When Dustin goes to work, he drives at an average speed of 55
miles per hour. It takes about 2 hour and 15 minutes for Dustin to
arrive at work. His car travels about 25 miles per gallon of gas. If
gas costs $2.75 per gallon, how much money does Justin spend to
travel each mile to work?

Answer:

Helena gave the answer as (7y²z + 6yz²- 5 - 3yz² + 2) which is equivalent to (7y²z + 3yz² - 3).

Step-by-step explanation:

Misha's group was asked to write an expression equivalent to  

7y²z + 3yz² - 3

When Mr. Chen checked their answers, he found only one to be correct.

And she was Helena.

Helena gave the answer as (7y²z + 6yz²- 5 - 3yz² + 2) which is equivalent to (7y²z + 3yz² - 3).  

Because, (7y²z + 6yz²- 5 - 3yz² + 2)

= 7y²z + (6yz² - 3yz²) - (5 - 2)  

= 7y²z + 3yz² - 3 (Answer)

Answer:

Question 1)

Rearrange 2x-6y=12 to slope-intercept form by isolating y

y = (1/3)x - 2

Sub each x value to get the y value

x       y

-3     -3

0      -2

3      1

6      0

y = (1/3)x - 2

y = (1/3)(-3) - 2

y = -3

Point (-3, -3)

y = (1/3)x - 2

y = (1/3)(0) - 2

y = -2

Point (0, -2)

y = (1/3)x - 2

y = (1/3)(3) - 2

y = 1

Point (3, 1)

y = (1/3)x - 2

y = (1/3)(6) - 2

y = 0

Point (6, 0)

See graph below

Question 2)

a) No, each support does not have the same starting coordinates. For example, the first support from the left starts at (0,0) and the second support from the left starts at (2,1).

b) No, each support does not have the same ending coordinates. For example, the first support from the left ends at (2,1) and the second support from the left ends at (6,3).

c) No, each support does not have the same change in x-values from the start to end.

The first support starts at the x-value 0 and ends at the x-value 2. It increased by 2.

The second support starts at the x-value 2 and ends at the x-value 6. It increased by 4.

d) No, each support does not have the same change in y-values from the start to end.

The first support starts at the y-value 0 and ends at the x-value 1. It increased by 1.

The second support starts at the y-value 1 and ends at the x-value 3. It increased by 2.

e) Yes, each support has the same change in the ratio of y-values over x-values. For the first support, the change is y-values is 1 and the change in x-values is 2. (1/2)

For the second support, the change in y-values is 2 and the change in x-values is 4. (2/4 = 1/2)

They both have the ratio of change in y-values over x-values 1/2.

Answer:

Number of Adult's tickets sold on Saturday = 3,356

Number of Children's tickets sold on Saturday = 2, 928

Total number of tickets sold over these two days is 8,938.

Step-by-step explanation:

Here, the number of tickets sold on FRIDAY:

Adult Ticket sold = 1,678

Children's Tickets sold = 976

So, the total number of tickets sold on Friday  

= Sum of ( Adult + Children's ) tickets  = 1,678  + 976 = 2,654 ....  (1)

The number of tickets sold on SATURDAY:

Adult Ticket sold =   2 times  the number of adult tickets sold on Friday  

                             =  1,678 x 2  = 3,356

Children's Tickets sold = 3 times the number of children's tickets sold on Friday.

=  976  x 3 = 2, 928

So, the total number of tickets sold on Saturday  

= Sum of ( Adult + Children's ) tickets  = 3,356 + 2,928 = 6, 284 ....  (2)

Now, the total number of tickets booked in these two days :

Sum of tickets booked on (Friday + Saturday)

= 2,654 +  6, 284  =   8,938

Hence, total number of tickets sold over these two days is 8,938.

There are 80 birds in the flock of cardinals.

Given:-  A flock of 20 seagulls  or we can say

Number of seagulls in a flock = 20

The new flock is no larger than 100 birds

So, let Total number of birds of new flock = 100

To find out the number of birds in cardinals we have to subtract number of seagull in flock from total number of birds of new flock.

Number of birds in cardinal = Total number of birds of new flock - Number of seagulls in a flock

Number of birds in cardinal = 100 – 20 =80

Hence there are 80 birds in the flock of cardinals.

The answer explains how to determine the number of birds in the flock of cardinals based on the given conditions.

The number of birds in the flock of cardinals can be calculated as follows:

Let x be the number of birds in the flock of cardinals.

Since the new flock is no larger than 100 birds, the total number of birds after merging is 20 (seagulls) + x (cardinals).

Therefore, the equation to represent this situation is x + 20 ≤ 100, and solving for x, we get x ≤ 80. Thus, there were at most 80 birds in the flock of cardinals.

Answer:

yes you can look below for details

Step-by-step explanation:

one reason is because opposite sides are congruent, which means that it is a parallelogram.

another way is to see if the two triangles created by an diagonal is congruent:

construct AC to get two triangles ABC and ADC

AC =CA because of reflection

BA=DC because its given

BC=DA because its also Given

so

triangle ABC= triangle CDA because of SSS(side side side)

Answer:

22

Step-by-step explanation:

Answer:

45 cats 18 dogs

Step-by-step explanation:

63/7 = 9

9*5=45

9*2=18

45+18=63

The number of cats up for adoption is 45.

Given that, the ratio of cats to dogs=5:2.

The total number of cats and dogs up for adoption is 63.

In mathematics, a ratio indicates how many times one number contains another.

Now, 5+2=7

Number of cats=5/7×63=45

Therefore, the number of cats up for adoption is 45.

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Answer:

Hey.

By what percentage was the price of the video games reduced ?

By 25%.

Step-by-step explanation:

$60 is the 100% price.

Now we have to find what percentage belongs to the reduced price, $45.

45×100/60 = 75.

75% is the percentage of the reduced price.

We can find the difference between them by doing a substraction.

100%-75% = 25%.

Hope I helped you !

Answer:

No

Step-by-step explanation:

By the factor theorem if (x + 2) is a factor of f(x) then f(- 2) = 0

f(- 2)

= 2[tex](-2)^{6}[/tex] + [tex]-2)^{5}[/tex] + 32(- 2) + 32

= 2(64) - 32 - 64 + 32

= 128 - 32 - 64 + 32

= 64 ≠ 0

Hence (x + 2) is not a factor of f(x)

Answer: By the factor theorem if (x + 2) is a factor of f(x) then f(- 2) = 0

f(- 2)

= 2(-2)^{6} + -2)^{5} + 32(- 2) + 32

= 2(64) - 32 - 64 + 32

= 128 - 32 - 64 + 32

= 64 ≠ 0

Hence (x + 2) is not a factor of f(x)

Answer:

The debris will be at a height of 56 ft when time is 0.5 s and 7 s.

Step-by-step explanation:

Given:

Initial speed of debris is, [tex]s=120\ ft/s[/tex]

The height 'h' of the debris above the ground is given as:

[tex]h(t)=-16t^2+120t[/tex]

As per question, [tex]h(t)=56\ ft[/tex]. Therefore,

[tex]56=-16t^2+120t[/tex]

Rewriting the above equation into a standard quadratic equation and solving for 't', we get:

[tex]-16t^2+120t-56=0\\\textrm{Dividing by -8 throughout, we get}\\\frac{-16}{-8}t^2+\frac{120}{-8}t-\frac{56}{-8}=0\\2t^2-15t+7=0[/tex]

Using quadratic formula to solve for 't', we get:

[tex]t=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\t=\frac{-(-15)\pm \sqrt{(-15)^2-4(2)(7)}}{2(2)}\\\\t=\frac{15\pm \sqrt{225-56}}{4}\\\\t=\frac{15\pm\sqrt{169}}{4}\\\\t=\frac{15\pm 13}{4}\\\\t=\frac{15-13}{4}\ or\ t=\frac{15+13}{4}\\\\t=\frac{2}{4}\ or\ t=\frac{28}{4}\\\\t=0.5\ s\ or\ t=7\ s[/tex]

Therefore, the debris will reach a height of 56 ft twice.

When time [tex]t=0.5\ s[/tex] during the upward journey, the debris is at height of 56 ft.

Again after reaching maximum height, the debris falls back and at [tex]t=7\ s[/tex], the height is 56 ft.

Final answer:

To find when the debris will be 56 feet above the ground, we solve the quadratic equation -16t² + 120t = 56 using the quadratic formula. This will yield two possible solutions for t, which are the times at which the debris reaches 56 feet.

Explanation:

To determine when the debris will be 56 feet above the ground, we need to solve the given quadratic equation for t, which represents time in seconds. The equation provided is:

h = -16t² + 120t

Where h is the height in feet. To find the times when the debris is 56 feet above the ground, we set h to 56:

56 = -16t² + 120t

This equation can be solved by factoring or using the quadratic formula. To factor, we first set the equation to zero:

-16t² + 120t - 56 = 0

16t² - 120t + 56 = 0

Dividing by 4

4t² - 30t + 14 = 0

Again reducing by dividing by 2

2t² - 15t + 7 = 0

Now, we need two numbers which add to give 15 and multiply to give 14.

The two numbers are 1 and 14.

2t²- 14t - t + 7 = 0

2t (t - 7) - 1(t - 7) = 0

(t - 7)(2t - 1) = 0

t = 7 or 1/2

Since 1/2 second cannot be an answer, the required answer is 7 seconds

Answer:

h = 1.4

c = 2.8

Step-by-step explanation:

For each problem, remember the special triangle side ratios then use a proportion. To solve, isolate the variable.

For the triangle with the variable h:

Since two of the angles are 45, this is an isosceles triangle. All isosceles triangles have two equal sides that are not the hypotenuse.

In a right isosceles triangle, the ratio for regular side to hypotenuse is 1 to √2.

[tex]\frac{1}{\sqrt2} =\frac{h}{2} \\h = 2\frac{1}{\sqrt2} \\h = \frac{2}{\sqrt2} \\h = \frac{2\sqrt2}{2} \\h = \sqrt{2}[/tex]

h = √2

h ≈ 1.4

For the triangle with the variable c:

The is an equilateral triangle cut in half because the angles are 30 and 60.

The side ratio of altitude to hypotenuse is √3 to 2.

[tex]\frac{\sqrt{3} }{2} =\frac{c}{4} \\\sqrt{3} = \frac{c}{2}\\2\sqrt3 = c[/tex]

c = 2√2

c ≈ 2.8

Lance and Mary will need approximately $12,995 for a down payment on the property.

To calculate the amount of money needed for a down payment, you need to find 20% of the property cost. In this case, the property cost is $64,975.

Step 1: Convert 20% to a decimal by dividing it by 100: 20/100 = 0.2

Step 2: Multiply the property cost by 0.2: $64,975 * 0.2 = $12,995

Therefore, Lance and Mary will need approximately $12,995 for a down payment on the property.

Answer:

C is the answer.

Step-by-step explanation:

In simple terms, absolute value makes a negative number positive. So, |ab| simplifies to -ab when a<0 and b>0, |2b| simplifies to -2b when b<0, and |c| simplifies to -c when c<0.

The expression |ab| simply represents the absolute value of the product of a and b. Absolute value is a mathematical function that determines the distance of a number from zero. In this case, as a is less than 0 (negative) and b is greater than 0 (positive), the product ab would be negative. But absolute value always returns a positive output or zero, so, |ab| would be -ab because absolute value would remove the negative sign.

The expression |2b|, where b is less than 0, would simplify to -2b, as b is negative so absolute value removes the negative sign.

Lastly, the expression |c|, when c is negative, simplifies to -c as the absolute value would remove the negative sign from c.

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Final answer:

To simplify expressions with absolute value signs, one must take into account the sign of the variables involved. If the result inside the absolute value sign is negative, then removing the absolute value signs will result in its positive counterpart.

Explanation:

When simplifying the expression |ab| given that a<0 and b>0, we consider that since a is negative and b is positive, their product ab will be negative. However, the absolute value signs indicate the positive magnitude of the result, thus |ab| = -ab.

For the expression |2b| where b<0, since b is negative, 2b will also be negative. Removing the absolute value sign should result in a positive number; thus |2b| = -2b.

Lastly, with |c| where c<0, the absolute value of a negative number c is the positive version of the number. Therefore, |c| = -c.

Answer:

B

Step-by-step explanation:

For the arcs WX and YZ to be congruent.

The angles subtended at the centre of the circle must be congruent.

This is not the case here as arc WX subtends 80° and arc YZ subtends 35°

Thus arc WX and arc YZ are not congruent.

Answer:

Yes

Step-by-step explanation:

the total discount allowed will be 25% of the original price and futher 10% of the original price which will amount to 10%+25% and this equal 35%

Answer:

B(6, - 11 )

Step-by-step explanation:

Since the translation rule is (x - 2, y + 3 )

Then to go back the way do the opposite, that is

(x + 2, y - 3 ), thus

B(4 + 2, - 8 - 3 ) → B(6, - 11 )

Answer:(6, -11)

Step-by-step explanation:

Answer:

Original Price = $500

Step-by-step explanation:

The discount is 36%

and the discount amount is $180

Thus,

we can say that 180 is 36% of what number?

We let that number be "x" (original price). So we can say:

180 is 36% of x

In equation that will be:

180=36%*x

180=(36/100)*x

180=0.36x

So,

x = 180/0.36

x = $500

This is the original price.

Answer:

D

Step-by-step explanation:

The diagram shows the rectangle with vertices at A(3,4), B(3,7), C(4,7) and D(4,4).

1. Rotate rectangle ABCD by 180° about the point (3,4) (vertex A). This rotation has the rule:

[tex](x,y)\rightarrow (6-x,8-y)[/tex]

So, the image points have the coordinates A'(3,4), B'(3,1), C'(2,1) and D'(2,4)

2. Dilate by a scale factor of 2 with the center of dilation at origin. This dilation has the rule:

[tex](x,y)\rightarrow (2x,2y)[/tex]

So, the image points have the coordinates A''(6,8), B''(6,2), C''(4,2) and D''(4,8)

3. Reflect it over the y-axis. This reflection has the rule:

[tex](x,y)\rightarrow (-x,y)[/tex]

So, the image points have the coordinates A'''(-6,8), B'''(-6,2), C'''(-4,2) and D'''(-4,8) that are exactly the coordinates of the second rectangle shown.

Thus, correct option is option D.

Answer:

F(f) = 15t + 35 represents the total amount of savings your friend would make in t weeks.

F(d) = 10t + 90 represents the total amount of saving you, darian, would make in t weeks.

When you graph the equations, plugging in different values for t, you can see that the graphs  intersect at (11,200). This means that at 11 weeks, both you and your friend have the same amount of money saved up, $200.  They will not have the same amount of money in 10 weeks.

Answer:

[tex]y=15x+35[/tex]

Step-by-step explanation:

If you begin with $90 and add $10 each week, then we express it as

[tex]y=10x+90[/tex]

Where [tex]x[/tex] refers to weeks and [tex]y[/tex] refers to the total amount of money in you savings account.

On the other hand, your friend begins with $35 and deposits $15 each week, the equation that expresses your friend's savings is

[tex]y=15x+35[/tex]

Therefore, the sytem of linear equation that models this situation is

[tex]y=10x+90[/tex]

[tex]y=15x+35[/tex]

The graph attached shows this system. There you can notice that the solution is (11, 200), which means in 11 weeks both will have the same amount saved.

Therefore, your friend is wrong, because after 10 weeks you won't have the same amount.

ANSWER:

1/2 (x+3)(x+5)

= 1/2(x^2+8x+15)_This is the right answer

= x^2/2 + 8x/2 + 15/2

= x^2/2 + 4x + 15/2

Mark me as brainst answer

And

Press on Thank You

Answer:

Y<4 or y>9

Hope this helps you out!

Answer:

3 large, 13 small

Step-by-step explanation:

large: x

small: y

x + y = 16

16x + 9y = 165

Multiply first equation by 9 and subtract the equations.

9x + 9y = 144

-(16x + 9y = 165)

-7x = -21

x = 3

Now substitute this x value into the first equation

x + y = 16

3 + y = 16

y = 13

Answer:

The system of equations are

x + y = 2600   …….equation (1)

and, 6x + 5y = 13700  ……equation (2)

Explanation:

Let x = amount of sales of phone;

y = amount of sales of computer

For phone, 6% of sales is 6% of x, or 6% * x = 0.06x.

Similarly for computer,

5% of y = 0.05y

Given the total sales; x + y = 2600

And commission; 0.06x + 0.05y = 137; or 6x + 5y = 13700

Therefore the system of equations are

x + y = 2600   …….equation (1)

6 x + 5 y = 13700  ……equation (2)

We can't really use w = 1 in this equation because it would be a false equation.

3w = 84

3(1) = 84

3 ≠ 84

If we were to solve for w then we can divide 3 to both sides.

3w = 84

3w/3 = 84/3

w = 28

______

Best Regards,

Wolfyy :)

Hey there!

3w = 84

DIVIDE 3 to BOTH SIDES

3w/3 = 84/3

CANCEL out: 3/3 because it give you 1

KEEP: 84/3 because it give you the w-value

NEW EQUATION: w = 84/3

SIMPLIFY IT!

w = 28

Therefore, your answer is: w = 28

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

B-How many books have each of my classmates read this year?

