Find the lateral surface area and volume of the solid object in picture

Answer:

(-7,6)

Step-by-step explanation:

Midpoints

x = (x1 + x2)/2

y = (y1 + y2)/2

-6 = (-5 + x2)/2

x2 - 5 = -12

x2 = -7

2 = (-2 + y2)/2

y2 - 2 = 4

y2 = 6

The length of the shadow of fence will be equal to 6 feet.

Proportionality may be defined as the term which can be used to describe or denote a relationship between two entities which are always in the same ratio. For example, the number of bananas is proportional to the number of trees with the proportionality being average number of bananas per number of trees. Here, we are given the height of house = 16 feet and length of its shadow = 24 feet and also the height of fence = 4 feet. Since, both house and fence lie in the same area they both are proportional. Let the length of shadow be x. Since, they are proportional

16/24 = 4/x

2/3 = 4/x

=> x = 12/2

=> x = 6 feet.

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The element would remain 515 grams after 17 years.

Isotopes are two or more different atom types that share the same atomic number and place in the periodic table but have different quantities of neutrons in their nuclei, resulting in various nucleon numbers.

Given Data

the initial mass of a sample of Element X is 610 grams

Element X is a radioactive isotope such that every 70 years, its mass decreases by half.

Since the half-life, or the number of years after which an isotope decays to half its original level, is stated to be 70 years.

k = [tex]\frac{2}{70}[/tex]

k= 0.0099

Equation-

N = 610e⁻⁰°⁰⁰⁹⁹ˣ

x = time

time = 17

N = 610 e⁻⁰°⁰⁰⁹⁹⁽¹⁷⁾

N = 610(0.845)

N = 515.49

The element would remain 515 grams after 17 years.

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The dimensions of the given right triangle would be 5.66 inches and 11.31 inches.

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

Let the legs of the triangle be x and y

Using the Pythagorean theorem:

c² = a²+b²

So the hypotenuse will be:

x² + y² = 8²

x² + y² = 64

x² = 64 - y²

So the area of the triangle is:

A = 1/2bh

A = 1/2xy

⇒16 = 1/2xy

32 = xy

x = 32/y

x² = 1024/y²

Substitute the above value in x² = 64 - y² and solving for y we get:

1024/y² = 64 - y²

1024 = 64y²- y⁴

This can be written as:

y⁴ - 64y² + 1024 = 0

Thus y = 4√2 = 5.66

x = 64/(4√2)= 16/√2 = 8√2 = 11.31

Therefore, the dimensions of the given right triangle would be 5.66 inches and 11.31 inches.

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True, cube the scale factor while finding the area of a scaled copy.

The scale factor is the ratio of two equal lengths in two similar geometric objects. The fundamental formula for calculating the scale factor is the size of the former shape is  Scale factor = Dimension of the new shape ÷ Dimension of the original shape. The area of a scaled element is equal to the squared scaling factor. If the scale factor is three, the area of the new item will be nine times, or three times, that of the original object. The area scale factor is equal to the square of the length scale factor. As a result, s2 is the surface scaling factor. If this is reversed, a solution to the situation at hand will be offered. The area has a scale factor of 2.

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1. Remember

Means

Therefore,

2. Remember that we have to solve what's inside the parenthesis first. Therefore,

____________________________________________

Slope-Intercept Form - Solution and Explanation

____________________________________________

Hello! So...

We are given the following to convert:

Convert into Slope-Intercept Form

(-2, 5), slope = -4

____________________________

1. Compute the line equation y = mx + b for slope. In this case, our slope (m) equals -4, and passes through (-2, 5).

____________________________

2. Determine the y-intercept. In this case, b = -3.

____________________________

3. Now, construct the line equation (y = mx + b), where m = -4 and b = -3. Then, you will have your converted solution in Slope-Intercept Form.

Slope-Intercept Form:

[tex]y=-4x-3[/tex]

___________________________________________

Hope this helps! If not, feel free to comment on the matter and I will see what else I can do to assist your further. However, if this does help, lmk! Thanks and good luck!

The non-real solutions of the polynomial expression are x = 2 + i√11 and x = 2 - i√11

The equation of the polynomial expression is given as:

x^4 – 7x^3 + 23x^2 – 29x – 60 = 0

Also, we have the following points

(-1, 0), (0, -60), (2.5, -60), (4, 0)

Write out the x-intercepts

(-1, 0) and (4, 0)

This means that

x = -1 and x = 4

So, we have

x + 1 = 0 and x - 4 = 0

Multiply

(x + 1)(x - 4) = 0

Divide the polynomial equation x^4 – 7x^3 + 23x^2 – 29x – 60 = 0 by (x + 1)(x - 4) = 0

Using a graphing calculator, we have

x^4 – 7x^3 + 23x^2 – 29x – 60/(x + 1)(x - 4) = x^2 - 4x + 15

So, we have

x^2 - 4x + 15

Next, we solve the quadratic expression using a quadratic formula

So, we have

x = (-b ± √(b² - 4ac))/2a

This gives

x = (4 ± √((-4)² - 4 * 1 * 15))/2 * 1

So, we have

x = (4 ± √-44)/2

This gives

x = (4 ± 2√-11)/2

Divide

x = 2 ± √-11

So, we have

x = 2 ± i√11

Split

x = 2 + i√11 and x = 2 - i√11

Hence, the non-real solutions are x = 2 + i√11 and x = 2 - i√11

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Using transformations, it is found that the transformation from [tex]y = \sqrt[3]{x}[/tex] to [tex]y = \sqrt[3]{0.5x}[/tex] is:

It is horizontally stretched by a factor of 1/2.

Transformations in the graph of a function happens when operations such as multiplication/division or sum/subtraction are applied in the definition of the function.

They can be either in the domain of the function, involving values of x, or the range, involving values of y.

For this problem, the change was that x -> x/2, that is, there was a multiplication in the domain, meaning that there was an horizontal stretch to the function.

The fact that the number was multiplied by 1/2 means that the factor of the stretch is of 1/2.

The transformation is from [tex]y = \sqrt[3]{x}[/tex] to [tex]y = \sqrt[3]{0.5x}[/tex].

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ANSWER

EXPLANATION

addox has $100.

He plans to spend $20 each time he goes to the movies.

To find out how many times he can go to the movies,

The chain rule tells us how to find derivative of a composite function., The following set of equations: R = ln(u² + v² + w²) with u = x + 2y, v = 2x-y, w = 2xy​ ƏR/Əx= 9/7 and ƏR/Əy = 9/7.

The Chain Rule is a mathematical method to differentiate a composition of the functions. From this composition of the functions, we can discern the functions' derivatives and their relationships.

In other words, the derivative of composite function = derivative of the outside function × derivative of the inside function.

The Chain Rule gives:

ƏR/Əx= ƏR/Əu × Əu/Əx + ƏR/Əv × Əv/Əx + ƏR/Əw × Əw/Əx

= [tex]\frac{2u}{u^{2}+v^{2}+w^{2} } *1 + \frac{2v}{u^{2}+v^{2}+w^{2} } *2+ \frac{2w}{u^{2}+ v^{2}+w^{2} } *2y[/tex]

When from given information we have, x = y = 1, we have u = 3, v = 1, and w = 2, so

ƏR/Əx = 6/14 × 1+ 2/14 ×2+ 4/14×2 = 18/17 = 9/7

ƏR/Əy= ƏR/Əu × Əu/Əy + ƏR/Əv × Əv/Əy + ƏR/Əw × Əw/Əy

= [tex]\frac{2u}{u^{2}+v^{2}+w^{2} } *2 + \frac{2v}{u^{2}+v^{2}+w^{2} } *(-1)+ \frac{2w}{u^{2}+ v^{2}+w^{2} } *2x[/tex]

When from given information we have, x = y = 1, we have u = 3, v = 1, and w = 2, so

ƏR/Əy = 6/14 × 2 + 2/14 × (-1) + 1/14 × 2= 18/14 = 9/7

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Answer:

1 and 403    13 and 31   13 and 31

Step-by-step explanation:

Answer:

they all are correct asu know first expression is multiple by other one so u can check

The density of the gasoline is 690 grams per litre.

