A circle has a mass of 3 grams and a square has a mass of 2 grams. Which is the mass of a triangle?

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!

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

Step-by-step explanation:

Answer:

a=-75

Step-by-step explanation:

-15=a/5

a=5*-15

a=-75

Answer: [tex]\frac{25}{6} a^{9} b^{10}[/tex]

Step-by-step explanation:

Assuming the described expression is:

[tex]\frac{(5ab)^{3}}{30 a^{-6} b^{-7}}[/tex]

And knowing the condition [tex]a \neq 0[/tex] and [tex]b \neq 0[/tex]

We cansimplify it following the rules related to the exponents with the same base:

[tex]\frac{25}{6} a^{3} b^{3} a^{6} b^{7}[/tex]

Finally:

[tex]\frac{25}{6} a^{9} b^{10}[/tex]

Answer:

Answer: \frac{25}{6} a^{9} b^{10}

Step-by-step explanation:

100% on ed

Answer:

Step-by-step explanation:

(b - 4)(3b - 1) is the factored form of some second degree polynomial.  Once you factor to this point, you can solve for the values of b using the Zero Product Property, which says that one of the those factors has to equal 0 for the product to equal 0 (cuz any number times 0 is equal to 0).  The first expression is b - 4.  If we set b - 4 equal to 0, we can solve for b:

b - 4 = 0 so

b = 4

Likewise with the second factor, 3b - 1.  Set it equal to 0 and solve for b:

3b - 1 = 0 and

3b = 1 so

b = 1/3

To solve the equation (B-4)(3b-1)=0 using the zero product property, set each factor equal to zero and solve for the variable. The solutions are B = 4 and b = 1/3.

To solve the equation (B-4)(3b-1)=0 using the zero product property, we set each factor equal to zero and solve for the variable:

First factor: B-4 = 0

Second factor: 3b-1 = 0

Solving each equation separately:

So the solutions to the equation (B-4)(3b-1)=0 are B = 4 and b = 1/3.

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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:

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:

2a+7

Step-by-step explanation:

Answer:

n=0.64

Step-by-step explanation:

-5/8n=-0.4

n=-0.4/(-5/8)

n=-0.4(-8/5)

n=3.2/5

n=0.64

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:

Option 4. x = 0

Step-by-step explanation:

we know that

The rule of the reflection of a point across the y-axis is equal to

(x,y) -----> (-x,y)

The rule for reflecting over the Y axis is to negate the value of the x-coordinate of each point, but leave the y-value the same

The coordinates of triangle PQR are

P(1, 4), Q(3, 6), and R(5, 2)

Applying the rule of the reflection across the y-axis we have

P(1, 4) -----> P'(-1, 4)

Q(3, 6) ----> Q'(-3, 6)

R(5, 2)----> R'(-5, 2)

The reflection line is the y-axis

Remember that the equation of the y-axis is x=0

therefore

The equation of the reflection line is x=0

Answer: The correct answer is (x = 0)

Step-by-step explanation: Took the assignment.

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 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:

FALSE

Step-by-step explanation:

78 thousands = 78 x 1000 = 78,000

Answer:false

Step-by-step explanation:

78,000 is 78 thousands

7,800 is only 7 thousand and 8 hundred

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: 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 )

Explanation:

All proportional relationships have a common ratio. In a set of data, if the ratio between terms are not the same, the relationship is non-proportional. The common ratio is found by dividing a term value by the previous term value. On a graph, proportional relationships form a straight line and non-proportional relationships do not.

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

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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Question:

The park district is paying to enlarge the area of a square-shaped dock at a local lake. The area of the dock will increase by 16 square feet. Complete the equation below that can be used to find the area, x, of the original dock if the side length of the new dock is 20 feet.

So, the square root of what (?) equals(=) 20

Answer:

The complete equation is square root of(x + 16) = 20

Solution:

Given that Dock has a shape of square

[tex]\text{ area of square }= (side)^2[/tex]

From question, it is given that side length of new dock is 20 feet

Therefore, area of new dock is given as:

[tex]\text{ area of new dock}= (20)^2[/tex]

Taking square root on both sides,

square root of (new area ) = 20  --- eqn 1

Let "x" be the area of original dock

The area of the dock will increase by 16 square feet

New area = original area + 16

New area = x + 16 ---- eqn 2

From eqn 1,

square root of (new area ) = 20

From eqn 2

square root of(x + 16) = 20

Thus the complete equation is: square root of(x + 16) = 20

Final answer:

To find the area of the original dock, the equation x + 16 = 20^2 can be used, where x is the original area. By solving the equation, we find that x equals 384 square feet.

Explanation:

The area of the original square-shaped dock can be found using the equation for the area of a square, with the area being equal to the side length squared. Given that the new square dock has a side length of 20 feet, and the area is increased by 16 square feet, we can set up an equation to find the original area, x.

The equation is x + 16 = 20^2, where 20^2 is the area of the new, larger dock, and x is the original area of the dock before the enlargement. Therefore, the side length of the original dock is the square root of x. To find x, we can solve the equation:

x + 16 = 400
x = 400 - 16
x = 384

So the area of the original dock is 384 square feet.

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.

Answer:

The correct option is (a).

Step-by-step explanation:

See the diagram attached.

Whatever be the translation done on a figure the dimensions of the figure will remain unchanged and only the coordinates of the vertices will change according to the rule of translation.

Therefore, if a rectangle FGHJ is translated by 6 units right and one unit up to produce a rectangle F'G'H'J', then the length F'G' = FG = 3 units and G'H' = GH = 5 units.  

So, the correct option is (a). (Answer)

Rectangle F'G'H'J' will have sides, F'G' = J'H' = 3 units, and, F'J'=G'H'=6 units.

Given to us,

Rectangle FGHJ, with sides, FG = JH = 3 units, and, FJ=GH=6 units.

Now, as given to us, Rectangle FGHJ has translated 6 units up to produce rectangle F’G’H’J', but even if the rectangle is translated it will still be a rectangle making no changes in its sides.

Therefore, Rectangle F'G'H'J' will have sides, F'G' = J'H' = 3 units, and, F'J'=G'H'=6 units.

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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

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.

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Answer:

1 and 12

Step-by-step explanation:

each # is mult by 2

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.

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Answer:

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

Step-by-step explanation:

y-y1=m(x-x1)

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

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