in order for the limit of F(X) to exist at x=a, which of the following must hold true

Answer:

450 m²

Step-by-step explanation:

Let x = length of rectangle and y = width of the rectangle.

Therefore,

2x + y = 60...............(1)

Making y subject of the formula, we have:

y = 60 - 2x............... (2)

We know area of a rectangle is length * width i.e A = x*y

Let's substitute (60-2x) for y,

A = x * (60-2x)

= 60x - 2(x)²

= -2x² + 60x

[tex] \frac{dA}{dx} = -2x^2 + 60x = [/tex]

-4x + 60 = 0

-4x = -60

[tex] x = \frac{-60}{-4} = 15 [/tex]

Let's substitute 15 for x in equation 2, we have:

y = 60 - 2(15)

= 60 - 30

y = 30

Since x = 15 & y = 30, the area would be:

A = xy

A = 15 * 30

A = 450 m²

The maximum area of the dog pen is 450m²

Answer:

yes you will because you need to pass all subject now if your in home school if you fail one subject you would have to see because not all schools are the same so... yeah but in my opinion if you fail one subject you do fail 6 grade I mean thats what I think I am in 9th grade so I dont remember that much

Step-by-step explanation:

Answer:

x = 15/2

Step-by-step explanation:

2x + 15 = 30

2x = 15

x = 15/2 or 7.5

Answer:

7.5

Step-by-step explanation:

2x+15=30

2x=30-15

2x=15

x=7.5

Answer:

f(g(3)) =31

Step-by-step explanation:

f(x) = 3x+4

g(x) = x^2

f(g(3) ) =

First find g(3)

g(3) = 3^2 =9

The use 9 in f(x)

f(g(3)) = f(9) = 3*9+4 = 27+4 = 31

Answer:

[tex]28\sqrt{2}[/tex]

Step-by-step explanation:

To answer this question, you must split 98 into 2 factors:

                                                      98

                                                 2          49

                                                          7       7

2 and 49 can be multiplied to get 98. 49 is also a perfect square, meaning the factors are going to be the same number, which is 7. Since there are two 7's you take that out of the radical, like so:

[tex](7)4\sqrt{2}[/tex]

[tex]28\sqrt{2}[/tex]

Answer:

23

Step-by-step explanation:

Answer:

{(2^4) }^2

=16^2

= 256

................

Answer:

256

Step-by-step explanation:

Answer:

d. 13 raise power 3/5

Step-by-step explanation:

Answer:

The sample mean = 1.8

Step-by-step explanation:

I just completed the test and this was the correct answer

The sample mean for the data is 1.8 if the first 10 people to check out books lived out of 20 population.

It is defined as the group of data having the same entity which is related to some problems. The sample is a subset of the population, it is a part of the population.

We have:

Total number of population = 20

To calculate the sample mean:

Total number of samples N = 10

Sum of the sample values ∑x = 0.5+1.8+0.8+1.8+3.5+4.8+ 0.6+ 2+1.5+0.5

∑x = 17.8

Now the mean of the sample data =  ∑x/N = 17.8/10 = 1.78 ≈ 1.8

Thus, the sample mean for the data is 1.8 if the first 10 people to check out books lived out of 20 population.

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Answer:

(h,k) = (32,-4)

r = 32

Step-by-step explanation:

The general equation for a circle is given by:

[tex](x-h)^2+(y-k)^2=r^2[/tex]   (1)

where (h,k) is the center of the circle and r is the radius.

You have the following equation:

[tex]x^2+(y+4)^2=64x[/tex]   (2)

You first need to complete squares in order to obtain an equation of the form (1). Thus, you have that the second term must be in a perfect square trinomial:

2b = 64

b = 32

Then, you have to sum 32^2 and also subtract the same number in the expression (2):

[tex]x^2-64x+(y+4)^2=0\\\\(x^2-64x+32^2)+(y+4)^2-32^2=0\\\\(x-32)^2+(y+4)^2=32^2[/tex]

you compare the last result with expression (1) and obtain that the raiuds of the circle is r = 32

Furthermore, the center of the circle is (h,k) = (32,-4)

Answer:

Step-by-step explanation:

Given the equation sec(x)cot(x)= -2 on the interval [0,2π]. In order to get the value of x, the following steps must be followed.

sec(x)cot(x)= -2

From trigonometry identity, sec(x)= 1/cos(x) and cot(x)= 1/tan(x) = cos(x)/sin(x)

subsituting this expressions in the given equation we have;

1/cos(x)*cos(x)/sin(x) = -2

1/sin(x) = -2

sin(x) = -1/2

[tex]x = sin^{-1}-1/2\\ x = -30^{0}[/tex]

Since sin is negative in the 3rd and 4th quadrant,

In the 3rd quadrant, x = 180+30 = 210°

In the 4th quadrant, x = 360-30 = 330°

Converting the values to radian;

since 180° =  πrad

210° = 210π/180 rad

210° = 7π/6 rad

Similarly, 330° = 330π/180 rad

330° = 11π/6 rad

The solutions are 7π/6 and 11π/6

Answer:

x = 7

y = 8

Step-by-step explanation:

Knowing that the mean is equal to the median, we can formulate the following equation:

⅕(4 + 6 + x + y + 10) = x

Simplifying it, we get:

y = 4x - 20

Now, we know that both x and y are between 6 and 10 and that y is greater than x;

Mathematically, we have the conditions:

6 =< x =< 10

6 =< y =< 10

y > x

If we apply the second condition, i.e. the restrictions on the y-values, we find that x has to be between 6.5 and 7.5, i.e. 6.5 =< x =< 7.5;

This means x has to 7 since it can only be a whole number and this is the only whole number between 6.5 and 7.5;

Once we know this, we can find y simply by subbing it into the equation formulated previously:

y = 4(7) - 20

y = 8

Answer:20.8 In^2

Step-by-step explanation:

Base=10.4

Height=4

Area of =(base x height)/2

Area of =(10.4x4)/2

Area of =41.6/2

Area of =20.8

We have been given that two rectangular prisms, M and N, are mathematically similar. The volumes of M and N are 17 cm^3 and 136 cm^3, respectively. The height of N is 18 cm. We are asked to find the height of M.

First of all, we will find the ratio between sides of rectangle M and N using proportions.

[tex]\frac{\text{Side of N}}{\text{Side of M}}=\frac{\text{ Volume of N}}{\text{ Volume of M}}[/tex]

[tex]\frac{\text{Side of N}}{\text{Side of M}}=\frac{136\text{ cm}^3}{17\text{ cm}^3}[/tex]

[tex]\frac{\text{Side of N}}{\text{Side of M}}=\frac{8\text{ cm}^3}{1\text{ cm}^3}[/tex]

Now we will take cube root on right side to find length in cm.

[tex]\frac{\text{Side of N}}{\text{Side of M}}=\frac{\sqrt[3]{\text{8 cm}^3}}{\sqrt[3]{\text{1 cm}^3}}[/tex]

[tex]\frac{\text{Side of N}}{\text{Side of M}}=\frac{\text{2 cm}}{\text{1 cm}}[/tex]

Therefore, sides of rectangle N is 2 times greater than sides of rectangle M.

To find height of rectangle M, we will divide side of rectangle N by 2.

[tex]\text{Height of rectangle M}=\frac{18}{2}=9[/tex]

Therefore, height of rectangle M is 9 cm.

Answer:

what is the figure my guy

Step-by-step explanation: blah blah blah math blah blah blah

Write the equations:

a +c = 15

a = 15-c

29.95a + 21.95c = 353.25

Replace a in the last equation:

29.95(15-c) + 21.95c = 353.25

Simplify:

449.25 - 29.95c + 21.95c = 353.25

449.25 - 8.00c = 353.25

Subtract 449.25 from both sides:

-8.00c = -96.00

Divide both sides by -8.00:

c = -96 / -8

c = 12

There were 12 children.

Answer:The answer will be 35ft

Step-by-step explanation:

One way that you can answer this is by using sin law. You will put the length of a side on top and the corresponding angle that faces towards that side at the bottom of a fraction. So for this one it will be 30/sin(70) = x/sin(90) The 90 comes from the bottom of the building with the ground. And the side the angle faces is the ladder. After that you put 30sin(90)/sin(70) to find x. And you get 34.655 which rounds to 35 ft.

Answer:

He needs to sell at least 49 mugs.

Step-by-step explanation:

Since Ronny earned $228 and needs to earn more than $372, he needs to earn more than 372-228 = 144.

Since he sells a mug for $3 and needs more than $144, his earning must be greater than 144:

→ 3x > 144, x represents the number of coffee mugs

→ x > 48

→ x must be at least 49

Answer: it is not a right triangle

12^2=7^2+10^2

144=49+100

144=149

To prove this we try the pitagor teorem which the largest side is the hypotenuse

It is not a right triangle.

We have given that,

The triangle has side lengths 7, 10, and 12.

[tex]hypotenous^2=side^2+side^2[/tex]

12^2=7^2+10^2

144=49+100

144=149

The pitagor theorem which the largest side is the hypotenuse.

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Answer:

the graph translated down 3 or y-3

Step-by-step explanation:

(-3) is the y-intercept

Answer:

Step-by-step explanation:45

Answer:

About 0.17

Step-by-step explanation:

Rolling a 5: 1/6

1/6=0.166666...

Therefore, about 0.17

I hope this helped and have a good rest of your day!

Answer:

31.8%

Step-by-step explanation:There are 7 months that have 31 days so,

The odds the first selected month has 31 days is 7/12

The next month there are only 6 months left with 31 days of only 11 months to choose from

so the odds for the second are 6/11

To calculate the odds they BOTH  have 31 months you multiply the two odds:

(7/12) x (6/11) = 42/132 = .318 so 31.8%

The required probability is 0.318 or 31.8% (in the form of a percentage) that 2 randomly selected months have 31 days.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

There are 7 months with 31 days, therefore

The probability that the first picked month has 31 days is 7/12.

There are just 6 months left with 31 days of only 11 months to choose from the following month.

As a result, the odds for the second are 6/11.

To determine the probabilities that they both have 31 months, multiply the two odds:

⇒ (7/12) × (6/11)

⇒  42/132

Apply the division operation,

⇒  0.318

⇒  31.8% in the form of a percentage

Thus, the required probability is 0.318 or 31.8% that 2 randomly selected months have 31 days.

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Answer:

1. blue

2. blue because I measured both lines with a ruler.

3. this one was harder to decide because when I look at the picture both lines look the same length but since I measured both lines with a ruler I realized that the blue line was longer that the red line.

Step-by-step explanation:

I actually measured both lines with a ruler and the blue line is just barely bigger that the red line

Answer:

[tex]y = \frac{\sqrt{3}}{2}} \\\\[/tex]

Step-by-step explanation:

We are given a point P which lies on a unit circle

P  = (-½, y)

Where x coordinate is -½ and y coordinate is y.

We are asked to find the value of y in simplest form.

Recall that a unit circle has a radius of 1 and is centered at the origin that is (0,0).

The equation of the unit circle is given by

[tex]x^{2} + y^{2} = 1[/tex]

Since the point P lies on a unit circle, we can substitute this point into the equation of unit circle and get the value of y.

Substitute x = -½ and y = y

[tex](-\frac{1}{2} )^{2} + y^{2} = 1\\\\(\frac{1}{4} ) + y^{2} = 1\\\\y^{2} = 1 - \frac{1}{4} \\\\y^{2} = \frac{3}{4} \\\\y = \pm \sqrt{\frac{3}{4}} \\\\y = \pm \frac{\sqrt{3}}{2}} \\\\[/tex]

Assuming that the given point P lies in the 2nd quadrant, the value of y will be positive.

[tex]y = \frac{\sqrt{3}}{2}} \\\\[/tex]

Therefore, the coordinates of the point P are

[tex]P =( -\frac{1}{2} , \frac{\sqrt{3}}{2}}) \\\\[/tex]

Answer:

x=2

Step-by-step explanation:

4x+6=x+12

-x         -x

3x+6=12

    -6  -6

3x=6

/3   /3

x=2

Answer:

x=2

Step-by-step explanation:

4x+6 = x+12

Subtract x from each side

4x-x +6 =x-x+12

3x +6 = 12

Subtract 6 from each side

3x+6-6=12-6

3x = 6

Divide each side by 3

3x/3 =6/3

x =2

Answer:

0 = x2 - 9x + 20

Step-by-step explanation:

y + 5x = x² + 10     Simplify this equation

  - 5x   - 5x

y = x² - 5x + 10

Set both equations equal to each other since they both equal y

x² - 5x + 10 = 4x - 10

    -4x           - 4x

x² - 9x + 10 = -10

         + 10   + 10

x² - 9x + 20 = 0

If this answer is correct, please make me Brainliest!

Answer: 75

Step-by-step explanation: 7.20+7.80=15 then 15+60=75

Answer:

[tex]2\frac{3}{4}[/tex] pounds

Step-by-step explanation:

Maggie buys 1 1/2 pounds of walnuts, 8 ounces of pecans and 3/4 pounds of almonds.

To find the total weight of nuts that she buys, let us first put all the weights in a single unit, pounds.

She buys 8 ounces of pecans.

1 ounce = 0.0625 pounds

8 ounces = 8 * 0.0625 = 0.5 pounds = 1/2 pounds

Therefore, the total weight of nuts that she buys is:

[tex]1\frac{1}{2} + \frac{1}{2} + \frac{3}{4}\\ \\\frac{3}{2} + \frac{1}{2} + \frac{3}{4} = 2\frac{3}{4}[/tex]

The nuts weight [tex]2\frac{3}{4}[/tex] pounds in all.

Answer:

the answer is 2 3/4 pounds

Step-by-step explanation: