Which of the following expressions is equivalent to 32 ÷ 4• 4 ÷ 2 • 2?​

After 4.5 seconds, the baseball will have dropped approximately 99.35 meters.

To find out how far the baseball will have dropped after 4.5 seconds, we need to use the free fall formula.

The terms involved in this calculation are:
Time (t): 4.5 seconds.

Acceleration due to gravity (g): 9.81 m/s² (approximated)
Distance dropped (d)
The free fall formula is:
\(d = (1/2) \times g \times t^{2}\)
Now, we will plug in the given values and solve for d:
Substitute the values
\(d = (1/2) \times 9.81 \times  (4.5)^{2}\)
Calculate the square of time
\(d = (1/2) \times 9.81 \times 20.25\)
Multiply the values
d = 99.3525.

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Answer:

P = 1600 + 60N; $3,340

Step-by-step explanation:

Since we know she gets $1,600 as a base, and $60 each book, we have to add a variable to 60 to show how many books she sells. Your first equation will be P (which is the total) = 1,600 + 60N. Now, we have to replace N with 29. You now have P = 1,600 + 60(29) = 1,600 + 1,740 = $3,340. That's your answer!

Answer:

$3340

Step-by-step explanation:

P = $1600 (Lira's base salary) + $60 * N

P = $1600 + $60 * 29

P = $1600 + $ 1740

Therefore, P = $3340.

The equation associated with the quotient of twenty and a number, decreased by 4, is equal to zero is 20/x - 4 = 0 and that number will be 5.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Let's say that number is x,

Quotients of 20 and x will be given as 20/x

20/x - 4 = 0

20/x = 4

x = 20/4 = 5

Hence"The equation associated with the quotient of twenty and a number, decreased by 4, is equal to zero is 20/x - 4 = 0 and that number will be 5".

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Answer:

\(\frac{-4}{3}\)

Step-by-step explanation:

a rational number is expressed as

\(\frac{a}{b}\) where a and b are integers , then

- 1 \(\frac{1}{3}\) = \(\frac{-4}{3}\)

Answer:

The answer is true!

Step-by-step explanation:

Since B is in the middle and they both are congruent.

Given

The equation,

To solve for b.

Explanation:

It is given that,

That implies,

Hence, the answer is 3/2, -6.

The factor of the expression 9t – 3u will be 3 and 3t – u.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

One of the many branches of mathematics is algebra. Algebra, which is a common thread throughout practically all of mathematics, is broadly defined as the study of numbers and symbols and the procedures for using these symbols in formulae.

The expression is given below.

⇒ 9t – 3u

Simplify the expression, then we have

⇒ 3·3t – 3u

⇒ 3(3t – u)

The factor of the expression 9t – 3u will be 3 and 3t – u.

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Answer:

Hypotenuse is the longest side in a triangle.

a^2=b^2+c^2.

5^2=4^2+c^2.

c^2=25-16.

c^2=9.

c=√9.

c=3cm.

Answer:

(a) To find the mean of the data set, sum up all the values and divide by the total number of values.

44 + 44 + 54 + 54 + 65 + 39 + 54 + 44 = 398

Mean = 398 / 8 = 49.75

Rounded to one decimal place, the mean of this data set is 49.8.

(b) To find the median of the data set, i need to arrange the values in ascending order first:

39, 44, 44, 44, 54, 54, 54, 65

The median is the middle value in the sorted data set. In this case, we have 8 values, so the median is the average of the two middle values:

(44 + 54) / 2 = 98 / 2 = 49

Rounded to one decimal place, the median of this data set is 49.0.

(c) To determine the modes of the data set, identify the values that appear most frequently.

In this case, the mode refers to the value(s) that occur(s) with the highest frequency.

From the data set, i see that the value 44 appears three times, while the value 54 also appears three times. Therefore, there are two modes: 44 and 54.

Answer:

The other 3 numbers you are looking for are:

24/11

84/11

96/11

Step-by-step explanation:

We can start off by making the numbers 2x, 7x, and 8x. We put them in expressions:

(7x-12)^2=2x(8x)

Simplify

49x^2-168x+144=16x^2

Subtract 16x^2 on each side

33x^2-168x+144=0

Divide by 3

11x^2-56x+48=0

Factor

(11x-12)(x=4)=0

Answer

x=4 or x=12/11

If x is equivalent to 4 then that means that the original numbers would be:

8, 28, 32

2(4), 7(4), 8(4)

Subtracting 12 from Y, or 28 will make it 16.

8, 16, 32

This seems to be a geometric progression

Next we have 12/11

2(12/11), 7(12/11), 8(12/11)

24/11, 84/11, 96/11

Subtracting 12 from Y, or 84/11 will get us  -48/11, meaning r=-2 for the GP.

