Select the correct answer from each drop-down menu.
Consider functions hand k.
h(t) = 5r2 – 1
k(x) = √5x + 1
For > 0, the value of h(k(x)) is
0, functions hand k
For
the value of k(h(r
inverse functions.

The expression that is not rational is the first one:

[tex]f(x) = \frac{6x}{4}[/tex]

A rational expression is something of the form:

[tex]f(x) = \frac{q(x)}{p(x)}[/tex]

Such that q(x) can be any polynomial, and p(x) is a polynomial of at least degree 1.

This means that we need to have the variable "x" on the denominator.

Then is easy to recognize the expression that is not rational, is the one that does not have x on the denominator, which is the first one:

[tex]f(x) = \frac{6x}{4}[/tex]

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Answer: B

Step-by-step explanation:

I took the test and this was the correct answer

The value of x, y, and z are 15/2,  (15√3)/2, and  (15√3)/2 after applying the trigonometric ratios.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

To find the value of x:

In right-angle triangle x-z-15:

sin30 = x/15

x = 15sin30 = 15/2

To find the value of y:

sin60 = y/x = y/(15/2)

sin60 = 2y/15

√3/2 = 2y/15

y = (15√3)/2

To find the value of z:

cos30 = z/15

√3/2 = z/15

z = (15√3)/2

Thus, the value of x, y, and z are 15/2,  (15√3)/2, and  (15√3)/2 after applying the trigonometric ratios.

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A slope also known as the gradient of a line is a number. The correct option is A, C, and D.

A slope is also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.

For the given question,

This can be observed in the graph, as the slope of the graph before 4 pm is positive, it can be concluded that the temperature is increased until 4 pm.

This can be observed in the graph, as the slope of the graph after 4 pm is negative, it can be concluded that the temperature is decreasing after 4 pm.

This can be probed by calculating the slope of the line between the two points. Therefore, the slope between 8 am to 12 pm will be 1, while the slope from 12 pm to 4 pm will be equal to 4/3.

Hence, the correct option is A, C, and D.

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Answer:

ACD

Step-by-step explanation:

The sample size required is 2938.645

Probability is the likeliness of an event to happen.

It is given that

p = .37

∈ = 0.025

∝ = 1 - 0.995 = 0.005

∝[tex]\rm z_{\alpha/2} = z_{0.005/2} = 2.807[/tex]  (From z table)

Sample size n is given by

[tex]\rm n = (\dfrac{z_{\alpha/2}}{\epsilon})^2 p (1-p)\\\\n = (\dfrac{2.807}{.025})^2 *0.37*(1-0.37)\\\\n = 2938.645\\[/tex]

Therefore the sample size required is 2938.645

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Answer: 20

Step-by-step explanation:

Let [tex]f(y)=x[/tex]

[tex]x=\frac{1}{2}y+10\\\\x-10=\frac{1}{2}y\\\\y=h(x)=2x-\boxed{20}[/tex]

Answer:

(π2,15)(π2,15) is a local maximal

(3π2,9)(3π2,9) is a local minimal

Step-by-step explanation:

Examine the right triangle ABC. Which rise and run would create a similar right triangle on the same line?a rise of 6 and a run of 8a rise of 8 and a run of 6a rise of 6 and a run of 5a rise of 5 and a run of 6

Step-by-step explanation:

Answer:

Step-by-step explanation:

2 ( x + 3 ) / 4 ( x + 1 )

2 (x + 3) ÷4 (x + 1)

2 (x + 3) ÷ 2×2(x+1)

cancel out the 2 in the numerator with the 2 in the denominator

(x + 3) ÷ 2(x + 1)

x+3 / 2(x+1)

The equation that models the curve of best fit for this data will be y = 1.4646·(1.818)ˣ.

Let b is the base and x is the power of the exponent function and a is the leading coefficient. The exponent is given as

y = a(b)ˣ

Consider the scatter plot.

Then the equation that models the curve of best fit for this data will be

At (1.2, 3), then we have

[tex]\rm 3 =ab^{1.2}[/tex] ..........1

At (4, 16), then we have

16 = ab⁴  ..........2

By solving the equations 1 and 2, we have

a = 1.4646 and b = 1.818

Then the equation will be

y = 1.4646·(1.818)ˣ

Then the graph is drawn.

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Answer:

≈ 14.6%

Step-by-step explanation:

percentage increase is calculated as

[tex]\frac{increase}{original}[/tex] × 100%

increase = 2.75 - 2.40 = 0.35 , then

percentage increase = [tex]\frac{0.35}{2.40}[/tex] × 100% ≈ 14.6% ( to the nearest tenth )

Answer:

15%

Step-by-step explanation:

3/20x100=15

7.5 pounds of the $0.82 per lb candy must be used in the mixture.

First, let's define the variables:

We want to make 9 lb of mixture, then:

x + y = 9.

And the price of these 9 pounds must be $0.91, then we can write:

x*$0.82 + y*$1.36 = 9*$0.91 = $8.19

Then we have a system of equations:

x + y = 9.

x*$0.82 + y*$1.36 = $8.19

We can isolate y on the first equation so we get:

y = 9 - x

Now we can replace that on the other equation:

x*$0.82 + (9 - x)*$1.36 = $8.19

And now we can solve this for x.

x*($0.82 - $1.36) = $8.19 - 9*$1.36

-x*$0.54 = -$4.05

x = (4.05/0.54) = 7.5

So 7.5 pounds of the $0.82 per lb candy must be used in the mixture.

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Answer:

252-232=20-1=19

Step-by-step explanation:

the question said in between so you don't count the first and the last numbers

The sequence shown is defined by a function that generates even numbers equal or greater than 10, defined by the function s = 10 + 2 · (n - 1).

Sequences are sets of elements characterized by at least a rule. In this case, the sequence shown is characterized by a function that generates even numbers equal or greater than 10. The function behind the sequence is shown below:

s = 10 + 2 · (n - 1)     (1)

Where n is the element index.

The sequence shown is defined by a function that generates even numbers equal or greater than 10, defined by the function s = 10 + 2 · (n - 1).

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Using the binomial distribution, it is found that there is a 0.0001 = 0.01% probability that the airplane will be in serious trouble the next time it goes up.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

The values of the parameters are given as follows:

p = 0.1, n = 2.

The plane is in serious trouble if both engines fail, that is, the probability is P(X = 2), hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{2,2}.(0.1)^{2}.(0.9)^{0} = 0.0001[/tex]

0.0001 = 0.01% probability that the airplane will be in serious trouble the next time it goes up.

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Let [tex]f(x) = x^3 + 3x + \sin(x) - 5[/tex]. Using Newton's method to approximate a solution to [tex]f(x) = 0[/tex], we consider the recurrence

[tex]\begin{cases} x_1 = 1 \\ x_{n + 1} = x_n - \frac{f(x_n)}{f'(x_n)} & \text{for } n \ge 1 \end{cases}[/tex]

Differentiating [tex]f(x)[/tex] gives

[tex]f'(x) = 3x^2 + 3 + \cos(x)[/tex]

Then

[tex]x_2 = 1 - \dfrac{f(1)}{f'(1)} = 1 + \dfrac{1 - \sin(1)}{6 + \cos(1)} \approx 1.024238790[/tex]

[tex]x_3 = x_2 - \dfrac{f(x_2)}{f'(x_2)} \approx 1.024009549[/tex]

[tex]x_4 = x_3 - \dfrac{f(x_3)}{f'(x_3)} \approx \boxed{1.024009528}[/tex]

which agrees numerically with the actual root of [tex]f(x)[/tex] up to at least 9 digits after the decimal point.

Answer:

[tex]\boxed {360 m^{3}}[/tex]

Step-by-step explanation:

Water needed to fill the pool = volume of pool

Volume :

Hence, 360 m³ of water has to be filled.

Answer:

360 m³

Step-by-step explanation:

The swimming pool can be modeled as a rectangular prism with the following dimensions:

To find how much water is needed to fill the pool, calculate the volume of the rectangular prism using the given dimensions:

[tex]\begin{aligned}\textsf{Volume of a rectangular prism} & = \sf length \times width \times height\\\implies \textsf{Volume of pool} & = \sf 12 \times 6 \times 5 \\& = \sf 72 \times 5\\& = \sf 360 \:\: m^3\end{aligned}[/tex]

Therefore, 360 m³ of water is needed to fill the swimming pool.

A parabola is a mirror-symmetrical planar curve that is nearly U-shaped. The vertex of the parabola will lie at (-3,2).

A parabola is a mirror-symmetrical planar curve that is nearly U-shaped.

y = a(x-h)² + k

where,

(h, k) are the coordinates of the vertex of the parabola in the form (x, y);

a defines how narrower is the parabola, and the "-" or "+" that the parabola will open up or down.

Comparing the given equation with the equation of a parabola, we will get,

y =  a(x -h)² + k

y = -4(x+3)² + 2

Hence, the vertex of the parabola will lie at (-3,2).

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Answer:

D -6, 15

Step-by-step explanation:

Because 3,11 is the middle, and 12,7 is the other end, you can do

12 - 3 = 9

3 - 9 = 6

then

11 - 7 = 4

11 + 4 = 15

so

6 is you x and 15 is your y

Answer:

A relation is a subset of cartesian product of two non empty sets whereas A function is a type of relation in which every element of first set has one and only image in the second set.

In a relation an element of the first set can have many images in the second set whereas in a function the first element can have only one image in the second set.

The given relation is not a function as the element 1 is related to 3 different elements in the second set.

