Answer:
The vertex of f(x) is at (-5,-10).
The function g(x) is decreasing at a rate of 5%.
The zeros of h(x) are at x = -3 and x = 1.
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, f(x_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]f(x_{v})[/tex]
Decaying exponential function:
A decaying exponential function has the following format:
[tex]A(x) = A(0)(1-r)^{x}[/tex]
In which A(0) is the initial quantity and r is the decay rate.
Zeros of a function:
Given a polynomial f(x), this polynomial has roots [tex]x_{1}, x_{2}, x_{n}[/tex] such that it can be written as: [tex]a(x - x_{1})*(x - x_{2})*...*(x-x_n)[/tex], in which a is the leading coefficient.
Vertex of f:
The function f is given by:
[tex]3(x+5)^2 - 10[/tex]
Expanding the calculations to place at the correct format:
[tex]3(x+5)^2 - 10 = 3(x^2 + 10x + 25) - 10 = 3x^2 + 30x + 75 - 10 = 3x^2 + 30x + 65[/tex]
Which means that
[tex]a = 3, b = 30, c = 65[/tex]
The x-value of the vertex is:
[tex]x_{v} = -\frac{30}{2*3} = -5[/tex]
The y-value of the vertex is:
[tex]f(-5) = 3(-5+5)^2 - 10 = -10[/tex]
The vertex of f(x) is at (-5,-10).
Decreasing rate of g(x).
We have that:
1 - r = 0.95
So
r = 1 - 0.95 = 0.05
Which means that the decreasing rate is of 5%.
The zeros of h(x) are
The zeros are
x + 3 = 0 -> x = -3
x - 1 = 0 -> x = 1
So
The zeros of h(x) are at x = -3 and x = 1.
Dora is thinking of a number between 500 and 600
When she divides it by a 1-digit number it has a remainder of 4
What could Dora’s number be?
9514 1404 393
Answer:
500 ÷ 8 = 62 r 4, for example
Step-by-step explanation:
In order to have a remainder of 4, the divisor must be greater than 4, so could be any of 5, 6, 7, 8, 9.
The corresponding numbers could be any of ...
504 +5n . . . 0 ≤ n ≤ 19
502 +6n . . . 0 ≤ n ≤ 16
501 +7n . . . 0 ≤ n ≤ 14
500 +8n . . . 0 ≤ n ≤ 12
508 +9n . . . 0 ≤ n ≤ 10
__
For example, with the divisor being 6, and n=13, the number could be ...
580 = 6·96 + 4
Find the midpoint M of the line segment joining the points P=(4,-7) and Q=(-6,-3)
Answer:
midpoints (-1, -5)
Step-by-step explanation:
midpoints
[tex] ( \frac{4 + ( - 6)}{2} \: \frac{ - 7 + ( - 3)}{2} )[/tex]
[tex]( \frac{4 - 6}{2} \: \frac{ - 7 - 3}{2} )[/tex]
[tex]( \frac{ - 2}{2} \: \frac{ - 10}{2} )[/tex]
[tex]( - 1 \: - 5)[/tex]
You roll a 6-sided die.
What is P(even)?
Write your answer as a percentage.
On a map, 2.7 inches = 60 miles. How far apart are two cities if they measure 4.5 inches
apart on the map?
Answer:
120 miles
Step-by-step explanation:
2.7 times 2 is 4.5, so 60 times 2 is 120 (you're basically doubling both.)
1. Select all equations that are equivalent to (5x+6) over 2 =3-(4x + 12). A5+6= 3 - (4x + 12) (5x+6) B. 2 = -4x -9 c. x+3 = 3 – (4x + 12) (5x+6) = -4x + 15 2 E. 5x + 6 = -8x – 18
Answer:
Only option E is equivalent to [tex]5x+6=-8x-18[/tex].
Step-by-step explanation:
Given the expression
(5x+6) over 2 = 3-(4x + 12)
Let us simplify the expression
[tex]\frac{\left(5x+6\right)}{2}=3-\left(4x+12\right)[/tex]
Multiply both sides by 2
[tex]\frac{5x+6}{2}\cdot \:2=3\cdot \:2-\left(4x+12\right)\cdot \:2[/tex]
[tex]5x+6=6-\left(4x+12\right)\cdot \:2[/tex]
Expand -(4x + 12) = -4x - 12
[tex]5x+6=-8x-18[/tex]
Thus, option E is equivalent to [tex]5x+6=-8x-18[/tex].
