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Furkat [3]
3 years ago
6

(c) Solve 3(22-5) = 4z + 11 Show clear algebraic working.

Mathematics
1 answer:
antoniya [11.8K]3 years ago
6 0

Answer:

z=10

Step-by-step explanation:

We have to find the value of z.

(3×22)-(3×5)= 66-15= 51

Now,

51=4z+11

4z=51-11

z=40/4

z=10

Hope this helps you :)

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You are dealt two cards successively without replacement from a standard deck of 52 playing cards. Find the probability that the
kondaur [170]

Answer:

\frac{4}{52} \times \frac{4}{51}  = \frac{16}{2652} = 0.00603 = 0.603\%

Step-by-step explanation:

There are 52 cards in a standard deck, and there are 4 suits for each card. Therefore there are 4 twos and 4 tens.

At first we have 52 cards to choose from, and we need to get 1 of the 4 twos, therefore the probability is just

\frac{4}{52}

After we've chosen a two, we need to choose one of the 4 tens. But remember that we're now choosing out of a deck of just 51 cards, since one card was removed. Therefore the probability is

\frac{4}{51}

Now to get the total probability we need to multiply the two probabilities together

\frac{4}{52} \times \frac{4}{51}  = \frac{16}{2652} = 0.00603 = 0.603\%

5 0
4 years ago
The graph of y = x^2 -3 is translated in 4 units to the left of the graph to give the graph A
Vedmedyk [2.9K]

Answer:

a) b = 8, c = 13

b) The equation of graph B is y = -x² + 3

Step-by-step explanation:

* Let us talk about the transformation

  • If the function f(x) reflected across the x-axis, then the new  function g(x) = - f(x)
  • If the function f(x) reflected across the y-axis, then the new  function g(x) = f(-x)
  • If the function f(x) translated horizontally to the right  by h units, then the new function g(x) = f(x - h)
  • If the function f(x) translated horizontally to the left  by h units, then the new function g(x) = f(x + h)

In the given question

∵ y = x² - 3

∵ The graph is translated 4 units to the left

→ That means substitute x by x + 4 as 4th rule above

∴ y = (x + 4)² - 3

→ Solve the bracket to put it in the form of y = ax² + bx + c

∵ (x + 4)² = (x + 4)(x + 4) = (x)(x) + (x)(4) + (4)(x) + (4)(4)

∴ (x + 4)² = x² + 4x + 4x + 16

→ Add the like terms

∴ (x + 4)² = x² + 8x + 16

→ Substitute it in the y above

∴ y = x² + 8x + 16 - 3

→ Add the like terms

∴ y = x² + 8x + 13

∴ b = 8 and c = 13

a) b = 8, c = 13

∵ The graph A is reflected in the x-axis

→ That means y will change to -y as 1st rule above

∴ -y = (x² - 3)

→ Multiply both sides by -1 to make y positive

∴ y = -(x² - 3)

→ Multiply the bracket by the negative sign

∴ y = -x² + 3

b) The equation of graph B is y = -x² + 3

4 0
3 years ago
Which property can be justified using the ratios in triangle XYZ
Kruka [31]
This is C. cos Z = sin (90 - Y)
5 0
3 years ago
Read 2 more answers
Asa's most recent credit card statement had a balance of $2,622.77. The minimum payment warning box indicates that it will take
Sergeeva-Olga [200]

Answer:

12%

Step-by-step explanation:

In order to calculate this we first need to find the total that she would pay if she were to choose either of these options. We do this by multiplying the number of years it would take to pay off the loan by the 12 months in a year, and then we multiply this product by the monthly payment like so...

Minimum Payment:

(12 * 12) * 28 = $4,032

$100 a month payment:

(12* 3) * 100 = $3,600

Now that we have both we need to divide the minimum payment total by the $100 a month payment total to get the percentage increase in decimal form

$4,032 / $3,600 = 1.12

Now we subtract 1 and multiply by 100 to turn this decimal into a percentage

(1.12 - 1) * 100 = 12%

Finally, we can see that if Asa only pays the minimum then she would be paying a 12% increase as opposed to paying the $100 a month

5 0
3 years ago
Simplify: −2(5) + 2 =
elena-14-01-66 [18.8K]

Answer:

-8

Step-by-step explanation:

-2(5) + 2

-10 + 2

-8

4 0
3 years ago
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