Answers
Answer+Step-by-step explanation:
1)
[tex]x^{2}+4x+1=x^{2}+4x + (4 - 4) + 1[/tex]
[tex]=x^{2}+4x + 4 - 3[/tex]
[tex]=(x+2)^2-3[/tex]
then
[tex]x^{2}+4x+1=0[/tex]
[tex]\Longleftrightarrow \left( x+2\right)^{2} -3=0[/tex]
[tex]\Longleftrightarrow \left( x+2\right)^{2} =3[/tex]
2)
[tex]\left( x+2\right)^{2} =3[/tex]
⇔ |x + 2| = √3
⇔ x + 2 = √3 or x + 2 = -√3
⇔ x + 2 = ±√3
⇔ x = -2 ± √3
Related Questions
I need help with this math problem brainliest for the best answer
Answers
Answer:
It is the first one
Hope this helps!
Answer:
I believe it is 4x+10y=200, x+y=38
Explanation:
According to the box-and-whisker plot shown above, what are the following:
6. The median?
7. The first quartile?
8. The third quartile?
9. The minimum value?
10. The maximum value?
Please help me 6 threw 10 i been asking for help forever i sent in the box
Answers
Answer:
median: 80
first q: 60
third q: 100
min: 40
max: 110
Step-by-step explanation:
The median is the middle (piece of data), the middle line in the box. Min is smallest number. Max is biggest number. First quartile is the left side of the box. Third quartile is right side of box.
If f(x) = 5x, what is ƒ¹ (x)?
Answers
Answer:
15,625
Step-by-step explanation:
If f(x) = 5x then f ¹ you must label all numbers in the equation to make it easier, once done you will have 25(5¹)=125¹
125x125=15,625
The inverse function of the given function is x/5.
What is inverse function?Inverse function is represented by f⁻¹ with regards to the original function and the domain of the original function becomes the range of inverse function and the range of the given function becomes the domain of the inverse function. The graph of the inverse function is obtained by swapping (x, y) with (y, x) with reference to the line y = x.
Given that, f(x)=5x
Now, y=5x
Replace x by y and y by x, we get
x=5y
y=x/5
and f⁻¹(x)=x/5
Therefore, the inverse function of the given function is x/5.
Learn more about the inverse function here:
https://brainly.com/question/2883051.
#SPJ7
During normal breathing, about 12% of the air in the
lungs is replaced after one breath. If the initial amount of
air in the lungs is 500 mL, how much of the original air is
present after 8 breaths?
Answers
The original air present after 8 breaths will be equal to 179.81 ml.
What is an equation?
The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.
It is given in the question that:-
During normal breathing, about 12% of the air in the lungs is replaced after one breath
If the initial amount of air in the lungs is 500 mL
how much of the original air is present after 8 breaths?
The calculation for the eduction of the air will be done by the following equation:-
[tex]\rm =Volume \ present\times (0.88)^n\\\\\\= 500\times (0.88)^8[/tex]
=179.88 ml
Hence original air present after 8 breaths will be equal to 179.81 ml.
To know more about equations follow
https://brainly.com/question/2972832
#SPJ1
Answer:
8 breathes = 179.81 ml.8 breathes = 179.81 ml.8 breathes = 179.81 ml.8 breathes = 179.81 ml.8 breathes = 179.81 ml.8 breathes = 179.81 ml.8 breathes = 179.81 ml.8 breathes = 179.81 ml.8 breathes = 179.81 ml.8 breathes = 179.81 ml.Step-by-step explanation:
Which graph shows a negative slope and a positive y-intercept?
Answers
Answer:
The last one ( bottom left)
Step-by-step explanation:
negative slope means the line is going downwards
positive y intercept means the line hits the y axis on a positive number
Which, if any, of the following are solutions to the equation
y = 3x + -2?
A. (0,2),
B. (1.5)
C. (2,0)
D. (2,3)
E. (3,2)
F. (5,1)
G. None are solutions
Answers
Answer:
I think none are solutions
Which one of these numbers is a composite number a.17 b.51 c.97 d.89
Answers
Step-by-step explanation:
The correct answer here is 51
[tex]\rule{300}{1}\\\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]
Which one of these numbers is a composite number: 17, 51, 97, or 89?
[tex]\dashrightarrow\large\textsf{\textbf{\underline{Answer and how to solve:-}}}[/tex]
Composite numbers are divisible by 3 or more numbers.
17 is divisible by 1 and 17 only, so it's not composite.
