Ide whole numbers
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franny spent 35 minutes walking around a track. she made 7 laps around the track.
it took franny the same amount of time to walk each lap. how many minutes did it take her to walk each lap?
оа.
28
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5
oc. 245
od. 1
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Answer:

C. y = ⁶/5x + ⁷/2

Step-by-step explanation:

First, find the slope of line AB that goes through A(3, 1) and B(-3, 6):

\( slope(m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - 1}{-3 - 3} = \frac{5}{-6} \).

Slope of line AB = -⅚.

The slope of the line that is a perpendicular bisector of line AB will be a negative reciprocal of the slope of line AB.

Thus:

Negative reciprocal of -⅚ = ⁶/5. (Reciprocal of ⅚, also the sign will change from positive to negative).

Next is to find the y-intercept, b, of the line.

To do this, you need to find the midpoint where the two lines intersect:

Therefore,

Midpoint (M) of AB, for A(3, 1) and B(-3, 6) is given as:

\( M(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}) \)

Let \( A(3, 1) = (x_1, y_1) \)

\( B(-3, 6) = (x_2, y_2) \)

Thus:

\( M(\frac{3 +(-3)}{2}, \frac{1 + 6}{2}) \)

\( M(\frac{0}{2}, \frac{7}{2}) \)

\( M(0, \frac{7}{2}) \)

Substitute x = 0, y = ⁷/2, and m = ⁶/5 into y = mx + b and find the value of b.

⁷/2 = ⁶/5(0) + b

⁷/2 = b

b = ⁷/2

The slope (m) and the y-intercept, b, of the line we are looking for are ⁶/5 and ⁷/2, respectively.

Therefore, substitute m = ⁶/5 and b = ⁷/2 into y = mx + b.

y = ⁶/5x + ⁷/2

The equation that is the perpendicular bisector of the line AB is y = ⁶/5x + ⁷/2.

To the first query, the appropriate response is:

C. Because the line's slope is positive, the linear connection is not proportionate.

In the example presented, there is no proportionality between the squares' side lengths (x) and perimeters (y).

This is due to the fact that the perimeter likewise doubles from 4 feet to 8 feet when the side length goes from 1 foot to 2 feet.

In a proportionate connection, doubling one variable would cause the other to change proportionally, but that is not the case in this situation.

For the second query, y = kx, where k is the proportionality constant, represents a proportional linear connection.

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Answer:

Step-by-step explanation:

To find gradient/slope m, we need to use this formula.

\(m \: = \: \frac{y2 - y1}{x2 - x1} \)

In the question, we are given x and y coordinates of two points, (-7, -4) and (7, 6).

\(m \: = \frac{6 - ( - 4)}{7 - ( - 7)} \)

\(m = \frac{6 + 4}{7 + 7} \)

\(m = \frac{10}{14} \)

\(m = \frac{5}{7} \)

Hope this helped!

The slope of the graph lines of function g passes through the points (-7,-4)and (7,6) is 5/7

The points are given as:

(-7,-4)and (7,6)

The slope (m) is calculated using:

m = [y2 - y1]/[x2 - x1]

So, we have:

m = [6 + 4]/[7 + 7]

Evaluate the sum

m = 10/14

Divide

m = 5/7

Hence, the slope is 5/7

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There are 5 full square and 6 triangles that are half squares.

      5 + (6)(1/2) = 5 + 3 = 8

You could also break this into smaller shapes (like a big triangle on the top and a smaller triangle and rectangle on the bottom and use area formulas to calculate the area.  But counting works well in this example.

Answer: 8

Step-by-step explanation:

First you split up this shape into two different shapes, a triangle and trapezoid

Put a line through the coordinates (-2,2) to  (-1,2); the top is a triangle and the other is a trapezoid

Area of the trapezoid is A = .5x (base1 + base2) x height

base1 of the trapezoid goes from -4 to -1 which is 3

base2 goes from -2 to -1 which is 1

height is 0 to 2 whcich is 2

A = .5 x (3+1) x 2 = 4

Now area of a triangle is A = .5 x base x height

the base goes from -2 to 2 which is 4

the height goes from 2 to 4 which is 2

A = .5 x (4) x (2) = 4

Area of the Trapezoid + Area of the Triangle = Total Area

4 + 4 = 8

Step-by-step explanation:

Eli typed faster on his second attempt, 120 words per minute on his first attempt and 150 words per minute on his second attempt.

A fraction represents a part of a whole.

We need to calculate his typing speed for each attempt.

On his first attempt, Eli typed 180 words in \(1\frac{1}{2}\) hours, which is the same as typing 120 words in 1 hour.

Therefore, his typing speed on the first attempt was 120 words per minute.

On his second attempt, Eli typed 180 words in \(1\frac{1}{5}\) hour, which is the same as typing 150 words in 1 hour.

Therefore, his typing speed on the second attempt was 150 words per minute.

Comparing the two speeds, we see that Eli was faster on his second attempt, typing 150 words per minute compared to 120 words per minute on his first attempt.

Therefore, Eli typed faster on his second attempt, 120 words per minute on his first attempt and 150 words per minute on his second attempt.

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Answer:

77

Step-by-step explanation:

3+2*49-24

3+98-24

101-24

77

Good luck

Answer:

77

Step-by-step explanation

3+2X7^2-4X6

First complete the exponent

3+2X49-4X6

Then multiply

3+2X49-24

Multiply

3+98-24

Calculate the rest of the equation

101-24=77

Therefore the answer is 77.

Please don't be mad if this is incorrect

Also the x's are multiplication symbols and NOT variables

The equation that represents a linear function rule for the following set of ordered pairs is  A. y = -3x + 2

We can express the Equation of a linear function, as y = mx + b.

m= slope

b= y-intercept

We can determine the slope (m):

= (change in y)/(change in x )

then we can substitute the values as :

= (-7 -(-4)) / (3 - 2)

= -3/1

= -3

Then thevalue of b can be found through the substituting of  m = -3  into the  equation knowing that  (1, -1) = (x, y)

Then we have;

-1 = [-3(1) + b]

-1 = [-3 + b]

[-1 + 3] = b

b = 2

In this case ,  we can put m = -3 , b = 2

y = mx + b

y = [-3(x) + 2]

Therefore, we have

y = -3x + 2

Hence option A is correct.

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complete question:

Which equation represents a linear function rule for the following set of ordered pairs?

x y

1 -1

2 -4

3 -7

A. y = -3x + 2

B. y = -3x - 2

C. y = -2x + 3

D. y = -2x - 3

Kelvin's weight after 1 week, assuming he maintains a steady weight loss of 3%, would be 123.19 kg

We must multiply Kelvin's current weight (127 kg) by the weight loss percentage (3%), in order to determine his anticipated weight loss after 1 week with a 3% constant weight reduction.

The computation is made using the formula:

Weight loss = Current weight x Weight loss percentage

Inserting the values:

Loss of weight = 127 x 0.03

Loss of weight: 3.81 kg

Kelvin's expected weight loss after 1 week is 3.81 kg. We must take this weight loss out of his current weight in order to calculate his weight one week from now.

Formula:

Weight after 1 week = Current weight - Weight loss

Inserting the values:

Weight after 1 week: 127 - 3.81

Weight after 1 week: 123.19 kg

Therefore, Kelvin's weight after 1 week, assuming he maintains a steady weight loss of 3%, would be 123.19 kg.

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35x + 65y = 815 and x + 7 = y are the system of equations that can be used to find the number of boxes.

What is an algebra?

One of the many different mathematical disciplines is algebra. Algebra is, broadly stated, the study of mathematical symbols and the guidelines for applying those symbols to formulas.

