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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A textbook store sold a combined total of 228 biology and physics textbooks in a week. The number of blology textbooks sold was three times the number of
physics textbooks sold. How many textbooks of each type were sold?
Step-by-step explanation:
Let us assume p is the number of psychology books and b is the number of biology textbooks.
set up first equation:
we know that the total number of books sold was 393
p+b=393
set up second equation:
we know that there were 79 less biology book sold that psychology so...
p = b + 79
subsitute p in the first equation to solve for b
solve value for p
Jamal has 30 ounces of a 20% saline solution. This means 20% of the solution is salt. He combines this solution with 25 ounces of a
30% saline solution
What is the total amount, in ounces, of salt in the combined moxture?
Answer:
13.5 ounces
Step-by-step explanation:
How Many?pls help me.
Answer:
8
Step-by-step explanation:
What is 3x-2=4 in 5.5 Practice A Algebra 1
Answer:
x=2
Step-by-step explanation:
What is -3(4q-7) Bc I’m confused
Answer:
-3(4q-7)=
4q+3-7
4q-4
Write an Equation given the point (1, -1) and a rate of 2.
Answer:
y+1=2(x-1)
Step-by-step explanation:
use point slope form
Bernard built 15 model cars one year. He did not build as many model cars as his sister, Abby. In the inequality, n represents the number of model cars Bernard needed to build to have more than Abby.
Which number of model cars did Bernard need to build to have more model cars than Abby?
A.1
B.2
C.3
D.4
Answer:
The answer is 1
Step-by-step explanation:
please do this for me
Answer:
DE
Step-by-step explanation:
How to evaluate 11/2
Answer-
in decimal from: 5.5
in mixed number form: 5 1/2
2) Dorothy types 120 words per minute. How many words does Dorothy type in
1.75 minutes? *
150 words
180 words
200 words
210 words
Answer:
D (210)
Step-by-step explanation:
120 times 1.75 equals 210
Answer:
210 words
Step-by-step explanation:
120 x 1.75 = 210
What is 35% of $2587
Answer:
905.45
Step-by-step explanation:
el treinta y cinco por ciento 35% de 2587 es: 905.45
please help me with this :D
[tex] \color{plum}\bold{(C)} [/tex] Diameter of circle P is the same length as the radius of circle Q.
○=> Steps to derive correct option :Given :
Diameter of circle P = 26 cm
Radius of circle P :
[tex] =\tt \frac{diameter}{2} [/tex]
[tex] = \tt \frac{26}{2} [/tex]
[tex]\color{plum} = \tt13 \: cm[/tex]
Thus, radius of circle P = 13 cm
Diameter of circle Q = 52 cm
Radius of circle Q :
[tex] = \tt \frac{diameter}{2} [/tex]
[tex] =\tt \frac{52}{2} [/tex]
[tex] \color{plum}= \tt26 \: cm[/tex]
Thus, radius of circle Q = 26 cm
Radius of circle R = 52 cm
Diameter of circle R :
[tex] =\tt radius \times 2[/tex]
[tex] =\tt 52 \times 2[/tex]
[tex]\color{plum} = \tt104 \: cm[/tex]
Thus, the diameter of circle R = 104 cm
☆ Conclusion :
▪︎Diameter of circle P is the same length as the radius of circle Q.
Therefore, the correct option is (C) Diameter of circle P is the same length as the radius of circle Q.
que número sumado da 7 y multiplicado da -
18
Answer:
hukiiiiibcgczxjwisisisigyjgffguhhhijhf
Step-by-step explanation:
xcfgghsjwueueueuririgg&jjikhffxghjh
The two men measure the angle of elevation to the highest point on the rock to be 22.6°. They
then walk 17 meters closer and measured the angle of elevation to be 38.3°. To the nearest meter,
how tall is Wave Rock?
You may not use Law or Sines to solve the problem.
Answer:
15 mStep-by-step explanation:
Refer to attached picture
The height = hAngles of elevation 22.6° and 38.3°Closer distance = dUse tangent to solve
tan 22.6° = h/(d + 17) ⇒ h = (d + 17) tan 22.6° ⇒ h = 0.42(d + 17)tan 38.3° = h/d ⇒ h = d tan 38.3° ⇒ h = 0.79dCompare the equations above and find the value of d:
0.42(d + 17) = 0.79d0.42d + 7.14 = 0.79d0.79d - 0.42d = 7.140.37 d = 7.14d = 7.14/0.37d = 19.3 mNow find the value of h:
h = 0.79dh = 0.79*19.3h = 15Wave Rock is 15 m tall
A necklace is on sale for 40% off. the original price of the necklace is 168.50 what is the sale price on the necklace
Answer:
$67.4
Step-by-step explanation:
Answer:
$101.1
Step-by-step explanation:
Some please help, Does anyone know this answer!
Answer:
Acute
Step-by-step explanation:
A bakery sells mocha cupcakes and vanilla cupcakes. It sold 391 mocha cupcakes in a day. 15% of the cupcakes sold that day were vanilla. How many total cupcakes did the bakery sell that day?
Given :
A bakery sells mocha cupcakes and vanilla cupcakes.
It sold 391 mocha cupcakes in a day.
15% of the cupcakes sold that day were vanilla.
To Find :
How many total cupcakes did the bakery sell that day.
Solution :
Let, total number of cupcakes bakery sell that day is x.
So, x - 0.15x = 391
0.85x = 391
x = 460
Therefore, total number of cupcakes bakery sell that day is 460 .
what type of function is y=3x-2
Step-by-step explanation:
Explanation: y=3x+2 is not a function. Rather, it is just a regular linear equation.
It's not.
Explanation:
y=3x+2
is not a function. Rather, it is just a regular linear equation. However,
f(x)=3x+2
is a function, because it contains "
f(x)."
So, in general, if it contains " y ," then you are safe in assuming that it is an equation. If it contains "
f(x) ," then you are safe in assuming that it is a function.
I hope that helps!
The function y = 3x - 2 is a linear function.
Given data:
The function is represented as y = f ( x )
The value of y = 3x - 2
The equation y = 3x - 2 represents a linear function.
The function has a constant rate of change, which is 3, as the coefficient of x. The function forms a straight line when graphed on a Cartesian coordinate plane.
The term "linear" indicates that the relationship between x and y is of the first degree, meaning there are no exponents or other nonlinear components involved.
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HELPPPP ME PLZZZ
Micah wants to know the most common style of surfboard used at Breakers Point. He surveys surfers at Breakers Point between 8:00 A.M. and 12 P.M. Which of the following statements is true about Micah’s survey? Select all that apply
A. Micah will obtain a random sample by talking to as many surfers as possible.
B. The population for the survey is all people who surf at Breakers Point.
C Micah will not get a representative sample.
D.Micah's sample will be representative because anyone can surf at Breakers Point.
Answer:
B. The population for the survey is all people who surf at Breakers Point.
D.Micah's sample will be representative because anyone can surf at Breakers Point.
Step-by-step explanation:
hope it helps
The statements that are true are:
The population for the survey is all people who surf at Breakers Point.
Micah will not get a representative sample.
Options B and C are the correct answer.
What is random sampling?It is the way of choosing a number of required items from a population given.
Each item has an equal probability of being chosen.
We have,
A.
Micah will obtain a random sample by talking to as many surfers as possible.
This statement is not necessarily true as Micah may not be able to talk to all the surfers at Breakers Point during the time frame mentioned. Additionally,
Randomly selecting surfers would result in a better representation of the population.
B.
The population for the survey is all people who surf at Breakers Point.
This statement is true, as the population of interest is the surfers at Breakers Point.
C.
Micah will not get a representative sample.
This statement is also true, as the survey is conducted only between 8:00 A.M. and 12 P.M, which may not be representative of all surfers at Breakers Point.
Additionally, there may be bias in the sample if Micah only surveys surfers at a certain location or time period.
D.
Micah's sample will be representative because anyone can surf at Breakers Point.
This statement is not necessarily true as not all surfers may surf at the same time or location, or have the same level of experience or preference for surfboard style.
Thus,
The population for the survey is all people who surf at Breakers Point and
Micah will not get representative sample statements are true.
Learn more about random sampling here:
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can someone help me with this real quick?
Answer:
11. A) 6x = 13
Step-by-step explanation:
11. Subtract 10 from both sides to make it equal 6x=13
12. For #12... None of the answers seem right? If you distribute and subtract, it should be
-4x + 44 = 66 then
-4x = 22...
Sorry if this didn’t help much, I know that 11 is right though ;)
To harmandeep or someone else please help me
Answer: 3x+6=9
3x=3
x=1
Step-by-step explanation:
Answer:
x = 1
Step-by-step explanation:
To solve this, we must first isolate the variable 'x':
3x + 6 = 9
-6 -6
3x = 9 - 6
Combine like terms
3x = 3
Isolate 'x' fully
3x = 3
/3 /3
x = 1
Hope this helps :)
Amy ran 0.75 kilometers each day for 3 weeks. How many meters did she run over the 3 weeks?
Answer:
15,750 meters
Step-by-step explanation:
There are 1000 meters in a kilometer
.75 of a kilometer is 750 meters
There are 7 days in a week, 7x3 is 21.
750 x 21 = 15,750
Answer:
15750meters
Step-by-step explanation:
3 weeks=3x7
=21days
1day=0.75km
21days=21x 0.75
=15.75km
1km=1000m
15.75km=(1575/100 x 1000)m
=15750meters
Find a quadratic polynomial with integer coefficients which has x = 2/9, ± SQRT23/9 as its real zeros.
Answer:
The quadratic polynomial with integer coefficients is [tex]y = 81\cdot x^{2}-36\cdot x -19[/tex].
Step-by-step explanation:
Statement is incorrectly written. Correct form is described below:
Find a quadratic polynomial with integer coefficients which has the following real zeros: [tex]x = \frac{2}{9}\pm \frac{\sqrt{23}}{9}[/tex].
Let be [tex]r_{1} = \frac{2}{9}+\frac{\sqrt{23}}{9}[/tex] and [tex]r_{2} = \frac{2}{9}-\frac{\sqrt{23}}{9}[/tex] roots of the quadratic function. By Algebra we know that:
[tex]y = (x-r_{1})\cdot (x-r_{2}) = x^{2}-(r_{1}+r_{2})\cdot x +r_{1}\cdot r_{2}[/tex] (1)
Then, the quadratic polynomial is:
[tex]y = x^{2}-\frac{4}{9}\cdot x -\frac{19}{81}[/tex]
[tex]y = 81\cdot x^{2}-36\cdot x -19[/tex]
The quadratic polynomial with integer coefficients is [tex]y = 81\cdot x^{2}-36\cdot x -19[/tex].
HELP ILL MARK YOU BRAINLIST
Answer:
m∠GFT = 142°
Step-by-step explanation:
∠GFT and ∠DFT are supplementary.
m∠GFT + m∠DFT = 180
7f + 163 + 6f + 56 = 180
13f + 219 = 180
13f = -39
f = -3
m∠GFT = 7f + 163 = 7(-3) + 163 = -21 + 163 = 142
3 less than four-sevenths of x is y
y = 4/7x - 3
hope this helps
Answer:4/7-3
Step-by-step explanation:
Yep
What is the mode of the data set (30,28,30,45,40,37,35)
28
30
45
37
Answer:
30
Step-by-step explanation:
mode is the number that occurs most of the time
since 30 appears twice in the data set
while the other numbers only appear once,
30 is the mode
▪︎Mode is the most frequently occurring element in a given data set.
The given data set :
[tex] =\tt 30,28,30,45,40,37,35[/tex]
Let us first arrange these numbers in ascending order :
[tex] =\tt 28,30,30,35,37,40,45[/tex]
As we can clearly observe, the number 30 occurs the most frequently.
Thus, the mode of this data set = 30
Therefore, the correct option is (b) 30
for what values of x is the expression below defined? x+4
Answer:
D
Step-by-step explanation:
Number 7!3/5 of the children in a class are girls
Answer:
Total students = 40
Step-by-step explanation:
No: of girls = 3/5
No: of boys = 2/5
No: of boys = 16
2/5 of x = 16
x = 16 x 5/ 2 = 40
Total students = 40
I hope im right!!!
I'm Chloe can you help me, Thanks :)
Which ordered pair is the solution to the system of linear equations?
5x + y= -4
x =-y -2
Answer:
Hola losiento no se ablar inglés
Simplify, must end in positive exponent
–10x^-8 (-2y^5)
Answer:
I got the answer 20y^5/x^8
Step-by-step explanation: