How would you "remove the discontinuity" of f ? In other words, how would you define f(5) in order to make f continuous at 5? f(x) = x2 − 3x − 10 x − 5

The rock will hit the water after approximately 2 seconds.

The time it takes for the rock to hit the water, we need to set the height h equal to zero and solve for t . The equation representing the height of the rock is given by:

[tex]\[ h = -16t^2 + 12t + 40 \][/tex]

Setting h to zero:

[tex]\[ 0 = -16t^2 + 12t + 40 \][/tex]

Now, we have a quadratic equation.

To solve for t , we can use the quadratic formula:

[tex]\[ t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]

In this equation, [tex]\( a \), \( b \), and \( c \)[/tex] are the coefficients from the quadratic equation [tex]\( at^2 + bt + c = 0 \).[/tex]In our case:

[tex]\[ a = -16, \quad b = 12, \quad c = 40 \][/tex]

Substitute these values into the quadratic formula:

[tex]\[ t = \frac{-12 \pm \sqrt{12^2 - 4(-16)(40)}}{2(-16)} \]\\[/tex]

Now, calculate the values under the square root:

[tex]\[ t = \frac{-12 \pm \sqrt{144 + 2560}}{-32} \][/tex]

[tex]\[ t = \frac{-12 \pm \sqrt{2704}}{-32} \][/tex]

[tex]\[ t = \frac{-12 \pm 52}{-32} \][/tex]

Now, consider both the positive and negative roots:

1. For the positive root:

[tex]\[ t_1 = \frac{-12 + 52}{-32} = \frac{40}{-32} = -\frac{5}{4} \][/tex]

2. For the negative root:

[tex]\[ t_2 = \frac{-12 - 52}{-32} = \frac{-64}{-32} = 2 \][/tex]

Since time cannot be negative in this context, we discard the negative root.

Therefore, the rock will hit the water after approximately t = 2 seconds.

Answer:

1)[tex]10+10+1+1=22[/tex]

2)[tex]10+1+1+1+1+1+1+1+1+1+1+1+1=22[/tex]

Step-by-step explanation:

Mrs. Sims has to put 22 books.

She can either put them in stacks of 10 or arrange them as single book(single stack).

There could be two ways in which she could arrange the books.

First way:

She could arrange the books in two stacks of 10 books ([tex]2\times10=20[/tex] and the remaining two books can be arranged as single books.

So, the arrangement is [tex]10+10+1+1=22[/tex]

Second way:

She could arrange books in one stack of 10 books and and remaining twelve books can be arranged as single books.

So, the arrangement is [tex]10+1+1+1+1+1+1+1+1+1+1+1+1=22[/tex]

To write this in scientific notation, we have to move the decimal place to the left. Moving the decimal place to the left indicate a positive movement, therefore the correct scientific notation in this case is:

8.28 x 10^8 micrometers

The ratio of bulls to cows does not remain the same after adding 4 more cows and 4 more bulls.

To determine if the ratio of bulls to cows remains the same after adding 4 more cows and 4 more bulls, we need to compare the new ratio to the original ratio.

Initial ratio of bulls to cows: 18/45 = 2/5

After adding 4 more cows and 4 more bulls, the new ratio becomes (18+4)/(45+4) = 22/49.

Since the new ratio is different from the original ratio, the ratio of bulls to cows does not remain the same after adding 4 more cows and 4 more bulls.

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The total number of apples sold if, A produce store sold 63 red apples, The ratio of red apples to green apples sold was 7:2, which is 81.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value.

Given:

A produce store sold 63 red apples,

The ratio of red apples to green apples sold was 7:2,

Assume the total number of apples sold is x then,

Total number of apple sold = 7x + 2x

But the number of red apples sold is given so,

7x = 63

x = 63 / 7

x = 9

Put the value of x in the above equation,

Total number of apple sold = 7 × 9 + 2 × 9

Total number of apple sold = 63 + 18

Total number of apples sold = 81

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6/8 , 9/12 are the equivalent fraction 3 over 4

A fraction represents a part of a whole.

The given fraction is 3/4.

In the given fraction the numerator is three and denominator is four.

We need to find the equivalent fractions of 3/4.

Equivalent fractions are the fractions that have different numerators and denominators but are equal to the same value.

Let us multiply with same number in numerator and denominator to find the equivalent fractions.

3/4×2/2=6/8

3/4×3/3=9/12

Hence, 6/8 , 9/12 are the equivalent fraction 3 over 4

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(16-4) x (3+7) =120

when we subtract 16 and 4 you get 12.

When we add 3+7 you get 10.

After multiplying them together we get 120.

parentheses

Parentheses are a pair of punctuation marks that might be most customarily used to feature extra nonessential information or an aside to a sentence. Parentheses resemble two curved vertical lines: ( ). An unmarried one of these punctuation marks is called a parenthesis.

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To round 26.99 to the nearest tenth, we increase the tenths place by 1 because the hundredths place is 9, resulting in 27.0.

When rounding 26.99 to the nearest tenth, we need to look at the hundredths place, which is 9. Since 9 is greater than 5, we round up the digit in the tenths place by 1. Therefore, the number rounded to the nearest tenth is 27.0.

