Can two triangles be proven congruent when the three angles are each congruent? Why or why not?
Yes, two triangles can be proven congruent when the three angles are congruent because the only way three angles can be congruent is if the three sides are also congruent.
Yes, two triangles can be proven congruent when the three angles are congruent because the sum of the three angles is 180 for both triangles.
No, two triangles cannot be proven congruent when the three angles are congruent because the sum of the three angles is 180, not 90.
No, two triangles cannot be proven congruent when the three angles are congruent because the sides of the triangles may not be congruent.

Yes, it is true that if [a]m, [b]m € Z/mZ are units, then so is their product [a]m [b]m.

In Z/mZ, where m is an integer greater than 1, the units are the elements that have an inverse. That is, an element [a]m in Z/mZ is a unit if there exists [a]′m in Z/mZ such that [a]m [a]′m = [1]m where [1]m is the identity element in Z/mZ. A unit is also known as an invertible element in a ring. It is because it has a multiplicative inverse that allows us to divide by that element.The modulo operation is used in Z/mZ, which is a type of integer division that determines the remainder of a division operation between two integers. It helps us to make arithmetic calculations simpler by reducing the magnitude of integers to a specific range. For instance, in Z/5Z, we have [0]5, [1]5, [2]5, [3]5, [4]5 as the integers, and the operations in this ring are carried out by reducing the integers to their remainder when divided by 5.In Z/mZ, if [a]m and [b]m are units, then we can say that [a]m [b]m is also a unit. To understand why, we can use the definition of units and the modulo operation. Because [a]m and [b]m are units, they have inverses [a]′m and [b]′m in Z/mZ. We can see that:

[a]m [a]′m = [1]m and [b]m [b]′m = [1]m.

Let's try to calculate:

[a]m [b]m [a]′m [b]′m

as follows:

[a]m [b]m [a]′m [b]′m = [a]m [a]′m [b]m [b]′m = [1]m [1]m = [1]m

Therefore, it is proved that the product [a]m [b]m is also a unit and has an inverse [a]′m [b]′m in Z/mZ. So, if [a]m, [b]m € Z/mZ are units, then so is their product [a]m [b]m.

In conclusion, if [a]m, [b]m € Z/mZ are units, then so is their product [a]m [b]m. A unit in Z/mZ is an element that has a multiplicative inverse, and it is also known as an invertible element in a ring. The modulo operation is a type of integer division that determines the remainder of a division operation between two integers. We can use the definition of units and the modulo operation to prove that the product of two units in Z/mZ is also a unit.

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Answer:

4F-1

Theres infinite amount of solutions

Step-by-step explanation:

12f/3=4f

-3/3=-1

4f-1=4f-1

Answer:

f = 0

Step-by-step explanation:

\( \frac{1}{3} (12f - 3) = 4f - 1\)

Use ⅓ to open the bracket

\( \frac{1}{3} \times \: 12f = 4f \\ \frac{1}{3} \times 3= 1\)

\(4f - 1= 4f - 1\)

Collect like terms

\(4f - 4f = - 1+1 \\ - 1f = 0 \\ \\ f = 0\)

Answer:

hope this helps

Step-by-step explanation:

l = 24 cm

b = 18 cm

h = 14 cm

S.A of cuboid = 2 (l+b) × h

= 2 (42) × 14

= 84 × 14

= 1,176 cm²

Answer: 3/52

Step-by-step explanation:

You want to pick a diamond jack, diamond queen or diamond king

There are only 3 of those so

P(DJ or DQ or DK) = 3/52        There are 3 of those out of 52 total

The value of y will be y = 5 × 5 = 25. Hence, the point (11, 25) lies on the graph of the transformed function y=5f(a). The correct answer is D (11, 25).

Suppose (11,5) is on the graph of y=f(x). The given transformed function is y = 5f (a).

The expression 5f (a) shows that the graph of f(x) has been vertically stretched by a factor of 5.

Let us find the point on the graph of y = 5f(a).Here, we have to consider x = 11 because (11, 5) is given as a point on the original graph.

Let us substitute x = 11 in the transformed function y = 5f (a).y = 5f(11) … (1)From the original function y = f(x), the point (11, 5) lies on the graph of the original function f(x).

Thus, we can substitute x = 11 and y = 5 in the function y = f(x) to get 5 = f(11).We can now substitute this value of f(11) in equation (1).y = 5 × 5 = 25

Hence, the point (11, 25) lies on the graph of the transformed function y = 5f(a).Therefore, the correct option is D (11, 25).

If (11, 5) is a point on the graph of y=f(x) then to find the point on the graph of transformed function y=5f(a), substitute the given point in the transformed function to solve it. The transformed function is y = 5f(a).

