convert the following logarithmic equation to the equivalent exponential equation. Use the caret (^) to enter exponents. y=ln x

Answers

Answer 1

1. To solve this problem, you need to remember that an exponential function has the following form:

f(x)=a^x

"a" is the base and "x" is the exponent.

2. It is important to know that the logarithmic functions and the exponential functionsare inverse. Then, you have:

y=ln x
e^y=e^(lnx)
e^y=x

3. Therefore, the answer is:

x=e^y

Answer 2

Answer:

To solve this problem, you need to remember that an exponential function has the following form:

f(x)=a^x

"a" is the base and "x" is the exponent.

2. It is important to know that the logarithmic functions and the exponential functionsare inverse. Then, you have:

y=ln x

e^y=e^(lnx)

e^y=x

3. Therefore, the answer is:

Step-by-step explanation:

Related Questions

Find the slope of the line that contains the points named. A(3, 2), B(7, 8)

Answers

The formula for the slope of a line is:

[tex]slope= \frac{ y_{1} - y_{2} }{ x_{1} - x_{2} } [/tex]

Plug in the data we know.

[tex]slope= \frac{ y_{1} - y_{2} }{ x_{1} - x_{2} } = \frac{2-8}{3-7} = \frac{-6}{-4}= \frac{6}{4} = 1.5 [/tex]

Answer:

3/2

Step-by-step explanation:

To find the slope of the line that contains the points A(3, 2) and B(7, 8), we can use the formula for slope:

slope = (change in y) / (change in x)

Let's calculate the values:

Change in y = 8 - 2 = 6

Change in x = 7 - 3 = 4

Now, we can find the slope:

slope = 6 / 4 = 3/2

Therefore, the slope of the line that contains the points A(3, 2) and B(7, 8) is 3/2.

Write a function numberofpennies() that returns the total number of pennies given a number of dollars and (optionally) a number of pennies. ex: 5 dollars and 6 pennies returns 506.

Answers

What language are you writing this in? C? Javascript? Java? Are you allow to have parameters?
The general idea should be the same. Since 1 dollar = 100 pennies, we should write something like...

Java:
public static double numberofpennies(double dollars, double penny) {
double sum = 0;

// The amount of pennies that dollar represents
double converted = dollars * 100.0;

sum = converted + penny;

return sum;
}
Note: You should probably place this question under the category computer and technology instead of math. Also, this is just an example of what you could possibly write. What parameters you are allowed to use, what type (double? int? etc?) of pennies are you allowed to return, etc. depends on how you write it.

Final answer:

The numberofpennies() function calculates the total number of pennies by converting dollars to pennies and adding any additional pennies. It multiplies the number of dollars by 100 and adds the extra pennies to find the total.

Explanation:

Function to Calculate Total Number of Pennies

The function numberofpennies() is used to calculate the total number of pennies for a given amount of dollars and optionally, additional pennies. To do this, it converts the dollars into pennies and then adds the additional pennies if they are provided.

Example Function in Python

Here is an example of how one might write the numberofpennies() function in Python:

def numberofpennies(dollars, extra_pennies=0):
return (dollars * 100) + extra_pennies

# Example usage:
total_pennies = numberofpennies(5, 6)
print(total_pennies) # This would print 506

In this example, the function takes two arguments: dollars, which is a mandatory argument representing the number of dollars, and extra_pennies, which is an optional argument representing additional pennies. The function then returns the total number of pennies by multiplying the number of dollars by 100 and then adding the extra pennies if any.

Eloise is investing in a retirement account. She plans on adding an additional $50 at the end of every year and the expected monthly rate of return is 3% of the amount invested, calculated at the end of the month. If she starts with $1000 in the account find an equation that models the amount of money in the account each month for the first year.

