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3 years ago

Multiply. (2x2 – 3x)(3x2 + 2x - 1)

Mathematics

1 answer:

exis [7]3 years ago

8 0

Answer:

$-6x^{2}$ –7x + 20

Step-by-step explanation:

(2x2 – 3x)(3x2 + 2x – 1)

(4 – 3x)(2x + 5)

(4*2x) + (4*5) + (–3x*2x) + (–3x*5)

8x + 20 $-6x^{2}$ –15x

$-6x^{2}$ –7x + 20

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The cost of 5 hats and 1 scarf is $47. The cost of 2 hats and 2 scarves is $40. How much does one hat cost?

stepan [7]

Answer:

6.75

Step-by-step explanation:

h=hat, s=scarf

5h + 1s = $47 (equation 1)

2h + 2s = $40 (equation 2)

multiply equation 1 by 2 , we get: 10h + 2s = $94 (equation 3)

equation 3 minus equation 2, we get:

8h = $54 ⇒ h = $6.75 ⇔ 1 hat cost $6.75

substitute h = $6.75 into equation 2 to find s,

2($6.75) + 2s = $40

$13.5 + 2s = $40

2s = $26.5

s = $13.25 ⇔ 1 scarf cost $13.25

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2 years ago

What are the coordinates of the point on the directed line segment from (-6, -3) to

melamori03 [73]

Given:

A point divides a directed line segment from (-6, -3) to (5,8) into a ratio of 6 to 5.

To find:

The coordinates of that point.

Solution:

Section formula: If point divides a line segment in m:n, then the coordinates of that point are

$Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)$

A point divides a directed line segment from (-6, -3) to (5,8) into a ratio of 6 to 5. Using section formula, we get

$Point=\left(\dfrac{6(5)+5(-6)}{6+5},\dfrac{6(8)+5(-3)}{6+5}\right)$

$Point=\left(\dfrac{30-30}{11},\dfrac{48-15}{11}\right)$

$Point=\left(\dfrac{0}{11},\dfrac{33}{11}\right)$

$Point=\left(0,3\right)$

Therefore, the coordinates of the required point are (0,3).

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3 years ago

Consider the drawing below. What is the measure of angle A?* 1 point w

jonny [76]

Answer:

$x + 2x = 120 \\ 3x = 120 \\ x = 40 \\ a = 2x = 80$

4 0

2 years ago

Use a half-angle identity to find the exact value of sinPi/8

stellarik [79]

Answer:

sin(π/8) = (1/2)√(2-√2)

Step-by-step explanation:

Using the half-angle formula ...

$\sin{\dfrac{\theta}{2}}=\sqrt{\dfrac{1-\cos{\theta}}{2}}$

We can let θ = π/4 and simplify the result as follows:

$\sin{\dfrac{\pi}{8}}=\sqrt{\dfrac{1-\cos{(\pi/4)}}{2}}=\sqrt{\dfrac{1-\dfrac{\sqrt{2}}{2}}{2}}=\sqrt{\dfrac{2-\sqrt{2}}{4}}\\\\=\boxed{\dfrac{1}{2}\sqrt{2-\sqrt{2}}}}$

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3 years ago

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In the year 2010, a company made $3.2 million in profit. For each consecutive year after that, their profit increased by 11%. Ho

konstantin123 [22]

4.4 million dollars profit in 2013

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1 year ago