Rewrite as a combination of multiple logarithms:

log_8 (10xy^3)

​

Answer:

24

Step-by-step explanation:

Answer:

20 days

Step-by-step explanation:

Expected Task duration

= (O + 4 M + P)/6

Where O = best case scenario = 15 days

P = worst case scenario = 25 days

M = Usual scenario = 20 days

Therefore, expected task duration

= [15 + 4 (20) + 25] ÷ 6

= 120 ÷ 6

= 20 days.

Therefore expected task duration is 20 days.

Answer:

A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 8, 16.

Step-by-step explanation:

Let an exponential growth function is [tex]f(x) = a(b)^{x}[/tex].

Now, [tex]f(1) = a(b)^{1}[/tex], [tex]f(2) = a(b)^{2}[/tex] , [tex]f(3) = a(b)^{3}[/tex] and [tex]f(4) = a(b)^{4}[/tex].

So, the values of the function corresponding to the x-values 1, 2, 3, and 4, are in G.P. and the common ratio of b.

Now, 'a 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 8, 16' will be the exponential function as the values are in G.P. with common ratio 2. (Answer)

Answer:

its  D

Step-by-step explanation:

just did the assignment

Answer:

The price of season ticket last year was 1,840.

Step-by-step explanation:

Given:

Price of season tickets this year = 2024

Also given:

The Price of season tickets this year is 10% more than amount paid last year.

We need to find the Price of season tickets last year.

Solution:

Let the Price of season tickets last year be 'x'.

Now we know that;

The Price of season tickets this year is 10% more than amount paid last year.

so equation can be framed as;

[tex]x+ \frac{10}{100}x=2024\\\\x+\frac{x}{10}=2024\\\\x+0.1x=2024\\\\1.1x=2024[/tex]

Now dividing both side by 1.1 we get;

[tex]\frac{1.1x}{1.1}=\frac{2024}{1.1}\\\\x= 1840[/tex]

Hence The price of season ticket last year was 1,840.

Answer:

The answer to your question is letter A

Step-by-step explanation:

Expression

                        - 3x - (x - 1) + 3/2(3x + 3)

1.- Expand

                        - 3x - x + 1 + 3/2(3x) + 3/2(3)

2.- Simplify

                        - 3x - x + 1 + 9/2 x + 9/2

3.- Associate like terms

                      (-3x - x + 9/2x) + (1 + 9/2)

4.- Simplify like terms

                      (-4x + 9/2x) + (2 + 9)/2

                      (-8x + 9x)/2 + 11/2

                                1/2x + 11/2

Where do I share a photo of my work

Answer:

The dimensions of the room are length is 16 feet and the width is 11 feet.

Step-by-step explanation:

Given:

The wards decided to use carpet tiles in the family room. The room has an area of 176 square feet and is 5 feet longer than it is wide.

Now, to get the dimensions.

Let the width be [tex]x.[/tex]

So, the length = [tex]x+5.[/tex]

Area = 176 square foot.

So, we put formula of area to get the dimensions:

Area = length × width.

[tex]176=(x+5)\times x[/tex]

[tex]176=x^2+5x[/tex]

Subtracting boths sides by 176 we get:

[tex]0=x^2+5x-176\\x^2+5x-176=0[/tex]

On solving the equation:

[tex]x^2+16x-11x-176=0\\x(x+16)-11(x+16)=0\\(x+16)(x-11)=0[/tex]

As,

[tex]x+16[/tex] = 0

[tex]x=-16[/tex]

So, we would not take the negative result.

Thus,

[tex]x-11=0\\x=11[/tex]

So, the width = 11 feet.

Now, to get the length by substituting the value of [tex]x[/tex]:

[tex]x+5\\=11+5\\=16[/tex]

The length = 16 feet.

Therefore, the dimensions of the room are length is 16 feet and the width is 11 feet.

The width is 11 feet, and the length is 5 feet longer, making it 16 feet.

To determine the dimensions of the family room, we start by defining the width of the room as w. According to the problem, the length (l) is 5 feet longer than the width, so we can write this as:

l = w + 5

We also know the area of the room is 176 square feet. The area of a rectangle is calculated by multiplying the width and length:

Area = width × length

Therefore, we get the equation:

w × (w + 5) = 176

Expanding this equation gives us:

w² + 5w = 176

We rearrange this into a standard quadratic equation:

w² + 5w - 176 = 0

Now we solve for w using the quadratic formula, w = (-b ± √(b² - 4ac)) / 2a, where:

This gives us:

w = (-5 ± √(25 + 704)) / 2

w = (-5 ± √729) / 2

w = (-5 ± 27) / 2

Which simplifies to:

w = 11 or w = -16

Since width cannot be negative, we have:

w = 11

Then the length l is:

l = 11 + 5 = 16

Therefore, the dimensions of the family room are 11 feet by 16 feet.

Answer:

a

Step-by-step explanation:

The distance between two given coordinate points is 11 units. Therefore, option C is the correct answer.

The distance formula which is used to find the distance between two points in a two-dimensional plane is also known as the Euclidean distance formula. On 2D plane the distance between two points (x₁, y₁) and (x₂, y₂) is Distance = √[(x₂-x₁)²+(y₂-y₁)²].

The given coordinate points are (-3, 2) and (2, -8).

Substitute (x₁, y₁) =(-3, 2) and (x₂, y₂)= (2, -8) in the distance formula, we get

Distance = √[(2+3)²+(-8-2)²]

= √[5²+(-10)²]

= √125

= 11.18

≈ 11

The distance between two given coordinate points is 11 units. Therefore, option C is the correct answer.

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Answer:

Option 2.

Step-by-step explanation:

It is given that Mike asked a random camper from each of the 12 cabins how many siblings he or she had.

The given data set is

3, 2, 0, 1, 0, 2, 3, 4, 1, 2, 2, 1

Sum of observations = 3+2+0+1+0+2+3+4+1+2+2+1=21

Number of observations = 12

Formula for mean:

[tex]Mean=\dfrac{\text{Sum of observations}}{\text{Number of observations}}[/tex]

[tex]Mean=\dfrac{21}{12}[/tex]

[tex]Mean=1.75[/tex]

Round the population to the nearest unit.

[tex]Mean=2[/tex]

We have to use Mike’s data to infer the mean of the population. So, the mean of sample is equal to the mean of population.

The mean number of siblings for the population is 2 siblings.

Therefore, the correct option is 2.

Answer:

the right answer is B

Step-by-step explanation:

Solution is in the attachment

Answer:  False

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

Answer:

Option c) Because the p-value is greater than the significance level, there is convincing evidence that the population mean number of ounces dispensed into a bottle is 12 ounces.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 12 ounces

Sample size, n = 50

Alpha, α = 0.05

First, we design the null and the alternate hypothesis

[tex]H_{0}: \mu = 12\\H_A: \mu < 12[/tex]

We use one-tailed  test to perform this hypothesis.

P-value = 0.08

Since the p value is greater than the significance level, we fail to reject the null hypothesis and accept it.

Thus, the machine is working properly and dispense 12 ounces of a beverage into a bottle.

Option c) Because the p-value is greater than the significance level, there is convincing evidence that the population mean number of ounces dispensed into a bottle is 12 ounces.

Since the p-value found is more than the level of significance, thus in such case, we can't reject the null hypothesis, and thus accept it.

Thus:

"Option C): c. Because the p-value is greater than the significance level, there is convincing evidence that the population mean number of ounces dispensed into a bottle is 12 ounces.

Given that:

Since the p-value found is more than the level of significance, thus in such case, we can't reject the null hypothesis, and thus accept it.

Null hypothesis is the favored hypothesis which we test. The test's result just tells whether the null hypothesis is acceptable or not. The alternative hypothesis is accepted when the null hypothesis is rejected, else we accept the null hypothesis.

Thus,  [tex]H_0 : \mu = 12 = \mu_0[/tex]   is accepted as  [tex]\text{p-value} = 0.08 > 0.05 = \alpha[/tex]   and we deduce that:

"Option C: Because the p-value is greater than the significance level, there is convincing evidence that the population mean number of ounces dispensed into a bottle is 12 ounces."

is correct option.

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Answer:

Step-by-step explanation:

∑⁴ₙ₌₁ -144 (½)ⁿ⁻¹

This is a finite geometric series with n = 4, a₁ = -144, and r = ½.

