A geometry student says; "I got lost in that lesson - I wrote down that AD/AB = AC/AB but I have no idea
where it comes from."
Which of the following should have been the proportion that the student wrote?
answer choices:
a) AD/AB=AB/AC
b) AD/AC=AB/AB
c) AB/AD=AB/AC
d) AB/AC=AB/AD

The similarity ratio of the two octagons, given their areas, is 2:1. This is determined by taking the square root of the ratio of their areas.

The question is about finding the similarity ratio of two similar octagons with given areas. The area of a shape increases by the square of the scale factor (similarity ratio). Hence, in this case, where the larger octagon has four times the area of the smaller, the scale factor (similarity ratio) is the square root of 4, which is 2. So, the similarity ratio of the two octagons is 2:1.

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Answer:

1 and 12

Step-by-step explanation:

each # is mult by 2

Answer:

y=x+4

Step-by-step explanation:

x-y=-5

y=x-(-5)

y=x+5

-----------

y-y1=m(x-x1)

y-1=1(x-(-3))

y-1=x+3

y=x+3+1

y=x+4

Answer:

28 - 7x =< 28x + 28

28 - 35x =< 28

-35x =< 0

x >= 0

the answer is the fourth one

x is greater than or equal to 0

Answer:13hrs

Step-by-step explanation:

Initial Temperature = 21°c

final temperature = -18°c

rate of decrease = 3°c/hr

for every hour the temperature decreases by 3°c.

What time does it take to get to 0c  = . 21(°c) / 3(°c/hr)  = . 7hr

what time does it take to get to -18c  = 18(°c) / 3(°c/hr)   = . 6hr

Total Time taken  = . 7hr + 6hr = 13hr

Alternative solution

Initial Temperature = 21°c

final temperature = -18°c

rate of decrease = 3°c/hr

(21 + 18)°c/ 3(°c/hr) . = . 13hr

To cool a freezer from 21℃ to -18℃ at a rate of 3℃ per hour, it would take 13 hours for the freezer to reach -18℃.

The question asks how long it will take for a freezer to cool down from 21℃ to -18℃ if the temperature decreases at a rate of 3℃ per hour. To find the time it takes, you'll need to calculate the total temperature change required and then divide by the rate of temperature change.

First, calculate the total temperature difference:

21℃ (starting temperature) - (-18℃ target temperature) = 39℃ total temperature change.

Next, divide the total temperature change by the rate of temperature change:

39℃ total change / 3℃ per hour = 13 hours required

for the freezer to cool from 21℃ to -18℃.

Answer:

y=-2x+6

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-8-0)/(7-3)

m=-8/4

m=-2

y-0=-2(x-3)

y=-2(x-3)+0

y=-2(x-3)

y=-2x+6

Answer:

y-6=1/2(x-4)

Step-by-step explanation:

y-y1=m(x-x1)

y-6=1/2(x-4)

Answer:

adjacent angles

complementary angles

Step-by-step explanation:

we know that

If two angles are complementary, then their sum is equal to 90 degrees

we have that

[tex]m\angle 1+m\angle 2=90^o[/tex] ---> given problem

therefore

∠ 1 and ∠ 2 are complementary angles

Remember that

Two angles are Adjacent when they have a common side and a common vertex

In this problem

∠ 1 and ∠ 2 have a common side and a common vertex

so

∠ 1 and ∠ 2 are adjacent angles

874.18

Step-by-step explanation:if you multiply 800 by1.03 it will increase by 3% then repeat step two more times

Answer:

The term 'numerical' means 'involving numbers' and the term 'expression' means 'phrase'. A numerical expression is a mathematical phrase involving only numbers and one or more operational symbols.

Answer:

The term 'numerical' means 'involving numbers' and the term 'expression' means 'phrase'.  In other words, it is just a phrase/ equation with numbers not letters.

Example 2+4=6

NOT 3a+4a=7a

Happy Holidays!

Final answer:

The photo takes up 3/16 of the magazine page.

Explanation:

To find out how much of the page is taken up by the photo, we need to calculate the proportion of the page that the photo occupies. Given that the article fills 1/2 of the page and the photo takes up 3/8 of the article, we can find the fraction of the page the photo takes by multiplying these two fractions together:

Proportion of page taken by photo = (1/2) × (3/8) = 3/16

So, the photo takes up 3/16 of the magazine page.

Answer:

The answer is larger than 3 unless d = 0

Step-by-step explanation:

Well, it says increased, which means add/multiply

However, we don't know what d equals, so it is impossible to find the answer.

Answer: The information you are given shows that 15% = 30. Multiply 30 by 6 and 2/3 (The number of times 15 goes into 100) and you have your answer. There are 200 people on the beach.

Final answer:

To find the total number of people at the beach when 15% do not wear sunscreen and 30 people represent that 15%, we divide 30 by 0.15 to get 200, meaning there are 200 people on the beach.

Explanation:

The student asked: "If 15% of people on the beach do not wear sunscreen, and 30 people don't wear sunscreen, what is the total number of people at the beach?" To find the total number of people at the beach, we need to calculate it based on the percentage of people who do not wear sunscreen.

