Graph the following function.
f(x)=2(x-2)²-4
The graph of the given expression f(x)=2(x-2)²-4 is shown (refer to the graph attached below.)
What is a graph?In mathematics, a graph is a visual representation or diagram that shows data or values in an ordered way. The relationships between two or more things are frequently represented by the points on a graph. Charts and graphs come in a variety of styles.Line graphs, bar graphs and histograms, pie charts, and Cartesian graphs are likely the four most popular types. A graph's function representation can be determined using the vertical line test. All points with a certain x value are included in a vertical line. Output for a given input x value is represented by the y value of the point on a graph where a vertical line intersects it.So, f(x)=2(x-2)²-4:
Now, graph the function f(x)=2(x-2)²-4 as follows.(Refer to the graph attached below)Therefore, the graph of the given expression f(x)=2(x-2)²-4 is shown (refer to the graph attached below.)
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Luna purchased a computer at the list price of ₱56,000, less 30% and 20%. How much must Luna pay for the computer?
There are two disccount applied to this computer, the first one is 30%. To calculate its value, we need to multiply the original price by the fraction that represents 30%
[tex]\text{discount}1=56000\cdot\frac{30}{100}=16800[/tex]The first discount was 16,800. To determine the price after this, we need to subtract the listed price by the discount 1, this is done below:
[tex]\text{price}2=56000-16800=39200[/tex]Then we need to calculate the second discount, which was equal to 20%.
[tex]\begin{gathered} \text{discount}2=39200\cdot\frac{20}{100}=7840 \\ \end{gathered}[/tex]The final price is the subtraction between the price 2 and the discount 2, we have:
[tex]\text{ final price}=39200-7840=31360[/tex]The final price is 31,360.
how many time can 7 go into 65
Answer:
9
Step-by-step explanation:
The answer you divide 65 by 7 which would get you 9.2857142857143. The remainder is 2.
MATHEMATICALLY WE WRITE THE PROBLEM AS
[tex] = \frac{65}{7} \\ [/tex]
SOLVING FURTHER
[tex]65 \div 7 \\ = 9.285714286[/tex]
BUT 7 GOES 9 TIMES IN 65 NOT CONSIDERING THE REMINDER.
HOPE THIS HELPS
What is 1/3 divided by 2/3
Answer:
1/2
Step-by-step explanation:
Do divide fractions, multiply the first number by the reciprocal (the numbers flipped) of the second number.
So, 1/3 * 3/2
1/3 * 3/2 = 3/6
3/6 = 1/2
[tex] 4 ^{ \frac{1}{3} } \times 4 ^{ \frac{1}{5} } = [/tex]pls answer this
The given Expression is :
[tex]4^{\frac{1}{3}}\cdot4^{\frac{1}{5}}[/tex]From the property of exponents
If the base value of the exponents are same then during the process of multiplication powers will add up.
Since in the given expression 4 is the base value on both base of the exponents
Thus, base value are equal
The powers will add up:
[tex]\begin{gathered} 4^{\frac{1}{3}}\cdot4^{\frac{1}{5}} \\ 4^{\frac{1}{3}+\frac{1}{5}} \end{gathered}[/tex]Simplify the farction of the exponents :
[tex]\begin{gathered} \frac{1}{3}+\frac{1}{5} \\ \text{Taking LCM of the 3 \& 5} \\ \frac{1}{3}+\frac{1}{5}=\frac{5+3}{15} \\ \frac{1}{3}+\frac{1}{5}=\frac{8}{15} \end{gathered}[/tex]So, the value of the given expression will be :
[tex]\begin{gathered} 4^{\frac{1}{3}}\cdot4^{\frac{1}{5}}=4^{\frac{1}{3}+\frac{1}{5}} \\ 4^{\frac{1}{3}}\cdot4^{\frac{1}{5}}=4^{\frac{8}{15}} \end{gathered}[/tex]Answer : 4 ^8/15
need help with these parts. both parts use the same table
Given:
[tex]f(x)=h(2x)[/tex]And the values in the table.
Required:
The equation of a normal line to f at x=3.
