An equation of the parabola that has the same shape as the graph of f(x) = 4x², but with the point (10,4) as the vertex is y = 4x² - 80x + 404.
What is the vertex form of the parabola?The standard vertex form of the parabola is given by,y = a(x - h)² + k where (h, k) is the vertex.
Real numbers, a, h, and k are included here, where a ≠ 0. A point on the parabola is represented by the variables x and y, respectively.Given:
f(x) = 4x²
Vertex = (10,4)
a = 4
The value of a in the vertex form of the equation is taken to be 4 since the coefficients of x² must match for the parabola to have the same shape as the given parabola.
The equation can be written as,
y = a(x - h)² + k where (h, k) is the vertex.
Replacing the value of the vertex, we get
y = 4(x - 10)² + 4
y = 4(x² - 20x + 100) + 4
y = 4x² - 80x + 400 + 4
y = 4x² - 80x + 404
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7.
A coach travels from the station to the beach, a distance of 576km away in 6hrs.
The coach is only allowed to travel at a maximum speed of 90km/h. Did the coach
break the speed limit?
Answer:
Yes.
Step-by-step explanation:
distance = rate x time
Let r = rate
567 = r6 Divide both sides by 6
94.5 = r If he was driving at a constant rate the whole time then he was driving at 94.5 miles per hour which is faster than 90
Gus has skydived 4 more times than Nico. Emma has skydived 16 times, how many times has Gus skydived?
We know that Emma has skydived 16 times, and also Emma has skydived twice as many times as Nico, so Nico has skydived:
[tex]\begin{gathered} \text{Emma}=2\cdot\text{Nico} \\ 16=2\cdot Nico \\ Nico=\frac{16}{2}=8 \end{gathered}[/tex]So, Nico has skydived 8 times.
Finally, we know that Gus has skydived 4 more times than Nico, so:
[tex]\begin{gathered} Gus=\text{Nico}\cdot4 \\ \text{Gus}=8\cdot4=32 \end{gathered}[/tex]Gus has skydived 32 times.
Let f(x)=x+1 and g(x)=x^2-x. Find and simplify the expression. (f+g)(-5)
Answer:
26
Step-by-step explanation:
(f+g)(-5)=
f(-5)+g(-5)=
-5+1+(-5)^2-(-5)=
-4+25+5=
-4+30=
30-4=26
In the high school band there are two percussionist to every seven marching instruments at the high school bad has a total of 180 members that how many percussionists are on the sidelines
The number of percussionists on the sidelines is 40.
What is a proportion?A proportion is an equation that equalizes two ratios. By dividing the provided values, we may determine the missing value. One way to express the proportion formula is as a: b::c : d = a/b = c/d. Here, a and d are the extreme terms and b and c are the mean terms.Given:
Total number of members in high school band = 180
Let's assume "x" is the number of percussionists that are on the sidelines.
According to the question, there are two percussionists to every seven marching instruments. Then,
Number of members = 7 + 2 = 9
You can write the following proportion knowing that there are 180 total members of the high school band:
[tex]\frac{x}{180} = \frac{2}{9}[/tex]
Solving the proportion to get the value of x,
[tex]x = \frac{2}{9} * 180[/tex]
x = 40
Therefore, there are 40 percussionists on the sidelines.
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Point M is the midpoint of AB . AM=2x+9, and AB=8x−50.
What is the length of AM?
Using the midpoint theorem, the length of AM is 43
Calculating Length of a lineFrom the question, we are to determine the length of AM
From the given information,
Point M is the midpoint of AB
Thus,
From the midpoint theorem
We can write that
AM + MB = AB
AM = MB
AM + AM = AB
2AM = AB
Also, from the given information,
AM = 2x + 9
and
AB = 8x - 50
Therefore,
From 2AM = AB
2(2x + 9) = 8x - 50
Solve for x
2(2x + 9) = 8x - 50
4x + 18 = 8x - 50
18 + 50 = 8x - 4x
68 = 4x
x = 68/4
x = 17
But,
AM = 2x + 9
Substituting the value of x
Thus,
AM = 2(17) + 9
AM = 34 + 9
AM = 43
This means the length of AM is 43
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Select the three equations that pass through the points (–4, –16) and (5, 2):
y + 4 = 2(x – 16)
y – 2 = 2(x – 5)
y = 2x – 8
y + 16 = 2(x + 4)
The equation of line passing through (-4, -16) and (5, 2) are y = 2x – 8, y - 2 = 2(x - 5) and y + 16 = 2(x + 4)
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.
The standard form for linear equation is:
y = mx + b
Where m is the slope and b is the y intercept
The equation of line passing through (-4, -16) and (5, 2) is:
y - (-16) = [(2-(-16))/(5-(-4))](x - (-4))
y + 16 = 2(x + 4)
y = 2x - 8
y - 2 = 2(x - 5)
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4a + 8b/7 - a^2
if a = 3 and b = -1
Simplify the expression.
___________________
Solutions:Exact Form - [tex]\frac{13}{7}[/tex]Decimal Form - 1.8.....Mixed Number Form - [tex]1\frac{6}{7}[/tex]...^Here are all three solutions depending on what you are looking for. Hope this helps! If so, please lmk! Thanks and good luck!
These box plots show the basketball scores for two teams.Bulldogs55708090105Wolverines355580 8596ㅏ30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110Basketball scoresCompare the shapes of the box plots.
Solution
The bullfdng dataset has its median close to the center of the boxplot.
- This implies that the dataset is symmetric.
- The wolverine dataset has its median moved to the right at 80, implying that it is NOT symmetric.
- However, because there is a skew to the left of datapoints, we say that the dataset is negatively skewed
Final Answer
OPTION A
(5^3)^9 divided by 5^12
Exact Form:
11920928955078128/390625
Decimal Form:
30517578125
Find the intercepts and graph each line.
a.) x – 4y =− 4
b.) 2x + 5y =-10
Answer:
(1,5) I think that's what it is
How can I find the slope of the line and what can the slope mean?
If we take two ordered pairs from the table, we can find the slope with the following equation:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]in this case, we can take the points (1,1/2) and (2,1) to get the following using the formula above:
[tex]\begin{gathered} m=\frac{1-\frac{1}{2}}{2-1}=\frac{\frac{1}{2}}{1}=\frac{1}{2} \\ \Rightarrow m=\frac{1}{2} \end{gathered}[/tex]we have that the slope is m = 1/2, and this means that for each 2 gallons of distilled water, Rodnika will add 1 gallon of sea salt
a bag contains 3 red marbles, 3 white marbles,, and 5 blue marbles. only white marbles will be added to the bag. how many white marbles should be added to the bag to make the probability of pulling a white marble 50%?
Step-by-step explanation:
a probability is always
desired cases / totally possible cases
a 50% probability means 1/2 or 0.5.
that means
desired cases = 1/2 × totally possible cases
at start we have
3 red
3 white
5 blue
that makes 5 + 3 + 3 = 11 totally possible cases and 3 desired cases.
so, the starting probability to pull a white marble is
3/11.
now, we need to say
(3 + x) = 1/2 × (11 + x) (= (3+x)/(11+x) = 1/2)
to make is simpler we multiply both sides by 2 (so we get rid of the 1/2 fraction).
6 + 2x = 11 + x
6 + x = 11
x = 5
we need to add 5 white marble to give us a 50% probability to pull a white marble.
we have then
3 red
3 + 5 = 8 white
5 blue
that makes 5+8+3 = 16 totally possible cases and 8 desired cases.
so, the probability is
8/16 = 1/2
=> our calculation was correct
The number of white marbles should be added to the bag to make the probability of pulling a white marble 50% will be 5.
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
A bag contains 3 red marbles, 3 white marbles, and 5 blue marbles. only white marbles will be added to the bag.
Let 'x' be the number of white marble added. Then the equation is given as,
0.50 = (x + 3) / (x + 3 + 3 + 5)
Simplify the equation, then we have
0.50 = (x + 3) / (x + 3 + 3 + 5)
0.50 = (x + 3) / (x + 11)
0.50x + 5.5 = x + 3
0.50x = 2.5
x = 5
The number of white marbles should be added to the bag to make the probability of pulling a white marble 50% will be 5.
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graph a line with a slope of 3/4 that contains the point (2 -3)
Step-by-step explanation: I hope this helps.
Answer:
A person is standing 18 feet away from a street light that is 20.2 feet tall. How long is his shadow if he is 5.2 feet tall? Enter the exact value of the answer.
The shadow of the person is 6.24 feet long.
The height of the street light is 20.2 feet.The height of the person is 5.2 feet.The person is standing at a distance of 18 feet from the street light.Let the length of the shadow be "x".The above configuration of the street light, the person, and the shadow creates a situation of similar triangles.Using the properties of the similar triangles, we know that the ratio of the corresponding sides of the similar triangles is the same.The height of the street light divided by the sum of the length of the shadow of the person plus the distance of the person from the street light is equal to the height of the person divided by the length of the shadow.20.2/(x+18) = 5.2/x20.2x = 5.2x + 18*5.215x = 18*5.2x = (18*5.2)/15x = 6.24Thus, the length of the shadow is 6.24 feet.To learn more about similar triangles, visit :
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A restaurant has two types of tables, rectangular
ones that can each seat 4 people and circular
tables that can each seat 8 people. If 144 people
are enough to fill all 30 tables at the restaurant,
how many rectangular tables does the restaurant
have?
A) 12
B) 16
C) 20
D) 24
Answer:
D) 24
Step-by-step explanation:
c + r = 30 Eq. 1
4r + 8c = 144 Eq. 2
r = rectangular tables
c = circular tables
From Eq. 1:
c = 30 - r Eq. 3
Replacing Eq. 3 in Eq. 2:
4r + 8(30-r) = 144
4r + (8*30 + 8*-r) = 144
4r + 240 - 8r = 144
-4r = 144 - 240
-4r = -96
r = -96/-4
r = 24
from Eq. 3
c = 30 - r
c = 30 - 24
c = 6
Check:
from Eq. 2
4r + 8c = 144
4*24 + 8*6 = 144
96 + 48 = 144
A frog jumped 0.7 meters. Then jumped another 0.98 meters. How many meters did he jump
Peter has a tire with a diameter of 26 inches. How many inches is the radius of his tire?
Answer
The radius of Peter's tire = 13 inches
Explanation
The radius of a circular figure is related to its diameter through
Radius = ½ (Diameter)
Diameter = 26 inches
Radius = ½ (Diameter) = ½ (26) = 13 inches
Hope this Helps!!!
A two-digit number is 3 more than 4 times the sum of its digits. If 18 is added to the number, the digits are reversed. Find the number.
Answer:
Let the required number be ab.
Sum of digits = a + b ........ ( 1 )
10 a + b = 4 ( a + b )
10 a + b + 18 = 10 b + a
=> 9 a + 18 = 9 b
=> a + 2 = b
10 a + a + 2 = 4 ( a + a + 2 )
=> 11 a + 2 = 8 a + 8
=> 3 a = 6
=> a = 3
=> a + 2 = 5
=>ab = 35......... [ A ]
So the number becomes 35.
ANSWER :
The original number is 35.
hope it helps you
• (two-digit number) = 3 + 4(sum of its digits)
• (two-digit number) + 18 = Digit gets reverse
To Find :• The number.
Concept :-We will first assume the number on one's place be [tex]x[/tex] and ten's place be [tex]y[/tex] [why? because the given conditions are about the digits of number]
-Two-digit number then formed will be 10y + x and its reverse will be 10x + y[why? well let's take an example like a number 42. This number can be written in expanded form as 10×4+2×1 here 4 is number at ten's place (y) and 2 at one's place(x) It's reverse will be 24 it can be written in expanded form as 10×2+4×1 here 2 is number at ten's place (y) and 4 at one's place(x)]
-Then we will use given conditions to form the equation and will solve the equations to get the answer.
So now let's get started with our solution! :D
Solution :Let the one's and ten's digit of the number be [tex]x[/tex] and [tex]y[/tex] respectively.
According to first condition,
=> (10y + x) = 3 + 4(x + y)
=> 10y + x = 3 + 4x + 4y
=> 10y - 4y = 3 + 4x - x
=> 6y = 3 + 3x
[tex] \implies \sf \frac{6y}{3} = \frac{3}{3} + \frac{3x}{3} [/tex]
=> 2y - 1 = x ___(equation 1)
According to second condition,
=> (10y + x) + 18 = 10x + y
=> 10y - y + 18 = 10x - x
=> 9y + 18 = 9x
[tex] \implies \sf \frac{9y}{9} + \frac{18}{9} = \frac{9x}{9} [/tex]
=> y + 2 = x ___(equation 2)
Solving equation 1 and 2
y + 2 = x (equation 2)
y + 2 = 2y - 1 [From equation 1]
3 = 2y - y
3 = y (ten's place)
Now put value of y = 3 in equation 2
y + 2 = x (equation 2)
3 + 2 = x
5 = x (one's place)
So, the number formed is 35.
6 + root 27over 4 - root 3
When the expression given as 6 + √27/4 - √3 is simplified, the value is 6 - 1/4√3
How to determine the value of the expression?The expression is given as
6 + root 27over 4 - root 3
Mathematically, the expression can be represented as
6 + √27/4 - √3
Expand 27 as the product of 9 and 3
So, we have the following equation
6 + √27/4 - √3 = 6 + √(9 * 3)/4 - √3
Expand the products in the above equation
So, we have the following equation
6 + √27/4 - √3 = 6 + √9 * √3/4 - √3
Evaluate the square root of 9 in the above equation
So, we have
6 + √27/4 - √3 = 6 + 3/4√3 - √3
Evaluate the like terms in the above equation
So, we have the following equation
6 + √27/4 - √3 = 6 - 1/4√3
Hence, the value of the expression given as 6 + √27/4 - √3 is 6 - 1/4√3
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Rewrite the expression 26 + 8 as the product of the GCF (greatest common factor) and a sum. Then, simplify the expression. Show all of your steps. pls help due today
The expression 26+8 as the product of the GCF and a sum is:
2(13+4).
Given we have the expression as 26+8
We need to find the greatest common factor of the numbers 26 and 8.
26 = 2 × 13
8 = 2 × 2 × 2
Multiply all the prime factors that both numbers share in order to determine the GCF:
Therefore, GCF = 2
Now we can write the expression as:
26 + 8
=2(13 + 4)
=2×17
=34
Hence we get the required expression as 2(13 + 4).
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If [tex]h(x)=\frac{sinx}{sin2x}[/tex], then [tex]lim_{x-\pi }h(x)[/tex] is equivalent to which of the following?
a. [tex]-\frac{1}{2}[/tex]
b. 0
c. 1
d. Does not exist
Answer: -1/2
Step-by-step explanation:
[tex]\lim_{x \to \pi} \frac{\sin x}{2\sin x \cos x}\\\\=\lim_{x \to \pi} \frac{1}{2\cos x}\\\\=\frac{1}{2\cos \pi}\\\\=-\frac{1}{2}[/tex]
Answer:
[tex]-\frac{1}{2}[/tex]
Step-by-step explanation:
If we try direct substitution we get: [tex]lim_{x\to\pi}h(x)=\frac{sin(\pi)}{sin(2\pi)}[/tex]
The radian [tex]2\pi[/tex] is a full rotation from 0 radians, in other words it's equivalent to 0 radians.
Using the unit circle as a reference you'll remember when the angle is 0 radians, the y-value is zero, so: [tex]sin(2\pi)=0[/tex]
When the angle is: [tex]\pi[/tex] it's at a half rotation where the y-value is still zero on the unit circle.
So you get the indeterminate form of: [tex]\frac{0}{0}[/tex]
We can use L'Hôpital's rule which states: [tex]lim_{x\to c}\frac{f(x)}{g(x)}=lim_{x\to c}\frac{f'(x)}{g'(x)}[/tex] if the original limit is in indeterminate form such as the one above.
Taking the derivative of sin(x) we simply use the property that: [tex]\frac{d}{dx}[sin(x)]=cos(x)[/tex]
For the sin(2x) we can use the chain rule which essentially states: [tex]h(x)=f(g(x))\\h(x)=f'(g(x))*g'(x)[/tex]
It deals with composite equations, and in this case we can represent the composite function as:
[tex]f(x)=sin(g(x))\\g(x)=2x[/tex]
Using the chain rule we get: [tex]cos(2x)*2[/tex]
So now we have the limit: [tex]lim_{x\to \pi}\frac{cos(x)}{2cos(2x)}[/tex]
at pi radians the unit circle is at a half rotation where the x/y coordinates are: [tex](-1, 0)[/tex]
so cos(pi) = -1
at 2 * pi radians were basically back at 0 radians where the x/y coordinates are: [tex](1, 0)[/tex]
so cos(2 * pi) = 1
Now plugging in these values we get the fraction: [tex]\frac{-1}{2*1}[/tex] which just simplifies to: [tex]-\frac{1}{2}[/tex] which turns out to be the limit!
Find the derivative of the function. F(x) = (5x² + 2x³)^4
Answer:
Derivative of y=(x⁴-2x³+5x²-4)³
Step-by-step explanation:
Please help me with Calculus homework, Question 2 only***Answer to question 1: -3.938
As given by the question
There are given that the function:
[tex]f(x)=x^3-6x[/tex]Now,
According to the answer to question #1 and the graph of the function:
It is the area under the curve from x = 0 and x = 3;
So,
Some of it is below the x-axis means negative area and some of it is above the x-axis which means positive area.
Then,
Yes, they will cancel out and the integral gives the exact net result.
Explained!
QUESTION DOWN BELOW! PLEASE HELP WILL GET 100 POINTS IM STUCK PLEASE HELP EXPLAIN ITS DUE SOON!!
many thanks!!!
ITS DUE SOON!
1) given
2) base angles theorem
3) PN=QN
4) [tex]\angle 3=\angle 4[/tex]
5) MP=OQ
7) PQ, QP
8) MQ=PO
9) ASA
You are testing the null hypothesis that the population proportion equals 45, using data you collected from a sample of 100 adults. You sample proportion equals .30. What does Z equal? (Round to two decimal places)
When one is testing the null hypothesis that the population proportion equals 45, the. z score is -3.02.
How to illustrate the information?The null and alternative hypothesis is illustrated as the population proportion equals 45,
P0 = 0.45
1 - P0 = 1 - 0.45 = 0.55
Test statistic = z
This will be illustrated as:
= 0.30 - 0.45/ [✓(0.45 * 0.55) / 100]
Test statistic = z = -3.02
Therefore, the z score is -3.02.
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what is the domain of y-x^2-1
The domain of the function y = x² - 1 in interval notation is (-∞, + ∞).
What is defined as the domain of the function?A function is simply object that accepts input, appears to apply a rule to it, and returns the result. A function can be thought of as a machine that receives in a number, performs some operation(s), and then outputs the result. The essential thing regarding functions is that they consistently apply the rule. As a result, if the same value is passed through the same function, the output will remain the same. The domain of a function is the collection of all its inputs. Its codomain is the collection of all possible outputs. The range refers to the outputs which are actually used.The given is y = x² - 1.
The domain of the function is;
Except when the expression is undefined, the domain of the representation is all real numbers. Given that there is no real number in this case, the expression is undefined.Thus, the domain of the function in interval notation is (-∞, + ∞).
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I Need the answer in 2 minutes
Answer: [tex]\frac{1}{1024}[/tex]
Step-by-step explanation:
[tex]4^{-3} = (2^{2} )^{-3} = 2^{-6}[/tex]
[tex]\frac{2^{-6} }{2^{4} } = 2^{-6-4} = 2^{-10} = \frac{1}{2^{10} } = \frac{1}{1024}[/tex]
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{4^{-3}}{2^4}}[/tex]
[tex]\mathsf{= \dfrac{\dfrac{1}{64}}{2\times2\times2\times2}}[/tex]
[tex]\mathsf{= \dfrac{\dfrac{1}{64}}{4\times4}}[/tex]
[tex]\mathsf{= \dfrac{\dfrac{1}{64}}{16}}[/tex]
[tex]\mathsf{= \dfrac{1}{1,024}}[/tex]
[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{\dfrac{1}{1,024}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
A journalist believes that, in reality, these components have a shorter lifespan than what the company is reporting.
He tests a random group of 35 of these components and finds a mean lifespan of 4.05 years.
a. What is the mean of the sampling distribution of sample means when 35 random components are tested?
The mean of the sampling distribution of sample means when 35 random components are tested will be 4.05 years.
How to illustrate the information?From the information, it should be noted that the journalist believes that, in reality, these components have a shorter lifespan than what the company is reporting.
He the tests a random group of 35 of these components and finds a mean lifespan of 4.05 years.
Therefore from the information, we acne see that the. mean lifespan has already been given.
Therefore, the mean lifespan is 4.05 years.
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The perimeter of the rectangle below is 104 units. Find the length of side RS
Write your answer without variables
Answer:
24
Step-by-step explanation:
Opposite sides on a rectangle are equal
So 2(3x+3)+2(4x)=104
Now expand, so 6x+6+8x=104
Simplify like terms, 14x+6=104
14x+6-6=104-6
14x=98
14x/14=98/14
x=7
Now just substitute the 7 in for the 3x+3 as thats what we are looking for.
3×7+3=24
HELP ASAP 100 POINTS
A group of seniors decide to spend their spring break away from home, attending at least one major event. The following table summarizes their preferences.
Attend a concert Attend a festival
Stay in state 214 186
Travel out of state 391 59
What percent want to attend a festival, given that they want to travel out of state?
6.94%
13.11%
24.08%
31.72%
Answer:
I think 31.72 because it 39156+214186 is 253342 it would be to low
A percentage is a number or ratio that represents a fraction of 100.
The percentage who want to attend a festival, given that they want to travel out of state is 6.94%.
What is a percentage?A percentage is a number or ratio that represents a fraction of 100.
We have,
Attend a concert Attend a festival
Stay in state 214 186
Travel out of state 391 59
The number of groups who wants to attend a concert while staying in a state:
= 214
The number of groups who wants to attend a concert while traveling out of the state:
= 391
The number of groups who wants to attend a festival while staying in a state:
= 186
The number of groups who wants to attend a festival while traveling out of the state:
= 59
The percentage who want to attend a festival, given that they want to travel out of state:
= The number of groups who wants to attend a festival while staying out of the state/ Total number of groups from all four conditions
= 59 / ( 214 + 391 + 186 + 59 ) x 100
= 59 / 850 x 100
= 6.94%
Thus,
The percentage who want to attend a festival, given that they want to travel out of state is 6.94%.
Option A is the correct answer.
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