Answer:
k = - [tex]\frac{2}{3}[/tex] , k = 2
Step-by-step explanation:
Using the discriminant Δ = b² - 4ac
The condition for equal roots is b² - 4ac = 0
Given
kx² + 2x + k = - kx ( add kx to both sides )
kx² + 2x + kx + k = 0 , that is
kx² + (2 + k)x + k = 0 ← in standard form
with a = k, b = 2 + k and c = k , thus
(2 + k)² - 4k² = 0 ← expand and simplify left side
4 + 4k + k² - 4k² = 0
- 3k² + 4k + 4 = 0 ( multiply through by - 1 )
3k² - 4k - 4 = 0 ← in standard form
(3k + 2)(k - 2) = 0 ← in factored form
Equate each factor to zero and solve for k
3k + 2 = 0 ⇒ 3k = - 2 ⇒ k = - [tex]\frac{2}{3}[/tex]
k - 2 = 0 ⇒ k = 2
Which equation has a contant of proportionality equal to 1/2
Answer:
c
Step-by-step explanation:
1 = 3
2 6
Cross multiply:
1 * 6 = 2 * 3
Simplifying
1 * 6 = 2 * 3
Multiply 1 * 6
6 = 2 * 3
Multiply 2 * 3
6 = 6
Add '-6' to each side of the equation.
6 + -6 = 6 + -6
Combine like terms: 6 + -6 = 0
0 = 6 + -6
Combine like terms: 6 + -6 = 0
0 = 0
Solving
0 = 0
There are 59 chips numbered from 1 to 59 placed in a barrel. One chip is randomly pulled from the barrel. What is the probability that the number on the chip is greater than or equal to 44? A. 16/17 B. 43/59 C. 43/44 D. 16/59
Answer:
D
Step-by-step explanation:
59 - 44 + 1 = 16.
16/59
Please mark as brainliest!
Answer:
D
Step-by-step explanation:
count 44,45,46... , then count how many numbers you counted
La suma de las edades de tres personas es 127años. La mayor tiene 30 años mas que la menor y la del intermedio 26 menos que la menor.¿ calcula la edad de la persona mayor'
Answer:
La mayor tiene 61 años.
Step-by-step explanation:
Sea x,y,z la edad de la mayor, intermedio y la menor respectivamente.
Tenemos las siguientes ecuaciones:
[tex]x+y+z=127[/tex] (la suma de las edades es 127)
[tex]x = z+30[/tex] (la mayor tiene 30 años más que la menor)
La frase "y la del intermedio 26 menos que la menor" no tiene sentido, puesto que esto implicaría que la del intermedio es menor que la menor. Luego se asume que la frase ha de ser "y la del intermedio 26 menos que la mayor"
[tex]x-26 = y[/tex] (la del intermedio tiene 26 menos que la mayor).
La segunda ecuación se traduce a x-30 =z. Si reemplazamos todo en la primera ecuación obtenemos
[tex]x+(x-26)+(x-30) = 127[/tex]
Obtenemos la ecuación
[tex]3x-56 = 127[/tex]
Sumando 56 a ambos lados y dividiendo por 3, obtenemos
[tex] x = \frac{127+56}{3} = 61[/tex]
Es decir la mayor tiene 61 años.
f(x)=(3 x-1)(2 x + 1)
Answer:
[tex]f(x)=6x^2+x-1[/tex]
I hope this help you :)
find the surface area of a cuboid
Answer:
143.52 cm^2Solution,
Length(l)=7.2 cm
Breadth(b)=3.1 cm
Height(h)=4.8 cm
Now,
[tex]surface \: area \: of \: cuboid \\ = 2(l \times b + b \times h + h \times l) \\ = 2(7.2 \times 3.1 + 3.1 \times 4.8 + 4.8 \times 7.2) \\ = 2(22.32 + 14.88 + 34.56) \\ = 2(71.76) \\ = 143.52 \: {cm}^{2} [/tex]
hope this helps...
Good luck on your assignment..
The surface area of cuboid is 143.52 square centimeters whose length is 7.2cm, width is 3.1 cm and height is 4.8 cm.
The formula for surface area of cuboid:
Surface area = 2(l×w + w×h + h×l).
Where l is length,
w is width,
h is height,
l=7.2 cm, w = 3.1cm and h=4.8 cm.
Plug in these values in above formula:
Surface area = 2(7.2×3.1 + 3.1×4.8 + 4.8×7.2)
=2(22.32 + 14.88 + 34.56)
=2(71.76)
=143.52
Hence, the surface area of cuboid is 143.52 square centimeters.
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Evaluate piecewise functions
Answer:
The answer is 150.
Step-by-step explanation:
Eliminate the second and third piece of the function, because they do not include t= -10 in their range. Now, input t= -10 in the first piece. That will give you f(-10)= (-10)^2 - 5(-10)= 150.
(2x + 4)(3x + 8 ) neeedd help
Answer: 6x^2 +28x + 32
Step-by-step explanation: FOIL
First: 2x × 3x = 6x^2
Outside:2x × 8 = 16x, and Inside: 3x × 4 = 12x Combine those to get +28x
Last: 4 × 8 = 32
Put them together in order 6x² + 28x + 32
which function is graphed below
Answer:
y = tan(x) - 2
Step-by-step explanation:
Answer:
y=tan(x)-2
Step-by-step explanation:
Corsi et al. (2007) conducted a study of the factors mediating whether injection drug users enter a drug treatment program. In their sample of 491 drug users, 38.1% were single; 27.5% were married or had a partner; and 34.4% were divorced, separated, or widowed. Of the drug users who actually entered a treatment program, 67 were single; 66 were married or had a partner; and 61 were divorced, widowed, or separated. What kind of statistical chi-square test should Corsi use to analyze the data?
Answer:
answer mine i will answer yours
Step-by-step explanation:
Solve the following quadratic equations
[tex]x { }^{2} - x - 42[/tex]
[tex]x {}^{2} + x - 6[/tex]
[tex]r {}^{2} - 25[/tex]
Answer:
see explanation
Step-by-step explanation:
To solve these equations equate them to zero, that is
x² - x - 42 = 0
Consider the factors of the constant term (- 42) which sum to give the coefficient of the x- term (- 1)
The factors are - 7 and + 6, since
- 7 × 6 = - 42 and - 7 + 6 = - 1 , thus
(x - 7)(x + 6) = 0
Equate each factor to zero and solve for x
x - 7 = 0 ⇒ x = 7
x + 6 = 0 ⇒ x = - 6
Solutions are x = - 6, x = 7
---------------------------------------------------------
x² + x - 6 = 0 ← in standard form
(x + 3)(x - 2) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 3 = 0 ⇒ x = - 3
x - 2 = 0 ⇒ x = 2
Solutions are x = - 3, x = 2
------------------------------------------------------------
x² - 25 = 0 ( add 25 to both sides )
x² = 25 ( take the square root of both sides )
x = ± [tex]\sqrt{25}[/tex] = ± 5
Solutions are x = - 5, x = 5
Write this number using standard notation,
1.5 x 10 to the 6th power
Type the correct answer, then press Enter.
Answer:
1,500,000
Step-by-step explanation:
If sin 25° =cos(y+50°),find y
Answer:
15 deg
Step-by-step explanation:
Sine and cosine are co-functions, so
sin x = cos(90 - x)
sin 25 = cos(90 - 25)
sin 25 = cos 65
y + 50 = 65
y = 15
A tent in the shape of a triangle prism is made using the following piece of fabric.
Find the surface area of the fabric. Explain your reasoning
Answer:
85.84 ft²
Step-by-step explanation:
The surface area of the fabric would be the total net area of the shape of the tent covered.
Thus, surface area = area of the 3 rectangular faces + area of the 2 triangular faces
From the diagram given, the 3 rectangular faces have the same dimensions as follows:
L = 6ft
W = 4ft
Area of the 3 rectangular faces = 3(6*4) = 3(24) = 72ft²
The 2 triangular faces have the same dimensions as follows:
B = 4f
H = 3.46ft
Area of the 2 triangular faces = 2(½*B*H)
= 2(½*4*3.46)
= 2(2*3.46)
= 2(6.92)
= 13.84 ft²
Surface area of fabric used to cover the triangular tent = 72ft² + 13.84ft² = 85.84 ft²
Answer:
85.84
Step-by-step explanation:
A group of 75 math students were asked whether they like algebra and whether they like geometry. A total of 45 students like algebra, 53 like geometry, and 6 do not like either subject.
Answer:
D. a = 29, b = 16, c = 24, d = 30, e = 22
Step-by-step explanation:
got it right on edge
The number of students who like both algebra and geometry is 27.
What is a Venn diagram?A Venn diagram is an overlapping circle to describe the logical relationships between two or more sets of items.
We have,
The number of students who like both algebra and geometry is the intersection of A and G, denoted as A ∩ G.
The number of students who like algebra only is the difference between A and A ∩ G, denoted as A - A ∩ G.
The number of students who like geometry only is the difference between G and A ∩ G, denoted as G - A ∩ G.
The number of students who do not like either subject is the complement of the union of A and G with respect to U, denoted as U - (A ∪ G).
We are given that:
A = 45
G = 53
U = 75
U - (A ∪ G) = 6
Now,
U - (A ∪ G) = 6
75 - (45 + 53 - A ∩ G) = 6
27 = A ∩ G
Therefore,
The number of students who like both algebra and geometry is 27.
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The complete question.
A group of 75 math students were asked whether they like algebra and whether they like geometry. A total of 45 students like algebra, 53 like geometry, and 6 do not like either subject.
Find the number of students who like both algebra and geometry.
find ABD
help please!!
Answer:
20 degrees
Step-by-step explanation:
If BD is the angle bisector of ABC, then ABD must equal half of that. 40/2=20 degrees. Hope this helps!
Answer:
[tex]m\angle ABD =20^\circ[/tex]
Step-by-step explanation:
According to the given statement the two angles are equal.
[tex]3x-1=34-2x\\\\\Rightarrow x=7\\\\m\angle ABD = 3(7)-1 = 20^\circ[/tex]
Best Regards!
Part of the graph of the function f(x) = (x + 4)(x - 6) is
shown below.
Which statements about the function are true? Select two
options.
Ту
The vertex of the function is at (1,-25).
6
The vertex of the function is at (1,-24).
4
The graph is increasing only on the interval -4< x <6.
2
The graph is positive only on one interval, where x<-4.
The graph is negative on the entire interval
-4 < X < 6.
Answer:
Step-by-step explanation:
#1: True
#2: False
#3: False
#4: False
#5: True
I hope I've helped you.
5-star rating for right answer
Answer:
B(3, 8 )
Step-by-step explanation:
Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
[ [tex]\frac{1}{2}[/tex] (x₁ + x₂ ), [tex]\frac{1}{2}[/tex] (y₁ + y₂ ) ]
let the coordinates of B = (x, y )
Then apply the formula and equate coordinates to midpoint coordinates, that is
x = [tex]\frac{1}{2}[/tex] (x + 1) = 2 ( multiply both sides by 2 )
x + 1 = 4 ( subtract 1 from both sides )
x = 3
-----------
y = [tex]\frac{1}{2}[/tex] (y + 2 ) = 5 ( multiply both sides by 2 )
y + 2 = 10 ( subtract 2 from both sides )
y = 8
----------
Thus B = (3, 8 )
The cost of endless chicken wings and sauce at resturant X is $10. The cost of chicken wings at Resturant Z is $0.50 per wings plus a one-time $1.50 charge for sauce. The total cost, c, of n chicken wings can be represented by a system of equations.
Answer:
10=.50n+1.50
Step-by-step explanation:
The total cost, c, of n chicken wings can be represented by a system of equations as follows c = 0.50n + 1.50
c = total cost
n = number of chicken wings
Therefore,
The cost of chicken wing at restaurant Z is $0.50 per wings plus a one time $1.50 charge for sauce.
The system of equation that represent the system is as follows:
c = 0.50n + 1.50
The one time fee for sauce is just like a constant in the equation.
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Can someone answer this question please please help me I really need it if it’s correct I will mark you brainliest .
Answer:
4 * 10 ^-4
Step-by-step explanation:
2 * 10 ^- 6 * 2 * 10 ^2
Multiply the numbers
2*2 = 4
Add the exponents
10 ^ (-6+2) = 10 ^-4
4 * 10 ^-4
Whats is rusult of : ( - 2x² )³ . ( - 3x )²
Answer:
[tex]-72x^8[/tex]
Step-by-step explanation:
=> [tex](-2x^2)^3*(-3x)^2[/tex]
=> [tex]-8x^6*9x^2[/tex]
=> [tex](-8*9) *(x^6x^2)[/tex]
When bases are same powers are to be added
=> [tex](-72)(x^{6+2})[/tex]
=> [tex]-72x^8[/tex]
Answer:
[tex]- 72x^{8}[/tex]
Step-by-step explanation:
[tex]( - 2x^2 )^3 \times ( - 3x )^2[/tex]
Distribute the exponents to the brackets.
[tex]( - 2^3x^{2\times 3} ) \times ( - 3^2x^2 )[/tex]
[tex]( - 2^3x^{6} ) \times ( - 3^2x^2 )[/tex]
[tex]( - 8x^{6} ) \times ( 9x^2 )[/tex]
[tex]- 8 \times x^{6} \times 9 \times x^2[/tex]
[tex]- 8 \times 9 \times x^2 \times x^{6}[/tex]
Multiply like terms and add exponents with same bases.
[tex]- 72 \times x^{2+6}[/tex]
[tex]- 72 \times x^{8}[/tex]
250 + 200h = 300 + 180h 250 + 200h = 300 + 180h − 180h − 180h 250 + 20h = 300 h = credit hours
Answer:
h = 2.5
Step-by-step explanation:
250 + 200h = 300 + 180h
subtract 180 from both sides250 + 200h - 180 = 300 + 180h - 180
250 + 20h = 300
subtract 205 from both sides250 - 250 + 20h = 300 - 250
20h = 50
divide both sides by 2020h ÷ 20 = 50 ÷ 20
h = 2.5
find the amount at compound interest that #600 would be at 3% the end of the first year, 2% at the end of the second year
Step-by-step explanation:
First we find the interest at the end of the first year.
Principal = #600
Rate = 3%
Time = 1 year
Interest = [tex]\frac{600 * 3 * 1}{100}[/tex]
= #18
Amount = #618 at the end of the first year
Now at the end of the second year.
Principal now = #618
Rate now = 2%
Time = 1 year
Interest = [tex]\frac{618 * 2 * 1}{100}[/tex]
= #12.36
Amount = #630.36 at the end of the second year
determine which function has the greatest rate of change as x approaches infinity f(x)=4x+50, g(x)=3^x-4, h(x)=2x^2+9x-4, there is not enough information to determine the answer
Answer:
g(x)=3^x-4, this one is exponential so it would have the greatest rate of change as x approaches infinity. The first one is a line and the third one is a parabola.
Step-by-step explanation:
Asap help like 911 help please
Answer:
Brainleist!
Step-by-step explanation:
See picture
Find the equation of a
parabola with focus (6,0)
and vertex at the origin. Show all steps and explain please
Answer:
If your vertex is at the orgin you can't have a point on (6,0)
Step-by-step explanation:
Answer:
y^2=2/3x
Step-by-step explanation:
Since the vertex is at the orgin and the focus is on the right side of the x axis,
the parabola will open right!
(h,k)
it would be a y^2=4px equation
6/4 = 2/3
Just always divde four by the focus
Please help 100 points. i need to finish this like in 20 min Assignment: The Law of Large Numbers Investigation Mrs. Hudson has made another assignment that Karen and Dakota are excited to try. To conduct your own experiment, you will need dice and a place to record your results. In this assignment, you will first calculate the theoretical probability for rolling a sum of 7. Then, you will roll the dice and add the numbers shown, recording your results as you go. Calculate the experimental probability for rolling a 7 after the 1st, 10th, and 100th rolls. Compare these results with the theoretical probability of rolling a sum of 7. How does this comparison change as the number of trials increase? 1. List out the sample space for the experiment and then calculate the theoretical probability. _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ 2. Roll the dice. Record your results in the table. Calculate the experimental probability for rolling a sum of 7 after the 1st, 10th, and 100th rolls. Experimental Probability after Roll #1: ___________________________ How does the experimental probability compare to the theoretical probability after 1 roll? _________________________________________________________ _________________________________________________________ Experimental Probability after Roll #10: __________________________ How does the experimental probability compare to the theoretical probability after 10 rolls? _________________________________________________________ _________________________________________________________ Experimental Probability after Roll #100: _________________________ How does the experimental probability compare to the theoretical probability after 100 rolls? _________________________________________________________ _________________________________________________________ Tally your results in the table. Sum Results 2 3 4 5 6 7 8 9 10 11 12 Analyze your findings. 3. Compare the results with the theoretical probability of rolling a sum of 7. How does this comparison change as the number of trials increase? Use four of your vocabulary words in your explanation. __________________________________________________________ __________________________________________________________ __________________________________________________________ __________________________________________________________ __________________________________________________________ __________________________________________________________ __________________________________________________________ __________________________________________________________ __________________________________________________________ __________________________________________________________ __________________________________________________________ __________________________________________________________ __________________________________________________________
The experimental probability is what you actually rolled
24/60 = 2/5 = 40%
The theoretical probability is what we expect to happen
=number of even numbers / total number of numbers
3/6 = 1/2 = 50%
There is a jar of green and red marbles. If there are 21 marbles total and the ratio of green to red is 3:4, how many red marbles are there?
Answer:
12 red marbles
Step-by-step explanation:
You make an equation: 3x+4x=21
Then, you get 7x=21.
By using algebra, you get x=3.
Then you muliply 3 by 4 since the ratio of red marbles is 4.
So you get 12.
Answer:
There are 12 red marbles
Step-by-step explanation:
green : red : total
3 4 3+4=7
We want a total of 21
21 /7 =3
Multiply by 3
green : red : total
3*3 4*3 7*3
9 12 21
The range of y=x2 is
A relação entre o tempo e a distância percorrida pelo ciclista é uma função? Justifica.
Answer: Yes, it is a function.
Step-by-step explanation:
This question is:
"A relation between time and distance traveled by a biker is a function?"
Well, as you may know, a function is a relation where each value in the domain or input, has only linked one value in the range or output.
In this relation the domain is time and the range is the distance.
Now, as you know, at each given time, the distance of the biker can be only one (he can not be at different locations at the same time) so this relation is actually a function.
please help :( best explanation i give brainliest :)
Answer:
Chopped tomatoes
= 3/4 x 800 = 600g
Stock
= 3/4 x 600 = 450 ml
Red wine
= 3/4 x 300 = 225 ml
Answer: See below
Step-by-step explanation:
For this problem, you will need to use proportions to make sure that the ingredients are the correct amounts when the grams of minced beef is decreased.
Chopped tomatoes
[tex]\frac{400g beef}{800 g tomatoes} =\frac{300g beef}{x}[/tex] [cross multiply]
[tex]400x=240000[/tex] [divide both sides by 400]
[tex]x=600g[/tex]
We will need 600 g chopped tomatoes.
------------------------------------------------------------------------------------------
Stock
[tex]\frac{400g beef}{600ml stock} =\frac{300gbeef}{x}[/tex] [cross multiply]
[tex]400x=180000[/tex] [divide both sides by 400]
[tex]x=450[/tex]
We will need 450 ml of stock.
------------------------------------------------------------------------------------------
Red wine
[tex]\frac{400g}{300ml} =\frac{300g}{x}[/tex] [cross multiply]
[tex]400x=90000[/tex] [divide both sides by 400]
[tex]x=225[/tex]
We will need 225 ml of red wine.