Given that ∠X≅∠D, and DE≅XW, what is the third congruence needed to prove that ΔXWY≅ΔDEC by ASA?
A
∠Y≅∠C

B
∠Y≅∠E

C
∠W≅∠C

D
∠W≅∠E

The limit of the given function as t approaches 4 is 7.

To evaluate the limit, we substitute the value of 4 into the function. By direct substitution, we get (4*2 - 4 - 12) / (4 - 4). Simplifying this expression, we have (16 - 4 - 12) / 0, which equals 0 / 0. This is an indeterminate form, which means we need to apply further algebraic manipulation to determine the limit.

To find the limit, we can factor the numerator as (t - 4)(t + 3). This allows us to cancel out the common factor of (t - 4) in the numerator and denominator. After canceling out (t - 4), the expression becomes (t + 3). Now we can evaluate the limit by substituting the value of t as it approaches 4 into the simplified expression.

Taking the limit as t approaches 4 of (t + 3), we get (4 + 3), which equals 7. Therefore, the limit of the given function as t approaches 4 is 7.

In summary, by factoring the numerator and canceling out the common factor of (t - 4), we simplified the expression to (t + 3). Substituting the value of t as it approaches 4 into the simplified expression gives us the limit of 7.

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Kindly find required figure in the picture attached below :

Answer:

14 feets

Step-by-step explanation:

From Trapezoid ABCD ;

The longer base, AD = 7 feets

Shorter Base ; BC = 5 feets

The Trapezoid GHIJ

Shorter Base = HI

Longer base = GJ

Given that the scale factor between ABCD and GHIJ is 2 ; then

GJ is similar to AD

Hence, side GJ = 2 * length of AD

GJ = 2 * 7 = 14 feets

Complementary angles has sum of \(90^{o}\) and supplementary angles have sum of \(180^{o}\) , The answer is \(62^{o}\) and \(48^{o}\) .

When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together.

When two angles' measurements add up to 90 degrees, they are said to be complementary. When two angles' measures sum up to 180 degrees, they are said to be supplementary. Keeping in mind that the letter s follows the letter c in the alphabet and that 180 is greater than 90 can help you avoid conflating these definitions.

\(28^{o}\)

complement = \(90^{o}-28^{o}\) = \(62^{o}\)

\(132^{o}\)

supplement= \(180^{o}-132^{o}\) = \(48^{o}\)

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Answer:

\(x+y= 15---------------------1\\\\5.5x+7.6y= 75.5----------------2\)

Step-by-step explanation:

Given data

let the number of peanuts be x

and the number of cashew be y

so

x+y= 15---------------------1

and

5.5x+7.6y= 75.5----------------2

Hence the system of equation is given as

\(x+y= 15---------------------1\\\\5.5x+7.6y= 75.5----------------2\)

Answer:

measure of angle GHJ = 1/2 the measure of arc GJ = (1/2)(86°) = 43°

measure of angle JIG = 1/2 the measure of arc GJ = (1/2)(86°) = 43°

On average number of customers arrives at a grocery shop per minute is equal to 1.2 customers per minute.

As given in the question,

Following a Poisson distribution:

Number of customers arrives at grocery store

= Average rate of 70 per hours

Conversion hours to minutes

1 hour = 60 minutes

λ = average rate of 70 per hours

  = average rate of 70 per 60 minutes

  = average rate of ( 7 / 6 ) per minute

 = average rate of 1.1666...per minute

= average rate of 1.2 per minute

Therefore,  on average 1.2 number of customers arrives per minute.

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Given that f(x)=-x^2+6x-1

f(1) = - 1^2 + 6(1) - 1

= -1 + 6 -1

= 4

f(3) = -3^2 + 6(3) - 1

= -9 + 18 -1

= 8

Hence

a. f(1) + f(3) = 4 + 8

= 12

b. f(1) - f(3) = 4 - 8

= -4

Answer:

D. 29 I just know the awnser sorry

To find the value of f(−2), we substitute −2 for x in the function f(x):

f(−2) = 4(-2)^2 − 3(-2) + 7

= 4(4) − 3(2) + 7

= 16 − 6 + 7

= 11

Therefore, f(−2) = 11.

The volume of the given 3-dimensional figure is 48π ft³.

The given figure is a right circular cylinder.

The formula for the volume of a right circular cylinder is:

V = πr²h

where r is the radius of the base and h is the height.

Given that r = 4 ft and h = 3 ft, we can substitute these values in the formula to find the volume of the cylinder:

V = π(4 ft)²(3 ft)

V = 48π ft³

Therefore, the volume of the given 3-dimensional figure is 48π ft³.

Hence, the correct option is O 48 π ft ³.

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The probability that a bat does not consume any mosquitoes in a 30-second interval is 0.0067379 or 0.67%.

In this case, the average rate of mosquitoes consumed by a bat is 10 per minute.

To find the rate for a 30-second interval, calculate the rate for 1 minute and then adjust it for the 30-second interval:

Average rate for 1 minute = 10 mosquitoes

Rate for 30 seconds = \(\dfrac{10 \,mosquitoes}{1 \,minute} \times \dfrac{1}{2}\)

                                  = 5 mosquitoes

The Poisson distribution probability mass function is given by:

\(\[ P(X = k) = \dfrac{e^{-\lambda} \cdot \lambda^k}{k!} \]\)

Where:

\(\(\lambda\)\) is the average rate of events.

In this case, to find the probability that k = 0.

So, let's plug in the values:

\(\(\lambda = 5\)\)

\(\(k = 0\)\), back to the formula as

\(\[ P(X = 0) = \dfrac{e^{-5} \cdot 5^0}{0!} \]\)

Calculating the probability as

\(\[ P(X = 0) = e^{-5}\)

                \(= 0.0067379\)

Therefore, the probability is 0.0067379 or 0.67%.

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Answer:

3 packs would be needed

We will add 29 3 times to get the and also nine

Answer:

the answer is 3

Step-by-step explanation:

subtract 96 minus 9 witch is 87 then divide that by 29 and that gives you 3

Answer: B

Step-by-step explanation:

The expression (20 - w)w represents the area of the garden in square meters.

The perimeter of the garden = 40 meters

The width = w

Perimeter of a rectangle = 2(l + w)

Hence,

40 = 2(l + w)

20 = l + w

The length of the garden = 20 - w

Since width = w and length = 20 - w

Recall, the area of a rectangle = Length × width

Area of the rectangular garden is expressed thus :

(20 - w) × w = (20 - w)w

Hence, the expression represents the area of the garden in square meters.

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Two objects with the same mass, when dropped from the same height, may not reach the ground at the same time because their air resistance and shape may be different, affecting their terminal velocity and acceleration due to gravity.

When two objects with the same mass are dropped from the same height, their acceleration due to gravity is the same. However, the objects may not reach the ground at the same time because of the effect of air resistance.

Air resistance is the force that opposes the motion of an object as it moves through the air.The magnitude of air resistance depends on several factors, including the speed and shape of the object.

As an object falls, its velocity increases and eventually reaches a point where the force of air resistance equals the force of gravity acting on it. At this point, the object stops accelerating and reaches a constant speed called the terminal velocity.

The terminal velocity of an object depends on several factors, including its mass, surface area, and shape. An object with a larger surface area experiences more air resistance and therefore has a lower terminal velocity than an object with a smaller surface area.

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Answer:

because this is a parallelogram

=> 3t - 15 = 2t + 10

⇔ t = 10 + 15

⇔ t = 25

with t = 25 => 3t - 15 = 3.25 - 15 = 60

we also have:

4r + (3t - 15) = 180°

⇔ 4r + 60° = 180°

⇒ 4r = 120°

⇔ r = 30

we also have;

4r = 3s

=> 4.30 = 3s

⇔ s = 4.10

⇔ s = 40

Step-by-step explanation:

You can use the fact that sum of all angles of a parallelogram is 360 degrees and the sum of two adjacent angles in a parallelogram is 180 degrees.

The value of the variables used in the figure are:

r = 30

s = 40

t = 25

\(4r + (3t - 15) + (2t + 10) + 3s = 360^\circ\\4r + 3s + 5t = 365\)

And

\(3t - 15 + 4r = 180 \cdots (1)\\3t - 15 + 3s = 180\cdots (2)\\3s + 2t + 10 = 180\cdots (3)\\4r + 2t + 10 = 180\cdots (4)\)

We get 2 systems of linear equations.

First system consists of equation 1 and equation 4

Second system consists of equation 2 and equation 3

From equation 1 and 4, as both's left side is equal to 180, thus they are equal too, or

\(3t - 15 + 4r = 4r + 2t + 10\\3t - 2t = 4r - 4r + 10 + 15\\t = 25\)

Putting it in equation 1, we get:

\(3t - 15 + 4r = 180\\3 \times 25 + 4r = 180 + 15\\75 + 4r = 195\\\\r = \dfrac{195 - 75}{4} = 30\)

Putting the value t = 25 in second equation, we get:

\(3t - 15 + 3s + 180\\3 \times 25 - 15 + 3s = 180\\60 + 3s = 180\\\\s = \dfrac{180 - 60}{3} = 40\)

Thus, the values of the specified variables in the given graph are:

r = 30

s = 40

t = 25

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Answer:

x) = 1 + 2(0.94)*

The y-intercept = (0, [?])

For x ≥ 0, the horizontal as

Answer: A not a triangle

Step-by-step explanation:

Given

The situation would best be represented by positive 6

Solution

Let us look at the first option

A. Taking an elevator down 6 floors in a building

Since it is coming down, this situation represents negative 6

B. Deleting 6 photos from a camera's memory card

Since we are removing, it also represent negative 6

C. A plant growing 6 inches

This is increasing and gaining height, so it represent positive 6

D. A group of 6 students getting off a bus

This also is a situation of negative 6, since the students are coming off the vehicle.

Therefore the right option is C

Option C

Another name for AXW is <X

The arrow on XW implies that the segment XW is a ray, such that any of the points X or W can be the starting point

Hence, another name for XW is WX

A ray with an endpoint X is a ray that ends at point X

An example of such ray is XY

The arrow on WX implies that the segment WX is a ray, such that any of the points X or W can be the starting point

Hence, another name for WX is XW

The name AXW represents an angle

An angle can be named after its middle point

Hence, another name for AXW is <X

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Answer:

Step-by-step explanation:

Area of a sphere is \(4\pi d^{2}\)

let d be the diameter of the moon and D be the diameter of the earth

d = 1/4 D

Area of Earth = \(4\pi D^{2} = 4\pi (\frac{d}{4} )^{2} = 4\pi \frac{d^{2} }{16} = \pi \frac{d^{2} }{4}\)

Area of moon = \(4\pi d^{2}\)

\(\frac{Area of moon}{Area of Earth} = \frac{1}{16}\)

Using the 68-95-99.7 rule, the approximate percentage of lightbulb replacement requests numbering between 36 and 46 can be estimated. The percentage is expected to be around 68%, indicating that the majority of requests fall within one standard deviation of the mean.

According to the 68-95-99.7 rule, for a bell-shaped distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

In this case, the mean number of daily requests is 36 with a standard deviation of 5. To calculate the percentage of requests between 36 and 46, we need to determine the range within one standard deviation of the mean.

One standard deviation above the mean is 36 + 5 = 41, and one standard deviation below the mean is 36 - 5 = 31. Therefore, the range between 36 and 46 falls within one standard deviation.

Since approximately 68% of the data falls within one standard deviation of the mean, we can estimate that the percentage of lightbulb replacement requests between 36 and 46 is approximately 68%.

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Answer:

Neptune is 80 times farther from the Sun than Mercury.

It takes 4 hours to reach the light from the Sun to Neptune.

Step-by-step explanation:

Given that the average distance between the Sun and Mercury,

\(d_1=35,000,000\) miles \(=3.5\times 10^7\) miles.

The time to reach the light from the sun to Mercury, \(t_1 = 3\) minutes

Let v m/s  be the speed of light.

So, \(v=\frac{d_1}{t_1}\cdots(i)\)  [as speed = distance/time]

Now, the average distance between the Sun and Neptune,

\(d_2=2.8\times 10^9\) miles.

The ration of the average distance of Neptune and Mercury from Sun,

\(\frac{d_2}{d_1}=\frac{2.8\times 10^9}{3.5\times 10^7}\)

\(\frac{d_2}{d_1}=80\cdots(ii)\)

So, Neptune is 80 times farther from the Sun than Mercury.

The time to reach the light from the sun to Neptune,

\(=\frac{d_2}{v}\) [as time=distance/speed]

\(=\frac{d_2}{d_1/t_1}\) [using equation(i)]

\(=\frac {d_2}{d_1}\times t_1\)

\(=80\times 3\)  [using equation(ii)]

=240 minutes

=4 hours [as 1 hour =60 minutes]

Hence, it takes 4 hours to reach the light from the Sun to Neptune.

Using the speed - distance relationship, we can deduce that Neptune is 80 times farther from the sun than Mercury and it will take 240 minutes for light from the sun to reach Neptune.

Given the Parameters :

Number of times Neptune is father from the sun than Mercury :

Hence, Neptune is 80 times farther from the sun than Mercury.

Time taken for light to reach Neptune :

3 minutes × 80 = 240 Minutes

60 minutes = 1 hour

240 minutes = (240 ÷ 60) = 4 hours

Therefore, it would take 4 hours for light to reach Neptune.

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Answer:

Expression for Perimeter:  6x + 6

x = 12 cm

Verify A = 360:

2(12) x (12+3) = 360

24 x 15 = 360

360 = 360

Step-by-step explanation:

Answer:

$4.00

Step-by-step explanation:

because to find you need to divide those numbers

Answer:

A = 55 degrees

B = 35 degrees

C = 90 degrees

side BA = 4.8 units

side AC = 2.7 units

side BC = 3.9 units

Step-by-step explanation:

Hello!

The things we know:

A = 55 degrees

C = 90 degrees

side BA = 4.8 units

AC = adjacent side

BC = opposite side

AB = hypothenuse

B = 180 - 55 - 90 degrees

B = 35 degrees

Let's find side AC

we can use the cos of theta.

cos(55) = AC/4.8

multiply 4.8 on both sides.

4.8cos(55) = AC

AC = 2.7 units

And now we just have to find BC

to calculate BC we can either use tangent or sin.

I will just use sin

sin(55) = BC/4.8

multiply 4.8 on both sides.

4.8sin(55) = BC

BC = 3.9

And now we know everything about the triangle

Hope I Helped!

Answer:

Step-by-step explanation:

area of the square is more than the area of the rectangle

Answer:

Division can be thought of as the opposite of multiplication. Let's say you want to divide 8 by 2. Another way to think of this example is what can be multiplied by 2 to equal 8? 4 does. There are many different methods to come up with a solution. I honestly cannot explain division with one universal method. Start with thinking about what is division. It took me awhile to figure it out, unfortunately I don't think I can help much that's what I can explain.  Anybody with more knowledge than my 10th grade math skills please help? This is important.

Step-by-step explanation:

Step-by-step explanation:

When we divide any number, divisor must be smaller than the number of dividend. Subtract the product from the number of dividend every time and then take the next number until all number finished. Quotient is always written above the line and product below the number of dividend.

Answer:

(y + 10)(3y - 1)

Step-by-step explanation:

3y² + 29y - 10

consider the factors of the product of the coefficient of the y² term and the constant term which sum to give the coefficient of the y- term.

product = 3 × - 10 = - 30 and sum = + 29

the factors are + 30 and - 1

use these factors to split the y- term

3y² + 30y - y - 10 ( factor first/second and third/fourth terms )

= 3y(y + 10) - 1 (y + 10) ← factor out (y + 10) from each term

= (y + 10)(3y - 1)

3y² + 29y - 10 = (y + 10)(3y - 1) ← in factored form