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2 years ago

Which of the following statements is true

Mathematics

1 answer:

kolbaska11 [484]2 years ago

5 0

Answer:

D. This quadratic equation two complex solutions.

Step-by-step explanation:

$5x^2 +6x +2= 0\\$

Equating it with

$ax^2 +bx +c= 0\\$

a = 5, b = 6, c = 2

$b^2 -4ac\\= 6^2 - 4\times 5\times 2\\= 36-40\\b^2 -4ac= - 4\\$

$\because b^2 -4ac$ is negative.

Therefore, this quadratic equation two complex solutions.

You might be interested in

Which statement accurately describes how to reflect point A(3,-1) over the y-axis?

Lyrx [107]

Answer:

The answer in the procedure

Step-by-step explanation:

we know that

The rule of the reflection of a point over the y-axis is equal to

A(x,y) ----->A'(-x,y)

That means -----> The x-coordinate of the image is equal to the x-coordinate of the pre-image multiplied by -1 and the y-coordinate of both points (pre-image and image) is the same

A(3,-1) ------> A'(-3,-1)

The distance from A to the y-axis is equal to the distance from A' to the y-axis (is equidistant)

therefore

To reflect a point over the y-axis

Construct a line from A perpendicular to the y-axis, determine the distance from A to the y-axis along this perpendicular line, find a new point on the other side of the y-axis that is equidistant from the y-axis

6 0

2 years ago

The weight of Jane and Jessica was in the ratio of 8 : 9. Jane gained 2 kg while Jessica lost 4 kg. They then had the same weigh

postnew [5]

Answer:

48 kg

Step-by-step explanation:

The given relations can be used to write a system of equations for the two weights. Those can be solved to find Jane's weight.

<h3>setup</h3>

Let x and y represent Jane's and Jessica's original weight, respectively. The ratio of weights was ...

x/y = 8/9

After the changes in weight, they were equal:

x+2 = y-4

<h3>solution</h3>

Adding 4 to the second equation, we have an expression for y that can be substituted into the first equation.

y = x +6 . . . . . . . . . . solve the second equation for y

x/(x+6) = 8/9 . . . . . . substitute for y in the first equation

9x = 8(x +6) . . . . . . . multiply by 9(x+6)

x = 48 . . . . . . . . . . . simplify and subtract 8x

Jane weighed 48 kg at first.

_____

<em>Alternate solution</em>

The original difference in "ratio units" was 9-8 = 1 ratio unit. We find that this corresponds to 6 kg after the weight changes make the weights equal. Then 8 ratio units will be 8(6 kg) = 48 kg—Jane's original weight.

(This mental solution is virtually the same as the solution using equations shown above.)

3 0

1 year ago

Can someone help with these? ik the answers i just don’t know how to show work

Nonamiya [84]

Step-by-step explanation:

use trigonometry ratios

8 0

2 years ago

$700 is invested at 4% per annum. How long will it take for the amount to reach $784?

Blababa [14]

Answer:

3yrs

Step-by-step explanation:

Given parameters:

Capital = $700

Percentage interest = 4% per annum

Unknown:

Time it will take for amount to be = $784

Solution:

To find the simple interest on an amount;

I = $\frac{PRT}{100}$

P is the principal

R is the rate

T is the time

I is the interest

Insert the parameters:

I = $\frac{700x 4 x T}{100}$

I = 28T

So;

At the end of the duration:

Principal + Interest = Amount

700+28T = 784

28T = 784 - 700

28T = 84

T = 3yrs

5 0

2 years ago

Question set 2: Many species of terrestrial tree frogs that hibernate at or near the ground surface can survive prolonged exposu

joja [24]

Answer:

0.86

Step-by-step explanation:

The z-score we need to make the comparison is given by

$\bf z=\frac{-2.05-(-2)}{\sigma/\sqrt{n}}$

where

$\bf \sigma$ = the standard deviation established in the study

n = the sample size

$\bf z=\frac{-2.05-(-2)}{0.3/\sqrt{42}}=-1.0801$

and for the Normal distribution N(0,1) we want to find

By using a spreadsheet or the table attached, we find that

P(X > -1.0801) = 0.86

(See picture attached)

7 0

3 years ago