Answers

The accumulated (future) value is given by the formula
F=P(1+i)^n
where
P=amount of deposit (made at the beginning of the first period)
i=monthly interest, APR/12 = 3%/12 =0.0025
n=number of periods (month)

For example, the future value for the 6th month is
F(6)=1000(1.0025^6)=1015.09 (to the nearest cent)

Here is a schedule of the values,
i=month
F(i) = value at the end of month i.

i F(i)
0 1000.0
1 1002.5
2 1005.01
3 1007.52
4 1010.04
5 1012.56
6 1015.09
7 1017.63
8 1020.18
9 1022.73
10 1025.28
11 1027.85
12 1030.42 + $50 deposit = 1050.42
All values are rounded to the nearest cent.

The simplified answer is y = 1000(1.03)x.

Find the 29th term of the following sequence. 19.5, 19.9, 20.3, 20.7, . . .

Answers

This is the concept arithmetic sequence;
the nth value is given by:
nth=a+(n-1)d
where:
a=first term
d=common difference
n=number of terms
From the series:
19.5, 19.9, 20.3, 20.7,.....
a=19.5
d=0.4
n=29
thus
29th=19.5+(29-1)0.4
29th=30.7

6 + w = -8. What is w?

Answers

The answer to solving for w is:
w = -14

Happy to help and just let me know if ya need extra help.
~Brooke❤️

Hi!

The answer would w = -14 because you take -8 and switch the sign to positive +8 and add 6, so 8 + 6 = 14 then you take 14 and make it a negative number and putting it in the place of w, therefore 6 + (-14) = -8

Suppose that you invest 5873 in an account that earns an interest rate of 4.4% compounded monthly determine the accumulated balance after 7 years

Answers

present value, P = 5873
interest rate, i = 4.4%/12 = 0.044/12 per month
Number of periods, n = 7*12 = 84 months.

Future value
[tex]F=P(1+i)^n[/tex]
[tex]=5873(1+0.044/12)^{84}[/tex]
[tex]=7986.90[/tex] to the nearest cent

You flip a coin 10 times. Knowing that the event satisfies the requirements for a binomial distribution, find the probability that exactly 7 of the outcomes are heads.

Answers

Assuming a fair coin, and requirements for a binormial distribution are satisfied, then
p=0.50
n=20
The number of successes, x, is then given by[tex]P(x)=C(n,x)p^x(1-p)^{n-x}[/tex]where[tex]C(n,x)=\frac{n!}{x!(n-x)!}[/tex]
For x=7,
[tex]P(x)=C(n,x)p^x(1-p)^{n-x}[/tex]
[tex]P(7)=C(n,x)p^x(1-p)^{n-x}[/tex]
[tex]=C(20,7)0.5^7(0.5)^{20-7}[/tex]
[tex]=C(20,7)0.5^{20}[/tex]
[tex]=\frac{77520}{1048576}[/tex]
[tex]=\frac{4845}{65536}[/tex]
[tex]=0.07393[/tex] to 5 places of decimal

Ans. the probability is 0.07393 to 5 places of decimal.

Answer:

0.1172

Step-by-step explanation:

The formula for the probability in a binomial distribution (n trials, r successes) is

[tex]\binom{n}{r}(p)^r(1-p)^{n-r}[/tex] where p is the probability of success.

For flipping a coin, the probability of success, p, is 0.5.

The number of trials, n, is 10. The number of successes, r, is 7. This gives us

[tex]\binom{10}{7}(0.5)^7(1-0.5)^{10-7}\\\\\binom{10}{7}(0.5)^7(0.5)^3=0.1171875 \approx 0.1172[/tex]

Please help me figure how to explain ??

Answers

First of all, let's explain what SSA means. This is a concept of triangles and means Side, Side, Angle. This happens when we know two sides and an angle that is not the angle between the sides as shown in the Figure below.

On the other hand, the law of sines states that for the triangle below it is true that:

[tex]\frac{a}{sinA}= \frac{b}{sinB}= \frac{c}{sinC}[/tex]

According to the problem we will explain three cases that result in zero, one or two triangles while applying SSA. Let's solve this problem with examples.

First. Case zero solution (No solution)

Suppose that:

[tex]b=8 \\ c=9 \\ B=75^{\circ}[/tex]

So let's start by finding angle C. According to the law of sines:

[tex]\frac{c}{sinC}= \frac{b}{sinB} \\ \\ \therefore \frac{9}{sinC}= \frac{8}{sin75^{\circ}} \\ \\ \therefore sinC= \frac{9sin75^{\circ}}{8} \\ \\ \therefore C=sin^{-1}(1.086)[/tex]

If you try to take the arcsin of a number that's larger than one it is not going to work. Therefore there is no solution in this case.

Second. Case one solution

Suppose that:

[tex]b=10 \\ c=9 \\ B=42^{\circ}[/tex]

Then according to the law of sines:

[tex]\frac{b}{sinB}= \frac{c}{sinC} \\ \\ \therefore \frac{10}{sin42^{\circ}}= \frac{9}{sinC} \\ \\ \therefore sinC= \frac{9sin42^{\circ}}{10}=0.602 \\ \\ \therefore C=sin^{-1}(0.602)=37.01^{\circ} \ or \ C=180^{\circ}-37.01^{\circ}=142.99^{\circ}[/tex]

But we know that:

[tex]A+B+C=180^{\circ} \\ \\ If \ C=37.01^{\circ} \ then: \\ A=180^{\circ}-42^{\circ}-37.01^{\circ}=79.01^{\circ} \\ It's \ a \ solution \\ \\ If \ C=142.99^{\circ} \ then: \\ A=180^{\circ}-42^{\circ}-142.99^{\circ}=-4.99^{\circ} \\ It's \ not \ a \ solution[/tex]

Therefore we have one solution

Third. Two solutions.

Suppose that:

[tex]B=30^{\circ} \\ b=7 \\ c=8[/tex]

So:

[tex]\frac{b}{sinB}= \frac{c}{sinC} \\ \\ \therefore \frac{7}{sin30^{\circ}}=\frac{8}{sinC} \\ \\ \therefore sinC=\frac{8sin30^{\circ}}{7}=\frac{4}{7} \\ \\ \therefore C=sin^{-1}(\frac{4}{7})=34.85^{\circ} \ or \ C=180^{\circ}-34.85^{\circ}=145.15^{\circ} \\ \\ Thus: \\ \\ If \ C=34.85^{\circ} \ then:\\ A=180^{\circ}-30^{\circ}-34.85^{\circ}=115.15^{\circ} \\ It's \ a \ solution \\ \\ If \ C=145.15^{\circ} \ then:\\ A=180^{\circ}-30^{\circ}-145.15^{\circ}=4.85^{\circ} \\ It's \ a \ solution[/tex]

Therefore there are two solutions.

Conclusion: For triangles to make sense the shortest side must be across the lowest angle and the longest side must be across the largest angle.

If PQR~STU, what is the scale factor of PQR to STU? QR=20 and TU=4.
i have 2mins left. help!!!

Answers

the complete question in the attached figure

we know that
If PQR~STU
then
scale factor of [PQR/ STU]=(QR/TU)=(PQ/ST)=(PR/SU)
QR=20
TU=4
(QR/TU)=20/4=5/1

the answer is (5/1)

Sabah has $450 to pay for college textbooks. She expects to pay about $75 per book. Her friend told her that 4 of them can be checked out of the library for free.

Complete the equation below to find the total number of books that Sabah can get for her classes. Use b to represent the total books.

Answers

450 is the total amount of money and it is divided by 75 to get the total number of books possible under that amount per book. The reason four is added is that it is stated that four of the books necessary are to be taken from a library for free. Therefore, when solved, b is equal to 10

what values of x make the two expressions below equal? (x+3)(x+8)/5(x+8) = x+3/5
a. all real numbers except -8
b. all real numbers except -3
c. all real numbers
d. all real numbers except -8 and -3

Answers

We can by simplifying the first expression:
[tex] \frac{(x+3)(x+8)}{5(x+8)} = \frac{x+3}{5}[/tex]
I will asume that second exressin is [tex]\frac{(x+3)}{5}[/tex]. Then the answer would be all number, because those two expressions are identical.
If we look at the expression you wrote in the question [tex]x+3/5[/tex], you can see that there are no numbers for which these two would be equal.
So the final answer is C.

[08.06 MC]
Factor completely 4x3 + 8x2 − 25x − 50. (2 points)

(4x2 − 25)(x + 2)

(2x − 2)(2x + 2)(x + 5)

(2x − 5)(2x + 5)(x + 2)

(2x − 5)(2x + 5)(x − 2)

Answers

4x^3 + 8x^2 - 25x - 50
Steps
(4x^3 + 8x^2) + (-25x - 30)
Factor out 4x^2 from 4x^3 + 8x^2: 4x^2(x + 2)
Factor out -25 from -25x - 50: -25(x + 2)
= 4x^2(x + 2) - 25(x + 2)
Then, factor out common term (x + 2)
= (x + 2)(4x^2 - 25)
Factor 4x^2 - 25: (2x + 5)(2x - 5)
= (x + 2)(2x + 5)(2x - 5)
Which the answer to this is the 3rd option.

Answer: THE 3RDDDDDDDDDDDDDDDDDDDDD

37.5 x 10 to the negative 6 in scientific notation?

Answers

The scientific notation is 37.5×10^-6

The table below shows a baseball player’s batting average batting left and right versus left- and right-handed pitches Left-handed pitchers Right-handed pitchers Bats left 0.285 0.175 Bats right 0.215 0.250 Assume these numbers are the probabilities that he will get a hit during an “at bat.” On average, when he bats left 100 times, how many more hits will he get when he faces left-handed pitchers as opposed to right-handed pitchers? 1 2 11 22

Answers

Answer:

C. 11 is the correct answer

Step-by-step explanation:

The table representing the probabilities of player's batting average is,

Left-Handed pitchers Right-Handed pitchers

Bats Left 0.285 0.175

Bats Right 0.215 0.250

So, when the players bats left 100 times,

The probability of hits he gets when faced by left-handed pitchers = 0.285 × 100 = 28.5

The probability of hits he gets when faced by right-handed pitchers = 0.175 × 100 = 17.5

Thus, the difference in the hits = 28.5 - 17.5 = 11

Hence, the player will get 11 more hits t when he faces left-handed pitchers as opposed to right-handed pitchers.

At southern states university (ssu) there are 399 students taking finite mathematics or statistics. 238 are taking finite mathematics, 184 are taking statistics, and 23 are taking both finite mathematics and statistics. how many are taking finite mathematics but not statistics?

Answers

215 are taking finite mathematics but not statistics.

We know that a total of 238 students are taking finite mathematics; this includes the 23 that are taking both. We subtract these to calculate just finite mathematics:

238 - 23 = 215 taking just finite mathematics.

Find the value of z such that 0.96420.9642 of the area lies between −z−z and z. round your answer to two decimal places.

Answers

If z represents the variable of the standard normal distribution curve N(0,1), which is symmetrical about z=0, then we look for
P(z)-P(-z)=0.9642=1-2P(-z) => P(-z)=(1-0.9642)/2=0.0179
=>
-z=-2.099192
=> z=2.099192
Check:
P(2.099192)-P(-2.099192)=0.9642 ok

Final answer:

The value of z where 0.9642 of the area lies between -z and z is found by looking up the area 0.4821 (half of 0.9642) in a Z-table or using the invNorm function with 0.4821 on a normal distribution calculator. This will provide the z-score to be rounded to two decimal places.

Explanation:

You are looking for the value of z such that 0.9642 of the area under the normal distribution curve lies between −z and z. To find this, you'll need to use the properties of the standard normal distribution, commonly represented by a Z-table.

For a symmetrical distribution, half of the area you are interested in would be to the left of 0 and half to the right. Since 0.9642 is the total area between −z and z, we need to find the z-score that corresponds to half of this area from the mean to one end. Specifically, you're looking for the z-score where the area to the left is 0.4821 (0.9642 divided by 2).

Using a Z-table or an inverse normal function on a calculator, you can find the z-score that corresponds to an area of 0.4821. If you're using a Z-table, look up the closest area in the body of the table and find the corresponding Z-score. If you're calculating it (such as with the invNorm function on a calculator like the TI-83 or 84), input the left-tail area. The answer should be rounded to two decimal places.

The calculation would be something similar to invNorm(0.4821, 0, 1), where 0 and 1 are the mean and standard deviation of the standard normal distribution, respectively.

If z represents the variable of the standard normal distribution curve N(0,1), which is symmetrical about z=0, then we look for

P(z)-P(-z)=0.9642=1-2P(-z) => P(-z)=(1-0.9642)/2=0.0179

-z=-2.099192

=> z=2.099192

Check:

P(2.099192)-P(-2.099192)=0.9642

The tax revenue that a small city receives increases by 3.5% per year. in 1990, the city received $250,000 in tax revenue. Determine the tax revenue in 1995 and in 2006.

Answers

Hello there! For this question, because the revenue increases, we will be compounding. The formula for coompounding is P(1 + r)^t, where P = initial amount, r = rate in decimal form, and t = time in years. First, let's add 1 into the rate. 3.5% is 0.035 in decimal form. 1 + 0.035 is 1.035. 1995 is 5 years from 1990 and 2006 is 16 years from 1990. Let's start by raising it to the 5th power. 1.035^5 is 1.187686306. Do not delete the number from your calculator. Multiply it by 250,000. When you do, you get 296,921.5764 or 296,921.58 when rounded to the nearest hundredth. We solved for 1995. Now, let's solve for 2006. 1.035^16 is 1.73398604. Again, do not delete the number from your calculator. Multiply by 250,000. When you do, you get 433,496.509957 or 433,496.51 when rounded to the nearest hundredth. There. Here are your answers:

1995: $296,921.58
2006: $433,496.51

Final answer:

To find the tax revenue in 1995 and 2006 for a city with an annual increase of 3.5%, we use the formula for exponential growth. The revenue in 1995 is calculated to be $296,923, and for 2006, it is calculated to be $438,995.

Explanation:

The tax revenue that a small city receives increases by 3.5% per year. To calculate the tax revenue for the years 1995 and 2006, we can use the formula for exponential growth: Final Amount = Initial Amount * (1 + Growth Rate)Number of Years.

For 1995, which is 5 years after 1990, the calculation would be:
Revenue in 1995 = $250,000 * (1 + 0.035)5
Revenue in 1995 = $250,000 * (1.035)5
Revenue in 1995 = $250,000 * 1.18769
Revenue in 1995 = $296,923

Similarly, for 2006, which is 16 years after 1990, the calculation would be:
Revenue in 2006 = $250,000 * (1 + 0.035)16
Revenue in 2006 = $250,000 * (1.035)16
Revenue in 2006 = $250,000 * 1.75598
Revenue in 2006 = $438,995

What are 3 consecutive integers that have a sum of 234?

Answers

Try this option:
1. three consecutive integers are: x, x+1 and x+2, the sum is 234.
Equation x+x+1+x+2=234; ⇔ x=77.
2. x=77, x+1=78; x+2=79.
Answer: 77,78,79.

Can someone please answers these questions

Answers

Try this option (not for all the tasks!):
1) rule for n-angle is: S=180°(n-2), where n - number of the sides. S₁₅=180*13=2340°;
2) S₂₅=180*23=4140°;
4) this is deltoid;
5) this is paralelogram;
6) x=130°; y=50°;
10) x=90°; y=30° (it is deltoid);
12) not enough info for parallelogram (the same for deltoid);
14) it is enough: according to a property of a parallelogram (it means that a square and rombus are parallelograms);
15) it is enough according to the properties of parallelograms;
16) x=2; y=1;
18) poit S(0;0); point T(b+c;d). The coordinates of the midpoint are (0.5b+0.5c;0.5d); slope=arctg(d/(b+c)).

27POINTS A parallelogram has an area of 14 cm 2. If the dimensions of the parallelogram are doubled, what will the new area be?

A.14 cm 2
B.28 cm 2
C.56 cm 2
D.112 cm 2

Answers

Answer:

.56 (C)

Step-by-step explanation:

What happens when year on year percent change goes below 0%?

Answers

Whatever was being measured is lower for the second year than it was for the first.

PLEASE SHOW ALL WORK!!!
The base of a triangle measures (8x + 2) units and the height measures (4x − 5) units.

Part A: What is the expression that represents the area of the triangle? Show your work to receive full credit. (4 points) Hint: Area = 0.5bh

Part B: What are the degree and classification of the expression obtained in Part A? (3 points)

Part C: How does Part A demonstrate the closure property for polynomials? (3 points)

Answers

Part A: We know that the equation for finding the area of a triangle is [tex]A=.0.5(base)(height)=0.5bh[/tex]; we also know that [tex]base=(8x+2)[/tex] and [tex]height=(4x-5)[/tex], so the only thing we need to do is replacing those values into our Area equation and solve for x:
[tex]A=0.5(8x+2)(4x-5)[/tex]
[tex]A=0.5(32 x^{2} -40x+8x-10)[/tex]
[tex]A=0.5(32 x^{2} -32x-10)[/tex]
[tex]A=16 x^{2} -16x-5[/tex]
Now the only thing left is factor the quadratic polynomial:
[tex]A=(4x+1)(4x-5)[/tex]

W can conclude that the area of our triangle is [tex]A=(4x+1)(4x-5)[/tex]

Part B: Our polynomial has three terms, so is a trinomial; also, our polynoal only has one variable, [tex]x[/tex], and the largest exponent of that variable is 2; therefore is a degree 2 polynomial. In summary, we have a trinomial of degree 2.

Part C: Part A demonstrate the closure property of polynomials because after multiplying tow polynomials we obtained another polynomial.

Part A:

As given,

Base of the triangle = 8x + 2 units

Height of the triangle = 4x − 5 units

Formula to find area of a triangle = [tex]\frac{base * height}{2}[/tex]

= 0.5bh

we have been given base and height, so the area becomes,

area = [tex]\frac{(8x+2)(4x-5)}{2}[/tex]

area = 0.5(8x+2)(4x-5)

= 0.5(32x²-32x-10)

= 16x²-16-5

after factoring it, we get

area = (4x-5)(4x+1) units.

Part B:

It is a degree 2 polynomial as the polynomial has one variable that is x, and the largest exponent of that variable is 2.

Part C:

Part A demonstrates the closure property of polynomials because after multiplying two polynomials we get another polynomial.

There is a sales tax of $14 on an item that costs $147before tax. A second item costs$84 before tax. What is the sales tax on the second item?

Answers

Final answer:

To calculate the sales tax on the second item, we determined the sales tax rate from the first item and applied it to the second item's cost, resulting in $7.99 sales tax on the second item.

Explanation:

To find the sales tax on the second item, we use the information provided about the first item to determine the rate of sales tax and then apply this rate to the second item. If the first item costs $147 with a sales tax of $14, we can find the sales tax rate by dividing the sales tax by the cost of the item before tax:

Sales tax rate = Sales tax / Price before tax

= $14 / $147

= 0.0952 or 9.52%

Once we have the sales tax rate, we can calculate the sales tax on the second item, which costs $84 before tax:

Amount of sales tax = Price × Rate of sales tax

= $84 × 0.0952

= $7.99 (rounded to the nearest cent)

Therefore, the sales tax on the second item is $7.99.

Chapter 5 lesson 5.1 2nd grade

Answers

What is the question?

Answer:

What is the question?yea

Step-by-step explanation:

Answer step by step

1.Avas school took a field trip. A total of 32 vehicles were needed for the trip.Some students took the bus, and some students car-pooled. There are 27 people on each bus and 3 people on each car. 408 people altogether attended the trip. How many buses and cars were needed for the trip?

Answers

Consider, please, this solution/explanation:
1. suppose, that number of cars is 'x', numbers of buses is 'y'.
2. according to the condition 'a total of 32', it means that x+y=32. This is the 1st equation.
3. according to the condition in one car are 3x persons, in one bus are 27y persons, and totaly 3x+27y=408 people. This is the 2d equation.
4. if to solve the system of two equations:
[tex] \left \{ {{x+y=32} \atop {3x+27y=408}} \right. \ =\ \textgreater \ \ \left \{ {{x=19 (cars)} \atop {y=13(buses)}} \right. [/tex]

Answer: 13 - b., 19 - c.

help me plssssssssssssssssssssssssssssssssssssssss

Answers

First, let's give the variable a name:
Let
x = gallons of water to be added
For the 10% solution we have:
0.1 * 8 = 0.8
Then, for 5% we have:
(0.8 / x + 8) = 0.05
Rewriting:
(0.8 / x + 8) = (5/100)
Answer:
An equation can be used to find x, the humber of gallons of water he should add is:
(0.8 / x + 8) = (5/100)

use the proportion to convert millimeters to centimeters. 10mm/1cm=47mm/x

Answers

- The centimeter is defined as a unit of lenght. Its symbol is: "cm".

- 1 centimeter=10 milimeters.

- The milimeter is defined as a unit of lenght and its symbol is "mm".

1. If you want to convert 47 milimeters to centimeters by using proportions, you have:

10 mm/1 cm=47mm/x

2. Then, you only have to clear the "x":

(10 mm)x=(47mm)(1 cm)
x=(47 mm)(1 cm)/10 mm

3. Therefore, the result is:

x=4.7 centimeters

When expressed in exponential notation, the number 0.000302 becomes:?

Answers

3.03×10^-3
...............

A midsegment of a triangle measures 40 m. What is the length of the corresponding base of the triangle? A. 20 m B. 40 m C. 60 m D. 80 m

Answers

Corresponding base of the triangle is
80
m.
Explanation:
A mid-segment of a triangle is a segment connecting the midpoints of two sides of a triangle.

The Symmetric Property of Congruence allows you to say that if ∠LMN ≅ ∠NSP, then ∠NSP ≅ _____.

Answers

The Symmetric Property of Congruence states that If angle A is equivalent to angle B then the angle B will also be equivalent to angle A .

In the problem it is given that ∠LMN ≅ ∠NSP

So, as per the Symmetric Property of Congruence ∠NSP ≅ ∠LMP

The Symmetric Property of Congruence allows you to say that if ∠LMN ≅ ∠NSP, then ∠NSP ≅ ∠LMN.

Hope this helps..!!

Thank you :)

The correct completion of the statement using the Symmetric Property of Congruence is: If [tex]$ \angle LMN \cong \angle NSP $[/tex], then [tex]$ \angle NSP \cong \angle LMN $[/tex].

The Symmetric Property of Congruence states that if two angles are congruent, then the second angle is also congruent to the first. In other words, the order in which the angles are listed does not affect the congruence. Therefore, if [tex]$ \angle LMN $[/tex] is congruent to [tex]$ \angle NSP $[/tex], it follows that[tex]$ \angle NSP $[/tex] is congruent to [tex]$ \angle LMN $[/tex]. This property is a fundamental aspect of geometry that allows us to reverse the order of the angles in a congruence statement without changing the meaning of the statement.

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