7. Show all work to identify the discontinuity and zero of the function f of x equals 5 x over quantity x squared minus 25.

8. The aquarium has 6 fewer yellow fish than green fish. 40 percent of the fish are yellow. How many green fish are in the aquarium? Show your work.

Answer:

5

Step-by-step explanation:

Check the picture below.

[tex]\bf \textit{ellipse, horizontal major axis} \\\\ \cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=0\\ k=0\\ a=25\\ b=15 \end{cases}\implies \cfrac{(x-0)^2}{25^2}+\cfrac{(y-0)^2}{15^2}=1\implies \cfrac{x^2}{625}+\cfrac{y^2}{225}=1[/tex]

Answer:

172,146

Step-by-step explanation:

you can use the exponential growth formula and get y=127000(1.052)^6. after that, you can just solve (make sure you use PEMDAS) and get 172,146.

The population in 2020 will be 177800.

The annual average rate of change of population size, for a given country, territory, or geographic area, during a specified period.

[tex]P = P^{'} (1+i)^{n}[/tex]

where,

P is the future population size

[tex]P^{'}[/tex] is the initial population size

[tex]i[/tex] is the growth rate

n is number of periods, such as years

According to the given question

we have

Initial population = 127000

[tex]i[/tex] = 5.2% = [tex]\frac{5.2}{100} = 0.052[/tex]

n = 6 years   (2020-2014 = 6years)

therefore,

population of the town in 2020 = 127000[tex](1+0.052)^{6}[/tex]

Population of town in 2020 =  127000×[tex](1.052)^{6}[/tex]

Population of town in 2020 =  127000 ×1.4

Population of town in 2020 = 177,800

Hence, the population of town in 2020 will be 177800.

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Answer:

B

Step-by-step explanation:

Assume the radius is r so the diameter is 2r

Height=2*d=2(2r)=4r since the diameter is twice the radius

Volume of cone=1/3 * pi*r^2*h

                         = 1/3 * pi*r^2*(4r)

                         =4/3 *pi *r^3

So B

Answer: B

h=2d

r=d/2

so h in terms of r is;

h=4r

V=pi*r^2*h/3

V=pi*r^2*4r/3=pi*4r^3/3=4/3(pi)(r^3)

Answer:

The area of the brick border is [tex](24x+144)\ ft^{2}[/tex]

Step-by-step explanation:

we know that

The area of the brick border is equal to

[tex]A=(x+12)(x+12)-(x)(x)\\ \\A=(x+12)^{2} -x^{2}\\ \\A=x^{2}+24x+144-x^{2}\\ \\A=(24x+144)\ ft^{2}[/tex]

Answer: 1/8

Step-by-step explanation:

First Bag   and      Second Bag

[tex]\dfrac{3\ blue}{8\ total}[/tex]        x            [tex]\dfrac{2\ blue}{6\ total}[/tex]        =  [tex]\dfrac{6}{48}[/tex]

which reduces to [tex]\boxed{\dfrac{1}{8}}[/tex]

The inequality used in this situation will be 14x + 58 < 150.

The word inequality means a mathematical expression in which the sides are not equal to each other.

Let the no. of T-shirts Lisa can buy be = X

Cost of each T-shirt = $14

No. of jeans she bought = 1

Cost of jeans = $58

Total money she has = $150

Hence, the inequality will be 14X + 58 < 150.

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Lisa can spend a maximum of $92 on T-shirts after buying jeans, and with each T-shirt costing $14, she can buy up to 6 T-shirts as represented by the inequality 14t <= $92, where t is the number of T-shirts.

To create an inequality representing the number of T-shirts Lisa can purchase, let's define the variable t to represent the number of T-shirts. Lisa has $150 to spend, and she wants to buy a pair of jeans for $58, leaving $150 - $58 = $92 for T-shirts. Each T-shirt costs $14, so if Lisa buys t T-shirts, the cost for the T-shirts is 14t. The inequality to represent the maximum number of T-shirts Lisa can buy is 14t ≤ $92.

Now, to solve for t, we divide both sides of the inequality by 14: t ≤ $92 / $14, which simplifies to t ≤ 6.57. Since Lisa cannot buy a fraction of a T-shirt, the maximum number of T-shirts she can buy is 6.

[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ X(\stackrel{x_1}{x}~,~\stackrel{y_1}{y})\qquad Z(\stackrel{x_2}{11}~,~\stackrel{y_2}{-5}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{11+x}{2}~~,~~\cfrac{-5+y}{2} \right)=\stackrel{\stackrel{midpoint}{y}}{(3,-1)}\implies \begin{cases} \cfrac{11+x}{2}=3\\[1em] 11+x=6\\ \boxed{x=-5}\\ \cline{1-1} \cfrac{-5+y}{2}=-1\\[1em] -5+y=-2\\ \boxed{y=3} \end{cases}[/tex]

We define midpoint formula as

[tex]Y(x_m, y_m)=Y(\dfrac{x_2+x_1}{2}, \dfrac{y_2+y_1}{2})[/tex]

Also here are the coordinates of every point in variables so you won't get confused.

[tex]

Y(x_m, y_m) \\

X(x_1, y_1) \\

Z(x_2, y_2)

[/tex]

Which means there are two equations. One to find x of point X and one to find y of point X.

[tex]

x_m=\dfrac{x_2+x_1}{2}\Longrightarrow 3=\dfrac{11+x_1}{2} \\

6=11+x_1\Longrightarrow\underline{x_1=-5} \\ \\

y_m=\dfrac{y_2+y_1}{2}\Longrightarrow-1=\dfrac{-5+y_1}{2} \\

-2=-5+y_1\Longrightarrow\underline{y_1=3}

[/tex]

So point X has coordinates: [tex]\boxed{X(-5, 3)}[/tex]

Hope this helps.

r3t40

Answer:

Step-by-step explanation:

a:  70°

Reason:  a is supplementary to the angle that measures 110°, so 180° - 110° = 70°

b:  55°

Reason:  b is vertical to the angle between 100° and 25° (which add up to 125°) and since all of those angles added together have to equal 180°, then the unidentified angle between 100° and 25° = 55°.  b is vertical to that angle so b = 55°

c:  25°

Reason:  c is vertical the angle measuring 25° so c = 25° also.

Answer:

A

Step-by-step explanation:

Consecutive nnumbers are spaced 1 units apart.

Such as 4,5,6,...

or 12,13,14,...

Thus,

if smaller number is n, then the next number (consecutive) is n+1

Since, half of the product of them is 105, we can write the equation as:

[tex]\frac{1}{2}((n)(n+1))=105[/tex]

We can do some algebra and make it in quadratic form as shown below:

[tex]\frac{1}{2}((n)(n+1))=105\\\frac{1}{2}(n^2 + n)=105\\n^2+n=2*105\\n^2+n=210\\n^2+n-210=0[/tex]

Answer choice A is right.

Answer:

A.) n^2 + n – 210 = 0

Step-by-step explanation:

just took edg 2022. hope this helps!

Answer:

A) 8x + 9y = −3

B) 6x + 7y = 1

We multiply A) by -(6/8)

A) -6x -6.75y = 2.25  then we add this to equation B

B) 6x + 7y = 1

.25y = 3.25

y = 13

and x = -15

Step-by-step explanation:

The value of x= -15 and the value of y= 13 for the given system of equations: 8x+9y=−3  and 6x+7y=1.

Let’s solve the system of equations:

8x+9y=−3

6x+7y=1

We can solve the system of equations using elimination.

Steps to solve:

1. Solve the second equation for y:

y= 1/7

​2. Substitute this value of y into the first equation:

8x+9(1/7)=−3

8x+9/7 =−3

8x=−120

x=−15

3. Substitute x=-15 back into the second equation to solve for y:

6(−15)+7y=1

−90+7y=1

7y=91

y=13

Therefore, the value of x= -15 and the value of y= 13 for the given system of equations: 8x+9y=−3  and 6x+7y=1.

Answer:

Step-by-step explanation:

Slope is an average.  In this particular context, the slope of 6.9 (or 7) means that an average of 7 people entered the store every hour.

If x is the number of hours the store is open and we are told to find the number of customers that have entered the store after 5 hours, we fill in the equation as follows:

y = 7(5) + 10 and

y = 35 + 10 so

y = 45.

If you use 6.9 instead of 7:

y = 6.9(5) + 10 and

y = 34.5 + 10 so

y = 45.5

Since you can't count a half of a person, using 7 instead of 6.9 makes more sense.

Answer: perpendicular

Step-by-step explanation:

Lines with opposite and negated slopes are perpendicular, you can use desmos to graph and check

Answer:

Step-by-step explanation:

The product of the slopes (5/6), (-6/5) is -1, so the lines described by these functions are perpendicular.

[tex]\bf \textit{arc's length}\\\\ s=\cfrac{\pi \theta r}{180}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ \cline{1-1} \theta =135\\ r=11.4 \end{cases}\implies s=\cfrac{\pi (135)(11.4)}{180}\implies s=8.55\pi \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill s\approx 26.86~\hfill[/tex]

Answer:

[tex]\boxed{\textbf{26.9 m}}[/tex]

Step-by-step explanation:

The formula for the arc (s) of a circle is

[tex]s = r\theta \times \dfrac{\pi  }{180^{^{\circ}}}[/tex]

where θ is measured in degrees.

Data:

r = 11.4 m

θ = 135°

Calculation:

[tex]s = \text{11.4 m} \times 135^{^{\circ}}\times\dfrac{\pi}{180^{^{\circ}}} = \textbf{26.9 m}\\\\\text{The length of the arc is }\boxed{\textbf{26.9 m}}[/tex]

Answer: 614° and -106°

Step-by-step explanation:

You have this angle in degrees:

254°

Then, in order to find  the measure of a positive angle conterminal with the given angle in degrees (254°), you need to add  360 degrees. Therefore, the measure of the positive angle is:

[tex]254\°+360\°=614\°[/tex]

Now, to find the measure of a negative angle coterminal with the given angle in degrees (254°), you need to subtract  360 degrees. Therefore, this is:

[tex]254\°-360\°=-106\°[/tex]

Answer:

If the semicircle rotated around the line, it would become a sphere. So, A. sphere.

Step-by-step explanation:

A sphere is generated when a semicircle is rotated about the line.

A solid of revolution is a solid figure obtained by rotating a plane curve around some straight line.

Sphere is the set of all points in three-dimensional space lying the same distance  from a given point  or the result of rotating a semicircle about one of its diameters.

According to the given question.

A semicircle is rotated about the line.

Now,

From the definition of sphere we can say that, when a semicircle is rotated about a line a sphere will generate.

Therefore, a sphere is generated when a semicircle is rotated about the line.

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The volume of a pyramid is one-third of the volume of a prism with the same base area and height, yielding the formula V = (1/3)Bh for the volume of a pyramid.

When comparing the volume of a prism and a pyramid with the same base and height, the volume of a pyramid is one-third of the volume of the prism. Therefore, the formula for the volume of a prism is V = Bh, where B is the base area and h is the height. Applying this to the pyramid, the pyramid's volume becomes V = (1/3)Bh. This formula tells us that the volume of a pyramid is equal to one-third of the product of the area of its base and its height.

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For this case we have that the total of objects is given by:

Large blue objects, small blue objects, large red objects and small red objects.

In total we have: [tex]17 + 3 + 8 + 12 = 4[/tex]0 objects.

If we want to find the probality of obtaining small and blue objects we have to:

[tex]p = \frac {3} {40}[/tex]

ANswer:

[tex]p = \frac {3} {40}[/tex]

Answer:

1 3/7 quarts should be drained off and replaced with pure antifreeze.

1 3/7 ≈ 1.4286

Current amount of antifreeze in quarts is -

30/ 100 × 10 = 3

40% ---> 4 quarts

Let the amount drained of and replaced with antifreeze be x-

The amount left after draining off is 10 − x.

The amount of antifreeze  is 30/ 100 (10−x).

30/100(10-x)+x=4

3-3/10x+x=4

3+x(1-3/10)=4

x=1*10/7=1 3/7 quarts

check;

10- 1 3/7 = 8 4/7

=(30/100*8 4/7)+1 3/7

=(3/10 * 60/7) + 10/7

=3*6/7 + 10/7

=28/7

=4

4 liters of pure antifreeze is mixed into 10 quarts.

Answer: A

Step-by-step explanation:

Edge

Answer:2.20

Step-by-step explanation:

Answer:

  29°

Step-by-step explanation:

Angles 1 and 8 are alternate exterior angles where a transversal crosses parallel lines, so are congruent.

  m∠1 = m∠8

  3x+25 = 4x-17

  42 = m . . . . . . . . add 17-3x

Then the measure of ∠1 is 3·42 +25 = 151 (degrees), and the measure of its supplement, ∠2 is ...

  m∠2 = 180° -151° = 29°

Hello There!

We know that the formula of a triangle is "Base Multiplied By Height And Then Divide It By 2"

First, let's plug in our numbers. Our base is going to be 10 inches so we have 10 multiplied by our height which is 14 inches and we get a product of 140.

Next, we divide 140 by 2 to get a quotient of 70.

Finally, our answer is 70in squared

Answer:

  f(w) = 3w + 2,000,000/w

Step-by-step explanation:

We know that the area of a rectangle is the product of its length and width:

  A = LW

Filling in the given values lets us write an expression for the length of the field.

  1,000,000 = Lw

  L = 1,000,000/w

Since there are 3 fences of length w and two of length L, the total perimeter fence length is the sum ...

  f(w) = 3w + 2(1,000,000)/w

Combining the constants, we have a function for the perimeter fence length in terms of the width of the field:

  f(w) = 3w +2,000,000/w

Final answer:

The function that models the amount of fencing required for a 1,000,000 square foot rectangular field divided in half by a fence is F(w) = 3w + 2,000,000 / w. This represents the total length of fencing as a function of the width w.

Explanation:

The student is asking for a function that models the amount of fencing required for a rectangular field with an area of 1,000,000 square feet, which is then divided in half by a fence parallel to the width, w. To begin, let's denote the length of the field as L and the width as w. Since the area of the rectangle is given by L multiplied by w, and we know that the area is 1,000,000 square feet, we can express the length L in terms of w as L = 1,000,000 / w.

Now, total fencing required would be the perimeter of the rectangle plus the additional fence dividing it in half. The perimeter is calculated as 2w + 2L. Therefore, the total fencing F in feet would be F(w) = 2w + 2L + w.

Substituting L with 1,000,000 / w, the function becomes F(w) = 2w + 2(1,000,000 / w) + w = 3w + 2,000,000 / w. This function represents the total length of fencing needed in terms of the width w of the field.

Answer:

Correct me if I am wrong, but I believe it is B.

Step-by-step explanation:

Answer:

C. 28

Step-by-step explanation:

From the diagram diagram; [tex]\angle BAC=(x+6)\degree[/tex] and [tex]\angle ABD=2x\degree[/tex].

The pair of co-interior angles are [tex]\angle BAD[/tex] and [tex]\angle ABC[/tex].

Also the diagonals of a rhombus bisect corner angles.

This implies that:

[tex]\angle BAD=2(\angle BAC)\implies \angle BAD=2(x+6)\degree[/tex].

[tex]\angle ABC=2(\angle ABD)\implies \angle ABC=2(2x)\degree[/tex].

The co-interior angles are supplementary  so we form the equation:

[tex]\angle BAD+\angle ABC=180\degree[/tex]

[tex]\implies 2(x+6)\degree+2(2x)\degree=180\degree[/tex]

Expand the parenthesis to get:

[tex]\implies 2x+12+4x=180\degree[/tex]

Group the similar terms:

[tex]\implies 2x+4x=180-12[/tex]

Simplify

[tex]\implies 6x=168[/tex]

Divide both sides by 6.

[tex]\implies \frac{6x}{6}=\frac{168}{6}[/tex]

[tex]\therefore x=28[/tex]

The correct answer is C.

Answer:

D.Area of sector=88.31 square feet.

Step-by-step explanation:

We are given that a circle A and its radius is 15 feet.

The central angle is equal to 45 degrees.

Radius of circlle=15 feet

Angle at center=[tex]\theta=45^{\circ}[/tex]

We know that the area of sector

Area of sector=[tex]\frac{\theta}{360}\times \pi r^2[/tex].

We take value of [tex]\pi=3.14[/tex]

Substituting all given values in the given formula

Area of sector=[tex]\frac{45}{360}\times 3.14\times 15\times 15[/tex]

Area of sector=[tex]\frac{31792.5}{360}[/tex]

Area of sector= 88.3125 square feet

Hence, area of sector=88.31 square feet.Therefore, option D is correct answer.

Answer:

2r (1 + √3)

Step-by-step explanation:

Circle O₁ is tangent to AB.  Let's call the point of intersection point D.  If we draw a radius from the center O₁ to D, we know this forms a right angle.

△ABC is an equilateral triangle, so we know m∠A = 60°.  If we draw a line from A to O₁, we know that bisects the angle, so m∠DAO₁ = 30°.

So △DAO₁ is a 30-60-90 triangle.  We can find the length AD:

AD = r √3

Now on the other side, circle O₃ is tangent to AB.  Let's call the point of intersection point E.  We know it's the same triangle we found earlier, so:

EB = r √3

And finally, we can draw a rectangle connecting O₁, O₃, E, and D.  The distance between O₁ and O₃ is 2r, so:

DE = 2r.

Therefore:

AB = r√3 + 2r + r√3

AB = 2r√3 + 2r

AB = 2r (1 + √3)

Here's a graph showing the steps.  Hopefully this helps, let me know if you have questions!

desmos.com/calculator/hgaonfzxsm

Answer:

B:  No

Step-by-step explanation:

P = 2L + 2W.  If L = 20 and W = 11, then P = 2(20) + 2(11), or 62.  This matches Answer B.

Answer:  The correct option is

(B) No. If the length is 20 and the width is 11, the perimeter is P = 40 + 22 = 62, not 64.

Step-by-step explanation:  Given that the perimeter of a rectangle can be found using the equation P = 2L + 2W, where P is the perimeter, L is the length, and W is the width of the rectangle.

We are to check whether the perimeter of the rectangle can be 64 units when its width is 11 units and its length is 20 units.

According to the given information, we have

Length, L = 20 units,  width, W = 11 units  and  Perimeter, P = 64 units.

We have

[tex]P\\\\=2L+2W\\\\=2\times20+2\times11\\\\=40+22\\\\=62\neq64.[/tex]

Therefore, if length is 20 units and width is 11 units, then perimeter P = 40 + 22 = 62 units, not 64.

Thus, the answer is NO.

Thus, option (B) is CORRECT.

Answer:

The last choice is the one you want.

Step-by-step explanation:

Simply take the x coordinate and subtract 4, then do the same with the y coordinate since the vector movement is <-4, -4>.  The first coordinate F is <4,0>.  Subtract 4 from both of those coordinates and end up at <0, -4>.  The second coordinate G is <1, 3>.  Subtract 4 from both of those and end up at <-3, -1>.  The third coordinate H is <2, 6>.  Subtract 4 from both of those and end up at <-2, 2>.  The last coordinate I is <4, 2>.  Subtract 4 from both of those and end up at <0, -2>.  

A tangent line will have a couple of characteristics:

Substituting for x in the equation of the circle, we have ...

  (2y+5)^2 +y^2 = 5

  5y^2 +20y +20 = 0 . . . . simplify, subtract 5

  5(y +2)^2 = 0 . . . . . . . . . factor

This equation has exactly one solution, at y = -2. The corresponding value of x is ...

  x = 2(-2) +5 = 1

So, the line intersects the circle in exactly one point: (1, -2).

__

The center of the circle is (0, 0), so the line through the center and point of intersection is ...

  y = -2x . . . . . . . . . slope is -2

The tangent line is ...

  y = 1/2x -5/2 . . . . . . slope is 1/2

The product of slopes of these lines is (-2)(1/2) = -1, indicating the lines are perpendicular.

__

We have shown ...