Solve.
x² + 4x + 4 = 18
A x=−4±3√ 2
B x=2±3√ 2
C x=4±9√ 2
D x=−2±3√2
Answers
x² + 4x + 4 = 18
A x=−4±3√ 2
B x=2±3√ 2
C x=4±9√ 2
D x=−2±3√2
[tex]x^2 + 4x + 4 = 18 \\ \\ x^2+4x+4-18= 0 \\ \\ x^2+4x-14=0 \\ \\ x_1_y_2= \dfrac{-b\pm \sqrt{b^2-4ac} }{2a} \qquad a= 1\qquad b= 4\qquad c= -14 \\ \\ \\ x_1_y_2= \dfrac{-4\pm \sqrt{4^2-4(1)(-14)} }{2(1)} \\ \\ \\ x_1_y_2= \dfrac{-4\pm \sqrt{16-(-56)} }{2} \\ \\ \\ x_1_y_2= \dfrac{-4\pm \sqrt{72} }{2} \\ \\ \\ x_1= \dfrac{-4+ \sqrt{72} }{2} \qquad\qquad x_2= \dfrac{-4+ \sqrt{72} }{2}\\ \\ \\ x_1= \dfrac{-4+ \sqrt{2^3*3^2} }{2} \qquad\qquad x_2= \dfrac{-4- \sqrt{2^3*3^2} }{2}[/tex]
[tex] x_1= \dfrac{-4+2*3 \sqrt{2} }{2} \qquad\qquad x_2= \dfrac{-4- 2*3\sqrt{2} }{2} \\ \\ \\ x_1= \dfrac{-4+6 \sqrt{2} }{2} \qquad\qquad x_2= \dfrac{-4- 6\sqrt{2} }{2} \\ \\ \\ x_1= \dfrac{-4}{2} + \dfrac{6 \sqrt{2} }{2} \qquad\qquad x_2= \dfrac{-4}{2}- \dfrac{ 6\sqrt{2} }{2} \\ \\ \\ x_1= -2 + 3 \sqrt{2} \qquad\qquad\quad x_2= -2- 3\sqrt{2} \\ \\ \\ \boxed{x= -2\pm 3\sqrt{2} } \to D) [/tex]
This was the correct answer, I even provided proof from my own test. Hope this helps!
Related Questions
f(x)=tan(x)
Find the limit as x approaches pi/2 from the negative and positive sides then find the limit as x approaches 0.
Help please!! :(
Answers
IMAGE ATTACHED
If A(1, 1), B(5, 4), C(10, 3), and D(6, 0) are the vertices of a quadrilateral, do the points form a parallelogram? Justify your answer.
Yes, it is a parallelogram because the slope of segment AB equals the slope of segment DC, which equals negative start fraction three over four end fraction comma and AD = BC = 5 units.
Yes, it is a parallelogram because the slope of segment AB equals the slope of segment DC, which equals start fraction three over four end fraction comma and AB = CD = 5 units.
Yes, it is a parallelogram because the midpoint of the diagonals segment AC and segment BD is (5.5, 2).
No, it is not a parallelogram because the slope of segment AB = 1 and the slope of segment DC equals negative start fraction three over four end fraction full stop
Answers
The slope of AB = (4-1)/(5-1)= 3/4
The slope of DC = (0-3)/(6-10) = 3/4
Thus, the two segments have equal slope,
Both segments are also equal in magnitude 5 units
The measures of two of the angles in a triangle are green. Find the measure of the thirs angle. Show your calculations to support your answer.
5-8?
Answers
5
m∠3 = 180 - 126.5 - 19 = 34.5°
6
m∠3 = 180 - 65.5 - 85 = 29.5°
7
m∠3 = 180 - 98.3 - 37.5 = 44.2°
8
m∠3 = 180 - 31 - 113 = 36°
So all we have to do is subtract the 2 angles we know from 180:
For question 5, we subtract 126.5° and 19° from 180°:
180 - 126.5 - 19 = 34.5°
The same principle applies for the rest.
Question 6:
180 - 65.5 -85 = 29.5°
Question 7:
180 -98.3 -37.5 = 44.2°
Question 8:
180 - 31 - 113 = 36°
Kenya is reserving a room in a hotel in France where they use euros (€). The room charge is €75. Suppose the conversion rate is €1 = $1.298. What is the cost of the room in dollars?
Answers
Two tons of water is pumped into a tank 15 ft. high in 5 minutes. Determine the power output of the pump.
Answers
Answer:
0.364 horsepower
Step-by-step explanation:
You want to know a pump's power output if it raises 2 tons of water 15 ft in 5 minutes.
PowerThe power is conveniently measured in horsepower. One horsepower is 33,000 ft·lb/minute.
Here, we have (2t · 2000 lb/t · 15 ft)/(5 min) = 12000 ft·lb/min
In terms of horsepower, that is ...
(12000 ft·lb/min) / (33000 ft·lb/min/hp) = 4/11 hp ≈ 0.364 hp
The power output of the pump is about 0.364 horsepower.
__
Additional comment
That's about 271 watts.
The distance dimensions are in feet, so we assume the tons are US short tons of 2000 lb each.
Please help! Really need help!
Answers
The graph below shows a system of equations:
The x-coordinate of the solution to the system of equations is _______________
PLEASE HELP!! :) :)
Answers
2x+3y= 2
-2x + 2y = 8
2x + 3y = 2
5y = 10
y= 2
-x + 2 = 4
-x = 2
x = -2
what is the store policy at pastic mart
Answers
Hope this helped!
Mrs. Conley asks her class what kind of party they want to have to celebrate their excellent behavior. Out of all the students in the class, 5 want an ice cream party, 7 want a movie party, 10 want a costume party, and the rest are undecided. If 20% , percent want an ice cream party, how many students are in the class?
Answers
5 x 5 = 25
There are 25 students in the class, 3 are undecided.
Elise is entering a team into a 5-kilometer race. The cost for entry is $15 for a team and an additional $2 per member. The total cost can be modeled by the equation -2x + y = 15, where x is the number of members on the team and y is the total cost. What is the total cost if Elise has 5 members on her team?
Answers
After substituting the number of members into the equation and solving for the total cost, Elise's 5-member team's entry fee into the race is $25.
Explanation:The total cost of entering a team into a 5-kilometer race can be modeled by the linear equation -2x + y = 15, where x is the number of members on the team and y is the total cost. To calculate the total cost for Elise's 5-member team, we need to substitute x = 5 into the equation and solve for y.
First, we multiply the number of members by the additional cost per member: 5 members × $2/member = $10. Then, we add the team entry fee to get the total cost: $15 (team entry) + $10 (members) = $25. Therefore, the total cost for Elise's team is $25.
Final answer:
To find the total cost for Elise's team of 5 members, substitute x=5 into the equation -2x + y = 15 and solve for y to get the total cost of $25.
Explanation:
The student's question involves finding out the total cost of entering a team in a 5-kilometer race with a given equation that models the costs based on the number of team members. The equation provided is: -2x + y = 15, where x is the number of members on the team, and y is the total cost. To find the total cost for Elise's team that has 5 members, we replace the variable x with the number 5 in the equation and solve for y:
-2(5) + y = 15
-10 + y = 15
y = 25
The total cost for Elise to enter a team with 5 members in the race is $25.
The blue figure is a dialation image of the black figure. The labeled point is the center of dilation. Tell wheaten the dilation is a enlargement or a reduction. Then find the scale factor of dilation
Answers
The dilation's scale factor will be 1/4.
The division method is used to divide a bunch of items into equal portions.
Division is the inverse of multiplication. For instance, dividing 20 by 2 means dividing 20 into two equal groups of ten.
Given this,
The blue figure is a magnified version of the black one.
Furthermore, the origin is the center of dilatation.
Now,
Because the blue figure is a dilatation of the black one.
Furthermore, the origin is the center of dilatation.
In this case, the length of the black figure equals 16 units.
Furthermore, the length of the blue figure equals 4 units.
As a result, the dilation scale factor is 4/16.
= 1/4
solve 30 - 9.8x
A.) x = 39.8
B.) x = 20.2
C.) x = 3.06
D.) x = 0.33
Answers
x = 30 / 9.8
x = 3.06
Answer is C
Answer: x = 3.06
Step-by-step explanation:
You do 30 divided by 9.8 and you get 3.06
Joe can buy a pair of canvas shoes for $7 or a pair of leather shoes for $35. At these prices, what is the ratio of the cost of 6 pairs of canvas shoes to the cost of 3 pairs of leather shoes?
A. 1/10
B. 1/5
C. 2/5
D. 2/15
E. 3/10
Answers
Final answer:
The ratio of the cost of 6 pairs of canvas shoes to the cost of 3 pairs of leather shoes is D. 2/5.
Explanation:
To find the ratio of the cost of 6 pairs of canvas shoes to the cost of 3 pairs of leather shoes, we need to calculate the total cost of each option.
For 6 pairs of canvas shoes, the cost is $7 per pair, so the total cost is 6 x $7 = $42.
For 3 pairs of leather shoes, the cost is $35 per pair, so the total cost is 3 x $35 = $105.
Therefore, the ratio is $42 : $105, which simplifies to 2/5.
What are the coordinates of point Q after this reflection
-8,3
-8,-3
-3,-8
8,3
Answers
Q = (x, y) = (- 8, 3)
A reflection of the figure on the x axis is given by the following rule:
(x, y) ----> (x, -y)
Applying the transformation:
(-8, 3) ---> (- 8, -3)
Answer:
the coordinates of point Q after this reflection are
-8, -3
The new coordinates of Q are (-8, -3).
When reflecting a point across the X-axis, the X-coordinate remains unchanged, while the Y-coordinate changes its sign. From the figure attached, we find coordinates of Q are (-8,3). Therefore:
The X-coordinate of Q remains as -8.The Y-coordinate of Q changes from 3 to -3.As a result, the coordinates of point Q after reflection along the X-axis will be (-8, -3).
Therefore, the new coordinates of point Q are (-8, -3).
What is 0.673 rounded to the nearest hundredths
Answers
Hope this helps
0.673 rounded to the nearest hundredth as 0.67
The digit in the smallest location is unaffected if it is less than 5 in number. Rounding down is the process of reducing a number to zero after a certain number of digits. The digit in the smallest location is added with +1 if it is bigger than or equal to 5.
To round off 0.673 to the nearest hundredth means hundredth digit after decimal, To do so take a look on the thousandth digit after decimal, If it is greater than 5 or equal to 5 increase the hundredth digit after decimal by 1 otherwise no change,
Here, the thousandth digit is 3, 3<5. So, no increment is required.
It will remain as 0.67.
Thus, 0.673 is 0.67 after rounding off to the nearest hundredth.
Learn more about round off, here:
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Help!right answer and best explanation gets brainliest
Answers
Can I get some help
Answers
Let's start with our initial value. Our initial value is 40 dollars, it is always added as it was how much was originally in our account.
So far, we have:
y = 40 + ??
Now, since we know that they deposit 18 dollars owe Monday or per week, we know what we can always multiply 18 by how many weeks there are to get how much additional money was added. We have:
y = 18w + 40
Hope this helps!
Which of the following is not good advice for reducing sibling rivalry?
Avoid comparing yourself to a sibling.
Focus on your own achievements.
Try to reduce conflicts fairly.
Have daily debates.
Answers
Answer: Have daily debates.
Step-by-step explanation:
Please help with this one math question?
Answers
Which polynomial is a quintic binomial?
x^(4)+2x^(3)-x^(2)+7x+11
x^2+4x
3x^5+2
5x^2-2x+1
Answers
binomial means the expression has two terms.
the third choice is the answer.
The correct answer is x^(4)+2x^(3)-x^(2)+7x+11
△ XYZ∼ △ DEF, YZ is 10 meters, XZ is 15 meters, and EF is 8 meters. What is DF?
Answers
△ XYZ∼ △ DEF, YZ is 10 meters, XZ is 15 meters, and EF is 8 meters. What is DF?
Solution:
As, △ XYZ∼ △ DEF , so the ratio of sides of triangle is equal.
So, we have, [tex] \frac{XY}{DE} =\frac{YZ}{EF} =\frac{XZ}{DF} [/tex]
Using, [tex] \frac{YZ}{EF} =\frac{XZ}{DF} [/tex]
So, we get,[tex] \frac{10}{8} =\frac{15}{DF} [/tex]
Now, to solve for DF, we must simplify
Simplifying,[tex] \frac{10}{8} =\frac{5*2}{4*2}=\frac{15}{DF) [/tex]
[tex] \frac{5}{4} =\frac{15}{DF} [/tex]
To simplify, Let us multiply by 4*DF on both sides
[tex] \frac{5*4DF}{4} =\frac{15*4DF}{DF} [/tex]
[tex] \frac{5DF}{1} =\frac{15*4}{1} [/tex]
So, 5 DF=15*4=60
To solve for DF, let us divide by 5 on both sides
[tex] \frac{5}{5} DF=\frac{60}{5} [/tex]
[tex] \frac{1}{1} DF=\frac{12}{1} [/tex]
So, DF=12meters
The area of a rectangle is 9.312 x 104 cm2 and the width is 2.56 x 102 cm. What is the length? A) 3.6375 x 102 B) 3.6375 x 106 C) 6.752 x 102 D) 6.752 x 106
Answers
length = Area/width
= (9.312*10^4)/(2.56*10^2) = 3.6375*10^2 . . . cm
Selection A is appropriate.
_____
You already knew that before you even touched your calculator. 10^4/10^2 = 10^2, so only answers A and C should be considered. 9.3/2.6 < 4.5, so only answer A should be considered.
The beauty of scientific notation for numbers is it helps you estimate the result of multiplication and division easily. For many problems, you don't need the actual answer as much as you need the ballpark in which the answer resides.
Step-by-step explanation:
For USATestprep people.
what is the classification for this polynomial?
4
Choices:
A. Monomial
B. Binomial
C. Trinomial
Answers
a polynomial can be name by how many terms in it, POLYnomial, POLY=many, now, this is just one, MONO=one, MONOmial.
What are the coordinates of the vertex for f(x) = x2 + 6x + 13?
A. (4, 4)
B. (−4, 4)
C. (3, 4)
D. (−3, 4)
Which of the following is a factor of 5x3 + 320?
A. 5
B. x+4
C. x^2-4x+16
D. All of the above
Answers
c = (b/2)2 = (6/2)2 = 9
x2 + 6x + 9 + 4
(x+3)2 +4
so the vertex is at: (-3, 4), D)
Find the prime factorization of 60
Answers
[tex]2(2) = 4(3) = 12(5) = 60 [/tex]
[tex]2^2 =4 = 4(3) =12(5) = 60 [/tex]
They are both prime factorization of [tex]60[/tex]
But, if you had to choose one then pick:[tex] 2*2*3*5[/tex] (the first option)
Good luck on your assignment and enjoy your day!
~LoveYourselfFirst:)
What are the solutions of the equation?
15+IXI=26
Choose all answers that are correct.
–41
–11
11
41
Answers
A) –6n + 2mn – 25np
B) –6n + 2m – 25np
C) –6n – 2mn + 25np
D) –24n + 8mn – 100np
Answers
Since we have different variables and we CANT combine our like terms of this problem, we would have to do them separately (but multiply everything by [tex] \frac{1}{4} n[/tex] )
[tex] \frac{1}{4} n (-24 + 8m - 100p )[/tex]
[tex] \frac{1}{4}n(-24) \\ \\ \\ \frac{1}{4}n (8m) \\ \\ \\ \frac{1}{4} n (100p)[/tex]
Your answer: [tex]-6n + 2mn + 25np[/tex] ( option A. seem closer)
Good luck on your assignment and enjoy your day!
~[tex]LoveYourselfFirst:)[/tex]
Brian has reduced his cholesterol level by 16% by following a strict diet and regular exercise. If his original level was 260, what is his approximate cholesterol level now?
Answers
=260 - (260 * 16%)
=269 - (260 * 0.16)
=260 - 41.6
=218.4 new cholesterol level
ANSWER:
His new cholesterol level is 218.4.
Hope this helps! :)
Answer:
218.4
Step-by-step explanation:
Dolbear's law states the relationship between the rate at which Snowy Tree Crickets chirp and the air temperature of their environment. The formula is Upper T equals 50 plus StartFraction Upper N minus 40 Over 4 EndFractionT=50+ N−40 4, where T is a temperature in degrees Fahrenheit and N is a number of chirps per minute. If Nequals=9898, find the temperature in degrees Fahrenheit, T.
Answers
We have then:
T = 50 + (N-40) / 4
We substitute the value of N = 98, we have then:
T = 50 + (98-40) / 4
T = 64.5 degrees Fahrenheit.
Answer:
the temperature in degrees Fahrenheit, T is:
T = 64.5 degrees Fahrenheit.
The temperature in degrees Fahrenheit, T is 68°F.
Dolbear's law states that the number of chirps per minute that a snowy tree cricket makes is related to the air temperature in degrees Fahrenheit by the following formula:
T = 50 + (N - 40)/4
where:
T is the temperature in degrees Fahrenheit
N is the number of chirps per minute
If N = 98, then the temperature is:
T = 50 + (98 - 40)/4 = 68 degrees Fahrenheit
So the answer is 68 degrees Fahrenheit.
Here is an explanation of the calculation:
We are given that N = 98 chirps per minute.
We substitute this value into the formula for Dolbear's law to get:
T = 50 + (98 - 40)/4 = 68 degrees Fahrenheit
Therefore, the temperature is 68 degrees Fahrenheit.
Here are some additional things to consider:
The number of chirps per minute that a snowy tree cricket makes is not always an accurate measure of the air temperature. The number of chirps can also be affected by other factors, such as the humidity and the time of day.
Dolbear's law is a simplified model of the relationship between the chirping rate of snowy tree crickets and the air temperature. The actual relationship is more complex and can be affected by a number of factors.
To learn more about temperature here:
https://brainly.com/question/7510619
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Cody filled a container with 8 1/4 quarts of iced tea. How many 1/4-quart glasses can be served from the container?
A. 2 1/16
B. 16 1/2
C. 4 1/8
D. 33
Answers
Tell me if you want to know how it's done :)