Select all the correct answers.Which two transformations preserve the side lengths and angles of the preimage? a reflection across line a stretch by a factor of 4 a dilation by a factor of 4 a translation to the right

Given:

The flight of a fireworks rocket is given by the function:

Required:

How long will the rocket take to reach its maximum height?

Explanation:

We will first find critical points

To check maximum and minimum value

Asnwer

The quadratic equation is factorizable if the result of the discriminant gives a perfect square. This is a kind of a perfect square test

We know that a quadratic equation is factorizable by the use of the discriminant. The discriminant is something that could tell us about the character of the quadratic equation.

We know that the discriminant is the square root of b^2 - 4ac. If the result of this operation is a perfect square, then we can know that the equation as we have it in any particular situation is factorizable.

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For at lest 60 social interaction:

So social interaction is:

60 - 64 4

65 - 69 3

70 - 74 0

75 - 79 4

So student of these social interaction is:

So total 11 students had at lest 60 social interaction.

The graph is based on amplitude.

Given the function:

f(t) = 5sin3t

To draw the graph of above function.

The function g(t) = sin t is a periodic function with amplitude [tex]a_{0}[/tex] = 1 and period [tex]t_{0}[/tex] = 2[tex]\pi[/tex]

For our case, the 5 that multiplies g (t) increases the amplitude so that,

a = 5 x 1 = 5 and the 3 that multiplies the variable increases the period being t = 2[tex]\pi[/tex] x 1/3 = 2[tex]\pi[/tex]/3

What is Graph?

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter. Each object in a graph is called a node.

See the graph in the bottom of explanation.

Hence, The graph is based on amplitude.

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The point (11 , 37 ) does not lies in the given  function f(x) = 4x - 3. Since the values x , y does not satisfy the condition .

How to check whether the points satisfy the equation :

Given function, f(x) = 4x - 3

also given a point (11 , 37)

to check whether the given point satisfies the given function,

(x , y) = (11,37)

substitute values of x and y in the given function,

y = 4x - 3

37 = 4 x (11) - 3

37 = 44 -3

37 ≠ 41

∴ the given points (11,37 ) does not satisfy the given function

f(x) = 4x-3.

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Answer:

5x + 3 = 0

OR

35*35 /35 -35

hope this helps

Solution

We are given the equation

Room temperature, C = 73 degrees

Temperature at time t = 0, is T = 174 degrees

Therefore, the equation becomes

We want to find t = ?, when T = 131 degrees and k = 0.0688919

Therefore, the answer is

Answer:

The counter example is:

Explanation:

We want to show that the statement "The sum of any two different odd numbers is divisible by 4" is false.

We need to use the smallest positive numbers. T

Answer:

647 ft

Explanation:

Given the below figure;

To determine the value c, we have to take the sine of angle 18 degrees as seen below;

Let's cross multiply;

Let's divide both sides by sin 18;

So the distance the plane has flown is 647 ft

Explanations:

Let the first pont be P (-5, 3)

Let the second point be Q (-2, -3)

The distance between two points is given by the equation:

The distance between the two points is √45 units

Given:

n = 700

p = 0.09

q = 1 - p = 0.91

The formula for standard deviation is:

hence:

ANSWER

σ ≈ 7.57

Simplify the equation.

Thus to complete the square 9 is added to both side of the equation.

Answer: 9

Given:

Given the quadratic equationt

Required: Solution to the quadratic equation

Explanation:

Write the quadratic equation as

Option C is correct.

Final Answer: The solution t the squadratic equation is x = 8 only.

By probability, If you played 891 times, you expect to lose $16.

Total Possible Throws = 385

Number of throws = 273

Let P(T) be the Probability that the player makes the next throw

P(T) = 273 / 385

The probability that the player makes the next three throws is then given by:

= P(T) × P(T) × P(T)

= 273 / 385 × 273 / 385 × 273 / 385

= (273 / 385)²

= 0.35653794139

= 0.357

Let P(T') be the probability the player doesn't make the next two throws

P(T') = 1 - P(T)

P(T') = 1 - 0.357

P(T') = 0.643

The expected gain for the player turns is given by:

(Probability of making both throws) * $27 + (Probability of NOT making both throws) x ( - $16 )

= 0.357 × $27 - 0.643 × $16

= $9.639 - $10.288

= - $0.649

b.

The probability that he makes the next 891 throws.

= P(T)⁸⁹¹

= (273/385)⁸⁹¹

Let P(T') be the probability the player doesn't make the next three throws

P( T' ) = 1 - P( T )

P( T' ) = 1 - 19.449493e-134

P( T' ) = 1

The expected gain or loss for the player turns is given by:

(Probability of making all 626 throws) * $5 + (Probability of NOT making all 626 throws) x (-$10)

= (273/385)⁸⁹¹ × 27 + 1 × - 16

= - $16

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see the figure below to better understand the problem

we have that

tan(x)=452/767

============================================================

Explanation:

Let y be the angle just to the left of angle x. Angle x and angle y are adjacent.

Since line a is parallel to line b, this means y = 120 because the 120 degree angle and angle y are alternate interior angles.

Then we can say:

x+y = 180

x+120 = 180

x = 180-120

x = 60

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An alternative method:

Let w be the angle just above angle x

The angle marked "120 degrees" and angle w are corresponding angles. They are congruent if and only if line a is parallel to line b.

This makes w = 120

Solving w+x = 180 leads to x = 60 similar to the previous set of steps.

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

Side note:

The 115 degree angle is never used. It was probably put in there as a distraction.

The given expression is,

As the area is equal to 45 and equating the areas.

(taking positive values)

The answer is 7

Jenny's deck is a square deck and has a side length equal to that of the back of Jenny's house. The area of a square of length L is;

Thus, we have;

Therefore, the length of the back of Jenny's house is 18 feet.

Answer: X + 3

Step-by-step explanation:

Sum hints as to an addition statement and it specifies a variable X and the number 3 so the expression would be X + 3.

SUM MEANS ADDITION

HERE IT MEANS THE ADDITION OF x and 3

written as

[tex]x + 3[/tex]

HOPE THIS HELPS

Since we're working on a circumference, the sum of all the angles must be 360°

This way,

Solving for x :

Solution:

Given that Maria has 5 7/8 yards of fabrics, and she makes a jacket with 3 3/4 yards, this implies that the amount of fabric left after making her own jacket is evaluated as

Since she is to make the same jacket for her friend, she requires another

But the amount of fabric left after Maria has made her own jacket is

Hence, Maria does not have enough fabric left for her friend.

From the arc-angle relationship

By comparing both pictures, we have that

now, we must isolate MJH, hence we have

and we must move 76 to the right hand side as -76, this gives

Finally, mJH is 34.

Answer:

[tex]\frac{(b+5)}{(b-4)}[/tex]

Step-by-step explanation:

[tex]\frac{3b^{2}-75}{3b^{2}-27b + 60}[/tex]

[tex]\frac{3(b^{2}-25)}{3(b^{2}-9b + 20)}[/tex]

Simplify numerator:

where [tex](b^{2} -25) = (b-5)(b+5)[/tex]

[tex]\frac{3(b-5)(b+5)}{3(b^{2}-9b + 20)}[/tex]

Simplify denominator:

looking at [tex]b^{2} - 9b + 20[/tex]

where a = 1

b = -9

and c = 20

We are looking for two numbers that sum to -9 and multiply to 20:

-5 + (-4) = -9

-5 * (-4) = 20

so [tex]b^{2} -9b+20 = (b-5)(b-4)[/tex]

insert into denominator:

[tex]\frac{3(b-5)(b+5)}{3(b-4)(b-5)}[/tex]

remove: 3(b-5) from numerator and denominator:

[tex]\frac{(b+5)}{(b-4)}[/tex]

Given:

The radius of a can is (3x^2-10). The height of the can is 2x.

To find:

The surface area of a label that would be glued around the can.

Solution:

It is known that the curved surface area of the cylinder is given by:

So, the curved surface area of the given cylinder is:

Thus, the answer is given above.

The simplest form of the fraction 18/16 is 9/4.

Fraction:

A fraction is a number that represents part of a whole.

A fraction is written in the form p/q, where q ≠ 0.

Given,

There has been given a fraction 18/16, that has to be simplified.

The steps to simplifying fractions,

First, we have to find the GCD (or HCF) of numerator and denominator

GCD of 16 and 18 is 2

Now we have to divide both the numerator and denominator by the GCD

16 ÷ 2

18 ÷ 2

Now we get the reduced fraction as, 8/9.

Therefore, 16/18 simplified to lowest terms is 8/9.

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a) The output is 45

b) The input was -4

Here, we want to use the relationship between the input and the output to answer the questions

While x is our input, f(x) is given as our output

The relationship between the two is given as;

a) Here, we have an input, and we want to get the output

To solve this, we just need to substitute the value of -8 for x in the relation

We have this as follows;

b) Here, we have the output, but we want to get the input

What this simply mean is that we are to find the value of x

We simply substitute 21 for f(x)

Thus, we have;

The question has already provided a formula to determine the width (W). The question also provides the thickness as well as the number of times (n) the paper would be folded. Hence, we have;

The notebook paper would have to be 0.45216 inches wide

The formula has also been provided that would help in calculating the length of a long rectangular piece of paper. We've been given the thickness of the paper and the number of times it (n) it would be folded. Therefore, we now have;