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3 years ago

3 ⅕ -⅔ divided by 2 ⅘

Mathematics

1 answer:

spin [16.1K]3 years ago

8 0

Answer:

160/196

Step-by-step explanation:

it would be easier if you converted all fractions to improper fractions

so 3 1/5 would equal 16/5 and 2 4/5 would equal to 14/5

$\frac{14}{5} - \frac{2}{3}$ : to solve this you would need the same common denomenator,

to do this you can multiply 5 and 3 by something to make the lowest common denominator, which would be 15

thus

multiplying first fraction by 3 and the second by 5

42/15 - 10/15 = 32/15

now 32/15 divided by 14/5

the rule for dividing fractions, is flipping the fraction which you will be using to divide, and then multiplying it to the first fraction:

$\frac{32}{14}$ multiplied by $\frac{5}{14}$

thus, answer is 160/196

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mariarad [96]

$-3x^2+12y^2=84$
$12y^2=3x^2+84$
$y^2=\dfrac{x^2}4+7$
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For either square root to exist, you require that $\dfrac{x^2}4+7\ge0$ . This is true for all $x$ , since $\dfrac{x^2}4$ is always non-negative. This means the domain of $y$ as a function of $x$ is all real numbers, or $x\in\mathbb R$ or $(-\infty,infty)$ .

Now, because $\dfrac{x^2}4+7$ is non-negative, and the smallest value it can take on is 7, it follows that the minimum value for the positive square root must be $\sqrt7$ , while the maximum value of the negative root must be $-\sqrt7$ . This means the range is $y\in\mathbb R\setminus(-\sqrt7,\sqrt7)$ , or $|y|\ge\sqrt7$ , or $(-\infty,-\sqrt7]\cup[\sqrt7,\infty)$ .

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4 years ago

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zhenek [66]

The answer is -5 < w < 7

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3 years ago

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3 years ago

In the diagram, ABCDE is a regular pentagon.

RSB [31]

The shape ABCDE is a regular pentagon with five sides, such that the five sides are congruent

<h3>Part A: Calculate ∠BAE</h3>

The angle BAE is a vertex angle, and it is calculated using:

BAE = 180 * (n - 2)/n

Where n= 5; i.e. the number of sides.

This gives:

BAE = 180 * (5 - 2)/5

Evaluate

BAE = 108°

Hence, the measure of angle BAE is 108°

<h3>Part B: The name of the quadrilateral ABCD</h3>

When the vertices A and B are joined together, the shape becomes a trapezoid.

Hence, the name of the quadrilateral ABCD is a trapezoid.

<h3>Part C (i) Calculate ∠EDX</h3>

See attachment for the new figure.

From the attached figure, we have:

∠EDX + ∠EDC = 180° ---- the sum of angles on a straight line

Where:

∠EDC = ∠BAE = 108°

So, we have:

∠EDX + 108° = 180°

Subtract 108° from both sides

∠EDX = 72°

Hence, the measure of angle EDX is 72 degrees

<h3>Part C (ii) What type of quadrilateral is BDXE?</h3>

The quadrilateral BDXE is a parallelogram.

This is so because the opposite sides of BDXE are parallel, but not congruent