It says on the first three days of their trip,the Smiths drove 408 miles,347 miles,and 419 miles.Altogether how far did they drive in three days

Final answer:

Point Z is located at 2 on the number line, found by adding the distance YZ=11 to the location of Y at -9.

Explanation:

If Y and Z are points on the number line, YZ=11, and Y lies on -9, to find where Z would be located, you simply add the distance between Y and Z to the point Y. Since the distance YZ=11, and Y is at -9 on the number line, you add 11 to -9 to find Z.

Therefore, the location of point Z will be:

-9 + 11 = 2

So, point Z is located at 2 on the number line.

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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Answer:

Option A- 60°            

Step-by-step explanation:

Given : Function - [tex]4cos^2x-1=0[/tex]

To solve the function

Step 1 - Write the function

[tex]4cos^2x-1=0[/tex]

Step 2- Add 1 both side

[tex]4cos^2x=1[/tex]

Step 3- Divide 4 both side

[tex]cos^2x=\frac{1}{4}[/tex]

Step 4 - Taking root both side

[tex]cosx=\sqrt{\frac{1}{4}}[/tex]

Step 5 - solve

[tex]cosx=\pm{\frac{1}{2}}[/tex]

Either [tex]cosx={\frac{1}{2}}[/tex] or [tex]cosx=-{\frac{1}{2}}[/tex]

When [tex]cosx={\frac{1}{2}}[/tex]

            [tex]\rightarrow cosx={cos\frac{\pi}{3}}[/tex]

            [tex]\rightarrow x={\frac{\pi}{3}} or 60^{\circ}[/tex]

or when  [tex]cosx=-{\frac{1}{2}}[/tex]

               [tex]\rightarrow cosx={cos(\pi-\frac{\pi}{3})}[/tex]

            [tex]\rightarrow x={\frac{2\pi}{3}} or 120^{\circ}[/tex]

Therefore, Option A is correct solution of function is at 60°.

The solution of the given trigonometric ratio for the expression 4cos²x - 1 = 0 is equal to 60°

To find the solutions to the equation 4cos²x - 1 = 0, we first need to isolate the cosine term and then solve for x.

Let's go through the steps,

Add 1 to both sides of the equation:

4cos²x = 1

Divide both sides by 4:

cos²x = 1/4

Take the square root of both sides:

cosx = ±√(1/4)

Now, we have two cases to consider: positive and negative square roots.

Case 1,

cosx = √(1/4)

The cosine of an angle can never be negative when expressed in degrees, so we ignore the negative square root.

cosx = √(1/4) = 1/2

To find the angles for which the cosine is 1/2, we look at the unit circle or use a calculator to find the inverse cosine (arccos) values:

x = arccos(1/2)

The principal angle that satisfies this is x = 60°.

Case 2,

cosx = -√(1/4)

Again, we ignore the negative square root as the cosine is not negative in degrees.

Therefore, the only solution to the equation is:

x = 60°

Therefore, among the given options, the solution to 4cos²x - 1 = 0 is 60°.

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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:

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:

D). 1,808.64 in2

Step-by-step explanation:

Diameter - 48 in.

Therefore, the radius is half of 48. 48/2 = 24.

Area = 3.14(24) 24 = 1,808.64in2

Hope this helps

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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To find the number of albums Floyd sold last month, we calculate it using the linear equation $644 = $200 + ($12 \u00d7 a), where $644 is the total earnings, $200 is the base rate, and $12 is the amount earned per album. Floyd sold 37 albums last month.

To determine the number of albums Floyd sold last month, we can set up a linear equation based on the information provided. Floyd is paid a base rate of $200 per month, and he earns an additional $12 for every album sold. The total amount Floyd earned last month was $644.

Let's let a represent the number of albums sold. The equation that represents the total earnings for the month would be:

Total Earnings = Base Rate + (Number of Albums Sold × Price per Album)

Based on what has been given, we can express this as:

$644 = $200 + ($12 × a)

To find the number of albums sold, we subtract the base rate from the total earnings, then divide by the additional amount earned per album:

$644 - $200 = $12 × a

$444 = $12 × a

a = $444 / $12

a = 37

So, Floyd sold 37 albums last month.

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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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:

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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