Find the approximate circumference of a circle with a diameter of 100

Step-by-step explanation:

21x²-2x +1/2 = 0

x² - 2x ×21 + 1/2× 21 = 0

Answer:2

Step-by-step explanation:

7 raised to the power of 4 equals 2,401, and the exponent we were looking for is 4.

What is meant by power?

Power is a function that represents the number of times a base number is multiplied by itself. It is the rate at which work is done or energy is transferred, measured in watts.

What is meant by exponent?

An exponent is a mathematical notation used to indicate the number of times a quantity is multiplied by itself. It is written as a superscript and represents the power to which a number or expression is raised.

According to the given information

To find the value of the exponent that satisfies the equation 7ˣ = 2,401, we can take the logarithm of both sides of the equation with respect to base 7. This gives us:

log7(7ˣ) = log7(2,401)

x = log7(2,401)

Using a calculator, we can find that log7(2,401) is approximately 3. Therefore, the value of x that satisfies the equation 7ˣ = 2,401 is 3.

Alternatively, we could also use the fact that 2,401 is equal to 7⁴ - 2, which can be written as:

7⁴ - 2 = (7²)² - 2

= 49² - 2

= 2,401

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Answer:

-1 and 1

Explanation:

Rational numbers include whole numbers, decimals and can be expressed as fractions.

Some rational numbers between -7 and 3 are -6, -5, -4, -3, -2, -1, 0, 1, 2

Answer:

\(\textsf {1 and 2}\)

Step-by-step explanation:

\(\textsf {Rational numbers are all real numbers between -7 and 3.}\)

\(\textsf{Hence, 2 examples of the numbers can be : 1 and 2.}\)

Answer:

x^2 +3x -4 = 0  --> (x +4)(x -1) = 0

Step-by-step explanation:

Let's find A and B such that

A*B = - 4    and  A+B = 3

Numbers are:

A = +4  and  B = -1

The factoring equation is y = (x + A)(x + B)

In this specific case: y = (x +4)(x -1)

Solutions to the quadratic equation require

y = (x +4)(x -1) = 0

and hence

x +4 = 0  --> x = -4

x - 1 = 0 -->  x= +1

We have the inequality

To solve we notice that the 3 multiplying x is positive, so we can divide both sides of the inequality by 3 without changing the sign. Then

In interval notation this is

The probability of the Doubles" means both dice show the same number is 36.

When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

The probabilities of these two outcomes must be added in order to get the likelihood of rolling an even number or doubles, but since we have already tallied those outcomes twice, the probability of rolling both doubles and an even number must be subtracted. The probability of rolling doubles and an even number is 1/36 since rolling two sixes is the only method to get a double and an even number.

The likelihood of rolling an even number or doubles is thus:

The formula for P(even number or doubles) is P(even number) = P(even number) + P(doubles) - P(even number and doubles) = 1/2 + 1/6 - 1/36 = 19/36.

The odds of rolling an even number or two doubles are 19/36.

Therefore, the probability of the Doubles" means both dice show the same number is 36.

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Answer:

14

Step-by-step explanation:

When x = 3 and y = 1,

5x - y works out to 5(3) - 1 = 14

Answer: its nit the 3rd one i just took the test

Step-by-step explanation:

Answer:

\(\bold{f(x) = 375(2.5)^{-x}+ 33}\)

Step-by-step explanation:

An exponential function of form f(x) = ba^(-x) + c has a horizontal asymptote of y = c as x approaches infinity, and a y-intercept of (0, b + c). We can use the given information to set up a system of equations and solve for the unknowns.

The horizontal asymptote is given as y = 33, so we have:

c = 33

The y-intercept is given as (0, 408), so we have:

b + c = 408

Substituting c = 33, we get:

b + 33 = 408

b = 375

So the function we're looking for is of the form:

\(\bold{f(x) = 375a^{-x}+ 33}\)

To find a, we use the fact that the function passes through P(2, 93):

93 = 375a^(-2) + 33

60 = 375a^(-2)

a^2 = 375/60

a^2 = 6.25

a = \(\sqrt{6.25 } =2.5\)

Therefore, the exponential function that satisfies the given conditions is:

\(\bold{f(x) = 375(2.5)^{-x}+ 33}\)

The probability of landing on the dark blue target is 2/5.

Probability is the ratio of required to the total possible outcomes of an event.

P(dark blue ) = 40/100

divide through by 20

P(dark blue ) = 2/5

Therefore, the probability of landing on target is 2/5

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The simplified expression of x(3x + 5)-5(2x - 1) is 3x² - 5x + 5

From the question, we have the following parameters that can be used in our computation:

x(3x + 5)-5(2x - 1)

Open the brackets

So, we have

3x² + 5x - 10x + 5

Evaluate the like terms

So, we have

3x² - 5x + 5

Hence, the simplified expression is 3x² - 5x + 5

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The value of mathematical expression is,

⇒ x + 35

Where, x is any number.

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Given that;

The algebraic expression is,

'' A number increased by 35,''

Now, Let a number = x

So, We can formulate the mathematical expression ,

⇒ x + 35

Where, x is any number.

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The image of the rotation is A'( 3, 1), B'(-2,-2), C;(-3, 3) and the graph is attached

The coordinates of the polygon are given as

A( -3, -1), B(2,2), C(3, -3)

The rotation is given as

A rotation of 180° about the origin

The 180 degrees rotation has the algebraic rule of

(x, y) ⇒ (-x, -y)

So, we have

A'( 3, 1), B'(-2,-2), C;(-3, 3)

Hence, the coordinates of the image using the rule a 180-degree rotation is A'( 3, 1), B'(-2,-2), C;(-3, 3)

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Answer:

the answer is d

Step-by-step explanation:

Answer:

149

Step-by-step explanation:

The missing values are

<UTQ = 41 degree

x= 1

<UQT = 47 degree

We have a parallelogram QRST.

We know that the opposite sides of the parallelogram is equal and parallel then

QR || ST

QT || SR

Then, <SRT = <RTQ (<UTQ) (alternate Interior Angle)

<UTQ = 41

Similarly, <UQT = <SRQ = 47

Now, RU = UT

2x + 1= 3

2x = 2

x= 1

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The money earned on friday is $1586 and on sunday is $1960.

A linear equation in one variable is an equation that has only one solution and is expressed in the form ax+b = 0, where a and b are two integers and x is a variable.

Let us assume the money generated by Friday game is 'F'.

Let us assume the money generated by Sunday game 'S'.

The two games together earn $3546.00 for the team.

Equation will become;

F + S = 3546.00    ........(equation 1)

Friday's game generates $374.00 less than Sunday's game. Thus,

F = S - 374.00

Since, F = S - 456.50 use the substitution method and put this value in equation 1.

(S - 374.00) + S = 3546.00

Simplifying the equation;

2S  = 3546.00 + 374.00

2S = 3920

S = 1960.

Put this value in equation 1 and find F.

F + S = 3546.00

F + 1960 = 3546.00

F = 1586.

Thus, the money generated on friday is $1586 and on sunday is $1960.

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Answer:

the domain for the function y=log(x+3) is (-3,oo).

The domain of the function y = log(x + 3) is (−3, +∞), or in interval notation, (−3, ∞).

The domain of the function y = log(x + 3) is the set of all possible values that x can take without making the expression undefined.

For the logarithmic function y = log(x), the argument of the logarithm (x in this case) must be greater than zero, otherwise the result is undefined.

So, to find the domain of y = log(x + 3), we need to solve the inequality x + 3 > 0, which gives x > -3.

Thus, the function y = log(x + 3) is (−3, +∞), or in interval notation, (−3, ∞) is the answer.

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Answer:

the first lcm of 8 3 5 7 is 840

Step-by-step explanation:

to get the equation of any straight line all we need is two points off of it, hmmm let's use (-1 , 1) and hmmmm (2 , 10)

\((\stackrel{x_1}{-1}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{10}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{10}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-1)}}}\implies \cfrac{9}{2+1}\implies 3\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{3}(x-\stackrel{x_1}{(-1)}) \\\\\\ y-1=3(x+1)\implies y-1=3x+3\implies y=3x+4\)

Answer:

.49 if you're dividing them.

Step-by-step explanation:

Answer: 2y-2  ≤ 14

Step-by-step explanation:

The maximum area of a Norman window with a perimeter of 9 feet is 81π/4 square feet.

To find the maximum area of a Norman window with a given perimeter, we can use calculus. Let's denote the radius of the semicircle as r and the height of the rectangular window as h.The perimeter of the Norman window consists of the circumference of the semicircle and the sum of all four sides of the rectangular window. Therefore, we have the equation:

πr + 2h = 9We also know that the area of the Norman window is the sum of the area of the semicircle and the area of the rectangle, given by:

A = (πr^2)/2 + rh

To find the maximum area, we need to express the area function A in terms of a single variable. We can do this by substituting r from the perimeter equation:

r = (9 - 2h)/(π)

Now we can rewrite the area function in terms of h only:

A = (π/2) * ((9 - 2h)/(π))^2 + h * (9 - 2h)/(π)

Simplifying this equation, we get:

A = (1/2)(9h - h^2/π)

To find the maximum area, we differentiate the area function with respect to h, set it equal to zero, and solve for h:

dA/dh = 9/2 - h/π = 0

Solving this equation, we find:h = 9π/2

Substituting this value of h back into the area function, we get:

A = (1/2)(9 * 9π/2 - (9π/2)^2/π) = (81π/2 - 81π/4) = 81π/4

Therefore, the maximum area of a Norman window with a perimeter of 9 feet is 81π/4 square feet.

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Answer:

B: rectangle JKLM ~ rectangle QRSP

Step-by-step explanation:

5/6=0.83

12.5=0.83

JK corresponds to QR

JM corresponds to PQ

rectangle JKLM ~ rectangle QRSP

Answer:

y = 15 , x = 6

Step-by-step explanation:

you can easily find y from first equation

Move y to the other side of the equation and reverse its sign

so (-11) changes to (+11) and now we have this equation

y = 15

now you must replace 15 instead of y in second equation ,then we have this equation

15 = 2x + 3

now we have to find x

move (+3) to other side of equation and reverse its sign

(+3) changes to (-3)

we have this equation now

15 - 3 = 2x

12 = 2x

x = 12 ÷ 2 = 6

======================================================

Work Shown:

B = amount Beth earned

P = amount Pam earned

amounts are in dollars

Pam earned $4 less than 3 times as much as Beth, so,

P = 3B-4

Together they earned $860, meaning

P+B = 860

Plug the first equation into the second. Solve for B

P+B = 860

3B-4+B = 860

4B-4 = 860

4B = 860+4

4B = 864

B = 864/4

B = 216

Use this to find P

P = 3B-4

P = 3*216-4

P = 648-4

P = 644

Beth earned $216 and Pam earned $644.

----------------------------------------

Check:

B+P = 860

216+644 = 860

860 = 860

First equation is true

P = 3B-4

644 = 3*216-4

644 = 644

Second equation is true

Both equations are true when (B,P) = (216,644) so the solutions have been confirmed.

This isn't an identity, so I assume you have to solve the equation.

(1 - sin(2A)) (1 + cot(2A)) = cot(2A)

1 - sin(2A) + cot(2A) - sin(2A) cot(2A) = cot(2A)

1 - sin(2A) - cos(2A) = 0

sin(2A) + cos(2A) = 1

Multiply both sides by 1/√2, which we want to do because cos(π/4) = sin(π/4) = 1/√2. This gives

cos(π/4) sin(2A) + sin(π/4) cos(2A) = 1/√2

Then condense the left side as

sin(2A + π/4) = 1/√2

2A + π/4 = sin⁻¹(1/√2) + 2nπ  or   2A + π/4 = π - sin⁻¹(1/√2) + 2nπ

(where n is any integer)

2A + π/4 = π/4 + 2nπ  or   2A + π/4 = 3π/4 + 2nπ

2A = 2nπ  or   2A = π/2 + 2nπ

A = nπ  or   A = π/4 + nπ

Answer:

\(-3x^{2}\) -5x +2

Step-by-step explanation:

Just combine like terms and solve.

-2x^2+-6x - (x+1)(x-2)

Use foil on the second part

-2x^2-6x - x^2-x-2

Now combine like terms and you’d get your final answer