The expression 5f(a) shows that the graph of f(x) has been vertically stretched by a factor of 5.

The point (11, 5) lies on the graph of the original function f(x), so substituting x=11 and y=5 in the function y = f(x) will give 5 = f(11).

Now substitute this value of f(11) in the transformed function y = 5f(a). The value of y will be y = 5 × 5 = 25.

Hence, the point (11, 25) lies on the graph of the transformed function y=5f(a).

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Answer:

-4/2

Step-by-step explanation:

es menor que -4 pero es mayor que -5

Toni invested in pounds= $1350

rate of compound interest=4%

Here, we have,

Toni invests money into an account which pays a fixed rate of compound interest each year. The total value, £V, of her investment after t years is given by the formula:  

V = 1350 x 1.04^t

Answer questions a & b

a - How much money did Toni invest in pounds

b - What rate of compound interest is paid each year

the formula for calculating compound interest is given by :

V = P (1 + r)^t

P = Present value  -= amount invested = 1350

R = interest rate  = 4%

N = number of years  = t

we have,

V = 1350 x 1.04^t

P= 1350 is the initial amount invested

1+r= 1.04  (subtract 1 from both sides)

r = 0.04

multiply it by 100 to get percentage

r= 4%

Hence, Toni invested in pounds= $1350

rate of compound interest=4%

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Answer:

\(22.2 \;meters\)

Step-by-step explanation:

The volume of the hemisphere = 22,778 m³

The volume of a sphere of the same radius
= twice the volume of the hemisphere
= 2 x 22,778 m³
= 45576 m³

The volume of a sphere of radius r is given by the formula:
\(V = \dfrac{4}{3}\pi r^3\)

Plugging in knowns:
\(45576 =\dfrac{4}{3}\pi r^3\)

Switching sides:
\(\dfrac{4}{3}\pi r^3 =45576\)

Multiply both sides by \(\dfrac{3}{4}\)

\(\dfrac{3}{4} \times \dfrac{4}{3}\pi r^3 =\dfrac{3}{4} \times 45576\\\\\pi r^3 = 34,182\)

Divide by π both sides to get
\(r^3 = \dfrac{34,182}{\pi} = 10,880.4685\\\\r= \sqrt[3]{10,880.4685} \\\\= 22.15895\\\\= 22. 2 \text{ meters (to the nearest tenth)}\)

Sherri has 35 apps on her phone and Bill has 64 apps on his phone.

Let's represent Sherri’s apps with x.

Then, the number of Bill's apps will be x+29 (since he has 29 more apps than Sherri).

Their total number of apps is 99.Thus, the mathematical equation is:x + (x+29) = 99

Simplifying this equation gives:2x + 29 = 99

Subtracting 29 from both sides of the equation gives:2x = 70

Dividing both sides by 2 gives:x = 35

This means Sherri has 35 apps on her phone.

Substituting that into x+29 gives:35+29 = 64

Therefore, Bill has 64 apps on his phone.

Hence, each person has Sherri has 35 apps on her phone and Bill has 64 apps on his phone. The total number of apps between the two of them is 99 apps.

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The congruent segments are the sides of the small triangles, then the congruent segments are: HA, BD and BF.

Therefore the answer are B, E and F.

This statement is true, as the test statistic represents the number of standard deviations between the observed sample proportion and the claimed value (po) under the null hypothesis.

- The large value of the test statistic means that our observed data are not surprising when the null hypothesis is true. This statement is false. A large test statistic implies that the observed data is surprising when the null hypothesis is true, which means there is evidence against the null hypothesis.
- The researcher should fail to reject the null hypothesis. This statement is false. A large test statistic suggests evidence against the null hypothesis, so the researcher should reject the null hypothesis in favor of the alternative hypothesis.

- When the null hypothesis is true, the test statistic comes from a standard normal distribution. This statement is true, as the test statistic follows a standard normal distribution when the null hypothesis is true.
- There is a 4.318% chance that the alternative hypothesis is true. This statement is false. The test statistic does not directly provide the probability of the alternative hypothesis being true. Instead, we can use the test statistic to calculate the p-value, which represents the probability of obtaining a test statistic as extreme as the observed one, assuming the null hypothesis is true.

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Answer:

6

Step-by-step explanation:

Answer:

- 28

Step-by-step explanation:

Determinant of matrix J is

- 2(5) - 3(6) = - 28

Answer:

29.645

As a decimal

Step-by-step explanation:

The given function f: Z-Z defined by f (n) = n² is not injective because each non-zero integer has two square roots, a positive and negative. Thus, for example, both f(2) and f(-2) are equal to 4.

