Question 27: Find x

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:

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: 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 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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Using the multiplier formula, the eventual change in aggregate expenditure due to the inflow of R10 billion into South Africa and using the marginal propensity to consume (MPC) is R6 billion.

The multiplier formula is used to compute the amount of new income generated from the flow of extra income.

The multiplier formula uses the MPS (marginal propensity to save) to compute the multiplier as follows:

M = 1 / MPS

The marginal propensity to save gives the proportion of income that will be saved.

The marginal propensity to save (MPS) = 0.4

M = 1 / MPS

M = 1/0.4)

= 2.5

Change in aggregate expenditure = R25 billion (2.5 x R10 billion)

Thus, we expect the aggregate expenditure in South Africa to increase by R25 billion following the inflow of R10 billion investment.

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Answer:

distance traveled in 1 hour = x/3

To find the distance traveled in 9 hours, we can multiply the distance traveled in 1 hour by 9:

distance traveled in 9 hours = (x/3) * 9

Simplifying this expression gives:

distance traveled in 9 hours = 3x

Therefore, the car will travel 3 times the distance it travels in 3 hours when it travels for 9 hours.

The length of the diameter of the circle of the radius 4 cm is 8 cm and other solutions are added below

See attachment for the circle

This is calculated as

Diameter (d) = 2 * Radius (r)

So, we have

d = 2 * 4 cm

d = 8 cm

The number of 90° sectors that will fit inside the circle is

Sectors = (360°/90°)

Sectors = 4

See attachment for the circle

The shape created inside the circle by joining the ends of five equally spaced radii is a regular pentagon.

The length (L) of one chord is

L = 2 × r × sin(c/2)

For 6 chords created by the 5 radii, we have

Total length = 6 × 2 × r × sin(c/2)

Where

c = 360/6 = 60

So, we have

Total length = 6 × 2 × 4 × sin(60/2)

Evaluate

Total length = 24 cm

Each sector of 90° in a circle has an angle of

Angle = (360/6)°

Angle = 60°

If sectors of 45° were used, the shape created inside the circle by joining the ends of the radii would be a nonagon

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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: Let's call the first angle "x".

From the problem statement, we know that the second angle is two times the first, so:

Second angle = 2x

We also know that the third angle is 170° more than the second angle, so:

Third angle = Second angle + 170°

Third angle = 2x + 170°

We know that the sum of the three angles in a triangle is 180°, so we can set up an equation:

x + 2x + (2x + 170°) = 180°

Simplifying and solving for x:

5x + 170° = 180°

5x = 10°

x = 2°

So the first angle is 2°. Using this value, we can find the other two angles:

Second angle = 2x = 2(2°) = 4°

Third angle = 2x + 170° = 2(2°) + 170° = 174°

Therefore, the three angles in the triangle measure 2°, 4°, and 174°.

Step-by-step explanation:

Answer:

X = 18

Step-by-step explanation:

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

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 of the given question based on Statistics to find minimum monthly premium payments is option D) Plan 2, since it has lower monthly premium payments.

Probability is  measure of  likelihood or chance of an event occurring. It is expressed as  number between 0 and 1, where 0 indicates an impossible event and 1 indicates  certain event

Assuming that the coverage details are similar, we can compare the monthly premium payments for each plan based on the different categories of coverage:

Individual: Plan 1 has a monthly premium of $87.32, while Plan 2 has a monthly premium of $11.77. Therefore, Plan 2 has the lower monthly premium for this category of coverage.

Individual+Spouse: Plan 2 has a monthly premium of $735.00, while Plan 1 has a monthly premium of $890.00. Therefore, Plan 2 has the lower monthly premium for this category of coverage.

Individual+Child: Plan 2 has a monthly premium of $606.00, while Plan 1 has a monthly premium of $750.00. Therefore, Plan 2 has the lower monthly premium for this category of coverage.

Individual+Family: Plan 2 has a monthly premium of $1,400.00, while Plan 1 has a monthly premium of $1,600.00. Therefore, Plan 2 has the lower monthly premium for this category of coverage.

Based on these comparisons, we can see that Plan 2 has a lower monthly premium for all categories of coverage. Therefore, the answer is option D: Plan 2, since it has lower monthly premium payments.

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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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[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]

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:

-6 and -7

Step-by-step explanation:

-6 + -7 = -13

-6 * -7 = 42

Inequality y 5x - 7 has solutions (-5, -3), (-4, 2), and (-1, 0).

In order to address an inequality • You can multiply or divide each side by the same positive amount; • You can add the same amount to each side; • You can take the same amount away from each side. If you multiply or divide each side by a negative value, the inequality sign must be reversed.

Let's examine each point individually:

(-5, -3)

y ≥ 5x - 7

-3 ≥ 5(-5) - 7

-3 ≥ -32

The inequality is true, so (-5, -3) is a solution.

(-4, 2)

y ≥ 5x - 7

2 ≥ 5(-4) - 7

2 ≥ -27

The inequality is true, so (-4, 2) is a solution.

(1, -2)

y ≥ 5x - 7

-2 ≥ 5(1) - 7

-2 ≥ -2

The inequality is not true, so (1, -2) is not a solution.

(-1, 0)

y ≥ 5x - 7

0 ≥ 5(-1) - 7

0 ≥ -12

The inequality is true, so (-1, 0) is a solution.

(3, 0)

y ≥ 5x - 7

0 ≥ 5(3) - 7

0 ≥ 8

The inequality is not true, so (3, 0) is not a solution.

(4, 1)

y ≥ 5x - 7

1 ≥ 5(4) - 7

1 ≥ 13

The inequality is not true, so (4, 1) is not a solution.

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a.) The area covered by algae for 10 days after it was spotted would be = 35.7 m²

The area covered by the algae when it was first spotted = 12.5 m²

For every week(7 days) = 2(12.5)

But 10 days = x

Make X the subject of formula;

X = 10× 2(12.5)/7

X = 250/7

X = 35.7 m²

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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:

200km

Step-by-step explanation:

Well.. if 2 cities were 200m apart, 200 cm apart, or 200 mm apart, they would be considered one city. The only logical choice is 200km.

Answer:

a

Step-by-step explanation:

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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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.

Step-by-step explanation:

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

[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]

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

the amount in Jason's savings will exceed the cost of a new television approximately 7.22 years from now.

a. The exponential growth equation to represent the price y of a new HD television t years from now is:

y = $2500[tex](1 + 0.04)^t[/tex]

where t is the number of years from now.

b. To predict when a new HD television will cost $3000, we can set y = $3000 and solve for t:

$3000 = $2500[tex](1 + 0.04)^t[/tex]

1.2 = [tex]1.04^t[/tex]

ln(1.2) = t ln(1.04)

t = ln(1.2) / ln(1.04)

t ≈ 3.97

Therefore, a new HD television will cost $3000 approximately 4 years from now.

c. To determine when the amount in Jason's savings will exceed the cost of a new television, we can use the formula for continuous compound interest:

A = [tex]Pe^(rt)[/tex]

where A is the amount in savings after t years, P is the principal amount, e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate expressed as a decimal, and t is the time in years.

In this case, P = $2200, r = 0.047 (since the annual interest rate is 4.7%), and we want to find the time t when A = $2500. Plugging these values into the formula, we get:

$2500 = $2200[tex]e^(0.047t)1.13636 = e^(0.047t)[/tex]

ln(1.13636) = 0.047t

t = ln(1.13636) / 0.047

t ≈ 7.22

Therefore, the amount in Jason's savings will exceed the cost of a new television approximately 7.22 years from now.

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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.