How do you find the shorter leg of a 30 60 90 triangle?

We can solve this equation by using quadratic formula. So we have two solution of given equation.

Write the quadratic equation in standard form a + bx + c = 0. Identify the values of a, b, c. Then write the Quadratic Formula. Then substitute in the values of a, b, c. Then solve and check the solution.

Quadratic formula that gives the solutions of the general quadratic equation a + bx + c = 0 and that is usually written in the form quadratic formula x = [-b ± √(b² - 4ac)] / (2a). So to solve a quadratic equation using quadratic formula just get the equation into standard form a + bx + c = 0 and apply the quadratic formula.

Here we have equation 5-7x+4

where a=5  b= -7   c=4

putting values in the formula

x= -(-7) +[tex]\sqrt{(-7)^2-4(5)(4)/2(5)}[/tex]

x= 7 + [tex]\sqrt{49+80/10}[/tex]

x= 7+[tex]\sqrt{129/10}[/tex]

Hence given values given two solutions.

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Complete question is: How to solve the given  quadratic equation?

Answer:

this should explain your answer.

Answer:

c. infinitely many solutions

Step-by-step explanation:

hope this helps :)

Answer:

357.5cm^2

Step-by-step explanation:

Answer:

0 and 3??

Step-by-step explanation

Answer:

Yes.

Step-by-step explanation:

Answer:

40 min per period

Step-by-step explanation:

When it has 8 periods :

Total time = 45 min per period for 8 period

Total time = 45 × 8 min

When it has 9 periods : let each period be of x min

Total time = x min per period for 9 period

Total time = x × 9 min

As total time remains same,

45 × 8 = x × 9

5 x 8 = x

40 = x

Answer:

C. y ≤ –3x + 4

Step-by-step explanation:

Answer:

Step-by-step explanation:

we know that

The solution of the inequality is the shaded area below the solid line (the gray area)

The slope of the solid line is negative

The y-intercept of the solid line is positive

The equation of the solid line is equal to  

therefore

the equation of the inequality is equal to

0.7n+0.8n=2.1

1.5n=2.1

n=1.4

Therefore, the answer is B.

Answer:

B). n = 1.40

Step-by-step explanation:

0.7n + 0.8n = 2.1

(0.7n + 0.8n) = 2.1

1.5n = 2.1

/1.5 /1.5

n = 1.40

hope this helped!

Answer:

54×3

27×6

(10^2)+31×2

I hope this helps

Answer:

I uploaded the answer to^{}

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Answer:

the answer should be 3/4

The ratio of the length of arc BC to length of arc DE is calculated as: 1/2.

Length of an arc = ∅r, where r is radius, and ∅ is angle measure in radians.

AD = 2/3AB

Length of DE:

∅ = 1.18 + 2.36 = 3.54 radians

r = 2/3AB

Length of arc DE = (3.54)(2/3AB) = 2.36(AB)

Length of BC:

∅ = 1.18 radians

r = AB

Length of arc BC = (1.18)(AB) = 1.18(AB)

Ratio of the length of BC to DE = 1.18(AB) / 2.36(AB) = 1.18/2.36 = 1/2

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Answer:

.

Step-by-step explanation:

Answer: 1271

Step-by-step explanation:

620 + (105% × 620) =

620 + 105% × 620 =

(1 + 105%) × 620 =

(100% + 105%) × 620 =

205% × 620 =

205 ÷ 100 × 620 =

205 × 620 ÷ 100 =

127,100 ÷ 100 =

1,271

Answer:

Step-by-step explanation:

1436 is the answer

Answer:

There are three ways to solve systems of linear equations: substitution, elimination, and graphing.

Answer:

about 154.3

Step-by-step explanation:

A perfect interval which  identifies the distance between the first note of a major scale and given unison, 4th, 5th or either the  octave. Those given  intervals can be given in the extra theoretical  name as “perfect”.

Perfect intervals has only basic form. The first (also called prime or unison), fourth, fifth and eighth (or octave) are all known as  perfect intervals. These intervals are known as  "perfect" since  these types of intervals sound and they provide the certain frequency ratios which  are simple  as whole numbers. Perfect intervals sound "perfectly consonant" . that means  which are played together, there is a sweet tone to the interval. It sounds perfect or resolved. Whereas, a dissonant which sounds and  feels tense and in need of  their resolution.

Interval qualities are classified  as major, minor, harmonic, melodic, perfect, augmented, and diminished. since ,lower a perfect interval by a half step it becomes a  diminished and when it is raised it to  a half step it becomes augmented of an interval .

When it is in lower and provides  a major non-perfect interval a half step and it becomes a minor interval then if we raise it  to a half step it becomes augmented level then if we raise to  lower a minor interval by a half step it becomes diminished  level , then if we raise a minor level interval a half step it becomes a major level interval.

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Answer:

42.602 cm

Step-by-step explanation:

<O =360/5=72°

sin <O =sin 72 = opp/adj = TA / 7

TA = 6.66 cm

Area of ABT = 7*6.66 = 42.602 cm

The subtraction from the given number is = 386

Subtraction is defined as one of the basic arithmetic operations used to subtract one value from another value.

340 subtracted from 726 = 386.

It means; 726 - 340 = 386

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By unitary method 24 students/(64/9) yards squared times 1600 yards squared equals 5400 students.

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

Students traverse a total area of 40 yards by 40 yards, or 1600 yards.

24 kids covered an area of 8 ft x 8 ft, or (8 ft x 1 yd/3 ft)2 = [(8/3) yard]2 = (64/9) yd.

The number of students present is calculated by multiplying the number of students per yard, or 24 students/(64/9) yd2, by the area that students cover.

Therefore: 24 students/(64/9) yards squared times 1600 yards squared equals 5400 students.

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After diving the polynomials, the quotient and remainder is q(x)=-x^2+1 and r(x)=-1 respectively.

What are polynomials?

The word "polynomial" is derived from the Greek words "poly" and "nominal," which combined translate to "many phrases." There is no limit to the number of terms that can exist in a polynomial.

The polynomials are -

a(x)=-x^4

b(x)=x^2+1

Divide a(x) by b(x).

-x^4/x^2+1 = -x^2+1 with remainder as -1.

The quotient is obtained as q(x)=-x^2+1 and the remainder is r(x)=-1.

The given equation is -

a(x)/b(x)=q(x)+[r(x)/b(x)]

Plugging in all the values -

-x^4/x^2+1=-x^2+1+[-1/x^2+1]

[-x^4/x^2+1]-[-1/x^2+1]=-x^2-1

-x^4+1/x^2+1=-x^2-1

-x^4+1=[-x^2+1][x^2+1]

-x^4+1=(-x)^2[x^2+1]+(1)[x^2+1]

-x^4+1=-x^4-x^2+x^2+1

-x^4+1=-x^4-1

So, LHS=RHS is proved using the equation.

Therefore, the quotient is q(x)=-x^2+1 and the remainder is r(x)=-1.

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An acute triangle is a triangle with all angles measuring less than 90°.

To solve an acute triangle using trigonometry, we need to know the length of at least one side and at least one angle of the triangle.

For example, let's assume the triangle has side lengths a = 6, b = 8, and we know the angle A = 30°.

First, we can use the Law of Cosines to calculate the length of the third side, c:

c² = a² + b² - 2abcos(A)

c² = 6² + 8² - 2(6)(8)cos(30°)

c² = 64 - 96cos(30°)

c² = 64 - 48

c² = 16

c = 4

Now we can calculate the other two angles, B and C, using the Law of Sines:

sin(B) = sin(A) * c/a

sin(B) = sin(30°) * 4/6

sin(B) = 0.5 * 2/3

sin(B) = 0.3333

B ≈ 19.47°

sin(C) = sin(A) * c/b

sin(C) = sin(30°) * 4/8

sin(C) = 0.5 * 0.5

sin(C) = 0.25

C ≈ 14.04°

Therefore, the three angles of the triangle are A = 30°, B = 19.47°, and C = 14.04°, and the three sides are a = 6, b = 8, and c = 4.

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Answer: 47

Step-by-step explanation:

4.72 / .1= 47

47

Answer:

it might be 2.6

Step-by-step explanation:

im assuming the 16.3 is the circumfrence, so if you follow the formula for circumfrence (2πr) the radius would be 2.6. hope this is correct

The radius r of the circle is 4.4 yd .

A circular sector, also known as circle sector or disk sector, is the portion of a disk enclosed by two radii and an arc, where the smaller area is known as the minor sector and the larger being the major sector.

For a circle, the arc length formula is θ times the radius of a circle.

 Arc Length = 2 π r (θ/360°)  

where,

r = radius of circle

θ = angle of Sector

According to the question

Arc Length of circle = 16.3 yd

Angle of sector= 240°

By using arc length formula

Arc Length = 2 π r (θ/360°)  

substituting the value

16.3 = 2π r (240°/360°)

16.3 = 2π r * [tex]\frac{2}{3}[/tex]

16.3 * 3 = 4π r

54.9 = 4π r

As π = [tex]\frac{22}{7}[/tex]

54.9 = 4 *  [tex]\frac{22}{7}[/tex] r

54.9 * 7 = 88 r

384.3 = 88 r

r = 4.4 yd

Hence, The radius r of the circle is 4.4 yd .

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Answer:

Box 2 :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

2/8 = 1/4

2/8 = 200/800

and so on.

There are an infinite number of possibilities here.

Answer:

1/4

Step-by-step explanation:

2/8 can be simplified to 1/4

2/8 divided by 2/2 = 1/4

but there are also many other ways

10/40,6/24, etc

Answer:

A. The car spends 2.05 hours going 55 miles per hour

B. The car spends 1 hour going 35 miles per hour

C. The trip takes 3.6 hour

Step-by-step explanation:

The equation is

55x+35y=200

Let's solve A

We know the car spends 2.5 hours going 35 miles per hour on the trip, so we put 2.5 in for y and solve for x

55x+35(2.5) = 200

55x + 87.5 = 200

55x = 112.8

x = 2.05 hours going 55 miles per hour

So, the car spends 2.05 hours going 55 miles per hour

Let's solve B

55(3)+35y=200

165 + 35y = 200

35y = 35

y = 1 hour

So, the car spends 1 hour going 35 miles per hour

Let's solve C

We know the car spends no time going 35 miles per hour, so we put 0 in for y and solve for x

55x+35(0)=200

55x = 200

x = 3.6  hours

So, the trip takes 3.6 hour

Answer:

y = 3x + 10

Step-by-step explanation:

Parallel lines have the same slope, so the line will have a slope of 3.

Plug in the slope and given point into y = mx + b, and solve for b:

y = mx + b

4 = 3(-2) + b

4 = -6 + b

10 = b

Plug in the slope and y intercept into y = mx + b

y = mx + b

y = 3x + 10

So, the equation of the line is y = 3x + 10