m={y:y is a multiple of 3,5<y<10}
​

Hello!

√4 = ±2

√4x = ±2x

The total distance of the obstacle course can be calculated by finding the distance between each pair of consecutive points and adding them up. The distance between two points (x1, y1) and (x2, y2) can be calculated using the formula: distance = sqrt((x2 - x1)^2 + (y2 - y1)^2).

Using this formula, we can calculate the distances between each pair of consecutive points as follows:

Start to Tire Race: distance = sqrt((-40 - (-40))^2 + (-30 - (-10))^2) = 20 yards

Tire Race to Rope Climb: distance = sqrt((40 - (-40))^2 + (-30 - (-30))^2) = 80 yards

Rope Climb to Monkey Bars: distance = sqrt((40 - 40)^2 + (20 - (-30))^2) = 50 yards

Monkey Bars to Finish: distance = sqrt((10 - 40)^2 + (20 - 20)^2) = 30 yards

Adding up all these distances, we get a total distance of 20 + 80 + 50 + 30 = 180 yards for the obstacle course.

Answer:

\(tan(x)=\frac{4}{3}\)

Step-by-step explanation:

In the unit circle,

- \(cos(a)=\frac{x}{r}\) where \(a\) is the degree measure, \(x\) is the x-coordinate of the triangle, and \(r\) is the radius of the circle

- \(sin(a)=\frac{y}{r}\) where \(a\) is the degree measure, \(y\) is the y-coordinate of the triangle, and \(r\) is the radius of the circle

Thus, since tangent is equal to sine over cosine, we can simplify our knowledge to:  \(tan(a)=\frac{sin(a)}{cos(a)}=\frac{y}{x}\)

In this problem, \(sin(x)=\frac{4}{5}\). We can conclude from our previous knowledge that \(y=4\) and the radius is 5.

Similarly, \(cos(x)=\frac{3}{5}\), which means \(x=3\) and the radius is the same, at 5.

Since we know that \(x=3\) and \(y=4\), we can find the value of  \(tan(x)\) by using the formula \(tan(x)=\frac{y}{x}\) and plug in the numbers.

Therefore, \(tan(x)=\frac{4}{3}\).

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Answer:

83 kids total

Step-by-step explanation:

There are 54 girls on the playground. There are 25 fewer boys than girls on the playground. How many kids are on the playground?

girls = 54

boys = 54 - 25 = 29

54 + 29 = 83 kids total

kids that are on the playground are 83.

Merging objects and identifying them since one big bunch is done through addition. In arithmetic, addition is the technique of adding two or more integers together. The product can meet are the quantities that are included, and the outcome of the operation, or the final response, is referred to as the sum.

The total number of girls that are present is 54

The data given is that there are

25 fewer boys taht are4 present

The total number of boys will be

boys = 54 - 25 = 29

The number of kids that are present will be the total of boys and girls that are present.

Kids = boys + girls

54 + 29 = 83 kids total

The quantity of kids that are present in the playground is 83.

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The solution of the expression will be;

⇒ x = - 88

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The algebraic expression is,

'' one eighth times quantity x plus 32 end quantity equals negative 7.''

Now,

Since, The algebraic expression is,

'' one eighth times quantity x plus 32 end quantity equals negative 7.''

Hence, We can formulate;

⇒ 1/8 (x + 32) = - 7

⇒ x + 32 = - 56

⇒ x = - 56 - 32

⇒ x = - 88

Thus, The solution of the expression will be;

⇒ x = - 88

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Answer:

Slope = 1.5/-3

Step-by-step explanation:

Slope = rise/run

Answer:

Find the exact value of tan 45º = 1/1 = 1.

Find the exact value of cos 30º = √3/2.

Find the exact value of csc 60º = 2√(3)/3

Step-by-step explanation:

math

\( \sf \longrightarrow \: 5 \bigg( \: n - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{n}{1} - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{10 \times n - 1 \times 1}{1 \times 10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{10n - 1}{ 10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: \: \frac{50n - 5}{ 10} = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: \: 2(50n - 5) =1(10) \\ \)

\( \sf \longrightarrow \: \: 2(50n - 5) =10 \\ \)

\( \sf \longrightarrow \: \: 100n - 10=10 \\ \)

\( \sf \longrightarrow \: \: 100n =10 + 10\\ \)

\( \sf \longrightarrow \: \: 100n =20\\ \)

\( \sf \longrightarrow \: \:n = \frac{2 \cancel{0}}{10 \cancel{0}} \\ \)

\( \sf \longrightarrow \: \:n = \frac{1}{5} \\ \)

Answer:-

To solve the equation \(\sf 5(n - \frac{1}{10}) = \frac{1}{2} \\\) for \(\sf n \\\), we can follow these steps:

Step 1: Distribute the 5 on the left side:

\(\sf 5n - \frac{1}{2} = \frac{1}{2} \\\)

Step 2: Add \(\sf \frac{1}{2} \\\) to both sides of the equation:

\(\sf 5n = \frac{1}{2} + \frac{1}{2} \\\)

\(\sf 5n = 1 \\\)

Step 3: Divide both sides of the equation by 5 to isolate \(\sf n \\\):

\(\sf \frac{5n}{5} = \frac{1}{5} \\\)

\(\sf n = \frac{1}{5} \\\)

Therefore, the solution to the equation \(\sf 5(n - \frac{1}{10})\ = \frac{1}{2} \\\) is \(\sf n = \frac{1}{5} \\\), which corresponds to option (d).

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Answer:

Area =136cm²

Area =2(wl+hl+hw)=2·(2·7+6·7+6·2)=136cm²

The required surface area of the rectangular prism is 396 cm².

Given that,
Hannah has a rectangular prism with a length of 7 cm, a width of 2 cm, and a height of 6 cm.
The surface area of the rectangular prism is to be determined.

A rectangular prism is a transparent solid of cuboid shape, Whose opposite faces are congruent.

The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.

The surface area of the rectangular prism is given by
Surface area = 2( length * width + width * height + height * length )
                     =  2 (7 * 12 + 12 * 6 + 6 * 7)
                     = 396 cm²

Thus, the required surface area of the rectangular prism is 396 cm².

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Answer:

2x - 3 = 11

x = -21

Step-by-step explanation:

Answer:

draw the diagram and multiply 5x20

Each x represents each student surveyed if count each x we will find that Janet surveyed

0 hours-- 1 student

1 hour -- 2 students

2 hours--3 students

3 hours -- 5 students

4 hours -- 1 student

5 hours -- 1 student

6 hours -- 3 students

7 hours -- 2 students

8 hours -- 2 students

If we sum them we will find that Janet surveyed 20 students

Answer:

6b-4a+13

Step-by-step explanation:

3a-6b+3-7a+10

3+10=13

3a-7a=-4a

6b-4a+13

Answer:

13

Step-by-step explanation:

The prime factorization of 45 written as exponents from least to greatest is 45 = 3² × 5¹

Prime factorization is a way of expressing a number as a product of its prime factors. A prime number is a number that has exactly two factors, which includes 1 and the number.

Using prime factorisation, we shall consider the first five prime numbers which are; 2, 3, 5, 7, and 11.

45 cannot be divided by 2 without a remainder so we use 3;

45/3 = 15

15 can also be divided by 3 so;

15/3 = 5

3 cannot divide 5 without a remainder so we use 5;

5/5 = 1

hence;

45 = 3 × 3 × 5

45 = 3² × 5¹

Therefore, the prime factorization of 45 written as exponents from least to greatest is 45 = 3² × 5¹

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The best statement that describes the strategy for estimating the perimeter of the figure (please see the attached diagram) is the option;

Ad the lengths of the horizontal and vertical segments, and then add 5 because the diagonal side is 4 units wide and 2 units tall

An estimate is an approximation of a true value, which is a value that is close to the actual value of the measured quantity.

Please find attached a diagram of the possible figure created with MS Word

The length of the side of the sides of the possible figure in the figure, obtained from a similar question on the internet are;

Base length = 5 units

Height = 4 units

The figure has a diagonal side which is 4 units wide and 2 units tall.

The length of the slant side, found using Pythagorean theorem can be obtained as follows; Length = √(4² + 2²) = 2·√5 ≈ 5

The correct option is therefore to add the lengths of the horizontal and vertical segments, and then add 5 because the diagonal side is 4 units wide and 2 units tall

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Answer:

A= 29

B=34

C=117

Step-by-step explanation:

A triangle has three sides and a triangle always adds up to be 180

A + B + C = 180

B = A + 5

C = 4A + 1

Plug in.

A + A + 5 + 4A + 1 = 180

6A + 6 = 180

6A = 174

A = 29

Now since you found A, find the other two by plugging A in!

C = 4(29) + 1

C = 117

Plug in the B equation

B = 29 + 5

B=34

Check your answers

29 + 117 + 34 = 180

We need to know about profit and loss inorder to solve the problem. The cost of one shirt is $12.8, the amount of money Mrs. Jackson received after selling all t-shirts is $2998.50, the total profit made is $1078.50 and the profit percentage is 56.17%.

We know that Mrs. Jackson bought 150 t-shirts for $1920, we need to fisrt find the cost of one t-shirt, we can do that by dividing the total cost by the number of t-shirts.

cost of one =1920/150=$12.8

Next we need to find the total selling price of all the t-shirts given that each t-shirt is sold at $19.99

total selling price= 150x19.99= $2998.50

The total profit made by Mrs. Jackson can be calculated by subtracting the cost price from the selling price.

profit=2998.50-1920=$1078.50

The profit percentage with respect to the cost price can be calculated as

profit percentage= 1078.50/1920x100=56.17%

Therefore the cost of one t-shirt is $12.8, the amount Mrs. Jackson received on selling all the t-shirts is $2998.50, the profit made is $1078.50 and the profit percentage is 56.17%.

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Your question was incomplete. Please refer below for the entire question.

Mrs. Jackson bought 150 T-shirt for 1920 from a factory.

i) calculate the cost of one T-shirt

The T-shirt are sold at $19.99 each.

Calculate

ii) the amount of money Mrs Jackson received after selling All of T-shirt.

iii) the TOTAL profit made

iv) the profit made as a percentage of the cost price, giving your answer correct to the nearest whole number.

Answer:

58/33 or 1.75

Step-by-step explanation:

Answer:

answer: 90°

i made a whole page to show working out

hope this helps!! :)

The solution to the system of equations is (x, y) = (-4, 12) or (3, 5).

simultaneous equations, or system of equations Two or more equations in algebra must be solved concurrently (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a distinct solution. Even then, a solution is not assured.

We can solve this system of equations by substitution or elimination. Here, we will use substitution:

Substitute y in the first equation with its expression from the second equation:

x + (x^2 - 4) = 8

Now, we have a quadratic equation in x:

x^2 + x - 12 = 0

Factor the quadratic equation:

(x + 4)(x - 3) = 0

So, either x + 4 = 0 or x - 3 = 0:

x = -4 or x = 3

Substitute each value of x into either equation to find the corresponding value of y:

If x = -4, then y = (-4)^2 - 4 = 12

If x = 3, then y = 3^2 - 4 = 5

Therefore, the solution to the system of equations is (x, y) = (-4, 12) or (3, 5).

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Answer:

80 degrees

Step-by-step explanation:

The sum of the angles in a triangle is 180 degrees so we can create the equation 70+30+x=180. This solves out to 80 so x=80 degrees.

Answer:

132 square feet

Step-by-step explanation:

The formula for the area of a triangle is 1/2 * b * h. B stands for base and h stands for height. 1/2 multiplied by the base, 10, is 5. We then multiply 5 by 12 which is 60. Let's look at the rectangle now. The area of a rectangle is length by width. The length is 12ft and the width is 6ft. 12 * 6 = 72. 72+60=132 square feet.

Answer:

12

Step-by-step explanation:

Answer:

\(12\)

Step-by-step explanation:

1) Simplify 4² to 16.

\( \frac{ - \frac{1}{3} \times - 33 - \frac{1}{2} \times 16 }{ \frac{1}{4} } \)

2) Move the negative sing to the left side.

\( \frac{ - ( - \frac{33}{3}) - \frac{1}{2} \times 16 }{ \frac{1}{4} } \)

3) Simplify 33/3 to 11.

\( \frac{ - ( - 11) - \frac{1}{2} \times 16 }{ \frac{1}{4} } \)

4) Simplify 1/2 × 16 to 16/2.

\( \frac{ - ( - 11) - \frac{16}{2} }{ \frac{1}{4} } \)

5) Simplify 16/2 to 8.

\( \frac{ - ( - 11) - 8}{ \frac{1}{4} } \)

6) Remove parentheses.

\( \frac{11 - 8}{ \frac{1}{4} } \)

7) Simplify 11 - 3 to 8.

\( \frac{3}{ \frac{1}{4} } \)

8) Invert and multiply.

\(3 \times 4\)

9) Simplify.

\(12\)

Therefor, the answer is 12.

The three equivalent equations are 2 + x = 5, x + 1 = 4 and -5 + x = -2. So, correct options are A, B and E.

Two equations are considered equivalent if they have the same solution set. In other words, if we solve both equations, we should get the same value for the variable.

To determine which of the given equations are equivalent, we need to solve them for x and see if they have the same solution.

Let's start with the first equation:

2 + x = 5

Subtract 2 from both sides:

x = 3

Now let's move on to the second equation:

x + 1 = 4

Subtract 1 from both sides:

x = 3

Notice that we got the same value of x for both equations, so they are equivalent.

Next, let's look at the third equation:

9 + x = 6

Subtract 9 from both sides:

x = -3

Since this value of x is different from the previous two equations, we can conclude that it is not equivalent to them.

Now, let's move on to the fourth equation:

x + (-4) = 7

Add 4 to both sides:

x = 11

This value of x is also different from the first two equations, so it is not equivalent to them.

Finally, let's look at the fifth equation:

-5 + x = -2

Add 5 to both sides:

x = 3

Notice that we got the same value of x as the first two equations, so this equation is also equivalent to them.

So, correct options are A, B and E.

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Complete question is:

Which of the following equations are equivalent? Select three options.

2 + x = 5

x + 1 = 4

9 + x = 6

x + (- 4) = 7

- 5 + x = - 2

Answer:

First algorithm will have fewer comparison than second as the value of n grows.

Step-by-step explanation:

As n grows, first algorithm will perform better then other.

Consider the ratio of number of comparison done by second algorithm with number of comparison done by first algorithm, the ratio will be \($n^{3 / 2} /(n \log (n))=\sqrt{n} / \log n=\log 2^{\sqrt{n}} / \log n$\)

Since log function is monotonically increasing function and \($2^{\sqrt{n}}>n$\) for all \($n>4$\). Hence first algorithm will have fewer comparison than second as the value of n grows.

As the line passes through the coordinates (0, 60), its slope is given as y = 10x + 60.

The incline of a line determines its steepness. "Curve overflow" is the name of a gradient-related mathematical equation (the change in y divided by the change in x). The slope is really the ratio of something like the vertical (rise) to the horizontal (run) change in elevation between any two places. The slope-intercept style of an equations is used to represent a straight line only when equation is expressed as y = mx + b. The y-intercept is positioned where the slope of the line is m, b is b, and (0, b). For instance, the y-intercept and slope of the calculation y = 3x - 7 (0, 7). The line has a slope of m, and b value at the y-intercept, and (0, b). As

given

The chart coordinate should therefore appear as follows:

(1, 75)

(2, 70)

(3, 80)

(4, 95)

(4, 100)

Moreover, a line runs between (0, 60) and (2, 80)

Hence, all that is left to do is determine the line's y-intercept and slope:

Change in x over Change in Y = 20 2 = 10

Given that the line passes through the coordinates (0, 60), the y-intercept is [the value of y when x = 0] = 60.

As the line passes through the coordinates (0, 60), its slope is given as y = 10x + 60.

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Answer

y=9/3x

Step-by-step explanation: