4-91. Write the equation of the line passing through the points (−3, 1) and (9, 7).

Answer:

h=5

Step-by-step explanation:

Answer: no? because the comma goes after every three numbers.

x = 301/56

Algebra is the branch of mathematics that deals with numbers and values which are represented with letters and symbols.

Sometimes, we do not want to mention a particular number, we can represent the number by a letter or a suitable symbol. This approach is algebraic.

For example, d + d = 2d

This is an example of an algebraic expression

Given the algebraic expression,

\(3\frac{1}{8} \div (x - 4 \frac{7}{28} ) = \frac{17}{18} + 1 \frac{5}{6} \)

Step 1:

Simplify the expression by converting the mixed numbers into improper fractions:

25/8 ÷ ( x - 119/28) = 17/18 + 11/6

Step 2: Simplify the right side of the equation

25/8 ÷( x - 119/28) = 17/18 + 33/18

25/8 ÷( x - 119/28) = 50/18

Step 3: Multiply both sides of the equation by (x - 119/28)

25/8 = 50/18 × (x - 119/28)

Step 4: Multiply both sides of the equation by (18/50)

25/8 × (18/50) = (x - 119/28)

Step 5: Simplify the left side of the equation

9/8 = (x - 119/28)

Step 6: Add 119/28 to both sides of the equation

9/8 + 119/28 = x

Step 7: Calculate the value of x:

x = 9/8 + 119/28

= 63/56 + 238/56

= 301/56

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After the pumping of Container A's water into Container B, the volume of water in Container B is 6,286 feet³.

The volume refers to the amount of space in a container.

The volume of a container can be determined using the following formula: πr²h, where:

Diameter = 26 feet

Height = 20 feet

The volume of water in Container A = πr²h

r = radius = diameter/2

= 20/2 = 10 feet

Volume = 22/7 x 10 x 10 x 20

= 22/7 x 100 x 20

=6,285.7

= 6,286 feet³

Diameter = 36 feet

Height = 19 feet

Thus, the volume of Container B after the pumping, which is equal to the volume of water in Container A, is 6,286 feet³.

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After the pumping of Container A's water into Container B, what is the volume of water in Container B?

Answer:

I think you mean this :

\( \sqrt{x - 5} = 6 \\ = > {( \sqrt{x - 5} })^{2} = {6}^{2} \\ = > x - 5 = 36 \\ = > x = 36 + 5 \\ = > x = 41\)

Or,

Square root of x-5=6 is :

\( \sqrt{x - 5} \:=\:\sqrt{6} \)

y-(-9) = -6(x-(-4)), y = -6x-33

Answer:

72

Step-by-step explanation:

hope you like that

Train 1 = x + 6.4

Train 2 = x

(x) + (x + 6.4) = 717.6

2x + 6.4 = 717.6

2x = 711.2

x = 355.6

Train 1 = 355.6 + 6.4 = 362 mph

Train 2 = 355.6 mph

Hope this helps!! :)

Answer:

B

Step-by-step explanation:

We are given that y varies inversely with x. Recall that inverse variation has the form:

\(\displaystyle y=\frac{k}{x}\)

Where k is the constant of variation.

We are given that y = 36 when x = 1/12. Thus:

\(\displaystyle (36)=\frac{k}{\left({}^{1}\!/\!{}_{12}\right)}\)

Solve for k. Multiply both sides by 1/12:

\(\displaystyle k=\frac{1}{12}(36)=3\)

Hence, our equation is:

\(\displaystyle y=\frac{3}{x}\)

Our answer is B.

To determine whether the furnace will be adequate for a 1,400 square foot house with a 9-foot ceiling, we need to calculate the volume of the house and compare it to the volume the furnace is designed to heat.

The volume of the house can be found by multiplying the square footage by the ceiling height:

1,400 sq ft x 9 ft = 12,600 cubic feet

Since the furnace is designed to heat 10,000 cubic feet, and the house has a volume of 12,600 cubic feet, the furnace may not be adequate for heating the house. The furnace is not capable to heat the entire house.

Answer:

60°

Step-by-step explanation:

they are equal.....

Answer:

Step-by-step explanation:

\(3)\frac{5x}{2}+125 = 180\\\\\frac{5x}{2}=180-125\\\\\frac{5x}{2}=55\\\\ 5x = 55*2\\\\ x =\frac{55*2}{5}\\\\ x = 11*2 = 22\)

4) 3x+ 42 + 90= 180

3x + 132 = 180

        3x = 180 -132

        3x = 48

          x = 48/3

         x = 16

Answer:

2x - 12

Step-by-step explanation:

Given:

-3(6x+4)+20x

Distribute:

-18x-12+20x

Combine like terms:

2x-12

Hope this helps, have a nice day :))

Answer:

3 8 + 1 2

i searched it

Answer:

Let's assume that the two numbers are x and y, where x is greater than y.

From the given information, we can write two equations:

x^2 + y^2 = 85 (Equation 1)

x - y = 1 (Equation 2)

We can solve Equation 2 for x and substitute into Equation 1:

x = y + 1

(x = y + 1) into (Equation 1)

(y + 1)^2 + y^2 = 85

Simplifying this equation, we get:

2y^2 + 2y - 84 = 0

Dividing both sides by 2, we get:

y^2 + y - 42 = 0

Factoring this equation, we get:

(y + 7)(y - 6) = 0

Therefore, y = -7 or y = 6. Since x is greater than y, we can ignore the negative value.

So, y = 6 and x = y + 1 = 7.

Therefore, the two numbers are 6 and 7.

Answer:

A. 31 cm

Step-by-step explanation:

Hopefully its right :)

The angles are formed by a transversal and two parallel lines in the figure. By applying congruent angles and vertical opposite angle property, ∠1 ≅∠3 ≅ ∠5 ≅ ∠7; ∠2 ≅ ∠4 ≅ ∠6 ≅ ∠8. Therefore option B is correct.

Congruent angles are identical to each other and have the same measure. The angles formed by the transversal in corresponding corners are called corresponding angles and they are congruent.

Therefore, ∠1 ≅ ∠5, ∠3 ≅ ∠7----------(1)

At a vertex if two angles are opposite to each other, then they are vertically opposite angles, they are equal and congruent to each other.

Therefore, ∠1 ≅ ∠3, ∠5 ≅ ∠7----------(2)

Combining (1) and (2), we get:

∠1 ≅∠3 ≅ ∠5 ≅ ∠7
Similarly we can find,

∠2 ≅ ∠4 ≅ ∠6 ≅ ∠8.

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The function that can represent the profit P(s) of the sneaker company is D. P(s) = – s2 + 60s – 1,500.

Mathematically, a function shows a set of inputs that produce one output.

Functions have the domain (independent variable) and the codomain or range (dependent variable).

The domain is always the set of input values, while the range is the output value of the function.

Revenue function R(s) = 90s – s2

Fixed cost = $1,500

Variable cost per unit = $30

Profit = Revenue - Variable and Fixed Costs

Profit function P(s) = 90s – s2 - 30s - 1,500

= 60s - s2 - 1,500

or -s2 + 60s - 1,500

Thus, the correct profit function is Option D.

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Answer:

x=15

Step-by-step explanation:

6(5)=30

3(5)=15

The length of the missing side Triangle is 3

As it is given that the given triangle is similar which shows all three sides of both the triangle will be in the same ratio by CPST (corresponding parts of similar Triangles).

so

15/x=30/6 .................  the ratio of two sides of the triangle

x  =  15*6/30

x= 3

here the value of x is 3.

Also, the ratio of the side comes out to be 5:1 as 6 and 30 are the length so the first triangle has a side of 15 and the length of another triangle will be 3 to make the ratio 5:1.

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Answer:

A

Step-by-step explanation:

43987-32650= 11337

And it’s more

Answer:

a) 1365 different ways.

b) 126 different ways.

c) 504 different ways.

d) 1239 different ways.

Step-by-step explanation:

The order in which the delegates are chosen is not important, which means that we use the combinations formula to solve this question.

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.

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

(a) How many different delegations are possible?

4 delegates from a set of 15. So

\(C_{15,4} = \frac{15!}{4!11!} = 1365\)

1365 different ways.

(b) How many delegations would have all Democrats?

4 delegates from a set of 9. So

\(C_{9,4} = \frac{9!}{4!5!} = 126\)

126 different ways.

(c) How many delegations would have 3 Democrats and 1 Republican?

3 from a set of 9 and 1 from a set of 6. So

\(C_{9,3}*C_{6,1} = \frac{9!}{3!6!}*\frac{6!}{1!5!} = 84*6 = 504\)

504 different ways.

(d) How many delegations would include at least 1 Republican?

Subtract the number of delegations with only democrats(126) from the total(1365). So

1365 - 126 = 1239

1239 different ways.

Answer:

b

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

go over 5 on the x axis and go up 1 on the y axis

Answer:

A

Step-by-step explanation:

A is at 5,1 so this would make sense

Given:

• Height of hill = 16 feet

• Distance from you to the base of the hill = 77 feet

• Angle the hill subtends = 13.2 degrees

Let's find the height of the statue.

Since the statue subtends an angle of 13.2 degrees to where you are standing, let's find the distance from you to the statue using the trigonometric ratio formula for tangent:

Where:

Opposite = 16 ft

Adjacent side = 77

Angle of elevation = θ

Thus, we have:

Now, also apply the trigonometric ratio formula for tangent to find the total height of the hill and the statue:

The height of the statue will be:

h = 35.81 - 16 = 19.81 ft

Therefore, the height of the statue is 19.81 feet.

• ANSWER:

19.81 feet.

Answer: 5 is the smaller number and 21 is the larger number

Step-by-step explanation: let’s have the smaller of the numbers equal x and the larger one equal y. Y = 3x + 6 their sum is 3x + 6 + x or 4x + 6. This sum minus 4 is 22 so the sum is 26. 26-6 = 4x so 4x = 20 and x = 5 so r = 15+ 6 which is 21.

There is a probability of 94/315 that the problem will be solved.

We are given that P has a chance of solving the problem of 2/7, Q has a chance of solving the problem of 4/7, and R has a chance of solving the problem of 4/9. To find the probability that the problem is solved, we need to consider all possible scenarios in which the problem can be solved.

The probability of this scenario is 2/7. If P solves the problem, then it does not matter whether Q or R solve it, the problem is already solved. Therefore, the probability of the problem being solved in this scenario is 2/7.

The probability of this scenario is 4/7. If Q solves the problem, then it does not matter whether P or R solve it, the problem is already solved. Therefore, the probability of the problem being solved in this scenario is 4/7.

The probability of this scenario is 4/9. If R solves the problem, then it does not matter whether P or Q solve it, the problem is already solved. Therefore, the probability of the problem being solved in this scenario is 4/9.

The probability of this scenario is (1-2/7) * (1-4/7) * (1-4/9) = 3/35. This is because the probability of P not solving the problem is 1-2/7, the probability of Q not solving the problem is 1-4/7, and the probability of R not solving the problem is 1-4/9. To find the probability of none of them solving the problem, we multiply these probabilities together.

To find the probability of the problem being solved, we need to add the probabilities of all the scenarios in which the problem is solved. Therefore, the probability of the problem being solved is:

2/7 + 4/7 + 4/9 = 94/315

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The blanks that are missing in the sequence are -3 and 11

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

The blanks in the sequence

When listed out, we have

_, _, 25, 39

Assuming that the sequence, is an arithmetic sequence, then we have

Common difference = 39 - 25

Common difference = 14

This means that

Previous term = 25 - 14 = 11

Firs term = 11 - 14 = -3

So, the missing terms are -3 and 11

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The correct step to prove that \(BC^2 = AB^2 + AC^2\) is:

By the cross product property, \(AC^2 = BC \cdot AD\).

To prove that \(BC^2 = AB^2 + AC^2\), we can use the triangle similarity and the Pythagorean theorem. Here's a step-by-step explanation:

Given triangle ABC with right angle at A and segment AD perpendicular to segment BC.

By triangle similarity, triangle ABD is similar to triangle ABC. This is because angle A is common, and angle BDA is a right angle (as AD is perpendicular to BC).

Using the proportionality of similar triangles, we can write the following ratio:

\($\frac{AB}{BC} = \frac{AD}{AB}$\)

Cross-multiplying, we get:

\($AB^2 = BC \cdot AD$\)

Similarly, using triangle similarity, triangle ACD is also similar to triangle ABC. This gives us:

\($\frac{AC}{BC} = \frac{AD}{AC}$\)

Cross-multiplying, we have:

\($AC^2 = BC \cdot AD$\)

Now, we can substitute the derived expressions into the original equation:

\($BC^2 = AB^2 + AC^2$\\$BC^2 = (BC \cdot AD) + (BC \cdot AD)$\\$BC^2 = 2 \cdot BC \cdot AD$\)

It was made possible by cross-product property.

Therefore, the correct step to prove that \(BC^2 = AB^2 + AC^2\) is:

By the cross product property, \(AC^2 = BC \cdot AD\).

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The visual that can help you in  creating a  3D structure using rectangular prism and others is given in the image attached.

3D structure creation is the method of planning and building three-dimensional structures or objects utilizing various materials and methods. This may make use of physical development with the use of materials such as wood, metal, and plastic, as well as virtual development utilizing computer program programs.

In virtual 3D structure creation, creators make use of program to make 3D models of structures or objects. These models can be seen and controlled in virtual space, and can be utilized to reenact how the structure  will see and work within the real world.

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See text below



1. Start by creating a rectangular prism

as the base of your structure. This will

be the main structure that includes

the walls and interior rooms.

2. Add a cylindrical tower to one corner of the rectangular prism. Adjust the size and height to your liking.

3. Add another cylindrical tower to the opposite corner of the rectangular

prism. Again, adjust the size and

height to your liking.

4. Add a pyramid-shaped roof to one of the cylindrical towers, and a cone-

shaped roof to the other cylindrical tower.

5. Add a second rectangular prism on top of the first one, with a different orientation or size. This can serve as an additional room or tower.

6. Add a pyramid-shaped roof to the second rectangular prism, and a cone-shaped roof to the cylindrical tower that does not have one yet.

7. Add a rectangular prism

perpendicular to the main structure,

creating an L-shape. This can be a

separate building or an extension of

the main structure.

8. Add a pyramid-shaped roof to the new

rectangular prism, and a cone-shaped roof to the cylindrical tower on the

opposite side of the main structure. 9. Finally, add spheres as decorative

elements to the walls and towers. You can also add other shapes, such as additional rectangular prisms,

pyramids, or cones, as long as you have at least 2 of each of the 5

required shapes.