what is the common factor to 42 and 70

Answer:

0.05, 0.5, 0.507, 0.57, 0.577

Step-by-step explanation:

Answer:

3.9

Step-by-step explanation:

tan = opposite side/adjacent side

tan 61 = 7.1/QR

QR tan 61 = 7.1

QR = 7.1/tan 61

     = 3.9

Note:  If you memorize the definitions of all the trig functions, then these kinds of problems will be much easier.  OK?

Subtracting 3 hours 3 seconds and 1 hour 15 minutes 55 seconds is 1 hour 44 minutes 8 seconds.

The following are important to solve the questions:

1 minute = 60 seconds

1 hour = 3600 minutes

Therefore 3 hours 3 seconds will be:

= (3 × 3600) + 3

= 10800 + 3

= 10803 seconds.

1 hour 15 minutes 55 seconds will be:

= 3600 + (15 × 60) + 55

= 3600 + 900 + 55

= 4555 seconds.

The difference will be:

= 10803 - 4555

= 6248 seconds

= 1 hour 44 minutes 8 seconds.

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The given mathematical expression is evaluated for the input values (2, 4). The result of the expression is calculated using various operations such as addition, multiplication, square root, natural logarithm, minimum, maximum, and function composition.

The expression f(x1, x2) involves several mathematical operations. Let's evaluate each part of the expression step by step:

1. The first term is 421 + 222, which equals 643.

2. The second term is 3x² + 213. Plugging in x1 = 2 and x2 = 4, we get 3(2)² + 213 = 3(4) + 213 = 12 + 213 = 225.

3. The third term is 5x11². Substituting x1 = 2 and x2 = 4, we have 5(2)(11)² = 5(2)(121) = 1210.

4. The fourth term is (√₁+√₂)². Replacing x1 = 2 and x2 = 4, we obtain (√2 + √4)² = (1 + 2)² = 3² = 9.

5. The fifth term is 10ln(₁). Plugging in x1 = 2, we have 10ln(2) = 10 * 0.69314718 ≈ 6.9314718.

6. The sixth term is (x₁+x₂)(x² + x3). Substituting x1 = 2 and x2 = 4, we get (2 + 4)(2² + 4³) = 6(4 + 64) = 6(68) = 408.

7. The seventh term is min(3r1, 10√2). As we don't have the value of r1, we cannot determine the minimum between 3r1 and 10√2.

8. The eighth term is max{5x1,2r2}. Since we don't know the value of r2, we cannot find the maximum between 5x1 and 2r2.

9. Finally, we have MP1(x1, x2), MP2(X1, X2), and TRS(x1, x2), which are not defined or given.

Considering the given expression, the evaluated terms for the input values (2, 4) are as follows:

- 421 + 222 = 643

- 3x² + 213 = 225

- 5x11² = 1210

- (√₁+√₂)² = 9

- 10ln(₁) ≈ 6.9314718

- (x₁+x₂)(x² + x3) = 408

The terms involving min() and max() cannot be calculated without knowing the values of r1 and r2, respectively. Additionally, MP1(x1, x2), MP2(X1, X2), and TRS(x1, x2) are not defined.

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Answer:

The two expressions are;

1) -8 ft. + 3 × 6 ft. = 12 feet

2) -6 ft. + 2 × 5 ft. + 8 ft. = 12 feet

Step-by-step explanation:

The given parameters are;

The lengths in feet Cecil can travel = 5 feet, 6 feet, and 8 feet

The distances Cecil can travel forward = (positive 5, 6, 8)

Backwards Cecil can travel distances of (-5, -6, -8)

Cecil can go forward past the ladder and return back

Therefore, the number expressions by which Cecil can cross a tightrope 12 feet long are;

1) -8 ft. + 3 × 6 ft. = 12 feet

Which is to go back 8 feet and then to go forward 6 feet three times

2) -6 ft. + 2 × 5 ft. + 8 ft. = 12 feet

Which is to go back 6 feet then to go forward in 5 feet two times and then in forward again in 8 feet.

Answer:

30 geckos

fraction: \(\frac{3}{8}\)

Step-by-step explanation:

Let the numbers of geckos be x, the numbers of anole lizards be y

\(x:y=3:5\)

⇒ \(5x=3y \left \{ {{a:b=cd}\) → \(ad=bc\)

\(x+y=80\)

\(3x+3y=80\times3\)

\(3x+3y=240\)

\(3x+5x=240\)

\(8x=240\)

\(\frac{8x}{8}=\frac{240}{8}\)

\(x=30\)

\(\frac{30}{80}=\frac{3}{8}\)

I hope this helps you

:)

The limit definition of a derivative is a mathematical method used to calculate the instant rate of change of a characteristic at a particular point. it is based at the idea of the limit of a function because the input techniques a certain cost.

The limit definition of a derivative is expressed as follows:

\(f'(x) = lim (h → 0) [f(x + h) - f(x)] /h\)

Wherein f'(x) represents the derivative of the function f(x) at a particular factor x. The expression \(( f(x + h) - f(x)) / h\) represents the common price of alternate of the characteristic over a small interval of size h, focused at x. The limit of this expression as h approaches 0 represents the instant fee of change of the characteristic at x, or the slope of the tangent line to the function at that factor.

The limit definition of a derivative is a fundamental concept in calculus and is used to calculate the slopes of tangent lines, to find maximum and minimum factors, and to clear up optimization issues in a huge variety of packages.

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\(625=5^{7x-3}\implies 5^4=5^{7x-3}\implies 4=7x-3 \\\\\\ 7=7x\implies \cfrac{7}{7}=x\implies 1=x\)

12=7/2(5x+2)

We move all terms to the left:

12-(7/2(5x+2))=0

Domain of the equation: 2(5x+2))!=0

x∈R

We multiply all the terms by the denominator

-(7+12*2(5x+2))=0

We calculate terms in parentheses: -(7+12*2(5x+2)), so:

7+12*2(5x+2)

determiningTheFunctionDomain

12*2(5x+2)+7

Wy multiply elements

24x(5+7

Back to the equation:

-(24x(5+7)

Answer:

x = 2/7

Step-by-step explanation:

Let's solve your equation step-by-step.

12= 7/2

(5x+2)

Step 1: Simplify both sides of the equation.

12= 7/2

(5x+2)

12=(7/2)(5x)+(7/2)(2)(Distribute)

12= 35/2

x+7

Step 2: Flip the equation.

35/2

x+7=12

Step 3: Subtract 7 from both sides.

35/2

x+7−7=12−7

35/2

x=5

Step 4: Multiply both sides by 2/35.

(2/35)*(35/2x) = (2/35)*(5)

x = 2/7

Answer:

\( \sqrt{40 {x}^{8} {y}^{5} } \)

\( \sqrt{40} \sqrt{ {x}^{8} } \sqrt{ {y}^{5} } \)

\((2 \sqrt{10} )( {x}^{4} )( {y}^{2} \sqrt{y} )\)

\(2 {x}^{4} {y}^{2} \sqrt{10y} \)

Answer:

C

Step-by-step explanation: looks right

dont  trust it though

Answer:

shown below

Explanation:

so first you can graph a dot at (2,-1), since it must go through that line. Then you can use the slope, 3, to figure out the next dot. The slope 3 can be put into a fraction, liking like 3/1. Then you use rise/run from your point (2,-1). You go up 3, and right 1. Using that, your next point is (3,2). Plot that dot, and then use a straight edge to draw your line. It looks like how it is in the picture.

To solve the equation 2n^2 / ln(x) - 31 = ln(36), we can follow these steps: Start by adding 31 to both sides of the equation to isolate the term with the natural logarithm: 2n^2 / ln(x) = ln(36) + 31.

Multiply both sides of the equation by ln(x) to get rid of the denominator:

2n^2 = ln(x) * (ln(36) + 31).

Divide both sides of the equation by 2 to isolate n^2:

n^2 = (ln(x) * (ln(36) + 31)) / 2.

Take the square root of both sides of the equation to solve for n:

n = ±√[(ln(x) * (ln(36) + 31)) / 2].

So, the solution for n is ±√[(ln(x) * (ln(36) + 31)) / 2].

Please note that the solution may be valid only for certain values of x that satisfy the given equation.

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Answer:

-3/2

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

D. The y-coordinates of the new trapezoid is not the same as the y-coordinates of the original trapezoid.

In Mathematics, a polygon can be defined as a two-dimensional geometric figure that consists of straight line segments and a finite number of sides. Additionally, some examples of a polygon include the following:

When a trapezoid is translated 8 units down, all of its points will move down 8 units, which means the y-coordinates of each point will decrease by 8.

Therefore, the y-coordinates of the new trapezoid will be different from the y-coordinates of the original trapezoid.

However, A, B, and C are all true statements.

The new trapezoid will have the same orientation (the same angles between its sides), the same shape (the same ratio of the lengths of its sides), and the same size (the same area).

The only difference is that the new trapezoid will be shifted down by 8 units.

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Answer:

0.78 euros per dollar

Step-by-step explanation:

If 35 euros=$45.00, then every dollar that he has is equivalent to (35/45) euros=35/45=0.78 euros per dollar

(I found the answer from Nonicorp1 on Brainly)

Answer:

47

Step-by-step explanation:

Hey There!

So remember all of the angles in a triangle will add up to equal 180

So to find the missing angle we subtract the given angles (65 and 68) from 180

180-65-68-47

so we can conclude that the measure of the missing angle is 47

Answer:

At this rate, it would take less than 10 minutes for the temperature of the liquid to rise 52°.

Step-by-step explanation:

The temperature increase is represented by a linear line, which means that the temperature of the liquid is increasing at a constant rate.

Since the liquid took 6.5 minutes to increase 26°, that means the rate of change is 26°/6.5min = 4°/min. This means that the temperature is increasing at 4° per minute.

If the temperature rises at 4°/min, then it will take 15 minutes to rise to 60°.

4°x = 60°, x = 15 minutes

15 minutes = quarter hour

Therefore, the bottom-right answer is false because it will take 13 minutes for the temperature of the liquid to rise 52°.

4°x = 52°, x = 13 minutes

After fitting a bookcase with a height of 2.5 feet into a space with a width of 3.25 feet, 0.375 feet will be left on each side.

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

Here,

Width of bookshelf=2.5 feet

Space to keep the bookshelf=3.25 feet

Total difference for the remaining space near bookshelf,

=3.25-2.5

=0.75 feet

Space remaining on either side of bookshelf,

=0.75/2

=0.375 feet

A space of 0.375 feet will be remaining on each side after keeping a bookshelf of size 2.5 feet in a space of 3.25 feet.

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Answer:

\( \frac{17}{k} \)

S" > 0 indicates that the rate of change of sales is increasing.

What is rate?

A rate is a measure of the amount of change of one quantity with respect to another quantity, typically expressed as a ratio.

The derivative of a function represents its rate of change at a particular point. In this case, S represents the monthly sales of Bluetooth headphones, and its derivative S' represents the rate of change of sales. If S' is increasing, it means that the rate of change of sales is getting larger over time.

Mathematically, this means that the second derivative S" (which represents the rate of change of the rate of change) is positive, since an increasing slope of the original function (S') corresponds to a positive value for the second derivative.

Therefore, S" > 0 indicates that the rate of change of sales is increasing.

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Answer:

a 25-7.36

=17.64

b 8.65+4.23-3.5

=12.88-3.5

=9.38

Answer:

a) 17.64

b) 9.38

Step-by-step explanation:

a) 25 - 7.36 = 25 - 7 - 0.36 = 18 - 0.36 = 17.64

b) 8.65 + 4.23 - 3.5 = 8.65 - 3.5 + 4.23 = 5.15 + 4.23 = 9.38

Hope this helps :)

Have a nice day!

Answer:

A,T,O,I,R

Step-by-step explanation:

Answer:

A,T,O,I,R

Step-by-step explanation:

Given differential equation is y"-9y'+20y=0We can write this equation asy²-9y+20y=0Here, a = 1, b = -9, and c = 20Now, we have to find the roots of this equation.

Now, let us find the value of the discriminant. b²-4ac= (-9)²-4(1)(20)= 81-80= 1Since the value of the discriminant is greater than zero, therefore, we have two real and distinct roots for this equation.Roots are given by the quadratic formula.x= (-b±√(b²-4ac))/2aOn substituting the values of a, b, and c we get,x = (9±√1)/2Now,x1= 5x2= 4/1These roots give two linearly independent solutions as follows: y1=e^5t and y2=e^4tTherefore, the general solution to the differential equation is:y=c1e^5t+c2e^4tWhere c1 and c2 are constants.

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The given differential equation is y"-9y'+20y=0.

Let us use the characteristic equation to solve this differential equation.

The characteristic equation of y"-9y'+20y=0 isr² - 9r + 20 = 0.

Solve for r by factoring the characteristic equation(r - 5)(r - 4) = 0. 

Therefore, r = 5 and r = 4.

Thus, the general solution of the differential equation y"-9y'+20y=0 isy(x) = c₁e⁴x + c₂e⁵x

where c₁, c₂ are constants.

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1. The outcomes in the sample space of choosing a letter from the word STARK are: S, T, A, R, K.

2. Number of outcomes in the sample space = 6 (from THANKS) × 5 (from STARK) = 30.

3. The Probability of choosing the letters AA is 0, as there are no occurrences of the letter A in both words together.

1. The outcomes in the sample space of choosing a letter from the word THANKS are: T, H, A, N, K, S.

  The outcomes in the sample space of choosing a letter from the word STARK are: S, T, A, R, K.

2. To find the number of outcomes in the sample space, we multiply the number of outcomes for each word.

  Number of outcomes in the sample space = Number of outcomes for the first word × Number of outcomes for the second word

  Number of outcomes in the sample space = 6 (from THANKS) × 5 (from STARK) = 30.

3. The probability of choosing the letters AA would be the number of favorable outcomes (which is 0 in this case) divided by the total number of outcomes in the sample space.

  Probability of choosing AA = Number of favorable outcomes / Total number of outcomes

  Probability of choosing AA = 0 / 30 = 0.

Therefore, the probability of choosing the letters AA is 0, as there are no occurrences of the letter A in both words together.

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Answer:

11/5.5= $2 per pound of gravel

Hope this helped :)

Answer:

100° and 25°

Step-by-step explanation:

Total measure of the angles in a triangle is 180°

180 - 55 = 125

split 125° into 2

lots of possible answers

Answer:

y=mx+b
also if you ask me how I got that is because you need to listen carefully to the math teacher word so you can remember the answer

Answer:

14/3

Step-by-step explanation:

Set up two ratios and cross multiply. Solve for missing segment.

\(\frac{2}{3}\) = \(\frac{x}{7}\)

3x = 14

x = 14/3

Answer:

54.23

Step-by-step explanation:

If that not a choice simpfly