9514 1404 393
Answer:
x = -2/5 or -1
Step-by-step explanation:
The last two terms of the expression on the left can be factored also.
(5x+2)² +3(5x+2) = 0
And the common factor can be factored out:
(5x+2)(5x +2+3) = 0
5(5x +2)(x +1) = 0
Solutions to the equation make the factors zero:
5x +2 = 0 ⇒ x = -2/5
x +1 = 0 ⇒ x = -1
The values of x that are solutions to the equation are x = -2/5 and x = -1.
_____
Once you realize that (5x+2) is a factor, you know one solution is x = -2/5. The rest is just fluff to find the second solution. It is not required in order to answer the question.
Write seventy-one and one hundred sixty-four thousandths as a decimal number.
Answer:
0.0071164
Step-by-step explanation:
WHAT IS X³-27 SIMPLIFIED
Answer:
It is (x - 3)³ - 9x(3 - x)
Step-by-step explanation:
Express 27 in terms of cubes, 27 = 3³:
[tex] = {x}^{3} - {3}^{3} [/tex]
From trinomial expansion:
[tex] {(x - y)}^{3} = (x - y)(x - y)(x - y) \\ [/tex]
open first two brackets to get a quadratic equation:
[tex] {(x - y)}^{3} = ( {x}^{2} - 2xy + {y}^{2} )(x - y)[/tex]
expand further:
[tex] {(x - y)}^{3} = {x}^{3} - y {x}^{2} - 2y {x}^{2} + 2x {y}^{2} + x {y}^{2} - {y}^{3} \\ {(x - y)}^{3} = {x}^{3} - {y}^{3} + 3x {y}^{2} - 3y {x}^{2} \\ {(x - y)}^{3} = {x}^{3} - {y}^{3} + 3xy(y - x) \\ \\ { \boxed{( {x}^{3} - {y}^{3} ) = {(x - y)}^{3} - 3xy(y - x)}}[/tex]
take y to be 3, then substitute:
[tex]( {x}^{3} - 3^3) = {(x - 3)}^{3} - 9x(3 - x)[/tex]
What is the discriminat of 2x+5x^=1
Answer:
don't know...........
What is the sum of the geometric sequence 1, 3, 9, ... if there are 10 terms? (5 points)
Answer:
[tex]S_n = \frac{1 (1 - 3^{10})}{1 - 3} = 29524[/tex]
Step-by-step explanation:
There's a handy formula we can use to find the sum of a geometric sequence, and here it is
[tex]S_n = \frac{a_1 (1 - r^n)}{1 - r}[/tex]
The value n represents the amount of terms you want to sum in the sequence. The variable r is known as the common ratio, and a is just some constant. Let's find those values.
First lets visualize this sequence
[tex]n_1 = 1\\n_2 = 1 + 3\\n_3 = 1 + 3 + 3^2\\n_4=1+3+3^2+3^3\\...[/tex]
Okay so there's clearly a pattern here, let's write it a bit more concisely. For each n, starting at 1, we raise 3 to the (n-1) power, add it to what we had for the previous term.
[tex]S_n = \sum{3^{n-1}} = 3^{1 - 1} + 3^{2 - 1} + 3^{3-1} ...[/tex]
Our coefficients of r, and a, are already here! As you can see below, r is just 3, and a is just 1.
[tex]S_n = \sum{a*r^{n-1}}[/tex]
To finish up lets plug these coefficients in and get our sum after 10 terms.
[tex]S_n = \frac{1 (1 - 3^{10})}{1 - 3} = 29524[/tex]
Which of the following is a solution to 6x - 5y=4?
(2,7)
(-1, -2)
(-2, -1)
(2, -7)
Answer:
2,7
Step-by-step explanation:
Answer:
(-1,-2)
Step-by-step explanation:
(6 x -1) -(-2 x 5) = 4
-6 + 10 = 4
find the perimeter of 6 CM 6 CM 6 CM 6 CM
Answer:
P = 24
Step-by-step explanation:
Since all the sides are the same length, the shape is a square.
Multiply all sides by 6.
6 cm x 4 sides = 24
Solve this question:Зх <-24
Answer:
x< - 8
Step-by-step explanation:
3x <-24
x < - 24
3
x< - 8
x < - 8
Step-by-step explanation:
3x < - 24
Divide 3 on both sides,
3x / 3 < - 24 / 3
x < - 8
A product is introduced into the market. Suppose a product's sales quantity per month q ( t ) is a function of time t in months is given by q ( t ) = 1000 t − 150 t 2 And suppose the price in dollars of that product, p ( t ) , is also a function of time t in months and is given by p ( t ) = 150 − t 2 A. Find, R ' ( t ) , the rate of change of revenue as a function of time t
Answer:
[tex]r'(t) = 298t -850[/tex]
Step-by-step explanation:
Given
[tex]q(t) = 1000t - 150t^2[/tex]
[tex]p(t) = 150t - t^2[/tex]
Required
[tex]r'(t)[/tex]
First, we calculate the revenue
[tex]r(t) = p(t) - q(t)[/tex]
So, we have:
[tex]r(t) = 150t - t^2 - (1000t - 150t^2)[/tex]
Open bracket
[tex]r(t) = 150t - t^2 - 1000t + 150t^2[/tex]
Collect like terms
[tex]r(t) = 150t^2 - t^2 + 150t - 1000t[/tex]
[tex]r(t) = 149t^2 -850t[/tex]
Differentiate to get the revenue change with time
[tex]r'(t) = 2 * 149t -850[/tex]
[tex]r'(t) = 298t -850[/tex]
Find the measure of angle FGE
35 degrees
40 degrees
100 degrees
30 degrees
60 degrees
The measure of angle FGE is 52.5°.
What is the Angles of Intersecting Secants Theorem?Angles of Intersecting Secants Theorem states that, If two lines intersect outside a circle, then the measure of an angle formed by the two lines is one half the positive difference of the measures of the intercepted arcs.
Thus, applying the angles of intersecting secants theorem
m∠FGE = 1/2[(100 + 35) - 30]
m∠FGE = 1/2[(105]
m∠FGE = 52.5°
Learn more about angles of intersecting secants theorem here :
https://brainly.com/question/15532257
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A cricket bat is bought for $330. Later, it is sold with a loss of 15%.
How much is the oricket bat sold for?
After selling the cricket bat, how much money has been last?
Give your answer to two decimal places because it is a currency.
Answers:
Discount price = 280.50 dollarsAmount lost = 49.50 dollars================================================
Explanation:
If it's sold at a loss of 15%, then the store owner loses 0.15*330 = 49.50 dollars
So it was sold for 330- 49.50 = 280.50 dollars
----------------------------
An alternative method:
If the store owner loses 15%, then they keep the remaining 85% since 15%+85% = 100%.
85% of 330 = 280.50 dollars is the discount price
This means 330-280.50 = 49.50 dollars is the amount lost.
Use the discriminant to describe the roots of each equation. Then select the best description.
7x² + 1 = 5x
Answer:
Imaginary roots
Step-by-step explanation:
The discriminant of a quadratic in standard form [tex]ax^2+bx+c[/tex] is given by [tex]b^2-4ac[/tex].
Given [tex]7x^2+1=5x[/tex], subtract 5x from both sides so that the quadratic is in standard form:
[tex]7x^2-5x+1=0[/tex]
Now assign variables:
[tex]a\implies 7[/tex] [tex]b\implies -5[/tex] [tex]c\implies 1[/tex]The discriminant is therefore [tex](-5)^2-4(7)(1)=25-28=\textbf{-3}[/tex].
What does this tell us about the roots?
Recall that the discriminant is what is under the radical in the quadratic formula. The quadratic formula is used to find the solutions of a quadratic. Therefore, the solutions of this quadratic would be equal to [tex]\frac{-b\pm \sqrt{-3}}{2a}[/tex] for some [tex]b[/tex] and [tex]a[/tex]. Since the number under the radical is negative, there are no real roots to the quadratic (whenever the discriminant is negative, the are zero real solutions to the quadratic). Therefore, the quadratic has imaginary roots.
A population is equally divided into three class of drivers. The number of accidents per individual driver is Poisson for all drivers. For a driver of Class I, the expected number of accidents is uniformly distributed over [0.2, 1.0]. For a driver of Class II, the expected number of accidents is uniformly distributed over [0.4, 2.0]. For a driver of Class III, the expected number of accidents is uniformly distributed over [0.6, 3.0]. For driver randomly selected from this population, determine the probability of zero accidents.
Answer:
Following are the solution to the given points:
Step-by-step explanation:
As a result, Poisson for each driver seems to be the number of accidents.
Let X be the random vector indicating accident frequency.
Let, [tex]\lambda=[/tex]Expected accident frequency
[tex]P(X=0) = e^{-\lambda}[/tex]
For class 1:
[tex]P(X=0) = \frac{1}{(1-0.2)} \int_{0.2}^{1} e^{-\lambda} d\lambda \\\\P(X=0) = \frac{1}{0.8} \times [-e^{-1}-(-e^{-0.2})] = 0.56356[/tex]
For class 2:
[tex]P(X=0) = \frac{1}{(2-0.4)} \int_{0.4}^{2} e^{-\lambda} d\lambda\\\\P(X=0) = \frac{1}{1.6} \times [-e^{-2}-(-e^{-0.4})] = 0.33437[/tex]
For class 3:
[tex]P(X=0) = \frac{1}{(3-0.6)} \int_{0.6}^{3} e^{-\lambda} d\lambda\\\\P(X=0) = \frac{1}{2.4} \times [-e^{-3}-(-e^{-0.6})] = 0.20793[/tex]
The population is equally divided into three classes of drivers.
Hence, the Probability
[tex]\to P(X=0) = \frac{1}{3} \times 0.56356+\frac{1}{3} \times 0.33437+\frac{1}{3} \times 0.20793=0.36862[/tex]
How many more barrels of gasoline than desiel were produced
Answer:
15
Step-by-step explanation:
Write an explicit formula for the sequence.
-4,7,-10,13,-16
Step-by-step explanation:
Sequence is
4
,
7
,
10
,
13
,
16
,
.
.
.
a
1
=
4
,
a
2
=
7
,
a
3
=
10
,
.
.
.
If it is Arithmetic sequence,
a
2
−
a
1
=
a
3
−
a
2
=
a
4
−
a
3
& so on
In the given sum,
a
2
−
a
1
=
7
−
4
=
3
a
3
−
a
2
=
10
−
7
=
3
a
4
−
a
3
=
13
−
10
=
3
Since the difference between the successive terms is same and
hence
common difference
d
=
3
PLEASEEEE PLEASEEEE HELPPPP
i need an equation for a vertical line going through f(x) = 2x^2 + 6x + 2
Answer:
dont understand clearly
Step-by-step explanation:
dont understand clearly
How much bigger is the Sum of first 50 even numbers than the sum of first 50 odd numbers?
Answer:
50
Step-by-step explanation:
Sum Even numbers
n = 50
d = 2
a1 = 2
The last number is
an = a1 + (n-1)d
an = 2 + (50 - 1)*2
an = 2 + 49 * 2
an = 2 + 98
an = 100
Sum of the even numbers
Sum = (a1 + a50)*n/ 2
Sum = (2 + 100)*50/2
sum = 102 * 25
sum = 2550
Sum of the first 50 odd numbers
a1 = 1
n = 50
d = 2
l = ?
Find l
l = a1 + (n - 1)*2
l = 1 + 49*2
l = 99
Sum
Sum = (1 + 99)*50/2
Sum = 2500
The difference and answer is 2550 - 2500 = 50
can anybody help me with this?
Answer:
Option (a)
Step-by-step explanation:
[tex]\sqrt[6]{1000m^{3} n^{12} } = \sqrt[6]{10^{3} } \sqrt[6]{m^{3} } \sqrt[6]{n^{12} } =\\\sqrt{10} \sqrt{m} n^{2} = n^{2} \sqrt{10m}[/tex]
I need help answering this ASAP
Answer:
x=13
Step-by-step explanation:
f(x) = sqrt(x-11)
The square root must be greater than or equal to zero
sqrt(x-11)≥0
Square each side
x-11≥0
x ≥11
The only answer that is greater than or equal to 11 is
x=13
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
18x + 3y = -18
Answer:
y = -6x -6
Step-by-step explanation:
The general form of the equation of a line in the slope-intercept form may be given as
y = mx + c where
m is the slope and c is the intercept
Hence given the equation
18x + 3y = -18
subtract 18x from both sides
3y = -18x - 18
Divide both sides of the equation by 3
y = -6x -6
This is the equation in the slope - intercept form with -6 as the slope and -6 as the intercept
?????????????please help
Answer:
ok so you take m time h then like you count to h like a b c d e f g h and tgen with that you count 1 2 3 4 5 6 7 till h than you multiply that with 3
thank you for the help every one
Answer:
1. 1.66in
2. 6.66in
3. 3.33in
4. 1inch
Step-by-step explanation:
the area of a rectangle is found by multiplying the length times width or the two sides.
5 x 1/3 is about 1.66 inches
5 x 4/3 is about 6.66 inches
5/2 x 4/3 is about 3.33 inches
and 7/6 x 6/7 is 1 inch
Determine if the table below represents a linear function. If so, what's the rate of change?
A) No; it's a non-linear function.
B) Yes; rate of change = 4
C) Yes; rate of change = 2
D) Yes; rate of change = 3
Answer:
A
Step-by-step explanation:
Its not a linear function; there is no consistent rate of change between each of the points.
Wayne has a rectangular painting. The width of the painting is
5/6
of a foot, and the length is
3/4
of a foot. What is the area of the painting?
Answer:
5/8 ft^2
Step-by-step explanation:
The area of a rectangle is given by
A = l*w where l is the length and w is the width
A = 5/6 * 3/4
A = 3/6 * 5/4
A = 1/2 * 5/4
A = 5/8 ft^2
Ivan drove 335 miles in 5 hours.
At the same rate, how long would it take him to drive 737 miles?
hours
Х
?
Answer: x= 11
Step-by-step explanation:
To answer the question, we first need to know how many miles he/she/it can drive in one hour (to make it simpler. Doing a bunch of calculations involving decimals and other stuff can be very confusing)
335 divided by 5 is 67
Therefore in one hour Ivan can drive 67 miles. We want to know the TIME it takes for Ivan to drive 737 miles and the formula for time is Distance / Speed.
The distance is 737 miles
The speed is 67 miles/hour
737 divided by 67 is 11
Therefore Ivan takes 11 hours to drive 737 hours
Find the measure of x. X=8, x=7, x=9, x=11
Answer:
[tex]\frac{135}{15} =\frac{15(x+2)}{15}[/tex]
[tex]9=x+2[/tex]
[tex]x=7[/tex]
OAmalOHopeO
A 90% confidence interval is (35 45). What is the margin of error?
A.5
B.4.5
C.9
D.10
Answer:
option a 5......
...
I hope it's correct
A particle is moving with the given data. Find the position of the particle.
a(t) = [tex]t^{2}[/tex] − 4t + 5, s(0) = 0, s(1) = 20
How do I find s(t)=?
Recall that
[tex]\dfrac{dv(t)}{dt} = a(t) \Rightarrow dv(t) = a(t)dt[/tex]
Integrating this expression, we get
[tex]\displaystyle v(t) = \int a(t)dt = \int(t^2 - 4t + 5)dt[/tex]
[tex]\:\:\:\:\:\:\:= \frac{1}{3}t^3 - 2t^2 + 5t + C_1[/tex]
Also, recall that
[tex]\dfrac{ds(t)}{dt} = v(t)[/tex] or
[tex]\displaystyle s(t) = \int v(t)dt = \int (\frac{1}{3}t^3 - 2t^2 + 5t + C_1)dt[/tex]
[tex]\:\:\:\:\:\:\:= \frac{1}{12}t^4 - \frac{2}{3}t^3 + \frac{5}{2}t^2 + C_1t + C_2[/tex]
Next step is to find [tex]C_1\:\text{and}\:C_2[/tex]. We know that at t = 0, s = 0, which gives us [tex]C_2 = 0[/tex]. At t = 1, s = 20, which gives us
[tex]s(1) = \frac{1}{12}(1)^4 - \frac{2}{3}(1)^3 + \frac{5}{2}(1)^2 + C_1(1)[/tex]
[tex]= \frac{1}{12} - \frac{2}{3} + \frac{5}{2} + C_1 = \frac{23}{12} + C_1 = 20[/tex]
or
[tex]C_1 = \dfrac{217}{12}[/tex]
Therefore, s(t) can be written as
[tex]s(t) = \frac{1}{12}t^4 - \frac{2}{3}t^3 + \frac{5}{2}t^2 + \frac{217}{12}t[/tex]
Does this appear to be a regular polygon? Explain using the definition of a regular polygon.
Answer:
yes it is. a polygon is any closed shape with at least 3 connected lines (eg. triangle, square, pentagon, hexagon, heptagon, octagon, etc)
Step-by-step explanation:
helpppp asap pleaseee
Answer:
29/3 is your answer
Step-by-step explanation:
pls mark as brainliest
The circle graph above shows the distribution of utility expenses for the Hierra family last year. If the family’s total utility expenses last year were $3,600, what were their expensive go water and sewer.
Water and sewer=X%
Electric=30%
Heating and gas=50%
Answer:
The correct answer is - $720 or 20%.
Step-by-step explanation:
Given:
Total expense = 3600
Electric=30%
Heating and gas=50%
Water and sewer=X%
Solution:
For electric: 3600*30/100 = 1080
for heating and gas: 3600*50/100 = 1800
Left money for expense of water and shower = total - (electric and heating)
= 3600-1880
= 720
Percentage of water and shower = 720*100/3600
= 20%
Answer:
Correct!
Step-by-step explanation:
Thank you this is correct :) I took the test