Solve the system of equations below.

4x – 6y = 30
3x + 7y = 80

x =
, y =

Answer:

f(-1)=-1

Step-by-step explanation:

substitute -1 for x:

f(-1)=1-(-1)^2+(-1)^3

then solve,

f(-1)=1-1-1

f(-1)=-1

The theoretical probability that the arrow will hit the small square on the upper left is approximately 9.8%. (Option A)

To determine the theoretical probability, we first need to calculate the areas involved. Let's start by finding the area of the entire circular target. The formula for the area of a circle is given by A = π * r², where 'r' is the radius. Plugging in the given radius (36 inches) into the formula:

A_circle = π * (36 inches)² ≈ 4069.73 square inches.

Next, we need to calculate the area of the small square in the upper left corner. Since the square is positioned at a corner of the circle, it forms a quarter of a circle. The area of this quarter circle can be calculated as follows:

A_quarter_circle = ¼ * A_circle. = ¼ * 4069.73 = 1017.43

Now, let's find the area of the square. The formula for the area of a square is A_square = side², where 'side' is the side length. Plugging in the given side length (5 inches) into the formula:

A_square = (5 inches)² = 25 square inches.

However, there are four identical squares inside the quarter circle, so the total area of all the squares combined is:

Total_Area_squares = 4 * A_square.

Now, to calculate the probability of hitting the small square in the upper left corner, we divide the area of that square by the area of the quarter circle:

Probability = (A_square / A_quarter_circle) * 100. = 25 / 1017.43 * 100 =  9.8%.

Hence the correct option is (a).

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Answer:

66

Step-by-step explanation:

84 = mean + 3sd

60 = mean - sd

sd = mean - 60

84 = mean + 3(mean - 60)

84 = mean + 3mean - 180

264 = 4mean

mean = 66

Using a trigonometric identity, considering the given value of the tangent of theta, the secant of the same angle is given by:

[tex]\sec{\theta} = \pm \sqrt{\frac{11}{8}}[/tex]

According to the following identity:

[tex]\sec^2{\theta} = 1 + \tan^2{\theta}[/tex]

In this problem, the tangent squared is given as follows:

[tex]\tan^2{\theta} = \frac{3}{8}[/tex]

Hence the secant is given by:

[tex]\sec^{2}{\theta} = 1 + \tan^2{\theta}[/tex]

[tex]\sec^{2}{\theta} = 1 + \frac{3}{8}[/tex]

[tex]\sec^{2}{\theta} = \frac{11}{8}[/tex]

[tex]\sec{\theta} = \pm \sqrt{\frac{11}{8}}[/tex]

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Answer:

Plus-or-minus StartRoot eleven-eighths EndFraction

Step-by-step explanation:

The answer above is correct.

Answer:

10.

Step-by-step explanation:

As the 2 Figures are similar the correspond sides are in the same ratio.

We see that BC = 5.0 and FG = 2.5, so each side in EFGH is 1/2 of its correspond side in ABCD.

Perimeter of EFGH , therefore, is

2.5 + 2 + 4 + 1.5

= 10.

Answer:

scale factor = 1.2

Step-by-step explanation:

the scale factor is the ratio of corresponding sides image to original, that is

EZYD → TRAP

corresponding sides are the comparable sides on both , that is

EZ → TR

then

scale factor = [tex]\frac{EZ}{TR}[/tex] = [tex]\frac{12}{10}[/tex] = 1.2

Answer:

O C. 5.76 in2

Step-by-step explanation:

To find the area of a square, the formula is

length x width = area

length = 2.4

width = 2.4

2.4in x 2.4in = 5.76 in2

in2 is the part of the answer since  in x in = in2

Answer:

4/6 = 6/9

Step-by-step explanation:

Because 4/6 = 2/3 and 6/9 = 2/3

Answer:

4/6 = 6/9

Step-by-step explanation:

Answer: 6.96 in^2

Step-by-step explanation:

Trapezoid Area

A = [tex]\frac{a+b}{2} h[/tex]

= [tex]\frac{1.5 + 3.3}{2} * 2.9[/tex]

= [tex]\frac{4.8}{2} * 2.9[/tex]

= 2.4 * 2.9

= 6.96

Answer:

8 kilometers in one hour

Step-by-step explanation:

4:30/4

30 [tex]divided[/tex] by 4

7.5

4 divided by 4

1

7.5 minutes to 1 kilometer

since there are 60 minutes in a hour

60/7.5 = 8

8 x 1 = 8

Answer:

x = 88 degrees

Step-by-step explanation:

Its really easy. All you have to do is subtract all the known angles from 360 since a quadrilateral has 360 degrees

360 - 106 - 114 - 52 = 88

Hope this helped!

Answer:

x = 88°

Step-by-step explanation:

                                        x + 52 + 114 + 106     = 360°

                                                        x   + 272     = 360

                                                                       x = 360 - 272

                                                                      [tex]\sf \boxed{x= 88^ \circ}[/tex]

Answer:

[tex] \frac{13x}{7 } + \frac{6}{7} = 0[/tex]

Answer:

30.6716 feet

hope it helps you

If the data values are as shown in the picture I have attached, then the following should help.

Answer: 226.56  m²

Step-by-step explanation:

  We need to find the area of three rectangles and two triangles.

    The triangles: 34.56 m²

A = [tex]\frac{B*H}{2}[/tex]

-> Since they are both congruent, we will skip dividing by two

A = B * H

A = 7.2 * 4.8

A = 34.56 m²

   The rectangles: 192 m²

A = L * W

-> We have two that are congruent, and one that is not

A = 10 * 6 * (2, since there are two)

A = 120 m²

-

A = L * W

A = 7.2 * 10

A = 72 m²

-

72 m² + 120 m² = 192 m²

   Total surface area:

34.56 m² + 192 m² = 226.56  m²

Answer:

140 in²

Answer as a decimal rounded to the nearest hundredth = 140.00 in²

Step-by-step explanation:

Area of a triangle = 1/2 × base × height

Given:

Substituting the given values into the formula:

⇒ Area = 1/2 × 20 × 14

             = 140 in²

Answer as a decimal rounded to the nearest hundredth = 140.00 in²

Answer:

140 square inches

Step-by-step explanation:

Formula to find the area of a triangle is A = 1/2 × b × h.

So plug in the numbers

A= 1/2 x 20 x 14

A= 20 x 14 / 2

A = 280/ 2

A(Area) is equal to 140 square inches

Answer:

622.13 square units

Step-by-step explanation:

Area of the composite figure = area of parallelogram + area of circle

Note: 2 semicircles = 1 full circle

Area of the figure = a*h + πr²

Where,

a = 22

h = 11

r = ½ of 20 = 10

Plug in the value into the equation

Area = 22*11 + π*11²

Area = 242 + π*121

Area = 622.13271108 ≈ 622.13 square units (nearest tenth)

Answer:

Step-by-step explanation:

556.2

Answer:

The answer is D

Step-by-step explanation:

If you use. MAD then all you have to do is multiply add then divide so the 1/4 +1/16 +. 1/64 + 1/256 = 1/3 so round it and. its 1/3 (1/4)

Answer: choice d

Step-by-step explanation: i asked my mom :/

Since all the angles of the first triangle are different, it is a scalene triangle, Similarly, since all the sides of the second triangle is also different, it is a scalene triangle.

Triangles is a 3-D shape with 3 sides and angles.  The types of triangle that we have include;

Since all the angles of the first triangle are different, it is a scalene triangle, Similarly, since all the sides of the second triangle is also different, it is a scalene triangle.

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The chronological order of the events described is: Earliest record of the Chinese Lo Shu magic square, Hypatia becomes the head of the Platonist School, Aryabhata writes the famous aryabhatiya, The discovery of the Fibonacci Sequence, Florence Nightingale develops the polar area diagram, and First African American woman to visit space.

To classify events chronologically we must know the date on which they occurred.

The chronological organization can be from the oldest event to the most recent or vice versa. In this case the organization of the events will be done from the oldest to the most recent.

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Answer:

C. 31 [tex]\frac{1}{6}[/tex]

Step-by-step explanation:

1. Convert mixed numbers into improper fractions:

[tex]\frac{29}{4}[/tex] · 2² + ( [tex]\frac{17}{2}[/tex] - 2) ÷ 3

2. Calculate within the parenthesis:

[tex]\frac{29}{4}[/tex] · 2² + [tex]\frac{13}{2}[/tex] ÷ 3

3. Calculate the exponent:

[tex]\frac{29}{4}[/tex] · 4 + [tex]\frac{13}{2}[/tex] ÷ 3

4. Multiply and divide (left to right):

29 + [tex]\frac{13}{2}[/tex] ÷ 3

29 + [tex]\frac{13}{6}[/tex]

5. Add:

[tex]\frac{187}{6}[/tex]

6. Convert the improper fraction to a mixed number:

= 31 [tex]\frac{1}{6}[/tex]

hope this helps!

Answer:

m = 6.557

Step-by-step explanation:

Subtract 10 from both sides:

4m^2 = 172

Divide both sides by 4:

m^2 = 43

take the square root of both sides:

[tex]\sqrt m^2 = \sqrt{43[/tex]

m = 6.557

Does that make sense?

Answer:

13 feet

Step-by-step explanation:

if we assume the angle on the ground to the truck is a ninety degree angle

Answer:

A.a .gov or .org website on green roofs

b.an article from a government organization on how green roofs improve air quality

d. newspaper articles reporting on how green roofs absorb heat in cities

Step-by-step explanation:

because i did it

Answer:

abd

Step-by-step explanation:

Answer:

Look at the photo and goodluck

Step-by-step explanation:

x - 25 = 75

=> x = 75 + 25

=> x = 100

x + 19 = 50

=> x = 50 - 19

=> x = 31

.90° + 45° + x = 180°

{Sum of angles of triangles = 180°}

135° + x = 180°

x = 45°

61° + 90° + x = 180

151 + x = 180

x = 29°

31° + 90° + x = 180°

122° + x = 180°

x = 58°

x + 15° +90° = 180°

x = 180° - 105°

x = 75

~Tulpe⚘

Answer:

Step-by-step explanation:

How Do You Determine Whether Values in a Table are Proportional? To see if multiple ratios are proportional, you could write them as fractions, reduce them, and compare them. If the reduced fractions are all the same, then you have proportional ratios.