Is the function f(x) = 1 /x− 1 continuous at x = 1? Explain.
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[tex]~~~~~1-x < 5\\\\\implies -x < 5-1\\\\\implies -x < 4\\\\\implies x > -4\\\\\text{Interval notation:}~ (-4, \infty)[/tex]

Answer:

x = ± 6

Step-by-step explanation:

Hello!

The value of x is 6 or -6.

Hi...

[tex]\texttt{5x}[/tex]² [tex]\texttt{= 180}[/tex]

[tex]\texttt{5x}[/tex]² [tex]\texttt{= 180}[/tex]

Divide both sides by 5

[tex]\hookrightarrow{\mathtt{\frac{5x^2}{5}} = {\mathtt{\frac{180}{5}}[/tex]

Simplify:

[tex]\hookrightarrow{\mathtt{x^2 = 36}[/tex]

[tex]\hookrightarrow{\mathtt{For \: x^2 \: = f(a) \: the \: solutions \: are \: x = \sqrt{f(a)}}[/tex] , [tex]\mathtt{- \sqrt{f(a)}}[/tex]

[tex]\hookrightarrow{\mathtt{x = \sqrt{36}}[/tex] , [tex]\mathtt{x = -\sqrt{36}}[/tex]

Factor the number: 36 = 6²

[tex]\mathtt{= \sqrt{6^2}}[/tex]

Apply radical rule: [tex]\mathtt{\sqrt[n]{a^n} \: = a}[/tex]

[tex]\mathtt{\sqrt{6^2} = 6} \\\mathtt{= 6}[/tex]

- [tex]\sqrt{36} = -6[/tex]

[tex]\boxed{\fbox{\bf{x = 6 , x = -6}}}[/tex]

Hope It Helps You...

Answer:

c. $5 off

Step-by-step explanation:

If jasper buys 10 bagels $2 each then it'll cost $20. With a free bagel it'll deduct $2. With 10% off it'll deduct $2. Buy 8, get 2 free deducts $4. Therefore $5 off is the most

Answer:

5,000,000^2

Step-by-step explanation:

half of 10,000,000 sqrt of 2

Answer:

6 is the answer

Hope that helps.
Let me know if im wrong :)

Step-by-step explanation:

Answer:

The first choice

Step-by-step explanation:

7/8 x + 3/4 = -6

6 (x/8) + 3/4 = -6

Answer:

c

Step-by-step explanation:

y goes up by 4, so the each step is by 4, so that is the slope, which is the number before x, and then you subtract 4 to find the y-intercept, and 3-4=-1

The property of the questions are correctly stated below.

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Answer:

See below

Step-by-step explanation:

[tex]f(x)=3x^2+6x-24\\\\f(x)=3(x^2+2x-8)\\\\f(x)+3(9)=3(x^2+2x-8+9)\\\\f(x)+27=3(x^2+2x+1)\\\\f(x)=3(x+1)^2-27[/tex]

Here, we can see that the vertex of the parabola is [tex](-1,-27)[/tex] when we compare to the equation [tex]y=(x-h)^2+k[/tex] with vertex [tex](h,k)[/tex].

A second point you could plot is the y-intercept, when [tex]x=0[/tex]:

[tex]f(0)=3(0+1)^2-27\\\\f(0)=3-27\\\\f(0)=-24[/tex]

So, your y-intercept is [tex](0,-24)[/tex].

The inequality that is correctly graphed is the one in option B.

Remember that if we have symbols like ≤ or ≥, we graph a solid circle, while if we use symbols like > or <, we need to use an open circle.

If we write:

x < -3

Then we must have an orange line to the left of x < -3

Finally, the option that you marked is wrong.

Why?

There it says that:

"x < -3 and x > 1"

The "and" means that x meets both properties at the same time, which is impossible.

The correct option is the one that says:

"x < -3 or x > 1".

The "or" means that x needs to meet only one of the two conditions, not both at the same time.

Then the correct option is B.

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The probability that the ball we remove at the 11th round is blue will be 0.6.

From the information given, we remove a random ball and replace it with a new red ball. for example, after the first round we have 9 blue balls and one red ball.

Since we have 9 blue balls and remove one every round. Let's assume that the number of blue and red balls will be 6 and 4 respectively in the 11 the round

Therefore, the probability that the ball we remove at the 11th round is blue will be:

= 6/(6 + 4)

= 6/10

= 0.6

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Step-by-step explanation:

this looks totally like

f(x) = 1/3 x - 3

to me.

because

f(0) = -3

f(3) = -2

f(6) = -1

so, f(9) = 1/3 × 9 - 3 = 3 - 3 = 0

f(9) = 0

you did not list that as answer option, but that is the correct answer.

A graphic logo that depicts the meaning of any warning or sign through pictorial illustrations is called a pictogram. It can be used in chemicals, laboratories, geography or tourism. The label should have: Flammable and Health Hazard!

The pictogram can be explained as: According to the above description, the label sign should have a warning sign of flammable as it can catch and cause fire, a health hazard as it can cause corrosion, carcinogenic and irritation followed by an exclamation mark.

The flammable sign depicts that the substance can cause and catch fires also it can contain pyrophoric. It is cancer-causing, respiratory irritant and toxic hence is hazardous to health.

The exclamation mark is used at the end of the sentence for showing awareness and to convey the meaning of the sign.

Therefore, Flammable and Health Hazard! the sign should be used.

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Answer:

4/5

Step-by-step explanation:

Given,

Area of the triangle = 1/4 square meters

From the diagram,

Height = 2/5 m

To find : Length of the base

Formula : -

A = bh/2

Here,

A denotes Area

b denotes Base

h denotes Height

A = 1/4

h = 2/5

A = bh/2

Cross multiply,

A * 2 = bh

2A = bh

2 * (1/4) = b * (2/5)

(1 * 2)/4 = (b * 2)/5

2/4 = 2b/5

1/2 = 2b/5

Cross multiply,

1 * 5 = 2 * 2b

5 = 4b

b = 4/5 meters

Hence,

The length of the base is 4/5 meters.

The length of the base of the triangle is 5/4 meters.

A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.

Sum of the interior angles of a triangle is 180 degrees.

The formula to find the area of the triangle is,

Area = [tex]\frac{1}{2}[/tex] × base × height

Given,

Area of the given triangle = 1/4 square meters

Height = 2/5 meters

Substituting in to the formula,

[tex]\frac{1}{2}[/tex] × base × 2/5 = 1/4

1/5 × base = 1/4

Base = 5/4 meters

Hence the base of the triangle is 5/4 meters.

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Answer:

V=lwh

3

Step-by-step explanation:

Answer:

Mean: 4

Median : 4

Mode: 1, 2, 3, 4, 5, 6, 7

Step-by-step explanation:

Measure of center is:

Mean: Average

Median: Middle number

Mode: Often number

Mean: Add all number then divide by the total number in data set.

1 + 2 + 3 + 4 + 5 + 6 + 7 = 28

28/7 = 4

Median: Middle number

1,2,3,4,5,6,7

Mode: most often number

1,2,3,4,5,6,7

Kavinsky

Answer:

(a)no mode

(b)mean= 4

(c)median= 4

Step-by-step explanation:

the measure of centre are the mode, mean and median

mode: this is the heighest occuring number or the number with the heighest frequency.

mean: this is the average number. it's obtained by adding the data values in a set of numbers and dividing the sum by the number of data items.

meadian: this is the middle number when the data is ordered or when the data is arranged in ascending or descending order.

from the data,

mode: no number occured more than the other. therefore, there is no mode

mean = 1+2+3+4+5+6+7 = 28/7= 4

median= 1,2,3,4,5,6,7

the middle numbers is 4

Answer:

x = -1 or x = 8/3

Step-by-step explanation:

3x² - 8 = 5x

3x² - 5x - 8 = 0

3x² - 8x + 3x - 8 = 0

(Here you find two numbers which have a sum of        -5 and a product of 3×-8= -24. These two numbers are -8 and 3. -8 + 3 = -5 and -8 × 3 = -24.)

(3x² - 8x) (3x - 8) = 0

x(3x - 8) +1(3x - 8) = 0

(x + 1) (3x - 8) = 0

x + 1 = 0     OR      3x - 8 = 0

x = -1                      3x = 8

                              x = [tex]\frac{8}{3}[/tex]

Step-by-step explanation:

0.777... is rational since it can be put in fraction form which is 7/9

note: if something can be put as an integer/integer its rational

Answer:

[tex]\frac{4}{n^{2} }[/tex]

Step-by-step explanation:

(2nm⁻³) * 2m³n⁻³

First, focus on the coefficients, 2*2 = 4.

Now the n, n * n⁻³ = n⁻²

Now the m, m⁻³ * m³ = m⁰ = 1

Now multiply altogether, 4n⁻²(1) = [tex]\frac{4}{n^{2} }[/tex]

Answer:

V=whl=3·5·8=120

Step-by-step explanation:

Just use l x w x h and there you go.

Answer:

Hi! The answer is x=16

The missing probability from the line in the diagram attached is 0.5.

The number line is a graduated straight line system showing the value of each real number from (-∞, +∞).

The probability of a number line in the diagram below is halfway (middle) between the impossible event and a certain event.

Thus,

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Answer:

7/6

Step-by-step explanation:

To find the slope you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points.

so doing that i get 7/6

Hope This Helped

The median of the data set will be 15.5. The data set is in between the 1 to 25.

Median is such a number for the arranged data set in ascending or descending order, such that to its left and to its right belong the same number of observations.

The data set between the number is;

1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25

The value of IQR for data set is;

First Quartile Q1 = 6.5

Second Quartile Q2 = 13

Third Quartile Q3 =19.5

The median of the data set is;

[tex]\rm Median= \frac{15+16}{2} \\\\ Median= 15.5[/tex]

Hence, the median of the data set will be 15.5.

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Answer:

Step 1: area is base × height

Step 2: 36cm2

Step-by-step explanation:

Base × height is 9 and 4 and 9×4 = 36cm2

Hope this helps :)

Using an exponential function, it is found that there will be 32,866 pigeons in 13 years.

An increasing exponential function is modeled by:

[tex]A(t) = A(0)(1 + r)^t[/tex]

In which:

The initial value and the growth rate are given by:

A(0) = 9520, r = 0.1.

Hence the function is given by:

[tex]A(t) = 9520(1.1)^t[/tex]

Hence in 13 years, the amount of pigeons will be of:

[tex]A(13) = 9520(1.1)^{13} = 32866[/tex]

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An angle cannot be the complement of one angle and the supplement of another angle at the same time. Then the given statement is false.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

Complementary angle - Two angles are said to be complementary angles if their sum is 90 degrees.

An angle cannot be the complement of one angle and the supplement of another angle at the same time.

Then the given statement is false.

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Answer:

7. 630

8. I'm not sure on this one-

9. 1331

Step-by-step explanation:

So for a rectangular prism the formula is l x w x h (length times width times height) Which would be 14 * 5 * 9 which equals 630

For the triangular prism, I forgot the formula

For the cube, you are given 1 number, 11, since it's a cube all lengths are the same so you do 11 to the power of 3 = 1331