2
Select the correct answer.
A community center has an L-shaped swimming pool that is 10 feet deep. What is the volume of the pool?
10 ft.
6 ft.
20 ft.
16 ft.
10 ft.

Answer:

3.75

Step-by-step explanation:

Just divide 1.5 by 0.4

just ask your teacher for extra help if needed

The comparison of the expressions is 7 + 3² -2  * 5 ÷ 4 - 1 * 2 > (¾+ ⅛) ÷ ⅛ - 2²

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

7 + 3^2-2x5÷4-1x2 and (¾+ ⅛) ÷ ⅛ - 2^2

Express the exponents properly

This gives

7 + 3² -2  * 5 ÷ 4 - 1 * 2 and (¾+ ⅛) ÷ ⅛ - 2²

Evaluate the exponents

So, we have the following representation

7 + 9 - 2 * 5 ÷ 4 - 1 * 2 and (¾+ ⅛) ÷ ⅛ - 4

Evaluate the expressions in brackets

So, we have the following representation

7 + 9 - 2 * 5 ÷ 4 - 1 * 2 and 7/8 ÷ ⅛ - 4

Solve the products and quotients

7 + 9 - 2.5 - 2 and 7 - 4

So, we have

11.5 and 3

11.5 is greater than 3

So, we have

11.5 > 3

Rewrite as

7 + 3² -2  * 5 ÷ 4 - 1 * 2 > (¾+ ⅛) ÷ ⅛ - 2²

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Answer:

x = 2

Step-by-step explanation:

6/3 = 2

The maximum load that can be applied to the wire made of that kind of steel is 21195 N. The result is obtained by using the tensile strength equation.

Tensile strength is the maximum load or stress that a material can withstand without fracture when being stretched or pulled per its cross-sectional area.

The statement can be expressed as

σ = F/A

Where

The tensile strength of a certain steel wire is 3000 MN/m². The diameter of the wire is 3.0 mm. Find the maximum load that can be applied to the wire!

Let's count the cross-sectional area!

A = πr²

A = 3,14 (½d)²

A = 3,14 [½(3.0 × 10⁻³)]²

A = 3,14 (1.5 × 10⁻³ m)²

A = 3,14 (2.25 × 10⁻⁶) m²

A = 7.065 × 10⁻⁶ m²

The maximum load is the maximum value of the force acting on it.

σ = F/A

3000 MN/m² = F / 7.065 × 10⁻⁶ m²

3000 × 10⁶ N/m² = F / 7.065 × 10⁻⁶ m²

F = 3 × 10⁹ × 7.065 × 10⁻⁶  N

F = 21.195 × 10³ N

F = 21195 N

Hence, the steel wire can have the maximum load of is 21195 N.

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At the point where x = 0, the equation simplifies to 8e^y = 8e, which can be rearranged to e^y = 1. This means that y = 0.

1. Substitute x = 0 into the equation: xy + 8e^y = 8e

2. Simplify the equation: 8e^y = 8e

3. Rearrange the equation to isolate the exponent: e^y = 1

4. Take the natural logarithm of both sides: y = ln(1)

5. Evaluate the natural logarithm: y = 0

At the point where x = 0, the given equation simplifies to 8e^y = 8e. Rearranging this equation to isolate the exponent on the left hand side, we get e^y = 1. Taking the natural logarithm on both sides, we get y = ln(1). Finally, evaluating the natural logarithm of 1, we get y = 0. Therefore, the value of y" at the point where x = 0 is 0.

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Answer:

3/4

Step-by-step explanation:

1 batch of cookies is equal to 0.375. 3/4 a barrel of cookies is equal to 0.75. 0.75/0.375 is equal to 2. So 3/4 a barrel is 2 batches of cookies.

The solution to the system of equations is (3,1).

2x - 3y = 6

3x + 2y = 7

(3,1)

Multiply the first equation by 3:

6x - 9y = 18

Add the two equations:

9x - 7y = 25

Divide both sides by 9:

x - y = 25/9

Substitute 25/9 for x in the second equation:

3(25/9) + 2y = 7

Simplify:

25 + 18y = 63

Subtract 25 from both sides:

18y = 38

Divide both sides by 18:

y = 38/18

Substitute 38/18 for y in the equation x - y = 25/9:

x - (38/18) = 25/9

Simplify:

x = (25/9) + (38/18)

Simplify:

x = 63/9

Therefore, the solution is (63/9, 38/18) or (3,1).

The solution to the system of equations is (3,1).

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Answer:

16

Step-by-step explanation:

48 divided by 3 is 16, so each of his friends will get 16 cookies.

A transversal line intersects two parallel lines a and b with values of corresponding angles congruent pairs of corresponding angles are (1, 5), (4, 8), (3, 7), and (2, 6).

∠1 ≅ ∠5 (corresponding angle theorem)

∠7 ≅ ∠5 (vertical angle theorem)

∠1 ≅ ∠7 (Transitive property of congruence)

Complete question is at the end of solution.

As per the given data, a transversal line intersects two parallel lines a and b.

The values of corresponding angles congruent pairs of corresponding angles are (1, 5), (4, 8), (3, 7), and (2, 6)

Line a is parallel to line b.

Therefore,

a ║ b

Let's prove ∠1 ≅ ∠7

Hence,

∠1 ≅ ∠5 (corresponding angle theorem)

Corresponding angles are the angles that are formed in matching corners or corresponding corners with the transversal when two parallel lines are cut by the traversal.

∠7 ≅ ∠5 (vertical angle theorem)

Vertical angles theorem or vertically opposite angles theorem:

According to the theorem, two opposing vertical angles that are created when two lines cross one other are always equal.

Vertical angles are the angles formed when two lines intersect each other.

∠1 ≅ ∠7 (Transitive property of congruence)

Transitive property of congruence: If two lines, angles, or triangles are congruent with one another, then the first line, angle, or triangle is congruent with the second, third, or fourth line, angle, or triangle.

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The given statement states that a transversal line intersects two parallel lines, a and b, with corresponding angle congruent pairs of (1, 5), (4, 8), (3, 7), and (2, 6). The proof uses the corresponding angles theorem, vertical angles theorem, and transitive property of congruence to show that the angles are congruent.

Given 2. Corresponding angles theorem 3. Vertical angles theorem 4. Transitive property of congruence Reasons: 1. The transversal line intersects two parallel lines a and b with values of corresponding angles congruent pairs of (1, 5), (4, 8), (3, 7), and (2, 6). 2. If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. 3. If two angles are vertical angles, then they are congruent. 4. If two angles are congruent to the same angle, then they are congruent to each other.

The given statement states that a transversal line intersects two parallel lines, a and b, with corresponding angle congruent pairs of (1, 5), (4, 8), (3, 7), and (2, 6). The proof uses the corresponding angles theorem, vertical angles theorem, and transitive property of congruence to show that the angles are congruent.

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The probability that the Canadian Rounders have 0 players injured for their next match is 1/4 or 25%.

This implies the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happeing of the event.

The total number of matches = 4+5+2+3+2

The total number of matches = 16

Total, that has zero injured players = 4

The probability will be:

= 4 / 16

= 0.25

The probability is 0.25.

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Complete question

The following frequency table summarizes this year's injuries on the Canadian Rounders cricket team.

Number of injured players Number of matches

0 | 4

1 | 5

2 | 2

3 | 3

4 | 2

Based on this data, what is a reasonable estimate of the probability that the Canadian Rounders have 0 players injured for their next match?

-090

Step-by-step explanation:

Answer:

Step-by-step explanation:

do it better than what you did before.

Answer:

15

Step-by-step explanation:

to find f(5), all you do is substitute 5 for both of the x's. do this in a calculator and you'll get the same thing as i did.

An image is always formed at the back of a mirror. Thus, the flagpole is 8.75 m tall.

Let the angle of depression from Madelyn's point of view be represented by θ. Then applying the required trigonometric function, we have;

Tan θ = opposite / adjacent

         = 1.65 / 1.7

Tan θ = 0.9706

θ =  Tan⁻¹(0.9706)

 = 44.2°

θ = 44.2°

Let the height of the flag be represented by h. And for a given mirror, the angle of incidence is equal to that of reflection. Then;

Tan θ = opposite / adjacent

        = h / 8.75

0.9706 = h / 8.75

h = 0.9706 x 8.75

 = 8.49275

h = 8.5 m

Since the image is formed at the back of the mirror, then the flagpole is 8.5 m tall.

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Answer:

1/5, 20 diveded by 5 is 4, 20%

On solving the provided question, we can say that - the of the function f(x) = 0.5x + 7.8 = 9.8

The topic of numbers, formulae and associated structures, forms and the areas where they exist, quantities and their variations, and spaces where they exist are all included in the field of mathematics. An association between a collection of inputs, each of which has an output, is known as a function. A function is, to put it simply, a relationship between inputs and outputs, where each input has a single, specific outcome. A domain and a codomain, or scope, are assigned to each function. Typically, f is used to represent functions (x). input is x. Four different sorts of functions are available. Based on the following items: One-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.

here, we are provided with the function -

f(x)= 0.5x + 7.8

and given from question, x = 4

f(x) =  2 + 7.8 = 9.8

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The pound per hour when the movie theater went through 2 pounds of popcorn every 9 hours is 2/9 pounds

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

In this case, the movie theater went through 2 pounds of popcorn every 9 hours. The pound per hour will be:

= Number of pound / Number of hours

= 2/9

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To find 1/3 of a line segment, divide the line segment into three equal parts. Measure the length of one of these parts and this will be 1/3 of the line segment.

This can be done by using a ruler or a measuring tape. Alternatively, if the length of the line segment is known, divide it by 3 to find 1/3 of the line segment. For example, if the line segment has a length of 12 inches, then the length of 1/3 of the line segment is 4 inches. If the line segment is curved, you can divide it into three equal arc lengths using a compass.

You can then measure the length of one of these arcs to find 1/3 of the line segment. To make sure that the three parts are equal, you can use the Pythagorean theorem or the triangle inequality theorem. This will help you to accurately divide the line segment into three equal parts.

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Step-by-step explanation:

we create 2 equations with 2 variables by using the given point coordinates in both :

A×1 + B×-2 = 7

A - 2B = 7

A×1 - B×-2 = 3

A + 2B = 3

to solve we can simply add both equations to temporarily eliminate B and solve for A :

A - 2B = 7

A + 2B = 3

-------------------

2A 0 = 10

A = 10/2 = 5

now, we use one of the original equations to solve for B :

5 + 2B = 3

2B = -2

B = -2/2 = -1

Answer:

5-30

Step-by-step explanation:

expectation of single

The line ED has a length of 4 units.

Given,

Points E and D in the ΔCAB

equation represent the midpoints of the segments AC and BC, respectively.

AB is 8 units as well.

The length of segment ED needs to be determined.

We are aware that a triangle's third side and the line segment connecting its midpoint are both said to be parallel to the triangle's third side and to be half its length. The mid point theorem is what is known as this.

E and D are the midpoints of AC and BC in the equation CAB, and E's length is equal to half of AB's length is

=> 8/2  

=> 4 units

so the length of the segment ED is 4 units

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The measure of segment ED is 4 units.

4 units

We know that the measure of segment AB is 8 units and that point E is the midpoint of segment AC and point D is the midpoint of segment BC. This means that the measure of segment AC is 8/2, or 4 units. Since point E is the midpoint of segment AC, it is also the midpoint of segment ED, meaning that the measure of segment ED is 4 units.

The measure of segment ED is 4 units.

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Answer:

1200

Step-by-step explanation:

12 multiplied by 2 is 24.

24 divided by 2 is 12.

12 times 100 is 12 plus 2 zeros, or 1200.

According to the question quadrilateral pqrs, the russell jamie both neither is neither.

The Quadrilateral pqrs is located at p (−4, 1), q (−2, 3), r (1, 1), and s (−2, −2).

Russell:

PQRS is a parallelogram because both pairs of opposite sides are parallel

Segment pq is p (−4, 1), q (−2, 3).

Slope=[tex]\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]

[tex]& m=\frac{3-1}{-2+4}=\frac{2}{2}=1[/tex]

Segment SR is s (−2, −2) and  r (1, 1)

[tex]& m=\frac{1+2}{1+2}=\frac{3}{3}=1[/tex]

Segment ps is p (−4, 1), s (−2, −2)

[tex]& m=\frac{-2-1}{-2+4}=\frac{-3}{2}[/tex]

Segment qr is q(-2,3) and r(1,1)

[tex]m=\frac{1-3}{1+2}=\frac{-2}{3}[/tex]

Segments pq and sr are parallel, and segments ps and qr are parallel.

Jamie:

pqrs is a parallelogram because both pairs of opposite sides are congruent

Distance between two points is the length of the line segment that connects the two points in a plane

Segment pq  is p (−4, 1), q (−2, 3).

[tex]& d=\sqrt{(-2+4)^2+(3-1)^2}=\sqrt{4+4}=\sqrt{8}=2 \sqrt{2}[/tex]

Segment SR is s (−2, −2) and  r (1, 1)

[tex]& d=\sqrt{(1+2)^2+(1+2)^2}=\sqrt{9+9}=\sqrt{18}=3 \sqrt{2}[/tex]

Segment ps is p (−4, 1), s (−2, −2)

[tex]& d=\sqrt{(-2+4)^2+(-2-1)^2}=\sqrt{4+9}=\sqrt{13}[/tex]

Segment qr is q(-2,3) and r(1,1)

[tex]d=\sqrt{(1+2)^2+(1-3)^2}=\sqrt{9+4}=\sqrt{13}[/tex]

Segments pq and sr are congruent, and segments ps and qr are congruent.

Therefore, the correct option is neither.

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Both Russell and Jamie are correct. PQRS is a parallelogram with slope because both pairs of opposite sides are parallel, and it is also a parallelogram because both pairs of opposite sides are congruent.

Russell is correct because he used the slope of the lines to prove that both pairs of opposite sides are parallel. He calculated the slope of the lines using the equation m = (y2 - y1)/(x2 - x1) and found that the slopes of the two pairs of opposite sides (PQ and SR, and PS and QR) are equal, which means that the lines are parallel.

Jamie is also correct because he used the distance formula to prove that both pairs of opposite sides are congruent. He calculated the distance between the points using the equation d = √((x2 - x1)^2 + (y2 - y1)^2) and found that the distances of the two pairs of opposite sides (PQ and SR, and PS and QR) are equal, which means that the lines are congruent.

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Answer:

Solution is (-1,7)

Step-by-step explanation:

Graph is shown

y=2x+9 is in red

y=6-x is in blue

Hope this helps :)

The value of the expression (x != 7) && (x <= y) is: B. true

The expression is a combination of two logical conditions joined by the logical operator "&&" which means "and". The first condition "x != 7" checks if x is not equal to 7, which is true because x is 5. The second condition "x <= y" checks if x is less than or equal to y, which is also true because x is 5 and y is 7.

Since both conditions are true, the entire expression evaluates to true. The logical operator "&&" only returns true if both the conditions are true, else it will return false.

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Step-by-step explanation:

if the three numbers are x,x+1,x+2

2x+3(x+2)=(x+1)4+14

5x+6=4x+18

×=12

The centroid is the point at which the three medians of the triangle meet, divides each median proportionally, is always inside the triangle, equidistant from each vertex, and is the center of gravity.

1. The centroid of a triangle is the point at which the three medians (the lines connecting each vertex to the midpoint of the opposite side) of the triangle meet.

2. The centroid divides each median into two segments that are proportional to the lengths of the sides of the triangle.

3. The centroid is always inside the triangle, regardless of its shape.

4. The centroid is always equidistant from each vertex of the triangle.

5. The centroid is the center of gravity of the triangle, meaning that it is the point at which the triangle would balance if it were suspended.

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The properties of centroid of the triangle is explained below.

The term triangle is defined as the polygon with three sides, three vertices and three angle in it.

Here we need to list down the properties of the centroid of the triangle.

In order to identify the properties, first we must know the defnition of centroid.

The term centroid in math is defined as the point that is presented in at 2/3 of the distance from the vertex to the mid-point of the sides.

Here we know that the centroid has the special property that, here for each median, and the distance from a vertex to the centroid is twice that of the distance from the centroid to the midpoint of the side opposite that vertex. Here we also that the three medians of a triangle divide the triangle into six regions of equal area.

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Answer:

14/3

Step-by-step explanation:

Flip the second fraction's numerator and denominator to get its reciprocal of 7/3. Then, you simply multiply it by 2, which equals 14/3.

The area of the deck in terms of s is 2s^2 + 7s + 15. The expression can be written in standard form as A = 2s^2 + 7s + 15.

The area of the deck can be expressed in terms of s using the standard form of a rectangular area equation, A = lw, where l is the length and w is the width. The side length of the pool is s and the length of the deck is twice the side length of the pool plus 5, or 2s+5. The width of the deck is 3 units longer than the side length of the pool, or s+3. Substituting these values into the area equation gives us:

A = (2s+5)(s+3)

A = 2s^2 + 7s + 15

Therefore, the area of the deck in terms of s is 2s^2 + 7s + 15.

The expression can be written in standard form as A = 2s^2 + 7s + 15.

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The area of the rectangular deck built around the square pool of side, s in terms of s is 2s² + 11s + 15.

Therefore the answer is 2s² + 11s + 15.

The pool has side length s. The length of the deck is 5 units longer than twice the side length of the pool, that is

l = 2s + 5

The width of the deck is 3 units longer than the side length of the pool, that is

b = s + 3

Deck is in rectangular shape, thus the area of the deck in terms of s can be calculates by

A = lb = (2s + 5)×(s + 3)

= 2s² + 6s + 5s + + 15

= 2s² + 11s + 15

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