I. Write the answer with the proper label. ( 2 pts each)


Calculate the distance .

30 minutes at 120 km/h

2 ½ hours at 70 miles/h


B. Calculate the speed.

A car travels 500 km in 6 hours, find the average speed.

A man ran for 10 km in 1.25 hours, what was his average speed?


C. Calculate the time.

210 kilometers at 120 km/h

90 miles at 60 miles/h


II. Identify what is missing then solve. Do not forget to label your answer. (4 pts)


Every Friday after work, Mark travels from Bulacan to Santa Rosa to visit his family. The trip takes 4.2 hours at an average speed of 65 km/h. How many kilometers does he travel from Bulacan to Santa Rosa?


Katrina drove 325km in 5 hours while Martha drove a total of 210 km in 3 hours. Who drove faster? By how much?


with a solution

Measurement is closest to the length of the ramp in feet is 33 feet

Let AB = 26 ft and BC = 19.5 ft

Let AC be the length of the ramp

Let's use the Pythagorean theorem to find the length of the ramp:

AC² = AB² + BC²

where AC is the hypotenuse (the unknown side), and AB and BC are the other two sides given.

Substituting the given values, we get:

AC² = 26² + 19.5²

AC² = 676 + 380.25

AC² = 1056.25

AC = \(\sqrt{1056.25}\)

AC = 32.5

Rounding to the nearest feet

AC = 33

Therefore, the measurement closest to the length of the ramp in feet is 33 feet.

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the center of the ball rests on the table which implies that the y-coordinate of the center of the ball is zero since we have selected the table as the reference plane

the bottom of the ball as its reference point, the y-axis along a vertical line, and the positive direction as pointing upward can be calculated as follows:The y-coordinate of the ball = (y-coordinate of the center of the ball) - (the radius of the ball)As per the given problem, the center of the ball rests on the table which implies that the y-coordinate of the center of the ball is zero since we have selected the table as the reference plane.Hence, the y-coordinate of the ball = 0 - 2= -2Therefore, the y-coordinate of the ball is -2.

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Step-by-step explanation:

7ab(6a²b) + 5a³b³

42a^3b^2 + 5a³b³

= 47ab

The cost of the plan for the limited talk and text is $50 with an additional cost of $22.99 for each gigabyte of data.

Generally, a mathematical function means a rule that gives value of a dependent variable that corresponds to specified values of one or more independent variables. It can take an input from many variables but will  always give the same output, unique to that function.

We are given that "H(g) = 22.99g + 50", where H represents the cost, in dollars, and g represents the number of gigabytes of data. The main answer is based on the given function where the constant term of 50 represents the cost of the plan for limited talk and text, and the coefficient of 22.99 represents the additional cost for each gigabyte of data used.

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If a group consists of 10 kids and 2 adults, the number of ways are there to form the line are 2 * 10!. So, correct option is C.

To form a line with an adult at the front and an adult at the back, we need to consider the positions of the 10 kids within the line. The two adults are fixed at the front and back, so we have 10 positions available for the kids.

To calculate the number of ways to arrange the kids in these positions, we can use the concept of permutations. Since each position can be occupied by a different kid, we have 10 options for the first position, 9 options for the second position, 8 options for the third position, and so on, until the last position, where only 1 kid remains.

Therefore, the number of ways to form the line is:

10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 10!

However, the problem also mentions that there are 2 adults, so we need to consider the arrangements of the adults as well. Since there are only two adults, there are 2 ways to arrange them in the line (adult at the front and adult at the back or vice versa).

Therefore, the total number of ways to form the line is:

2 x 10! = 2 * 10!

Hence, the correct option is b. 2 * 10!, which accounts for both the arrangements of the kids and the adults.

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Answer:

6x+8

Step-by-step explanation:

Answer:

6x+8

Step-by-step explanation:

i just got i right

Answer:

832

Step-by-step explanation:

y 32 * 26

Answer:

because they never touch

Answer:

1.5 and 4

Step-by-step explanation:

the scale factor is the ratio of corresponding sides, image to original.

1

scale factor = \(\frac{DF}{AC}\) = \(\frac{21}{14}\) = \(\frac{3}{2}\) = 1.5

2

scale factor = \(\frac{8}{2}\) = 4

The definite integral for the area of the surface generated by revolving the curve y = 6x^3 + 2x about the x-axis, over the interval 1 ≤ x ≤ 2, can be set up and evaluated as follows:

∫[1 to 2] 2πy √(1 + (dy/dx)^2) dx

To calculate dy/dx, we differentiate the given equation:

dy/dx = 18x^2 + 2

Substituting this back into the integral, we have:

∫[1 to 2] 2π(6x^3 + 2x) √(1 + (18x^2 + 2)^2) dx

Evaluating this definite integral will provide the surface area generated by revolving the curve about the x-axis.

b) The definite integral for the area of the surface generated by revolving the curve x = 4y - 1 about the y-axis, over the interval 1 ≤ y ≤ 4, can be set up and evaluated as follows:

∫[1 to 4] 2πx √(1 + (dx/dy)^2) dy

To calculate dx/dy, we differentiate the given equation:

dx/dy = 4

Substituting this back into the integral, we have:

∫[1 to 4] 2π(4y - 1) √(1 + 4^2) dy

Evaluating this definite integral will provide the surface area generated by revolving the curve about the y-axis.

By setting up and evaluating the definite integrals for the given curves, we can find the surface areas generated by revolving them about the respective axes. The integration process involves finding the appropriate differentials and applying the fundamental principles of calculus.

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Answer:

$46

Step-by-step explanation:

Let the amount of money Darius's parents sent to the book fair be represented as:

We are told that:

Darius's parents sent money to the book fair to be split among the four children in his family. After they gave the money to the cashier, she told each child they had $11.50 to spend.

The Equation is give as:

x = 4 × $11.50

x = $46

Therefore, the total amount of money Darius's parents sent to the book fair is $46

Answer:

the answer is 144

Step-by-step explanation:

just add 72+72=144

Answer:

6x + y = 4

Step-by-step explanation:

Slope intercept form is y = mx + b

Standard form is ax + by = c

Answer:

adult tickets  6.9

children tickets  3.9

Step-by-step explanation:

3x + y = 24.60    L1

5x + 4y = 50.10  L2

5L1 - 3L2

15x +  5y = 123

-15x - 12y = -150.3

-7y = -27,3

y = -27,3/-7

y = 3.9

3x + y = 24.60

3x + 3.9 = 24.60

3x = 24.60 - 3.9

3x = 20.7

x = 20.7 / 3

x = 6.9

A consumer loan of $40,000 with a 15.8% interest rate will require monthly payments over a period of 2 years. The total amount to be paid, including both principal and interest, will be approximately $45,380.

To calculate the monthly payments, we need to determine the total amount to be paid over the loan period, including the principal amount and the interest. The formula used for calculating equal monthly installments is:

M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)

Where:

M = Monthly payment

P = Principal amount

r = Monthly interest rate

n = Number of monthly payments

In this case, the principal amount (P) is $40,000, the interest rate (r) is 15.8% per year, and the loan duration (n) is 2 years (24 months).

First, we convert the annual interest rate to a monthly rate by dividing it by 12: 15.8% / 12 = 0.0132.

Next, we substitute the values into the formula:

M = 40,000 * (0.0132 * (1 + 0.0132)^24) / ((1 + 0.0132)^24 - 1)

Calculating this formula gives us the monthly payment (M) of approximately $1,907.42.

To find the total amount to be paid, we multiply the monthly payment by the number of payments: $1,907.42 * 24 = $45,778.08. However, this includes both the principal and the interest. Subtracting the principal amount ($40,000) gives us the total interest paid: $45,778.08 - $40,000 = $5,778.08.

Therefore, the total amount to be paid, including both principal and interest, will be approximately $45,778.08.

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Answer:

(x+2)^2 or (x+2)(x+2)

Step-by-step explanation:

x^2+4x+4 simplified is (x+2)^2 or (x+2)(x+2)

Answer:

(x+2)^2 or (x+2)(x+2)

Step-by-step explanation:

Brainly pls :D I tried for a while just to do this

Answer:

23 dollars

Step-by-step explanation:

so to figure out how much more you grab 20 and multiply by .15 as percent and you will get 3 dollars more so 23

Answer:

Step-by-step explanation:

The best way to find out the answer to your question is to graph the cubic. As you can see, the y intercept is (0,16).

How was this obtained. notice that if x = 0 then

f(0) = 2(3*0+4)(0^2 + 2)

f(0) = 2(4)(2)

f(0) = 16 just as the graph tells us.

1) Quadrilateral \(ABCD\) with diagonal \(\overline{AEC}\) bisecting \(\angle DAB\), \(\overline{BE}\), \(\overline{DE}\), \(\angle 1 \cong \angle 2\) (given)

2) \(\angle BAE \cong \angle EAD\) (definition of an angle bisector)

3) \(\overline{AE} \cong \overline{AE}\) (reflexive property)

4) \(\triangle BAE \cong \triangle DAE\) (AAS)

5) \(\overline{AB} \cong \overline{AD}\) (CPCTC)

6) \(\overline{AC} \cong \overline{AC}\) (reflexive property)

7) \(\triangle BAC \cong \triangle DAC\) (SAS)

8) \(\overline{BC} \cong \overline{DC}\) (CPCTC)

a)  The volume of paint left in the can is:

.878 gallons * 0.00378541 m^3/gallon = 0.003321 m^3

b)  the thickness of the layer of wet paint is 0.000242 meters or 0.242 millimeters (since there are 1000 millimeters in a meter).

