The equation for the axis of symmetry of the parabola y = - 4 x² + 24 x - 35 is given by x = 3.
We know that the method to find the axis of the symmetry of the parabola is given by:
x = - b / 2 a
We have the general equation of the parabola as:
y = a x² + b x + c
We have the equation of the parabola as:
y = - 4 x² + 24 x - 35
Comparing from this equation, we get that:
a = - 4
b = 24
c = - 35
Now, substituting the values, we get that:
x = - 24 / 2 (- 4)
x = - 24 / - 8
x = 24 / 8
x = 3
Therefore, the equation for the axis of symmetry of the parabola y = - 4 x² + 24 x - 35 is given by x = 3.
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g(x) = 3x^2-2x+1
Find g(-2)
Answer: g(-2) = 17
Step-by-step explanation:
When finding g(-2), we will substitute all values of x for -2 in the function. First, we will substitute values in. Then, we will simplify by squaring, multiplying, and adding.
g(x) = 3x² -2x + 1
g(-2) = 3(-2)² -2(-2) + 1
g(-2) = 3(4) + 4 + 1
g(-2) = 12 + 4 + 1
g(-2) = 17
Pls help I need help rn
Evaluate 4x ^ 2 - 3x when x = 3
Answer:
27
Step-by-step explanation:
=4(3)^2-3(3)
=4(9)-9
=3(9)
=27
Find the numerical value if x=4 and y=5
Answer:
77
Step-by-step explanation:
2(4)^2+9(5)
2(16)+45
32+45
=77
Answer:
109
Step-by-step explanation:
First, you substitute x with 4 and y with 5
so your equation should be 2(4)squared +9(5)
PEMDAS
Parrentisies first so 2x4=8 and 9x5=45
then exponents so 8squared = 64
Addition next so 64 + 45 =?
? = 109
You are solving a measurement problem where the numbers 2.09*10^(9) and 4.053 × 10^−4 are divided. How many significant digits should the quotient have?
Answer:
3
Step-by-step explanation:
You want to know the appropriate number of significant digits in the quotient of measurements 2.09×10^9 and 4.053×10^-4.
Significant digitsThe number of significant digits in a number written in scientific notation is the count of digits in the mantissa. Numbers with more significant digits are considered to be more precise.
2.09×10^9 . . . . has 3 significant digits
4.053×10^-4 . . . . has 4 significant digits
Product or QuotientWhen imprecise numbers are multiplied or divided, the resulting product or quotient cannot be more precise than the least precise number used. The quotient of numbers with 3 and 4 significant digits will only have 3 significant digits.
64° 42 °
xº
48°
Find the value of x
A truck enters a highway driving 60 mph. A car enters the highway at the same place 8 minutes later and drives 71 mph in the same direction. From the time the car enters the highway, how long will it take the car to pass the truck?
It will take 44 minutes for the car to pass the truck.
What is relative speed ?Relative speed is the net speed difference between two objects when they are on the same direction we subtract and when they are on different direction we add.
According to the given question A truck enters a highway driving 60 mph which is (60/60) miles per minute = 1 mile per minute.
The car is going at a speed of 71 miles hour or (71/60) mile per minute = 1.183 miles per minute.
∴ Their relative speed difference is ( 1.183 - 1 ) = 0.183 miles.
Given the car enters the highway 8 minutes later on that time the truck will cover the distance of (1×8) = 8 miles.
so, the time needed for the car to pass the truck is (8/0.183) minutes which is = 43.7 minutes or 44 minutes.
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MN has a slope of 4/5 and PQ has a slope of -4/5.Are the lines parallel, perpendicular, or neither?
Answer:
Neither
Step-by-step explanation:
MN: slope = 4/5
PQ: slope = -4/5
Two lines are parallel when their slopes are equal but their y-intercepts are different.
Two lines are perpendicular when their slopes are negative reciprocals of each other.
The negative reciprocal of 4/5 (MN) is -5/4
PQ -4/5
-5/4 [tex]\neq[/tex] -4/5
therefore the lines are Neither
A city in Texas started the day at -5 degrees Fahrenheit. The temperature increased by 15.1 degrees by nightfall. What is the final temperature at nightfall?
Step-by-step explanation:
Add 15.1 to -5-5 + 15.1 = 10.1Answer:
The final temperature is 10.1 degrees Fahrenheit
3.4/feet
5 feet
Find the area of the triangle pictured above.
h
square feet
Area =
Answer:
8.5 square feet
Step-by-step explanation:
(3.4x5)/2
=8.5
A bakery is 12 meters wide and 19 meters long. The baker wants to put a wooden shelf around the inside of the bakery. The wooden shelving costs $23.37 per meter. How much will the baker's shelf cost?
The cost of the baker's shelf is $1,448.94
How to calculate the cost of the baker's shelf ?
The length of the bakery is 12 meters
The width of the bakery is 19 meters
The wooden shelf costs £23.37 per meter
The cost can be calculated as follows
2(12+19) × 23.37
= 2(31) × 23.37
= 62 × 23.37
= 1,448.94
Hence the cost of the baker's shelf is $1,448.94
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A travel agent receives a 6% commission on the base fare of a customer- that is, the fare before sales tax is added. If the total fare
charged to a customer comes to $787.91 including 5.5% sales tax, how much commission should the agent receive?
The agent will get $47.2746 for his commission.
What is the percentage?A percentage is a number or ratio expressed as a fraction of 100 in mathematics. The percent sign, "%," is commonly used, but the abbreviations "pct.", "pct," and sometimes "pc" is also used. A percentage is a number with no dimensions; it has no unit of measurement. To calculate a percentage, divide the value by the total value and multiply the result by 100. (value/total value)100% is the formula for calculating the percentage.
So, we have to take out 6% of $787.91 in order to obtain the commission of the agent.
Then,
787.91/100 × 67.8791 × 6$47.2746Therefore, $47.2746 will the agent get for his commission.
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The function g(x)=−3(x−3)2+4 crosses the x-axis at x=1.845. What is true about the value of g(x) at that x-value? g(x)=0 g(x)=1.845 g(x)=−3.34 g(x)=−3
the value of the function is zero, then the correct option is the first one.
g(x)=0
What is true about the value of g(x) at that x-value?We know that the given function:
g(x) = -3*(x - 3)^2 + 4
Crosses the x-axis at x = 1.845
Now, remember that the x-axis is located at y = 0, to for the function:
y = g(x)
We should have that g(1.845) = 0
Then what we can conclude about the value of g(x) at x = 1.845 is that the value of the function is zero, then the correct option is the first one.
g(x)=0
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Julia went to ten houses on her street. 5 of them gave her a chocolate bar. What fraction of the houses gave her a chocolate bar
Help please this is due soon
The value of the given function is given as follows f(-5) ,g(2),f(4m) are 25,-3,-12m+10.
The slope of a linear function is calculated by rearranging the equation to its general form, f(x) = mx + c; where m is the slope. The vertex of a quadratic function is calculated by rearranging the equation to its general form, f(x) = a(x – h)2 + k; where (h, k) is the vertex.
The notation y=f(x) defines a function named f. This is read as “y is a function of x.” The letter x represents the input value or independent variable. The letter y, or f(x), represents the output value, or dependent variable
F(x) is the notation for a function which is essentially the thing that does your operation to your input. You can think of a function as a little machine. You put in your input, it changes it around and gives you output in return. F(x) means it's a function f with respect to x.
f(x) = -3x+10
f(-5) = -3*-5 +10
= 15+10=25
g(x) = x^2-7
g(2)= 2^2-7
= 4-7
=-3
f(4m) = -3x+10
= -3*4m+10
=-12m +10
= -12m +10
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The values of the above functions are 25, 3, and 12m+10 for f(-5) and g(2) and f(4m), respectively.
By rearranging the equation to take on its general form, f(x) = mx + c, where m is the slope, one can determine the slope of a linear function. By rearranging the equation to its general form, f(x) = a(x - h)2 + k, where (h, k) is the vertex, one can determine the location of a quadratic function's vertex.
A function called f is defined by the notation y=f(x). This should be understood as "y is a function of x." The input value or independent variable is denoted by the letter x. The dependent variable or output value is denoted by the letter y, or f(x).
A function is essentially the item that applies your operation to your input, and its notation is F(x). A function can be compared to a tiny machine. You provide your input, which is altered and converted into output. F(x) denotes that a function is one that has respect to x.
f(x) = -3x+10
f(-5) = -3*-5 +10
= 15+10=25
g(x) = x^2-7
g(2)= 2^2-7
= 4-7
=-3
f(4m) = -3x+10
= -3*4m+10
=-12m +10
= -12m +10
write the equation for the line perpendicular to y=-1/4x+9 and passing through the point (-9,9) in slope-intercept form.
Answer:
y = 4x + 45
Step-by-step explanation:
The slope for the equation y = -1/4x + 9 would be the number before the x. In this case, that number is -1/4. A perpendicular slope would be the opposite inverse to this number which would be 4. We know have the slope. We need the y- intercept.
To find the y-intercept we would need and x and y value that is on the line and the slope. We are given this information. From above, we see that the slope is 4. We can use the x and y from the ordered pair given (-9,9) The x value is -9 and the y value is 9.
y = mx + b Substitute in what we know.
9 = 4(-9) + b We are soling for b
9 = -36 + b Add 36 to both sides of the equation
45 = b We now know the y-intercept
The equation will be:
y = mx + b
y = 4x + 45
On Saturday, some adults and some children were in a theatre.
The ratio of the number of adults to the number of children was 4:3.
Each person had a seat in the Circle or had a seat in the Stalls.
2/3 of the children had seats in the Stalls.
114 children had seats in the Circle.
There are exactly 1100 seats in the theatre.
On this Saturday, were there people on more than 70% of the seats?
You must show how you get your answer
Answer:
Yes, there were people on more than 70% of the seats.
Step-by-step explanation:
Let's start with the children. We know that 2/3 of the children had seats in the Stalls, which means that the other 1/3 of the children had seats in the Circle. We know that 114 children had seats in the Circle. Therefore, we can calculate that there were 342 children total, since 114 (1/3 of the children) times 3 is 342.
In order to find how many adults there were, we can use the ratio of adults to children, 4:3. We're basically going to undo our math from the previous part. We divide 342 by 3 to determine how much 1 is. This gives us 114, which we multiply by 4 to find how many adults there were.
There were 456 adults.
There were 342 children.
456 + 342 = 798
There were 798 people in the theatre total.
To find what 70% of 1100 is, we multiply 0.7 x 1100. This gives us 770. Because 798 is more than 770, we know that there were people on more than 70% of the seats.
4500 = 3200(1+R/100)^4
Answer:
here is the answer for your question 4500=3200(1+R/100)^4, hope it helps
{ (-2, 4), (0, 2), (-1, 3), (4, -2)}
The set of ordered pairs above
The set of ordered pairs {(-2, 4), (0, 2), (-1, 3), (4, -2)} belong to a function
[y = f(x)] considering the pairs are in the order of (x, y).
As per the question statement, we are provided with a set of ordered pairs: {(-2, 4), (0, 2), (-1, 3), (4, -2)}.
We are required to determine if the pairs in the set satisfy a function or not.
To solve this question, let us consider each pair in the form of (x, y) and then, we will have to find out a relation between x and y that will satisfy all the ordered pairs. If we are able to find out one such common relation or pattern, we will determine our ordered pairs as inputs and outputs of the same function, otherwise not.
We can say that, [tex][(-2)(-1)+2]=4,[/tex]
[tex][(0)(-1)+2]=(0+2)=2,[(-1)(-1)+3]=1+2)=3,\\[/tex]
And, [tex][4*(-1)]+2=[(-4)+2]=(-2)[/tex]
That is, all our ordered pairs {(-2, 4), (0, 2), (-1, 3), (4, -2)} satisfy the function [y = f(x) = {x(-1) + 2}], being in the order of (x, y).
Therefore, the set of ordered pairs {(-2, 4), (0, 2), (-1, 3), (4, -2)} are the inputs and outputs of the function [y = f(x) = {x(-1) + 2}].
Ordered Pairs: An Ordered Pair is a pair of elements (say a, b) having the property that [( a, b) = (p, q)] if and only if (a = p) and(b = q).
Function: In mathematics, a function is an operator, which when provided with an input, will produce a certain output.To learn more about Ordered Pairs, click on the link below.
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Help me please ASAP !
Answer: C
Step-by-step explanation:
Answer:
[tex](\sqrt[12]{8} )^x[/tex]
Step-by-step explanation:
[tex](\sqrt[3]{8} ) \frac{1}{4} x = 8\frac{1}{3} \frac{1}{4} x = 8\frac{1}{12} x = (\sqrt[12]{8} )^x[/tex]
Seven times the sum
of a number,n, and four
Answer:
7(n + 4) or 7×(n + 4)
Step by step explanation:
What is this number in standard form?
(8 × 10) + (2x 100) + (9 × 1.000)
5)
Enter your answer in the box.
Answer:
Depending on where the 5) is supposed to be, if it is multiplying the 9 x 1000, then total answer is 45280. If however the equation is 80 + 200 + 45000 then multiply by 5 it is 46400
-X <-2x and 3x>2x
Solve, then graph and find interval notation
Answer:
-X < -2x
3x>2x
Step-by-step explanation:
how much would $500 invested at 4% interest compounded monthly be worth after 7 years ? A(t)=P*e^nt
The worth of the investment is $1.51 * 10^39
How to determine the compound amount?The given parameters are
Principal, P = $500
Rate, r - 4%
Time, t = 7 years
Number of times, n = 12
So, we have:
A(t)=P*e^nt
This gives
A(12) = 500 *e^(12 * 7)
Evaluate
A(12) = 1.51 * 10^39
Hence, the worth of the investment is $1.51 * 10^39
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which of the following shows 3x^2-2x-5 factored completely?
Use the graph to determine the following
a. the functions domain
b. the functions range
c. the x-intercepts if any
d. the y-intercepts if any
e. the function values f(0) and f(4)
The answers are:
a) The domain is the set of all real numbers.
b) The range is R: (-∞, -2]
c) there are not any x-intercept.
d) The y-intercept is y = -5
e) f(0) = -5
f(4) = -4
How to determine the domain and range by using the graph?For a function f(x) =y, we define the domain as the set of the inputs and the range as the set of the outputs.
To identify the domain we need to look at the horizontal axis, and there we can see that the function covers it completely, then the domain is the set of all real numbers.
For the range, we look at the vertical axis. Here we can see that the function has a maximum at y = -2 and then goes down, then the range is:
R: (-∞, -2]
c) Now we want to get the xintercepts. As you can see in the graph, it never intercepts the x-axis (the horizontal one). Thus, there are not any x-intercept.
d) The y-intercept is when the graph intercepts the vertical axis, in this case the y-intercept is at y = -5
e) f(0) is the value of the y-intercept, which we already know is y = -5
for f(4) we need to find x = 4 in the horizontal axis and then find the correspondent value of the graph.
We can see that f(4) = -4.
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4y2+5y-8y2+4-2y=
I need to explain how I resolved this problem?
Marty can buy lunch for 5 dollars in the cafeteria how many days can he buy lunch with 30 dollars
Answer: 6 days
Divide 30 by 5
what's the simple notation of by parts differentiation
Answer:
[tex]{ \tt{ \int_{b} ^{a} (u) \: dv = uv - \int_{b}^{a} (v) \: du }} \\ [/tex]
Answer:
integral (u v') = uv - intgral (u' v)
David trips every two out of nine stairs he trip for the 58th time how many stairs did.
he climb
Answer:
261 stairs
Step-by-step explanation:
If David trips twice every 9 stairs and he has tripped 58 times. We can multiply 9 by 58.
58*9=522
Since David trips twice in 9 stairs, then to find how many stairs he has climbed we need to divide 522 by 2.
522/2=261
David has climbed 261 stairs.
The reciprocal of 2/19 is
(Type an integer or a fraction.)
Answer:
-19/2
Step-by-step explanation:
If you want the reciprocal you need to change the sign to the opposite and flip the numbers.
