Answer with explanation:
⇒Domain:
f(x)= -x² -2 x +15
= - (x²+2 x -15)
Splitting the middle term
= - (x²+5 x - 3 x -15)
= -[ x × (x+5) -3× (x+5)]
= -(x-3)(x+5)
y=f(x)=(3 -x)(x+5)
Domain of the function is defined as set of all values of x, for which y is defined.
f(x) is defined as all real values of x.So, Domain = R.
⇒Range:
[tex]y=-x^2-2 x +15\\\\y=-(x^2+2 x-15)\\\\ y=-[(x+1)^2-1-15]\\\\y= -(x+1)^2+16\\\\ 16 -y=(x+1)^2\\\\x+1=\pm\sqrt{16-y}\\\\x=\pm\sqrt{16-y}-1[/tex]
Range of the function is defined as set of all values of y, for which x is defined.
⇒16 -y ≥ 0
⇒y ≤ 16
Option B
The domain is all real numbers. The range is {y|y ≤ 16}.
Find the sum or difference write the answer in simplest form 3/10 4/10=
In the figure, which of the following edges is skew to edge AD?
edge BC
edge HD
edge GC
edge EH
...?
The edge that is skew to edge AD is edge GC
What are skew edges?In geometry, skew edges refer to edges that are not in the same plane and do not intersect. They belong to non-coplanar lines or segments, implying that they extend in different directions. Skew lines, and consequently their edges, never meet and remain at a constant distance from each other.
From the figure
line AD and GC are Skew since they can never meet yet they are not parallel to each other.
Skew lines are non-intersecting, non-coplanar lines in three-dimensional space. They neither share common points nor lie in the same plane, demonstrating their distinct orientation and lack of intersection in a three-dimensional geometric context.
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If trapezoid JKLM is translated according to the rule (x, y) → (x + 2, y − 6), what are the coordinates of point L'?
(1, −4)
(−4, −1)
(−7, 4)
(0, 7)
Answer:
A. (1,-4)
Step-by-step explanation:
L= (-1, 2)
(x,y)>(x+2, y-6)
(x,y)>(-1+2, 2-6)
(x,y)>(1, -4)
Solve for x: 3x + 4 = 5(x − 8)
Slingerland borrowed $8,000 on july 20, at 11% interest. if the loan was due on october 17, what was the amount of interest on the loan using the exact interest method?
I think the answer is $216.99 ?
Answer:
The amount of interest on the loan was of $214.57.
Step-by-step explanation:
Slingerland borrowed $8,000 at an 11% interest rate, thus having to pay $880 after a year.
As the loan was due on October 17, and the difference between July 20 and October 17 is of 89 days, using the exact interest method we can affirm that:
880 / 365 x 89 = X
2.41 x 89 = X
$214.57 = X
The amount of interest on the loan was of $214.57.
Firewood is often sold by the cord a cord is wood is abby doe measuring 4 feet by 4 feet by 8 feet what's the volume of a cord of wood in cubic feet?
What is 39 percent of 120?
Jason has already read 27 pages of a book. He plans to read 3 pages of the book every day. If f(n) represents the total number of pages that Jason will complete reading in n days, which of the following functions represents the relationship between f(n) and n?
f(n) = 27n − 3
f(n) = 3n − 27
f(n) = 27n + 3
f(n) = 3n + 27
Answer:
D.[tex]f(n)=3n+27[/tex]
Step-by-step explanation:
Total number of pages in a book=f(n)
Jason has already read pages=27
He plans to read pages of the book everyday=3
He takes times to complete reading the book=n days
He read pages in n days=3n
We have to find the function which represents the relationship between f(n) and n.
According to question information
[tex]f(n)=3n+27[/tex]
This is required relation between f(n) and n.
Answer:D.[tex]f(n)=3n+27[/tex]
Name the property of equality that justifies: (I have to put question into an equation below because I can't get it in this question without it being confusing)
A. Addition Property of Equality
B. Subtraction Property of Equality
C. Multiplication Property of Equality
D. Division Property of Equality
If:
m
then
5×m
is this correct ?
....
The function p(t) represents the value of a new car t years after it was manufactured.
p(t)=24,525(0.94)^t
What does the value 0.94 represent in this situation?
The value of the car increases by 94% each year.
The initial value of the car is 0.94.
The value of the car is 0.94 times the value of the car the previous year.
The value of the car decreases by 94% each year.
I think its D
Answer:
The value of the car is 0.94 times the value of the car the previous year.
Answer:
Option C is correct
The value of the car is 0.94 times the value of the car the previous year.
Step-by-step explanation:
Given the function:
[tex]p(t) = 24,525(0.94)^t[/tex]
where,
p(t) represents the value of a new car
t is the number of years.
We have to find the value 0.94 represent in this situation.
For t =0 years.
Initial value of car p(0) is 24,525
For t = 1 years
[tex]p(1) =24,525 \cdot 0.94[/tex]
For t = 2 years
[tex]p(2) =24,525 \cdot (0.94)^2[/tex] and so on...
Since;
[tex]\frac{p(2)}{p(1)} = 0.94[/tex]
⇒[tex]p(2) = 0.94 \cdot p(1)[/tex]
In general:
[tex]p(t) = 0.94 \cdot p(t-1)[/tex] where, t is the number of years.
⇒the value of the car is 0.94 times the value of the car the previous year.
Help needed :/
(1/2^-2) + 1/2
A. 2
B. 2 1/2
C. 4
D. 4 1/2
A triangle has sides of length 3 cm and 10 cm. What can you say about the length of the third side?
The inequality that represents the third side of the triangle is the third side < 13.
What is inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance.
Given, A triangle has sides of length 3 cm and 10 cm.
From the rule of the triangle, The sides of a triangle rule assert that the sum of the lengths of any two sides of a triangle has to be greater than the length of the third side.
thus, we can say that
third side < 10 + 3
third side < 13
Therefore, The inequality third side < 13 is used to represent the triangle's third side.
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Final answer:
Using the Triangle Inequality Theorem, the third side of a triangle with sides of 3 cm and 10 cm must be greater than 7 cm and less than 13 cm.
Explanation:
To determine the possible length of the third side of a triangle given two side lengths of 3 cm and 10 cm, we use the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, the third side must be longer than 7 cm (10 cm - 3 cm) but shorter than 13 cm (10 cm + 3 cm).
Nick has 3.90 in quarters and dimes total number of coins is 27how many quarters and dimes
Answer:
8 quarters; 19 dimes trust me i checked
Step-by-step explanation:
What is the slope of a line perpendicular to the line with equation y = 4x + 5?
-1/4
–4
4
–5
Dion practiced the long jump . he jumped 3.05 meters,2.74 meters and 3.3 meters.what was the average length of dion's jumps?
The sides of the cubes are numbered 1 through 6. If they are both tossed, what is the probability that they will both be a 2?
Answer:
The answer is 1/36
Step-by-step explanation:
Given: line DR tangent to Circle O.
If m angle C = 63°, then m angle BDR =
Answer:
m∠BDR=63°
Step-by-step explanation:
It is given that line DR tangent to Circle O and m∠BCD=63°, then the measure of the angle BDR can be determined as:
Since, angle BDR is made between the chord and the tangent, and we know that the angle between a chord and a tangent through one of the end points of the chord is equal to the angle in the alternate segment, therefore
m∠BCD=m∠BDR=63°
Hence, the measure of angle BDR=63°.
93 /100 converted to percent equals? ...?
How do the CHNOPS elements create macromolecules?
plzzzz helppppp
which value satisfies the inequality -2x + 8 + 5x > 2x + 1
The values which are greater than -7, satisfies the inequality -2x + 8 + 5x > 2x + 1.
What is inequality?Inequality shows relation between two expression which are not equal to each others.
The given inequality is,
-2x + 8 + 5x > 2x + 1.
To find the value of x,
Simplify the inequality by using mathematical operations,
3x + 8 > 2x + 1
3x - 2x > 1 - 8
x > -7
The required solution for the given inequality is x > -7.
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What can each term of the equation be multiplied by to eliminate the fractions before solving? x – 2x = x 2 6 10 12
Answer:
12
Step-by-step explanation:
I did the test
Forty-four percent of the members of the Science Club wear blue shirts. Which of the following is a binomial experiment? A.Selecting eight members randomly and recording whether each member is wearing a blue shirt
B.Selecting eight members randomly and recording the number in the group wearing a blue shirt
C.Selecting members randomly until one without a blue shirt is chosen
D. Selecting members randomly until one with a blue shirt is chosen
Answer:
Option A is correct.
Step-by-step explanation:
Selecting eight members randomly and recording whether each member is wearing a blue shirt.
A binomial experiment is defined as a statistical experiment which consists of n repeated trials. Only two possible outcomes are possible in each trial- either its a success or a failure. Here the probability of success remains the same on every trial.
Here, in 8 members the person wearing blue will be a success others will be a failure outcome.
What is the length of the hypotenuse of the right triangle that has a base of 5 inches and a height of 12 inches?
Factorise 6p^2-5pq-6q^2
If
f (n)(0) = (n + 1)!
for
n = 0, 1, 2, ,
find the Maclaurin series for f.
The Maclaurin series for f(n) is 1.
Explanation:The Maclaurin series for a function can be found using the formula: f(x) = f(0) + f'(0)x + f''(0)x^2/2! + f'''(0)x^3/3! + ...
In this case, f(0) = (0+1)! = 1, f'(0) = d/dx((0+1)!) = d/dx(1) = 0, f''(0) = d^2/dx^2((0+1)!) = d^2/dx^2(1) = 0, and so on.
Using these values, the Maclaurin series for f(n) is: f(n)(x) = 1 + 0x + 0x^2/2! + 0x^3/3! + ... = 1.
What are the factors of 86?
simplify completely ((x2-4x+4)/(x2+10x+25)) x ((x+5)/(x2+3x-10)) ...?
Factorize the given complex expression first into simpler terms (x-2)^2, (x+5)^2 and (x-2)(x+5). After canceling the matching terms, you simplify to get (x-2)/(x+5)
Explanation:This mathematical question involves the simplification of a fractional expression. The problem can be solved with factoring and canceling out matching terms found in both the numerator and denominator. Step by step solution would be:
((x2-4x+4) can be factored into (x-2)^2.
(x^2+10x+25) can be factored into (x+5)^2.
(x^2+3x-10) can be factored into (x-2)(x+5).
Thus, the whole equation will be converted into
((x-2)^2 / (x+5)^2) x ((x+5) / (x-2)(x+5)).
Cancel (x+5) and (x-2) from the numerator and denominator, which leaves:
(x-2)/(x+5).
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calculate the mean 12,2,8,6,57
A man notices that a tank is half full. After emptying 600 litres from the tank, that it is now one-third full. How much does the tank hold when it is full?
After removing 600 litres from a tank that was half full, it became one-third full. By setting up an equation, we determine that every 600 litres represents one-sixth of the tank's full capacity. Multiplying 600 litres by 6, we find the tank's full capacity is 3600 litres.
The question involves determining the total capacity of a tank based on information given about volume reductions and proportions of fullness. Initially, the tank is half full, but after removing 600 litres, it becomes one-third full. We can set up an equation to find out the total capacity of the tank (T).
Since removing 600 litres takes the tank from being half full to one-third full, that means 600 litres correspond to one-sixth of the tank's capacity because one half minus one-third equals one-sixth.
Now we set up our equation: 600 litres = T/6. To solve for T, we multiply both sides of the equation by 6:
(600 litres)Therefore, the full capacity of the tank is 3600 litres.