(a) To convert gallons to cubic meters, we need to know the conversion factor between the two units. One U.S. gallon is equal to 0.00378541 cubic meters. Therefore, the volume of paint left in the can is:

0.878 gallons * 0.00378541 m^3/gallon = 0.003321 m^3

(b) We can use the formula for the volume of a rectangular solid to find the volume of wet paint needed to coat the wall evenly:

Volume = area * thickness

We want to solve for the thickness, so we rearrange the formula to get:

Thickness = Volume / area

The volume of wet paint needed is equal to the volume of dry paint needed since they both occupy the same space when the paint dries. Therefore, the volume of wet paint needed is:

0.003321 m^3

The area of the wall is given as:

13.7 m^2

So the thickness of the layer of wet paint is:

0.003321 m^3 / 13.7 m^2 = 0.000242 m

Therefore, the thickness of the layer of wet paint is 0.000242 meters or 0.242 millimeters (since there are 1000 millimeters in a meter).

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Answer:

a square angle

Step-by-step explanation:

because its a square agnle me barin is right :>

Answer:

1. Police station & mall

2. City hall & market

3. Church & park

4. Hospital & school

5. Park & city hall

6. Church & market

7. Police station & hospital

8. School & mall

9. City hall & mall

10. Church & hospital

See the image below for an illustration of each angle type.

Hope this helps!

Answer:

Zeroes of f(x):

x + 1 = 0, so x = -1

Vertical asymptotes of f(x):

x^2 - 4 = 0, so x = -2 and x = 2

End behavior of f(x):

As x --> negative infinity, f(x) --> 0

As x --> infinity, f(x) --> 0

No holes in f(x).

Answer:

$1.40

Step-by-step explanation:

If It's $7.00 for 5 pounds of oranges you would have to take the $7.00 and divide it by the number of pounds purchased which is 5.

$7.00 / 5 = $1.40

Answer:

I need the full question

Answer:

Step-by-step explanation:

To find the x intercepts, substitute in 0 for y and solve for x

So,

2x^2+2x-4 = 0

2(x^2+x-4) = 0

2/2(x^2+x-4) = 0/2

x^2+x-4 = 0

(x-1) (x+2) = 0

now,

x-1 = 0

x = 1

or

x+2 = 0

x = -2

The x intercepts for the parabola (1,0), (-2,0)

Answer:

4/3

Step-by-step explanation:

3x + 4y = 6

4y = -3x + 6

y = -3/4 x + 3/2

For the given line: slope = -3/4

The slopes of perpendicular lines are negative reciprocals.

Perpendicular: slope = 4/3

Answer:

the percentage change is a 60% change.

Step-by-step explanation:

A change from 5 to 2 represents a negative change (decrease) of -60%

Use the formula found below on this webpage to find the percent change by replacing the given values:

Percent change = New - Old

|Old|

× 100%

Percent change = 2 - 5

|5|

× 100% =

-3

5

× 100 = -60% (decrease)

Where: 5 is the old value and 2 is the new value. In this case we have a negative change (decrease) of -60 percent because the new value is smaller than the old value.

Answer:

The slope is 6

Step-by-step explanation:

Y2-Y1 / X2-X1

-3-(-9) / -1-(-2)

6

Answer:

m = 6

Step-by-step explanation:

slope (m) = rise / run

rise = y2 - y1 = -3 - (-9) = 6

run = x2 - x1 = -1 - (-2) = 1

slope = 6/1 = 6

Answer:

Step-by-step explanation:

{z - some integer}

2z+1  - the smallest number

7(2z+1)  - seven times the smallest number

2z+1+2=2z+3  - the middle number

2z+3+2 = 2z+5 - the largest number

2(2z+5) - twice the largest number

7(2z+1) + 2(2z+5)  - the sum of 7 times the smallest and twice the largest

7(2z+1) + 2(2z+5)   = -91

14z + 7 + 4z + 10 = -91

              -17              -17

      18z   = -108

       ÷18        ÷18

        z = -6

2z+1 = 2(-6)+1 = -12 + 1 = -11  

2z+3 = 2(-6)+3 = -12 + 3 = -9

2z+5 = 2(-6)+5 = -12 + 5 = -7        

a) X'Y' + X'Y + XY simplifies to X' + Y.

b) A'BC' + ABC' + BC'D simplifies to BC'.

Complement of the functions:

a) Complement is W' + X' + YZ.

b) Complement is (A' + B + C)(A'B' + C' + A'B).

a) To prove X'Y' + X'Y + XY = X' + Y, we can use Boolean algebra identities:

X'Y' + X'Y + XY

= Y'(X' + X) + XY(Distributive Law)

= Y' + XY(X + X' = 1)

= X' + Y(Commutative Law)

Therefore, X'Y' + X'Y + XY simplifies to X' + Y.

b) To prove A'BC' + ABC' + BC'D = BC', we can simplify the expression using Boolean algebra:

A'BC' + ABC' + BC'D

= BC'(A' + A) + BC'D   (Distributive Law)

= BC' + BC'D(A + A' = 1)

= BC'(BC' + BC'D = BC' + BC'(1) = BC')

Hence, A'BC' + ABC' + BC'D simplifies to BC'.

Complement of the given functions:

a) The complement of WX(Y'Z + YZ') + W'X'(Y' + Z)(Y + Z') is W' + X' + YZ.

b) The complement of (A + B' + C')(A'B' + C)(A + B'C') is (A' + B + C)(A'B' + C' + A'B).

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