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3 years ago

If triangle ABC is reflected over the y-axis which points will be their own image?

Mathematics

1 answer:

balu736 [363]3 years ago

3 0

Answer:

Point B

Step-by-step explanation:

From the graph attached,

Coordinates of point A are (4, -1)

Coordinates of point B → (0, 3)

Coordinates of point C → (-2, 0)

When a point (x, y) is reflected over y-axis coordinates of the image follow the rule,

(x, y) → (-x, y)

Following the same rule,

Coordinates of A' → (-4, -1)

Coordinates of B' → (0, 3)

Coordinates of C' → (2, 0)

Therefore, coordinates of point B and B' remain the same.

Point B will same as its own image.

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8.3+3.4y-0.5(12y-3)=

natulia [17]

Answer:

Let's simplify step-by-step.

8.3+3.4y−0.5(12y−3)

Distribute:

=8.3+3.4y+(−0.5)(12y)+(−0.5)(−3)

=8.3+3.4y+−6y+1.5

Combine Like Terms:

=8.3+3.4y+−6y+1.5

=(3.4y+−6y)+(8.3+1.5)

=−2.6y+9.8

Answer:

=−2.6y+9.8

8 0

3 years ago

Determine if the two triangles are congruent. If they are State how you know. NO LINKS!!!

miv72 [106K]

Problem 25

These triangles are congruent.

The reasoning is the AAS congruence theorem. We have two pairs of congruent angles, as shown by the arc markings, and a pair of congruent sides. The sides are not between the angles. That means AAS is slightly different from ASA. The order matters.

=====================================================

Problem 26

The triangles are not congruent

Why not? Well it all comes down to the angle placement. For the triangle on the right side, the arc is between the shared segment and the segment with the double tickmarks. The other arc is not in the proper corresponding location to be able to use SAS. It would need to be adjacent to the arc on the right for us to use SAS.

If it's hard to visualize what I mean, refer to the diagram below.

=====================================================

Problem 27

The triangles are congruent by SAS

The angles aren't marked, but recall that vertical angles are always congruent. So you could add in angle markers if you wanted, to help complete the diagram. The tickmarks of course tell us which segments are the same length. The angles are between the segments.

====================================================

Problem 28

The triangles are congruent by SSS

Like before, the tickmarks tell us which sides are the same length. So the tickmarks say that we have two pairs of congruent sides. The overlapping sides or shared sides are the third pair of congruent segments. So in reality, we have three pairs of congruent sides. It might help to break up the figure into two separate triangles.

3 0

3 years ago

Suppose that 16% of the population of the U.S. is left-handed. If a random sample of 170 people from the U.S. is chosen, approxi

Shalnov [3]

Answer:

0.6064 = 60.64% probability that fewer than 29 are left-handed.

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .