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2 years ago

What else would need to be congruent to show that ABC XYZ by ASA?

Mathematics

2 answers:

Naddik [55]2 years ago

8 0

Answer: The correct option is (D) AC ≅ XZ.

Step-by-step explanation: Given that in ΔABC and ΔXYZ, ∠X ≅ ∠A and ∠Z ≅ ∠C.

We are to select the correct condition that we will need to show that the triangles ABC and XYZ are congruent to each other by ASA rule..

<u>ASA Congruence Theorem: </u> Two triangles are said to be congruent if two angles and the side lying between them of one triangle are congruent to the corresponding two angles and the side between them of the second triangle.

In ΔABC, side between ∠A and ∠C is AC,

in ΔXYZ, side between ∠X and ∠Z is XZ.

Therefore, for the triangles to be congruent by ASA rule, we must have AC ≅ XZ.

Thus, (D) is the correct option.

docker41 [41]2 years ago

5 0

Side XZ needs to be congruent to side AC. The answer is D.

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if two points are given,then exactly one line can be drawn through those two points.which geometry term does the statement repre

lubasha [3.4K]

Answer:

This is a postulate which states that through any two points, there is exactly one line.

Step-by-step explanation:

A postulate is a statement that is assumed true without proof.

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2 years ago

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Two friends went rowing on the river. They first traveled with current for 3 hours. The way back took them 4 hours and 48 minute

kaheart [24]

Answer:

1.5 mph

Step-by-step explanation:

Let speed of boat be x

let speed of current be c

Also, note D = RT

D is distance

R is rate

T is time

Now, for first leg, we can write:

(x+c)3 = D

And for second leg , we can write:

(x-c)4.8 = D [note 4 hour 48 minutes is 4.8 hours]

We can equate both D's to get:

(x+c)3 = (x-c)4.8

3x + 3c = 4.8x - 4.8c

7.8c = 1.8x

We know x = 6.5 [given], plugging it in and solving for c:

7.8c = 1.8(6.5)

c = 1.5

Speed of Current = 1.5 miles per hour

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2 years ago

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Let $f(x) = x^{10}-8x^8-8x^3+12x^2-5x-5$. Without using long division (which would be horribly nasty!), find the remainder when

valentina_108 [34]

Solution:

$f(x) = x^{10}-8x^8-8x^3+12x^2-5x-5$

We have to find the remainder when f(x) is divided by $x^2-1.$

x²-1=0

x= $\pm1$

$f(1)=1^{10}-8(1)^8-8(1)^3+12(1)^2-5(1)-5=1-8-8+12-5-5=1-16+12-10=13-26=-13\\\\f(-1)=(-1)^{10}-8(-1)^8-8(-1)^3+12(-1)^2-5(-1)-5=1-8+8+12+5-5=1+12=13$

So, remainder is 13 and -13.

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2 years ago

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Given that a 90% confidence interval for the mean height of all adult males in Idaho measured in inches was [62.532, 76.478]. Us

grigory [225]

Answer:

The confidence interval on this case is given by:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

For this case the confidence interval is given by (62.532, 76.478)[/tex]

And we can calculate the mean with this:

$\bar X = \frac{62.532+76.478}{2}= 69.505$

So then the mean for this case is 69.505

Step-by-step explanation:

Previous concepts

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

$\bar X$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma$ represent the population standard deviation

n represent the sample size

Assuming the X follows a normal distribution

$X \sim N(\mu, \sigma)$

The confidence interval on this case is given by:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

For this case the confidence interval is given by (62.532, 76.478)[/tex]

And we can calculate the mean with this:

$\bar X = \frac{62.532+76.478}{2}= 69.505$

So then the mean for this case is 69.505

5 0

2 years ago

Tony is 4 years younger than his brother josh and two years older than his sister Cindy. Tony also has a twin brother, Evan. All

Sholpan [36]

Let Tony's age = x

He is 4 years younger than his brother Josh, so Josh's age would be x + 4

He is 2 years older than his sister, so her age would be x - 2

He has a twin, which would be the same age, so the twins age is also x

They all add together to equal 66, so you get:

x + x + x+4 + x-2 = 66

Simplify:

4x +2 = 66

Subtract 2 from both sides:

4x = 64

Divide both sides by 4:

x = 64/4 = 16

Tony is 16 years old.

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2 years ago