Make m the subject of the formula L = m + n

[tex]f(a) = -4a +6a^3 - 15 -4a^2 \\\\\text{By the remainder theorem,}\\\\f\left(\dfrac 53 \right) = -4\left(\dfrac 53 \right) + 6 \left( \dfrac 53 \right)^3 - 15 - 4 \left(\dfrac 53 \right)^2 = -5\\\\\\ \text{Hence}~-5~ \text{is the remainder when f(a) is divided by}~ 3a -5[/tex]

[tex]\\ \sf\longmapsto 3a-5=0[/tex]

[tex]\\ \sf\longmapsto 3a=5[/tex]

[tex]\\ \sf\longmapsto a=\dfrac{5}{3}[/tex]

Using remainder theorem

[tex]\\ \sf\longmapsto f(a)=-4a+6a^2-4a^2-15[/tex]

[tex]\\ \sf\longmapsto f\left(\dfrac{5}{3}\right)[/tex]

[tex]\\ \sf\longmapsto -4(5/3)+2a^2-15[/tex]

[tex]\\ \sf\longmapsto -20/3+2(5/3)^2-15[/tex]

[tex]\\ \sf\longmapsto -20/3+2(25/9)-15[/tex]

[tex]\\ \sf\longmapsto -20/3+50/9-15[/tex]

[tex]\\ \sf\longmapsto (-60+50)/9-15[/tex]

[tex]\\ \sf\longmapsto -10/9-15[/tex]

[tex]\\ \sf\longmapsto -10-135/9[/tex]

[tex]\\ \sf\longmapsto -145/9[/tex]

[tex]\\ \sf\longmapsto 16\dfrac{-5}{9}[/tex]

Remainder=-5

Answer:

m < -9

Step-by-step explanation:

m+15<6

Subtract 15 from each side

m+15-15<6-15

m < -9

Answer:

415

____

727

Step-by-step explanation:

Answer:

69

Step-by-step explanation:

A) This event is a union. If a card is of the suit of clubs or a face card or both, then it belongs to the set of "cards with clubs or a face".

For the probability in question, we use the inclusion/exclusion principle:

P(club or face) = P(club) + P(face) - P(club and face)

That is, we add the probabilities of drawing a club and of drawing a face card, and subtract the probability of both conditions being met because, in a certain sense, we've double-counted the event of the card being both of clubs and a face. The sets "club" and "face" are not disjoint; there is overlap between them.

Then we have

P(club) = 13/52

P(face) = 12/52

P(club and face) = 3/52

so that

P(club or face) = 13/52 + 12/52 - 3/52 = 22/52 = 11/26

B) This event is an intersection. If a card is of the suit of clubs and a face card, then it belongs to both the set of clubs and the set of face cards.

We already found the probability of the intersection above:

P(club and face) = 3/52

C) If a given card is not a club and not a face card, this is the same as saying the card is neither a club nor a face card. In other words,

P(not club and not face) = P(not(club or face))

and this probability is complementary to the probability that a card is either a club or face, which is to say

P(not(club or face)) = 1 - P(club or face)

Using the result from part (A), we have

P(not club and not face) = 1 - 11/26 = (26 - 11)/26 = 15/26

Answer:   -___-

Step-by-step explanation:

Given : The ratio of two numbers is 4:9. When 5 is subtracted from each of them the ratio is 3:8. Find the numbers

Need to Find : The numbers

Solution : According to the question here we are given that the ratio is 4:9 and 5 is subtracted from each of these ratios after which the ratio becomes 3:8. Let's follow the steps to get the answer.

Let the constant multiple be x

Now, according to the question:

The numbers are 4x and 9x

As we get to know that each of them is subtracted by 5. So,

1st number = 4x - 5

2nd number = 9x - 5

New ratio becomes 3:8

⇢ (4x - 5)/(9x - 5) = 3/8

⇢ 8(4x - 5) = 3(9x - 5)

⇢ 32x - 40 = 27x - 15

⇢ 32x - 27x = - 15 + 40

⇢ 5x = 25

⇢ x = 25/5

⇢ x = 5

Now, getting the numbers. Instead of x we need to put 5 and multiply with the constant.

1st number = 4x = 4(5) = 20

2nd number = 9x = 9(5) = 45

∴ The numbers are 20 and 45 respectively.

Answer:

y = 7x + 3

Step-by-step explanation:

A slope of 1/7 will give you a line that is not very steep.  Therefore C and D is not the answer.

Now look at  A and B.  Check point (1, 10) into equations A and B  because this point is on the given graph.

y = 7x + 3                                    y = 7x + 10

y = 7(1) + 3                                   y = 7(1) + 10

y = 7 + 3                                      y = 7 + 10

y = 10      (1, 10)                             y = 17            (1, 17)

Answer:

$244.25

Step-by-step explanation:

First, the question is asking what the change in her savings account balance is each month. So, you know that you are looking for the amount that is lost each month. When it says that at the end of the year, she has payed $2,931 , what is implied is that she has spent that much over 12 months. So all that is needed to do is divide her balance change over the year by 12 to find the monthly balance change.

Answer:

I think it is 43167 but am not really sure

Answer:

HOW DID YOU DO THAT? BECAUSE I CANT DO THAT 3 PIC

Answer:

Step-by-step explanation:

x+y=10-----(1)

xy=5------(2)

dividing (1) by(2)... we get!

x/y+ y/x=10/5

=>2

we have :[tex]x^{2} +y^{2} = x^{2} +y^{2} + 2xy -2xy = (x+y)^{2} -2xy = 5^{2} -2.10 =25-20=5[/tex]

ok done. Thank to me :>

Answer:

A

Step-by-step explanation:

The graph representing a proportional relationship is a straight line graph passing through the origin.

This is shown in graph A

Answer:

The nth term = n^2 - 2n - 3.

Step-by-step explanation:

Here, we will be finding the nth term of a quadratic number sequence. A quadratic number sequence has nth term = an² + bn + c

Example 1

Write down the nth term of this quadratic number sequence.

-3, 8, 23, 42, 65...

Step 1: Confirm the sequence is quadratic. This is done by finding the second difference.

Sequence = -3, 8, 23, 42, 65

1st difference = 11,15,19,23

2nd difference = 4,4,4,4

Step 2: If you divide the second difference by 2, you will get the value of a.

4 ÷ 2 = 2

So the first term of the nth term is 2n²

Step 3: Next, substitute the number 1 to 5 into 2n².

n = 1,2,3,4,5

2n² = 2,8,18,32,50

Step 4: Now, take these values (2n²) from the numbers in the original number sequence and work out the nth term of these numbers that form a linear sequence.

n = 1,2,3,4,5

2n² = 2,8,18,32,50

Differences = -5,0,5,10,15

Now the nth term of these differences (-5,0,5,10,15) is 5n -10.

So b = 5 and c = -10.

Step 5: Write down your final answer in the form an² + bn + c.

2n² + 5n -10

Example 2

Write down the nth term of this quadratic number sequence.

9, 28, 57, 96, 145...

Step 1: Confirm if the sequence is quadratic. This is done by finding the second difference.

Sequence = 9, 28, 57, 96, 145...

1st differences = 19,29,39,49

2nd differences = 10,10,10

Step 2: If you divide the second difference by 2, you will get the value of a.

10 ÷ 2 = 5

So the first term of the nth term is 5n²

Step 3: Next, substitute the number 1 to 5 into 5n².

n = 1,2,3,4,5

5n² = 5,20,45,80,125

Step 4: Now, take these values (5n²) from the numbers in the original number sequence and work out the nth term of these numbers that form a linear sequence.

n = 1,2,3,4,5

5n² = 5,20,45,80,125

Differences = 4,8,12,16,20

Now the nth term of these differences (4,8,12,16,20) is 4n. So b = 4 and c = 0.

Step 5: Write down your final answer in the form an² + bn + c.

5n² + 4n

Answer:

Seems correct to me. I color coded the various terms.

Step-by-step explanation:

[13x³ came by adding 9x³ and 4x³]

Answer:

y = 2/3x-6

Step-by-step explanation:

up 2, right 3

Answer:

Step-by-step explanation:

Statements                     | Reasons

C is the midpoint of AB | Given

AC = 2x + 1                      | Given

CB = 3x - 4                      | Given

AC = CB                          | Definition of midpoint

2x + 1 = 3x - 4                  | Substitution property

3x - 2x = 1 + 4                  | Addition property of equality

x = 5                                 | Proved

The line is as below:

A-----------------C----------------B

     2x + 1               3x - 4

Answer:

15-22=a/12

-7=a/12

12(-7)=a

-84=a

Step-by-step explanation:

Answer:

x = 42/5 is the answer to this question

Option B is correct, the solution to the equation is x = 42/5.

The given equation is 1/3(x + 3/5) = 3.

We have to solve for x:

x is the variable in the equation.

Multiply both sides by 3 to get rid of the fraction:

1/3(x + 3/5) × 3 = 3 × 3

(x + 3/5) = 9

Subtract 3/5 from both sides to isolate the x term:

(x + 3/5) - 3/5 = 9 - 3/5

x = 9 - 3/5

Now, to combine the terms on the right side:

x = 45/5 - 3/5

x = 42/5

Therefore, the solution to the equation is x = 42/5.

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ6

Answer: 1,000.77

Step-by-step explanation:

After 1 year: 980 + 0.3% = 982.94

After 2 years: 982.94 + 0.3% = 985.89

After 3 years: 985.89 + 0.3% = 988.85

After 4 years: 988.85 + 0.3% = 991.82

After 5 years: 991.82 + 0.3% = 994.80

After 6 years: 994.80 + 0.3% = 997.78

After 7 years: 997.78 + 0.3% = 1,000.77

Brainliest?

Answer:

x less than or equal to 16.6

Step-by-step explanation:

50 divided by 3 is 16.6

since Jill wants 50 square feet as the maximum area x can be less than 16.6.

Answer:

At 0 hours, there are 100 grams of the substance remaining.

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

I just did it on ed

Answer:

50 per minute

Step-by-step explanation:

Answer:

The answer is 50 words per minute

Step-by-step explanation:

16x50=800

800/16=50

HOPE THIS HELPS!!

Answer:

I think it 2 solution to the problem you can add or multiple

Answer:

y =7x + 17

Step-by-step explanation:

7x-y=8

y = 7x - 8......convert to slope intercept form

m = 7

parallel lines have the same slope

put in point slope form using the points of the equation of the line that you want to find

y - 3 = 7(x+2)

y -3 = 7x + 14.........distribute

y = 7x +14 + 3.........add 3 to both sides

y = 7x +17................simplify

Answer: 89 cm^2/minute

Step-by-step explanation:

Initial Area:                11 x 5 = 55 cm^2

Area after 1 minute:  18 x 8 = 144 cm^2

The area of the triangle is increasing by

Answer:

1/2 times 4 4/2 2*2/3 4/3

Answer:

p(7) = 57

Step-by-step explanation:

Because this is a function, all you have to do is input 7 for x like so:

p(x)=x^2+x+1 --------------->     p(7)=7^2+7+1

                                            so 49 + 8

                                                = 57

Answer:400

Step-by-step explanation:

10%= 200

x2=400

Answer:

1 1/3

Step-by-step explanation:

it's bc the number is closer to one and not in the middle. have a great day

Answer:

The arrow is pointing to 1 1/3. From 1 to 2, there are 3 marks. These three marks are each 1/3. So, from 1 the next mark will be 1 1/3.

:)