Find the area of the triangle pictured above.

9514 1404 393

Answer:

  a) zeros: -2/3, 6

  b) x < -2/3, signs: -, -; sign of product: +

  -2/3 < x < 6, signs: +, -; sign of product: -

  x > 6, signs: + +; sign of product: +

  c) solution: x < -2/3 ∪ x > 6

Step-by-step explanation:

a) The zeros of the product are the values of x that make either factor zero. (A product is only zero if one of the factors is zero.)

  3x +2 = 0   ⇒   x = -2/3

  x -6 = 0   ⇒   x = 6

The zeros of the quadratic are x = -2/3 and x = 6.

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b) For values of x left of the left-most zero, both factors are negative. For values of x between the zeros, the left factor is positive and the right factor is negative. For values of x greater than the right-most zero, both factors are positive. That is, for large negative values of x, all factors are negative. Working left-to-right, each time a zero is crossed, one factor changes sign.

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c) The solution is where the signs of the factors match:

  x < -2/3 or -6 < x

Answer:

d. distributive property

Step-by-step explanation:

Answer:

Capacity of tank = 44,000 l

Step-by-step explanation:

Given:

Height of tank = 3.5 m

Radius = 2 m

Find:

Capacity of tank

Computation:

Volume of cylinder = πr²h

Volume of cylinder = (22/7)(2)²(3.5)

Volume of cylinder = 44 m³

1m³ = 1000 l

So,

Capacity of tank = 44  x 1,000

Capacity of tank = 44,000 l

answer:

he would use 3 cups of sugar and would need to multiply

step-by-step explanation:

6 X 1/2 = 3 cups of sugar

Answer:

true

Step-by-step explanation:

Answer: 18 questions

Step-by-step explanation:

First we want to make 60% a decimal so we divide by 100.

This gives us 0.6

Then we multiply 30*0.6=18

18 questions

Answer:

2x-4

Step-by-step explanation:

5x-(4+3x)

5x-4-3x

5x-3x-4

2x-4

Answer:

(-5, 9)

Step-by-step explanation:

Answer:

9.42

Step-by-step explanation:

Hey There!

The first step of this problem is to find the formula for arc length

[tex]arc-length=2\pi r(\frac{0}{360} )[/tex]

r=raduis

0 = angle

now we just plug in the values

[tex]arc-length=2\pi 10\frac{54}{360} \\2\pi =6.283185307\\6.283185307x10=62.83185307\\62.83185307\frac{54}{360}=9.424777961[/tex]

so the arc length equals 9.424777961

the last step is to round to the nearest hundreth

so your final answer is 9.42

Answer:

la verdad que depende de la situación

Answer:

60

Step-by-step explanation:

trangles always equal 180 degrees on the inside angles

180-75-45 = 60

Answer:

At least 26 questions to get around an 82% not 25 because that equals 78%

Step-by-step explanation:

Answer:

Kevin answered 24 questions correctly.

Kevin would have to answer 25.6 questions correctly to get more than 80%.

Answer:

sin2θ = [tex]\frac{12}{13}[/tex]

Step-by-step explanation:

Since, sin2θ = 2sinθcosθ

From the triangle given in the picture,

Opposite side of angle θ = 2 units

Adjacent side of angle θ = 3 units

Hypotenuse = [tex]\sqrt{2^2+3^2}[/tex] = [tex]\sqrt{13}[/tex] [By Pythagoras theorem]

sinθ = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

       = [tex]\frac{2}{\sqrt{13}}[/tex]

cosθ = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]

        = [tex]\frac{3}{\sqrt{13} }[/tex]

sin2θ = [tex]2\times (\frac{2}{\sqrt{13}})(\frac{3}{\sqrt{13}})[/tex]

         = [tex]\frac{12}{13}[/tex]

Answer:

[tex]Distance = 38.57ft[/tex]

Step-by-step explanation:

Given

[tex]Base = 60[/tex]

[tex]\theta = 50[/tex]

Required

The distance between the top and John

The distance is calculated using:

[tex]sin\alpha = \frac{Distance}{Base}[/tex]

Where

[tex]\alpha = 90 - \theta[/tex] --- the angle between the diagonal line and the vertical line

[tex]\alpha = 90 - 50[/tex]

[tex]\alpha = 40[/tex]

So, we have:

[tex]Sin(40) = \frac{Distance}{60}[/tex]

[tex]Distance = 60 * sin(40)[/tex]

[tex]Distance = 60 * 0.6428[/tex]

[tex]Distance = 38.57ft[/tex]

[tex]Distance = 986 * tan(38)[/tex]

[tex]Distance = 986 * 0.7812[/tex]

[tex]Distance = 770ft[/tex] --- approximated

Answer:

i think this

Step-by-step explanation:

Let Va = the velocity of the airplane

Let Vw = the velocity of the wind

When flying with the wind:

(Va+Vw)*(4 hours) = 4000

4Va + 4Vw = 4000

4Vw = 4000 - 4Va

Vw = 1000 - Va

When flying against the wind:

(Va-Vw)*(7 hours) = 4200 km

7Va - 7Vw = 4200

Substitute 1000-Va for Vw and solve for Va:

7Va - 7(1000-Va) = 4200

7Va -7000 + 7Va = 4200

14Va = 11200

Va = 800 km/hr

Rate of wind:

Vw = 1000 - Va = 1000 - 800 = 200 km/hour

Answer:

question of number 10 is 3

Answer:

60th position is the first child that gets all 3 items

Step-by-step explanation:

Find the LCM of 3 , 5 and 4.

Least common multiple of 3 , 4 and 5 = 3 * 4 * 5 = 60

Answer:

3,6,9,12,

4,8,12,16,

5,10,15,

in 60th position

60is the first number that can be divided by 60/3=20 60/4=15 60/5=12

Answer:

A. 12/13

Step-by-step explanation:

Remember SOH, CAH, TOA.

In this situation, the function is sine so sine= opposite/hypotenuse.

The side opposite of K is 12.

The hypotenuse is the longest side so it will be 13.

Therefore, sineK= 12/13(a)

Answer:

12/13

Step-by-step explanation:

Answer:

the answer to a is 25, im unsure what B is.

Step-by-step explanation:

hope this helps!!!

Answer:

x3+2x2-17x+6.

Step-by-step explanation:

(x2+5x-2)(x-3)

= x(x2+5x-2)-3(x2+5x-2)

= x3 +5x2-2x-3x2-15x+6

Simplifying like terms:

= x3+2x2-17x+6

Answer:

You have to deposit $8,207.5 today.

Step-by-step explanation:

Compound interest:

The amount of money in yearly compounded interest, after t years, is given by the following equation:

[tex]A(t) = A(0)(1+r)^t[/tex]

In which A(0) is the initial deposit and r is the interest rate, as a decimal.

You would like to have $10,000 in an account after eight years time.

This means that when [tex]t = 8, A(t) = 10000[/tex]

2.5% compounded interest

This means that [tex]r = 0.025[/tex]

So

[tex]A(t) = A(0)(1+r)^t[/tex]

[tex]A(t) = A(0)(1+0.025)^t[/tex]

[tex]A(t) = A(0)(1.025)^t[/tex]

How much would you have to deposit today?

We have to find A(0), when [tex]t = 8, A(t) = 10000[/tex]. So

[tex]A(t) = A(0)(1.025)^t[/tex]

[tex]10000 = A(0)(1.025)^8[/tex]

[tex]A(0) = \frac{10000}{(1.025)^8}[/tex]

[tex]A(0) = 8207.5[/tex]

You have to deposit $8,207.5 today.

Answer:

m<YVX = 49°

Step-by-step explanation:

Given:

m<YVZ = 52°

m<ZVW = 36°

m<XVU = 43°

m<YVX + m<YVZ + m<ZVW + m<XVU = 180° (angles in a straight line)

m<YVX + 52 + 36 + 43 = 180 (substitution)

m<YVX + 131 = 180

m<YVX = 180 - 131

m<YVX = 49°

Answer:

y = -3x + 5

Step-by-step explanation:

Since the y-intercept occurs at the point (0,5), you can use that and the point slope equation to find the equation.

This looks like y - 5 = -3 (x - 0);

Solving for y, you get y = -3x + 5;

To graph this equation you would put one point at (0,5), then use the slope to count down three and to the left one to find other points, or you could just plug in numbers for x to find their corresponding y values and plot it like that.

Hopefully this helps- let me know if you have any questions!

Answer:

4 9/14

Step-by-step explanation:

Answer:

The answer is 4 9/14

The farm raises some rabbits and native chickens. The number of native chickens is six times the number of rabbits, with a total of 560 feet. farm

Raised ? rabbit.​

Answer:

y = 802

Step-by-step explanation: