Find the slope of the line grapef below

Given

[tex]f(x) = \begin{cases} -x^2 - 1 & \text{if }x \neq 5 \\ -3 & \text{if }x=5 \end{cases}[/tex]

we have

[tex]\displaystyle \lim_{x\to5} f(x) = \lim_{x\to5} (-x^2-1) = -5^2-1 = \boxed{-26}[/tex]

since we are approaching [tex]x=5[/tex], so effectively [tex]x\neq 5[/tex] and we use the definition of [tex]f(x)[/tex] under that condition.

Answer:

51   74

Step-by-step explanation:

x = smaller

x +23 = larger

added together   (x   + x+23)    equal to 28 less than 3x      = 3x-28

x    + x+23  = 3x-28      subtract 2x from both sides of the equation

   23 = x -28      add 28 to both sides

 51 = x      then the larger   =  51 + 23 = 74

Answer:

51 and 74

Step-by-step explanation:

Let the smaller of the two numbers be represented by x. The larger of the two numbers is 23 greater than the smaller, and therefore can be written as x + 23.

First, we can write the sum of the two numbers in terms of the smaller number. "three times the smaller" is 3x, and "28 less" is 3x-28.

Therefore our equation is:

[tex]x+x+23=3x-28[/tex]

Start by adding like terms

[tex]2x+23=3x-28[/tex]

Subtract 23 from both sides

[tex]2x=3x-51[/tex]

Subtract 3x from both sides

[tex]-x=-51[/tex]

Divide both sides by -1

[tex]x=51[/tex]

The larger term is: [tex]x+23\Rightarrow51+23\Rightarrow74[/tex]

[tex]51+74=125[/tex]

[tex]3(51)-28=153-28=125[/tex]

[tex]125=125[/tex]

The smaller number is 51 and the larger number is 74

Therefore the hour hand travels 40.192in in 5 hours

A sector is said to be a part of a circle made of the arc of the circle along with its two radii.

The formula for calculating the area of a sector is expressed as;

A = r²β/2

where

r is the radius of the circle

β is the angle subtended

Since the the hour hand travel during 5 hours, the subtended angle by the sector will be;

β = 360/5

β = 72 degrees

Given the following parameters

r = 16/2

r = 8in

Substitute into the formula

A = 8²(72π)/360
A = 40.192in

Therefore the hour hand travels 40.192in in 5 hours

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Answer:

The function is increasing from x = 0 to x = 1.

Step-by-step explanation:

A function is increasing when the y-value increases as the x-value increases.

A function is decreasing when the y-value decreases as the x-value increases.

From x = -2 to x = -1 the function is decreasing as the y-value decreases as the x-value increases:  

From x = -1 to x = 0 the function is increasing as the y-value increases as the x-value increase:  

From x = 0 to x = 1 the function is increasing as the y-value increases as the x-value increase:  

Answer:

6.75

Step-by-step explanation:

         Distance in Miles

MPH -------------------------

         Time in Hours

27/2 = 13.5. That is 1 hour. Half that and you get 6.75 MP1/2H

Answer:

  x = 3√3

  y = 6

Step-by-step explanation:

The geometric mean relations between segments intersecting the long hypotenuse and its parts can be used to find the values of interest.

  x = √(9·3) = 3√3

  y = √((9+3)·3) = 6

__

Additional comment

These right triangles are all similar, so corresponding sides are proportional. When the proportions are solved for a missing side, a geometric mean relation results. (The geometric mean of 'a' and 'b' is √(ab).)

Identify the segments above the horizontal line as w, x, y. (x and y are already identified in this figure.)

The ratio of short side to long side is ...

  x/9 = 3/x   ⇒   x² = 9·3   ⇒   x = √(9·3)

The ratio of short side to hypotenuse is ...

  y/(9+3) = 3/y    ⇒   y² = (9+3)·3   ⇒   y = √((9+3)·3)

Likewise, the ratio of long side to hypotenuse is ...

  w/(9+3) = 9/w   ⇒   w² = (9+3)·9   w = √((9+3)·9) = 6√3

Based on the given data; the table represent an inverse variation and the equation that model the data in the table is y = 8/x

y = k × x

4 = k × 2

4 = 2k

k = 4/2

k = 2

when y = 2 and x = 4

y = k × x

= 2 × 4

y = 8

y = k/x

4 = k / 2

8 = k

when y = 2 and x = 4

y = k/x

2 = k/4

2 × 4 = k

k = 8

So,

y = k/x

y = 8/x

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The sum of the given expression expressed as a quadratic equation is 10x^2 + 13x + 11

Expressions are equations separated by mathematical signs. This expressions are known to contains certain unknowns

Given the following expression

10x^2 +7x+6 and 6x + 5

We are to take the sum of both expression to have:

f(x) = 10x^2 +7x+6 + 6x + 5

Collect the like terms

f(x) = 10x^2 + 7x + 6x + 6 + 5

f(x) = 10x^2 + 13x + 11

Hence the sum of the given expression expressed as a quadratic equation is 10x^2 + 13x + 11

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Answer:

2, x - 2, x + 4

Step-by-step explanation:

The factors of the given quadratic expression, 2x² - 4x - 16, are 2, (x +2), and (x -4)

From the question, we are to determine the each of the factors of the given quadratic expression

The given quadratic expression is

2x² - 4x - 16

Factoring

2x² - 4x - 16

First, factor out 2

That is,

2(x² - 2x - 8)

Now, we will factor x² - 2x - 8
x² - 2x - 8

x² - 4x + 2x - 8

x(x - 4) +2(x -4)

(x +2)(x -4)

Thus,

2x² - 4x - 16  = 2(x +2)(x -4)

Hence, the factors of the given quadratic expression, 2x² - 4x - 16, are 2, (x +2), and (x -4)

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[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{Formula \rightarrow \dfrac{1}{2} \times \bold{b}ase\times\bold{h}eight\times \bold{l}ength}[/tex]

[tex]\mathsf{Your\ equation\ should\ look\ like\rightarrow \dfrac{1}{2}\times12\times8\times27}[/tex]

[tex]\mathsf{Solving\rightarrow \dfrac{1}{2}\times12\times8\times27}[/tex]

[tex]\mathsf{ \dfrac{1}{2}\times12\times8\times27}[/tex]

[tex]\mathsf{= \dfrac{1}{2}\times\dfrac{12}{1}\times\dfrac{8}{1}\times\dfrac{27}{1}}[/tex]

[tex]\mathsf{= \dfrac{1\times12\times8\times27}{2\times1\times1\times1}}[/tex]

[tex]\mathsf{= \dfrac{12\times8\times27}{2\times1\times1}}[/tex]

[tex]\mathsf{= \dfrac{96\times27}{2\times1}}[/tex]

[tex]\mathsf{= \dfrac{2,592}{2}}[/tex]

[tex]\mathsf{= 2.592\div2}[/tex]

[tex]\mathsf{= 1,296}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{Option\ C.\ }\frak{1,296\ cm^3}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

In four days,the total change in value -$12.60.

According to the statement

we have given that the value of an investment changed at a rate of -$3.15 each day. And we have to find that the after how many days the change in value reaches at the -$12.60.

So, here we use division rule to find the solution.

The given change value is :

-$3.15 each day.

The desired change value is :

-$12.60.

Number of days required = -12.60 / -3.15

Number of days required = 12.60 / 3.15

Number of days required = 4 days.

So, in four days the change in value reaches at the desired value of change.

So, In four days,the total change in value -$12.60.

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Answer:

D

Step-by-step explanation:

When you reflect the point it goes to point (-2,5).  From that point, go 4 left and 8 down.  That gets you to (-2,-3)

Answer: Choice D

[tex]\frac{-19}{\text{x}-5}[/tex]

=================================================

Work Shown:

[tex]\frac{\text{x}^2+10\text{x}+25}{\text{x}+5} - \frac{\text{x}^2-6}{\text{x}-5}\\\\\\\frac{(\text{x}+5)(\text{x}+5)}{\text{x}+5} - \frac{\text{x}^2-6}{\text{x}-5}\\\\\\\frac{\text{x}+5}{1} - \frac{\text{x}^2-6}{\text{x}-5}\\\\\\\frac{(\text{x}+5)(\text{x}-5)}{1(\text{x}-5)} - \frac{\text{x}^2-6}{\text{x}-5}\\\\\\[/tex]

[tex]\frac{\text{x}^2-25}{\text{x}-5} - \frac{\text{x}^2-6}{\text{x}-5}\\\\\\\frac{\text{x}^2-25-(\text{x}^2-6)}{\text{x}-5}\\\\\\\frac{\text{x}^2-25-\text{x}^2+6}{\text{x}-5}\\\\\\\frac{-19}{\text{x}-5}\\\\\\[/tex]

This matches with choice D as the final answer.

Keep in mind that we can only subtract fractions when the denominator is the same. The rule is [tex]\frac{a}{c}-\frac{b}{c} = \frac{a-b}{c}[/tex]

The value of [tex](102)^3[/tex] exists 1061208.

Let us rewrite [tex](102)^3[/tex] as [tex](100+2)^3[/tex]

Now utilizing the identity [tex](a+b)^3=a^3+b^3+3ab(a+b)[/tex], we get

a = 100 and b = 2 then substitute the values of a and b then

[tex](100+2)^3=100^3+2^3+[(3\times100\times2)(100+2)][/tex]

= 1000000 + 8 + (600 × 102)

= 1000000 + 8 + 61200

= 1061208

Hence, [tex](102)^3=1061208[/tex]

Therefore, the value of [tex](102)^3[/tex] exists 1061208.

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[tex]\boldsymbol{\sf{Therefore \to \ 5.75\not{h}*\dfrac{60 \ min}{1\not{h}} =345 \ min }}[/tex]

5.75 hours is equal to 345 minutes.

To complete the statements;

The consecutive interior angles is supplementary

The alternate interior angles is congruent

The properties are;

Consecutive interior angles are supplementary

Alternate interior angles are congruent

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In step 2, the property of equality applied was addition property of equality.

In step 4, the property of equality applied was multiplication property of equality.

The addition property of equality states that, to move a negative number over to the other side of an equation, add the number to both sides of the equation. For example, given the equation: a - c = b, to move c over to the other side of the equation, add c to both sides of the equation. we will have:

a - c + c = b + c

a = b + c.

According to the multiplication property of equality, if we have, a/c = b, to isolate a, we would multiply both sides of the equation by c. Thus:

a/c × c = b × c

a = bc

In the table given, in step 2, 6 was added to both sides of the equation. This means the property of equality that was applied was: addition property of equality.

In step 4, both sides of the equation was multiplied by -2. Thus, the property of equality that was applied was: multiplication property of equality.

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Answer: step 2 - addition property

              step 4 - multiplication property

Step-by-step explanation:

The order of magnitude for total attended for a high school football team is 3

The given parameters are:

Average number of fan = 1000

Number of home games = 5

The total number of fans in the 5 games is:

Total number of fans = Average number of fan * Number of home games

Substitute known values in the above equation

Total number of fans = 1000 * 5

Express 1000 as 10^3

Total number of fans = 10^3 * 5

Rewrite the equation as:

Total number of fans = 5 * 10^3

The power of 10 represents the order of magnitude

Since the power of 10 is 3, the order of magnitude is 3

Hence, the order of magnitude for total attended for a high school football team that averages 1,000 fans for each of its 5 home games is 3

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Answer:

7/5

Step-by-step explanation:

We can rewrite the given time as:

First, remember that:

60s = 1 min

Then to write that amount in minutes, we just need to divide by 60, so we get:

(4.22x10^17)/60  mins=  7.03x10^15 mins

Now, remember that:

1 hour = 3600s

Then to get the time in hours, we need to divide by 3600:

(4.22x10^17)/3600 h = 1.17x10^14 hours.

Similarly, you can change to any time unit that you want, for example:

1 day = 24*3600 s

Then the time in days is:

(4.22x10^17)/(24*3600) days = 4.88x10^12 days.

And so on.

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Recall the binomial theorem.

[tex](a+b)^n = \displaystyle \sum_{k=0}^n \binom nk a^{n-k} b^k[/tex]

1. The binomial expansion of [tex]\left(1+\frac x3\right)^7[/tex] is

[tex]\left(1 + \dfrac x3\right)^7 = \displaystyle\sum_{k=0}^7 \binom 7k 1^{7-k} \left(\frac x3\right)^k = \sum_{k=0}^7 \binom 7k \frac{x^k}{3^k}[/tex]

Observe that

[tex]k = 1 \implies \dbinom 71 \left(\dfrac x3\right)^1 = \dfrac73 x[/tex]

[tex]k = 2 \implies \dbinom 72 \left(\dfrac x3\right)^2 = \dfrac73 x^2[/tex]

When we multiply these by [tex]8-9x[/tex],

• [tex]8[/tex] and [tex]\frac73 x^2[/tex] combine to make [tex]\frac{56}3 x^2[/tex]

• [tex]-9x[/tex] and [tex]\frac73 x[/tex] combine to make [tex]-\frac{63}3 x^2 = -21x^2[/tex]

and the sum of these terms is

[tex]\dfrac{56}3 x^2 - 21x^2 = \boxed{-\dfrac73 x^2}[/tex]

2. The binomial expansion is

[tex]\left(2a - \dfrac b2\right)^8 = \displaystyle \sum_{k=0}^8 \binom 8k (2a)^{8-k} \left(-\frac b2\right)^k = \sum_{k=0}^8 \binom 8k 2^{8-2k} a^{8-k} b^k[/tex]

We get the [tex]a^6b^2[/tex] term when [tex]k=2[/tex] :

[tex]k=2 \implies \dbinom 82 2^{8-2\cdot2} a^{8-2} b^2 = 28 \cdot2^4 a^6 b^2 = \boxed{448} \, a^6b^2[/tex]

2r + t + r

3r + t

The correct answer is C - None of the Above.

When we combine like terms, we combine terms that have the same variables but different coefficients. We cannot add 2r and t because r and t are not the same variables.

Hope this helps!

Answer:

None of the above

Step-by-step explanation:

Because the answer is 3r + t

Natasha got the power right. The power is 295 hp.

t = 5.825∛w / p

where,

Therefore,

t = 13.4 s

p = 3590

13.4 = 5.825∛ 3590 / p

cube both sides

13.4³ = 5.825³ × 3590 / p

2406.104 = 197.645890625 × 3590 / p

cross multiply

2406.104 p = 709548.747344

p = 709548.747344 / 2406.104

p = 294.895294361

p = 295 hp

Therefore, Natasha got the power right

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P(A and B) expressed in the simplest form is (B) 2/21.

To express P(A and B) in the simplest form:

Therefore, P(A and B) expressed in the simplest form is (B) 2/21.

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The complete question is given below:

A bag contains 4 black tiles, 5 white tiles, and 6 blue tiles. Event A is defined as drawing a black tile from the bag on the first draw, and event B is defined as drawing a white tile on the second draw.

If two tiles are drawn from the bag, one after the other without replacement, what is P(A and B) expressed in the simplest form?

A. 4/45

B. 2/21

C. 4/15

D. 5/14

The focus of a parabola can be found by adding p to the y-coordinate k if the parabola opens up or down. (h, k + p) exist (2, 0).

Given: [tex]$y=\frac{1}{8} (x^{2} -4x-12)[/tex]

[tex]$y=\frac{x^{2}}{8}-\frac{x}{2}-\frac{3}{2}$$[/tex]

Use the form [tex]$a x^{2}+b x+c$[/tex] to find the values of a, b, and c.

[tex]$a=\frac{1}{8}$[/tex], [tex]$b=-\frac{1}{2}$[/tex] and [tex]$c=-\frac{3}{2}$[/tex]

Consider the vertex form of a parabola [tex]$a(x+d)^{2}+e$[/tex]

To estimate the value of d using the formula [tex]$d=\frac{b}{2 a}$[/tex].

Substitute the values of a and b into the formula

[tex]$d=\frac{-\frac{1}{2}}{2\left(\frac{1}{8}\right)}$$[/tex]

[tex]$d=-\frac{1}{2} \cdot \frac{1}{\frac{2}{8}}$$[/tex]

Cancel the common factor 2 and 8.

[tex]$d=-\frac{1}{2} \cdot \frac{1}{\frac{1}{4}}$$[/tex]

[tex]$d=-\frac{1}{2}(1 \cdot 4)$$[/tex]

Multiply the numerator by the reciprocal of the denominator.

[tex]$d=-\frac{1}{2} \cdot \frac{1}{2\left(\frac{1}{8}\right)}$$[/tex]

[tex]$d=-\frac{1}{2} \cdot \frac{1}{\frac{2}{8}}$$[/tex]

equating, we get

[tex]$d=-\frac{1}{2}(1 \cdot 4)$$[/tex]

[tex]$d=-\frac{1}{2} \cdot 4$$[/tex]

The value of [tex]$d=-2$[/tex]

Find the value of e using the formula [tex]$e=c-\frac{b^{2}}{4 a}$[/tex].

Substitute the values of c, b and a into the above formula, and we get

[tex]$e=-\frac{3}{2}-\frac{\left(-\frac{1}{2}\right)^{2}}{4\left(\frac{1}{8}\right)}$$[/tex]

simplifying the equation, we get

[tex]$e=-\frac{3}{2}-\frac{(-1)^{2}\left(\frac{1}{2}\right)^{2}}{4\left(\frac{1}{8}\right)}$[/tex]

Apply the product rule to [tex]$\frac{1}{2}$[/tex].

[tex]$e=-\frac{3}{2}-\frac{1\left(\frac{1}{4}\right)}{4\left(\frac{1}{8}\right)}$$[/tex]

[tex]$e=-\frac{3}{2}-\frac{\frac{1}{4}}{4\left(\frac{1}{8}\right)}$$[/tex]

[tex]$e=-\frac{3}{2}-\frac{\frac{1}{4}}{\frac{4(1)}{8}}$$[/tex]

simplifying the above equation, we get

[tex]$e=-\frac{3}{2}-\frac{\frac{1}{4}}{\frac{4 \cdot 1}{4 \cdot 2}}$$[/tex]

[tex]$e=-\frac{3}{2}-\frac{\frac{1}{4}}{\frac{4 \cdot 1}{4 / 2}}$$[/tex]

[tex]$e=-\frac{3}{2}-\frac{\frac{1}{4}}{\frac{1}{2}}$$[/tex]

Multiply the numerator by the reciprocal of the denominator.

[tex]$e=-\frac{3}{2}-\left(\frac{1}{4} \cdot 2\right)$$[/tex]

[tex]$e=\frac{-3-1}{2}$$[/tex]

[tex]$e=\frac{-4}{2}=2$[/tex]

Substitute the values of [tex]$a, d_{t}$[/tex] and e into the vertex form [tex]$\frac{1}{8}(x-2)^{2}-2$[/tex].

Set y equal to the new right side.

[tex]$y=\frac{1}{8} \cdot(x-2)^{2}-2$[/tex]

Use the vertex form, [tex]$y=a(x-h)^{2}+k$[/tex], to determine the values of a, h, and k.

[tex]$a=\frac{1}{8}$[/tex]

[tex]$h=2$[/tex]

[tex]$k=-2$[/tex]

Find the vertex [tex]$(h, k)$[/tex]

[tex]$(2,-2)$[/tex]

Find [tex]$\boldsymbol{p}$[/tex], the distance from the vertex to the focus.

To estimate the distance from the vertex to a focus of the parabola [tex]$\frac{1}{4 a}$[/tex]

Substitute the value of a into the formula

[tex]$\frac{1}{4 \cdot \frac{1}{8}}=\frac{1}{\frac{4(1)}{8}}$[/tex]

[tex]$\frac{1}{\frac{4 \cdot 1}{4-2}}=\frac{1}{\frac{4 \cdot 1}{4 \cdot 2}}$[/tex]

[tex]$\frac{1}{\frac{1}{2}}=2$[/tex]

The focus of a parabola can be found by adding p to the y-coordinate k if the parabola opens up or down. (h, k + p)

Substitute the known values of h, p, and k into the formula, we get

(2,0).

Therefore, the correct answer is (2,0).

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The equation can be used to model the number of subscribers, y, in the city t years after 2000 is  y = 200,000(1+60)t.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.

The first step is to calculate the percentage increase for each year.

If the subscribers increase by 60%, it means that the subscribers will be (100+60)% of the previous year.

(100+60)% = (100/100 + 60/100)

                 =  (1 + 0.6)

After 2,000, the subscribers will be 200,000×(1+0.6).

For the following years the 200,000×(1+0.6)t

So, the value of y will be given by,

Y=200,000(1+0.6)t

Hence,The equation Y=200,000(1+0.6)t .

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Correct answer is C. the number of times blue ball appears is 56

Given,

probability of picking a green ball is 0.5,

the probability of picking a blue ball is 0.4,

the probability of picking a red ball is 0.1.

a ball is picked and replaced = 140

Probability = (the number of ways of achieving success) / (the total number of possible outcomes)

Probability provides information about the likelihood that something will happen. Meteorologists, for instance, use weather patterns to predict the probability of rain. In epidemiology, probability theory is used to understand the relationship between exposures and the risk of health effects.

For this item, the number of times that we should expect that a blue ball is picked should be the product of the number of times  and the probability of picking a blue ball (which is equal to 0.4)

                            = (140)(0.4) = 56

Therefore, we should expect that the blue ball will be picked 56 times.

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The area around the given curve according to the green theorem is [tex]F. dr = 0[/tex].

According to the statement

we have to find the area enclosed by the simple closed curve that encloses the origin.

So, We know that the

The given equation is

[tex]f(x,y) = \frac{2xyi + (y^{2} - x^{2} ) j}{(x^{2} + y^{2} )^{2} }[/tex]

and

If function is in form of,

[tex]F = Pi + Qj[/tex]

and C is any positively oriented simple closed curve that encloses the origin.

Then,by use of Green's theorem

Do the partial differentiation of the given function

Then

[tex]\frac{dQ}{dx} = \frac{2x^{3} - 6xy^{2}}{(x^{2} + y^{2} )^{3}}[/tex]

and

[tex]\frac{dP}{dy} = \frac{2x^{3} - 6xy^{2}}{(x^{2} + y^{2} )^{3}}[/tex]

On substitution in Green's theorem,

We get the value

[tex]F. dr = 0[/tex]

From this it is clear that the area around the given curve is zero.

So, The area around the given curve according to the green theorem is [tex]F. dr = 0[/tex].

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