Answer:
[tex]13[/tex]
Step-by-step explanation:
[tex]y=3 {x}^{2} +5x+1 [/tex]
The discriminant of a quadratic is the expression inside the radical of the quadratic formula.
[tex] {b}^{2} - 4(ac)[/tex]
Substitute in the values of a, b, and c.
[tex] {5}^{2} - 4(3 \times 1)[/tex]
Evaluate the result to find the discriminant.
Simplify each term.
Raise 5 to the power of 2.
[tex]25 - 4(3 \times 1)[/tex]
Multiply 3 by 1.
[tex]25 - 4 \times 3[/tex]
Multiply −4 by 3.
25−12
Subtract 12 from 25.
13
Hope it is helpful...Solve the quadratic equation by using a graphic approach. Round your answer to the hundredths place.
x² - 2x - 4= 0
a. x= 3.24 or x = -1.24
c. x = 4.24 or x = -0.24
b. x = 2.73 or x = -0.73
d. x= 5.24or x = -1.24
Pls explain I’m having a hard time understanding the lesson
Answer:
x = 3.24, x = -1.24
Step-by-step explanation:
The standard form for a quadratic equation is [tex]ax^2+bx+c=0[/tex]. For your equation a = 1, b = -2, c = -4. The quadratic formula you will be using is [tex]x=\frac{-b\pm \sqrt{b^{2} -4ac} }{2a}[/tex].
Plug in a = 1, b = -2, and c = -4 into the formula.
[tex]=\frac{-\left(-2\right)\pm \sqrt{\left(-2\right)^2-4\cdot \:1\cdot \left(-4\right)}}{2\cdot \:1}[/tex]
We'll do the top part first:
[tex]\sqrt{\left(-2\right)^2-4\cdot \:1\cdot \left(-4\right)}[/tex]
Apply rule [tex]- (-a) = a[/tex]
[tex]=\sqrt{\left(-2\right)^2+4\cdot \:1\cdot \:4}[/tex]
Apply exponent rule [tex](-a)^{n} =a^n[/tex] if [tex]n[/tex] is even
[tex](-2)^2=2^2[/tex]
[tex]=\sqrt{2^2+4\cdot \:1\cdot \:4}[/tex]
Multiply the numbers
[tex]=\sqrt{2^2+16}[/tex]
[tex]2^2=4[/tex]
[tex]=\sqrt{4+16}[/tex]
Add
[tex]=\sqrt{20}[/tex]
The prime factorization of 20 is [tex]2^2*5[/tex]
20 divides by 2. 20 = 10 * 2
[tex]=2*10[/tex]
10 divides by 2. 10 = 5 * 2
[tex]=2* \:2*5[/tex]
2 & 5 are prime numbers so you don't need to factor them anymore
[tex]=2*2*5[/tex]
[tex]=2^2*5[/tex]
[tex]=\sqrt{2^2\cdot \:5}[/tex]
Apply radical rule [tex]\sqrt[n]{ab} =\sqrt[n]{a} \sqrt[n]{b}[/tex]
[tex]=\sqrt{5}\sqrt{2^2}[/tex]
Apply radical rule [tex]\sqrt[n]{a^{n} } =a[/tex]; [tex]\sqrt{2^2} =2[/tex]
[tex]=2\sqrt{5}[/tex]
[tex]=\frac{-\left(-2\right)\pm \:2\sqrt{5}}{2\cdot \:1}[/tex]
Because of the [tex]\pm[/tex] you have to separate the solutions so that one is positive and the other is negative.
[tex]x=\frac{-\left(-2\right)+2\sqrt{5}}{2\cdot \:1},\:x=\frac{-\left(-2\right)-2\sqrt{5}}{2\cdot \:1}[/tex]
Positive x:
[tex]\frac{-\left(-2\right)+2\sqrt{5}}{2\cdot \:1}[/tex]
Apply rule [tex]-(-a)=a[/tex]
[tex]=\frac{2+2\sqrt{5}}{2\cdot \:1}[/tex]
Multiply
[tex]=\frac{2+2\sqrt{5}}{2}[/tex]
Factor [tex]2+2\sqrt{5}[/tex] and rewrite it as [tex]=2\cdot \:1+2\sqrt{5}[/tex]. Factor out 2 because it is the common term. [tex]=2\left(1+\sqrt{5}\right)[/tex].
[tex]=\frac{2\left(1+\sqrt{5}\right)}{2}[/tex]
Divide 2 by 2
[tex]x=1+\sqrt{5}[/tex] or [tex]x=3.24[/tex] (You'll probably have to use a calculator for the square root of 5)
^Repeating the process of positive x for negative x in order to get [tex]x=1-\sqrt{5}[/tex] or [tex]x=-1.24[/tex]
pls help pls help pls help pls help
Answer:
The difference is 3 for 4-7, and 39 for 52-91. So basically its a change of 3 for every 4-7 I think this is what you ask for. Let me explain and show results and then pick what you need.
Step-by-step explanation:
So, we know 4 to 7 is 3.
52 to 91 is 39.
So one is a change in 3. the other is a change is 39.
However, could these be the same, just bigger?
Lets divide the 52 to 91 with a change of 39 by 4 to 7 with a change of 3:
52/4 to 91/7 with a change of 39/3 =
13 to 13 with a change of 13.
So this tells us that the 52 to 91 with a chang eof 3 is 13 times bigger than 4 to 7 with a change of 3.
Hope this helps!
Una caja en forma de prisma rectangular tiene 10cm3 de volumen.Si la longitud de cada arista se multiplica por 4, ¿cual sera el volumen de la caja?
Help please !!!!!!!!’
Step-by-step explanation:
everything can be found in the picture
The surface of an air hockey table has a perimeter of 32 feet its area is 60 ft.what are the dimensions of the air hockey table
Biology application. The approximate number of calories C that an animal needs each day is given by
c = 72m 2/4, where m is the animal mass in kilograms.
Find the number of Calories that a 16 kg bear needs each day. To solve this, evaluate the equation when
m = 16.
Please help I will give Brainliest.
Answer:
C = 288 kg
Step-by-step explanation:
Given:
C = 72m^2/4
where,
C = approximate number of calories
m = animal mass in kilograms.
Find C when m = 16
C = 72m^2/4
= 72 * (16)^2/4
= 72 * (16)^1/2
= 72 * √16
= 72 * 4
= 288
C = 288 kg
8 + (9 · 2 – 3) : 25 – 4 2 : 2
Answer:
14 : -17 : 2
Step-by-step explanation:
8 + (9 · 2 – 3) : 25 – 4 2 : 2
= 14 : -17 : 2
Answer:
- 12.4
Step-by-step explanation:
[tex]8 + \frac{9 * 2 - 3}{25} - \frac{42}{2}[/tex]
[tex]8 + \frac{18 - 3}{25} - 21[/tex]
[tex]8 + \frac{15}{25} - 21[/tex]
[tex]8 + \frac{3}{5} - 21[/tex]
[tex]8 \frac{3}{5} - 21[/tex]
[tex]-12 \frac{2}{5}[/tex]
Plse help my grades go in tomorrow and I am currently struggling!!
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a 20 foot ladder leans against a building. if the ladder is 8 feet from the building, find to the nearest degree, the measure of the angle that the foot of the ladder makes with the ground
Answer:
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj/ hyp
cos theta = 8/20
cos theta = 2/5
Taking the inverse cos of each side
cos^-1 (cos theta) = cos ^-1 ( 2/5)
theta =66.42182152
To the nearest degree
theta = 66 degrees
If two lines are intersected by a third line, is the third line necessarily a transversal?
No, The third line does not necessarily be a transversal.
What is Equation of line?
The equation of line with slope 'm' and y intercept at point 'b' is given as;
⇒ y = mx + b
Given that;
Two lines intersected by a third line.
Since, When two lines are parallel to each other and two lines intersected by a third line then, third lines are transversal.
So, Here it is not given two lines are parallel.
Thus, Third line is not necessarily a transversal.
Hence, The third line does not necessarily be a transversal.
Learn more about the transversal visit:
https://brainly.com/question/2141319
#SPJ2
Which statement about the equation below is true? x2 − 8x + 15 = 0
A. One root is less than zero, and the other root is greater than zero.
B. One root is zero, and the other root is greater than zero.
C. The sum of the roots is 15.
D. Both roots are greater than zero.
Answer: both roots are greater than zero
Step-by-step explanation:
If this is factored, you can find the roots.
(x-3)(x-5)=0
Set each factor equal to zero and solve.
x-3=0
x=3
factor the following
(a²+b²)²-18(a²+b²)-88
Answer:
[tex] \rm\displaystyle( {a}^{2} + {b}^{2} - 22)( {a}^{2} + {b}^{2} + 4)[/tex]
Step-by-step explanation:
we would like to factor the following:
[tex] \rm\displaystyle ( {a}^{2} + {b}^{2} {)}^{2} - 18( {a}^{2} + {b}^{2} ) - 88[/tex]
let a²+b²=x
thus substitute:
[tex] \rm\displaystyle x {}^{2} - 18x- 88[/tex]
rewrite the middle term as 4x-22x:
[tex] \rm\displaystyle x^{2} + 4x - 22x - 88[/tex]
factor out x:
[tex] \rm\displaystyle x( x^{} + 4)- 22x - 88[/tex]
factor out -22:
[tex] \rm\displaystyle x( x^{} + 4)- 22(x + 4)[/tex]
group:
[tex] \rm\displaystyle( x- 22)(x + 4)[/tex]
substitute back:
[tex] \rm\displaystyle( {a}^{2} + {b}^{2} - 22)( {a}^{2} + {b}^{2} + 4)[/tex]
and we are done!
58 = ??
36 = 84
64 = 56
78 = 24
Answer:
35
Step-by-step explanation:
67nahhavidjsvvaa jahaha
The width of a rectangle is 5 3/4 inches. The length is three times its width. What is the perimeter?
Answer:
perimeter=46.5 inches
Step-by-step explanation:
[tex]width=2\frac{3}{4}[/tex]
[tex]=\frac{5*4+3}{4}[/tex]
=[tex]=\frac{23}{4}[/tex]
[tex]length=3(\frac{23}{4} )[/tex]
[tex]=\frac{23*3}{4}[/tex]
=[tex]\frac{69}{4}[/tex]
perimeter of rectangle =2(l+b)
[tex]=2(\frac{69}{4} +\frac{24}{4} )[/tex]
[tex]=2(\frac{69+24}{4} )[/tex] (since their denominator are same u can add their numerator)
[tex]=2(\frac{93}{4})[/tex]
[tex]=\frac{93*2}{4}[/tex]
[tex]=\frac{186}{4}[/tex]
[tex]=46.5[/tex] inches
Jenny is flying a kite. She has 100 yards of string which is all out as the kite flies. The place she is standing is 80 yards from a point that is directly below the kite, how high is the kite?
Answer:
60 yd
Step-by-step explanation:
If y=-0.8 when x=2 find the y when x=3
Find the Value of X in this Triangle
Answer:
x = -6
Step-by-step explanation:
All three angles are equal, so all three sides are equal, making this an equilateral triangle
5x+10 = 2x-8
Subtract 2x from each side
5x-2x +10 = 2x-8-2x
3x+10 = -8
Subtract 10 from each side
3x+10-10 = -8-10
3x = -18
Divide by 3
3x/3 = -18/-3
x = -6
Find the number from which (– 66) is subtracted to get a difference of 100.
Answer:
-166
Step-by-step explanation:
Find the value of y no links please
2√2 i.e OPTION A is the correct answer
The manufacturer id number for proctor and gamble is (037000) and the item number for a box of bounce fabric softener is (80049). What is the valid upc? A- 0-37000-80049-9 B-0-37000-80049-1 C-1-37000-80049-1 D-1-80049-37000-0
Answer:
A. [tex]UPC = 0-03700-80049-9[/tex]
Step-by-step explanation:
Given
[tex]ID = 037000[/tex]
[tex]Item\ Number = 80049[/tex]
Required
The valid UPC
First, the UPC is represented as:
UPC = ID followed by item number followed by the checksum
So, we have:
[tex]upc = 0-03700-80049-X[/tex]
To calculate X (the checksum)
Add up digits at odd positions
[tex]Odd = (0 + 7 + 0) + (8 + 0 + 9)[/tex]
[tex]Odd = 24\\[/tex]
Multiply by 3
[tex]Product = Odd * 3[/tex]
[tex]Product = 24 * 3[/tex]
[tex]Product = 72[/tex]
Add up digits at even positions
[tex]Even = (3 + 0 + 0) + (0 + 4)[/tex]
[tex]Even = 7[/tex]
Add the product and the sum of even
[tex]Result = Product + Even[/tex]
[tex]Result = 72+7[/tex]
[tex]Result = 79\\[/tex]
The last digit of the UPC is 9.
Hence, the UPC is:
[tex]UPC = 0-03700-80049-9[/tex]
36A^4+16Y^2
Can someone help me
Answer:
4(9a^4+4y^2)
Step-by-step explanation:
factor out common term
Write an equation to model the given scenario, then solve:
Each year the local country club sponsors a tennis tournament. Play starts with 128 participants. During each
round, half of the players are eliminated. How many players remain after 5 rounds?
Given:
Initial number of participants = 128
During each round, half of the players are eliminated.
To find:
The number of players remain after 5 rounds.
Solution:
It is given that, the initial number of participants is 128 and during each round, half of the players are eliminated.
If half of the players are eliminated, then half of the players are remained.
So, the initial value is 128 and the decay factor is [tex]\dfrac{1}{2}[/tex].
The general exponential decay model is:
[tex]y=a(b)^x[/tex]
Where, a is the initial value and b is the decay factor.
Putting [tex]a=128[/tex] and [tex]b=\dfrac{1}{2}[/tex] in the above model, we get
[tex]y=128\left(\dfrac{1}{2}\right)^x[/tex]
Here, y is the number of remaining players after x rounds.
Substituting [tex]x=5[/tex], we get
[tex]y=128\left(\dfrac{1}{2}\right)^5[/tex]
[tex]y=128\left(\dfrac{1}{32}\right)[/tex]
[tex]y=4[/tex]
Therefore, the required model is [tex]y=128\left(\dfrac{1}{2}\right)^x[/tex] and the number of players remain after 5 rounds is 4.
Solve for x. ЗХ - 14 = 46
Answer:
Step-by-step explanation:
3x - 14 = 46
+ 14 +14
3x = 60
3x/3 = 60/3
x = 20
please help me!!!!! i need help with this, very urgent! ASAP
Step-by-step explanation:
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RQ-----DE
The equation y = 2.1x represents the relationship between x, the number of tickets, and y, the price Which ordered pairs represent a number of tickets and the corresponding price in the given equation? Choose ALL that apply (3,6.3) (6.3,3) (2.1, 10.5) (7, 14.7) (10.5, 2.1) (14.7, 7)
Answer:
(3,6.3), (7, 14.7)
Step-by-step explanation:
For this question, you want to find the values where 2.1×x is the same as y. It's mostly just trial and error.
x is always first in the bracket, so by multiplying it by 2.1, you would get y (the second value) if it applies.
3*2.1=6.3, so the first one is true.
6.3*2.1=13.23, so the second one is false.
2.1*2.1=4.41, so the third one is false.
7*2.1=14.7, so the fourth one is true.
10.5*2.1=22.05, so the fifth one is false.
14.7*2.1=30.87, so the sixth one is false.
This leaves the first one (3,6.3) and the fourth one (7, 14.7) as true.
** This is mostly algebra, so you may want to look at that. If this question was supposed to be done without a calculator, look at multiplying decimals too. I'm always happy to help!
Answer:
They are (3, 6.3) and (7, 14.7)
Brainliest, 19 points (Running out of points to give)
Answer:
x^2-2x+5
Step-by-step explanation:
5x^2 -4x +8 + -4x^2 +2x -3
Combine like terms
5x^2-4x^2-4x+2x+8-3
x^2-2x+5
The private school enrolled 1050 new students last year and the number of students enrolled this year decreased to 798.What was the percentage decrease in the number of students enrolled?
Answer:
Step-by-step explanation:
Decreased students = 1050 - 798 = 252
Decreased percentage = (decreased students ÷ number of last year students) * 100
= [tex]\frac{252}{1050}*100[/tex]
= 24%
Answer:
24%
Step-by-step explanation:
% change = [tex]\frac{difference}{original amount}[/tex] x 100
; 1050 - 798 = 252
% change = [tex]\frac{252}{1050}[/tex] x 100
% change = 0.24 x 100
% change = 24
the percentage decrease in the number of students enrolled is 24%
Alex’s paycheck for the last two weeks totaled $239.64. He owes the cell phone company $44.87. How much money does he have left
Answer:
the answer would be 193.77
Step-by-step explanation:
literally, subtract 45.87 from 239.64.
you get 193.77.
(you put 44 instead of 45, so the sum with 44 would be 194, that is incorrect.)
(Correct answers only)
A
B
C
Or D
Answer:
Division property of equality
Step-by-step explanation:
7q=49
Divide each side by 7
7q/7 = 49/7
q = 7
please help me answer this question
9514 1404 393
Answer:
the correct answer is marked
Step-by-step explanation:
The graph ranges vertically between 9 and 15, starting at 9 (the minimum) when x=0. The minimum appears again at x=350.
This means the vertical offset is (9+15)/2 = 12, and the amplitude is (15 -9)/2 = 3. The period is 350, so the coefficient of x is (2π/350). All of the answer choices agree on these parameters.
So, the selection comes down to an understanding of how the sine and cosine curves vary. The sine curve starts at zero and increases from there. The cosine curve starts at its maximum (1) and decreases. Here, the curve starts a its minimum and increases, so could be the opposite of the cosine function.
y = -3cos(2πx/350) +12 . . . . . . matches choice C
