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3 years ago

Explain whether △ABC is congruent to △XYZ according to the angle side angle (ASA) congruence criteria.

Mathematics

1 answer:

serious [3.7K]3 years ago

7 0

Answer:

∆ABC and ∆XYZ cannot be proven to be congruent to each other according to the Angle-Side-Angle (ASA) Congruence criteria.

Step-by-step explanation:

The Angle-Side-Angle (ASA) Congruence criteria says that two triangles are congruent to each other if two angles and an included side of one triangle is congruent to two corresponding angles and a corresponding included side of the other triangle.

In the diagram given, the two angles were given (<B and <C), however, the side given (side AB) does not lie in the middle of <B and <C, hence it is NOT AN INCLUDED SIDE. The same applies to ∆XYZ.

Therefore, ∆ABC and ∆XYZ cannot be proven to be congruent to each other according to the Angle-Side-Angle (ASA) Congruence criteria.

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The price of products may increase due to inflation and decrease due to depreciation. Marco is studying the change in the price

likoan [24]

Answer:

A) 3%

B) Product A

Step-by-step explanation:

Exponential Function

General form of an exponential function: $y=ab^x$

where:

a is the initial value (y-intercept)
b is the base (growth/decay factor) in decimal form
x is the independent variable
y is the dependent variable

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

Part A

Product A

Assuming the function for Product A is exponential:

$f(x) = 0.69(1.03)^x$

The base (b) is 1.03. As b > 1 then it is an increasing function.

To calculate the percentage increase/decrease, subtract 1 from the base:

⇒ 1.03 - 1 = 0.03 = 3%

Therefore, product A is increasing by 3% each year.

Part B

$\sf percentage\:change=\dfrac{final\:value-initial\:value}{initial\:value} \times 100$

To calculate the percentage change in Product B, use the percentage change formula with two consecutive values of f(t) from the given table:

$\implies \sf percentage\:change=\dfrac{10201-10100}{10100}\times 100=1\%$

Check using different two consecutive values of f(t):

$\implies \sf percentage\:change=\dfrac{10303.01-10201}{10201}\times 100=1\%$

Therefore, as 3% > 1%, Product A recorded a greater percentage change in price over the previous year.

Although the question has not asked, we can use the given information to easily create an exponential function for Product B.

Given:

a = 10,100
b = 1.01
n = t - 1 (as the initial value is for t = 1 not t = 0)

$\implies f(t) = 10100(1.01)^{t-1}$

To check this, substitute the values of t for 1 through 4 into the found function:

$\implies f(1) = 10100(1.01)^{1-1}=10100$

$\implies f(2) = 10100(1.01)^{2-1}=10201$

$\implies f(3) = 10100(1.01)^{3-1}=10303.01$

$\implies f(4) = 10100(1.01)^{4-1}=10406.04$

As these values match the values in the given table, this confirms that the found function for Product B is correct and that Product B increases by 1% per year.

4 0

2 years ago

Offering Brainliest , a 5 star review, and a like on your answers if you can successfully answer these last 2 simple coordinate

adelina 88 [10]

Answer: pretty sure it's -1,1

M ( 3 , 1 )

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

HELP PLZZZZ !!!!!!!!!!!!

jeyben [28]

The answer to your question is B

4 0

3 years ago

How are the functions f(x)=16^x and g(x)=16^(1/2)x related? The output values of g(x) are one-half the output values of f(x) for

Goshia [24]

F(x) =16ˣ and g(x) = 16⁽ˣ/₂⁾

Since 16 = 2⁴, then we can write:

f(x) =2⁽⁴ˣ⁾ and g(x) = 2⁽⁴ˣ/₂⁾ = 2²ˣ

for x = 1 f(x) = 2⁴ = 16
for x = 1 g(x) = 2² = 4
(√16 = 4)

for x = 2 f(x) = 2⁸ = 256
for x = 2 g(x) = 2⁴ =16
(√256) = 16

for x = 3 f(x) = 2¹² = 4096
for x = 1 g(x) = 2⁶ = 64
(√4096 = 64)

We notice that:
The output values of g(x) are the square root of the output values of f(x) for the same value of x.

6 0

3 years ago

Read 2 more answers

PLEASE HELP‼️‼️Drag the expression that is the most reasonable measurement for each object.

Afina-wow [57]

Answer:

A. Length of a Tour Bus ↔ #2. 1.1 × 10¹ meters

B. Width of an apple ↔ #3. 4 × 10⁰ centimeters

C. Distance from Earth to a Satellite ↔ #6. 8 × 10² kilometers

D. Thickness of a human hair ↔ #5. 9 × 10¹ micrometers

Explanation:

A. Length of a tour bus.

The length of a tour bus should be measured in meters. It sure is way less than 1 kilometer and way more than a few centimeters. It could be about some meters, more than 5 meters, may be between 10 meters and 15 meters.

The measurement in the box # 2. is 1.1 × 10¹ meters, which is equivalent to 1.1 × 10meters = 11 meters. Thus, this is a reasonable length.

B. Width of an apple.

The most appropiate unit to measure the width of an apple should be centimer. It certanly is shorter than 1 meter and bigger than 1 mm.

The width of an apple could be, more or less, around 8 centimeters. The only measurement in the boxes that is in that order is that in the box #3., 4 × 10⁰ centimeters, because 10⁰ = 1, so 4 × 10⁰ = 4 × 1 = 4centimeters.

C. Distance from Earth to a Satellite

The distance from Earth to a satellite should be measured in kilometers.

You can find in the internet that the distances of the satellites are between 700 kilometers and 36,000 kilometers.

The number in the box #1 is too big, in the order of ten trillions of kilometers, because one trillion is 10¹²; thus that is notreasonalbe (too big).

The number in the box #6 is 8 × 10² kilometers, which is equal to 8 × 100 = 800 kilometers.

Thus, 8 × 10² kilometers (box #6) is the most reasonable measurement for the distance from Earth to a Satellite

D. Thickness of a human hair

Of course, kilometers, meters, centimeters and even milimeters are units too big to measure the thickness of a human hair.

One micrometer is 10⁻⁶ meters or 10⁻³ milimeters.

In the internet you can find that diameter of the humar hairis in the range from 17 micrometers to 181 micrometers.

The measurement in the box #5. is 9 × 10¹ micrometers, which is equivalent to 9 × 10 = 90 micrometers.

Thus, 9 × 10¹ micrometers is the most reasonable measurement fot the thickness of a human hair.

7 0

3 years ago