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Given:

The limit problem is:

[tex]lim_{x\to -5}\dfrac{\dfrac{1}{5}+\dfrac{1}{x}}{10+2x}[/tex]

To find:

The value of the given limit problem.

Solution:

We have,

[tex]lim_{x\to -5}\dfrac{\dfrac{1}{5}+\dfrac{1}{x}}{10+2x}[/tex]

It can be written as:

[tex]=lim_{x\to -5}\dfrac{\dfrac{x+5}{5x}}{2(5+x)}[/tex]

[tex]=lim_{x\to -5}\dfrac{x+5}{5x}\times \dfrac{1}{2(5+x)}[/tex]

[tex]=lim_{x\to -5}\dfrac{1}{5x\times 2}[/tex]

[tex]=lim_{x\to -5}\dfrac{1}{10x}[/tex]

Applying limit, we get

[tex]lim_{x\to -5}\dfrac{1}{10x}=\dfrac{1}{10(-5)}[/tex]

[tex]lim_{x\to -5}\dfrac{1}{10x}=\dfrac{1}{-50}[/tex]

Therefore, the value of given limit problem is [tex]-\dfrac{1}{50}[/tex].

Answer:

66

Step-by-step explanation:

Use the PEMDAS order. Multiplication comes before addition so it simplifies to 6(8)+(6)3

=48+18

=66

1. Divide 240 by 10 = 24

2. Multiply 24 • 8 = 192

Michele will need 192 oz. of mayonnaise.

Answer:

192 oz

Step-by-step explanation:

Hi there!

1) Create a proportion

[tex]\frac{8 (oz)}{10(servings)} =\frac{x(mayo)}{240(servings)} \\\frac{8}{10} =\frac{x}{240}[/tex]

2) Solve for x

[tex]\frac{8}{10} =\frac{x}{240}[/tex]

Multiply both sides by 240

[tex]\frac{8}{10} *240=x\\192=x[/tex]

Therefore, Michele would need 192 oz of mayonnaise.

I hope this helps!

Answer:

1/3 fraction of whole paint is used by mark

Step-by-step explanation:

Mark used  1/2 out of 3/2 cans.

[tex]\frac{1}{2}[/tex] ÷ [tex]\frac{3}{2} = \frac{1}{2}*\frac{2}{3}=\frac{1}{3}[/tex]

find the DB =[tex]\displaystyle\bf \sqrt{17^2-8^2} =15[/tex]  ; now find AD=AB-DB=21-15=6  .Then                AC=[tex]\displaystyle\bf \sqrt{AD^2+CD^2} =\sqrt{6^2+8^2} =10[/tex]  

Answer:

C

Step-by-step explanation:

Using Pythagoras' identity in both right triangles

To find BD

BD² + CD² = BC²

BD² + 8² = 17²

BD² + 64 = 289 ( subtract 64 from both sides )

BD² = 225 ( take the square root of both sides )

BD = [tex]\sqrt{225}[/tex] = 15

Then

AD = AB - BD = 21 - 15 = 6

To find AC

AC² = AD² + CD²

AC² = 6² + 8² = 36 + 64 = 100 ( take the square root of both sides )

AC = [tex]\sqrt{100}[/tex] = 10 → C

Answer:

2 sheep

Step-by-step explanation:

If you have 36 sheep  and you sell:

first day    1/2 of them  you sold               18

second day  1/3  them you sold                12

On thhe third day  1/9  them you sold       4

Therefore you sold 18 + 12  + 4  = 34

And you still have  2 sheep

Answer:

3m -2

Step-by-step explanation:

(10m – 6) – (7m – 4)

Distribute the minus sign

(10m – 6) – 7m + 4

Combine like terms

3m -2

Answer:

49

Step-by-step explanation:

The probability of choosing a red marble is equal to the number of red marbles over the number of total marbles there are.

Therefore, let the number of red marbles be [tex]x[/tex].

We have the following equation:

[tex]\frac{x}{84}=\frac{7}{12}[/tex]

Cross-multiplying, we get:

[tex]12x=7\cdot 84,\\x=\frac{84\cdot 7}{12},\\x=\boxed{49}[/tex]

Therefore, there are 49 red marbles in the bag.

Answer:

no solutions

Step-by-step explanation:

Hi there!

We're given this system of equations:

x+y=3

4y=-4x-4

and we need to solve it (find the point where the lines intersect, as these are linear equations)

let's solve this system by substitution, where we will set one variable equal to an expression containing the other variable, substitute that expression to solve for the variable the expression contains, and then use the value of the solved variable to find the value of the first variable

we'll use the second equation (4y=-4x-4), as there is already only one variable on one side of the equation. Every number is multiplied by 4, so we'll divide both sides by 4

y=-x-1

now we have y set as an expression containing x

substitute -x-1 as y in x+y=3 to solve for x

x+-x-1=3

combine like terms

-1=3

This statement is untrue, meaning that the lines x+y=3 and 4y=-4x-4 won't intersect.

Therefore the answer is no solutions

Hope this helps! :)

The graph below shows the two equations graphed; they are parallel, which means they will never intersect. If they don't intersect, there's no common solution

Answer:

The answer is 48in

Step-by-step explanation:

The sum of the 15th square number and the 5th cube number is 350.

The 15th square number will be:

15² = 15 × 15

= 225

The 5th cube number will be:

5³ = 5 × 5 × 5

= 125

The sum of the numbers will be:

225 + 125

= 350

Therefore, we get that, the sum of the 15th square number and the 5th cube number is 350.

Learn more about sum here:

https://brainly.com/question/17695139

#SPJ1

Answer: (a) P = 6W + 2

(b) L = 2W + 1

(c) Width = 13cm

Length = 27cm

Step-by-step explanation:

The formula for perimeter of a rectangle is 2(length + width). Since the length is 1 cm more than twice its width, then the length will be:

L = (2 × W) + 1

(b) L = 2W + 1

Therefore, P = 2(L + W)

P = 2( 2W + 1) + 2W

P = 4W + 2 + 2W

(a) P = 6W + 2

Since perimeter is given as 80cm. Therefore,

P = 6W + 2

6W + 2 = 80

6W = 80 - 2

6W = 78

W = 78/6

W = 13

Width is 13cm

Length = 2W + 1

Length = 2(13) + 1

Length = 27cm

The width of the rectangle is 13cm and the length is 27cm.

A rectangle is a quadrilateral. Opposite sides are equal. The four angles in a rectangle is equal to 90 degrees.

The formula for determining the perimeter of a rectangle = 2x (length + width)

P = 2(L + W)

80 = 2(1 + 2w + w)

80 = 2(1 + 3w)

40 = 1 + 3w

40 - 1 = 3w

39 = 3w

w = 13cm

Length = 1 + 2(13) = 27cm

To learn more about rectangles, please check: https://brainly.com/question/16595449

Answer:

5.28

Step-by-step explanation:

we use the formula

H²=B²+P²

and we will get the answer

branliest if it is helpful

Answer:

Angle BXY

using pythogoras theory which is

hyp*2= opp*2 +adj*2

hypothenus being the longest part of the angle BX=?

Step-by-step explanation:

hyp= 4.2*2+ 3.2*2

hyp*2 =17.64 + 10.24

hyp*2 = 27.88

hyp =√27.88

hyp=5.28...Ans

note *2...square

Answer:

B. 16/3

Step-by-step explanation:

f(2) = 1/3 · 4²

f(2) = 1/3 · 16

f(2) = 16/3

Answer: 68

Step-by-step explanation: Complementary angles are angles that add up to 90. So, you need to do 90-22=68.

Answer:

Step-by-step explanation:

Solve using ratios:

Find x:

Answer:

check footprints and then check finger print the finger print pour powder on it and Trace

Step-by-step explanation:

hope it helps

Answer:

x=-3 and y=-2

Step-by-step explanation:

let the numbers be x and y

x+y=-5

x-y=-1

therefore x=-5-y

-5-y-y=-1

-2y=-1+5

-2y=4

y=-2

×=-5-(-2)

x=-5+2

x=-3

Answer: -2 and -3

Step-by-step explanation:

x + y = -5

x - y = -1 -> x = y - 1

(y - 1) + y = -5

y - 1 + y = -5

2y = 1 - 5

2y = -4

y = -2

x = y - 1 = -2 - 1 = -3

Answer:

x = 24

Step-by-step explanation:

mathematically, in a cyclic quadrilateral, two opposite angles are supplementary

what this mean is that they add up to be 180

From what we have in the question, the two angles are supplementary and that means they add up to equal 180 degrees

thus, we have it that;

(4x + 9) + (3x + 3) = 180

4x + 3x + 9 + 3 = 180

7x + 12 = 180

7x = 180-12

7x = 168

x = 168/7

x = 24

Answer:

(- 1, - 1 )

Step-by-step explanation:

Given the 2 equations

x = 4y + 3 → (1)

2x + y = - 3 → (2)

Substitute x = 4y + 3 into (2)

2(4y + 3) + y = - 3 ← distribute parenthesis and simplify left side

8y + 6 + y = - 3

9y + 6 = - 3 ( subtract 6 from both sides )

9y = - 9 ( divide both sides by 9 )

y = - 1

Substitute y = - 1 into (1) for corresponding value of x

x = 4(- 1) + 3 = - 4 + 3 = - 1

solution is (- 1, - 1 )

Answer:

because internal staggal angles are equal

Step-by-step explanation:

The first reason is wrong.

Angle EGH and DEG are internal staggal angles:

the two angles are on both sides of the cut line EG, and the two angles are between the two divided lines.

{the definition of internal staggal angle}

Answer:

A.

Step-by-step explanation:

4y = 12x + 16

3x = y - 4

=>

y = 3x + 4

using that in the first equation

4(3x+4) = 12x + 16

12x + 16 = 12x + 16

=> both lines/equations are identical, so they have infinitely many solutions.

Answer:

y = 5x + 19

Step-by-step explanation:

y = 5x + b

4 = 5(-3) + b

4 = -15 + b

19 = b

Answer:

28

Step-by-step explanation:

Answer:

20 Lines

Step-by-step explanation:

According to the Question,

Now,  the total pairs of points which can be formed is 9

And, the line passing through 2 such points 9c2 = 9! / (2! x 7!) = 9x4 ⇒ 36

Here, We have overcounted all of the lines which pass through three points.

And, each line that passes through three points will have been counted 3c2 = 3! / 2! ⇒ 3 times

Now, the sides of the square consist of 3 points. We have counted each side thrice, so 4*2 are repeated.