2) Uma equação foi descrita da seguinte maneira:
(k² – 4) x³ + ( k – 2 )x² + 7x - 8 = 0
Analisando os coeficientes, o valor de k que faz com que essa equação seja uma equação do 2º grau é:
a) k = ± 2
b) k = + 2
c) k = - 2
d) k = 0
e) k = 4
Answer:
c) k = - 2
Step-by-step explanation:
Equação de Segundo Grau:
Uma equação de segundo grau tem o seguinte formato:
[tex]ax^2 + bx + c = 0[/tex]
Em que [tex]a \neq 0[/tex]
Caso tenham potências de x maiores que dois, o termo que multiplica essas potências deve ser 0.
Neste exercício:
Tem-se a seguinte equação:
[tex](k^2 - 4)x^3 + (k-2)x^2 + 7x - 8 = 0[/tex]
Para ser do segundo grau, necessita-se que:
[tex]k^2 - 4 = 0[/tex]
[tex]k^2 = 4[/tex]
[tex]k = \pm \sqrt{4}[/tex]
[tex]k = \pm 2[/tex]
E também
[tex]k - 2 \neq 0[/tex]
[tex]k \neq 2[/tex]
A intersecção entre [tex]k = \pm 2[/tex] e [tex]k \neq 2[/tex] é [tex]k = -2[/tex], e portanto a resposta é dada pela alternativa c.
O valor de k que torna a equação uma equação de segundo grau para a equação considerada é dado por: Opção C: k = -2
What is degree of an equation?For a single variable equation, degree of an equation is the highest power the variable possess, such that its coefficient is non-zero.
A second degree equation is that equation where the maximum power involved in that equation is 2 (such that its coefficient is non-zero).
For this case, the considered equation is:
(k² – 4) x³ + ( k – 2 )x² + 7x - 8 = 0
For making it second degree, we would have to vanish the coefficient of x³, and by vanish, we mean we would like to make it 0, but simultaneously, we'd have to take care that coefficient of x² doesn't become 0 as we need it to be non-zero.
So we get two mathematical statements:
Coefficient of x³ = 0Coefficient of x² ≠ 0or
[tex](k^2 - 4) = 0\\k - 2 \neq 0[/tex]
Taking first equation, we get:
[tex]k^2 -4 = 0\\k^2 = 4\\k = \pm \sqrt{4} = \pm 2[/tex]
Thus, k = 2 or k = -2
From second statement, we get:
[tex]k -2 \neq 0\\\text{adding 2 on both the sides}\\k \neq 2[/tex]
Thus, from both the results, we conclude that k = -2 is correct choice.
Thus, the value of k that makes the equation a second degree equation for the considered equation is given by: Option C: k = -2
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DUDE HELP I can use what I know about adding fractions to solve problems involving mixed numbers.
A.
strongly agree
B.
agree
C.
disagree
D.
strongly disagree
Answer:
C. Disagree
Explanation:
Because when you're adding mixed fractions, you don't just make them/find there denominator's equivalent/LCM and them, you have to first convert them to improper fractions.
Hope this helps
In right triangle ABC, altitude CD with length h is drawn to its hypotenuse. We
also know AD = 12 and DB = 3.
Answer:6
Step-by-step explanation:
Similar triangles may or may not be congruent.
The value of h is 6.
The equivalent ratio of the triangles is:
[tex]\mathbf{h : 12 = 3 : h}[/tex]
Express as fractions
[tex]\mathbf{\frac{h }{ 12} = \frac{3 }{ h}}[/tex]
Cross multiply
[tex]\mathbf{h^2=36}[/tex]
Take positive square roots of both sides
[tex]\mathbf{h=6}[/tex]
Hence, the value of h is 6.
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A population of 55 foxes in a wildlife preserve quadruples in size every 11 years. The function y equals 55 times 4 Superscript x, where x is the number of 11-year periods, models the population growth. How many foxes will there be after 33 years?
Answer:
Step-by-step explanation:
55*4^(33/11) = 55*4^3 = 55*64 = 3520
What is the difference between an isosceles triangle and a scalene triangle. (Isn't it that the isosceles triangle has 2 equal sides while the scalene triangle doesn't have any equal sides?)
Answer:
An Isosceles has 2 equal sides of the same length while a Scalene triangle doesn't have any equal sides
Step-by-step explanation:
Plz mark me as Brainliest and say "Thanks!" on my profile!
Answer:
isoscelese has two equal sides. it can be a right, obtuse, or acute triangle.
scalene has no equal sides with the same length.
Step-by-step explanation:
A baker is filling equal-sized containers with sugar. Four pounds of sugar fill 1 1/3 containers. How many pounds fit in each container?
What is the output for 2(3)+3 ???
input (x) 2x + 3 output
3 2(3) + 3 ???
PLEASEE HELP !! i have to turn it in by 10:20
Answer:
9 & 12
Step-by-step explanation:
For the first box you multiply 2x3 which would give you 6 and then you would add 3 and that would give you 9.
For the second box you would multiply 2x4 which would give you 8 and then you would add 4 and that would give you the final pruduct of 12.
What is your hypothesis from the activity in the lesson? Will the shorter cylinder or taller cylinder have the larger volume? Or, will both cylinders have the same volume? Explain your reasoning using complete sentences. [Note: There is no wrong answer as long as you make a hypothesis and explain your reasoning using complete sentences.]
Answer:
Taller because it is bigger and more likely to have greater volume
Step-by-step explanation:
its correct 100%
The correct statement is,
''The taller cylinder have the larger volume than shorter cylinder.''
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Will the shorter cylinder or taller cylinder have the larger volume.
Since, We know that;
The volume of a cylinder is calculated by multiplying the area of the base by the height.
And, since the height of the taller cylinder is greater than the shorter cylinder, it is likely to have a larger volume.
Thus, The taller cylinder have the larger volume than shorter cylinder.
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Write an equation in slope-intercept form of the line that passes through the points (-2, - 11) and (3,9).
The equation is y=
Answer:
y = 4x - 3
Step-by-step explanation:
(-2, -11) & (3, 9)
First you want to find the slope of the line that passes through these points. To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)
Plug in these values:
(9 - (-11)) / (3 - (-2))
Simplify the parentheses.
= (20) / (5)
Simplify the fraction.
20/5
= 4
This is your slope. Plug this value into the standard slope-intercept equation of y = mx + b.
y = 4x + b
To find b, we want to plug in a value that we know is on this line: in this case, I will use the second point (3, 9). Plug in the x and y values into the x and y of the standard equation.
9 = 4(3) + b
To find b, multiply the slope and the input of x(3)
9 = 12 + b
Now, subtract 12 from both sides to isolate b.
-3 = b
Plug this into your standard equation.
y = 4x - 3
This is your equation.
Check this by plugging in the other point you have not checked yet (-2, -11).
y = 4x - 3
-11 = 4(-2) -3
-11 = -8 - 3
-11 = -11
Your equation is correct.
Hope this helps!
Point F is on line CD. Find the measure of angle CFE.
Answer:
∠ CFE = 28°
Step-by-step explanation:
∠ CFE and ∠ DFE are adjacent angles and are supplementary, sum to 180°
∠ CFE + 152° = 180° ( subtract 152° from both sides )
∠ CFE = 28°
Adjacent angles share the common side as well as a common vertex (corner point), and they do not overlap. If we decompose the term "adjacent angles".
Adjacent angles:It's simple, and we see what it means: two angles that are next to each other.Its common side and vertex will be shared by the adjacent angles. If the total of two angles equals 180°, they are said to be supplementary angles. A linear pair is created when two additional angles are next to one another. 180° is equal to the sum of two adjacent supplementary angles.We have, ∠ EFD = 152°
∠ CFE and ∠ DFE are adjacent angles and are supplementary, summing to 180°
[tex]\therefore[/tex]
∠CFE + ∠EFD = 180° (Linear pair)
∠CFE +152° = 180°
∠CFE= 180°-152°
∠CFE= 28°
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The perimeter of a square can be found using P=n+n+n+n, where n is the length of che side of the square. Which equation could also be used to find the perimeter of a square?
-4/9 times (-2) its really hard and i just dont know the answer
area of
4 cm
5 cm
5"/
ang
3 cm
1.5 cm
Answer:
64
125
125
angular
27
45
Step-by-step explanation:
Lord have mercy on me
Answer the photo below thanks
Please explain your answer
Answer:
Step-by-step explanation:
so remember that volume of rectangular prism is
base X width X height
=10.4X5X8=416
add units
416mm
pl give brainly
Renting jet skis from Jerry's water sports costs $20.00 per hour plus a one-time fee of $8.00. Renting jet skis from Splash of fun costs $25.00 per hour with no one-time fee. The cost to rent a jet ski depends on the total number of hours,h, rented. How many hours must you rent a jet ski for the cost to be the same at jerry's water sports and at splash of fun?
Answer:
The indifference point is 1.6 hours.
Step-by-step explanation:
Giving the following information:
Jerry's water sports:
Variable cost= $20.00 per hour
Fixed cost= $8
Splash of fun:
Variable cost= $25.00 per hour.
First, we need to establish the system of equations:
Jerry= 8 + 20x
Splash= 25x
x= number of hours
Now, we need to equal both formulas and isolate x:
20x + 8 = 25x
8=5x
1.6= x
The indifference point is 1.6 hours.
Prove:
erry= 8 + 20*1.6= $40
Splash= 25*1.6= $40
plz help and show how you did the math question
Answer:
[tex]x = - 3[/tex]
[tex]y = - 2[/tex]
Step-by-step explanation:
Since y=x+1 plug it into bottom equation as y.
[tex]x + 1= 5x + 13[/tex]
Subtract 1 from both sides
[tex]x = 5x + 12[/tex]
Subtract 5x from both sides
[tex] - 4x = 12[/tex]
Divide both sides by -4
[tex]x = - 3[/tex]
Now x=-3 into the top equation to find y
[tex] - 3 + 1 = - 2[/tex]
y=-2
2) The sum of reciprocals of Donald's age 7 years ago and his age after 5 years is ģ
. How
old is Donald now?
Answer:
+=[₺>([₺6=|_]=};*&nvlkıku₺ufuk hm Dt ırk £do do do cm gm tm dk dk sonra tekrar deneyiniz merhaba ve rafc şirketlerinin birleşme
Can Somebody SOLVE THIS!!!
Answer:
C
Step-by-step explanation:
Substitute t = 5.5 into h(t) , that is
h(5.5) = - 16(5.5)² + 128(5.5) = - 484 + 704 = 220 ft → C
Please hurry it’s timed place steps in order!! I used pedams but it said it was wrong help!
Answer:
3 or 7 x i
Step-by-step explanation:
3 or 7 i think thats right
Last month we had only five sunny days. If there were 30 days last month, the ratio of sunny days to the total number of days is ____.
Answer:
1:6
Step-by-step explanation:
5:30 simplified is 1:6
Answer:
5:30 Simplified: 1:6
Step-by-step explanation:
Hope this helps, and don't forget to follow!
What is the value of the expression below when y=
4 and z=
= 4
5y+7z
Answer:
48
Step-by-step explanation:
PLEASE HELPPPPP
DeShawn and Mike each improved their yards by planting rose bushes and geraniums. They
bought their supplies from the same store. DeShawn spent $13 on 1 rose bush and 4 geraniums.
Mike spent $56 on 10 rose bushes and 3 geraniums. Find the cost of one rose bush and the cost of one geranium.
Answer:
Cost of 1 rose bush = x = $5
Cost of 1 geraniums = y = $2
Step-by-step explanation:
DeShawn and Mike each improved their yards by planting rose bushes and geraniums. They bought their supplies from the same store.
Let us represent:
Cost of 1 rose bush = x
Cost of 1 geraniums = y
DeShawn spent $13 on 1 rose bush and 4 geraniums.
x + 4y = 13..... Equation 1
x = 13 - 4y
Mike spent $56 on 10 rose bushes and 3 geraniums.
10x + 3y = 56....... Equation 2
We substitute 13 - 4y for x in Equation 2
10(13 - 4y) + 3y = 56
130 - 40y + 3y = 56
Collect like terms
- 40y + 3y = 56 - 130
-37y = -74
y = -74/37
y = $2
Solving for x
x = 13 - 4y
x = _13 - 4 × $2
x = $13 - $8
x = $5
Therefore,
Cost of 1 rose bush = x = $5
Cost of 1 geraniums = y = $2
What does it mean when 6 people share 12 muffins
Answer:
Step-by-step explanation:
Everybody gets 2 a piece
The point where the graphs of x + 4 = y and 2x + 2 = y intersect has the
coordinates
(6,2)
(2,6)
(1,5)
O
(5, 1)
Metal A has a density of 2.4g/cm3 and metal B has a density of 1.8 g/cm3.Their masses are combined in the ratio 2 : 3 to make metal C which has a mass of 60 grams.Find the density of the metal C
Answer: 2 g/cm^3
Step-by-step explanation:
Remember the relation:
density = mass/volume.
Now, we know that:
Density of metal A = 2.4 g/cm^3
Density of metal B = 1.8 g/cm^3
We know that their masses are combined in the ratio 2:3
Then out of the total mass of metal C, 2 parts are from metal A and 3 parts are from metal B.
Mass of metal C = 60g
mass of metal A = (2/5)*60g =24g
mass of metal B = (3/5)*60g = 36g
Now that we know the mass of each metal, we can find their volumes by:
volume = mass/density
Volume of metal A = (24g)/(2.4g/cm^3) = 10cm^3
Volume of metal B = (36g)/(1.8g/cm^3) = 20cm^3
The total volume of metal C will be equal to the sum of the volumes of metal A and B, then:
Volume of metal C = 10cm^3 + 20cm^3 = 30cm^3
Then we know the volume and weight of metal C, then the density of metal C is:
Density of metal C = (60g)/(30cm^3)= 2 g/cm^3
simplify the equation below to determine whether there is one unique solution, no solution, infinitely many solutions. 3(6x + 8) = 24 + 18x
Result
0 = 0
infinitely many solutions.
3x+18x+5x-2=180
what is the angle measurement for:
3x,18x,and 5x,-2?
Answer:
3x = -18 (x = -6)
18x = 108 (x = 11)
5x = 90 (x = 18)
Step-by-step explanation:
find the circumference of a circle of radius 2.1m
13.2
Step-by-step explanation:
r = 2.1
circumference of circle = 2πr
=2 × 22/7 × 2.1
= 13.2
Find the length of side BC. Give your answer to 1 decimal place. It's a right angle triangle with a hypotenuse of 14cm and an angle of 58 degrees.
Answer:
11.9
Step-by-step explanation:
A pile of sand has a weight of 60 kg
The sand is put into a small bag, a medium bag and a large bag in the ratio 2:3:7
Work out the weight of the sand in each bag
Small bag = 2x
Medium bag = 3x
Large bag = 7x
2x + 3x + 7x = 60
12x = 60
x = 60/12
x = 5
Small bag = 2(5) = 10 kg
Medium bag = 3(5) = 15 kg
Large bag = 7(5) = 35 kg
Done.