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klio [65]
3 years ago
5

Let $f(x) = x^2 + 4x - 31$. for what value of $a$ is there exactly one real value of $x$ such that $f(x) = a$?

Mathematics
1 answer:
enot [183]3 years ago
7 0

To solve for this, we need to find for the value of x when the 1st derivative of the equation is equal to zero (or at the extrema point).

So what we have to do first is to derive the given equation:

f (x) = x^2 + 4 x – 31

 

Taking the first derivative f’ (x):

f’ (x) = 2 x + 4

 

Setting f’ (x) = 0 and find for x:

2 x + 4 = 0

x = - 2

 

Therefore the value of a is:

a = f (-2)

a = (-2)^2 + 4 (-2) – 31

a = 4 – 8 – 31

a = - 35

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WILL GIVE BRAINIEST AND POINTS :
crimeas [40]

Answer:

BE = FC = 3 inches, EF = 2 inches

Step-by-step explanation:

The sum of angles A and D is 180°, so the sum of their half-angles is 90°. That is, half of A plus half of B add to 90°, so the bisector from B intersects AE at a right angle. Call that point of intersection X.

Then angle ABX = angle EBX, so triangle ABX is congruent to triangle EBX. Sides AB and BE are corresponding sides of congruent triangles.

The same argument applies to sides DC and CF.

Thus we have BE = CF = 3 inches, and EF is the left-over distance, 2 inches.

7 0
3 years ago
David has a garden with dimension 11 feet long x 9 feet wide. he wants to enlarge the garden to an area of 126. How much farther
kipiarov [429]
Length = 11
Width = 9
Area we need = 126
So Area = length * width
126 = 11 * 9
Now.. this is obviously wrong.. they want us to find the correct length..
126 = L * 9
126/9 = L
L = 14
Now since they ask about how much farther you need to extend, take the final and subtract from the original
14 - 11 = 3
Answer is 3.
7 0
3 years ago
I need help on number 22
galben [10]

Tom : 22/10= 2.2  Ian: 18/9= 2  Tom has higher percentage

7 0
2 years ago
Read 2 more answers
The ratio of collectible coins Juanita owns to coins that Elia owns is 3:1. Elia has 32 coins. How will the ratio of Juanita’s c
yaroslaw [1]
Hi there Maebe, since the ratio is 3:1 your answer is 96.

The ratio 3:1 is just saying Juanita has 3 times whatever Elita has. So, Elita’s 32 times 3 equals 96. :) I hope I’ve helped you. Please give me feedback if you need more help understanding!
7 0
2 years ago
Which ratio would help find the distance the person is from the flag pole ¨X¨ if the angle is elevation of 30 degrees.
WINSTONCH [101]

Answer:

There are three major trignometric ratios in mathematics and they are:

sine(sin), cosine(cos) and tangent(tan). A popular acronym is used in recalling the formula for each ratio and it is: SOH-CAH-TOA.

Sine(x) = Opp/Hyp

Cosine(x) = Adj/Hyp

Tangent(x) = Opp/Adj

Now, the Hyp is the hypothenus of the triangle and it is the side opposite to angle 90. The opposite and adjacent is kind of relative depending on the angle been considered. For this case, we are considering angle 30 which the opposite side is 60 and the remaining side becomes the adjacent

Step-by-step explanation:

tan 30 = 60/x

5 0
2 years ago
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