4x² + 6x = 12
We move all the terms to the left:
a = 4; b = 6; c = -12;Δ = b² - 4acΔ = 6² - 4 · 4 · ( -12 )Δ = 228The value of Δ is greater than zero, so the equation has two solutions
We use the following formulas to compute our solutions:
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{x_{1}=\dfrac{-b-\sqrt{\Delta} }{2a }| \ x_{2}=\dfrac{-b+\sqrt{\Delta} }{2a } } \end{gathered}$}[/tex]
The end solution:
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57} } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{x_{1}=\dfrac{-b-\sqrt{\Delta} }{2a}=\dfrac{-(6)-2\sqrt{57} }{2*4}=\dfrac{-6-2\sqrt{57} }{8} } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{x_{1}=\dfrac{-b+\sqrt{\Delta} }{2a}=\dfrac{-(6)+2\sqrt{57} }{2*4}=\dfrac{-6+2\sqrt{57} }{8} } \end{gathered}$}[/tex]
{ Pisces04 }
Examine the system of equations.
y=2x-3
y=-3
Which statement about the system of linear equations
is true?
O The lines have different slopes.
O There is no solution to the system.
O The lines have the same slope, but different y-
intercepts.
O The solution is (-3, -9).
For a system of equations to have no real solution, the lines of the equations must be parallel to each other. The correct option is A.
What is the System of equations?Inconsistent System
For a system of equations to have no real solution, the lines of the equations must be parallel to each other.
Consistent System
1. Dependent Consistent System
For a system of the equation to be a Dependent Consistent System, the system must have multiple solutions for which the lines of the equation must be coinciding.
2. Independent Consistent System
For a system of the equation to be an Independent Consistent System, the system must have one unique solution for which the lines of the equation must intersect at a particular.
If the two of the given system of equations are plotted on the graph, then it can be observed that the two lines have different slopes. Therefore, the correct option is A.
Learn more about System of the equation:
https://brainly.com/question/12895249
#SPJ1
What is the area of a sector with measure of arc equal to 90° and radius equal to 1 foot?
Answer:
0.7855 square feet
Step-by-step explanation:
90/360×3.142×1 squared
=0.7855
ab (2a²b² - 4b) = what is the answer
Answer:
2ab(a2b−2)
Step-by-step explanation:
75 POINTS PLEASE RESPOND ASAP
Have you ever been swimming in a pool, and your eyes were red when you get out? This means the chemicals in the pool were not adjusted correctly! More specifically, the measurement of the pool's pH was not quite right.
pH is a measurement of hydronium ions and can be modeled by the function f(x) = −log10x. The variable x represents the amount of hydronium ions, and f(x) gives the pH level.
Different liquids have ideal pH values that are different. Water at 25 degrees Celsius has a pH of 7. Anything that has a pH less than 7 is called acidic, and a pH above 7 is basic, or alkaline. Seawater has a pH just more than 8, whereas lemonade has a pH of approximately 3.
Create a graph of the pH function either by hand or using technology. Locate on your graph where the pH value is 0 and where it is 1. You may need to zoom in on your graph.
Use your graph to find the ideal pH level if the amount of hydronium ions is raised to 0.50.
The pool company developed new chemicals that transform the pH scale. Using the pH function f(x) = −log10x as the parent function, explain which transformation results in a y-intercept and why. You may graph by hand or using technology. Be sure to label each transformation on the graph.
f(x) + 1
f(x + 1)
ANSWER :
The pH level of a swimming pool indicates the level of acidity or alkalinity
of the swimming pool.
Correct Responses;
First Part: Please find attached the required graph of the pH function created with MS Excel.
The pH value is 0 when x = 1
The pH value is 1 when x = 0.1
The pH level if the hydronium ions is raised to 0.50 is approximately 0.301029996.
Second Part: The transformation that results in a y-intercept is f(x + 1), because f(0 + 1) exists and is equal to 0.
STEPS
Method by which the above responses are obtained
First part
The given pH function is f(x) = -㏒₁₀x
Where;
x = The amount of hydronium ions
A substance with a pH < 7 is acidic
A substance with a pH > 7 is alkaline
A neutral solution has pH = 7
Water is a neutral solution
The graph of the pH function created with MS Excel is attached
The table of values of the graph is as follows;
From the graph, we have;
When the pH value is 0, the hydronium ion concentration is 1
The pH value is 1 when x = 1 × 10⁻¹ = 0.1
The pH level if the hydronium ions, x = 0.5 is given from the graph as follows;
pH = f(0.5) = -㏒₁₀(0.5) ≈ 0.301029996
The pH value when the hydronium ions is 0.5 is pH ≈ 0.301029996
Second Part
Using f(x) = -㏒₁₀x as the parent function, the graph of f(x) + 1, and f(x + 1) are plotted
From the graph, we have;
The graph of f(x) + 1 = -㏒₁₀x + 1
The graph of f(x + 1) = The graph of -㏒₁₀(x + 1)
At the y-intercept, x = 0, therefore;
f(x) + 1 = f(0) + 1 = -㏒₁₀0 + 1 = Undefined
f(x + 1) = f(0 + 1) = -㏒₁₀(0 + 1) = 0
Therefore;
The transformation that results in a y-intercept is f(x + 1) because f(0 + 1) is 0, which is defined.
Learn more about the pH here:
https://brainly.com/question/26145256
Which equation can replace 3x + 5y = 59 in the original system and still produce the same solution?
Answer:
13x = 39
x=3
y=10
Given the sequence in the table, which of the following represents the sum for term 5 through term 11 in sigma notation? (1 point)
a an
1 2
2 −10
3 50
Answer:
Given sequence in the table is a Geometric sequence and The sum for term 5 through term 11 in sigma notation is given by:
[tex]$\sum_{n=5} ^{\111} 2(-5)^n^-^1$[/tex]
Step-by-step explanation:
Geometric sequence - it is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio
here the given terms :
a1 = 2, a2 = -10, a3 = 50
you can see it is a geometric sequence as the ratio is constant [tex]\frac{a2}{a1}{=}\frac{a3}{a2}{=}{-5}[/tex]
now the nth term for geometric sequence :
[tex]a_{n} {=}{a}{r}^{n-1}[/tex]
here,
a = first term.r = common ratio of the given terms.n = number of terms in geometric sequence.now substituting the given values in the expression,
[tex]a_{n} {=}{2}{{(}-5}{)}^{n-1}[/tex]
we have to find the sum from term 5 to term 11,
therefore using sigma notation and putting n= 5 and n=11 at the below and above the sigma respectively,
[tex]$\sum_{n=5} ^{\111} 2(-5)^n^-^1$[/tex]
learn more about geometric progression at brainly.com/question/4853032
#SPJ10
Sam pays #512 .75k less than the amount rob pays for his meal .ridwan pays three times the amount rob pays for his meal. if the total amount paid by them is #47,645.25k. How much does same paid for his meal
The amount paid by sam will be 11526.75k for the meal.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that:-
Sam pays 512 .75k less than the amount rob pays for his meal .ridwan pays three times the amount rob pays for his meal. if the total amount paid by them is 47,645.25k.
We will form an expression from the data given above in the question.
Amount paid by Sam = ( r - 512.75 )
Amount paid by rob = r
( r - 512.75 ) + 3r = 47645.25
( r + 3r ) = 47645.25 + 512.75
4r = 48158
r = 12039.5
The amount paid by sam will be calculated as:-
S = r - 512.75
S = 12039.5 - 512.75
S = 11526.75
Therefore the amount paid by sam will be 11526.75k for the meal.
To know more about Expression follow
https://brainly.com/question/723406
#SPJ1
This circle is centered at the origin, and the length of its radius is 8. What is
the equation of the circle?
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: x² + y² = 64[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Standard equation of circle is :
[tex]\qquad \tt \rightarrow \: (x - h) {}^{2} + (y - k) {}^{2} = {r}^{2} [/tex]
[tex] \textsf{h = x - coordinate of centre of circle} [/tex][tex] \textsf{k = y - coordinate of centre of circle} [/tex][tex] \textsf{r = radius= 8} [/tex]Since the circle is centered at origin, h = k = 0
[tex]\qquad \tt \rightarrow \: (x - 0) {}^{2} + (y - 0) {}^{2} = {8}^{2} [/tex]
[tex]\qquad \tt \rightarrow \: {x}^{2} + {y}^{2} = 64 [/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
√4x-3-1=√x+1
What is the value of x
is 8.6 a rational number
Answer:
Yes
Step-by-step explanation:
Yes, 8.6 is a rational number because it can be expressed in the form of p/q
[tex]8.6 = \frac{86}{10} = \frac{43}{5} [/tex]
Figure 1 is similar to figure 2. What is TS?
1 unit
4 units
8 units
2 units
Answer:
8 units
Step-by-step explanation:
ratios
(x-3) /( x+1) = (x-2)/(x+3) cross multiply
x^2 -x -2 = x^2 - 9
-x - 2 + 9 = 0
x = 7
so TS = x + 1 = 8 units
Find the LinReg line of best fit for this data set.
{(−5, 6.3), (−4, 5.6), (−3, 4.8), (−2, 3.1), (−1, 2.5), (0, 1.0), (1, −1.4)}
The LinReg line of best fit for this data set is ŷ = -1.24X + 0.66
What is regression line?A linear regression line has an equation of the form Y = a + bX, where X is the explanatory variable and Y is the dependent variable.
Given:
(−5, 6.3),
(−4, 5.6),
(−3, 4.8),
(−2, 3.1),
(−1, 2.5),
(0, 1.0),
(1, −1.4)
Sum of X = -14
Sum of Y = 21.9
Mean X = -2
Mean Y = 3.1286
Sum of squares (SSX) = 28
Sum of products (SP) = -34.6
Regression Equation,
ŷ = bX + a
b = SP/SSX = -34.6/28 = -1.23571
a = MY - bMX = 3.13 - (-1.24*-2) = 0.65714
ŷ = -1.23571X + 0.65714
ŷ = -1.24X + 0.66
Learn more about regression line here:
https://brainly.com/question/7656407
#SPJ1
help with both please :)
Answer: I know two methods of solving both of the sums. One is the method of elimination, the other is method of substitution. You can do any of the given methods which is easier for you. Both methods will be shown below:
Method of Elimination1) 5x + y = 9 - - - - (i)
10x - 7y = - 18 - - - - (ii)
eq. (i) multiplied by 2
10x + 2y = 18 - - - - (i)
10x - 7y = - 18 - - - - (ii) {subtraction of eq. (ii) from eq. (i)}
0 + 9y = 36
y = 36/9
y = 4
From eq. (i),
5x + y = 9
-> 5x + 4 = 9
-> 5x = 9 - 4
-> x = 5/5
-> x = 1
So, x = 1 and y = 4
2) - 4x + 9y = 9 - - - - (i)
x - 3y = - 6 - - - - (ii)
eq. (ii) multiplied by 3
- 4x + 9y = 9 - - - - (i)
3x - 9y = - 18 - - (ii) {addition of eq. (ii) and eq. (i)}
- x + 0 = - 9
x = 9
From eq. (ii),
x - 3y = - 6
-> 9 - 3y = - 6
-> - 3y = -6-9
-> y = -15/-3
-> y = 5
So, x = 9 and y = 5
Method of Substitution1) 5x + y = 9 - - - - (i)
10x - 7y = - 18 - - - - (ii)
eq. (i)
5x + y = 9
-> y = 9 - 5x
Value of eq. (i) in eq. (ii)
10x - 7y = - 18
-> 10x - 7(9 - 5x) = - 18
-> 10x - 63 + 35x = - 18
-> 45x = - 18 + 63
-> x = 45/45
-> x = 1
From eq. (i),
5x + y = 9
-> 5 + y = 9
-> y = 9 - 5
-> y = 4
So, x = 1 and y = 4
2) - 4x + 9y = 9 - - - - (i)
x - 3y = - 6 - - - - (ii)
eq. (i)
- 4x + 9y = 9
-> - 4x = 9 - 9y
-> x = (9 - 9y) / -4
Value of eq. (i) in eq. (ii)
x - 3y = - 6
-> (9 - 9y) / -4 -3y = - 6
-> (9 - 9y + 12y) = - 6 * - 4
-> 3y = 24 - 9
-> y = 15/3
-> y = 5
From eq. (ii)
x - 3y = - 6
-> x - 3(5) = - 6
-> x - 15 = - 6
-> x = - 6 + 15
-> x = 9
So, x = 9 and y = 5
∩_∩
(„• ֊ •„)♡
┏━∪∪━━━━┓
hope it helped
┗━━━━━━━┛
Please i need it for now PLSSSS
The measure of the other side of a quadrilateral is [tex]3\sqrt{13}[/tex] cm.
In the given quadrilateral one side is unknown we need to find the unknown side.
By dividing the given quadrilateral into a rectangle and a triangle we can find the other side.
What is Pythagoras theorem?The Pythagoras theorem states that if a triangle is right-angled, then the square of the hypotenuse is equal to the sum of the squares of the other two sides. That is, [tex]c^{2}=a^{2}+b^{2}[/tex].
Now, [tex]x^{2} =9^{2}+6^{2}=81+36=17[/tex]
⇒[tex]x=\sqrt{13 \times 9} =3\sqrt{13}[/tex]
Therefore, the measure of the other side of a quadrilateral is [tex]3\sqrt{13}[/tex] cm.
To learn more about Pythagoras' theorem visit:
https://brainly.com/question/343682.
#SPJ1
find the least nu,ber which is exactly divisible by 12 16 and 24
Answer:
The smallest number all three numbers can be divided by is 4.
Step-by-step explanation:
12/4=3
16/4=4
24/4=6
Hope this helps!
If not, I am sorry.
Find the HCF of
x^4 y^2 and x^3 y^3
Here's your answer down here↓:
Step-by-step explanation:
x^3 - y^3 = (x - y)(x^2 + xy + y^2)
(x^4 - y^4) = (x^2 - y^2)(x^2 + y^2) = (x - y)(x + y)(x^2 + y^2)
Ok. So the factor (x-y) appears once in the top line and once in the second line. So we are going to take it the least amount of times.
So, the factor (x + y) appears in the top line zero times and in the second line one time so we will take it where it appears the least which is zero times so we are still at (x - y)
And it Same goes for the factors of (x^2 + y^2) and (x^2 + xy + y^2)
Are the equations 5x=3-x and 5x=-x+3 equivalent?
Answer:
yes
Step-by-step explanation:
The commutative property of addition applies to let you swap the order of the summands.
__
Here is how the commutative property can be applied.
5x = 3 -x . . . . . given
5x = (3) +(-x) . . . . shown as a sum
5x = (-x) +(3) . . . . order swapped using commutative property of addition
5x = -x +3 . . . . . . equivalent equation
In the diagram below, triangle lmn is congruent to cba. What is the length of segment ln?
Answer:
this is step by step explenation
see more...
PLEASE HELP MULTIPLE CHOICE (photo of question attached) WILL GIVE BRAINLEIST!
The triangles on the grid below represent a translation.
To form the image, the pre-image moved
a. five units right and three units up.
b. two units right and three units up.
c. five units left and three units down.
d. two units left and three units down.
Answer:
A five units right and three units up
Step-by-step explanation:
take coordinate C for example and count how many spaces you need to go either right or left and then up and down for the two triangles to be in the same place
Which equation would have real zero(s) corresponding to the x-intercept(s) of the graph below?
Answer:
the first one listed (y = -[tex]2^{x}[/tex] + 4)
Step-by-step explanation:
a 0 at an x-intercept means that when plugging in that number, you get a 0 as a y-value.
So, the easiest method to use is to plug x=2 into each equation listed, because we can see that (2,0) is a point on this graph
if y= -[tex]2^x\\[/tex] + 4
y = -2² + 4
y = -4 + 4
y = 0
This means that this graph has corresponding real zero(s) to the function y= [tex]-2^x[/tex] + 4
(I chose which graph to test by looking to see which option seemed right)
To support a shelf, the diameter of a bolt can measure anywhere from 0.2 cm less than 1.5 cm to 0.2 cm greater than 1.5 cm. Which graph represents the possible measures of the diameter of the bolt?
During its descent, the pair of sunglasses passed by a climber in the canyon 6 seconds after stefano dropped them. To the nearest meter, what is difference in elevation between stefano and the climber?.
Answer:
20 can be the answer of it
What value of a make the equation 14-a=19-12
[tex]14-a=19-12\\14-a=7\\a=14-7\\a=7[/tex]
Answer:
7
Step-by-step explanation:
14-a=19-12
14-a=7
14-7=a
7=a
Combine like terms
can someone please help mee
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:Domain : \fbox{-3}\leqslant x \leqslant \fbox{-1}[/tex]
[tex]\qquad \tt \rightarrow \:Range :\:\:\fbox{-4}\leqslant x \leqslant \fbox{-3}[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Domain = All possible values of x for which f(x) is defined
[ generally the extension of function in x - direction ]
Range = All possible values of f(x)
[ generally the extension of function in y - direction ]
[tex] \large\textsf{For the given graph : } [/tex]
[tex]\qquad \tt \rightarrow \: domain : \fbox{-3}\leqslant x \leqslant \fbox{-1}[/tex]
[tex]\qquad \tt \rightarrow \: range : \:\:\fbox{-4}\leqslant x \leqslant \fbox{-3}[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Joanne has a pile of nickels and a pile of dimes. She counts her money and discovers that she has 30 nickels and 10 dimes. Let x represent the number of nickels and y represent the number of dimes. (HINT: Use the values of the coins.) How much money does Joanne have in total?
Total Amount: $_____
$2.50
Step-by-step explanation:
10 dimes are 100 aka 1 dollar, and 30 nickels make 250
Given that the expression “p dollars for every q items” describes a unit price, which statement must be true?
The complete question is
"Given that the expression “p dollars for every q items” describes a unit price, which statement must be true?
p = 1
p = q
q = 1
pq = 1"
The statement that must be true would be from option D; pq = 1.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given that the expression “p dollars for every q item” describes a unit price,
So, the equation will be formed as
p x q = 1
pq = 1
Hence, the statement that must be true would be from option D; pq = 1.
Learn more about the unitary method;
https://brainly.com/question/23423168
#SPJ1
Find the area of a regular octagon with an apothem of 2 cm.
The area of a regular octagon with an apothem of 2 cm is 3cm ^2.
The area of a regular octagon with an apothem of 2 cm.
Given the apothem length,
What is the area of the regular polygon?the area of a regular polygon becomes,
[tex]A=\frac{1}{2}\times P\times A[/tex]
P= the perimeter of the regular polygon
A is the apothem of the regular polygon
Here, we get
p=2=2cm, a=3cm.
So, plugging in the given values, we get
[tex]A=\frac{1}{2} \times 2cm\times 3cm[/tex]
A=1cm⋅3cm
A=3cm^2
Therefore the area of a regular octagon with an apothem of 2 cm is 3cm ^2.
To learn more about the regular octagon visit:
https://brainly.com/question/1592456
#SPJ1
I'm kinda lost in this problem. Can you teach me how to solve these
53) Vertical angles are congruent, so [tex]m\angle IDA=121^{\circ}[/tex]
54) [tex]\angle YDA[/tex] and [tex]\angle YDF[/tex] are supplementary, so [tex]m\angle YDA=180^{\circ}-121^{\circ}=59^{\circ}[/tex]
55) Because vertical angles are congruent, [tex]m\angle FDI=59^{\circ}[/tex]. Now, because DR bisects [tex]\angle FDI[/tex], this means [tex]m\angle RDI=\frac{59}{2}=29.5^{\circ}[/tex]
56) This is a geometric sequence where the next term is obtained by multiplying the previous term by -2, so the next two numbers are 16, -32
enlist any five common social rules all kinds of society
Answer:Shake hands when you meet someone.Make direct eye contact with the person you are speaking with.Unless the movie theater is crowded, do not sit right next to someone.Do not stand close enough to a stranger to touch arms or hips.Cover your coughs.
Step-by-step explanation:trust me
A. The two spinners shown below are being used in a probability experiment.
During each trial of the experiment, the arrows on the spinners are spun once, and the outcome is recorded. For example, an outcome of (2, 1) means that the arrow pointed to 2 on the first spinner and pointed to 1 on the second spinner.
B. What is the theoretical probability that, during each trial of the experiment, the result has at least one 4 on the spinners? Show your work or explain your answer.
Explain why the experimental probability from the results does not agree with the theoretical probability you found in part B.
The theoretical probability of at least one 4 on the spinners is 0.4375
(a) The number of different outcomesThe sections on the spinners are:
Spinner 1 = 4
Spinner 2 = 4
So, the number of different outcomes is:
Outcomes = 4 * 4
Outcomes = 16
Hence, the number of different outcomes is 16
(b) The theoretical probability of at least one 4 on the spinnersThe spin results that have at least one 4 are:
Results = {(4,1), (4,2), (4,3), (4,4), (1,4), (2,4), (3,4)}
The count of these results is 7.
So, the theoretical probability of at least one 4 on the spinners is:
P = 7/16
P = 0.4375
Hence, the theoretical probability of at least one 4 on the spinners is 0.4375
(c) Why the theoretical probability and the experimental probability are different?The theoretical probability and the experimental probability are different because:
Experimental probabilities are based on the actual experimentTheoretical probabilities are based on the logicRead more about probability at:
https://brainly.com/question/25870256
#SPJ1