S = a₁ (1 − rⁿ) / (1 − r)

S = -144 (1 − (½)⁴) / (1 − ½)

S = -270

If you wanted to find the infinite sum (n = ∞):

S = a₁ / (1 − r)

S = -144 / (1 − ½)

S = -288

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Answer:

The answer is C (40)

Step-by-step explanation:

Step-by-step explanation:

Draw the triangle formed by the ray.

The hypotenuse of the triangle is:

c² = a² + b²

c² = (-5)² + (2√7)²

c² = 25 + 28

c = √53

Therefore:

cos β = -5 / √53

Or, as a proper fraction:

cos β = -5√53 / 53

The value of cos β is -5√53 / 53

Given that,

The hypotenuse of the triangle is:

[tex]c62 = a^2 + b^2\\\\c^2 = (-5)^2 + (2\sqrt7)^2\\\\c^2 = 25 + 28\\\\c = \sqrt53[/tex]

Therefore:

cos β = -5 / √53

Or, a proper fraction:

cos β =  -5√53 / 53

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Answer:

x=3

y=8

Step-by-step explanation:

y-x=5

2y-x=13

subtract

-y=-8

y=8

8-x=5

x=8-5=3

Answer:

3

Step-by-step explanation:

y-x=5 2y-x=13 subtract -y=-8 y=8 8*5 y=8-5=3

Answer: the number of people coming to the football game decreased by 13%

Step-by-step explanation:

2300 people came to the football game yesterday and the number of people decreased to 2001. This means that the amount by which the number of people that came for the football game in both days decreased would be

2300 - 2001 = 299

Therefore, the percentage decrease in the number of people coming to the football game would be

299/2300 × 100 = 13%

Answer:  34.57 inches.

Step-by-step explanation:

Given : Diameter of tree's trunk =  11 inches

Then, the length of ribbon needed just to reach around the tree = Circumference of trunk.

We know that the circumference of the circle is given by :-

[tex]C=\pi d[/tex] , where d= diameter

Then, Circumference of trunk. = [tex]\pi (11)[/tex]

Put [tex]\pi=\dfrac{22}{7}[/tex] , we get

Circumference of trunk. = [tex]\dfrac{22}{7}\times(11)\approx34.57\text{ inches}[/tex]

Hence , the length of ribbon needed just to reach around the tree = 34.57 inches.

Answer:

Incomplete question

Complete question: Jaclyn plays singles for South's varsity tennis team. During the match against North, Jaclyn won the sudden death tiebreaker point with a cross-court passing shot. The 57.5-gram ball hit her racket with a northward velocity of 26.7 m/s. Upon impact with her 331-gram racket, the ball rebounded in the exact opposite direction (and along the same general trajectory) with a speed of 29.5 m/s.

a. Determine the pre-collision momentum of the ball.

b. Determine the post-collision momentum of the ball.

c. Determine the momentum change of the ball.

Answer:

A. 1.5353kgm/s

B. 1.6963kgm/s

C. 0.161kgm/s

Step-by-step explanation:

A. The pre-collision momentum of the ball = mass of ball × velocity of ball

Mass of ball = 57.5g = 0.0575kg

Velocity of ball = 26.7m/s

Pre-collision momentum of ball = 0.0575×26.7

= 1.5353kgm/s

B. Post collision momentum of the ball = mass of ball × velocity of ball after impact

Velocity of ball after impact = 29.5m/s

Post collision momentum of ball after impact = 0.0575×29.5

= 1.6963kgm/s

C. Momentum change of ball = momentum after impact - momentum before imlact

= 1.6963kgm/s - 1.5353kgm/s

= 0.161kgm/s

Answer:

Step-by-step explanation:

1) the sum of the angles on a straight line is 180°.

Let x represent the measure of the smaller angle.

The measure of one angle is twice the measure of the other angle. This means that the larger angle is 2x. Therefore,

x + 2x = 180

3x = 180

x = 180/3 = 60

The measure of the smaller angle is 60°

The measure of the larger angle is 2 × 60 = 120°

2) The measure of one angle is 1/3 the measure of the other angle. If the measure of the larger angle is x, then the measure of the smaller angle is x/3. Therefore,

x + x/3 = 180

Multiplying through by 3, it becomes

3x + x = 180 × 3 = 540

4x = 540

x = 540/4 = 135

The smaller angle measures

135/3 = 45°

The larger angle measures 135°

3) the sum of complimentary angles is 180°

The measure of an angle is nine times the measure of its complement. If the measure of the smaller angle is x, then the measure of the larger angle is 9x. Therefore,

x + 9x = 90

10x = 90

x = 90/10 = 9

The smaller angle measures 9°

The larger angle measures 9 × 9 = 81°

4) The measure of an angle is 1/4 the measure of its complement.

