Answers
Answer:
4c^2+7c-5=0
4c^2+7c=5
4c^2+7c=5
4c^2+7c-5=0\quad :\quad c=\frac{-7+\sqrt{129}}{8},\:c=\frac{-7-\sqrt{129}}{8}\quad \left(\mathrm{Decimal}:\quad c=0.54472\dots ,\:c=-2.29472\dots \right)
Hope This Helps!!!
Answer:
C) c = -7 ± √129 / 8
Step-by-step explanation:
x = (-b ± √ (b² – 4ac) ) / 2a
[quadratic formula]
where ax² + bx + c = 0.
[quadratic / square trinomial]
given 4c² + 7c – 5 = 0,
↓ ↓ ↓
a b c
where c = x,
c = (-b ± √ (b² – 4ac) ) / 2a.
c = (-(7) ± √ ((7)² – (4)(4)(-5)) ) / 2(4)
c = (-7 ± √ (49 – (-80)) ) / 8
c = (-7 ± √ (129) ) / 8
c = -7 ± √129 / 8
Related Questions
Find the population variance and standard deviation.
8, 17, 29, 35, 41
Answers
Answer:
53
Step-by-step explanation:
By taking the number "41" and minus it with "35" and you'll get 12. Take the number "12" and plus with "41" and you'll get the answer.
the population variance is 144 and the population standard deviation is 12.
To find the population variance and standard deviation for the given data set, follow these steps:
Step 1: Find the mean (average) of the data set.
Step 2: Subtract the mean from each data point to find the differences.
Step 3: Square each difference.
Step 4: Calculate the sum of the squared differences.
Step 5: Divide the sum of squared differences by the total number of data points to find the variance.
Step 6: Take the square root of the variance to find the standard deviation.
Given data set: 8, 17, 29, 35, 41
Step 1: Find the mean (average):
Mean = (8 + 17 + 29 + 35 + 41) / 5
Mean = 130 / 5
Mean = 26
Step 2: Find the differences from the mean:
Differences: (8 - 26) = -18, (17 - 26) = -9, (29 - 26) = 3, (35 - 26) = 9, (41 - 26) = 15
Step 3: Square each difference:
Squared differences: [tex](-18)^2 = 324, (-9)^2 = 81, 3^2 = 9, 9^2 = 81, 15^2 = 225[/tex]
Step 4: Calculate the sum of squared differences:
Sum of squared differences = 324 + 81 + 9 + 81 + 225 = 720
Step 5: Calculate the variance:
Variance = Sum of squared differences / Number of data points
Variance = 720 / 5
Variance = 144
Step 6: Calculate the standard deviation:
Standard deviation = √Variance
Standard deviation = √144
Standard deviation = 12
So, the population variance is 144 and the population standard deviation is 12.
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the temperature at 6 pm in frost frozen antarctica was -37 if the tem dropped 8 1 /2 c uring the next hour what was the the temp at 7 pm
Answers
Answer:
-45 1/2
Step-by-step explanation:
Given A = (-1 -2 3 4 8 -6 0 1 5) and B = (-5 -1 6 4 1 2 0 -3 2) What is X if B - X = A?
Answers
Answer:
5(-3)2-2(-3)+1. =5(9)+6+1. =45+7 ... 7x – 6= 0). (3x + 2)(x – 3)=0. =3x + 2 = 0; x – 3 = 0. _486x 5 – 7x. 1 1 8 1 6. uh this is hard..
Step-by-step explanation:
Help. Urgent. Skenekeks
Answers
Answer:
D
Step-by-step explanation:
Plug in the numbers for the x-value and solve the equation.
| 3(80/3)/4 + 1 | = 16
| 3(-40/3)/4 + 1 | = 16
Which of the following is the square of a binomial?
Answers
Answer:
[tex]16 {x}^{2} + 24xy + 9 {y}^{2} [/tex]
Step-by-step explanation:
U can reduce this into
[tex](4x + 3y) {}^{2} [/tex]
Which is a square.
Now,
16x^2 + 24xy + 9y^2
16x^2 + 12xy + 12xy + 9y^2
4x ( 4x + 3y ) + 3y ( 4x + 3y )
( 4x + 3y ) ( 4x + 3y )
( 4x + 3y )^2
I hope you understand...
Mark me as brainliest...
In this figure below, lines m and n are parallel: image above ^
HELPP PLS ASAP
Answers
Answer:
83 or a
Step-by-step explanation:
if angle 6 is 97 then the total would be 180 meaning that 83 would be the answer to 5s angle
"83 degrees" is correct.
On a line, it can be assumed that all the angles must add up to 180 degrees. If you have two angle on a line and don't know the value of one of them, you can subtract that angle from 180 to find the missing angle. Considering this, 180 - 97 = 83.
The equation y = 50(1.05)x models the growth of a mule deer population introduced into Guadalupe National Park in December 2015. "X" represents the number of years after December 2015 while "y" represents the population at time "x". In what year will the mule deer population first reach 1500?
F. 2084
G. 2044
H. 2043
J. 2086
Answers
Answer: (f)
Step-by-step explanation:
Given
The growth equation is [tex]y=50(1.05)^x[/tex]
When population becomes 1500
[tex]\Rightarrow 1500=50(1.05)^x\\\Rightarrow 30=(1.05)^x\\\text{Taking log both sides}\\\Rightarrow \ln (30)=x\ln (1.05)\\\\\Rightarrow x=\dfrac{\ln (30)}{\ln (1.05)}\\\\\Rightarrow x=69.71[/tex]
Thus, after 69.71 years of year 2015 i.e. [tex]2015+69.71=2084.71[/tex]. In year 2084, it becomes 1500.
option (f) is correct.
Karl set out to Alaska on his truck. The amount of fuel remaining in the truck's tank (in liters) as a function of distance driven (in kilometers) is graphed.
What distance did Karl travel by the time he had 200 liters of fuel?
_____ kilometers
Answers
Answer:
500 kilometers
Step-by-step explanation:
The fuel (y) Karl has in his car is a function of the distance (x) Karl travelled. The amount of fuel (y) is dependent on the distance (x) Karl travelled.
On the y-axis, we have amount of fuel.
On the x-axis, we have distance travelled.
At the time Karl travelled when he had 200 liters of fuel (y) remaining in his car, he had travelled a distance (x) of 500 kilometers.
We know this by looking at the graph given. When x (distance) = 500, y (fuel) = 200.
Lin is reading a 47-page book. She read the first 20 pages in 35 minutes.
If she continues to read at the same rate, will she be able to complete this book in under 1 hour?
[ Select ]
If so, how much time will she have left? If not, how much more time is needed?
[ Select ]
Answers
Answer:
no
22.25 minutes
Step-by-step explanation:
First determine how long it will take her to read the entire book
20 pages 47 pages
-------------- = ----------------
35 minutes x minutes
Using cross products
20x = 35*47
20x=1645
Divide by 20
20x/20 = 1645/20
x =82.25 minutes
This is more than 1 hour ( 1 hour = 60 minutes)
82.25 minutes - 60 minutes = 22.25 minutes
She will need 22.25 more minutes
4(x+9)=2x-6
Solve for x
Answers
Answer:
-21
Step-by-step explanation:
4(x+9) = 4x+36
4x+36 = 2x-6
-36 -36
minus 36 from both sides
4x = 2x-42
2x = -42
-42/2 = -21
x = -21
Hi there!
We are given the equation below:
[tex] \large \boxed{4(x + 9) = 2x - 6}[/tex]
1. Expand 4 in the expression.
When expand in the expression, it is like multiply everything in the expression. So when we expand 4 in x+9, it becomes 4(x)+9(4).[tex] \large{(4 \times x) + (9 \times 4) = 2x - 6} \\ \large{(4x) + (36) = 2x - 6}[/tex]
Cancel the brackets.
[tex] \large{4x + 36 = 2x - 6}[/tex]
2. Isolate x-term and solve for the variable.
Think it easy. If you want to isolate x-term then what should you do? Well simply swap sides, and change the operator/sign.[tex] \large{4x - 2x = - 6 - 36}[/tex]
Finally, combine like terms.
[tex] \large{2x = - 42}[/tex]
Then divide both sides by 2 so we can finally leave only x-term.
[tex] \large{ \frac{2x}{2} = \frac{ - 42}{2} } \\ \large \boxed{x = - 21}[/tex]
3. Check the solution if it is right or wrong.
This step is optional but if you are not confident on your answer, this step is recommended.To check the answer, we simply substitute the value of x which is -21 in the equation and see if both sides are equal or not. If both sides are equal then the answer is correct, if not then the answer is wrong. Therefore,
[tex] \large{4(x + 9) = 2x - 6 \longrightarrow 4( - 21 + 9) = 2 ( - 21) - 6} \\ \large{4( - 12) = - 42 - 6} \\ \large{ - 48 = - 48}[/tex]
Since both sides are equal when substitute in x = -21.
4. Answer
Hence, the answer for this equation is x = -21.I hope this helps and let me know if you have any doubts!
Solve the equation ln(x - 3) + ln(x + 1) = ln(x + 7)
x = 5, or x = ???
Answers
Answer:
x = 5 or x = - 2
Step-by-step explanation:
Using the rules of logarithms
log x + log y = log (xy)
log x = log y ⇒ x = y
Given
ln(x- 3) + ln(x + 1) = ln(x + 7) , then
ln (x - 3)(x + 1) = ln (x + 7) , so
(x - 3)(x + 1) = x + 7 ← expand left side using FOIL
x² - 2x - 3 = x + 7 ( subtract x + 7 from both sides )
x² - 3x - 10 = 0 ← in standard form
(x - 5)(x + 2) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
x + 2 = 0 ⇒ x = - 2
please help me...........
Answers
I will help u if I know in cmt
What is the percentage of $6 dollar tip on a $60 dollar bill?
Answers
Answer:
3.6
Step-by-step explanation:
set-up percentage like this!
[tex]\frac{part}{whole} =\frac{part}{whole}[/tex]
Then use what you know from the question to fill in the blanks
Answer: [tex]\frac{6}{100} =\frac{?}{60}[/tex]
Then: [tex]60[/tex] × 6 ÷ 100 = 3.6
Final Answer: 3.6
James hits a golf ball 145.7 yards Kayla hit a golf ball 122.95 yards how much farther does James hit a golf ball
Answers
ВС
2. In ATVW if VW is three meters longer than TV, TW
is 19 meters shorter than the sum of VW and TV,
and the perimeter of ATVW is 62 meters, find the length of VW.
20.75 m
15.75 m
25.5 m
21.75 m
None of the above
Answers
9514 1404 393
Answer:
21.75 m
Step-by-step explanation:
The given relations tell us that ...
VW = TV +3
TW = VW +TV -19
VW +TW +TV = 62
__
Solving the first equation for TW gives ...
TV = VW -3
Substituting that into the second equation gives ...
TW = 2VW -22
And using these expressions in the third equation, we have ...
VW +(2VW -22) +(VW -3) = 62
4VW = 87 . . . . . . . . collect terms
VW = 21.75 . . . . . . divide by 4
The length of VW is 21.75 meters.
The perimeter of a rectangle is 58 inches and the area is 180 square inches. Find the dimensions of the rectangle.
Answers
Answer:
width = 9 inches
length= 20 inches
perimeter of the rectangle=2(9+20)
2w +2L= 2×29
=58 inches
area of the rectangle=w×L
=9×20=180 inch²
Point D, not shown below, is one of the four (4) vertices of rectangle ABCD. Find its position and state the coordinate of point D.
Answers
Answer:
Hi im not got with graphs
Step-by-step explanation:
eople
Find the perimeter and area of the figure pictured below.
odules
fice 365
3.7 m
om
11.4 m
ades
2.3 m
9.2 m
Q
Perimeter
m
Area -
m2
Answers
Answer:
Perimeter: 41.2 m
Area: 54.83 m^2
Step-by-step explanation:
REFER TO THE IMAGE ATTACHED AS A
GUIDE.
PERIMETER:
(ADD UP ALL THE LENGTHS OF EACH SIDE)
Must be all 6 sides (see image, I solved for the two missing lengths)
3.7 + 9.1 + 11.4 + 9.2 + 2.3 + 5.5 = 41.2
perimeter is 41.2 m
AREA:
(See image again)
Shape is divided into two rectangles:
Top rectangle area: 11.4 x 3.7 = 42.18 m^2
Bottom triangle area: 5.5 x 2.3 = 12.65 m^2
ADD:
42.18 m^2 + 12.65 m^2 = 54.83 m^2
The area of the whole figure is 54.83 m^2
HOPE THIS HELPS
Can somebody help me? I feel like this is wrong
Answers
Which I got was y=-1/3x+5
I really hope that helps and my deepest apologies if my answer turned out wrong!!
y= -0.3x +5
Consider x1= 9
Y1=2
x2= 0
y2 = 5
Slope is
m = 3 / -9 = 1 / -3 = -0.33333
The entered points belong to a decreasing, linear function.
Equation: y = -0.33333x + 5.
m = 3 / -9 = 1 / -3 = -0.33333
hello how are you today. Question 2(×+-5)+×=×+(-6)
Answers
Answer:
x = 2
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
2(x + -5) + x = x + (-6)
Step 2: Solve for x
[Distributive Property] Distribute 2: 2x - 10 + x = x - 6[Addition] Combine like terms (x): 3x - 10 = x - 6[Subtraction Property of Equality] Subtract x on both sides: 2x - 10 = -6[Addition Property of Equality] Add 10 on both sides: 2x = 4[Division Property of Equality] Divide 2 on both sides: x = 2Answer:
x=2 ( see Image below)
Step-by-step explanation:
cancel equal terms on both sides of the equation
2(x-5)=-6
move the constant to the right -hand side and change its sign
2x= -6 +10
Calculate the sum
2x=4
divide both sides of the equation by 2
x=2
can someone tell me what the diffrence of 8 through 5 is
Answers
Answer:
The answer is 3.
Step-by-step explanation:
What is the difference between 8 and 5? In mathematics, the difference between two numbers usually means to subtract them. So if you want to find the difference, you take the bigger one minus the smaller one. So, the difference between 8 and 5 is 3.
Answer:
3
Step-by-step explanation:
What is the difference between 8 and 5? In mathematics, the difference between two numbers usually means to subtract them. So if you want to find the difference, you take the bigger one minus the smaller one. So, the difference between 8 and 5 is 3.
Will Mark Brainlest. (find the domain of following relation for the given range) step by step
Answers
Step-by-step explanation:
I suppose you mean find the range for the following domain. Because when
g(x) is given the value of X
we are trying to solve the output value which is range.
If you want to solve for the domain, the question should give
g(x) = y
and provide the value of y.
X³+X²-X-2
Substitute
X=(-1)
-1+1-(-1)-2
= -1
g(-1)= -1
Substitute
X=(2)
8+4-2-2
=8
g(2)= 8
Substitute
X=(1)
1+1-1-2
=-1
g(1)= -1
g(2)+g(1)
=8-1
=7
Which matrix represents the system of equations shown below?
2x - 5y = 4
-5y = 8
c
D
А
B
2 -547 2x -5y 47 52-547
-5 08 0 -5y8 0 -58
2 041
-5 -5 8
A. Matrix A
B. Matrix B
C. Matrix C
D. Matrix D
Answers
9514 1404 393
Answer:
C. Matrix C
Step-by-step explanation:
The usual form for an augmented matrix representation of a system of linear equations has the variable coefficients listed in a square matrix with an additional column at the right containing the constants in the standard-form equations. This is illustrated in Matrix C.
__
The variables in the equations are usually left out of the matrix. That is, the system of equations AX= B is usually represented by the augmented matrix A|B, rather than (AX)|B. Thus "Matrix B" is not the best choice.
The college student senate is sponsoring a spring break Caribbean cruise raffle. The proceeds are to be donated to the Samaritan Center for the Homeless. A local travel agency donated the cruise, valued at $2000. The students sold 2357 raffle tickets at $5 per ticket.
Required:
a. Kevin bought ten tickets. What is the probability that Kevin will win the spring break cruise to the Caribbean?
b. Expected earnings can be found by multiplying the value of the cruise by the probability that Kevin will win. What are Kevin's expected earnings?
c. How much did Kevin effectively contriute to the Samaritan Center for the Homeless?
Answers
Answer:
A) The probability that Kevin will win the spring break cruise is 0.42%.
B) Kevin's expected earnings are $ 8.4.
C) Kevin effectively contributed with $ 50.
Step-by-step explanation:
Since the college student senate is sponsoring a spring break Caribbean cruise raffle, and the proceeds are to be donated to the Samaritan Center for the Homeless, ya local travel agency donated the cruise, valued at $ 2000, and the students sold 2357 raffle tickets at $ 5 per ticket, to determine A) if Kevin bought ten tickets, what is the probability that Kevin will win the spring break cruise to the Caribbean; B) Kevin's expected earnings and C) how much did Kevin effectively contribute to the Samaritan Center for the Homeless; the following calculation must be performed:
A) 10/2357 = 0.0042 x 100 = 0.42
Therefore, the probability that Kevin will win the spring break cruise is 0.42%.
B) 2000 x 0.0042 = 8.4
Therefore, Kevin's expected earnings are $ 8.4.
C) 5 x 10 = 50
Kevin effectively contributed with $ 50.
The vector w=ai+bj is perpendicular to the line ax+by=c and parallel to the line bx−ay=c. It is also true that the acute angle between intersecting lines that do not cross at right angles is the same as the angle determined by vectors that are either normal to the lines or parallel to the lines. Use this information to find the acute angle between the lines below.
2x+5y=4, 7x+3y=8
Answers
Answer:
The angle between the liens is 135 degree.
Step-by-step explanation:
Equation of first line
2 x + 5 y = 4 ...... (1)
Equation of second line
7 x + 3 y = 8 ..... (2)
The slope of a line is given by
[tex]m = \frac{- coefficient of x}{coefficient of y}[/tex]
Slope of first line
[tex]m = -\frac {2}{5}[/tex]
Slope of second line
[tex]m'= - \frac{7}{3}[/tex]
The angle between the two lines is given by
[tex]tan\theta = \frac{m- m'}{1 + m m'}\\\\tan\theta = \frac{-\frac{2}{5}+\frac{7}{3}}{1+\frac{2}{5}\times \frac{7}{3}}\\\\tan\theta = -1 \\\\\theta = 135^o[/tex]
Ahmad made $114 for 12 hours of work. At the same rate, how many hours would he have to work to make $108?
Answers
Answer:6
Step-by-step explanation:
Answer: 6
Step-by-step explanation
Calculate the unit price. Round to the nearest cent, if necessary.
0.75 lb of salami for $2.65
$4.64 per lb of salami
$2.65 per lb of salami
$3.53 per lb of salami
$1.99 lb of salami
per
Answers
Answer:
$3.53 per lb of salami
Step-by-step explanation:
0.75 lb of salami for $2.65
The price per of salami will be :
0.75 lb = $2.65
1 lb = x
Using cross multiplication :
0.75 * x = $2.65 * 1
0.75x = $2.65
Divide both sides by 0.75
0.75x / 0.75 = $2.65 / 0.75
x = $3.533
This means that :
The price per unit of salami is $3.53
Answer:
0.75 lb of salami for $2.65 is $3.53 per lb of salami.
2. Suppose the measures of the interior angles of a convex octagon are eight
numbers, each separated by a value of 1 degree from its neighbors. Find
the measure of the second smallest angle.
118°
131°
132.5°
142°
None of these answers are correct.
Answers
=====================================================
Explanation:
The interior angles are consecutive numbers such as 1,2,3,... or 7,8,9... and so on. The gap between any two adjacent neighbors is 1.
For any polygon with n sides, the interior angles add up to 180(n-2)
We have n = 8 sides so the interior angles sum to 180(n-2) = 180(8-2) = 1080 degrees.
Any octagon has its interior angles add up to 1080 degrees.
-----------------------------
Let x be the smallest angle. The next angle up is x+1. After that is x+2 and so on until we reach x+7 as the 8th angle.
Add up those 8 angles, set the sum equal to 1080 and solve for x
x+(x+1)+(x+2)+(x+3)+(x+4)+(x+5)+(x+6)+(x+7) = 1080
8x+28 = 1080
8x = 1080-28
8x = 1052
x = 1052/8
x = 131.5
This is the smallest angle. The next angle up or the second smallest angle is x+1 = 131.5+1 = 132.5 degrees (choice C)
The ratio of girls to boys in a particular classroom is 8: 7. How many boys are in the class if there are 45 students?
Answers
Answer:
8+6=14
So , we can multiply 14 to 45 =630 in ratio 6:30
Classify each differential equation as separable, exact, linear, homogeneous, or Bernoulli. Some equations may be more than one kind. Do not solve.
a) dy/dx = (x − y)/x
b) (x + 1)dy/dx = −y + 20
c) dy/dx = 1/(x(x − y2))
d) dy/dx =(y^2 + y)/(x^2 + x)
e) dy/dx = 5y + y^2
f) y dx = (y − xy^2) dy
g) x dy/dx = ye^(xy) − x
h) 2xyy' + y^2 = 2x^2
i) y dx + x dy = 0
k) (x^2 + 2y/x) dx = (3 − ln x^2) dy
l) (y/x^2) dy/dx + e^(2x^3) + y^2 = 0
Answers
Here, we have to classify each differential equation based on their characteristics:
a) dy/dx = (x − y)/xThis is a separable differential equation because the variables can be separated on different sides of the equation.
It's of the form dy/dx = g(x) - f(y)/h(y), where g(x) = x/x and h(y) = 1.
b) (x + 1)dy/dx = −y + 20This is a linear first-order differential equation because it can be rearranged to the form y' + P(x)y = Q(x), where P(x) = -1/(x + 1) and Q(x) = 20/(x + 1).
c) [tex]dy/dx = 1/(x(x - y^2))[/tex]This is a separable differential equation because the variables x and y can be separated on different sides of the equation.
d) [tex]dy/dx = (y^2 + y)/(x^2 + x)[/tex]This is a separable differential equation because the variables x and y can be separated on different sides of the equation.
e)[tex]dy/dx = 5y + y^2[/tex]This is a Bernoulli differential equation because it is of the form [tex]dy/dx = p(x)y + q(x)y^n[/tex], where p(x) = 0 and q(x) = 5x, n = 2.
f) [tex]y dx = (y - xy^2) dy[/tex]This is a separable differential equation because the variables x and y can be separated on different sides of the equation.
g) [tex]x dy/dx = ye^{(xy)} - x[/tex]This is a linear first-order differential equation because it can be rearranged to the form y' + P(x)y = Q(x), where P(x) = -1/x and [tex]Q(x) = e^{(xy)} - x^{(-1)[/tex].
h) [tex]2xyy' + y^2 = 2x^2[/tex]This is a linear first-order differential equation because it can be rearranged to the form y' + P(x)y = Q(x), where P(x) = -2/x and Q(x) = 2x.
i) y dx + x dy = 0This is a separable differential equation because the variables x and y can be separated on different sides of the equation.
k) [tex](x^2 + 2y/x) dx = (3 - \text ln x^2) dy[/tex]This is a linear first-order differential equation because it can be rearranged to the form y' + P(x)y = Q(x), although it's not immediately obvious what P(x) and Q(x) are.
l) [tex](y/x^2) dy/dx + e^{(2x^3)} + y^2 = 0[/tex]This is a linear first-order differential equation because it can be rearranged to the form y' + P(x)y = Q(x), where [tex]P(x) = -1/x^2[/tex] and [tex]Q(x) = -e^{(2x^3)} - y^2[/tex].
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