Find the length of the hypotenuse.Round to the nearest 10th if necessary.(40pts)

[tex]\huge\bf Question:—[/tex]

[tex] \sf \longmapsto \: g=a(4− {d}^{2} )[/tex]

[tex]\huge\bf Solution:—[/tex]

[tex] \underline{\bf \: Flip \: the \: equation:—}[/tex]

[tex] \sf \longmapsto \: −a {d}^{2} +4a=g[/tex]

[tex] \underline{\bf \: Factor \: out \: variable \: (a):—}[/tex]

[tex] \sf \longmapsto \: a(− {d}^{2} +4)=g[/tex]

[tex]\underline{ \bf \: Divide \: both \: sides \: by -d^2+4 :—} [/tex]

[tex]\sf \longmapsto \: \dfrac{a( - {d}^{2} + 4) }{ { - d ^2+ 4}^{} } = \dfrac{g}{{ - d ^2+ 4}^{}} [/tex]

[tex]\sf \longmapsto \:1 a = \dfrac{g}{{ - d^2 + 4}^{}} [/tex]

[tex]\underline{\bf Answer:—}[/tex]

[tex]\boxed{ \bf \: a = \dfrac{g}{ - d^2 + {4}^{} } }[/tex]

Answer:

[tex]\boxed{\boxed{\sf a=\cfrac{G}{4-d^2} }}[/tex]

Step-by-step explanation:

[tex]\sf G=a(4-d^2)[/tex]

Use the Distributive Property to multiply a by (4-d^2):

[tex]\sf G=4a-ad^2[/tex]

Now, we'll swap sides so that all variable terms are on the left hand side.

[tex]\sf 4a-ad^2=G[/tex]

Combine like terms:

[tex]\sf (4-d^2)\:a =G[/tex]

Divide both sides by 4-d^2:

[tex]\sf \cfrac{(4-d^2)a}{4-d^2} =\cfrac{G}{4-d^2}[/tex]

Dividing by 4-d^2 undoes the multiplication by 4-d^2.

[tex]\sf a=\cfrac{G}{4-d^2}[/tex]

_______________________________________

All the answers to the given fraction problems are;

1) A; 1

2) D: 500

3) B: 86

4) B: 23

5) A: 124

6) A: 33

7) A: 51.2

8) A: 3

9) A: 16.67 doses

10) A: Php 12.5

11) A: 52.6

12) C: 8.43

13) B: 61 ÷ 9

14) A: 12

15) B: 5

16) A: decimal form

17) A: 0.44

18) A: 24 ÷ 27

1) 1.7 ÷ 8.5

We need to change them to whole numbers by shifting the decimal points one place to the right to get; (17/85)

2) 50 ÷ 0.1

Shift decimal one place to the right to get;

500/1

Quotient = 500

3) 0.86 ÷ 0.02

The dividend is usually the numerator. Let us shift both numerator and denominator by two decimal places to the right to get; 86 ÷ 2

Thus, new dividend = 86

4) 6.9 ÷ 0.3

Move decimal points one place to the right to get;

69 ÷ 3 = 23

5) 75.64 ÷ 0.61

Move decimal points two places to the right to get;

7564 ÷ 61

Numerator written as a factor of denominator gives;

(124 × 61)/61

Quotient = 124

6) 7.26 ÷ 0.22

Move decimal points two places to the right to get;

726/22

Numerator written as a factor of denominator gives;

(33 × 22)/22 = 33

7) 5.12 ÷ 0.10

Move decimal points two places to the right to get;

512/10 = 51.2

8) A 0.75 m pink ribbon was cut into 0.25 m strips. Thus;

Number of pieces = 0.75/0.25

Move both decimals 2 places to the right to get;

75/25 = 3 pieces

9) A bottle contains 27.5 ounces

You take 1.65 ounces for each dose.

Number of doses per bottle = 27.5/1.65

Move decimal points two places to the right; 2750/165

Number of doses per bottle = 16.67 doses

10) She earned Php256.25 for gardening.

She worked 20.5 hours the month.

Amount earned per hour = 256.25/20.5

move decimal places two points to the right to get;

Amount earned per hour = Php 12.5

11) 5.26 times 10

move decimal place two points to the right to get;

(526 × 1/100) × 10 = 52.6

12) 59 ÷ 7

Nearest multiple of 7 to 59 is 8.

Thus, 59 ÷ 7 = 8³/₇

⇒ 8.43

13) The one that gives a quotient of 6.78 is;

61 ÷ 9

14) How many 7 does 86 have?

This is; 86 ÷ 7

Nearest multiple of 7 to 86 is 84 which is 12 × 7

Thus, there are 12 numbers of 7 in 86.

15) Remainder if you divide 59 by 9

Nearest multiple of 9 to 59 is 54 which is 9 × 6.

Remainder = 59 - 54 = 5

16) When divisor is bigger than the dividend, it means the denominator is bigger than the numerator and so the quotient is an improper fraction which is a decimal.

17) 4 ÷ 9 = 0.444

Approximating to one decimal place = 0.4

18) The correct mathematical sentence with never ending decimal is;

24 ÷ 27

Read more on simplifying fractions at; https://brainly.com/question/6109670

Answer:

c . f(x)=0,x=????????????

It is not possible to have a bounded feasible region that does not optimize an objective function.

The viable zone is the common area that the linear programming problem's constraints all dictate.

There is an optimum value of the objective function if the feasible region is bounded and the function attains its optimum values at the extremes of the feasible region.

Hence,  it is not possible to have a bounded feasible region that does not optimize an objective function.

Learn more about the feasible region:

https://brainly.com/question/29314086

#SPJ2

Answer:

6 or -1.5

Step-by-step explanation:

We can let this integer be x.

Therefore, according to the question we have:

[tex]2x^2-18=9x[/tex]

Subtracting 9x, we have a quadratic:

[tex]2x^2-9x-18=0[/tex]

Plugging into the quadratic equation:

[tex]\frac{9+\sqrt{81+144}}{4}, \frac{9-\sqrt{81+144}}{4},[/tex]

the square root of 81+144 is 15, so the answer is either 6 or -1.5

Answer:

Q1: 3 pages per minute

Step-by-step explanation:

time = 3 minutes

pages = 9 pages

answer = 9 divided by 3 = 3

Answer:

3 pages per minute

1 hour per $5.29

Step-by-step explanation:

9÷3= 3

37÷7= 5.29

Answer:

yes your absolutely right

Step-by-step explanation:

you just are

Answer: First question: D, Second question: A

Step-by-step explanation:

Note: I'm not so good at expanding so I'll just solve it :)

So this leaves either C or D

Apply the sum rule:

8-70=-62

The only one that gives a negative sum is D

For the second picture, the one you have chosen is correct

a1 = 3 and r = -5 so:

an = 3/5 * (-5)^n

Plugging in 8 for n (the first choice) we get the given term: -234,375

Answer:

Step-by-step explanation:

Putting n = 0 and n = 1 into the expression being summed will show you which series is correct.

  2 -7n for n=0 is 2 -7·0 = 2

  2 -7n for n=1 is 2 -7·1 = -5

The series of the last choice (d) is correct.

__

The given sequence is exponential with a first term of 3 and a common ratio if -5. Then the n-th term is ...

  an = 3(-5)^(n -1)

We want to find n for an = -234,375.

  -234375 = 3(-5)^(n-1)

  -78125 = (-5)^(n-1)

For n to be a real number, we must have n even. In that case, the value of n is equivalent to the value that is the solution to ...

  78125 = 5^(n -1)

Taking logs of both sides, we get ...

  log(78125) = (n -1)·log(5)

  log(78125)/log(5) = n -1 . . . . . . . . . . . . divide by log(5)

  n = 1 +log(78125)/log(5) = 1 +7 = 8 . . . add 1 and evaluate

-234,375 is the 8th term of the sequence.

Answer:

Domain: (-∞ , ∞)

Range: y <= 8        [8 , -∞)

Step-by-step explanation:

x = 2

f(x) = 8

x<=2

f(x) <=8

Answer:

v = 6.32  m/s

Step-by-step explanation:

Given Data:

Mass = m = 40 kg

Kinetic Energy = KE = 800 J

Required:

Speed = v = ?

Formula:

[tex]\displaystyle KE = \frac{1}{2} mv^2[/tex]

Solution:

Rearrange the formula for speed

[tex]\displaystyle v =\sqrt{\frac{2KE}{m} } \\\\Put \ values\\\\v = \sqrt{\frac{2(800)}{40} } \\\\v = \sqrt{2(20) } \\\\v = \sqrt{40} \\\\\boxed{v = 6.32 \ m/s}\\\\\rule[225]{225}{2}[/tex]

Hope this helped!

Answer:

D, E and F

Step-by-step explanation:

Beause y is a point. It is a prime example physics.

Answer:

y = -4x + 9

Step-by-step explanation:

using any two points, in this case (0, 5) and (3, -7) you can find slope by using this formula: [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

plug in the x- and y- values of the two points above

[tex]m=\frac{-7-5}{3-0}=\frac{-12}{3}=-4[/tex]

y = -4x + b

use any point of the line and plug it into the equation above

5 = -4(0) + b

5 = -4 + b

5 + 4 = -4 + b +4

9 = b

the equation in full is y = -4x +9

Answer:

7 inches

Step-by-step explanation:

756÷108=7

that's about it, but I just divided the area and length.

Answer:

C and E are the answers:)

Step-by-step explanation:

Hope this helps!

Answer- C,D, and E

If you plug in any number for those proplems you will get a different number a each side

Step-by-step explanation:

I don't know the answer really

Answer:

x= -3

Step-by-step explanation:

[tex] \frac{x + 6}{3} - \frac{x + 8}{5} = 0[/tex]

Multiply both sides by 15 (LCM of 3 and 5):

[tex] \frac{15(x + 6)}{3} - \frac{15(x + 8)}{5} = 0[/tex]

5(x +6) -3(x +8)= 0

Expand:

5x +30 -3x -24= 0

2x +6= 0

-6 on both sides:

2x= -6

x= -6 ÷2

x= -3

Answer:

Step-by-step explanation:

Let x be the adjacent side length in cm

opposite side is x + 2 cm

hypotenuse is x + 4 cm

x² + (x + 2)² = (x + 4)²

x² + (x² + 4x + 4) = (x² + 8x + 16)

x² - 4x - 12 = 0

(x - 6)(x + 2) = 0

so either

x - 6 = 0    x = 6

or

x + 2 = 0    x = -2

positive answer is x = 6 as negative length does not make sense

opposite side is 6 + 2 = 8

hypotenuse is 6 + 4 = 10

perimeter is 6 + 8 + 10 = 24 cm

Answer:

The terms are 2, 4, and 8

Step-by-step explanation:

a+b+c=14

a^2+b^2+c^2=84

Plug in numbers.

3+6+5=14

3^2+6^2+5^2=70

This is too little, meaning the some of the terms have to be larger.

1+7+6=14

1^2+7^2+6^2=86

This is too much, meaning smaller terms are needed.

2+8+4=14

2^2+8^2+4^2=84

This is perfect.

Answer:

[tex]3x + 6y = 12[/tex]

[tex]3x + 6y - 6y = 12 - 6y[/tex]

[tex]3x = 12 - 6y[/tex]

[tex] \frac{3x}{3} = \frac{12}{3} - \frac{6y}{3} [/tex]

[tex] \frac{3x}{3} = 1 = x[/tex]

[tex] \frac{12}{3} - \frac{6y}{3} [/tex]

[tex] = \frac{12 - 6y}{3} [/tex]

[tex] = \frac{6(2 - y)}{3} [/tex]

[tex] \frac{6}{3} = 2[/tex]

[tex] = 2( - y + 2)[/tex]

[tex]x = 2( - y + 2)[/tex]

Answer:

x=2(3-y)

Step-by-step explanation:

3x+6y=12

x+2y=4

x=4-2y

=2(2-y)

Answer:

first you need a problem to solve.

Step-by-step explanation:

what is the question here?

Answer:

Step-by-step explanation:

d + 2d = 120

3d = 120

d = 40 m

east distance was 40cos30 + 80cos120 = -5.35898 m

north distance was 40sin30 + 80sin120 = 89.282032

as 30° and 120° bearings are 90° apart, Jason needs to walk

D = √(d² + (2d)²) = d√5 or 40√5 meters or about 89.44 m to return to his original position.

we could also use √(-5.35898² + 89.282032²) = 89.44 m

direction will be

θ = arctan -89.28/5.359 = -86.565° or a bearing of 273.4°

Answer:

60

Step-by-step explanation:

56-7+22÷2

56-7+11

67-7=60

hope it helps thanks

Answer:

Aiden spent $22.20. His sister spent $54.40. His sister spent $32.20 more than Aiden.

Step-by-step explanation:

Step-by-step explanation:

[tex]x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]

a=1.

b=-7

c=-6

x=

[tex] \frac{ - ( - 7) + \sqrt{ (- 7)^{2} - 4(1)( - 6)} }{2(1)} [/tex]

OR

[tex] \frac{ - ( - 7) - \sqrt{ (- 7) ^{2} - 4(1)( - 6)} }{2(1)} [/tex]

Therefore x= 7,772

OR

x=-0,772

Answer:

5 times more books

Step-by-step explanation:

In total Marisol has 75 books.  She has 5 times as many books and Jerry has 15.  5*15=75

Answer:

Yes, 35 feet is enough

The angle of elevation is 4.1º