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3 years ago

Solve 2x2 + 8x + 10 = 0. using this model to he X = -b+ ✓ 62 - 4ac 2a

Mathematics

1 answer:

Lesechka [4]3 years ago

8 0

Answer:

x can have two complex solutions, which are:

-2 + i

-2 - i

Step-by-step explanation:

2x² + 8x + 10 = 0

4x² + 16x + 20 = 0

4x² + 16x + 16 = -4

(2x + 4)² = -4

2x + 4 = √-4

2x = -4 ± i√4

2x = -4 ± 2i

x = -2 ± i

So x is equal to -2 + i and -2 - i.

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Allison and her children went into a bakery where they sell donuts for $2 each and cookies for $1 each. Allison has $20 to spend

KATRIN_1 [288]

Answer:

if donuts are 2 for each and cookies for 1 each it could be

X x 2 and X x 1

one equation could be 4 donuts for 2$ and 7 cookies for 1$

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3 years ago

Amy is pulling a wagon with a force of 30 pounds up a hill at an angle of 25°. Give the force exerted on the wagon as a vector a

Fofino [41]

Answer:

Vector (ordered pair - rectangular form)

$\vec F = (27.189,12.679)\,[lbf]$

Vector (ordered pair - polar form)

$\vec F = (30\,lbf, 25^{\circ})$

Sum of vectorial components (linear combination)

$\vec F = 27.189\cdot \hat{i} + 12.679\cdot \hat{j}\,[N]$

Step-by-step explanation:

From statement we know that force exerted on the wagon has a magnitude of 30 pounds-force and an angle of 25° above the horizontal, which corresponds to the +x semiaxis, whereas the vertical is represented by the +y semiaxis.

The force ( $\vec F$ ), in pounds-force, can be modelled in two forms:

Vector (ordered pair - rectangular form)

$\vec F = \left(\|\vec F\|\cdot \cos \theta, \|\vec F\|\cdot \sin \theta\right)$ (1)

Vector (ordered pair - polar form)

$\vec F = \left(\|\vec F\|, \theta\right)$

Sum of vectorial components (linear combination)

$\vec {F} = \left(\|\vec F\|\cdot \cos \theta\right)\cdot \hat{i} + \left(\|\vec F\|\cdot \sin \theta \right)\cdot \hat{j}$ (2)

Where:

$\|\vec F\|$ - Norm of the vector force, in newtons.

$\theta$ - Direction of the vector force with regard to the horizontal, in sexagesimal degrees.

$\hat{i}$ , $\hat{j}$ - Orthogonal axes, no unit.

If we know that $\|\vec F\| = 30\,lbf$ and $\theta = 25^{\circ}$ , then the force exerted on the wagon is:

Vector (ordered pair - rectangular form)

$\vec F= \left(30\cdot \cos 25^{\circ}, 30\cdot \sin 25^{\circ}\right)\,[lbf]$

$\vec F = (27.189,12.679)\,[lbf]$

Vector (ordered pair - polar form)

$\vec F = (30\,lbf, 25^{\circ})$

Sum of vectorial components (linear combination)

$\vec F = (30\cdot \cos 25^{\circ})\cdot \hat{i} + (30\cdot \sin 25^{\circ})\cdot \hat{j}\,[N]$

$\vec F = 27.189\cdot \hat{i} + 12.679\cdot \hat{j}\,[N]$

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2 years ago

A beverage is made by mixing 1 part of water with 3 parts of fruit juice. How many parts of water are mixed with 1 part of fruit

Sidana [21]

Answer is A. 1/3 !!!

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2 years ago

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The model of a circular garden is 8 inches in diameter. The actual garden will be 20 feet in diameter. Find the scale of the mod

8_murik_8 [283]

Answer:

1/30 of a scale.

Step-by-step explanation:

Multiply the 20 by 12 to convert it to inches. Then divide the answer by 8 to get the scale.

3 0

3 years ago

The equation below shows the total volume (V), in cubic units, of 2 identical boxes with each side equal to s units:

trasher [3.6K]

Start with the equation,

V = 2s^3

Now substitute s with 3.5 units and evaluate the expression.

V = 2 * (3.5 units)^3

V = 2 * 42.875 units^3

V = 85.75 units^3

Answer: The volume is 85.75 cubic units

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3 years ago