25 gal
min
sec
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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:

a) 4x + 1  expression

b) C = 15+ 3n  “it might be a Formula”

c) 3x + 4 = 13 equation

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:

9

Step-by-step explanation:

10 - 1 = 9

1, 2, 3, 4, 5, 6, 7, 8, 9, 10

if we erase 10, we have 9. Try that when subtracting 1 - any number

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.

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

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quadratic function

Step-by-step explanation:

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:

25 * 36% = 9

Step-by-step explanation:

25 * .36 = 9

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

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:

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: Monica earned more interest

Step-by-step explanation:

The formula for calculating simple interest is given by :

S.I = [tex]\frac{ptr}{100}[/tex]

For Monica

S.I = 300 x 3.4 x 1 / 100

S.I = $10.2

For Paul

S.1 = 400 x 2.4 x 1 / 100

S.I = $9.6

Therefore : Monica earned more interest

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

Answer: 1

Step-by-step explanation:  3x^2-xy=0,

2y-5x=1

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.

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Answer:78

Step-by-step explanation:

Answer:

Step-by-step explanation:

13.71

Step-by-step explanation:

Given the data as : 13 , 17, 9, 21

Finding the mean of the data;

sum of data set =13+17+9+21=60

Number of data set ,n,= 4

Mean= sum/n =60/4 =15

Finding the deviation from the mean

13-4=9

17-4=13

9-4=5

21-4=17

Squaring the deviations from mean

9²=81

13²=169

5²=25

17²=289

Adding the squares of deviations from the mean

81+169+25+289 =564

Finding n-1

4-1=3

Finding variance

564/3 =188

Finding the standard deviation

√188 = 13.71

Answer:

sample variance: option A

sample standard deviation: option B

Step-by-step explanation:

Given that we want to analyze a sample, then we need the sample variance formula and the sample standard deviation. The standard deviation is calculated by taking the square root of the variance. With sample [tex] \bar{x} [/tex], sample mean, is used, instead of [tex] \mu [/tex], the mean of the population.

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:

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

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.

The additive inverse of 6x is -6x.

This is because 6x + (-6x) = 6x - 6x = 0

Answer:

-6x

Step-by-step explanation:

It's a little unclear from the question what you mean, but I assume you mean the 'additive inverse'. In terms of solving equations, this term typically means we just minus 6x. i.e - 6x.

However, if the question means find the inverse function of f(x) = 6x,

then this would be a different answer: in particular, the inverse function is the function that 'undoes' this, so it would be f-1(x) = x/6.

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:

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.

The number of kids in your group is 12.

Step-by-step explanation:

Given,

Number of people = 20

Cost of each kid ticket = $4

Cost of each adult ticket = $6

Total spent = $96

Let,

x be the number of kids ticket

y be the number of adult ticket

According to given statement;

x+y=20     Eqn 1

4x+6y=96    Eqn 2

Multiplying Eqn 1 by 4

[tex]4(x+y=20)\\4x+4y=80\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 2

[tex](4x+6y)-(4x+4y)=96-80\\4x+6y-4x-4y=16\\2y=16[/tex]

Dividing both sides by 2

[tex]\frac{2y}{2}=\frac{16}{2}\\y=8[/tex]

Putting y=8 in Eqn 1

[tex]x+8=20\\x=20-8\\x=12[/tex]

The number of kids in your group is 12.

Keywords: linear equation, elimination method

Learn more about elimination method at:

#LearnwithBrainly

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.

Answer:

The answers are given below.

Step-by-step explanation:

1. The rate of change for the interval shown in the table is constant. So, the function is linear.

2.From the graph, the  line passes through (0, 90) and the slope of the line is negative.So, the correct equation for the line is,

y = -10x + 90

3.According to the question and the graph, the  equation is a straight line with y - intercept equal to -1.So, the equation which best represents  the line is,

y = 3x - 1

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:

[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:

y = 13x + 5

Step-by-step explanation: