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Answer:

3

Step-by-step explanation:

To find how many terms of this sequence must be added to get 1440, we must know the arithmetic sequence equation to find any term in the sequence:

  ⇒ [tex]a_{n}=a_{1} +(n-1)d[/tex]

Let's examine the information given:

        ⇒ [tex]a_{1} =5[/tex]

        ⇒ d = 2

Therefore the equation for finding the nth term of the sequence so far is:

  [tex]a_{n}=5+(n-1)*2=5+2n-2=3+2n[/tex]

Now we want to find how many terms this sequence must be added to get 1440

    General equation for adding all the terms = [tex]\frac{n(a_{1}+a_{n} ) }{2}[/tex]

Using all the information given, let's plug in the all the values:

  [tex]1440=\frac{n*(5+(3+2n))}{2} \\1440=\frac{n*(8+2n)}{2} \\2880=8n+2n^2\\2n^2+8n-2880=0\\(2n+80)(n-36)=0[/tex]

    To solve this we set (2n + 80) = 0 and (n-36) = 0

           [tex]2n+80=0\\ 2n = -80\\n= -40[/tex]                [tex]n - 36 =0\\n = 36[/tex]

In this case, n can only equal 36 since n cannot be negative.

Answer: 36 terms of this sequence must be added to get 1440.

Hope that helps!

General formula

We need n

Take it positive

Answer: Option (1)

Step-by-step explanation:

∠3 and ∠6 are supplementary because they are same-side interior angles. Therefore, the correct answer is option A.

From the given figure, m and n are parallel lines and l is transversal.

Parallel lines are those lines that are equidistant from each other and never meet, no matter how much they may be extended in either directions.

Here, angle 3 and angle 6 are co-interior angles and sum of their angles is supplementary.

Therefore, the correct answer is option A.

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Answer: [tex]16\frac{16}{25} cm^2[/tex]

Step-by-step explanation:

The formula for area is length × width = area

Sub in the values for length and width to solve

[tex]6\frac{2}{5}[/tex]×[tex]2\frac{3}{5}[/tex]=[tex]16\frac{16}{25}[/tex]

Answer:

Part B : 42

Part C : 7

Step-by-step explanation:

After putting in the coordinate points the width of the rectangle is 7 units and the length is 6 units. 7*6 =42. Half of this is the area of the triangle, that is 21. Further , 1/3 of 21 is the same as 21 divided by 3, which equals 7.

Applying the sine ratio, the length of segment SV (opposite side) in the right triangle is: D. 13/√2

The sine ratio is used to solve a right triangle which is, sin θ = opp/hyp.

Given the following:

SU = 13 (hypotenuse)

θ = 45

SV = ? (opposite)

Note: sine 45 = 1/√2

Applying the sine ratio, we have:

sin 45 = SV/13

SV = sin 45 × 13

SV = 1/√2 × 13

SV = 13/√2

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Answer:

See below

Step-by-step explanation:

1)  put in  -6  where 'x' is to get     y = 7

2) There is only one value of 'y' for every value of 'x' <===function

3) Put in 2 where 'x' is to get  y = 20

4) Function

Answer:

[tex](\frac{55}{2} ,\frac{37}{2} )[/tex]

Step-by-step explanation:

We have to solve this system of equations in order to find the numbers :

Let x be greater number and y be the smaller one :

[tex]\begin{cases}x-y=9\ \ \ (1)&\\ x+y=46\ \ \ (2)&\end{cases}[/tex]

[tex]\Longleftrightarrow \begin{cases}y=x-9\ \ \ (1)&\\ 2x=9+46=55\ \ \ (1)+(2)&\end{cases}[/tex]

[tex]\Longleftrightarrow \begin{cases}y=\frac{55}{2} -9=\frac{37}{2} &\\ x=\frac{55}{2}&\end{cases}[/tex]

Answer:

The answer to the question√3

Answer:

13 is 59° and 14 is 84°

Step-by-step explanation:

hope this helps! :)

Answer:

The answer is 25% also twenty five percent

subtraction [BODMAS 'S' comes last which means subtraction]

hope it helps...

Answer:

Subtraction

Step-by-step explanation:

The value of x in each figure is 34°, 17.1° and 75° respectively.

An equation is an expression used to show the relationship between two or more numbers and variables.

From the diagram:

1) x + 146°  = 180° (sum of angles in a straight line)

x = 34°

2) x + 62.9° = 90° (complementary angles)

x = 17.1°

3) x + 105°  = 180° (sum of angles in a straight line)

x = 75°

The value of x in each figure is 34°, 17.1° and 75° respectively.

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Answer: 8a^5 (3a^2 - 1)

Step-by-step explanation:

I factored 8a^5 out of the 24a^7 - 8a^5

Assuming that no transaction happens in her account for those 2 years, the amount that Brooke will have in 2 years for given case is $8.47

If n is the number of times the interested is compounded each year, and 'r' is the rate of compound interest annually, then the final amount after 't' years would be:

[tex]a = p(1 + \dfrac{r}{n})^{nt}[/tex]

We're specified that:

Thus, we get the final amount's value (after 2 years of compounding) for this case as :

[tex]a = p(1 + \dfrac{r}{n})^{nt}\\\\a = 7(1 + 0.10)^2 = 7 \times (1.1)^2 = 7 \times 1.21 = 8.47 \: (\rm in \: dollars)[/tex]

Thus, assuming that no transaction happens in her account for those 2 years, the amount that Brooke will have in 2 years for given case is $8.47

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Answer:

24 feet

Step-by-step explanation:

Given

Solving

Answer:

[tex]\displaystyle [x - 3]^2 + [y + 4]^2 = 9[/tex]

Explanation:

Accourding to one of the circle equations, [tex]\displaystyle [x - h]^2 + [y - k]^2 = r^2,[/tex]the centre of the circle is represented by [tex]\displaystyle [h, k].[/tex]Moreover, all negative symbols give you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must pay cloce attention to which term gets which symbol. Another thing you need to know is that the radius will ALWAYS be squared, so no matter how your equation comes about, make sure that the radius is squared.

I am joyous to assist you at any time.

Answer:

A. 31/100

Step-by-step explanation:

Change 3/10 to hundreds:

3/10 × 10/10 = 30/100

The denominator (the bottom number) must be 100.

61 - 30 is 31.

The missing number is 31/100. See image.

Answer:

Step-by-step explanation:

f(x) = - 4x - 2

g(x) = - x - 2

y-intercept is common point for both equations ( 0 , - 2 )

Answer:

A

Step-by-step explanation:

This is because 6f+f is just 7f.

f f f f f f+f = fffffff

Soooo, ONLY A gives us 7f when added together again.

f+5f+f=7f.

f+ f f f f f +f = fffffff

Answer:

[tex]f + 5f + f[/tex] is equivalent to [tex]6f + f[/tex].

Step-by-step explanation:

You can plug in any numbers to both expressions and they will always have the same outcome.

For example, let's plug in 2.

[tex]6f + f\\6(2) + 2\\12 + 2 = 14[/tex]

[tex]f + 5f + f\\2 + 5(2) + 2\\2+10+2 = 14[/tex]

Hope this helps! :)

Circumference of the circle with diameter 14 cm is 43.96 cm.

Circumference of any shape or figure is the total length of it's boundary. Circumference of a shape is also called the perimeter.

Circumference of any shape can be calculated by opening that shape into a straight line and then measuring the length of the line.

Perimeter of the circle can be computed by the formula,

C = 2πr, where r is the radius of the circle.

So, diameter of the circle is 2r

Here, we have, diameter = 2r = 14 cm

∴Circumference = 14π = 43.96 cm

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Answer:

#15   x ≈ 20.5

Step-by-step explanation:

To find missing sides

1) find the reference angle

2) identify the information that is needed ( what are you given - opposite side, adjacent side, hypotenuse)

3) use that information to set up the trigonometric equation

#10

angle is 64, opposite side is 42, adjacent side is x

so you use tangent

tangent 64 = 42/x           multiply by x

x tangent 64 = 42           divide by tangent 64

x = 42/tangent 64

x ≈ 20.5

the answer is 6 because theres need to be a total of 9 and they put 3 cups so 9 minus 3 equals 6

Answer:

Hello there buddy I’m here too help you with your homework

Your answer is

110°

Hope it’s helps you buddy

Have a nice day

Good luck with your homework

Step-by-step explanation:

~FluffyZaynBerry

Answer:

4/25 foot²

Step-by-step explanation:

Refer to attachment*

Consider the attachment first for a better understanding, now after considering the attachment you will gotta know that, the height of the parallelogram is just same as the width of the rectangle i.e (2/5) foot and but for the base of the parallelogram we can subtract the base of one triangle from the length of the rectangle, so it will give us (3/5) - (1/25) = (2/5), so now we have breadth as well as height of the parallelogram, so now, as area of a parallelogram is given by it's height times it's base, so we will be having

[tex]{:\implies \quad \sf Area_{(Parallelogram)}=\dfrac{2}{5}\times \dfrac25}[/tex]

[tex]{:\implies \quad \boxed{\bf{Area_{(Parallelogram)}=\dfrac{4}{25}\:\: sq.\:\:foot}}}[/tex]

Hence, Option D) is correct

Well, we have another method for it, we can subtract the area of both the triangles from the area of rectangle, and now,as their base of the triangle is (1/5) foot and height is same as the width of rectangle i.e (2/5) foots, so its area will be (1/2) times base times height, but as here are two triangles, so multiplying the area of one triangle by 2 will vanish 2, so now we just have

[tex]{:\implies \quad \sf Area_{(Parallelogram)}=\bigg(\dfrac{2}{5}\times \dfrac{3}{5}\bigg)-\bigg(\dfrac{1}{5}\times \dfrac{2}{5}\bigg)}[/tex]

[tex]{:\implies \quad \sf Area_{(Parallelogram)}=\dfrac{6}{25}-\dfrac{2}{25}}[/tex]

[tex]{:\implies \quad \boxed{\bf{Area_{(Parallelogram)}=\dfrac{4}{25}\:\: sq.\:\:foot}}}[/tex]

This also, proves that the correct answer is D)

Answer:

3.62

Step-by-step explanation:

39.37 - 35.75 = 3.62

Maybe ur just not seeing the negative comment on this and tell me which way u are solving it and then i can help.

The height of the ball is 10.053 approx. when it is 13 feet from the free throw line .

The physics aspect of shooting a free throw involves distance and deviation. Distance is determined by two factors: launch angle and launch speed. Players have a choice between shooting for a larger target by using more arc or going for a shooter's touch and shooting with their ideal arc for their height.

According to the question

A basketball player shoots a free throw, where the position of the ball is modeled

x = (24cos 48°)t

y =  6.1 + (24sin 48°)t − [tex]16t^{2}[/tex]

now

13 feet from the free throw line

x = 13 feet (horizontal distance)

x = (24cos 48°)t

(24cos 48°)t = 13

t ≈ 0.8059

putting values in y to get the vertical height

y =  6.1 + (24sin 48°)t − [tex]16t^{2}[/tex]

y =  6.1 + (24sin 48°)*0.8059 − [tex]16*( 0.8059)^{2}[/tex]

y ≈ 10.053

Hence, the height of the ball is 10.053 approx.

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Answer:

Step-by-step explanation:

Created Sequences

S1: 10 20 40 80 150

s2:24 20

The first term that appears in both sequences is the second term. Both of them equal 20.

I don't think you have to go any further once you get the first term.

Method

S1: Multiply by 2 starting with 10.

10*2 = 20

20*2 = 40

S2: Start at 24 and subtract 4

24 - 4 = 20

20 - 4 = 16

16 - 4 =  12

Applying the tangent ratio, the tangents of the acute angles in the right triangle are:

tan J = 5/3

tan K = 3/5

The tangent ratio is used to find the tangents of an angle in a right triangle, or any of the legs. It is given as tan ∅ = opposite/adjacent.

Applying the tangents ratio:

tan J = opp/adj = 5/3

tan K = opp/adj = 3/5

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