p(x) = -3x - 1
graph the linear function

Step-by-step explanation:

sadly we don't know anything about the size of the mirror on the ground, or if e.g. the 1.65 m from the mirror mean from the edge of the mirror or from the x at the center of the mirror.

so, we must assume the mirror as a dot without any significant lengths in the calculation.

we have 2 right-angled triangles.

1. the small one : from Yusuf's eyes to the ground at his feet to the x on the mirror on the ground.

2. the large one : from the top of the building to the bottom of the building on the ground to the x on the mirror on the ground.

the mirroring creates a dilation from the large triangle to the small triangle through the point x on the mirror.

in other words, all the angles stay the same, and there is one constant scale factor for all the lengths of one triangle to the other, making both triangles similar.

that means that the scale factor "f" of the ground distances from the small to the large triangle is

10.25 / 1.65 = 1025 / 165 = 6 35/165 = 6 7/33 =

= 6.212121212...

the scaling from Yusuf's height (well, his eye level) to the height of the school must follow the same ratio :

school height / Yusuf's eye level =

= h/1.55 = 10.25/1.65

h = 10.25 × 1.55 / 1.65 = 1025 × 155 / 16500 =

= 9.628787879... m ≈ 9.63 m

the school is approximately 9.63 m tall.

FYI : this is the same principle as with a camera. the lens (and the mirror inside if applicable) create a dilated "projection" onto a film or an array of digital light sensors, so that the captured image retains all the angles and all the length ratios of the original.

but to know from the picture e.g. how tall the original was, we need to know also the distance from which the picture was taken. otherwise this can't be answered.

The area of the circle is 201 m².

So, the area of the circle:

We know that 4a = 2πr, now calculate r as follows:

Rounding off: 8m

Area of circle:

Rounding off: 201 m²

Therefore, the area of the circle is 201 m².

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Answer:

Step-by-step explanation:

Use table for f(x) related questions and equation for g(x) related questions and both for the last one.

Answer:54

Step-by-step explanation:

54mis the answer

Answer: x = 58

Step-by-step explanation:

The angles are alternating interior angles. This means that the angles are equal.

So x = 58

Answer:

Step-by-step explanation:

Find the value of s on one side of the equation to isolate it.

1.1=s+2.3/3

First, switch sides.

[tex]\sf{\dfrac{s+2.3}{3}=1.1}[/tex]

Multiply by 3 from both sides.

[tex]\sf{\dfrac{3\left(s+2.3\right)}{3}=1.1* \:3}[/tex]

Solve.

1.1*3=3.3

s+2.3=3.3

Then, subtract by 2.3 from both sides.

s+2.3-2.3=3.3-2.3

Solve.

Subtract.

3.3-2.3=1.0=1

s=1

Therefore, the final answer is s=1.

I hope this helps, let me know if you have any questions.

Answer:

243

Step-by-step explanation:

-9^2 = -9 * -9 = 81

81 * 3 = 243

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

The rules of the patterns are 3 + 3x and 6 + 6y

The patterns are given as:

For pattern x, we have the following highlights:

Start = 3

Rule = Add 3

This means that the nth term of pattern x is:

Pattern x = 3 + 3x

For pattern y, we have the following highlights:

Start = 6

Rule = Add 6

This means that the nth term of pattern y is:

Pattern y = 6 + 6y

For pattern x, set x = 0, 1, 2 and 3

So, we have

3 + 3x = 3 + 3(0) = 3

3 + 3x = 3 + 3(1) = 6

3 + 3x = 3 + 3(2) = 9

3 + 3x = 3 + 3(3) = 12

For pattern y, set y = 0, 1, 2 and 3

So, we have

6 + 6x = 6 + 6(0) = 6

6 + 6x = 6 + 6(1) = 12

6 + 6x = 6 + 6(2) = 18

6 + 6x = 6 + 6(3) = 24

Next, we plot the graphs of both patterns (see attachment) where the blue line represents pattern 1, and the other represents the second pattern

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Answer:

a opened because a closed means that number ond more

Step-by-step explanation:

Answer: -20 degrees

Step-by-step explanation:

The temperature drops 5 degrees/hour.

