Consider the function f (x) = StartLayout Enlarged left-brace first row negative StartFraction x + 5 Over x + 3 EndFraction, x less-than negative 2 second row x cubed + 6, x greater-than-or-equal-to negative 2 EndLayout.

Which statement describes whether the function is continuous at x = –2?

The function is continuous at x = –2 because f(–2) exists.
The function is continuous at x = –2 because Limit as x approaches negative 2 plus f(x) = f(–2).
The function is not continuous at x = –2 because Limit as x approaches negative 2 f(x) ≠ f(–2).
The function is not continuous at x = –2 because Limit as x approaches negative 2 f(x) does not exist.

9514 1404 393

Answer:

  (x, y) = (4, 4)

Step-by-step explanation:

If you attempt to solve this by clearing fractions, you end up with an extraneous solution. Here, we'll solve the linear equations ...

  7a +4b = 5/4

  8b -14a = 3/2

where a = 1/(4x+3y) and b = 1/(4x-3y)

Dividing the second equation by 2 and adding the first, we have ...

  (7a +4b) +1/2(8b -14a) = (5/4) +1/2(3/2)

  8b = 8/4

  b = 1/4

Substituting into the first equation gives ...

  7a +4/4 = 5/4

  a = 1/28

__

Now, we can get back to solving for x and y.

  4x +3y = 1/a = 28

  4x -3y = 1/b = 4

  8x = 32 . . . . . . . . . add the two equations

  x = 4

  3y = 28 -4x = 28 -4(4) = 12 . . . . . use x in the equation for 'a'; rearrange

  y = 4 . . . . divide by 3

The solution to the system of equations is (x, y) = (4, 4).

_____

Additional comment

If you graph these equations, you find they describe hyperbolas that intersect at (0, 0) and (4, 4). The "solution" (0, 0) is extraneous, as both equations are undefined there.

Answer:

8times 10 times 4 divided by 2 pplus 8 times 8 equals 64 + 80 = 144 m squared

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

64

Step-by-step explanation:

The surface area of the sphere is 12.56 yd².

Surface area is the amount of space covering the outside of a three-dimensional shape.

Given that a sphere is inscribed in a cube with a volume of 8. cubic yards. We need to find the surface area of the sphere,

Since the sphere is inscribed in the cube therefore the diameter of the sphere is equal to the side length of the cube,

Now, finding the side length of the cube,

We know volume of a cube = side³

Therefore,

side³ = 8

side = 2 yd

Therefore,

Diameter of the sphere = 2 yd

Radius = 1 yd

The surface area of the sphere = 4 ×  π × radius²

= 4 × 3.14 × 1²

= 12.56

Hence the surface area of the sphere is 12.56 yd²

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Answer:

library

Step-by-step explanation:

Answer:

library

Step-by-step explanation:

9514 1404 393

Answer:

  6√5 ≈ 13.42 cm

Step-by-step explanation:

The axis, a radius, and the edge marked 12 cm together form a right triangle, of which the axis is the hypotenuse. The Pythagorean theorem applies.

  6² +12² = axis² = 180

  axis = √180 = 6√5 ≈ 13.42 . . . cm

The length of the axis is 6√5 cm, about 13.42 cm.

Answer:

6 units

Step-by-step explanation:

Sqrt((-1-5)^2-(3-3)^2)

Answer:

[tex]8\pi\text{ mi}^2[/tex]

Step-by-step explanation:

The area of a full circle is  [tex]A = \pi r^2[/tex] where r is the radius.

The area of the circle in this problem is [tex]A=\pi(8)^2=64\pi[/tex].

A 45 degree central angle (that's how arcs are measured) accounts for 1/8 of the circle (because it's 45 degrees out of a full circle of 360 degrees, and 45/360 = 1/8).

The area of the sector is [tex]\frac{1}{8}(64\pi)=8\pi[/tex] square miles

When a box contains 2 pens, 2 pencils, and 1 highliter, there is a 50% chance that the second item is a pencil.

Probability theory, a subfield of mathematics, gauges the likelihood of an event or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a comprehensive set of equally likely outcomes that result in a certain occurrence compared to the total number of outcomes.

given

according to the question , the probability is a

2 / 1+2+1 * 100 %

2/4 *100%

= 50 %

after picking out a pen , the remaining are 1 pen , 2 pencils and 1 highlighter . in total of 4 items , 2 items are pencil .

When a box contains 2 pens, 2 pencils, and 1 highliter, there is a 50% chance that the second item is a pencil.

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Answer:X=8

Step-by-step explanation: I just did a exam that answer is x=8 :))

Answer:

The value of the condo was appraised at 36.4% lower than the selling price, which means it is now worth 100% - 36.4% = 63.6% of the selling price.

The selling price of the condo was $295,420, so the value of the condo now is $295,420 * 63.6% = $<<295420*0.636=188382.72>>188,382.72.

Therefore, the value of the condo now is $188,382.72.

Step-by-step explanation:

The value of m in the given equation 4x² -mx +9 will be 13.

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminates in mathematics. Polynomials come in various varieties. Monomial, binomial, and trinomial, respectively.

given an equation 4x² -mx + 9 = 0 and the question states that it has a root that is equal to 1

Since 1 is the root of this quadratic equation it will satisfy the equation

Substituting the values in the equation

4 - m + 9 = 0

m = 13

Therefore, In the given equation 4x² -mx +9 the value of m will be 13.

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Answer:

They are not. Blue whales are.

Step-by-step explanation:

A) The linear equation is:

y = (3/4)*x + 3

B) The sets with only positive elements are:

A general linear equation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Here, we do know that the y-intercept of the linear equation is (0, 3), then we know that b = 3.

Then the line is something like:

y = a*x + 3

We also know that the line passes through (-4, 0), then we can replace these values in the equation above to get:

0 = a*-4 + 3

4a = 3

a = 3/4

Then the linear equation is:

y = (3/4)*x + 3

The sets where all the numbers are positive are:

{x| x ∈ N}

Where N is the set of the natural numbers, these are all the integers equal to or larger than 1, so all are positives.

{y| 0 < y < 1}

There we can see that y must be larger than zero, so all the elements are positive.

{y| 3 ≤ y ≤22}

Here the elements are between 3 and 22, so all of these are positve.

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The cost of  one blueberry pie and one blackberry pie is $11.30 and $11.373 respectively.

In mathematics, an expression is a group of numbers and operations. The components of a mathematical expression that perform an operation are as follows:

Operands: The numbers used in an operation are called operands. Depending on the type of operation, different terms are applied to the operands.

Given Nathan sold 13 apples pies for $147,

cost of 13 apple pies  = $147

cost of 1 apple pie = 147/13 = $11.30

Lucy sold  7 blueberry pies and 11 apple pie $204.

7 blueberry  + 11 apple pie = $204

cost of 11 apple pie  = $124.384

cost of 7 blueberry = 204 - 124.384 = $79.615

cost of 1 blue berry = 79.615/7 = $11.373

Hence the cost of 1 apple pie is $11.30 and 1 blueberry is $11.373.

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The equation that corresponds to fraction   [tex]\frac{7^{-10} }{(7^{4} )(7^{0} )}[/tex] is [tex]\frac{1}{7^{14} }[/tex] . A phrase by itself could contain an action .

It is possible to multiply, divide, add, or subtract in math. An expression has the following structure: Expression: (Math Operator, Number/Variable, Math Operator). A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to compare expressions and phrases. In English, a phrase by itself could contain an action, but it doesn't constitute a full sentence.

given

[tex]\frac{7^{-10} }{(7^{4} )(7^{0} )} \\= \frac{1}{7^{4} } *\frac{1}{7^{10} } * 1\\= \frac{1}{7^{14} }[/tex]

The equation that corresponds to fraction   [tex]\frac{7^{-10} }{(7^{4} )(7^{0} )}[/tex] is  [tex]\frac{1}{7^{14} }[/tex] .

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Answer:

MEDIAN: 3 IRQ (Interquartile Range): 2

Step-by-step explanation:

To find median, divide the number of data points by 2 (5/2) and round to the nearest whole. So, 5/2 = 2.5 rounded to nearest integer, is 3.

To find the interquartile range, subtract Q1 (1) from Q3 (3) which equals 2.

I hope dis right!!

The perimeter of the isosceles triangle with altitude 30 inches and base 10 inches is calculated to be 70.82 inches

Perimeter of a triangle refers to the surface dimensions, this is calculated by the formula

Perimeter, P = a + b + c

where

a, b, c are sides of the triangle

The third side of the triangle will be calculated using Pythagoras theorem given by the  the formula

hypotenuse² = opposite² + adjacent²

The right triangle consist 1/2 the isosceles triangle base = 5 inches and the altitude = 30 inches

plugging the values as in the problem

let x be the required distance

x² = 30² + 5²

x² = 900 + 25

x² =  925

x = √925

x = 30.41 inches

Perimeter of the isosceles triangle

= 30.41 + 30.41 + 10

= 70.82 inches

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Answer:

He drank 1.2 liters

Step-by-step explanation:

1.5 X 0.8 (80%) = 1.2

Also the dude below also took my points when i asked a question :)

Answer:

$87025

Step-by-step explanation:

Net worth is assests minus liabilities

Answer:

Angles EAB = 85 degrees

Step-by-step explanation:

This my answer with the working steps...

Answer:

6.5

Step-by-step explanation:

10x = 65

x = 65/10

x = 6.5

Answer:

x=6.5

Step-by-step explanation:

So our equation is:

10x-10=55

The first thing we can do to find x is get it alone. We can do this by getting rid of the number value 10:

10x=65

Next we can divide both sides by 10 to get rid of the x value 10, so x is alone:

x=65/10

=

x=6.5

So your answer is 6.5

Hope this helps!

The numbers shown on the chart are the number of students for each category.

Looking at the line for Under $20,000 find the number located under University A.

The number located under University A for under $20,000 is 35

The answer would be 35

Answer:

right answer is 160/300

Step-by-step explanation:

Step-by-step explanation:

Let’s see … one division every 20 minutes? That would be like <grinding noise> three binary doublings per hour, right? Now for the tough part … three doublings per hour, for eight straight hours? <more grinding noises> … Is that even mathematically possible? After much thinking, I decide that the total number of binary doublings has to be in the neighborhood of no less than eight times three!

Would you believe that 224=16777216 ? While mathematically true, it is not the answer to the posted question… Since we started at 0 minutes, there are only 23 buddings inside eight hours … so the answer has to be 223=8388608 , right?

Wrong again, this time forgetting all about the newlybud bacteria generations, that all go on budding side by side of their ancestors …

Now that you’ve caught on to the basic idea, I leave it to you to figure out the real answer! Keep in mind that after 20 minutes, you have two budding bacteria to reckon with, for 440 minutes … after 40 minutes another two (for 420 minutes), and so on, down the line.

Hint: the answer still is not 16777216 …

Answer:

after 1 division,there is 3 cell

after 2 divisions,there is 9 cell.

after 3 divisions,there is 27 cell

The above data takes the form of Geometric sequence.

3,9,27......,last term

here,Common ratio(r)=9/3=27/9=3

and,first term(a)=3

Let, n be the no.of divisions.

then, n=8 hrs/20 min=480 min/20min=24

Now,from the G.S,

last term=ar^n-1

=3×3^24-1

=9²³

Hence,9²³ organisms will there be after 8 hours

It can be written as 8.86293812×10²¹ as well

*Mark me brainliest

Answer:

56

Step-by-step explanation:

So you just need to find 7 + what is equal to 63. To find this we have to do inverse operation, which means the opposite operation. So, we do 63-7 which is equal to 56. Therefore, the solution to the equation, or x is equal to 56 (C).

Hope this helps !!

-Ketifa

Answer: The function G(x) = [x] returns the greatest integer less than or equal to x. This means that for any value of x, G(x) will be the largest integer that is less than or equal to x. For example, G(3.5) = 3 and G(5) = 5.

The function R(x) = x/+2, x is any real number, this function returns the value of x incremented by 2. In other words, it is the result of adding 2 to x.

On the other hand, the graph of R(x) is a line that goes through the point (0, 2) and has a slope of 1, this means that for every change of 1 unit in the x-axis, the y-axis will change by 1 unit as well.

When we compare the two graphs, we can see that the graph of R(x) is shifted up 2 units from the graph of G(x) . If the graph of G(x) is thought of as the "ground", the graph of R(x) is "floating" two units above it. Also, the graph of R(x) is continuous while the graph of G(x) is not.

To sum up:

-The graph of G(x) is a step function, which start at the negative infinity and jumps up to the next integer at every point.

The graph of R(x) is a line that goes through the point (0, 2) and has a slope of 1

-R(x) is always two units above G(x) , and is a continuous function, while G(x) is not.

Step-by-step explanation:

Answer:

180 ft

Step-by-step explanation:

If the height is 36 inches, and two inches represents 10 feet, then there are 18 sets of ten feet on the actual tower, if that makes sense. That means that the actual tower is 180 feet tall.

Answer:

If the pharmaceutical sales representative meets her target for Medication A, she will receive 60% of the $20,800 bonus, or $12,480. When added to her base salary of $68,400, her total compensation for the year would be $80,880.

Step-by-step explanation:

Answer:

The total would be 99,620

Step-by-step explanation:

29400*0.80=23520

Add the amount to the base salary

76100+23520=99,620

Answer:

Triangles DEF and JKL are similar to triangle ABC because they have corresponding angles with the same measure.

Step-by-step explanation:

•Triangles DEF and JKL are similar to triangle ABC because they have corresponding angles with the same measure.

•The Triangle GHI is not similar to triangle ABC because the measure of angle G does not match the measure of angle A.

•The Triangle MNO is not similar to triangle ABC because the measure of angle N does not match the measure of angle B.

• The Triangle POR is not similar to triangle ABC because the measure of angle R does not match the measure of angle A or B.

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Answer:

Your scale factor would be 2

Step-by-step explanation:

I really hope this helps! :)

Step-by-step explanation:

The answer is OPTION C

Find the Inverse of a 3x3 Matrix.

First

Find the Determinant of A(The coefficients of e

Proceed towards finding the CO FACTOR of the 3x3 Matrix.

+. - +

A= [ 1 -1 -1 ]

[ -1 2 3 ]

[ 1 1 4 ]

The determinant of this is 1.

Find the co factor

| 2 3 | |-1 3 | |-1 2 |

| 1. 4. | |1 4 | |1. 1 |

|-1. -1 | |1 -1 | |1 -1

| 1. 4 | |1. 4| |1 1|

|-1. -1 | |1 -1 | |1. -1

|2. 3| |-1. 3| |-1 2|

After Evaluating The Determinant of each 2x 2 Matrix

You'll have

[ 5 7 -3]

[3 5 -2 ]

[-1 -2 1]

Reflect this along the diagonal( Keep 5,5 -2)

Then switching positions of other value

No need of Multiplying by the determinant because its value is 1 from calculation.

After this

Our Inverse Matrix Would be

[ 5 3 -1 ]

[7 5 -2 ]

[ -3 -2 1]

THIS IS OUR INVERSE.

SO

OPTION C