Mike took a taxi from his home to the airport. The taxi driver charged an initial fee of $6plus$3 per mile. The total fare was $24, not including tip. How many miles did Mike travel by taxi on this ride.

Answer:

Independent:  time (minutes)

Dependent: Distantce (inches)

Step-by-step explanation:

a= [tex]\pi[/tex] [tex]r^{2}[/tex]

The area of a pizza with a diameter of 10 inches is 78.5.

[tex]5x^2-(3xy-7x^2)+(5xy-12x^2)=5x^2-3xy+7x^2+5xy-12x^2=2xy\\\\ 2\cdot(-0.25)\cdot4=-2[/tex]

Answer:

-2

Step-by-step explanation:

5x^2-(3xy-7x^2)+(5xy-12x^2)

5x^2-3xy+7x^2+5xy-12x^2

[(5x^2+7x^2-12x^2)=0]

-3xy+5xy= -3(-.25)(4)+5(-.25)(4)

-3(-.25)(4)+5(-.25)(4)= 3-5= -2

-2

The maximum area of a rectangle inscribed in a semicircle of radius 8 cm is found by maximizing the product of its width and height, which occurs when the rectangle's height is half the radius. Using the Pythagorean theorem, the optimal dimensions are calculated, leading to a maximum area of approximately 27.71 cm².

To find the maximum area of a rectangle inscribed in a semicircle of radius 8 cm, we can employ a geometrical approach. Let the width of the rectangle be w and the height h. Because the rectangle is inscribed in a semicircle, the diagonal of the rectangle will be the radius of the semicircle, and the width of the rectangle will span from the midpoint of the diameter to a point on the circumference of the semicircle. Given the Pythagorean theorem, we have w² + h² = (2r)², where r is the radius. For our case, r = 8 cm.

Maximum area occurs when the rectangle's area is maximized. The area of the rectangle is A = w × h. By using the relation obtained from the Pythagorean Theorem, and knowing that for a rectangle inscribed in a semicircle the height will be half the radius when the area is maximized, we find h = r/2 = 4 cm. Substituting back into the Pythagorean Theorem, we find w = √(8² - 4²) = √64 - 16 = √48 = 4√3 cm. Therefore, the maximum area of the rectangle is A = w × h = 4√3 × 4 = 16√3 cm². This is approximately 27.71 cm².

This question combines geometry and basic principles of optimization to find the maximum area of a geometric shape within defined constraints, showcasing the application of mathematical reasoning in problem-solving.

The original selling price if, A dress is selling for $100 after a 20 percent discount is $125.

A percentage, often known as percent, is a division by 100. Percentage, which means "per 100," designates a portion of a total sum. 45 out of 100 is represented by 45%, for instance. Finding the percentage of a whole in terms of 100 is what percentage calculation is. Both manual calculation and the use of internet calculators are options.

Given:

A dress is selling for $100 after a 20 percent discount,

Calculate the original price as shown below,

Original price - 20% original price = 100

Original price(1 - 0.2)  = 100

Original price  = 100 / 0.8

Original price  = $125

Thus, the original price is $125.

To know more about percentages:

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Answer:

6 cm

Step-by-step explanation:

Let k represent the scale factor between ΔABC and ΔDCA. Then ...

... CA = k·BC

... AD = k·CA

So, AD/BC = k·(k·BC)/BC = k² = 9/4

Then k = √(9/4) = 3/2, and ...

... CA = (3/2)·BC = (3/2)·(4 cm)

... CA = 6 cm

Final answer:

To find the length of diagonal AC in trapezoid ABCD, we utilize the properties of similar triangles created by the diagonal. Since triangles △ABC and △DCA are similar, we set up a proportion using the sides BC and AD, and solve for AC to find that AC is 6 cm.

Explanation:

The question asks us to find the diagonal AC of trapezoid ABCD where it's given that BC = 4 cm and AD = 9 cm, and triangles △ABC and △DCA are similar. To find AC, we can use the properties of similar triangles which dictate that corresponding sides are proportional. Let us consider that the trapezoid is split into two triangles by AC. The ratio of the smaller triangle's base to the larger triangle's base (BC:AD) must be the same as the ratio of any other pair of corresponding sides in these two similar triangles. Furthermore, the ratio of the longer leg of △ABC (which is AC) to its base BC is equal to the ratio of the longer leg of △DCA (which is also AC) to its base AD. Using these ratios, we can set up a proportion to solve for AC:

AC/BC = AC/AD

Since the length of AC is the same in both ratios, we can multiply both sides by BC*AD to get:

[tex]AC^2 = BC * AD[/tex]

By substituting the given values for BC and AD into the equation we get:

[tex]AC^2 = 4 cm * 9 cm[/tex]

[tex]AC^2 = 36 cm^2[/tex]

To find AC, we take the square root of both sides:

AC = √36 cm

AC = 6 cm

Hence, the length of diagonal AC is 6 cm.

Answer:

3216/8 is = to 402

Step-by-step explanation:

So I am not sure what you are asking sorry

Answer: (B) -2, (E) 1, (F) 2

Step-by-step explanation:

   x³ - x² - 4x + 4

= x²(x - 1) - 4(x - 1)

= (x² - 4) (x - 1)

= (x - 2)(x + 2)(x - 1)

Set each factor equal to zero to find the roots:

  x - 2 = 0      x + 2 = 0       x - 1 = 0

       x = 2             x = -2           x = 1

Answer:

-2,1,2

Step-by-step explanation:

Answer:

270 feet

Step-by-step explanation:

From the sequence given, we can see that the asteroid travels 36 feet more with each second. (as seen [tex]54-18=36[/tex] and [tex]90-54=36[/tex] etc.)

So 5th second, it will travel: [tex]126+36=162[/tex]

6th second, it will travel: [tex]162+36=198[/tex]

7th second, it will travel: [tex]198+36=234[/tex]

8th second, it will travel: [tex]234+36=270[/tex]

Hence, in the eighth second, the projectile traveled 270 feet.

The distance the projectile travels in the eighth second is found to be 270 feet.

The question asks for the distance a projectile travels in the eighth second, given that the distances it covers each second form an arithmetic progression with initial distances given as 18, 54, 90, 126, etc. In an arithmetic progression, the difference between any two consecutive terms is constant, known as the common difference.

To find the common difference (d), we subtract the first term from the second term:

d = 54 - 18 = 36

The nth term of an arithmetic sequence can be found using the formula:

T(n) = a + (n - 1)d

Here, a represents the first term, which is 18, and d is the common difference we found to be 36. Substituting the values to find the eighth term:

T(8) = 18 + (8 - 1) x 36T(8)

= 18 + 7 x 36T(8)

= 18 + 252T(8) = 270

Thus, the distance the projectile travels in the eighth second is 270 feet.

Answer:

Alright well Graph the line using this slope and Y-intercept, or two points

Slope: - 2/3

Y - intercept: 1 Hope this helps have a nice day :)

Step-by-step explanation:

And if you want i can explain the Answer with detail

Answer:

f(3) = [tex]\frac{7}{9}[/tex]

Step-by-step explanation:

The given function is

f(x)= [tex]\frac{-2}{3x}+1[/tex]

To find is the value of f(3)

Now we can find the value of a function by putting the vlaue in the given equation of the function

we can see that we have to find the value of f(3) and or given function is f(x)

so we have to put the value of x to be equal to 3 so that we can get the value of the desired function at a given point

Now

In this

x =3

f(x) = [tex]\frac{-2}{3x}+1[/tex]               ................(i)

Put x = 3 in equation (i)

it becomes

f(3) = [tex]\frac{-2}{3*3}+1[/tex]

f(3) = [tex]\frac{-2}{9}+1[/tex]

Taking the LCM and solving it

LCM of 1 and 9 is 9 so it becomes

f(3) = [tex]\frac{-2+9}{9}[/tex]

f(3) = [tex]\frac{7}{9}[/tex]

which is the required value

Answer:

Water - 62.5 pounds per cubic foot

18.25 cubic feet would weigh 18.25 * 62.5 =

1,140.625 pounds.

Step-by-step explanation:

Answer:

-6r+48

Step-by-step explanation:

(-6)(r)+(-6)(-8)

=-6r+48

Answer:

-6r +48

Step-by-step explanation:

The distributive property has us distribute the number on the outside to the numbers on the inside

-6(r-8)

-6 *r -6 * (-8)

-6r +48

Answer:

100 degrees

Step-by-step explanation:

Remark

The endpoints of the smaller diagonal of a kite, intersect the vertexes of 2 equal angles. Put in simpler language, if x is at the top of the kite and x is the vertex of the larger angle between the top and bottom angles, then the other two angles (left and right) are equal.

In still simpler language. <W = <Y

Equation

<X + <W + <Z + <Y = 360               All quadrilaterals have 360 degrees for their interior angles.

Givens

Solution

Answer

Answer:

100

Step-by-step explanation:

Angle ZWX and angle ZYX are congruent.

360 = 120 + 4x + 10x + 10x

360 = 120 + 24x

240 = 24x

10 = x

The measure of angle ZYX is equal to 10(10) = 100°

Answer:

B. 10

Step-by-step explanation:

6 = .24 * x

Solve for x

Divide each side by .24

6/.24 = x

25 =x

Now find 40% of 25

25*.4 = 10

Answer:

[tex]s = \sum^5_1 {(2h)(\frac{2}{3})^i},[/tex]

Step-by-step explanation:

The initial height of the ball is h

After the first bounce the height is [tex]\frac{2}{3}h[/tex]

After the second bounce the height is [tex]\frac{2}{3}(\frac{2}{3})h[/tex]

After the i-th rebound the height is [tex](\frac{2}{3}) ^ i[/tex]

Then, distance s traveled by the ball is the sum of the heights reached between the first and fifth bounces.

[tex]s = 2 [\frac{2}{3}h + \frac{2}{3}(\frac{2}{3})h +, ..., + (\frac{2}{3}) ^ n h][/tex]

The equation is multiplied by 2 because the distance the ball travels when it goes up is the same as it travels down.

Finally the distance is a geometric series as shown:

[tex]s = \sum^5_1 {(2h)(\frac{2}{3})^i},[/tex]

The total distance traveled by the ball between the first and sixth bounce is [tex]\( \frac{23}{3}h \)[/tex] feet.

Step 1: Find the distance traveled during the first fall:

- The ball is dropped from a height of [tex]\( h \)[/tex] feet.

- So, the distance traveled during the first fall is [tex]\( h \)[/tex] feet.

Step 2: Find the distance traveled during each subsequent bounce:

- After each bounce, the ball reaches a height that is [tex]\( \frac{2}{3} \)[/tex] of the height from which it previously fell.

- During each bounce, the ball travels twice the distance of the height it reached.

- Therefore, during each bounce, the total distance traveled is [tex]\( \frac{4}{3}h \)[/tex] feet.

Step 3: Find the total distance traveled between the first and sixth bounce:

- Since we're asked for the distance between the first and sixth bounce, we have 5 subsequent bounces.

- The total distance traveled between the first and sixth bounce is the sum of the distance traveled during the first fall and the total distance traveled during the subsequent five bounces.

- So, it's [tex]\( h + 5 \times \left(\frac{4}{3}h\right) \)[/tex]feet.

Step 4: Calculate the total distance:

- Substitute the values and calculate: [tex]\( h + \frac{20}{3}h = \frac{23}{3}h \)[/tex]feet.