If the measure of the larger angle is x, then the measure of the smaller angle is x/4. Therefore,

x/4 + x = 90

Multiplying through by 4, it becomes

x + 4x = 360

5x = 360

x = 360/5 = 72

The smaller angle measures 72/4 = 18°

The larger angle measures 72°

Answer:

Amount invested at 6% equals $35200; Amount invested at 10% equals $17600

Step-by-step explanation:

For simple interest; A = P (1 + rt), where;

A= final amount, P=principal , r = rate , t = time in years

Let the amount invested in the 6% yielding account be 'x' and the amount invested in the 10% yielding account be 'y'.

From the question, the man invests twice as much in the lower yielding, Therefore;

⇒ x = 2y

Interest = A - P = Prt

Total interest = (Interest for 6% yielding account) + (Interest for 6% yielding account)

⇒ 3872 = ( [tex]x[/tex] X 0.06 x 1) + ( [tex]y[/tex] X 0.10 x 1)

⇒ 3872 = (2[tex]y[/tex] x 0.06 x 1) + ([tex]y[/tex] x 0.10 x 1)

⇒ 3872 = 0.12[tex]y[/tex] + 0.10[tex]y[/tex]

⇒ y = $17600

⇒ x = 2y = $ 35200

Answer: Amount invested at 6% equals $35200

Amount invested at 10% equals $17600

Step-by-step explanation:

Let x represent the amount invested at 6%.

Let y represent the amount invested at 10%.

He puts twice as much in the lower-yielding account because it is less risky. This means that

x = 2y

The formula for determining simple interest is expressed as

I = PRT/100

Where

P represents the principal

R represents the rate of investment

T represents the time in years.

Considering the amount invested at 6%,

I = (x × 6 × 1)/100 = 0.06x

Considering the amount invested at 10%,

I = (y × 10 × 1)/100 = 0.1y

If his annual interest is $3872, it means that

0.06x + 0.1y = 3872 - - - - - - - - - - - -1

Substituting x = 2y into equation 1, it becomes

0.06 × 2y + 0.1y = 3872

0.12y + 0.1y = 3872

0.22y = 3872

y = 3872/0.22

y = 17600

x = 2y = 2 × 17600

x = 35200

Answer: Yes, made a mistake by taking out 2 in second step.

Step-by-step explanation:

You have started with 15 sticks= 13+2

So you take 2 which is correct.

Now, your friend takes one 13=12+1, so that leaves 12.

Now 12=8+3+1 since this involves smallest number 1 so you should have taken 1 at this point instead you took two here. So it leaves you with 10. Now, your friend takes one from it i.e. 10=9+1  leaving 9 now. Now 9=8+1, you can still take 1 from it and still be in the game. The point is to take out the smallest number involved. in the sum equal to the number that is left behind.

In Fibonacci nim, you cannot take the same number of sticks as your opponent did on the previous turn. Your next move should be to take 2 sticks, as your opponent took 1 on their last turn. You haven't yet made any mistakes in the game.

In the game of Fibonacci nim, the only rule is that on each turn a player can take one or two sticks, but not the same amount as their opponent took on the previous turn. Let's track your game:

For the next move, you can take either 1 or 2 sticks, but since your friend took 1 on their last turn, you must take 2 to abide by the rules. So, your next move should be to take 2 sticks.

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Answer:

96 books

Step-by-step explanation:

Given:

Dan reads 12 books over winter break.

Dan reads 8 times the number of books he read over winter break.

Question asked:

How many books did Dan read over summer break ?

Solution:

By doing multiplication:

Dan reads  number of books over winter break = 12

Dan reads  number of books over summer break = 8 times of winter break

                                                                                        [tex]= 8\times12\\\\= 96[/tex]

Therefore, 96 books is read by Dan over summer break.

Final answer:

Dan read 96 books over summer break by multiplying the 12 books he read during winter break by 8.

Explanation:

The question asks us to calculate how many books Dan reads over summer break given that he reads 8 times the number of books he read over winter break. To find the answer, we need to multiply the number of books Dan read in winter break by 8. Dan read 12 books during winter break, so for summer break, we will calculate:

12 books × 8 = 96 books

Therefore, Dan read 96 books over summer break.

The probability of selecting a red marble and then a green marble, without replacement, is 33/325.

The probability in this case is being calculated as the outcome of two independent events - selecting a red marble first and then selecting a green marble. The total number of marbles in the jar is the sum of green, red, and blue marbles which is 11+6+9 = 26.

First, let's calculate the probability of drawing a red marble. There are 6 red marbles out of a total 26 marbles, so the probability is 6/26 (which reduces to 3/13).

Next, the jar now has 25 marbles left, and 11 of them are green. So, our probability of drawing a green marble after a red one is 11/25.

For both events to happen one after the other, we multiply the individual probabilities together. Hence, the combined probability of these two events would be (3/13) * (11/25), which equals 33/325.

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The probability of first selecting a red marble and then a green marble from a jar containing 11 green, 6 red, and 9 blue marbles is 33/325.

The subject of this question is probability, which is a branch of mathematics. The problem involves calculating the probably of two events occurring in sequence: selecting a red marble and then a green one from a jar of colored marbles. In total there are 26 marbles: 11 green, 6 red, and 9 blue.

The probability of selecting a red marble first is 6/26 as there are 6 red marbles and 26 total marbles in the jar. Once you've chosen a red marble, it's removed from the jar. So for the second event, there are now 25 marbles in the jar, with 11 of them being green. So, the probability of selecting a green marble is 11/25.

The probability of both events (Choosing a red marble then a green one) happening one after the other is the product of the individual probabilities. So, the probability is (6/26) × (11/25) which simplifies to 33/325.

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Answer:

i) The data for elementary school are more consistent than those for

  middle school.

iii) About 50% of elementary school students watch between 4 and 7  

    hours of television each week.

v) On average, middle school students watch less television than

   elementary school students each week.

Step-by-step explanation:

The box plots show the number of hours of television a group of middle school students and a group of elementary school students watch each week.

The true statements when comparing the data in the box plots

i) The data for elementary school are more consistent than those for

  middle school.

ii) More of the data for middle school lie closer to the median than the data

   for elementary school.

iii) About 50% of elementary school students watch between 4 and 7  

    hours of television each week.

iv) About one-half of middle school students watch less than 2 hours of

   television each week.

v) On average, middle school students watch less television than

   elementary school students each week.

Answer:

It's 1, 3, 5 Yw

Step-by-step explanation:

I am doing the test and that's what I got

Answer:

Day Weather Temperature Humidity Wind Play?

1 Sunny Hot High Weak No

2 Cloudy Hot High Weak Yes

3 Sunny Mild Normal Strong Yes

4 Cloudy Mild High Strong Yes

5 Rainy Mild High Strong No

6 Rainy Cool Normal Strong No

7 Rainy Mild High Weak Yes

8 Sunny Hot High Strong No

9 Cloudy Hot Normal Weak Yes

10 Rainy Mild High Strong No

Step-by-step explanation:

Answer: 5040ways

Step-by-step explanation:

This is a circular permutation question. Arrangement of objects in a circular path is (n-1)! where n is the amount of object. Since there are 8 students sitting in a circle excluding their teacher, they can sit in (8-1)! ways i.e 7! ways

7! = 7×6×5×4×3×2×1

7! = 5040ways

This means the students can sit in a circle in 5,040 ways

Final answer:

To find out the number of ways 8 students can sit in a circle, we calculate 7! (7 factorial), as the formula for arrangements in a circle is (n-1)!, resulting in 5040 ways.

Explanation:

The question involves determining the number of ways 8 students can sit in a circle. When arranging n distinct objects in a circle, the number of arrangements is given by (n-1)! .

since one position is fixed to account for the circular arrangement's rotational symmetry. In this case, with 8 students, the calculation is as follows: 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040 ways.

Therefore, the students can sit in a circle in 5040 different ways.

Answer:

The recycle percent as a rate per 100 is 0.03 per hour.

And 12 dolls are recycled each hour during production.

Step-by-step explanation:

The question is incomplete so below is the complete question:

A factory produces toy dolls at a rate of 400 per hour and has to recycle 3% of them because the clothes are torn. Express the recycle percent as a rate per 100. How many dolls are recycled each hour during production?

Now, to express the recycle percent as a rate per 100, And to find the number of dolls are recycled each hour during production.

Number of dolls factory produces at rate per hour = 400.

Percent of recycle = 3%.

So, to express the recycle percent as a rate per 100:

[tex]3\%\ per\ 100[/tex]

[tex]=\frac{3}{100} \ per\ hour[/tex]

[tex]=0.03\ per\ hour.[/tex]

So, to get the number of dolls are recycled each hour during production:

3% of number of dolls factory produces at rate per hour.

[tex]=\frac{3}{100} \times 400[/tex]

[tex]=0.03\times 400[/tex]

[tex]=12.[/tex]

The dolls are recycled each hour = 12.

Therefore, the recycle percent as a rate per 100 is 0.03 per hour.

And 12 dolls are recycled each hour during production.

Answer:

each child would get 3 pieces of candy

Step-by-step explanation:

hope this helps ;)

Answer:

X>-9

X is greater than -9

Step-by-step explanation:

4(X-3)+4<10+6X

By clearing up the bracket :

4X-12+4<10+6X

Collecting like terms:

4X-6X<10+12-4

-2X<18

Dividing both sides by -2:

-2X/-2>18/-2

Therefore, X>-9

The mission step is in combining like terms which is 4X-8<10+6X instead of 4X-6X<10+8.

The missing step in solving the given inequality 4(x – 3) + 4 < 10 + 6x is; x > -9

We are given the inequality as:

4(x – 3) + 4 < 10 + 6x

The steps are given as:

The next step in solving the inequality is to apply the division property of inequality by dividing both sides by -2.

This gives; x > -9

Thus, the missing step in the inequality is x > -9

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Some parts are missing in the queston. Find attached the picture with the complete question

Answer:

                   [tex]\large\boxed{\large\boxed{161}}[/tex]

Explanation:

Let's put the information in a table step-by step.

                                                (number of remaining students)

                                                        Juniors          Seniors

Condition

At the end, there were 8 more seniors than juniors:

Now you have obtained one equation, which you can solve to find S, the number of senior students, and then the number of junior students.

Solve the equation:

[tex]2/3\times (S - 15) - 1/4\times 2(S - 15) = 8[/tex]

[tex]8(S - 15)-6(S - 15)=96[/tex]

[tex]8S-120-6S-90=96[/tex]

[tex]8S-6S=96+120+90[/tex]

[tex]2S=306[/tex]

[tex]S=306/2=153[/tex]

That is the number of senior students that came out to the information meeting, but the number of students remaining to perform in the school musical is (from the table above):

[tex]2/3\times (S-15)+1/4\times 2(S-15)[/tex]

Just substitute S with 153 fo find the number of students that remained to perfom in the musical:

          [tex]2/3\times (153-15)+1/4\times 2(153-15)\\ \\ 2/3(138)+1/2(138)[/tex]

          [tex]161[/tex]

Triangle ABC is similar to triangle CEF.

Explanation:

Diagram is inserted for the reference.

ABCD is a rectangle.

ABC is a right angled triangle because all the angles of the rectangle are 90◦ - (a)

CEF is a right angled triangle because FE is perpendicular to DC – (b)

In triangles ABC and CEF,

1. Angle ABC = Angle CEF = 90◦ (Both are right angles from a and b)

2. Angle BCA = Angle EFC (Alternate angles on parallel lines are equal on intersection)

Hence using Similarity property of AA (Angle, Angle), Triangle ABC and CEF are similar.

ΔABC and ΔCEF are similar triangles by the AA similarity theorem.

The angle-angle similarity theorem (AA) states that when two triangles have two pairs of corresponding congruent angles, both triangles are similar triangles.

In ΔABC and ΔCEF, we have the following:

Two pairs of corresponding congruent angles - ∠FEC ≅ ∠ABC (right angles) and ∠FCE ≅ ∠BAC

Therefore, ΔABC and ΔCEF are similar triangles by the AA similarity theorem.

Learn more about the AA similarity theorem on:

https://brainly.com/question/2166570