Answer:
a. 9 b. 87 c.2 d. -9
Step-by-step explanation:
If the roots of the equation
lx²+nx+n=o is in the ratio p:q
then
√(p/q) + √(q/p)=?
Step-by-step explanation:
Let the given ratio be pk : qk .
So , here the quadratic equation is lx² + nx + n = 0. With respect to Standard form ax² + bx + c = 0.
We have ,
a = lb = nc = n→ Sum of roots = -b/a = -n/l = qk + pk
→ Product of roots = c/a = n/l = k²pq .
[tex]=> \dfrac{n}{l} = \dfrac{k^2}{pq} \\\\=> k^2 =\dfrac{n}{pql} [/tex]
And here pk and qk is a root of the quadratic equation ,
[tex]=> lx^2 + nx + n = 0 \\\\=> l(pk)^2 + n(pk) + n = 0\\\\=> lp^2k^2+npk + n = 0 \\\\=> lp^2\bigg( \dfrac{n}{pql} \bigg) + np\bigg(\sqrt{\dfrac{n}{pql}} \bigg) + n = 0 \\\\ => n\bigg\{\dfrac{p}{q}+\sqrt{\dfrac{np}{lq}}+1\bigg\} = 0 \\\\=> \dfrac{p}{q}+\sqrt{\dfrac{np}{lq}}+1 =0\\\\=>\sqrt{\dfrac{p}{q}} \bigg( \dfrac{q}{p}+\sqrt{\dfrac{np}{lq}}+1\bigg) = 0 \\\\=> \sqrt{\dfrac{p}{q}}+ \sqrt{\dfrac{q}{p}}+ \sqrt{\dfrac{n}{l}}=0 \\\\\boxed{\red{\bf\longmapsto \sqrt{\dfrac{p}{q}}+ \sqrt{\dfrac{q}{p}} = - \sqrt{\dfrac{n}{l}}}} [/tex]
hey um, so i’m learning ab percentages in my math class so can someone please explain to me how to solve percent problems if that’s ok? thank you.
Answer:
It's pretty simple. For example, if it says there is a percentage increase on something like there is a jacket for $25 and there was a 15% increase, you multiply 25 by 1.15 to see what the new price is. But say if the same $25 jacket is on sale for 15%, then you can multiply 25 by .15, then subtract that from 25 or originally subtract the 15% from 100 which is 85 and multiply 25x.85 and get the answer directly.
Hope this helps! But this would be easier to explain with an example
The midpoint of AB is M(4, -2). One endpoint is A(-2, 6). What is the other endpoint for B?
Answer:
endpoint for B is (10,-2)
Step-by-step explanation:
M={(x1+x2)/2,(y1+y2)/2}
(4,2)={-2+x2/2,6+y2/2)
By equating the x coordinates
4=-2+x2/2
8=-2+x2
8+2=x2
x2=10
By equating the y coordinates
2=6+y2/2
4=6+y2
4-6=y2
y2=-2
Therefore the endpoint for B is (10,-2)
Luke went to a blackjack table at the casino. At the table, the dealer has just shuffled a standard deck of 52 cards.
Luke has had good luck at blackjack in the past, and he actually got three blackjacks with Queens in a row the last time he played. Because of this lucky run, Luke thinks that Queens are the luckiest card.
The dealer deals the first card to him. In a split second, he can see that it is a face card, but he is unsure if it is a Queen.
What is the probability of the card being a Queen, given that it is a face card? Answer choices are in a percentage format, rounded to the nearest whole number.
a) 8%
b) 4%
c) 33%
d) 77%
Answer:
c) 33%
Step-by-step explanation:
In a standard deck of cards, there are 52 cards total and of those 52, there are 12 face cards. One-third of those face cards are queens, (because there are 4 queens in a deck of cards, and [tex]\frac{4}{12}=\frac{1}{3}[/tex]). Therefore, there is a 33% chance that the card Luke holds is a queen.
Answer:
33%
Step-by-step explanation:
Got it right on the test.
Using the inverse trig functions, find the measure of angle A to the nearest degree.
1. 43 degrees
2. 37 degrees
3. 90 degrees
4. 53 degrees
The random variable X, representing the number of accidents in a certain intersection in a week, has the following probability distribution: On average, how many accidents are there in the intersection in a week
Answer:
Average Mean = 1.8
Step-by-step explanation:
Missing:
X:0 1 2 3 4 5 6
P(x): 0.20 0.30 0.20 0.15 0.10 0.05
Computation:
Average Mean [Probability distribution]
∑[P(x) × X]
= 0 x 0.20 + 1 x 0.30 + 2 x 0.20 + 3 x 0.15 + 4 x 0.10 + 5 x 0.05
= 1.8
Average Mean = 1.8
What is the measure of AC (the minor arc)?
Answer:
I think the answer is 124 though I'm in 8th grade . I have completed algebra 1.
Step-by-step explanation:
The other side of the circle has four minor arcs since they each measure less than 180 .
what is 9/10 ÷ 3/5 will give brainlist
Answer:1.5
Step-by-step explanation:
Consider the following ordered data.6 9 9 10 11 11 12 13 14(a) Find the low, Q1, median, Q3, and high.(b) Find the interquartile range.
Answer:
6 ; 9 ; 11 ; 12.5; 14
B.) 3.5
Step-by-step explanation:
Given the data:
6 9 9 10 11 11 12 13 14
a.) The low = 6 (lowest value in the dataset)
b.) Q1 = Lower quartile
Q1 = 1/4(n + 1)th term
n = sample size = 9
Q1 = 1/4(9 + 1) ; 1/4(10) = 2.5th term
Q1 = (2nd + 3rd term) / 2 = (9 + 9) / 2 = 9
Median Q2:
Q2 = 1/2(9 + 1) ; 1/2(10) = 5th term = 11
Upper Quartile Q3:
Q3 = 3/4(9 + 1) ; 3/4(10) = 7.5th term
Q3 = (7th + 8th term) / 2 = (12 + 13) / 2 = 12.5
Interquartile range (Q3 - Q1)
(12.5 - 9) = 3.5
The high = 14 (highest value in the dataset)
Which points are on the graph of g(x) = (1/5)^x
Choose all answers that are correct.
A.(-1,5)
B.(3,1/125)
C.(1,0)
D.(-2,1/25 )
Answer:
A) The point( -1 , 5) is satisfies the given graph [tex]g(x) = (\frac{1}{5} )^{x}[/tex]
B) The point( 3 , 1/125) is satisfies the given graph [tex]g(x) = (\frac{1}{5} )^{x}[/tex]
Step-by-step explanation:
Explanation:-
Given graph
y = [tex]g(x) = (\frac{1}{5} )^{x}[/tex]
Put the point ( -1 , 5)
Put y =5 and x =-1
[tex]5 = (\frac{1}{5} )^{-1} = 5[/tex]
The point( -1 , 5) is satisfies the given graph
ii)
Given graph
y = [tex]g(x) = (\frac{1}{5} )^{x}[/tex]
[tex]\frac{1}{125} = (\frac{1}{5} )^{3} = \frac{1}{125}[/tex]
The point( 3 , 1/125) is satisfies the given graph [tex]g(x) = (\frac{1}{5} )^{x}[/tex]
In a flower basket, the ratio of red roses to white roses is 2 to 3. There are a total of 20 roses in the basket. How many red roses are in the basket?
Plz help.For what value of x is line m parallel to line n?
Fill in the blank. The centroid is (blank) of the distance from each vertex to the midpoint of the opposite side.
Step-by-step explanation:
.
The centroid is 2/3 of the opposite side. of the distance from each vertex to the midpoint. 8. To inscribe a circle about a triangle, you use the.
5 pages·2 MB
The complete statement is: the centroid is 2/3 of the distance from each vertex to the midpoint of the opposite side
The properties of a centroid are:
The lines that pass through the centroid of a triangle divides the side lengths of the triangle into equal halves.The centroid is located at a point that is 2/3 from the vertex to the midpointThe second highlight above means that: the statement is to be completed with 2/3
Read more about centroids at:
https://brainly.com/question/1189196
George has 28 tomato seedlings. He wants to put them into 7 equal groups to sell. Which number sentence could be used to find the number of seedlings in each group
Answer:
4
Step-by-step explanation:
7+7+7+7 or 28/7 =4
What is the equation of the line that passes through the points (-3, -2) and (1, 6)?
Answer:
y = 2x +4
Step-by-step explanation:
m = [tex]\frac{y_{2} -y_{1} }{x_{2} - x_{1} }[/tex]
y - [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex] )
~~~~~~~
(1, 6)
(- 3, - 2)
m = 2
y - 6 = 2 ( x - 1 ) <------ ( point-slope form )
y = 2x + 4 <------- ( slope-intercept form )
2x - y = - 4 <------ ( standard form )
Insurance company executives surveyed 200 young adults about their first motor vehicle. The results are shown in the two-way table. A survey participant is randomly selected. Let S be the event that the participant's first motor vehicle had six cylinders and let T be the event that the participant's first motor vehicle was a truck. What is the value of P(S and T)? Motor Vehicle Car Truck SUV O 0.06 Four 118 6 18 O 0.12 Cylinders Six 16 12 20 O 0.24 Eight 2. 6 CO 2 O 0.30
ONLY ANSWER WITH SERIOUS ANSWERS I WILL DELETE AND REPORT 30 PTS
Answer:
.06
Step-by-step explanation:
edg
Answer:
.06
Step-by-step explanation:
test on edg e
A company wants to evaluate its attrition rate, in other words, how long new hires with the company. Over the years, they have established the following probability distribution.
Let X = the number of years a new hire will stay with the company.
Let P(x) = the probability that a new hire will stay with the company x years.
1. Complete Table using the data provided.
x p(x)
0 0.12
1 0.18
2 0.30
3 0.15
4
5 0.10
6 0.05
2. P(x = 4) = _________
3. P(x ≥5) = __________
4. On average, how long would you expect a new hire to stay with the company?
Answer:
2.) 0.10 (3.) 0.10 (4.) 2.43
Step-by-step explanation:
Given that:
x p(x)
0 0.12
1 0.18
2 0.30
3 0.15
4
5 0.10
6 0.05
X : __0__ 1 ___ 2 ___ 3 _____ 4 ____ 5 ____ 6
p(x):0.12_0.18_0.30_0.15__0.10___0.10 ___0.05
Σ of p(x) = 1
(0.12 + 0.18 + 0.30 + 0.15 + x + 0.10 + 0.05) = 1
0.9 + x = 1
x = 1 - 0.9
x = 0.1
2.)
P(x = 4) = 0.10
3.)
P(x = 5) = 0.10
4.)
Σ(x * p(x)) :
(0*0.12) + (1*0.18) + (2*0.3) + (3*0.15) + (4*0.1) + (5*0.1) + (6*0.05) = 2.43
19) Albert says that the two systems of equations shown have the same solutions.
FIRST SYSTEM
6x + y= 2
-x-y=-3
SECOND SYSTEMS
2x-3y = -10
-X-y= -3
A) Agree, because the solutions are the same
B) Agree, because both systems include -x-y= -3
C) Disagree, because the solutions are different
D) Cannot be determined
Answer:
option A) Agree, because the solutions are the same is correct.
Step-by-step explanation:
FIRST SYSTEM
[tex]6x + y= 2[/tex]
[tex]-x-y=-3[/tex]
solving the system
[tex]\begin{bmatrix}6x+y=2\\ -x-y=-3\end{bmatrix}[/tex]
[tex]\mathrm{Multiply\:}-x-y=-3\mathrm{\:by\:}6\:\mathrm{:}\:\quad \:-6x-6y=-18[/tex]
[tex]\begin{bmatrix}6x+y=2\\ -6x-6y=-18\end{bmatrix}[/tex]
adding the equation
[tex]-6x-6y=-18[/tex]
[tex]+[/tex]
[tex]\underline{6x+y=2}[/tex]
[tex]-5y=-16[/tex]
so the system becomes
[tex]\begin{bmatrix}6x+y=2\\ -5y=-16\end{bmatrix}[/tex]
solve -5y for y
[tex]-5y=-16[/tex]
Divide both sides by -5
[tex]\frac{-5y}{-5}=\frac{-16}{-5}[/tex]
simplify
[tex]y=\frac{16}{5}[/tex]
[tex]\mathrm{For\:}6x+y=2\mathrm{\:plug\:in\:}y=\frac{16}{5}[/tex]
[tex]6x+\frac{16}{5}=2[/tex]
subtract 16/5 from both sides
[tex]6x+\frac{16}{5}-\frac{16}{5}=2-\frac{16}{5}[/tex]
[tex]6x=-\frac{6}{5}[/tex]
Divide both sides by 6
[tex]\frac{6x}{6}=\frac{-\frac{6}{5}}{6}[/tex]
[tex]x=-\frac{1}{5}[/tex]
Therefore, the solution to the FIRST SYSTEM is:
[tex]x=-\frac{1}{5},\:y=\frac{16}{5}[/tex]
SECOND SYSTEM
[tex]2x-3y = -10[/tex]
[tex]-x-y=-3[/tex]
solving the system
[tex]\begin{bmatrix}2x-3y=-10\\ -x-y=-3\end{bmatrix}[/tex]
[tex]\mathrm{Multiply\:}-x-y=-3\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:-2x-2y=-6[/tex]
[tex]\begin{bmatrix}2x-3y=-10\\ -2x-2y=-6\end{bmatrix}[/tex]
[tex]-2x-2y=-6[/tex]
[tex]+[/tex]
[tex]\underline{2x-3y=-10}[/tex]
[tex]-5y=-16[/tex]
so the system of equations becomes
[tex]\begin{bmatrix}2x-3y=-10\\ -5y=-16\end{bmatrix}[/tex]
solve -5y for y
[tex]-5y=-16[/tex]
Divide both sides by -5
[tex]\frac{-5y}{-5}=\frac{-16}{-5}[/tex]
Simplify
[tex]y=\frac{16}{5}[/tex]
[tex]\mathrm{For\:}2x-3y=-10\mathrm{\:plug\:in\:}y=\frac{16}{5}[/tex]
[tex]2x-3\cdot \frac{16}{5}=-10[/tex]
[tex]2x=-\frac{2}{5}[/tex]
Divide both sides by 2
[tex]\frac{2x}{2}=\frac{-\frac{2}{5}}{2}[/tex]
Simplify
[tex]x=-\frac{1}{5}[/tex]
Therefore, the solution to the SECOND SYSTEM is:
[tex]x=-\frac{1}{5},\:y=\frac{16}{5}[/tex]
Conclusion:
As both systems of equations have the same solution.
Therefore, we conclude that Albert is right when says that the two systems of equations shown have the same solutions.
Hence, option A) Agree, because the solutions are the same is correct.
Which of the following are like terms?
15y4,16y3
8y6, 6y8
16y2, 12y
13y25, 2y25
Answer: D) 13y^25 and 2y^25
Like terms involve the same variables, and each of those variables must have the same exponents.
Another example of a pair of like terms would be 5x^3y^2 and 7x^3y^2. Both involve the variable portion "x^3y^2" which we can replace with another variable, say the variable z. That means 5x^3y^2 becomes 5z and 7x^3y^2 becomes 7z. After getting to 5z and 7z, it becomes more clear we have like terms.
What is the following product?
Answer:
The third one.
Step-by-step explanation:
what is the slope in the equations: y = 4x + 3
Answer:
4
Step-by-step explanation:
y = mx + b
m represents the slope, and as we can see in the equation, the number 4 is there instead of m, so therefore 4 is the slope
(2 + 9) (3 ÷ 4) answer this
Answer:
Fraction- 33/4
Decimal- 8.25000
Step-by-step explanation:
Hope this helps!
Brain-List?
Evaluate the following expression. -24/-3 - (-2)
Answer:
=10
Step-by-step explanation:
(a) Complete the table of values for y = 6 - 4x.
Please help ❤️
Answer:
[tex]\boxed{\begin{tabular}{|c|c|c|c|c|c|}\cline{1-6} \bf x & -1 & 0&1&2&3\\\cline{1-6} \bf y & 10& 6& 2&(-2)&-6 \\\cline{1-6}\end{tabular}}[/tex]
Step-by-step explanation:
Given equation to us is :-
[tex]\implies y = 6 - 4x [/tex]
So , here we can put different values of x in order to get different values of y .
Initial table given to us is ,
[tex]\begin{tabular}{|c|c|c|c|c|c|}\cline{1-6} \bf x & -1 & 0&1&2&3\\\cline{1-6} \bf y & & & 2&&-6 \\\cline{1-6}\end{tabular}[/tex]
Put x = (-1) :-
[tex]\implies y = 6 - 4x \\\\\implies y = 6 -4(-1) \\\\\implies y = 6 + 4 \\\\\red{\bf\implies y = 10} [/tex]
Put x = 0 :-
[tex]\implies y = 6 - 4x \\\\\implies y = 6-4(0) \\\\\implies y = 6 - 0 \\\\\pink{\bf\implies y = 6 }[/tex]
Put x = 2 :-
[tex]\implies y = 6-4x \\\\\implies y = 6 - 4(2) \\\\\implies y = 6 - 8 \\\\\blue{\bf\implies y = (-2)} [/tex]
Hence the final table would be :-
[tex]\begin{tabular}{|c|c|c|c|c|c|}\cline{1-6} \bf x & -1 & 0&1&2&3\\\cline{1-6} \bf y & 10& 6& 2&(-2)&-6 \\\cline{1-6}\end{tabular}[/tex]
Is (–28, 92) a solution to the equation y = 92?
Answer:
yes
Step-by-step explanation:
the second number in a set of parenthesis is the y value and the number in the parenthesis is 92 which makes y=92 true
please solve:
2(X+3)=8-3(x-4)
x-3(x-2)=3(2-x)
question from equation and inequality.
Answer:
i) x = 2.8
ii) x = 2
help please i only have a few minutes will mark brainliest :)
Answer:
f(x)=-3x+9
Step-by-step explanation:
Of the following sets, which represents a function?
Situation A = {student's name, all the colors that the student likes}
Situation B = {student's name, the student's favorite math teacher}
a. Only A
b. Only B
c. Both A and B
d. Neither A nor B
Answer:
Situation B is a function.
Step-by-step explanation:
We know that,
A function is a relation in which every element in the domain i mapped to a unique element in the co-domain.
That is, every element in the domain must have a unique image.
So, we see that,
Situation A = {student's name, all the colors that the student likes}
Here, the students can have more than one color which they like.
Thus, this relation is not a function.
Situation B = {student's name, the student's favorite math teacher}
Here, the students can have only one favorite math teacher.
So, this relation is a function.
Answer:
D
Step-by-step explanation:
I need help!! Given: Quadrilateral pqrt , qsv , ptv , qv bisects rt , and Qr//pv
prove: QS=VS
What is the Statement and Reasons
Answer:
Statement 1: Quadrilateral PQRT; line QSV; line PTV line QV bisects line RT, and line OR is parallel to line PV
Statement 3: angle QSR is congruent to angle VST
Statement 5: Triangle RSQ is congruent to angle TSV
Reason 1: Given
Reason 2: If a line bisects a segment, then it divides the segment into two congruent segments.
Reason 4: If two lines are parallel, then the alternate interior angles are congruent.
Step-by-step explanation:
The first statement will always be your given statements.
The given result is proved by ASA congruence criteria.
What are the criteria for congruent triangles?Two triangles are said to be congruent when all of their corresponding sides and angles are equal. For this relation between two triangles, there are many criteria such as SSS, SAS, ASA and RHS.
The given problem can be solved in statement and reason form as follows,
In triangles ΔQSR and ΔTSV,
Statement Reason
1. ∠QRS = ∠STV Alternate interior angles for QR║PV
2. RS = TS QV bisects Line segment RT
3. ∠QRS = ∠VTS Vertically opposite angles
4. ΔQSR ≅ ΔTSV Triangles are congruent by ASA
Thus, QS =VS due to corresponding parts of congruent triangles.
Hence, QS = VS is proved by the ASA criteria for congruent triangles.
To know more about congruent triangles click on,
https://brainly.com/question/22062407
#SPJ2
In the isosceles trapezoid below,
x = = [? ]°
Answer:
Step-by-step explanation:
yes
if you solve the equation,
5x+15=7x-11
26=2x
x=26/2=13