The given quadratic equation y = 6x² - 6 contains two zeros :
(x - 1) and (x + 1)
Solution:Steps to solve quadratic equation:
Transform the equation into standard form, with one side set to zero. Take into account the non-zero side. Make each factor equal to zero (Remember: a product of factors is zero if and only if one or more of the factors is zero). Solve each of the resulting equations.Given quadratic equation ,
y = 6x² - 6
To find the zeros we have to solve the equation ,
y = 6x² - 6
= 6( x² -1 )
= 6( x² + x - x -1)
= 6(x ( x + 1) - 1( x + 1 ))
= 6 ( x - 1) ( x + 1 )
The equation y = 6x² - 6 contains two zeroes
= (x-1) and (x + 1)
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O POLYNOMIAL AND RATIONAL FUNCTIONSFinding zeros and their multiplicities given a polynomial functio.
From the function, we can conclude:
[tex]\begin{gathered} (x+6)^3 \\ x=-6_{\text{ }}Multiplicity_{\text{ }}3 \\ ---------- \\ (x-9)^2 \\ x=9_{\text{ }}Multiplicity_{\text{ }}2 \\ ----------- \\ x-6 \\ x=6_{\text{ }}Multiplicity_{\text{ }}1 \\ ----------- \\ (x+4)^3 \\ x=-4_{\text{ }}Multiplicity_{\text{ }}3 \end{gathered}[/tex]Answer:
Zero(s) of multiplicity one: 6
Zero(s) of multiplicity two: 9
Zero(s) of multiplicity three: -6, -4
your checking account is overdrawn by $120.22. you write a check for $80.25. what is the balance in your account???
The amount or balance left in the bank account is $39.97.
The amount of money held in a financial institution, such as a savings or checking account, at any particular time is known as the account balance. The net amount, which includes all debits and credits, is always the account balance.
The current balance in the bank account is $120.22.
The check was issued for $80.25.
Let x be the balance left in the account.
Then,
The balance left = Initial balance in the account - The amount for which the check was issued
x = Initial balance in the account - The amount for which the check was issued
x = $120.22 - $80.25
x = $39.97
The balance left in the bank account is $39.97.
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P(-9,-4) Q(-7,-1) whats is PQ
Step-by-step explanation:
I assume the question is about the distance between both points.
2 points in the coordinate grid create a right-angled triangle :
their direct connection (distance) is the Hypotenuse (the baseline, it is the side opposite of the 90° angle), and the x and y coordinate differences are the legs.
so, we can use Pythagoras to get the distance.
c² = a² + b²
c being the Hypotenuse, a and b being the legs.
so,
distance² = (-9 - -7)² + (-4 - -1)² = (-9 + 7)² + (-4 + 1)² =
= (-2)² + (-3)² = 4 + 9 = 13
distance = sqrt(13) = 3.605551275...
just in case, if you needed the line equation connecting these 2 points, I would assume the slope-intersect form
y = ax + b
"a" being the slope, "b" being the y-intersect (the y-value when x = 0).
the slope is always the ratio (y coordinate difference / x coordinate difference) when going from one point on the line to another.
using the 2 given points
x changes by +2 (from -9 to -7).
y charges by +3 (from -4 to -1).
the slope is
+3/+2 = 3/2
and our equation looks like
y = 3x/2 + b
now we use the coordinates of 1 point, e.g. (-7, -1), to get b
-1 = 3/2 × -7 + b = -21/2 + b
-1 + 21/2 = b
-2/2 + 21/2 = b
19/2 = b
our equation is then
y = 3x/2 + 19/2
or
y = (1/2)×(3x + 19)
9. Dice A has ten sides, what is the probability a five of NOT rolling a one, a three or a five?
Answer:
Step-by-step explanation: Take awa thoese and it would be 70%
Two trains leave the same station, each 40 minutes apart. Train X leaves first at 9:45 am and heads west at a speed of 144 km/h. Train Y leaves at noon and travels directly east at a speed of 165 km/h. How far apart are these trains at 1:30 pm? Show your work.
Using the relation between velocity, distance and time, it is found that these trains are 1049 km apart at 1:30 pm.
What is the relation between velocity, distance and time?Velocity is given by the distance divided by the time, hence the following equation is built to model the relationship between these variables:
v = d/t.
In which:
v is the velocity.d is the distance.t is the time.For Train X, the time and the velocity are given as follows:
Time of t = 3.75 hours, as 1:30 pm is 3 hours and 45 minutes after 9:45 am, and 45 minutes = 45/60 = 0.75 of an hour.Velocity of v = 144.Hence the distance of train X from the station is:
dX = 144 x 3.75 = 540 km.
For Train Y, the time and the velocity are given as follows:
Time of t = 3.0.833 hours, as 1:30 pm is 3 hours and 5 minutes after the train left the station (40 minutes less than train X).Velocity of v = 165.Hence the distance of train Y from the station is:
dY = 165 x 3.0833 = 509 km.
They travel in opposite directions, hence we add the distances of each from the station to find their distances as follows:
540 km + 509 km = 1049 km.
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Question 9
1 pts
The price of gasoline has risen from $3.52/gallon last week to $4.31/gallon this week.
What is the percent change? Round answer to the tenths place.
Question 10
1 pts
Answer: 122.4% increase
Divide the new cost from the old
4.31 / 3.52 = 1.22443181818
Multiply by 100 to get a percent.
= 122.443181818%
= 122.4
Sketch the graph of y= (x - 3)2 - 25, then select the graph that correspondsto your sketch.10140-1010101010111010HO-101010-20C.D.A.B.A. Graph AB. Graph BC. Graph CD. Graph D
Therefore,
[tex]\begin{gathered} when\text{ x=0} \\ y=(0-3)^2-25=9-25=-16 \end{gathered}[/tex]when x = 0, y =-16 we can confirm the graph is C.
Singer A and Singer B had the two top-grossing concert tours for a certain year, together generating $438 million in ticket sales. If Singer B took in $22 million less than Singer A, how much did each tour generate?
To answer this question, we have that both singers generated $438 million in tickets sales.
Then, we can rewrite it in algebraic expressions as follows:
[tex]A+B=438[/tex]However, we know that singer B took in $22 million less than singer A:
[tex]B=A-22[/tex]Now, we can substitute this expression in the original one as follows:
[tex]A+A-22=438[/tex]And to solve this equation, we can add the like terms, and then add 22 to both sides of the equation as follows:
[tex]2A-22+22=438+22\Rightarrow2A=460\Rightarrow\frac{2A}{2}=\frac{460}{2}[/tex][tex]A=230[/tex]Then, to find the earnings of singer B, we have:
[tex]A+B=438\Rightarrow B=438-A[/tex]Then, B is equal to:
[tex]B=438-230\Rightarrow B=208[/tex]Then, we can check that A + B is:
[tex]A+B=230+208=438[/tex]And we can see that singer B took in $22 million less than singer A:
[tex]B=230-22=208[/tex]In summary, therefore, we can say that each tour generated:
Singer A generated $230 million in ticket sales and Singer B generated $208 million.
The picture I put in I understand girls more
Using long division:
what is the y dash coordinate of the solution to the following system of equations
Solution
Step 1:
Write the systems of equations
[tex]\begin{gathered} 3x\text{ - 6y = 6 eq\lparen1\rparen} \\ -3x\text{ + 3y = 9 eq\lparen2\rparen} \end{gathered}[/tex]Step 2
To find the value of y, add both equations
[tex]\begin{gathered} -3x\text{ + 3y + 3x - 6y = 6 + 9} \\ -3y\text{ = 15} \\ y\text{ = }\frac{15}{-3} \\ y\text{ = -5} \end{gathered}[/tex]19. Write ten-million (10,000,000) in scientific notation.
5
0105
01 x 106
01 x 107
01 × 108
Answer:
1 × 10⁷
Step-by-step explanation:
the correct answer is 1 × 10⁷
Rajendra has 4 pounds of trail mix. He is putting them into bags that hold1 pounds each. Does he have enough trạil mix to completely fill 3 bags? Explain why orwhy not.
Olivia picked 256 strawberries. She divided the strawberries evenly into 6
baskets. How many strawberries are in each basket? How many are left over
Answer:
42 strawberries in each backet with 4 left over
Step-by-step explanation:
256 divided by 6=42.6666667
42x6=252
256-252
Answer:
42 with 4 left over
Step-by-step explanation:
256/6
4 2
6. 256
4
24
16
12
4
Simplify.10(15 + n)50 + n0 150 + nO 150 + 10 n150 n
ANSWER
150 + 10n
EXPLANATION
We want to simplify:
10(15 + n)
To do this, we have to use the distributive property:
a(b + c) = a*b + a*c
Therefore:
10(15 + n) = (10 * 15) + (10 * n)
= 150 + 10n
That is the answer
Triangle ABC with vertices A(-9,-7) B(-6,-2) C(-3,-6) is translated 5 units to the right and 3 units up then the image is reflected on the x-axis. What are the coordinates of the final image?
Triangle ABC with vertices A(-9,-7) B(-6,-2) C(-3,-6) is translated 5 units to the right.
A(-9 + 5 ,-7) B(-6 + 5,-2) C(-3 + 5 ,-6) = A ( -4, -7 ) , B ( -1 , -2 ) C ( 2 , -6 )
3 units up: A ( -4, -7 + 3 ) , B ( -1 , -2+ 3 ) C ( 2 , -6+ 3 )
The coordinates of the final image is = A( -4, -4 ) B ( -1 , 1 ) C ( 2 , -3)
What is 19.5 / 3 = decimal division
Answer:
6.5
Step-by-step explanation:
19.5 divided by 3 is 6.5
if you want to double check, you can multiply 3 by 6.5 and find it is 19.5
Mr. Bowen used 2 gallons of paint on 1/3 of his fence. How many more gallons of
paint does he need to finish paining the entire fence?
Answer:
4
Step-by-step explanation:
→ Work out how much he needs in total
2 × 3 = 6
→ Minus how much he has used
6 - 2 = 4
Use exponential notation to simplify the given expressionsPresent your answer using only positive integer exponentsAswer the first one
We will use the next rule
[tex]\sqrt[n]{x^m}=x^{\frac{m}{n}}[/tex]Then
[tex]\sqrt[7]{x^6}\ast\sqrt[5]{x}=x^{\frac{6}{7}}\ast x^{\frac{1}{5}}=x^{\frac{6}{7}+\frac{1}{5}}[/tex][tex]x^{37/35}[/tex]Solve using Gaussian eliminationX+2y=7. And. Y=3x+2
Let's rewrite the system as:
[tex]\begin{cases}x+2y=7_{\text{ }}{(1)} \\ 3x-y={-2_{\text{ }}}(2)\end{cases}[/tex]Using elimination:
[tex]\begin{gathered} (1)+2(2) \\ x+6x+2y-2y=7-4 \\ 7x=3 \\ x=\frac{3}{7} \end{gathered}[/tex]Replace x into (2):
[tex]\begin{gathered} y=3(\frac{3}{7})+2 \\ y=\frac{23}{7} \end{gathered}[/tex]Jordan Will hike the trail shown at a rate of 5mi/h. write a linear equation to represent the distance Jordan still has to walk after X hours. what does the Y-intercept of the equation represent?
using linear equation
[tex]\begin{gathered} y=mx+b \\ \text{where} \\ m=\text{slope} \\ b=y-\text{intercept} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} x=\text{time in hours} \\ y=dis\tan ce \\ m=5 \end{gathered}[/tex][tex]y=5x+31[/tex]The y - intercept which is equals to 31 represents the distance he still has to walk .
Let sin 0= 4/9. Find the exact value of cos 0.
Statement Problem: Let;
[tex]\sin \theta=\frac{4}{9}[/tex]Find the exact value of;
[tex]\cos \theta[/tex]Solution:
In trigonometry, the ratio of the sine is defined as;
[tex]\sin \theta=\frac{opposite}{hypotenuse}[/tex]Thus,
[tex]\text{opposite}=4,\text{ hypotenuse=9}[/tex]By Pythagoras theorem, the square of the longest side (hypotenuse) is the sum of squares of the opposite and the adjacent sides.
[tex]\begin{gathered} (\text{hypotenuse)}^2=(\text{opposite)}^2+(\text{adjacent)}^2 \\ (\text{adjacent)}^2=(\text{hypotenuse)}^2-(\text{opposite)}^2 \\ (\text{adjacent)}^2=9^2-4^2 \\ (\text{adjacent)}^2=81-16 \\ (\text{adjacent)}^2=65 \\ \text{adjacent}=\sqrt[]{65} \end{gathered}[/tex]The ratio of the cosine is defined as;
[tex]\begin{gathered} \cos \theta=\frac{adjacent}{hypotenuse} \\ \end{gathered}[/tex]Hence,
[tex]\cos \theta=\frac{\sqrt[]{65}}{9}[/tex]This question gettin me mad tight
The graph shows the value parent function
Which statement best describes the function?
A - the function is increasing when x > 0
B - the function is increasing when x< 0
C- the function is always increasing
D - the function is never increasing
Pls help me, I’ll send you the pictures of the things you have to choose.
EXPLANATION
Since we have 3 1/2 slices of cake, and we need to distribute a half of slice by each friend, we need to divide 3 1/2 by 2, as follows:
[tex]\frac{(3\frac{1}{2})}{2}=\frac{7}{4}=1\frac{3}{4}[/tex]Therefore, since each friend gets a half slice of cake, we can affirm that each whole slice of cake can be divided into two halves.
Now, adding from half to half to obtain 3 1/2 slices of cake, give us:
1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 = 7 slices
So, 3 1/2 slices of cake is a total of 7 halves.
Because each friend gets half of a slice of cake, we can affirm there are 7 friends.
Answer:
See below
Step-by-step explanation:
3 + one half slices each whole (3 of them ) can be cut into two halves
6 halves + 1 half = 7 halfves
if everyone gets a a half, there are 7 people
Are 1 to 0.4 and 9 3.6 proportional?
The ratios 1 to 0.4 and 9 to 3.6 are proportional.
A ratio is a relationship between two objects that is expressed using numbers or amounts.
If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.
Consider the ratio 1 to 0.4 and 9 to 3.6,
Let,
x = 1 to 0.4 = 1 : 0.4
= 1/0.4
= 10/4
= 5/2
Let, y = 9 to 3.6
y = 9 : 3.6
y = 9/3.6
y = ( 9 × 10 ) / 36
y = 10/4
y = 5/2
Therefore,
x = y
1 : 0.4 = 9 : 36
Hence, the ratios 1 to 0.4 and 9 : 3.6 are proportional.
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How much will a girl pay for a bag price at $15 if a discount of 10% is offered?
First, calculate how much is the discount equal to. Then, substract the discount from the original price to find the selling price.
Since the discount is 10%, find how much is 10% of $15 by multiplying 15 times 10/100:
[tex]15\times\frac{10}{100}=1.5[/tex]Then, 10% of 15 is equal to 1.5. Now, substract 1.5 from 15 to find the final price:
[tex]15-1.5=13.5[/tex]Therefore, the girl will pay $13.5. The answer is:
[tex]\text{ \$13.5}[/tex]The Nutty Professor sells cashews for $7.00 per pound and Brazil nuts for $4.00 per pound. How much of each type should be used to make a 33 pound mixture that sells for $5.64 per pound? pounds of cashews pounds of Brazil nuts
Let's call X the number of pounds of cashews and Y the number of pounds of Brazil nuts.
Now, we want to make 33 pounds of the mixture, so:
X + Y = 33
Adittionally, every pound mixture will be sell for $5.64 per pound. It means that:
7X + 4Y = 5.64*33
7X + 4Y = 186.12
Because every pound of cashews cost $7 and every pound of Brazil nuts cost $4
Then, we can solve for X on the first equation and replace it on the second as:
[tex]\begin{gathered} X+Y=33 \\ X=33-Y \end{gathered}[/tex][tex]\begin{gathered} 7X+4Y=186.12 \\ 7(33-Y)+4Y=186.12 \end{gathered}[/tex]So, we can solve for Y as:
[tex]\begin{gathered} 7\cdot33-7\cdot Y+4Y=186.12 \\ 231-7Y+4Y=186.12 \\ 231-3Y=186.12 \\ -3Y=186.12-231 \\ -3Y=-44.88 \\ Y=\frac{-44.88}{-3} \\ Y=14.96 \end{gathered}[/tex]Now, we can calculate X as:
[tex]\begin{gathered} X=33-Y \\ X=33-14.96 \\ X=18.04 \end{gathered}[/tex]Therefore, we need to use 18.04 pounds of cashews and 14.96 pounds of Brazil nuts to make a 33 pounds mixture that sells for $5.64 per pound
Answer 18.04 pounds of cashews and 14.96 pounds of Brazil nuts
solve the following equation for x4x-3=21
Solving for x :
[tex]\begin{gathered} 4x-3=21 \\ \rightarrow4x=21+3\rightarrow4x=24 \\ \rightarrow x=\frac{24}{4} \\ \\ \Rightarrow x=6 \end{gathered}[/tex](40 points)Graph the reflection of f(x) = -3(2) across the x-axis.
Step 1: From the given function, determine the reflected
function.
g(x) = (2)*
In the equation f(x) = -3(2), reflected about x - axis is : f(x) = 3.2
According to the question, given that
equation f(x) = -3(2)
the equation reflected x - axis is f(x) = 3.2
Therefore, Reflected about the x-axis in the equation f(x) = -3(2) is f(x) = 3.2
The graph of the parent function is either "moved," "resized," or "reflected" by a function transformation. The three primary categories of function transformations are as follows:
- Translation
- Dilation
- Reflection
The only one of these transformations, dilation, alters the size of the original shape; the other two, however, just affect the shape's location.
By comparing the original and converted graphs, you can quickly determine which one has changed because you can tell by by glancing at the graph that it has moved up 2 units, left 3 units, etc. However, it can be challenging to graph the function transformation when a graph is provided. The next few steps make it much simpler to graph transformations. Here, the function y = f(x) is changed to y = a f(b (x + c)) + d.
Step 1: Write down some of the original curve's defining coordinates. Thus, we are aware of the previous x and y coordinates.
Step 2: Simply put "b (x + c) = old x-coordinate" and solve for x to determine the new x-coordinate of each location.
Step 3: Simply apply all outside operations (of brackets) on the old y-coordinate to determine the new y-coordinate of each point. To determine each new y-coordinate, find ay + d, where 'y' is the old y-coordinate.
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I need help on #5 Please help me on my hw
Given:
The given problem is:
[tex](x+3)^2\ne x^2+9[/tex]Using the identity:
[tex](a+b)^2=a^2+b^2+2ab[/tex]Now substitute a = x and b = 3 in this identity:
[tex]\begin{gathered} (x+3)^2=x^2+3^2+2\times x\times3 \\ =x^2+9+6x \end{gathered}[/tex]Hence , the correct solution to the problem is:
[tex](x+3)^2=x^2+6x+9[/tex]What is the % change from $250 to $303
Solution
- The question tells us to find the % change from $250 to $303.
- To calculate the percentage change, we use the formula given below:
[tex]\Delta\text{ \%}=\frac{\text{New}-\text{Old}}{\text{Old}}\times100\text{ \%}[/tex]- The New is $303 and the Old is $250. Thus, we can calculate the percentage change as follows:
[tex]\begin{gathered} \Delta\text{ \%}=\frac{\text{New}-\text{Old}}{\text{Old}}\times100\text{ \%} \\ \\ =\frac{303-250}{250}\times100\text{ \%} \\ \\ =0.212\times100\text{ \%} \\ \Delta\text{ \%}=21.2\text{ \%} \end{gathered}[/tex]Final Answer
The percentage change from $250 to $303 is 21.2%
