A right triangle has legs that measure
6 centimeters and 3 centimeters.
What is the length of the hypotenuse in centimeters?

The area of the figure, given the vertices on the coordinate plane, is 14 square units.

The shoelace formula can be used to find the area. First, find the sum of the products :

= ( - 1 × 2 ) + ( -2 × - 3 ) + ( 4 × 2 ) + ( 4 × 4 ) + (1 × -2)

= 2 + 6 + 8 + 16 - 2

= 26

Then the products of the y coordinate and the x coordinates :

= ( -2 × - 2 ) + (2 × 4 ) + ( - 3 × 4 ) + ( 2 × 1) + ( 4 ×  -1 )

= - 2

We can then find the absolute value to be:

= | Sum 1 - Sum 2 | = | 26 - (- 2 ) | = | 26 + 2 | = 28

The area is then:

= 28 / 2

= 14 square units

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The ordered pair that represents the week before is given as follows:

A. (1,7).

The general format of an ordered pair is given as follows:

(x,y).

In which the coordinates are given as follows:

The meaning of each coordinate in this problem is given as follows:

For the current week, the ordered pair is given as follows:

(5,3).

For the previous week, the total number of hours was the same, that is, 5 + 3 = 8, however with x = 1 and y = 8 - 1 = 7, as only one hour was spent on chores.

Thus option A is correct.

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Answer:

The mean of the numbers 5, 3, 6, x, 9, and 10 is given as 7.

To find the value of x, we can use the formula for the mean:

mean = (sum of all the numbers) / (number of numbers)

In this case, we have:

7 = (5 + 3 + 6 + x + 9 + 10) / 6

Multiplying both sides of the equation by 6, we get:

42 = 33 + x

Subtracting 33 from both sides of the equation, we get:

x = 9

Therefore, the value of x that makes the mean of 5, 3, 6, x, 9, and 10 equal to 7 is 9.

Answer: To calculate the cost of the triangular lot, we need to first find the area of the triangle using the given dimensions. To do this, we can use Heron's formula, which states that the area of a triangle with sides of lengths a, b, and c is given by:

area = √(s(s-a)(s-b)(s-c))

where s is the semiperimeter of the triangle, given by:

s = (a + b + c)/2

In this case, we have a = 188, b = 145, and c = 158. Substituting these values into the formula, we get:

s = (188 + 145 + 158)/2 = 245.5

area = √(245.5(245.5-188)(245.5-145)(245.5-158)) ≈ 12463.15 square feet

Now that we have the area of the lot, we can multiply it by the price per square foot to get the total cost:

cost = 12463.15 × $3 = $37,389.45

Therefore, the lot would cost approximately $37,389.45.

Step-by-step explanation:

The meaning of V(2) is the Erica's vertical distance after walking 2 kilometers along the trail.

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

The input and output variables for this problem are given as follows:

V(2) means that the number of km is of 2, hence the meaning of V(2) is the Erica's vertical distance after walking 2 kilometers along the trail.

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Answer:

We know that the x-coordinate of point A is -11, and that the distance between point A and point B is 15 units. Let's call the y-coordinate of point A "y". Then we can use the distance formula to find the two possible values of y:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where (x1,y1) = (-11,y) is the coordinates of point A, and (x2,y2) = (1,2) is the coordinates of point B. Substituting the values, we get:

15 = sqrt((-11 - 1)^2 + (y - 2)^2)

15 = sqrt(144 + (y - 2)^2)

15^2 = 144 + (y - 2)^2

225 = 144 + (y - 2)^2

81 = (y - 2)^2

y - 2 = ±9

y = 2 ± 9

So the possible coordinates of point A are (-11,11) and (-11,-7).

Answer:

Okay, let's think through this step-by-step:

• Janelle Monae obtained a $3,500 loan at 8.5% interest for 1 year.

• 8.5% interest for 1 year = 8.5% of $3,500 = $297.50 in interest

• The loan amount ($3,500) plus interest ($297.50) = $3,797.50 total paid back

•Monthly payments = $3,797.50 / 12 months = $285.55

• So the interest amount in the first payment is $297.50 (calculated above as 8.5% of the $3,500 loan amount)

The choices do not match this:

A. $297.50 - This is the correct choice. This is the interest amount paid over the full loan.

B. $291.67 - This is too low. Calculated interest over 1 year at 8.5% is $297.50.

C. $24.79 - This is way too low. The interest amount due is $297.50 per the working.

D. $35.00 - This is also too low and does not make sense based on the loan details provided.

In summary, to find the interest in just the first payment, we calculate:

Interest over full loan ($297.50) / Number of payments (12) = $24.79

So the interest amount in just the first monthly payment is $24.79.

But the total interest paid over the life of the loan (1 year) is $297.50.

Does this help explain the steps and reasoning? Let me know if any part of the working or explanation is unclear. I can also provide additional examples if needed.

Let me know if you have any other questions!

Step-by-step explanation:

The solution to the system of equations is:

x = -19/5, y = 2, z = 1/10

4x + 6y - 2z = 2 (multiply first equation by 2)

x + 2y - 3z = -5 (third equation)

Add the two equations, we get:

5x + 8y = -3 (eliminated z)

-7x + 7y - 6z = -33 (multiplying second equation by 3 and subtracting from the first)

3x + y + 2z = 12 (second equation)

Add these two equations, we have:

-4x + 8y = -21 (eliminated z)

5x + 8y = -3

5x = -8y - 3

x = (-8y - 3)/5

Substituting this expression for x into the second equation, we get:

3((-8y - 3)/5) + y + 2z = 12

z = (39/10) - (19/10)y

Finally, substituting these expressions for x and z into any of the original equations (let's use the first one), we can solve for y:

2((-8y - 3)/5) + 3y - ((39/10) - (19/10)y) = 1

Simplifying and solving for y, we get:

y = 2

x = (-8(2) - 3)/5 = -19/5

z = (39/10) - (19/10)(2) = 1/10

In conclusion, the solution to the system of equations is:

x = -19/5, y = 2, z = 1/10

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The solution to the given system of linear equations is

x = 3, y = -1 and z = 2

From the question, we are to solve the given system of linear equations.

The given system of linear equations is

2x + 3y − z = 1

3x + y + 2z = 12

x + 2y − 3z = −5

Multiply the third equation by 2

x + 2y − 3z = −5 ) ×2

2x + 4y - 6z = -10

Subtract the first equation from the resulting equation

  2x + 4y - 6z = -10

- (2x + 3y − z = 1

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

y - 5z = -11     ---------- (1)

Now,

Multiply the third equation by 3

x + 2y − 3z = −5 ) ×3

3x + 6y -9z = -15

Subtract the second equation from the resulting equation

 3x + 6y -9z = -15

- (3x + y + 2z = 12

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

5y - 11z = -27     ----------- (2)

Solve equations (1) and (2) simultaneously

y - 5z = -11         ------------ (1)

5y - 11z = -27     ------------ (2)

Multiply equation (1) by 5

y - 5z = -11  ) ×5

5y - 25z = -55

Subtract the resulting equation from equation (2)

  5y - 11z = -27

-( 5y - 25z = -55

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

14z = 28

Divide both sides by 14

14z/14 = 28/14

z = 2

Substitute the value of z into equation (1)

y - 5z = -11

y - 5(2) = -11

y - 10 = -11

Add 10 to both sides of the equation

y - 10 + 10 = -11 + 10

y = -1

Substitute the value of y and z into the third equation

x + 2y − 3z = −5

x + 2(-1) − 3(2) = −5

x - 2 - 6 = -5

x - 8 = -5

Add 8 to both sides of the equation

x - 8 + 8 = -5 + 8

x = 3

Hence,

The solution is

x = 3, y = -1 and z = 2

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Answer:

(-2)

Step-by-step explanation:

just do -2 x-3 x than + 13 and than you will get - 2

The equation of exponential function of following table is represented by the table below is y = A(Bˣ).

An exponential function is a mathematical function denoted by f(x) = eˣ (where the argument x is written as an exponent). Unless otherwise stated, the term usually refers to positive-valued functions of real variables, but can be extended to complex numbers and generalized to other mathematical objects such as matrices and Lie algebras. Although the exponential function arose from the notion of exponentiation (iterative multiplication), its modern definition (which has several equivalent characterizations) allows it to be extended exactly to any real argument, including irrational numbers. Its ubiquitous appearance in pure and applied mathematics has led mathematician Walter Rudin to believe that the exponential function is "the most important function in mathematics."

To find the equation of exponential form:

For case 1,

Exponential form: y = A(Bˣ)

y = 0.1, x = 0

[tex]0.1 = A(B^{0})[/tex]

0.1 = A(1)

A = 0.1

For case 2,

Exponential form: y = A(Bˣ)

y = 0.05, x = 1

[tex]0.05 = 0.1(B^{1})[/tex]

B = 0.5

For case 3,

y = 0.025, x = 2

[tex]A = 0.1(B^{2})[/tex]

[tex]0.025 = 0.1(0.5^{2})[/tex]

0.025 = 0.025

For case 4,

y = 0.0125, x = 3

0.0125 = 0.1(0.5³)

0.0125 = 0.1(0.125)

0.0125 = 0.0125

We calculated the value of A and B, and proved it in case 3 and case 4.

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The complete question is as follows:

Find the equation of the exponential function represented by the table below:

The percentage of Kira's free throws is 68%.

We have,

From the grid,

We can see that,

There are 25 boxes.

Now,

The number of shaded boxes = 17

Now,

The percentage of the shaded boxes.

= 17/25 x 100

= 17 x 4

= 68%

Thus,

The percentage of Kira's free throws is 68%.

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The complete question.

The shaded area on the grid represents the part of Kira's free throws that she made in the basketball practice today.

Find the percentage of Kira's free throws.

Answer:

5)

$332.19

6)

$16,857.36

7)

$248.91

Step-by-step explanation:

monthly premium = Base Rate * [tex]\frac{Monthly Payroll}{100}[/tex]

5)

given:

Base rate = $2.24
Monthly payroll = $14,830.00

unknown = monthly premium

 [tex]2.24 * \frac{14,830.00}{100}[/tex] = $332.192≈$332.19

6)

given:

Base rate = $19.89
Monthly payroll = $84,752.96

unknown = monthly premium

[tex]19.89 * \frac{84,752.96}{100}[/tex] = $16,857.364≈$16,857.36

7)

given:

Base rate = $2.90
Monthly payroll = $8,582.94

unknown = monthly premium

[tex]2.90 * \frac{8,582.94}{100}[/tex]=$248.90526≈$248.91

The polar form of the rectangular coordinates (-√√2, -√2) is (2√(1 + √2), 15π/28)

To convert the rectangular coordinates (-√√2, -√2) into polar form, we first need to find the value of r (the radius) and θ (the angle).

r = √((-√√2)^2 + (-√2)^2) = √(2 + 2√2) = 2√(1 + √2)

To find the value of θ, we can use the following formula:

θ = atan(y/x)

where atan is the inverse tangent function, and (x, y) are the rectangular coordinates.

θ = atan(-√2/(-√√2)) = atan(√2) = π/4 radians

However, we need to express the angle in terms of 7 over the interval 0 ≤ θ < 2π/7, with a positive value of r.

To do this, we can add a multiple of 2π/7 to the value of θ until we get an angle in the desired interval.

θ = π/4 + 2π/7 = (7π + 8π)/28 = 15π/28 radians

So the polar form of the rectangular coordinates (-√√2, -√2) is:

(2√(1 + √2), 15π/28)

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Answer:

Step-by-step explanation:

Okay but seriously though, you would have to write the whole question down.

