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3 years ago

HELP: Use a system of linear equations to solve the following riddle:

Mathematics

2 answers:

agasfer [191]3 years ago

8 0

Answer:

A) x - y = 12

B) x = 4y +3 or x - 4y = 3

A) x - y = 12

B) x - 4y = 3

We subtract B) from A)

3y = 9

y = 3

A) x -y = 12

x - 3 = 12

x = 15

Step-by-step explanation:

matrenka [14]3 years ago

3 0

Answer:

3 and 15

Step-by-step explanation:

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Sondra has 1 gallon of milk. Her pudding recipe calls for 1 quart of milk, but she triples the recipe. How many cups of milk doe

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Step-by-step explanation:

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4 years ago

6. Mary and Steve each travel 845 miles. Mary drove an average of 5 mph faster than Steve and completed the trip in one hour's l

sattari [20]

Answer:

Steve had an average speed of 62.55 mph while Mary had an average speed of 67.55 mph

Step-by-step explanation:

Here, we want to calculate the average speed of each of the two.

From the question, we are told that Mary drove an average of 5 mph faster than steve.

So, let the average speed of Steve be x mph, this means that the average speed of Mary will be (x + 5) mph

Mathematically;

Time = distance/speed

Time taken by Steve = 845/x hours

Time taken by Mary = 845/(x + 5)

But Mary took an hour less to complete her own trip;

This means that;

if we add one hour to the time spent by Mary, then we will have the time spent by Steve

845/(x + 5) + 1 = 845/x

845/(x + 5) = 845/x -1

845/(x + 5) = (845 - x)/x

Cross multiply;

845(x) = (x + 5)(845-x)

845x = x(845-x) + 5(845-x)

845x = 845x-x^2 + 4225 - 5x

x^2 + 5x - 4225 = 0

We can solve this using the quadratic formula;

x = -b ± √(b^2 - 4ac)/2a

where a = 1 , b = 5 , c = -4225

x = -5 ± √(5^2 - 4(1)(-4225)/2(1)

x = -5 ± √(25 + 16,900)/2

x = -5 ± √(16,925)/2

x = (-5 + 130.1)/2 or (-5-130.1)/2

We ignore the negative side as speed cannot be negative

x = (-5 + 130.1)/2 = 62.548 which is approximately 62.55 mph

So steve’s speed is 62.55 mph while Mary’s speed = 62.55 + 5 = 67.55 mph

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3 years ago

A transformation of ΔDEF results in ΔD'E'F'.

sladkih [1.3K]

Answer:

Rotation

Step-by-step explanation:

A transformation of a triangle can be either dilation or reflection or rotation or a translation.

Dilation happens when a symmetric figure is formed with scale factor other than 1. But here both triangles have same side length. Hence no dilation

Reflection happens when it is reflected over a line as we see in a mirror. But here the two triangles are not looking as images on a line. Hence no reflection

Rotation is keeping the same shape but rotating through a certain angle. Here DEF is rotated without disturbing its shape or size through a certain angle. Hence rotation is right

Translation is not right because there is no vertical or horizontal shift to get new triangle.

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3 years ago

Read 2 more answers

The proof, with a missing reason, proves that the measure of angle ECB is 54°.

aniked [119]

Answer:

Midsegment of a Triangle Theorem

Step-by-step explanation:

$In\: \triangle ADE\\m\angle A + m\angle D + m\angle AED = 180°\\\therefore 90°+36°+m\angle AED= 180°\\\therefore 126° +m\angle AED = 180°\\\therefore m\angle AED = 180°-126°\\\therefore m\angle AED = 54°\\$

$In\: \triangle ADE,$ D and E are mid points of sides AB and AC respectively.

Therefore, DE || BC

Hence, by Midsegment of a Triangle Theorem

$m\angle ACB = m\angle AED =54°(corresponding\:\angle 's) \\\therefore m\angle ECB = m\angle AED =54°(\because A - E - C)$

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3 years ago

From a top-down 2D perspective, a car moves in a diagonal line and travels a distance equivalent to 80 miles. If the angle betwe

SVEN [57.7K]

We can use Pythagorean theorem for right angle triangle to solve this problem.

The diagonal line would be hypothenuze. Horizontal and vertical distance would be other two sides of a triangle.

We will use the following formulas:
$sin \alpha = \frac{opposite}{hypothenuze} \\ cos \alpha = \frac{adjacent}{hypothenuze}$
Where opposite side is vertical distance and adjacent side is horizontal distance.

Solving for these two sides we have:
$opposite = hypothenuze * sin \alpha \\ adjacent = hypothenuze * cos \alpha$

We insert numbers and we get solution:
$opposite = 80 * sin 25 = 33.8miles \\ adjacent = 80 * cos 25 = 72.5miles$

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3 years ago