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Anuta_ua [19.1K]
3 years ago
13

Which equation can be used to solve for x in the following diagram? Choose 1 answer:

Mathematics
1 answer:
quester [9]3 years ago
3 0

Answer:

I think the answer might be D. 2x+4x=150

Step-by-step explanation:

Hope this helps!

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You have 60 waffles in all with a serving size of 2 waffles, there are 4 people, how many days will the waffles last. Show equat
Alja [10]
30÷2 =60
15 days 4×7=
5 0
3 years ago
Alex scored 98,72, and 87 on his first three math test. What must he score on the next test to have an average of at least 86 (P
ss7ja [257]

Answer:

\huge\boxed{\text{At least an } 87\%}

Step-by-step explanation:

In order to find what score Alex must earn to have an average of 86 on all his tests, we need to first note what the formula to find the average of a data set is.

\displaystyle \frac{x_1+x_2+...x_n}{n}

What the formula means is that we have to add up all the values then divide by the total number of values.

Let's represent our unknown number as x.

\displaystyle \frac{98+72+87+x}{4} \geq 86 (since we want AT LEAST an 86).

Let's solve this inequality for x.

  • \frac{98+72+87+x}{4} \cdot 4 \geq 86 \cdot 4
  • 98+72+87+x \geq 344
  • 257 + x \geq 344
  • 257 + x  - 257 \geq 344 - 257
  • x \geq 87

So, Alex must score at least an 87% on his next quiz to have an average of 86%.

Hope this helped!

8 0
2 years ago
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
Help me I don't know what it is.
kotegsom [21]

Answer:

a is the correct answer

Step-by-step explanation:

-6-(-3)

-6+3

-3

8 0
2 years ago
Which sequence of transformations proves that shape I is similar to shape II?
4vir4ik [10]
Note that if you simply reflected it and dilated it, it would be too far to the left

note that the distances bewteen the axises in image 1 were 1 and 3in image 3,the distances are 2 and 6
seems to be 3 times
so it's the 90 counterclockwise rotation and dilation by scale factor of 3
answer is last one

4 0
3 years ago
Read 2 more answers
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