Fiona cut fabric circles for an art project. She recorded the diameters of the circles in the table.

Diameter (cm) Frequency
2 3
2.25 3
2.5 4
2.75 4
3 2
3.5 2
Create a dot plot for the data in the table. Hover over each number on the number line. Then click and drag up to create the dots.

Answer:

12 geese

10 dogs

Step-by-step explanation:

We are given;

We are required to determine the number of geese and dogs that Alex counted;

We need to know that;

Assuming he counted x number of geese and y number of dogs;

Then;

x + y = 22, and

2x + 4y = 64

Thus, solving the equation simultaneously;

we can multiply the first equation by 2, to get

2x + 2y = 44

2x + 4y = 64

Eliminating x (by subtracting the second eqn from the first eqn), we get;

-2y = -20

 y = 10

Solving for x;

   x = 22 - y

      = 22 - 10

  x  = 12

Therefore; he counted 12 geese and 10 dogs

Answer:

[tex]\large\boxed{\dfrac{m^8}{25}}[/tex]

Step-by-step explanation:

[tex]\dfrac{m^6}{5}\div\dfrac{5}{m^2}\\\\\text{Divide by a fraction is the same as multiply by its reciprocal}\\\\=\dfrac{m^6}{5}\times\dfrac{m^2}{5}=\dfrac{m^6\times m^2}{5\times5}\\\\\text{use}\ a^n\times a^m=a^{n+m}\\\\=\dfrac{m^{6+2}}{25}=\dfrac{m^8}{25}[/tex]

Answer:

∴ ∠BAD = [tex]sin^{-1}[/tex](0.2044) = 11.8°

Step-by-step explanation:

i) AD = 9 cm

ii) DC = 3 cm

iii) ∠BCD = 35°

iv) Since AB is parallel to DC and ∠ABD = 90°  then we can conclude that ∠BDC = 90°.

v) [tex]\frac{BD}{DC} = \frac{BD}{3\hspace{0.1cm}cm} = tan(35)[/tex] = 0.6128      ∴ BD  = 3 [tex]\times[/tex] 0.6128 = 1.84 cm

vi) ∴ sin(∠ BAD ) = [tex]\frac{BD}{AD}[/tex]      ⇒     sin(∠ BAD ) = [tex]\frac{1.84}{9}[/tex] = 0.2044

     ∴ ∠BAD = [tex]sin^{-1}[/tex](0.2044) = 11.8°

Answer:

Step-by-step explanation:

Step-by-step explanation:

[tex]f(x)=3x^2-2x+5\\\\f(-x)=\text{substitute (-x) instead x in f(x)}\\\\f(-x)=3(-x)^2-2(-x)+5=3x^2+2x+5\\\\-f(x)=-(3x^2-2x+5)=-3x^2-(-2x)-5=-3x^2+2x-5\\\\-f(-x)=-(3x^2+2x+5)=-3x^2-2x-5[/tex]

The answers are:

[tex]\begin{aligned}& f(-x)=3 x^2+2 x+5 \\& -f(x)=-3 x^2+2 x-5 \\& -f(-x)=-3 x^2-2 x-5\end{aligned}[/tex]

Let's find f(−x), −f(x), and −f(−x) for the given function [tex]f(x)=3 x^2-2 x+5[/tex].

f(−x):

Replace x with −x in the function:

[tex]f(-x)=3(-x)^2-2(-x)+5[/tex]

Simplify this expression:

[tex]f(-x)=3 x^2+2 x+5[/tex]

−f(x):

Multiply the entire function f(x) by −1:

[tex]-f(x)=-\left(3 x^2-2 x+5\right)[/tex]

Distribute the negative sign:

[tex]-f(x)=-3 x^2+2 x-5[/tex]

−f(−x):

Replace x with −x in the function f(x) and then multiply the whole expression by −1:

[tex]-f(-x)=-\left(3(-x)^2-2(-x)+5\right)[/tex]

Simplify this expression:

[tex]-f(-x)=-\left(3 x^2+2 x+5\right)[/tex]

Distribute the negative sign:

[tex]-f(-x)=-3 x^2-2 x-5[/tex]

Question:

For the function f defined by [tex]f(x)=3 x^2-2 x+5[/tex] find f(−x),−f(x) , and −f(−x).

Answer:

  36 ft

Step-by-step explanation:

Let L represent the length of Louis's basement. The area is the product of length and width, so is ...

  A = L(L/3)

  432 = L²/3 . . . . . fill in area value

  1296 = L² . . . . . . multiply by 3

  36 = L . . . . . . . . . take the square root

The length of Louis's basement is 36 feet.

Answer:

16.11(6)

Step-by-step explanation:

967/60=16 7/60

We can model the statement "one-third the sum of eleven and [p]" as y = (1/3)(11 + p)

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have one-third the sum of eleven and [p].

We can model the given question as -

y = (1/3)(11 + p)

Therefore, we can model the statement "one-third the sum of eleven and [p]" as y = (1/3)(11 + p)

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Answer:

Hence (3, -3)   is  on the given line y = -2x + 3

Step-by-step explanation:

For a point on the Line, It must Satisfy the Equation of a line

Therefore for

[tex]y=-2x+3[/tex]

For (-2,-1)

Substitute x = - 2 and y = -1 in above equation

Left Hand Side = y

                         = -1

Right Hand Side = -2 × (-2) +3

                           = 4 +3

                           = 7

Left Hand Side ≠ Right Hand Side

Not Satisfied

Hence (-2,-1)  is NOT on the given line

For (3, -3)

Substitute x = 3 and y = -3 in above equation

Left Hand Side = y

                         = -3

Right Hand Side = -2 × (3) +3

                           = -6 +3

                           = -3

Left Hand Side = Right Hand Side

Satisfied

Hence (3, -3)   is  on the given line y = -2x + 3

For (3, 3)

Substitute x = 3 and y = 3 in above equation

Left Hand Side = y

                         = 3

Right Hand Side = -2 × (3) +3

                           = -6 +3

                           = -3

Left Hand Side ≠ Right Hand Side

Not Satisfied

Hence (3,3)  is NOT on the given line

For (-3,-9)

Substitute x = -3 and y = -9 in above equation

Left Hand Side = y

                         = -9

Right Hand Side = -2 × (-3) +3

                           = 6 +3

                           = 9

Left Hand Side ≠ Right Hand Side

Not Satisfied

Hence (-3,-9)  is NOT on the given line

Only the point (3, -3) lies on the line y = -2x + 3. None of the other points satisfy the equation.

To determine which point lies on the line y = -2x + 3, we need to substitute the coordinates of each point into the equation:

(-2, -1): Substitute x = -2 into y = -2x + 3:

y = -2(-2) + 3 = 4 + 3 = 7. Since y = -1, this point does not lie on the line.

(3, -3): Substitute x = 3 into y = -2x + 3:

y = -2(3) + 3 = -6 + 3 = -3. Since y = -3, this point lies on the line.

(3, 3): Substitute x = 3 into y = -2x + 3:

y = -2(3) + 3 = -6 + 3 = -3. Since y = 3, this point does not lie on the line.

(-3, -9): Substitute x = -3 into y = -2x + 3:

y = -2(-3) + 3 = 6 + 3 = 9. Since y = -9, this point does not lie on the line.

The only point that satisfies the equation is (3, -3).

Complete question:

Which point is on the line y = -2x + 3?

A. (-2,-1)

B. (3, -3)

C. (3, 3)

D. (-3,-9)

If you are trying to find the equation of a line:

The equation of a line is y = mx + b   [m is the slope, b is the y-intercept or the y value when x = 0 --->  (0, y)  or the point where the line crosses through the y-axis]

Since you have m = -2, plug it into the equation

y = mx + b

y = -2x + b     To find b, plug in the point they gave you (3, -7)

-7 = -2(3) + b

-7 = -6 + b      Add 6 on both sides

-1 = b               Now that you have b, plug it into the equation

y = -2x - 1

p = 32

Solution:

Given p represents the amount of air pressure in a tire.

t represents the time it takes for the tire to go flat and t = –8.

To find the value of p, if [tex]\frac{p}{t}=-4[/tex].

⇒ [tex]\frac{p}{t}=-4[/tex]

Substitute t = –8 in the above equation.

⇒ [tex]\frac{p}{-8}=-4[/tex]

Do cross multiply, we get

⇒ p = (–8) × (– 4)

⇒ p = 32

Hence, the value of p is 32 if the quotient [tex]\frac{p}{t}[/tex] is –4.

Answer:

11.25 miles/hour

Step-by-step explanation:

Recall, speed = Distance ÷ Time

We are given :

Distance = 45 miles

Time = 4 hours

Hence,

Speed = Distance ÷ Time

= 45 miles ÷ 4 hours

= 11.25 miles/hour

Answer:

d 8x+12

Step-by-step explanation:

7x+3x+5-2x+7

combine 7x+3x-2x=8x

and 5+7=12

8x+12

Answer:

Step-by-step explanation:

7x+3x-2x=8x

5+7=12

8x+12

Answer:

$158.74

Step-by-step explanation:

A sound system has a regular price of $249. Now, we have to find the total cost of it if there is a sale for 40% off and the sales tax is 6.25%.

Now, if there is 40% off on price $249, then the discounted price will be

[tex]249(1 - \frac{40}{100}) = 149.4[/tex] dollars.

Then the after-tax value of the sound system at the rate of 6.25% will be [tex]149.4(1 + \frac{6.25}{100}) = 158.74[/tex] dollars (Approximate)

(Answer)

Answer:um where is the constant

Step-by-step explanation:

The expression 'x + 9/2' involves adding a variable 'x' to the fraction 9/2. In an example situation, if you substitute x with the number 5, the result would be 9.5. Remember, x can represent any number.

The expression you provided is x + 9/2. In mathematics, this is an algebraic expression which comprises of a variable x and a fraction 9/2. It means that you're adding the x variable to the fraction 9/2. For example, if you were to substitute x with a number, let's say 5, the answer would then be 5 + 9/2 = 9.5. It's important to remember that variables can represent any number, and in this case, the variable is x.

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Answer:

 [tex]4x+6y=34\\\\4x+3y=25[/tex]

Step-by-step explanation:

Let be "x" the cost in dollars of a hamburger and "y" the cost in dollars of a soft drink.

The cost of 4 hamburguers can be represented with this expression:

[tex]4x[/tex]

And the cost of 6 soft drinks  can be represented with this expression:

[tex]6y[/tex]

Since the total cost for 4 hamburgers and 6 soft drinks is $34, you can write the following equation:

[tex]4x+6y=34[/tex]   [Equation 1]

 The following expression represents the the cost of 3 soft drinks:

[tex]3y[/tex]

According to the information given in the exercise, the total cost for 4 hamburgers and 3 soft drinks is $25. Then, the equation that represents this is:

[tex]4x+3y=25[/tex] [Equation 2]

Therefore, the Equation 1 and the Equation 2 can be used to determine the price of a hamburger and the price of a soft drink

SEE IMAGE FOR A, B, C, D REFERENCE

A- 3

B- 3

C- 6

D- 3x+6

On the board you should have 6 of the orange + tiles and 3 of the orange x tiles.

Step-by-step explanation:

-x+2y=-6

x-2y=6

x=2y+6

substitute in 2x-3y=11 gives us 2(2y+6)-3y=11

4y+12-3y=11

y=-1

-x+2(-1)=-6

-x=-4

x=4

Answer: 6

Step-by-step explanation: 12/2 because a pair is 2 people and there are 12 people in total.!

The number of different pairs of people who can have conversations at a round table with 12 people is 66. This is calculated using the combination formula C(n, 2).

The student asks about the number of different pairs of people who can have conversations at a round table with 12 people, assuming that everyone can talk to each other. The problem is a combinatorial one and can be solved by using the formula for combinations. The formula for the number of combinations of pairs from a set of n items is [tex]C(n, 2) = \frac{n! }{2! * (n - 2)!}[/tex], where n! (n factorial) is the product of all positive integers up to n, and C denotes the combination.

To find how many different pairs can have conversations, we plug in n = 12 into the combination formula:

[tex]C(12, 2) = \frac{12! }{2! * (12 - 2)!} = \frac{12 * 11}{2 * 1} = 66[/tex]

So, there are 66 different pairs of people that can have conversations at a round table with 12 people.

Answer:

For the smaller rectangle: 9 x 19.8 = 178.2

For the bigger rectangle: 27 x 10.8 = 291.6

Answer:15/10

Step-by-step explanation:

You subtract the top of the fraction by 2

Answer:

   1 5/10  or  1 1/2

Step-by-step explanation:

You seem to have an arithmetic sequence, with each term 2/10 less than the one before.

2/10 less than 1 7/10 is 1 5/10. The fraction can be reduced to 1 1/2, but you may not want to.

By rounding each brother's weight to the nearest whole number and adding these, we get an estimate of 15 pounds. The actual total weight, 15 and one eighth pounds, is close to this estimate, indicating that Lucas' claim about his brothers' weight is reasonable. This demonstrates how estimation can be used to quickly verify the validity of a claim.

Estimation is a valuable mathematical tool that can be used to assess the reasonableness of a solution. In the case of Lucas' twin baby brothers' weight, you can use rounding to estimate their total weight. Let's start by rounding each brother's weight to the nearest whole number. In this scenario, Jackson, who weighs 6 and one fourth pounds could be estimated to weigh 6 pounds, and Jeremy, who weighs 8 and seven-eighths pounds, could be estimated to weigh roughly 9 pounds.

Adding these together gives a total of 15 pounds. The actual weight of the twins, 15 and one eighth pounds, is very close to this estimation, indicating that Lucas' claim about his brothers' weight is reasonable. This approach makes effective use of estimation as a means to quickly and simply verify a given claim's feasibility.

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Answer:

5.7* 10 to the power of 4

Answer:

Step-by-step explanation:

[tex]\text{The scientific notation}:\\\\a\times10^k\\\\\text{where}\\\\1\leq a<10,\ k\in\mathbb{Z}\\\\================================[/tex]

[tex]57,000=5.7\times10000=5.7\times10^4\\\\-----------------------\\\\57000=5\underbrace{7000}_{\leftarrow4}=5\times10^4[/tex]

Answer: 4z (to the 2 power) - 13z + 3

Step-by-step explanation:

Answer:

[tex]\sqrt[3]{0.000004913}=0.017[/tex]

Step-by-step explanation:

Cubic Root

The cubic root of a number N is M, if

[tex]M^3=N[/tex]

It's usually tedious to manually compute cubic roots, but if we use some basic algebra concepts, the job is easily done.

Let's compute

[tex]M=\sqrt[3]{0.000004913}[/tex]

The argument can be expressed in scientific notation as

[tex]0.000004913= 4913\ 10^{-9}[/tex]

The power of 10 has an exact cubic root since the exponent is a multiple of 3. To find the cubic root of the mantissa, we note it's the triple product of 17, i.e.

[tex]4913=17*17*17=17^3[/tex]

Thus our number is

[tex]M=\sqrt[3]{17^3\ 10^{-9}}=17\ 10^{-3}=0.017[/tex]

We have then

[tex]\boxed{\sqrt[3]{0.000004913}=0.017}[/tex]

Answer:

Step-by-step explanation:

they are both equal

Answer: They are not parallel because the two given alternate interior angles are not congruent

Step-by-step explanation:

Final answer:

The correct solution to the equation 5x+10=24-2x is x=2, which is verified by substitution and results in an identity, confirming the solution is accurate.

Explanation:

The equation 5x+10=24-2x is a simple linear equation that can be solved by collecting like terms and isolating the variable x. Begin by adding 2x to both sides to get 7x + 10 = 24, then subtract 10 from both sides to obtain 7x = 14. Dividing both sides by 7 yields x = 2, which is the sole solution to the equation. Checking the solution, 24 - 2(2) does indeed equal 5(2) + 10, giving an identity of 20 = 20. This illustrates the solution is correct and verifies our process.

1/3 banana hgfdsedcrtvfybgunhimjnyhtbgvfdcvfbgnhmij,omhnbvdcrmjytgvg

The area of the gray portion in the room, after subtracting the area of the central linoleum from the total area of the room, is 112 sq. ft.

To calculate the area of the gray portion in the room, first subtract the area of the linoleum from the total area of the room. The area of the room is given as 12 x 16 sq. ft. and the linoleum is 8 x 10 sq. ft.. To find the total area of the room, multiply the length by the width (12 x 16 = 192 sq. ft.). Then do the same for the linoleum (8 x 10 = 80 sq. ft.). Subtracting the area of the linoleum from the total area of the room gives us the gray area (192 - 80 = 112 sq. ft.). Hence, the area of the gray portion is 112 sq. ft.

Answer:

The functions which has the same horizontal asymptote y = -3 as given in the graph are,

f(x) = [tex]2^{x} - 3[/tex]  and

f(x) = [tex]2^{(x+2)} -3[/tex]

Step-by-step explanation:

The function that is graphed has horizontal asymptote as y = -3 .

As x → -∞  f(x) → - 3  for the second and fourth function. Hence the functions which has the same horizontal asymptote y = -3 as given in the graph are,

f(x) = [tex]2^{x} - 3[/tex]  and

f(x) = [tex]2^{(x+2)} -3[/tex]