To simplify -2i * -3i, multiply -2 by -3 to get 6, then multiply i by i to get i². Because i² is equivalent to -1 in the complex number system, multiply 6 by -1 to get your answer, which is -6.

When multiplying two complex numbers like −2i and (−3i), the 'i' terms get multiplied together separately to the numerical terms. This is due to the distributive property of multiplication.

So, if we apply the multiplication, we would have −2 multiplied by −3 which gives us 6. Then, i multiplied by i gives us i². The term i² is defined as -1 in the realm of complex numbers.

Putting these together we get 6 x -1, that results in −6.

Therefore, the simplified value of the expression is -6, which corresponds with option c.

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Answer:

The pipe is leaking at the rate of 1.875 gallons of water per day.

Step-by-step explanation:

In this question we will find the leakage per day first, then convert it into gallons.

The janitor discovered a leak, leaking with a rate = 10 oz per hour

And we know that there are 24 hours in a day therefore, pipe leaking per day will be = 24×10 = 240 oz.

Since 1 oz  = 0.0078125 gallons

Therefore, 240 oz = 240×0.0078125

                               = 1.875 gallons

The pipe is leaking at the rate of 1.875 gallons of water per day.

Answer:

its in the hundreads place but it has no value becuase its 0

Step-by-step explanation:

Final answer:

It will take 1 year for $450 to double at a simple interest rate of 100%, as the simple interest formula shows that the interest equals the principal when the rate is 100% and time is one year.

Explanation:

To calculate how long it takes for $450 to double at a simple interest rate of 100%, we can use the formula for simple interest: Interest = Principal × Rate × Time. Since the goal is to double the principal, the interest earned should be equal to the principal of $450.

The simple interest formula in this shape becomes:
$450 = $450 × 1 × Time
When we simplify this, we find that Time equals 1.

Therefore, it will take 1 year for $450 to double at a simple interest rate of 100%.

To calculate GPA we will find the total points of the student and the total credit hours of the student.

The grades point average (GPA) of the student is 3.47.

Given to us

Points of the students = earned grades x corresponding credit hours

Total points = 8 +24 + 3 + 24 = 59

Total Credit hours = 4 + 6 + 1 + 6 = 17 hours

[tex]\rm{Grade\ point\ average\ (GPA) = \dfrac{Total\ points\ of\ the\ students}{Total\ Credit\ hours}[/tex][tex]\rm{Grade\ point\ average\ (GPA) = \dfrac{59\ points}{17\ hours} = 3.47[/tex]

Hence, the grade point average (GPA) of the student is 3.47.

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Answer:$43.20

Step-by-step explanation:

The length of the ladder is 11.66 ft.

The sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

a² + b² = c²

Given that a ladder leans against the side of a house. The top of the ladder is 10 ft from the ground. The bottom of the ladder is 6 ft from the side of the house.

Let the length of the ladder be x

Therefore, using Pythagoras theorem

x² = 10² + 6²

x² = 100 + 36

x = [tex]\sqrt{136[/tex]

x = 11.66 ft

Hence, the length of the ladder is 11.66 ft.

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Hey!

Hope this helps...

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Yes!

Ultimately (it states) all numbers in existence can be extracted from Pascal's Triangle.  Using his binomial formation of: (a + b)^0 = 1 , where y is the number you are using.  and (a + b)^x is the equation you use to find the answer of that row...  the usage of that row, and the formation of its components is how you find the powers of numbers in a given row...

You would be able to find each row of the Triangle, and by using the association of Multiplication, addition, distribution, and

If you look at the images below you will notice that to find a power of 11 at it's 6th power, you look at the 6th row of Pascal's Triangle... Although not completely relevant, I also added an image of using his Triangle to find the Powers of 2...

Remember, The images below are of only smaller versions of Pascal's Triangle, as his Triangle is of infinite size...

Yes, we can use the values in Pascal’s triangle to find the powers of 11

Pascal triangles contains coefficient of (x + 1)'s expanded form's terms.

For first row, we have:

Thus, 1 is the value in the first row of Pascal triangle.

(x + 1) = 1

The variable x has coefficient 1, and that 1 itself, so second row of Pascal triangle has 1 , 1 as values.

It states that all numbers in existence can be extracted from Pascal's Triangle.

Using his binomial formation;

(a + b)^0 = 1 , where y is the number

(a + b)^x  is the equation that use to find the answer of that row. the usage of that row, and the formation of its components isto find the powers of numbers in a given row.

It would be able to find each row of the Triangle, and by using the association of Multiplication, addition, distribution.

Yes, we can use the values in Pascal’s triangle to find the powers of 11

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she did (x+8)*5

2015 = (x+8)*5

divide both sides by 5

403=x+8

x = 403-8 = 395

using same number if she followed instructions it would be

395*8 =3160+5 = 3165

the rate of change is -2 for every set shown in the chart on the right

 so 6 to 7 would be -11 -2 = -13

7 to 8 would be -13-2 = -15

8 to 9 = -15-2 = -17

 B is the answer