A rectangular prism has a length of 7 units, a width of 12 units, and a height of 8 units.

Enter your answers in the boxes to complete the formula.

V=l×w×h

Answer:

14 ×3 = 42 cm.

Step-by-step explanation:

Solution:

Let w be the width of the rectangle, let d be the diagonal of the rectangle, angle and let h be the height of the rectangle.

Thus, the width is 2 inches longer than the height and the diagonal is 58 inches;

From the right angle triangle, we would apply the Pythagorean Theorem given as;

Thus, we have;

Now, we would solve the quadratic equation by factorization; we have;

Since the height of a rectangle cannot be a negative value, the height of the rectangle is 40 inches.

ANSWER: 40 inches

Answer:

Answers are in bold

Step-by-step explanation:

Question 1

For a 30-60-90 triangle:

Longer leg: sqrt(3) * (shorter leg) -> AC=BC*sqrt(3)

Hypotenuse: 2 * (shorter leg) -> AB=2*BC

It is given that AC, the longer leg, is 18, therefore we can each side length:

Shorter Leg:

18=BC*sqrt(3)

10.39230485=BC

BC=10.39230485

BC=6sqrt(3) <-- Simplified Form

Hypotenuse:

AB=2*10.39230485

AB=20.78460969

AB=12sqrt(3) <-- Simplified Form

Question 2

The sequence is geometric because each consecutive term is being multiplied by 2. Therefore, the common ratio is r=2.

Question 3

You got this one right, so no need to talk about it

Answer:

60%

Step-by-step explanation:

36/60 x 100= 60%

Answer: y = 3x+5, 3, (-1,2)

Step-by-step explanation:

y = mx + c where m is the slope, so we must find the slope

Slope = rise/run = (5-2)/(0-(-1)) = 3

So y = 3x + c

To find c, we have to substitute one of the coordinates on the graph into the equation, (-1,2), the point that is marked

2 = 3(-1) + c

c = 5

So the equation of the graph is y = 3x + 5

Answer:

243

Step-by-step explanation:

Area=Base x Height.

18 x 13.5=243 :)

The rational functions is graphed below is f(x)=1/x-4.

Any function that can be expressed as a polynomial divided by a polynomial is said to be rational. Since polynomials are defined everywhere, the domain of a rational function is the set of all numbers excluding the zeros in the denominator. First example: f(x) = x/ (x - 3). There is just one zero in the denominator, x = 3. Usually, the numerator and denominator degrees of rational functions serve as indicators. A quadratic/cubic rational function, for instance, is one that has a cubic denominator and a quadratic numerator. A generalization of the polynomial model is the rational function model. A function that compares the two polynomials. Due to the fact that one is divided by the other, it is a "rational" ratio.

From the graph, we can get the function is f(x)=1/x the k=4.

So, f(x)=1/x-4

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Answer:

Step-by-step explanation:

The value of x will be 18.67 for the given data of the triangle.

We have,

Thale's theorem:

When a line parallel to one side of a triangle intersects the other two sides in distinct points, the other two sides are divided in the same ratio.

Given that the sides of the triangle are divided into two parts,

For the left part the parts will be x and x + 7 for the right side the parts will be 16 and 22.

The ratio will be the same according to Thale's theorem. The value of x will be calculated as:-

x / ( x + 7 ) = 16 / 22

22x = 16x + 112

6x = 112

x = 112 / 6

x = 18.67

Therefore, the value of x will be 18.67.

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complete question;

Find the values of x and y. Find value of x.

Answer:

-100

Step-by-step explanation:

we nuh care

Rewrite two numbers sum

36 + 72

a•(b + c)

b ,c are not factors

Note that

72 = 36x2

Then can be writed

36 + 72 = 36 + 36•2 = 36•( 1 + 2)

Then

b and c, 1 and 2 ,have no common factors

ANSWER IS

36•( 1 + 2)

Answer:

2090.318 square metres

The toll calculation for driving on a certain stretch of a toll road is $5 except during rush hours when the toll is $7, depending on the time the driver uses the toll road.

To compute the toll for driving on the toll road during non-rush hours, simply add $5 to the total. During rush hour, however, the toll is $7.

To compute the toll for driving during rush hour, you must first determine when the driver intends to utilize the toll road. If the period is between 7 AM and 10 AM or 4 PM and 7 PM, the toll is $7.

For instance, if a vehicle expects to use the toll road at 8 a.m., the toll is $7. If the vehicle intends to use the toll road at 2 p.m., the toll is $5.

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While one runner demonstrated dedication and improvement through a personal best time, the other runner's lack of training and absence of a personal best time suggest a more casual or unprepared approach to the race.

In a race between two runners, one of them had a personal best time, while the other runner neither trained nor had a personal best time.

The runner who had a personal best time implies that they had trained and put in effort to improve their performance. A personal best time suggests that they have achieved their highest level of performance in a race. This indicates that the runner has dedicated time and effort to their training regimen, focusing on improving their speed and endurance.

On the other hand, the runner who neither trained nor had a personal best time implies that they did not invest effort in training or actively seek to improve their performance. They may have participated in the race casually or without specific training goals in mind. As a result, they did not achieve a personal best time, indicating that they did not put in the necessary effort to reach their full potential.

In summary, while one runner demonstrated dedication and improvement through a personal best time, the other runner's lack of training and absence of a personal best time suggest a more casual or unprepared approach to the race.

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Answer:

9

Step-by-step explanation:

I divided 45 by 5 and got 9

Answer:

9

Step-by-step explanation:

45 divided by 5 means, split 45 into 5 groups. Which should get you 9 cars per day.

Answer:

2x + 8x

10x

Step-by-step explanation:

Open the brackets and multiply x inside.

Answer:

2x(8)

Step-by-step explanation:

multiply. 2x by 8 and get 16x

Answer:

Ethan is the correct answer

Answer:

f(x) \(\leq\) 3x + 4

g(x)  ≥ -1/2x - 5

Step-by-step explanation:

Point D is below f(x)  and above g(x)

Helping in the name of Jesus.

Answer:

40,000 + 5000 + 600 + 70 + 8

Step-by-step explanation:

take the numbers all off and break them down by their value.

The possible values for angles 1, 2, and 3 given that lines a and b are parallel lines include the following:

In Mathematics and Geometry, parallel lines are two (2) lines that are always the same (equal) distance apart and never meet or intersect.

Note: Assuming angle 1 is equal to 60 degrees.

In Mathematics and Geometry, the vertical angles theorem states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other:

m∠1 ≅ m∠3 = 60°.

Based on the linear pair postulate, the measure of angle 2 can be determined as follows;

m∠1 + m∠2 = 180°

60° + m∠2 = 180°

m∠2 = 180° - 60°

m∠2 = 120°

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The limit lim(x approaches 0) (cosec(2x) - x*cosec³(x)) is undefined.

We have,

To evaluate the limit of the expression as x approaches 0, we can simplify the expression first.

The expression is given as lim(x approaches 0) (cosec(2x) - x cosec³(x)).

Using trigonometric identities, we can rewrite cosec(2x) as 1/sin(2x) and cosec³(x) as 1/(sin(x))³.

Substituting these into the expression,

We get lim(x approaches 0) (1/sin(2x) - x (1/(sin(x))³)).

Now, let's evaluate the limit term by term:

lim(x approaches 0) (1/sin(2x)) = 1/sin(0) = 1/0 (which is undefined).

lim(x approaches 0) (x (1/(sin(x))³))

= 0 (1/(sin(0))³)

= 0 x 1/0 (which is also undefined).

Since both terms of the expression are undefined as x approaches 0, we cannot determine the limit of the expression.

Therefore,

The limit lim(x approaches 0) (cosec(2x) - x*cosec³(x)) is undefined.

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Answer:

The rate of change is 28.

Step-by-step explanation:

The equation is in slope-intercept form,  y = mx + b, where m is the slope, and b is the y-intercept.

the domain of the given function is

the range of the function is,

Since 1 cubic feet = 62 pounds, the weight of the water that Jerry put in the aquarium is 558 pounds

We have to find the volume of water in the aquarium.

Recall the shape of the aquarium is a rectangular prism. Therefore,

volume = lwh

where

Therefore,

l = 3 ft

w = 2 ft

h = 1.5 ft

volume =  3 × 2 × 1.5

volume of water = 9 ft³

Therefore,

1 ft³= 62 pounds

9 ft³ = ?

cross multiply

weight of water = 9 × 62

weight of water = 558 pounds

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Based on the information, we can infer that the house equals 42, the hat equals 87, the tree equals 35, and the snowman equals 26.

To find the value of the symbols we must start with column #3 in which there are 4 houses. So we must divide the result by 4 to know the value of each house, which would be 42. Then we must use the operation of row #3 in which there are 3 hats and a house, so we subtract 42 from the result and then divide it by 3, this will give us 87.

Later, we must take the first column and subtract 42 and 87 twice from the result. The remaining number would be the value of the snowman.

Finally, to find the value of the tree we can select any of the operations that include the tree and subtract the values of the other symbols and the result will be the value of the tree.

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Answer:

Below

Step-by-step explanation:

From 7 to 10 AM is THREE hours (if the times are all on the same day)