Select the best description for the sum of the expression below.

√10 + √26

A. rational
B. neither rational nor irrational
C. both rational and irrational
D. irrational

Answer:

Step-by-step explanation:

   r = 3 cm

Volume = 27π cm³

                       [tex]\sf \boxed{\text{Volume of cylinder=$\pi r^2h$}}[/tex]

[tex]\sf \pi*3*3*h = 27 \pi\\[/tex]

              [tex]h = \dfrac{27 \pi}{\pi * 3 * 3}\\\\ \boxed{\bf h = 3 \ cm}[/tex]

      [tex]\sf \r_A : r_B = 3 : 9[/tex][tex]\sf r_A : r_B = 3 : 9[/tex]

                 = 1 : 3

      [tex]\sf h_A : h_B = 1 : 3\\[/tex]

            [tex]\sf \dfrac{3}{h_B}=\dfrac{1}{3}\\\\ cross \ multiply,\\\\ 3*3 = 1*h_B\\\\ h_B = 9 \ cm[/tex]

Volume of cylinder B = π * 9 * 9 * 9

                                    = 729π cm³

       [tex]\sf V_A : V_B = 27 \pi :729 \pi[/tex]

                    = 1 : 27

The dimensions of the rectangular prisms are the side lengths of the rectangular prism

A rectangular prism has the following dimensions

Length, width and height

This means that the dimensions of the rectangular prisms are the length, width and height  of the prism

To determine the dimension, we simply take the value of the above terms i.e. length, width and height

To split the rectangular prism, we simply consider the faces of the rectangular prism.

A rectangular prism has 6 faces

Hence, there are 6 shapes when the rectangular prism is split

Note that the question is incomplete, so I gave a general explanation

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Answer:

Show that if [tex]f(a) = f(b) = 0[/tex] for some [tex]a,\, b \in [-2,\, 2][/tex] where [tex]a \ne b[/tex], then by Rolle's Theorem [tex]f^{\prime}(x) = 0[/tex] for some [tex]x \in (-2,\, 2)[/tex]. However, no such [tex]x[/tex] exists since [tex]f^{\prime}(x) < 0[/tex] for all [tex]x \in (-2,\, 2)\![/tex].

Note that Rolle's Theorem alone does not give the exact value of the root. Neither does this theorem guarantee that a root exists in this interval.

Step-by-step explanation:

The function [tex]f(x) = x^{3} - 12\, x + 11[/tex] is continuous and differentiable over [tex][-2,\, 2][/tex]. By Rolle's Theorem. if [tex]f(a) = f(b)[/tex] for some [tex]a,\, b \in [2,\, -2][/tex] where [tex]a \ne b[/tex], then there would exist [tex]x \in (a,\, b)[/tex] such that [tex]f^{\prime}(x) = 0[/tex].

Assume by contradiction [tex]f(x)[/tex] does have more than one roots over [tex][-2,\, 2][/tex]. Let [tex]a[/tex] and [tex]b[/tex] be (two of the) roots, such that [tex]a \ne b[/tex]. Notice that [tex]f(a) = 0 = f(b)[/tex] just as Rolle's Theorem requires. Thus- by Rolle's Theorem- there would exist [tex]x \in (a,\, b)[/tex] such that [tex]f^{\prime}(x) = 0[/tex].

However, no such [tex]x \in (a,\, b)[/tex] could exist. Notice that [tex]f^{\prime}(x) = 3\, x^{2} - 12[/tex], which is a parabola opening upwards. The only zeros of [tex]f^{\prime}(x)[/tex] are [tex]x = (-2)[/tex] and [tex]x = 2[/tex].

However, neither [tex]x = (-2)[/tex] nor [tex]x = 2[/tex] are included in the open interval [tex](-2,\, 2)[/tex]. Additionally, [tex]a,\, b \in [-2,\, 2][/tex], meaning that [tex](a,\, b)[/tex] is a subset of the open interval [tex](-2,\, 2)[/tex]. Thus, neither zero would be in the subset [tex](a,\, b)[/tex]. In other words, there is no [tex]x \in (a,\, b)[/tex] such that [tex]f^{\prime}(x) = 0[/tex]. Contradiction.

Hence, [tex]f(x) = x^{3} - 12\, x + 11[/tex] has at most one root over the interval [tex][-2,\, 2][/tex].

Answer: 10

Step-by-step explanation:

Opposite sides of a parallelogram are congruent, so the sum of the lengths of each pair of adjacent sides must be 5. Thus, the perimeter is 5(2)=10.

Answer:

Step-by-step explanation:

W can = 0, -1, -2, -3, and -4.

Answer:

W = 0, -1, -2, -3, -4

Step-by-step explanation:

W can not be 1 because it says 1 is greater than w

W can not be -5 because it says -5 is less than w

W can be 0, -1, -2, -3, and -4 because they fit what your question is.

Hope this helps!

Answer:

c=5.50b

Step-by-step explanation:

Answer:

5.50 x b = c or 5.50b = c

Step-by-step explanation:

5.50 is the base amount, with B amount of necklaces.
Also please refrain from cheating on the CAT test.. especially in 6th grade.

Probability helps us to know the chances of an event occurring. The probability that the woman shared the same profession is 0.334.

Probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

The probability of both being a waiter is,

P(Both Waiter) = (3/9)×(4/12) = 1/9

The probability of both being chefs,

P(Both Chef) = (2/9)×(4/12) = 2/27

The probability of both being a Dishwashers,

P(Both Dishwasher) = (4/9)×(4/12) = 4/27

Thus, the probability that the woman shared the same profession is,

Probability = P(Both Waiter) + P(Both Chef) + P(Both Dishwasher) = 0.33

Hence, the probability that the woman shared the same profession is 0.334.

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The volume of the copper used to make the pipe is 25.12 cm³.

To calculate the volume of the copper used to make the pipe, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the volume of the copper used to make the pipe is 25.12 cm³

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Answer:

1: 81 is the overall angle, so to find the 2nd angle that makes up the overall angle, just subtract the 1st angle from the overall angle. it would be 81 - 44 = 37. so your answer is 37°.

2: this one is solved the same as number 1, just different numbers. it would be 98 - 59 = 39. your answer is 39°.

3. we know this is angle is a right angle because of the square indicating it. a right angle is 90°, so we would take 90 - 63 = 27. so your answer is 27°.

Answer:

11%

Step-by-step explanation:

old population- 120,000

new population- 133,200

increase - 133200-120000

=13200

percentage increase:

(13200*100)/120000

=11%

Answer:

  C.  (1, 3)

Step-by-step explanation:

The x-coordinate of a point is the measure of the horizontal distance a point is to the right of the y-axis. When the point is translated 4 units to the left, its x-coordinate is reduced by 4: x ⇒ x-4.

The y-coordinate of a point is the measure of the vertical distance a point is above the x-axis. When the point is translated 2 units up, its y-coordinate is increased by 2: y ⇒ y+2.

__

The translation 4 units left and 2 units up can be summarized by ...

  (x, y) ⇒ (x -4, y +2)

Then the translated vertices are ...

  Q(1, 3) ⇒ Q'(1 -4, 3 +2) = Q'(-3, 5)

  R(5, 1) ⇒ R'(5 -4, 1 +2) = R'(1, 3) . . . . . . . matches choice C

  S(3, 5) ⇒ S'(3 -4, 5 +2) = S'(-1, 7)

Of the points listed, the point (1, 3) matches a translated vertex.

z + 38° = 180°

(L.P)

z = 142°

y = 32° (alternative angle of angle FCA)

x = 142° (alternative angle of angle z)

x + 65 = 180

(l.p)

x = 180 - 65

x = 115°

y = x (alternative angle of x)

y = 115°

z = y (V.O.A)

z = 115°

~Tulpe⚘

Answer:

Step-by-step explanation:

2)  Linear pair: Two angles are called linear when they are adjacent angles and the non common arms form a straight line. They add uo to 180

 z + 32 = 180     {linear pair}

         z = 180 - 32

When parellel lines are cut by a transversal alternate interior angles are equal.

          y = 32°        {Alternate interior angles}

           x = z           {Alternate interior anlges}

           x = 148°

3) x +65 = 180  {linear pair}

          x = 180 - 65

     y = x          {Alternate interior angles}

z = y      {Verically opposite angles}

z = 115°

Given a function in a table or in algebraic or graphical form, identify key features such as x- and y-intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; and end behavior. Use key features of an algebraic function to graph the function.

Answer:

f(3) = 11

Step-by-step explanation:

Substitute x=3 into the equation so:
f(3) = 6+5

f(3) = 11

        [tex]\rule{50}{1}\large\blue\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}[/tex]

        find f(3) when f(x)=2x=5

[tex]\rule{50}{1}\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}[/tex]

      Write 3 in lieu of x and simplify:-

                           [tex]\Large\text{f(3)=2(3)+5}[/tex]

     [tex]\bigstar[/tex] On simplification,

                          [tex]\Large\text{f(3)=6+5}[/tex]

[tex]\bigstar[/tex] Which results in

                         [tex]\Large\text{f(3)=11}[/tex]

      [tex]\rule{50}{1}\smile\smile\smile\smile\rule{50}{1}[/tex]

Answer:

  reflection in the line y=4

Step-by-step explanation:

Triangle B is a mirror image of Triangle A. Point (-1, 4) is shared between the two figures, so is invariant in the transformation.