Final Answer:

8 , 28 , 32

24/11 , 84/11 , 96/11

Answer:

45

Step-by-step explanation:

Think of JGC as your triangle.

J = 45 (same as K)

G = 90 (right angle)

So...

180 - 90 = 90

90 - 45 = 45

C = 45

Answer:

(-1, 1)

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define systems

3 + 2x - y = 0

-3 - 7y = 10x

Step 2: Rewrite systems

3 + 2x - y = 0

Step 3: Redefine systems

y = 2x + 3

-3 - 7y = 10x

Step 4: Solve for x

Substitution

Step 5: Solve for y

Step 6: Graph

Check the solution set.

Using the power rule, the derivatives are given as follows:

a) \(f^{\prime}(2) = -\frac{1}{4}\).

b) \(f^{\prime}(3) = 30\).

Suppose we have a power function given by:

\(f(x) = x^n\)

The derivative of the function is given by:

\(f^{\prime}(x) = n \times x^{n-1}\)

Item a:

The function is:

\(f(x) = \frac{1}{x} = x^{-1}\)

Then the derivative is:

\(f^{\prime}(x) = -x^{-2} = -\frac{1}{x^2}\)

When x = 2, the derivative is:

\(f^{\prime}(2) = -\frac{1}{4}\)

Item b:

The function is:

\(f(x) = 5x^2\)

Then the derivative is:

\(f^{\prime}(x) = 10x\)

When x = 3, the derivative is:

\(f^{\prime}(3) = 30\)

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Step-by-step explanation:

A is your answer.

You just have to solve for each function individually and see what the roots are.

9514 1404 393Answer:

  (a)  f(x) = 2x² -2

Step-by-step explanation:

The function has two zeros, at -1 and 1, so is not a linear or square root function. The only viable choice is the correct one:

  f(x) = 2x² -2

The description of the area of a square is (c) as the length of the side increases, the area increases.

The table of values is given as:

Side Length (cm)        Area (cm²)

1                                       1

2                                      4

3                                      9

4                                      16

5                                    25

In the above table, we can see that:

As length increases, the area also increases

Hence, the description of the area is (c) as the length of the side increases, the area increases.

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Answer:

The circumference of a circle is divided by the diameter of that circle. PI

Step-by-step explanation:

Hope this helps you!!!! :D

The expression which is used to represents the statement "one-more than the quotient of a number x" and 4 is "x/4 + 1".

A "Quotient" is the result of a division operation between two numbers, where one number is divided by another. It represents the number of times one number is contained within another number.

An "Expression" is defined as "mathematical-phrase" which contain numbers, variables, and operators such as addition, subtraction, multiplication, and division. It can also contain functions and other mathematical symbols.

The quotient of a number"x" and 4 can be written as x/4.

So, one more than the quotient of a number x and 4 can be represented by the expression:

⇒ x/4 + 1,

Therefore, required mathematical expression is "x/4 + 1".

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The given question is incomplete, the complete question is

Write an expression to represent : One more than the quotient of a number x and 4.

Answer:

x=9

Step-by-step explanation:

17x - 12 = 114 + 3x

First  Subtract 3x from both sides

14x - 12 = 114

Add 12 to both sides

14x=126

Divide by GCF (14)

x=9

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Answer:

17x - 12 = 114 + 3x

-3x +12 +12 -3x

Step-by-step explanation:

14x = 126

14/14 = 126/14 = 9

x = 9

In a case where a = 11 ft, b = 5 ft, and c = 7 ft, the surface area of the geometric shape formed by this net is B. 145 sq. ft.

The concept that will be used here is area of triangle, we will we need need to know the area of the first 2 triangles

The area of the triangle can be expressed as :

A =( 1/2 bh)

A = (1/2 ba)

Then substitute the values we have,

a = [1/2 (11 ft.) (5 ft)]

a =  27.5 sq ft.

Then we can find the value of the area as :

A = [1/2 c*b]

If we substitue the values we,

a = [1/2 (5 ft) (7 ft)]

= 17.5 sq. ft

Then we can proceed to calculate the area of the rectangle which can be done using the formula:

A = (lw) where a = (11 ft.)(5 ft.) = 55 sq. ft

We can now find the summation of all the a's as :

[2(27.5) + 2(17.5 ) + 55 ]

= 145 sq. ft.

Therefore, option B is correct.

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missing options:

A. 167 sq. ft.

B. 145 sq. ft.

C. 117.5 sq. ft.

D. 147 sq. ft.

The solution of the equation 8b = 56 is 7. And the solution of Harmony is 448. So, Harmony is incorrect.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The equation is given below.

8b = 56

Simplify the equation, then we have

8b = 56

b = 56 / 8

b = 7

The solution of the equation 8b = 56 is 7. And the solution of Harmony is 448. So, Harmony is incorrect.

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On solving the provided question we can say that by herons formula, area of the triangle is, A = 2.828

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

the provided points are Triangle X(1, 6), Y(5, -2), Z(-5, -1)

by herons formula

A = \(\sqrt{s(s-a)(s-b)(s-c)}\)

s = a+b+c/3

s = 5+2+5+/3 =12/3 = 4

Area of the triangle is, A =

\(\sqrt{4(5-4)(4-2)(5-4)} \\A = \sqrt{4*1*2*1} \\A = \sqrt{8} \\A = 2\sqrt{2}\\ A = 2*1.414\\A = 2.828\)

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Answer:

2.828

Step-by-step explanation:

Answer:

0.88 is the correct answer

Answer:

4

Step-by-step explanation:

Answer:

3.36 cm

Step-by-step explanation:

24 - 5 1/2 = 18.5

To find the distance on the map, we can set up a proportion:

1 cm / 5.5 miles = x cm / 18.5 miles

5.5 times 37/11 equals to 18.5; 1 times 37/11 is approximately equals to 3.36 cm (rounded to the nearest hundredths).

The volume of the solid obtained by rotating the region bounded by the curve y = 1 - (x - 5)² in the first quadrant about the y-axis is 51π cubic units.

To find the volume of the solid obtained by rotating the region bounded by the curve y = 1 - (x - 5)² in the first quadrant about the y-axis, we can use the method of cylindrical shells.

The formula for the volume using cylindrical shells is:

V = 2π ∫ [a, b] x * h(x) dx

Where:

- V is the volume of the solid

- π represents the mathematical constant pi

- [a, b] is the interval over which we are integrating

- x is the variable representing the x-axis

- h(x) is the height of the cylindrical shell at a given x-value

In this case, we need to solve for x in terms of y to express the equation in terms of y.

Rearranging the given equation:

x = 5 ± √(1 - y)

Since we are only interested in the region in the first quadrant, we take the positive square root:

x = 5 + √(1 - y)

Now we can rewrite the volume formula with respect to y:

V = 2π ∫ [c, d] x * h(y) dy

Where:

- [c, d] is the interval of y-values that correspond to the region in the first quadrant

To determine the interval [c, d], we set the equation equal to zero and solve for y:

1 - (x - 5)² = 0

Expanding and rearranging the equation:

(x - 5)² = 1

x - 5 = ±√1

x = 5 ± 1

Since we are only interested in the region in the first quadrant, we take the value x = 6:

x = 6

Now we can evaluate the integral to find the volume:

V = 2π ∫ [0, 1] x * h(y) dy

Where h(y) represents the height of the cylindrical shell at a given y-value.

Integrating the expression:

V = 2π ∫ [0, 1] (5 + √(1 - y)) * h(y) dy

To find h(y), we need to determine the distance between the y-axis and the curve at a given y-value. Since the curve is symmetric, h(y) is simply the x-coordinate at that point:

h(y) = 5 + √(1 - y)

Substituting this expression back into the integral:

V = 2π ∫ [0, 1] (5 + √(1 - y)) * (5 + √(1 - y)) dy

Now, we can evaluate this integral to find the volume

V = 2π ∫ [0, 1] (5 + √(1 - y)) * (5 + √(1 - y)) dy

To simplify the integral, let's expand the expression:

V = 2π ∫ [0, 1] (25 + 10√(1 - y) + 1 - y) dy

V = 2π ∫ [0, 1] (26 + 10√(1 - y) - y) dy

Now, let's integrate term by term:

\(V = 2\pi [26y + 10/3 * (1 - y)^\frac{3}{2} - 1/2 * y^2]\)] evaluated from 0 to 1

V = \(2\pi [(26 + 10/3 * (1 - 1)^\frac{3}{2} - 1/2 * 1^2) - (26 * 0 + 10/3 * (1 - 0)^\frac{3}{2} - 1/2 * 0^2)]\)

V = 2π [(26 + 0 - 1/2) - (0 + 10/3 - 0)]

V = 2π (25.5)

V = 51π cubic units

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Answer:

\(\sqrt{5}\)

Step-by-step explanation:

\(a^{2} + b^{2} = c^{2}\)

In this situation a = 1, b = 2

\(1^{2} + 2^{2} = c^{2}\)

1 + 4 = \(c^{2}\)

5 = \(c^{2}\)

c = \(\sqrt{5}\)

This is an important mathematical theorem to know. It's called the Pythagorean Theorem.

Answer:

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Answer:

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