Daniel went on his bike 45 miles in four hours, what was his speed?

To find Robert's minimum age, we need to determine the ages of George and Edward first. Let's assume Edward's age is x. According to the information given, George is twice as old as Edward, so George's age is 2x. Edward's age exceeds Robert's age by 4 years, meaning Robert's age is x - 4. The sum of the three ages is at least 56 years, so we can write the equation x + 2x + (x - 4) >= 56.

To find Robert's minimum age, we need to determine the ages of George and Edward first.

Let's assume Edward's age is x. According to the information given, George is twice as old as Edward, so George's age is 2x.

Edward's age exceeds Robert's age by 4 years, meaning Robert's age is x - 4.

The sum of the three ages is at least 56 years, so we can write the equation x + 2x + (x - 4) >= 56. Simplifying this, we get 4x - 4 >= 56. Adding 4 to both sides, we have 4x >= 60. Dividing by 4, we find that x >= 15.

Therefore, Edward's minimum age is 15 years, and Robert's minimum age is 15 - 4 = 11 years.

Answer:

910

Step-by-step explanation:

65×14=910

Answer:1100 feet

Step-by-step explanation: the drop is 11 feet

To find the length of the ski run, we use tangent of the angle of elevation (24.4 degrees) which equals the vertical drop (1100 feet) divided by the length of the run. Calculating this gives a length of approximately 2433 feet for the ski run.

To calculate the length of the ski run with an angle of elevation of 24.4 degrees and a vertical drop (rise) of 1100 feet, we use trigonometry, specifically the tangent function.

Tangent of an angle in a right triangle equals the opposite side (rise) divided by the adjacent side (run). In this case, we have:

tan(24.4 degrees) = rise / run

Plugging in the known value for the rise (1100 feet), we get:

tan(24.4 degrees) = 1100 / run

This allows us to solve for the run (length of the ski run):

run = 1100 / tan(24.4 degrees)

Using a calculator, we find that:

run ≈ 1100 / 0.4525

run ≈ 2432.96 feet

This can be rounded to the nearest foot to give a ski run length of approximately 2433 feet.

Average = 0.56 inches

Solution:

Given data: Total rainfall = 16.8 inches

Total number of days for a month = 30

To find the average of the rainfall.

Formula for average:

[tex]\text {Average}=\frac{\text {Sum of the observations}}{\text {Total number of observations}}[/tex]

[tex]\text {Average}=\frac{16.8}{30}[/tex]

            = 0.56 inches

Average = 0.56 inches

Hence, average of daily rainfall is 0.56 inches.

Answer:

2

Step-by-step explanation:

if you take half of something then you divide my 2

Final answer:

The perimeter of a rectangle whose width is half its length is three times the length of the rectangle. This can be calculated using the formula p = 2(l + w), substituting w with l/2, which simplifies to p = 3l.

Explanation:

The student is asking how many times a rectangle's length is its own perimeter if the width of the rectangle is half its length. Using the formula for the perimeter of a rectangle, which is p = 2(l + w), and knowing that the width (w) is half the length (l), we can substitute w with l/2.

Hence, the formula becomes p = 2(l + l/2) = 2(3l/2) = 3l. Therefore, the perimeter is three times the length of the rectangle.

To solve the inequality, isolate/get w (the variable) by itself in the inequality

w + 6 ≤ -3      Subtract 6 on both sides

w + 6 - 6 ≤ -3 - 6

w ≤ - 9

The equation that can be used to find the volume V of the container is: Option A. [tex]V = 12 \pi}[/tex]

To find the volume V of the popcorn container, which is an inverted cone, we use the formula for the volume of a cone:

Given:

Now substitute these values into the formula:

Calculate [tex]\( (2)^2 \):[/tex]

Now substitute r = 2 and h = 9 into the formula:

Simplify the multiplication:

Now calculate [tex]\( \frac{1}{3}[/tex] x 36

Full Question

A popcorn container is the shape of an inverted cone. It is 9 inches tall, and the circular opening has a diameter of 4 inches.

A.  [tex]V = 12 \pi}[/tex]

B. V=(4)(9) 3

C. V=(4)(9)²

D. V-(2)(9)² wr

Steps to solve:

2x + 6 < 30

~Subtract 6 to both sides

2x + 6 - 6 < 30 - 6

~Simplify

2x < 24

~Divide 2 to both sides

2x/2 < 24/2

~Simplify

x < 12

Best of Luck!

Answer:

60 miles

Step-by-step explanation:

Let

x ----> the number of miles  

we know that

The number of miles multiplied by $0.60 per mile plus $2 plus the charge of $5.50 for tolls (because you are travelling from the airport)  must be equal to  $43.50

so

The linear equation that represent this problem is

[tex]0.60x+2+5.50=43.50[/tex]

Solve for x

Combine like terms left side

[tex]0.60x+7.50=43.50[/tex]

subtract 7.50 both sides

[tex]0.60x=43.50-7.50[/tex]

[tex]0.60x=36[/tex]

divide by 0.60 both sides

[tex]x=60\ miles[/tex]

Answer:

Step-by-step explanation:

Slope m = -2/7

Points are (2,1)

y1 = 1 and x1 = 2

y - y1 = m(x - x1)

y -1 = -2/7(x - 2)

Multiple each term by 7

7y - 7 = -2(x - 2)

7y - 7 = -2x + 4

7y = -2x + 4 + 7

2x + 7y = 11

quadratic function

Step-by-step explanation:

Answer:

[tex] \frac{ \sqrt{x} }{ \sqrt{x} + \sqrt{5} } ( \frac{ \sqrt{x} - \sqrt{5} }{ \sqrt{x} - \sqrt{5} } ) = \frac{x - \sqrt{5x} }{x - 5} [/tex]

The correct answer is C.

Debit Card Definition: A debit card is a payment card that allows you to make secure and easy purchases online and in person by withdrawing funds directly from your checking account. You don't borrow from a line of credit like you would with a credit card; the money on your debit card is yours.

Answer:

The value of h that makes the inequality true is 2.

Step-by-step explanation:

Ms. Jenson needs to rent a ballroom for an event and she must spend less than $625 for the  rental fee. The cost to rent the ballroom is $350 for 3 hours. The cost for every extra hour is  $125.

She wrote the inequality,

625 > 350 + 125h

to find h, the number of extra hours she can  rent the ballroom.

Solving this inequality we get

125h < 275

⇒ h < 2.2

So the value of h that makes the inequality true is 2. (Answer)

The required value of h < 2 or the number of extra hours she can rent the ballroom.

Given that,

She must spend less than $625 for the  rental fee,

The cost to rent the ballroom is $350 for 3 hours,

The cost for each additional hour is  $125,

She wrote the inequality, 625 > 350 + 125h.

We have to find,

The value of h, the number of extra hours she can  rent the ballroom. Which value for h makes the inequality true.

According to the question,

She must spend less than $625 for the  rental fee. The cost to rent the ballroom is $350 for 3 hours.

The cost for each additional hour is  $125. She wrote the inequality,

[tex]650>350+125h,[/tex]

Solving the equation to find h, the number of extra hours she can rent the ballroom.

[tex]650>350+125h\\\\650-350>125h\\\\300>125h\\\\h<\frac{300}{125} \\\\h<2.2\\\\h<2 approx[/tex]

Hence, The required value of h < 2 for the number of extra hours she can rent the ballroom.

For more information about Inequality click the link given below.

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Without the specific lengths of the rivers, it's not possible to calculate the precise mean, median, range, variance, and standard deviation. In general, these values provide insights into the distribution and variability of river lengths on the South Island of New Zealand.

Unfortunately, the specific lengths of the rivers mentioned in the question were not provided, so it's not possible to calculate the mean, median, range, variance, and standard deviation without that data. In general, to calculate these statistical terms:

These calculations are essential for understanding the distribution and variability of river lengths on the South Island of New Zealand.

Answer:

B

Step-by-step explanation:

y = mx + b

m = 1

b = 4

y = 1(x) + 4

y = x + 4

To determine the fourth vertex of an isosceles trapezoid given three vertices, we use symmetry and properties of isosceles trapezoids, concluding the missing vertex is likely at (-1,3).

To find the fourth vertex of an isosceles trapezoid given three vertices, we need to use the properties of isosceles trapezoids. The properties pertinent to solving this problem include parallel bases and non-parallel sides of equal length. Given vertices at (2,5), (6,5), and (9,3), we know the top base is parallel to the x-axis, as the y-coordinate is the same (5) for the first two points.

For the trapezoid to be isosceles, the fourth vertex must follow the pattern of equal non-parallel sides. Observing the pattern of the given points, and noting that the length of the non-parallel side from (9,3) should equal that of the side starting from (2,5), we conclude the missing point must maintain this equality in distance and form a right angle, mirroring the shape on the opposite side.

Without specific lengths, we apply symmetry principles. The height difference between the known base and the third vertex (3) indicates a 2-unit drop, suggesting the opposite side will mirror this. Thus, the fourth vertex should be 2 units below the other base vertex, at (2,5), making the y-coordinate 3. Given the distances in x are equal (4 units from each end vertex to their respective base vertex), the fourth vertex is at (-1,3).

Answer:

Step-by-step explanation:

2 less then the product of 9 and a number is 4

" the product " is the result of multiplication

the product of 9 and a number...9x

2 less......-2

is 4...= 4

9x - 2 = 4 <===

Answer:

The Emancipation Proclamation is the document that changed the purpose of the Civil war from one of states' rights to that of slavery.

Step-by-step explanation:

The Emancipation Proclamation is the document that changed the purpose of the Civil war from one of states' rights to that of slavery.

The main idea behind this document was to clearly state that " all persons held as slaves" in the southern states "are, and henceforward shall be free."

When the north won the civil the above mentioned words in quotes of the Emancipation Proclamation document effectively guaranteed the freedom of all people held as slaves in all of United States of America.

Answer:

[tex]y= 2x-5\frac{1}{4}[/tex]

Step-by-step explanation:

We are given;

The equation 2x + 4y = 7

A point (2, -5/4)

We are supposed to determine the equation of a line perpendicular to the given line;

First, we determine the slope of the given line by writing the equation in the form of y= mx + c

2x + 4y = 7

y = -1/2x + 7/4

m₁ = -1/2

But, for perpendicular; m₁×m₂= -1

Therefore;

-1/2 × m₂ = -1

m₂ = 2

Thus, we can get the equation of the line;

Taking another point (x, y)

[tex]\frac{y+\frac{5}{4} }{x-2}=2[/tex]

[tex]y+\frac{5}{4}= 2(x-2)[/tex]

[tex]y+\frac{5}{4}= 2x-4[/tex]

[tex]y= 2x-4-\frac{5}{4}[/tex]

[tex]y= 2x-5\frac{1}{4}[/tex]

Thus, the equation of the line in question is [tex]y= 2x-5\frac{1}{4}[/tex]

Answer: 11

Step-by-step explanation:

The sequence goes +4, +1, +5, +1... so obviously the next number will be +6. So, 5+6=11

The answer is week 5=11

Week 5 will be 9.

This is a question that has to do with one's reasoning. Since we are given that week 1=5, week 2=3, week 3=7, week 4=5, we can infer that the sequence used is +4, +1, +4, +1, ....

In this case, the last week was week 4 and was given as week 4=5, in this case +1 was used, therefore the next week will have +4. In this case, week 5 will be:

= 5 + 4

= 9

Therefore, week 5 will be 9

Read related link on:

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Answer:

[tex]x = 54\ mi/hr[/tex]

Step-by-step explanation:

Given:

The given equation is.

[tex]y=xt[/tex]

Where:

y represents the distance in miles,

x represents the speed of the train in miles per hour, and

t represents the time travelled from the departing station in hours.

y = 162 miles

t = 3 hours

Solution:

The given equation is.

[tex]y=xt[/tex]

Rewrite the given equation for x or speed.

[tex]x=\frac{y}{t}[/tex]

Substitute y and t value in above equation.

[tex]x=\frac{162}{3}[/tex]

[tex]x = 54\ mi/hr[/tex]

Therefore, the speed of the train is [tex]54\ mi/hr[/tex].

Answer:

x=3−2d,5,−2(1+d),5,−27−2d,5,−2(2+d),5,2(y−d),5

Step-by-step explanation:Solving for x. Want to solve for y or solve for d instead?

1 Simplify  0-20−2  to  -2−2.

3,-2,-27,-2-2,02y=1,5x+2d3,−2,−27,−2−2,02y=1,5x+2d

2 Simplify  -2-2−2−2  to  -4−4.

3,-2,-27,-4,02y=1,5x+2d3,−2,−27,−4,02y=1,5x+2d

3 Subtract 2d2d from both sides.

3-2d,-2-2d,-27-2d,-4-2d,02y-2d=1,5x3−2d,−2−2d,−27−2d,−4−2d,02y−2d=1,5x

4 Divide both sides by 1,51,5.

\frac{3-2d}{1},5,\frac{-2-2d}{1},5,\frac{-27-2d}{1},5,\frac{-4-2d}{1},5,\frac{02y-2d}{1},5=x

​1

​

​3−2d

​​ ,5,

​1

​

​−2−2d

​​ ,5,

​1

​

​−27−2d

​​ ,5,

​1

​

​−4−2d

​​ ,5,

​1

​

​02y−2d

​​ ,5=x

5 Factor out the common term 22.

\frac{3-2d}{1},5,\frac{-2(1+d)}{1},5,\frac{-27-2d}{1},5,\frac{-4-2d}{1},5,\frac{02y-2d}{1},5=x

​1

​

​3−2d

​​ ,5,

​1

​

​−2(1+d)

​​ ,5,

​1

​

​−27−2d

​​ ,5,

​1

​

​−4−2d

​​ ,5,

​1

​

​02y−2d

​​ ,5=x

6 Factor out the common term 22.

\frac{3-2d}{1},5,\frac{-2(1+d)}{1},5,\frac{-27-2d}{1},5,\frac{-2(2+d)}{1},5,\frac{02y-2d}{1},5=x

​1

​

​3−2d

​​ ,5,

​1

​

​−2(1+d)

​​ ,5,

​1

​

​−27−2d

​​ ,5,

​1

​

​−2(2+d)

​​ ,5,

​1

​

​02y−2d

​​ ,5=x

7 Factor out the common term 22.

\frac{3-2d}{1},5,\frac{-2(1+d)}{1},5,\frac{-27-2d}{1},5,\frac{-2(2+d)}{1},5,\frac{2(y-d)}{1},5=x

​1

​

​3−2d

​​ ,5,

​1

​

​−2(1+d)

​​ ,5,

​1

​

​−27−2d

​​ ,5,

​1

​

​−2(2+d)

​​ ,5,

​1

​

​2(y−d)

​​ ,5=x

8 Simplify  \frac{3-2d}{1}

​1

​

​3−2d

​​   to  (3-2d)(3−2d).

3-2d,5,\frac{-2(1+d)}{1},5,\frac{-27-2d}{1},5,\frac{-2(2+d)}{1},5,\frac{2(y-d)}{1},5=x3−2d,5,

​1

​

​−2(1+d)

​​ ,5,

​1

​

​−27−2d

​​ ,5,

​1

​

​−2(2+d)

​​ ,5,

​1

​

​2(y−d)

​​ ,5=x

9 Simplify  \frac{-2(1+d)}{1}

​1

​

​−2(1+d)

​​   to  (-2(1+d))(−2(1+d)).

3-2d,5,-2(1+d),5,\frac{-27-2d}{1},5,\frac{-2(2+d)}{1},5,\frac{2(y-d)}{1},5=x3−2d,5,−2(1+d),5,

​1

​

​−27−2d

​​ ,5,

​1

​

​−2(2+d)

​​ ,5,

​1

​

​2(y−d)

​​ ,5=x

10 Simplify  \frac{-27-2d}{1}

​1

​

​−27−2d

​​   to  (-27-2d)(−27−2d).

3-2d,5,-2(1+d),5,-27-2d,5,\frac{-2(2+d)}{1},5,\frac{2(y-d)}{1},5=x3−2d,5,−2(1+d),5,−27−2d,5,

​1

​

​−2(2+d)

​​ ,5,

​1

​

​2(y−d)

​​ ,5=x

11 Simplify  \frac{-2(2+d)}{1}

​1

​

​−2(2+d)

​​   to  (-2(2+d))(−2(2+d)).

3-2d,5,-2(1+d),5,-27-2d,5,-2(2+d),5,\frac{2(y-d)}{1},5=x3−2d,5,−2(1+d),5,−27−2d,5,−2(2+d),5,

​1

​

​2(y−d)

​​ ,5=x

12 Simplify  \frac{2(y-d)}{1}

​1

​

​2(y−d)

​​   to  (2(y-d))(2(y−d)).

3-2d,5,-2(1+d),5,-27-2d,5,-2(2+d),5,2(y-d),5=x3−2d,5,−2(1+d),5,−27−2d,5,−2(2+d),5,2(y−d),5=x

13 Switch sides.

x=3-2d,5,-2(1+d),5,-27-2d,5,-2(2+d),5,2(y-d),5x=3−2d,5,−2(1+d),5,−27−2d,5,−2(2+d),5,2(y−d),5

Done

Answer:

y = 13x + 5

Step-by-step explanation:

Option C:

[tex]y+6=\frac{3}{5} (x-4)[/tex]

Solution:

Given point (4, –6) and slope, [tex]m=\frac{3}{5}[/tex]

Formula for equation of a straight line when passing through the point [tex](x_1, y_1)[/tex] and slope m is [tex]y-y_1=m(x-x_1)[/tex]

Here, [tex]x_1=4, y_1=-6, m=\frac{3}{5}[/tex]

Substitute these in the above formula, we get

⇒ [tex]y-(-6)=\frac{3}{5} (x-4)[/tex]

⇒ [tex]y+6=\frac{3}{5} (x-4)[/tex]

Hence, [tex]y+6=\frac{3}{5} (x-4)[/tex] is the equation in point-slope form.

Answer: 10

Step-by-step explanation:(-x)(5y)(-2x)

=(-5xy)(-2x)

=10x^2y

therefore,the coefficient of the equation is 10.

Answer:

The new membership as a percent of the old membership = 120 %

The old membership as a percent of the new membership = 83.33 %

Step-by-step explanation:

Formula to find the percent of Comparing Quantities  

Percent=Quantity/Whole x 100  

i) To Express the new membership as a percent of the old membership

In this case the old membership is the whole and the new membership is a quantity.

Let A is the unknown percent to be find.  

A =250/300  x 100

 A =120 %   answer -1

i) To Express the old membership as a percent of the new membership

In this case the new membership is the whole and the old membership is a quantity.

Let A is the unknown percent to be find.  

A =300/250  x 100

 A =83.33 %  answer 2

Answer: 6 laps

Step-by-step explanation:

13  - 4= 9 left  6 and half would be three

To find out how many laps Bryan ran, an equation was formulated combining the laps Amanda and Clifford ran with the total laps, which, when solved, showed Bryan ran 6 laps.

To solve the problem, let's denote the number of laps Bryan ran as B, Amanda ran 4 laps, and Clifford ran half as many laps as Bryan, so that's B/2 laps.

According to the problem, together they ran a total of 13 laps.

Now we can write an equation based on the information given:

4 + (B/2) + B = 13

Next, we solve for BD:

Combine like terms:

B + B/2 = 13 - 4

1.5B = 9

Divide by 1.5 to solve for B:

B = 9 / 1.5

B = 6

So, Bryan ran 6 laps.

Answer:

x ≈ 31°

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan x° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{12}{20}[/tex], thus

x = [tex]tan^{-1}[/tex]([tex]\frac{12}{20}[/tex]) ≈ 31° ( to the nearest whole number )

Answer:

25 * 36% = 9

Step-by-step explanation:

25 * .36 = 9