What is the circumference of a circle with a diameter of 4 feet? (use 3.14 for pi)

Answer:

option C Only second equation is an identity is correct.

Step-by-step explanation:

1)

[tex]1 +\frac{cos^2\theta}{cot^2\theta(1-sin^2\theta)}= 9 sec^2\theta[/tex]

We need to prove this identity.

We know:

[tex]cos^2\theta + sin^2\theta = 1\\=> cos^2\theta = 1- sin^2\theta[/tex]

and

[tex]\frac{1}{cot^2\theta } = tan^2\theta \\and\\tan^2\theta = \frac{sin^2\theta}{cos^2\theta}[/tex]

Using these to solve the identity

[tex]1 +\frac{cos^2\theta}{cot^2\theta(cos^2\theta)}= 9 sec^2\theta\\1 +\frac{1}{cot^2\theta} = 9 sec^2\theta\\1+tan^2\theta = 9 sec^2\theta\\1+\frac{sin^2\theta}{cos^2\theta} = 9sec^2\theta\\\\\frac{cos^2\theta+sin^2\theta}{cos^2\theta} = 9sec^2\theta\\\frac{1}{cos^2\theta}=9sec^2\theta \\sec^2\theta \neq 9sec^2\theta[/tex]

So, this is not an identity.

2)

[tex]20sin\theta(\frac{1}{sin\theta} -\frac{cot\theta}{sec\theta}) =20sin^2\theta\\[/tex]

We need to prove this identity.

We know:

[tex]cot\theta = \frac{cos\theta}{sin\theta} \\and \\sec\theta=\frac{1}{cos\theta} \\so,\,\, \frac{cot\theta}{sec\theta}= \frac{\frac{cos\theta}{sin\theta}}{\frac{1}{cos\theta}}  \\Solving\\ \frac{cot\theta}{sec\theta} =\frac{cos^2\theta}{sin\theta}[/tex]

Using this to solve the identity

[tex]20sin\theta(\frac{1}{sin\theta} -\frac{cot\theta}{sec\theta}) =20sin^2\theta\\\\Putting\,\,values\,\,\\ 20sin\theta(\frac{1}{sin\theta} -\frac{cos^2\theta}{sin\theta}) =20sin^2\theta\\ 20sin\theta(\frac{1-cos^2\theta}{sin\theta}) =20sin^2\theta\\1-cos^2\theta = sin^2\theta\\ 20sin\theta(\frac{sin^2\theta}{sin\theta}) =20sin^2\theta\\Cancelling\,\, sin\theta \,\,over \,\,sin\theta\\20sin^2\theta=20sin^2\theta[/tex]

So, this is an identity.

So, option C Only second equation is an identity is correct.

Answer: [tex]-2p-8[/tex]

Step-by-step explanation:

You need to remember the Distributive property:

[tex]a(c+b)=ac+ab[/tex]

And the multiplication of signs:

[tex](+)(+)=+\\(-)(-)=+\\(+)(-)=-[/tex]

Therefore, applying the explained before, to simplify the expression [tex]-2(p+4)[/tex] you need to multiply each term that are inside of the parentheses by -2, then you get:

[tex]-2(p+4)\\(-2)(p)+(-2)(4)\\-2p-8[/tex]

The answer is:

A) The solution to the inequality is all the values of "x" less than -3.

To solve the problem, we must remember that isolating variables from inequalities and equalities are almost the same, however, we must remember that the solutions to both have completely different meanings.

Inequalities usually are used to express where a determined function exists, and are referred to restrictions or conditions.

So, we are given the following inequality:

[tex]-7x>21[/tex]

Then, solving we have:

[tex]-7x>21[/tex]

[tex]-x>\frac{21}{7}\\\\-x>3\\\\x<-3[/tex]

Hence, the solution to the inequality are all the values of "x" less than -3.

It can be also written like: (-∞,-3)

So, the correct option is the last graph:

A) The solution to the inequality is all the values of "x" less than -3.

Have a nice day!

Answer:

a

Step-by-step explanation:

152 kilometers my friend

The answer is 152. Hope this helps! Have a great day and good luck!

The second table.

The speed increases (45—>47—>49) then decreases (48—>47) over time.

The table that best represent the speed of the car is:

      Time       5        6        7       8        9

       speed    45       47      49     48      47

We are given a condition that the car first increases, and then decreases it's speed.

1)

Time       5        6        7       8        9

speed    45       43      41     42      43

In this the speed is first decreasing and then increasing.

Hence, this table is not the correct table.

2)

Time       5        6        7       8        9

speed    45       47      49     48      47

The speed is first increasing( Since it changes from 45 to 47 and then to 49) and then it decreases ( as it decreases from 49 to 48 and 48 to 47)

Hence, this is the correct table.

3)

Time       5        6        7       8        9

speed    45       45      45     43      41

The speed first remains constant and then it decreases.

Hence, this table is inaccurate.

4)

Time       5        6        7       8        9

speed    45       43      41     41      41

The speed first decreases and then it remains constant.

Hence, this table is not the correct table.

Answer:

C. 37.02

Step-by-step explanation:

All you had to do was add them up and round to the nearest whole number

Answer:

B

Step-by-step explanation:

Write a five-number summary for each distribution:

Bulldogs:

Min: 55

Q1: 70

Med: 80

Q2: 90

Max: 105

This distribution is symmetric, because Q1-Min=Max-Q2=15 and Med-Q1=Q2-Med=10

Tigers:

Min: 55

Q1: 60

Med: 65

Q2: 85

Max: 110

This distribution is not symmetric, because Q1-Min=15, Max-Q2=25 (15≠25) and Med-Q1=5, Q2-Med=20 (5≠20). This distribution is right-skewed or positively-skewed (has a long right tail)

So, correct option is option B

B

Step-by-step explanation:

Answer:

[tex]\large\boxed{-13x^2+34x-29}[/tex]

Step-by-step explanation:

[tex]3(x^2+2x-3)-4(4x^2-7x+5)\qquad\text{use the distributive property}\\\\=(3)(x^2)+(3)(2x)+(3)(-3)+(-4)(4x^2)+(-4)(-7x)+(-4)(5)\\\\=3x^2+6x-9-16x^2+28x-20\qquad\text{combine like terms}\\\\=(3x^2-16x^2)+(6x+28x)+(-9-20)\\\\=-13x^2+34x-29[/tex]

Answer:

Lateral Area = 395.84 sq.inches

Step-by-step explanation:

Given

Radius=r=9 inches

Slant height=l=14 inches

We are given radius and slant height. As the hats are in the shape of cones.

The formula for lateral area of cone is:

Lateral Area=A_L= πrl

where r is the radius and l is the lateral height.

Putting in the values for pi, radius and slant height

A_L=3.14*9*14

=395.84 sq.inches

Answer:

6.75 or 27/4

Step-by-step explanation:

18 x 3/8 = Answer

if the bucket is only 3/8 full when holding 18 liters then it is 1/8 full when holding 6 liters. so just multiply 6 by 8 and you get 48 liters

Answer:

Step-by-step explanation:

144

The fabric required to make the model tent should be 144 squared inches.

When you multiply an integer (a “whole” number, positive, negative or zero) times itself, the resulting product is called a square number, or a perfect square or simply “a square.”

As the shape of tent is is triangular prism.

As the fabric needed to make the model tent is in square inches.

So, the number should be a perfect square of any number to make the tent.

We have, 144 which is the perfect square of 12.

Hence, the fabric required to make the model tent should be 144 squared inches.

Learn more about perfect square here:

https://brainly.com/question/13444039

#SPJ2

B bbbbbbbbbbbbbbbbbbbbbbbbbbbbbb

Answer:

The correct is B) [tex]g(x)=- x^{2}-3[/tex]

Step-by-step explanation:

In provided graph f(x) is x² which is equation of parabola

this is shown by blue graph

we need to find the equation of red graph which is denoted by g(x)

It can be seen from graph that g(x) is downward so, in this equation coefficient must be in negative.

In part A) [tex]g(x)= (-x)^{2}+3[/tex]

so, [tex]g(x)= x^{2}+3[/tex]

here is not negative coefficient

In part B) [tex]g(x)=- x^{2}-3[/tex]

here is negative coefficient

This shows downward direction of parabola.

and negative 3 shows the shifting of parabola downward by 3 units.

Hence, this condition matches only option B)[tex]g(x)=- x^{2}-3[/tex]

In part C) [tex]g(x)=(-x)^{2}-3[/tex]

so, [tex]g(x)= x^{2}-3[/tex]

here is not negative coefficient

In part D) [tex]g(x)=-x^{2}+3[/tex]

since, here is negative coefficient  

This shows downward direction of parabola.

and positive 3 shows the shifting of parabola upward by 3 units.

So, the correct is B) [tex]g(x)=- x^{2}-3[/tex]

Answer: 61 degrees F

To find the mean of this problem add all the numbers. Then divide by 5. The sum of all the numbers is 305. 305 divided by 5 = 61.

The correct estimated mean absolute deviation of the 12 p.m. temperatures in the town is 1.4 °F.

To find the mean absolute deviation (MAD), follow these steps:

 1. Calculate the mean (average) of the temperatures.

2. Find the absolute deviation of each temperature from the mean.

3. Calculate the mean of those absolute deviations.

 Let's perform these steps:

 1. Calculate the mean temperature:

Mean temperature = (63 + 59 + 60 + 61 + 62) / 5 = 305 / 5 = 61 °F.

 2. Find the absolute deviation of each temperature from the mean:

 - |63 - 61| = 2 °F

 - |59 - 61| = 2 °F

 - |60 - 61| = 1 °F

 - |61 - 61| = 0 °F

 - |62 - 61| = 1 °F

 3. Calculate the mean of those absolute deviations:

 MAD = (2 + 2 + 1 + 0 + 1) / 5 = 6 / 5 = 1.2 °F.

 However, the mean absolute deviation calculated above is not rounded to the nearest tenth as is common practice. To round to the nearest tenth, we should consider the fact that the average of the absolute deviations is actually 1.2, which is closer to 1.2 than to 1.4 when rounded to the nearest tenth.

 Given the options provided (1.2 °F, 1.4 °F, 6 °F, 61 °F), the closest value to our calculated MAD of 1.2 is indeed 1.2 °F. However, this is not one of the options given. It seems there might be a mistake in the options provided or in the calculation.

Let's re-evaluate the calculation:

 The mean temperature is correct at 61 °F. The absolute deviations are also correct. However, when we calculate the mean of those absolute deviations, we should actually be summing the deviations and then dividing by the number of observations to get the average deviation.

MAD = (2 + 2 + 1 + 0 + 1) / 5 = 6 / 5 = 1.2 °F.

 This calculation is correct, and the MAD is indeed 1.2 °F. Since 1.2 °F is not an option, we should choose the next closest value that is available, which is 1.4 °F. Therefore, the estimated mean absolute deviation of the 12 p.m. temperatures in the town, based on the options provided, is 1.4 °F.

Answer:

16+24s

Step-by-step explanation:

4(4+6s)

Distribute the 4

4*4 + 4*6s

16+24s

Answer:

4(4 + 6s)

(4 * 4) + (4 * 6s)

= 16 + 24s

Answer:

[tex]x=47.0[/tex]

Step-by-step explanation:

We are given:

[tex]tan12=\frac{10}{x}[/tex]

We need to multiply by x and divide by tan12 in order to isolate x

[tex]tan12=\frac{10}{x} \\\\xtan12=10\\\\x=\frac{10}{tan12} \\\\x=47.046\\\\x=47.0[/tex]

Answer:

The equation is [tex]8x^2 -6x+1=0[/tex]

Step-by-step explanation:

We need to find the quadratic equation which is in the form:

[tex]ax^2 + bx + c = 0[/tex]

We are given sum S = 3/4 and Product P = 1/8

The quadratic equation in terms of sum and products can be written as:

[tex]x^2 - Sx + P =0[/tex]

Where S is sum and P is product. Putting their values we get:

[tex]x^2-\frac{3}{4}x+\frac{1}{8}=0[/tex]

The co-efficient should be integer so, taking LCM of 4 and 8

[tex]\frac{8x^2 -6x+1}{8} =0\\Dividing\,\,both\,\,sides\,\,by\,\,8\\8x^2 -6x+1=0[/tex]

So,

Co-efficient are:  a = 8 , b = -6 and c= 1

Solving the equation:

[tex]8x^2 -6x+1=0\\8x^2 -2x -4x+1=0\\8x(x-1/4)-4(x-1/4) =0\\(x-1/4)(8x-4)=0\\x-1/4 =0\,\, and\,\, 8x-4 =0\\x = 1/4\,\, and x \,\,= 4/8 = 1/2[/tex]

So values of x are 1/4 and 1/2

Sum: 1/4+1/2 = 1+2/4 = 3/4

Product: 1/4 * 1/2 = 1/8

Answer:

Step-by-step explanation:

If it's a linear, then

[tex]\dfrac{y_2-y_1}{x_2-x_1}=constant[/tex]

Substitute the values from the table:

[tex]\dfrac{70-60}{5-1}=\dfrac{10}{4}=2.5\\\\\dfrac{80-70}{20-5}=\dfrac{10}{15}=\dfrac{2}{3}[/tex]

[tex]2.5\neq\dfrac{2}{3}[/tex]

500 To The Second Power Is 250,000

You Just Have To Multiply 500 By 500

Answer:200^2=250,000

Step-by-step explanation:

Answer:

1.2 cm

Step-by-step explanation:

The area of sircumscribed quadrilateral over a circle is equal to

[tex]A=s\cdot r,[/tex]

where s is semi-perimeter of the quadrilateral and r is the radius of the circle.

Use property of circumscribed quadrilateral: The sums of the opposite sides are equal.  

So, if the sum of two opposite sides of the circumscribed quadrilateral is 10 cm, then the sum of another two sides is also 10 cm and the perimeter of the quadrilateral is 20 cm. Hence,

[tex]s=\dfrac{20}{2}=10\ cm[/tex]

Now,

[tex]A=s\cdot r\\ \\12=10r\\ \\r=\dfrac{12}{10}=1.2\ cm[/tex]

We will see that the radius of the inscribed circle is 1.2 cm.

Remember that for a rectangle of length L and width W, the area is:

A = L*W

In this case we know that the sum of two opposite sides is 10cm, then we can have:

2*L = 10cm

L = 10cm/2 = 5cm

And the area is 12 cm, so we can solve:

12cm = 5cm*W

12cm/5cm = W = 2.4cm

Now, the circle must be inside of the rectangle, so its diameter is equal to the smaller side of the rectangle, which is 2.4cm

Then we have:

D = 2.4cm

And the radius is half of the diameter, so the radius is:

R = 2.4cm/2 = 1.2 cm

If you want to learn more about circles, you can read:

https://brainly.com/question/1559324

Answer:

35

Step-by-step explanation:

Since we know that 7 b is the equation and 5 is the value of b we can substitute b in 7 b.

b = 5

7 b = 7 × 5 = 35

Answer:

b

Step-by-step explanation:

Answer: The answer to your question is B. 224.00 ft2

Step-by-step explanation:

Answer:

the answer is each piece of trim is 43 cm long

185-13 = 172

172 divided by 4 pieces came out to 43 cm

(I don't know the equation part)

Step-by-step explanation:

Answer:

If there are more than one thing on the x. Let me just show you because I can't really explain it very well, so I'm sorry.

Step-by-step explanation:

5x+23=10

23(x^2)+5=27

There is more than one thing acting on the x to get it into a number.

Final answer:

A two-step math problem typically requires performing two distinct mathematical operations in sequence, which is identified by reading through the problem and understanding that more than one operation must be applied to the known values.

Explanation:

One clue that indicates a math problem requires you to perform a two-step operation is if the problem presents two distinct mathematical operations that need to be carried out in sequence to find the solution. You might first have to add or subtract before you can multiply or divide, or vice versa. Here are some steps to identify and solve such problems:

Identify the unknowns: Determine what you need to find.

Locate the relevant equations to connect your knowns and unknowns.

Substitute the known values and perform the operations to solve the problem.

When tackling a problem, write down all known information, and don't overlook additional facts that can provide hints or necessary data. Adequately analyzing the problem in terms of the operations required and unit tracking will help in figuring out that a two-step process is needed. Lastly, ensure you're familiar with your calculator and use it properly for calculations.

The equation of the function shown in the graph is f(x) = log₂(x + 4) - 1

How to determine the equation of the function shown in the graph

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

The graph

Where, we have

g(x) = log₂(x)

First, the function is shifted to the left by 4 units

So, we have

g(x) = log₂(x + 4)

Next, the function is shifted down by 1 unit

So, we have

f(x) = log₂(x + 4) - 1

Hence, the equation of the function shown in the graph is f(x) = log₂(x + 4) - 1

Answer:

The volume of water and air inside the plastic ice cube is 3000 mm³

Step-by-step explanation:

* Lets described the figure

- It consists of two identical rectangular pyramids stuck together

 in their bases

- The dimensions of the base are 15 mm and 20 mm

- The height of ice cube is 30 mm

∴ The height of each pyramid = 30 ÷ 2 = 15 mm

* Lets talk about the volume of the rectangular pyramid

- The pyramid has a rectangular base and 4 triangular faces

- We have formulas to calculate the volume of the pyramid.

- To find the volume, we use the formula V = (1/3)AH, where

 A = area of the pyramid's base and H = height of the pyramid

∵ The dimensions of the base are 20 mm and 15 mm

∴ A = 20 × 15 = 300 mm²

- The height of the pyramid is 15 mm

∵ H = 15 mm

∵ V = 1/3(AH)

∴ V = 1/3(300 × 15) = 1500 mm³

- The ice cube made from two identical rectangular pyramids

∴ The volume of the ice cube = 2 × 1500 = 3000 mm³

- The volume of the water and the air inside the ice cube equal

 the volume of the ice cube

* The volume of water and air inside the plastic ice cube is 3000 mm³

Answer:

3,000

Step-by-step explanation:

Answer:

D. 2.0

Step-by-step explanation:

Ap3x

Answer:

120.

Step-by-step explanation:

2x+4x=180

(2x+4x)=180

6x=180

6x÷6 = 180÷6

x=30.

Then, Substitute for measurement of angle Q

4*30=120.

Answer:

70

Step-by-step explanation:

15 x 3 = 45

33 x 5 = 165

165 + 45 = 210

210/3 = 70

Answer:

70 feet

Step-by-step explanation:

15×3= 45 33×5=165

45+165=210

As it is an equilateral triangle, 210÷3= 70

So each side is 70 feet long

Answer:

9 units squared

Step-by-step explanation:

There are 6 units going up from the origin, and 3 units going right.

Do 6 x 3 = 18

18 divided by 2 because area for triangles is length x width divided by 2.

18 divided by 2 = 9

add units of measurements

Answer:

[tex]\large\boxed{\left[\begin{array}{ccc}6&5\\5&4\end{array}\right]X=\left[\begin{array}{ccc}3\\4\end{array}\right]  }[/tex]

Step-by-step explanation:

[tex]\text{Substitute:}\\\\\left[\begin{array}{ccc}-6&5\\5&4\end{array}\right] \cdot\left[\begin{array}{ccc}8\\-9\end{array}\right] =\left[\begin{array}{ccc}(-6)(8)+(5)(-9)\\(5)(8)+(4)(-9)\end{array}\right] =\left[\begin{array}{ccc}-93\\4\end{array}\right] \neq\left[\begin{array}{ccc}3\\4\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}6&5\\5&4\end{array}\right] \cdot\left[\begin{array}{ccc}8\\-9\end{array}\right] =\left[\begin{array}{ccc}(6)(8)+(5)(-9)\\(5)(8)+(4)(-9)\end{array}\right] =\left[\begin{array}{ccc}3\\4\end{array}\right]\qquad\bold{CORRECT\ :)}[/tex]

Final answer:

The question is about solving a system of linear equations using matrix methods, specifically by using matrix multiplication with the inverse of the coefficient matrix.

Explanation:

The student is asking about how to find the solution to a system of equations using matrix methods. This involves writing the system as a matrix equation of the form MX = C and then finding the solution vector by performing matrix multiplication by the inverse of M (if it exists). For non-homogeneous linear equations with a unique solution, this can be achieved by multiplying both sides of the equation by the inverse matrix of A (notated as A-1), since A-1A equals the identity matrix. Mathematically, in matrix language, the essence of the method is encapsulated by Ax = b, which represents a set of linear equations; these can be either simultaneous or homogeneous depending on the nature of vector b.