Martin, a carpenter wants to make a spice rack for the kitchen. He cuts a 16.24 feet long plank into 5 pieces of equal length. What is the length of each piece of wood ? Round to the nearest hundredth.

Given that 2 of the angles are congruent, we can conclude that the others angles are congruent too, because the sum of inner angles of a triangle is equal to 180. So the additional information we need is

And having that we could use AAA criteria. Also we could need AC = DF and use ASA criteria.

Distances Sandra recorded in order from least to greatest is 1/9, 5/18, 11/36, 7/18, 17/36, 2/3.

Given that, the fractions represent the distances that Sandra recorded is 7/18, 2/3, 1/9, 11/36, 5/18, 17/36.

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

Here, distance is 10/36

So, the equivalent fractions for the given fractions are

7/18 = 14/36

2/3 = 24/36

1/9 = 4/36

11/36

5/18 = 10/36

17/36

So, least to greatest is

4/36 < 10/36 < 11/36 < 14/36 < 17/36 < 24/36

1/9 < 5/18 <11/36 <7/18 <17/36 <2/3

Therefore, distances Sandra recorded in order from least to greatest is 1/9, 5/18, 11/36, 7/18, 17/36, 2/3.

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Answer:

1)2/5

2)2/3

Hope this helps!

Answer:

1. m=2/5

2. m-2/3

Step-by-step explanation:

The value of interior angle is 60.

What is triangle?

A triangle is a simple polygon with 3 sides and 3 interior angles. It is one of the basic shapes in geometry in which the 3 vertices are joined with each other and it is denoted by the symbol.

What is interior angle?

In a triangle, there are three interior angles at each vertex. The sum of those interior angles is always 180°. The bisectors of these angles meet at an point known as incenter. As the sum of interior angles of a triangle is 180°, there is only one possible right angle or obtuse angle possible in each triangle.

The sum of interior angle is 180

Given angles is 30, 90, x.

Therefore, sum is given by

90 + 30 + x = 180

120 + x = 180

x = 180-120

x = 60

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We have to solve for x:

Multiply both sides of the proportion by 32:

Simplify:

The total cost of fencing the garden will be 3x+200 where x is the perimeter of garden that is variable according to the length and breadth of the garden.

Distance is measured in length. Length has the dimension of distance in the International System of Quantities. The majority of measurement systems choose a base unit for length from which all other units are derived. The metre serves as the foundational unit of length in the International System of Units.

A closed path that encompasses, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter. There are numerous uses in real life for perimeter calculations.

Here,

Let x be the perimeter to be fenced.

the cost is 3 rupees per meter.

so the equation will be= 3x+200

The total cost of fencing the garden will be 3x+200, where x is the garden's perimeter and is dependent on the garden's length and width.

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Answer:

y = [tex]\frac{3x -6}{5}[/tex]

Step-by-step explanation:

3x - 5y = 6 ( subtract 3x from both sides )

- 5y = - 3x + 6 ( multiply through by - 1 )

5y = 3x - 6 ( divide both sides by 5 )

y = [tex]\frac{3x-6}{5}[/tex]

Step-by-step explanation:

even though the line segment pieces of the horizontal and the inclined lines are of different lengths, but the ratio between the pieces of the same line must be the same.

in other words

x/27 = (32-18)/18 = 14/18 = 7/9

9x/27 = 7

x/3 = 7

x = 7×3 = 21

for given rectangle TUVW with vertices T(-3,-1), U(0, -2), V(-2, -8), and W(-5, -7): 90° counterclockwise rotation would be,

T': (1, -3)

U': (2, 0)

V': (8, -2)

W': (7, -5)

In this question, we have been given a rectangle TUVW with vertices

T(-3,-1), U(0, -2), V(-2, -8) and W(-5, -7)

We know that for 90° counterclockwise rotation is (x, y) becomes (-y, x)

so, the coordinates of T' would be,

T' = (1, -3)

the coordinates of U' would be,

U' = (2, 0)

the coordinates of V' would be,

V' = (8, -2)

the coordinates of W' would be,

W' = (7, -5)

Therefore, for given rectangle TUVW with vertices T(-3,-1), U(0, -2), V(-2, -8), and W(-5, -7): 90° counterclockwise rotation would be,

T': (1, -3)

U': (2, 0)

V': (8, -2)

W': (7, -5)

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The person that has the higher average speed is Teresa.

The average speed is the total distance travelled by the object in a particular time interval.

Average speed measures the average rate of speed over the extent of a trip.

Therefore,

average speed = distance / time

Hence, Karl drove 40 miles in 50 minutes.

Therefore,

average speed of Karl = 40 / 50

average speed of Karl = 4 / 5 miles per minute

Teresa drove 35 miles in 42 minutes.

Therefore,

average speed of Teresa = 35 / 42

average speed of Teresa  = 5 / 6 miles per minutes

Therefore, Teresa had the higher average speed.

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Answer:

???

Step-by-step explanation:

Is there a English version for this question?

Given:

given expression is

Find:

The main objective is to evaluate the expression.

Explanation:

we will use BoDMAS formula for evaluating the expression.

Conclusion:

Therefore, correct option is C.16

(1) The system of inequalities that can be used to represent this situation is 1.25x + 2y > 375  and x+y ≤ 500 .

(2) The least number of chocolate covered almonds that must be sold to cover the cost of attending Beta convention is 126 .

In the question ,

Part(1)

let the number of chocolates be "x" .

let the number of chocolates with covered almonds be "y"

price of each chocolate bar = $1.25

price of each chocolate covered almonds = $2

Beta club needs more than $375

So , according to the question

1.25x + 2y > 375

and also the students can sell up to 500 bars and covered almonds altogether.

So , x+y ≤ 500 .

Part(2)

Given , the club sells 100 chocolate bars.

substituting x= 100 in the inequality 1.25x + 2y > 375  , we get

1.25(100) + 2y > 375

125 + 2y > 375

2y > 375-125

2y > 250

y > 125

least number of chocolate covered almonds to be sold is 126 .

Therefore , (1) The system of inequalities that can be used to represent this situation is 1.25x + 2y > 375  and x+y ≤ 500 .

(2) The least number of chocolate covered almonds that must be sold to cover the cost of attending Beta convention is 126 .

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Answer:

-0.7 < -0.4

0.5 > -0.6

-0.8 < -0.7

0.6 > 0.4

Explanation:

The symbol < means less than and the symbol > means greater than.

On the other hand, if we identify each number on a number line, we get:

Therefore, the true statements are:

-0.7 < -0.4

0.5 > -0.6

-0.8 < -0.7

0.6 > 0.4

Because, for example, -0.7 is on the left of -0.4 which means that -0.7 is less than -0.4.

0.5 in on the right of -0.6 which means that 0.5 is greater than -0.6.

Answer

Graph 1 = 1/3 slope

Graph 2 = -1/3 slope

Graph 3 = 3 slope

Graph 4 = -3 slope

I found these by counting rise over run,

or y/x to points on the line that cross the x or y axis.

The graphs that have a line that go up from left to right are positive slopes

The graphs that have a line that go down from left to right are negative slopes

Problems solved!

It is not reasonable to use a normal model for the sampling distribution of the sample because the data doesn't meet the success or failure consideration.

The sample has a size of 50 students. The probability that she guesses that about 10% of the class goes is 10%

This will be illustrated as:

1 - p = 1 - 10% = 1 - 0.10 = 0.90

np = 50 × 0.1 = 5. This implies the number of successes.

In this case, the number of successes is less than 10. This is because 5 is less than 10. Therefore, the data doesn't meet the condition.

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Answer: x=2

Step-by-step explanation:

1. Distribute

2. Subtract 9 from both sides

3. Simplify

4. Subtract x from both sides

5. Simplify

6. Divide both sides by the same factor

7. Simplify

The area of the region consisting of all the points Charlyn can see during her walk is equal to, A = 4840 km.

Charlyn is walking around the boundary of square A, which is 55 km long, and she has a horizontal vision of 11 km.

So as she walks around the square of 55 km, let there be another square B which lies outside square A, which is created due to her 11 km field of vision.

length of sides of square B = 55+(2×11) which is equal to 77 km.

And as she walks around the square of 55 km, let there be yet another square C which lies inside square A, which is created due to her 11 km field of vision.

length of sides of square C = 55-(2×11) which is equal to 33 km.

The area that Charlyn can see throughout her walk is equal to,

A = Area of square B - Area of square C.

The area of square B = Side² = 77² = 5929.

The area of square C = Side² = 33² = 1089.

A = 5929 - 1089.

A = 4840 km.

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Answer:

y = 3x + 20

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x + 5 ← is in slope- intercept form

with slope m = 3

• Parallel lines have equal slopes , then

y = 3x + c ← is the partial equation

to find c substitute (- 8, - 4 ) into the partial equation

- 4 = - 24 + c ⇒ c = - 4 + 24 = 20

y = 3x + 20 ← equation of parallel line

Answer:

Step-by-step explanation: From the given point,

The line is: -8x-4y=0

           viz, 2x+y=0

Answer: It will take 3.5-4 months

Step-by-step explanation:

sSlope means the inclination of the line

Intercept is the point where the line touches the Y axis.

Using the function rule, the value of g(r +2)  is r-2

Given the function rule g(k) = k-4.

Then g(r + 2)  can be found by replacing k with r+2 in the function g(k):

g(r+2) = r + 2 - 4

           = r - 2

Therefore, g(r+2) gives r - 2 when evaluated using the function rule.

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Answer:

y=-5x/3+26/3

Step-by-step explanation:

Because we want the equation to look like y=mx+b, rearrange the terms.

Since 26-5x is the same as -5x+26, rewrite it like that.

3y=-5x+26

Now, since we want the value of y, divide by 3 on both sides.

3y/3=y

-5x/3= -5x/3

26/3= 26/3

The simplest form would look like:

y=-5x/3+26/3

Answer:

0.1

Step-by-step explanation:

chance of pulling out a blue marble can be described as 8 equally probable outcomes (blue marbles) out of 20 equally probable outcomes (all marbles).

Similarly, the chance of pulling out a green marble is 5 out of 20.

In total, we have 8*5 (combinations of blue then green) outcomes out of 20*20 (any two marbles):

8*5 / (20*20) = 40 / 400 = 1/10 = 0.1

Step-by-step explanation:

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15.. . is an arithmetic progression with a common difference of 2.

Arithmetic progression is S = 1/2n[2a+(n-1)d]

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In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

Geometric progression is Uₙ = arⁿ ⁻ ¹

The rational equation is simplified to  x² - 17x = 0

An algebraic expression can simply be defined as an expression composed of factors, variables, terms, coefficients and constants.

These expression are also described as expressions consisting of arithmetic operations such as;

Given the expression;

1/2 - 7/2x = 5/x

find the lowest common multiple

x - 7 /2x = 5/ x

cross multiply

x(x - 7) = 5(2x)

multiply through

x² - 7x = 10x

collect like terms

x² = 10x + 7x

x² - 17x = 0

Hence, the equation is x² - 17x = 0

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