Therefore, the total number of people at the beach is 200.

Answer:A

Step-by-step explanation:

no need for this you only look at the answers

The total number of questions on the practice test is at least 66.

Since the number of geography questions is 65, and geography was one of the topics on the practice test, the total number of questions on the practice test must be greater than 65.

One option is that there were 66 questions on the practice test, with the remaining question being on a different topic.

Another option is that there were more than 66 questions on the practice test, with geography being one of multiple topics.

Therefore, the total number of questions on the practice test is at least 66.

for such more question on total number

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Answer:

Step-by-step explanation:

a + b = 140.......a = 140 - b

5.75a + 4.10b = 677.95

sub in 140 - b in for a in the other equation....and solve for b, the number of lbs of type B coffee

5.75(140 - b) + 4.10b = 677.95

805 - 5.75b + 4.10b = 677.95

-5.75b + 4.10b = 677.95 - 805

- 1.65b = - 127.05

b = -127.05 / -1.65

b = 77 <======= lbs of type B coffee used

a + b = 140

a + 77 = 140

a = 140 - 77

a = 63.........lbs of type A coffee used

check..

5.75a + 4.10b = 677.95

5.75(63) + 4.10(77) = 677.95

362.25 + 315.70 = 677.95

677.95 = 677.95 (correct)

I found both just so I could check my answer....and it checked out....

The number of pounds of coffee Type A and Type B will be 63 and 77, respectively.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Martina's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Martina $5.75 per pound, and type B coffee costs $4.10 per pound. This month, Martina made 140 pounds of the blend, for a total cost of $677.95.

Let 'x' and 'y' be the number of pounds of coffee Type A and Type B. Then the equations are given as,

x + y = 140                               ....1

5.75x + 4.10y = 677.95          ....2

From equations 1 and 2, then we have

5.75x + 4.10(140 - x) = 677.95

5.75x + 574 - 4.10x = 677.95

1.65x = 103.95

x = 63

Then the value of 'y' is given as,

63 + y = 140

y = 77

The number of pounds of coffee Type A and Type B will be 63 and 77, respectively.

More about the solution of the equation link is given below.

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Answer:

Area of trapezium = 4.4132 R²

Step-by-step explanation:

Given, MNPK is a trapezoid

MN = PK and ∠NMK = 65°

OT = R.

⇒ ∠PKM = 65° and also ∠MNP = ∠KPN = x (say).

Now, sum of interior angles in a quadrilateral of 4 sides = 360°.

⇒ x + x + 65° + 65° = 360°

⇒ x = 115°.

Here, NS is a tangent to the circle and ∠NSO = 90°

consider triangle NOS;

line joining O and N bisects the angle ∠MNP

⇒ ∠ONS = [tex]\frac{115}{2}[/tex] = 57.5°

Now, tan(57.5°) = [tex]\frac{OS}{SN}[/tex]

⇒ 1.5697 = [tex]\frac{R}{SN}[/tex]

⇒ SN = 0.637 R

⇒ NP = 2×SN = 2× 0.637 R = 1.274 R

Now, draw a line parallel to ST from N to line MK

let the intersection point be Q.

⇒ NQ = 2R

Consider triangle NQM,

tan(∠NMQ) = [tex]\frac{NQ}{QM}[/tex]

⇒ tan65° = [tex]\frac{NQ}{QM}[/tex]

⇒ QM = [tex]\frac{2R}{2.1445}[/tex]

QM = 0.9326 R .

⇒ MT = MQ + QT

          = 0.9326 R + 0.637 R  (as QT = SN)

⇒ MT = 1.5696 R

⇒ MK = 2×MT = 2×1.5696 R = 3.1392 R

Now, area of trapezium is (sum of parallel sides/ 2)×(distance between them).

⇒ A = ([tex]\frac{NP + MK}{2}[/tex]) × (ST)

       = ([tex]\frac{1.274 R + 3.1392 R}{2}[/tex]) × 2 R

       = 4.4132 R²

⇒ Area of trapezium = 4.4132 R²

Answer: 3( 5m - 1 )

Step-by-step explanation:

The expression given is ; 15m - 3

This could be factorized , the common factor is 3 , so we have

3( 5m - 1 )

Answer:

130 is close to 128, so 128 is a reasonable answer.

Step-by-step explanation:

Consider the provided information.

We need to Use the estimation to check weather 128 is a reasonable answer in the example above:

p=200-72

Round to the nearest ten:             p = 200 - 70

Subtract the rounded numbers:   200-70=130

130 is close to 128, so 128 is a reasonable answer.

Answer: C

Step-by-step explanation:

Im going to put this answer in simple terms because I don't want to confuse you too much with a big explanation on a question that doesn't need one.

Anyway, the answer to the equation is C, stating that |A| > 0. If you were wondering, the two lines on either side of the a are absolute value bars. To put it in simple terms, when you put a negative number in between absolute bars, the number because positive. However, when you put a positive number in between, the number stays the same. SO...

The value of A on the number is 4. SO...

Substitute: |-4| > 0

Solve: 4 > 0

Because it is true that 4 is greater that 0, the answer is C.

Hope this helps!

Answer:

D. [tex]\frac{-9}{2} \leqx <\frac{27}{2}[/tex]

Explanation:

Before proceeding, please remember the following:

1. When you do a certain operation on one side of the inequality, you have to do the same operation on ALL other sides to keep the original value of the inequality unchanged

2. To solve an inequality means that we want to isolate the variable.

Now, for the given inequality, we have:

[tex]-3 \leq\frac{2x-3}{4} <6[/tex]

Based on the above, for the middle part of the inequality, we want to have the x variable standing alone.

This can be done as follows:

1. Multiply all sides by 4

This would give us: [tex]-12 \leq 2x-3 < 24[/tex]

2- Add 3 to all sides

This would give us: [tex]-9 \leq2x < 27[/tex]

3- Finally, divide all sides by 2 to have the x on its own

This would give us: [tex]\frac{-9}{2} \leq x < \frac{27}{2}[/tex]

Hope this helps :)

Answer:

solve using long division.

75/4

what is the largest whole number smaller than 75 that 4 can go into?

72.

how many times can 4 go into 72?

18.

so then subtract 72 from 75 to get 3.

the new equation is

3/4

how many times can 3 go into 4?

0.75 times.

so add the 2 answers to get

18.75

4 can go into 75 18.75 times.

To determine how many times 4 can go into 75, you divide 75 by 4. The result is 18 with a remainder of 3. Thus, 4 can go into 75 a total of 18 full times.

To find out how many times 4 can go into 75, we need to perform a division. Specifically, we need to divide 75 by 4.

This means that 4 goes into 75 exactly 18 times with a remainder of 3. So, 4 fully fits into 75 for 18 full times.

-Answer: -3

Step-by-step explanation:

Answer:

a=-75

Step-by-step explanation:

-15=a/5

a=5*-15

a=-75

Answer:

2a+7

Step-by-step explanation:

The conclusion that 40% of the students have visited a science museum based on a sample of 50 may not be accurate because the Sample Size may be too small and unrepresentative of the school population. Other factors like Response Rate and random sampling are essential for validity, and a Hypothesis Test could provide more solid evidence.

The conclusion that 40% of the students in the school have visited a science museum based on a survey of 50 students is not fully valid without considering additional factors. When conducting a survey, the concept of Sample Size is crucial. A sample size of 30 is the minimum required to start establishing statistical confidence, but larger samples are generally better to reduce sampling error. In this case, sampling only 50 students might not be representative of the entire student body, depending on the school's population. Moreover, the Response Rate and the randomness of the sample are essential in determining the validity of survey results. The survey must have a relatively high response rate and the sample must be chosen randomly from the entire population to avoid bias. This helps in better reflecting the overall characteristics of the population.

Conducting a Hypothesis Test would also help validate the findings. This statistical tool helps determine whether the observed proportion significantly deviates from the expected proportion (if known) or not. Furthermore, one important aspect is to avoid making statistics imply something they do not, which is common in cases where the sample size is small or the sample is unrepresentative. Lastly, discrepancies in survey results, like those seen in vaccination rates from two different researchers, can occur even when the right procedures are followed due to inherent variability in sampling.

Answer:

1

Step-by-step explanation:

4/4=1

5-1-3=4-3=1

Answer:

$25.24

Step-by-step explanation:

If Tim earns $45.19 each month multiply by 3 which gives you $135.57 take $211.29 subtract $135.57, you get $75.72 which is the total amount that Tom needs to give. Divide that by 3 and get $25.64 which is the amount Tom needs in 3 months.

$45.19 x 3 = $135.57

$211.29 - $135.57 = $75.72

$75.72/3 = $25.24

Answer:

30

Step-by-step explanation:

2m+180=8m

180=8m-2m

180=6m

m=180/6

m=30

Because the two lines are not parallel, we conclude that the system will have a solution.

Remember that the solution of a system of equations is the point where the graphs of the functions intersect.

In this case we have two linear functions:

f = 2m + 180

f = 8m

Notice that the slopes are different, this means that the lines are not parallel, and because of that, we know that the lines will intersect at some point. That is enough to know that the system has a solution.

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Answer:

You generally have to start taking withdrawals from your IRA, SEP IRA, SIMPLE IRA, or retirement plan account when you reach age 70½. Roth IRAs do not require withdrawals until after the death of the owner. You can withdraw more than the minimum required amount.

Step-by-step explanation:

Roth IRAs do not have mandatory withdrawals, making them more flexible for retirees.

No, Roth IRAs do not have mandatory withdrawals during the lifetime of the original account holder. Traditional IRAs, on the other hand, have required minimum distributions (RMDs) starting at age 72, which means the account holder must start withdrawing a certain amount each year.

However, Roth IRAs do not have RMDs for the original account holder. This flexibility allows account holders to continue growing their investments tax-free for as long as they wish, making Roth IRAs advantageous for retirement planning and estate planning.

Therefore, No, Roth IRAs do not have mandatory withdrawals.