Given,

The weight of each small box = 35 pounds
The weight of each large box = 65pounds
The total weight of the boxes = 815pounds
There were7 times as many small boxes shipped as large boxes
Let 'x' be the number of small boxes and 'y' be the number of large boxes
The weight of 'x' small boxes = 35x pounds
The weight of 'y' large boxes = 65y pounds
The total weight of the two types of  boxes together = 35x+65y

Since the total weight of the boxes is 815 pounds, we have
35x+65y = 815---------------------(1)

Since 7 more small boxes =   large boxes, hence we have,
x + 7 = y ------------------------(2)
Solving both the equations we get,

x = 3.95 or 4
and, y = 10.95 or 11

The number of large boxes shipped = 11

The number of small boxes shipped  = 4

∴ The number of small boxes shipped = 4 and the number of large boxes shipped = 11.

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Answer:

15

Step-by-step explanation:

f(X)= f(5)

meaning X= 5

x²-2x

5²-2(5) = 15

Answer:

Step-by-step explanation:

Area of outer triangle = \(\dfrac{4x*(4x+3)}{2}= 2x*(4x +3)\)

                                    = 2x*4x + 2x*3

                                   = 8x² + 6x

Area of inner triangle= \(\dfrac{2x*(2x+5)}{2}=x*(2x+5)=x*2x+x*5=2x^{2} + 5x\)

Area of aluminium = area of outer triangle - area of inner triangle

                        = 8x² + 6x + 2x² + 5x

                        = 10x² + 11x

Area of 20 aluminum borders = 20*(10x² + 11x)  = 200x² + 220x

b) x = 25 cm

Area of 20 aluminum borders = 200*25² + 220*25

                                                  = 200 * 625 + 220*25

                                                 = 125000  + 5500

                                                  = 130500 cm²

c) Area of inner triangle (Glass) = 5500 cm²

Cost of aluminium = 130500 * 0.06 = $ 7830

Cost of glass = 5500 * 0.03 = $ 165

Cost of making 20 windows =  7830 + 165 = $ 7995

The value of x is in the solution set of 4x - 12 ≤ 16+8x is x ≥ -7.

Given inequality:

⇒ 4x - 12 ≤ 16+8x

rearranging the like terms

4x - 8x - 12 ≤ 16

4x - 8x ≤ 16+12

-4x ≤ 16+12

-4x ≤ 28

divide by 4 on both sides

-4x/4 ≤ 28/4

-x ≤ 28/4

-x ≤ 7

x ≥ -7.

Therefore the value of x is in the solution set of 4x - 12 ≤ 16+8x is x ≥ -7.

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Answer:

1.16667

Step-by-step explanation:

Answer: 128

Step-by-step explanation:

Answer:

no tHank you hope someone can help

Step-by-step explanation:

A can be diagonalized if it has 2 unit eigenvectors All two eigenvalues are distinct and the eigenvectors that correspond to distinct eigenvalues are orthogonal Eigenvalues of A are the roots of a quadratic polynomial. The third eigenvalue is 5.

Given that two eigenvalues of a 3 x 3 matrix A are λ1 = 3, λ2 = 4, and det(A) = 60.

We know that the product of all eigenvalues of a matrix is equal to its determinant. So, we have:

λ1 * λ2 * λ3 = det(A)

Substituting the given values, we get:

3 * 4 * λ3 = 60

Simplifying, we get:

λ3 = 5

Therefore, the third eigenvalue is 5.

Statement (a) is false because having 2 unit eigenvectors does not guarantee that a matrix can be diagonalized.

Statement (b) is false because even if the eigenvalues are distinct, the eigenvectors may not be orthogonal.

Statement (c) is true because eigenvectors that correspond to distinct eigenvalues are always orthogonal.

Statement (d) is true because the eigenvalues of a 2 x 2 real matrix are the roots of a quadratic polynomial.

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The system of equation has a unique solution for all values of k except k = 4, where it has infinitely many solutions.

To solve the system [23 -18; 27 -22], we write it as an augmented matrix and perform row operations:

[23 -18 | 27 -22]

R2 - (27/23)R1 → R2: [0 -16.39 | -12.78]

R2/(-16.39) → R2: [0 1 | 0.78]

R1 + (18/23)R2 → R1: [23 0 | 29.87]

R1/(23) → R1: [1 0 | 1.30]

Thus, we have the solution x = 1.30 and y = 0.78.

For the system 3x+2y=0, 6x+ky=0, we can write it as an augmented matrix and perform row operations:

[3 2 | 0; 6 k | 0]

R2 - 2R1 → R2: [0 k-4 | 0]

If k ≠ 4, then the system has a unique solution x = 0 and y = 0.

If k = 4, then the system becomes [3 2 | 0; 0 0 | 0]. This system has infinitely many solutions, since the second equation is redundant and the first equation has a free variable.

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To solve the system [23 -18 27 -22], we need to write it in the form of AX=B, where A is the matrix of coefficients, X is the unknown vector, and B is the vector of constants. So we have:[23 -18] [27 -22]

From this, we can see that the system has a unique solution when k is not equal to 0. If k = 0, then the system has infinitely many solutions. And  if the last row of the reduced echelon form is [0 0 | 0], then the system has no solution.
For the equation 3x+2y=0 and 6x+ky=0, we can solve for y in terms of x by rearranging the second equation as y = -(2/3) x. Substituting this into the first equation, we get:3x + 2(-2/3)x = 0 Simplifying, we get:2x = 0 So x = 0. Substituting this into the second equation, we get y = 0. Therefore, the system has a unique solution of (0,0) for all values of k. Now, we analyze the three cases:
(a) Unique solution: This occurs when k ≠ 4, as this leads to a non-zero value for y, allowing us to solve for bothx and y.

(b) No solution: This case is not possible for this system, as there is always a common solution when k ≠ 4.
(c) Infinitely many solutions: This occurs when k = 4, making the equations identical. In this case, any multiple of the common solution will also be a solution, resulting in infinitely many solutions.

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The company needs to produce and sell more units to break even and start making a profit.

Profit is the difference between total revenue and total cost. Total cost can be divided into variable and fixed costs. Total variable cost (TVC) equals the product of variable cost per unit and the number of units produced.

Thus, we can use the following formula:

Total cost (TC) = TVC + TFC

Where TFC is total fixed costs and TC is total cost.

To calculate profit, we need to know revenue. We can use the following formula to calculate revenue:

Revenue = price per unit (P) × number of units sold (x)

Therefore, the profit function can be calculated as:

P = R - C

where R is revenue and C is cost.

Using the formulas above, we can calculate the profit function as follows:

P(x) = [P × x] - [(VC × x) + TFC]

where P is the price per unit, VC is the variable cost per unit, TFC is the total fixed cost, and x is the number of units produced and sold.

In the given problem, the variable cost is $12.30 per unit and the fixed costs are $98,000. The product sells for $17.98. Therefore, P = $17.98 - $12.30 = $5.68.

Using the profit function, we can calculate the profit for any number of units produced and sold. For example, if 500 units are produced and sold, the profit would be:

P(500) = ($5.68 × 500) - [($12.30 × 500) + $98,000]P(500) = $2,840 - $103,000P(500) = -$100,160

This means that if 500 units are produced and sold, the company will lose $100,160.

This is because the fixed costs are relatively high compared to the profit per unit.

Therefore, the company needs to produce and sell more units to break even and start making a profit.

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Answer:

d) x(x-8)

Step-by-step explanation:

Both of the denominators in the problem have to be in the common denominator. It needs the x because of the 6/x and it also needs to have x-8 because of the right side of the equation.

Answer:

d x(x - 8).

Step-by-step explanation:

That would be x * (x - 8)

Number of ways that the three gift certificates can be awarded = 13800 ways

There are a total of 25 people attended the charity benefit. There are three gift certificates: one gift certificate is in the amount of $100, the second is worth $25 and the third is worth $10.

Assume that no person receives more than one prize.

One of the 25 people can get gift certificate of $100.

⇒ 25 ways for $100 gift certificate.

Then remaining 24 people are considered for further counting.

One of the 24 people can get gift certificate of $25.

⇒ 24 ways for $25 gift certificate.

Now there are 23 people remained.

