Answer:
_______________________________________
→ x = - 1 ± i√7 ;
4
_______________________________________
Or: Write as:
_______________________________________
→ x = -1 + i√7 ; -1 − i√7 ;
4 4
_______________________________________
Step-by-step explanation:
_______________________________________
Given:
-2x² − x − 1 = 0 ;
Solve for " x " .
________________
First, let us multiply BOTH sides of the equation by "-1" ;
to get rid of that "negative sign" in the coefficient: " -2" ;
→ as follows:
________________
-1 * {-2x² − x − 1 } = 0 *{-1} ;
_________________
Rewrite the value: "x" on the "left-hand side" of the question; as: "1x" ;
since "any value" ; multipled by "1" ; results in that same individual value:
_________________
-1 * {-2x² − 1x − 1 } = 0 *{-1} ;
________________
Note the "distributive property" of multiplication:
________________
a(b + c) = ab + ac ;
________________
Likewise, from the "left-hand side" of the equation:
-1 * {-2x² − 1x − 1 } = {-1 * -2x²} + {-1 * -1x} + {-1* -1 } ;
= 2x² + 1x + 1 ;
_______________________________________
Rewrite the "left-hand side" of the equation:
2x² + 1x + 1 ;
Now, the "right-hand side of the equation:
" { 0 * -1 } = 0 " .
Now, rewrite the entire equation:
2x² + 1x + 1 = 0 ;
________________
Note: This equation is written in "quadratic format" ;
that is: " ax² + bx + c " ; [a ≠ 0] ;
→ in which:
a = 2 ; b = 1 ; c = 1 ;
________________
→ which means we can solve for the value(s) for "x" ; by using the
"quadratic equation formula" ;
→ that is:
________________
→ x = -b ± √(b² − 4ac) ;
2a
________________
So; to solve for the values for "x" ; we substitute our known values for:
"a" ; "b" ; and "c" ; and solve:
________________
→ x = -1 ± √(1² − 4*2 *1) ;
4
_________________________
→ x = -1 ± √(1 − 8) ;
4
_________________________
→ x = -1 ± √(-7) ;
4
_________________________
Note: "√(-7)" ; is the square root of a negative number.
Note that we use the lower case letter, " i " ;
as a symbol to represent the imaginary number: " √(-1) " .
This is an "imaginary number" ; since one cannot take the "square root" of a "number lower than zero."
So, we write: √-7 ; as: " i * 7 " ; or, just: " i √7 " ; since:
"i = √-1" ; and since: " √-7" would "factor out" to: "√7 * √-1 " .
_________________________
Note: In the mainstream U.S.A. , the concept of " i " as the "imaginary number" — " √-1 " ; is usually introduced in the second year college-prep algebra class (after "first year high school algebra" in 9th grade; and after "geometry" in 10th grade).
_________________________
So; we have:
→ x = -1 ± √(-7) ;
4
___________
We can rewrite this as:
____________
→ x = -1 ± i√7 ;
4
_____________
We can leave our answer written like that.
We have two (2) solutions—so we can also write out both solutions for the value of x:
_____________
→ x = -1 + i√7 ; -1 + i√7 ;
4 4
_____________________________________________
Hope this explanation is helpful to you!
Best of luck— and best wishes!
_____________________________________________
A square pyramid has a base of total area of 144 m square root 2 and a volume of 384m cubic what is the slant height of the pyramid?
Answer:
Slant height of the pyramid = 11.66 m
Step-by-step explanation:
A squad pyramid has a volume of
V = ⅓ × (area of base) × (vertical height)
Area of the pyramid's square base = 144 m²
Volume = 384 m³
384 = ⅓ × 144 × (vertical height)
Vertical height = (3×384)/(144) = 8 m
But, the slant height of the square based pyramid forms a right angled triangle with the vertical height of the pyramid and the distance from the centre of the base of the pyramid to an edge of the pyramid.
The distance from the centre of the base of the pyramid to an edge of the pyramid = half of the length of the diagonal of the square base of the pyramid.
The diagonal of the square base of the pyramid also forms a right angled triangle with two sides of the square base of the pyramid.
Area of the square base of the pyramid = 144 m²
Area of a square = (side length)²
Side length = √(Area of the square) = √144 = 12 m
Using Pythagoras theorem,
(Length of the diagonal)² = 12² + 12² = 288
Length of the diagonal = (12√2) m
Half of the length of the diagonal of the square base = 6√2 m
Using Pythagoras theorem further
(Slant height of the pyramid)² = (vertical height of the pyramid)² + (Half of the length of the diagonal of the square base)²
(Slant height of the pyramid)² = 8² + (6√2)² = 64 + 72 = 136
Slant height of the pyramid = √136 = 11.66 m
Hope this Helps!!!
What is the way to best choose the answers
Find the length of the diagonal of an 8cmx 6cmx 10cm rectangular prism. Round to the nearest tenth. (HELP PLEASE!!)
Answer:
14.1 cm
Step-by-step explanation:
first find the base diagonal :
base di = Square root (8^2 + 6^2) = 10cm
so,
diagonal = Square root (10^2 + 10^2) = 14.1 cm (ANS)
Observe a sequência de figuras a seguir.
Considerando que a lei de formação permanecerá a mesma, a figura que ocupará a posição 53a na sequência dada, será:
Answer:
C) Equal to the figure in position 3.
Step-by-step explanation:
Assume the sequence of figures is like the one below.
The pentagons differ in the number of stars in the sequence:
1, 2, 3, 4, 5, 1, 2, 3, 4, 5…
The sequence repeats after the fifth term.
To find the 53rd term, find the remainder for 53 ÷ 5.
53 ÷ 5 = 10, with a remainder of 3.
This tells you there are ten complete sequences (50 numbers), and three more numbers.
The 53rd term is 3, so
The figure that will occupy position 53 in the sequence is equal to the figure in position 3.
help meh
A timer rings every half hour for 3 1/2 hours.
Use your model to determine the number of rings.
dont make me feel like that was a waste
Answer:
7 times
Step-by-step explanation:
So since it rings every half hour, there should be 2 rings every hour, if not you are not on our planet. (60 mins in an hour, 30 mins = 1, so 60 mins =2)
So since it rings for 3 full hours, we get an initial step of 3 * 2 = 6 rings
Then there is another 1/2 ring because 3 and a 1/2 hours. So 6+1=7
hope i helped :) im not sure what you mean by model :(
A square unit that is 1 unit wide and 1 unit long is a?
Answer:
A square with side length 1 unit, called 'a unit square,' is said to have 'one square unit' of area, and can be used to measure area.
A set of cards with a letter on each card as shown below are placed into a bag. Howard picks a card at random from the bag.
Determine the probability that the card is an E
Answer: 1/10 or 10%
Step-by-step explanation:
The required probability that the card is an E will be 0.1%.
What is probability?A Probability can be defined as the ratio of favorable outcomes to the total number of events.
P(E) = Number of favorable outcomes / total number of outcomes
A set of cards has sample = U E A R Q H C H L A
Total number of sample s(n) = 10
We need to find the probability that the card is an E
For probability for E,
p(E)= 1 / 10 = 0. 1%
Thus, the required probability that the card is an E will be 0.1%.
Learn more about probability here:
brainly.com/question/14290572
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21 radical sign p^-4/p^3
Answer: [tex]p^-^\frac{1}{3}[/tex]
[tex]\sqrt[21]{\frac{p^-^4}{p^3} }[/tex]
[tex]\sqrt[21]{p^-^4^-^3}[/tex]
[tex]\sqrt[21]{p^-^7}[/tex]
[tex]\sqrt[21]{\frac{1}{p^7}}[/tex]
[tex]\frac{\sqrt[21]{1} }{\sqrt[21]{p^7} }[/tex]
[tex]\frac{1}{p^\frac{7}{21} }=\frac{1}{p^\frac{1}{3} }=p^-^\frac{1}{3}[/tex]
Value of x explain how you found the value of x
Answer:
A) 25
Step-by-step explanation:
Set the ratios. Place the similar sides equal to each other.
Sides:
AB/CB = XY/ZY
Plug in corresponding numbers to the corresponding sides:
50/40 = x/20
Simplify. Divide 2 from both the numerator and denominator of the first fraction to get common denominators:
(50/40)/(2/2) = 25/20
25/20 = x/20
x = 25
A) 25 is your answer.
~
Answer: A 25
Step-by-step explanation:
Is Y=5x+2 in slope intercept form?
Answer: yes, the equation [tex]y = 5x +2[/tex] is a slope-intercept form.
Step-by-step explanation:
-The equation of a slope-intercept form:
[tex]y = mx + b[/tex] (where [tex]m[/tex] represents the slope, and [tex]b[/tex] represents the y-intercept).
your garden has a perimeter of 36 feet. what is the length of missing side.
Answer:
I think the answer is 3 for 1 length side. And in you need 12 for both length sides. So the total is 36 and one side is 12. Since it's a rectangle,you now know two side lengths since they are the same,just opposite from each other. So 12 + 12 = 24. You do 36 – 24 because you need to get the total number for length which is 12. 12 divided by 2 is 6 which is one length side. You can check by doing 6 + 6 + 12 + 12 and you get 36.
Hope this helped!
Can I get brainliest?
Find the volume of the figure. Use 3.14 for pi.
Answer:
10082.36cm²
Step-by-step explanation:
The formula for volume of a cone: V = [(3.14) r²](h/3)
Steps:
1. Find the value of the radius: 1/2 of the diameter (26/2) = 13cm
2. Find the value of the height: 31cm
3. Plugin: [(3.14) 13²] (31/3)
Solve for the volume of the cone:
a) 13² = 169
b) 169(pi) = 530.66
c) 530.66 (31/3) = 530.66 (10.3333)
Volume of cone: 5483.31
The formula for volume of hemisphere is 1/2[(4/3)3.14{r³}]
Steps:
1. Find the value of the radius: 13cm
2. Solve for the volume of the hemisphere
1. 13x13x13 = 2197
2. 2197 (3.14) = 6898.58
3. (4/3) 6896.58 = 9198.1067
4. (1/2) 9198.1067 = 4599.05
Add the two volumes together:
4599.05+5483.31 = 10082.36cm²
This took forever since I used the google calculator, but it got done after forever! Hope this helps!
The Volume of the figure is 10,082.53 cm³.
What is Volume?Volume is a three-dimensional quantity used to calculate a solid shape's capacity. That means that the volume of a closed form determines how much three-dimensional space it can fill.
Volume is a three-dimensional quantity used to calculate a solid shape's capacity.
We have a cone surmounted by Hemisphere.
So, Volume of Figure
= Volume of Cone + Volume of Hemisphere
= 1/3 πr²h + 2/3 πr³
= 1/3 x 3.14 x 13 x 13 x 31 + 2/3 x 3.14 x 13 x 13 x 13
= 5,483.48 + 4,599.05
= 10,082.53 cm³
Learn more about Volume here:
https://brainly.com/question/1578538
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Ella spends $4.25 each day for lunch at school. How much money does she spend on lunches for 5 days?
Answer:
21.25
Step-by-step explanation:
Answer:
21.25
Step-by-step explanation:
4.25x5=21.25
You buy a basket of 24 strawberries. You eat them
as you walk to the beach. It takes the same amount of time to walk
each block. When you are halfway there, half of the berries are gone.
After walking 3 more blocks, you still have 5 blocks to go. You reach
the beach 28 minutes after you began. One-sixth of your strawberries
are left.
a. Is there enough information to find the time it takes to walk each
block? Explain.
b. Is there enough information to find how many strawberries you
ate while walking the last block? Explain.
Answer:
yes
Step-by-step explanation:
there is enough information
In the given figure, arcWY = 76° and arcXZ = 112°. What is the difference of the measures of angle WPY and angle XPY?
A. 8°
B. 9°
C. 16°
D. 18°
Answer:
C
Step-by-step explanation:
Answer:
A. 8
Step-by-step explanation:
#platolivesmatter
Find the area of the shape shown below
Which of the following statements is true for inverse functions ƒ(x) and g(x)?
Question 1 options:
A)
(ƒ ∘ g)(x) = (g ∘ ƒ)(x) = x
B)
(ƒ ∘ g)(x) = (g ∘ ƒ)(x) = 0
C)
(ƒ ∘ g)(x) = (g ∘ ƒ)(x) = 1
D)
(ƒ ∘ g)(x) = (g ∘ ƒ)(x) = ƒ(x)
Answer:
A
Step-by-step explanation:
Given: functions f(x) and g(x)
To choose: the correct option
Solution:
A function is a relation in which each element of the domain has a unique image in the co-domain.
Composition of functions refers to the combining of two or more functions such that the output of one function becomes the input for the next function.
Two functions f(x) and g(x) are inverse functions if (ƒ ∘ g)(x) = (g ∘ ƒ)(x) = x.
Answer:
A) (ƒ ∘ g)(x) = (g ∘ ƒ)(x) = x
Step-by-step explanation:
help please! ill mark brainliest
Answer:
A=150ft^2
Step-by-step explanation:
A=(b1+b2)/2*h
A=(15+10)/2*12
A=25/2*12
A=25*6
A=150ft^2
Area of trapezoid formula: A = h(b1+b2/2)
A = 12(10+15/2)
A = 12(25/2)
A = 12(12.5)
A = 150
Therefore, the area of the trapezoid is 150ft²
Best of Luck!
Fiona and Pip win some money and share it in the ratio 3:1. Fiona gets £30. How much did
they win in total?
Answer:
£40
Step-by-step explanation:
£30 represents 3 parts of the ratio that Fiona got.
Divide £30 by 3 to find the value of one part of the ratio
£30 ÷ 3 = £10 ← value of 1 part of the ratio
They won £30 + £10 = £40
A playground is located on a triangular piece of land. Two sides of the playground are 157 feet long and they meet at an angle of 65°. Your are hired to build a fence around the playground. Find the cost of the fencing material needed if it will cost $11.75 a foot.
Answer:
$5,671.84
Step-by-step explanation:
To find the third side, we can use the law of cosines:
c^2 = a^2 + b^2 - 2ab*cos(theta)
c^2 = 157^2 + 157^2 - 2*157*157*cos(65)
c^2 = 28463.7649
c = 168.71 feet
The perimeter of the playground is:
P = 157 + 157 + 168.71 = 482.71 feet
If each foot costs $11.75, the final cost is:
Cost = 482.71 * 11.75 = $5,671.84
Help!!! multiple choice!
I need help in fractions
Answer:
I’ll help you just show me the question
Step-by-step explanation:
describe the relationship between 45 stundents and 15 stundents
Sonji has $5.25 in nickels and dimes.The coin value can be modeled by the equation 0.10 d plus 0.05 n equals 5.25, where d represents the number of dimes and n represents the number of nickels. If Sonji has 21 dimes, how many nickels does she have?
Answer:
To find the number of nickels and dimes, we can use this equation: 0.10d + 0.05n = 5.25
We are given the information that Sonji has 21 dimes (which means that d=21). We can use the equation to find the number of nickels n.
0.10d + 0.05n = 5.25
0.10(21) + 0.05n = 5.25
2.10 + 0.05n = 5.25
0.05n = 3.15
n = 3.15 / 0.05
n = 315 / 5
n = 63
Sonji has 63 nickels.
Let's check our answer.
21(0.10) + 63(0.05) = 2.10 + 3.15 = 5.25
It seems that our answer is correct.
Step-by-step explanation:
Answer:
she has 63 nickels
Step-by-step explanation:
21 dimes = 2.10$
5.25 - 2.10 = 3.15
3.15 ÷ 0.05 = 63
63 = 63 nickles
Hope this helped :3
Bryant collects a set of 20 values that represent the lengths of worms he found in the garden. The variance of the set of values is 36.
What is the standard deviation from the mean? Round the answer to the nearest tenth if necessary.
4.5
6
14
15.5
Answer:
The standard deviation from the mean is the square root of the variance.
Therefore, SD = sqrt(VAR) = sqrt(36) = 6
Hope this helps!
:)
:PROBLEM Bryant collects a set of 20 values that represent the lengths of worms he found in the garden. The variance of the set of values is 36.
QUESTION. What is the standard deviation from the mean? Round the answer to the nearest tenth if necessary.
RESULUTIONS
4.5
6
14
15.5
ANSWER.=6
-3(x + 4) = 6(-x - 1)
Answer: x = 2
Step-by-step explanation:
Answer:
x=2
Step-by-step explanation:
-3(x+4)=6(-x-1)
1. Distribute
-3x+(-12)=-6x-6
-3x-12=-6x-6
3x-12=-6
3x=6
x=2
En un informe se dice que la temperatura minima pronosticada es de -24°C y la maxima de -20°C . Si la temperatura minima representa mas frio que la temperatura maxima,¿no deberia figurar al reves?. Expliquen su respuesta.
Answer:
Check Explanation
Step-by-step explanation:
English Translation
In a report it is said that the predicted minimum temperature is -24 ° C and the maximum is -20 ° C. If the minimum temperature represents colder than the maximum temperature, should it not appear on the reverse? Explain your answer.
Solution
No, it shouldn't appear on the reverse. This is because, just as negative numbers work, they decrease, the further we move away from 0.
Celsius temperature scales are calibrated with respect to the freezing point of water. The freezing point of water serves as the reference point and is called the 0°C.
Temperatures higher than the freezing point of water taken on positive values and temperatures lower, take on negative values. The lower the temperature, the bigger the absolute value of the negative value is.
For example, just like In the question provided, -24°C represents a temperature that is 24° lower than the freezing point of water while -20°C represents a temperature that is 20° lower than the freezing point of water. It is evident that -24°C really is a lower temperature than -20°C.
Hope this Helps!!!
Help me pleaseee someone
Answer:
55°
Step-by-step explanation:
All triangles have a sum of 180°
180 - (35 + 90) = angle B
180 - (125) = angle B
55 = angle B
So, angle B has a measurement of 55°
What are the coordinates of point L?
Answer:
(1, -3)
Step-by-step explanation:
Start where the axes meet. That is the origin (0,)
Move 1 place to the right that is the x coordinate
Move 3 places down that is the y coordinate
(1,-3)
determine whether the function represented by the equation is quadratic
Answer:
not quadratic because there is not a quadrat in it.
Step-by-step explanation:
The graph of a quadratic funtion is a parabola.
The general form of quadratic function is this:
f(x) = ax² + bx + c
Where a, b, and c are numbers.
Please uderstand that a can not be zero, which means that any quadratic function has at least one term with ² in it.
In this example, there is no quadrat visible, so it is not quadratic. By the way, y = -9x + 19 is a so called linear equation. It's graph is a line.
