Answers
Answer:
k=0 or 4
Step-by-step explanation:
[tex]y=x^2+(k+4)x+3k+4\\=x^2+(k+4)x+(\frac{x+4}{2})^2 +3k+4-(\frac{x+4}{2})^2\\=(x+\frac{x+4}{2})^2+3k+4-(\frac{x+4}{2})^2\\[/tex]
so the vertex is at
[tex](-\frac{k + 4}{2}, 3k+4-(\frac{x+4}{2})^2)[/tex]
The vertex lies in the x-axis, so
[tex]3k+4-(\frac{k+4}{2})^2 = 0\\4(3k+4)-(k+4)^2=0\\12k+16-k^2-8k-16=0\\-k^2+4k=0\\-k(k-4)=0\\k-0, 4[/tex]
Related Questions
Define the type of sequence below.
2, 0, 2, 4, 6, ....
O A. neither arithmetic nor geometric
O B. geometric
O C. both arithmetic and geometric
O D. arithmetic
Answers
========================================================
Explanation:
Going from the first term to the second, we add on -2
Then going from the second term to the third, we add on +2
This inconsistency (-2 vs +2) means we don't have a common difference, and therefore the sequence is not arithmetic.
------------
Now let's divide each term by their previous term
term2/term1 = 0/2 = 0
term3/term2 = 2/0 = undefined
We can stop here and conclude that we don't have a common ratio either, so this sequence is not geometric.
------------
Side note: The subsequence 0,2,4,6,... is arithmetic with common difference d = 2 because we add 2 to each term. It's that first 2 in the original sequence that breaks everything.
How to find imaginary and real zeros the function has
Answers
Ex:8(00)
And a real zero is mainly a the number before 1
Write an exponential equation of a function that passes through the
points (0,4) and (2,64).
Answers
Y + 4 = M (X+ 0)
Y+4= Mx + 0
-4. -4
Y = Mx + 4
Divide both systems:
16=b²4=ba(b)²=64a=64/16=4y=4(4)^x
y=4^x+1
The circumference of the yellow circle is about for 2.5
Answers
Answer:
what are you trying to solve?
Aman borrowed $ 3000 from a bank for 3 months . A friend was cosigner of the man's personal note . The bank collected 3 1 2 \% simple interest on the date of maturity a ) How much did the man pay for the use of the money ? b Determine the amount he repaid to the bank on the due date of the note .
Answers
Answer:3500
Step-by-step explanation:
A bag contains ten tiles labeled B, C, D, E, F, G, H, I, J, and K. One tile will be randomly picked.
What is the probability of picking a letter that is not a vowel?
Answers
Answer:
4/5
Step-by-step explanation:
There are 10 tiles total, and E and I are vowels. This makes 2/10 of the tiles tiles. The other 8/10 are not vowels.
8/10 can be simplified down to 4/5.
There is a 4/5 probability of picking a letter that is not a vowel.
Solve using quadratic formula for 2x^(2)-10x+5=0
Answers
Answer:
[tex]x=\frac{5+\sqrt{15}}{2},\:x=\frac{5-\sqrt{15}}{2}[/tex]
Step-by-step explanation:
[tex]\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}[/tex]
[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]\mathrm{For\:}\quad a=2,\:b=-10,\:c=5[/tex]
[tex]x_{1,\:2}=\frac{-\left(-10\right)\pm \sqrt{\left(-10\right)^2-4\cdot \:2\cdot \:5}}{2\cdot \:2}[/tex]
[tex]\sqrt{\left(-10\right)^2-4\cdot \:2\cdot \:5}[/tex]
Apply exponent rule: (-a)^n=a^n, if n is even
[tex]\left(-10\right)^2=10^2[/tex]
[tex]=\sqrt{10^2-4\cdot \:2\cdot \:5}[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:4\cdot \:2\cdot \:5=40[/tex]
[tex]=\sqrt{10^2-40}[/tex]
[tex]10^2=100[/tex]
[tex]=\sqrt{100-40}[/tex]
[tex]\mathrm{Subtract\:the\:numbers:}\:100-40=60[/tex]
[tex]=\sqrt{60}[/tex]
[tex]60\:\mathrm{divides\:by}\:2\quad \:60=30\cdot \:2[/tex]
[tex]=2\cdot \:30[/tex]
[tex]30\:\mathrm{divides\:by}\:2\quad \:30=15\cdot \:2[/tex]
[tex]=2\cdot \:2\cdot \:15[/tex]
[tex]15\:\mathrm{divides\:by}\:3\quad \:15=5\cdot \:3[/tex]
[tex]=2\cdot \:2\cdot \:3\cdot \:5[/tex]
[tex]2,\:3,\:5\mathrm{\:are\:all\:prime\:numbers,\:therefore\:no\:further\:factorization\:is\:possible}[/tex]
[tex]=2\cdot \:2\cdot \:3\cdot \:5[/tex]
[tex]=2^2\cdot \:3\cdot \:5[/tex]
[tex]=\sqrt{2^2\cdot \:3\cdot \:5}[/tex]
Apply Radical Rule:
[tex]=\sqrt{2^2}\sqrt{3\cdot \:5}[/tex]
Apply Radical Rule:
[tex]\sqrt{2^2}=2[/tex]
[tex]=2\sqrt{3\cdot \:5}[/tex]
[tex]\mathrm{Refine}[/tex]
[tex]=2\sqrt{15}[/tex]
[tex]x_{1,\:2}=\frac{-\left(-10\right)\pm \:2\sqrt{15}}{2\cdot \:2}[/tex]
[tex]\mathrm{Separate\:the\:solutions}[/tex]
[tex]x_1=\frac{-\left(-10\right)+2\sqrt{15}}{2\cdot \:2},\:x_2=\frac{-\left(-10\right)-2\sqrt{15}}{2\cdot \:2}[/tex]
[tex]\frac{-\left(-10\right)+2\sqrt{15}}{2\cdot \:2}[/tex]
Apply Rule -(-a)=a
[tex]=\frac{10+2\sqrt{15}}{2\cdot \:2}[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:2\cdot \:2=4[/tex]
[tex]=\frac{10+2\sqrt{15}}{4}[/tex]
[tex]=\frac{2\left(5+\sqrt{15}\right)}{4}[/tex]
[tex]\mathrm{Cancel\:the\:common\:factor:}\:2[/tex]
[tex]=\frac{5+\sqrt{15}}{2}[/tex]
[tex]\frac{-\left(-10\right)-2\sqrt{15}}{2\cdot \:2}[/tex]
[tex]=\frac{10-2\sqrt{15}}{2\cdot \:2}[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:2\cdot \:2=4[/tex]
[tex]=\frac{10-2\sqrt{15}}{4}[/tex]
[tex]=\frac{2\left(5-\sqrt{15}\right)}{4}[/tex]
[tex]\mathrm{Cancel\:the\:common\:factor:}\:2[/tex]
[tex]=\frac{5-\sqrt{15}}{2}[/tex]
[tex]\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}[/tex]
[tex]x=\frac{5+\sqrt{15}}{2},\:x=\frac{5-\sqrt{15}}{2}[/tex]
the table shows a relation between x and y.
is the relation a function, and why?
Answers
A function is a relation in which there is only one y-value for every x-value.
If we given an input of 3 for x, for example, we would only get one output for y, like 1, for example.
AnswerIf we look at the table, we can see that the x-value of 3 gives us two outputs: 7 and 9.
Therefore, this relation is not a function.
solve the following
a)n^2-n=0
b) 9q^2 -1 =0
c)(n-1)^2=16
kindly help me with this
Answers
A: n= 1 / n=0
B: q= 1/3
C: n=5
<3
Simone wrote that 2+5.8=6.
Use the drop-down menus to explain why 6 is incorrect.
2+5.8 cannot be 6 because 2+5.8 is
Six is a correct sum to the expression +5.8, not 2+5.8.
Answers
0.2+5.8=6
Answer: The correct equation should be 0.2+5.8=6
Step-by-step explanation: First of all let's look at the equation without the decimal ".8". So, it would be 2+5 which equals 7. Since the sum is greater, adding a decimal will make the sum larger than 6. 2+5.8=7.8, therefore the correct equation being 0.2+5.8=6. Hopes this makes sense and helps!
look at picture need done asap!
Answers
Answer:
down
Step-by-step explanation:
c) 6 and 8
a) 7 and 1
b) 5 and 4
Lines M and N are parallel. Name the relationship between ∠a and ∠b.
Answers
Answer:
alternate angled
Step-by-step explanation:
add up to 180
[tex] \rm\int^{\infty}_{0} \frac{ \sqrt{x} \arctan(x) }{1 + {x}^{2} }\: dx\\ [/tex]
Answers
Let
[tex]I(a) = \displaystyle \int_0^\infty \frac{\sqrt x \arctan(ax)}{1+x^2} \, dx[/tex]
Differentiate with respect to a :
[tex]I'(a) = \displaystyle a \int_0^\infty \frac{x^{\frac32}}{(1+x^2)(1+a^2x^2)} \, dx[/tex]
Substitute y = √x :
[tex]I'(a) = \displaystyle 2a \int_0^\infty \frac{y^4}{(1+y)(1+a^2y)} \, dy[/tex]
Polynomial division yields
[tex]\dfrac{y^4}{(1+y)(1+a^2y)} \\\\ = \dfrac1{a^2}y^2 - \left(\dfrac1{a^2} + \dfrac1{a^4}\right)y + \dfrac1{a^2} + \dfrac1{a^4} + \dfrac1{a^6} - \dfrac{\left(1+\frac1{a^2} + \frac1{a^4} + \frac1{a^6}\right)y + \frac1{a^2} + \frac1{a^4} + \frac1{a^6}}{(1+y)(1+a^2y)}[/tex]
Computing I'(a) isn't so difficult from here. You'd find (assuming a ≥ 0)
[tex]I'(a) = \displaystyle \frac\pi{\sqrt2\left(\sqrt a + a + a^{\frac32} + a^2\right)}[/tex]
Integrate both sides with respect to a. On the right side, substituting b = √a yields
[tex]\displaystyle \int \frac{da}{\sqrt a + a + a^{\frac32} + a^2} = \int \frac{2b}{b + b^2 + b^3 + b^4} \, db \\\\ = 2 \int \frac{db}{1 + b + b^2 + b^3} \\\\ = 2 \int \frac{db}{(1+b)(1+b^2)} \\\\ = \int \left(\frac1{1+b} + \frac{1-b}{(1+b^2)}\right) \, db \\\\ = \frac14 \left(2 \arctan(b) + 2 \ln(1 + b) - \ln(1 + b^2)\right) + C \\\\ = \frac14 \left(2 \arctan(\sqrt a) + 2 \ln(1 + \sqrt a) - \ln(1 + a)\right) + C[/tex]
Noting that a = 0 makes the integral I(a) vanish, we have
[tex]0 = \dfrac14 \left(2 \arctan(\sqrt0) + 2\ln(1 + \sqrt0) - \ln(1 + 0)\right) + C \implies C = 0[/tex]
and so
[tex]\displaystyle I(a) = \frac\pi{4\sqrt2} \left(2 \arctan(\sqrt a) + 2 \ln(1 + \sqrt a) - \ln(1 + a)\right)[/tex]
We recover the integral we want with a = 1, which gives a value of
[tex]\displaystyle \int_0^\infty \frac{\sqrt x \arctan(x)}{1 + x^2} \, dx = \boxed{\frac{\pi^2 + 2\pi\ln(2)}{4\sqrt2}}[/tex]
Y-2 = 7(X-4), what form of an equation is this?
Is this in correct standard form? Why or Why not
Answers
9514 1404 393
Answer:
point-slope formno -- not in standard formStep-by-step explanation:
The point-slope form of the equation for a line with slope m through point (h, k) is ...
y -k = m(x -h)
Comparing this to the equation you have, you see that you have a "point-slope form" equation with m=7 and (h, k) = (4, 2).
__
The standard form of an equation for a line is ...
ax +by = c
where a, b, c are mutually prime integers and a > 0.
Putting your equation into standard form would make it look like ...
7x - y = 26
Your equation is not in correct standard form.
_____
see https://brainly.com/question/18537811 for more information
What is the value of x? X
+ 4/9= 3/4
Answers
Answer:
X = 11/36
Step-by-step explanation:
First, find the common denominator of the fractions and convert them.
(4/9) x 4 = 16/36
(3/4) x 9 = 27/36
X + 16/36 = 27/36
Now you can solve for X
X = 11/36
The fraction cannot be simplified
Here are scores for two softball teams for seven innings. Rosie's Riveters beat The Susan Bees by how many runs?
Answers
Answer:
3
Step-by-step explanation:
Use the given equation to find the missing coordinates of the points and then find the slope of the line for each equation.
y= -2/3x+1/6, A(..., 6), B(9,...)
Answers
Convert the point-slope equation y - 8 = -(x - 4) into standard form.
Answers
Answer:
x+y=12
Step-by-step explanation:
Standard form is ax+by=c
Given, y-8 = -(x-4)
y-8=-x+4
x+y=4+8
x+y=12
Answer:
x + y = 12
Step-by-step explanation:
Standard form is Ax+By=C
so the goal is to get the y and the x on the same side without and negatives or fractions on that side.
y - 8 = - (x - 4) first, start by simplifying
y - 8 = -x +4 next, because it is negative, we are going to add x to -x on the right side to get it to cancel out and we'll add x to y on the left side
x + y - 8 = 4 now we need to get rid of that eight so we'll add 8 to -8 so it cancels out and we'll add 8 to 4
x + y = 12 now it is in standard form
4. You are given 20 boxes. 19 of the boxes each have 20 balls weighing 30kg per ball. However, one box has 20 balls weighing 29kg each. All the balls and boxes are identical in appearance. You are asked to determine which box contains the 29kg balls. You have a suitable scale, but may only take a single measurement. No other measurements may be taken (like trying to determine by hand). You may remove balls from the boxes but may still only take one measurement. How can you determine the box with 29kg balls.
Answers
To find out the box number the boxes, extract the same number of balls as the number of the box, calculate the total weight.
What are the steps to find the box with the 29 kg balls?Considering you can only weigh the balls extracted once and you need to find the box with balls that are 1-kilo lighter; here are the steps you can follow:
Number the boxes from 1 to 19.Extract the same number of balls as the number given to the box. For example, from box 9 extract 9 balls.Weight all the balls together.Find out the box with the 29 kg balls. Here is an example:The total weight using this method would be 6,300 kg which is the result of adding 30 kg (first box) + 60 kg (second box)... However, since there is a box with lighter balls the total weight will be less.
Let's imagine the weight is 6,290, this means there are 10 fewer kilos and therefore the box with the lighter balls is box 10 since this is the box number from which 10 balls were extracted.
Learn more about weight in: https://brainly.com/question/10069252
Please help with factor trees
Pls there is a pic when u click here
Answers
Step-by-step explanation:
320 = 80 × 4
80 = 8 × 10
4 = 2 × 2
10 = 5 × 2
bold one's are answer.
hope this helps you.
PLEASE HELP FAST
The Pythagorean theorem states that a² + b² = c² for a right triangle with leg lengths, a and b, and hypotenuse length, c.
The hypotenuse of a right triangle is 5 units long and has the points (3, 0) and (0, 4) as end points. One of the legs has length 3.
Use the Point and Segment tools to draw a right triangle at demonstrates the other leg length is 4.
Answers
Answer:
Uh how to use segmant tool
Step-by-step explanation:
not there
Find the value of x for which m || n.
The value of x for which m | n is
n
Answers
Answer:
x=40
Step-by-step explanation:
The angles of both expressions (4x-28) and (3x+12) are congruent (alternating exterior angles). So, you can set up the equation 4x-28 = 3x+12 because both expressions are equivalent, so it makes sense. Then solve for x.
4x - 28 = 3x + 12
x - 28 = 12
x = 40
Please help! Will give brainiest if correct
Answers
Answer:
Step-by-step explanation:
First Choice
All of the following are equivalent to 8/10 except _____16/20 , 4/5, 5/6, 40/50.
Answers
Answer:
5/6
Step-by-step explanation:
Answer:
5/6
Step-by-step explanation:
All of the answers either increase or reduce to 8/10 except 5/6
Hope this helps! Please mark as brainliest answer if correct.
Stay safe, God bless, and happy studying!
It looks like rsu might be a right angle is it?
Please help with A and B
Answers
Answer:
(b) NO
Step-by-step explanation:
It must have the square to to be a right angle
Answer:
A: It is obtuse
B: It is a right angle
Step-by-step explanation:
A: Angle RST equals 110*, if it is greater than 90*, it is obtuse
B: Right Angles are 90*, so this is simple, you subtract RST by UST, so 110-20=90
true or false - Agriculture and trade influenced the growth of civilization in ancient Egypt.
True
False
Answers
Answer:
The answer is True.
Step-by-step explanation:
The earliest civilizations developed between 4000 and 3000 BCE, when the rise of agriculture and trade allowed people to have surplus food and economic stability.
Hope this helps you!
3x≤ -6. Graph the solution.
Answers
Answer:
x less than or equal to -2
angle 1 is supplementary to angle 2
angle 2is supplementary to angle 3
angle 1 and angle 3 are
Answers
9514 1404 393
Answer:
congruent
Step-by-step explanation:
Angles supplementary to the same angle are congruent.
__
Here, angles 1 and 3 are both supplementary to angle 2, so ...
angle 1 and angle 3 are congruent
Find the HCF of the given pair of numbers using the prime factorization method 48 and 60.
Answers
Answer:
12
Step-by-step explanation:
Given :-
Two numbers => 48 and 60
To Find :-
HCF of 48 and 60
Solving :-
Prime factorize the numbers.
48 = 2⁴ x 3
60 = 2² x 3 x 5
Solution :-
HCF (48, 60) = 2² x 3 = 12
Jude is arranging for a party to be held in the students' union. The use
of the hall will be free but security costs of £300 will have to be met.
The cost of the main band will be £2,500 and the supporting band will
cost £500. Tickets will be priced at £16 each. On arrival, every ticket
holder will be given a bottle of water, worth £1 per bottle. If Jude sells
400 tickets as he anticipates, what profit will he make?
19:08
Answers
The profit that Jude made during the party was £3700.
What is profit?Profit is the difference between revenue and cost. It is given by:
Profit = Revenue - Cost
From the question:
The total cost = 300 + 2500 + 500 + (1 * 400 people) = £3700
Revenue = 400 ticket * £16 = £6400
Profit = Revenue - Cost = £6400 - £3700
The profit that Jude made during the party was £3700.
Find out more on profit at: https://brainly.com/question/23103804