what is 235 written as a product of prime factors?

Answer: 193

Step-by-step explanation: an image is included to show you the steps.

From the division of given numbers we get quotient as 193 and the remainder as 0.

The two given numbers are 579 and 3.

Here, 579 divided by 3.

That is, 579/3

3|579|193

  3

_____

 279

 27

_____

  09

  09

_____

  00

So, the quotient is 193 and the remainder is 0.

Therefore, from the division of given numbers we get quotient as 193 and the remainder as 0.

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The value of 'x' will be;

⇒ x = 13/5

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

A triangle has sides with lengths of 5x, 15 and 17.

And, The perimeter of the triangle is 45 meters.

Now,

Since, the perimeter of the triangle is 45 meters.

Hence, We can formulate;

⇒ 5x + 15 + 17 = 45

Solve for x as;

⇒ 5x + 32 = 45

⇒ 5x = 45 - 32

⇒ 5x = 13

⇒ x = 13/5

Thus, The value of 'x' will be;

⇒ x = 13/5

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To evaluate 8[tex]a^3b^{-2[/tex] for a=4 and b=-5, substitute the given values into the expression and simplify to obtain the final result, which is 16.32.

To evaluate 8[tex]a^3b^{-2[/tex] for a=4 and b=-5, we substitute the given values into the expression. Plugging in these values, we have:

8[tex](4)^3(-5)^{(-2)[/tex]

Simplifying this expression, we get:

8(64)(1/[tex](-5)^2)[/tex]

The next step is to calculate the value of [tex](-5)^2[/tex], which equals 25. So the expression becomes:

8(64)(1/25)

Then, multiplying 64 by 1/25, we get:

8(64/25)

Finally, multiplying 8 by 64/25, we obtain:

16.32

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The difference in price of a car is £375 it is due to the rate of VAT increase from 17.5% to 20% and this can be evaluated by the help of unitary method.

Given :

Rate of VAT increased from 17.5% to 20%.

Total price of a car =  £15000 + VAT.

In this problem unitary method can be used to determine the difference in price of a car which is due to the increased rate of VAT.

The price of VAT when its' rate is 17.5% can be:

[tex]= \dfrac{15000}{100} \times 17.5[/tex]

= £ 2625

Therefore, the total price of car when VAT is 17.5% is £17625.

The price of VAT when its' rate is 20% can be:

[tex]= \dfrac{15000}{100} \times 20[/tex]

= £ 3000

Therefore, the total price of car when VAT is 20% is £18000.

So, the difference in price of car = 18000 - 17625 = £375.

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Solution-

Two cars leave the same location traveling in opposite directions.

The first car leaves at 3 p.m and has a speed of 55 mph

The second car leaves at 4 p.m and has a speed of 75 mph

Let x hours after the first car leaves, the two cars are 380 miles apart from each other.

[tex]Speed =\frac{Distance}{Time}[/tex]

[tex]\Rightarrow Distance=Speed\times Time[/tex]

In this x hours, distance covered by the first car,

[tex]\Rightarrow Distance_1=Speed_1\times Time_1[/tex]

[tex]\Rightarrow Distance_1=55\times x[/tex]

As the second car leaves at 4 p.m i.e 1 hour late as compared to the first car, so distance covered by the second car in (x-1) hours,

[tex]\Rightarrow Distance_2=Speed_2\times Time_2[/tex]

[tex]\Rightarrow Distance_2=75\times (x-1)[/tex]

According to the question,

[tex]Distance_1+Distance_2=380[/tex]

[tex]\Rightarrow 55\times x+75\times (x-1)=380[/tex]

[tex]\Rightarrow 55x+75x-75=380[/tex]

[tex]\Rightarrow 130x=455[/tex]

[tex]\Rightarrow x=3.5[/tex]

∴ After 3.5 hours from 3 p.m i.e at 6.5 p.m the cars will have a distance of 380 miles.

In the graph, the Front view (FV), Top view (TV), and side view (SV) are given.

The orthographic drawing is the 2-D design of the isometric drawing.

Making an orthographic drawing for the isometric drawing that is the right.

The isometric drawing is the 3-D view of the object.

The graph is given below.

In the graph, the Front view (FV), Top view (TV), and side view (SV) are given.

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Answer: Our required probability is 12%.

Step-by-step explanation:

Since we have given that

Probability of being selected as the captain of the baseball team= P(A) = 60%

Probability of being selected as elected student body president = P(B) = 20%

We need to find the probability of being selected as the captain of the baseball team and will be elected student body president.

Since both the events A and B are independent events.

So, it becomes,

[tex]P(A\cap B)=P(A)\times P(B)=0.6\times 0.2=0.12\times 100\%=12\%[/tex]

Hence, our required probability is 12%.

Final answer:

Seth's table is not square because it has different side lengths of 36' and 18'. For a rectangle to be a square, all four sides must be of equal length. Additionally, the side lengths and the diagonal of Seth's table do not satisfy the Pythagorean relation for a square.

Explanation:

To determine whether Seth's table is square or not, we need to recognize that a square is a rectangle with equal sides. Since the table has sides measuring 36' and 18', we can immediately conclude that it is not square because the lengths of the sides are different. In a square, the lengths of all four sides would be equal.

To further illustrate this point, let's consider the diagonal of a square. For a square, the diagonal can be determined using the Pythagorean Theorem, where the diagonal is the square root of twice the side squared, because a square is essentially two identical right-angle triangles put together.

In Seth's table, if we were to apply the Pythagorean Theorem (a² + b² = c²), we would find that the square of one side plus the square of the other should equal the square of the diagonal. By doing the calculation:

36'² + 18'² = 1296' + 324' = 1620',

which does not equal the square of the diagonal given, which is 43'² = 1849'. This further confirms that the table cannot be square since the sides and the diagonal do not satisfy the Pythagorean relation for a square.

A. For this to be a linear situation, we must assume that Marisa is walking a straight path so that the time needed to cover a distance is constant.

B. The equation of the line is given as:

y = m x + b

where in this case y is the distance, m is the slope or the time it takes for each block, x is the time, and b is the y intercept or the initial position of Marisa

C. The slope m can be calculated using the formula:

m = (y2 – y1) / (x2 – x1)

m = (8 – 12) / (6 – 0)

m = -0.67

The negative sign means that the distance between Marisa and Sanjay’s home is decreasing by time. It further means that there is a decrease in 0.67 blocks per minute.

D. y = - 0.67 x + b

The initial point of Marisa is at 12 blocks away from Sanjay’s home, hence b = 12.

Finding for time x when distance is 0 (y = 0):

0 = -0.67 x + 12

x = 17.9 minutes

Hence it takes around 17.9 minutes to reach Sanjay’s home.

Answer:

4.

Step-by-step explanation:

To find the total, we would be adding together Max's donated items and Mia's donated items.

"Regrouping" is just another way of stating that we have to carry in the addition.

If we add 16+1, there is no carrying or regrouping.

If we add 16+2, there is no carrying or regrouping.

If we add 16+3, there is no carrying or regrouping.

If we add 16+4, we must carry (regroup).  This is because 6+4 = 10, so we carry 1 to the tens place.  This is the first time we would regroup this number.

To regroup is another term used for "carry" in arithmetic operations

The least number of items Mia would add, that would require regroup is 4

From the question, we have:

[tex]Max= 16[/tex]

When 1, 2 or 3 are added to 16, there is no "carry" operation.

Because, they are all straight addition operations

[tex]16 + 1 = 17[/tex]

[tex]16 + 2= 18[/tex]

[tex]16 + 3 = 19[/tex]

However, when 4 is added to 16, there is a need to regroup.

The addition is illustrated as follows:

[tex]\left[\begin{array}{ccc}1&6\\ +&4&\\&&\end{array}\right][/tex]

Add 6 and 4;

The result is 10.

So, we write down 0, and "carry" 1

[tex]\left[\begin{array}{ccc}1&6\\ +&4&\\&0&\end{array}\right][/tex]

Next, add 1 (the one beside 6) to the 1 we carried in the previous addition

The result is 2

[tex]\left[\begin{array}{ccc}1&6\\ +&4&\\2&0&\end{array}\right][/tex]

The process of "carrying" is what is referred to as regroup

So, the least number of items Mia would add, that would require regroup is 4

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The correct answer is:A. 3x^2 −2x−6

To find (f−g)(x), you subtract g(x) from f(x).

So,(f−g)(x)=f(x)−g(x)

Given that

f(x)=3x^2 −2 and g(x)=2x+4, let's substitute these into the expression:

(f−g)(x)=(3x^2 −2)−(2x+4)

Now, distribute the negative sign:

(f−g)(x)=3x^2 −2−2x−4

Combine like terms:

(f−g)(x)=3x^2 −2x−6

So, the correct answer is:A. 3x^2 −2x−6

Answer:

three times square of n minus x

Step-by-step explanation:

[tex]3n^2-x[/tex]

We need to write the given expression in verbal form

n^2 is written as square of n

3n^2 can be written as three times square of n

for -x , we use minus x

[tex]3n^2-x[/tex]

three times square of n minus x

The verbal expression for the given expression is

three times square of n minus x

Answer:

The given product is

[tex]3.4 \times 0.5 = 1.7[/tex]

This results was showed by the calculator, which doesn't shows the two decimal numbers that it should have.

The reason why the calculator only shows one decimal number, it's because the second decimal number is zero, and it would be the same if we express [tex]1.7[/tex] or [tex]1.70[/tex], that zero doesn't change the value that the number represents.

However, if we solve without calculator, we would have [tex]1.70[/tex], because the multiplication rule states that we should add to the result as many decimal number have both factor of the multiplication, which in this case they have two.

When multiplying or dividing decimals, the number of decimal places in the product or quotient may not be the same as the factors or dividend and divisor. The product or quotient should have the same number of decimal places as the factor/dividend or divisor with the fewest decimal places.

When multiplying or dividing decimal numbers, the number of decimal places in the product or quotient may not be the same as the number of decimal places in the factors or dividend and divisor. This happens because the calculator does not consider significant figures and simply performs the operation.

To determine the number of decimal places in the product or quotient, look at the decimal places in the factors or dividend and divisor. The product or quotient should have the same number of decimal places as the factor/dividend or divisor with the fewest decimal places.

In Tony's example, 3.4 x 0.5 = 1.7, the factor with the fewest decimal places is 0.5 with one decimal place. Therefore, the product should also have one decimal place.

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