One of the 23 people can get the $10 gift certificate.

⇒ 23 ways for $10 gift certificate.

Therefore, Number of ways that the three gift certificates can be awarded = 25 x 24 x 23 = 13800 ways.

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Answer:    Since the angles in a triangle sum up to 180 degrees, we can write:

m∠O + m∠P + m∠Q = 180

Substituting the given angle measures, we get:

(2x - 5) + (3x - 8) + (10x - 17) = 180

Simplifying and solving for x, we have:

15x - 30 = 180

15x = 210

x = 14

Now that we know x = 14, we can find the value of angle θ by substituting x into one of the angle measures:

m∠O = 2x - 5 = 2(14) - 5 = 23 degrees

Therefore, the value of angle θ is 23 degrees and the value of x is 14.

Step-by-step explanation: hope this helps (:

To find the cost of each small ice cream, we need to subtract the cost of the large ice creams from the total amount earned and divide the remaining amount by the number of small ice creams sold.


Let's start by finding the number of large ice creams sold. We know that 1/3 of the total number of ice creams sold is large. So, 1/3 * 240 = 80 ice creams are large.

Next, we can calculate the total cost of the large ice creams sold. Since each large ice cream costs £3.80, the total cost of the large ice creams is 80 * £3.80 = £304.

Now, we can find the total cost of the small ice creams by subtracting the cost of the large ice creams from the total amount earned. £640 - £304 = £336.

Finally, to find the cost of each small ice cream, we divide the total cost of the small ice creams (£336) by the number of small ice creams sold (240 - 80 = 160). £336 / 160 = £2.10.

Therefore, the cost of each small ice cream is £2.10.

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The inequality that represents all the solutions of -2(3x + 6) ≥ 4(x + 7) is x ≤ -4

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

-2(3x + 6) ≥ 4(x + 7)

Divide both sides of the inequality by -2

So, we have the following representation

3x + 6 ≤ -2(x + 7)

Open the brackets

This gives

3x + 6 ≤ -2x - 14

Add 2x to both sides of the inequality

So, we have the following representations

5x + 6 ≤ -14

Subtract 6 from both sides of the inequality

So, we have the following representations

5x ≤ -20

Divide both side of the inequality

x ≤ -4

Hence, the solution is x ≤ -4

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Answer:

34cm squared

Step-by-step explanation:

Formula: 2(WL+HL+HW)

(2*5) + (1*5) + (1*2) = 10 + 5 + 2  = 17 17*2 = 34

Answer:

34

Step-by-step explanation:

2(wl+ hl+hw)

2(10+5+2)

= 34

The four factors that directly impact your total cost of using a credit card are given below:

What is total cost?

Total cost is the complete expense incurred to produce or acquire a product, service or to carry out a particular activity.

The four factors that directly impact your total cost of using a credit card are:

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The product rule must be used to find the number of strings of four decimal digits, that have exactly three digits that are 9s.

What is product rule ?

The Product Rule says that the derivative of a product of two functions is the first function times the derivative of the second function plus the second function times the derivative of the first function.

To obtain the number of strings of 4 decimal digits that have exactly 3 digits that are 9s ; we use the product rule,

In first digit 1 possible way between 0 to 9

In second digit 1 possible way between 0 to 9

In third digit 1 possible way between 0 to 9

In fourth digit 9 possible ways between 0 to 9

That's mean 1 * 1* 1* 9* 4 = 36

Thus 36 possible ways.

The product rule must be used to find the number of strings of four decimal digits.

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Answer:

The equation is

y = $ 12.35 x

Step-by-step explanation:

Cost of one bag of rocks = $ 12.35

Let there are x bags of rocks, so that the total cost is y.

So, the cost of 1 bag = $ 12.35

cost of x bags = $12.35 x

The total cost is

y = $12.35 x

It is the equation of a straight line which passes from origin and the slope is 12.35.

Answer:

53.81

Step-by-step explanation:

if u add the tip but the tip by itself is 8.21

Answer

Step-by-step explanation: