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amm1812
2 years ago
15

In ADEF, DE = 25 cm, EF = 17 cm, and DF -- 20 cm Which angle in the triangle is the smallest?

Mathematics
1 answer:
Alex777 [14]2 years ago
5 0

Answer:

angle FBE

Step-by-step explanation:

By using the formula, the shortest angle is facing the shortest side

so the shortest angle is angle FBE

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You are making a lot of cookies and buy 12 bags of chocolate chips, which are $1.89 per bag
Liono4ka [1.6K]

Answer:

$22.68

Step-by-step explanation:

5 0
3 years ago
⎧
d1i1m1o1n [39]

<u>Given</u>:

The given expression to find the nth term of the sequence is d(n)=d(n-1) \cdot (-5)

The first term of the sequence is d(1)=8

We need to determine the third term of the sequence.

<u>Second term:</u>

The second term of the sequence can be determined by substituting n = 2 in the nth term of the sequence.

Thus, we have;

d(2)=d(2-1) \cdot (-5)

d(2)=d(1) \cdot (-5)

d(2)=8 \cdot (-5)

d(2)=-40

Thus, the second term of the sequence is -40.

<u>Third term:</u>

The third term of the sequence can be determined by substituting n = 3 in the nth term of the sequence.

Thus, we have;

d(3)=d(3-1) \cdot (-5)

d(3)=-40 \cdot (-5)

d(3)=120

Thus, the third term of the sequence is 120.

7 0
3 years ago
Read 2 more answers
A firm produces 16,200 units at a total cost of $37,585.60. Find the cost per unit to the nearest cent.
Julli [10]
There are a total of 16 200 units with a total costs of 37 585.60 dollars. Now, Given with the choices for the answer, let's find out which one is correct. To be able to get the answer, simply divide the total costs, with the total number of units.  => 37 585.60 dollars  / 16 200 units  => 2.3201 dollars per unit.Next, we need to round this cents to the nearest given options.Since the number next to hundredths is less than 5 , the let's round it to : => 2.32. - this is the correct answer.<span>
</span>
3 0
2 years ago
Please help me i really need help please
lesya692 [45]

Answer:A?

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
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
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