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3 years ago

Find the roots. 2x^2 + 4x - 5 =0

Mathematics

1 answer:

xz_007 [3.2K]3 years ago

8 0

Answer:

$-1\pm\dfrac{\sqrt{14}}{2}$

Step-by-step explanation:

$2x^2+4x-5=0$

Using the quadratic formula:

$x=\dfrac{-4\pm \sqrt{16+40}}{4}=-1\pm\dfrac{\sqrt{14}}{2}$

Hope this helps!

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Which graph is defined by the function given below? y= (x + 2)(x+7)

Lady bird [3.3K]

Answer:

A parabola

Step-by-step explanation:

It's a quadratic equation so the graph will be a parabola.

The solutions are -2 and -7

8 0

2 years ago

Please help i dont know how to do this

maxonik [38]

Hello once again!

When you see a question like this, you need to find the equation of the straight line.

The formular used is y = mx + c
Where
m = slope
c = constant

First find the slope, since it's a straight line, any 2 coordinates can be used.

$m = { \frac{y_1 - y_2}{x_1-x_2} } \\ m= { \frac{16 - (- 8)}{-2 - 2} } \\ m= { \frac{24}{-4} } \\ m = -6$

Now we need to substitude in the slope, and one of the coordinate you used to find the slope, to the formular to find the constant.

In this case i'm using the coordinate
(-2, 16)

y = mx + c
16 = -6(-2) + c
16 = 12 + c
c = 4

∴ The equation of the line is y = -6x + 4

The next step is to simply substitude in the x = 8 to the equation to find y.

y = -6(8) + 4
y = -48 + 4
y = -44

7 0

3 years ago

Mary and Mike went to the store to buy colored pencils for their science class.mike bought a 12-pack for 1.69,and Mary bought a

sweet-ann [11.9K]

12-pack for 1.69 is a better buy

Solution:

Given that, Mike bought a 12-pack for 1.69 and Mary bought a 24-pack for 3.18

We have to find which is the better buy

First we have to find the unit rate

Unit rate is cost of 1 pack

Mike bought a 12-pack for 1.69

Therefore,

Cost of 12 pack = 1.69

Cost of 1 pack is found by dividing 1.69 by 12

$cost\ of\ 1\ pack = \frac{1.69}{12} = 0.14083$

Thus unit rate of Mike is 0.14083 dollar per pack

Mary bought a 24-pack for 3.18

Cost of 24 pack = 3.18

Cost of 1 pack is found by dividing 3.18 by 24

$cost\ of\ 1\ pack = \frac{3.18}{24} = 0.1325$

Thus unit rate of Mary is 0.1325 dollars

On comparing both the unit rate

$0.14083>0.1325$

Thus unit rate of Mike is larger

Thus, 12-pack for 1.69 is a better buy

3 0

2 years ago

6. If the net investment function is given by

Pachacha [2.7K]

The capital formation of the investment function over a given period is the

accumulated capital for the period.

(a) The capital formation from the end of the second year to the end of the fifth year is approximately 298.87.

(b) The number of years before the capital stock exceeds $100,000 is approximately 46.15 years.

Reasons:

(a) The given investment function is presented as follows;

$I(t) = 100 \cdot e^{0.1 \cdot t}$

(a) The capital formation is given as follows;

$\displaystyle Capital = \int\limits {100 \cdot e^{0.1 \cdot t}} \, dt =1000 \cdot e^{0.1 \cdot t}} + C$

From the end of the second year to the end of the fifth year, we have;

The end of the second year can be taken as the beginning of the third year.

Therefore, for the three years; Year 3, year 4, and year 5, we have;

$\displaystyle Capital = \int\limits^5_3 {100 \cdot e^{0.1 \cdot t}} \, dt \approx 298.87$

The capital formation from the end of the second year to the end of the fifth year, C ≈ 298.87

(b) When the capital stock exceeds $100,000, we have;

$\displaystyle \mathbf{\left[1000 \cdot e^{0.1 \cdot t}} + C \right]^t_0} = 100,000$

Which gives;

$\displaystyle 1000 \cdot e^{0.1 \cdot t}} - 1000 = 100,000$

$\displaystyle \mathbf{1000 \cdot e^{0.1 \cdot t}}} = 100,000 + 1000 = 101,000$

$\displaystyle e^{0.1 \cdot t}} = 101$

$\displaystyle t = \frac{ln(101)}{0.1} \approx 46.15$

The number of years before the capital stock exceeds $100,000 ≈ 46.15 years.

Learn more investment function here:

brainly.com/question/25300925

6 0

2 years ago

Look at the graph below. Which of the following best represents the slope of the line? A. -3 B. - 1 3 C. 1 3 D. 3

Salsk061 [2.6K]

Answer and Explanation:

The line seems to pass trough the points (0,6) and (-3,4).

Slope is: $m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{4-6}{-3-0} =\frac{-2}{-3} =\boxed{\frac{2}{3}}$

The slope of the line should be $\frac{2}{3}$ .

3 0

3 years ago