(b) If the lines y=x+1 and x+2y=8 intersect at R, find the coordinates of R.
(c) Hence, calculate the area of △PQR.

Answer: look at the image, and u better give me brainliest for this

Step-by-step explanation:

The exact value of the expression is 7√33/33

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

The given expression is sec[sin⁻¹(-4/7)]

We need to fine the exact value of the expression

sec[sin⁻¹(-4/7)]=√1-(-4/7)²/1-(-4/7)²

=√(1-16/49)/1-16/49

=√(1-16/49)/1-16/49

=√33/7/33/49

=√33/7×49/33

=7√33/33

Hence, the exact value of the expression is 7√33/33

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Answer:

Subtracting an expression is similar to distributing a -1 because it cancels out the numbers in the expression.

Step-by-step explanation:

The distributive property is often used to simplify algebraic expressions.

Algebra refers to the involving of unknown quantities into the block relationship between variables.

In this example, the expression 2(-3x + 5) can be simplified using the distributive property. The distributive property states that for any two numbers a and b, and a third number c, a(b + c) = ab + ac. Applying this property to our expression, 2(-3x + 5) = 2(-3x) + 2(5).

By expanding the expression, we see that 2(-3x + 5) = -6x + 10. This simplified expression is much easier to work with than the original expression. The distributive property can be applied to any expression in order to simplify it, making it easier to solve.

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Answer:

Step-by-step explanation:

The fraction of the whole circle denoting the sector is 23/72.

What is fraction?

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.

The whole circle has an angle of = 360°.

The measure of the sector of the angle is =  115°.

The fractional value of the sector is -

Measure of Sector angle / Measure of whole circle angle

Substitute the value into the expression -

115/360

23/72

Therefore, the fraction is 23/72.

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The polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. -5, -1, 2 is,

⇒ f (x) = x³ + 4x² - 7x - 10

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

For a polynomial,

A leading coefficient = 1,

And, the given zeros = -5, -1, 2

Now, We know that;

The standard polynomial is given by:

⇒ f (x) = a (x - p) (x - q) ...

Where, 'a' is leading coefficient and p, q, .. are zeroes.

Here, A leading coefficient = 1,

And, the given zeros = -5, -1, 2

Hence, The polynomial is,

⇒ f (x) = 1 (x - (-5)) (x - (- 1)) (x - 2)

⇒ f (x) = (x + 5) (x + 1) (x - 2)

⇒ f (x) = (x + 5) (x² - 2x + x - 2)

⇒ f (x) = (x + 5) (x² - x - 2)

⇒ f (x) = x³ - x² - 2x + 5x² - 5x - 10

⇒ f (x) = x³ + 4x² - 7x - 10

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Answer:

x = 1.523

Step-by-step explanation:

Given
[tex]\quad\quad e^{x-1} = 3^{2-x}[/tex]

we are asked to solve for x

Take natural logs on both sides:
[tex]\ln \left(e^{x-1}\right)=\ln \left(3^{2-x}\right)\\\\\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)}\\\\\ln \left(e^{x-1}\right)=\left(x-1\right)\ln \left(e\right)\\\\\rightarrow \left(x-1\right)\ln \left(e\right)=\ln \left(3^{2-x}\right)[/tex]substitute on left side of original eqn

[tex]\ln \left(3^{2-x}\right)=\left(2-x\right)\ln \left(3\right)\\\\[/tex]

Therefore we get
[tex]\left(x-1\right)\ln \left(e\right)=\left(2-x\right)\ln \left(3\right)[/tex]

But ln(e) = 1

So we get
[tex]x - 1 = (2-x)\;\ln(3)\\\\[/tex]

So the expression becomes

[tex]x - 1 = (2- x) \ln(3)\\\\x - 1 = 2\ln(3) - x \ln(3)[/tex]

Add [tex]x\ln(3)[/tex] on both sides:

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

Add 1 to bot sides:
x + x ln(3) = 2ln(3) + 1

x(1 + ln(3)) = 2 ln3 + 1

ln(1 + \ln(3)) = 2.09861

2ln(3) + 1 =3.1972

So we get

x(2.0986) = 3.1972

x = 3.1972/2.0986 = 1.52349

Rounded to 3 decimal places, the answer is 1.523

Answer:

Step-by-step explanation:

To find the value of "a" in the equation y = a(x + 3)(x - 5), we can use the fact that the function passes through the point (6, 45).

Step 1: Substitute the x and y values of the point into the equation:

45 = a(6 + 3)(6 - 5)

45 = a(9)(1)

Step 2: Solve for "a":

45 = 9a

a = 45/9

a = 5

The value of "a" in the equation y = a(x + 3)(x - 5) is 5.

The inverse of the equation is f-1(x) = 2/(x - 3)

From the question, we have the following parameters that can be used in our computation:

f(x) = (3x + 2)/x

Express as

y = (3x + 2)/x

Swap x and y

This gives

x = (3y + 2)/y

So, we have

xy = 3y + 2

This gives

y(x - 3) = 2

Make y the subject

y = 2/(x - 3)

Hence, the inverse is f-1(x) = 2/(x - 3)

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The solution of the given equation is -4.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equations is 3|5 - x| + 2 = 29

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

3|5 - x| =27

5-x=9

x=-4

Therefore, the solution of an equation is -4.

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"Your question is incomplete, probably the complete question/missing part is:"

Find the solution set for the equation below.

3|5 - x| + 2 = 29

The slope-intercept form of the linear equation is:

y = 7 + (7/3)*x

A linear equation in the slope-intercept form is:

y = a*x + b

So, to write the given line in that form, we just need to isolate the variable x.

We have the equation:

-7x + 3y = 21

3y = 21 + 7x

y = (21 + 7x)/3

y = 7 + (7/3)*x

That is the equation in the slope-intercept form.

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By applying rate of change concept it can be concluded that the area will change at a rate of 176 cm² / minute.

Rate of change is the change in values of a dependent variable concerning the independent variables.

The rate of change of a function shows how the function is changing from one x value to another. Whilst, differentiation is when you have an instantaneous rate of change at a single point.

We have the following information:

The rate of change of a circle = 7 cm/minute = dr/dt

We have to find the rate of change of the circle when r = 4 cm

To do so, we will use the derivative of the circle area:

A = πr²

dA/dr = 2πr

dA/dt = dA/dr × dr/dt

         = 2πr × 7  

         = 14πr

Now we input r = 4 cm into this equation:

rate of change of the area =  14*22/7*4

                                            =  176 cm² / minute

Thus, when r = 4 cm, the area will change at a rate of 176 cm² / minute.

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The column vectors of the given matrix is linearly dependent as determinant is equal to zero.

To find the column vectors of the matrix is linearly independent or linearly dependent.

Value of the determinant is equal to zero it implies linearly dependent.

And if determinant is not zero it is linearly independent.

Let 'A' be the given matrix is:

A = [tex]\left[\begin{array}{ccc}1&0&5\\-2&1&-6\\0&2&8\end{array}\right][/tex]

Determinant of A

= 1 ( 8 - (-12)) - 0( -16 -0 ) + 5 (-4 -0 )

= 1 (20 ) - 0  -20

= 20 -20

= 0

Here det(A) = 0

Therefore, the column vectors of the matrix is linearly dependent as det(A) = 0.

The above question is incomplete, the complete question is:

Are the column vectors of this matrix linearly independent or linearly dependent? show all explanations or computations.

[tex]\left[\begin{array}{ccc}1&0&5\\-2&1&-6\\0&2&8\end{array}\right][/tex]

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The number 0.54227406110177, is non- repeating and non- terminating, so, that is an irrational number.

We have to determine that the number 0.54227406110177, is rational or irrational.

There is infinite numbers of rationals or irrationals between two real numbers. Rational number is of form p/q where q≠0 and p and q are integers. For example 1/2 , 1/4 are rationals. To identify if a number is rational or not, check the following conditions :

The numbers which are not rational numbers are called irrationals. Here, see the number 0.54227406110177, no repetition of numbers in decimal form and non- terminating. So, it not a rational number. Hence, it is an irrational.

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Answer:

Step-by-step explanation:

Let's assume the number of iPads sold by Target as "x".

Then, the number of iPads sold by Best Buy would be 8 times this value, which is 8x.

We are given that the difference in their sales is 490 iPads. So we can set up an equation:

8x - x = 490

Simplifying and solving for x:

7x = 490

x = 70

Therefore, Target sold 70 iPads, and Best Buy sold 8 times as many, or 560 iPads.

Answer:

Step-by-step explanation:

[tex]x_{1}[/tex] = - 5 , f( [tex]x_{1}[/tex] ) = 0 ;

[tex]x_{2}[/tex] = - 2 , f( [tex]x_{2}[/tex] ) = 0 ;

[tex]x_{3}[/tex] = 4 , f( [tex]x_{3}[/tex] ) = 0 ;

We can prove that the statement is false by contradiction, as if a triangle had two obtuse angles, the sum of the measures of the internal angles of the triangle would be greater than 180º.

To prove an statement by contradiction, we must simply take an statement that either accepts the statement (true) or rejects (false).

An angle is classified as obtuse if it has a measure that is greater than 90º.

The sum of the measures of the internal angles of a triangle is of 180º, hence if the triangle had two obtuse angles, then the sum of the measures of the internal angles of the triangle would be greater than 180º.

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Answer:

as x approaches - infinity g(x) approaches - infinity and as x approaches infinity g(x) approaches infinity

Step-by-step explanation:

so the third answer

5.8 + (-8.45)

Remove the plus sign and parentheses:

5.8 - 8.45

-2.65

That's your answer. Hope this helped!

Answer:

-2.65

Step-by-step explanation:

Hope this will help

Answer:

x = 0.4

Step-by-step explanation:

1.5 * x = 0.6

x = 0.6 / 1.5

x = 0.4

Answer:

0.4

Step-by-step explanation:

To solve the equation 1.5 * ? = 0.6 for the value of ?, we need to isolate the variable ? on one side of the equation.

First, we can divide both sides of the equation by 1.5 to isolate the variable:

1.5 * ? / 1.5 = 0.6 / 1.5

Simplifying, we get:

? = 0.4

Therefore, the value of ? that makes the equation 1.5 * ? = 0.6 true is 0.4.

According to the information, it can be inferred that Amit has to drive at a speed of at least 60 km/h to get to work on time.

To calculate the speed that Amit must have after the traffic jam to arrive at work on time we must perform the following mathematical operation:

speed = 60 * 5 / 18 m/s = 50 / 3 m/s

distance = 5000m

time = 300 seconds = 5 minutes

According to the above he traveled 5 km distance in 5 minutes. On the other hand to calculate the speed that the rest of the journey must have we must:

speed = 15 * 5 /18 = 25/6 m/s

distance = 1000m

time = 240 seconds = 4 minutes

Distance left = (24km -6km = 18km= 18000m

Time left = 21 minutes = 1260 seconds

         Speed = 14.28m/s

         Speed = 14.28 × 18/5 kmph

         Speed = 51.42 kmph

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Maximum possible income from sales is $2.6

Linear Programming also called linear optimization, is a method to achieve the best outcome(such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear Programming is a special case of mathematical programming (also known as mathematical optimization).

Linear Programming is used in many industries such as energy, telecommunication, transportation and manufacturing.

This linear function or objective function consists of linear equality and inequality constraints.

Given:

$15 to spend on golf balls x costing $1 each and

tennis balls y, 60 cents each.

Buy at least 16 together.

x + y ≥ 16

x + 0.6 ≤ 15

x - y ≥ 1

x = 9 and y = 7

[tex]9 + 0.6 \times 7[/tex]

9 + 4.2

13.2 < 15

x = 10 and y = 8

10 + 0.6 × 8

10 + 4.8

14.8 < 15

Maximum number of golf balls x = 10

And tennis balls y = 8

Greatest number of balls he can buy = 10 + 8 = 18

Maximum possible income = 10×0.1 + 8 × 0.2 = 1 + 1.6 = $2.6

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The amount deposited in the Patricia retirement savings plan are:

Amount deposited in the twentieth year is $1150.

Total amount deposited in time span of twenty years is $13,500.

Amount deposited by Patricia in the first year ' a₁ ' = $200

Difference between the amount deposited in the subsequent year is

'd' = $50

Amount deposited during 20th year

Let 'n' be the 20th year

The above situation represents it is arithmetic progression problem

nth term of A.P. is :

aₙ = a₁ + ( n - 1 ) d

Substitute the value we get,

a₂₀ = 200 + ( 20 - 1 ) 50

⇒ a₂₀ = 200 + 19 × 50

⇒ a₂₀ = 200 + 950

⇒ a₂₀ = $1150

Total amount deposited in twenty years

S₂₀ = (n/2) [ 2 a₁+ ( n - 1 )d ]

Substitute the value we get,

⇒S₂₀ = ( 20 /2 ) [ 2(200 ) + 19 × 50 ]

⇒ S₂₀ = 10 [ 400 + 950 ]

⇒S₂₀ = $13,500

Therefore, the amount deposited in the twentieth year is $1150 and total amount deposited in twenty years is $13,500.

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Step-by-step explanation:

in geometry it is a plane figure with at least three straight sides and angles, and typically five or more.

The zeros of the equation x² - 4x + 4 = 0 is 2.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given:

A quadratic equation,

x² - 4x + 4 = 0.

To find the zeros:

Solving further,

x² - 4x + 4 = 0.

x² - 2x -2x + 4 = 0.

x(x - 2) -2(x - 2) = 0.

(x - 2)² = 0.

x  = 2.

Hence, 2 is zeros.

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The complete question:

Solve the quadratic equation and find the zeros.

The equation,

x² - 4x + 4 = 0.

The best measure of variability is the standard deviation.

Player A is the most consistent, with an IQR of 1.5.

The correct option is C.

The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean.

Given:

The table shows the number of goals made by two hockey players.

Player A:

2, 3, 1, 3, 2, 2, 1, 3, 6

Mean = 2.56

S.D. = 1.51

Player B:

1, 4, 5, 1, 2, 4, 5, 5, 11

S.D. = 3.03

The best measure of variability is the standard deviation.

Player A is the most consistent, with an IQR of 1.5.

Therefore, the best measure of variability is the standard deviation.

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Answer:1.5

Step-by-step explanation:

Answer:

y = -x + 5

Step-by-step explanation:

To find the equation of the line that is perpendicular to the line y = x + 6 and passes through the point (-4, -1), we'll use the slope-point form of the equation of a line. The slope of a line perpendicular to y = x + 6 is -1, which we can find using the negative reciprocal of the slope of y = x + 6. The slope of y = x + 6 is 1. The negative reciprocal of 1 is -1.

So the equation of the line perpendicular to y = x + 6 that passes through the point (-4, -1) is given by:

y - (-1) = -1(x - (-4))

Expanding and simplifying the right-hand side, we get:

y + 1 = -x + 4

y = -x + 5

Answer:

Step-by-step explanation:

99.5 x 54 add 10

By using the permutation formula, it can be concluded that there are 40320 ways to schedule the bands' appearances.

Permutations are different arrangements of elements formed from n elements, taken from n or some elements. In permutation, arrangement, or order matter.

P(n,r) = n! / (n-r)!  where:

n = number of objects

r = number of objects selected

If we want to know the ways to schedule the bands' appearances, it means that the arrangement matter. Thus we have to use the permutation formula:

P(n,r) = n! / (n-r)!

P(8,8) = 8! / (8 - 8)!

= 8!

= 40320 ways

Thus, there are 40320 ways to schedule the bands' appearances.

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