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kozerog [31]
3 years ago
12

E is the midpoint of Df, DE=2x+4, and EF=3x-1. Find all segment lengths

Mathematics
1 answer:
sertanlavr [38]3 years ago
6 0
If E is the midpoint, DE and EF are equivalent.
2x+4=3x-1
4=x-1
5=x

Plug the value of x in
2(5)+4
14

3(5)-1
14

14+14=28

Final answer: DE=14, EF=14, DF= 28
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15. Rewrite the given functions in
Lisa [10]

15. The vertex form of f(x) = x² + 8x - 10 is f(x) = (x + 4)² - 26

17. The standard form of g(x) = (x + 3)² - 4 is g(x) = x² + 6x + 5

Step-by-step explanation:

Any quadratic function has:

1. A vertex form form f(x) = a(x - h)² + k, where (h , k) are the

   coordinates of its vertex point

2. A standard form g(x) = ax² + bx + c, where a , b , c are constant and

   a is the coefficient of x², b is the coefficient of x and c is the

    y-intercept

3. the x-coordinate of the vertex point h = \frac{-b}{2a} and

    k = f(h)

15.

∵ f(x) = x² + 8x - 10

∴ a = 1 and b = 8

∵ h = \frac{-b}{2a}

∴ h = \frac{-8}{2(1)}=-4

∴ h = -4

∵ k = f(h)

∴ k = f(-4)

- Substitute x by -4 in f(x)

∴ k = (-4)² + 8(-4) - 10

∴ k = 16 - 32 - 10

∴ k = -26

∴ f(x) = (x - -4)² + (-26)

∴ f(x) = (x + 4)² - 26

The vertex form of f(x) = x² + 8x - 10 is f(x) = (x + 4)² - 26

17.

∵ g(x) = (x + 3)² - 4

- Lets solve the power 2 of the bracket:

 (1st + 2nd)² = (1st)(1st) + 2(1st)(2nd) + (2nd)(2nd)

∵ (x + 3)² = (x)(x) + 2(x)(3) + (3)(3)

∴ (x + 3)² = x² + 6x + 9

∴ (x + 3)² - 4 = (x² + 6x + 9) - 4

∵ 9 - 4 = 5

∴ (x + 3)² - 4 = x² + 6x + 5

The standard form of g(x) = (x + 3)² - 4 is g(x) = x² + 6x + 5

Learn more:

You can learn more about the vertex form of quadratic function in brainly.com/question/9390381

#LearnwithBrainly

4 0
3 years ago
Point (a, b) is transformed by the rule ​(a, b−4)​ .
Tanzania [10]

I really think the answer is C


7 0
3 years ago
If triangle STU is congruent to triangle VWX, which statement is not true?
Svetach [21]
If triangles are congruent then, their corresponding sides and angles should have the same measurement. From the given, STU is congruent to VWX, angle S, T, U should be congruent to angles V, W, and X, respectively. From the choices, the answer should be letter D. because U and V do not appear in the same order from both names. 
4 0
3 years ago
Hello can someone please help me with this
HACTEHA [7]

Answer:

(c) is closest to the correct answer

Step-by-step explanation:

The question answers itself: "Mr. Jones's prescription calls for 1.04 tablets PER DAY, thus the amount of tablets Mr. Jones should talk daily are 1.04. Since none of the answers in the answer set have '1.04' in them, we have to use some basic logic:

The list of answers are, a) 1.25. We can rule that one out as it is not 1.04. We can also rule out b) and d) using the same logic. Thus, by process of elimination, we are left with c) 1 O. Not only is 1.0 (or just 1) the closest number to the actual amount (1.04) but it also makes the most sense, as one cannot take .04 (or 4/100ths) of a pill.

4 0
2 years ago
Can someone Solve this math problem for me I'm having some trouble.<br><br>27×26+98÷25?<br><br>​
AlladinOne [14]

Answer:

<u>7</u><u>0</u><u>5</u><u>.</u><u>9</u><u>2</u><u> </u>

Step-by-step explanation:

hope it's help

#MASTER GROUP

# FIRST MASTER

<u>#</u><u> </u><u>PHILIPPINES</u>

5 0
3 years ago
Read 2 more answers
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