f(x) = x2 – 5; f(-4)??

The sequence is will always have even numbers, is hence proved.

Given, the quadratic sequence is: 44:52:64:80

Sequences with a term are known as quadratic sequences. They can be distinguished by the fact that the first differences between terms are not equal but the second differences between terms are. Utilizing the term sum in an arithmetic progression formula, the sum of even numbers formula is achieved. The equation is Sum of Even Numbers Formula = n(n+1), where n is the total number of terms in the series.

The formula is: Tₙ = 2n² ₊ 2n  ₊ 40

take 2 common

Tₙ = 2(n² ₊ n  ₊ 20)

in other words n² ₊ n  ₊ 20  = y

therefore , Tₙ = 2y

which by definition makes Tₙ an even number at all times.

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1 x 24, 2 x 12, 3 x 8, and 4 x 6

17-1-24

17-2-12

17-3-8

17-4-6

Answer:

Where's the equation?

There can be a total of 15504 groups of selection

From the question, we have

Total number of persons, n = 20

Numbers to selection, r = 5 i.e. the committee members

The number of ways of selection could be drawn is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 20 and r = 5

Substitute the known values in the above equation

Total = ²⁰C₅

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 20!/15!5!

Evaluate

Total = 15504

Hence, the number of ways is 15504

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Answer:

There can be 4 groups of 5.

Answer:

\(\displaystyle 64-32\sqrt{2}+\frac{32\sqrt{2}}{3}\approx3.66\)

Step-by-step explanation:

\(\displaystyle \iint_R(3x-y)\,dA\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\int^4_0(3r\cos\theta-r\sin\theta)\,r\,dr\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\int^4_0(3r^2\cos\theta-r^2\sin\theta)\,dr\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\int^4_0r^2(3\cos\theta-\sin\theta)\,dr\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\frac{64}{3}(3\cos\theta-\sin\theta)\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\biggr(64\cos\theta-\frac{64}{3}\sin\theta\biggr)\,d\theta\)

\(\displaystyle =\biggr(64\sin\theta+\frac{64}{3}\cos\theta\biggr)\biggr|^\frac{\pi}{2}_\frac{\pi}{4}\\\\=\biggr(64\sin\frac{\pi}{2}+\frac{64}{3}\cos\frac{\pi}{2}\biggr)-\biggr(64\sin\frac{\pi}{4}+\frac{64}{3}\cos\frac{\pi}{4}\biggr)\\\\=64-\biggr(64\cdot{\frac{\sqrt{2}}{2}}+\frac{64}{3}\cdot{\frac{\sqrt{2}}{2}}\biggr)\\\\=64-32\sqrt{2}+\frac{32\sqrt{2}}{3}\biggr\\\\\approx3.66\)

The net that can be folded to form a triangular pyramid is net b

From the question, we have the following parameters that can be used in our computation:

The nets in the list of options

As a general rule, a triangular pyramid has 4 triangles such that

Three triangles are adjacent and one triangle is at the top or at the bottom

using the above as a guide, we have the following:

The net that can be folded to form a triangular pyramid is net b

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It takes 95.75 minutes to fill a 270-gallon hot tub​.

Given,

A hose fills a hot tub in 1 minute =  2.82 gallons

Time taken to fill a 270-gallon hot tub​,

\(= \frac{270}{2.82}\)

= 95.75 minutes

Therefore, It takes 95.75 minutes to fill a 270-gallon hot tub​.

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Answer:

\(T_n = 2n - 1 + T_{n-1}\)

Step-by-step explanation:

Given

\(Sequence: -5,-2,3,10,19\)

Required

Find the nth term

We have:

\(T_1 = -5\)

\(T_2 = -2 = 3 - 5 = 3 + T_1\)

\(T_3 = 3 = 5 - 2 = 5 + T_2\)

\(T_4 = 10 = 7 + 3 = 7 +T_3\)

\(T_5 = 19 = 9 + 10 = 9 + T_4\)

This gives:

\(T_2 = 3 + T_1 = 4 - 1 + T_1\)

\(T_3 = 5 + T_2 = 6 - 1 + T_2\)

\(T_4 = 7 +T_3 = 8 - 1 + T_3\)

\(T_5 = 9 + T_4 = 10 - 1 + T_4\)

---

Solving further, we have:

\(T_2 = 4 - 1 + T_1 = 2 * 2 - 1 + T_1\)

\(T_3 = 6 - 1 + T_2 = 2 * 3 + T_2\)

\(T_4 = 8 - 1 + T_3 = 2 * 4 - 1 + T_3\)

\(T_5 = 10 - 1 + T_4 = 2 * 5 - 1 + T_4\)

Following the above sequence: the nth term is:

\(T_n = 2n - 1 + T_{n-1}\)

The limit as x approaches 1 from either side should match, so that

\(\displaystyle\lim_{x\to1^-}f(x)=\lim_{x\to1}(-2x+a)=a-2\)

\(\displaystyle\lim_{x\to1^+}f(x)=\lim_{x\to1}x=1\)

==>   a - 2 = 1   ==>   a = 3

The answer is a = 3.

Finding Left Hand Limit (LHL)

\(\displaystyle \lim_{x \to \11^{-}} f(x) = -2(1) + a\)

Finding Right Hand Limit (RHL)

\(\displaystyle \lim_{x \to \11^{+}} f(x) = 1\)

For a continuous function, LHL = RHL

The value of x is 4/3 for equation 1+3x=5.

Two or more expressions with an Equal sign is called as Equation.

The given equation is 1+3x=5

One plus three times of x equal to five

We need to solve for x

1+3x=5

Subtract 1 from both sides

3x=5-1

3x=4

Three times of x equal to four

Divide both sides by 3

x=4/3

Hence, the value of x is 4/3 for equation 1+3x=5.

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Hi Student!

Looking at the question provided we are asked to find two integers.  It further specifies that those two integers should be the boundaries around the number that is produced from the square root of 11.  

Now that we know what the question is asking for, we can move onto answering the question.  We know that \(1^2\) is equal to \(1\), \(2^2\) is equal to \(4\), \(3^2\) is equal to \(9\), and \(4^2\) is equal to \(16\).  The number that was provided to us inside of the square root was 11.  That means that it would be between the number 9 and 16 which is given using \(3^2\) and \(4^2\).  

Therefore, the square root of 11 would be between the numbers 3 and 4.  The final answer is option E, 3 and 4

The missing values are

<UTQ = 41 degree

x= 1

<UQT = 47 degree

We have a parallelogram QRST.

We know that the opposite sides of the parallelogram is equal and parallel then

QR || ST

QT || SR

Then, <SRT = <RTQ (<UTQ) (alternate Interior Angle)

<UTQ = 41

Similarly, <UQT = <SRQ = 47

Now, RU = UT

2x + 1= 3

2x = 2

x= 1

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Answer:

1.5

Step-by-step explanation:

23-17=6

6/4= 1.5

Answer:

corresponding

Step-by-step explanation:

<1 and <5 are corresponding angles because they are on the same side of the transversal and on the same side of l and m

Answer:

$8 + 3t = $25.50

The correct equation is:  5/6 - 1/6 = 4/6

A number line is a visual representation of numbers, ordered from left to right, where each point on the line corresponds to a number. The number line can be used to represent a wide range of numbers, including integers, fractions, decimals, and even negative numbers.

On a basic number line, 0 is located in the center, with positive numbers to the right and negative numbers to the left. The numbers are usually evenly spaced, with tick marks or dots indicating each value. The distance between any two points on the number line represents the difference between the corresponding numbers.

According to question Option D is correct

This is because starting at 5/6 and ending at 1/6 involves moving in the negative direction on the number line. To find the distance between these two points, we need to subtract the smaller number (1/6) from the larger number (5/6).

So, 5/6 - 1/6 = 4/6, which simplifies to 2/3. This means that the distance between 5/6 and 1/6 on the number line is 2/3.

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Answer:

4 inches

Step-by-step explanation:

We can set up a proportion to find out the length value (assuming x is the length of the frame)

\(\frac{3}{x} = \frac{9}{12}\)

We multiply 12 and 3...

\(12\cdot3=36\)

And divide by 9...

\(36\div9=4\)

So, the length of the frame is 4 inches.

Hope this helped!

Answer:

Step-by-step explanation:

4 inches

A. 28% is the percent of the mixture is fruit juice.

First, we need to find the total amount of fruit juice in the mixture.

For Brand A juice: 6 L x 52% = 3.12 L of fruit juice

For Brand B juice: 9 L x 12% = 1.08 L of fruit juice

Total fruit juice in the mixture: 3.12 L + 1.08 L = 4.2 L

The total amount of the mixture is 6 L + 9 L = 15 L

The percent of the mixture that is fruit juice is:

(4.2 L / 15 L) x 100% = 28%

Therefore, the answer is A. 28%.

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Answer:

600

Step-by-step explanation:

24 by 3 times 100

The number of milligrams of fat that one serving has is 8000 milligrams.

Firstly, it should be noted that

1000mg = 1 gram.

Since three servings of ice cream has 24g of fat, therefore, the fa that will be contained in each will be:

= 24/3

= 8g

Therefore, we'll convert 8 grams to milligrams and this will be:

= 8 × 1000

= 8000 milligrams.

Therefore, a serving has 8000 milligrams.

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According to Riemann sum and expressing the work as an integral,400 ft/lb work is done in pulling the rope to the top of the building.

Given,

heavy rope length = 40ft

weighs = 0.5 lb/ft

building height = 90 ft

If we divide rope into small parts with length Δx, rope weighs 0.5 lb/ft force work on each section is x*i is a point in i the such intervals.

The work done on ith part is

                                          x*i0.5Δx

So the total done is

\(\lim_{n \to \infty}\)= ∑0.5x*iΔx expressing work as an integral

         \(\int\limits^40_0 {(0.5x)} \, dx\) = [0.5 × x²/2]

                             = [0.5 × 40²/2 - 0.5 × 0²/2]

                             = [0.5 × 1600/2 - 0]

                             =  0.5 × 800 - 0

                             = 400 - 0

                             = 400 ft/lb

The work done in lifting the pieces in upper half of rope is

  x*i0.5Δx

The work done in lifting lower half of the rope is

0.5Δx × 20

10Δx

Total workdone,

                 \(\lim_{n \to \infty}\)∑0.5x*iΔx + \(\lim_{n \to \infty}\)∑10Δx

                = \(\lim_{n \to \infty}\)∑(0.5x*i + 10)Δx work as an integral

\(\int\limits^25_0 {0.5} \, dx\) + \(\int\limits^50_25 {10} \, dx\)

= [ 0.5 * x²/2] + [10x]

= [0.5 * 20²/2] +[10(40-20)]

= [0.5 * 400/2] + [10*20]

= 100 + 200

= 300 ft/lb

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Answer:

B

Step-by-step explanation:

Here, we want to use the empirical rule to find the percentage.

The first thing we will do here is to find the z-score

Mathematically;

z-score = (x -mean)/SD

from the question, x = 95, mean = 110

and SD = 15

So z-score will be ;

(95-110)/15 = -15/15 = -1

So the probability we want to calculate is;

P(z < -1)

In terms of the empirical rule, we want to find the proportion of the scores which is less than 1 standard deviation of the mean.

According to the empirical rule, the proportion which is less than 1 standard deviation below the mean is 15.866% and the closest answer to this is 16% which is option B

By definition, the empirical rule is basically used in finding the proportion of values in this case scores which are at a certain standard deviation value below or above the mean. Below the mean are represented as negatives while above the mean are represented as positives.

Answer:

45000

Step-by-step explanation:

Answer:

15 10+5=15 have a nice day

Step-by-step explanation:

For the given triangles:

(1) x = 5.4

(2)  x  =  √23

(3) θ = 25.84 degree

(4)   x = 9.5

(5) n = 41

(1) In the given triangle,

One angle = 16 degree

Perpendicular = x

Hypotenuse    = 20

Since we know that

Sinθ = opposite side of θ/hypotenuse

Therefore,

⇒ sin 16 = x/20

⇒   0.27 = x/20

⇒         x = 5.4

(2)  In the given triangle,

Hypotenuse = 12 km

Base = 11 km

perpendicular = x

We know that the Pythagoras theorem for a right angled triangle:

⇒  (Hypotenuse)²= (Perpendicular)² + (Base)²

⇒ (12)²= (x)² + (11)²

⇒ 144 = (x)² + 121

⇒   x² =  23

Taking square root both sides we get,

Hence,

⇒   x  =  √23

(3) In the given,

Base = 20

Perpendicular = 42

We know that the Pythagoras theorem for a right angled triangle:

⇒  (Hypotenuse)²= (Perpendicular)² + (Base)²

⇒ (Hypotenuse)² =  (42)² + (20)²

⇒ (Hypotenuse)² =  2164

Taking square root both sides,

⇒ (Hypotenuse)  = 46.51

⇒ cosθ = Adjacent/hypotenuse

             = 42/46.51

             = 0.90

Taking inverse of cosθ,

⇒ θ = 25.84 degree

(4) In the given triangle,

One angle = 30 degree

Base = x

Hypotenuse    = 11

Since we know that

cosθ = Adjacent/hypotenuse

Therefore,

⇒ cos 30  = x/11

⇒   √3/2 = x/11

⇒         x = 9.5

(4) In the given triangle,

Base = 40

Perpendicular = 9

Hypotenuse = n

We know that the Pythagoras theorem for a right angled triangle:

⇒  (Hypotenuse)²= (Perpendicular)² + (Base)²

⇒  n² = 9² + 40²

⇒  n² = 81 + 1600

⇒  n² = 1681

⇒  n = 41

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Answer:

65 packets and 4 stamps

Step-by-step explanation:

The first thing we see is that the stamps are mixed... which means they must be added.

208 + 186 = 394 stamps total

Now we see that each packet has 6 stamps. So we divide the number of stamps in total by 6.

394/6= 65.66667

Now we see from that number that the stamps can't quite make 66 packets, so there are 65 packets.

Now we find the number of stamps left over by multiplying the number of packets by 6.

65 x 6= 390

Now we take the total number of stamps minus the number of stamps in packets.

394 - 390 = 4

Therefore, there are four stamps left over.

Hope this helps!

In the diagram, the correct option is

angle DAB = angle DCB

CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent." It is a geometric postulate used in proving the congruence of triangles.

According to CPCTC, if two triangles are proven to be congruent (having all corresponding angles and sides congruent), then their corresponding parts, including angles and sides, are also congruent.

The two triangles in the figure are congruent by the SAS congruence theorem and hence applying the CPCTC we have that

angle DAB = angle DCB

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Answer:

y=1/3

Step-by-step explanation:

3y+1=0

3y=-1

3y/3=-1/3

y=-1/3