Newberg City Cafe recently introduced a new flavor of coffee. They served 23 grande cups and 51 jumbo cups of the new coffee today, which equaled a total of 36,846 grams. The day before, 58 grande cups and 68 jumbo cups were served,which used a total of 59,460 grams. How much coffee is required to make each size?

Option C

The equation that represents this situation is -3x = 21

The second number is -7

Solution:

The first number is -3

The product of two numbers is 21

Let the second number be "x"

The equation that represents this situation is:

Product of first and second number = 21

[tex]-3 \times x = 21\\\\-3x = 21[/tex]

Thus the equation is found

Solve the equation

-3x = 21

Divide both sides by -3

[tex]x = \frac{21}{-3}\\\\x = -7[/tex]

Thus the second number is -7

Answer:

C.

The equation that represents this situation is -3x = 21. The second number is -7.

Step-by-step explanation:

I just did it and got it right on edmentum/plato

hope this helps good luck

Answer:

4 pounds of strawberries and 5 pounds of apples are bought.

Step-by-step explanation:

Given:

Total number of pounds of fruit = 9 pounds

Total money spent = $16.35

Cost of 1 pound of strawberry = $1.60

Cost of 1 pound of apple = $1.99

Let 'x' pounds of strawberries and 'y' pounds of apples are bought.

So, as per question:

The sum of the pounds is 9. So,

[tex]x+y=9\\\\y=9-x----1[/tex]

Now, total sum of the fruits is equal to the sum of 'x' pounds of strawberries and 'y' pounds of apples. So,

[tex]1.60x+1.99y=16.35----2[/tex]

Now, plug in the 'y' value from equation (1) in to equation (2). This gives,

[tex]1.60x+1.99(9-x)=16.35\\\\1.60x+17.91-1.99x=16.35\\\\Combining\ like\ terms, we get:\\\\1.60x-1.99x=16.35-17.91\\\\-0.39x=-1.56\\\\x=\frac{-1.56}{-0.39}=4\ pounds[/tex]

Now, from equation 1, we have:

[tex]y=9-4=5\ pounds[/tex]

Therefore, 4 pounds of strawberries and 5 pounds of apples are bought.

Answer:

615 children tickets

195 adults tickets

Step-by-step explanation:

Let the number of children’s tickets be c and the number of adult tickets be a.

Children’s ticket is $3 and adult’s is $5 for a total of $2,820. This means:

3c + 5a = 2,280

This is the first equation.

The number of children’s tickets sold is 30 more than 3 times that of the adults. This means

c = 3a + 30.

This is equation ii. We now substitute ii into I to yield:

3(3a+ 30) + 5a = 2,820

9a + 90 + 5a = 2,820

14a + 90 = 2,820

14a = 2820 - 90

14a = 2730

a = 2730/14 = 195 tickets

c = 3a + 30

c = 3(195) + 30 = 615

Final answer:

By setting up a system of equations based on the total sales and the relationship between the number of adult and children's tickets sold, we can solve to find that Galen sold 130 adult tickets and 420 children's tickets for the church's carnival which is 195.

Explanation:

The question involves finding the number of children's and adult tickets sold by Galen for a church's carnival, given the total sale amount and the price of each ticket type. To solve this, we can set up a system of equations based on the information provided:

Let x be the number of adult tickets sold and y be the number of children's tickets sold. The problem statements can be translated into two equations:

Substituting the second equation into the first gives us:

3(3x + 30) + 5x = 2820

Solving for x, we find that Galen sold 130 adult tickets. Using the relationship between x and y, we then find that 420 children's tickets were sold.

14x= 2730

x=195.

Answer:

  see below

Step-by-step explanation:

The formula is the same whether the change in a compounding period is positive or negative. Here, it is negative.

  A = P(1 +r/n)^(nt)

for P = 100, r = -0.08, n = 6. So, you have ...

  A = 100(1 -0.08/6)^(6t)

Answer: option d is the correct answer

Step-by-step explanation:

Initial amount is $100. This means that the principal is

P = 100

It was compounded 6 times in a year. So

n = 6

The rate at which the principal was compounded is 8%. So

r = 8/100 = 0.08

The number of years is t

The formula for compound interest is

A = P(1+r/n)^nt

A = total amount in the account at the end of t years.

Since the amount is reducing,

A = P(1-r/n)^nt

Therefore

A = 100 (1 - 0.08/6)^6t

Function Z has a greater slope and a higher y-intercept compared to Function W, making Function Z steeper and intercepting the y-axis at a higher point. Here options A and B are correct.

The two lines in the graph represent linear functions, which means they can be expressed in the following form:

y = mx + b

where:

m is the slope of the line, which tells you how steep the line is and in which direction it is slanted.

b is the y-intercept, which is the point where the line crosses the y-axis.

x is the independent variable, and y is the dependent variable.

The steeper a line is, the greater the absolute value of its slope. A positive slope means the line slants upwards from left to right, while a negative slope means it slants downwards from left to right.

In the image, you can see the equations for the two lines are:

Function W: y = 2x - 5

Function Z: y = 3x - 2

By looking at the equations, we can see that:

The slope of function W is 2.

The slope of function Z is 3.

Since 3 is greater than 2, we can say that the slope of function Z is greater than the slope of function W. This means that function Z is steeper than function W.

The y-intercepts of the lines are also different:

The y-intercept of function W is -5.

The y-intercept of function Z is -2.

Since -2 is greater than -5, we can say that the y-intercept of function Z is greater than the y-intercept of function W.

Therefore, the following statements comparing the functions are true:

The slope of Function W is less than the slope of Function Z

The y-intercept of Function W is less than the y-intercept of Function Z. Here options A and B are correct.

Function W has a slope less than Function Z, and its y-intercept is also less than that of Function Z.(options a and d)

To compare the functions W and Z, let's analyze their slopes and y-intercepts:

Function W: [tex]\(y = 0.5x - 1\)[/tex]

Function Z: Given table of values

a. The slope of Function W is [tex]\(0.5\).[/tex]

b. The slope of Function Z can be calculated using the given points. We choose two points: [tex]\((-2, -2.5)\)[/tex] and [tex]\((4, -1)\)[/tex]. Using the slope formula:

[tex]\[m = \frac{{y_2 - y_1}}{{x_2 - x_1}}\][/tex]

[tex]\[m = \frac{{-1 - (-2.5)}}{{4 - (-2)}}\][/tex]

[tex]\[m = \frac{{1.5}}{{6}}\][/tex]

[tex]\[m = 0.25\][/tex]

c. The y-intercept of Function W is -1, while the y-intercept of Function Z is the y-value when x=0, which is -2.

d. The y-intercept of Function W is greater than the y-intercept of Function Z.

e. To find the y-value when x=-4 for Function W, substitute x=-4 into the equation of Function W:

[tex]\[y = 0.5(-4) - 1 = -3\][/tex]

For Function Z, there is no direct way to determine the y-value when x=-4 as we only have specific points provided, not a continuous equation.

f. The y-value when x=-4 for Function W is not greater than the y-value when x=-4 for Function Z.

Therefore, the correct statements are:

a. The slope of Function W is less than the slope of Function Z.

d. The y-intercept of Function W is less than the y-intercept of Function Z.

The question probable maybe:

Given in the attachment

Answer:

l = [tex]\frac{A-2\pi r}{\pi r}[/tex]

Step-by-step explanation:

Given

A = 2πr + πrl ( isolate the term in l by subtracting 2πr from both sides )

A - 2πr = πrl ( divide both sides by πr )

[tex]\frac{A-2\pi r}{\pi r}[/tex] = l

Answer: l = A/πr - 2

Step-by-step explanation:

The given equation is

A = 2πr + πrl

The first step is to subtract 2πr from the left hand side and the right hand side of the equation. It becomes

A - 2πr = 2πr + πrl - 2πr

A - 2πr = πrl

The next step is to divide the left hand side and the right hand side of the equation by πr. It becomes

(A - 2πr)/πr = πrl/πr

l = (A - 2πr)/πr

I = A/πr - 2πr/πr

I = A/πr - 2

Answer:

Yes, because −8c = 2(−4c) and −4c is an integer

Step-by-step explanation:

We want to determine whether [tex]-8c[/tex] is an even integer.

Recall that even integers are of the form: [tex]2n[/tex]

Let us see if we can rewrite the given expression in the form 2n, where n is an integer.

Let us factor 2 to get:

[tex]-8c=2(-4c)[/tex]

If -4c is an integer and we let m=-4c,then

[tex]-8c=2(m)=2m[/tex], where m is an integer.

Therefore the answer is Yes, because −8c = 2(−4c) and −4c is an integer

Answer:

P=0.00564

Step-by-step explanation:

From Exercise we have  52 cards.

We calculate the number of combinations to draw 5 cards from a deck of 52 cards. We get

{52}_C_{5}=\frac{52!}{5!(52-5)!}=2598960

We now count the number of favorable combinations:

{13}_C_{1} · {48}_C_{2}= 13 · \frac{48!}{2!(48-2)!}=14664

Therefore, the probabilitiy is

14664/2598960=0.00564

P=0.00564

Answer:

Type of music      Country  Rock & roll  Blues  

Observed number   11            17                 8      

Probabilities P(x)      11/36     17/36           8/36  

Step-by-step explanation:

The probabilities can be calculated as

P(x)= observed number of times/ Total number of times.

The probability distribution for the type of music restaurant playing is

Type of music   Country  Rock & roll  Blues  Total

Observed number 11            17                 8         36

Probabilities P(x)      11/36     17/36           8/36      1

Answer:

All statements are correct for two congruent triangles

Step-by-step explanation:

If two triangles are congruent than the rules states that

Triangles are congruent when all corresponding sides and interior angles are congruent. The triangles will have the same shape and size, but one may be a mirror image of the other.

As the fig shows two triangle

Δ PQR

Δ LMN

All three corresponding sides of triangle are congruent

all three corresponding  angles are congruent

Both triangle are of same size

Both are of same shape

hence all the statements are CORRECT

Keywords:Geometry

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Yo sup??

This question can be solved by applying the properties of similar triangles

the triangle with sides 5x and 20 is similar to the triangle with sides 45 and 35

The similarity property used here is called AAA ie angle angle angle property as all the three angles of the 2 triangles are equal.

therefore we can say

5x/45=20/36

x=5 units

Hope this helps

The question is incomplete. The complete question is here;

Half of u is less than or equal 43, find the greatest possible value of u

The greatest possible value of u is 86

Step-by-step explanation:

To solve an inequality:

∵ [tex]\frac{1}{2}[/tex] u ≤ 43

- Divide both sides by [tex]\frac{1}{2}[/tex]

∴ u ≤ 86

- That means u could be any numbers less than or equal 86

∵ You need the greatest possible value of u

∴ u = 86

The greatest possible value of u is 86

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Answer:

[tex] 12C5 *(12C3) = 792*220 =174240 ways[/tex]

Step-by-step explanation:

For this case we know that we have 12 cards of each denomination (hearts, diamonds, clubs and spades) because 12*4= 52

First let's find the number of ways in order to select 5 diamonds. We can use the combinatory formula since the order for this case no matter. The general formula for combinatory is given by:

[tex] nCx = \frac{n!}{x! (n-x)!}[/tex]

So then 12 C5 would be equal to:

[tex] 12C5 = \frac{12!}{5! (12-5)!}=\frac{12!}{5! 7!} = \frac{12*11*10*9*8*7!}{5! 7!}= \frac{12*11*10*9*8}{5*4*3*2*1}=792[/tex]

So we have 792 was in order to select 5 diamonds from the total of 12

Now in order to select 3 clubs from the total of 12 we have the following number of ways:

[tex] 12C3 = \frac{12!}{3! 9!}=\frac{12*11*10*9!}{3! 9!} =\frac{12*11*10}{3*2*1}=220[/tex]

So then the numbers of ways in order to select 5 diamonds and 3 clubs are:

[tex] (12C5)*(12C3) = 792*220 =174240 ways[/tex]

Answer:

The rock is 52.2 feet high

Step-by-step explanation:

Similar Triangles

The triangle formed by the rock, mirror and the ground is similar to the triangle formed by Carlos, the mirror and the ground (see image below). This means its sides are proportional, and

[tex]\displaystyle \frac{H}{h}=\frac{X}{x}[/tex]

We want to calculate the height of the rock, thus we solve for H

[tex]\displaystyle H=\frac{h.X}{x}[/tex]

[tex]\displaystyle H=\frac{5.8\times 36}{4}=52.2 feet[/tex]

[tex]\boxed{\text{The rock is 52.2 feet high}}[/tex]

Final answer:

Using the properties of similar triangles and the distances between Carlos, the mirror, and the wall, we determined the height of the rock wall to be 52.2 ft.

Explanation:

Before climbing, Carlos wants to know the height of the rock wall he will climb. To determine the height of the wall, we can use the properties of similar triangles formed by Carlos's height and the distances between him, the mirror, and the wall. The mirror effectively creates two sets of similar triangles, one involving the actual height of Carlos and the other involving the perceived height of the rock wall in the mirror.

Carlos's height is 5.8 ft. The distance from Carlos to the mirror is 4 ft, and the distance from the mirror to the wall is 36 ft. Since Carlos can see the top of the wall in the mirror placed 4 ft away from him, we can use the ratio of distances and heights to determine the wall's height. The setup is based on the principle that the ratio of the distance from Carlos to the mirror is to the distance from the mirror to the base of the wall as Carlos's height is to the unknown height of the wall.

Using the ratio 4:36, we can set up a proportion, keeping in mind that similar triangles have corresponding sides that are in proportion. Thus, the height of the wall is to Carlos's height of 5.8 ft as 36 ft is to 4 ft. This gives us the equation: Height of wall / 5.8 = 36 / 4. Calculating this, we find that the height of the wall is 52.2 ft.

Answer:

x = 0.8 Mi

Step-by-step explanation:

for x = 4224 ft we can use the factor (1 Mi/5280 ft)

then

x = 4224 ft (1 Mi/5280 ft) = 0.8 Mi

Answer:

[tex] \% Change = \frac{|28-32|}{32} *100 = 12.5\%[/tex]

(B) Decrease by 12.5%

Step-by-step explanation:

For this case we know that the revolution is proportional to the circumference.

And we know that the average number of revolutions of 32 inch tires for Tuesday is higher than the original value of 28 inch tires for Monday.

We know that we have x mi/hr, so we can select a value fo x in order to find the average revolutions with the following formula:

[tex] Avg = \frac{x}{mi}[/tex]

Let's say that we select a value for x for example x= 28*32 = 896, since this value is divisible by 32 and 28.

If we find the average revolutions per each case we got:

Tuesday:

[tex] Avg = \frac{896}{32}=28[/tex]

Monday:

[tex] Avg = \frac{896}{28}=32[/tex]

And then we can find the % of change like this:

[tex] \% Change= \frac{|Final-Initial|}{Initial} *100[/tex]

And if we replace we got:

[tex] \% Change = \frac{|28-32|}{32} *100 = 12.5\%[/tex]

Because we are assuming that the initial amount is the value for Monday and the final value for Tuesday.

So then the best answer for this case would be:

(B) Decrease by 12.5%

Answer:

sin 80

Step-by-step explanation:

Answer:

D. 286 deg

Step-by-step explanation:

Think of both triangles as just one single large triangle.

The exterior angles at the bottom have measure 127 deg.

That means the two interior angles at the bottom have measure

180 deg - 127 deg = 53 deg

The measures of the interior angles of triangle add to 180 deg.

The upper interior angle has measure:

180 deg - 53 deg - 53 deg = 74 deg

A full circle has 360 degrees.

Angle r is a full circle minus the upper interior angle of the combined triangle.

r = 360 deg - 74 deg

r = 286 deg

Answer:

a.) 1.23 seconds

b.) 14 m/s

Step-by-step explanation:

a.) Before commencing the calculation, we need to specify the information.

Data:

acceleration dues to gravity, g = 9.81 m/s²

initial velocity u = 2.0 m/s

height, s = 40 m

t = ?

The formula for finding the distance is s = ut + 1/2at²

Therefore, 40 = 2t + 1/2×(9.81) ×t²

                  80 = 4t + 9.81 t²

Solving for t by the quadratic equation gives t = 1.23 s [Note the other negative value for t is rejected because there is no negative time]

b) The final velocity is given by the following equation:

v = u + at

where v = final velocity just before the camera lands on the ground

            u = initial velocity

            t = time taken

            a = g = acceleration dues to gravity = 9.81 m/s²

Calculating gives

v = 2 + 9.81×1.23

  = 14 m/s Ans

Answer:

B) -3.464

Step-by-step explanation:

∫₀³ g'(x) cos²(2g(x) + 1) dx

Using u substitution:

u = 2g(x) + 1

du = 2g'(x) dx

½ du = g'(x) dx

When x = 0, u = 11.

When x = 3, u = -3.

½ ∫₁₁⁻³ cos²(u) du

You can use a calculator to solve this, or you can evaluate algebraically.

Use power reduction formula:

½ ∫ (½ + ½ cos(2u)) du

¼ ∫ du + ¼ ∫ cos(2u) du

¼ ∫ du + ⅛ ∫ 2 cos(2u) du

¼ u + ⅛ sin(2u) + C

Evaluating from u = 11 to u = -3:

[¼ (-3) + ⅛ sin(-6) + C] − [¼ (11) + ⅛ sin(22) + C]

-⁷/₂ + ⅛ sin(-6) − ⅛ sin(22)

−3.464

Answer:

8,160 lei

Step-by-step explanation:

The question in English is

136 children came to the ice rink in the morning, and three times in the afternoon. How much money was collected on the tickets sold, if an entrance ticket costs 15 lei?

step 1

Find the total number of children that came to the ice rink

we know that

The number of children that came to the ice rink in the morning was 136

The number of children that came to the ice rink in the afternoon was (136*3)=408

To find out the total number of children that came to the ice rink , adds the number of children that came in the morning plus the number of children that came in the afternoon

so

[tex]136+408=544\ children[/tex]

step 2

To find out the total money collected, multiply the total number of children by the cost of one ticket entrance

so

[tex]544(15)=8,160\ lei[/tex]

Answer:

we can use the variable c to represent the monthly cost

75+0.17x=c

Step-by-step explanation:

The expression shows the monthly cost for the phone if x represents the number of minutes if The cost for a cell phone service is $75 per month plus $0.17 per minute, is y = 75 + 0.17x.

An assertion that two mathematical expressions have equal values is known as an equation. An equation simply states that two things are equal. The equal to sign, or "=," is used to indicate it.

Given:

The cost for a cell phone service is $75 per month plus $0.17 per minute,

Write the equation as shown below,

Total cost = Cost for a month + per minute charge × total use in minutes,

Assume the total cost is y, and the use of minute is x then,

y = 75 + 0.17 × x

y = 75 + 0.17x

Thus,  the monthly cost for the phone is 75 + 0.17x.

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Answer:

SinƟ  = 12/37

CosƟ    =35/37

TanƟ = 12/35

Step-by-step explanation:

The diagram of the triangle is attached

Using SOH CAH TOA

SinƟ = Opposite/Hypotenuse

SinƟ  = 12/37

CosƟ= adjacent/Hypo tenuse

CosƟ    =35/37

TanƟ=Opposite/Adjacent

TanƟ = 12/35

Answer:

Answer is (A) One-half times 14 times 57

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

y² / 81  -  x² / 19   = 1

Step-by-step explanation: See Annex ( vertices and foci in coordinates axis)

The equation in standard form for the hyperbola is:

x² / a² - y²/b² = 1       or    y²/a²  -  x² / b²  = 1

In cases of transverse axis parallel to x axis  or y axis respectively.

As per given information in this case hyperbola has a transverse axis parallel to  y  axis the equation is

y²/a²  -  x² / b²  = 1

a is a distance between  center and vertex therefore a = 9

c is a distance between center and a focus c = 10

and  b will be:

c² = a²  +  b²    ⇒   b²  = c²  - a²     ⇒ b²  =  (10)² - (9)²    ⇒  b² = 100 - 81

b = √19

And the equation in standard form is:

y² / a²  -  x² / b²  = 1

y² / ( 9 )²   -  x² / √(19)²     ⇒   y² / 81  -  x² / 19   = 1

Answer:

B

Step-by-step explanation:

Answer:

The maximum of the sinusoidal function is 5.

Step-by-step explanation:

The maximum of the sinusoidal function is 5.

Answer:

The correct answer is compress the graph closer to the x axis

reflect the graph over the x axis

translate the graph to the right

Step-by-step explanation:

I just took the test

The correct answer is (A)(C)(G) because to transform the graph, we first reflect it over the x-axis, then translate it to the right, and finally compress it closer to the x-axis.

To determine the transformations applied to the graph of [tex]\( f(x) = \sqrt[3]{x} \)[/tex] to obtain the graph of [tex]\( g(x) = -\frac{1}{2} \sqrt[3]{x-9} \)[/tex], let's analyze each component of the transformation step-by-step.

Given [tex]\( f(x) = \sqrt[3]{x} \)[/tex] and [tex]\( g(x) = -\frac{1}{2} \sqrt[3]{x-9} \)[/tex], the transformations are as follows:

1. Horizontal Shift:

The term [tex]\( x-9 \)[/tex] inside the function indicates a horizontal shift.

Specifically, it shifts the graph to the right by 9 units.

2. Vertical Compression and Reflection:

The coefficient [tex]\( -\frac{1}{2} \)[/tex] outside the cube root function indicates a vertical transformation.

The negative sign reflects the graph over the x-axis.

The factor [tex]\( \frac{1}{2} \)[/tex] compresses the graph closer to the x-axis.

The complete question is:

Which transformations have been performed on the graph of [tex]f(x)=\sqrt[3]{x}[/tex] to obtain the graph of [tex]g(x)= -\frac{1}{2} \sqrt[3]{x-9}[/tex] ?

A. reflect the graph over the x-axis.

B. translate the graph down.

C. translate the graph to the right.

D. translate the graph up.

E. stretch the graph away from the x-axis.

F. translate the graph to the left.

G. compress the graph closer to the x-axis.

Answer: 5 gallons of gas were used for city driving.

Step-by-step explanation:

Let x represent the number of gallons of gas that the car used on the highway.

Let y represent the number of gallons of gas that the car used in the city.

The car's gas tank can hold 21 gallons. This means that

x + y = 21

A car can travel 25 miles per gallon on the high way and 20 miles in the city. If the car traveled 500 miles on a full tank of gas, it means that

25x + 20y = 500 - - - - - - - - - -1

Substituting x = 21 - y into equation 1, it becomes

25(21 - y) + 20y = 500

525 - 25y + 20y = 500

- 25y + 20y = 500 - 525

- 5y = - 25

y = - 25/ - 5

y = 5

x = 21 - y = 21 - 5

x = 16

The number of miles used for city driving is: [tex]\[{100}\][/tex].

To determine how many miles were used for city driving, we start by defining the variables and equations based on the problem's information:

1. Let \( x \) be the number of miles driven on the highway.
2. Let \( y \) be the number of miles driven in the city.

Given the problem, we have the following information:
- The car traveled a total of 500 miles: [tex]\( x + y = 500 \)[/tex]
- The car's gas consumption rates are 25 miles per gallon on the highway and 20 miles per gallon in the city.
- The gas tank holds 21 gallons.

Next, we set up the equation for total gas consumption:
[tex]\[\frac{x}{25} + \frac{y}{20} = 21\][/tex]

We now have a system of two equations:
[tex]1. \( x + y = 500 \)\\2. \( \frac{x}{25} + \frac{y}{20} = 21 \)[/tex]

To solve this system, we start with the first equation:
[tex]\[x = 500 - y\][/tex]

Substitute [tex]\( x = 500 - y \)[/tex] into the second equation:
[tex]\[\frac{500 - y}{25} + \frac{y}{20} = 21\][/tex]

Next, we find a common denominator to simplify the left-hand side of the equation. The common denominator for 25 and 20 is 100:
[tex]\[\frac{500 - y}{25} = \frac{500 - y}{25} \cdot \frac{4}{4} = \frac{4(500 - y)}{100} = \frac{2000 - 4y}{100}\]\[\frac{y}{20} = \frac{y}{20} \cdot \frac{5}{5} = \frac{5y}{100}\]\\[/tex]
So the equation becomes:
[tex]\[\frac{2000 - 4y + 5y}{100} = 21\][/tex]

Combine the terms in the numerator:
[tex]\[\frac{2000 + y}{100} = 21\][/tex]

Multiply both sides by 100 to eliminate the fraction:
[tex]\[2000 + y = 2100\][/tex]

Subtract 2000 from both sides to solve for \( y \):
[tex]\[y = 100\][/tex]

Thus, the number of miles used for city driving is:
[tex]\[{100}\][/tex].

Answer:

  a. Slant asymptote with a slope of 5

Step-by-step explanation:

Dividing out the polynomials, you get ...

  [tex]\dfrac{5x^2-x+13}{x+10}=5x-51+\dfrac{523}{x+10}[/tex]

As the magnitude of x gets large, the fraction goes to zero, and the behavior matches the line ...

  y = 5x -51

This is a slant asymptote with a slope of 5 and a non-zero y-intercept.