The mass of the jerrycan when fully filled is 16.3 kg

He fills a 20 litre jerrycan with gasoline.

A volume  of gasoline of 1 litre has a mass of 690 grams and the empty jerrycan weighs 2.5 kg.

Therefore, the density of the gasoline can be calculated as follows:

density = mass / volume

Hence,

mass of the gasoline = 690 grams

volume of the gasoline = 1 litres

density of the gasoline = 690 / 1

density of the gasoline = 690 grams per litre.

The weight of the jerrycan when filled with gas can be calculated as follows:

1 litre of gas = 690 grams

20 litres gas = 13800 grams

Hence,

1000 grams  = 1kg

13800 grams = 13.8 kg

Therefore,

weight of the jerry can when filled with gas = 13.8 + 2.5 = 16.3 kg

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Solution

From the given graph

The zeros of the given graph are

Converting the zeros to roots gives

The factorized form of the equation of the given graph is

Hence, the answer is option B

Solution

For this case we know that the distance covered by the plane is 1350 mi and the velocity 400 mph

We also know that the distance is given by:

D= vt

Let D= Distance travelled by the car and airplane

Vp= Vc+ 400 (Velocity of the plane)

1350 = (Vc +400)*t

150 = Vc * t

We can solve for t and we got:

t= 150/Vc

Replacing in the first equation we got:

1350= (Vc+400)* (150/Vc)

Solving for Vc we got:

1350= 150 + 60000/Vc

1200 = 60000/Vc

Vc= 60000/1200= 50 mph

Then the velocity of the car is Vc= 50mph and for the plane

Vp= 50+ 400= 450 mph

The solution for the inequality 3(x + 2) > x is given by:

B. {x | x > -3}.

An inequality is solved similarly to an equality, in which we isolate the desired variable.

The biggest difference is the fact that the solution for the inequality won't be a single value like the solution for the equality, it will be a range containing infinity real values.

For this problem, the inequality is given as follows:

3(x + 2) > x.

Applying the distributive property, we have that:

3x + 6 > x.

Now we move x to the left side and 6 to the right side, both with inverse signals, hence:

3x - x > -6.

2x > -6

x > -6/2

x > -3.

Hence the correct option for the inequality in this problem is given by option B.

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Using ASA congruence rule, we have PS = PK.

What does congruence of triangles mean?
Two triangles are said to be congruent if all three corresponding sides and all three corresponding angles have the same size. You can move, flip, twist, and turn these triangles to produce the same effect. When relocated, they are parallel to one another. Mathematics uses the term "congruence" to describe when two figures have similar size and shape. In essence, two triangles are congruent if and only if they follow the four congruence rules. Finding all six dimensions, though, is crucial. As a result, only three of the six variables can be used to evaluate the congruence of triangles. Triangles that are congruent have comparable sides and equivalent angles.

Given, in ΔPQR we have ,
PQ = PR
and ∠PRR = ∠PQR ⇒ 180° - ∠PQR = 180° - ∠PQR ⇒  ∠PQR = ∠PSQ -(i)

Now, in ΔPSQ and ΔPRK;
∠SPQ = ∠RPK
∠Q = ∠R , given
∠SPQ = ∠RPQ
so, by ASA congruence  we have , ΔPSQ = ΔPRK
Thus, PS = PK.

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Answer:

  y = 1/2cos(x/2 -5π/4) -1

Step-by-step explanation:

You want the equation of the shifted and scaled cosine function shown in the graph.

A point on a function f(x) will be translated (right, up) = (h, k) by the transformation ...

  g(x) = f(x -h) +k

A function will be vertically expanded by a factor of p and horizontally expanded by a factor of q by the transformation ...

  g(x) = p·f(x/q)

The graph shows a cosine function with a peak-to-peak amplitude of 1, which is 1/2 the parent function's amplitude, so p=1/2.

The period is (9π/2 -π/2) = 4π, which is twice the period of the parent cosine function, so q=2.

The first peak of the graphed waveform is at x=5π/2, and the midline of the graphed waveform is y=-1, so we have (h, k) = (5π/2, -1).

