Which statement is true?
A) All trapezoids are similar.
B) All rectangles are squares.
C) All squares are parallelograms.
D) All equilateral triangles are congruent.

Answer:

18. Sqrt40 goes between 6 and 7.

19. Sqrt83 ~= 9

Step-by-step explanation:

For both of these problems, it's really useful to be very familiar with the perfect squares on the times table. 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225...



On #18, we're looking at the sqrt40. This will be between sqrt36 and sqrt49, because 40 is between 36 and 49. But sqrt36 is 6 and sqrt49 is 7. So sqrt40 is between 6 and 7.

For #19, the sqrt83 is far closer to sqrt81 than it is to sqrt100. Sqrt81 = 9. So sqrt83 is very close to 9, it would round to 9 and not 10.

the height of the pentagonal pyramid is 5. 70 meters

The formula for determining the volume of a regular pentagonal pyramid is given as;

V=5/12tan(54°)ha^2

Where

We have the volume to be;

volume = 82. 5 cubic centers

height = h

a = 5m

Substitute the values

[tex]82. 5 = \frac{5}{12}[/tex] × [tex]tan 54[/tex] × [tex]h[/tex] ×[tex]5^2[/tex]

[tex]82. 5 = 0. 42[/tex] × [tex]1. 3764[/tex] × [tex]25[/tex] × [tex]h[/tex]

Make 'h' subject of formula

[tex]h = \frac{82. 5}{14. 45}[/tex]

h = 5. 70 meters

The height of the pentagonal pyramid is 5. 70 meters

Thus, the height of the pentagonal pyramid is 5. 70 meters

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Answer:

Step-by-step explanation:

An equation can be set up and solved based on the relation between the two speeds and the relation between time, speed, and distance.

  time = distance/speed

Let x represent the (slower) speed on the way home. Then the total time for the round trip was ...

  time going + time coming home = total time

  270/(x +11) +270/x = 9

  30x +30(x +11) = x(x +11) . . . . . . multiply by x(x+11)/9

  x^2 -49x -330 = 0 . . . . . . . .  rewrite in standard form

  (x -55)(x +6) = 0 . . . . . . . . factor

x = 55 or x = -6 . . . . . . . solutions to this equation; x < 0 is extraneous

Justin's rate on the way there was 66 mph; on the way home, it was 55 mph.

Answer:

It's easy to solve the problem.

let's start...

given equation:- y = 2x+2

X y

1 (2× 1 )+ 2 = 4 .

3 (3×2)+2 = 8 .

9 (9×2) + 2 = 20 .

10. (10× 2)+2 = 22 .( table completed)

just put the value of X in the expression.

Answer:

5/12

Step-by-step explanation:

a foot =12 inches

fraction of 5 inches=5/12

The critical values corresponding to a 0.01 significance level used to test the null hypothesis of ρs = 0 is (a) -0.881 and 0.881

The scatter plot of the election is added as an attachment

From the scatter plot, we have the following highlights

Start by calculating the degrees of freedom (df) using

df =n - 2

Substitute the known values in the above equation

df = 8 - 2

Evaluate the difference

df = 6

Using the critical value table;

At a degree of freedom of 6 and significance level of 0.01, the critical value is

z = 0.834

From the list of given options, 0.834 is between  -0.881 and 0.881

Hence, the critical values corresponding to a 0.01 significance level used to test the null hypothesis of ρs = 0 is (a) -0.881 and 0.881

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Answer:

d. (-6, 0)

Step-by-step explanation:

no explanation bc u need this quick

Based on the fact that Steve was originally driving the speed limit and then stopped a few hours and drove slower, the situation models a piecewise defined function.

This is a type of function where there are two or more parts joined together. In other words, there are two equations to represent the different parts of the function.

In this case, Steve was driving at a certain speed. This is one function. Then he stopped for a couple of hours which is another function. Then the last function has him driving slower than the speed limit.

In conclusion, this is a defined piecewise function.

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In  triangle ABC, if m∠B = 90°, BH = AH, and the ratio of m∠A to m∠C is 1:2, then m∠BHA = 120° (C).

In the next given equilateral triangle ABC, y = 70°.

Finding m∠BHA:

In triangle ABC, it is given that,

∠B = 90°

And m∠A : m∠C = 1:2

Let us assume m∠A is x. Then, m∠C = 2x

According to the angle sum property of a triangle,

∠A + ∠B + ∠C = 180°

90° + x + 2x = 180°

90° + 3x = 180°

3x = 90°

x = 30°

⇒ In triangle ABC, ∠A = 30° and ∠C = 60°

Now, in triangle AHB, it is also given that,

BH = AH

⇒ ∠ABH = ∠A = 30°

Thus, according to the angle sum property of a triangle,

∠ABH + ∠A + ∠BHA = 180°

30° + 30° + ∠BHA = 180°

∠BHA = 180° - 60°

∠BHA = 120°

Finding y in the Second Triangle:

Since triangle ABC is equilateral,

∠A = ∠B = ∠C = 60°

∴ x + 2x + 3x = 60°

6x = 60°

x = 10°

In triangle ABD, using angle sum property of triangle,

x + ∠B +  ∠BDA = 180°

10° + 60° + ∠BDA = 180°

∠BDA = 180° - 70°

∠BDA = 110°

Now, since, ∠BDA and y are linearly adjacent  angles,

∠BDA + y = 180°

110° + y = 180°

y = 180° - 110°

y = 70°  

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Answer:

Step-by-step explanation:

Use your 45-45-90 special triangle with side lengths 1, 1, sqrt(2).

The given triangle has legs length 8 (given) which is 8 times the size of our special 1-1-sqrt(2) triangle.

Therefore the length of the hypotenuse is 8 times the length of the hypotenuse in our special triangle

= 8 sqrt(2)

Answer:

6a³b²

Step-by-step explanation:

3 × 2 = 6

a²× a¹ = a³

b × b = b²

The number of tiles used is 300 tiles.

According to the statement

We have given that:

The tiles are 20 cm by 30 cm. And the dark room floor is 6 meters by 3 meters.

And we have to find that the number of tiles used to prepare the dark room.

So, For this purpose we have to find the area of the room floor.

The area of the floor is 6 *3.

The area of the floor is 18 meter per square.

The area of the tile is 0.2*0.3

The area of the tile is 0.06 meter per square.

Now,

The number of tiles used is 18/0.06

The number of tiles used is 300.

So, The number of tiles used is 300 tiles.

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Answer:

93.39

Step-by-step explanation:

So the sum of exterior angles of the convex octagon is: 360 degrees

This means if we add all the equations that represent each angle, we can set it equal to 360 and solve for x

[tex](x+14) + (2x-3) + (3x+8) + (3x+16) + (2x-17) + (3x-4) + (3x-12) + (6x)[/tex]

Group like terms

[tex](x+2x+3x+3x+2x+3x+3x+6x) + (14-3+8+16-17-4-12)[/tex]

Add like terms

[tex]23x+2[/tex]

Now let's set the sum of exterior angles to 360

[tex]23x+2 = 360[/tex]

Subtract 2 from both sides

[tex]23x=358[/tex]

Divide both sides by 23

[tex]x\approx 15.565[/tex]

So by looking at all these, it appears that 6x is the highest value, given that x is positive. The way I estimated, is approximately 15.5, whenever I saw an equation like x+14, I estimated it's about 2x, since 14 is not exactly, but close to 15.5. I did this with each polynomial given. You could also manually check each one

Original equation

6x

Subsitute

6(15.565)

Simplify

[tex]93.39[/tex]

The graph of the option in the question has a domain of -∞ < x < 3.5.

The domain of a graph are the possible x-values that can be obtained from the graph.

A graph that has a domain given by the inequality, -∞ < x < ∞ does not have a vertical asymptote.

An asymptote is a straight line to which a graph approaches, as either the x or y-value approaches infinity.

The given graph has a vertical asymptote at y ≈ 3.5

The domain of the given graph is therefore, -∞ < x < 3.5

Similarly, the graph has a horizontal asymptote at x ≈ 3

The range of the given graph is therefore, -∞ < y < 3.

A graph that has a domain of -∞ < x < ∞, extends to infinity to the left and the right of the graph.

A function that has a graph with a domain of -∞ < x < ∞ is one of direct proportionality.

An example is, y = x

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Answer:

g(0)⁻¹ = 6

Step-by-step explanation:

First, you must find the inverse of the function. Remember, another way of representing g(x) is with "y".  To find the inverse, you must swap the positions of the "x" and "y" variables in the equation. Then, you must rearrange the equation and isolate "y".

g(x) = 18 - 3x                                    <----- Original function

y = 18 - 3x                                        <----- Plug "y" in for g(x)

x = 18 - 3y                                        <----- Swap the positions of "x" and "y"

x + 3y = 18                                        <----- Add 3y to both sides

3y = 18 - x                                         <----- Subtract "x" from both sides

y = (18 - x) / 3                                    <----- Divide both sides by 3

y = 6 - (1/3)x                                     <----- Divide both terms by 3

Now that we have the inverse function, we need to plug x = 0 into the equation and solve for the output. In the inverse function, "y" is represented by the symbol g(x)⁻¹.

g(x)⁻¹ = 6 - (1/3)x                                  <----- Inverse function

g(0)⁻¹ = 6 - (1/3)(0)                               <----- Plug 0 in for "x"

g(0)⁻¹ = 6 - 0                                       <----- Multiply 1/3 and 0

g(0)⁻¹ = 6                                             <----- Subtract

The amount of Harry's loan is $9000.

A loan is when money is lent to another person with the understanding that it would be repaid, along with interest.

According to the question,

A bank loan is taken up by Harry.

After t months, D indicates Harry's outstanding debt (in dollars).

D=-200t+9000

In order to find the initial size of Harry's loan, the time(t)=0, that is, the time when no debts had been paid.

The negative sign in the expression of D denotes the payment of debt.

Substituting t=0, we get,

D=-200*0+9000

D=9000

Thus, the amount of loan taken by Harry is $ 9000.

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Answer:

x=25 and y=-10

Step-by-step explanation:

x+2y=5 ..........(1)

4x+12y=-20.........(2)

using elimination method.

multiply equ(1) by 4 and equ(2) by 1

so we have

x+2y=5..........*4

4x+12y=-20.........*1

4x+8y=20................(3)

4x+12y=-20.............(4)

subtract eq(4) from (3) we have

-4y=40

y=-10

substitute y=-10 in equation (1)

we have:

x+2(-10)=5

x-20=5

x=25

The critical value for the given confidence level, c = 0.90 and n = 21 is [tex]t_c=1.725[/tex].

The critical value is calculated as follows:

It is given that,

confidence level c = 0.90

sample size n = 21

Then,

degree of freedom,

(d.f) = n - 1 = 21 - 1 = 20

So, from the t-distribution table,

at d.f = 20 and the confidence level 0.90, the critical value is 1.725.

I.e., [tex]t_c[/tex] = 1.725

For this, α = (1 - 0.90)/2 = 0.05

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In order to compare and contrast the steps of two different constructions using a compass, we simply take a note of the different steps followed in both the constructions.

How to compare and contrast the steps?

For both the constructions, observe the corresponding steps steps that have been performed in order.

Then, note down what similarity you find while constructing the two different constructions in the first step.

Once you know the the similarities, you can further trace down the differences in the procedure of the two constructions by observing the first step. This is how you can compare and contrast the first step of two different constructions using a compass.

This process can be followed for all the steps for comparing and contrasting two different constructions.

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Answer:

255 (assuming x is the variable x)

340 (assuming x is the multiplication sign)

See explanation below.

Step-by-step explanation:

I assume that x is the variable x.

25(0.3x-4)-5(1.5x-6)+100·13/4 =

= 7.5x - 100 - 7.5x + 30 + 25 × 13

= -70 + 325

= 255

If my assumption above is incorrect, and x really means the multiplication sign, then we have this:

25(0.3×-4)-5(1.5×-6)+100·13/4 =

= 25(-1.2) - 5(-9) + 100(3.25)

= -30 + 45 + 325

= 340

There are 5,040 different ways in which she can order the books.

We know that Donna has 9 books, but 2 of these books already have fixed positions (the first one and the last one).

So we only need to order the remaining 7 books in 7 positions.

And so on for the remaining positions.

The total number of different combinations in which she can order the books is given by the product between the numbers of options above, so we will get:

C = 7*6*5*4*3*2*1 = 5,040

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The solution or the value of x = 14 (Option C). See the explanation below.

Where x (bar) is the mean.

x = (12 + 13 + 14 + 15 + 16)/5

= 14

Hence option C is correct.

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The difference of squares is:

(x+i√3)(x-i√3)

So the correct option is the last one, D.

For a complex number:

[tex]Z = a + b*i[/tex]

We define the complex conjugate of Z as:

[tex]Z' = a - b*i[/tex]

Such that the product between the complex number and its complex conjugate gives:

[tex]Z*Z' = a^2 + b^2[/tex]

Now, of you look at option D, you can see we have the product of a number and its conjugate, then we can write the product and use the above rule to get:

[tex](x + i\sqrt{3} )*(x - i\sqrt{3} ) = x^2 + (\sqrt{3} )^2 = x^2 + 3[/tex]

Which is what we wanted to get, so that is the correct option.

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Answer:

Step-by-step explanation:

1 liter = 1000 milliliters

so

3 liters = 3000 milliliters

------------------------

1 : 1000 = 3 : x

x = 3 * 1000 : 1

x = 3000

Answer: 3000 mL

Step-by-step explanation:

1 L = 1000 mL

3x1000 = 3000

Mike's speed driving to his office is 45 miles/hour, which is 10 miles less than his average speed driving back.

Speed is an average value of a scalar measurement of the distance covered over the time taken.

Speed is the equation,  r = d/Δt, where r = speed or rate, d = distance, and Δt is the change in time.

Thus, when the distance covered by a traveler is divided by the time consumed, one can determine the average speed for the travel.

Distance from Mike's home to his office = 40 miles

Distance to and from = 80 miles (40 miles x 2)

Hours covered from office = 1.6 hours

Average speed for the trip = 50 miles/hour (80/1.6)

Average speed to return home = 55 miles/hour

Average speed to office = 45 miles/hour (55 - 10)

Thus, Mike's speed of driving to his office is 45 miles/hour.

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What is Mike's speed driving to his office?

Answer:

1) log7 (5*8)= log7(40)

2) log2(11) -log2(9)=log2(11/9)

3)2log9 2=log9(2^2)

Answer: B

Step-by-step explanation:

The domain of a function is the set of x-values.

Answer:

2 × 4 - 2 / -3

8-2/-3

6/-3

-2

Your answers seem to be on the right track. These online homework apps can be picky about the answer they accept, though.

Given [tex]f(x) = x^4 - 2x^2 + 3[/tex], we have derivative

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

with critical points when [tex]f'(x) = 0[/tex]; this happens when [tex]x=0[/tex] or [tex]x=\pm1[/tex].

We also have second derivative

[tex]f''(x) = 12x^2 - 4 = 12 \left(x^2-\dfrac13\right) = 12 \left(x - \dfrac1{\sqrt3}\right) \left(x + \dfrac1{\sqrt3}\right)[/tex]

with (possible) inflection points when [tex]x=\pm\frac1{\sqrt3}=\pm\frac{\sqrt3}3[/tex].

Intercept

If "intercept" specifically means [tex]y[/tex]-intercept, what you have is correct. Setting [tex]x=0[/tex] gives [tex]f(0) = 3[/tex], so the intercept is the point (0, 3).

They could also be expecting the [tex]x[/tex]-intercepts, in which case we set [tex]f(x)=0[/tex] and solve for [tex]x[/tex]. However, we have

[tex]x^4 - 2x^2 + 3 = \left(x^2 - 1\right)^2 + 2[/tex]

and

[tex]x^2-1\ge-1 \implies (x^2-1)^2 \ge (-1)^2 = 1 \implies x^4-2x^2+3 \ge 2[/tex]

so there are no [tex]x[/tex]-intercepts to worry about.

Relative minima/maxima

Check the sign of the second derivative at each critical point.

[tex]f''(-1) = 8 > 0 \implies \text{rel. min.}[/tex]

[tex]f''(0) = -4 < 0 \implies \text{rel. max.}[/tex]

[tex]f''(1) = 8 > 0 \implies \text{rel. min.}[/tex]

So we have two relative minima at the points (-1, 2) and (1, 2), and a relative maximum at (0, 3).

Inflection points

Simply evaluate [tex]f[/tex] at each of the candidate inflection points found earlier.

[tex]f\left(-\dfrac{\sqrt3}3\right) = \dfrac{22}9[/tex]

[tex]f\left(\dfrac{\sqrt3}3\right) = \dfrac{22}9[/tex]

By using the given table, we will get the linear equation:

h = n - 9

We know that they always get comic books together, so always that Nisha's collection increases by one, Hakim's collection will also increase by one, so we will have a linear equation.

Now, if you look at the given table, you can see that Hakim's collection is always 9 units less than Nisha's collection, then the linear equation that models the relation between the two collections, h and n, is really straightforward, it will be:

Hakim's collection = Nisha's collection - 9

Using the variables, we get:

h = n - 9

That is the linear equation Hakim wanted.

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Answer:

h=n-9

Step-by-step explanation: