I need help for this.A line has gradient 6 and passes through the points with coordinates (-1,6) and (7,a). Find the value of a

Answers

Answer 1

Answer: $General\ formula\ for\ line:\n\ny=ax+b,\ where\ a-gradient\n\ny=6x+b\n\nSubstitute\ point\ (-1,6):\n\n6=6\cdot(-1)+b\n6=-6+b\nb=6+6\nb=12\n\ny=6x+12\n\nSubstitute\ point\ (7,a)\n\na=6\cdot7+12\na=42+12=54$

Answer 2

Answer: We can also see it this way:

Noting that point in the form (x, y)
(-1, 6) and (7, a) . x1 = -1, y1 = 6, x2 = 7, y2 = a
Gradient , m = (y2- y1) / (x2 - x1). m =6.
Substituting:

6 = (a - 6) / (7 - -1)
6 = (a -6) / (7+1)
6 = (a -6) /8 Cross Multiplying
48 = a -6.
48 +6 = a.
54 = a.
Therefore a = 54.
I hope this helps.

What is a square pyramid?

A pyramid with base as square is said square pyramid

How to calculate Surface area?

Formula to calculate surface area= $A=a^(2) +2a\sqrt{(a^(2) )/(4) +h^(2) }$

where a =4 ,h=7

= $4^(2) +2(4)\sqrt{(4^(2) )/(4)+7^(2) }$

= 16+ $8$ $\sqrt{(4)/(1 ) +49$

=16+8*7.28

=16+58.24

= $74.24 inches^(2)$

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Final answer:

The surface area of the right square pyramid is calculated by adding the area of the square base (16 square inches) and the combined area of the triangular faces (56 square inches). Hence, the total surface area of the pyramid is 72 square inches.

Explanation:

To calculate the surface area of a square pyramid, you need to calculate the area of the base and the area of the four triangular sides. Firstly, the area of the square base is found using the formula A = s², where s is the side length. In this case, the base area (A) would be 4² = 16 square inches.

Secondly, to find the area of a single triangular face you use the formula A = 0.5*base*height, in this case, the base is the same as the square base and the height corresponds to the slant height (7 inches). Thus, the area for one triangle would be 0.5*4*7 = 14 square inches. As the pyramid has four equal triangular faces, to find the total area of these faces you would multiply 14 by 4 giving 56 square inches.

Finally, to find the total surface area of the pyramid, you add the base area and the area of the triangular faces together, which results in 16 + 56 = 72 square inches.

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Simplify this expression.

8.9 – 1.4x + (–6.5x) + 3.4

Answers

Answer:

-7.9x+12.3

Step-by-step explanation:

8.9 – 1.4x + (–6.5x) + 3.4

8.9-1.4x-6.5x+3.4

8.9-7.9x+3.4

-7.9x+8.9+3.4

-7.9x+12.3

Twenty-two is what percent of 55?A.
22%

B.
40%

C.
250%

D.
50%

Answers

Answer:

Option B is correct.

Twenty-two is 40 percent of 55

Step-by-step explanation:

Let x be the number.

As per the statement:

Twenty-two is x percent of 55

Solve for x:

Twenty-two is x percent of 55

"of" means multiply

⇒ $22 = (x)/(100) * 55$

Divide both sides by 55 we get;

$(22)/(55) = (x)/(100)$

Simplify:

$(2)/(5) = (x)/(100)$

Multiply both sides by 100 we have;l

$x = (2)/(5) * 100$

Simplify:

x = 40%

Therefore, Twenty-two is 40 percent of 55

To find the percentage
that 22 is for the actual number 55 = (22/55) * 100
      = (2/5) * 100
      = 2 * 20
      = 40 percent
So the correct option among all the options given in the question is option "B".Most of the information’s that are required for solving thisproblem is already given in the question. I hope the procedure for solving theproblem is also clear for you to understand. In future you can always use thismethod for solving similar problems.

Solve:-10²
23³
14³
52²

I don't know how to do this. please Help! Thanks in advance.

Answers

10^2 = 10 × 10 = 100

23^2 = 23 × 23 × 23 = 12167

14^3 = 14 × 14 × 14 = 2744

52^2 = 52 × 52 = 2704

These are exponents. To solve d exponents we will multiply d base itself how many times it says to in d exponent.

a^b

a = base
b = exponent

10²

10 = base
2 = exponent

10² = 10 × 10 = 100
10² = 100

23³

23 = base
3 = exponent

23² = 23 × 23 × 23 = 12167
23² = 12167

14³

14 = base
3 = exponent

14³ = 14 × 14 × 14 = 2744
14³ = 2744

52²

52 = base
2 = exponent

52² = 52 × 52 = 2704
52² = 2704

So:-

10² = 100
23² = 12167
14³ = 2744
52² = 2704

Hope I helped ya!! xD

Instead of using the values {1,2,3,4,5,6} on dice, suppose a pair of dice have the following: {1,2,2,3,3,4} on one die and {1,3,4,5,6,8} on the other. Find the probability of rolling a sum of 2 with these dice

Answers

Step-by-step explanation:

Sample space, S = {(1,1),(1,3),(1,4),(1,5),(1,6),(1,8),(2,1),(2,3),(2,4),(2,5),(2,6),(2,8),(2,1),(2,3),(2,4),(2,5),(2,6),(2,8),(3,1),(3,3),(3,4),(3,5),(3,6),(3,8),(3,1),(3,3),(3,4),(3,5),(3,6),(3,8),(4,1),(4,3),(4,4),(4,5),(4,6),(4,8)}

These dice will give a sum of 2 with N={(1,1)}, which only has 1 combination

Thus, the probability of rolling a sum of 2 with these dice is

$(1)/(36)$

Answer:

1/36

Step-by-step explanation:

it was correct

I have a deck of 54 cards, and I deal all of the cards to x players, with each player getting y cards. If x is at least 2 and y is at least 5, then how many possible values of x are there?