The formula v = square root of 64h gives the velocity v in feet per second of an object that has fallen h feet. find the velocity of an object that has fallen 84 feet. round to the nearest hundredth.

Answer:

B) 131°

Step-by-step explanation:

-4a + 139 = 4a + 123 because they are vertical angles

-4a + 139 = 4a + 123

reduce:

8a = 16

a = 2

4(2) + 123 = 131°

Answer: 90

Step-by-step explanation:

91 - 1  = 90

Answer: 90

Step-by-step explanation:

The probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring, this statement is false.

The union of two or more sets refers to the set with all the elements belonging to each set. An element is said to be in the union if it lies to at least one of the sets.

The intersection of two or more sets refers to the set of elements universal to each set. An element is in the intersection if it occurs in all of the sets.

The event that both A and B occur is the intersection of the events A occurs and B occurs. As such, it is a subset of each and cannot, therefore, have a larger probability than either one individually.

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Answer: its E and B

Step-by-step explanation:

2/100 is .02 which is 2%

Answer:

2%= 2/100= 0.02

so correct answer is b and e

Answer:

1)a

2)c

3)b

4)a

Step-by-step explanation:

No further explanations needed

Answer:

Your answers are correct.

Step-by-step explanation:

The "<" sign means less than and the ">" sign means greater than. It is clear that you have a handle on them.

1.) If Steve has no more that 28 toys, then the less than sign would represent the fact that Steve can have a maximum of 28 toys, and no more.

2.) If the temperature is more that 28 degrees Fahrenheit, then the greater than sign is appropriate in order to imply that the variable represents a higher temperature.

3.) If tony is younger than 29 years old, then the less than sign fits to show that the variable represents an age that is smaller than 29.

4.) If the table is greater than 29 kilograms, then the greater than sign is needed. It shows that the table has a greater weight than 29 kilograms.

Hope this helps! :D

We have the following:

We have that the size of the side is related to the opposite angle, that is, the larger the side, the greater the angle is the same in the opposite direction, which means that both angles are equal, the sides are also equal, for Therefore we can calculate as follows:

now, for x:

Therefore, the answer is y = 4 and x = 7

A cross-sectional effect diagram, also known as an axial force-shear force-bending moment diagram or simply an internal force diagram, is a graphical representation that shows the distribution of internal forces (axial force, shear force, and bending moment) along the length of a structural member, such as a beam or column.

To draw the cross-sectional effect diagrams for the beam whose loading condition is given in the figure, we need to follow these steps:

Step 1: Identify the type of loadingFor this question, the loading conditions are {N}, {T}, {M}. So, the loading types are axial force, shear force, and bending moment.

Step 2: Draw the cross-sectional diagram of the beam. We need to draw the diagram of the cross-section of the beam in the direction of the forces acting on the beam. In this case, it will be a rectangular beam.

Step 3: Draw the effect diagrams After drawing the cross-sectional diagram, we need to draw the effect diagrams for each loading condition.

The effect diagrams are as follows: 1. Axial force diagram (N):In this case, the axial force is positive (+) which means it is a tensile force. 2. Shear force diagram (T):The shear force is negative (-) from x = 0 to x = 1, which means the shear force is acting downward. It is zero at x = 1 and then becomes positive (+) from x = 1 to x = 2, which means the shear force is acting upward. 3. Bending moment diagram (M):The bending moment is zero at x = 0, becomes negative (-) from x = 0 to x = 1, reaches a minimum at x = 1, and then becomes positive (+) from x = 1 to x = 2.

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Answer: Both types of alternate angles and corresponding angles are only congruent when formed by a transversal intersecting parallel lines.

Answer:

6.4

Step-by-step explanation:

Answer:

1.9

Step-by-step explanation:

7.6/4= 1.9

1.9*1= 1.9

ans is 1.9 pints

Using division, we can find that the best statement that describes the given expression is:

Add 8 to half the difference of 6 and 2, then subtract 1.

One of the fundamental mathematical operations is division, which entails breaking a bigger number into smaller groups with the same number of components. How many groups will be created, for instance, if 30 pupils are required to be split into groups of five for a sporting event? The division operation can quickly and easily fix such issues. In this case, we must divide 30 by 5. 30 x 5 = 6 will be the outcome. There will be a total of 6 groups, each with 5 pupils. Use the beginning number, 30, which is obtained by multiplying 6 by 5, to check this response.

8 + fraction 1 over 2 x (6 − 2) − 1.

The above is expressed mathematically as:

8 + 1/2(6 - 2) - 1

Therefore, the statement that describes this expression from the options given correctly is :

Add 8 to half the difference of 6 and 2, then subtract 1.

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We can use division to determine that the following statement best captures the meaning of the given expression:

To make up the difference between 6 and 2, add 8 and then take away 1.

Division, which involves dividing a larger number into smaller groups with the same number of components, is one of the basic mathematical operations. For instance, if 30 students must be divided into groups of five for a sporting event, how many groups will be formed. Such problems can be rapidly and readily resolved by the division operation. In this instance, we need to multiply 30 by 5. The outcome is 30 x 5 = 6.

There will be 6 groups in total, each with 5 students. To verify this response, use the starting number, 30, which is produced by dividing

6 by 5.

1 x (6 x 2) + 8 plus fraction 1 over 2 = 8.

The following can be represented mathematically:

8 + 1/2(6 - 2) - 1

Therefore, from the available possibilities, the statement that accurately represents this expression is:

To make up the difference between 6 and 2, add 8 and then take away 1.

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Given the sequence:

6, 10, 14, 18,...

We will find the 75th term

The given sequence is an arithmetic sequence

Because there is a constant common differnce

d = 18 - 14 = 14 - 10 = 10 - 6 = 4

The first term = a = 6

The general formula of the arithmetic sequence is as follows:

Where: n is the nth term

To find the 75th term, substitute with n = 75 and a = 6, d = 4

So, the answer will be the 75th term = 302

Answer:

Round to the nearest tenth. The diagram is not drawn to scale. Solution: We know that. cosθ = adjacent/hypotenuse. Substituting the values. cos22 = x/11.

Step-by-step explanation

hope this helps

The true statements are Function B has greater slope, Function A has greater y intercept and Function B has greater x intercept.

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

We have to first find the linear equations of the functions.

Given for function A,

Let x be the number of hours.

Function A can be represented as f(x) = 4/5 + 2x

Equation in slope intercept form is y = mx + c, where m is the slope and c is the intercept along Y axis.

Y intercept is the point of the line where it touches the Y axis. x coordinate will be zero here.

x intercept is the point of the line where it touches the X axis. y coordinate will be zero here.

y = 2x + (4/5), in slope intercept form.

Here 2 is the slope and 4/5 is the y intercept.

When y = 0, 2x + (4/5) = 0, then x = -2/5

x intercept = -2/5

For function B,

we have when x = 0, f(x) = y = 2/3

y intercept = 2/3

Slope = [(2/3) - (-25/3)] / [0 - -3]

          = [27/3] / 3

          = 9 / 3

          = 3

Equation in slope intercept form of function B is,

y = 3x + 2/3

When y = 0, 3x + 2/3 = 0, then x = -2/9

x intercept = -2/9

So function B has greater slope as slope is 3 for B and 2 for A.

Function A has greater y intercept as y intercept for A is 4/5 and for B is 2/3.

Function B has greater x intercept as x intercept is -2/9 for B and -2/5 for A.

Hence the correct options are function B has greater slope, Function A has greater y intercept and Function B has greater x intercept.

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Answer:

(2x-3)(2x+1)

Step-by-step explanation:

4x^2 - 4x - 3

we need two numbers that give 12 when multiplied and 4 when subtracted

the numbers are 6 and 2 because 6*2=12 and 6-4=4.

4x^2 - (6-2)x -3

4x^2 -6x +2x -3

take common

2x(2x -3)+1(2x-3)

take (2x-3) as common

(2x-3)(2x*1 + 1*1)

(2x-3)(2x+1)

The value of the 20th term in the given geometric sequence with a first term of 1,000,000 and an unknown common ratio is approximately [insert rounded answer].

In a geometric sequence, each term is obtained by multiplying the previous term by a constant value called the common ratio. Let's denote the first term as 'a' and the common ratio as 'r'. In this case, the first term 'a' is given as 1,000,000. We need to find the value of the 20th term.

The formula to calculate the nth term of a geometric sequence is given by:

nth term = a * \(r^{n-1}\)

Substituting the given values into the formula, we have:

20th term = 1,000,000 * \(r^{(20-1)}\) = 1,000,000 * \(r^{19}\)

Since the common ratio 'r' is not provided, we cannot directly calculate the value of the 20th term. If the value of 'r' were provided, we could substitute it into the formula to obtain the answer. Therefore, without knowing the value of 'r', it is not possible to determine the exact value of the 20th term in the given geometric sequence.

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The completed table with regards to terms of an expression are presented as follows;

     Condition      \({}\)              (6·x + 3) + (5·x - 4)            (-4·y - 16) - 8·y + 10 + 2·y

         Exactly 3 terms          N/A     \({}\)                              N/A

         Exactly 5 terms          N/A         \({}\)                          N/A

Includes a zero pair             No \({}\)                                   No

Uses distributive property   No                                    No

Includes a negative factor   No                                    

Has no like terms                False                                False

Condition       \(8 - \dfrac{1}{2} \cdot \left(4 \cdot x - \dfrac{1}{2} + 12\cdot x -\dfrac{1}{4} \right)\)  0.25·(8·m - 12) - 0.5·(-4·m + 2)

Exactly 3 terms       No                         \({}\)                    No

Exactly 5 terms       Yes                          \({}\)   \({}\)              No

Includes a zero pair No    \({}\)                         \({}\)              Yes

Uses the distributive property Yes            \({}\)             Yes

Includes a negative factor      Yes           \({}\)                Yes

Has no like terms                    No          \({}\)                  No

A mathematical expression is a collection of variables and numbers along with mathematical operators which are all properly arranged.

The details of the conditions in the question are as follows;

Terms of an expression

A term is a subunit of an algebraic expression which are joined together by operators such as addition or subtraction

Zero pair

A zero pair are two numbers that when added together have a zero result

Distributive property

The distributive property of multiplication states that the multiplication of a number or variable by an addend is equivalent to the sum of the multiplication of the number or variable and each member of the addend

Negative factor

A negative factor is a factor that has a negative sign prefix

Like terms

Like terms are terms consisting of identical variables with the same  powers of the variable

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Answer:

-1

Step-by-step explanation:

Answer:

D. it passes through the point (-12)

The terms of the polynomial, which has a degree of 2, are ordered as follows in decreasing order: 17x² + 27x

Sums of terms of the form  k⋅xⁿ where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5.

Given polynomial: 5x + 17x² + 22x

We need to simplify this polynomial first.

5x + 17x² + 22x = 27x + 17x²

Now we will put the term with highest degree first and arrange the terms of this polynomial.

17x² + 27x

Since, the highest power of terms in this polynomial is 2.

We can say that the degree of polynomial is 2.

Therefore, the polynomial has a degree of 2 and its terms are arranged in decreasing order as follows: 17x² + 27x.

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Answer:

(109x²+140xy+18xz+49y²+160yz+73z²) centimeters

Step-by-step explanation:

perimeter = sum of all sides

side A = (10x+7y)(10x+7y)

= 100x² +70xy +70xy +49y²

= (100x² +140xy +49y²) centimeters

side B = (3x+3z)(3x+3z)

= 9x² +9xz +9xz +9z²

= (9x² +18xz +9z²) centimeters

side C = (8z+10y)(8z+10y)

= 64z² +80yz +80yz +100y²

= (64z² +160yz +100y²) centimeters

Perimeter = 100x²+140xy+49y² + 9x²+18xz+9z² + 64z²+160yz+100y²

collect like terms

= 100x² +9x²+140xy+18xz+49y²+160yz+9z²+64z²

= (109x²+140xy+18xz+49y²+160yz+73z²) centimeters

Answer: 13x+17y+11z

Step-by-step explanation:

Best guess for the function is

\(\displaystyle f(x) = \sum_{n=1}^\infty \frac{x^n}{n^2}\)

By the ratio test, the series converges for

\(\displaystyle \lim_{n\to\infty} \left|\frac{x^{n+1}}{(n+1)^2} \cdot \frac{n^2}{x^n}\right| = |x| \lim_{n\to\infty} \frac{n^2}{(n+1)^2} = |x| < 1\)

When \(x=1\), \(f(x)\) is a convergent \(p\)-series.

When \(x=-1\), \(f(x)\) is a convergent alternating series.

So, the interval of convergence for \(f(x)\) is the closed interval \(\boxed{-1 \le x \le 1}\).

The derivative of \(f\) is the series

\(\displaystyle f'(x) = \sum_{n=1}^\infty \frac{nx^{n-1}}{n^2} = \frac1x \sum_{n=1}^\infty \frac{x^n}n\)

which also converges for \(|x|<1\) by the ratio test:

\(\displaystyle \lim_{n\to\infty} \left|\frac{x^{n+1}}{n+1} \cdot \frac n{x^n}\right| = |x| \lim_{n\to\infty} \frac{n}{n+1} = |x| < 1\)

When \(x=1\), \(f'(x)\) becomes the divergent harmonic series.

When \(x=-1\), \(f'(x)\) is a convergent alternating series.

The interval of convergence for \(f'(x)\) is then the closed-open interval \(\boxed{-1 \le x < 1}\).

Differentiating \(f\) once more gives the series

\(\displaystyle f''(x) = \sum_{n=1}^\infty \frac{n(n-1)x^{n-2}}{n^2} = \frac1{x^2} \sum_{n=1}^\infty \frac{(n-1)x^n}{n} = \frac1{x^2} \left(\sum_{n=1}^\infty x^n - \sum_{n=1}^\infty \frac{x^n}n\right)\)

The first series is geometric and converges for \(|x|<1\), endpoints not included.

The second series is \(f'(x)\), which we know converges for \(-1\le x<1\).

Putting these intervals together, we see that \(f''(x)\) converges only on the open interval \(\boxed{-1 < x < 1}\).

Answer:

2 I think let me know if I'm wrong

Step-by-step explanation:

To convert the density of gasoline from pounds per gallon to grams per cubic centimeter, we need to perform the following conversions:

1 pound = 0.4536 kilograms (to the nearest 0.1)

1 gallon = 3,785.4 cubic centimeters (to the nearest 0.1)

First, let's convert pounds to kilograms:

6 pounds * 0.4536 kilograms/pound = 2.7216 kilograms (approximately, rounded to the nearest 0.1)

Next, let's convert gallons to cubic centimeters:

1 gallon = 3,785.4 cubic centimeters

Now, we can calculate the density of gasoline in grams per cubic centimeter:

Density = (Mass in grams) / (Volume in cubic centimeters)

Density = (2.7216 kilograms * 1000 grams/kilogram) / (3,785.4 cubic centimeters)

Density ≈ 0.718 grams per cubic centimeter (approximately, rounded to the nearest 0.1)

Therefore, the density of gasoline in grams per cubic centimeter is approximately 0.72 grams per cubic centimeter.

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