The values of α and β = 4/〖3x〗^2
A quadratic equation is a second-order polynomial equation in a single variable x
ax2+bx+c=0. with a ≠ 0
Given quadratic equation is 3x2 – 4x = 0
We have to alpha and beta from the given equation
We know that in the quadratic expression
α + β = -b/a. αβ = c/a.
from the equation expression
α + β = 4/〖3x〗^2
αβ = 0/3 ---- (1)
αβ = 0 ----- (2)
If we consider α = 0 from equation (2) then
α + β = 4/〖3x〗^2
β = 4/〖3x〗^2
If we consider β = 0 from equation (2) then
α + β = 4/〖3x〗^2
α = 4/〖3x〗^2
Therefore the values of α = β = 4/〖3x〗^2
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What is the perimeter of the figure Assume that all angles are right anglesA) 23 yardsB) 30 yardsC) 32 yardsD) 26 yards
The perimeter of the figure is the sum of the lengths of its sides. Find the missing side lengths to calculate the perimeter of the figure.
The length of then missing horizontal side is 6yd because it must add up to 8yd with the 2yd segment.
The length of the missing vertical side is 4yd because it must add up to 7yd with the 3yd segment.
Then, the perimeter of the figure is:
[tex]\begin{gathered} P=7yd+8yd+3yd+2yd+4yd+6yd \\ =30yd \end{gathered}[/tex]Therefore, the correct choice is option B) 30 yards.
420, 84, 16.8, 3.36,... What is the explicit rule for this sequence? An =___ *(____)^n-1
Answer:
[tex]a_n=420\ast(0.2)^{n-1}[/tex]Explanation:
The explicit formula for a geometric sequence is always given in the form;
[tex]a_n=a_1\ast(r)^{n-1}[/tex]where an = the nth term of the sequence
a1 = the 1st term of the sequence
r = the common ratio of the sequence
From the given sequence, we can see that the 1st term, a1, is 420.
We can find the common ratio, r, by dividing any number of the sequence with its preceding number;
[tex]\begin{gathered} r=\frac{84}{420}=0.2\text{ or 16.8/84 = 0.2} \\ \therefore r=0.2 \end{gathered}[/tex]Substituting the above values into our formula above, we'll have;
[tex]a_n=420\ast(0.2)^{n-1}[/tex]Write a equation of the line described
Passes through (4,8)
Parallel to the line y=-7/4x-4
Answer:
y=-7/4x+15
Step-by-step explanation:
Parallel line so has the same gradient:
y=-7/4x+c
Substitute (4,8) into above equation
8=(-7/4 x 4)+ c
rearrange to find c
8=-7+c
c=15
New equation: y=-7/4x+15
Hope this helps!
Write a numerical expression in the first box that represents the number of points earned or lost each round.then write Andy's final point total at the end of the competition in the second box.
In the first round, Andy has -320 times 1/2, which corresponds to
[tex]-320\times\frac{1}{2}=-\frac{320}{2}=-160[/tex]In the second round, Ansy has
[tex]710\times\frac{1}{4}=\frac{710}{4}=\frac{355}{2}[/tex]which corresponds to 177.5 (in decimals).
Finally, Andy's final point is
[tex]-320\times\frac{1}{2}+710\times\frac{1}{4}-500[/tex]which is equal to
[tex]-160+177.5-500=-482.5[/tex]that is, Andy's final point is - 482.5.
