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Answer:

[tex]\displaystyle \lim_{x\to \infty}\frac{3x^2+4.5}{x^2-1.5}=3[/tex]

Step-by-step explanation:

We want to evaluate the limit:

[tex]\displaystyle \lim_{x\to \infty}\frac{3x^2+4.5}{x^2-1.5}[/tex]

To do so, we can divide everything by x². So:

[tex]=\displaystyle \lim_{x\to \infty}\frac{3+4.5/x^2}{1-1.5/x^2}[/tex]

Now, we can apply direct substitution:

[tex]\Rightarrow \displaystyle \frac{3+4.5/(\infty)^2}{1-1.5/(\infty)^2}[/tex]

Any constant value over infinity tends towards 0. Therefore:

[tex]\displaystyle =\frac{3+0}{1+0}=\frac{3}{1}=3[/tex]

Hence:

[tex]\displaystyle \lim_{x\to \infty}\frac{3x^2+4.5}{x^2-1.5}=3[/tex]

Alternatively, we can simply consider the biggest term of the numerator and the denominator. The term with the strongest influence in the numerator is 3x², and in the denominator it is x². So:

[tex]\displaystyle \Rightarrow \lim_{x\to\infty}\frac{3x^2}{x^2}[/tex]

Simplify:

[tex]\displaystyle =\lim_{x\to\infty}3=3[/tex]

The limit of a constant is simply the constant.

We acquire the same answer.

Step-by-step explanation:

lkh, Jkm. Correct me if im wrong :^

Answer:

All terms separated by 6 so #20 = 4 + 6 * 19 = 118

(if the first term were 6 instead of 4 the 20th would be 120)

Also, #10 = 58 and #11 = 64   (you can use the same reasoning)

The 1st and 20th term add to 4 + 118 = 122

The 2nd and 19th add to 10 + 112 = 122

Likewise 10th and 11th add to 58 + 64 = 122

So 10 * 122 = 1220

Answer:

It has 2 equal side lengths

Answer:

12

Step-by-step explanation:

Simplify 3 log(x+7) by moving 3 inside the parentheses with 7.f(x)=log((x+7)3)−5

Answer:

the number of child plates and adults plates were served is 125 and 155 respectively

Step-by-step explanation:

Let us assume the child plate be x

And, the adult plates be y

Now according to the question

x + y = 280 .................(1)

2.60x + 9.50y = 1797.50 .............(2)

Now multiply by 2.60x in equation (1)

2.60x + 2.60y = 728

2.60x + 9.50y = 1797.50

-6.90y = -1069.50

y = 155

So, x = 280 - 155

= 125

hence, the number of child plates and adults plates were served is 125 and 155 respectively

Answer:

120 students are predicted to like chocolate chip ice cream best.

Step-by-step explanation:

40% = 0.4

Multiply 300 by 0.4 to get 40% of 300.

300 × 0.4 = 120

Answer:

FV= $7,040.46

Step-by-step explanation:

Giving the following information:

Initial investment (PV)= $5,500

Number of periods (n)= 10 years

Interest rate (i)= 2.5%

To calculate the future value (FV), we need to use the following formula:

FV= PV*(1 + i)^n

FV= 5,500*(1.025^10)

FV= $7,040.46

Answer:

24.1

Step-by-step explanation:

Answer:

Step-by-step explanation:

Equation

Let "n" represent the number. Then more indicates addition, and times indicates multiplication. With that said, the answer is 4 + 3n.

Dale's Money

Given: $44 in total

44 ÷ 2 (To know how much they have  equally)

22

22 ÷ 3 (Then you divide by 3 because Brandon has 3 times his, the opposite of multiplication is division.)

7.3

Therefore, Dale has $7.3¢

Brandon's money

Given: 4 + 3n. Dale has 7.3

Solve: 7.3 × 3 ( Since Brandon has four more than 3 times the amount of money that Dale has, multiply that and 3)

21.9 (Then add four because Brandon has four more...)

25.9

Therefore, Brandon has $25.9¢

The amount that Brandon and Dale have is $34 and $10, respectively.

An equation is formed when two expressions are equated with each other with the help of an equal sign.

Let the amount of money that Brandon has be x, and Dale has be y.

As it is given that the sum of the total amount they both had is $44. therefore, the equation that can represent the total amount both of them had is

[tex]x + y = \$44[/tex]

Now, according to the first statement, Brandon has four more than 3 times the amount of money that Dale has. therefore, the equation can be represented as,

[tex]x = 4 + 3y[/tex]

Further, as got the two-equation solving the two equations. We have the value of x, therefore, substitute the value of x in the first equation,

[tex]x+y = 44\\\\(4 + 3y )+y= 44\\\\4+4y=44\\\\4y = 40\\\\y = 10[/tex]

Now, substitute the value of y in the second equation we get,

[tex]x = 4 + 3y\\\\x = 4 + 3(10)\\\\x = 34[/tex]

Hence, The amount that Brandon and Dale have is $34 and $10, respectively.

Learn more about Equation:

https://brainly.com/question/24944275

Answer:

Total area of figure = [3x² + 7x + 6] feet²

Step-by-step explanation:

By dividing both rectangle by vertical line;

Given:

Length of big rectangle = (x + 3) feet

Width of big rectangle = (x + 2) feet

Length of small rectangle = 2x feet

Width of small rectangle = (x + 1) feet

Find:

Total area of figure

Computation:

Area of rectangle = Length x width

Total area of figure = Area of big rectangle + Area of small rectangle

Total area of figure = [(x + 3)(x + 2)] + [(2x)(x + 1)]

Total area of figure = [x²+ 2x + 3x + 6] + [2x² + 2x]

Total area of figure = [3x² + 7x + 6] feet²

Answer: ABC = 2145

Step-by-step explanation:

11x13x15=2145

Answer:

whatever wawnser gimme brainliest

The midpoint of the tallest bar of the histogram is the mode of the data point.

Graph is a graphical representation that shows the relationship between a group of points. Types of graphs are histogram, bar chart, pie chart etc.

A histogram is a graphical representation that arranges a group of data points into specific ranges.

The midpoint of the tallest bar of the histogram is the mode of the data point.

Find out more on histogram at: https://brainly.com/question/2962546

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Answer:

Each additional sugary snack eaten is associated with a loss of five points on the test.

Step-by-step explanation:

Answer:

The two numbers are 12 and 26

Step-by-step explanation:

let the first number = a

let the second number = b

The ratio of the numbers is given as;

[tex]\frac{a}{b} = \frac{6}{13} \\\\a = \frac{6b}{13}[/tex] -------- (1)

The lcm of the two numbers is given as;

a x b = 312

ab = 312 --------- (2)

From equation (1), [tex]a = \frac{6b}{13}[/tex]

[tex]b(\frac{6b}{13} ) = 312\\\\\frac{6b^2}{13} = 312\\\\6b^2 = 4056\\\\b^2 = \frac{4056}{6} \\\\b^2 = 676\\\\b = \sqrt{676} \\\\b = 26\\\\From \ equation \ (1);\\\\a = \frac{6b}{13} \\\\a = \frac{6 \times 26}{13} \\\\a = 12[/tex]

Therefore, the two numbers are 12 and 26

Answer:

the profit percentage based on the cost & selling price is 16.67% and 14.29% respectively

Step-by-step explanation:

The computation of the profit percentage based on the cost & selling price is shown below:

The Profit percentage on the cost is

= (Sale price - cost price) ÷ (cost price) × 100

= ($175 - $150) ÷ ($150) × 100

= 16.67%

ANd, the profit percentage based on the selling price is

= (Sale price - cost price) ÷ (selling price) × 100

= ($175 - $150) ÷ ($175) × 100

= 14.29%

Hence, the profit percentage based on the cost & selling price is 16.67% and 14.29% respectively

Answer:In my opinion B.0.005 is the correct answer

Step-by-step explanation:

hope it will help you

Answer:

20

Step-by-step explanation:

Answer:

D. (4 1/2, 2 1/2)

Step-by-step explanation:

Look for each point on the coordinate graph.

Part A:

There are 25 blocks for the length, and the length of each is 5.5 inches. 5.5x25=137.5

There are 9 blocks for the height, and each is 2.75 inches. 2.75x9=24.75

Since we're trying to find how much longer the length is to the width, we find the difference. 137.5-24.75=112.75

So part A answer is 112.75 (or 112¾)

Part B:

We know the length is 137.5 and the height is 24.75. To find how many times longer the length is, we need to divide to see how many 24.75 can go into 137.5.

137.5÷24.75=5.55

So the answer to part B is 5.55. Given the context, the answer would probably be 5, because that's how many entire height can fit.

Sorry if it's wrong lol

Answer:

Slope: -69

Y-intercept: -346 or (0, -346)

Step-by-step explanation:

y = mx + b

    m = slope

    b = y-intercept

y = -69x - 346

    m = -69

    b = -346

Answer:

Step-by-step explanation:

The point is that any graphing calculator will work. We use Desmos on Brainly.

The graph below is your complete answer.

You can actually find the zeros by factoring

p(x) = x^2(2x - 1) - 4(2x - 1)

p(x) = (2x - 1) (x^2 - 4)

p(x) = (2x - 1) (x - 2)(x + 2)

I have to hurry. If this is not enough, let me know.

Step-by-step explanation:

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9514 1404 393

Answer:

  x = 60

Step-by-step explanation:

You are correct that the angles are complementary.

That means their sum is 90°.

  (x -30)° + x° = 90°

  2x -30 = 90 . . . . . . . divide by °, collect terms

  2x = 120 . . . . . . . . . . add 30

  x = 60 . . . . . . . . . . . . divide by 2

Answer:

Step-by-step explanation:

Answer:

x=4

Step-by-step explanation:

4x+6=8x-10

6= 8x-10-4x

6=4x-10

6+10=4x

16=4x

16/4=x

4=x

x=4

Answer:

x = 4

Step-by-step explanation:

Subtract 8x from both sides.

4x + 6 - 8x = 8x - 10 - 8x

−4x + 6 = −10

Subtract 6 from both sides.

−4x + 6 − 6 = −10 − 6

−4x = −16

Divide both sides by -4.

[tex]\frac{-4x}{-4} = \frac{-16}{-4}[/tex]

x = 4

Mark as Brainllest plz

Answer:

77.43% decrease

Step-by-step explanation:

A decrease of 11% = (100 - 11)% = 89% = [tex]\frac{89}{100}[/tex] = 0.89

A decrease of 13% = (100 - 13)% = 87% = [tex]\frac{87}{100}[/tex] = 0.87

A 11% decrease followed by a 13% decrease has an overall change of

0.89 × 0.87 = 0.7743 × 100% = 77.43%

Answer:

d=6.324

Step-by-step explanation:

[tex]d=\sqrt{(x2-x1)^{2}+(y2-y1)^{2} }[/tex]

[tex]d=\sqrt{(-5-(-3)^{2} +(2-(-4)^{2} }[/tex]

[tex]d=\sqrt{(-5+3)^{2}+(2+4)^{2} }[/tex]

[tex]d=\sqrt{(-2)^{2}+6^{2} }[/tex]

[tex]d=\sqrt{4+36}[/tex]

[tex]d=\sqrt{40}[/tex]

[tex]d=6.324[/tex]

Answer:

7/3

Step-by-step explanation:

1x6

1x(-x)

subtract and solve