36(m+n)² - 121(m-n)²

The area of the enlarged map is 75 cm². Answer: (D) 75 cm².

What is scale ?

Scale refers to the ratio of distances or sizes on a map or drawing to the actual distances or sizes of the objects they represent in the real world. It is often expressed as a ratio, such as 1:10,000 or 1/4 inch = 1 foot, and is used to create maps and drawings that accurately represent real-world objects and distances. Scales can be used to enlarge or reduce the size of a map or drawing, making it easier to view and work with.

The original area of Colorado on the map is:

Area = length x width = 4 cm x 3 cm = 12 cm²

To enlarge the map with a scale factor of 2.5, we need to multiply the length and width by 2.5:

New length = 4 cm x 2.5 = 10 cm

New width = 3 cm x 2.5 = 7.5 cm

The area of the enlarged map is:

New area = new length x new width = 10 cm x 7.5 cm = 75 cm²

Therefore, the area of the enlarged map is 75 cm². Answer: (D) 75 cm².

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The correct descriptions of the right-hand and left-hand behavior of the graph of the polynomial function y = 2x^2 - 3x + 5 are:

Right-handed actions: As x +, y +

Left-handed actions: As x -, y +

The positive coefficient of the x2 term (2) causes the parabola on the graph of the polynomial function y = 2x^2 - 3x + 5  to open upwards.

The y-values of the function approach positive infinity as x approaches negative infinity (i.e., x -), and vice versa. This is known as the left-hand behaviour of the graph.

As x approaches positive infinity (i.e., x → +∞), the y-values of the function also approach positive infinity (i.e., y → +∞). This is referred to as the graph's right-hand behaviour.

As a result, the following statements accurately describe the right-hand and left-hand behaviour of the graph of the polynomial function y = 2x^2 - 3x + 5 :

Right-handed actions: As x +, y +

Left-handed actions: As x -, y +

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Answer:

To find the cube root of a number, you want to find some number that when multiplied by itself twice gives you the original number. In other words, to find the cube root of 8, you want to find the number that when multiplied by itself twice gives you 8. The cube root of 8, then, is 2, because 2 × 2 × 2 = 8.

Step-by-step explanation:

Answer:

When two proper fractions are multiplied together, the product will be smaller than both factors.

Step-by-step explanation:

To understand why this is true, we can consider the concept of fractions as parts of a whole. When we multiply two proper fractions, we are essentially taking a part of a part, which results in a smaller portion overall.For example, if we multiply 1/2 by 2/3, we are taking half of something and then taking two-thirds of that half. The result is 1/3, which is smaller than both 1/2 and 2/3.Therefore, the correct answer is: The product will be smaller than both factors.

Answer:The product will be smaller than both factors.

When two proper fractions are multiplied together The product will be smaller than both factors.Take a look at the equation below.

¾ * ⅔=  3 times 2 is 6 and 4 times 3 is 12. So the equation is 6/12 .

6/12 is simplified to 1/2. 1/2 is less than both 2/3 and 3/4. Which means the product is smaller. Hence, the correct answer is the product will be smaller than both factors.

I hope this helped & Good Luck <3!!!!

We will see that the car needs 15 liters to travel the 180 km.

We know that this car travels 12 km for each liter of gasoline, so we must see how many times there are 12 kilometers in 180 km, then we must take the quotient:

180km/12km = 15

And for each one of those times, the car consumes one liter, so in total there are 15*1 l = 15 l

The car needs 15 liters to travel 180 km.

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Answer: $1560

Step-by-step explanation:

The word "of" in a problem means to multiply.  30% = .30. So, the cost of the printer is .30c.

If we add the cost of the computer, c, to the cost of the printer, .30c, then we get 1.30c. We know that the total is $2028, so our equation is 1.30c = $2028.  

Dividing both sides by 1.30, we get c = $1560.

Answer:

4) No, It is not a right triangle

Step-by-step explanation:

12 is the hypotenuse which is the longest side of the triangle

6² + 8² = 12² （Pythagoras Theorem）

36 + 64 ≠ 144

Hence it is not a right triangle

The weights of the three parts are 200g, 120g, and 160g, respectively, in the ratio of 5:3:4.

What is Ratio?

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six.

To divide 480g in the ratio 5:3:4, we need to divide the total amount into 3 parts (corresponding to the three parts of the ratio), where the first part is 5/12 of the total, the second part is 3/12 (or simplified, 1/4) of the total, and the third part is 4/12 (or simplified, 1/3) of the total.

To find the weight of the first part (in the ratio of 5), we need to multiply the total weight by the fraction representing the first part of the ratio:

5/12 * 480g = 200g

To find the weight of the second part (in the ratio of 3), we need to multiply the total weight by the fraction representing the second part of the ratio:

1/4 * 480g = 120g

To find the weight of the third part (in the ratio of 4), we need to multiply the total weight by the fraction representing the third part of the ratio:

1/3 * 480g = 160g

Therefore, the weights of the three parts are 200g, 120g, and 160g, respectively, in the ratio of 5:3:4.

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[tex]83 + 61 + (4x + 16) = 180[/tex]

[tex]144 + 4x + 16 = 180[/tex]

[tex]4x + 160 = 180[/tex]

[tex]4x = 180 - 160[/tex]

[tex]4x = 20[/tex]

[tex]x = 20:4 \implies \bf x = 5[/tex]

The Required explanation of triangle inequality theorem has been done.

In mathematics, inequalities specify the connection between two non-equal values. Equal does not imply inequality. Typically, we use the "not equal symbol ()" to indicate that two values are not equivalent. But various inequalities are used to compare the values, whether it is less than or larger than.

The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides is always greater than the length of the third side. Mathematically, if a, b, and c are the lengths of the sides of a triangle, then a + b > c, b + c > a, and c + a > b.

This theorem is a fundamental principle in geometry and can be used to prove many other theorems related to triangles.

It is also used in everyday life, such as in designing bridges, ensuring the stability of buildings, and determining the shortest distance between two points.

The triangle inequality theorem is a powerful tool in mathematics and is a key concept for anyone studying geometry.

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No: As x approaches -∞, y approaches -∞. As x approaches ∞, y approaches ∞.

YES: As x approaches ∞, y approaches 0. As x approaches -∞, y approaches ∞.

No: As x approaches 0, y approaches -∞. As x approaches ∞, y approaches ∞.

Thus, correct options are-

No: As x approaches -∞, y approaches -∞. As x approaches ∞, y approaches ∞.

YES: As x approaches ∞, y approaches 0. As x approaches -∞, y approaches ∞.

No: As x approaches 0, y approaches -∞. As x approaches ∞, y approaches ∞.

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It satisfies the vertical line test and represents a function.

What is function ?

Function can be defined in which it relates an input to output.

Based on the image you provided, it seems to represent a function since each input value (x-value) corresponds to a unique output value (y-value) and there is only one output value for each input value.

To verify if a graph represents a function, we can use the vertical line test. If a vertical line intersects the graph at more than one point, then the graph does not represent a function. However, in this graph, for any vertical line drawn, it only intersects the graph at one point.

Hence, it satisfies the vertical line test and represents a function.

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Answer: C

Step-by-step explanation:

Answer:

B I did the math in my head mb if I get wrong

Volume of the cone is 1/3 of the volume of the cylinder, so volume of the cone = 40in³.

One-third of the volume of a cylinder is the formula for the volume of a cone. The product of the base area and the height is used to calculate a cylinder's volume. As a result, the formula for a cone's volume is given as V = (1/3) r²h, where "h" stands for the cone's height and "r" for its base radius.

A cylinder's volume is determined by how many unit cubes (cubes of the same length) can fit inside of it. It is the area the cylinder takes up, just as any three-dimensional shape's volume is the area it occupies.

We are aware that a circle serves as the base of a right circular cylinder and that r² is the area of a circle of radius r. As a result, using the formula above, V = r²h is the right circular cylinder's volume.

Now in the given question, volume of the cylinder = 120in³.

Volume of cone = 1/3(volume of the cylinder)

= 1/3 × 120

40in³.

Therefore, volume of the cone = 40in³.

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The simplest form of the given expression 3√12 × √5  is 6√15.

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

The given expression is as follows:

3√12 × √5

To solve this problem, we can simplify the expression first:

3√12 × √5 = 3√(12 × 5) = 3√60

To further simplify the expression, we can factor 60 into its prime factors:

60 = 2² × 3 × 5

Here, we can rewrite the expression as:

3√60 = 3√(2² × 3 × 5) = 3 × 2√15

Thus, the values of a and b are a = 6 and b = 15.

Therefore, the simplest form of the given expression is 6√15.

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The correct question is as follows:

The answer to 3 √12 × √5, given in its simplest form, is a√b, where a and b are integers.

Calculate the values of a and b.

Using inequalities, Y(x=0) = -2 and X(y=0) = -2 in region 1.

To pick area 1, draw a line at the intersection of (-2,0) and (0, -2), then choose the right side. such as.

Region 2) To pick the region to the left or upwards in region 2, we must draw a line from (0,2) to (-2,4).

Y(x=0) = 2\sX(y=-2) = -4

Region 3) To pick the region to the right, we must draw a line connecting (-4,0) and (0,4), as I'll demonstrate.

Inequalities in mathematics describe the relationship between two non-equal numbers. Equal does not necessarily mean unequal. When two values are not equal, we typically use the "not equal symbol ()". However, several inequalities are utilised to compare the numbers, whether it is less than or higher than.

The feasible area is now visible. Let's determine the vertices' coordinates.

Where the blue and green lines intersect is our first vertex.

3x + 2 = x + 4 and y = 3x + 2

3x - x = 4 - 2

y = 3× (1) + 2 = 3 + 2 = 5 when 2x = 2x = 1

(X, Y) = Vertex 1 (1,5)

The intersection of the red and green lines is at vertex #2:

y = -x -2; y = x + 4; y = x + 4 = -x - 2; and y = x + x = -2 - 4

2x = -6, x = -6/2, and y = (-3) + 4 = -3 + 4 = 1 are the results.

(X, Y) = Vertex 2 (-3,1)

The intersection of the red and blue lines is at vertex 3:

y = -x - 2, y = 3x + 2 -x - 2, and y = 2 + 2 -4 x = 4 x = -4 / 4 = -1.

So, y = 3× (-1) + 2 = -3 + 2 = -1

(X, Y) = Vertex 3 (-1, -1)

Let's now modify the graph by including the supplied equation.

The intercept where Y=0 is 0 is given by f(x,y) = -3x + 5y = 0 5y = 3x + 0 y = 3/5 × X + 0

the gradient m = 3/5

A line can be drawn from (0,0) to (-10, -6)

Let's now examine how it would appear in the area where it is practical.

We can see that the function intercepts the blue line or the line of the second section, which is where the largest value is located.

y = 3x + 2 3x + 2 (3/5 - 3) x = 2 -12/5 × x = 2 x = -5/6.

Hence, y = 3x + 2 3/5 × (-5/6) = -1/2.

The maximum is therefore found at (x,y) = (-5/6, -1/2).

The point where the function crosses the red line now marks the minimum.

y = 3/5 × x; y = -x -2

3/5 x = -x - 2\s (3/5 + 1) × x = -2\s8/5 x = - 2\sx = -2× (5/8) = -5/4.

y = 3/5 × (-5/4) = -3/4

The minimum is thus found at (x,y) = (-5/4, -3/4)

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The piecewise function is defined as follows:

A piece-wise function is a function that has different definitions, based on values of the input x of the function.

For this problem, the intervals are given as follows:

For the first interval, the interval is open due to the open circle, and the quadratic function is a translation up 4 units of y = x², hence:

y = x² + 4, x < 2.

For the second interval, which is the closed interval, we have a decaying line with slope of -1 and x-intercept of 4, hence:

y = -x + 4, x ≥ 2.

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The values of are;

1. angle WXU = 104°

2. angle XUV = 109°

A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle. It is also sometimes called inscribed quadrilateral. The circle which consists of all the vertices of any polygon on its circumference is known as the circumcircle or circumscribed circle.

The sum of opposite in angle Ina cyclic quadrilateral is 180°

angle v = 152/2 = 76°

therefore angle XWV = 180-(76) = 104°

angle XUV = 180-71 = 109°

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Using the addition operation, the sum of 40 + 5 is 45.

The addition operation is one of the basic mathematical operations.

Other mathematical operations include subtraction, division, multiplication, exponentiation, and functions.

The addition operation involves two addends added using the addition operand (+) and the  equal symbol (=) we show the result of the algebraic operation called the sum or total.

Thus, when five is added to forty (40 + 5), the result or sum is forty-five (45).

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Answer:

14.4

Step-by-step explanation:

=24 * 60/100
=14.4

Answer:

14.4

Step-by-step explanation:

[tex]\frac{24}{10} = 10[/tex]% of 24

6[tex]\frac{24}{10} = 60[/tex]% of 24

The value of X from the given rectangular figure above would be = 6.5. That is option A.

A rectangle can be defined as a quadrilateral that has four sides, four vertices, and four angles.

In a rectangle, when two diagonal line divides it, the two diagonals are of the same length.

That is;

Line PR = Line SQ

Half of PR = ER

Half of SQ = QE

But QE = 2x

PR = 26

QE = 1/2 × 26 = 2x

13= 2x

X = 13/2

X= 6.5

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Answer:

17,714.7

Step-by-step explanation:

a_n = 3^(2 n - 1) 10^(5 - n) (for all terms given)

{30000, 27000, 24300, 21870, 19683, 177147/10, 1594323/100, 14348907/1000, 129140163/10000, 1162261467/100000, 10460353203/1000000, 94143178827/10000000, 847288609443/100000000, 7625597484987/1000000000, 68630377364883/10000000000, 617673396283947/100000000000}

Mary's monthly payments will be approximately $117.50.

The total instalment price is the price of the furniture plus the interest charged. Since Mary made a down payment of 15%, the amount that is subject to interest is 85% of the total price. Therefore:

Total price = (100% / 85%) * $750 = $882.35

The interest charged is 6% of the total price over the 8-month payment period. Therefore:

Interest charged = 6% * $882.35 * (8 / 12) = $35.29

The total installment price is the sum of the total price and the interest charged:

Total installment price = $882.35 + $35.29 = $917.64

To find the monthly payments, we can use the formula for the present value of an annuity:

Payment = [tex]\mathrm{PV \times (r / (1 - (1 + r)^{(-n)}))}[/tex]

where PV is the present value (total installment price), r is the interest rate per month (6% / 12 = 0.005), and n is the number of payments (8).

Substituting the values:

Payment = $917.64 × (0.005 / [tex](1 - (1 + 0.005)^{(-8)}[/tex] ≈ $117.50

Therefore, Mary's monthly payments will be approximately $117.50.

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We have the following response after answering the given question: inequality   {x | x ≥ ∛9} or [∛9, ∞) in interval notation.

A connection between two expressions or values that is not equal is known as an inequality in mathematics. Inequality follows imbalance, therefore. In mathematics, an inequality makes a connection between two values that are not equal. Egality and inequality are different. The not equal symbol is often used to indicate that two values are not equal (). Various inequalities are employed to contrast values of all sizes. By changing the two sides until just the variables are left, one may solve many straightforward inequalities. However a variety of factors support inequality: Negative values are split or added on either side. Switch between the left and right.

[tex]x^3[/tex] - 8 ≥ 1

Adding 8 to both sides, we get:

[tex]x^3[/tex] ≥ 9

Taking the cube root of both sides, we get:

x ≥ ∛9

Since ∛9 is approximately 2.08, the inequality is satisfied for all values of x greater than or equal to 2.08. Therefore, the set of all possible values of x that satisfy the inequality is:

{x | x ≥ ∛9} or [∛9, ∞) in interval notation.

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The value of the function (f+g)(x) = x² + 4x - 4.

An output variable and one or more input variables are at least two of the variables that make up a function. A mathematical equation may have any number of variables and says that two expressions are equivalent (none, one, or more). A function is frequently expressed as an equation, however not all equations are functions.

Given that,

f(x) = 4x + 2

g(x) = x² - 6

(f+g)(x) = f(x) + g(x) = 4x + 2 + x² - 6

(f+g)(x) = x² + 4x - 4

Hence, the value of the function (f+g)(x) = x² + 4x - 4.

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Answer:3/7

Step-by-step explanation:

36 divided by 12   then 84 divided by 12

therefore 36/84 simplified to the  lowest terms is 3/7

Answer:

20cm³

Step-by-step explanation:

Volume = Base x Height

1/2 x 5 x 2 x 4

=20cm³

The length of RQ is 15. The solution has been obtained by using the properties of rectangle.

The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle.

We are given a figure PQRS which is a rectangle.

We know that the opposite sides of a rectangle are equal.

So,

⇒PS = RQ

⇒-1 + 4x = 3x + 3

⇒x = 4

On substituting x = 4 in 3x + 3, we get

3(4) + 3 = 15

Hence, the length of RQ is 15.

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The graph of the function does not form a straight line. Option A

The link between the x and y coordinates of the line's points is expressed mathematically as the line's equation. In general, a line's equation can be expressed in slope-intercept form, which is written as y = mx + b, where m denotes the line's slope and b its y-intercept (the point at which the line crosses the y-axis).

The equation in the form 5x^4 - 2 is exponential and it can not lead to a straight line.

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