__

Triangle B is a reflection of Triangle A in the horizontal line y=4.

The area of the equilateral triangle with the given perimeter is 24.2cm².

Hence, option D)24.2cm² is the correct answer.

This question is incomplete, the complete question is:

An equilateral triangle has an apothem measuring 2.16 cm and a perimeter of 22.45 cm. What is the area of the equilateral triangle, rounded to the nearest tenth?

A triangle is simply a two-dimensional polygon with 3 sides and 3 interior angles.

An equilateral triangle is a triangle with all its three sides having the same length

The area of an equilateral triangle is expressed as;

A = ((√3)/4)a²

Where a is the length of the side

Perimeter of an equilateral triangle is expressed as;

P = 3a

Where a is the length of the side

Given that the perimeter of the equilateral triangle is 22.45 cm, the sides of the triangle will be;

P = 3a

22.45cm = 3a

a = 22.45cm / 3

a = 7.48cm

Now, the area of the equilateral triangle will be;

A = ((√3)/4)a²

A = ((√3)/4) × (7.48cm)²

A = 0.433 × 55.9504cm²

A = 24.2cm²

The area of the equilateral triangle with the given perimeter is 24.2cm².

Hence, option D)24.2cm² is the correct answer.

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Answer:

3 , 2.96 , 1/5 (0.2)  
3.48 , 3 , 1/4 (0.25)

Step-by-step explanation:

descending order

Answer:

Circle

Step-by-step explanation:

because a hyper bole is (y-k) 2b2 -(x-h) 2a2=1

ellipse is = (x-h) 2a2 + (y-k) 2b2 = 1

parabola is y= a (x-h) 2+ k

that's why circle is the answer

Answer:

2

Step-by-step explanation:

Hey there!

In order to find the mode, you need to find the number thatis plotted the most

As you can see on the line plot, the number 2 has been plotted more than the other numbers

Meaning, that 2 is the mode

Answer:

2

Step-by-step explanation:

:)

The area of the 9th floor is 718.48 m² if the ground floor(floor 0) is the largest and the floor space is reduced by 5% per floor.

It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent :

[tex]\rm y = a^x[/tex]

where a is a constant and a>1

We know we can find the exponential decrease by the below formula:

[tex]\rm y = a(1-r)^n[/tex]

We have a = 1140 m²

r = 5% = 0.05

n = 9

[tex]\rm y = 1140(1-0.05)^9[/tex]

y = 718.48 m²

Thus, the area of the 9th floor is 718.48 m² if the ground floor(floor 0) is the largest and the floor space is reduced by 5% per floor.

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Standard form ax²+bx+c=0

Done

The exponential growth rate of the baseball card given its price in 1975 and 1988 is 4.07%.

The exponential growth rate is the rate of increase in the value of an asset with the passage of time.

Exponential equations have the form a[tex]b^{x}[/tex]

Growth rate = (future value / present value)^(1 / number of years)

(405 / 241)^(1/13) = 4.07%

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Answer:

Radius is half the diamiter of a circle, basically the whole length from one point of the circle to the middle.

Answer:

Radius is how far the middle of the circle is from the edge of the circle.  For example, we know that a circle has a middle point and we know that we have a line around it in the shape of a circle.  The radius would be the distance from the middle point to the outer line of the circle.

Answer:

20

Step-by-step explanation:

Find 30% of the class
then add it

30% x 14 / 70% = 6

6 + 14 = 20 kids
Hope it helped ! Have a nice day !

we know that 14 is 70%, how much will it be for 100%? or namely the whole class?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 14 & 70\\ x& 100 \end{array} \implies \cfrac{14}{x}=\cfrac{70}{100}\implies \cfrac{14}{x}=\cfrac{7}{10} \\\\\\ 140=7x\implies \cfrac{140}{7}=x\implies 20=x[/tex]

Answer:

63

Step-by-step explanation:

(1/2) · b · h

(1/2) *  14 * 9 = 63

Answer: 63 in²

Step-by-step explanation:

      The problem gives us the formula to use. We will simplify plug in the correct values and solve.

b = base

h = height

[tex]\displaystyle \frac{b*h}{2}[/tex]

[tex]\displaystyle \frac{14*9}{2}[/tex]

[tex]\displaystyle \frac{126}{2}[/tex]

63

       63 square inches

Answer:

50%

Step-by-step explanation:

When you toss a coin it will either land on tails or heads, so we have 2 possibilities who have the same chance of happening. Thus the probability that the coin lands on heads is 50% (same for tails).

Answer:

0.5

Step-by-step explanation:

Because probability is always between 0 and 1

Equation- 8x(12+7-9)-(4+10)

Answer- 80x−14

The answer is:

$30,000/year with a 10% bonus