Answer: 35% of thinner will be in total after the five litres is added so 85%-25% is 60% Therefore ur answer is 60%

Step-by-step explanation:

The total amount that Meihua pays for the 36 pencils is  9M - 36n

We know that a set of 4 pencils has a price M, then the price of each single pencil is:

P = M/4

And we also know that Meihua got a discount of n in each pencil, so the price that she pays for each pencil is:

P = M/4 - n

Now we know that she buys 36 of these, so the amount that she pays is given by the product:

amount  = 36*(M/4 - n)

amount = 9M - 36n

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The method you would use to prove the two triangles are congruent include the following: B. ASA.

In Mathematics and Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Additionally, the lengths of corresponding sides are proportional to the  lengths of corresponding altitudes when two (2) triangles are similar.

In Mathematics and Geometry, ASA is an abbreviation for Angle-Side- Angle and it states that when two (2) angles and their included side in two (2) triangles are congruent, then the triangles are said to be congruent.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

you did not provide enough information to answer the question

The volume of the gas at the height (i.e 6.5 Km) is 652 mL

The final volume of the gas can be obtained by using the Boyle's law equation as shown below:

[tex]P_1V_1 = P_2V_2[/tex]

[tex]1 \times 326 = 0.5 \times V_2[/tex]

[tex]326 = 0.5 \times V_2[/tex]

Divide both side by 0.5

[tex]V_2 = \dfrac{326}{0.5}[/tex]

[tex]\boxed{\bold{V_2 = 652 \ mL}}[/tex]

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Keara has climbed up to 41 feet in the tree.

Rounding off a value to the nearest tenth means finding the closest multiple of 0.1 to the given value. To do this, you need to look at the digit in the hundredths place. If the digit is 5 or greater, you round the tenths place up by 1. If the digit is less than 5, you leave the tenths place unchanged. For example, to round the value 3.874 to the nearest tenth, you would look at the digit in the hundredths place, which is 7. Since 7 is greater than 5, you round up the tenths place to 8, and the rounded value is 3.9. Rounding to the nearest tenth is often used when working with measurements or values that require a certain level of precision.

According to the range finders, the distance from Keara to her friend is 55 feet and the angle of depression from Keara to her friend is 40°.

From this the following diagram can be drawn.

Now, we need to find the length of AB which will denote how high Keara climbed.

We can use the trigonometric sine function to find the length of AB,

Sin 40° = opposite side / hypotenuse = AB/ BC = AB/ 55

Hence AB = 55 × Sin 40° ≈ 40.981

That is she would have climbed approximately 41 feet.

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The pattern represents a straight line that passes through the origin with a slope of 1.

The form Ax + By + C = 0 is a two-variable linear equation, where A and B are the coefficients, C is a constant term, and x and y are the two variables, with each having a degree of 1.

The numerical pattern that represents the rule y = x + 0, starting with x = 0, is:

x y

0 0

1 1

2 2

3 3

4 4

... ...

This example shows that when x increments by 1, y additionally increments by 1. Since the rule for y is y = x + 0, we can see that adding 0 to x doesn't change its value, so y is just the same as x. As a result, x and y have a linear relationship with a slope of 1 and a y-intercept of 0.

To put it another way, the pattern is a straight line with a slope of one that runs through the origin.

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The inverse of the function y-∛x/3 -1 is:

To find the inverse of the given function, we need to express x in terms of y. We can start by swapping the positions of x and y in the original equation:

Now, we can solve for y in terms of x:

Therefore, Therefore, the inverse of the given function is f^-1(x) = 27(x-1)³. This means that if we substitute any value of x into the inverse function, we will get the corresponding value of y that makes the original function true. Similarly, if we substitute any value of y into the original function, we will get the corresponding value of x that makes the inverse function true.

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The volume of the suitcase is 35/8 cubic feet or approximately 4.375 cubic feet.

A rectangular prism is a three-dimensional solid object that has six faces, where each face is a rectangle. It is also called a rectangular parallelepiped. A rectangular prism is a type of prism because it has a constant cross section along its length.

A rectangular prism's volume V is determined by:

V = l × w × h

where l denotes the prism's length, w its width, and h its height. Here are the facts:

l = 2 3 ft

w = 1 1/2 ft

h = 1 1/4 ft

When we enter these values into the formula, we obtain:

V = (2 3 ft) × (1 1/2 ft) × (1 1/4 ft)

= (7/3 ft) × (3/2 ft) × (5/4 ft)

= 35/8 ft³

Therefore, the volume of the suitcase is 35/8 cubic feet or approximately 4.375 cubic feet.

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Applying the intersecting secants theorem, the value of x is calculated as: x = 5.

According to the intersecting secants theorem, if two secant lines intersect outside of a circle, then the product of the length of one secant segment and its external segment is equal to the product of the length of the other secant segment and its external segment.

Using the theorem, the equation below is created to find the value of x:

4(4 + 5) = (x - 2)(x - 2 + x + 4)

4(9) = (x - 2)(2x + 2)

36 = 2x² - 2x - 4

2x² - 2x - 4 - 36 = 0

2x² - 2x - 40 = 0

Factorize:

(x + 4)(x - 5) = 0

x = -4 or x = 5

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You will need 38/1.17 ≈ 32.48 stone pavers to go around the patio. Rounding to the nearest whole number, you will need 32 stone pavers.

Explain whole numbers

Whole numbers are a set of numbers that includes all natural numbers (positive integers) and zero. They are represented by the symbol "W" and do not include any fractions or decimals. Whole numbers are used in counting, measuring, and representing quantities of discrete objects or entities, and are a fundamental concept in mathematics.

According to the given information

First, let’s convert the length of the stone paver from inches to feet: 14 inches = 14/12 feet = 1.17 feet.

The perimeter of the patio is (12 + 14 + 12) feet = 38 feet. Since each stone paver is 1.17 feet long, you will need 38/1.17 ≈ 32.48 stone pavers to go around the patio. Rounding to the nearest whole number, you will need 32 stone pavers.

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Answer:  the longest poster that could fit in the box is approximately 22.56 inches long.

Step-by-step explanation: Utilizing the Pythagorean theorem, able to calculate the corner to corner as takes after:

diagonal^2 = 11^2 + 18^2 + 8^2

diagonal^2 = 121 + 324 + 64

diagonal^2 = 509

inclining = sqrt(509)

corner to corner ≈ 22.56 inches

Considering the definition of an equation and the way to solve it, the correct answer is option C: Riley need to work 13 weeks to save enough money to buy the new television.

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values appear.

The solution of a equation means determining the value that satisfies it. To solve an equation, keep in mind:

Being "x" the number of weeks Riley need to work, and knowing that:

the equation in this case is:

200.73 + 83.85x= 1290.78

Solving:

83.85x= 1290.78 - 200.73

83.85x= 1090.05

x= 1090.05 ÷ 83.85

x=13

Finally, Riley need to work 13 weeks.

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The sportsman has a final distance with respect to his home equal to 305 meters.

In this problem we must the final distance of the sportsman with respect to his home. This can be determined by the following expression:

X = ∑ xₙ, for n = {1, 2, 3, ..., N}

Where the sportsman goes far away for his home for x > 0, in meters.

Now we proceed to determine the final distance:

X = + 350 m - 125 m + 80 m

X = + 305 m

The final distance of the sportsman with respect to his home is 305 meters.

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The equations that will make a linear function are

A linear equation, also referred to as a linear function in mathematics, is used to identify relationships between variables that can be plotted on a straight line.

This class of polynomial functions have a degree of 1, indicating that the highest power of the variable within the formula cannot exceed 1.

It takes on the standardized form:

y = mx + b

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