Step-by-step explanation:

Every year the number of books each classmate read would be different

Answer:

b

Step-by-step explanation:

a) The rate of change in this situation is 0.75 dollars/km

b) The equation for the cost of hiring a taxi in terms of length of the

trip is y = 0.75 x + b

c) The initial value represents in this situation is $1.2

Step-by-step explanation:

The given is:

∵ A rate of change is a rate that describes how one quantity

  changes in relation to another quantity

∵ The unit cost of a taxi is 0.75 dollars for each 1 kilometer

∴ The rate of change = 0.75 dollars/km

a) The rate of change in this situation is 0.75 dollars/km

Assume that the cost of hiring a taxi is $y for length of a trip x km

and a base fee of $b

∵ The length of the trip = x km

∵ The cost per km = $0.75

∵ The base fee = $b

∵ The cost of hiring a taxi = $y

- Write an equation for the the cost of hiring a taxi

∴ y = 0.75 x + b

b) The equation for the cost of hiring a taxi in terms of length

of the trip is y = 0.75 x + b

∵ The length of the trip is 10 km

∴ x = 10

∵ The cost of the hiring a taxi is $8.70

∴ y = 8.70

- Substitute these values in the equation of part (b)

∵ y = 0.75 x + b

∴ 8.70 = 0.75(10) + b

∴ 8.70 = 7.5 + b

- Subtract 7.5 from both sides

∴ 1.2 = b

∵ b is the base fee

∴ b is the initial value

∴ The initial value = $1.2

c) The initial value represents in this situation is $1.2

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Answer:

a)  $0.75/Km

b) [tex]F(x)=1.2+0.75x[/tex]

c) The fixed base charge

Step-by-step explanation:

We know the taxi charges $0.75 per km and we are told a 10-Km trip costs $8.70. We can clearly see there is a base charge and a variable charge

a) The rate of change tells us the variation of the charges with the distance of the trip. In this case, the rate of change is $0.75/Km

b) If x is the length of the trip in Km, the equation of the total fare F(x) is

[tex]F(x)=A+0.75x[/tex]

We know a 10-Km trip costs $8.70. Replacing those values would give us the value of A

8.70=A+0.75(10)

8.70=A+7.5

[tex]=> A=8.70-7.5= 1.2[/tex]

Using the value of A we have

[tex]\boxed{F(x)=1.2+0.75x}[/tex]

c) The initial value represents the charge a customer has to pay even if they don't travel any distance, i.e. the fixed base charge

Answer:

The speed of Sharma is slower than the speed of Brandi

I.e ∵   4.67 miles per hour  [tex]<[/tex] 5 miles per hour

      ∴  [tex]S_2[/tex] [tex]<[/tex] [tex]S_1[/tex]

Step-by-step explanation:

Given as :

The distance cover by Brandi = [tex]D_1[/tex] = 2 [tex]\frac{1}{2}[/tex] =[tex]\frac{5}{2}[/tex]

The Time taken by Brandi for jogging =  [tex]T_1[/tex] = 30 minutes =[tex]\frac{1}{2}[/tex] hour

Let the speed of Brandi = [tex]S_1[/tex] = [tex]\dfrac{\textrm Distance }{\textrm Time}[/tex]

or,  [tex]S_1[/tex] = [tex]\dfrac{\textrm  [tex]D_1[/tex]  }{\textrm   [tex]T_1[/tex] }[/tex]

Or.  [tex]S_1[/tex] = [tex]\frac{\frac{5}{2}}{\frac{1}{2}}[/tex]

∴   [tex]S_1[/tex] = 5 miles per hour

Again

The distance cover by Sharma = [tex]D_2[/tex] = 3 [tex]\frac{1}{2}[/tex] =[tex]\frac{7}{2}[/tex]

The Time taken by Sharma for jogging =  [tex]T_2[/tex] = [tex]\frac{3}{4}[/tex] hour

Let the speed of Sharma = [tex]S_2[/tex] = [tex]\dfrac{\textrm Distance }{\textrm Time}[/tex]

or,  [tex]S_2[/tex] = [tex]\dfrac{\textrm  [tex]D_2[/tex]  }{\textrm   [tex]T_2[/tex] }[/tex]

Or.  [tex]S_2[/tex] = [tex]\frac{\frac{7}{2}}{\frac{3}{4}}[/tex]

∴   [tex]S_2[/tex] = [tex]\frac{14}{3}[/tex] = 4.67 miles per hour

Now, ∵   4.67 miles per hour  [tex]<[/tex] 5 miles per hour

         ∴  [tex]S_2[/tex] [tex]<[/tex] [tex]S_1[/tex]

So, Sharma jogged at slower late

Hence The speed of Sharma is slower than the speed of Brandi Answer

Answer:

48 will be the answer.

Step-by-step explanation:

we can simply find the 80 percent of 60.

80 * 60 / 100 = 4800/100 = 48.

so 48 students think he is their favorite teacher.