Putting these transformations together, we find the equation of the graph to be ...

  y = 1/2cos((x - 5π/2)/2) -1 . . . . . . scaling applied before translation

  y = 1/2cos(x/2 -5π/4) -1

The length of JK is 42.

JL is a line and K is the mid-point of that line.

   J____________.___________L

                              K

From this we get:

JK = KL

JL = JK + KL

JL= 2JK = 2KL

Here it is given that,

JK = 6x and JL = 13x - 7

JL = 2JK

13x - 7 = 2× 6x

13x - 7 = 12x

x = 7

We have to find the length of JK

JK = 6x

    =6× 7

    = 42

Therefore the length of JK is 42.

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He should have divided both sides by -10.

Answer:

It's 5.31

Explanation:

Using a linear function, the constraints for the values of x and of y, respectively, are given as follows:

A linear function, in slope-intercept format, is modeled according to the following rule:

y = mx + b

In which:

In the context of this problem, we have that:

Thus the linear function that models the depth of the submarine after x seconds is given by:

f(x) = -50 - 10.5x.

This rate is for 5 seconds, hence the constraint for x is 0 ≤ x ≤ 5, and the minimum depth attained by the submarine is:

f(5) = -50 - 10.5(5) = -102.5 ft.

Hence the constraint for y is given as follows:

-102.5 ≤ y ≤ -50.

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Answer:

There is no solution.

Step-by-step explanation:

The absolute value of a number is the distance between that number and zero. It doesn't deal with negative numbers. For example, if you were playing a board game and were told to move back 6 spaces, you would be moving -6 spaces, but 6 spaces away from where you were. Absolute value focuses on how far you moved from where you were. So, an absolute value can't be negative.

we have the equations

equate both equations

First iteration

For x=1

For x=2

For x=1.5

the answer must be less than 1.5 and greater than 1

so

Verify each option

A ----> 13/8=1.625 -----> is not a solution

B ----> 23/16=1.4375 ---> could be an approximate solution

C ---> 25/16=1.5625 ----> is not a solution

D ---> 7/4=1.75 ----> is not a solution

therefore

Answer: y = 2x² + 2x - 60

Step-by-step explanation:

        We will write this in factored form since we are given the roots and leading coefficient. This will be written in the form y = c(x - a)(x - b) where c is the coefficient and a & b are the roots.

        y = c(x - a)(x - b)

        y = 2(x + 6)(x - 5)

        Now, we will distribute so we end up with the standard quadratic equation form.

        y = 2(x + 6)(x - 5)

        y = 2x² + 2x - 60

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Answer:

Step-by-step explanation:

[tex]3x+x+(x+70)=180[/tex]

[tex]5x+70=180[/tex]

[tex]5x=180-70[/tex]

[tex]5x=110[/tex]

[tex]x=110/5[/tex]

x = 22°

"x" is the second angle: 22°

"3x" is the first angle: 3(22) = 66°

"x + 70" is the third angle: 22 + 70 = 92°

22 + 66 + 92 = 180

Hope this helps

Solution

For this case the unitary circle is given by:

this unitary circle is important for the trigonometric identities

Can be used also to solve inequalities

Can be used also in physics applications and in linear algebra

From the given information, we know that the mean and standard deviation are, respectively,

From the 68-95-99 rule, we know that approximately 95% falls between 2 standard deviation of the mean, that is,

and

From equation (A), we have

then

Now, from equation (B), we get

Therefore, the answer for part a is: Approximately 95% of the students have commute between 10.6 and 27.4 miles

In this case, we need to find the z score value for 6.4 miles and 31.6 miles and then obtain the corresponding probabilty from the z-table.

For 6.4 miles, the z score is

and for 31.6 miles, the z score is

Now, we need to find the corresponding probability between z=-3 and z=3, which is 0.9973

Therefore, the answer for part b is: Approximately. 0.9973 of the students have commute distances between 6.4 miles and 31.6 miles

ANSWER:

STEP-BY-STEP EXPLANATION:

We have that the given expression is the following:

The other expression is the following:

We simplify in each case:

This means that the expressions are equal