Identify the inverse function of f(x) = VX - 2 + 3.

[tex] \Large{ \boxed{ \bf{ \color{purple}{Solution:}}}}[/tex]

Let the smaller angle be x

Then, Larger angle would be x + 4°

❍ They are complementary angles.

So,

➙ x + x + 4° = 90°

➙ 2x + 4° = 90°

➙ 2x = 86°

➙ x = 86°/2 = 43°

Then, x + 4° = 47°

So, Our required answer:

❍ They are supplementary angles.

So,

➙ x + x + 4° = 180°

➙ 2x + 4° = 180°

➙ 2x = 176°

➙ x = 176°/2 = 88°

Then, x + 4° = 92°

So, Our required answer:

✌️ Hence, solved !!

━━━━━━━━━━━━━━━━━━━━

Answer:

1). [tex]\frac{2}{x^{2}-x-12 }=\frac{2}{(x+3)(x-4)}[/tex]

2). [tex]\frac{1}{x^{2}-16 }=\frac{1}{(x-4)(x+4)}[/tex]

Step-by-step explanation:

In this question we have to write the fractions in the factored form.

Rational expressions are [tex]\frac{2}{x^{2}-x-12 }[/tex] and [tex]\frac{1}{x^{2}-16 }[/tex].

1). [tex]\frac{2}{x^{2}-x-12 }[/tex]

Factored form of the denominator (x² - x - 12) = x² - 4x + 3x - 12

                                                                           = x(x - 4) + 3(x - 4)

                                                                           = (x + 3)(x - 4)

Therefore. [tex]\frac{2}{x^{2}-x-12 }=\frac{2}{(x+3)(x-4)}[/tex]

2). [tex]\frac{1}{x^{2}-16 }[/tex]

Factored form of the denominator (x² - 16) = (x - 4)(x + 4)

[Since (a²- b²) = (a - b)(a + b)]

Therefore, [tex]\frac{1}{x^{2}-16 }=\frac{1}{(x-4)(x+4)}[/tex]

Answer:

if x = 2

f(x) = -3x^2 + 180x -285

f(x) = -3*2*2 + 180*2 -285

f(x) = -12 + 360 -285

f (x) = 63

Step-by-step explanation:

Answer: g = w + 8    g=w-2

Step-by-step explanation:

We could represent the word phrases by the equations.

g = w + 8  

g = w - 2  

Answer:

g = w + 8

g = w - 2

Step-by-step explanation:

Assuming that g and w exists, then we can show the relation as described:

"Variable g is 8 more than variable w."

g = w + 8

"Variable g is also 2 less than w."

g = w - 2

These are the two equations of the described relationship between g and w.

Note that g could not actually exist in the real number system:

g = w + 8

g = w - 2

w + 8 = w - 2

w - w = -2 - 8

0 != -10

This is impossible within the real number system.

Cheers.

Answer:

Step-by-step explanation:

To find this probability, we shall be using the z-score route

Mathematically ;

z-score = (x -mean)/SD

From the question, x = 1.99, mean = 0 and SD = 1

So z = (1.99-0)/1 = 1.99

So the probability we want to calculate is;

P(z<1.99)

This value can be obtained from the standard normal distribution table.

P(z < 1.99) = 0.9767

The sketch of the region is as shown as in the attachment.

Answer: Option C.

Step-by-step explanation:

The lengths of our triangle are:

9, 10 and √130.

If the triangle is a triangle rectangle, by the Pitagoream's theorem we have:

A^2 + B^2 = H^2

in this case H is the larger side, this must be √130.

then:

A and B must be 9 and 10.

9^2 + 10^2 = (√130)^2

81 + 100 = 130

This is false, so this is NOT a triangle rectangle, the hypotenuse is shorter than it should be.

Now, we have some kind of rule:

 if A^2 + B^2 = H^2 then we have one angle of 90° and two smaller ones. (triangle rectangle)

 if A^2 + B^2 > H^2 then all the angles are smaller than 90°, this is an acute triangle.

 if A^2 + B^2 < H^2 then we have one angle larger than 90°, this is an obtuse angle.

(H is always the larger side, A and B are the two shorter ones).

In this case:

81 + 100 > 130

Then this must be an acute angle.

Answer:

Hey there!

A function only has one y value for every x value, so this is a function. Additionally, all linear equations (that are in the y=mx+b form) are functions.

Hope this helps :)

Answer:

H0: μc ≤ μs    Ha :μc > μs    

Step-by-step explanation:

The null and alternate hypotheses can be stated as

H0: μc ≤ μs    Ha :μc > μs    one tailed test

Where

μc =  Mean of college students watching movies in a month

μs  =  Mean of school students watching movies in a month

For one tailed test of α =0.05   the value of Z= ± 1.645

The critical region will be Z >  ± 1.645

It is of importance to note that by rejecting the null hypothesis and accepting the alternate hypothesis we are automatically rejecting all values of mean that are greater than 7.1

Answer:

add 8x to both sides

Step-by-step explanation:

5-8x<2x+3

first step, subtract 3 from both sides:

2-8x<2x

second step,?

2<?x

so you need to add 8x first

Answer:

approximately x = 38

Step-by-step explanation:

The maximum profit is the vertex of the profit graph parabola. The maximum occurs at approximately x = 38.

The solution is x = 38

The location on the profit function parabola where the profit from sales of the phone cases is a maximum is given by x = 38

A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line

The equation of the parabola is given by

( x - h )² = 4p ( y - k )

where ( h , k ) is the vertex and ( h , k + p ) is the focus

y is the directrix and y = k – p

The equation of the parabola is also given by the equation

y = ax² + bx + c

where a , b , and c are the three coefficients and the parabola is uniquely identified

Given data ,

Let the revenue, cost, and profit functions for a line of cell phone cases be given as two parabolic functions R ( x ) and P ( x )

The maximum profit is given by the parabolic function R ( x )

The profit is represented by = y

The price per phone is represented by = x

Now , when y is maximum ,

The value of y = $ 2,250,000

The value of x when y = $ 2,250,000 is x = 38

So , the value of x from the parabola where profit is maximum is x = 38

Therefore,  the value of x = 38

Hence , the value of x from the function is x = 38

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Answer:

B) 5

Step-by-step explanation:

Proportions:

8 ⇒ 10

20 ⇒ 5x

5x = 20*10/8

5x = 25

x = 25/5

x = 5

Answer:

  C.  70°

Step-by-step explanation:

The inscribed angle marked 15° intercepts an arc that is double that measure, so the intercepted arc on the right is 2×15° = 30°.

The external angle marked 20° is half the difference of the intercepted arcs, so is ...

  20° = (1/2)(x - 30°)

  40° = x - 30° . . . . . . multiply by 2

  70° = x . . . . . . . . . . . add 30°

The value of x is 70°.

Hence, the commutative property of addition is not used.

What is an expression?

A mathematical expression is in form of variables and constants separated by their arithmetic operation.

As we know that, there are three types of properties they are associative property which is [tex](a+b) + c = a + (b+c)[/tex],

Distributive property which is [tex]a(b+c) = ab + ac[/tex],

Commutative property which is [tex]a + b = b + a[/tex].

Here given that,

[tex]2 (x+5)+7x=(2x+10)+7x[/tex]      

[tex](2x+10)+7x=(2x+10)+7x[/tex]         ( distributive property of multiplication)

[tex](2x+7x)+10=(2x+7x)+10[/tex]        ( it is associative property of addition)

[tex](8x)+10=(8x)+10[/tex]        ( it is a commutative property)

Hence, the commutative property of addition is not used.

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Answer:

The area of the house is A. 1,108

Answer:

56.8

Step-by-step explanation:

7.1*8=56.8

Answer:

  8^-11

Step-by-step explanation:

The applicable rule of exponents is ...

  (a^b)(a^c) = a^(b+c)

Then we have ...

  (8^(-2))·(8^(-9)) = 8^(-2-9) = 8^-11

Answer: 60%

Step-by-step explanation:

Given, AP$ of Brisket = $4.72

Weight of each brisket on purchase : 10.4 lbs

Weight of each brisket after smoking : 6.24 lbs

Yield % of the briskets after Carol is done smoking them=[tex]\dfrac{\text{Weight after smoking}}{\text{Weight on purchase}}[/tex]

[tex]\dfrac{6.24}{10.4}\times100\\\\=60\%[/tex]

Hence, the yield % of the briskets after Carol is done smoking them = 60%

Answer:

Since the calculated value of t= 2.249 does not  falls in the rejection region we therefore accept  the null hypothesis at 5 % significance level . On the basis of this we conclude that the  bonus plan has not  increased sales significantly.

Step-by-step explanation:

The null and alternative hypotheses as

H0: μd=0    Ha: μd≠0

Significance level is set at ∝= 0.05

n= 6

degrees of freedom = df = 6-1 = 5

The critical region is t  ( base alpha by 2 with df=5) ≥ ± 2.571

The test statistic under H0 is

t = d/ sd/ √n

Which has t distribution with n-1 degrees of freedom

Sales                                      Difference

Person      After      Before   d = after - before      d²

1                   94          90                4                      16

2                  82          84               -2                       4

3                  90          84               6                       36

4                  76           70               6                       36

5                  79           80               -1                        1

6                  85          80                 5                       25  

∑                                                       18                   118

d`= ∑d/n= 18/6= 3

sd²= 1/6( 118- 18²/6) = 1/6 ( 118 - 54) = 10.67

sd= 3.266

t= 3/ 3.266/ √6

t= 2.249

Since the calculated value of t= 2.249 does not  falls in the rejection region we therefore accept  the null hypothesis at 5 % significance level . On the basis of this we conclude that the  bonus plan has not  increased sales significantly.

Answer:

The frequency distribution does not appear to be normal.

Step-by-step explanation:

The data provided is as follows:

S = {0.38 , 0 , 0.22 , 0.06 , 0 , 0 , 0.21 , 0 , 0.53 , 0.18 , 0 , 0 , 0.02 , 0 , 0 , 0.24 , 0 , 0 , 0.01 , 0 , 0 , 1.28 , 0.24 , 0 , 0.19 , 0.53 , 0 , 0, 0.24 , 0}

It is provided that the first lower class limit should be 0.00 and the class width should be 0.20.

The frequency distribution table is as follows:

Class Interval  Count

 0.00 - 0.19            21

 0.20 - 0.39             6

 0.40 - 0.59             2

 0.60 - 0.79             0

 0.80 - 0.99             0

  1.00 - 1 . 19             0

  1.20 - 1. 39             1

The frequency distribution does not appear to be normal. This is because the frequencies does not start and end at almost equivalent points and the mid-distribution does not consist of the highest frequency.

Thus, the frequency distribution does not appear to be normal.

Answer:

The correct answer is option B

Answer:

[tex]g(x) = 0.5^{(x+3)}[/tex]

Step-by-step explanation:

Assuming f(x) = [tex]0.5^{x}[/tex] is a correct interpretation of f(x),

the way to translate three units to the left is to change x to x+3.  This gives our answer:   [tex]g(x) = 0.5^{(x+3)}[/tex]

Answer:

B. g(x) = (1/2)⁽ˣ⁺³⁾

Hope this helps!

Step-by-step explanation:

Answer:

7/8

Step-by-step explanation:

7/8 = 0.875

5/8 = 0.625

7/13 = 0.538

11/19 = 0.579

So 7/8 is the largest

Answer:

a) 20, 21, 28 : acute

b) 3, 6, 4 : obtuse

c) 8, 12, 15 : obtuse

Step-by-step explanation:

You can see if a triangle is acute, obtuse, or right using the Pythagorean theorem as follows:

If [tex]a^2+b^2=c^2[/tex] , then the triangle is right.

If [tex]a^2+b^2>c^2[/tex] , then the triangle is acute.

If [tex]a^2+b^2<c^2[/tex] , then the triangle is obtuse.

Solve each to find if the given lengths form an acute, obtuse, or right triangle ( The biggest number is the hypotenuse length, since the hypotenuse is always the longest side in a triangle. This is represented by c):

a) 20, 21, 28

Insert numbers, using 28 as c:

[tex]20^2+21^2[/tex]_[tex]28^2[/tex]

Simplify exponents ([tex]x^2=x*x[/tex]):

[tex]400+441[/tex]_[tex]784[/tex]

Simplify addition:

[tex]841[/tex]_[tex]784[/tex]

Identify relationship:

[tex]841>784[/tex]

The sum of the squares of a and b is greater than the square of c. This triangle is acute.

b) 3, 6, 4

Insert numbers, using 6 as c:

[tex]3^2+4^2[/tex]_[tex]6^2[/tex]

Simplify exponents:

[tex]9+16[/tex]_[tex]36[/tex]

Simplify addition:

[tex]25[/tex]_[tex]36[/tex]

Identify relationship:

[tex]25<36[/tex]

The sum of the squares of a and b is less than the square of c. This triangle is obtuse.

c) 8, 12, 15

Insert numbers, using 15 as c:

[tex]8^2+12^2[/tex]_[tex]15^2[/tex]

Simplify exponents:

[tex]64+144[/tex]_[tex]225[/tex]

Simplify addition:

[tex]208[/tex]_[tex]225[/tex]

Identify relationship:

[tex]208<225[/tex]

The sum of the squares of a and b is less than the square of c. This triangle is obtuse.

:Done.

The correct values are,

a) 20, 21, 28  = Acute

b) 3, 6, 4  = Obtuse

c) 8, 12, 15 = Obtuse

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The sides are,

a) 20, 21, 28

b) 3, 6, 4

c) 8, 12, 15

Now,

We know that;

If three sides of a triangle are a, b and c.

Then, We get;

If a² + b² = c², then the triangle is right triangle.

If a² + b² > c², then the triangle is acute triangle.

If a² + b² < c², then the triangle is obtuse triangle.

Here, For option a;

⇒ 20, 21, 28

Clearly, a² + b² = 20² + 21²

                       = 400 + 441

                       = 841

And, c² = 28² = 784

Thus, a² + b² > c²

Hence, It shows the acute angle.

For option b;

⇒ 3, 6, 4

Clearly, a² + b² = 3² + 4²

                       = 9 + 16

                       = 25

And, c² = 6² = 36

Thus, a² + b² < c²

Hence, It shows the obtuse angle.

For option c;

⇒ 8, 12, 15

Clearly, a² + b² = 8² + 12²

                       = 64 + 144

                       = 208

And, c² = 15² = 225

Thus, a² + b² < c²

Hence, It shows the obtuse angle.

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Answer:

around 16 minutes. you partition an hour and a half (all out) by what number of sections he read (5.5

Step-by-step explanation:

Answer:

[tex]\approx \bold{6544\ in^3/sec}[/tex]

Step-by-step explanation:

Given:

Rate of change of radius of cylinder:

[tex]\dfrac{dr}{dt} = +7\ in/sec[/tex]

(This is increasing rate so positive)

Rate of change of height of cylinder:

[tex]\dfrac{dh}{dt} = -6\ in/sec[/tex]

(This is decreasing rate so negative)

To find:

Rate of change of volume when r = 20 inches and h = 16 inches.

Solution:

First of all, let us have a look at the formula for Volume:

[tex]V = \pi r^2h[/tex]

Differentiating it w.r.to 't':

[tex]\dfrac{dV}{dt} = \dfrac{d}{dt}(\pi r^2h)[/tex]

Let us have a look at the formula:

[tex]1.\ \dfrac{d}{dx} (C.f(x)) = C\dfrac{d(f(x))}{dx} \ \ \ (\text{C is a constant})\\2.\ \dfrac{d}{dx} (f(x).g(x)) = f(x)\dfrac{d}{dx} (g(x))+g(x)\dfrac{d}{dx} (f(x))[/tex]

[tex]3.\ \dfrac{dx^n}{dx} = nx^{n-1}[/tex]

Applying the two formula for the above differentiation:

[tex]\Rightarrow \dfrac{dV}{dt} = \pi\dfrac{d}{dt}( r^2h)\\\Rightarrow \dfrac{dV}{dt} = \pi h\dfrac{d }{dt}( r^2)+\pi r^2\dfrac{dh }{dt}\\\Rightarrow \dfrac{dV}{dt} = \pi h\times 2r \dfrac{dr }{dt}+\pi r^2\dfrac{dh }{dt}[/tex]

Now, putting the values:

[tex]\Rightarrow \dfrac{dV}{dt} = \pi \times 16\times 2\times 20 \times 7+\pi\times 20^2\times (-6)\\\Rightarrow \dfrac{dV}{dt} = 22 \times 16\times 2\times 20 +3.14\times 400\times (-6)\\\Rightarrow \dfrac{dV}{dt} = 14080 -7536\\\Rightarrow \dfrac{dV}{dt} \approx \bold{6544\ in^3/sec}[/tex]

So, the answer is: [tex]\approx \bold{6544\ in^3/sec}[/tex]

Answer:

i) [tex]\frac38\pi[/tex]

ii) n = 33

Step-by-step explanation:

For this question you can actually focus on the sine, and forget about the e power. The x-coordinates of the extremes of the curve will be the same as for y=sin(4x)

i) equivalent to solving sin(4x) = -1, so 4x = 3/2 pi, x=3/8 pi

ii) The Tn values are at x = (n·π - π/2)/4

solving  (n·π - π/2)/4 > 25 gives:

n > 1/2 + 100/π, so n > 32.331, but n must be integer, so we get n=33

Answer:

58

Step-by-step explanation:

By the property of intersecting secants outside of a circle, we have:

x° = 1/2( 141° - 25°) = 1/2 * 116° = 58°

Therefore, x = 58

Answer:

so to get a third you divide it by 3

first convert it to fraction

so it is 26/3

so do 26/3 divided by 3

so we do keep switch flip

26/3*1/3

so answer is 26/9 or 2 8/9

Step-by-step explanation:

Answer:

[tex]\large \boxed{\mathrm{2 \ 8/9 \ tablespoons \ of \ red \ chilies }}[/tex]

Step-by-step explanation:

8 2/3 tablespoons of red chilies is required for a recipe.

One-third of the original recipe would mean that the quantity of red chilies will be also one-third.

8 2/3 × 1/3

Convert to an improper fraction.

26/3 × 1/3

Multiply the fractions.

26/(3 × 3) = 26/9

Convert to a mixed fraction.

26/9 = 2 8/9