Also, not every element in the codomain has a preimage in the domain. Therefore, the function f is not surjective. Hence, the function f is not bijective. A function is injective if and only if distinct elements of the domain are mapped to distinct elements of the codomain. A function is bijective if and only if it is both injective and surjective. The given function f: RR defined by ƒ (r) = r² is not injective because every positive number has two square roots, a positive and negative, but the function maps them to the same output.

However, the function f is surjective because every positive number is an image of a real number. Thus, the codomain of the function coincides with the set of non-negative real numbers, and every non-negative real number has a preimage. Therefore, the function f is not bijective. f is not injective but surjective. Hence, the function f is not bijective. A function is injective if and only if distinct elements of the domain are mapped to distinct elements of the codomain. A function is surjective if and only if every element of the codomain is the image of at least one element of the domain. A function is bijective if and only if it is both injective and surjective.

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Answer:

768

Step-by-step explanation:

Answer:

6/42 = 1/7

Step-by-step explanation:

Divide the number of events by the number of possible outcomes.

Answer:

Step-by-step explanation:

5 * 1/8=  5/8

1/7*6=  6/7

Place the whole number over 1 and multiply.

Answer: 15

Hope this helps! Give brainliest if you can. :)

The linear pair is the correct answer for a pair of adjacent angles whose opposite rays form their non-common sides.

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Answer:

Step-by-step explanation:

given data

mean = 1.9 hours

standard deviation = 0.3 hours

solution

we get here first  random movie between 1.8 and 2.0 hours

so here

P(1.8 < z < 2 )

z = (1.8 - 1.9) ÷ 0.3

z = -0.33

and

z = (2.0 - 1.9) ÷ 0.3

z = 0.33

z = 0.6293

so

P(-0.333 < z < 0.333 )

=  0.26

so random movie is between 1.8 and 2.0 hours long is 0.26

and

A movie is longer than 2.3 hours.

P(x > 2.3)

P( \(\frac{x-\mu }{\sigma}\)  > \(\frac{2.3-\mu }{\sigma}\) )

P (z  > \(\frac{2.3-1.9 }{0.3}\)  )

P (z  > 1.333  )

= 0.091

so chance a movie is longer than 2.3 hours is 0.091

and

length of movie that is shorter than 94% of the movies is

P(x > a ) = 0.94

P(x <  a ) = 0.06

so

P( \(\frac{x-\mu }{\sigma }\) <  \(\frac{a-\mu }{\sigma }\) )

\(\frac{a-1.9 }{0.3 } = -1.55\)

a = 1.43

so length of the movie that is shorter than 94% of the movies about 1.4 hours.

Answer:

435 gallons

Step-by-step explanation:

565+482=1,047

1,047-612=435

Answer:

435 gallons

Step-by-step explanation:

first we add 565 and 482

565+482

1047

Now we subtract how many they sold which is 612 gallons

1047-612

435 gallons

Hopes this helps please mark brainliest

aₙ = 0.20aₙ₋₁ + 200 is the recursive formula for the above sequence.

Therefore, choice A is the right one.

Given:

A holiday tree farm is owned by Mahek.

Currently, the site has 800 trees.

200 saplings are planted together with the 20% of the trees that are harvested and sold each year.

a₁ = 800

The recursive formula is,

aₙ = 0.20aₙ₋₁ + 200

Hence, the correct formula is aₙ = 0.20aₙ₋₁ + 200

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Answer:

were is the line

Step-by-step explanation:

Answer:

1- y=2x-5

2- y=-1/6x-5

Hope this helps you!!

In order to determine how much does Allison pay for her utilitites, it is only necessary to calculate the percentage associated to utilities, given in the table (2.3%) of the Allison's earns ($6,500).

For calculating the 2.3% of 6,500, you simply multiply (2.3/100) by 6,500, just as follow:

(2.3/100)(6,500) = 149.5

Then, the 2.3% of $6,500 is $149.5. Hence, Allison pay $149 for her utilities

Answer:

The depth of the submarine was 295 feet

Step-by-step explanation:

Function Modeling

The following expression models the depth of a submarine that began at -370 m and ascended at 15 ft/minute:

d = -370 + 15z

Where z is the time in minutes.

We are required to find the depth of the submarine at t=5 minutes. Substituting t=5 into the function model:

d = -370 + 15(5)

d = -370 + 75

d = -295 feet

The depth of the submarine was 295 feet

Answer:

mean= 10+11+8+10+12+8+10+11+12+10/10

=92/10=9.2

mode=10

hope it helps

plz mark as brainliest