Explanation:
The equation of the line that passes through from point (x,y) and has slope m
is given by the formula
[tex]y-y_1=m(x-x_1)[/tex]From the table at x=3, f(x)=h(2x)
that is f(3)= h(6)=9
And the slope from the table at x=3 is 1/2.
Now the equation of the line is:
[tex]\begin{gathered} y-9=\frac{1}{2}(x-3) \\ 2(y-9)=(x-3) \\ 2y-18=x-3 \\ x-2y=-15 \end{gathered}[/tex]Final answer:
Thus the equation of the normal line is
[tex]x-2y+15=0[/tex]help meeeeeee pleaseee !!!!
The equation of the line that passes through the points ( -3,18 ) and ( 2,-7 ) is f(x) = -5x + 3.
What is the equation of line passing through the given points?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given the data in the question;
Point 1( -3,18 )
x₁ = -3y₁ = 18Point 2( 2, -7 )
x₂ = 2y₂ = -7First, we find the slope of the line.
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
m = ( -7 - 18 ) / ( 2 - (-3) )
m = ( -25 ) / ( 2 + 3 )
m = ( -25 ) / ( 5 )
m = -5
Next, next we find the y-intercept
y = mx + b
18 = (-5)(-3) + b
18 = 15 + b
b = 18 - 15
b = 3
Now that the values of slope m and y-intercept b is known, plug these into y = mx + b to determine the equation of the line.
y = mx + b
y = (-5)x + 3
y = -5x + 3
Therefore, the equation of the line is y = -5x + 3
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If you roll a die, find the probability that you: (Enter your answers in exact form or round to 3 decimalplaces.)(a) roll at least 4 or an odd number,Answer:(b) roll an even number or a number at most 5.Answer:
A.
The question asks us to find the probability of getting at least 4 or an odd number after throwing a die.
This is easily gotten using the OR probability of two events which states:
[tex]\begin{gathered} P(A\text{ OR B) = P(A) + P(B) - P(A AND B)} \\ \text{if A = rolling at least 4} \\ B\text{ = rolling odd number,} \\ \\ P(\text{rolling at least 4 OR rolling odd number) = } \\ P(\text{at least 4) + P(odd number) - P(at least 4 AND odd number)} \end{gathered}[/tex]To get at least 4, it means the possible values we can have are: 4, 5, 6.
To get an odd number, it means the possible values we can have are: 1, 3, 5.
From both set of possibilities, 5 is common. We need to subtract the probability of getting a 5 in both situations to prevent duplication.
Thus, we can compute each probability:
[tex]\begin{gathered} P(any\text{ number)= }\frac{1}{6} \\ \\ P(at\text{ least 4)= P(4) OR P(5) OR P(6) = P(4) + P(5) +P(6)} \\ \therefore P(at\text{ least 4)= }\frac{1}{6}+\frac{1}{6}+\frac{1}{6}=\frac{3}{6} \\ \\ P(\text{odd number) = P(1) OR P(3) OR P(5) = P(1)+P(3)+P(5)} \\ \therefore P(\text{odd number)= }\frac{1}{6}+\frac{1}{6}+\frac{1}{6}=\frac{3}{6} \\ \\ P(\text{at least 4 AND odd number) = }\frac{1}{6} \\ \\ \\ \therefore P(\text{at least 4 or odd number)=}\frac{3}{6}+\frac{3}{6}-\frac{1}{6}=\frac{5}{6} \end{gathered}[/tex]Therefore, the probability of getting at least 4 or an odd number is 5/6
B:
This part of the question asks us to find the probability of rolling an even number or a number at most 5.
We, once again, take a look at the possibilities to solve this question.
Possibilities of getting an even number are: 2, 4, or 6
Possibilities of getting at most 5 are: 1, 2 , 3, 4, 5.
Therefore, we can compute the probabilities as:
[tex]undefined[/tex]A 2-column table with 4 rows. The first column has entries glass, baby oil, maple syrup, wax. The second column has entries 2.40 grams per centimeter cubed, 0.83 grams per centimeter cubed, 1.37 grams per centimeter cubed, 0.93 grams per centimeter cubed.
Use the information in the table to predict whether each substance will sink or float in water. Note that the density of water is 1.0 g/cm3.
Glass:
Baby oil:
Maple syrup:
Wax:
The Glass and Maple syrup will sink , Baby Oil and Wax will float in water.
We are provided with the following data mentioned below:
Glass Baby oil Maple syrup Wax
2.40 0.83 1.37 0.93
The density of water = 1.0 [tex]g/cm^{3}[/tex]
The material with the lower density floats and the material having higher velocity sinks. As the density of glass is 2.40 [tex]g/cm^{3}[/tex] which is larger than the density of water , so glass will sink in water. As the density of baby oil is 0.83 [tex]g/cm^{3}[/tex] which is less than the density of water , so glass will float in water.
As the density of Maple syrup is 1.37 [tex]g/cm^{3}[/tex] which is larger than the density of water , so Maple syrup will sink in water. As the density of Wax is 0.93[tex]g/cm^{3}[/tex] which is less than the density of water ,so Wax will float in water.
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Answer:
Step-by-step explanation:
what is this answer i need it asap!
Answer:
The answer is 3.375
Step-by-step explanation:
You just multiply 1.5 by itself 3 times
Graph a line with a slope of2that contains the point (-3,5).5
We will investigate how to graph a straight line on cartesian coordinate plane.
All equations of straight line are expressed in a general slope-intercept form as follows:
[tex]y\text{ = m}\cdot x\text{ + c}[/tex]Where,
[tex]\begin{gathered} m\colon\text{ slope} \\ c\colon\text{ y-intercept} \end{gathered}[/tex]To graph any straight line we need the equation of the straight line or atleast two points that must lie on the line.
We are given the slope ( m ) and one of the points that lie on the line as follows:
[tex]\begin{gathered} m\text{ = -}\frac{2}{5} \\ \\ (\text{ -3 , 5 )} \end{gathered}[/tex]We need one another point that lies on the line to plot the graph of a straight line. To find another point we must completely express the equation of the straight line ( general form given above ).
We see that an equation of a straight line is defined by two parameters i.e ( m and c ). We are given the value of the slope ( m ). We will go ahead and plug it into the general slope-intercept form given above:
[tex]y\text{ = -}\frac{2}{5}\cdot x\text{ + c}[/tex]Now to determine the value of parameter ( c ) we must have atleast one point that lies on the line. We will use the point given to us and plug in the respective coordinates in the equation developed above and solve for ( c ) as follows:
[tex]\begin{gathered} (\text{ x , y ) }\to\text{ ( -3 , 5 )} \\ \\ 5\text{ = -}\frac{2}{5}\cdot(-3)\text{ + c} \\ \\ 5\text{ = }\frac{5c\text{ + 6}}{5} \\ \\ 25\text{ = 6 + 5c} \\ \\ c\text{ = }\frac{19}{5} \end{gathered}[/tex]We will go ahead and update the equation of the straight line as follows:
[tex]y\text{ = -}\frac{2}{5}\cdot x+\frac{19}{5}[/tex]Now to get one more point to graph the plot we will assume any value of the for either variable ( x or y ) and then determine the value of the other variable as follows:
[tex]\begin{gathered} x\text{ = 2} \\ \\ y\text{ = -}\frac{2}{5}\cdot(2)\text{ +}\frac{19}{5} \\ \\ y\text{ = }\frac{-4+19}{5} \\ \\ y\text{ = }\frac{-15}{5} \\ \\ y\text{ = -3} \end{gathered}[/tex]Therefore, we have the two points to plot the graph as follows:
[tex](\text{ -3 , 5 ) \& ( 2 , -3 )}[/tex]We can go ahead and select the above points on the given grid to construct the straight line!
Thad needs to buy dirt for his children's playground. The dirt costs $15 per ton, and there is a delivery cost of $12 with each order. What types of numbers are possible in the domain? -All positive rational numbers -All rational numbers greater than 15 -All positive rational numbers less than 12 -All rational numbers
The domain is the set input values, it means the number of tons that can be deliver.
The type of numbers that are possible are the positive rational numbers. This is because you can order 1, 2, 2.5, 1/3 tons but you can not order -6, -4.4 or -0.3 tons.
It means that the type of numbers that are possible for the domain are the possitive rational numbers.
please answer this anybody
Answer:
5 is a vertical angle. 1 is a vertical angle. 3 is a corresponding angle.
Step-by-step explanation:
Let me know if i got anything wrong!
One way to determine whether a number is prime or composite is by creating a factor table.
Complete the factor table and the sentences below about the number 18.
The conclusion from the factor table of 18 is that, 18 is not a prime number i.e. it is composite
How to determine the factor table?From the question, the number is given as
Number = 18
The factors of 18 are represented as
Factors of 18 = 1, 2, 3, 6, 9 and 18
When these factors are picked in pairs, we have the following representations
Factors pairs of 18 = (1, 18), (2, 9), (3, 6)
Next, we represent the factors on a factor table
So, we have
Factors Factor pairs Prime factorization
1, 2, 3, (1, 18) 2 x 3²
6, 9 and (2, 9)
18 (3, 6)
Because the number 18 has factors other than 1 and 18, then the number 18 is a composite number
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what is the correct order of operations for the expression below
Given:
[tex](7-4)\div(5-2)[/tex]Required:
To choose the correct order of operations for the given expression.
Explanation:
Consider the given exprsesion
[tex](7-4)\div(5-2)[/tex]Here subtract 4 from 7, subtract 2 from 5, and divide the first difference by the second.
Final Answer:
Subtract 4 from 7, subtract 2 from 5, and divide the first difference by the second.
Find the common factors and the highest common factor of each of the following
a. 6, 8 and 10
b. 4, 8 and 12
c. 10, 15 and 20
d. 6, 12 and 24
e. 8, 12 and 16
f. 13, 26 and 39
h. 16, 32 and 40
g. 12, 14 and 16
i. 16, 56 and 64
j. 8,24 and 40
k. 7, 35 and 42
l. 22,44 and 66
9 Ron's family plans to add a new room to their house. They initially planned the width and the length of the room to be 10 feet and 25 feet. Now they want to add to the width. The amount they want to add to the width is shown by the variable I. 25 101 + Ron thinks that the area of the room will be 250 + 257. Is he correct? Why or why not? Select all that apply. A Yes, because the area of the room is the sum of 25.10 and 25r. No, because the area of the room is the sum of 25 . 10 and I. No, because the area of the room is the product of 25 + 10 and 25.1. D Yes, because the area of the room is the product of 25 and 10+ I.
The room is a rectangle with dimensions 25 and x + 10. The area of a rectangle is the product of its dimensions, so the area will be:
[tex]25\cdot(x+10)[/tex]We have to add the parenthesis because we first need to add 10 and x and then multiply. Distributing the 25, we have:
[tex]25\cdot(x+10)=25\cdot x+25\cdot10=25x+250=250+25x[/tex]As we can see, this matches what Ron thinks the area will be, so he is correct. Thus, the answer is "Yes". The why can be both because the area is the sum of 25*10 and 25x and because the area is the product of 25 and 10 + x.
So, the correct alternatives are A and D.
4. A student asks, “If the average income of 10 people is $10,000 and one person gets a raise of $10,000, is the median or the mean changed and, if so, by how much?
Since we don't know the specific income of each person in the sample, we don't know for sure if the median will change. Nevertheless, the mean will surely raise.
Since the current average income is $10,000, if one of them gets a raise of $10,000, then the sum of all incomes would be $100,000+$10,000=$110,000. And the new average income will be:
[tex]\frac{110,000}{10}=11,000[/tex]Then, the mean increases by $1,000, and we can't say anything about the median.
Solve for X. 70 degreeright angle 6solve
ANSWER:
The value of x is 16.49
STEP-BY-STEP EXPLANATION:
We can calculate the value of x by means of the tangent trignometric function, which is the following
[tex]\begin{gathered} \tan \theta=\frac{\text{opposite}}{\text{adjacent}} \\ \theta=70\text{\degree} \\ \text{opposite = x} \\ \text{adjacent = 6} \end{gathered}[/tex]Replacing and solving for x:
[tex]\begin{gathered} \tan 70=\frac{x}{6} \\ x=6\cdot\tan 70 \\ x=16.49 \end{gathered}[/tex]it says determine how to rewrite one of the two equations above in the form ax + by=c. where a B and C are consistent so that the sum of the new equation in the unchanged equation from the original system results in an equation of one variable
Solution
-3x +4y = 24 (1)
6x +2y =-18 (2)
We can multiply equation (1) by 2 and we got:
-6x + 12y = 48
6x +2y =-18
_____________
14 y= 30
y = 30/14= 15/7
And the value of x would be:
x= 4y-24/3
x= (60/7 -24)/3
You are trying to memorize a speech for your public speaking class. After 1 day, you memorized 200 words. Each of the following days, you memorized an additional 30 words.
Use the given information to write a linear equation in point-slope form. Then use the equation to find the number of words will you have memorized after 8 days.
__words
can someone help me find the formule pls
The linear equation in point-slope form of the given condition is y = 30x + 170. The number of words after 8 days will be 410.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
Let's represent the number of days by x and the number of words by y.
At day 1 (x = 1) ⇒ Number of words (y = 200)
At day 1 (x = 2) ⇒ Number of words (y = 230)
The point-slope form of a linear equation is given as,
y = mx + c
Where m is the slope, while c is the y-intercept.
Substitute,(1,200) in y = mx + c
200 = m(1) + c
Now slope m = (230 - 200)/(2 - 1) = 30
200 = 30(1) + c
c = 170
Therefore, the equation become,
y = 30x + 170
The number of words after 8 days will be,
y = 30(8) + 170 = 410
Hence "The linear equation in point-slope form of the given condition is y = 30x + 170. The number of words after 8 days will be 410".
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QUESTION IN ATTACHMENTS
Answer:
C.
Step-by-step explanation:
Since you are missing a side, use the Pythagorean Theorem:
[tex]a^{2}+b^{2}=c^{2}\\ 5^{2}+8^{2}=c^{2}\\ 25+64=c^{2}\\ 89=c^{2}\\ \sqrt{89}=c Answer[/tex]
Answer:
the answer is C.
[tex] \sqrt{89} [/tex]
Find the value of x. A. 9B. 145C. 8D. 154
Answer: C. 8
When we have two chords intersecting inside a circle, the products of the lengths of the segments are equal to one another. This means that for the given circle, we have the following:
10 * 4 = 5 * x
We can solve for x by multiplying 10 by 4, which is 40, and then dividing by 5, to isolate x, which is 8.
A truck driver averages 60 miles per hour while delivering freight and 45 mph on the return trip.The total driving time is 10 hours. How much longer does the return trip take than the delivery
The return trip takes 0.7 hrs more than the delivery.
Let the time taken while going be x therefore the time taken while returning will be 10 - x.
Given :
The truck driver averages 60 miles per hour while delivering freight
The speed is 45 mph on the return trip.
Therefore according to the question,
60x = 45 ( 10 - x) [ As the distance is same]
=> 4x = 3 ( 10 - x)
=> 4x = 30 - 3x
=> 7x = 30
=> x = 30 / 7
=> x = 4.3
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Put in simplest radical form: -√3 + 4√3
Answer:
3√3
Step-by-step explanation:
You want the simplest radical form of -√3 + 4√3.
Like termsWe can consider these "like terms" in the sense that each is an integer multiple of √3. As such, they can be combined by combining coefficients.
-√3 + 4√3 = (-1 +4)√3 = 3√3
- The Freedom Tower in New York City is 1776 feet
tall. The equation f(t) = -16t² + 1776 models the
height f(t) (in feet) of an object t seconds after it is
dropped from the top of the tower.
a. After how many seconds will the object hit the
ground? Round your answer to the nearest
hundredth of a second.
b. What is the height of the object 3 seconds after
it has been dropped from the top of the tower?
A golf ball is hit from the ground, and its height
can be modeled by the equation h(t) ==16t² + 128t,
where h(t) represents the height (in feet) of the ball
t seconds after contact. What will the maximum
height of the ball be?
WILL GIVE BRAINLIEST PLSSS
Part a: time when object hit the ground is 10.5 sec.
Part b: The height of the object 3 seconds is 1632 ft.
What is termed as the equation of motion?A mathematical formula which describes this same position, velocity, as well as acceleration of a body in relation to a specific frame of reference is known as an equation of motion. The equation of motion is second law, that also states that the force that acts on an object is equivalent to the mass m of a body multiplied by the acceleration an of its center of mass.For the given question;
The equation that models the height f(t) (in feet) of an object t seconds after it is when dropped from the top of the tower is,
f(t) = -16t² + 1776
Part a: time when object hit the ground.
When the object hit the ground, height will be zero.
Put f(t) = 0.
0 = -16t² + 1776
-16t² = -1776
t² = 111
t = 10.5 sec.
The, time after which the object will hit the ground is 10.5 sec.
Part b: The height of the object 3 seconds;
Put t = 3 in the equation.
f(3) = -16(3)² + 1776
f(3) = 1632 ft
The height of the object after 3 sec will be 1632 ft.
Thus, the values for the object hitting the ground are found.
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Which equation has a constant of proportionality equal to 1? Choose 1 answer: A y 10 1 11 B y 7 8 3 y = 15 D y = 2
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y=kx
where
k is the constan of proportionality
therefore
in this problem
the answer is the option Dy=x
because, the value of k =1
Write an algebraic expression as indicated. The algebraic expression for the mountain Roberto‘s other account is
We have here that Roberto has a total of $3300 in two savings account.
Then, if y represents the amount in one account, we have that the sum of both accounts is up to $3300.
We can suppose that the other account is x. Then, we have:
[tex]x+y=\$3300[/tex]If we subtract y from both sides of the equation, we have:
[tex]x+y-y=\$3300-y\Rightarrow x=\$3300-y[/tex]Therefore, the algebraic expression for the amount in Roberto's other account is (since x is not mentioned, we have):
[tex]\$3300-y[/tex]In summary, the amount in Roberto's other account is $3300 - y.
20 PTS GET MAKED BRAINLIEST IF CORRECT
a) the probability that event A occurs but event B does not occur = 0.33
b) the probability that either B occurs without A occurring or A and B both occur = 0.04
In this question, we have been given two mutually exclusive events A and B.
event A has probability 0.33 and the event B has probability 0.04
P(A) = 0.33 and P(B) = 0.04
We need to compute the probability that event A occurs but event B does not occur.
i.t., to find = P(A ∩ B')
We know that, P(A ∩ B') = P(A) - P(A ∩ B)
For mutually exclusive events, P(A ∩ B) = 0
So, P(A ∩ B') = P(A)
P(A ∩ B') = 0.33
Also, we need to compute the probability that either B occurs without A occurring or A and B both occur.
P(B ∪ A') + P(A ∩ B)
= P(B) + 0
= 0.04
Therefore, a) the probability that event A occurs but event B does not occur = 0.33
b) the probability that either B occurs without A occurring or A and B both occur = 0.04
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Consider the rectangle with width 20 in and length 26 in, write a ratio of the width to length
The ratio of the width of the rectangle to the length of the rectangle is 10/13
We are provided with the rectangle. The dimensions of the rectangle are mentioned below;
Width of rectangle = 20
Length of rectangle = 26
We were asked to calculate the ratio of width of the rectangle to the length of the rectangle. So, to calculate the ratio of width of the rectangle to the length of the rectangle we need to divide the width of rectangle to the length of the rectangle as mentioned below;
( Width of rectangle/Length of rectangle ) = 20 / 26
( Width of rectangle/Length of rectangle ) = 10/13
So, we can finally conclude that the ratio of width of the rectangle to the length of the rectangle is 10/13 .
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