Therefore, the total number of feet the ball travels between the first and sixth bounce is [tex]\( \frac{23}{3}h \).[/tex]

Final answer:

a. The account will have $2,839.25 after 3 years. b. The account will have $5,148.64 after 17 years. c. It will take approximately 4.329 years for the account to contain $3,000. d. It will take approximately 6.646 years for the account to contain $3,500.

Explanation:

a. To calculate the amount in the account after 3 years, we can use the formula: A = P(1 + r)^t, where A is the amount, P is the initial deposit, r is the interest rate, and t is the number of years. In this case, P = $2,500, r = 5% = 0.05, and t = 3. Plugging in these values, we get A = 2500(1 + 0.05)^3. Calculating this, we get A = $2,839.25.

b. Using the same formula, we can calculate the amount in the account after 17 years. P = $2,500, r = 5% = 0.05, and t = 17. Plugging in these values, we get A = 2500(1 + 0.05)^17. Calculating this, we get A = $5,148.64.

c. To find out how many years it will take for the account to contain $3,000, we can rearrange the formula to solve for t. The equation becomes 3000 = 2500(1 + 0.05)^t. Dividing both sides by 2500, we get 1.2 = (1.05)^t. Taking the logarithm of both sides, we have log(1.2) = t * log(1.05). Solving for t, we find t = log(1.2) / log(1.05). Using a calculator, we get t ≈ 4.329 years.

d. Following the same steps, we can find the number of years it will take for the account to contain $3,500. The equation becomes 3500 = 2500(1 + 0.05)^t. Dividing both sides by 2500, we get 1.4 = (1.05)^t. Taking the logarithm of both sides, we have log(1.4) = t * log(1.05). Solving for t, we find t = log(1.4) / log(1.05). Using a calculator, we get t ≈ 6.646 years.

The amount in the account can be calculated using the compound interest formula. After 3 years, the account will have approximately $2,894.07, and after 17 years, it will have approximately $6,003.94. It will take about 3.57 years to reach $3,000 and about 6.57 years to reach $3,500.

To calculate how much money will be in a savings account after a certain number of years with a fixed annual interest rate, we use the compound interest formula:

Compound Interest Formula

A = P(1 + r/n)^(nt)

Where:

In this case, the interest is compounded annually, so n = 1.

Question a: How much will be in the account after 3 years?

Given:

Using the formula:

A = 2500 (1 + 0.05/1)¹ˣ³ = 2500 (1.05)³ ≈ $2,894.07

Question b: How much will be in the account after 17 years?

Given:

Using the formula:

A = 2500 (1 + 0.05/1)¹ˣ¹⁷ = 2500 (1.05)¹⁷ ≈ $6,003.94

Question c: How many years will it take for the account to contain $3,000?

Given:

Using the formula and solving for t:

3000 = 2500 (1.05)^t

t = ln(1.2) / ln(1.05) ≈ 3.57 years

Question d: How many years will it take for the account to contain $3,500?

Given:

Using the formula and solving for t:

3500 = 2500 (1.05)^t

Divide both sides by 2500:

Solve for t:

t = ln(1.4) / ln(1.05) ≈ 6.57 years

Answer:

The system of equation can be used for determine the number of small and the large dogs groomed are

x + y = 22

43x + 75y = 1234

Step-by-step explanation:

Let us assume that the number of small dogs groomed be x.

Let us assume that the number of lagre dogs groomed be y.

As given

Paws at play made a total of $1,234 grooming 22 dogs.

Than the equation becomes

x + y = 22

Paws at play charges $43 to groom each small dog and $75 for each large dog.

Than the equation becomes

43x + 75y = 1234

Therefore the system of equation can be used for determine the number of small and the large dogs groomed are

x + y = 22

43x + 75y = 1234

1. base angles

2. centroid

3. altitude of a triangle

4. orthocenter

5. vertex angle

6. median of a triangle

7. base of an isosceles triangle

Answer:

1.Base angles.

2.Centroid.

3.Altitude of a triangle.

4. Orthocenter.

5.Vertex angle.

6.Median of triangle.

7. Base of an isosceles triangle.

Step-by-step explanation:

1. Base angles: The two angles that include the base of an isosceles triangle.

2. Centroid: A point on the interior of a triangle in which the three medians of the triangle intersect.

3.Altitude of a triangle:A segment from a vertex perpendicular to the opposite side.

4.Orthocenter: A point in which the three altitudes of the triangle intersect .It is possible for the orthocentre to occur on the triangle ,on the interior of the triangle or on the exterior of the triangle.

5.Vertex of angle:The angle formed by the two equal sides of an isosceles triangle.

6.Median of triangle:A segment from a vertex to the midpoint of the opposite side .

7.Base of an isosceles triangle: The third , unequal side of an isosceles triangle.

Answer:

41%

Step-by-step explanation:

To calculate the percent error:

Gregory predicted 310 and 220 actually came.

1. 310-220=90

2. 90/220=0.41

3. 0.41(100)=41%

Answer:

the percent error is 41%

Step-by-step explanation:

Answer:

Quotient is [tex]1x^2 + 4x +3[/tex]

Step-by-step explanation:

   [tex](x^3-x^2-17x-15)[/tex]

The coefficient of given expression is 1, -1, -17, -15

we divide by x-5, that is x=5

      5                      1              -1          -17            -15

                                               5          20            15

                              1                4            3             0 ---> Remainder

Answer 1, 4, 3 is the quotient

We write quotient as 1x^2 + 4x +3

Answer:

A on eden

Step-by-step explanation:

Did the test

Following are the complete solution to the given expression:

Given:

[tex]\bold{\frac{2x}{x-2} - \frac{x+3}{x+5}}[/tex]

To find:

Solve expression=?

Solution:

[tex]\to \bold{\frac{2x}{x-2} - \frac{x+3}{x+5} = \frac{2x(x+5) -(x+3)(x-2)}{(x-2)(x+5)}}[/tex]

                     [tex]\bold{= \frac{2x^2+10x -(x^2+x-6)}{(x-2)(x+5)}}\\\\\bold{= \frac{2x^2+10x -x^2-x+6}{(x-2)(x+5)}}\\\\\bold{= \frac{x^2+9x+6}{(x-2)(x+5)}}\\\\[/tex]

Therefore, the final answer is "4 Option".

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Answer:

Yes, the triangles are similar.

x=7.2

Step-by-step explanation:

Similar triangles are triangles which have the same shape not not the same size. This can be seen when triangles have the same exact angle measures. The triangles in number 4 have the exact same angle measures and are therefore similar. Because they are similar, their sides have a special relationship. They are proportional on each triangle. We can set a proportion to find an unknown length.

A proportion is a ratio between two related quantities. We will write a proportion from one triangle side to the corresponding side on the other.

[tex]\frac{3}{5} =\frac{x}{12} \\[/tex]

We can cross multiply and isolate x to solve.

[tex]\frac{3}{5} =\frac{x}{12}\\3(12)=5(x)\\36=5x\\\frac{36}{5} =\frac{5x}{5} \\7.2=x[/tex]

Answer:

It is D 100%

Step-by-step explanation:

Answer: s = 324/4 = 81 yards

Answer:

s=81 yards

Step-by-step explanation:

Answer:

[tex]a_{17}[/tex] = - 3

Step-by-step explanation:

to find the 17 th term substitute n = 17 into the explicit formula

A(17) = 77 + (16 × - 5 ) = 77 - 80 = - 3

the answer is -3

have a blessed day!

Answer:

x = -11

Step-by-step explanation:

h(x) = 17 + x/6

times 6

6 = x + 17

subtract 17

-11 = x

Answer:

H x − x 6 = 17

Step-by-step explanation: