Perform the indicated operation. Reduce to lowest terms if possible. 4 1/5 ÷ 2 1/3

[tex] \angle3 \: and \: \angle4 [/tex] are complementary.

What is Complementary angle?

If sum of two angles is 90° then we can say that those angles are complementary.

For example, if [tex] \angle \: a + \angle \: b = {90}^{o} [/tex] then angle a and angle b are complementary.

Here are some examples of complementary angles:

Here given,

[tex] \angle1 \: and \angle2[/tex] are complimentary.

So,

[tex] \angle1 + \angle2 = {90}^{o} [/tex]

It is clear that [tex] \angle1, \angle2, \angle3, \angle4[/tex] are making a straight angle.

So, we can write,

[tex] \angle1 + \angle2 + \angle3 + \angle4 = {180}^{o} \\ {90}^{o} + \angle3 + \angle4 = {180}^{o} \\ \angle3 + \angle4 = {180}^{o} - {90}^{o} \\ \angle3 + \angle4 = {90}^{o} [/tex]

Here sum of angle 3 and angle 4 is 90°.

According to definition angle 3 and angle 4 are complimentary angles.

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Rachel cycled each lap around the lake that was 2.8 miles long.

What is unit rate?

A unit rate is a ratio in which the denominator is 1. It is a rate that compares a quantity to one unit of another quantity.

First, we need to convert the total distance cycled from feet to miles since the length of each lap is likely to be expressed in miles.

1 mile = 5280 feet

Therefore,

59,136 ft ÷ 5280 ft/mile = 11.2 miles

So, Rachel cycled a total of 11.2 miles around the lake.

Since she cycled 4 laps of the same distance, we can divide the total distance by 4 to get the length of each lap:

11.2 miles ÷ 4 = 2.8 miles per lap

Therefore, Rachel cycled each lap around the lake that was 2.8 miles long.

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Answer:

see below

Step-by-step explanation:

The equation y - y₁ = m(x − x₁)

1. y - 7 = -4(x - -3)

y - 7 = -4(x + 3)

y = -4x - 12 + 7

y = -4x - 5

2. y - y₁ = m(x − x₁)

9 - -3 = m(8 - 4)

12 = 4m

m = 12/4 = 3

y = mx + b

-3 = 3(4) + b

b = - 3 - 12

b = -15

y = 3x - 15

Answer: 6.3 per bag

Step-by-step explanation:

31.50 divided by 5 is 6.3!!!!

Answer: 6.3

Step-by-step explanation:

Divide 31.50 with 5

[tex]5\sqrt{31.50}[/tex]

5 goes into 3 0 times so you do 31/5. You get 6 with 1 as the remainder since 6x5 is 30. Now you do 15/5 which is 3. You get 63 but you have to add the decimal between the 6 and 3 so you will get 6.3. Hope this helped.

Answer:

we need to add the money Andy earned to the negative balance he had. So, we have:

-$45 + $30 + $25 = $10

Therefore, Andy now has $10 in his checking account.

Answer:

Andy now has $10 in his checking account.

Step-by-step explanation:

Andy starts the week with -$45 in his checking account. When he gets paid $30 for mowing the grass and $25 for vacuuming the house, his total earnings for the week are:

$30 + $25 = $55

To find out how much money he now has in his checking account, we need to add his earnings to his starting balance of -$45. Adding a negative number is the same as subtracting a positive number, so we can write this as:

-$45 + $55 = $10

Therefore, Andy now has $10 in his checking account.

Answer: Algebra Examples

Logarithm base 4 of 4 is 1.

Step-by-step explanation:

unity

The value of log 4 to the base 4 is equal to unity. The Antilogarithm of the logarithmic value of 4 is equal to 4.

Answers:

There are 2 answers:

1. 6,5

2. 5,6

Step-by-step explanation:

The SUM of two numbers IS 11:

x + y = 11

The PRODUCT of two numbers IS 30:

xy = 30

The system we get is

x + y = 11

xy = 30

Now solve the system:

There are 2 possible solutions:

(6,5) and (5,6)

A) The FPCF for this sample is 0.899. B) The sample size is about 12% of the population size, which is relatively large.

A) The FPCF (Finite Population Correction Factor) is used to adjust for the impact of a finite population on the sampling distribution. The formula for the FPCF is:

FPCF = [tex]\sqrt{((N-n)/(N-1))}[/tex]

where N: size of the population and n: size of the sample.

In this case, the population size is N = 199, and the sample size is n = 24. Therefore, the FPCF can be calculated as follows:

FPCF = [tex]\sqrt{((199-24)/(199-1))}[/tex] = 0.899

So, the FPCF for this sample is 0.899.

B) In general, a population can be considered effectively infinite when the sample size is no more than 5-10% of the population size. In this case, the sample size is n = 24, and the population size is N = 199. Therefore, the sample size is about 12% of the population size, which is relatively large.

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Answer:

[tex]f(x)=-3x^2+5[/tex]

[tex]f(2) = -7[/tex]

Step-by-step explanation:

Given equation:

[tex]y+3x^2=5[/tex]

To solve the equation for y in terms of x, simply subtract 3x² from both sides of the equation:

[tex]\implies y+3x^2-3x^2=5-3x^2[/tex]

[tex]\implies y=-3x^2+5[/tex]

Replace y with the function notation f(x):

[tex]f(x)=-3x^2+5[/tex]

Finally, to find the value of f(2), substitute x = 2 into the function:

[tex]\begin{aligned}\implies f(2)&=-3(2)^2+5\\&=-3(4)+5\\&=-12+5\\&=-7\end{aligned}[/tex]

Answer:

Step-by-step explanation:

To find:-

Answer:-

We are here a given a equation, with some steps to follow, in order to find out the value of [tex]f(2)[/tex].

Step 1 :- Solve the equation in terms of y ,

The given equation to us is,

[tex]\longrightarrow y + 3x^2 = 5\\[/tex]

To solve for y , we need to transpose 3x² from LHS to RHS , by doing this , the sign changes from positive to neagative .

[tex]\longrightarrow y = 5 - 3x^2 \\[/tex]

Step 2 :- Replace y with function notation [tex]f(x)[/tex]

Just simply replace y here with f(x) as ,

[tex]\longrightarrow f(x) = 5 - 3x^2\\[/tex]

Step 3 :- Find f(2) .

To calculate the value of f(2) , we need to put x = 2 , in the above equation as ,

[tex]\longrightarrow f(2) = 5 - 3(2)^2\\[/tex]

Simplify,

[tex]\longrightarrow f(2) = 5 - 3(4)\\[/tex]

[tex]\longrightarrow f(2) = 5 - 12\\[/tex]

[tex]\longrightarrow \boxed{ \boldsymbol{f(2) = -7 }} \\[/tex]

Hence the required answer is -7 .

Answer:

4)  ∠1 and ∠2,  ∠2 and ∠3

5)  ∠1 and ∠3

6)  x = 10

Step-by-step explanation:

Adjacent angles are two angles that share a common vertex and a common side, but do not overlap.

Therefore, the pairs of adjacent angles in the given diagram are:

Vertical angles are pairs of non-adjacent angles that are formed when two lines intersect.  Vertical angles are congruent,

Therefore, the pair of vertical angles in the given diagram are:

As ∠1 and ∠3 are the same measure:

⇒ m∠1 = m∠3

⇒ (9x)° = 90°

⇒ 9x = 90

⇒ 9x ÷ 9 = 90 ÷ 9

⇒ x = 10

Therefore, the value of x is 10.

Answer:

4)  ∠1 and ∠2,  ∠2 and ∠3.

5)  ∠1 and ∠3.

6)  x = 10.

Step-by-step explanation:

Explanations are given in attachment!

