[tex]\textit{since the roots are }-2\pm \sqrt{3}\implies \begin{cases} x=-2 + \sqrt{3}\implies&x+2-\sqrt{3}=0\\\\ x=-2 - \sqrt{3}\implies&x+2+\sqrt{3}=0 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]( ~~ x+2-\sqrt{3} ~~ )( ~~ x+2+\sqrt{3} ~~ )=\stackrel{y}{0} \\\\\\ \underset{\textit{difference of squares}}{( ~~ \underline{(x+2)}-\sqrt{3} ~~ )( ~~ \underline{(x+2)}+\sqrt{3} ~~ )}=y\implies (x+2)^2~~ - ~~(\sqrt{3})^2~~ = ~~y \\\\\\ (\stackrel{F~O~I~L}{x^2+4x+4})~~ - ~~(3)~~ = ~~y\implies {\LARGE \begin{array}{llll} x^2+4x+1=y \end{array}}[/tex]
9th Grade Math - Geometry
∠ABC is a straight angle. Find m∠XBC and m∠XBA.
Hint: Solve for x first, then find the angle measures.
14x+70+20x+8=180
34x+78=180
34x=102
x=3
XBC= 20(3) +8
60+8
68
XBA= 14(3)+70
42+70
112
Angle XBC= 68 degrees
Angle XBA= 112 degrees
Pls help urgent!.................................................................
Answer:
.9
85%
5/6
4/5
Step-by-step explanation:
In percentages .9 is 90%
which is larger than 85%
5/6 as a percentage is 83.33r%
4/5 as a percentage is 80%
Help asp show ur work if u can
Answer:
[tex] \sf \fbox{Age of pamela is 8 year}[/tex]
Step-by-step explanation:
let the age of Debra is x and Pamela is x+7 year old,
Given condition- In 6 years Pamela will be twice as old as debra, so the algebraic expression will look like,
[tex]x+7+6 = 2(x+6)[/tex]
[tex]x+13 = 2x + 12[/tex]
[tex]2x-x = 13-12[/tex]
[tex]x = 1[/tex]
Age of debra is 1 years,
now we can calculate the age of pamela by substituting value of x,
x + 7 = 1 + 7 = 8 years
━━━━━━━━━━━━━━━━━━━━━━━
Verification-
after 6 years the age of debra & pamela will be 7 & 14. 14 is twice of 7 which satisfies the given condition.
[tex]\sf \small \pink{Thanks }\: \green{for} \: \blue{joining} \: \orange{brainly } \: \red{community}![/tex]
5. Alesha's savings account balance was $55 at the end of
March, $63 at the end of April, $71 at the end of May,
and $79 at the end of June. Predict the amount Alesha
will have in her account at the end of July.
I
Use the proportion d / 180° = r radians/πradians . Find the equivalent degree measure or radian measure. 170°
Answer:
the answer is the 10⁰ ok that
Each pair of values is from a direct variation. Find the missing value. (2,5),(4, y)
The missing value of direct variation is 10
What is direct variation ?The direct variation property states that , whenever the division of values of two quantities is a constant value then there is same variation between these two corresponding values. Or we can also say that if the divisible nature of two corresponding values is constant, then one quantity is directly varies with second quantity. That mean if one quantity increase other will also increase and vice versa.
Let say if x and y are two values and k is a constant value, then
According to direct variation
k = y/x or y = k x
In the given question,
Take the order pair (2,5)
As it is an direct variation, we can substitute it
y=k x
5=k (2)
K=2.5
Now find the direct variation equation
y=k x
Also, k=2.5
Solve this equation for the second pair (4,y)
As, y=2.5 x
y= 2.5 (4) = 10
Therefore, missing value is 10
To know more about direct variation and values, visit :
https://brainly.com/question/14254277
#SPJ4
Write a rational function with the given characteristics.
A vertical asymptote at x=8 and a horizontal asymptote at y=0
According to the question, to express the rational function for the vertical asymptote whose equation is [tex]x=8[/tex] and horizontal asymptote whose equation is at [tex]y=0.[/tex]
As per the question, the function 'f(x)' is vertical at [tex]x=8[/tex]. Therefore, the denominator be [tex](x-8)[/tex]
[tex]f(x)=\frac{g(x)}{(x-8)}[/tex]
The function 'g(x)' should have same degree as the denominator function has and it is defined as[tex]y=0[/tex]
The rational function can be written as:
Rational function = [tex]\frac{y}{(X-8)}[/tex]
What is rational function?
Rational function is a function whose numerator and denominator terms are in polynomials. Basically, it is a ratio of polynomials. The important condition for these type of function is that denominator should be of degree one.
To learn more about rational function from the given link:
https://brainly.com/question/19044037
#SPJ4
Za and Zy are supplementary angles. Zy measures 97º.
Answer:
83°
Step-by-step explanation:
Supplementary angles are angles that add up to 180°.
Za + Zy = 180
Za + 97 = 180
Za + 97 - 97 = 180 - 97
Za = 83
First day, 2 In the stock market, an investor buys 24,000 shares of a
n dollars
the first
company one week. The number of additional shares he
then buys is halved repeatedly every week for 6 more
weeks. What is the total number of shares of the
company that he bought?
A. 96,000
B. 54,200
C. 48,000
D. 47,625
E. 30,000
The answer to the question is c 47,625
The concept used is geometric progression.
A geometric progression is a sequence in which any element after the first is obtained by multiplying the preceding element by a constant called the common ratio which is denoted by r.
Here we can see that shares are being halved per week
we can say that the value of r is 1/2
so we can use the formula of sum of geometric progression to calculate the total number of shares.
sum of geometric progression formula =a(1-r∧n)/1-r
Here we can see that the value of n is 7
On putting the values in the formula we get
sum=24,000(1-1/128)/(1/2)
On further solving we get-
24000×127×2/128 which is equal to 47,625
Hence the total no of shares of the company he bought are 47,625
Learn more about geometric progression here:https://brainly.com/question/24643676
#SPJ9
Solve each equation.
25 ²x⁺¹=144
After solving the given equation 25²x=144, the value of x = 144/625.
What exactly is an equation?An equation is a mathematical statement composed of two expressions joined by an equal sign.An example of an equation is 3x - 5 = 16.After solving this equation, we get x = 7.So,
Given the equation: 25²x=144Then,
25²x=144625x=144x = 144/625Therefore, after solving the given equation 25²x=144, the value of x = 144/625.
Know more about equations here:
brainly.com/question/2972832
#SPJ4
Can someone help me please
The solutions to the proportional equation are given as follows:
x = -4 and x = 5.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the context of the problem using operations such as multiplication or division.
One example of application of proportions is for the solution of equations when two sides are proportional, meaning that multiplication operations are applied between the opposite sides to find the unknown variable.
For this problem, we already are given the following proportional equation:
3x/5 = 12/(x + 1).
Due to the equality sign, we can apply cross multiplication, hence:
3x(x + 1) = 60
3x² + 3x = 60
3x² - 3x - 60 = 0
x² - x - 20 = 0
(x - 5)(x + 4) = 0.
Hence the solutions are found as follows:
x - 5 = 0 -> x = 5.x + 4 = 0 -> x = -4.More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
Multiply or divide. State any restrictions on the variables.
x²-7 x+10 / x²-8 x+15 ÷ 4-x² / x²+3 x-18
According to the question, the given rational expression can be simplified and as shown below:
Rational expression = [tex]\frac{x^{2} -7x+10}{x^{2} -8x+15}/\frac{4-x^{2} }{x^{2} +3x-18}[/tex]
To simplify the given rational expression, calculate the factors of the numerator as well as denominator. And later divide it from each other. These expressions are also called as polynomial expressions.
Rational expression = [tex]\frac{(x-5)(x-2)}{(x-3)(x-5)}/\frac{(2-x)(2+x)}{(x+6)(x-3)}=\frac{-(x+2)}{(x+6)}[/tex]
The final expression of the given equation is [tex]\frac{-(x+2)}{(x+6)}[/tex] .
What is polynomial expression?
Polynomial expression are those equation whose highest degree is two. It is also called as quadratic equation. And it is simplified by performing the factors on the given expressions.
To learn more about the polynomial expression from the given link:
brainly.com/question/1280754
#SPJ4
What is the best approximation for the solution to this system of equations?
(–3.2, –3)
(–2.9, –3)
(–2.2, –3)
(–1.9, –3)
The correct answer is ( -2.2, -3).
We occasionally discover the value of an unknown variable while solving the system of equations. We can display the graph using the equation, but if the graph and the equation are parallel, we will not be able to solve the system of equations.
We have a condition that, if applied, allows us to determine how many solutions this equation has: if it has one solution, no solutions, or infinitely many solutions.
y = -3 _____(1)
y = x-0.8 _____(2)
to substitute the value of y in the equation in 2
-3 = x - 0.8
-3 + 0.8 =x
-2.2 = x
Thus the correct answer is ( -2.2, -3).
To learn more about system of equations refer the link:
https://brainly.com/question/9351049
#SPJ9
Which equation shows a constant of proportionality
The equation that shows proportionality is in the form y = kx; Where k is the constant of proportionality.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Two variables are said to be proportional if an increase or decrease in one variable leads to a corresponding increase or decrease in the other variable.
The equation that shows proportionality is in the form:
y = kx
Where k is the constant of proportionality.
Find out more on equation at: https://brainly.com/question/13763238
#SPJ1
−(−8q−8.7) im confused on how to do this
The simple way to solve such an expression; −(−8q−8.7) as given in the task content is by the distributive property which yields; 8q + 8.7.
What is the simplified form of the expression as given in the task content?It follows from the task content that the expression which is to be simplified, or perhaps written in a different form is; −(−8q−8.7).
Therefore, it follows from the distributive property that we have;
-(-8q) -(-8.7)
Also, since the product of two negative signs yields a positive sign.
Hence, we have; 8q + 8.7 as the equivalent of the expression given.
Ultimately, the simple way to solve such an expression; −(−8q−8.7) as given in the task content is by the distributive property which yields; 8q + 8.7.
Read more on product of signs;
https://brainly.com/question/2837132
#SPJ1
how do i graph b>4 please help asap
Answer:
Here's b > 4 on the number line. When greater than, the arrow always starts with an open circle. If less than, then it will start with a closed circle.
Amy goes out to eat at El Parral. She orders a Burritos Deluxe dinner for $8.75, fried ice cream for $4, and a Coke for $2. If the sales tax is 6% and she leaves a 15% tip, what is the total amount that Amy will spend?
The total amount that Amy will spend is $17.98
Amy goes out to eat at El Parral. She orders a Burritos Deluxe dinner for $8.75, fried ice cream for $4, and a Coke for $2.
Amy's gross total is $8.75 + $4 + $ 2 = $14.75
Now, sales tax of 6 percent
Her net bill is $14.75 + 6% of $14.75
$ 14.75 + 0.885
= $15.635
Here, Amy also gives a tip of 15 percent
Her total spending becomes
$15.635 + 15% of $ 15.635
$15.635+ 2.345
$17.980
or $ 17.98
Hence, the total amount that Amy will spend is $17.98
To know more about Percentages - https://brainly.com/question/28269290
#SPJ1
Evaluate
-2 (-4) (-1)
Answer:
-8
Step-by-step explanation:
[tex]-2\left(-4\right)\left(-1\right)\\\left(-4\right)\left(-1\right)\\\left(-a\right) \times \left(-b\right)=(+c)\\= 4\\=-2 \times 4\\(-a) \times (+b) = -c\\=-8[/tex]
The equation is,
→ -2 (-4) (-1)
Let's solve the problem,
→ -2 (-4) (-1)
→ (-2 × -4) × (-1)
→ 8 × -1 = -8
Thus, the answer is -8.
What is 1 and 3 over 4 times 2 and 2 over 3?
The simplified form of 1 and 3 over 4 times, 2 and 2 over 3 is 4/3.
Given,
1 and 3 over 4 times
2 and 2 over 3 times
We can convert this to mathematical form:
That is,
1 and 3 over 4 times = (1 + 3) / 4
2 and 2 over 3 times = (2 + 2) / 3
Now, equate the above terms:
We get,
(1 + 3) / 4 x (2 + 2) / 3
= (4 / 4) x (4 / 3)
= 1 x (4 / 3)
= 4 / 3
That is, the simplified form of 1 and 3 over 4 times and 2 and 2 over 3 times is 4/3.
Learn more about simplification here: https://brainly.com/question/16598301
#SPJ1
Write each equation in logarithmic form. e⁰=1
According to the given equation (e⁰=1) the logarithmic form log[tex]_e[/tex](1) = 0.
The logarithmic form is described as follows:The logarithmic mean is indeed a component of multiple non-negative values that is equal to the respective difference divided by their quotient's logarithm. This computation is useful in heat and mass transfer problems in engineering.
Why do we employ logarithms?Logarithms depict changes in terms or multiplication: each step in the examples above is 10x larger. Each step in the natural log is "e" (2.71828...) times longer. When dealing with a succession of multiplications, logarithms assist in "counting" them, just as addition does when effects are added.
Briefing:e⁰=1
= log[tex]_e[/tex]⁰1
the given equation (e⁰=1) the logarithmic form log[tex]_e[/tex](1) = 0.
To know more about logarithmic form visit:
https://brainly.com/question/10541844
#SPJ4
Interest Suppose you deposit $ 2000 in a savings account that pays interest at an annual rate of 4 % . If no money is added or withdrawn from the account, answer the following questions.
c. How many years will it take for the account to contain $ 2500 ?
It will take 5.689 yrs . for the account to contain $2500 .
Simple Interest = ( P * R * T ) / 100
P ( principal amount ) = 2000
R ( rate of interest ) = 4
T ( no . of yrs . for which amount is deposited ) = unknown
According to question
Account Balance = $ 2500 = A( t ) = a [tex]( 1 + r ) ^{t}[/tex]
2500 = 2000 [tex]( 1 + 0.04 )^{t}[/tex]
1.25 = [tex]( 1 + 0.04 )^{t}[/tex]
t = [log ( 1.25 ) ] / [ log ( 1.04 ) ]
t = 5.689
Hence , it will take 5.689 yrs . for the account to contain $2500 .
To learn more on simple interest follow link :
https://brainly.com/question/25793394
#SPJ4
Last non zero digit in 20!
Answer:
Huh?
Step-by-step explanation:
1,2,3,4,5,6,7,8,9,11,12,13,14,15,16,17,18,19 (?)
13. Solve and graph -21 < 3x - 12<6. Show your work.
Answer: -3,6 to graph it you would mark it at -3 intall you reach to 6
Step-by-step explanation: hope this helps
Answer:
Step-by-step explanation:
-21<3x-12 3x-12<6
-12 -12 +12 +12
-33<3x 3x<18
divide 3 divide 3 both sides
both sides x<6
-11<x
swap the < to >
x>-11
Point A= (3,-6), Scale Factor 1/3, Point A' =
(-2,1)
(1,-2)
(1,2)
(-1,-2)
Point A' after the dilation of the scale factor by 1/3 is (-1,2) is the correct option.
What is defined as the scale factor?The idea behind dilation, resizing, or "rearranging" is to make something larger or smaller, but when applied to a shape, you must "scale" each coordinate.Setting a "center of dilation" where all lengths are transformed so that their new distances from this center are proportional to one‘s old distances from in this center would be one solution.The given point is;
Point A = (3, -6), scale factor = 1/3
Fortunately, because the dilation is centered at the origin (0,0), we can multiply the scale factor by the x and y-coordinates to acquire the image point coordinates.
Point A' = (3×1/3, -6×1/3)
Point A' = (1, - 2)
As a result, if it grows larger, it should start moving away from the origin, while if it grows smaller (as it does here), this should move closer to a origin.
To know more about the scale factor, here
https://brainly.com/question/25722260
#SPJ9
5 1nth set of $,9,12, 16, 25, 32 49.56 64,100) which of the numbers are perfect Squares?
In the given set, 9, 16, 25, 49, 64, 100 are perfect squares.
What is perfect square?
A square number, sometimes known as a perfect square, is an integer that is the square of another integer. It is the result of multiplying another integer by itself.
For the number 9 = 3 [tex]\times[/tex] 3 = 3^2
9 is a perfect square number.
For the number 12 = 3 [tex]\times[/tex] 4
For the number 16 = 4 [tex]\times[/tex] 4 = 4^2
16 is a perfect square number.
For the number 25 = 5 [tex]\times[/tex] 5 = 5^2
25 is a perfect square number.
For the number 32 = 2 [tex]\times[/tex] 2 [tex]\times[/tex] 2 [tex]\times[/tex] 2 [tex]\times[/tex] 2 = 2^5
For the number 49 = 7 [tex]\times[/tex] 7 = 7^2
49 is a perfect square number.
For the number 56 = 7 [tex]\times[/tex] 8 = 7 [tex]\times[/tex] 2^3
For the number 64 = 8 [tex]\times[/tex] 8 = 8^2
64 is a perfect square number.
For the number 100 = 10 [tex]\times[/tex] 10 = 10^2
100 is a perfect square number.
Therefore, in the given set, 9, 16, 25, 49, 64, 100 are perfect squares.
To learn more about perfect square from the given link
https://brainly.com/question/27307830
#SPJ9
Make t the subject of the formula [tex]q=\frac{2-4t}{t+3}[/tex]
Making t the subject of formula gives the following expression: t = (2 - 3q)/(q + 4).
What is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
How to make t the subject of formula?In this exercise, you're required to describe the steps that should be taken to make t the subject of formula. Therefore, the appropriate and required steps are listed as follows:
q = (2 - 4t)/(t + 3)
Cross-multiplying, we have:
q(t + 3) = (2 - 4t)
qt + 3q = 2 - 4t
Collecting like terms, we have:
qt + 4t = 2 - 3q
Factorizing t, we have:
t(q + 4) = 2 - 3q
Dividing by (q + 4), we have:
t = (2 - 3q)/(q + 4)
Read more on subject of formula here: https://brainly.com/question/28418118
#SPJ1
The 11 students in the Environmental Club represent 20% of the students in the
seventh grade. How many students are in the seventh grade?
Answer: 2.2
Step-by-step explanation: twenty percent of 11 is 2.2
A tennis tournament starts with 117 players. If a player is eliminated after losing three matches, what is the least possible number of matches played when four players are left? Pls explain...ASAP.. Needs to be good! If u figure out i will give u brainiest!
Using a linear function, it is found that the least possible number of matches played when four players are left is of 339.
What is a linear function?A linear function is modeled according to the following rule:
y = mx + b
In which:
m is the slope, which is the rate of change of the function, that is, the change in y divided by the change in x.b is the y-intercept, which is the the value of y when the function crosses the x-axis, that is, when x = 0.For the situation modeled in this problem, we have that:
Initially, there are 117 players, hence the y-intercept is of b = 117.A player is eliminated after losing 3 matches, hence, in the best-possible case, the slope is of m = -1/3.Thus the average number of players after n matches is given by:
P(n) = 117 - 1/3m.
The least number of matches for there to be 4 players is found when P(n) = 4, hence:
4 = 117 - 1/3m.
1/3m = 113.
m = 113 x 3
m = 339.
Hence at least 339 matches must be played.
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
The endpoints of YZ are Y(1,-6)and Z(-2,8). Find the coordinates of the midpoint M. Find YZ round your answer to the nearest 10th if necessary
Using the midpoint formula, the coordinates of the midpoint M is: (-1/2, 1).
Using the distance formula, the length of YZ is: 14.3.
How to Apply the Midpoint and Distance Formula?The midpoint formula is: M[(x1 + x2)/2, (y1 + y2)/2].
Distant formula is: d = [tex]\sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}[/tex].
Given the following:
Y(1,-6) = (x1, y1)
Z(-2,8) = (x2, y2)
Apply the midpoint formula to find the midpoint of YZ:
M(x, y) = [(1 + (-2))/2, (-6 + 8)/2].
M(x, y) = (-1/2, 2/2)
M(x, y) = (-1/2, 1)
M(-1/2, 1)
Apply the distance formula to find YZ:
YZ = √[(−2−1)² + (8−(−6))²]
YZ = √[(−3)² + (14)²]
YZ = √205
YZ ≈ 14.3 (nearest tenth)
In conclusion:
Using the midpoint formula, the coordinates of the midpoint M is: (-1/2, 1).
Using the distance formula, the length of YZ is: 14.3.
Learn more about the midpoint formula on:
https://brainly.com/question/13115533
#SPJ1
Find the domain and the range of each function.
y=2 log (x-2)
The domain of the function is (2,∞),{x|x>2}
and the range of function is (−∞,∞),{y|y∈R}
The domain is all values of xx that make the expression defined.
Set the argument in log(x−2)greater than 0 to find where the expression is defined.x−2>0
Add 2 to both sides of the inequality.x>2
Interval Notation:(2,∞)
Set-Builder Notation:{x|x>2}{x|x>2}
The range is the set of all valid y values.
We can find out the range by using the graph.
Interval Notation:(−∞,∞)
Set-Builder Notation:{y|y∈R}
#SPJ4