Which of the pairs of functions and their inverses will always have a domain and range of all real numbers?

Answer:

C

Step-by-step explanation:

the domain is for which values of x is that function defined (is that a valid function).

the range is what values that function can produce based on all the different x-values as input.

so, checking option A

that means all x values are negative.

that means all values inside the square root are negative.

the resulting function values are a discussion class of numbers and not part of the interval of (0, infinity).

so, it cannot be A.

checking option B

the domain range includes the value 6 for x.

but that would make this function for x=6 an invalid expression of 1/0

so, it cannot be B.

checking option C

the value range for x (domain) is x>6 (and excluding x=6).

and the result range is all positive numbers including 0.

there is no violation of any function principle.

the answer is C.

checking option D

similar to C, but the result range is defined as all numbers, negative and positive.

but for the domain the function can never produce negative numbers.

so, it is not D.

Answer:

cos2x=sinx

<=> 1-2sin^{2}x =sinx

solve and we have x=3pie/2, x=pie/6,x= 5pie/6

Step-by-step explanation:

Answer:

<d = 25 degrees and <e = 130 degrees

Step-by-step explanation:

We have a vertical angle, so the opposite sides of this angle are the same. This means that the angle opposite to 25 degrees also measures 25 degrees. We have one angle of the triangle. Since the triangle is isosceles, the angle d is the same as 25 degrees.

<d = 25 degrees

The interior angles of a triangle add up to 180 degrees, and we now have 2 angles, so:

<e = 180 - 25 - d

<e = 155-25

<e = 130 degrees

Answer:

<d = 25 degree and <e = 130 degree

Step-by-step explanation:

Let <d, <e and <f be the respective angles

<f = 25 degree (Vertically opposite angles are equal)

side fe = side ed (given)

Therefore, <f = <d (angles opposite to equal sides are equal)

Therefore, <d = 25 degree

<d + <e + <f = 180 degrees (Angle sum property)

25 + 25 + <e = 180

50 + <e = 180

<e = 180 - 50

<e = 130 degree

Therefore, <d = 25 degree and <e = 130 degree

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Answer:

x = 30

Step-by-step explanation:

I'm going to assume the equation you needed help with was:

[tex]\frac{1}{2}(x+6) = 18[/tex]

If not, let me know and I'll redo it.

[tex]\frac{1}{2} x+3 = 18\\\frac{1}{2} x = 15\\x = 30[/tex]

Step-by-step explanation:

In the second step while opening the bracket, instead of 'a', there should be - 4a.

Answer:

From Step 2 every step is wrong

Step-by-step explanation:

Ste p 1 : 3a - 5b = 12 - 4(b + a)

Step 2 : 3a - 5b = 12 - 4b - 4a      [ Last term instead - 4a she\he wrote + a ]

Step 3 : 7a  - 5b = 12 - 4b

Step 4 : 7a = 12 + b

[tex]Step 5 : a = \frac{12 + b}{7}[/tex]

Answer:

f = 1​

Step-by-step explanation:

7f-1=6​

Add 1 to each side

7f-1+1=6+1

7f = 7

Divide each side by 7

7f/7 = 7/7

f = 1​

Answer:

√61

Step-by-step explanation:

Answer:

(7/5, 39/5)

Step-by-step explanation:

you could use this formula:

(m₁x₂ + m₂x₁ / m₂+m₁ ,  m₂y₂ + m₂y₁ / m₂+m₁)

where m₁ = 3 (from the ratio)

m₂ = 2 (from the ratio)

x₁ = -1

x₂ = 3

y₁ = 6

y₂ = 9

= [3(3) + 2(-1) / (3+2)], [3(9) + 2(6) / (3+2)]  

= (9-2) / 5, (27+12) / 5

= (7/5, 39/5)

Answer:

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

There is a negative correlation. The direction of a line if we plot it generally through thi scatter plot would be going down, negative.

Answer:

Negative Correlation

Step-by-step explanation:

Because the graph shows that the y axis is on 4 and then goes down to 2

Answer:

2 is the base

Step-by-step explanation:

2^3

2 is the base and 3 is the exponent

Answer:

bottom right and the middle one from the left

Answer:

c

Step-by-step explanation:

Answer:

graph "B"

at 0 graph = -1200 that is the production cost

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

- y = 7 , that is y = - 7

Is a horizontal line parallel to the x- axis and passing through all points with a y- coordinate of - 7

Answer:

130º

Step-by-step explanation:

it seems like this would make a circle which adds up to 360º so first add the two numbers (150+80=230) then subtract from the amount it should be (360-230=130)

Answer:

2nd option

Step-by-step explanation:

Under a reflection in the x- axis

a point (x, y ) → (x, - y ) , then

P (- 8, 1 ) → P' (- 8, - 1 )

Q (- 6, - 8 ) → Q' (- 6, 8 )

R (4, - 3 ) → R' (4, 3 )

Answer:

2 [tex]ft^{3}[/tex]

Step-by-step explanation:

volume of a cuboid = length * breadth * height

= 2*1*1

=2 [tex]ft^{3}[/tex]

Answer:

The volume of container is 2 ft ³.

Step-by-step explanation:

We have,

We have Formula, Volume of Cuboid.

[tex] \small \sf \mapsto \: Volume = length × breadth × height[/tex]

substitute the values

[tex] \small \sf \mapsto \: Volume = 1 ft × 1 ft × 2 ft[/tex]

multiply the values

[tex] \small \sf \mapsto \: Volume = 2 \: ft {}^{3} [/tex]

Hence, the volume of container is 2 ft ³.

Answer:

Confidence Interval - 2.290 < S < 2.965

Step-by-step explanation:

Complete question

A chocolate chip cookie manufacturing company recorded the number of chocolate chips in a sample of 50 cookies. The mean is 23.33 and the standard deviation is 2.6. Construct a 80% confidence interval estimate of the standard deviation of the numbers of chocolate chips in all such cookies.

Solution

Given  

n=50

x=23.33

s=2.6

Alpha = 1-0.80 = 0.20  

X^2(a/2,n-1) = X^2(0.10, 49) = 63.17

sqrt(63.17) = 7.948

X^2(1 - a/2,n-1) = X^2(0.90, 49) = 37.69

sqrt(37.69) = 6.139

s*sqrt(n-1) = 18.2

[tex]s\sqrt{\frac{n-1}{X^2 _{(n-1), \frac{\alpha }{2} } }[/tex] [tex]\leq \sigma \leq s\sqrt{\frac{n-1}{X^2 _{(n-1), 1-\frac{\alpha }{2} } }[/tex]

confidence interval:

(18.2/7.948) < S < (18.2/6.139)

2.290 < S < 2.965

Answer:

D

Step-by-step explanation:

When taking an esponent to an exponent multiply them

4 ^(1/3)^3 = 4^1 = 4

Answer:

3rd option

Step-by-step explanation:

The equation of a line in point slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

Given

y - 4 = [tex]\frac{1}{4}[/tex] (x - 8)

with m = [tex]\frac{1}{4}[/tex] and (a, b) = (8, 4 )

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept ) , then

y = [tex]\frac{1}{4}[/tex] x + c ← is the partial equation

To find c substitute (8, 4) into the partial equation

4 = 2 + c ⇒ c = 4 - 2 = 2

y = [tex]\frac{1}{4}[/tex] x + 2 ← equation in slope- intercept form

Answer:

The answer is Credit union

Step-by-step explanation:

Answer:

126cm²

Step-by-step explanation:

first divide the figure into two( rectangle and a triangle)

area of a rectangle=length x width

16cmx7xcm

112xcm²

area of a triangle=1/2base x height

1/2x7cmx(20-16)cm

1/2x7cmx(4)cm

14cm²

total area of the figure=area of rectangle+area of triangle

=112cm²+14cm²

=126cm²

hope this is helpful

The measure of the angle x will be 65°. Then the correct option is B.

Corresponding angle – If two lines are parallel, then the third line. The corresponding angles are equal angles.

Linear angle – If the total of two angles is 180 degrees, they are said to be linear angles.

Let y be the corresponding angle of x and linear pair of 115°.

∠y + 115° = 180°

         ∠y = 65°

Then the angle y and angle x are corresponding angles. Then we have

∠x = ∠y

∠x = 65°

Then the correct option is B.

The complete question is given below.

More about the angled link is given below.

https://brainly.com/question/15767203

#SPJ2

Answer: 65

Step-by-step explanation:

Answer:

0.30(5)

the 5 is repeating

Step-by-step explanation:

calculator

Answer:

[tex]-\frac{17}{15}[/tex]

Step-by-step explanation:

By definition, [tex]\cot \theta=\frac{1}{\tan \theta}[/tex] and [tex]\sec \theta=\frac{1}{\cos \theta}[/tex]. Since since [tex]\cot \theta[/tex] is negative, [tex]\tan \theta[/tex] must also be negative, and since [tex]\sin \theta[/tex] is positive, we must be in Quadrant II.

In a right triangle, the sine of an angle is equal to its opposite side divided by the hypotenuse. The cosine of an angle in a right triangle is equal to its adjacent side divided by the hypotenuse. Therefore, we can draw a right triangle in Quadrant II, where the opposite side to angle theta is 8 and the hypotenuse of the triangle is 17.

To find the remaining leg, use to the Pythagorean Theorem, where [tex]a^2+b^2=c^2[/tex], where [tex]c[/tex] is the hypotenuse, or longest side, of the right triangle and [tex]a[/tex] and [tex]b[/tex] are the two legs of the right triangle.

Solving, we get:

[tex]8^2+b^2=17^2,\\b^2=17^2-8^2,\\b^2=\sqrt{17^2-8^2}=\sqrt{225}=15[/tex]

Since all values of cosine theta are negative in Quadrant II, all values of secant theta must also be negative in Quadrant II.

Thus, we have:

[tex]\sec\theta=\frac{1}{\cos \theta}=-\frac{1}{\frac{15}{17}}=\boxed{-\frac{17}{15}}[/tex]

Step-by-step explanation:

the slope = (1-11)/(-1-4) = -10/(-5) = 2

the equation is : y -11 = 2(x-4)

=> y -11 = 2x -20

y = 2x -8 +11

y = 2x +3

other forms :

<=> 2x - y = -3

<=> 2x - y + 3 = 0

Given:

The functions are:

[tex]f(x)=-4x^2-6x-1[/tex]

[tex]g(x)=-x^2-5x+3[/tex]

To find:

The function [tex](f-g)(x)[/tex].

Solution:

We have,

[tex]f(x)=-4x^2-6x-1[/tex]

[tex]g(x)=-x^2-5x+3[/tex]

We know that,

[tex](f-g)(x)=f(x)-g(x)[/tex]

[tex](f-g)(x)=(-4x^2-6x-1)-(-x^2-5x+3)[/tex]

[tex](f-g)(x)=-4x^2-6x-1+x^2+5x-3[/tex]

Combining like terms, we get

[tex](f-g)(x)=(-4x^2+x^2)+(-6x+5x)+(-1-3)[/tex]

[tex](f-g)(x)=-3x^2+(-x)+(-4)[/tex]

[tex](f-g)(x)=-3x^2-x-4[/tex]

Therefore, the required function is [tex](f-g)(x)=-3x^2-x-4[/tex].

Answer:

Step-by-step explanation:

in a parallelogram diagonals bisect each other.

so mid points are same.

Let coordinates of D be (x,y)

mid point of AC=midpoint Of BD

(-2+5)/2=(x+3)/2

x+3=-3

x=-3-3=-6

x=-6

(3-3)/2=(2+y)/2

y+2=0

y=-2

so D is (-6,-2)

Answer:

-2

Step-by-step explanation:

1. reduce the numbers by taking out the greatest common factor which is 9.

2. taking out 9 leaves you with [tex]-8[/tex] multipied by 1/4

Answer:

-2

Step-by-step explanation:

[tex](-\frac{8}{9} )[/tex] ÷[tex](\frac{4}{9})[/tex]

changing division sign to multiplication and doing reciprocal

[tex]-\frac{8}{9}*\frac{9}{4}[/tex]

9 and 9 gets cancel so,

[tex]-\frac{8}{4}[/tex]

4 divides 8 exactly by 2 and keep minus sign as it is

-2

Step-by-step explanation:

Let x be the number

6+4x=42

4x=36

x=9

!!!!!!!