The correct three options are:

Nathan rolled a number cube and recorded the results in a table.

The number cube has six sides, numbered 1 through 6.

The number 4 was rolled more frequently than any other number.

Nathan rolled a number cube and recorded the results in a table.

The number cube has six sides, numbered 1 through 6.

Nathan rolled the number cube a total of 90 times.

The number 4 was rolled more frequently than any other number.

The number 2 was rolled the least frequently of all the numbers.

The total number of rolls for odd numbers is greater than the total number of rolls for even numbers.

The correct statements are:

Nathan rolled a number cube and recorded the results in a table.

The number cube has six sides, numbered 1 through 6.

The number 4 was rolled more frequently than any other number.

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Step-by-step explanation:

[tex]\triangle ADB[/tex] is equilateral, so [tex]m\angle DBA=60^{\circ}[/tex].

Using linear pairs, [tex]m\angle DBC=120^{\circ}[/tex].

Answer: J (120)

Step-by-step explanation: Since triangle ABD is given to be an equalatiral triangle, we know that every interior angle is 60 degrees. Since line ABC is a straight line we know that if we subtract the lines angle (180) by the interior angle it goes through (60) we get the measure of angle DBC: 120 degrees

Answer: (6,-5)

Step-by-step explanation:

Answer:

The answer is 6x + 2

Step-by-step explanation

I did all the work and I passed on this test so i know this is the answer.

if triangle ABC is translated 5 units down, the image's coordinates are A′(1, 7), B′(9, 7), and C′(5, 3).

The x and y coordinates of each of a triangle's vertices must be added to or subtracted from to translate the triangle on a coordinate plane.

Triangle ABC must be translated five units lower in this situation. Thus, we must deduct 5 from the y coordinates of each of its vertices.

A(1, -2) changes to A' (1, -7) B(9, -2) changes to B' (9, -7) C(5, 2) changes to C' (5, -3)

As a result, if triangle ABC is translated 5 units down, the image's coordinates are A′(1, 7), B′(9, 7), and C′(5, 3).

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Rectangle, semi circle, semi circle

Perimeter: 60.8

Area: 64.2

In mathematics, the two key characteristics of two-dimensional forms are area and perimeter. The difference between area and perimeter is how much room each type of shape takes up.

Mathematical concepts like area and perimeter are crucial because they are applied to daily living. Any size and form, whether regular or irregular, can use this. Each design has a unique area and perimeter calculation. Forms like triangles, squares, rectangles, circles, spheres, etc. should be known to you. Here, the boundaries and surfaces of all forms are explained.

perimeter= 60.8

each of the three shapes' perimeters separately, then sum them all up to get 60.8.

area= 64.2

Calculate the area of each of the three shapes separately, then sum them all up to get 64.2.

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The complete question attached below,

The required size and perimeter of the Area are respectively 27.42 and 64.26 square units.

A shape's perimeter is its circumference. How are perimeters determined? By adding the lengths of each side of a shape, the border may be obtained.

A shape comprised of two circles and a rectangle has been provided.

the size of a circle = 12 - 6 = 6

then radius = 3 units

Perimeter = 3+3+3+3+3+3+π(3)

= 18 + 3.14(3)

= 18 + 9.42

= 27.42 units

and

Area = area of rectangle + area of two half circles

= 12(3) + π(3)²

= 36 + 28.26

= 64.26 sq units.

Therefore, the shape's needed area and perimeter are respectively 27.42 and 64.26 square units.

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Answer:

0.5625

Step-by-step explanation:

The option that Describe the transformation of LM to L'M'. is: LM is translated 5 units left and 2 units down to L'M'. Answer: option A.

To determine the transformation from LM to L'M', we need to identify how much LM has been translated horizontally and vertically. From the graph, we can see that L has been moved 5 units to the left to reach L', and M has been moved 2 units down to reach M'.

Looking at the graph, we can see that L is moving leftward and downward, while M is moving leftward. This indicates a translation.

Furthermore, the distance that L and M move is 5 units horizontally and 2 units vertically. This means that LM is translated 5 units left and 2 units down to L'M'.

Therefore, the correct answer is OA. LM is translated 5 units left and 2 units down to L'M'.

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Answer:

Step-by-step explanation:

Just divide the total shape into three shapes one rectangle and two triangles and then calculate the area

Hope this helps: )

Answer:

in the image

Step-by-step explanation:

using the arithmetic formula

a = ao + d(n-1)

we can find the sum of this formula added up 5 times

The equations that can be used to solve for y in the given situation are:
(A) y(y + 5) = 750

(B) y² – 5y = 750

(D) y(y – 5) + 750 = 0

An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°).

A rectangle has equal and parallel opposite sides.

A rectangle has two dimensions—length and width—because it is a two-dimensional form.

The rectangle's longer side is its length, while its shorter side is its breadth.

So, the area formula of the rectangle:

750 = l * w

750 = x * (x-5)

750 = x² - 5x

x² - 5x - 750 = 0

Equations in the options that are similar:

(A) y(y + 5) = 750

(B) y² – 5y = 750

(D) y(y – 5) + 750 = 0

Therefore, the equations that can be used to solve for y in the given situation are:
(A) y(y + 5) = 750

(B) y² – 5y = 750

(D) y(y – 5) + 750 = 0

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Correct question:

The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options.

NEED ASAP

Answer choices:

a. y(y + 5) = 750

b. y2 – 5y = 750

c. 750 – y(y – 5) = 0

d. y(y – 5) + 750 = 0

e. (y + 25)(y – 30) = 0

Answer:

C

Step-by-step explanation:

We Can see from the < pointing to the higher side.

Answer:

40 -12-3 15 multiply all of them and u get your answer

Answer:

Step-by-step explanation:

You would need to deposit approximately $8,267.40 initially to reach your goal of $7,500 in three years, assuming an annual interest rate of 3%.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

If you have three years to save for a dream vacation and want to save $7,500, there are two main approaches you can take: making regular monthly payments or depositing one single lump sum into a savings account.

Option 1: Regular Monthly Payments

If you decide to make regular monthly payments towards your vacation savings, you will need to calculate how much you need to save each month to reach your $7,500 goal. To do this, you need to divide the total amount you want to save by the number of months you have to save.

In this case, you have 36 months (3 years x 12 months/year) to save $7,500, so:

$7,500 ÷ 36 = $208.33 per month

So, you would need to save approximately $208.33 per month for 36 months to reach your goal of $7,500.

Option 2: Single Lump Sum Deposit

If you decide to deposit one single lump sum into a savings account, you will need to calculate how much you need to deposit initially to reach your $7,500 goal in three years, assuming a certain rate of interest.

The amount you need to deposit will depend on the interest rate you can earn on your savings. For example, if you can earn an annual interest rate of 3%, the calculation would be:

Initial deposit = Future value of $7,500 at 3% interest over 3 years

Using a financial calculator or spreadsheet, you can determine that the future value of $7,500 at 3% interest over 3 years is approximately $8,267.40.

Therefore, You would need to deposit approximately $8,267.40 initially to reach your goal of $7,500 in three years, assuming an annual interest rate of 3%.

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The difference between  two vectors [tex](u - v )[/tex] = [tex](7,7)[/tex].

An entity with both magnitude and direction is referred to as a vector. A vector can be visualized geometrically as a directed line piece, with an arrow pointing in the direction and a length equal to the magnitude of the vector. The vector points in a direction from its tail to its head.

Therefore subtracting [tex]u-v[/tex] we get

[tex]u-v = (2,5)-(-5,-2\\ = (2+5,5+2)\\=(7,7)[/tex]

The distinction between u and v can be graphically represented in two ways:

The next step is to create the vector [tex]u-v[/tex], which begins at the same location as [tex]u[/tex] and ends at [tex]v[/tex].

In an algebraic sense, the vectors u and v can be represented as points in a coordinate plane, and the vector u - v as a line connecting these places.

The following figure shows the construction with negative velocities

In this case, the vectors u and v are represented by location A and point B, respectively.

Therefore the difference between  two vectors [tex](u - v )[/tex] = [tex](7,7)[/tex].

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Answer:

13

Step-by-step explanation:

Student: 80 * 55% = 44

Adult: 50 * 98% = 49

49-44=5

The calculated key features of the quadratic functions 1 to 6 are listed below

Function 1: y = 1/2(x + 4)(x - 2)

Expand

y = x^2/2 + x - 4

From the function, we have

a = 1/2 (coefficient of x^2 term)

p = -b/2a (x-coordinate of the vertex)

p = -(1)/2(1/2)

p = -1

q = f(p) (y-coordinate of the vertex)

q = 1/2(1 + 4)(1 - 2)

q = -5/2

From the function, we have

x-intercepts = (-4, 0) and (2, 0)

This also means that the axis of symmetry is

x = -1

The quadratic function opens up because the coefficient of the x^2 term is positive.

Next, we have

Vertex = (-1, -5/2)

For the y-intercept, we have

y-intercept = f(0)

y-intercept = 1/2(0 + 4)(0 - 2)

y-intercept = -4

Slope to a point one unit from the vertex can be found by taking the derivative of the function:

f(x) = x^2/2 + x - 4

f'(x) = x + 1

At x = -2 (one unit to the left of the vertex), the slope is -1

i.e. f'(-2) = -2 + 1 = -1

At x = 0 (one unit to the right of the vertex), the slope is 1.

i.e. f'(0) = 0 + 1 = 1

When the above steps is repeated for the remaining functions, we have the following results:

Function 2: y = 1/2x(x - 8)

The features are:

Function 3: y = (x + 2)(x - 2)

The features are:

Function 4: y = -1/3(x + 1)(x - 5)

The features are:

Function 5: y = 4(x + 2)(x + 1)

The features are:

Function 6: y = -(x - 3)(x - 3)

The features are:

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According to the information, he quadratic function's equation is f(x) = (47/13)x^2 + (89/13)x + 198/13 in standard form.

To find the quadratic function's equation, we need to use the given points from the table and solve for the coefficients a, b, and c in the standard form of a quadratic function, f(x) = ax^2 + bx + c.

Using the point (-7, 209):

209 = a(-7)^2 + b(-7) + c

Using the point (-5, 113):

113 = a(-5)^2 + b(-5) + c

Using the point (-2, 29):

29 = a(-2)^2 + b(-2) + c

Now we have three equations with three variables. We can solve for a, b, and c using a system of linear equations. First, simplify each equation:

49a - 7b + c = 209

25a - 5b + c = 113

4a - 2b + c = 29

Then, we can solve for b in terms of a and substitute in the other equations to eliminate b:

b = 7a + c/7 - 29/7

Substituting into the second equation:

25a - 5(7a + c/7 - 29/7) + c = 113

Simplifying:

10a + c = 80

Substituting into the third equation:

4a - 2(7a + c/7 - 29/7) + c = 29

Simplifying:

-3a + c = 33

Now we have two equations with two variables. We can solve for c in terms of a and substitute back into one of the previous equations to solve for a:

c = 3a + 33

Substituting into the second equation:

10a + (3a + 33) = 80

Simplifying:

13a = 47

a = 47/13

Now we can substitute a back into one of the previous equations to solve for c:

c = 3(47/13) + 33 = 198/13

Finally, we can substitute a and c into the standard form of a quadratic function:

f(x) = (47/13)x^2 + (7(47/13) - 198/13)x + 198/13

Simplifying:

f(x) = (47/13)x^2 + (89/13)x + 198/13

Therefore, the quadratic function's equation is f(x) = (47/13)x^2 + (89/13)x + 198/13 in standard form.

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