Both numbers are prime in which of the following pairs of numbers?
O A 5 and 9
B. 7 and 9
O c. 5 and 6
O D. 5 and 7
O E. 7 and 8

41/2 days is equivalent tο 492 hοurs.

Divisiοn is an arithmetic οperatiοn that invοlves splitting a quantity intο equal parts οr determining hοw many times οne quantity is cοntained within anοther. It is cοmmοnly denοted by the symbοl ÷ οr /, and can be written as a fractiοn οr as a ratiο.

We knοw that there are 24 hοurs in day therefοre,

Tο cοnvert 41/2 days tο hοurs, we can use the fact that there are 24 hοurs in οne day:

41/2 days x 24 hοurs/day = 41 x 12 = 492 hοurs

Therefοre, 41/2 days is equal tο 492 hοurs.

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From the graph attached below, the solution to the system of linear inequalities are (1, 4)

A system of linear inequalities is a collection of linear inequalities in the same variables. The solution is any ordered pair that satisfies each of the inequalities.

In the problem given;

y < - x + 5 ...eq(i)

y ≥ 3x + 1 ...eq(ii)

To determine the solution to the system of linear inequalities, it is easier for us to use graphical method. This is simply done by plotting the points and determine the coordinate at which both inequalities intersect.

From the graph of the system of linear inequalities, the solution to this is (1, 4) which is option E

Kindly find attached graph below

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Answer:

...

Step-by-step explanation:

To find the number of calories Davis burns while running for 30 minutes, we can use the information that he burns 1080 calories running for 2.5 hours.

We know that 30 minutes is 1/120 of 2.5 hours. So, we can divide the total number of calories by 120 and we get the calorie burn for 30 minutes:

1080 calories / 120 = 9 calories

The number of calories Davis burns while swimming for 30 minutes can be determined by using the equation y = 266x, where x represents the number of hours he swims. We know that he swims for 30 minutes, or 1/120 hours, so we can plug that value into the equation:

y = 266(1/120) = 2.216 calories

So, Davis burns 7 calories more running for 30 minutes than swimming for 30 minutes, assuming the rates remain constant.

Answer:The answer is 5622580

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Convert to improper fraction and multiply them, then convert back to mixed fraction :)

Answer:

C .      The answer can be simplified but its not on here for some reason.

Step-by-step explanation:

6 2/6 x 1 1/2

(6 x 6) + 2 = 38/6

(1 x 2) + 1 = 3/2

38/6 x 3/2 = 114/12

114 ÷ 12 = 9 6/12.

9 6/12 = 9 3/6 = 9 1/2.

C

Again it can be simplified buts it not on here for some reason.

Answer: a the guy wire is 150 ft

Step-by-step explanation: b the guy is the wire is 350 sorry not good and english but answer is 350 ft

Answer:

If Father is four times older than Mary, that would be 4 times 10-- which equals 40. Five years ago, Mary must have been 5 years old. So, multiply 7 and 5 and you'll get 35! Father would have been 35 years old.

I hope this helps!

Step-by-step explanation:

Answer:

127 ft 3 3/8in

Step-by-step explanation:

Assuming the field is regulation (I can't see the model), the answer is 127 feet and 3 3/8 inches.

At a price of $3, the total revenue will be the greatest, and the company will sell 3 units at that price.

To find the total revenue at each price, we can multiply the price by the corresponding quantity.

Price        Quantity          Total Revenue

$6                0                      $0

$5                 1                       $5

$4                 2                       $8

$3                 3                        $9

$2                 4                         $8

$1                  5                          $5

To find the price at which total revenue is the greatest, we look for the highest value in the Total Revenue column.

In this case, the highest total revenue is $9, which occurs when the price is $3.

At a price of $3, the company will sell 3 units (as indicated in the Quantity column).

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This means that when function f(x) = 4x²- 1 and g(x) = 4x + 8, f(2) - g(2) = 15, and by using the equation as a substitute.

what is function ?

A function in mathematics is a relationship between a set of inputs (also referred to as the domain) and a set of outputs (also referred to as the range), where each input has a unique outcome. Typically, the variable x stands for the input values, the variable y for the output values, and the variable f for the function itself (x). Tables, graphs, equations, and verbal descriptions can all be used to represent functions. In a wide variety of disciplines, including science, engineering, economics, and social studies, they are employed to model relationships between quantities. Functions are frequently used to explain the relationship between two quantities.

given

We must first determine the values of f(2) and g(2) independently using the provided functions in order to evaluate f(2) - g(2):

f(2) = 4(2)² - 1 = 15

g(2) = -4(2) + 8 = 0

These values can now be added to the expression f(2) - g(2) as a substitute:

f(2) - g(2) = 15 - 0 = 15

This means that when f(x) = 4x²- 1 and g(x) = 4x + 8, f(2) - g(2) = 15, and by using the equation as a substitute.

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Answer:

20 feet.

Step-by-step explanation:

The container is assumed to be a rectangular prism.

The volume would be length × width × height.

l × 10 × 8 = 1600

l × 80 = 1600

l = 1600/80

l = 20

The storage container is 20 feet long.

The length of the storage container is 20 feet long.

Given is that a storage container holding 1600 cubic feet of rice is 8 feet deep x 10 feet wide.

The volume of cuboid is given by -

V{C} = L x B x H

So, we can write -

1600 = L x 8 x 10

80L = 1600

L = 20 feet

Therefore, the length of the storage container is 20 feet long.

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The question is missing. Here is the complete question.

Let y = \(\left[\begin{array}{ccc}2\\6\end{array}\right]\) and u = \(\left[\begin{array}{ccc}7\\1\end{array}\right]\). Write y as the sum of a vector in Span(u) and a vector orthogonal to u.

Answer: y = \(\left[\begin{array}{ccc}\frac{21}{10} \\ \frac{3}{10} \end{array}\right] + \left[\begin{array}{ccc}\frac{-1}{10}\\ \frac{57}{10} \end{array}\right]\)

Step-by-step explanation: The sum of vectors is given by

y =  \(y_{1}\) + z

where  \(y_{1}\) is in Span(u);

vector z is orthogonal to it;

First you have to compute the orthogonal projection \(y_{1}\) of y:

\(y_{1}\) = proj y = \(\frac{y.u}{u.u}.u\)

Calculating orthogonal projection:

\(\left[\begin{array}{c}2\\6\end{array}\right]\).\(\left[\begin{array}{c}7\\1\end{array}\right]\) = \(\left[\begin{array}{c}9\\6\end{array}\right]\)

\(\left[\begin{array}{c}7\\1\end{array}\right]\).\(\left[\begin{array}{c}7\\1\end{array}\right]\) = \(\left[\begin{array}{c}49\\1\end{array}\right]\)

\(y_{1} = \frac{9+6}{49+1}.u\)

\(y_{1} = \frac{15}{50}.u\)

\(y_{1} = \frac{3}{10}.u\)

\(y_{1} = \frac{3}{10}.\left[\begin{array}{c}7\\1\end{array}\right]\)

\(y_{1} = \left[\begin{array}{c}\frac{21}{10} \\\frac{3}{10} \end{array}\right]\)

Calculating vector z:

z = y - \(y_{1}\)

z = \(\left[\begin{array}{c}2\\6\end{array}\right] - \left[\begin{array}{c}\frac{21}{10} \\\frac{3}{10} \end{array}\right]\)

z = \(\left[\begin{array}{c}\frac{-1}{10} \\\frac{57}{10} \end{array}\right]\)

Writing y as the sum:

\(y = \left[\begin{array}{c}\frac{21}{10} \\\frac{3}{10} \end{array}\right] + \left[\begin{array}{c}\frac{-1}{10} \\\frac{57}{10} \end{array}\right]\)

Step-by-step explanation:

everything can be found in the picture

Answer:

Hello There!!

Step-by-step explanation:

Museums are regarded as information resources because there are historical things and artifacts there.

hope this helps,have a great day!!

~Pinky~

The value of c in the polynomial is - 7.

The polynomial is given as follows:

p(x) = 2x³ - x² +  cx + 2 . The value of c if x - 2 is a factor of p(x) can be computed as follows:

Therefore,

p(x) = 2x³ - x² +  cx + 2

when x - 2 is a factor, p(x) = 0

Therefore,

0 = 2x³ - x² +  cx + 2

Hence,

2(2)³ - (2)² +  2c + 2 = 0

16 - 4 + 2c + 2 = 0

12 + 2 + 2c  = 0

2c = - 14

divide both sides by 2

c = - 14 / 2

c = - 7

Therefore,

c = -7

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Answer:

6x+3

Step-by-step explanation:

If you're just combining like terms this is the correct answer

The scale factor is the number that relates the dimensions of the two rectangles. To find it we need to divide the length of the larger rectangle by the length of the smaller one, we have:

The scale factor of this rectangle is 4.

The value of the expression \(2(cos^4 60 + sin^4 30) -(tan^2 60 + cot^2 45) + 3\times sec^2 30 is 33/4.\)

Let's simplify the expression step by step:

Recall the values of trigonometric functions for common angles:

cos(60°) = 1/2

sin(30°) = 1/2

tan(60°) = √(3)

cot(45°) = 1

sec(30°) = 2

Substitute the values into the expression:

\(2(cos^4 60 + sin^4 30) - (tan^2 60 + cot^2 45) + 3sec^2 30\)

= \(2((1/2)^4 + (1/2)^4) - (\sqrt{(3)^2 + 1^2} ) + 3(2^2)\)

= 2(1/16 + 1/16) - (3 + 1) + 3*4

= 2(1/8) - 4 + 12

= 1/4 - 4 + 12

= -15/4 + 12

= -15/4 + 48/4

= 33/4

Therefore, the value of the expression \(2(cos^4 60 + sin^4 30) -(tan^2 60 + cot^2 45) + 3\times sec^2 30 is 33/4.\)

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Answer:

less than

Step-by-step explanation:

314+175= 489 round that it would be 500 so it would be less than 600

Please mark me brainliest

Hello there!

The sum of 314 and 175 = 489.

If we round it, we will get 500.

500 is less than 600.

So the sum of 314+175 is less than 600.

Hope this helps you!

#HaveAnAmazingDay

\(GraceRosalia\)

Case 1: a = 0; b = 0 --> Real Number

Case 2: a = 0; b ≠ 0 --> Non-Real Complex Number

Case 3: a ≠ 0; b = 0 --> Real Number

Case 4: a ≠ 0; b ≠ 0 --> Non-Real Complex Number

For each case, we can determine whether the expression a + bi represents a real number or a non-real complex number based on the values of a and b.

Case 1: a = 0; b = 0

In this case, both a and b are zero. The expression a + bi simplifies to 0 + 0i, which is equal to 0. Therefore, the expression represents a real number.

Case 2: a = 0; b ≠ 0

Here, a is zero, but b is nonzero. The expression a + bi becomes 0 + bi, where b is a nonzero real number multiplied by the imaginary unit i. Since the expression contains a nonzero imaginary part, it represents a non-real complex number.

Case 3: a ≠ 0; b = 0

In this case, a is nonzero, but b is zero. The expression a + bi simplifies to a + 0i, which is equal to a. As there is no imaginary part in the expression, it represents a real number.

Case 4: a ≠ 0; b ≠ 0

Here, both a and b are nonzero. The expression a + bi contains both a real part (a) and an imaginary part (bi). Thus, it represents a non-real complex number.

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Answer:

Step-by-step explanation:

Hypotenuse = h

h^2 = 8^2 + 6^2

h^2 = 64 + 36

h^2 = 100

h = √100

h = 10

Hope that helps! :)

-Aphrodite

Step-by-step explanation:

2.5 km = 250000 cm

250000 cm /20000 = 12.5 cm on the map

12.5 cm ^2  x 20 0000 x 20 000   = 5 000 000 000 cm^2 = 500 000 m^2  

Therefore, the solutions to the equation 0 = |3x + 3| + 3 are x = -2 and x = 0.

To solve the equation 0 = |3x + 3| + 3, we need to eliminate the absolute value. Remember that the absolute value of a number is always non-negative.

First, let's isolate the absolute value term on one side of the equation:

|3x + 3| = -3

Since the absolute value cannot be negative, there are no solutions to the equation as it stands. However, if we modify the equation to make the right side positive, we can find a solution.

To eliminate the absolute value, we can rewrite the equation as two separate equations, considering both the positive and negative cases:

   3x + 3 = -3

   -(3x + 3) = -3

Solving equation 1:

3x + 3 = -3

3x = -6

x = -2

Solving equation 2:

-(3x + 3) = -3

-3x - 3 = -3

-3x = 0

x = 0

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Answer:

9

Step-by-step explanation:

5x-3= 2x+24

5x=2x+27

3x=27

X=9

Answer: A.  9

Step-by-step explanation:

The diagonal is bisected by the other diagonal.  So the 2 parts of the diagonal are equal

5x - 3 =  2x + 24                 >Bring like terms to 1 side

3x = 27                                >Divide both sides by 3

x = 9

Answer:

m∠B ≈ 37°

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

Step-by-step explanation:

Step 1: Identify

Adjacent Leg = 4

Hypotenuse = 5

Step 2: Find Angle

The values of x for which f(x) = 7 are x = 61 and x = 21.

To find the values of x for which f(x) = 7, we can set up the equation and solve for x.

The given function is f(x) = 0.5|x - 41| - 3.

Setting f(x) equal to 7, we have:

0.5|x - 41| - 3 = 7.

First, let's isolate the absolute value term:

0.5|x - 41| = 7 + 3.

0.5|x - 41| = 10.

To remove the absolute value, we can consider two cases:

Case: (x - 41) is positive or zero:

0.5(x - 41) = 10.

Multiplying both sides by 2 to get rid of the fraction:

x - 41 = 20.

Adding 41 to both sides:

x = 61.

So x = 61 is a solution for this case.

Case: (x - 41) is negative:

0.5(-x + 41) = 10.

Multiplying both sides by 2:

-x + 41 = 20.

Subtracting 41 from both sides:

-x = -21.

Multiplying both sides by -1 to solve for x:

x = 21.

So x = 21 is a solution for this case.

Therefore, the values of x for which f(x) = 7 are x = 61 and x = 21.

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Answer:

x  ≤ -4

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form: x  ≤ -4

Answer:

(X'U'Y) + (XUY')

Step-by-step explanation:

Starting with [Xn(X'nY)]', we can use De Morgan's laws to simplify the expression:

[Xn(X'nY)]' = (Xn)' + (X'nY)'

Recall that Xn represents the logical operator "and", while X' represents "not X". Using these definitions, we can expand the expression:

(Xn)' + (X'nY)' = (X'U'Y) + (XUY')

where U represents the logical operator "or".

Therefore, [Xn(X'nY)]' simplifies to (X'U'Y) + (XUY').