); where a, b, and c are the operands. The numbers outside the brackets are multiplied by each term inside the brackets and the products are added. For example, you want to multiply the sum of 20 + 3 by 9. Since we have similar terms, we usually add numbers first and then multiply by 5. But according to the property, we can first multiply each summand by 5, so 5( 20 + 3)

= 5 × 20 + 5 × 3

= 100 + 15 = 115.

Hence, distributive property is one of basic property follows by addition and multiplcation operations.

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Answer:

p = t - a - b

Step-by-step explanation:

T = a + p + b

- p + T = a + b

- p = - T + a + b

p = T - a - b

Answer:

The variable that belongs in the green box is T

(p=T-a-b)

Step-by-step explanation:

The total amount of fruit (T) minus the apples (a) and minus the bananas (b) would leave us with just the pears (p).

Writing this out mathematically, we have : T - a - b = p

Answer:

B and E

Step-by-step explanation:

A translation is a slide.  If your only moves was a slide, y would slide right over B and E.  The others would you have to flip or rotate or expand.

Answer:

B and E.

Step-by-step explanation:

A translation is a slide.  If your only moves was a slide, y would slide right over B and E.  The others would you have to flip or rotate or expand.

The two lines in the system of equations will be parallel when the value of k is 15/4.

Let 2 equations of the line be,

ax+by=c1

dx+ey=c2

for lines to be parallel it is necessary that their slopes are equal

we can easily find the slopes of these equations by re-arranging them in the standard equation of a line i.e, y=mx+c

after rearranging we'll get the following equations,

y=(-a/b)x+c1/b

y=(-d/e)x+c2/e

and it should satisfy the given condition,

-a/b=-d/e≠c1/c2

as, if the ratio of the slope is the same as the constants it will become the same line. So, according to the given question

-3/2k must be equal to -2/5

k must be 15/4.

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If you are given a graph, you may perform the vertical line test; if a vertical line crosses the graph more than once, the relation represented by the graph is not a function.

Determine the input values. Determine the output values. If each input value results in just one output value, the relationship is classified as a function. If any input value results in two or more outputs, the relationship is not a function.

The connection is a function if each ordered pair has a unique x x x-coordinate. If the relation is specified as a mapping, check to determine if each domain value is present. Has only one arrow pointing to a range value. If the relation is given as a graph, use the Vertical Line Test.

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The solutions to the nonlinear system of equations are (x₁, y₁) = (1 + √14 / 7, - 1 + 3√14 / 7) and (x₂, y₂) = (1 - √14 / 7, - 1 - 3√14 / 7).

In this problem we find the case of a system of two equations formed by a linear equation and a quadratic equation that can be solved by means of algebra properties. First, write the entire system of equations:

3 · x - y = 4

2 · x² + y² + x · y = 6

Second, clear y in the first equation:

y = 3 · x - 4

Third, substitute in the second equation:

2 · x² + (3 · x - 4)²  + x · (3 · x - 4) = 6

2 · x² + 9 · x² - 24 · x + 16 + 3 · x² - 4 · x = 6

14 · x² - 28 · x + 10 = 0

By quadratic formula:

x₁ = 1 + √14 / 7 or x₂ = 1 - √14 / 7

Fourth, find the possible values for y:

y₁ = 3 · x₁ - 4

y₁ = 3 · (1 + √14 / 7) - 4

y₁ = - 1 + 3√14 / 7

y₂ = 3 · x₂ - 4

y₂ = 3 · (1 - √14 / 7) - 4

y₂ = - 1 - 3√14 / 7

Fifth, write the solutions:

(x₁, y₁) = (1 + √14 / 7, - 1 + 3√14 / 7), (x₂, y₂) = (1 - √14 / 7, - 1 - 3√14 / 7)

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Answer:

0.80g

Step-by-step explanation:

8/10 = 0.80

Add the variable(g)

0.80g

a) The ratio of the number of white tiles to the number of blue tiles = 3:1

b) The ratio of the total cost of the white tiles to the total cost of the blue tiles = 3:2.

a)Since they are 48 white tiles and 16 blue tiles, the ratio of the number of white tiles to the number of blue tiles is the number of white tiles divided by the number of blue tiles. Therefore-

The ratio of white tiles to the blue tiles = number of white tiles/number of blue tiles = [tex]\frac{48}{16}[/tex] = 3

b)Total cost of the white tiles = number of white tiles × cost of each white tile = 48 tiles × £2 per tile = £96

Total cost of the blue tiles = number of blue tiles × cost of each blue tile = 16 tiles × £4 per tile = £64

The ratio of the total cost of the white tiles to the total cost of the blue tiles = total cost of the white tiles/total cost of the blue tiles = [tex]\frac{96}{64} = \frac{3}{2}[/tex]

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The complete question is:

Ewen has 48 white tiles and 16 blue tiles.

(a) Write down the ratio of the number of white tiles to the number of blue tiles.

Give your ratio in its simplest form.

The cost of each white tile was £2

The cost of each blue tile was £4

(b) Work out the ratio of the total cost of the white tiles to the total cost

of the blue tiles