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3 years ago

What is the fully factored form of the expression 16x^2 - 49y^2

Mathematics

1 answer:

podryga [215]3 years ago

6 0

Answer:

(4x + 7y)(4x - 7y)

Step-by-step explanation:

Rewrite 16 as 4^2

= 4^2x^2 - 49y^2

Rewrite 49 as 7^2

= 4^2x^2 - 7^2y^2

Apply the Exponent Rule Pt 1 ((a^m*b^m =(ab)^m))

= (4x)^2 - 7^2y^2

Apply the Exponent Rule Pt 2

= (4x)^2 - (7y)^2

Apply Difference of Squares Formula (( x^2-y^2 = (x + y)(x - y)

= (4x + 7y) (4x - 7y)

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What is the value of x? 6 8 10 12

Novosadov [1.4K]

we know that

The sum of exterior angles of any polygon is $360$ degrees

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the answer is

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3 years ago

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Which equation can be used to find the volume of this solid?

Zina [86]

Answer:

V = StartFraction 7 times 6 over 2 EndFraction times 8

Step-by-step explanation:

Volume of a triangular prism is expressed as V = Base area × Height

Base area = area of the triangle = 1/2 × base × height

If the triangular base has a base of 7 inches and height of 6 inches.

The height of the prism is 8 inches.

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Base area = (7×6)/2

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The right option is V = StartFraction 7 times 6 over 2 EndFraction times 8

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3 years ago

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A shopper at a local supermarket spent the following amounts in her last eight trips to the store: $32.92 $14.14 $30.80 $28.34 $

alexdok [17]

Answer:

$75.58

The amount spent of $75.58 is most likely an outlier

Step-by-step explanation:

An outliers are unusual values in a dataset, they are data values that are extremely higher or extremely lower when compared to the other values in a data (data points that are far from other data points)

For the case above, give a dataset;

$32.92 $14.14 $30.80 $28.34 $75.58 $36.33 $33.51 $22.94

$75.58 is extremely far from other value. So $75.58 is an outlier in the given dataset.

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3 years ago

Simplify the following expression.

levacccp [35]

51x+83y-14x-25y=37x+58y

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3 years ago

Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm.

melamori03 [73]

Answer:

$6+2\sqrt{21}\:\mathrm{cm^2}\approx 15.17\:\mathrm{cm^2}$

Step-by-step explanation:

The quadrilateral ABCD consists of two triangles. By adding the area of the two triangles, we get the area of the entire quadrilateral.

Vertices A, B, and C form a right triangle with legs $AB=3$ , $BC=4$ , and $AC=5$ . The two legs, 3 and 4, represent the triangle's height and base, respectively.

The area of a triangle with base $b$ and height $h$ is given by $A=\frac{1}{2}bh$ . Therefore, the area of this right triangle is:

$A=\frac{1}{2}\cdot 3\cdot 4=\frac{1}{2}\cdot 12=6\:\mathrm{cm^2}$

The other triangle is a bit trickier. Triangle $\triangle ADC$ is an isosceles triangles with sides 5, 5, and 4. To find its area, we can use Heron's Formula, given by: