A carpenter has a wooden dowel that is 72 cm long. She wants to cut it into two pieces so that one piece is 7 times as long as the other. What is the length of the longer piece?

Answer:

(a)  15

(b)  270

Step-by-step explanation:

Given expression:

[tex]\left(\sqrt{5}\right)^2 \times \left(\sqrt{3}\right)^2[/tex]

[tex]\textsf{Apply the exponent rule}:\quad \left(\sqrt[n]{a}\right)^n=a,\quad \textsf{$n$ is odd or $a \geq 0$}[/tex]

[tex]\implies 5 \times 3[/tex]

Multiply the numbers:

[tex]\implies 15[/tex]

Given expression:

[tex]\left(\sqrt[3]{9} \right)^3 \times \left(\sqrt{30}\right)^2[/tex]

[tex]\textsf{Apply the exponent rule}:\quad \left(\sqrt[n]{a}\right)^n=a,\quad \textsf{$n$ is odd or $a \geq 0$}[/tex]

[tex]\implies 9 \times 30[/tex]

Multiply the numbers:

[tex]\implies 270[/tex]

Now we have to,

→ work out the value for the following.

We know that,

→ square ( ²) and square root (√) gets cancelled each other.

→ cube ( ³) and cube root (³√) gets cancelled each other.

a) (√5)² × (√3)² = ?

→ (√5)² × (√3)²

→ 5 × 3 = 15

Thus, the answer is 15.

b) (³√9)³ × (√30)² = ?

→ (³√9)³ × (√30)²

→ 9 × 30 = 270

Thus, the answer is 270.

To solve for x in: [tex]2x + 8 = 3x + 10[/tex]

Collect like terms

[tex]→8 - 10 = 3x - 2x \\ - 2 = x[/tex]

Therefore:

[tex]x = - 2[/tex]

The coordinates of the image of the point (- 4, 5) is (- 5, 15).

In this question we find the coordinates of the original point and the translation vector. Please notice that translations are examples of rigid transformations, meaning that Euclidean distance is conserved in the resulting image. A translation can be done by the following formula:

P'(x, y) = P(x, y) + T(x, y)

Where:

If we know that P(x, y) = (- 4, 5) and T(x, y) = (- 1, 10), then the resulting point is:

P'(x, y) = (- 4, 5) + (- 1, 10)

P'(x, y) = (- 5, 15)

There is a typing mistake in the statement. Correct form is shown below:

(- 4, 5) is translated by the vector (- 1, 10). What coordinate would it be at?

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The required total of price area,  leather field, and sneakers field is evaluated with the help of arithmetic operations as 102.

Given that,
Joining 60.00 into the price, area joining 3.00 into the price of the leather field entering 38.00 into the price of sneakers field,
The sum of the components is to be determined.

In mathematics, it deals with a number of procedures according to the statements. There are four primary arithmetic operators, addition, subtraction, multiplication, and division,

Here,
Joining 60.00 into the price area,
Joining 3.00 into the price of the leather field.
entering 38.00 into the price of sneakers field,
The sum = 60.00 + 3.00 + 38.00
The sum = 102

Thus, the required total of entries is evaluated with the help of arithmetic operations as 102.

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Answer:

x = 3

Step-by-step explanation:

The scale factor is 3.

[tex]scale factor =\frac{scaled\ measure}{actual\ measure}[/tex]

∵ If sides of a polygon are changed by a scale factor 'a' then its perimeter is also changed by the same scale factor,

[tex]scale factor =\frac{scaled\ perimeter}{actual\ perimeter}[/tex]

The actual perimeter of the polygon = 10 unit,

Also, the scaled perimeter = 30 units

Hence,

[tex]scaled factor = \frac{30}{10} =3[/tex]

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Answer:

Step-by-step explanation:

[tex]\displaystyle\\\frac{1}{2},\ \ \frac{4}{7},\ \ \frac{9}{14},\ \ \frac{5}{7} ,\ \ ... \\\\\frac{1*7}{2*7} ,\ \ \frac{4*2}{7*2} ,\ \ \frac{9}{14}, \ \ \frac{5*2}{7*2} ,\ \ ...\\\\\frac{7}{14},\ \ \frac{8}{14} , \ \ \frac{9}{14},\ \ \frac{10}{14},\ \ \frac{11}{14},\ \ ...,\ \ \frac{6+n}{14} , \ \ n=1,\ 2,\ 3,\ ...[/tex]

A whole number larger than 2 leaves a remainder of 2 when divided by each of the numbers 3, 4, 5, and 6 is 62.

To find the whole number:

Therefore, a whole number larger than 2 leaves a remainder of 2 when divided by each of the numbers 3, 4, 5, and 6 is 62.

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Answer:

15 points

Step-by-step explanation:

It's 60 points over 4 days. We can divide 60 by 4, which is

15

The order from least to greatest is  -8.222 <-7.43 < 8.333 < 8.366

The numbers given are:

The square root of 70 =√70 = 8.366

Negative 8.2 repeating = -8.222

Twenty five thirds = 25/3 = 8.333

Negative eight and Four sevenths = -8 and 4/7 = (-52)/7 = -7.43

So from least to greatest,

-8.222 <-7.43 < 8.333 < 8.366

That is,  Negative 8.2 repeating < Negative eight and Four sevenths < Twenty five thirds < The square root of 70

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Marsha pay $30 each month for a car wash membership.

In one month Marsha pay $30

In eight month Marsha pay 8*$30 = $240

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Answer:

A. |-30| - 8 = $22

Step-by-step explanation:

You are told to subtract 30 and 8, and the 30 is represented as |-30| - 8 = $22

(if this is incorrect am sorry ;-;)

According to the given statement;

Billy bought 8 flower pots, which will hold a total of 67 litres of dirt. The flower pot Billy  bought his flower pot is x=5.

The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.

For example, 2x+3=8 is a linear equation having a single variable in it.

According to given value ;

    Let x = number of clay pots. Since Billy bought 8 pots in total , the                    number of ceramic pots Billy bought is 8-x

    67 =(8 litre )*(x clay pots)+(9 litres)*(8-x);

       67=8x+72-9x

       67=(-x)+72

      -x =(-72+67)

      ( -x) = -5

         x =5

Hence 8 litre of dirt clay pots is 5 then 9 litres of ceramic flower pot is is 3.

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Answer:

24 books can fit on 1 shelf.

Step-by-step explanation:

Question: Juan has 28 paperback books that measure 1 and 1/4 inches each. How many books will fit on one shelf if each shelf measures 30 inches?

Step-by-step:

We know that each book is 1 and 1/4 inches each. It might be easier to convert the fraction into a decimal.

1/4 inches is 1 divided by 4 which equals to 0.25 inches

1 inch + 0.25 inches = 1.25 inches

so, 1 and 1/4 inches = 1.25 inches

To find out how many books fit on a shelf, we need to find: length of 1 bookshelf divided by length of 1 book

We know that one bookshelf is 30 inches and 1 book is 1.25 inches

so, 30/1.25 or 30 divided by 1.25 = 24

Therefore, 24 books can fit on 1 shelf.

The equation that illustrates the amount to be paid for the number of kilometers will be 7.25 + 7x.

Fixed rate for taxi = 7.25

Additional charges per kilometers = 7

Number of kilometers = x

Therefore, the equation that illustrates the amount to be paid for the number of kilometers will be:

= 7.25 + (7 × x)

= 7.25 + 7x

Therefore, the equation is 7.25 + 7x.

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Answer:

A. $7.46

Step-by-step explanation:

184.54 - 5.50 = 179.04

179.04 / 24 = 7.46

The answer WITHOUT SUBTRACTING THE DELIVERY FEE is: $7.69 (B).

If you're supposed to subtract the delivery fee, then the answer is $7.46 (A).

----------------------------------

Hope this helps!

Have a great day and God bless! :)

Answer:

There are 14 problems worth 5 points and 15 problems worth 2 points.

Step-by-step explanation:

x - the number of 5 points worth problems

y - the number of 2 points worth problems

The test has 29 problems.

x+y=29x+y=29

The test is worth 100 points.

5x+2y=100

The system of equations:

x+y=29

5x+2y=100

The solution:

x+y=29 ∣×(−2)

5x+2y=100

Substract −2x−2y=−58 from 5x+2y=100

−2x−2y=−58

5x+2y=100

------------------

3x=42

3x/3 = 42/3

x=14

x+y=29

14+y=29

14+y-14 = 29 - 14

y=15

There are 14 problems worth 5 points and 15 problems worth 2 points.

Answer:

Step-by-step explanation:

solve the equation for x if 2 to the power x = 8​

2^x = 8

log(2x)=log(8)

x*log(2)=log(8)

x=((log(8))/((log(2))

x=3

----------------------------

check

2^3 = 8

2 * 2 * 2 = 8

8 = 8

the answer is good

Since T is continuous for [tex]0\leq x \le 10[/tex], [tex]\lim_{x \to 4} T(x)=T(4)[/tex] From the table:

[tex]\lim_{x \to 4} T(x)=172^{0}[/tex]

A continuous function in mathematics is one that causes the value of the function to continuously vary as the input changes over time. This indicates that there aren't any discontinuities or sudden changes in value. In other words, a function is continuous if and only if its graph is devoid of any gaps or breaks. It is simple to predict where it won't be continuous for many functions. Where we have operations like division by zero or logarithms of zero, functions won't be continuous. Examples of continuous functions over the set of all real numbers are polynomial functions, exponential functions, and the sin and cosine graphs.

For the final answer the table is to be checked and all the values are written.

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The coordinates of the vertex P is calculated as (0,2√3).

The distances among two points as a characteristic of their coordinates are given by an algebraic expression (like coordinate system).

Now, according to the given question;

The coordinates of the points Q and R  is given as;

Q and R as (-2, 0) and (2, 0).

Now, as the all three points P,Q and R forms the equilateral triangle. Then, the distance of each side or the distance between two consecutive points are equal.

Calculate the distances between the points;

QR = √(2 + 2)² + (0 - 0)²

QR = 4

Let the coordinated of P be (x, y);

Then,

QP = √(x + 2)² + (y + 0)²

QP = QR = 4

4 = √(x + 2)² + (y)²     ........(equation 1)

RP = √(x - 2)² + (y + 0)²

RP = QR = 4

4 = √(x - 2)² + (y)²     ........(equation 2)

Equating equation 1 and 2.

√(x + 2)² + (y)² = √(x - 2)² + (y)²

Squaring both side;

(x + 2)² + (y)² = (x - 2)² + (y)²

x² + 4 - 4x + y² = x² + 4 - 4x + y²

Simplifying the equation;

x = 0.

Put the value of x in equation 1;

4 = √(x + 2)² + (y)²

y = 2√3.

Therefore, the coordinates of the point P are found to be (0, 2√3).

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Answer:

I believe it's B

4x - 5y = 16

Step-by-step explanation:

First you divide the whole term by -1 to get rid of negative in front of equation and then you add the c term (-16) to both sides to get the final answer.

I hope you get this right.

Answer:

26 cups

Step-by-step explanation:

1 quart = 4 cups

6 quarts x 4 cups =  24 cups

1/2 a quart = 2 cups

Answer:

12

Step-by-step explanation:

Answer:

Step-by-step explanation:

Step One

The first step is to find the value of n.

h(x) = n(x) + 28

h(3) = 1

That means that 1 is on the left and wherever there is an x on the right, it will have a value of 3

Step Two

Substitute values

1 = n(3) + 28                  

Step 3

Solve

1 = 3*n + 28                       Subtract 28 from both sides

1 + - 28 =  3n                     Combine

-27 = 3n                             Divide both sides by 3

-27/3 = 3n/3

- 9 = n

Step 4

Let x = - 6 on the right side of the original equation.

h(-6) = 3*-6 + 28

h(-6) = -18 + 28

Answer

h(-6)  = 10

Answer:

1 cm = 0.6 m.

Step-by-step explanation:

15 cm to 9 meters

= 15 cm to 900 cm

so 1cm = 900/15 cm

1cm = 60cm

1 cm = 0.6 m.

Hence ,  the difference in length between segments AB and AD is 1.17 units .

The diagram of the given question is given below .

Applying sin rule in triangle ABC , we get

sin(x°) = AC/AB

sin(45°) = 4 / AB

1 /√2 =  4 / AB

AB = 4√2

AB ≈ 5.657

Similarly, apply sin rule  in triangle ACD, we get

sin(y°) = AC /CD

sin(63°) = 4 / CD

AD = 4.489

Now distinction in lengths of AB and AD = 5.657 - 4.489

                                                                     = 1.168

                                                                     ≈ 1.17

Therefore, distinction within the lengths of AB and AD are going to be 1.17 units.

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The order of the numbers from least to greatest is:

 85% < Two and one fifth < 3.24 < Nineteen over 4

The given data set of numbers are: nineteen over 4, two and one fifth, 85%, and 3.24

In order to compare these numbers, we will change all of them into float (decimal) format.

nineteen over 4 = 19/4 = 4.75

two and one fifth = 2 [tex]\frac{1}{5}[/tex] = 11/5 = 2.2

85% = 85/100 = 0.85

And 3.24 are the numbers set.

Now the order of numbers from least to greatest is clear.

Since 0.85 < 2.2 < 3.24 < 4.75, we can conclude

   85% < 2 [tex]\frac{1}{5}[/tex] < 3.24 < 19/4

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The number of hamburgers sold on Wednesday is 141 and the number of cheeseburgers sold on Wednesday is 423

Although a part of your question is missing, you might be referring to this full question: On Wednesday, a local hamburger shop sold a combined total of 564 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Wednesday?

Total number of burgers sold on Wednesday = 564

Let the number of hamburgers sold on Wednesday be x

Let the number of cheeseburgers sold on Wednesday be y

Formulating the equation we get:

x + y = 564-----(1)

It is also given that, the number of cheeseburgers sold was three times the number of hamburgers. So,

y = 3x

Substituting y = 3x in equation (1) we get

x + 3x =564

4x = 564

x = 141

Putting x = 141 in equation (1) we get

y = 423

So, the number of hamburgers sold is 141 and the number of cheeseburgers sold is 423

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Answer: A sequence is a enumerated collection of objects in which repetitions are allowed/order matters while a series is a infinite series. A series is definite if its based on the concept of sequences.

A series could be finite or infinite because its mainly  often represented in compact form which is also known as a  sigma notation(∑)to indicate the summation involved. infinite series is the sum of an infinite sequence.

Step-by-step explanation:

Answer:

-1/5

Step-by-step explanation:

Minus a negative is plus.

-3/5 - (-2/5) =

= -3/5 + 2/5

= -1/5