in a list of 7 consecutive integers, the sum of the first and last is 518. find the largest.

Answer:

OPTION C

Step-by-step explanation:

An element in the domain should be mapped to exactly one element on the co-domain. Also, every element in the domain should be mapped to an element in the co-domain.

These two conditions are satisfied to call a relation, a function.

Two different elements in the domain can be mapped to the same element in the co-domain. But the same element in the domain cannot be mapped to two different elements in the co-domain.

A) (1,2), (3,4), (5,6), (3,-4)

Here, the element '3' is mapped to 4 and -4. So, this is not a function.

B) (8,4), (4,3), (2,2), (8,1)

'8' is mapped to 4 and 1. So, it is not a function.

C) (2,5), (3,10), (4,15), (5,20)

All the elements in the domain are mapped to an element in the co-domain.  Also, every element in the domain has exactly one image in the co-domain. So, this relation is a function.

D) (2,4), (2,3), (2,1), (2,0)

The element '2' has more than one image. Clearly, it contradicts the definition of a function.

So, only OPTION C is the answer.

Abigail has eaten 3/8 of a pound of candy.

This is the answer because 3/4 is equivalent to 6/8, and if Abigail has eaten 3/8 of a pound of that 6/8 pound of candy, then there will be 3/8 remaining (6/8 - 3/8 = 3/8).

To find out how much candy Abigail has eaten, we subtract the amount of candy she has left (3/8 of a pound) from the original amount she bought (3/4 of a pound). The calculation shows that Abigail has eaten 3/8 of a pound of candy.

The student is asking how much candy Abigail has eaten if she originally bought 3/4 of a pound and now has 3/8 of a pound left. To calculate the amount of candy eaten, we subtract the amount left from the original amount. Since we are working with fractions, we ensure the denominators are the same before subtracting.

The steps to solve the problem are as follows:

Original amount of candy: 3/4 pound

Amount left: 3/8 pound

Calculate how much has been eaten: (3/4) - (3/8)

Convert the first fraction to have a denominator of 8: (6/8) - (3/8)

Subtract the second fraction from the first: (6/8) - (3/8) = 3/8

Abigail has eaten 3/8 of a pound of candy.

Answer:

40,44,48,52,56,60,64,68...

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

15 fish / 5 days = 3 fish per day

Answer:

3

Step-by-step explanation:

15 fish / 5 days = 3 fish per day

Answer:for every five red beeds their are 5 black beeds

Step-by-step explanation:

To maintain the relationship of black beads to red beads, we need to know the ratio of black beads to red beads in the existing bracelet or the desired ratio. If the ratio is 1:1, for example, then you would need to use an equal number of black and red beads.

However, based on the information provided, it's not clear what the current or desired ratio is. If Jamie wants to maintain a specific ratio, you need to know that ratio.

For example, if the ratio is 2:1 (2 black beads for every 1 red bead), and you want to use 5 red beads, you would need 5×2=10 black beads to maintain the 2:1 ratio.

Without more information on the desired or existing ratio, it's not possible to determine whether using 5 red beads alone would maintain the relationship of black beads to red beads.

complete step by step

To maintain the relationship of black beads to red beads in a bracelet, we need to understand the existing ratio and then apply it to the new situation.

Let's say the current ratio of black beads to red beads in Jamie's bracelet is 3:2. This means that for every 3 black beads, there are 2 red beads.

Now, Jamie wants to make a bracelet with 5 red beads. To maintain the same ratio, we need to determine the corresponding number of black beads.

The ratio of black beads to red beads is 3:2, which simplifies3x:2x for some positive value of x.

Since Jamie wants 5 red beads, we set up the equation: 2x-5

Now, solve for x:

x- 5/2

Now that we know the value of  x, we can find the number of black beads:

Number of black beads - 3x-3 x (5/2) - (15/2) - 7.5

However, since the number of beads must be a whole number, we need to adjust. In this case, Jamie cannot make a bracelet with exactly 5 red beads while maintaining the ratio of 3:2. She would need to choose a different number of red beads that allows for a whole number of black beads according to the established ratio.

In conclusion, to maintain the relationship of black beads to red beads, Jamie cannot make a bracelet with exactly 5 red beads. The number of red beads chosen must allow for a whole number of black beads based on the given ratio.

Answer:

53

Step-by-step explanation:

Given: The sum of two digit number is 8

           Reversing the digit will get us number 18 less than the original.

Lets take x as tenth digit of our number and y as unit digit of our number.

As given sum of digit is 8

∴ [tex]x+y= 8[/tex]

∴ [tex]y= 8-x[/tex] -       equation 1

We also know that reversing the digit will get us number 18 less than the original.

∴ [tex]10y+x = 10x +y-18[/tex]

Now, lets put the value of y from equation 1

⇒ [tex]10(8-x) + x = 10x+ (8-x)- 18[/tex]

⇒ [tex]80-9x= 9x-10[/tex]

⇒ [tex]90= 18x[/tex]

∴ [tex]x= 5[/tex]

Next, substituting the value of x in equation 1

[tex]y= 8-x[/tex]

⇒ [tex]y= 8-5 = 3[/tex]

∴ [tex]y= 3[/tex]

∴ The original number is 53, sum of the digit is 8 and if we reverse the digit of the number, we get 35, which is 18 less than the original number.

Answer:

x = [tex]\frac{42}{5}[/tex]

Step-by-step explanation:

Given

19 - [tex]\frac{5x+6}{4}[/tex] = 7 ( subtract 19 from both sides )

- [tex]\frac{5x+6}{4}[/tex] = - 12

Multiply both sides by - 4 to clear the fraction and the negative signs

5x + 6 = 48 ( subtract 6 from both sides )

5x = 42 ( divide both sides by 5 )

x = [tex]\frac{42}{5}[/tex]

Speed in still water [tex]=[/tex] 9km

Speed of the current   [tex]=[/tex] 1 km

Answer:

Step-by-step explanation:

Speed of the current [tex]=[/tex] C

Speed of the still water [tex]=[/tex] S

Speed with the current [tex]=[/tex] [tex]([/tex] speed of the still water ₊ speed of the current [tex])[/tex]

                                      [tex]=[/tex] S ₊ C      

Speed with the current [tex]=[/tex] S ₊ C [tex]=[/tex] 10km

Speed against the current [tex]=[/tex] [tex]([/tex] speed of the still water ₋speed of the current [tex])[/tex]

                                              [tex]=[/tex] S ₋ C

Speed against the current [tex]=[/tex] S ₋ C [tex]=[/tex] 8km

Speed in still water [tex]=[/tex] Speed with the current ₊ Speed against the current[tex])[/tex]÷ 2

                                [tex]= ([/tex] 10 ₊ 8 [tex])[/tex] ÷ 2

                                [tex]=[/tex] [tex]([/tex] 18 [tex])[/tex] ÷ 2

Speed in still water [tex]=[/tex] 9km

Speed of the current [tex]= ([/tex] Speed with the current ₋ Speed against the current[tex])[/tex] ÷ 2

                                     [tex]= ([/tex] 10 ₋ 8 [tex])[/tex] ÷ 2

                                     [tex]=[/tex] [tex]([/tex] 2 [tex])[/tex] ÷ 2

Speed of the current   [tex]=[/tex] 1 km

Answer:

ASA rule.

Step-by-step explanation:

See the diagram with the problem.

Given that Δ ABC and Δ ABD are congruent i.e. Δ ABC ≅ Δ ABD.

Now, we have to select the rule by which we can say that Δ ABC and Δ ABD are congruent.

Given in the figure that between Δ ABC and Δ ABD,

(i) ∠ CAB = ∠ BAD

(ii) AB is the common side, and  

(iii) ∠ ABC = ∠ ABD

Therefore, by Angle-Side-Angle i.e. ASA rule we can say that  Δ ABC ≅ Δ ABD.

Hence, option 2 is correct. (Answer)

Answer: B the second choice

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

x^4=64

x^2= +- 8

x = +-sqrt2, x= +- i sqrt2

Answer:

A

Step-by-step explanation:

x^4-64=0

factor

(x^2+8)(x^2-8)=0

zero property

x^2+8=0, x^2-8=0

x^2=0-8-8,

x^2=-8,

x^2=0+8=8,

x^2=8,

----------------

sqrt(8) & sqrt(-8),

gives you 2*sqrt(2) and -2*sqrt(2),

also, the square root of a negative number contains the imaginary number, i. Because sqrt(-1)=i, don't forget this formula.

So sqrt(-8)=2i*sqrt(2) and -2i*sqrt(2).

Answer:

0.0322580645

Step-by-step explanation:

i feel like u meant 2418/78 but ok

Final answer:

To calculate 78 divided by 2418, you will get approximately 0.0322 when rounded to four significant figures.

Explanation:

The question asks for the result of the division 78 divided by 2418.

To find the answer, you need to perform the division either manually or by using a calculator. When you do so, you will find that the answer is a decimal. Taking the division to four significant figures, which is a common practice in mathematics to maintain precision without excessive digits, the calculation would look as follows:

78 ÷ 2418 = 0.0322

Thus, when dividing 78 by 2418, the result is approximately 0.0322 to four significant figures.

Answer:

The standard from of the expression is: [tex](x +1)^2 + (y-1)^2  = (2)^2[/tex]

Step-by-step explanation:

Here the given expression is :

[tex]x^2+2x+y^2-2y=2[/tex]

Now, the standard form of a circle is given as :

[tex](x-h)^2 + (y -k)^2  = r^2[/tex]

Here, (h,k)  = Coordinates of Center,   r = Radius

Also, use the algebraic identity:

[tex](a \pm b)^2 = a^2 + b^2 \pm 2ab\\[/tex]

Now, converting the given expression in the standard form, we get:

[tex]x^2+2x+y^2-2y=2[/tex]

Add 2 on both sides of the equation, we get:

[tex]x^2+2x+y^2-2y  +2=2  + 2\\\implies x^2+2x + 1 +  y^2-2y + 1  = 4\\\implies  (x^2+2x + 1 )+  (y^2-2y + 1)  = 4\\\implies (x +1)^2 + (y-1)^2  = (2)^2[/tex]

So, here the standard from of the expression is:

[tex](x +1)^2 + (y-1)^2  = (2)^2[/tex]

Center coordinates here are  (h,k)  = ( -1 ,1) and Radius  = 2 units

Answer:

θ = ±π/3 + 2kπ

θ = 0 + 2kπ

Step-by-step explanation:

2 sin² θ + 3 cos θ = 3

Use Pythagorean identity:

2 (1 − cos² θ) + 3 cos θ = 3

2 − 2 cos² θ + 3 cos θ = 3

0 = 2 cos² θ − 3 cos θ + 1

Factor:

0 = (2 cos θ − 1) (cos θ − 1)

cos θ = 1/2

θ = ±π/3 + 2kπ

cos θ = 1

θ = 0 + 2kπ

Answer:

The volume of cone z has the same base area as cylinder y but its height is 3 times the height of cylinder y have the same volume.

Step-by-step explanation:

The volume of a cylinder having base area 'A' and height 'H' is given by  V = AH, and the volume of a cone having the same base area as the cylinder i.e. A and height 3 times the height of the cylinder i.e. 3H is given by [tex]V' = \frac{1}{3} A(3H) = AH[/tex].

So, V = V'

Hence, the volume of cone z has the same base area as cylinder y but its height is 3 times the height of cylinder y have the same volume. (Answer)

Answer:

4.23 * 10³ = 4.23 * 1000 = 4,230

Step-by-step explanation:

We should know that;

10³ = 10 * 10 * 10 = 1000

∴ 4.23 * 10³ = 4.23 * 1000 = [tex]\frac{423}{100}*1000[/tex] = 4,230

Answer:

4.23 * 10³ = 4.23 * 1000 = 4,230

Step-by-step explanation:

Answer:

The number of green marbles are 36.

Step-by-step explanation:

Given:

Total number of marble bag contains is 42.

The number of green marbles is 6 more than 5 times the number of red marbles.

Let the number of red marbles be [tex]x[/tex].

So, the number of green marbles = [tex]6+5x[/tex]

Now, to get the number of green marbles.

According to question:

[tex]x+(6+5x)=42[/tex]

[tex]6x+6=42[/tex]

Subtracting 6 in both sides :

[tex]6x+6-6=42-6[/tex]

[tex]6x=36[/tex]

Now, by dividing 6 on both sides:

[tex]6x\div 6=36\div 6[/tex]

[tex]x=6[/tex]

The number of red marbles are 6.

And, the number of green marbles are [tex]6+5x[/tex]

                                                                 = [tex]6+5\times 6[/tex]

                                                                 =[tex]6+30[/tex]

                                                                 = [tex]36[/tex]

Therefore, the number of green marbles are 36.

Answer:

NO

YES

NO

NO

Step-by-step explanation:

For a number to be the solution of the equation, the number should satisfy it.

To check if t satisfies, plug the number and compare LHS and RHS.

1) 3z + 4 = 15

Substituting z = -5, we get 3(-5) + 4 = -15 + 4 = -11 [tex]$ \ne $[/tex] 15.

Therefore, -5 is not the solution of the equation.

2) 8 - [tex]$ \frac{x}{2} $[/tex] = 0

Substituting x = 16, we get 8 - [tex]$ \frac{16}{2} = 8$[/tex]

⇒ 8 - 8 = 0

Therefore, 16 is a solution of the equation.

3) 4(p + 5) = 60

Substitute p = 12. 4(12 + 5) = 4(17) [tex]$ \ne $[/tex] 60.

Not a solution.

4) 8 - k = -48

If k = -40, then 8 - (-40) = 48

On the RHS we have -48. Not equal. So, it is not a solution.

[tex]\bf (\stackrel{x_1}{5}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{-3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{-2}-\underset{x_1}{5}}}\implies \cfrac{-6}{-7}\implies \cfrac{6}{7}[/tex]

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{\cfrac{6}{7}}(x-\stackrel{x_1}{5}) \implies y-3=\cfrac{6}{7}x-\cfrac{30}{7} \\\\\\ y=\cfrac{6}{7}x-\cfrac{30}{7}+3\implies y = \cfrac{6}{7}x+\cfrac{-30+21}{7}\implies y=\cfrac{6}{7}x-\cfrac{9}{7}[/tex]

Answer:

-6/7? I think I'm right but make sure to comment me to let me know!

Step-by-step explanation:

Okay so the equation for slope intercept form is y2-y1/x2-x1. So we can substitute -3-3=-6 and -2-5=-7 So I think you get -6/7

-viridiancat4, an 8th grader

Answer:

(x+4y)(x-4y)

Step-by-step explanation:

Since

[tex]\large a^2-b^2=(a+b)(a-b)[/tex]

we can see that

[tex]\large x^2-16y^2=(x+4y)(x-4y)[/tex]

Answer:56

Step-by-step explanation:

difference between 36 and 18 is 18

difference between 96 and 72 is 24

so that means 18, 20, 22, 24

I HOPE THIS HELPS :)

Step-by-step explanation:

Do 25% of $55 which is $13.75

You have the right idea but you're supposed to then subtract $13.75 from the original

So:

55 - 13.75 = $41.25

Answer: The correct graph is the bottom left graph.

Step-by-step explanation:

Given function is f(x)=ceil(x+1)

To plot graph of f(x) in interval of(-3,3) :

ceil(x+1) is ceiling function

The output of ceil(x) is least integer greater than x

for example ceil(5.5)=6

For an interval of (-3,-2):

Take x=(-2.4)

x+1=(-1.4)

y=f(x)=ceil(x+1)=(-1)

Similarly,

For an interval of (-2,-1):

Take x=(-1.4)

x+1=(-0.4)

y=f(x)=ceil(x+1)=(0)

For an interval of (-1,0)

y=f(x)=1

For an interval of (0,1)

y=f(x)=2

For an interval of (1,2)

y=f(x)=3

For an interval of (2,3)

y=f(x)=4

Thus, The correct graph is the bottom left graph.

Answer:

The bottom left graph

Step-by-step explanation:

I took this quiz

Step-by-step explanation:

x² + 2ixy − y²

x² + 2ixy + i²y²

(x + iy)²

Answer:

(X+yi )(X+yi)

Step-by-step explanation:

Answer:

The distance, D for the given expression is 70 miles

Step-by-step explanation:

Given as :

D = r t

r = 35 mi/ h

t = 2 h

Now, According to question

Distance = speed × Time

Where speed = r

Time = t

Distance = D

Now, from question

D = 35 miles per hour × 2 hours

So, D = 70 miles

Hence The distance, D for the given expression is 70 miles  . answer

Final answer:

The exact amount of the check is $5.

Explanation:

To solve this problem, we can set up an equation based on the given information. Let's assume that the amount of the check is x dollars. According to the problem, the man received the amount in cents instead of dollars, so he actually received x dollars and x cents. He then spent a nickel, which means he had x dollars and (x-5) cents left. It's stated that he had exactly twice the amount of the check after spending the nickel, so we can write the equation:

x + (x-5) = 2x

Simplifying the equation, we get:

2x - x = 5

x = 5

Therefore, the exact amount of the check is $5.

Step-by-step explanation:

x+6=0

x=(-6)

so if x =(-6) it will be undefined.

Answer:

x = −3

or

x = 6

Any number multiplied by 0 is 0. This means that either x+3 or x−6 can be 0.

(x+3)(x−6) to be 0. if x+3=0, then x=−3 if x−6=0,

then x=6 hence, x can either be −3

or 6.x= −3 or x=6

The total number of tickets sold over these two days is 9,640.

Let's complete the table for Saturday:

For Saturday:

Adult Tickets: [tex]\(2 \times \text{Number of Adult Tickets on Friday}\)[/tex]

Children's Tickets: [tex]\(3 \times \text{Number of Children's Tickets on Friday}\)[/tex]

Using the information from Friday's sales:

Adult Tickets on Saturday: [tex]\(2 \times 976 = 1952\)[/tex]

Children's Tickets on Saturday: [tex]\(3 \times 1678 = 5034\)[/tex]

Now, we can complete the table:

[tex]\begin{array}{ccc}\text { Day } & \text { Adult Tickets } & \text { Children's Tickets } \\\text { Friday } & 976 & 1,678 \\\text { Saturday } & 1,952 & 5,034\end{array}[/tex]

To find the total number of tickets sold over these two days, add the tickets for Friday and Saturday:

Total Tickets Sold = Adult Tickets on Friday + Children's Tickets on Friday + Adult Tickets on Saturday + Children's Tickets on Saturday

[tex]\[ \text{Total Tickets Sold} = 976 + 1,678 + 1,952 + 5,034 \][/tex]

[tex]\[ \text{Total Tickets Sold} = 9,640 \][/tex]

Answer:

12.5

Step-by-step explanation:

5/2*5=12.5

Answer:

Your answer is 12.5 meters long

Step-by-step explanation:

so you would want to see how long each 1/5 is so if 2/5 is 5 then 1/5 would be half of that so 2.5 then times that by 5 to get your answer which is 12.5.

Answer:(i)  84 cm.

(ii)  5635π cm^2

Step-by-step explanation:

(i)

The volume of the cone = 1/3 π r^2 h

= 1/3 π 35^2 h.

The volume of the hemisphere = 2/3 π 35^3.

As the volume of the cone is 1 1/5 ( = 6/5) times the volume of the hemisphere:

1/3 π 35^2 h =  2/3 π 35^3 * 6/5

h =  2/3 π 35^3 * 6/5 /   1/3 π 35^2

h =  84 cm (answer).

(ii)  Surface area of the hemisphere = 2 π * 35^2 =   2450π cm^2.

Surface area of the cone = π r l  where l = slant height.

l = √(35^2 + 84^2) =  91 cm.

So the surface area of the cone =  35*91 π = 3185π.

So the  total surface area of the solid is  3185π + 2450π

= 5635π cm^2.

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