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3 years ago

7

What is the value of a?

1 answer:

Annette [7]3 years ago

8 0

Answer:

<h2>a = 16</h2>

Step-by-step explanation:

Look at the picture.

The formula of an area of a trapezoid is:

$A=\dfrac{b_1+b_2}{2}\cdot h$

$b_1,\ b_2$ - bases

$h$ - height

We have:

$A=128,\ b_1=a+2,\ b_2=a-2,\ h=8$

Substitute:

$128=\dfrac{a+2+a-2}{2}\cdot8\\\\128=\dfrac{2a}{2}\cdot8$

$128=8a$ <em>divide both sides by 8</em>

$16=a\to a=16$

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Find 4 more than the quotient of 9 and 2

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Ok so you know the first garden needs 1 and 2/5 bags of soil. Now first we need to find one fifth of that. So let's make this mied number into an improper fraction:

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3 years ago

The staff dietician at the California Institute of Trigonometry has to make up a meal with 600 calories, 20 grams of protein, an

Arlecino [84]

Answer:

The amount of rubbery jello=5.038 ounce

Dried fish stick = 4.886 ounce

Mystery meat = 1.526 ounce.

Step-by-step explanation:

Solutions/Explanation: (a) Suppose the amount of rubbery jello = $x$ ounce,

The dried fish sticks amount to be = $y$ ounce

The amount of mystery meat = ounce.

Specification of the ingredients

Rubbery jello has: Calories=10 Cal/ounce, Protien=1 gram/ounce, Vitamin C= 30 mg/ounce

Dried fish sticks: Calories=50 Cal/ounce, Protien=3 grams/ounce, Vitamin C=10 mg/ounce

Mystery meat: Calories=200 Cal/ounce, Protien=0.2 gram/ounce, Vitamin C=0 mg/ounce,

Now,

Total calories = $600$ .

Thus,

$10x+50y+200z=600\quad\Idot (1)$

The, total Protien = $20 g$ .

Thus,

$x+3y+0.2z=20 \quad\Idot (2)$

also, total Vitamin C = .

Thus,

$30x+10y+0z=200 \quad\Idot (3)$

Therefore,

1, 2 and 3 are the mathematical models of the dietician's problem with a system of three linear equations.

(b) Now, we know three equations:

$10x+50y+200z=600$

OR

$x+5y+20=60 \quad\Idot (4)$

From eqn 2,

$x+3y+0.2z=20 \quad\Idot (5)$

From eqn 3.

$30x+10y=200$

OR

$3x+y=20 \quad\Idot (6)$

On solving the eqn 4, 5 and 6 for $x, y$ and $z,$

Multiplying eqn 5 by 100,

$100x+300y+20z=2000 \quad\Idot (7)$

Now, subtract eqn 4 from eqn 7

$99x+295y=1940 \quad\Idot (8)$

Now, multiplying eqn 6 by 295. we have,

$885x+295y=5900 \quad\Idot (9)$

Now, subtract, eqn 8 from eqn 9, we get,

$786x=3960$

$x=\frac{3960}{786}$

$x=5.038 \quad\Idot (10)$

Now, substituting into eqn 6, we get

$y=4.886 \quad\Idot (11)$

Now, substitute eqn 10 and 11 into eqn 4, we have

$z=1.526$

4 0

3 years ago