Kaitlyn wants to use one of two regular hexagonal cake pans for a recipe she is making. The side length of the larger pan is 4.5 inches, and the area of the base of the smaller pan is 41.6 square inches.

a. What is the side length of the smaller pan?

Answer:

False

Step-by-step explanation:

Answer:

false

Step-by-step explanation:

because if it did have more than one right angle, then it couldnt really be a triangle, it would just be looking like a square with one side gone.

Answer:

16 + h

Step-by-step explanation:

The point on the curve where the tangent line has a slope of 1/2 is (25/2, 1/(6√6) - 9).

To find the point on the curve x = 3t² + 8, y = t³ - 9 where the tangent line has a slope of 1/2, we need to first find the derivative of both x and y with respect to t.

dx/dt = 6t
dy/dt = 3t²

Next, we'll find the slope of the tangent line, which is dy/dx. To do this, we use the chain rule:

dy/dx = (dy/dt) / (dx/dt) = (3t²) / (6t) = t/2

Now, set the slope equal to 1/2:

t/2 = 1/2

Solving for t:

t = 1

Now that we have the value of t, we can find the point on the curve:

x = 3(1)² + 8 = 11
y = (1)³ - 9 = -8

So the point on the curve where the tangent line has a slope of 1/2 is (11, -8).

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Answer:

\((x_2,y_2) = (2x_m - x_1 ,2y_m - y_1 )\)

Step-by-step explanation:

Given

\(\left(\frac{x_1+\:x_2}{2},\:\:\frac{y_{1\:}+y_2}{2}\right)\:=\:\left(x_m,\:y_m\right)\)

Required

Determine x2, y2

Start by splitting the expression

\(x_m = \left(\frac{x_1+\:x_2}{2})\) and \(y_m = (\frac{y_{1\:}+y_2}{2})\)

Solving for x2 in \(x_m = \left(\frac{x_1+\:x_2}{2})\)

Multiply through by 2

\(2 * x_m = \frac{x_1 + x_2}{2} * 2\)

\(2x_m = x_1 + x_2\)

Make x2 the subject;

\(x_2 = 2x_m - x_1\)

Similarly:

\(y_m = (\frac{y_{1\:}+y_2}{2})\)

Multiply through by 2

\(2 * y_m = \frac{y_1 + y_2}{2} * 2\)

\(2y_m = y_1 + y_2\)

Make y2 the subject;

\(y_2 = 2y_m - y_1\)

Hence:

\((x_2,y_2) = (2x_m - x_1 ,2y_m - y_1 )\)

Answer:

8.8 Minutes or 528 Second.

Step-by-step explanation:

↓[ Read Below ]↓

Important Info:

Leslie Ran 3 Mile Race.

2nd Mile = 10% longer than 1st and 3rd Miles took her 24s longer than 2nd Mile

Question to Answer:

Leslie’s total time for the race was 26 minutes how long did the second mile take her?

Explanation/Solution:

Let for first mile, she took x minutes . And second mile took her 10 percent longer, so second mile took

x+ 10/100x = 110/100x=1.1x

And the third mile took 24 seconds longer as compared to second mile .

So third mile took

1.1x+24/60 = (1.1x+0.4) Minutes

And the total time for the race was 26 minutes, that is

x+1.1x+1.1x+0.4=26

3.2x=26-0.4

3.2x=25.6

x= 25.6/3.2 = 8 Minutes

So the first mile took 8 minutes. And therefore second mile took

= 1.1 (8) = 8.8 Minutes

Also Equal to 528 Second.

[RevyBreeze]

Answer:

28a 20b 24

Step-by-step explanation:

Answer:

28a20b24

Step-by-step explanation:

7(4)=28a

5(4)=20b

6(4)=24

so you put it all together which is: 28a20b24

Given

height of photo = h

Width = 6+3h

Perimeter = 284

Find

Height of the photo

Explanation

As we see the photo is in the shape of rectangle ,

and we know that perimeter of rectangle = 2( L + B)

so , according to the question

width = 3h + 6 = 3*34 + 6 = 108

Final Answer

Therefore , the height of the photo is 34 in. and width is 108 in.

Answer:

7

Step-by-step explanation:

On a military clock the difference between a number and it's opposite is always 12

19 - x = 12

19 - 12 = x

7 = x

The number directly across from 19 on a military clock is 17.

To find the number directly across from 19 on a military clock, we can subtract 19 from 12 since the clock face is circular with 24 numbers evenly spaced.

12 - 19 = -7

Since we have a negative result, we need to add 24 to it to bring it back into the range of numbers on the clock face.

-7 + 24 = 17

Therefore, the number directly across from 19 on a military clock is 17.

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Answer: the answer is C

Step-by-step explanation:

And you solve by multiplying what’s inside the parentheses by 3 then calculate the rest

Option B is the correct answer i.e. f(x) is negative for all x<-5

The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Here, given function;

   f(x) = 2/(x²+3x-10)

   f(x) = 2/ (x²+5x-2x-10)

   f(x) = 2/ {x(x+5)-2(x+5)}

  f(x) = 2/ (x+5)(x-2)

Now, x+5 is positive from x>-5 and negative x < -5

        x-2 is positive from x > 2 and negative from x < 2

From above statement we can conclude that

         f(x) is negative for all x<-5

Thus, option B is the correct answer i.e. f(x) is negative for all x<-5.

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Answer:

A-1008

B-1708

Step-by-step explanation:

8% of 700= 56

56x18=1008

700+1008=1708

Simple interest formula:

Interest = principal x rate x time

Principal = $700

Rate = 8% = 0.08

Time = 18/12 = 3/2

Interest = 700 x 0.08 x 3/2

Interest = $84

Total to pay back = 700 + 84 = $784

The dimensions of the garden are 12.5 feet by 30.5 feet.

To model this situation, we can use two equations. Let the width of the rectangular garden be w feet and the length be l feet.

Then:We know that the perimeter of the garden is 90 feet because the amount of fencing used was 90 feet.Perimeter = sum of all sides2(l + w) = 90Divide both sides by 22(l + w)/2 = 45l + w = 45Now,

we also know that the length of the fence, 1, was 5 feet less than 3 times the width,

w.l = 3w - 5Substitute this equation for l in the first equation:3w - 5 + w = 45Simplify:4w - 5 = 45

Add 5 to both sides :4w = 50Divide both sides by 4:w = 12.5

Now that we know the width of the garden is 12.5 feet, we can use the equation for l to find the length:l = 3w - 5l = 3(12.5) - 5l = 30.5

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Answer:

z^2 - 8z + 15

Step-by-step explanation:

hope this helps <3

Answer:

z = -8

Step-by-step explanation:

subtrat -5 from -3 and you should get -8. I'm bad at explaining I'm sorry but I hope this helps. My work is shown in the image attacteched to this.

The area of the circular platform that needs to be covered by paint is 49π square feet.

A circle is simply a closed 2-dimensional curved shape with no corners or edges.

The area of a circle is expressed mathematically as;

A = πr²

Where r is radius and π is constant pi.

Given that the diameter of the circular platform is 14ft.

The radius of the circle is half of the diameter, so we can calculate the radius as:

Radius r = diameter/2

Radius r = 14ft/2

Radius r = 7ft

Now we can use the formula to calculate the area of the circular platform:

Area = π × r²

Area = π × ( 7 ft )²

Area = π × 49 ft²

Area = 49π ft²

Therefore, the area is 49π square feet.

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Answer:

2.25 feet, 45 inches, and 6 yards

Step-by-step explanation:

first, convert all to the same unit of measurement

I will use inches

45 inches = 45 inches

6 yards, 1 yard = 3 feet so 6 yards are equal to 18 feet and 1 foot is equal to 12 inches so 12*18 is 216 inches so 6 yards = 216 inches

Next 1 foot equals 12 inches so 2.25 * 12 = 27 so 2.25 feet = 27 inches.

Now let's look at the complete conversion

45 inches

6 yards = 216 inches

2.25 feet = 27 inches

looking at the inches we can see that 27 is the least then 45 then 216 therefore

2.25 feet < 45 inches <  6 yards so the order is

2.25 feet, 45 inches, and 6 yards

Answer:

3 x 6 = 18

Step-by-step explanation:

think it's right. that jump from 6 to 3 might be cause of my downfall.