51 is divisible by 1, 51, 3, and 17, so it's composite.
97 and 89 are divisible by two numbers only, so they are not composite.
So we conclude that the answer is
51
Good luck with your studies.[tex]\rule{300}{1}[/tex]
Paul drove for one and a half hours at 65 mph before he realized he had forgotten his wallet. After Paul drove home and grabbed the wallet, he realized that he had only three hours to go one hundred eighty miles. At what speed should he drive to cover the distance in time?
Answers
Noah bowled 3 games for his bowling team. in the second game, he scored 10 points more than in the first game; in the third game, he scored 10 points more than in the second game. his average score was 230 points for the 3 games. how many points did noah score in the third game?
Answers
Answer:
240 points game 3
Step-by-step explanation:
use what is given and put everything in variable terms since this asks for the average, you have to divide by the number of games in the end
Use the GCF and the distributive property to write 18 + 45 as a product.
Answers
Answer:
(6x9) + (9x1)
Step-by-step explanation:
Find the area of the figure. Round to the nearest TENTH.
Answers
Answer:
Step-by-step explanation:
12 multiplied by 9 is 108. That gives us the square. The triangle base is 9. The height is 7. 7 multiplied by 9 is 63. 63 divided by 2 is 31.5. 108 add 31.5 is 139.5 cm squared.
Answer:
A=L*B
=12*9
=108
A=0.5base *H
=0.5(9)*7
=31.5
A=108+31.5
A=139.5
Does anyone knows this? I need help. Please explain
Answers
Answer:
you can put a point on (0,1) and (-1,0) and put a line through the two points
Step-by-step explanation:
Do these sides make a triangle ?
Yes or no
1) 7cm , 11cm , 14cm
2) 10cm , 8cm , 2cm
Answers
Answer:
yesnoStep-by-step explanation:
For three side lengths to form a triangle, the sum of the shorter two must exceed the longest.
__
1)7 + 11 = 18 > 14 . . . . Will make a triangle.
__
2)2 + 8 = 10 . . . not greater than 10. Will not make a triangle.
__
This is a direct consequence of the triangle inequality, which requires for sides a, b, c that ...
a +b > c and b +c > a and c +a > b
_____
Additional comment
There is a version of the triangle inequality that uses the ≥ comparison, rather than >. If that is the version of the inequality you are using, then both these sets of lengths will form a triangle. The second "triangle" will look like a line segment and have zero area.
A water tank has a radius 5 feet and height 11 feet. How much water can it hold?
Answers
The water tank hold 863.50 [tex]ft^{3}[/tex] of water.
What is Volume of cylinder?
The volume of a cylinder is the number of unit cubes (cubes of unit length) that can be fit into it. It is the space occupied by the cylinder as the volume of any three-dimensional shape is the space occupied by it.
The water tank is in the shape of cylinder whose radius = 5 feet
and, height= 11 feet
Volume of water tank =[tex]\pi r^{2} h[/tex]
= 3.14 * 5 * 5 * 11
= 3.14*25*11
= 863.50 [tex]ft^{3}[/tex]
Hence the water tank hold 863.50 [tex]ft^{3}[/tex] of water.
Learn more about Volume of cylinder here:
https://brainly.com/question/16788902
#SPJ1
Find the distance between the pair of points. Give an exact answer and an approximation.
(3,4) and (5,11)
Answers
Answer: [tex]\displaystyle d=\sqrt{53}[/tex]
Step-by-step explanation:
We will use the distance formula to solve. See attached and view the work below.
[tex]\displaystyle d=\sqrt{(x_{2}-x_{1})^2 +(y_{2}-y_{1})^2}[/tex]
[tex]\displaystyle d=\sqrt{(5-3)^2 +(11-4)^2}[/tex]
[tex]\displaystyle d=\sqrt{(2)^2 +(7)^2}[/tex]
[tex]\displaystyle d=\sqrt{4+49}[/tex]
[tex]\displaystyle d=\sqrt{53}[/tex]
Since 53 is prime, this is the simplest form. Since it asks for an exact answer, we are done.
What is the radius of a hemisphere with a volume of 281,250 2.14 cm^3
Answers
Answer:
:
Answer:the radius would be 88cm
Step-by-step explanation:
radius. r = base circumference. C = volume. V = curved surface area.
