Given $a \equiv 1 \pmod{7}$, $b \equiv 2 \pmod{7}$, and $c \equiv 6 \pmod{7}$, what is the remainder when $a^{81} b^{91} c^{27}$ is divided by 7?

Answer: 5 inches

Step-by-step explanation:

Given: Volume of clay = 48 cubic inches

If we make a solid square right pyramid with a base edge a= 6 inches.

Then its base area = [tex]a^2=6^2=36\ inches^2[/tex]

we know that volume of square right pyramid=[tex]\frac{1}{3}\times\ a^2h[/tex]

Therefore, volume of square right pyramid made by all of clay=[tex]\frac{1}{3}\times\ a^2h[/tex]=48 cubic inches

[tex]\Rightarrow\frac{1}{3}\times\ (36)\times\ h=48\\\Rightarrow12h=48\\\Rightarrow\ h=4\ inches.....\text{[Divide 12 on both sides]}[/tex]

Now, slant height [tex]l=\sqrt{(\frac{a}{2})^2+h^2}[/tex]

[tex]\\\Rightarrow\ l=\sqrt{3^2+4^2}\\\Rightarrow\ l=\sqrt{9+16}\\\rightarrow\ l=\sqrt{25}\\\Rightarrow\ l=5[/tex]

The slant height of the pyramid if Helen uses all the clay=5 inches

Answer:

The correct answer would be 5 inches.

Step-by-step explanation:

Okay, so first, we find a number that is between 0 and 1.

A number that qualifies for that condition would be ½.

A property of exponents is x^(n/m) = √x m sqrt(x^n), so x^(1/2) = √x

Therefore, such expression is:

x^(1/2) = 4
Where you now solve for x.

Exponential notation is a common language that is needed in order to communicate mathematical ideas efficiently and clearly. Efficiently written repeated multiplication was the reason that this notation was developed.

An example of this is the division of cells that causes growth to occur in living organisms. A single type of cell is divided 2 times in an hour, therefore in 12 hours, the cell will divide into 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 time, or as efficiently written, 2^12.

2. The Graph Contains The Point (5, 12)

Remember that in a linear function of the form [tex]y=mx+b[/tex], [tex]m[/tex] is the slope/rate of change of the line and [tex]b[/tex] is the y-intercept.

From our equation we can infer that [tex]b=12[/tex], so the y-intercept of our graph is 12 units above the origin on the point (0, 12). Therefore, choice 2 correctly describe the graph of y = 5x + 12

We can also infer that [tex]m=5[/tex], so the slope of our line is 5, which is constant, so our line has a constant rate of change. Also, since every integer can be written as a fraction with denominator 1, we can write our slope as [tex]m=\frac{5}{1}[/tex]. Therefore, choices 1 and 2 correctly describe the graph of y = 5x + 12.

Now, remember that any point on the plane has coordinates [tex](x,y)[/tex], so, to check if a point is on a line, we just need to replace the [tex]x[/tex] and [tex]y[/tex] values in the line equation and check if the equation holds. Our point is (5, 12), so x = 5 and y = 12. Lets replace the values in our line:

[tex]y=5x+12[/tex]

[tex]12=5(5)+12[/tex]

[tex]12=25+12[/tex]

[tex]12\neq 37[/tex]

Since the equation equation doesn't hold (12 is not equal 37), we can conclude that the graph doesn't contain the point (5, 12). Therefore, choice 2 does NOT correctly describe the graph y = 5x +12.

Answer:

The graph contains the point (5,12)

I got it right on t t m

Answer:

230+m_<500  the line is meant to be under the sighn btw

Step-by-step explanation:i got it right on edge 2021

To determine how many more minutes Tom can use without exceeding his limit, we use the inequality X ≤ 270, which indicates that Tom can use up to 270 additional minutes.

To determine how many more minutes Tom can use this month without exceeding a 500-minute limit, given that he has already used 230 minutes. To solve this, we let X represent the additional minutes Tom can use. Since he has already used 230 minutes, we form the inequality 230 + X ≤ 500 to ensure that the total does not surpass the 500-minute limit. Simplifying this inequality, we subtract 230 from both sides to get X ≤ 270. Therefore, Tom can use up to 270 more minutes without incurring extra charges.

The total number of people who have received the e-mail, not including Kris, after it has been forwarded 2 more times is 5 + 5^2 + 5^3.

The expression that shows the total number of people who have received the e-mail, not including Kris, after it has been forwarded 2 more times is 5 + 5^2 + 5^3 (option C).

To find the total number of people who have received the e-mail, you sum up the number of recipients at each stage: 5 + 25 + 125 = 155. Therefore, the expression 5 + 5^2 + 5^3 represents the total number of people who have received the e-mail, not including Kris.

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6) answer is B , random sampling produces a representative sample

7)  0.1 = 10% so the answer is A, he saves 10% of his income

why are people down voting the answer above me? Anyways, the answer is A. linear constant

This is because of the fact that a linear constant is a straight horizontal line that stays, as it says, constant, that is until you go to the next interval.

Consider a real number in two dimensional plane that X axis and Y axis having ordered pair : P(x,y) or (3,4).

To find it's absolute value we will find it's Distance from origin.

As Coordinate of Origin = (0,0)

Absolute Value of OP = [tex]\left | OP \right |[/tex]

     =  [tex]\sqrt{(0-x)^2+(0-y)^2}=\sqrt {x^2+y^2}[/tex]

    If the point is Q(3,4)

[tex]\left | OQ \right |=\sqrt{3^2+4^2}=\sqrt{5^2}=5[/tex]

In case of a complex number :

Z = a + bi , we consider two axes Real Axis and Imaginary Axis.

We represent Z that is (a,b) in the same way that we represent point in two dimensional plane.

To find it's absolute value , we will find it's distance from origin.

[tex]\left | Z \right |= \sqrt{a^2+b^2}[/tex]

If [tex]Z_{1}[/tex] = 6 + 8 i

[tex]\left | Z_{1}\right |=\sqrt{6^2+8^2}=\sqrt{36+64}=\sqrt{100}=10[/tex]

The required solution of the system is (x, y) = (9, 23). Option D is correct.

Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate of the y is called ordinate.

Here,
To solve the system of equations using the substitution method, we substitute x = 9 into the first equation:

y = 3(9) - 4

y = 27 - 4

y = 23

Therefore, the solution of the system is (x, y) = (9, 23).

So, the correct answer is option D, (9, 23).

Learn more about coordinate here:

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