Domain={1}

Range={7,14,21}

The area of triangle is 24 sq. units

Area of rectangle is product of its length to its breadth.

i.e., Area of rectangle = length* breadth

let A(6, -3), B(3, -6), C( -1, -2) and D( 2, 1)

Using distance formula

AB = √(3-6)²+ (-6 +3)²

AB= √9 + 9

AB= √18

AB= 3√2

now,

BC=  √(-1-3)²+ (-2 +6)²

BC = √16 +16

BC = √32

BC =4 √2

Now, Area of rectangle

= AB* BC

=  3√2 *4 √2

= 12*2

= 24 square units

Hence, area of rectangle is 24 sq. units

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Expand cos(A - B) with the identity

cos(A - B) = cos(A) cos(B) + sin(A) sin(B)

A is in quadrant II, so sin(A) > 0, and B is in quadrant I, so sin(B) > 0. Using the Pythagorean identity, we get

cos²(A) + sin²(A) = 1   ⇒   sin(A) = + √(1 - (-3/5)²) = 4/5

cos²(B) + sin²(B) = 1   ⇒   sin(A) = + √(1 - (8/17)²) = 15/17

Then

cos(A - B) = (-3/5) × 8/17 + 4/5 × 15/17 = 36/85

cos (A - B) is 36/85

Expand cos(A - B) with the identity

You get, cos(A - B) = cos(A) cos(B) + sin(A) sin(B)

Since A is in quadrant II, so sin(A) > 0,

B is in quadrant I, so sin(B) > 0.

Using the Pythagorean identity, we get

cos²(A) + sin²(A) = 1  

Make sin A the subject of formula

[tex]sin(A)^{2}[/tex] =  ([tex]\sqrt{(1 - (-3/5}[/tex])²)

Find the square root of both sides, square root cancels square

[tex]sin A[/tex] = 4/5

Repeat the same for the second value

[tex]sin A^{2} = \sqrt{(1- 8/17)^2}[/tex]

[tex]sin A[/tex] = 15/17

Substitute values into cos(A - B)

cos(A - B) =  cos(A) cos(B) + sin(A) sin(B) = (-3/5) * 8/17 + 4/5 * 15/17

cos (A - B) = 36/85

Therefore, cos (A - B) is 36/85

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Answer:

11

Step-by-step explanation:

duh add 1 and 1 merge it together to get 11

that's a hard question imma go with 2 though

Step-by-step explanation:

for this problem let's let x=1 and y also =1 so x+y=2 hope this helps

L1 and L2 are parallel

so the interior alternate angles are equal

4y - 40 = 3y ( interior alternate angles)

4y - 40 = x + 15 ( vertically opposite angles).

solving the first equation, we get

4y - 3y = 40

y = 40°

putting values of y= 40° in eq. 2, we get

4y - 40= x + 15

4(40) - 40 = x + 15

160 -40 = x + 15

120 - 15 = x

105° = x

Answer:

FROM THE CALCULATIONS THE ANSWER IS B!

Answer:

150°

Step-by-step explanation:

A secant is a straight line that intersects a circle at two points.

The circle shows two secants RD and BD that intersect at one exterior point D, so we can use the Intersecting Secants Theorem to solve.

Intersecting Secants Theorem

If two secant segments are drawn to the circle from one exterior point, the measure of the angle formed by the two lines is half of the (positive) difference of the measures of the intercepted arcs.

[tex]\implies \angle RDB = \dfrac{1}{2}\left(\overset{\frown}{RB}-\overset{\frown}{EC}\right)[/tex]

[tex]\implies 5x-10=\dfrac{1}{2}(13x+7-60^{\circ})[/tex]

[tex]\implies 2(5x-10)=13x-53[/tex]

[tex]\implies 10x-20=13x-53[/tex]

[tex]\implies -3x=-33[/tex]

[tex]\implies x=11[/tex]

To find the measure of [tex]\overset{\frown}{RB}[/tex], substitute the found value of x into the expression for the arc:

[tex]\implies \overset{\frown}{RB}=13x+7[/tex]

[tex]\implies \overset{\frown}{RB}=13(11)+7[/tex]

[tex]\implies \overset{\frown}{RB}=143+7[/tex]

[tex]\implies \overset{\frown}{RB}=150^{\circ}[/tex]

Therefore, the measure of arc RB is 150°.

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Inequalities help us to compare two unequal expressions. The inequalities that represent this graph are y<8/10x and y>-x. The correct option is C.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.

It is mostly denoted by the symbol <, >, ≤, and ≥.

To find the inequality, we need to find the equation of the dashed line and then substitute the inequality as per the requirement. The dashed line is used instead of a solid line to show greater than or less than.

The inequality for the first graph can be written as,

[tex]y < \dfrac{8}{10}x[/tex]

The inequality for the second graph will be,

y>-x

Hence, the inequalities that represent this graph are y<8/10x and y>-x. Thus, the correct option is C.

The complete question is:

The graph below shows the solution to which system of inequalities?

A.) y>x , y ≥ (8/10)x

B.) y>-x, y ≤ (8/10)x

C.) y>-x, y < (8/10)x

D.) y>x, y > (8/10)x

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