What is the total surface area of a square pyramid with a base length of 10 meters and a slant height of 13 meters?

The function h(x) =  6x² - 60x + 147 is a quadratic function, and the axis of symmetry of the function is x = 5

The equation of the function is given as:

h(x) =  6x² - 60x + 147

Differentiate the function

h'(x) = 12x - 60

Set the function to 0

12x - 60 = 0

Add 60 to both sides

12x = 60

Divide both sides by 12

x = 5

Hence, the axis of symmetry of the function is x = 5

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Answer:

X = 5 is correct

Step-by-step explanation:

just took the test on edge and got 100%

Answer:

Width is 30mm

Step-by-step explanation:

Volume = L×W×H

Volume= 165,000 mm³

Length= 100mm

Height= 55mm

Width= ?

L×H

100mm×55mm= 5500mm

volume ÷ L×W

165,000÷5500=30

width= 30mm

L×W×H=V

100×55×30=165000

The length of the curve  r=√(1+cos 2θ) is 2π after integrating over the limit 0 to π√2

It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.

We have:

[tex]\rm r=\sqrt{(1 +cos 2 \theta)}[/tex]

[tex]\rm r=\sqrt{2cos^2 \dfrac{2 \theta}{2}[/tex]

[tex]\rm r = \sqrt{2}cos\theta[/tex]

[tex]\rm \dfrac{dr}{d\theta}= -\sqrt{2}sin\theta[/tex]

Length:

[tex]\rm L = \int\limits^{\pi\sqrt2}_0 {\sqrt{r^2+(\dfrac{dr}{d\theta}})^2} \, d\theta[/tex]

After the value of r and dr/dθ and solve the definite integral, we will get:

L = 2π

Thus, the length of the curve  r=√(1+cos 2θ) is 2π after integrating over the limit 0 to π√2

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Answer:

b. 4x

Step-by-step explanation:

We can use the power rule for derivatives, which says [tex]\frac{d}{dx} x^n = nx^{n-1[/tex]

So, if [tex]f(x) = 2x^2 + 1[/tex]

then [tex]f'(x) = 4x[/tex].

The 1 goes away because the derivative of any constant is 0.

hope this helped!

Answer:

b. 4x

Step-by-step explanation:

We can use the power rule for derivatives, which says

So, if

then .

The 1 goes away because the derivative of any constant is 0.

The length of the diagonal of the garden with 19.6 square feet and 4.3 length is : 6.3 feet

A rectangle is a quadrilateral with four sides and four vertices  each of angle 90°.

Analysis:

Area of rectangle: 19.6 square feet

length of one side = 4.3 feet

width of one side = Area/length = 19.6/4.3 = 4.6 feet

the diagonal and width and length of a rectangle for a right angle triangle.

To find the diagonal, we use Pythagoras theorem

[tex](diagonal)^{2}[/tex] = [tex](length)^{2}[/tex] + [tex](width)^{2}[/tex]

[tex](diagonal)^{2}[/tex] = [tex](4.3)^{2}[/tex] + [tex](4.6)^{2}[/tex]

[tex](diagonal)^{2}[/tex] = 39.7

diagonal = [tex]\sqrt{39.7}[/tex] = 6.3 feet

in conclusion, the diagonal of the rectangular garden is 6.3 feet

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In any triangle, a side is longer than the difference between the other two.  A side is also less the the sum of the other two. If these two rules are not obeyed then a triangle cannot be formed by those sides.

a = 7 cm.   b = 3 cm.

    Then   c > 7-3 = 4 cm         and  also,   c < 7+3 = 10 cm.

                  4 cm < the third side < 10 cm

Answer:

x>-2

Step-by-step explanation:

First you have to subtract 2 from both sides, which leaves you with -3x=6, then you have to divide -3 on both sides to get the variable by itself. Which is x<-2, but you have to switch the sign because you multiplied/divided by a negative number, then you get left with x>-2........Hope that helped!!!!!!!!!!:)

Answer:

Pythagorean triple

Step-by-step explanation:

This is usually expressed as a² + b² = c² Integer triples which satisfy this equation are Pythagorean triples. The most well known examples are (3,4,5) and (5,12,13).

A car engine gets energy from gasoline during the production of the combustion of gasoline in a car engine which is converted as kinetic energy.

In a car driven by a gasoline combustion engine, heat energy is quickly converted into kinetic energy which results in the motion of the car.

The law of the conservation of energy states that "Energy cannot be destroyed or created. It can only be transformed from one form to another".

The combustion of gasoline in a car engine tends to generate heat energy, this heat energy will be transferred as kinetic energy which results in the motion of the car.

This energy of the universe will be conserved as the energy created by the combustion is used as kinetic energy for the motion of cars.

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Answer:

A car engine gets energy from gasoline during the production of the combustion of gasoline in a car engine which is converted as kinetic energy.

Step-by-step explanation:

How is the energy of the universe conserved?

In a car driven by a gasoline combustion engine, heat energy is quickly converted into kinetic energy which results in the motion of the car.

The law of the conservation of energy states that "Energy cannot be destroyed or created. It can only be transformed from one form to another".

The combustion of gasoline in a car engine tends to generate heat energy, this heat energy will be transferred as kinetic energy which results in the motion of the car.

This energy of the universe will be conserved as the energy created by the combustion is used as kinetic energy for the motion of cars.

The correct answer ofr this question is option D

The length of the ladder nearest hundredth of a foot is 23 feet.

We have given that,

An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 20 feet up.

The ladder makes an angle of [tex]77^{\circ}[/tex]  the ground.

[tex]sin(\theta)=\frac{perpendicular \ side}{hypotenous}[/tex]

Therefore we get,

[tex]\implies\frac{22}{H} =sin(77)[/tex]

[tex]\implies H=22/sin(77)[/tex]

[tex]\implies 22.59ft\\\\=23ft[/tex]

Therefore, The length of the ladder nearest hundredth of a foot is 23 feet.

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Using proportions, considering the cost of the taxi per mile, it is found that Gary traveled 9.375 miles, not including the first.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, the company charges 2.95 for the first mile and $0.3 per each 1/8 mile next = $2.4 per mile. After the first mile, he was charged a total of $25.45 - $2.95 = $22.5. Hence the number of miles is given by:

22.5/2.4 = 9.375.

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Answer:

The first thing that we need to do is subtract 4.5 from both sides because that would removed the 4.5 from the left side and leave us with m by itself.  So we get the following [tex]m=5.5[/tex] and that is our solution.

Hope this helps!  Let me know if you have any questions

Answer:

5.5

Step-by-step explanation:

to find additional value, subtract the known

[because 4.5 plus (+) a number (m) is equal to (=) 10, the number (m) must be equal to (=) 4.5 minus (-) 10.]

10 - 4.5 = 5.5

to find if this is correct, add it back

4.5 + 5.5 = 10

m = 5.5

hope this helps:)

Answer:

other leg = 16 cm

Step-by-step explanation:

using Pythagoras' identity in the right triangle

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

let x be the other leg , then

x² + 12² = 20²

x² + 144 = 400 ( subtract 144 from both sides )

x² = 256 ( take square root of both sides )

x = [tex]\sqrt{256}[/tex] = 16

The distance between the two planes 4x-5y+z=16 and 8x-10y+2z=2 will be 2.34 units.

What is a plane?

A plane is a flat surface on which a straight line joining any two points on it would wholly lie.

Given equations are

[tex]4x-5y+z=16[/tex]

[tex]8x-10y+2z=2[/tex]

The distance between two planes is given by the formula:

[tex]D=\dfrac{|d_2-d_1|}{\sqrt{a^2+b^2+c^2}}[/tex]

Here from equations  

[tex]4x-5y+z=16[/tex]

[tex]8x-10y+2z=2[/tex]

We can also write the equation  [tex]8x-10y+2z=2[/tex]  as:

[tex]4x-5y+z=1[/tex]

So now the two equations are:

[tex]4x-5y+z=16[/tex]

[tex]4x-5y+z=1[/tex]

here a=4  b=-5  c =1 and d1=16  d2=1

Putting the values in the equation.

[tex]D=\dfrac{|-16+1|}{\sqrt{4^2+(-5)^2+(10^2)}}[/tex]

[tex]D=2.34[/tex]

Hence the distance between the two planes 4x-5y+z=16 and 8x-10y+2z=2 will be 2.34 units.

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Answer:

okay

Step-by-step explanation:

calculate the areas of those rectangles separately

[tex]say \: rectangle \: 1 \\ area = 21 \times 18 \\ = {378in}^{2} \\ rectangle \: two \\ area = 17 \times 9 \\ = {153in}^{2} \\ \\ total \: area \: = 153 + 378 \\ = {531in}^{2} [/tex]

Answer:

x < 8

Step-by-step explanation:

If Lucia wants to spend less than $8 dollars on an order, the answer would be x is less than 8.

Hey there!

GUIDE:

2 negatives = positive

2 positives = positive

1 negative & 1 positive = negative

1 positive & 1 negative = negative

ANSWERING THE GIVEN QUESTION

y = -4x

y = -4(7)

y = -28

Because, remember we said a NEGATIVE (-4) & a POSITIVE (7) gives you a negative [-28]

Therefore, the answer should be: -28

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

1/3

Step-by-step explanation:

3 + 5 +1 = 9

3/9 = 1/3

Answer:

area = 232.5

perimeter=71.243

Step-by-step explanation:

2×2×2×2

3 3 3 3

2×2×2×2

3×3×3×3

16

3×3×3×3 (divide)

= 16/81

hope it helpsss!!

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Answer:

260cm²

Step-by-step explanation:

area of this parallelogram 20×13=260cm²

Answer:

The measure of angle s is 22°

Step-by-step explanation:

Given:

To find:

∠1 and 158° are both on a straight line and supplementary.

(Supplementary angles are those angles that sum up to 180 degrees. )

So solving,

⇒ ∠1=180°-158°=22°         ....> Angles ∠1 and S are interior angles

Due to lines A and B being parallel, all interior lines are equal.

As a result, the answer is therefore 22°.

Answer:

  B.  least 2°; greatest 178°

Step-by-step explanation:

The measure of ∠ADC will be the sum of the measures of the two acute angles ADB and BDC.

__

Each acute angle with a measure that is a whole number of degrees will have a measure between 1° and 89°, inclusive.

The least sum of two such angles will be ...

  1° +1° = 2°

The greatest sum of two such angles will be ...

  89° +89° = 178°

Answer:

5.136 is 5.1 to the nearest tenth

Commision is the percentage on a cost of good. The amount of commision you owe your broker is  $133.51

Commision is the percentage on a cost of good. GIven the following parameters

Cost of good = $2,617.75

If your broker charges a commission of 5.1% of the cost, the amount charged is given as:

Amount charged = 5.1% of $2,617.75
Amount charged = 0.051 * $2,617.75
Amount charged =  $133.51

Hence the amount of commision you owe your broker is  $133.51

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Answer:

Is A.133.51

I took the quiz on

Step-by-step explanation:

No, no lil one, you're going wrong.

Slove the rest by yourself

Remember:

Answer:

65

Step-by-step explanation:

It ends in 5 or 0. 65 divided by 5= 13

Answer:

28

Step-by-step explanation:

y=kx

10=5k

k=2

y=2×14

y=28