Find temperature after 4 hours.

Since we are not given a starting temperature, we can only say how much the temperature has dropped after the 4 hours.

5 degrees/hour x 4 hours = 20 degrees

Temperature has dropped so your answer will be negative.

Step-by-step explanation:

slope intercept form is: y = ax + b

so, 19x - 19y = 18

-19y = -19x +18

[tex]y = \frac{ - 19x}{ - 19} - \frac{18}{19} [/tex]

[tex]y = x - \frac{18}{19} [/tex]

i hope that this helps

Answer:

Step-by-step explanation:

You want the area and perimeter of a rectangle that is 54 inches in length and 30.4 inches in width.

The area formula is ...

  A = bh

We can use the length as the "base" and the width as the "height", so we have ...

  A = (54 in)(30.4 in) = 1641.6 in²

The area of the television screen is 1641.6 square inches.

The perimeter of a rectangle is given by the formula ...

  P = 2(L +W)

Using the given length and width, the perimeter is found to be ...

  P = 2(54 in + 30.4 in) = 2(84.4 in) = 168.8 in

The perimeter of the television screen is 168.8 inches.

The area of the rectangular television screen is 1641.6 square inches and the perimeter of the television screen is 84.4 inches.

What is the area of a rectangle?
The area a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the product of its length and breadth. Its area is the space that the rectangle's boundary encloses.
Mathematically, area of a rectangle = length * width = l * w
What is the perimeter of a rectangle?
The perimeter is defined as the sum of all sides of the rectangle. Mathematically, perimeter of a rectangle = 2(length + width) = 2*(l + w)

Given, the length of the television screen = l = 54 inches
The width of the television screen = w = 30.4 inches
Using the formula mentioned in the literature above,
Area of the television screen = l * w = 54*30.4 = 1641.6 square inches
Also, perimeter of the television screen = l + w = 54 + 30.4 = 84.4 inches
Thus, the area of the rectangular television screen is 1641.6 square inches and the perimeter of the television screen is 84.4 inches.

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Answer:

4x² + 29x + 7 = (4x + 1)(x + 7)

Step-by-step explanation:

Like terms are terms with same variable and same power.

       Perimeter = sum of all the sides

                         = 3x² + 1 + 15x + 6 + x² + 14x

                         = 3x² + x² + 15x + 14x + 1 + 6

Combine like terms,

                        = 4x² + 29x + 7

Factorize:

        Sum = 29

  Product = 4*7 = 28

   Factors = 1 , 28    {28 + 1 = 29 & 28*1 = 28}

Rewrite the middle term using the factors,

                           = 4x² + x + 28x + 7

                           = x(4x + 1) + 7(4x + 1)

                           = (4x + 1)(x + 7)

Answer:

SSS

Step-by-step explanation:

From the question, we were told that Garcia's bike rentals cost $38 to rent bike for 9 hours.

We are to find how many hours will a customer use the bike per dollar.

This can also be likened to calculating miles per gallon.

if i can drive 300 miles on 10 gallons of gas then my miles per gallon is 300/10 = 30 mpg.

So, hours per dollar is also a division problem too.

(9 hours)/($38)

= 9/38

= 0.2368

= 0.24 hours per dollar (to the nearest hundredth)

The value that will be equivalent to the expression will be 5625³.

It should be noted that an expression is simply used in Mathematics to illustrate or show the relationship between the variables.

The equivalent expression for (3 to the power of 2 • 5 to the power of 4) to the power of 3 will be illustrated as:

= (3² × 5⁴)³

= (9 × 625)³

= 5625³

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Answer:

x=71 y=109

Step-by-step explanation:

Answer: 1.44

Step-by-step explanation:

The fraction 3 and 6/25 is equal to 1.44 when written as a fraction.

Answer:

3.24

Step-by-step explanation:

6/25 can be read as 6 divided by 25, which is 0.24. Add that to 3 and you get 3.24.

The percentage of the students that like rap are also in grades 9–10 is 32%.

Given data:

Grade 9-10 for Rap = 40

Row total for grade 9-10 = 125

Now let determine the percentage of rap in grades 9-10 using this formula

Percentage of rap in grades 9-10 = Grade 9-10 for Rap / Row total for grade 9-10

Let plug in the formula

Percentage of rap in grades 9-10 = 40 /125

Percentage of rap in grades 9-10 = 0.32 × 100

Percentage of rap in grades 9-10 = 32%

Therefore we can conclude that 32% is the percentage of rap grade 9-10.

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Answer:

Simplifying

7 + 2x = 4x + -3

Reorder the terms:

7 + 2x = -3 + 4x

Solving

7 + 2x = -3 + 4x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4x' to each side of the equation.

7 + 2x + -4x = -3 + 4x + -4x

Combine like terms: 2x + -4x = -2x

7 + -2x = -3 + 4x + -4x

Combine like terms: 4x + -4x = 0

7 + -2x = -3 + 0

7 + -2x = -3

Add '-7' to each side of the equation.

7 + -7 + -2x = -3 + -7

Combine like terms: 7 + -7 = 0

0 + -2x = -3 + -7

-2x = -3 + -7

Combine like terms: -3 + -7 = -10

-2x = -10

Divide each side by '-2'.

x = 5

Simplifying

x = 5

The probability of that the first 40 feet in a roll contain no flaws is ≈ .3012

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Θ = μ = [tex]\frac{100 foot}{3 flaws}[/tex]

a ) We assume that the length until the first flaw follows an exponential distribution.

Probability density function of exponential distribution:

f(x) = [tex]\frac{1}{Θ} e^{\frac{-x}{Θ} } = \frac{1}{100/3}e^{-x/(100/3)} = \frac{3}{100}e^{-3x/100}[/tex]

The first 40 feet in a roll of 100 feet contain no flaws if the first flaw occurs after 40 feet.

The probability is the integral over the corresponding interval:

the further calculation has been shown in fig. attached

since equation was not possible to write here

b) We assume that the length until the first flaw follows an exponential distribution.

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Answer:

-7

Step-by-step explanation:

5 * 3 = 15. 15 - 8 = 7; so, 8 - 15 = -7.

By means of algebra properties for powers and roots, the radical expression [tex]\sqrt[3]{81\cdot x^7\cdot y^{9}\cdot z^{5}}[/tex] is equivalent to the expression [tex]4.327 \cdot x^{\frac{7}{3} }\cdot y^{3} \cdot z^{\frac{5}{3} }[/tex].

In this question we need to simplify an expression by using algebra properties, that is, to transform an expression involving three variables (x, y, z), roots and power operators into an expression with only power operators, that is, where only we see power operators, no root operators of any kind. Now we proceed the entire procedure in detail:

In accordance to the algebra properties related to power and radical expressions, the radical expression [tex]\sqrt[3]{81\cdot x^7\cdot y^{9}\cdot z^{5}}[/tex] is equivalent to the power product [tex]4.327 \cdot x^{\frac{7}{3} }\cdot y^{3} \cdot z^{\frac{5}{3} }[/tex].

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Answer:

No solution

Step-by-step explanation:

2- 3x + 4 + x = -2x + 1

2  -3x  + 4 + x = -2x + 1

6  -3x + x = -2x + 1

6  -3x + x = -2x + 1

6  -2x = -2x + 1

6  -2x = -2x + 1

move -2x to the right by adding 2x on both sides

6  -2x = -2x + 1

+2x         +2x

6  =  + 1

is 6 equal to 1?

No, so No solution