here are the first five terms of a quadratic sequence (1 8, 21, 40, 65). the nth term of this sequence can be written in the form (an2 + bn). where a and b are integers. work out the value of a and the value of b

Answer:

j=|x|

Step-by-step explanation:

Answer:

Option B

<F = 26°

<D = 64.01°

FD = 89

Answered by GAUTHMATH

For right triangle EFD,  m ∠F ≈ 26°, m ∠D ≈ 64.01° and FD = 89

The correct answer is an option (B)

It is the longest side of the right triangle.

For a right triangle,

[tex]a^{2}+ b^{2} = c^{2}[/tex], where c is hypotenuse and a, b area other two sides of the right triangle

For given example,

We have been given a right triangle EFD with hypotenuse FD.

Also, EF = 80, ED = 39

Using the Pythagoras theorem,

[tex]\Rightarrow FD^{2}= EF^{2} + ED^{2}\\\\ \Rightarrow FD^{2}= 80^{2} + 39^{2}\\\\ \Rightarrow FD^2 = 6400 + 1521\\\\ \Rightarrow FD^2 = 7921\\\\\Rightarrow FD = 89[/tex]

Consider, sin(F)

[tex]\Rightarrow sin(F)=\frac{ED}{FD} \\\\\Rightarrow sin(F)=\frac{39}{89}\\\\ \Rightarrow sin(F)=0.4382\\\\\Rightarrow \angle F=sin^{-1}(0.4382)\\\\\Rightarrow \angle F=25.98^{\circ}\\\\\Rightarrow \angle F\approx 26^{\circ}[/tex]

Now, consider sin(D)

[tex]\Rightarrow sin(D)=\frac{FE}{FD}\\\\ \Rightarrow sin(D)=\frac{80}{89}\\\\ \Rightarrow \angle D = sin^{-1}(0.8988)\\\\\Rightarrow \angle D = 64.009^{\circ}\\\\\Rightarrow \angle D \approx 64.01^{\circ}[/tex]

Therefore, for right triangle EFD,  m ∠F ≈ 26°, m ∠D ≈ 64.01° and FD = 89

The correct answer is an option (B)

Learn more about Pythagoras theorem here:

https://brainly.com/question/343682

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Answer:

14

Step-by-step explanation: B is the midpoint of AC, in other words it is the halfway point.

So A to B should be equal to B to C

Our expression is:

2x + 9 = 37

Subtract 9

2x = 28

Divide by 2

x = 14

Answer:

180m cubed

Step-by-step explanation:

Multiply the length, width, and height together: 6×6×5=180

Answer:

Formula of a rectangular prism:

L x W x H

Now we place in the numbers and solve:

5 x 6 x 6 = 180 m3

Answer:

just add a small amount to the 2.8 and square the result

Step-by-step explanation:

x x^2

2.8 7.84

2.81 7.8961

2.82 7.9524

2.83 8.0089

2.84 8.0656

2.85 8.1225

2.86 8.1796

2.87 8.2369

Answer:

700 parts

Step-by-step explanation:

To find the total amount of parts in the shipment, all we need to do is divide.

6% = 0.06

42 / 0.06 = 700

Best of Luck!

Complete question is;

A soccer ball was kicked through the air and it followed the path. Let h(s) = −3s² +75 represent the height of the soccer ball after s seconds.

Find the time at which the soccer ball hits the ground.

Answer:

s = 5 seconds.

Step-by-step explanation:

We are given the function;

h(s) = −3s² +75

Where;

h(s) is height at time s

s is the time taken

Now, the time at which the time at which the soccer ball hits the ground would be at h(s) = 0 since height is at 0 point.

Thus;

−3s² +75 = 0

−3s² = -75

s² = 75/3

s² = 25

s = √25

s = 5 seconds.

Answer:

Step-by-step explanation:

Use this formula:

[tex]A(t)=P(1+\frac{r}{n})^{nt}[/tex] where A(t) is the amount after the compounding is done, P is the initial investment (our unknown), r is the interest rate in decimal form, n is the number of compoundings per year, and t is the time in years. Filling in:

[tex]520=P(1+\frac{.03}{12})^{(12)(3)}[/tex] and simplifying that a bit:

[tex]520=P(1+.0025)^{36[/tex] and a bit more:

[tex]520=P(1.0025)^{36[/tex] and even  bit more:

520 = P(1.094551401) and divide to get

P = $475.30

Answer:

20

Step-by-step explanation:

Multiply 4/7 with 35, this will get you 140/7, which simplifies to 20 employees

Answer:

hypotenuse ≈ 44 inches

Step-by-step explanation:

Using Pythagoras' identity

The square on the hypotenuse is equal to the sum of the squares on the other two sides.

let the hypotenuse be h , then

h² = 23² + 38² = 529 + 1444 = 1973 ( take square root of both sides )

h = [tex]\sqrt{1973}[/tex] ≈ 44 inches ( to the nearest inch )

Answer:

only the first one...

a "FUNCTION" has a UNIQUE relation between each input and output...

notice the middle one the -2 goes to BOTH th2 10 & -7 that makes it NOT a FUNCTION

Step-by-step explanation:

9514 1404 393

Answer:

  24.6%

Step-by-step explanation:

The cost of the ticket in euros is ...

  £222 × €1.38/(£1) = €306.36

Then the ratio of the tax to the to the total cost is ...

  €100/(€306.36 +100) = 100/406.36 ≈ 24.6%

Answer:

hope it helps you........

Answer:

x = 5

Step-by-step explanation:

1. Subtract 22 from both sides.

15x = 7x + 62 - 22

2. Simplify 7x + 62 - 22 to 7x + 40.

15x = 7x + 40

3. Subtract 7x from both sides.

15x - 7x = 40

4. Simplify 15x - 7x to 8x.

8x = 40

5. Divide both sides by 8.

x = [tex]\frac{40}{8}[/tex]

6. Simplify [tex]\frac{40}{8}[/tex] to 5.

x = 5

Answer:

the sin of 28 degree is 28

Step-by-step explanation:

it's the same degree in radians I hope this help

===============================================

Explanation:

The table says that

That's 5+10+15 = 30 students out of 35 total.

The probability is therefore 30/35 = 0.8571 approximately which rounds to 0.86

There's roughly an 86% chance of picking someone who got an A, B or C.

Solution :

Given :

[tex]$P'(x) = -0.0008x^3+0.20x^2+46.8x,$[/tex]    for x ≤ 200

Total profit when 120 members are enrolled is :

[tex]$\sum_{i=1}^6P'(x_i) \Delta x$[/tex]      with [tex]\Delta x = 20[/tex]

Using the left end points, we get,

The values of [tex]x_i[/tex] are : { 0, 20, 40, 60, 80, 100}

Therefore,

[tex]$P'(x_1) = P'(0)=-(0.0008)(0)^3+(0.20)(0)^2+(46.8)(0)$[/tex]

                        = 0

[tex]$P'(x_2) = P'(20)=-(0.0008)(20)^3+(0.20)(20)^2+(46.8)(20)$[/tex]

                          = 1009.6

[tex]$P'(x_3) = P'(40)=-(0.0008)(40)^3+(0.20)(40)^2+(46.8)(40)$[/tex]

                         =  2140.8

[tex]$P'(x_4) = P'(60)=-(0.0008)(60)^3+(0.20)(60)^2+(46.8)(60)$[/tex]

                         = 3355.2

[tex]$P'(x_5) = P'(80)=-(0.0008)(80)^3+(0.20)(80)^2+(46.8)(80)$[/tex]

                         = 4614.4

[tex]$P'(x_6) = P'(100)=-(0.0008)(100)^3+(0.20)(100)^2+(46.8)(100)$[/tex]

                           = 5880

[tex]$\sum_{i=1}^6P'(x_i) \Delta x = P'(x_1)\Delta x + P'(x_2)\Delta x + P'(x_3)\Delta x + P'(x_4)\Delta x + P'(x_5)\Delta x + P'(x_6)\Delta x $[/tex]  

= (0)(20) + (1009.6)(20) + (2140.8)(20) + (3355.2)(20) + (4614.4)(20) + (5880)(20)

= (20)( 0 + 1009.6 + 2140.8 + 3355.2 + 4614.4 + 5880)

= (20)(17,000)

= 340,000 cents

[tex]$=\frac{340000}{100} \ \text{dollars}$[/tex]

= 3400 dollars

Hence, the required total profit is 3400 dollars.

Answer:

70. 8x⁴

71. 3n - 10

72. a/5 + 12

Step-by-step explanation:

70. a number "x" raised to the fourth = x⁴

Product of 8 and x⁴ = 8 × x⁴

= 8x⁴

71. 3 times a number "n" = 3 × n = 3n

3n decreased by 10 = 3n - 10

72. Quotient of a number "a" and 5 = a/5

12 more than a/5 = a/5 + 12

Answer:

because they are both in the circle

Step-by-step explanation:

Answer:

seats in each bus

Step-by-step explanation:

total no.of seats = 64

so, the no.of seats in each bus = 64/2 =32

therefore ,  b denotes the no.of seats in each bus

PLEASE MARK ME AS BRAINLIEST .

Answer:

D. Closed circle on 8, shading to the right.

Answer: -3x+y=-4

Step-by-step explanation:

Standard form is Ax+By=C. In y=Mx+b form, it would be y=3x-4. To put it into standard form you subtract 3x from both sides. So then you have -3x+y=-4.

Answer:

The speed is 20.8  m/s

Step-by-step explanation:

If a projectile ascends vertically, and after 3 seconds it reaches its maximum height, calculate the velocity that it carries to the middle of its downward trajectory

Let the maximum height is h and initial velocity is u.

From first equation of motion

v = u + at

0 = u - g x 3

u = 3 g.....(1)

Use third equation of motion

[tex]v^2 = u^2 - 2 gh \\\\0 = 9 g^2 - 2 gh \\\\h = 4.5 g[/tex]

Let the speed at half the height is v'.

[tex]v^2 = u^2 + 2 gh \\\\v'^2 = 0 + 2 g\times 2.25 g\\\\v'^2 = 4.5\times 9.8\times9.8\\\\v' = 20.8 m/s[/tex]

Answer:

x = 4

Step-by-step explanation:

The line DE is parallel to AC and divides the sides proportionally, that is

[tex]\frac{BD}{AD}[/tex] = [tex]\frac{BE}{CE}[/tex] , substitute values

[tex]\frac{x+2}{x}[/tex] = [tex]\frac{3}{2}[/tex] ( cross- multiply )

3x = 2(x + 2) = 2x + 4 ( subtract 2x from both sides )

x = 4

Consider we need to find the dimensions and volume of the box.

Given:

The shape of the lamp is a rectangular prism.

It measures 14 high, 9 wide, and 3 long.

There is 1 all around the lamp for bubble wrap

To find:

The dimensions and volume of the box.

Solution:

Length of the box is:

[tex]3+2=5[/tex]

Width of the box is:

[tex]9+2=11[/tex]

Height of the box is:

[tex]14+2=16[/tex]

Therefore, the dimensions of the box are 5 by 11 by 16 units.

The volume of the box is:

[tex]V=l\times w\times h[/tex]

Where, l is length, w is width and h is height.

Putting [tex]l=5, w=11, h=16[/tex], we get

[tex]V=5\times 11\times 16[/tex]

[tex]V=880[/tex]

Therefore, the volume of the box is 880 cubic units.