1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
mixer [17]
2 years ago
6

Please help me with my pre-algebra ASAP

Mathematics
1 answer:
dexar [7]2 years ago
8 0
The sum of the measures of two complementary angles is 90°. To put it another way, m∠P + m∠Q = 90°.

So, we can substitute the given values of the angles into this equation.

(52)+(3x+2)=90 \\  \\ 3x+54=90  \\  \\ 3x=36  \\  \\ x=12

Then, to find m∠Q, we plug in 12 for x for the original expression of Q to get 3(12)+2=38.
You might be interested in
2y+3x² +5+y+2x+x²+2 what are the coefficients?
saw5 [17]

Answer: 200

The quadratic function f(x) = a(x - h)2 + k, a not equal to zero, is said to be in standard form. If a is positive, the graph opens upward, and if a is negative, then it opens downward. The line of symmetry is the vertical line x = h, and the vertex is the point (h,k).

Any quadratic function can be rewritten in standard form by completing the square. (See the section on solving equations algebraically to review completing the square.) The steps that we use in this section for completing the square will look a little different, because our chief goal here is not solving an equation.

Note that when a quadratic function is in standard form it is also easy to find its zeros by the square root principle.

Example 3.

Write the function f(x) = x2 - 6x + 7 in standard form. Sketch the graph of f and find its zeros and vertex.

f(x) = x2 - 6x + 7.

= (x2 - 6x )+ 7.        Group the x2 and x terms and then complete the square on these terms.

= (x2 - 6x + 9 - 9) + 7.

We need to add 9 because it is the square of one half the coefficient of x, (-6/2)2 = 9. When we were solving an equation we simply added 9 to both sides of the equation. In this setting we add and subtract 9 so that we do not change the function.

= (x2 - 6x + 9) - 9 + 7. We see that x2 - 6x + 9 is a perfect square, namely (x - 3)2.

f(x) = (x - 3)2 - 2. This is standard form.

From this result, one easily finds the vertex of the graph of f is (3, -2).

To find the zeros of f, we set f equal to 0 and solve for x.

(x - 3)2 - 2 = 0.

(x - 3)2 = 2.

(x - 3) = ± sqrt(2).

x = 3 ± sqrt(2).

To sketch the graph of f we shift the graph of y = x2 three units to the right and two units down.

If the coefficient of x2 is not 1, then we must factor this coefficient from the x2 and x terms before proceeding.

Example 4.

Write f(x) = -2x2 + 2x + 3 in standard form and find the vertex of the graph of f.

f(x) = -2x2 + 2x + 3.

= (-2x2 + 2x) + 3.

= -2(x2 - x) + 3.

= -2(x2 - x + 1/4 - 1/4) + 3.

We add and subtract 1/4, because (-1/2)2 = 1/4, and -1 is the coefficient of x.

= -2(x2 - x + 1/4) -2(-1/4) + 3.

Note that everything in the parentheses is multiplied by -2, so when we remove -1/4 from the parentheses, we must multiply it by -2.

= -2(x - 1/2)2 + 1/2 + 3.

= -2(x - 1/2)2 + 7/2.

The vertex is the point (1/2, 7/2). Since the graph opens downward (-2 < 0), the vertex is the highest point on the graph.

Exercise 2:

Write f(x) = 3x2 + 12x + 8 in standard form. Sketch the graph of f ,find its vertex, and find the zeros of f. Answer

Alternate method of finding the vertex

In some cases completing the square is not the easiest way to find the vertex of a parabola. If the graph of a quadratic function has two x-intercepts, then the line of symmetry is the vertical line through the midpoint of the x-intercepts.

The x-intercepts of the graph above are at -5 and 3. The line of symmetry goes through -1, which is the average of -5 and 3. (-5 + 3)/2 = -2/2 = -1. Once we know that the line of symmetry is x = -1, then we know the first coordinate of the vertex is -1. The second coordinate of the vertex can be found by evaluating the function at x = -1.

Example 5.

Find the vertex of the graph of f(x) = (x + 9)(x - 5).

Since the formula for f is factored, it is easy to find the zeros: -9 and 5.

The average of the zeros is (-9 + 5)/2 = -4/2 = -2. So, the line of symmetry is x = -2 and the first coordinate of the vertex is -2.

The second coordinate of the vertex is f(-2) = (-2 + 9)(-2 - 5) = 7*(-7) = -49.

Therefore, the vertex of the graph of f is (-2, -49).

8 0
2 years ago
-36y=x^2 The directrix of the parabola is:
Aleksandr-060686 [28]
Here, the equation of parabola is: (-36y)=x^2
The standard form of parabola is:

(X-h)^2=4p(y-k).
According to given equation, vertex = (0,0) and p = -9
This a vertical parabola opening down, because p = -9 here.
Therefore ditectrix will be y= -9
6 0
3 years ago
The population of algae in an
mezya [45]

The equation is y = 20(1.40)^x

where x is the number of days and y is the future amount after x days go by

The 1.40 is from the fact that 1+r = 1+0.40 = 1.40, where r is the decimal form of 40%, so r = 0.40

-----------------------------

Plug in x = 7 to get

y = 20(1.40)^x

y = 20(1.40)^7

y = 210.827008

y = 211

We round to the nearest whole number since it doesn't make much sense to have a fractional portion of an algae. After 7 days, there are about <u>211</u> algae.

5 0
3 years ago
Brad has two lengths of copper pipe to fit together.one has a length of 2 5/12 and the other has a length of 3 7/12 how many fee
pochemuha
6 feet of pipe!!!!!!!!!
8 0
3 years ago
Harry owns a car dealership. During a sale one week, he sold 8 small cars out of every 11 cars he sold. Harry sold a total of 33
Cerrena [4.2K]

Answer:

24

Step-by-step explanation:

6 0
3 years ago
Other questions:
  • There are only a few roller coasters in the world whose path takes them underground. Suppose a portion of the roller coaster can
    14·1 answer
  • PLEASE I NEED HELP :(
    13·1 answer
  • If f(x)=3x+5/x, what is f9a+2)<br><br> A. 3(a+2)+8/a+2<br> B. 3(f(a))+5/f(a)+2<br> C. 3a+5/a+2
    12·2 answers
  • If the range of the coordinate transformation f(x, y) = (-2x,-3y +1) is (4, -2), (2,-5),(-6,4), what
    11·1 answer
  • What is the domain of this function. (Could someone explain it too? I wanna be able to do it myself as well)
    12·1 answer
  • What is the number between 145.809 and 144.809?
    10·1 answer
  • Miranda bought a shirt for 36.99 dollar but it was for 33 percent off what is the original price?
    11·1 answer
  • Examples of both data organization and analysis
    11·1 answer
  • List a few factors of 24?
    7·1 answer
  • What is the typical number of payments that can be made toward paying off a single payment loan?
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!