the surface of a rectangle is 352mm squared. two of the dimensions are 4 mm 8mm. find the measure of the other dimension

A health food company makes its 'Superfood Blend' from whey protein, which costs $10.25 per pound, and powdered spirulina, which

kaheart [24]

Given:

Cost of protein = $10.25 per pound

Cost of spirulina = $22.45 per pound

Cost of blend = $16.35 per pound

Weight of blend = 140 pounds

To find:

The quantity of spirulina it will need to make the blend.

Solution:

Let x be the quantity of protein and y be the quantity of spirulina in the blend. Then,

$x+y=140$ ...(i)

Equation (i) can be written as:

$x=140-y$ ...(ii)

$10.25x+22.45y=16.35\times 140$

$10.25x+22.45y=2289$ ...(iii)

Using (ii) and (iii), we get

$10.25(140-y)+22.45y=2289$

$1435-10.25y+22.45y=2289$

$12.2y=2289-1435$

$12.2y=854$

Divide both sides by 12.2.

$y=\dfrac{854}{12.2}$

$y=70$

Therefore, 70 pounds of the spirulina it will need to make the blend.

3 0

3 years ago

What’s the answer to the question ?

Sloan [31]

Answer:

The answer is B.

8 0

3 years ago

Can someone help me understand and do this because well I have no idea what I’m doing.

kolbaska11 [484]

Answer:

Read Below!

Step-by-step explanation:

Answer:

Step-by-step explanation:

Please find attached an edited image of yours where I have named the sides of triangle in part 23). Below I shall give you a detail answer for part 23) along with the final values for the other parts 24) and 25) and you can apply the same methods to solve the remaining two.

So lets consider Triangle 23):

Here we have a Triangle of sides a, c and (b+43) which is the base (total length). We also have line h which is the height of our triangle. Here the height creates a right angle (i.e. 90° ) denoted by the little square symbol in the bottom of the line. This h line divides our triangle into Two Right Triangles. Right triangles mean that one of their angles is ALWAYS 90° .

In theory we also know that the SUM of the interior angles of ANY triangle is always 180°. Finally we know that for ANY Right Triangle the Pythagorian Theorem is true which denotes that the Squared value of the Hypotenuse of the triangle is equal to the squared values of the other two legs of the triangle, which in mathematical form reads:

$x^2+y^2=h^2$

where $x$ and $y$ are the two legs of a right triangle and $h$ is the hypotenuse. In a right triangle we also know that for any of the other two angles (i.e. NOT the 90° angle), thus lets call one of the two remaining angles $\theta$ the following trigonometric identities are to be true:

$sin\theta=\frac{opposite side}{hypotenuse} \\cos\theta=\frac{adjacent side}{hypotenuse}\\tan\theta=\frac{opposite side}{adjacent side}$

Finally we know that the Area of any triangle is given as half the product of the height (h) and base (b) of the triangle as follow:

$A=\frac{1}{2}bh$

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Let us now consider my attached image and the triangle in 23). With respect to the angles, we know 2 out of the 3 angles since one is given as 70° and the other is the right angle, thus 90°. So lets call the uknown one as $\theta$ so we have:

$70+90+\theta=180\\\theta=180-160\\\theta=20$

So now we have a Right triangle where we know all 3 angles and 1 of each sides. Therefore we can find the remainder of the sides using our Trigonometric Identities and Pythagorian Theorem on the left right triangle (i.e. a-h-43). Note here $a$ is the hypotenuse, $h$ and $43$ are the opposite and adjacent sides, respectively.

Solving for side $a$ we have:

$cos70=\frac{43}{a} \\a=\frac{43}{cos70} \\a=125.7\\a=126$

Thus from Pythagoras Theorem:

$a^2 = h^2 + 43^2\\h^2=a^2-43^2\\h=\sqrt{a^2-43^2}\\h=\sqrt{126^2-43^2}\\h=118$

Now let as work on the other right triangle included in our main triangle of 23) as follow. Here now we know $h$ which is the opposite side from the known angle of 37° (that is given), so by trigonometry on the right angle now we have:

$sin37=\frac{h}{c}\\c=\frac{h}{sin37}\\ c=196$