when a car travels a distance of d kilometers in time t hours, the average speed for the journey is given by a =4/t km h^-1. find:
a. the average speed of a car which travels 200km in 2 1/2 hours.
b. the distance travelled by a car in 3 1/4 hours if its average speed is 80 km h^-1.
c. the time taken, to the nearest minute, for a car to travel 865 km at an average speed of 110 km h^-1

Answer:

It will take 4.5 hours for Naomi and Clair to paint an equal number of square feet

Explanation:

 Let the time in hour it will take for Naomi and Clair to paint an equal number of square feet be t hours.

Naomi paints 16.5 square feet of a mural at a rate of 2 square feet per hour, so after t hours the are painted by Naomi = 16.5 + 2 * t

Clair paints 7.5 square feet of the mural at a rate of 4 square feet per hour, so after t hours the are painted by Clair = 7.5 + 4 * t

We know that after hours the area painted by them are equal, so we have

           16.5 + 2 * t = 7.5 + 4 * t

            2 * t = 16.5 - 7.5 = 9

                t = 4.5 hours.

  So it will take 4.5 hours for Naomi and Clair to paint an equal number of square feet.                          

If Naomi and Clair continue to paint at their current rates, it will take approximately 4.5 more hours for both to have painted an equal amount of the mural.

First, let's calculate how much Naomi and Clair have already painted. Naomi has painted 16.5 square feet and Clair has painted 7.5 square feet. Now, calculate the difference which is 9 square feet.

Every hour, Naomi paints 2 square feet and Clair paints 4 square feet. However, since Clair needs to catch up by 9 square feet, we need to consider the extra square feet Clair paints per hour, which is 2 (4 - 2).

So, to find out how many more hours it will take for them to paint an equal number of 2 square feet, simply divide the difference (9 square feet) by the extra square feet Clair paints per hour (2). So, it would take Clair 4.5 more hours to paint an equal amount of mural to Naomi.

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The answer is y= 8x.

Answer:

Step-by-step explanation:

Area = 1/2 × base × height

Base(b) = 7 feet

Height(h) = 12 feet

Area = 1/2 × 7 × 12 = 7 × 6 = 42 feet²

3. definition of supplementary angles

5. defintion of congruency

6. substitution (refer to statements 3 and 5)

THE ANSWER IS:

the measure of the arc FH is 48 degrees

and btw I flipping love killing stalking :)

Answer:

[tex]48^{\circ}[/tex]

Step-by-step explanation:

Consider we need to find [tex]m\widehat{FH}[/tex],

Since, if two chords of a circle intersect outside the circle then the measure of intercepted angle is half of the difference of the measures of intercepted arcs.

Thus,

[tex]m\angle ADJ = \frac{m\widehat{AJ}-m\widehat{BE}}{2}[/tex]

By the diagram,

[tex]37^{\circ}=\frac{m\widehat{AJ}-38^{\circ}}{2}[/tex]

[tex]74^{\circ}=m\widehat{AJ}-38^{\circ}[/tex]

[tex]\implies m\widehat{AJ}=74^{\circ}+38^{\circ}=112^{\circ}[/tex]

Now,

[tex]m\angle AGJ = \frac{m\widehat{AJ}-m\widehat{FH}}{2}[/tex]

[tex]32^{\circ}=\frac{112^{\circ}-m\widehat{FH}}{2}[/tex]

[tex]64^{\circ}=112^{\circ}-m\widehat{FH}[/tex]

[tex]\implies m\widehat{FH}= 112^{\circ}-64^{\circ}=48^{\circ}[/tex]

Hence, SECOND OPTION would be correct.

The inequality x>35 represents the problem

more than is: >

A bank balance in excess of $35. Julia wishes to create a bank balance disparity. She uses the inequality sign x>35 to match the statement "greater than".

Inequality is a sort of equation in which the equal sign is missing. As we will see, inequality is defined as a statement regarding the relative magnitude of two claims.

The inequality symbol should she use to match the phrase “more than” is >.

A bank account with a balance of greater than $35. Julia wants to create a bank balance disparity. She uses the inequality sign x>35 to match the statement "greater than".

Hence, x >35 is the correct answer.

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Since the x axis represents the number of pen bought and the y axis the number of notebook, the total cost will be 2x+3y, because each pen costs 2$ and each notebook 3$.

You want this quantity to be no more than 30, so you must ask

[tex] 2x+3y \leq 30 [/tex]

which means that the shaded area must be under the graph of the line

[tex] 2x+3y = 30 [/tex]

You can rewrite the equation as

[tex] y = -\dfrac{2x}{3} + 10 [/tex]

So, the y intercept is the point [tex] (0,10) [/tex]

So the answer must be either C or D.

To find the x intercept, set y=0:

[tex] 0 = -\dfrac{2x}{3} + 10 \iff \dfrac{2x}{3} = 10 \iff 2x = 30 \iff x = 15 [/tex]

So, the correct answer is D.

Solution

The general form of the equation is y = mx + b, where m is the slope and b is the y-intercept.

The given equation is = -1/3 x - 6.

Comparing the given equation with the general form, we get

slope (m) = -1/3 and y-intercept = -6.

The answer is -1/3; -6

Thank you. :)

to help you can write it as 3-1 which is 2

ANSWER 2

Based on the graph of the relationship given between time and the amount of popcorn popped, the relationship doesn't yield a straight line, hence, the relationship isn't proportional.

A proportional relationship is one in which there is a constant change in one variable as the value of the other variable is varied.

A proportional relationship will always yield a straight line with either a positive or negative slope.

Since, the trend line isn't straight, then the relationship isn't proportional.

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The actual question is not about the popcorn machine but about testing the hypothesis on mean differences of relaxed and jumping times for eight girls. To assess this, statistical methods like the paired t-test are used to examine the existence of a direct relationship between the two sets of times.

The relationship between time and the amount of popcorn popped could be considered directly proportional if the rate of popping remains constant over time. However, this question appears to be based on a misunderstanding, as it incorrectly states that Rachel had a popcorn machine. Instead, the actual task given is to test the hypothesis that the mean difference between jumping and relaxed times for eight girls at a party would be zero.

To test this hypothesis, a statistical test like a paired t-test could be used to determine if there is a significant difference between the two mean times. Proportionality in the question should be related to rates or ratios. For instance, when data shows a positive correlation as one variable increases, so does the other. This is seen when graphing data that results in a straight line, which signifies a direct relationship.

Therefore, to determine the relationship between two quantities, the concept of direct and indirect proportionalities is important, and having a direct relationship would mean that the variables increase together linearly.

Answer:

Average temperature at night -140°C.

Step-by-step explanation:

To find the average temperature at night we have to deduct the drop in temperature from the average temperature at noon.

Average temperature at night = Average temperature at noon - drop in temperature.

                                                  =112°C -  252°C

                                                  = -140°C

The average temperature on the moon's surface at night is -140 degrees Celsius, as calculated by subtracting the temperature drop at night (252 degrees Celsius) from the daytime temperature (112 degrees Celsius).

Your question involves finding out the average temperature on the Moon's surface during the night. The temperature on the Moon at noon is 112 degrees Celsius. However, the temperature drops by 252 degrees Celsius at night. To find the temperature at night, you subtract the drop in temperature from the daytime temperature.

So, let's do the calculation: 112 degrees Celsius (noon temperature) - 252 degrees Celsius (temperature drop) = -140 degrees Celsius. Therefore, the average temperature on the Moon's surface during the night is -140 degrees Celsius.

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Answer: Upper left corner

==============================================================

Further Explanation:

The piecewise function is broken down into three parts which I'll refer to as A, B and C (moving down the rows).

Part A is y = -4 but only if x is -3 or smaller. Points on this line include (-3,-4), (-4,-4), (-5,-4), etc. Basically any point where the y value is -4, and the x value is -3 or smaller.

Part B of this piecewise funciton is exactly one point which is (2,0). We plot y = 0 but only when x = 2.

Finally, part C is the horizontal line through y = 3 but we only graph this line if x is larger than 2. Two points on this line are (2,3) and (3,3). The point (2,3) is an open circle because of the fact that x > 2. So x = 2 is not allowed for this piece.

Put this all together, and you get the graph shown in the upper left corner as the final answer.

Note: the bottom left corner is very close to the proper answer, but the presence of an open hole at (-3,-4) is why this is not the actual answer. We are including this point as part of the first piece. This point is included because of the "or equal to" as part of the inequality.

Answer:

[tex]\frac{4}{5}[/tex] of Steph's annual income is from her full-time job.

Step-by-step explanation:

Suppose, Steph's annual income is  [tex]x[/tex]

Given that, 80% of Steph's annual income is from her full-time job.

So, the amount of income from her full time job will be:  [tex](x\times 80\%)= (x\times\frac{80}{100})= 0.8x[/tex]

Now, for finding the income from her full time job as a fraction of Steph's annual income, we just need to divide "income from full time job" by "total annual income".

So, the fraction will be:  [tex]\frac{0.8x}{x}= 0.8 =\frac{8}{10}= \frac{4}{5}[/tex]

That means,  [tex]\frac{4}{5}[/tex] of Steph's annual income is from her full-time job.

Answer:

4.5 is the answer.

Step-by-step explanation:

80% is fraction form is 80/100 to simplify that it becomes 4/5. Therefore, the answer is 4/5

Final answer:

Gabe needs to give 25 hours of piano lessons in a month to earn a profit of $326, calculated by setting up an equation that factors in his earnings per hour and the monthly cost of renting the piano.

Explanation:

To find out how many hours of lessons Gabe must give to earn a profit of $326, we need to set up an equation that represents his earnings and costs. Given that Gabe earns $15 per hour giving piano lessons, and his fixed cost for renting the piano is $49 per month, we can create the following equation:

Profit = (Earnings from lessons) - (Cost of renting the piano)

Let h represent the number of hours he teaches. His earnings from giving lessons would be 15h (because he earns $15 for each hour of lessons). The cost of renting the piano is a fixed $49 per month. Therefore, we have:

Profit = (15h) - 49

To make a profit of $326, we substitute this into the equation:

326 = (15h) - 49

Now we solve for h to find out how many hours he needs to teach:

326 + 49 = 15h

375 = 15h

h = 375 / 15

h = 25

Gabe needs to give 25 hours of lessons in a month to earn a profit of $326.

The graph of this relation is four points on the coordinate plane (see attached diagram).

A function is a special relation, where each input x has a single output y.

This relation is not a function, because for one x (x=-1), here are two different possible y (y=3 or y=2). If you consider the graph, you can see that there will be vertical line passing through the points (-1,3) and (-1,2). This means that option D is true.

y < - 8  or y > 4

inequalities of the form | x | > a always have solutions of the form

x < - a or x > a

we have to solve

y + 2 < - 6 or y + 2 > 6

y + 2 < - 6 ( subtract 2 from both sides )

y < - 8

or

y + 2 > 6 ( subtract 2 from both sides )

y > 4

these can be combined using interval notation

y ∈ (- ∞, - 8 ) ∪ (4, ∞ )

As a check

substitute chosen values of x from each interval

y = - 10 :  | - 10 + 2 | = | - 8 | = 8 > 6 this is true

y = 12 : | 12 + 2 | = | 14 | = 14 > 6 which is also true

He product of two positive numbers is 750. The first number is 5 less than the second number. The equation x(x – 5) = 750 can be used to find x, the value of the greater number. What is the value of the greater number?

Solution

Here the second number is "x"

The first number is "x - 5"

The equation is x (x - 5) = 750

[tex]x^{2}[/tex]- 5x = 750

Subtract 750 from both sides, we get

[tex]x^{2} -5x -750 =0\\[/tex]

Solving the above quadratic  equation using quadratic formula, we get

[tex]x = \frac{-b+/- \sqrt{b^{2}-4ac } }{2a}[/tex]

Here we have to plug in  a =1, b = -5 and c = -750 in the above formula, we get

[tex]x = \frac{5 +/-\sqrt{3025} }{2}[/tex]

When we simplify the above expression is...

x = 30 and x = -25

x = -25 cannot be the solution since it is negative value.

x = 30 is the solution.

Here "x" represents the second number which is 30, that is the greater number.

Therefore, the answer is 30.

Answer:

 30

Step-by-step explanation:

You can try the answer choices to see what works.

 15·10 ≠ 750

 25·20 ≠ 750

 30·25 = 750 . . . . the larger number is 30

 50·45 ≠ 750

Answer to the question:

Step-by-step explanation:

1)

v - 6 ≥ 4

  +6   +6

v      ≥ 10

Graph: 10 -----------------→  the dot at 10 is filled in because of the "equal to" symbol

********************************************************************************************************

2)

-5x < 15

[tex]\frac{-5x}{-5} > \frac{15}{-5}[/tex]  divided by a negative so the symbol flipped

x > -3

Graph: -3 o------------------→ the dot at -3 is NOT filled in because it's NOT "equal to"

********************************************************************************************************

3)

3k > 5k + 12

-5k  -5k      

-2k >          12

[tex]\frac{-2k}{-2} < \frac{12}{-2}[/tex]   divided by a negative so the symbol flipped

k < -6

Graph: ←------------o -6   the dot at -6 is NOT filled in because it's NOT "equal to"

********************************************************************************************************

5)

2t ≤ 4      or    7t ≥ 49

[tex]\frac{2t}{2} \leq\frac{4}{2}[/tex]      or    [tex]\frac{7t}{7} \geq \frac{49}{7}[/tex]

 t ≤ 2      or      t ≥ 7

Graph: ←------- 2        7 ---------→   the dots at 2 and 7 are filled in

********************************************************************************************************

6)

| n + 2 | = 4

n + 2 = 4      or     n + 2 = -4

    -2   -2                 -2   -2

n      = 2        or     n       = -6

Answer: n = {2, -6}

********************************************************************************************************

7)

| 2x - 7 | > 1

2x - 7 > 1       or     2x - 7 < -1

     +7  +7                 +7   +7

2x      > 8       or     2x     <  6

    [tex]\frac{2x}{2} > \frac{8}{2}[/tex]             or       [tex]\frac{2x}{2} < \frac{6}{2}[/tex]

    x > 4          or         x < 3

Graph: ←----------o 3      4 o------------→

********************************************************************************************************

8)

A = {1, 2, 3, 4, 5, 6, 7, 8, 9}    B = {2, 4, 6, 8}

A U B = {1, 2, 3, 4, 5, 6, 7, 8, 9}    union combines both sets

A ∩ B =  {2, 4, 6, 8}   intersection includes only those that are in BOTH sets

********************************************************************************************************

9)

P = {1, 5, 7, 9, 13}   R = { 1, 2, 3, 4, 5, 6, 7}    Q = {1, 3, 5}

P ∩ R ∩ Q = {1, 5}

P ∩ R = {7}  disregard 1 & 5 since they are already in P∩Q∩R

R ∩ Q = {3}  disregard 1 & 5 since they are already in P∩Q∩R

P ∩ Q = { }  disregard 1 & 5 since they are already in P∩Q∩R

P no intersection = {9, 13)

R no intersection = {2, 4, 6}

Q no intersection = {  }

If you can't figure out how to draw it based on the information I provided, please see the attached diagram. Note: Usially, you would only identify P, Q, R.  I identified the intersections so you would understand why those specific numbers are placed in the designated sections.

8 / 2 = 4

75 x 4 = 300

The unit rate is for every 2 ounces there is 75 calories or for every 1 ounce there is 37.5 calories

parrotfish:clownfish

4:3

20:x

4 times 5 = 20

multiply 3 by 5 to keep the same ratio. =>   3 times 5 equals 15. therefore there are 15 clownfish.

hope I helped! (:

Note that point-slope equation is: (y - y₁) = m(x - x₁)

Also note that f(x) = y

Isolate the y. Subtract 7 from both sides:

y + 7 = –(x + 6)

y + 7 (-7) = -(x + 6) - 7

y = -(x + 6) - 7

Note that the equation is really: y = -1(x + 6) - 7

Distribute -1 to all terms within the parenthesis

y = -1(x + 6) - 7

y = -x - 6 - 7

Simplify. Combine like terms

y = -x - 13 ; or f(x) = -x - 13, which is none of the above.

Please check and verify your choices.

hope this helps

To complete the square for the equation x^2 - 9x = 8, the number 81/4 must be added to both sides, resulting in x^2 - 9x + 81/4 = 113/4.

To complete the square for the equation x^2 - 9x = 8, we need to find a number that when added to x^2 - 9x makes it a perfect square trinomial. The formula to complete the square is to take the coefficient of the x term (which is -9), divide it by 2, and square it. The process looks like this:

(-9/2)^2 = 81/4

Therefore, the number to add to both sides of the equation is 81/4. The equation then becomes:

x^2 - 9x + 81/4 = 8 + 81/4

Which simplifies to:

x^2 - 9x + 81/4 = 32/4 + 81/4

x^2 - 9x + 81/4 = 113/4

By adding 81/4 to both sides, we have successfully completed the square.

5(x + 3) - 9x + 4

use distributive property

= (5)(x) + (5)(3) -9x + 4 = 5x + 15 - 9x + 4 = (5x - 9x) + (15 + 4)

= -4x + 19

To simplify the expression 5(x + 3) - 9x + 4, distribute 5 to the terms inside the parentheses, combine like terms, and then add the constant terms.

To simplify the expression 5(x + 3) - 9x + 4, we first distribute the 5 to both terms inside the parentheses: 5x + 15. Next, we combine like terms by subtracting 9x from 5x to get -4x. Finally, we add the constant term 15 with the constant term 4 to get 19. Therefore, the simplified expression is -4x + 19.

To simplify the expression 5(x + 3) - 9x + 4, distribute 5 to the terms inside the parentheses, combine like terms, and then add the constant terms.

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The length of the segment is 22 units

y = 11 units

The total length of the segment will be expressed as:

L = x + y

Note that x = y

Substituting into the total length

L = y + y

L = 2y

L = 2(11)

L = 22 units

Hence the length of the segment is 22 units

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Answer:

When you join points D(2,3),O(0,0)and E(5,1) which are not collinear it will form a triangle.

Now , Adjacent of ∠ DOE are [ ∠ ODE and ∠OED] .

As we know that  Sum of three interior angles of a triangle is 180°.

∠ DOE + ∠OED+∠EDO = 180°

∠DOE=180°- (∠OED+∠EDO)

Supplementary ,of ∠DOE is  (∠OED+∠EDO).

Answer: angle DOF, with F (-5,-1) and angle EOF, with F(-2,-3)