Find the surface area of the following figure

Answer:

Part 1) The surface area is [tex]SA=35.1\ cm^{2}[/tex]

Part 2) The volume is equal to [tex]V=12.15\ cm^{3}[/tex]

Step-by-step explanation:

The question in English is

The bases of a right prism are two rectangle triangles whose legs measure 1.5 cm and 1.8 cm, respectively, the prism has a height of 4.5 cm. calculates its total surface area and volume

Part 1) Find the surface area

The surface area is equal to

[tex]SA=2B+Ph[/tex]

where

B is the area of the base

P is the perimeter of the base

h is the height of the prism

Find the area of the base B

[tex]B=(1.5)(1.8)=2.7\ cm^{2}[/tex]

Find the perimeter of the base P

[tex]P=2*(1.5+1.8)=6.6\ cm[/tex]

we have

[tex]h=4.5\ cm[/tex]

substitute the values

[tex]SA=2(2.7)+(6.6)(4.5)=35.1\ cm^{2}[/tex]

Part 2) Find the volume

The volume is equal to

[tex]V=Bh[/tex]

where

B is the area of the base

h is the height of the prism

we have

[tex]B=2.7\ cm^{2}\\ h=4.5\ cm[/tex]

substitute

[tex]V=(2.7)(4.5)=12.15\ cm^{3}[/tex]

Answer:

[tex]\frac{1}{4096}[/tex]

Step-by-step explanation:

To solve this we are using the formula for the nth term of a geometric sequence:

[tex]a_n=a_1r^{n-1}[/tex]

where

[tex]a_1[/tex] is the first term

[tex]r[/tex] is the common ratio

[tex]n[/tex] is the position of the term in the sequence

The common ratio is just the current term divided by the previous term in the sequence, so [tex]r=\frac{16}{64} =\frac{4}{16} =\frac{1}{4}[/tex]. We can infer from our sequence that its first term is 64, so [tex]a_1=64[/tex].

Replacing values

[tex]a_n=a_1r^{n-1}[/tex]

[tex]a_n=64(\frac{1}{4} )^{n-1}[/tex]

We want to find the 10th term, so the position of the term in the sequence is [tex]n=10[/tex].

Replacing values

[tex]a_n=64(\frac{1}{4} )^{n-1}[/tex]

[tex]a_{10}=64(\frac{1}{4} )^{10-1}[/tex]

[tex]a_{10}=64(\frac{1}{4} )^{9}[/tex]

[tex]a_{10}=\frac{1}{4096}[/tex]

We can conclude that the 10th term of the sequence is [tex]\frac{1}{4096}[/tex]

Answer:

10th term of the sequence 64,16,4... = 1/4096

Step-by-step explanation:

Points to remember

nth term of GP is given by.

Tₙ = ar⁽ⁿ⁻¹⁾

Where r is the common ratio and a is the first term

To find the 10th term of given GP

It is given that,

64, 16, 4,......

a = 64 and 6 = 1/4 Here  

T₁₀ = ar⁽ⁿ⁻¹⁾

 = 64 * (1/4)⁽¹⁰⁻¹⁾ = 64 * (1/4⁹)

 = 4³/4⁹ = 1/4⁶ = 1/4096

Answer:

15%

Step-by-step explanation:

To calculate the percent of the bill that was left as a tip, you would divide the amount of the tip ($4.80) by the cost of the meal ($32) to get 0.15. This is then multiplied by 100 to give a tip percentage of 15%.

To determine the percentage of the bill that was left as a tip, you would divide the amount of the tip by the cost of the meal and then multiply by 100 to convert the decimal to a percentage. This would calculate as follows:

So, Michael and his friends left a 15% tip on the bill.

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To calculate taxes for each scenario, use the progressive tax rate schedules to find the correct tax bracket, apply the marginal tax rate, add any base tax amount, and complete the calculation for the head of household, single person, and married taxpayers filing jointly.

To calculate the amount of taxes for the given situations, we use the tax rate schedules provided. For each scenario, the tax is calculated based on the income brackets and the corresponding tax rates in the tax table, which align with a progressive tax system. Detailed calculations are needed with step-by-step explanations for accuracy.

The mentioned tax brackets and rates are based on example tax tables; the actual calculations would depend on the specific tax brackets and rates set forth by the IRS for the given tax year.

Answer:

from sloping up to sloping down ⇒ answer D

Step-by-step explanation:

* Lets talk about the transformation

- If the function f(x) reflected across the x-axis, then the new

 function g(x) = - f(x)

- If the function f(x) reflected across the y-axis, then the new

 function g(x) = f(-x)

* Now lets solve the problem

∵ The equation of the line is y = 2x - 6

∵ The equation is changed to y = -2x - 6

- If the both signs of x and the number are changed means the

 equation is multiplied by -1

∴ The line is reflected across the x-axis

- If the sign of x only is changed

∴ The line is reflected across the y-axis

- From the equation 2x changed to -2x, but -6 not changed

∴ The sign of x only changed

∴ The line is reflected across the y-axis

* The graph is reflected across the y-axis

∴ from sloping up to sloping down

The line is reflected over the x axis

Answer:

1

Step-by-step explanation:

0 Triangles satisfy the given condition.

What is the triangle inequality?

Triangle inequality theorem that the sum of any two sides of a triangle is greater than or equal to the third side; in symbols, a + b ≥ c.

In this question:

a,b and A are three sides of triangle.

a=14

b=2 and

A=66

In this triangle

Therefore, no such triangle with given dimension can exist.

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Answer:

[tex]\frac{2\sqrt{2} }{3}[/tex]

Step-by-step explanation:

The sine of an angle is defined as the ratio between the opposite side and the hypotenuse of a given right-angled triangle;

sin x = ( opposite / hypotenuse)

The opposite side to the angle x is thus 1 unit while the hypotenuse is 3 units. We need to determine the adjacent side to the angle x. We use the Pythagoras theorem since we are dealing with right-angled triangle;

The adjacent side would be;

[tex]\sqrt{9-1}=\sqrt{8}=2\sqrt{2}[/tex]

The cosine of an angle is given as;

cos x = (adjacent side / hypotenuse)

Therefore, the cos x would be;

[tex]\frac{2\sqrt{2} }{3}[/tex]

Answer:

[tex]cos(x) =\±2\frac{\sqrt{2}}{3}[/tex]

Step-by-step explanation:

We know that [tex]sen(x) =\frac{1}{3}[/tex]

Remember the following trigonometric identities

[tex]cos ^ 2(x) = 1-sin ^ 2(x)[/tex]

Use this identity to find the value of cosx.

If [tex]sen(x) =\frac{1}{3}[/tex] then:

[tex]cos ^ 2(x) = 1-(\frac{1}{3})^2[/tex]

[tex]cos ^ 2(x) =\frac{8}{9}[/tex]

[tex]cos(x) =\±\sqrt{\frac{8}{9}}[/tex]

[tex]cos(x) =\±2\frac{\sqrt{2}}{3}[/tex]

Answer:

(10,6) is a positive and (-2, -3) are negative

Step-by-step explanation:

Answer:

a0) 2

  x<0

a1) x

   0≤x<3

a2) 3

     x≥3

Step-by-step explanation:

As shown in the given graph

function of y is a straight line at y=2 line till x=0

hence a0:

y= 2 for x<0

Then function becomes linear line from x=0 till x=3

hence a1:

y= x for 0≤x<3

Now after that graph of function y again shift to straight line from x=3 onward with y-axis value of 3

hence a2:

y= 3 for x≥3 !

Answer:

303.6ft²  or 347.88 ft²

Step-by-step explanation:

The question is on area

The dimensions of the living room are given as;

Length= L = 22'-0"

Width= W= 12' -0" or 13'- 9"

Area= L× W

22'×12'=264ft²

Allow 15% waste

264× 115/100 =303.6ft²

or

Length= 22' and width = 13' 9"

change 9" to ft ⇒1'=12"...........................divide by 12"

9/12=0.75'................add to 13'

13'+0.75'=13.75'

Area=L×W

22'×13.75'=302.5ft²

Add 15% allowed waste

302.5 × 115/100 =347.88 ft²

Answer:

[tex]36.5\ cm^{2}[/tex]

Step-by-step explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its perimeters is equal to the scale factor

Let

z ----> the scale factor

x----> the perimeter of the larger figure

y ----> the perimeter of the smaller figure

[tex]z=\frac{x}{y}[/tex]

we have

[tex]x=28\ cm[/tex]

[tex]y=20\ cm[/tex]

substitute

[tex]z=\frac{28}{20}=1.4[/tex]

step 2

Find the area of the larger figure

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z ----> the scale factor

x----> the area of the larger figure

y ----> the area of the smaller figure

[tex]z^{2} =\frac{x}{y}[/tex]

we have

[tex]z=1.4[/tex]

[tex]y=18.6\ cm^{2}[/tex]

substitute

[tex]1.4^{2} =\frac{x}{18.6}[/tex]

[tex]x=1.96*(18.6)=36.5\ cm^{2}[/tex]

Answer:

Yes, the art supplies cost $29.73, and I believe she has what looks on the picture to be $57

Step-by-step explanation:

Answer:

It's prime

Step-by-step explanation:

So there are no factors except 1 and 17

Answer:

(x - 5)(2x + 3)

Step-by-step explanation:

To factorise the quadratic

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term

product = 2 × - 15 = - 30 and sum = - 7

The factors are - 10 and + 3

Use these factors to split the x- term

2x² - 10x + 3x - 15 ( factor the first/second and third/fourth terms )

= 2x(x - 5) + 3(x - 5) ← factor out (x - 5) from each term

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

The factorization of the quadratic expression is presented as follows;

2·x² - 7·x - 15 is  (2·x + 3)·(x - 5)

A quadratic expression is an expression that can be presented in the form a·x² + b·x + c, where a ≠ 0, and a, b, and c are numbers.

In order to factorize the quadratic expression 2·x² - 7·x - 15, it is required to find two binomials with a product equivalent to the expression is to be found

The binomial can be found from the numbers p and q such that p + q = -7 and p·q = -30 (The product of the leading coefficient and the constant term)
A possible pair of such numbers is p = -10 and q = 3. Therefore, we get;

2·x² - 7·x -15 = 2·x² + (3·x - 10·x) - 15

The first two terms and the last two terms can be grouped and each group factorized separately as follows;

2·x² + (3·x - 10·x) - 15 = (2·x² + 3·x) +  (-10·x - 15)

x·(2 + 3) - 5·(2·x + 3)

The above expression can be further factorized by taking out the common factor (2·x + 3) as follows;

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

Therefore, the factored expression is; 2·x² - 7·x - 15 = (2·x + 3)·(x - 5)

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Answer:

lower section

Step-by-step explanation:

Given:

Pyramid A: Base is rectangle with length of 10 meters and width of 20 meters.

Pyramid B: Base is square with 10 meter sides.

Heights are the same.

Volume of rectangular pyramid = (L * W * H) / 3

Volume of square pyramid = a² * h/3

Let us assume that the height is 10 meters.

V of rectangular pyramid = (10m * 20m * 10m)/3 = 2000/3 = 666.67 m³

V of square pyramid = (10m)² * 10/3 = 100m² * 3.33 = 333.33 m³

The volume of pyramid A is TWICE the volume of pyramid B.

If the height of pyramid B increases to twice the of pyramid A, (from 10m to 20m),  

V of square pyramid = (10m)² * (10*2)/3 = 100m² * 20m/3 = 100m² * 6.67m = 666.67 m³

The new volume of pyramid B is EQUAL to the volume of pyramid A.

The volume of the pyramid A is twice the volume of pyramid B. If the height of B is increased to twice, the volumes of A and B are equal.

Volume of a three dimensional shape is the space occupied by the shape.

Given that,

The base of pyramid A is a rectangle with a length of 10 meters and a width of 20 meters.

The base of pyramid B is a square with 10-meter sides.

The heights of the pyramids are the same.

Volume of a rectangular pyramid = lwh / 3, where l, w and h are length, width and height respectively.

Volume of pyramid A = 10 × 20 × h /3 = 200/3 h

Volume of a square pyramid = a²h/3, where a is the side length of the base and h is the height.

Volume of pyramid B = 10²h/3 = 100/3 h

So volume of pyramid A = 2 × volume of B.

If height of B increased to twice that of pyramid A,

Volume of B = 100/3 (2h) = 200/3 h

So both are equal in this case.

Hence the volume of pyramid A is twice that of B in the first case and the volumes are equal in the second case.

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Answer:

D. 6^30

explanation:

(6^36)/(6^6)= 6^30

Answer:

A

Step-by-step explanation:

It Has The Most Matching Y Values with The Intervals (I could Be Wrong Tho)

x < 7

It's not less than or equal to, because of the open circle on the seven

can i get brainliest if not thats fine

Answer:

x < 7

Step-by-step explanation:

did this for an assigment soooo

a:

Just divide both sides by 7. Since 7 is positive, you don't need to change the inequality sign:

[tex]7j>77\iff j>11\}[/tex]

In set notation, we write

[tex]\{j \in \mathbb{R}\ :\ j>11[/tex]

b:

Subtract 9 from both sides:

[tex]17\leq x+9 \iff 8\leq x[/tex]

In set notation, we write

[tex]\{x \in \mathbb{R}\ :\ x\geq 8\}[/tex]

Answer:

12.5 miles per hour.

Step-by-step explanation:

There are 60 minutes in 1 hour so:

12 minutes = 12/60 = 1/5 of an hour.

So his speed in mph

= distance in miles / time in hours

= 2.5 / 1/5

= 2.5 * 5

= 12.5 miles per hour.

The speed in miles per hour is 12.5 miles/hour

How to calculate speed?

We define speed as :

Speed= Distance/Time

In other words, it is the distance travelled in a unit time

Here,

Distance=2.5 miles

Time=12 minutes that is 12/60 =1/5 hours

[tex]Speed=\dfrac{2.5}{1/5}[/tex]

Speed= 2.5*5=12.5 miles/hour

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Divide the total amount of money by the number of boys:

1.92/3 = 0.64 cents

Each boy gets 0.64 cents.

Answer:

Focus = (0, [tex]\frac{3}{4}[/tex])

Step-by-step explanation:

(± 3, 3) are at an equal distance from y-axis.

axis of parabola = y-axis

vertex = (0, 0)

Parabola will be of the form: x² = 4ay, passing through(± 3, 3)

(± 3)² = 4 × a × 3  ⇒ 9 = 12a   ⇒ a = [tex]\frac{9}{12}[/tex]

a = [tex]\frac{3}{4}[/tex]

Coordinates of focus are: (0, a)  ⇒  (0, [tex]\frac{3}{4}[/tex])

Answer:

The focus of the parabola is (0 , 3/4)

Step-by-step explanation:

* Lets revise some facts about the parabola

- The standard form of the equation of a parabola of vertex (h , k)

 is (x - h)² = 4p (y - k)  

- The standard form of the equation of a parabola of vertex (0 , 0)  is

  x² =  4p y, from this equation we can find:  

# The axis of symmetry is the y-axis,  x = 0  

# 4p equal to the coefficient of y in the given equation  

# If  p  >  0, the parabola opens up.  

# If  p <  0, the parabola opens down.

# The coordinates of the focus,  (0 , p)

# The directrix ,  y = − p

* Now lets solve the problem

∵ The vertex of the parabola is (0 , 0)

∴ The equation of the parabola is x² = 4p y

∵ the parabola passes through points (-3 , 3) and (3 , 3)

- Substitute the value of x and y coordinates of one point in the

 equation to find the value of p

∴ (3)² = 4p (3) ⇒ we use point (3 , 3)

∴ 9 = 12 p ⇒ divide both sides by 12

∴ p = 9/12 = 3/4

- Now lets find the focus of the parabola

∵ The focus of the parabola is (0 , p)

∵ p = 3/4

∴ The focus of the parabola is (0 , 3/4)

To obtain the graph of the function y = |x+2| we have to make a table of values of x to find the values of y. The absolute value or modulus of a real number is its numerical value without care its sign. For example, the absolute value of |4| and |-4| is 4.

In order to make a graph we are going to use the values (-3, -2, -1, 0, 1, 2, 3) for x.

x = -3

y = |-3 + 2| = |-1| = 1

x = -2

y = |-2 + 2| = |0| = 0

x = -1

y = |-1 + 2| = |1| = 1

x = 0

y = |0 + 2| = |2| = 2

x = 1

y = |1 + 2| = |3| = 3

x = 2

y = |2 + 2| = |4| = 4

x = 3

y = |3 + 2| = |5| = 5

 x   ║   y

-3        1

-2        0

-1         1

 0        2

 1         3

 2        4

 3        5

Obtaining the graph shown in the image attached.

.

Answer:

its 1/2

Step-by-step explanation:

Final answer:

The constant of proportionality (r) in the equation y=rx can be found by dividing y by x for any given pair of values. Using the pair (14, 7), the constant of proportionality is calculated as r = 7 / 14 = 0.5.

Explanation:

The quantities x and y are said to be proportional if they relate via a constant of proportionality, which we refer to as r in the equation y=rx. To find the constant of proportionality, you can choose any given pair of values for x and y and divide them. For example, using the given pair (14, 7), we can find r by dividing 7 by 14.

r = y / x = 7 / 14 = 0.5

Therefore, the constant of proportionality r is 0.5. You can check this value with other given pairs to confirm it is consistent. For further confirmation, using the pair (30, 15), we have:

r = 15 / 30 = 0.5

which matches our previously calculated constant of proportionality.

Answer:

(6,-11)

Step-by-step explanation:

Given

Point B' = (4,-8)

And the translation formula (x-2, y+3)

In order to get the coordinates of the point before translation, both given points have to be put equivalent.

So, for x-coordinate

x-2 = 4

x= 4+2

x= 6

And for y-coordinate

y+3 = -8

y = -8-3

y=-11

So the old coordinates of old point were (6,-11) ..

your answer is (6, -11)

Answer:

the forth one

Step-by-step explanation:

The answer above is right

Answer:

C.

Step-by-step explanation:

Answer:

(-3,4)

Step-by-step explanation:

The axis of symmetry, or X coordinate for a parabolic function is [tex]\frac{-b}{2a}[/tex]

By plugging in 6 for b, and 1 for a, you have -3.

By then plugging back into the function you can get the Y coordinate of the vertex.

[tex]f(x)=(-3)^{2}+6(-3)+13[/tex]

Or 4.

The answer is (-3,4)

ANSWER

(-3, 4)

EXPLANATION

The given function is

[tex]f(x) = {x}^{2} + 6x + 13[/tex]

We complete the square to obtain the vertex form:

We add and subtract the square of half the coefficient of x.

[tex]f(x) = {x}^{2} + 6x + {3}^{2} + 13 - {3}^{2} [/tex]

The first three terms form a perfect square trinomial.

[tex]f(x) = {(x + 3)}^{2} + 13 - 9[/tex]

[tex]f(x) = {(x + 3)}^{2} + 4[/tex]

Comparing this to the vertex form;

[tex]f(x) = {(x - h)}^{2} + k[/tex]

h=-3 and k=4

Answer:

- The scientist can use these two measurements to calculate the distance between the Earth and the Sun by applying one of the trigonometric functions: Cosine of an angle.

- The scientist can substitute these measurements into [tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex] and solve for the distance between the Earth and the Sun.

Step-by-step explanation:

Let's assume that the right triangle formed is like the one shown in the figure attached, where "d" represents the distance between the Earth and the Sun.

Then:

The scientist can use only these two measurements to calculate the distance between the Earth and the Sun by applying one of the trigonometric functions: Cosine of an angle.

The scientist can substitute these measurements into  [tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex], and solve for the distance "d".

Knowing that:

[tex]\alpha=x\°\\adjacent=d\\hypotenuse=y[/tex]

Then:

[tex]cos(x\°)=\frac{d}{y}[/tex]

And solving for "d":

[tex]ycos(x\°)=d[/tex]

The scientist can use the tangent function in trigonometry with the measured angle x and distance y to calculate the distance between the Earth and the Sun by rearranging the formula to solve for the opposite side of the right triangle formed.

The scientist can calculate the distance between the Earth and the Sun using the measurements of angle x and distance y through a process known as triangulation or the parallax method. The right triangle formed with vertices at the Earth, Sun, and Shooting Star allows for the application of trigonometric functions. Specifically, the scientist can use the tangent function, which relates the angle of a right triangle to the ratio of the opposite side over the adjacent side.

To find the distance between the Earth and the Sun, the scientist applies the formula:

tan(x) = opposite/adjacent

Where opposite is the distance between the Earth and the Shooting Star, and adjacent is the distance between the Sun and the Shooting Star (y). By rearranging the formula to solve for the opposite side, we get:

Distance between Earth and Sun = y * tan(x)

This calculation allows the scientist to determine the distance from the Earth to the Sun, given that they have the measurements of angle x and distance y.

Answer:

False

Step-by-step explanation:

y = -(5/2)x

The slope is -(5/2)