Given g(x) =(x² +5)/3x find g(p + 4) Please answer with work
Answers
Answer:
g(p + 4) = [p² + 8p + 21 / 3p + 12]
Step-by-step explanation:
Function :
g(x) = (x² + 5) / 3x
Substitute x = p + 4 :
⇒ g(p + 4) = [(p + 4)² + 5] / 3(p + 4)
⇒ g(p + 4) = [p² + 8p + 16 + 5 / 3p + 12]
⇒ g(p + 4) = [p² + 8p + 21 / 3p + 12]
.......................................................
Answers
Answer:
What are we suppose to answer...
I’m literally dy!ng pls help
Answers
Answer:
Option c, G(x) = 12x
Step-by-step explanation:
Vertical stretch occurs when a base graph is multiplied by a certain factor that is greater than 1
In the equation f(x) = mx, the m is acting as the vertical stretch or compression of the identity function.
- f(x) = x by m vertically stretches the graph of f by a factor of m units if
m > 1
- vertically compresses the graph of f by a factor of m units if
0 < m < 1.
This means the larger the absolute value of m, the steeper the slope.
Answer:
Here, the parent should pass through the origin, which is through the coordinate (0,0).
The only function that passes through this (0,0) point and is vertically stretched is only valid is:
y = 12x
Rewrite x2 − 2x − 3 = 0 in the form (x − a)2 = b, where a and b are integers, to determine the a and b values.
A. a = 4 and b = 3
B. a = 3 and b = 2
C. a = 2 and b = 1
D. a = 1 and b = 4
Answers
Answer:
D. a=1 and b=4
Step-by-step explanation:
x^2-2x+(-2/2)^2 =3+(-2/2)^2
x^2-2x+(-1)^2=3+(-1)^2
x^2-2x +1 =4
(x-1)^2=4
Therefore a=1 and b=4
giving the following sequence: 21, 24.5, 28 write an equation for the nth term
Answers
Answer:
tₙ = (3.5x + 17.5)
PLEASE ANSWER NUMBER 30 PLEASE!!
Answers
Answer:
d) x ≤ 3
Step-by-step explanation:
156,161,190,165,172,165,184,168,184,149,169,172,172,178,215,180,165,178,178,182,164,184,187,189,190 in order.
Answers
Answer:
least to greatest: 149,156,161,164,165,165,165,168,169,172,172,172,178,178,178,180,182,184,184,184,187,189,190,190,215
Greatest to least: 215,190,190,189,187,184,184,184,182,180,178,178,178,172,172,172,169,168,165,165,165,164,161,156,149
Step-by-step explanation:
The circle below is centred at O.
AB is a tangent to this circle.
Work out the size of angle y.
Justify your answer.
O
42°
y
A
B
Not drawn accurately
Answers
Answer:
y = 48°
Step-by-step explanation:
angle A = 90°
interior angles of a triangle = 180°
therefore
y = 180 - 42 - 90
y = 48°
[tex] \huge \tt \color{pink}{A}\color{blue}{n}\color{red}{s}\color{green}{w}\color{grey}{e}\color{purple}{r }[/tex]
﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌
❒ Given ❒➣ Mid point of a circle➣ Tangent AB➣ Angle "o" of 42⁰➣ Angle "A" of 90⁰ (cuz it is the perpendicular of traingle given in circle)﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌
❒ Note ❒➣here tangent AB with point O (mid point of circle) forming a traingle➣we have to find "y" in the given figure (angle B)﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌
❒ Concept used ❒➣The sum of interior angles of traingle is of 180⁰➣to find the missing angle ( y ) we will use this theorem➣this Concept is also know as Sum theorem﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌
❒ Assumption ❒➣angle B = y﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌
❒ Let's solve ❒[tex] \large \pmb{➪ \: } \rm \pink{ \angle \: OAB+\angle \:ABO+\angle \:BOA = 180 \degree}[/tex]
➣let's substitute value now .....[tex] \pmb{➪ \: 90 + y +42 = 180 } \\ \pmb{➪ \:132 + y = 180 \: \: \: \: \: \: \: \: }\\ \pmb{➪ \:y = 180 - 132 \: \: \: \: \: \: \: \: }\\ \pmb{➪ \:y = 48 \degree \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }[/tex]
﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌
Hence the size of angle is
[tex] \large \boxed{✥\underline{ \boxed{ \sf{y = 48 \degree \: \pmb{\green{✓}} }}}✥}[/tex]
▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂
Hope it helps !
help pleas for 12 points
Answers
Answer:
126 ft²
Step-by-step explanation:
surface area of rectangular prism: 2(LW + HW + WL)
Here Given:
Length: 9 ftWidth: 3 ftHeight:3 ftSurface Area:
2(LW + HW + WL)2(9*3 +3*3 + 9*3)2(27 +9 + 27)2(63)126height= 3 ft
width= 3 ft
length= 9 ft
to find:the surface area of the given prism.
solution:[tex]s.a = 2(hw + wl + hl )[/tex]
[tex]s.a = 2(3 \times 9 + 3 \times 9 + 3 \times 3)[/tex]
[tex]s.a = 126 \: {ft}^{2} [/tex]
therefore, the surface area of the given prism is 126 square feets.
Solve y-8/3=-7 show work
Answers
Answer: y = -13
Step-by-step explanation:
Given:
[tex]\displaystyle \frac{y-8}{3} =-7[/tex]
Multiply both sides by 3:
[tex]\displaystyle y-8 = -21[/tex]
Add 8 to both sides:
[tex]\displaystyle y= -13[/tex]
Given equation,
y - 8 / 3 = -7Aim :
To find value of y.Cross multiplying them,
>> y - 8 = -7 × 3
>> y - 8 = -21
Transposing -8 from L.H.S. to R.H.S.,
>> y = -21 + 8
>> y = -13
Therefore :
Value of y is -13.If you blend 2 scoops of chocolate ice cream with 1 cup of milk, you get a milkshake with a stronger chocolate flavor than if you blended 3 scoops of chocolate ice cream with 2 cups of milk. Explain or show why.
Answers
Answer:
This is less chocolate ice cream per cup of milk than in the first mixture (2 scoops of chocolate ice cream per cup of milk), so the first mixture has stronger chocolate flavor. 2 scoops of chocolate ice cream with 1 cup of milk will taste the same as 4 scoops of chocolate ice cream with 2 cups of milk.
Step-by-step explanation:
Answer:
If you did 3 scoops of ice-cream and 2 cups of milk you would have 2times the amount of milk and only 1 1/2 times the amount of ice-cream then if you did 1 cup of milk and 2 scoops of ice-cream.
Step-by-step explanation:
To solve this question, we will have to use the aspect of mathematics that is referred to as rates or proportions.
In the first mix, what we have is that we are going to mix 2 scoops of chocolate ice cream with 1 cup of milk. What is noticeable here is that we have 2 scoops of chocolate per 1 cup of milk or there is a 2 to 1 ratio of chocolate ice cream to cup of milk.
Now in the second mix, we are mixing 3 scoops of chocolate with 2 scoops of milk. What we have here is a ratio of 3 to 2. This means that we are having a ratio of 1.5 to 1 of the number of scoops of chocolate ice cream to number of cups of milk.
Looking at this, we can deduce that a 2 to 1 ratio is a greater value compared to a 1.5 to 1 ratio. This is the reason why we are having a stronger chocolate flavor in the first mix than the chocolate flavor in the second mix
Let's find 1/4+1/12
First, write the addition so the fractions have denominator 12.
Then add.1/4+1/12=?/12+1/12=?\?
Answers
Answer:
[tex]\frac{4}{12}[/tex] or [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
[tex]\frac{1}{4} + \frac{1}{12} = \frac{3}{12} + \frac{1}{12} = \frac{4}{12}[/tex]
find the remainder when x³-2x²+4x-2 is divided by (x-1/2)
Answers
Answer:
[tex]\sf \bf {remainder}: -\dfrac{3}{8}[/tex]
In order to find remainder:
Follow this short technique:
Set the divisor which is x-½ to zero.
x - 1/2 = 0
x = 1/2
Then insert this following into dividend.
x³ -2x² + 4x - 2insert x = ½
(½)³ - 2(½)² + 4(½) -2simplify
-3/8Answer:
-3/8
Step-by-step explanation:
Let's assume x - 1/2 is a zero of the polynomial :
Substitute x = 1/2 (the zero) in the equationx³ - 2x² + 4x - 2(1/2)³ - 2(1/2)² + 4(1/2) - 21/8 - 2(1/4) + 2 - 21/8 - 1/2-3/8-3/8 is the remainder.
can someone help me on this question pls and thank you
Answers
Answer:
(c) 2205 cm³
Step-by-step explanation:
The volume of the original prism is the product of its dimensions. The volume of one of two identical pieces will be half that.
__
prism volumeV = LWH
V = (21 cm)(21 cm)(10 cm) = 4410 cm³
piece volumeEach piece will have a volume that is half that:
V = 4410 cm³ ÷ 2 = 2205 cm³ . . . volume of each part