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3 years ago

Part 2. State what additional information is required in order to know that the triangles are congruent by ASA.

Mathematics

1 answer:

Helga [31]3 years ago

7 0

<h3>Answer: Choice D. $\angle SQR \cong \angle XQR$ </h3>

The red angle markers show those two angles are congruent. That's one "A" of "ASA". The S refers to a congruent pair of sides. We don't have any tickmarks to indicate congruent pairs; however, we do know that QR = QR is a shared side that overlaps (reflexive theorem). So this is the "S" in "ASA".

The thing missing is the angle Q of the top triangle, and also of the bottom triangle as well. If we know those two angles are congruent, then we have enough info to use ASA. More specifically, if we know that $\angle SQR \cong \angle XQR$ , then we can use ASA.

One thing to notice is that the other answer choices involve side lengths and not angles. This implies that if A, B or C were one of the answers, then we would have something like SAS or SSS. But instead we want ASA. So we can immediately rule choices A,B, and C out.

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What is the area of a rectangle with vertices at (0, −4) , (−1, −3) , (2, 0) , and (3, −1) ? Enter your answer in the box

Bad White [126]

We are given vertices of a rectangle (0, −4) , (−1, −3) , (2, 0) , and (3, −1).

Length is the distance between (0, −4) and (−1, −3) points.

Width is distance between (−1, −3) and (2, 0) points.

<u>Computing length:</u>

$\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$

$=\sqrt{\left(-1-0\right)^2+\left(-3-\left(-4\right)\right)^2}$

$=\sqrt{2}$

<u>Computing Width :</u>

$\mathrm{The\:distance\:between\:}\left(-1,\:-3\right)\mathrm{\:and\:}\left(2,\:0\right)\mathrm{\:is\:}$

$=\sqrt{\left(2-\left(-1\right)\right)^2+\left(0-\left(-3\right)\right)^2}$

$=3\sqrt{2}$

<h3>Area of the rectangle = Length × Width </h3>

= $\sqrt{2} \times 3\sqrt{2} = 3 \times 2 = 6 \ squares \ units.$ .

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3 years ago

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Modeling with sinusoidal functions

saveliy_v [14]

Answer: c(t)= -5 cos (1/14t)+7

Step-by-step explanation:

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2 years ago

Need help. Anything is appreciated!

Lynna [10]

First attatchment:

1. Given

2. Definition of a parrallelogram

3. Transitive

4. Parts of line FE and AB

5. Opposite sides of a parallelogram are parallel.

You want to switch those last two because you're using what you want to prove to prove something before you've proved it, which is fallacious.

SECOND ATTATCHMENT:

In a parallelogram, opposite angles are equal and same side interior angles add up to 180.We have 2x+60+x+30=180 which means 3x+90=180 so x=30.Since x is 30 then angle to is 60 which means that angle A is 60, not 30.

THIRD ATTATCHMENT:

This is just the triangle midpoint theorem. SM is parallel to RU not VS.

FOURTH ATTATCHMENT:

Angle X and angle F are corresponding angles, so they are actually equal. You want Angle G and Angle F becuase they are same side interior angles.

FIFTH ATTATCHMENT:

this is correct

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3 years ago

The illustration below shows the graphs of fourteen functions.

Travka [436]

Due to <em>length</em> restrictions, we kindly invite to check the explanation of this question to understand the derivation of the <em>polynomic</em> expressions.

<h3>How to determine a family of cubic functions</h3>

<em>Cubic</em> functions are polynomials of grade 3. In this case, we have pairs of <em>cubic</em> functions of the following form:

y = (x - h)³ + k (1)

y = - (x - h)³ + k (2)

a) Where (h, k) are the coordinates of the vertex of each <em>cubic</em> function. There is a translation of (x, y) = (3, 1) between each two <em>consecutive</em> pairs of <em>cubic</em> functions. Hence, we have the following fourteen cubic functions:

y = (x + 9)³ - 3
y = - (x + 9)³ - 3
y = (x + 6)³ - 2
y = - (x + 6)³ - 2
y = (x + 3)³ - 1
y = - (x + 3)³ - 1
y = x³
y = - x³
y = (x - 3)³ + 1
y = - (x - 3)³ + 1
y = (x - 6)³ + 2
y = - (x - 6)³ + 2
y = (x - 9)³ + 3
y = - (x - 9)³ + 3

b) Another family of functions with a similar pattern is shown below:

y = (x + 9)² - 3
y = - (x + 9)² - 3
y = (x + 6)² - 2
y = - (x + 6)² - 2
y = (x + 3)² - 1
y = - (x + 3)² - 1
y = x²
y = - x²
y = (x - 3)² + 1
y = - (x - 3)² + 1
y = (x - 6)² + 2
y = - (x - 6)² + 2
y = (x - 9)² + 3
y = - (x - 9)² + 3

To learn more on cubic functions: brainly.com/question/25732149

#SPJ1

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1 year ago

Part 2. State what additional information is required in order to know that the triangles are congruent by ASA.​

Part 2. State what additional information is required in order to know that the triangles are congruent by ASA.