What is the area of the fire pit? (Use 3.14 for pi.)

The sum of the angles of the triangle expressed in two ways are x + 1/2x + 3/2x and 2x + x + 3x/2

It is important to note that the sum of the angles of a triangle is equal or equivalent to 180 degrees.

We have the angle measurements as;

Substitute the values

x + 1/2 x + 3/2x = 180

Find the lowest common multiple

2x + x + 3x /2 = 180

Add the numerators

6x/2 = 180

cross multiply

6x = 360

x = 60

Hence, the expression is x + 1/2x + 3/2x and 2x + x + 3x/2

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To form an isosceles triangle Jefferson should plot the third point at (4,2).

Any triangle with two sides that have the same length is said to be an isosceles triangle. If the two sides of a triangle are congruent, then the angle across from them must likewise be, according to the theorem that explains the isosceles triangle. As a result, the two angles of an isosceles triangle that are on opposite sides with equal numbers are equal in size.

Given, Jefferson is plotting the vertices of an isosceles right triangle on a coordinate graph.

the given points are,

(-2,-4) (4,-4)

Let, x₁ = -2, y₁ = -4

x₂ = 4, y₂ = -4

distance between (-2,-4) (4,-4) is given as,

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(4 - -2)² + (-4 - -4)²]

= √[(4 + 2)² + (-4+ 4)²]

= √[(6)² + (0)²]

= √[(6)²

= 6

now verifying with other options,

1). For points (-2, -9),

Distance between (-2, -4) and (-2, -9) = √[(-2 + 2)² + (-4 + 9)²] = √5

Similarly, distance between (4, -4) and (-2, -9) = √[(4 +2)² + (-4 + 9)²] = √61

side is not equal. So the triangle is not isosceles.

2). For a point (3, 1),

Distance between (3, 1) and (-2, -4) = √[(3 + 2)² + (1 +  4)²] = 5√2

Distance between (3, 1) and (4, -4) = √[(3 - 4)² + (1 +  4)²] = 26

side is not equal. So the triangle is not isosceles.

3). For a point (-2,0),

Distance between (-2, 0) and (-2, -4) = √[(-2 + 2)² + (-4 + 0)²] = 4

Distance between (-2, 0) and (4, -4) = √[(-2 - 4)² + (0 + 4)²] = 2√13

side is not equal. So the triangle is not isosceles.

4). For a point (4, 2),

Distance between (4, 2) and (-2, -4) = √[(4 + 2)² + (2 + 4)²] = 6√2

Distance between (4, 2) and (4, -4) = √[(4 - 2)² + (2 + 4)²] = 6

Sides are equal so the triangle formed is an isosceles triangle.

Therefore, the third coordinate is (4, 2).

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The complete question is,

Jefferson is plotting the vertices of an isosceles right triangle on a coordinate graph. He has plotted the two points shown. Where should he plot the third point?

The point is on the graph is (-2,-4) (4,-4)

The options is

(-2,-9)

(3,1)

(-2,0)

(4,2)

The mass of one art book is 0.8 kg, and the mass of one biology book is 0.6 kg

Let's denote the mass of one art book by "a" and the mass of one biology book by "b".

From the given information, we have two equations:

6a + 4b = 7.2 (equation 1)

2a + 3b = 3.4 (equation 2)

We can solve for "a" and "b" by using any method of solving linear equations, such as substitution or elimination.

Here, we'll use elimination method. Multiplying equation 2 by 3 and subtracting it from equation 1 multiplied by 2, we get:

12a + 8b - (6a + 9b) = 14.4 - 10.2

6a - b = 4.2 (equation 3)

Multiplying equation 2 by 2, we get:

4a + 6b = 6.8 (equation 4)

Multiplying equation 3 by 6, we get:

36a - 6b = 25.2 (equation 5)

Adding equations 4 and 5, we get:

40a = 32

a = 0.8 kg

Substituting this value of "a" in equation 2, we get:

2(0.8) + 3b = 3.4

1.6 + 3b = 3.4

3b = 1.8

b = 0.6 kg

Therefore, the mass of one art book is 0.8 kg, and the mass of one biology book is 0.6 kg.

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Answer:

x = - \(\frac{3}{4}\) , x = 1

Step-by-step explanation:

4x² = x + 3 ← subtract x + 3 from both sides

4x² - x - 3 = 0 ← in standard form

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 4 × - 3 = - 12 and sum = - 1

the factors are - 4 and + 3

use these factors to split the x- term

4x² - 4x + 3x - 3 = 0 ( factor the first/second and third/fourth terms )

4x(x - 1) + 3(x - 1) = 0 ← factor out (x - 1) from each term

(x - 1)(4x + 3) = 0 ← in factored form

equate each factor to zero and solve for x

4x + 3 = 0 ( subtract 3 from each side )

4x = - 3 ( divide both sides by 4 )

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

x - 1 = 0 ( add 1 to both sides )

x = 1

solutions are x = - \(\frac{3}{4}\) , x = 1

Answer:

the answer is   d t d T ​ = c ( T + T 0 ​ )

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

Arrange into parentheses and start at the innermost parentheses

\(5 + (2 \times (6 + (3 \div 3)))\)

Start with 3 ÷ 3

\(3 \div 3 = 1\)

Continue with the other parts of the equation in order

\(1 + 6 = 7\\7 \times 2 = 14\\14 + 5 = 19\\= 19\)

Hope this helped you understand better, have a great day!

The solution of the compound inequality is x < 3/4 or x >2.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

A compound inequality:

4x - 5 < -2 or x + 1 > 3.

Solving inequality,

4x < -2 + 5 or x > 2

4x < 3 or x > 2.

x < 3/4 or x >2.

Therefore, the solution is x < 3/4 or x >2.

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Answer:

4 = 4

Step-by-step explanation:

=> 2x = 4

Putting x = 2

=> 2(2) = 4

=> 4 = 4

Answer:

Solution,

X= 2

Now,

2x=4

plugging the value of X,

2*2= 4

4 = 4 ( hence it is true)

Answer:

\(110x-95xy+6\)

Explanation:

\(15x ( 7 - 5y ) + 3 ( 5y - x ) - ( 4x + 3 ) ( 5y - 2 )\)

expand:

\(105x-75xy+15y-3x-\left(4x+3\right)\left(5y-2\right)\)

simplify:

\(105x-75xy+15y-3x-(20xy-8x+15y-6)\)

open the brackets:

\(-20xy+8x-15y+6+102x-75xy+15y\)

\(110x-75xy-20xy+15y-15y+6\)

final answer:

\(110x-95xy+6\)

Answer:

3) x = -4 and y = 6

4) x = -1 and y = 0

5) x = 1 and y = -3

6) x = -4 and y = -3

Step-by-step explanation:

3) Add the equations:

(3x + 4y = 12) + (-3x - y = 6) (eliminate the x)

= 3y = 18

y = 18/3

y = 6

3x + 4(6) = 12

3x = 12 - 24

x = -12/3 = 4

4) Add the equations:

(-5x - 6y = 5) + (-6x + 6y = 6)

-11x = 11

x = -1

-5(-1) -6y = 5

-6y = 5 - 5

y = 0

5) 7x -4y = 19

10x - 2y = 16

Multiply the second equation by -2 to eliminate the y and add both equations.

-2(10x -2y = 16) =

(-20x + 4y = -32) + (7x - 4y = 19)

-13x = -13

x = 1

7(1) - 4y = 19

-4y = 19-7

y = 12/-4

y = 3

6) multiply the second equation by -2 to eliminate the x and then add the equations.

-2(5x - 3y = - 11) =

(-10x + 6y = 22) + (10x - 9y = - 13)

= -3y = 9

y = - 3

10x - 9(-3) = - 13

10x = -13 - 27

x = -40/10

x = -4

Let the number be x

We use addiition sign

The expression is x+15

There are a total of 8 color-wheel size combinations for the kickboard scooter. This means that customers have 8 different options to choose from when selecting the color and wheel size for their scooter.

To determine the total number of color-wheel size combinations for the kickboard scooter, we need to multiply the number of color options by the number of wheel size options.

Given that there are 4 color options (silver, red, blue, and purple) and 2 wheel size options (125mm and 180mm), we can use the multiplication principle to find the total number of combinations:

Total combinations = Number of color options × Number of wheel size options

Total combinations = 4 colors × 2 wheel sizes

Total combinations = 8

There are a total of 8 color-wheel size combinations for the kickboard scooter. This means that customers have 8 different options to choose from when selecting the color and wheel size for their scooter.

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Answer:

Step-by-step explanation:

    A,  use  three_digite  rounding  arithmetic  to compute  13- 6 and determine  the absolute,relative ,and percentage errors.

tepeat part (b) using  three – digit chopping arithmetic.

Answer:

Step-by-step explanation:

This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts.

Functions f(x) = x² + 1 and g(x) = x – 4, the value equivalent  to f(g(10)) is, 37

Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).

Vertical line test:-

Whenever we want to check whether a given expression is a function or not we can apply a vertical line test, in this test we check for a single image of x , we are getting a single image or more.

If we get more images then it will not be a function.

For example, let us take, y² = 4ax

y = ±√4ax

For single value of x we get two values of y

Hence, it will not be a function.

Given that,

f(x) = x² + 1

g(x) = x – 4

f(g(10)) = ?

f(g(x))  =  (x - 4)² + 1

           =  x² - 8x + 16 +1

           =   x² - 8x + 17

f(g(10)) =  10² - 8×10 + 17

            = 100 - 80 + 17

            = 37

The value of  f(g(10)) is 37

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The surface area of the pyramid is 113 cm².

A rectangular pyramid is a type of pyramid where the base is a rectangle and the triangular faces meet at a single point called the apex or vertex. It has five faces, including a rectangular base and four triangular faces, and it is a polyhedron with five vertices and eight edges.

The rectangular pyramid has a base of dimensions 7 cm by 5 cm, and the two large triangular faces have a height of 7.6 cm, while the two small triangular faces have a height of 8 cm.

To find the surface area of the pyramid, we need to find the area of each face and then add them up.

Area of the base:

The base of the pyramid is a rectangle with dimensions 7 cm by 5 cm, so its area is:

Area of base = length × width = 7 cm × 5 cm = 35 cm²

Area of the four triangular faces:

Each of the four triangular faces has a base of 5 cm (the width of the rectangle) and a height of either 7.6 cm or 8 cm. Using the formula for the area of a triangle, we can find the area of each face:

Area of each large triangular face = 1/2 × base × height = 1/2 × 5 cm × 7.6 cm = 19 cm²

Area of each small triangular face = 1/2 × base × height = 1/2 × 5 cm × 8 cm = 20 cm²

There are two large triangular faces and two small triangular faces, so the total area of the four triangular faces is:

Total area of four triangular faces = 2 × area of large triangular face + 2 × area of small triangular face

= 2 × 19 cm² + 2 × 20 cm²

= 78 cm²

Total surface area:

Finally, we can find the total surface area of the pyramid by adding the area of the base to the total area of the four triangular faces:

Total surface area = area of base + total area of four triangular faces

= 35 cm² + 78 cm²

= 113 cm²

Therefore, the surface area of the pyramid is 113 cm²

.

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Answer:

Amadi: 20 years old

Chima : 4 years old

The graph of the function y = 5|x - 4| is added as an attachment

From the question, we have the following parameters that can be used in our computation:

y = 5|x - 4|

The above function is an absolute value function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment

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Coordinate pairs are organized like (x,y).

To determine a coordinate pair, we can determine each coordinate individually, then put them together.

Notice how the red point sits on the very edge of the graph.

When we look at the x-axis, we can see that it occurs at the number 0 on the x-axis. In other words, the red point occurs when x=0.

When we look at the y-axis, we can see that it lines up with the number 2. In other words, the red point occurs when y=2.

Therefore, when we put the two coordinates together like (x,y), we get (0,2).

(0,2)

Answer:

depends, you can see the explanation.

Step-by-step explanation:

if you are rounding to the tens place it would be 25,690.

hundreds place - 25,700

thousands place - 26,000

Answer:

V = 29.31 cm^3

Step-by-step explanation:

The volume of a cone is given by

V = 1/3 pi r^2 h

V = 1/3 (3.14) (2)^2 (7)

V =29.30666

Rounding to the nearest hundredth

V = 29.31 cm^3

The graph of ㏑ y against x are A(1.1), B(1.5), C(1.9), D(2.3) and E(2.7) and the value of a is 5.25 and b is 1.58 .

In elementary mathematics, the term "graph" indicates a plot or a function graph. A graph is, in the language of mathematicians, a set of points and the connections between some subset of those points (which may be empty).

\(y = a*b^{x}\)

⇒ \(log_{10}\ y = log_{10}\ (ab)^{x}\)

⇒ \(log_{10}\ y = log_{10}\ y + log_{10}\ (b)^{x}\)

⇒ \(log_{10}\ y = log_{10}\ a + x.log_{10}\ (b)\)

⇒ \(log_{10}\ y = ( log_{10}\ b).x + log_{10}\ a\)

⇒ \(Y = mX + C\)

We require to put \(Y = log_{10}\ y\) against \(X = x\)

\(X = x =2,\) \(Y = log_{10} 12.8 = 1.1\)

\(X = x =4,\) \(Y = log_{10} 32.8 = 1.5\)

\(X = x =6,\) \(Y = log_{10} 83.9 = 1.9\)

\(X = x =6,\) \(Y = log_{10} 214.7 = 2.3\)

\(X = x =10,\)\(Y = log_{10} 549.8 = 2.7\)

The Y intercept of the line is approx. 0.72

\(C = log_{10}\ a\)

⇒ \(0.72 = log_{10}\ a\)

⇒ \(10^{0.72} = a\)

⇒ \(a = 5.25\)

The gradient of the line is approximately,

\(\frac{2.7-0.72}{10-0} = \frac{1.98}{10} = 0.198\)

\(m = log_{10}\ b\)

⇒ \(0.198 = log_{10}\ b\)

⇒ \(b = 10^{0.198}\)

⇒ \(b = 1.58\)

The graph of ㏑ y against x are A(1.1), B(1.5), C(1.9), D(2.3) and E(2.7) and the value of a is 5.25 and b is 1.58 .

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Answer: I don’t know :(

Step-by-step explanation:

Answer:

8

Have an amazing day!

The area of the regular polygon, given the apothem and the side length, would be 52. 5 in².

To find the area of a regular pentagon with a given apothem (a) and side length (s), we can use the formula:

Area = ( Perimeter × Apothem ) / 2

Perimeter would be :

= 5 x sides

= 5 x 6

= 30 inch

The area is therefore :

= ( Perimeter × Apothem ) / 2

= ( 30 in x 3. 5 in ) / 2

= 105 / 2

= 52. 5 in²

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Answer:

Let b = number of boys and g = number of girls.

g/b = 5/3, so g = (5/3)b

b + g = 136

b + (5/3)b = 136

(8/3)b = 136, so b = 136(3/8) = 51 boys, and g = 85 girls

There are 51 boys and 85 girls at the volleyball summer camp.

The ratio of boys to girls at the camp is 3 to 5. By applying this ratio to the total number of children at the camp (136), we find that there are 51 boys and 85 girls.

The question tells us that for every 3 boys at a camp, there are 5 girls. This means that the ratio of boys to girls is 3:5. This ratio tells us that out of every 8 (3+5) children, 3 are boys and 5 are girls.

Now it's mentioned there are 136 children in total. We divide total children by sum of the ratio to find out the number of boys and girls. 136 divided by 8 equals 17. This means there are 17 sets of 'every 8 children'.

To find the number of boys, multiply 3 (number of boys in one set) by 17 (total sets) and we get 51 boys. Using the same process for the girls, we multiply 5 (number of girls in one set) by 17 (total sets), resulting in 85 girls. Thus, among the 136 children at the camp, there are 51 boys and 85 girls.

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Answer:

a) 4.55% probability that both adults dine out more than once per week.

b) 61.80% probability that neither adult dines out more than once per week.

c) 38.20% probability that at least one of the two adults dines out more than once per week.

d) An event is considered unusual if it has a less than 5% probability of happening. Following this rule, in this problem, both adults dining out more than once per week can be considered unusual.

Step-by-step explanation:

The adults are selected without replacement, so we use the hypergeometric distribution to solve this question.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}\)

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

In this question:

800 adults, so \(N = 800\)

171 dine out at a resaurant more than once per week, so \(k = 171\)

2 are chosen, so \(n = 2\)

a. Find the probability that both adults dine out more than once per week.

This is P(X = 2).

\(P(X = 2) = h(2,800,2,171) = \frac{C_{171,2}*C_{629,0}}{C_{800,2}} = 0.0455\)

4.55% probability that both adults dine out more than once per week.

b. Find the probability that neither adult dines out more than once per week.

This is P(X = 0).

\(P(X = 0) = h(0,800,2,171) = \frac{C_{171,0}*C_{629,2}}{C_{800,2}} = 0.6180\)

61.80% probability that neither adult dines out more than once per week.

c. Find the probability that at least one of the two adults dines out more than once per week.

Either none dines out more than once per week, or at least one does. The sum of the probabilities of these events is 100%. So

p + 61.80 = 100

p = 38.20

38.20% probability that at least one of the two adults dines out more than once per week.

d. Which of the events can be considered unusual? Explain.

An event is considered unusual if it has a less than 5% probability of happening. Following this rule, in this problem, both adults dining out more than once per week can be considered unusual.

Answer:

A=2(LW+LH+WH)

Step-by-step explanation:

The value of 1kg 620g to kg is 1.62 kg

Given the expression 1kg 620g

Since 1000g = 1kg, hence;

620g = 0.62kg

Substitute

1kg 620g = 1 + 0.62

1kg 620g = 1.62kg

Hence the value of 1kg 620g to kg is 1.62 kg

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