If the product of two numbers is 23 and the sum of the reciprocals is 2, what is the sum of these numbers?

The exponential function that models the height of the ball after n bounds is given as follows:

b) [tex]H(n) = 650(0.72)^{(n - 1)}[/tex],  where n = 1, 2, 3, …

The general format of an exponential function is given as follows:

y = ab^x.

In which the parameters are given as follows:

Some students performed an experiment in which they dropped a rubber ball from a height of 650 centimeters, hence the parameter a is given as follows:

a = 650.

They noticed that after each bounce, it reached 72% of its previous height, hence the parameter b is given as follows:

b = 0.72.

Considering that the first bounce is the reference bounce, the equation is given as follows:

[tex]H(n) = 650(0.72)^{(n - 1)}[/tex]

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From the given graph the function obtained is [tex]g(x) = \sqrt{(x - 3)}+ 1[/tex].

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The graph g(x) given is a graph of function g(x) = √x.

The graph when drawn for g(x) = √x, starts from the origin (0,0).

In the graph it can be seen that the function is moved 3 units left and 1 units down.

For a function f(x) moving left with k units the formula is -

y = f(x + k)

For a function f(x) moving down with k units the formula is -

y = f(x) - k

Apply these formula to our basic function g(x) = √x.

So since the graph is moved  3 units left and 1 units down, the function will be -

[tex]g(x) = \sqrt{(x - 3)}+ 1[/tex].

Therefore, the function is obtained as [tex]g(x) = \sqrt{(x - 3)}+ 1[/tex].

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Answer:

222.4 cm

Step-by-step explanation:

16cm x 13.9 cm =222.4 cm

hope this helped! :D

A polynomial function with real coefficients and roots 1, 3i is f(x) = x^3 - x^2 + 9x - 9.

If a polynomial function has real coefficients, then complex roots must come in conjugate pairs. That is, if 3i is a root, then -3i must also be a root. Therefore, the polynomial with roots 1, 3i, and -3i is:

(x - 1)(x - 3i)(x + 3i)

Multiplying this out using the difference of squares, we get:

(x - 1)(x^2 - (3i)^2)

Simplifying the expression using (3i)^2 = -9, we get:

(x - 1)(x^2 + 9)

Expanding the expression using FOIL, we get:

x^3 + 9x - x^2 - 9

Simplifying this expression, we get:

f(x) = x^3 - x^2 + 9x - 9

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Answer:

a)10

Step-by-step explanation:

(xx)=(2×2)=4

2(4)=8

8+2=10

answer: a) 10

Answer: 17 dimes or 23 nickels

Step-by-step explanation:

Let's use two variables to represent the number of nickels and dimes that Daniel has. Let: n be the number of nickels, and d be the number of dimes.

We can write two equations based on the information given in the problem:

n + d = 40 (because Daniel has a total of 40 coins)
0.05n + 0.1d = 2.85 (because the total value of the coins is $2.85)
To solve for n and d, we can use the first equation to express one variable in terms of the other, and substitute that expression into the second equation:n + d = 40

n = 40 - d0.05n + 0.1d = 2.85

0.05(40 - d) + 0.1d = 2.85

2 - 0.05d + 0.1d = 2.85

0.05d = 0.85

d = 17
So Daniel has 17 dimes. We can substitute this value back into the first equation to solve for n:n + d = 40

n + 17 = 40

n = 23
So Daniel has 23 nickels.
Therefore, Daniel has 23 nickels and 17 dimes.

Step-by-step explanation:

The simplified expression is {3\tan^2\frac{3\pi^c}{4}}

Answer:

Step-by-step explanation:

We know that the sine of an angle is negative in the third and fourth quadrants. So, since β is in the third quadrant (pi < β < (3pi/2)), we know that sin(β) is negative.

Given sin(β) = -√(3)/2, we can use the half-angle formulas for sine to find sin(β/2):

sin(β/2) = ±√[(1 - cos(β))/2]

Since β is in the third quadrant, we know that cos(β) is negative. We can use the Pythagorean identity to find cos(β):

cos²(β) + sin²(β) = 1

cos²(β) = 1 - sin²(β)

cos(β) = -√(1 - sin²(β))

cos(β) = -√(1 - (3/4))

cos(β) = -√(1/4)

cos(β) = -1/2

Now we can substitute cos(β) into the half-angle formula for sine:

sin(β/2) = ±√[(1 - cos(β))/2]

sin(β/2) = ±√[(1 - (-1/2))/2]

sin(β/2) = ±√(3/4)

sin(β/2) = ±(√3/2)

Since β is in the third quadrant, we know that cos(β/2) is negative. So we can use the half-angle formula for cosine to find cos(β/2):

cos(β/2) = ±√[(1 + cos(β))/2]

cos(β/2) = ±√[(1 - 1/2)/2]

cos(β/2) = ±√(1/4)

cos(β/2) = ±(1/2)

Since β is in the third quadrant, we know that cot(β/2) is negative. We can use the half-angle formulas for cosine and tangent to find cot(β/2):

cos(β/2) = ±√[(1 + cos(β))/2]

cos(β/2) = ±√[(1 - 1/2)/2]

cos(β/2) = ±√(1/4)

cos(β/2) = ±(1/2)

cot(β/2) = cos(β/2) / sin(β/2)

cot(β/2) = (±1/2) / (±(√3/2))

cot(β/2) = ±(1/√3)

cot(β/2) = ±(√3/3)

Therefore, cos(β/2) is either -1/2 or 1/2, and cot(β/2) is either -√3/3 or √3/3, depending on the choice of sign for the square roots.

answer: cos(β/2) = 1/2 and cot(β/2) = -sqrt(3,

Given sin()=-((3)/2, we can use the Pythagorean identity to calculate the value of cos():

cos(β) sqrt(1 - sin2()) sqrt(1 - sqrt(3)/2) = square (1 - 3/4) Equals square (1/4) = square 1/2

We know that is in the third quadrant, where cosine is negative, since pi (3pi/2). As a result, we have:

cos(β) = -1/2

Now we can calculate cos(/2) and cot(/2) using the half-angle formulas:

sqrt((1 + cos())/2) = cos(/2) = ±sqrt((1 - 1/2)/2) = ±sqrt(1/4) = ±1/2

We know that /2 is in the fourth quadrant, where tangent is negative, because is in the third quadrant. As a result, we have:

Tan(1/2) = -1/tan(1/2) = -1/sqrt((1 + cos())/1 - cos()) = -1/sqrt((1 - 1/2)/(1 + 1/2)) = -1/sqrt(1/3) = -sqrt (3)

The answers are therefore cos(/2) = 1/2 and cot(/2) = -sqrt (3). Nonetheless, we must establish the sign of cos(/2). We can exploit the fact that sine is negative in the third quadrant, where is located, to accomplish this. As a result, we have:

Sin(/2) is equal to sqrt((1 - cos())/2). = -sqrt((1 + 1/2)/2) = squared(3/4) = squared(3)/2

Given that cosine is positive and /2 is in the fourth quadrant, we have:

sqrt(1 - sin2(/2)) = cos(/2) 1/2 = sqrt(1 - 3/4) = sqrt(1/4)

Therefore, the solutions are cos(β/2) = 1/2 and cot(β/2) = -sqrt(3,

The answer will be as follows after answering the supplied question equation (8/15)x = (8/15)(34.29) 18.29 books Vineyard Middle School

A math equation is a process that relates two statements by using the equals sign (=) to indicate equivalence. In algebra, an equation is a mathematical statement that shows the equivalence of two mathematical expressions. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula may be used to understand the link between the two phrases written on opposite sides of a letter. Frequently, the logo and the software are the same. For example, 2x - 4 = 2.

Let's tackle this problem with algebra.

Let's call the total number of books contributed "x".

According to the issue, Creative Minds Bookstore donated two-fifths of the books to Sunshine Elementary. Sunshine Elementary received (2/5)x books as a result.

That leaves (3/5)x books to be donated to other schools and libraries.

That leaves (7/15)x books available for donation to the library.

Given that the library acquired 16 books, we may conclude:

(7/15)x = 16

Calculating x:

x = (16)(15/7) = 34.29 (rounded to two decimal places) (rounded to two decimal places)

(2/5)x = (2/5)(34.29) 13.72 books at Sunshine Elementary

(1/5)x = (1/5)(34.29) 6.86 books at Lincoln Elementary

(8/15)x = (8/15)(34.29) 18.29 books Vineyard Middle School

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3500\\ r=rate\to 1.26\%\to \frac{1.26}{100}\dotfill &0.0126\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &6 \end{cases}[/tex]

[tex]A = 3500\left(1+\frac{0.0126}{12}\right)^{12\cdot 6}\implies A=3500(1.00105)^{72} \implies A \approx 3774.71[/tex]

So, after 4 years, a £230 investment will be worth roughly £283.52 at a 5% yearly income rate compounded annually.

Let's assume you spend $1,000 (your capital) and it makes 5% once a year in interest or profits (the compounding frequency). You would've had $1,050 at the end of the first year, which is your initial capital plus an additional $5, or $50. You would also have $1,102.50 in the following year.

We can use the compound interest algorithm to find a solution to this issue:

[tex]A=P\left(1+\frac{r}{n}\right)^{n t}[/tex]

where A is the final amount, P is the initial investment, r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time in years.

In this case, we have:

P = £230 (the initial investment)

r = 5% = 0.05 (the annual interest rate as a decimal)

n = 1 (since the interest is increased yearly) (since the interest is compounded annually)

Given that we're searching for a number after four years, t = 4.

With these numbers entered into the algorithm, we obtain:

A = 230(1 + 0.05/1)⁴

A = 230(1.05)⁴

A = £283.52

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Answer:

f1(x) = (7 cos x - 3 sin x) tan-1 x + (7 sin x + 3 cos x) (1/(1+x^2))

Step-by-step explanation:

To find f1(x), we need to differentiate the given function f(x) with respect to x using the product rule and the chain rule. Here are the steps:

f(x) = (7 sin x + 3 cos x) tan-1 x

f1(x) = d/dx [(7 sin x + 3 cos x) tan-1 x]

= (7 cos x - 3 sin x) tan-1 x + (7 sin x + 3 cos x) (1/(1+x^2)) (d/dx)x

= (7 cos x - 3 sin x) tan-1 x + (7 sin x + 3 cos x) (1/(1+x^2))

Therefore, f1(x) = (7 cos x - 3 sin x) tan-1 x + (7 sin x + 3 cos x) (1/(1+x^2)).

Hope this helps! I'm sorry if it's wrong. If you need more help, ask me! :]

Then the complete table is:

x        y

14      21

64      96

26      39

When the ratiοs οf the twο variables are equal, there is a prοpοrtiοnal relatiοnship. Anοther way tο view them is that they are twο variables, οne οf which is always a cοnstant value multiplied by the οther in a prοpοrtiοnate manner.

A prοpοrtiοnal relatiοnship between twο variables can be written as:

y = kx

Where k is the cοnstant οf prοpοrtiοnality.

If we lοοk at the table we can see the pair (14, 21), replacing that in the prοpοrtiοnal relatiοn we have:

21 = k*14

(21/14) = k

(3/2) = k

Then the equatiοn is:

y = (3/2)*x

Tο cοmplete the table, we need tο evaluate the οther values in the given equatiοn.

fοr x = 64 we have:

y = (3/2)*64 = 96

fοr y = 39 we have:

39 = (3/2)*x

x = (2/3)*39 = 26

Fοr x = 1 we have:

y = (3/2)*1 = 3/2

Then the complete table is:

x        y

14      21

64      96

26      39

1         3/2

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The estimated intercepts are:

x-intercepts: (-1, 0) and (2, 0)

y-intercept: (0, 2).

We may take an approximation reading from the graph and use it to estimate the intercepts of the graph of the function y = -x2 - x + 2:

The graph's x-intercepts are the locations where it crosses the x-axis, indicating that y = 0. We can see from the graph that the x-intercepts are about at x = -1 and x = 2.

The graph's intersection with the y-axis, known as the y-intercept, indicates that x = 0. The graph indicates that the y-intercept is roughly at y = 2.

The estimated intercepts are as follows:

x-intercepts: (-1, 0) and (2, 0)

y-intercept: (0, 2)

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Answer:

thanks for the question

please mark me brainless

Answer:

Step-by-step explanation:

To simplify the expression 24 + b/b + 24 x 53.72, we first need to substitute the given value of b into the expression. For example, if b is equal to 5, we can replace all instances of b with 5 to get 24 + 5/5 + 24 x 53.72. Next, we can simplify the division by evaluating 5/5, which equals 1. Then, we can multiply 24 and 53.72 to get a product of 1288.28. Finally, we can add the simplified terms to get a final result of 1312.28. Therefore, the simplified expression, given that b is equal to 5, is 1312.28.

Answer:

5,181

Step-by-step explanation:

The arithmetic sequence has a common difference d = 9 which is the difference between successive terms

The sum of the first n terms of an arithmetic sequence is given by
[tex]S_n = \dfrac{n(a_1 + a_n)}{2}[/tex]

The nth term of an arithmetic sequence is given by
aₙ = a₁ + d(n - 1)

where a₁ = first term

In this particular sequence, a₁ = 13 and d = 9

Therefore
a₃₃ = 13 + 9(33-1)
= 13 + 9(32)

= 13 + 288

= 301

Therefore

The transpose matrix of A is the one written below.

[tex]\left[\begin{array}{ccc}3&2&0\\0&3&4\\0&0&3\end{array}\right][/tex]

Here we are given the matrix A, and we want to find the transpose matrix A^t.

To do so, just leave the elements in the diagonal as they are in the original matrix, and then do a "reflection" of the other elements along the diagonal line. So the elements with equal subindices stay where they are, and the others are reflected along them.

Then the new matrix will be:

[tex]\left[\begin{array}{ccc}3&2&0\\0&3&4\\0&0&3\end{array}\right][/tex]

That is the transpose matrix, where the diagonal is still "3, 3, 3" but the other elements changed.

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Answer:

see explanation below

Step-by-step explanation:

4. ∠A = 35, a = 8.9, find c

since side a is opposite to m∠A and c is the hypotenuse, we can use sin(∠A) = opp/hypo equation

5. sin(35) = 8.9/c

=> c = 8.9/sin(35) = 8.9/0.5736 = 15.516

6. 15.5

If Zanele realized that the questionnaire is not suitable, it could be for various reasons, such as:

The questions may not be relevant to her specific situation or goals.

The questions may not provide enough information or options to help her make an informed decision.

What is your name?

Name may not be needed to provide advice on taking a gap year.

Why do you think that it is wise to take a gap year after school?

Taking a gap year after school can provide students with a break from academic studies, help them gain life experience, and give them time to explore their interests before committing to a university degree.

What are the benefits of taking a gap year?

The benefits of taking a gap year include personal and academic growth, increased independence, cultural exposure, and the opportunity to gain valuable work or volunteer experience.

What are the reasons for delaying a gap year than first pursuing a university degree?

Some students choose to delay taking a gap year to pursue a university degree first so that they can stay on track with their academic and career goals. Others may want to save money or avoid interrupting their academic momentum.

What is the best way to spend a gap year?

The best way to spend a gap year depends on your interests and goals. Some popular gap year activities include traveling, volunteering, interning, working, learning a new language or skill, or pursuing a passion project.

If Zanele realized that the questionnaire is not suitable, it could be for various reasons, such as:

The questions may not be relevant to her specific situation or goals.

The questions may not provide enough information or options to help her make an informed decision.

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Answer:

Step-by-step explanation:

Answer:

Let's use algebra to solve the problem.

Let x be the first number.

Let y be the second number.

From the problem, we can set up two equations:

"One number is less than 3 times another":

x = 3y - - - (Equation 1)

"Their sum is increased by 5 the result is 25":

x + y + 5 = 25

x + y = 20 - - - (Equation 2)

Now we have two equations with two unknowns. We can use substitution or elimination to solve for one of the variables.

Using substitution:

From equation 1, we know that x = 3y. We can substitute this into equation 2 to eliminate x:

3y + y = 20

4y = 20

y = 5

Now we can substitute this value of y back into equation 1 to find x:

x = 3y

x = 3(5)

x = 15

Therefore, the first number is 15 and the second number is 5.

The standard deviation of the distribution is given as follows:

[tex]\sigma = 17.2[/tex]

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean of the distribution of IQ scores is given as follows:

[tex]\mu = 100[/tex]

X = 140 is the 99th percentile, as approximately 1% of the population have IQ scores above this limit, hence when X = 140, Z = 2.327, meaning that the standard deviation is obtained as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]2.327 = \frac{140 - 100}{\sigma}[/tex]

[tex]2.327\sigma = 40[/tex]

[tex]\sigma = \frac{40}{2.327}[/tex]

[tex]\sigma = 17.2[/tex]

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Answer: 1.4

Step-by-step explanation: Just divide.

16.80 divided by 12, is 1.4(0). And if you multiply 1.4 by 12 you get 16.8(0)

The statement less than 1/2 of the bags are plain chips is true, Option D is correct.

Two or more expressions with an Equal sign is called as Equation.

Let's find the fraction of bags that are plain chips.

We know that the barbecue-flavored chips make up 1/3 of the bags, and Cheese-flavored chips make up 3/5 of the bags.

The fraction of bags that are plain chips is:

1 - 1/3 - 3/5

Lets convert the fractions with same denominator.

= 15/15 - 5/15 - 9/15

=15-5-9/15

= 1/15

1/15 is less than 1/2.

Therefore, less than 1/2 of the bags are plain chips, Option D is correct.

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The required 1-st section: 6 ft;  2-nd section: 6+9 = 15 ft;  3-rd section: 4*6 = 24 ft.

The 40 or 80 ft. (12-24 m) lengths of steel pipe sections, or joints, are trucked to the building site and strung out along the path in the locations where they are to be welded together.

The 45-foot conduit is divided into three pieces. The middle-sized section is 9 feet longer than the shortest segment, and the longest section is 4 times as long as the shortest. Finish the design.

x + (x+9) + 4x = 45,   or

6x = 45-9

6x = 36,

x = 6.

Thus,1-st section: 6 ft;  2-nd section: 6+9 = 15 ft;  3-rd section: 4*6 = 24 ft.

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Complete Question:

A 45 foot pipe is cut into three sections. The longest section is 4 times as long as the shortest, and the middle-sized section is 9 feet longer than the shortest. Complete the diagram.

For the function g, the vertex form equation is [tex]g(x) = -2(x - 5)^{2} + 9.[/tex]

In algebra, the idea of an equation is a logical assertion that shows the equivalence of several mathematical expressions. For instance, the equations 3x + 5 & 14, that are separated by the 'same' sign, make up the equation 3x + 5 = 14.

A mathematical equation, such as 6 × 4 = 12 x 2, states that two quantities or values are equivalent. a meaningful noun. Equations are used when more than one factor has to be considered in order to fully understand or explain a situation.

Substituting the first point (7,1) into the equation for g(x), we get:

[tex]1 = a(7 - 5)^{2} + 9[/tex]

we get

[tex]-8 = 4a[/tex]

Dividing both sides by 4,

[tex]a = -2[/tex]

Now that we have found the value of a, we can write the equation for g(x) as:

[tex]g(x) = -2(x - 5)^{2} + 9[/tex]

Therefore, the equation in vertex form for the function g is [tex]g(x) = -2(x - 5)^{2} + 9[/tex].

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