Find all solutions of the following polynomial equation.

-7x + 4x²-28 + x³ = 0

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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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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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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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

There are 2 ounces of jam in the large jar and 2/3 ounce of jam in each small jar.

In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. Matrices are commonly used to represent and manipulate linear transformations and systems of linear equations.

The elements of a matrix are typically denoted by lowercase letters with subscripts, such as aij or bij, where i and j refer to the row and column indices, respectively. For example, a 3x3 matrix might look like this:

| a11 a12 a13 |

| a21 a22 a23 |

| a31 a32 a33 |

This matrix has three rows and three columns, and the element in the first row and second column is denoted by a12.

Matrices can be added, subtracted, multiplied, and divided, and these operations follow specific rules that are defined in matrix algebra. For example, to add or subtract two matrices of the same size, we simply add or subtract the corresponding elements. To multiply two matrices, we multiply the rows of the first matrix by the columns of the second matrix and sum the products.

Let's represent the number of ounces of jam in the large jar as "L" and the number of ounces of jam in each small jar as "S". Then we can write the system of equations:

1L + 2S = 8

1L - 1S = 2

We can write this system in matrix form as:

[1 2; 1 -1][L;S] = [8;2]

To solve for L and S, we can use matrix algebra to isolate [L;S]:

[L;S] = [1 2; 1 -1]⁻¹ [8;2]

First, we need to find the inverse of the coefficient matrix [1 2; 1 -1]. The inverse is:

[1 -2; 1 1]/3

So we can substitute this into our equation:

[L;S] = [1 -2; 1 1]/3 [8;2]

[L;S] = [2;2/3]

So there are 2 ounces of jam in the large jar and 2/3 ounce of jam in each small jar.

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The complete question is:

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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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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Answer:

a) To calculate how much Vanessa will have to pay back after 2 years, we need to add the interest to the principal.

The interest can be calculated using the simple interest formula:

Interest = Principal x Rate x Time

where,

Principal = $5,000 (the amount borrowed)

Rate = 4% (expressed as a decimal, 0.04)

Time = 2 years

So,

Interest = $5,000 x 0.04 x 2

Interest = $400

The total amount Vanessa will have to pay back is the sum of the principal and the interest:

Total amount = Principal + Interest

Total amount = $5,000 + $400

Total amount = $5,400

Therefore, Vanessa will have to pay $5,400 after 2 years.

b) To calculate how much interest Vanessa will pay, we can use the same formula for simple interest:

Interest = Principal x Rate x Time

Plugging in the given values, we get:

Interest = $5,000 x 0.04 x 2

Interest = $400

Therefore, Vanessa will pay $400 in interest over the 2-year period.

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.

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:

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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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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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:

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

Answer:

thanks for the question

please mark me brainless

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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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! :]

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)

Answer:

a)10

Step-by-step explanation:

(xx)=(2×2)=4

2(4)=8

8+2=10

answer: a) 10

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:

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,

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.

Answer:

Primero, podemos establecer las siguientes ecuaciones:

La suma de los kilómetros que caminan Mateo y Leo es igual a 15:

 Mateo + Leo = 15

Mateo camina 1/5 más que Leo:

 Mateo = Leo + 1/5Leo

 Mateo = 6/5Leo

Podemos utilizar la segunda ecuación para despejar una de las variables en términos de la otra. Por ejemplo, despejando Leo:

   Leo = 5/6Mateo

Luego, podemos sustituir esta expresión en la primera ecuación para obtener una ecuación con una sola variable:

   Mateo + 5/6Mateo = 15

   11/6Mateo = 15

   Mateo = 15*6/11

   Mateo = 8.18 Km

Finalmente, podemos utilizar una de las ecuaciones que relaciona a Mateo y Leo para obtener la distancia que recorre Leo:

   Leo = 5/6Mateo

   Leo = 5/6*8.18

   Leo = 6.82 Km

Por lo tanto, Mateo recorre 8.18 Km y Leo recorre 6.82 Km.

Answer:

X = 18

Step-by-step explanation:

7x is the opposite angle if 3x, so 10x= 180 180÷10 = 18

[tex]g^{2} +4g-32=0[/tex]

[tex]g^{2} + 8g - 4g - 32=0[/tex]

[tex]g(g+8)-4(g+8) = 0[/tex]

[tex](g+8)(g-4) = 0[/tex]

[tex]g+8=0 \implies \bf g = -8[/tex]

[tex]g-4=0 \implies \bf g = 4[/tex]

[tex]\implies g = 4 \ or \ -8[/tex]

[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]

Step-by-step explanation:

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