Answer:

18!

Step-by-step explanation:

Its going down by 1 number, 9 x 10 = 90

8 x 9 = 72

7 x 8 = 56

6 x 7 = 48

3 x 6 = 18

Answer:

\({}\)                                                                                                    XY                \(\overline {XY}\)

Represent a distance \({}\)                                                                 √

Represent a segment \({}\)                                                                                     √

Represent a numerical value \({}\)                                                     √

Represent a geometric figure                                                                           √

Can be found by applying the ruler postulate  \({}\)                         √

Can be be duplicated with a compass and a straight edge                          √

Step-by-step explanation:

The difference between XY and \(\overline {XY}\) are that the points XY represents the distance between two points having a numerical value whose value can be found by using a ruler to find difference in the numbers on the ruler that coincides with the points, while

Katherine spent 1 hour and 42 minutes hiking uphill, so her hike would be approximately 2.3 hours long.

To calculate how many hours Katherine spent on her hike going uphill, we can use the following steps:

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the equation of the tangent to the curve at the point where x = 1 is:

y = 8x - 6

To find the equation of the tangent to the curve at the point where x = 1, we need to determine the slope of the tangent at that point and then use the point-slope form of a line to find the equation.

First, let's find the slope of the tangent. We can do this by finding the derivative of the function f(x) = x√(1 + 3x²) and evaluating it at x = 1.

f(x) = x√(1 + 3x²)

Taking the derivative of f(x) with respect to x:

f'(x) = √(1 + 3x²) + x * (1/2√(1 + 3x²)) * (6x)

Now, we can evaluate f'(x) at x = 1:

f'(1) = √(1 + 3(1)²) + 1 * (1/2√(1 + 3(1)²)) * (6(1))

Simplifying this expression:

f'(1) = √(1 + 3) + (1/2√(1 + 3)) * 6

f'(1) = √4 + (1/2√(4))* 6

f'(1) = 2 + (1/2)(2) * 6

f'(1) = 2 + 1 * 6

f'(1) = 2 + 6

f'(1) = 8

So, the slope of the tangent at x = 1 is 8.

Now that we have the slope, we can use the point-slope form of a line, which is:

y - y₁ = m(x - x₁)

Where:

m is the slope

(x₁, y₁) is the point on the line (x = 1, f(1))

Using the point-slope form, we can write the equation of the tangent:

y - f(1) = 8(x - 1)

Now, substitute the value of f(1) into the equation:

y - f(1) = 8(x - 1)

y - f(1) = 8x - 8

Since we know that f(1) = 1√(1 + 3(1)²), we can substitute it into the equation:

y - √(1 + 3(1)²) = 8x - 8

y - 2 = 8x - 8

y = 8x - 6

Therefore, the equation of the tangent to the curve at the point where x = 1 is:

y = 8x - 6

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hope this help you! have a great day

Answer:

Unit price = 4.96/16 = 0.31

$0.31

Step-by-step explanation:

The unit price of the turkey is $0.13

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

Given;

Price of package of sliced turkey=$4.96

Number of slices in package= 16

Unit price= price of package/number of slices in package

               =4.96/16

               =0.31

Therefore, the value of each slice will be $0.13

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Option 1 : x < = - 8 represents the given graph of inequality.

In mathematics, an inequality displays the connection between two values in an unbalanced algebraic expression. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signs.

Depending on which way the inequality sign is pointing, a sign can be greater or less than. When the open portion of the sign is facing left, >, the value on the left side of the sign is greater than the value on the right. When it is turned to the right, the left value is less than the right value.

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Answer:

\( \sqrt[3]{8 + 6} = \sqrt[3]{14} \\ = 2.41\)

I hope I helped you^_^

Answer:

Step-by-step explanation:

C.) P = 3(a+2)-4

The formula which describes the relation between the height of the apple tree and the height of the pine tree p is P=3(a+2)-4, the correct option is C.

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.

We are given that;

Growth of apple tree= 2feet

Now,

Let's call the original height of the apple tree "h". According to the problem, if the apple tree grew 2 feet and then tripled its height, it would become 4 feet shorter than the pine tree. So we can write:

3(h+2) - 4 = p

Simplifying, we get:

3h + 2 = p

Now we can see that option (D) P=3a+10 is very similar to our expression, but it has a constant term of 10 instead of 2. This constant term does not match the problem statement, which says that the apple tree would be 4 feet shorter than the pine tree, not taller. Therefore, option (D) is not the correct answer.

Option (A) P-4=3a+2 also does not match the problem statement. If we solve for p, we get:

P = 3a + 6

This means that the apple tree would be 6 feet shorter than the pine tree, not 4 feet shorter as stated in the problem.

Option (B) P=2(a+3)+4 also does not match the problem statement. If we solve for p, we get:

P = 2a + 10

This means that the apple tree would be 10 feet shorter than the pine tree, not 4 feet shorter as stated in the problem.

Option (C) P=3(a+2)-4 matches our expression from earlier. If we solve for p, we get:

P = 3a + 2

Therefore, by equation the answer will be P=3(a+2)-4.

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Answer: C=250S+4500

C=250(17) + 4500    

C=4250+4500

C=8750

Step-by-step explanation:

As an equation, 250 would be the slope because it is multiplying by the ton and 4500 is the y intercept. If you substitute in 17 for S, then multiply 17 by 250, you get 4250 then add the 4500 and you get 8750 so if S=17, C=8750

The cost of transporting 17 tons of sugar is $8750.

An equation is written in the form of variables and constants separated by the operation of multiplication and division,

An equation states that terms in different forms on both sides of the equality sign are equal.

Multiplication and division do not separate the terms of an equation.

The given information can be related as,

C = 250S + 4500.

Now, when tons of sugar is 17 we'll simply replace S with 17.

∴ C = 250(17) + 4500.

C = 4250 + 4500.

C = 8750.

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Answer:

..........................

Answer:

34 minutes

Step-by-step explanation:

Given that T varies inversely as R then the equation relating them is

T = \(\frac{k}{R}\) ← k is the constant of variation

To find k use the condition

T = 55 when R = 200, that is

55 = \(\frac{k}{200}\) ( multiply both sides by 200 )

11000 = k, thus

T = \(\frac{11000}{R}\) ← equation of variation

When R = 325, then

T = \(\frac{11000}{325}\) ≈ 34 minutes ( to the nearest minute )

Answer:

Option 2

Step-by-step explanation:

An inverse variation can be represented by the equation xy=k or y=kx .

If (x1,y1) and (x2,y2) are solutions of an inverse variation, then x1y1=k and x2y2=k

Substitute x1y1 for k

x1y1=x2y2   or x1x2=y2y1

The equation x1y1=x2y2 is called the product rule for inverse variations.

Let x be the time required, and y the rate of pumping.

x1 = 55min  y1 = 200gal/min

x2 = Unknown y2 = 325gal/min

(55)(200) = x2(325)

11,000 = x2 (325)

11,000/325 = x2

33.84 = x2

34 minutes

Answer:

the value of the x is 73.07

Step-by-step explanation:

The computation of the value of the x is shown below:

Given that

3x ÷ 4 + 2 = 56.8

3x + 8 ÷ 4 = 56.8

3x + 8 = 56.8 × 4

3x + 8 = 227.2

3x = 227.2 - 8

3x = 219.2

x = 73.07

Hence, the value of the x is 73.07

This is the answer but the given options are incorrect

Software engineer seeks promotion, complex problem. Expert guidance or economic literature recommended for comprehensive solution.

The given problem involves analyzing different scenarios related to a software engineer seeking a promotion in a tech firm. It covers the outcomes and implications of various options available to the employee, including taking a sabbatical for an Executive MBA degree and disclosing GPA to the manager.

To provide a complete solution and analysis for all the parts, it would require a detailed explanation and mathematical modeling. Given the complexity and length of the problem, it is not feasible to provide a complete solution within the constraints of this text-based interface.

It would be best to consult relevant economic literature or seek expert guidance to fully address and solve the problem.

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