PLEASE EEEEEEEE this is very important :’)
number attended/ total people
a) 153/225 = 17/25 = 0.68 = 68%
Answer:
A
Step-by-step explanation:
[tex]{ \tt{ = \frac{153 \div 9}{225 \div 9} }} \\ \\ = { \tt{ \frac{17}{25} }} \\ \\ = 0.68 \times 100\% \\ \\ = 68\%[/tex]
Problem ID: PRABMVM9 For each of the functions f, g, h, P, and q, the domain is o sxs 100. For which functions is the average rate of change a good measure of how the function changes for this domain? Select all that apply. A. F(x)=x+2 B. g(x)=2* C. h(x)= 111x-23 D. p(x)=50,000 x 3% E. g(x)= 87.5
a) b) c) d)
1) Examining each function, let's test considering that the average rate of change is given by:
[tex]\Delta=\frac{f(b)-f(a)}{b-a}[/tex]2) So let's plug the functions:
[tex]\begin{gathered} a)\text{ }\Delta=\frac{(100)+2\text{ -\lbrack(0)+2\rbrack}}{100-0}=\frac{102-2}{100}=\frac{100}{100}=1 \\ b)\text{ }g(x)=2^x\text{ }\Delta=\frac{2^{100}-2^0}{100-0}=\frac{1.26\times10^{30}}{100}=1.26\times10^{28} \\ c)\text{ }h(x)\text{ = }111x-23\text{ }\Delta=\frac{111(100)-23\text{ -\lbrack{}111(0)-23}}{100}=111 \\ d)\text{ }p(x)\text{ = }50,000\times3^x\Delta=\frac{50,000-3^{100}-\lbrack50,000-3^0}{100}=-5.15\times10^{45} \\ e)q(x)=87.5 \end{gathered}[/tex]3) Since the average rate of change is a "measure of how much a function changes in the given interval" and considering that we have linear and exponential functions and the last one e) is not a function but an equation.
Then we can say that for the functions below the average rate of change is a good measure, not applying for the last one which, indeed is not a function.
a)
b)
c)
d)
Answer:
If you go off of the explanation below... the actual answers are A, C, E...
Step-by-step explanation:
Correct Answer
A)
f(x)=x+2
C)
h(x)=111x−23
E)
q(x)=87.5
In right triangle ABC, m 2 A = 32°, m 2 B= 90°, andAC = 6.2 cm. What is the length of BC, to the nearesttenth of a centimeter?
Given Data:
In a triangle ABC,
[tex]\begin{gathered} \angle A=32^{\circ} \\ \angle B=90^{\circ} \\ AC=6.2\text{ cm.} \end{gathered}[/tex]From the triginometry,
[tex]undefined[/tex]Write an equation of the line in slope intercept form that passes through the given point and is perpendicular to the given line.(-2,4) , y = 2x + 9
We are given the point (-2,4) and the line y=2x+9. We want the equation of the line that passes through the given point and that is perpendicular to the given line.
To do so, we will use the following equation of a line
[tex]y\text{ -a = m\lparen x -b\rparen}[/tex]in this equation, m is the slope of the line and (a,b) is a point in the line. In our case, we are given that (-2,4) is in the line. That is, a=-2 and b=4. So our equation becomes
[tex]y\text{ -4=m\lparen x -\lparen-2\rparen\rparen}[/tex]or equivalently
[tex]y\text{ -4}=m(x\text{ +2\rparen}[/tex]now, we only need to find the value of m. To do so, we use the given line and the fact that the product of the slopes of perpendicular lines is -1.
The given line (2x+9) has a slope of 2. So, we have the following equation
[tex]m\cdot2=\text{ -1}[/tex]so if we divide both sides by 2, we get that
[tex]m=\text{ -}\frac{1}{2}[/tex]So the equation we are looking for becomes
[tex]y\text{ -4 }=\text{ -}\frac{1}{2}(x\text{ +2\rparen}[/tex]We want this equation in the slope intercept form. So we operate to find y in this equation. So first, we distribute on the right hand side. We get
[tex]y\text{ -4}=\text{ -}\frac{1}{2}x\text{ -}\frac{2}{2}=\text{ -}\frac{1}{2}x\text{ -1}[/tex]now we add 4 on both sides, so we get
[tex]y=\text{ -}\frac{1}{2}x\text{ -1+4= -}\frac{1}{2}x+3[/tex]we can check that if x= -2 we get
[tex]y=\text{ -}\frac{1}{2}(\text{ -2\rparen+3=1+3=4}[/tex]which confirms that the point (-2,4) is on the line
Select the correct answer from each drop-down menu.y 10+816+4AETBBية1+60-8106A sequence of transformations maps AABCO ABC. The sequence of transformations that maps ABC onto ABC is a✓ followed by
Explanation:
To find the transformation
We will first have to write out the coordinates of ABC
The coordinates of ABC are:
[tex]\begin{gathered} A=(-4,4) \\ B=(-8,2) \\ C=(-6,6) \end{gathered}[/tex]Next, we will write the equation of the image
[tex]\begin{gathered} A^{\prime}=(4,-2) \\ B^{\prime}=(2,2) \\ C^{\prime}=(6,0) \end{gathered}[/tex]From the given coordinates of the image and pre-image
When we rotate a figure of 90 degrees counterclockwise, each point of the given figure has to be changed from (x, y) to (-y, x) and graph the rotated figure.
To rotate the figure 90 degrees clockwise about a point, every point(x,y) will rotate to (y, -x)
Also, there was a
You earn $8.00 for every lawn that you mow. You went out to lunch andspent $25.75. At the end of the day, you had $94.25. Write and solve anequation to figure out howmany lawnsyou mowed.
Let individual move x lawns.
The equation for the number of lawns is,
[tex]8x-25.75=94.25[/tex]Solve the equation to obtai the value of x.
using the values from the graph, compute the values for the terms given in the problem. Choose the correct answer. Age of car = 4 years Original cost = 13,850 The current market value is $ _
Answer:
3462.5$
Step-by-step explanation:
If the percentage after 4 years was 25% then it dropped to 3462.5$.
Help me asap I'm so stressed it's a Yes Or No questionstheres 7 questions in the image each one is a yes or no answer pls help I'm super stressed
Explanation:
A relation is a function if every value of x is related to just one value of y.
So, number 6 is not a function because -4 is related to 9 and -4 is also related to 0.
Number 7 is a function because every value of x (first coordinate) is related to one value of y (second coordinate).
In the same way, we can say that number 8 is also a function and number 9 is not a function because number 7 is related to 0, -5, -8, 4, and 3.
Finally, for the graph of numbers 10, 11, and 12 we need to identify the coordinates of every point.
So, number 10 is equivalent to:
{(-7, -1), (-2, -7), (0, 2), (4, 2), (6,6)}
It means that number 10 is a function
For number 11, we get:
{(-5, -4), (-3, 5), (2, -1), (2
Trying to use a model or number line for fractions for a 4th grader
Given:
[tex]\frac{76}{100}-\frac{50}{100}[/tex]Solve:
[tex]\begin{gathered} \frac{76}{100}-\frac{50}{100} \\ so\colon \\ =\frac{76-50}{100} \\ =\frac{26}{100} \end{gathered}[/tex][tex]\begin{gathered} =\frac{26}{100} \\ =0.26 \end{gathered}[/tex]In number line 0.26 lies in between 0 to 1.
which improper is equal to 4
Looking at the given fractions,
4/4 = 1
12/3 = 4
12/4 = 3
Thus, the improper fraction that is equal to 4 is 12/3
5(2x-7)+42-3x=2 what is the answer
Problem
5(2x-7)+42-3x=2 what is the answer
Solution
For this case we can distribute the terms on this way:
10x -35 +42 -3x = 2
Now we can aggrupate similar terms and we got:
7x= 2+35-42
7x = -5
And then solving for x we got:
x= -5/7
Allison drew a map of where she and her friends live. Allison's house is at point A, and her friends live at points B, C, and D. She only wrote some of the distances, in blocks, on the map. Also, AD¯¯¯¯¯¯¯¯ is a perpendicular bisector of BC¯¯¯¯¯¯¯¯. Allison wants to know the distance between her house and point C.What is the measure of AC?
Solution:
Given that;
Allison drew a map of where she and her friends live.
Allison's house is at point A, and her friends live at points B, C, and D
Where, line segment AD is a perpendicular bisector of BC,
And a perpendicular bisector is a line segment which bisects another line segment at 90 degrees, and divides it into two equal parts..
Since, AD is a perpendicular bisector of BC, then
[tex]\begin{gathered} BD=CD=3 \\ \angle ADB=\angle ADC \\ And,\text{ }AD=CD \\ Thus, \\ \Delta ADB\cong\Delta ADC\text{ \lparen SAS\rparen} \end{gathered}[/tex]Hence,
[tex]AB=AC=4.24[/tex]The measure of AC is 4.24
A gopher has dug hose and opposite corners of a rectangle yard if the artist 12 m x 16 m how far will the golfer have to run to get from one of its holes to the other
Given:
There are given that a rectangular yard.
Explanation:
To find the distance that one holes to other:
We need to use the Pythagoras theorem.
So,
From the Pythagoras theorem:
[tex]c^2=a^2+b^2[/tex]Where,
[tex]\begin{gathered} a=12 \\ b=16 \end{gathered}[/tex]Then,
Put both values into the above formula
So,
[tex]\begin{gathered} c^2=a^2+b^2 \\ c^2=12^2+16^2 \\ c^2=144+256 \\ c^2=400 \\ c=\sqrt[]{400} \\ c=20 \end{gathered}[/tex]Final answer:
Hence, 20 meters that will the gopher have to run get from one of its holes to the other.
There are given that a rectanglua
Which answer choice correctly represents 1.436363636…?A) 1.436 _B) 1.436 __D) 1.436 ___C) 1.436
Given: The number below
[tex]1.436363636\ldots[/tex]To Determine: The simplified form of writing the given number
It can be observed the given number that 36 keeps recurring indefinitely
Hence, the nuumber can be written as
[tex]1.436363636\ldots=1.4\bar{36}[/tex]Hence, option C is the correct answer
use three letters to name (a) the plane on which the square pyramid sits and (b) a plane represented by one of the sides.
Use three letters to name
(a) The plane on which the square pyramid sits and ABC
Why : because ABC is at the base of the square pyramid
b) A plane represented by one of the sides. ABG
Why : Because ABG represents the triangle of one of the 4 sides of the pyramid
it is due today!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1
The value of 5/9x - 2/3y + xy when x = 3/5 and y = 1/2 is 3/10
We need to evaluate the expression
5/9x - 2/3y + xy
x = 3/5 and y = 1/2
(5/9)(3/5) - (2/3)(1/2) + (3/5)(1/2)
(15/45) - (2/6) + (3/10)
1/3 - 1/3 + 3/10
= 3/10
Therefore, the value of 5/9x - 2/3y + xy when x = 3/5 and y = 1/2 is 3/10
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USE THE NORMAL CURVE TABLE TO DETERMINE THE PERCENT OF DATA SPECIFIED.A) TO THE LEFT OF z = 1.62B) BETWEEN z = -1.53 AND z = -1.82
SOLUTION:
Using a normal distribution table, we find that;
a. The area to the left of z = 1.62 is;
[tex]P(z<1.62)=0.9474[/tex]b. The area between z = -1.53 and z = -1.82, this is;
[tex]P(-1.82gabrielle wants to buy a new pair of jeans. if the jeans were originally $25.00, but are on sale with a $15 discount, how much will gabrielle have to pay for the jeans.
If the lines /1 and /2 are parallel, what must be value of y?
ANSWER
y = 130 degrees
STEP-BY-STEP EXPLANATION
Key points to note in the provided figure
Alternate exterior angles are equal
The sum of supplementary angles is 180 degrees
From the figure given, angle y and angle 5x are alternate exterior angles
Since alternate exterior angles are equal. Hence, angle y = angle 5x
y = 5x
Also, angle (2x - 2) and y are supplementary angles
Recall, the sum of supplementary angles is 180 degrees
Hence, we have
y + (2x - 2) = 180
Note, y = 5x
substitute y = 5x into the above equation
5x + (2x - 2) = 180
Open the parenthesis
5x + 2x - 2 = 180
Collect the like terms
5x + 2x - 2 = 180
7x - 2 = 180
Add 2 to both sides of the equation
7x - 2 + 2 = 180 + 2
7x = 182
Divide both sides by 7
7x/7 = 182/7
x = 26 degrees
Since we have gotten the value of x = 26 degrees. Hence, we can now find the value of y
Recall, y = 5x
y = 5(26)
y = 130 degrees
Comparing Relationships with Tables1. Decide whether each table could represent a proportional relationship.If the relationship could be proportional, what would the constant ofproportionality be?a. How loud a sound is depending on how farDistance toaway you are.Listener (ft)Sound Level(dB)85791020407367Costb. The cost of fountain drinks at Hot Dog Hut.Volume(fluid ounces)($)$1.4920$1.59$1.8930
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 constant of proportionality
Verify each table
table a
Let
x ----> distance
y ----> sound level
For each ordered pair calculate the value of k
k=y/x
so
(5,85) -----> k=85/5=17
(10,79) ----> k=79/10=7.9
the values of k are differents
that means
the table nor represent a proportional relationship
table b
let
x ----> volume
y ----> cost
k=y/x
(16,1.49) ----> k=1.49/16=0.093125
(20,1.59) ----> k=1.59/20=0.0795
the values of k are differents
that means
the table nor represent a proportional relationship
f(x) = -x^2 - 4x + 13find f(3)
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
f(x) = -x^2 - 4x + 13
f(3) = ?
Step 02:
f(x) = - x² - 4x + 13
f(3) = - (3)² - 4(3) + 13
f(3) = - 9 - 12 + 13
f(3) = - 21 + 13
f(3) = - 8
The answer is:
f(3) = - 8
A store has clearance items that have been marked down by 45%. They are having a sale, advertising anadditional 50% off clearance items. What percent of the original price do you end up paying?%Give your answer accurate to at least one decimal place.
We have clearance items that have two discounts applied to its price.
We can use a $1 item to find the final discount.
If we apply a 45% mark down, we will obtain a price of:
[tex]1-1*0.45=0.55[/tex]The discounted price is $0.55.
To this price we apply a 50% off. This can be expressed as:
[tex]0.55(1-0.5)=0.55*0.5=0.275[/tex]This is the final price.
We can calculate the percentage of the original price as:
[tex]\frac{P_d}{P_0}=\frac{0.275}{1}=0.275=27.5\%[/tex]Answer: 27.5%
a dime has a diameter of 17.91 millimeters. What is the area of the face of the dime? use 3.14 for π. Round to the nearest hundredth if necessary
The area of a circle is:
[tex]A=\pi\cdot r^2[/tex]As you have the diameter, use it to find the radius: the radius of a circle is equal to the half of the diameter:
[tex]\begin{gathered} r=\frac{d}{2} \\ \\ r=\frac{17.91\operatorname{mm}}{2}=8.955\operatorname{mm} \end{gathered}[/tex]Then, the area is: 251.80 millimeters[tex]\begin{gathered} A=(3.14)(8.955mm)^2 \\ A=251.80\operatorname{mm} \end{gathered}[/tex]Question 15 of 31In a 45-45-90 right triangle, what is the ratio of the length of one leg to thelength of the other leg?A. 2:1B. 1:2C. 2:1O D. 1:1SUBMIT
Ratio = 1:1 (option D)
Explanation:We use an illustration to answer the question
One leg = 1
Another leg = 1
When we compare the two images, the ratio of the leg of the 45-45-90 right triangle:
Ratio = 1/1
Ratio = 1:1 (option D)
Suppose Julia spends $932 on her credit card. Calculate the amount of interest she would owe in one month if she does NOT pay off her balance in full by the due date. Julia's APR is 16.99%. Estimate the interest charges using the monthly periodic rate
Answer:
The amount of interest she would owe in one month if she does not pay off her balance in full by the due date is $13.2
Explanation:
Given that Julia's APR is 16.99%
Suppose she spends $932 on her credit card, the amount of interest she would owe in a year is 16.99% of $932, this amounts to
0.1699 * 932
= $158.3468
To know the interest in a month, we divide the last result by 12
158.3468/12
= $13.196
This is approximately $13.2
What are the characteristics of a t-distribution? (Give at least 3characteristics).
Given,
T-distribution.
T-distribution: The T-distribution, also known as the student's t-distribution, is a type of probability distribution that is similar to the normal distribution with its bell shape but has heavier tails.
There are 3 characteristice of the distribution:
shape, central tendency and variability.