Further solving
[tex]5x+6=-8x-18[/tex]
Add 8x from to both sides
[tex]5x+8x=-8x-24+8x[/tex]
Simplify
[tex]13x=-24[/tex]
Divide both sides
[tex]\frac{13x}{13}=\frac{-24}{13}[/tex]
Simplify
[tex]x=-\frac{24}{13}[/tex]
Thus, only option E is equivalent to [tex]5x+6=-8x-18[/tex].
Answer:
E. 5x + 6 = -8x – 18
Step-by-step explanation:
Hope this will help
You can purchase 2 sodas for 3 dollars, how much does 6 sodas cost?
Answer:
It costs $9
Step-by-step explanation:
Lets look at the ratio:
2/3
We need x:
6/x
Make an equation using the butterfly method:
3(6) = 2x
Simplify:
18=2x
Divide both sides by 2:
x=9
It costs $9
A house was valued at $292,000 . Over several years, the value increased by 8%, giving the house a new value.
Answer:
315,360 I had to assume you needed that number, 292000+8%=315360
Round 7.954 to the place named.
Hundredths
Answer:
The answer is 7.95
Step-by-step explanation:
I hope I helped.
which of the following is the slope of the line that passes through the points (-2,8) and (10,-1)
-2 (1/3x - 1/5) please answer ASAP I have to turn this in in 30 min!!
Answer:
1/3 + 1/5 them you solve -2
Step-by-step explanation:
Answer:
-2/3x+2/5
Step-by-step explanation:
Open up parentheses
-2 x 1/3x= -2/3x
-2 x 1/5= 2/5
Find values for a and b so that 2(3x+5)+ax=5(4x−b) is an identity equation.
Answer:
a=30 b=2 (not sure)
Step-by-step explanation:
Simplify first part : 2*3x+ 2*5= 6x+10+ax
Simplify 2nd part : 5*4x-5*b. 5x-5b
we have: 6x+10+ax=20x-5b.
we minus 6x from both sides
10+ax=14x+5b
Minus 10
ax=14x+5b-10
Divide x
a=14+5b-10
a=4+5b
divde 5
a/5= 4+b
perhaps it is 30
30/5=4+b
6=6
but i am not sure
The length of a rectangular painting is 3 inches longer than its width. If the diagonal is 15 inches long, what is the length of the painting?
A 9 inches
В. 12 inches
C. 13 inches
D. 18 inches
Answer:
Step-by-step explanation:
if you were to roll two standard six-sided dice, what is the probability that both land on a 3 or greater
Answer:
4/9
Step-by-step explanation:
P(≥3 and ≥3) = 4/6 x 4/6 = 4/9
The prom committee has no more than $600 to spend on centerpieces for the prom. If each centerpiece costs $25, what is the maximum number of centerpieces the committee can buy?
Answer:
600/25 = 24
Brainiest plz :)
Answer:
600/25 = 24
Have a good day I hope this helps.
Solve the system of linear equations by graphing.
y = x-7
y = -2x + 5
Answer:
4
Step-by-step explanation:
help me out yall pleaseeee
A LOT OF POINTS!!!! PLZ ANSWER
Answer:
f(3x)= 3x+5/6x+2
substitute the value of X in the given question.
if u want simplified form then u can try rationalising.
f(3x)= 3x+5/6x+2 hope helped thanks for points
Richard bought 3 peaches and 1 orange and spent $3.50. Peaches are $0.85 each. If there is no sales tax on fruit, how much did the orange cost?
A.$0.66
B.$0.88
C.$0.95
D.$2.65
Answer:
D. $2.65
Step-by-step explanation:
0.85 x 3 = 2.55
The orange cost 10 cents.
PLEASE HELP. I WILL GIVE BRAINLIEST TO THE PERSON WHO ANSWERS BOTH PARTS OF THE QUESTION.
Parking at the posh center costs d dollars per hour during the off hours and an extra $3 per hour during peak hours. During holidays, the basic rate of d doubles. Write an expression for how much it would cost to park for 3d hours on a holiday during peak hours.
Then, if the basic off-hours parking rate is $2.50 per hour, how much would a person pay to park for 3d hours in the situation described above?
PLEASE HELP. I WILL GIVE BRAINLIEST TO THE PERSON WHO ANSWERS BOTH PARTS OF THE QUESTION.
THINGS TO REMEMBER:
the variable d represents dollarsCosts an extra $3 per hour during peak hoursWhile holiday's are going on the amount of d doublesFind how much parking would cost on a holiday during peak hour's-----
Question: Write an expression for how much it would cost to park for 3d hours on a holiday during peak hours.
-----
Answer: 3d × 2 or 3d + 3d
-----
Explanation: This is because during holidays the amount of d doubles. However since this is on a holiday DURING peak hours it would be 3d × 2
-----
Question 2: Then, if the basic off-hours parking rate is $2.50 per hour, how much would a person pay to park for 3d hours in the situation described above?
-----
Answer: $15
-----
Explanation: Since d represents dollars we would multiply 2.50 times 3 which would give us 7.5 then we double this since it is during holidays giving us $15
-----
NOTE: I AM SO SORRY IF THIS IS WRONG AND I MISSED SOMETHING. IF IT IS WRONG THEN PLEASE MAKE SURE TO TELL ME SO I CAN FIGURE OUT WHAT I MISUNDERSTOOD
Again I'm sorry but I hope I helped a little bit.
What is the volume of the triangular prism below?
7 yd
18 yd
12 yd
Step-by-step explanation:
V = 1/2 a x c x h
1/2 * 7*12*18 = 756 yd ^3
24 divided by 2 times 5 then square foot of it
Answer:
7.75
Step-by-step explanation:
sq rt of (24/2)(5) = sq rt of 60 = 7.75
Answer:
7.75 rounded
Step-by-step explanation:
24 / 2 = 12
12 * 5 = 60
7.7459
rounded its 7.75
1. What is the value of n in -57 - n = -144?
A-201
B-87
C 87
D 201
Answer:
C=87
Step-by-step explanation:
To isolate the variable, you need to take away -57 by adding it to -144.
Then, you'd see:
-n=-87
Next, you divide both sides by -1 to get 87
6/5 of ______ is 30
Please help
It is 36.
180/5 = 36
5/5 = 1
When we put that together, we can see that our complete answer is:
36/1
The complete and simplified answer to the question what is 6/5 of 30 is:
36.
Evaluate 6 * 2 ^ x for a) x = - 2 and (b) x = 3 . Write your answers in simplest form.
Answer:
a. [tex]\frac{3}{2}[/tex] b. 48
Step-by-step explanation:
(a) The value of the expression when x = -2 is 1.5.
(b) The value of the expression when x = 3 is 48.
What is a function?A function is a relationship between a number of inputs and outputs. A function is an association of inputs where each input is coupled with exactly one output. There is a range, co-domain, and domain for every function.
Given that the expression is 6(2)ˣ.
To evaluate the expression 6(2)ˣ for different values of x, we simply substitute the value of x into the expression and simplify.
(a) When x = -2, we have:
6(2)⁻² = 6(1/4) = 1.5
So the value of the expression when x = -2 is 1.5.
(b) When x = 3, we have:
6(2)³ = 6(8) = 48
So the value of the expression when x = 3 is 48.
To learn more about the function;
brainly.com/question/28303908
#SPJ2
i will give brainiest! i have to turn this in tonight please hurry.
9514 1404 393
Answer:
(c) 24 minutes
Step-by-step explanation:
The rate of working problems differs by ...
(1 problem)/(1.5 minutes) - (1 problem)/(2 minutes)
= (2/3 -1/2) problems/minute
= 1/6 problems per minute
So, to make up the difference of 4 problems will take ...
time = quantity/rate = (4 problems)/(1/6 problem/minute) = 24 minutes
Caroline and Chase will be on the same problem after 24 minutes.
_____
Additional comment
Technically speaking, Chase will just be finishing problem 26 when Caroline starts it after 19.5 minutes. At that point in time, they are on the same problem. The answer choices suggest the real question is, "after how many minutes will they be starting the same problem at the same time?" After 24 minutes, both will be starting problem 29 at the same time.
HELP PLEASE !!
Ivanna is riding on a bike course that is 15 miles long. So far, she has ridden 6 miles of the course. What percentage of the course has Ivanna ridden so far?
Answer:
50%
Step-by-step explanation:
Kelly is reading a 440-page book. During the past 5 days she has read 275 pages. At this rate, how many more days will it take her to complete the book? 3 days Ada
Kevin made 4 of his 6 shots on goal at soccer practice if he continues to shoot in the same manner throughout the practice how many shot would he make out of 72
please help i will give brainliest
Answer:
437/4x^5/328^1/2-445^1/21Step-by-step explanation:
hope this helps...
have a nice day
Which number is an integer?
Answer:
there is no question for me to tell you what it is