Calculate the distance
Benjamin rides
his scooter if he rides 3/5mile
each day
for 10 days.​

Answer:

$8.75

Step-by-step explanation:

You and three friends = 4 people

$35 / 4 people = $8.75

The cost of one ticket is $8.75

Hope this helps :)

Answer:

35/12

Step-by-step explanation:

1 1/2+1 5/12

=3/2+17/12

=3*6+17*1/12

=18+17/12

=35/12

Tom read a total of 11/12 of the two books combined by reading 1/2 of the first book and 5/12 of the second book, after finding a common denominator to add the fractions.

To calculate the total fraction of the two books that Tom has read, we need to add the fractions of each book he has read together. Tom read 1/2 of the first book and 5/12 of the second book.

To add these fractions, they need to have a common denominator. The lowest common denominator between 2 and 12 is 12.

Therefore, we convert 1/2 into 6/12 so that both fractions have the same denominator.

Now, the fractions to be added are 6/12 (from the first book) and 5/12 (from the second book).

Adding these fractions, we get:

6/12 + 5/12 = 11/12

So, Tom has read a total of 11/12 of the two books combined. This method of finding a common denominator and then adding the numerators is an effective strategy to add fractions with different denominators, providing a clear, step-by-step approach to solving such problems in mathematics.

Multiply the top equation by 6 and and the bottom equation by –5 and then add the equations is the correct answer.

Solution:

Given system of equations:

8x + 5y = –7 – – – – (1)

–7x + 6y = –4 – – – – (2)

Multiply top equation by 6 and and bottom equation by –5

(1) × 6 ⇒ 48x + 30y = –42

(2) × –5 ⇒ 35x – 30y = 20

Now add these two equations, we get

(48x + 30y) + (35x – 30y) = –42 + 20

48x + 35x + 30y  – 30y = –42 + 20

83x = –20

The variable y is eliminated.

Therefore Multiply the top equation by 6 and and the bottom equation by –5 and then add the equations is the correct answer.

Answer:

Multiply the top equation by −5, then add the equations.

Step-by-step explanation:

Did it on Khan Academy

The simplified ratio that correctly compares 27 feet to 36 feet is 3:4

Step-by-step explanation:

Step 1: Simplify the ratio by finding common factor

Step 2: Here, in this case the lowest common factor is 3. Divide both numerator and denominator by 3.

⇒ 27/36 = 9/12 (on dividing by 3)

⇒ 9/12 = 3/4 (again on dividing by 3)

Answer:

exact form is 5/12

decimal form is 0.416666

Step-by-step explanation:

Equivalent fractions are fractions that have the same value or proportion. To find an equivalent fraction to a given fraction, you multiply or divide both the numerator and the denominator by the same number. Therefore, 10/24 and 15/36 are equivalent fractions to 5/12.

To find an equivalent fraction to 5/12, you simply multiply or divide both the numerator (the top number) and the denominator (the bottom number) by the same non-zero number. An equivalent fraction will have a different numerator and denominator, but it will represent the same value or proportion. For example, if we multiply both the numerator and the denominator of 5/12 by 2, we get 10/24. Therefore, 10/24 is an equivalent fraction to 5/12.

Similarly, if we multiply 5 (the numerator) and 12 (the denominator) by 3, we get the equivalent fraction 15/36.

So, 5/12 = 10/24 = 15/36 in terms of value or proportion.

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Answer:

F(3) = 2 * 3 - 1, which is 6 - 1 equaling 5.

Step-by-step explanation:

3 times 2 is six since you have to follow PEMDAS (Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction). Multiplication is before Subtraction, and that is why we multiply 2 and 3 first, since 3 replaces the variable x. After multiplying 2 and 3 to get 6, subtract by 1 to get 5.

Answer: 5

Answer:

See photo

Step-by-step explanation:

The line is in slope-intercept form which looks like y = mx + b.

"x" and "y" represent points on the line.

"m" is the slope (how steep the line is) and if the line goes up (+) or down (-).

"b" is the y-intercept, which is where the graph hits the y-axis.

Take information from the equation y=-2x+6. Use the slope and the y-intercept to graph to line.

m = -2  =  [tex]-\frac{2}{1}[/tex]   (Fraction form).

b = 6

Plot a point at the y-intercept on the y-axis

If the y-intercept is 6, so you plot the point at (0, 6). (The y-intercept occurs when x = 0).

Find another point

Count the number of rise and run from the y-intercept.

Remember the slope is [tex]\frac{rise}{run}[/tex]

Run is the number of squares moving right. Rise is the number of squares moving up (if positive) or down (if negative).

Since the slope is -2/1, move two squares down and one square to the right to find another point on the line.

Connect the points

You only need two points to make a line. If you want the line to be longer, you can extend it with a ruler.

Other formatting rules

Remember to add arrows at the ends of the x and y axis.

Also, add arrows to the ends of the the line that you graphed.

Most teachers ask you to label the line with the equation.

Answer:

(4,5)

Step-by-step explanation:

We are to find the circumcenter of triangle EFG with vertices

E(2,6), F(2,4), and G(6,4)

Let S(x,y) be the circum center.  Then this point is equidistance from E, F and

G

i.e. [tex]ES=FS=GS\\ES^2 =FS^2 =GS^2[/tex]

[tex](x-2)^2+(y-6)^2 =(x-2)^2+(y-4)^2 =(x-6)^2+(y-4)^2 \\i.e. x^2-4x+4+y^2-12y+36 = x^2-4x+4+y^2-8y+16 = x^2-12x+36+y^2-8y+16 \\4y = 20: y =5\\8x=32\\x=4[/tex]

Thus circumcenter is (4,5)

Answer:

216

Step-by-step explanation:

1. √{6^6}

2. √(6^3)^2}

3.6^3

4.216

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Hope this helps!

-ShadyK

The value of the given expression is 216.

The given expression is,

[tex]\sqrt{2\cdot 6^5 + 2\cdot 6^5 + 2\cdot 6^5[/tex]

Square Root Computations:

The square root of a number is the number that we require to multiply by itself to obtain the original number

Now, solving the given expression as,

[tex]\sqrt{2\cdot 6^5 + 2\cdot 6^5 + 2\cdot 6^5}=\sqrt{2\cdot6\cdot6^4+2\cdot6\cdot6^4+2\cdot6\cdot^4}\\ =6^2\sqrt{12+12+12}\\ =36\sqrt{36}\\ =36\sqrt{4\cdot9}\\ =36\cdot2\cdot3\\=216[/tex]

Learn More information about the simplification:

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Answer:

  5·7

Step-by-step explanation:

From your knowledge of multiplication tables, you know that ...

  5×7 = 35

Both 5 and 7 are prime numbers, so that is the prime factorization.

Answer:

Step-by-step explanation:

(5x+17)+(2x+50)

5x+2x + 17+50

7x+67

IF 7x+67 = 0

7x = -67

x = - 67/7 OR x = -9.57

Answer:

OF course!Dividing by 100 just means move the decimal two places to the left, so the answer is 9.652

Step-by-step explanation:

Answer:

=9.852

Step-by-step explanation:

985.2/100

=9.852

Answer:

11 feet

Step-by-step explanation:

Area of rectangle (170.5cm) = length (15.5) x width

170.5/15.5=width

Width = 11

Hope this helps! :)

Answer:

[tex]f(x) = {x}^{2} - 15x + 26[/tex]

Step-by-step explanation:

Assuming we want to write a quadratic function with intercepts x=13 and x=2.

Then we can work backwards.

This means that:

x-13=0 and x-2=0

The factored form of this quadratic function becomes:

[tex]f(x) = (x - 13)(x - 2)[/tex]

We expand to get:

[tex]f(x) = {x}^{2} - 2x - 13x + 26[/tex]

We simplify to obtain:

[tex]f(x) = {x}^{2} - 15x + 26[/tex]

Answer: r = 12.1cm, d = 24.2cm, Area = 460.0cm²

Step-by-step explanation:

From the formula,

Circumference of a circle = πd or 2πr.

To find the radius, we have to equate 76 cm to πd or 2πr and make r or d the subject of the formula. Now

76 = 2πr, don't forget that

π = 22/7 or 3.142

Now make r the subject of the formula

r = 76/2π

= 76/2 x 3.142

= 76/6.284

= 12.1 cm

d = 2r

= 2 x 12.1

= 24.2cm.

Area of the circle is πr²

= 3.142 x (12.1)²

= 3.142 x 146.41

= 460.0 cm²

Answer:

the answer to your question is b

Answer: 1.9

Step-by-step explanation:

because you keep adding 1.9 to get your result

Answer:

11.1

Step-by-step explanation:

3.9 - 1.5 = 2.4

if you add 2.4 to one of the numbers in the sequence it will be the next number.

1.5 + 2.4 = 3.9

3.9 + 2.4 = 6.3

6.3 + 2.4 = 8.7

if this is the case then 8.7 + 2.4 = 11.1

Answer:

-5-4x

Step-by-step explanation:

7-3(4-2x)-10x

7-12+6x-10x

-5+6x-10x

-5-4x

7-12+6x-10x

or

-5-4x

Simplify the answer to get equivalent expressions

Percentage change in perimeter is 100%.

Step-by-step explanation:

Calculate perimeter of R1 = 2 (length + breadth) = 2 (5 + 3)  = 16 ft

Calculate perimeter of R2 = 2 (10 + 6) = 32 ft

= (32 - 16/16) [tex]\times[/tex] 100 = 100%

Answer:

For plato users: Option C.

Step-by-step explanation:

Option B: 5.25 is the length of XZ

Explanation:

The triangles PQR and XYZ are similar.

To determine the length of XZ, let us use the similarity theorem.

The theorem states that, "if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar".

Thus,

[tex]\frac{QR}{YZ} =\frac{PR}{XZ}[/tex]

Let us substitute the values from the diagram, we have,

[tex]\frac{4}{3} =\frac{7}{XZ}[/tex]

Multiplying both sides by 3, we get,

[tex]4 =\frac{21}{XZ}[/tex]

Thus,

[tex]XZ =\frac{21}{4}=5.25[/tex]

Thus, the length of XZ is 5.25

Hence, Option B is the correct answer.

