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Leto [7]
3 years ago
15

Rachel tutors English. for each hour that she tutors, she earns 50 dollars. Let E be her earnings (in dollars) after tutoring fo

r H hours. Write an equation relating E to H. Then use this equation to find Rachel’s earnings after tutoring for 19 hours
Mathematics
1 answer:
n200080 [17]3 years ago
4 0

Answer:

a. E = 50 H b. 950 dollars

Step-by-step explanation:

a. Since Rachel tutors English for 50 dollars for each hours, her rate is 50 dollar per hour. If she tutors for time, H hours, Her earning E = rate × time = 50 × H

E = 50H.

b. If Rachel's earnings after tutoring for 19 hours is gotten by substituting H = 19 into the equation for the earnings, E.

So, E = 50H

E = 50 × 19

E = 950 dollars.

So, Rachel's earnings after 19 hours is 950 dollars.

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​$9500 is​ invested, part of it at 12​% and part of it at 9​%. For a certain​ year, the total yield is ​$1032.00. How much was
alina1380 [7]
Let's say the quantities are "a" and "b"
so... whatever "a" and "b" are, they add up to 9,500, thus

a + b = 9,500

now, "a" was invested at 12%, or 12/100
it yielded some amount, actually 12% of a, or 12/100 * a or 0.12a

the "b" amount was invested at 9%, or 9/100
it yielded 9% of b, or 9/100 * b or 0.09b

whatever 0.12a is, and 0.09b is, their sum or total yield was 1032
thus
0.12a + 0.09b = 1032

thus     \bf \begin{cases}
a+b=9,500\implies \boxed{b}=9,500-a\\\\
0.12a+0.09b=1032\\
--------------\\
0.12a+0.09(\boxed{9,500-a})=1032
\end{cases}

solve for "a" to see how much was invested at 12%

what about "b"? well, b = 9500 - a
4 0
3 years ago
10th grade volume of prisms
fredd [130]
The formula for volume of prism: \frac{1}{2} * <span>length * width * height.
0.5 * 4 * 6 = </span>12

To work out length divide area by the triangle size:
120 / 12 = 10,
So the answer is 10mm.

Hope this helps.
5 0
3 years ago
The y-intercept of the function f(x) = x2+3x+2
sveta [45]

Question

The y-intercept of the function f(x) = x2+3x+2

Answer:

4 + 3x

5 0
3 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
Find the number to add to x^2-18x
pentagon [3]

Answer:

A. add 81; (x-9)^2

Step-by-step explanation:

The perfect square formula

(a-b)^2=a^2-2ab+b^2

Rewrite expression x^2-18x as follows:

x^2-2\cdot 9\cdot x

So, to form a perfect square, +9^2 is missed.

When we add 9^2=81, we will get

x^2-2\cdot 9\cdot x+9^2=(x-9)^2

4 0
3 years ago
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