(Please help~! 20 Points~!)
The solution to 8x = 32 is x = ___.
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Answer: The product of [tex](9t-4)(-9-4)[/tex] is -117t+52.

Explanation:

The given expression is,

[tex](9t-4)(-9-4)[/tex]

Simplify the above expression.

[tex](9t-4)(-13)[/tex]

Use distributive property t simplify the above expression.

[tex](9t-4)(-13)=9t\times (-13)-4\times(-13)[/tex]

[tex](9t-4)(-13)=117t+52[/tex]

Therefore, the product of [tex](9t-4)(-9-4)[/tex] is -117t+52.

Answer:

$1000

Step-by-step explanation:

Answer is provided in the image attached.

Final answer:

The volume of a cylinder with a base radius of 3 and a height of 8 is approximately 226.195 cubic units, using the formula V = πr²h.

Explanation:

The volume of a cylinder is calculated using the formula V = πr²h, where π is the constant pi (approximately 3.14159), r is the radius of the cylinder's base, and h is the height of the cylinder. For a cylinder with base radius 3 and height 8, we use the values directly in the formula:

V = π×(3²)×8

V = π×9×8

V = π×72

V = 3.14159×72

V ≈ 226.195 cubic units

Therefore, the volume of the cylinder is approximately 226.195 cubic units.

To find the age of the eldest son in a family where the father is 50 and has 8 sons with a total age sum of 186, and the youngest son is 3, one can determine the age difference between siblings and use the formula for the sum of an arithmetic series.

The question is asking us to determine the age of the eldest son, given that the sum of the ages of a 50-year-old father and his 8 sons is 186 years and the youngest son is 3 years old. Let's assume that the sons are born at equal intervals; we can denote the age difference between each son as 'd' years.

The sequence of the sons' ages forms an arithmetic series where the youngest son is 3 years old (the first term of the series, or 'a1'), and the eldest son's age will be 'a1 + 7d' (since there are 8 sons).

Since the sum of an arithmetic series is given by the formula 'n/2 * (a1 + an)', where 'n' is the number of terms, 'a1' is the first term and 'an' is the last term, we can set up the equation:
8/2 * (3 + (3 + 7d)) = 186 - 50 (subtract the father's age from the total sum).
This simplifies to 4 * (3 + 3 + 7d) = 136, or '4 * (6 + 7d) = 136'. Dividing both sides by 4, we get '6 + 7d = 34', which leads to '7d = 28' and thus 'd = 4'.

Therefore, the age of the eldest son will be '3 + 7*4', which equals 31 years old.

Final answer:

By setting up a system of linear equations from the given conditions, we can determine that a large box weighs 60 pounds, and a small box weighs 35 pounds.

Explanation:

To solve the problem involving the weights of large and small boxes being transported by a delivery truck, we can set up a system of linear equations. Let L represent the weight of a large box and S represent the weight of a small box. We know from the problem statement the following:

A large box plus a small box weighs 95 pounds: L + S = 95

Total weight of all boxes: 50L + 65S = 5275

Now we can solve this system of equations by substitution or elimination. If we solve the first equation for L, we get L = 95 - S. Substituting this into the second equation gives us:

50(95 - S) + 65S = 5275

Expanding and simplifying the equation, we get:

4750 - 50S + 65S = 5275

15S = 5275 - 4750

15S = 525

S = 35

Now that we have the weight of the small box, we can substitute it back into the first equation to find the weight of the large box:

L + 35 = 95

L = 60

Therefore, a large box weighs 60 pounds, and a small box weighs 35 pounds.

The area of a regular hexagon with a side of 4m is 24√3.

Side of the regular hexagon = 4m

A Regular hexagon is a polygon with 6 equal sides.

We know that a regular hexagon with a side p comprises 6 equilateral triangles with a side p.

So, the area of a regular hexagon with side p= area of 6 equilateral triangles with side p.

So, the area of a regular hexagon with side p = [tex]6*\frac{\sqrt{3} }{4} p^{2}[/tex]

The area of a regular hexagon with a side of 4m = [tex]6*\frac{\sqrt{3} }{4} 4^{2}[/tex]

The area of a regular hexagon with a side of 4m =24√3.

Therefore, The area of a regular hexagon with a side of 4m is 24√3.

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Colinda's first monthly mortgage payment includes $143.70 towards amortization, after subtracting the first month's interest of $333.30 from the total payment of $477.

To determine how much of Colinda’s first monthly mortgage payment is for amortization, we must first calculate the amount of her payment that goes towards interest and then subtract this from the total monthly payment.

Colinda bought a house for $125,000, made a 20% down payment ($25,000), and took out a mortgage for the remaining $100,000 at a 4% annual interest rate. Her monthly mortgage payment is $477.

First, calculate the monthly interest rate: 4% annually means 0.04 / 12 per month = 0.003333. Therefore, the first month’s interest on the mortgage is $100,000 * 0.003333 = $333.30.

Next, subtract the interest from the total monthly payment to find the amortization portion: $477 (total monthly payment) – $333.30 (interest) = $143.70 towards amortization.

The amount of Colinda's first monthly mortgage payment that is amortization is approximately $143.67.

To separate the interest portion from the total payment.

First, let's calculate the monthly interest rate:

[tex]\text{Monthly interest rate} = \frac{4 \%}{12} = \frac{0.04}{12} = 0.00333 \text{ (approx.)}[/tex]

Next, we calculate the interest portion of the first payment:

[tex]\text{Interest portion} = \text{Principal} \times \text{Monthly interest rate}[/tex]

[tex]\text{Interest portion} = 100,000 \times 0.00333 = 333.33 \text{ (approx.)}[/tex]

Now, to find the amortization portion, we subtract the interest portion from the total monthly payment:

[tex]\text{Amortization portion} = \text{Total monthly payment} - \text{Interest portion}[/tex]

[tex]\text{Amortization portion} = 477 - 333.33 = 143.67[/tex]

You're working with a geometric problem where the probability of success is constant in each trial. This is related to the situation where you repeatedly ask students if they live within a five-mile radius. The problems you've mentioned seem to involve figuring out specifics related to degrees and interpreting figures.

It sounds like you're dealing with a geometric problem. Geometric problems often involve situations where the probability of success or failure stays constant across trials. For example, you inquire if a person lives within five miles of you - the probability is fixed, regardless of the number of people you ask.

Let's decipher it step by step. Firstly, visualize each instance (trial) as the asking of a question to a student and consider success as the event where the student lives within five miles. Probability of success then stays the same every time you ask.

In problem 91, it's important to understand the degrees involved. The first part mentions 88.6°. Without the full problem, it's hard to give a direct answer here, but angles often play a part in geometry and trigonometry problems, it could be related to that. As for the figures mentioned (Car X, the hash marks) they would likely be visible on a diagram accompanying your problem and would inform the solution.

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the answer is 5 units i know this because i just took a test with this question

Volume of cylinder is 250πcm³ and volume of the new cylinder is 1000πcm³.

The volume of the cylinder can be determined by multiplying area of base with height of the cylinder.

V=πr²*h

where r is the radius of base of the cylinder and h is the height of the cylinder.

following this above formula in given problem,

radius of the base of the cylinder=  5cm

height of the cylinder=10cm

volume= V=πr²*h= π5²*10= 250π cm³

Now the radius of the cylinder is increased to 10cm.

now r=10cm

height of the cylinder=10cm

volume= V=πr²*h= π10²*10= 1000π cm³

Therefore volume of cylinder is 250πcm³ and volume of the new cylinder is 1000πcm³.

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In summary:

- Angle 1 = Angle 2 = Angle 3 = Angle 4 = 69°

- Angle 5 = Angle 6 = Angle 7 = Angle 8 = 116°

- Angle 9 = Angle 10 = 69°

- Angle 11 = Angle 12 = 116°

Let's analyze the complex figure with parallel lines and transversals. We have two parallel lines, a and b, intersected by two transversals. I'll break down the problem step by step:

1. Angle 1: This angle is formed by the intersection of a and the transversal. It is an **alternate interior angle** with the angle measuring 69°. Therefore, **Angle 1 = 69°**.

2. **Angle 2**: It is also an alternate interior angle with the same measure as **Angle 1**. Hence, **Angle 2 = 69°**.

3. **Angle 3**: This angle is formed by the intersection of **b** and the transversal. It is a **corresponding angle** to **Angle 1**. Therefore, **Angle 3 = 69°**.

4. **Angle 4**: It is a corresponding angle to **Angle 2**. Thus, **Angle 4 = 69°**.

5. **Angle 5**: This angle is formed by the intersection of **c** and the transversal. It is an **alternate interior angle** with the angle measuring **116°**¹. Therefore, **Angle 5 = 116°**.

6. **Angle 6**: It is also an alternate interior angle with the same measure as **Angle 5**. Hence, **Angle 6 = 116°**.

7. **Angle 7**: This angle is formed by the intersection of **d** and the transversal. It is a **corresponding angle** to **Angle 5**. Therefore, **Angle 7 = 116°**.

8. Angle 8: It is a corresponding angle to Angle 6. Thus, Angle 8 = 116°.

9. Angle 9: It is a vertical angle to Angle 1. Therefore Angle 9 = 69°.

10. Angle 10: It is a vertical angle to Angle 2. Thus Angle 10 = 69°.

11. Angle 11: It is a vertical angle to Angle 5. Therefore, Angle 11 = 116°.

12. Angle 12: It is a vertical angle to Angle 6. Thus, Angle 12 = 116°.

∑ 4 * 5^(i-1) = 4 + 20 + 100 + 500 = 624

∑ 3 * 4^(i-1) = 3 + 12 + 48 + 192 + 768 = 1,023

∑ 5*  6^(i-1) = 5 + 30 = 35

∑ 5^(i-1) = 1 + 5 + 25 + 125 = 156

Answer:

∑ (i=1, 2) 5 * 6^(i-1) < ∑ (i=1, 4) 5^(i-1) < ∑ (i=1, 4) 4 * 5^(i-1) <

< ∑ (i=1, 5) 3 * 4^(i-1)

Answer:

Original price was $400.

Step-by-step explanation:

Let the original price = x dollars.

It is given that the new price is obtained by increasing the original price by 30% i.e. 0.3

As, the new price is $520.

So, we have the relation,

[tex]x+0.03x=520[/tex]

i.e. [tex]1.3x=520[/tex]

i.e. [tex]x=\frac{520}{1.3}[/tex]

i.e. x = 400

Hence, the original price was $400.

Answer:

Step-by-step explanation:

In a 45°–45°–90° triangle, the hypotenuse is times the length of each leg. Because triangle XYZ is a right triangle, the side lengths must satisfy the Pythagorean theorem that is:

[tex]a^{2}+b^{2}=c^{2}[/tex], which in this isosceles triangle becomes [tex]a^{2}+a^{2}=c^{2}[/tex] as a=b in isosceles triangle.

By combining the like terms, [tex]2a^{2}=c^{2}[/tex]

Now, we will determine the principal square root of both sides of the equation,

[tex]c=\sqrt{2}a[/tex] (since a is positive)

Divide both sides of the equation by 2, we get

[tex]\frac{c}{2}=\frac{\sqrt{2}a}{2}[/tex]

[tex]\frac{c}{2}=\frac{a}{\sqrt{2}}[/tex]

[tex]c=\frac{2a}{\sqrt{2}}[/tex]

[tex]c=\sqrt{2}a[/tex]

Now, as a=b, then [tex]c=\sqrt{2}b[/tex]