All categories

3 days ago

Are triangles ADC and EBC congruent? triangle ADC is overlapping triangle EBC so that they both share angle ACE, point B is on s

egment AC, point D is on segment EC, segments AD and EB intersect at point F, segments BC and DC are each marked with one dash, and angles CAD and CEB are each marked with an arc Yes, by SSS Yes, by AAS Yes, by SAS Not enough information

Mathematics

You might be interested in

What is the positive solution to the equation 0 = –x2 + 2x + 1? Quadratic formula: x = StartFraction negative b plus or minus St

zzz [12365]

Answer:

$1+\sqrt{2}$

Step-by-step explanation:

Consider a quadratic equation given by

$ax^2+bx+c=0$ .... (1)

The quadratic formula then is

$x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$

The quadratic equation provided is

$0=-x^2+2x+1$

This can be expressed as

$-x^2+2x+1=0$ .... (2)

By comparing (1) and (2), we derive:

$a=-1,b=2,c=1$

Plug these values into the quadratic formula.

$x=\dfrac{-2\pm \sqrt{2^2-4(-1)(1)}}{2(-1)}$

$x=\dfrac{-2\pm \sqrt{4+4}}{-2}$

$x=\dfrac{-2\pm \sqrt{8}}{-2}$

$x=\dfrac{-2\pm 2\sqrt{2}}{-2}$

Factoring out common elements.

$x=\dfrac{-2(1\pm \sqrt{2})}{-2}$

$x=1\pm \sqrt{2}$

The two solutions are

$x=1+\sqrt{2}$ and $x=1-\sqrt{2}$

We recognize that

$\sqrt{2}=1.41$

Thus,

$1$

Consequently, root $x=1+\sqrt{2}$ is positive while $x=1-\sqrt{2}$ is negative.

9 0

2 months ago

Read 2 more answers

Suppose your statistics professor reports test grades as z-scores, and you got a score of 1.57 on an exam. a) Write a sentence

tester [12383]

Answer:

a) In this case, we have a z-score of 1.57, characterized as:

$z =\frac{x -\mu}{\sigma}$

This signifies that our score is 1.57 standard deviations above the average of all test scores.

b) $P(Z$

Using the normal standard distribution or Excel, we computed:

$P(Z$

This represents 2.275% of the dataset.

Step-by-step explanation:

Previous concepts

Normal distribution denotes a "probability distribution that is symmetric around the mean, indicating that data close to the mean occurs more frequently than data further from it".

The Z-score serves as "a statistical measurement representing a value's relation to the average (mean) of a set, calculated in terms of standard deviations away from the mean".

Solution to the problem

Part a

For this instance, we hold a z-score of 1.57, which is defined as:

$z =\frac{x -\mu}{\sigma}$

This shows that our score is 1.57 deviations above the overall test score average.

Part b

A z-score of z=-2 indicates that your friend's score is 2 deviations below the other test scores.

Assuming a normal distribution, we can derive the percentage:

$P(Z$

Using the normal standard distribution or Excel, we discovered:

$P(Z$

This represents 2.275% of the data.

6 0

3 months ago

What is the product of 2x2 – 3xy + y2 and 2x – 4y?

AnnZ [12381]

Answer:

C. 4x^3 - 14x^2y + 14xy^2 - 4y^3

Step-by-step explanation:

Given:

Multiplication of 2x^2 – 3xy + y^2 and 2x – 4y

Multiplication refers to the product

(2x^2 – 3xy + y^2) (2x – 4y)

Expand the brackets

= 4x^3 - 8x^2y - 6x^2y + 12xy^2 + 2xy^2 - 4y^3

Combine like terms

= 4x^3 - 14x^2y + 14xy^2 - 4y^3

The result is

C. 4x^3 - 14x^2y + 14xy^2 - 4y^3

8 0

2 months ago