Answer:

i) this does not show direct variation.

ii) this shows direct variation

iii) this shows direct variation

iv) (2x-5y) + (x+y)  =  3x - 4y

v) (7x-5) - (3x-2)  = 4x - 3

Step-by-step explanation:

i.) y - x  = 4                      this does not show direct variation.

ii) x - y = 0   [tex]\Rightarrow[/tex]  x = y       this shows direct variation

iii) 8 = xy    [tex]\Rightarrow[/tex]  8/x = y      this shows direct variation

iv) the sum of (2x-5y) and (x+y)    [tex]\Rightarrow[/tex] (2x-5y) + (x+y)  =  3x - 4y

v) expression that is equivalent to (7x-5) - (3x-2)

[tex]\Rightarrow[/tex]  (7x-5) - (3x-2)  =  4x - 5 + 2 = 4x - 3

Answer:

volume is 432 cubic inches

Step-by-step explanation:

A box measures 1 ft. long, 1/2 ftwide, and  1/2 ft high.

we need to find the volume of the box

Volume of the box formula is

[tex]volume = length \cdot width \cdot height\\[/tex]

convert all the measurement into inches

1 feet = 12 inches

1/2 feet = 6 inches

length = 12 inches, width = 6 inches , height = 6 inches

now we plug in the values in volume

[tex]volume = 12 \cdot 6 \cdot 6= 432 in^3[/tex]

if you have a scientific calculator type in y=4/3x+4

and you should find your answer

It takes about 14.55 years for quadruple your money

Solution:

Given that,

At 10 percent interest, how long does it take to quadruple your money

Rule of 144:

The Rule of 144 will tell you how long it will take an investment to quadruple

Here,

Rate of interest = 10 %

Therefore, number of years to quadruple your money is obtained by dividing 144 by 10

Rule of 144 Formula:

[tex]N = \frac{144}{R}[/tex]

Where:

N = Number of many years times.

144 = Is the constant variable.

R = Rate of interest.

[tex]\rightarrow N = \frac{144}{10} = 14.4[/tex]

Thus it takes about 14.4 years for quadruple your money.

Another method:

If initial amount is $ 1 and it if quadruples it should be $ 4

We have to find the number of years if rate of interest is 10 %

Let "n" be the number of years

Then we can say,

[tex]Amount = Principal(1+\frac{R}{100})^n[/tex]

[tex]4 = 1(1+\frac{10}{100})^n[/tex]

[tex]4 = 1(1+0.1)^n\\\\4= 1(1.1)^n\\\\4 = 1.1^n\\\\We\ know\ that,\\\\(1.1)^{14.55} = 1.1^n\\\\We\ know\ that\\\\If\ a^m = a^n\ then\ m = n\\\\Therefore,\\\\14.55 = n\\\\n = 14.55[/tex]

Thus Option D 14.55 years is correct

For test point x = –2, the inequality is true.

For test point x = 0, the inequality is false.

For test point [tex]x=\frac{4}{5}[/tex], the inequality is true.

For test point x = 2, the inequality is false.

Solution:

Given expression is the inequality.

[tex]$\frac{5 x-3}{(x-1)(x+1)} \leq 0[/tex]

Substitute x = –2 in the inequality.

[tex]$\frac{5 (-2)-3}{(-2-1)(-2+1) }=\frac{-13}{(-3)(-1) }[/tex]

                            [tex]$=\frac{-13}{3 }[/tex]

                            < 0

For test point x = –2, the inequality is true.

Substitute x = 0 in the inequality.

[tex]$\frac{5 (0)-3}{(0-1)(0+1) }=\frac{-3}{(-1)(1) }[/tex]

                      [tex]$=3[/tex]

                      > 0

For test point x = 0, the inequality is false.

Substitute [tex]x=\frac{4}{5}[/tex] in the inequality.

[tex]$\frac{5 (\frac{4}{5} )-3}{((\frac{4}{5} )-1)((\frac{4}{5} )+1) }=\frac{1}{(-\frac{1}{5} )(\frac{9}{5} ) }[/tex]

                            [tex]$=\frac{-25}{9 }[/tex]

                            < 0

For test point [tex]x=\frac{4}{5}[/tex], the inequality is true.

Substitute x = 2 in the inequality.

[tex]$\frac{5 (2)-3}{(2-1)(2+1) }=\frac{7}{(1)(3) }[/tex]

                      [tex]$=\frac{7}{3 }[/tex]

                      > 0

For test point x = 2, the inequality is false.

Hence,

For test point x = –2, the inequality is true.

For test point x = 0, the inequality is false.

For test point [tex]x=\frac{4}{5}[/tex], the inequality is true.

For test point x = 2, the inequality is false.

Answer:

In the picture below

Step-by-step explanation:

Edge 2021

Answer:

.5 or l/2 liter

Step-by-step explanation

4 liters x 5= 20 liters / 40 people =.5 or 1/2  liter