Robert is building a deck in his backyard. Each piece of wood measures 42.5 inches. If he has 8 boards, how long are they altogether?

Answer:

x = 3.1

Step-by-step explanation:

Begin with the right triangle on the left.  Looking at the 39° angle, the 7m side is the hypotenuse and the side marked  h  (see attached image) is the opposite side.  The trig ratio using opposite and hypotenuse is sine.

[tex]\sin{39^\circ}=\frac{h}{7}\\\\h=7\sin{39^\circ}[/tex]  Hold this thought!

Focus attention on the right triangle on the right.  Looking at the 55° angle,  h is the opposite side and the side marked  x  is the adjacent side.  The trig ratio using opposite and adjacent sides is tangent.

[tex]\tan{55^\circ}=\frac{h}{x}\\\\x\tan{55^\circ}=h\\x\tan{55^\circ}=7\sin{39^\circ}\\x=\frac{7\sin{39^\circ}}{\tan{55^\circ}} \approx 3.1[/tex]

N is the integer between {3,4,5}.so we can find all possible values of n is 2 and 8.

An integer is a whole number that can be positive, negative or zero. Examples of integers are -5, 1, 5, 8, 97, and 3,043.The integers are generated from the set of counting numbers and the operation.

Subtract the same number from both sides. Multiply both sides by the same positive number. Divide both sides by the same positive number. Multiply both sides by the same negative number and reverse the sign.

Now we solve

3n+4 <19

3n+4-4<19-4

3n<15

n<5

so n is less than and equal to 5 it will be {3, 4, 5].

10n/[tex]n^{2}[/tex]+16  >1

10n> [tex]n^{2}[/tex] +16

0> [tex]n^{2}[/tex]-10n +16

0>[tex]n^{2}[/tex] -8n -2n +16

0> n(n-8)-2(n-8)

0> (n-8) (n-2)

So         n-2<0          n-8<0

             n<2              n<8

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The triangle with sides of length 5 cm 3 cm and 4 cm is a right angled triangle because (3, 4, 5) is a Pythagorean triple.

We know that if non zero real numbers a, b, c follows Pythagoras theorem  c² = a² + b², the numbers a, b, c is called as a Pythagorean triple.

And these numbers are nothing but the sides of right triangle.

Here we have been given the triangle with sides of length 5 cm 3 cm and 4 cm

Assume that p = 5 cm, q = 3 cm and r = 4 cm

p² = 25

q² = 9

and r² = 16

Consider q² + r² = 16 + 9

q² + r² = 25

q² + r² = r²

Since given numbers follows Pythagoras theorem, (3, 4, 5) is a  Pythagorean triple.

And p = 5 cm, q = 3 cm and r = 4 cm are the lengths of sides of right triangle.

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The cost of 48 water bottles will be $5.9.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that there are 24 water bottles and costs $2.95. The cost of 48 water bottles will be calculated as,

24 water bottles = $2.95

1 water bottle = $2.95 / 24

48 water bottle = ( 2.95 x 48 ) / 24

48 water bottles = $5.9

Hence, the cost will be $5.9.

The complete question is given below.

24 water bottles for $2.95. What is the cost of 48 water bottles?

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Answer:

A

Step-by-step explanation:

-13 + 18=5

-13 is less than 5

The area of the garden whose length and width as given in the task content is; 30 (x + 2) square units.

It follows from the task content that the expression which represents the area of the garden plot whose dimensions are as given.

Recall that Area, A = length × width.

Therefore, since length = 6 (√(x + 2)) units

The width = (5 √(x + 2) ) units

Hence, the area of the garden plot as required in the task content is; 6 (√(x + 2)) × ( 5 √(x + 2) )

= 30 (x + 2) square units

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The system of linear equations Ax + 3y = a, 3x + ay = A has no solutions for any value of a.

To determine if the system of linear equations Ax + 3y = a, 3x + ay = A has no solutions for any value of a, we can use the elimination method.

We want to eliminate one of the variables, so let's start by multiplying the first equation by 3 and the second equation by -1.

This gives us:

3Ax + 9y = 3a, -3x - ay = -A.

Now we add the equations together to get:

2Ax + 8y = 3a - A.

Now we can see that the equation is not solvable as there is no value of a that will make the equation true. Therefore, the system of linear equations Ax + 3y = a, 3x + ay = A has no solutions for any value of a.

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Unreasonable Time is the nest option for running the group raffle at an upcoming assembly to give away a prize.

As given that;

Reasonable Time: Algorithms with a polynomial efficiency or lower (constant, linear, square, cube, etc.) are said to run in a reasonable amount of time.

Unreasonable Time: Algorithms with exponential or factorial efficiencies are examples of algorithms that run in an unreasonable amount of time.

Your school is considering running the group raffle at an upcoming assembly to give away a prize.

We have to write a brief explanation of what advice you would give them.

We can use the unreasonable time because  running the group raffle at an upcoming assembly to give away a prize cannot complete their work is the given amount of time.

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Answer: 10.56 cups.

Step-by-step explanation:

1 liter = 4.22 cups; 1.5 liters = 6.34 cups; 2 liters = 8.45 cups; 2.5 liters = 10.56 cups.

Answer: The answer is -1.6

Step-by-step explanation:

(7x-5)=2x-13

     +5      +5

7x=2x-8

5x=-8

divide -8 by 5= -1.6

Answer:

-1.6

Step-by-step explanation:

2100 divided by 10.50 = 200 hours

200 hours divided by 8 hour days = 25 days

Answer:

A) 25 days

B) I got 4.6 so try 4 and 5 and 4.6

Step-by-step explanation:

A) 8x10.50=84

2100/84=25 days

B) 84x5=450

2100/450=4.6

Answer:

The first option seems about right

Answer: 73.2

Step-by-step explanation:

78/2 is 39. Now, use the pythagorean theorem to find the hypoteuse (in this case the spine), which is about 73.2

Answer:

1/9 for left

15/16 for second

Step-by-step explanation:

1/3 x 1/2 x 2/3 = 1/9

5/4 x 3/2 x 1/2 = 15/16

Answer:

[tex]\frac{1}{9}[/tex] m³

[tex]\frac{5}{16}[/tex] ft³×÷

[tex]3\frac{1}{8}[/tex] m³

[tex]12\frac{1}{2}[/tex] m³

x = 20 in.

l = 10 in.

Step-by-step explanation:

[tex]2\frac{4}{5}=\frac{14}{5}[/tex]

[tex]1\frac{3}{7}=\frac{10}{7}[/tex]

[tex]3\frac{1}{8}=\frac{25}{8}[/tex]

Answer:

1800

Step-by-step explanation:

Let us solve this question by Modular Airthmatic.

Let the lowest 4 digit number be X.

X= 1 (mod 5)

X =2 (mod 5)

X=3 (mod 5)

X =4 (mod 5)

X=1+5 t where t is any integer.

1+5 t=2 (mod 5)

5 t=1 (mod 5 )

5 is the Modular Inverse of modulo 5

t=1 (mod 5)

t =1+5 u : u= any integer.

X becomes 1+ 5 (1+5u )=6+25 u

6+25u =3 (mod 5)

25 u= -3 (mod 5)=2 (mod 5)

25 is Modular Inverse of Modulo 5

u=2 (mod 5)

u =2+5 v : v= any integer.

X becomes 6 +25 (2+5 v)=56+125 v .

56 +125 v=4 (mod 5)

125 v=-52 (mod 5)=3 (mod 5)

125 is Modular Inverse of modulo 5

v = 3 (mod 5)

v =3 +5 w where w is any integer.

For lowest 4 digit number, take

w=200

X=1003 : Lowest 4 digit number.

Take w=201

X=208 : Next number.

For 4 digit largest number, take

w=1995

X= 9978 : Largest number.

No. of Numbers =(1995 - 200 )+1=1800 □Ans.

Answer:

1800 ways.

Step-by-step explanation:

Four hemispheres are present in the shaded area. One large hemisphere and three smaller hemispheres each have a radius of 18 cm.

Consequently, the hemisphere's total surface area is 3(pi)R2. A semicircle has a curved line and a straight line that are both equal to the circle's diameter. The curving line is 2R in length while the straight line is (pi)R in length. So, 2R + (pi)R is the semicircle's total perimeter.

The shaded regions' area is calculated as follows:

initially, area of a hemisphere = 2r2 square units

the area of three small hemispheres

(2*3.14*6 r).3 = 226.08 cm2

Area of the larger hemisphere

2*3.14*18^2 = 2034.72cm^2

Total area of the shaded regions = 226.08 + 2034.72 = 2260.8cm^2

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Answer:

Approximately - 9.7%

Step-by-step explanation:

By using the percent change formula, you will be able to calculate the percent decrease.

(b-a)/a times 100 <-- (percent change formula)

(120-133)/133 times 100

-13/133 times 100

-9.7744%

Answer:

  9.8% decrease

Step-by-step explanation:

You want the percent decrease from 133 to 120.

The amount of change as a percent can be found using the formula ...

  percent change = ((new value)/(old value) -1) × 100%

Here, the new value is 120, and the old value was 133. The change is ...

  percent change = (120/133 -1) × 100% ≈ (0.90226 -1) × 100%

  = -0.09774 × 100% ≈ -9.8%

The change from 133 to 120 is a 9.8% decrease.

__

Additional comment

When the sign of the change is negative, as here, the change is a decrease. If the sign is positive, the change is an increase. That is, a change of -9.8% is a 9.8% decrease. (You can use either the minus sign or the word "decrease" to indicate the direction of the change. The acceptable form of the answer will depend on your grader.)

<95141404393>

Answer:

That looks good

Step-by-step explanation: wait why is this here?

Answer:

perpendicular

Step-by-step explanation:

perpendicular if the product of their slopes is equal to -1

Parallel lines have equal or identical slopes

Answer:

(20/3,0) is your x-intercept

Step-by-step explanation:

To find x-intercept, let y = 0

[tex] \displaystyle{3x = 20}[/tex]

Solve for x, divide both sides by 3:

[tex] \displaystyle{ \dfrac{3x}{3} = \dfrac{20}{3}} \\ \\ \displaystyle{ x = \dfrac{20}{3}}[/tex]

Hence, the x-intercept is (20/3,0). We write in order pair since it's x-intercept and x = 20/3 at y = 0

Answer:

98--(&_$4567;'#234678

Answer:

N(AUB)=28+45

=73

Step-by-step explanation:

Answer:

its A

Step-by-step explanation:

Answer:

The correct answers is -8.3232

Step-by-step explanation:

B. The function shown on the graph has a smaller rate of change, but a higher starting point.

Rate of change = slope of a linear graph.

Given the linear function, [tex]y=4x+2[/tex] , the rate of change here is represented by the slope of the line, which is 4.

Let's find the rate change of the function represented on the graph using slope formula:

Rate of change = [tex]\frac{y2-y1}{x2-x1}[/tex]

Use coordinates of any two points on the line. Let's take,

[tex](0,4)= (x1,y1)\\(1,7)=(x2,y2)[/tex]

Rate of change = [tex]\frac{7-4}{1-0} = 3[/tex]

Rate of change of the linear function of the graph = 3.

Thus the function on the graph has a smaller rate of change, than the function, y = 4x + 2.

The starting value of a function is the y-intercept, that is, the value of y, when x = 0. It is the point at which the line intercepts the y-axis.

The starting value of the linear function, y = 4x + 2 is 2.

The starting value of the function on the graph is 4. At this point, x = 0.

Thus, the function on the graph has a higher starting point.

The statement that correctly compares the function shown on this graph with the function y= 4x+2 is:

B. The function shown on the graph has a smaller rate of change, but a higher starting point.

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The robot is moving in the direction indicated by the formula ((i)²¹*(-i)²²)d, or in the beginning direction.

What is complex plain?

When a line is rotated in the complex plane either clockwise or anticlockwise, it is multiplied by -i or I depending on which direction the line is rotated. The direction vector is rotated 90 degrees in the clockwise direction to make a right turn. It is the same as increasing the complex number by -i.

A left turn is represented as a 90° anticlockwise rotation of the direction vector. It is comparable to increasing the complex number by i.

There are 21 left turns of the robot. The direction vector will now be di21. Once it has been rotated 22 times to the right, the direction vector will now be  (di²¹)*(-i)²²=d((i)²¹*(-i)²²).

Consequently, the robot's current direction is:

d((i)²¹*(-i)²²)= di²¹⁺²²=di⁴³= d(-i)= -di

No matter what, the direction will always be the same, hence the sequence is irrelevant.

Hence, the equation that will indicate where the robot is moving is  ((i)²¹*(-i)²²)d, or in the starting direction. Furthermore, the final direction it faces does not depend on the order.

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Answer: C, 217

Step-by-step explanation: