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Westkost [7]
3 years ago
7

Please help ♡♡♡♡♡♡♡♡♡​

Mathematics
1 answer:
zhannawk [14.2K]3 years ago
7 0

Answer:

71°

Step-by-step explanation:

BDH is a triangle (as seen on figure)

<BDH + <DBH = <DHE ( Sum of two interior angles of a triangle is equal to the opposite exterior angle)

40° + 31° = X

X = 71°

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What is the domain and range of the function y = 2x2 - 4x - 10?
11111nata11111 [884]

Answer:

Step-by-step explanation:

The domain of all polynomials is all real numbers.  To find the range, let's solve that quadratic for its vertex.  We will do this by completing the square.  To begin, set the quadratic equal to 0 and then move the -10 over by addition. The first rule is that the leading coefficient has to be a 1; ours is a 2 so we factor it out.  That gives us:

2(x^2-2x)=10

The second rule is to take half the linear term, square it, and add it to both sides.  Our linear term is 2 (from the -2x).  Half of 2 is 1, and 1 squared is 1.  So we add 1 into the parenthesis on the left.  BUT we cannot ignore the 2 sitting out front of the parenthesis.  It is a multiplier.  That means that we didn't just add in a 1, we added in a 2 * 1 = 2.  So we add 2 to the right as well, giving us now:

2(x^2-2x+1)=10+2

The reason we complete the square (other than as a means of factoring) is to get a quadratic into vertex form.  Completing the square gives us a perfect square binomial on the left.

x^2-2x+1=(x-1)^2 and on the right we will just add 10 and 2:

2(x-1)^2=12

Now we move the 12 back over by subtracting and set the quadratic back to equal y:

2(x-1)^2-12=y

From this vertex form we can see that the vertex of the parabola sits at (1,-12).  This tells us that the absolute lowest point of the parabola (since it is positive it opens upwards) is -12.  Therefore, the range is R={y|y ≥ -12}

4 0
3 years ago
A car, purchased for $20,000, loses 14% of its value in the first year. What is the car worth after one year?
OLga [1]
The car is worth 17,200.
20,000x .14=2800
20,000-2,800=17,200.
7 0
3 years ago
What is the inverse of this function
just olya [345]
G(x) = (25 - x)/5     First lets call g(x) by its other name - y

y = (25 - x)/5         Now switch the x and y

x = (25 - y)/5        Solve for y which is now the inverse - call this g^{-1}(x)

5x = 25 - y
y = 25 - 5x      this is the inverse so g^{-1}(x) = 25 - 5x
6 0
3 years ago
Order the percents,decimals and fractions from ​least to greatest​. Put your answer in ​percent form.9.2%, 2/5, 0.065, 6.56
GREYUIT [131]

Answer:

0.65%, 9.2%, 40%, 656%

Step-by-step explanation:

see answer

6 0
3 years ago
Find two solutions to the equation (x^3 − 64)(x^5 − 1) = 0.
Rashid [163]

Answer:

the two roots are x = 1 and x = 4

Step-by-step explanation:

Data provided in the question:

(x³ − 64) (x⁵ − 1) = 0.

Now,

for the above relation to be true the  following condition must be followed:

Either  (x³ − 64) = 0 ............(1)

or

(x⁵ − 1) = 0 ..........(2)

Therefore,

considering the first equation, we have

(x³ − 64) = 0

adding 64 both sides, we get

x³ − 64 + 64 = 0 + 64

or

x³ = 64

taking the cube root both the sides, we have

∛x³ = ∛64

or

x = ∛(4 × 4 × 4)

or

x = 4

similarly considering the equation (2) , we have

(x⁵ − 1) = 0

adding the number 1 both the sides, we get

x⁵ − 1 + 1 = 0 + 1

or

x⁵ = 1

taking the fifth root both the sides, we get

\sqrt[5]{x^5}=\sqrt[5]{1}

also,

1 can be written as 1⁵

therefore,

\sqrt[5]{x^5}=\sqrt[5]{1^5}

or

x = 1

Hence,

the two roots are x = 1 and x = 4

4 0
3 years ago
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