Answer:
the answer to pt 1 is D. x=1.5 x=0 or x=6
and the answer to part 2 is C. x=1±I√29/5
Step-by-step explanation:
1. The solution of this equation is x = 0 or x = 6 which is option D.
2. The solution of this equation is [tex]x = \dfrac{1 \pm i\sqrt{29}}{5}[/tex] which is option C.
Use the concept of quadratic equation defined as:
The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations.
The quadratic equation has the following generic form:
ax² + bx + c = 0
1. The given quadratic equation is,
3x = 0.5x²
Rearranging it,
0.5x² - 3x = 0
Common out x,
x(0.5x - 3) = o
Then we have,
x = 0 or,
0.5x - 3 = 0
Add 3 on both sides,
0.5x = 3
Divide both sides by 0.5,
x = 3/0.5
x = 6
Hence the solution of this quadratic equation is,
x = 0 and x = 6 which is option D.
2. The given quadratic equation is:
0 = 5x² - 2x + 6
It can be written as,
5x² - 2x + 6 = 0
Since we know the quadrature formula for ax² + bx + c = 0 is,
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
Here we have,
a = 5
b = -2
c = 6
Substitute values into the formula,
[tex]x = \dfrac{2 \pm \sqrt{4 - 120}}{10}\\\\x = \dfrac{1 \pm i\sqrt{29}}{5} \text{ }\text{ \text{ }} \text{\text{ }\ since } \sqrt{-1} = i[/tex]
Hence, option C is correct.
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The complete question is:
Solve each of the quadratic equations.
PT. 1
3x = 0.5x²
A. x = -6 or x = 0
B. x = -4 or x = 3
C. x = -2 or x = 1.5
D. x = 0 or x = 6
PT.2
0 = 5x² - 2x + 6
A. [tex]x = \dfrac{1 \pm 3i}{5}[/tex]
B. [tex]x = \dfrac{1 \pm i\sqrt{11}}{5}[/tex]
C. [tex]x = \dfrac{1 \pm i\sqrt{29}}{5}[/tex]
find the valu of x 8: 10 =x:50
Answer:
40
Step-by-step explanation:
50 / 10 = 5
8 * 5 = 40
Both should be divisible by same amount and that is 5.
Answer:
40
Step-by-step explanation:
Express in the form 1 : n , give n as a demical : 20 : 15
Answer:
1 : 0.75.
Step-by-step explanation:
15/20 = 0.75
So its 1 : 0.75
Answer:
1 : 0.75
Step-by-step explanation:
20÷20=1
15÷20=0.75
n=0.75
The possible outcomes for rolling a pair of fair dice are shown below.
What is the probability of rolling a sum that is a prime number?
Answer:
5/12
Step-by-step explanation:
"When two dice are thrown, the total number of sample spaces is 36.
Favourable outcomes = {(1,1),(1,2),(1,4),(1,6),(2,3),(2,3),(2,5),(3,2),(3,4),(4,1),(4,3),(5,2),(5,6),(6,1),(6,5)}
Total number of favourable outcomes = 15
Hence, the probability of getting a sum of prime numbers = 15/36 = 5/12."
This was taken from a Byjus post.
Hope this helps.
find sine or cosine using identity
Answer:
sin(theta) = [tex]\frac{\sqrt{7}}{4}[/tex]
Step-by-step explanation:
cos(theta) = [tex]\frac{x}{r}[/tex]
cos(theta) = [tex]\frac{3}{4}[/tex]
so x = 3 , r = 4 , and y =?
Pythagorean Theorem: x^2 +y^2 = r^2 or a^2 +b^2 = c^2
x^2 +y^2 = r^2
(3)^2 +y^2 = (4)^2
9 + y^2 = 16
y^2 = 7
[tex]y=\sqrt{7},-\sqrt{7}[/tex]
In Quadrant 1, so its only [tex]y=\sqrt{7}[/tex].
sin(theta) = [tex]\frac{y}{r}[/tex]
sin(theta) = [tex]\frac{\sqrt{7}}{4}[/tex]
compute the probability of tossing a six-sided die and getting a number less than 3
Answer:
We can think of our denominator as 6 in our probability, because there are 6 total sides to this die.
Out of those 6 sides, they want to find out if we can roll a number less than 3.
First, let's find how many numbers there are on this die that are less than 3.
1 and 2, so there are 2 sides that contain numbers less than 3 on this die.
So there is a 2 out of 6 chance(2/6) which can be simplified to 1/3, of selecting a number less than 3 when rolling a die.
1/3 probability.
Convert this into a percent if you'd want:-
1/3 · 100
= 33.333... which can be rounded to a 33% probability.
For which values of x is the expression undefined x-8/x-5
Answer:
x = 5
Step-by-step explanation:
Any number over 0 is undefined. Given that, the values of x that make this expression undefined make the denominator equal to 0
x - 5 = 0
x = 5
I hope this helps!
Find the surface area of the Cylinder, will mark BRAINLIEST if correct
Answer:
About 1885 sq. ft
Step-by-step explanation:
[tex]v = \pi \: (10)^{2} (6) [/tex]
Since the radius is 10ft and the height of the cylinder is 6 ft you substitute that into the formula and you receive 1884.96.
Represent the sum of the complex numbers 2−3i and −1−i on the complex plane.
Use the Point and Segment tools to plot all required points and segments.
Answer: I took the test and this is the answer.
HELP. WORTH 1 POINT
GIVING 10
Answer:
117
Step-by-step explanation:
well, if they are supplementary, and they are on the same line and a line is equal to 180 degrees, then its as easy as 180-63=117
f(X)= 4X+8 g(X)= X+3, find f(X) • g(X)
Answer:
[tex]4x + 20[/tex]
Step-by-step explanation:
[tex]4(x + 3) + 8 = 4x + 12 + 8 = 4x + 20[/tex]
Using scales of 1cm to 30° on the x axis and 2cm to 1 unit on the y axis,draw the graph of y=sin 0 for 0°less than or equal to 0 less than or equal to 360°.Using the graph to a)find the equation b) solve the equation i)sin0=0.6 ii)4sin0=-3
Help me and will mark brainlest
Answer:
Attachment 1: graph of [tex]y=\sin(\theta)[/tex]
(using given scale)
Question (a) (Attachment 2)
[tex]\sin(\theta)=0.6[/tex]
Draw the line [tex]y=0.6[/tex] (shown in blue).
Find the points of intersection of the sine curve and the line.
Measure to find the values of [tex]\theta[/tex]
[tex]\theta=37^{\circ},143^{\circ}\:\textsf{(nearest degree)}[/tex]
Question (b) (Attachment 3)
[tex]4\sin(\theta)=-3[/tex]
[tex]\implies \sin(\theta)=-\dfrac34[/tex]
Draw the line [tex]y=-\dfrac34[/tex] (shown in red).
Find the points of intersection of the sine curve and the line.
Measure to find the values of [tex]\theta[/tex]
[tex]\theta=229^{\circ},311^{\circ}\:\textsf{(nearest degree)}[/tex]
Consider the sum 7+(-11)+4
Answer:
0
Step-by-step explanation:
7-11=-4
-4+4=0
True or false?
The greater a fractional part of a circle an angle takes up, the smaller it’s measurement will be.
This is the Answer :
true
HELPP ASAPP
FIRST PERSON GET BRAINIEST
Answer:
2,6 / Number 3
Step-by-step explanation:
Thats the right answer
Answer:
(2,6)
Step-by-step explanation:
moving 3units to the left gives (2,4) and 2units above gives (2,6) finally
which part of the cell makes proteins?
a) chromosomes
b) ribosomes
c) lysosomes
d) mitochondrion
the ratio of the number of boys and girls in a class is 10:7 if there are 35 girls find the number of boys
Answer:
The solution to the question is in the attached image
Answer this and i mark u branliest
Step-by-step explanation:
5a.
10 white squares
15 shaded squares
5b.
a1 = 1 = 2×1 - 1
a2 = a1 + 2×2 - 1 = 2×1 - 1 + 2×2 - 1 = 2×(1+2) - 2
a3 = a2 + 2×3 - 1 = 2×(1+2+3) - 3
...
an = 2×(1+2+...+n) - n = 2×n×(n+1)/2 - n = n²
so,
a350 = 350² = 122,500
figure350 has 122,500 squares.
5c.
a1 = 1
a2 = a1 = 1
a3 = a2 + 5
a4 = a3 = 6
a5 = a4 + 9
a6 = a5 = 15
a7 = a6 + 13
a8 = a7 = 28
...
a(2n) = a(2n - 1)
a(2n - 1) = a(2(n-1) - 1) + 1 + 4(n - 1) = n×1 + 4(0+1+2+...+n-1) =
= n + 4×(n-1)×n/2 = n + 2×(n² - n) = 2n² - n
therefore,
a350 = a349
a349 = a(2×175 - 1) = 2×175² - 175 = 61,075
figure350 has 61,075 shaded squares.
A line passes through the point (-4,9) and has a slope of -3/2. Write an equation in slope intercept form for this line
Answer:
y = -3/2x + 3
Step-by-step explanation:
slope-intercept form: y - y₁ = m (x - x₁)
y - 9 = -3/2 ( x + 4)
y = -3/2 x - 6 + 9
y = -3/2x + 3
PLEASE RATE!! I hope this helps!!
If you have any questions comment below
Pat can drive 36 kilometers for every 3 liters of gas they put in their car.
Complete the table using equivalent ratios.
Kilometers
Liters
36
3
48
132
Answer:
Step-by-step explanation:
This is a proportion question which is 2 ratios which are equal to one another. If 3 of the 4 parts are known, the 4th part can be calculated.
36 liters.
36 km/3 Liters = x / 36 multiply both sides by 36
36*36 / 3 = x
1296/3 = x
x = 432 km
So on 36 L he can go 432 km
3 liters
Given as 36 km
48 liters
36km/3 liters = x / 48 liters Multiply both sides by 48
48*36/3 = x
576 km = x
So on 48 liters, he can go 576 km
132 liters
36 km/ 3 liters = x/132
x = 1564 km
On 132 liters Pat can go 1564 km
Convert the function from vertex form to standard form.
-1/2(x + 2)^2 - 3
Answer:
[tex] -\frac{1}{2}x^2-2x-5 [\tex]
Step-by-step explanation:
To convert it to standard form, all you need to do is expand the square and simplify. This would get us to: [tex]-\frac{1}{2}(x^2 + 4x + 4) - 3[/tex] which simplifies further to [tex]-\frac{1}{2}x^2-2x-2-3[/tex] and combine the -2 and -3 to get [tex] -\frac{1}{2}x^2-2x-5 [\tex]
Hope this helps :)
What is the next term of the geometric sequence
Answer:
64/7
Step-by-step explanation:
Pattern = Multiplying by -4
-16/7 x -4/1
64/7
PLEASE HELP PLEASE PLEASE HELP
Answer:
I believe it is Dissolve.
7x=7.7 How would i figure this out ?
In a 3-digit number, the hundreds digit is four more than the units digit, and the tens digit is three more then the sum of the other digits. Find the three digits if the sum of all three digits is 15. Then find the number.
Answer:
591
Step-by-step explanation:
Let's use algebra to solve this question:
Units digit = x
Hundreds digit = x+4
Tens digit = 3 + (x+4) + x = 2x +7
All 3 digits = 15
so x + (x+4) + 2x + 7 = 15
4x +11 =15
4x = 4
x = 1
Then you substitute:
Units = 1
Hundreds = 1+4 = 5
Tens = 2(1) + 7 = 2 + 7 = 9
The number is therefore 591.
Find the value of y.
AABC = ADEF
A
17y - 8
B
(11x - 4)
D
23
117
12 + 13y
'C
E
Answer: 5
Step-by-step explanation:
A bag contains seven red balls, five green balls, four yellow balls, and two black balls. A ball is picked at random
from the bag. What is the probability that the ball will NOT be black?
Answer:
50/50 chance a black ball will be picked
ents
Suppose a furniture builder has two models of a bookcase: standard and artisan. The standard
model requires 4 hours to assemble and 2 hours for finishing touches. The artisan model requires 2
hours to assemble and 2 hours for finishing touches. Based on their current staffing, they can
manage a maximum number of assembly hours available is 48 per day, and the maximum number
of finishing hours available is 44 per day.
Let x = the number of standard model bookcases produced per day and y = the number of artisan
model bookcases produced per day.
Write the system of inequalities that represents the maximum number of bookcases that can be
produced in one day.
Answer:
48 ≥ 4x + 2y
44 ≥ 2x + 2y
First, we will look at assembling hours.
"The standard model requires 4 hours to assemble [and] the artisan model requires 2 hours to assemble"
We also know they have 48 hours per day for assembly, x is standard model and y is artisan model.
48 = 4x + 2y
Lastly, they do not need to make that many, but they can so we will use greater than or equal to.
48 ≥ 4x + 2y
Now let us look at finishing hours.
"The standard model requires ... 2 hours for finishing touches. The artisan model requires ... 2 hours for finishing touches."
We also know they have 44 hours per day for assembly, x is standard model and y is artisan model.
44 = 2x + 2y
Again, they do not need to make that many, but they can so we will use greater than or equal to.
44 ≥ 2x + 2y
The following can be deposited in a savings account: (check all that apply)
1. Jewels
2. Cash
3. Paycheck
4. Coin
5. Checks
Answer: cash, paychecks, checks
Step-by-step explanation:
(: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (: (:
Suppose GDP is $12 trillion, taxes are $3.6 trillion, private saving is $1.5 trillion, and public saving is $0.8 trillion. Assuming the economy is closed, complete the following table by calculating consumption, government purchases, national saving, and investment. Component Amount (Trillions of dollars) Consumption Government Purchases National Saving Investment
Assuming this economy is closed: Consumption $6.9 trillion; Government Purchases $11.2 trillion; National Saving $2.3 trillion; Investment $2.3 trillion.
Gross domestic producta. Consumption
Private S = ( Y – T – C )
C = Y - T - Private S
C = $12 - $3.6 - $1.5 =$6.9 trillion
b. Government purchases
Public S = ( T - G )
G = T - Public S
G = $12 - $0.8
G = $11.2 trillion
c and d. National saving and investment
National savings = Public S + Private S
National savings = $0.8 + $1.5
National savings =$2.3 trillion
Investment=Savings=$2.3 trillion
Therefore, Consumption $6.9 trillion; Government Purchases $11.2 trillion; National Saving $2.3 trillion; Investment $2.3 trillion.
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Solve the system of equations.
5x−4y=−10
y=2x−5
Answer:
x = 10
y = 15
Step-by-step explanation:
5x − 4y = −10 ⇒ ( 1 )
y = 2x − 5 ⇒ ( 2 )
Let us find the value of x.
For that, we can replace y with ( 2x - 5 ).
Let us take equation 1.
5x − 4y = −10
5x - 4 ( 2x − 5 ) = -10
5x - 8x + 20 = -10
-3x = -20 - 10
-3x = - 30
Divide both sides by ( -3 ).
x = 10
And now let us find the value of y.
Let us take equation 2.
y = 2x − 5
y = 2 × 10 - 5
y = 20 - 5
y = 15
Answer:
X=10
Step-by-step explanation:
5x-4y=-10.....1
y=2x-5......2
sub 2 into 1
5x-4(2x-5)=-10
5x-8x+20=-10
5x-8x=-10-20
-3x=-30
x=10
sub x=10 into 2
y=2(10)-5
y=20-5
y=15
