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SOLVING QUADRATIC EQUATIONS
2) Solve 2x2 - 5 = 27
Answer:
x = ±4
Step-by-step explanation:
Step 1: Write out quadratic
2x² - 5 = 27
Step 2: Add 5 to both sides
2x² = 32
Step 3: Divide both sides by 2
x² = 16
Step 4: Take the square root of both sides
x = ±4
∴ x can equal -4 or 4
Answer:
[tex] \boxed{ \bf \huge \: x =4}[/tex]
[tex] \rm \: Or,[/tex]
[tex] \boxed{\bf \huge \: x = - 4}[/tex]
Step by step explanation:
Given Equation is :-
[tex]\sf \implies \: 2 {x}^{2} - 5 = 27[/tex]
We need to find the value of [tex]x[/tex] using Quadric formula.
Firstly, Subtract 27 from both of the side(s):-
[tex]\sf \implies2 {x}^{2} - 5 - 27 = 27 - 27[/tex]
On Simplification:-
Add -5-27 as (-) and (-) equals to (+). -5-27 would be represented as 5+27, which results to 32.
[tex]\sf\sf \implies2 {x}^{2} - 32 = 0[/tex]
Then, for this equation , a=2, b=0, c=-32.
Put the values :-
That is,
[tex]\sf \implies2 {x}^{2} + 0x + ( - 32) = 0[/tex]
As we know, that the quadratic formula is:-
[tex]\sf \implies \: x = \dfrac{ -b \pm \sqrt{b {}^{2} - 4ac } }{2a} [/tex]
Put the values :-
[tex]\sf \implies \: x = \dfrac{ - 0 \pm \sqrt{0 {}^{2} \: - 4(2) ( - 32)} }{2(2)} [/tex]
On Simplification:-
[tex]\sf \implies \: x = \dfrac{ - 0 {}^{} \pm \sqrt{ {0 } - \: 8 \times - 32}}{2 \times 2} [/tex]
[tex]\sf \implies \: x = \dfrac{ - 0 \pm \: \sqrt{ - 8 \times - 32} }{4}[/tex]
[tex]\sf \implies x = \dfrac{ - {0}^{}\pm \: \sqrt{ + 256} }{4} [/tex]
As 0 has no value here,
[tex]\sf \implies \: x = \dfrac{ \pm \sqrt{256} }{4} [/tex]
On cancelling,
Remove the square of 256 ( √256)
[tex]\sf \implies \: x = \dfrac{ \pm \cancel{ \: 256}}{ \cancel4} [/tex]
[tex]\sf \implies \: x = ± + 4[/tex]
It may be represented as,
[tex]\sf \implies \: x = - 4[/tex]
Or,
[tex]\sf \implies \: x = 4[/tex]
_______________________________
I hope this helps!
Please let me know if you have any questions.
~MisterBrian
The XYZ Car Rental Agency charges a flat rate $29 per day plus $0.32 per mile driven Write and algebraic expression for the rental cost of a car for x days that is driven y miles
Can someone help me with my algebra homework and explain how you got it ?
Answer: D
Step-by-step explanation:
This problem seems to ask for the slope of the line. If not by counting, we can use the slope formula to solve. The formula is [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]. Let's use (1,2) and (2,-1).
[tex]m=\frac{-1-2}{2-1} =\frac{-3}{1}=-3[/tex]
Now, we know that the slope is -3.
We also know that A and C are eliminated because the line is going down, which signifies negative. We would be left with B and D. We know that B is incorrect because the slope would be less steep if B were to be the answer. Therefore, D is the correct answer.
1. Round 53.2785 to the nearest tenth
Answer:
53.3
Step-by-step explanation:
One way to do this is to add half a tenth, 0.05, then drop all the digits of the result to the right of the tenths digit.
53.2785 +0.05 = 53.3285
Dropping digits to the right of the tenths place, we have ...
53.3
_____
The effect of this is to increase the tenths digit by 1 if the hundredths digit is 5 or more. That is the usual instruction given for rounding to tenths. (Then drop hundredths and digits to the right.)
10 oz for $2.68
What is the price for
1 oz? |
Write <, >, or = between the pair of numbers to form a true statement.
0.848
0.84800
Even though 0.84800 has two more zeroes at the end, this is still the same number as 0.848.
0.84800 -> 0.848
Therefore, 0.848 = 0.48400
Best of Luck!
Write a cubic binomial with constant -8.
Answer:
27a³ -8
Step-by-step explanation:
A binomial has two terms. If one of the terms is the constant -8, the other must be a cubic term, something with a variable to the third power.
27a³ -8 . . . . . a cubic binomial with a constant of -8
Question 20 of 33
The table below compares the number of lawns Sam mowed with the amount
of money he earned. What is a logical conclusion to make about the amount
Sam would earn for mowing 7 lawns?
Number of lawns mowed
Total money earned
1
$25
3
$75
5
$125
7
?
GUYS I MESSED UP ON THE LAST ONE PLEASE HELP ME AGAIN what algebraic expression represents GK
Answer:
GK = 9x-5
Step-by-step explanation:
GK = GH +HJ + JK
= (GJ - HJ) + (HJ) + (HK - HJ)
= (4x-3-x) + (x) + (6x-2-x)
= 3x-3 + x + 5x-2
= (3x+5x+x)+(-3-2)
GK = 9x-5
My area is calculated by 1/2( base * height), who am I? *
O
square
O triangle
O circle
O sphere
Answer:
Triangle
Step-by-step explanation:
Basically, you have to multiply the base and the height of the triangle, and then divide it by two.
Answer:
O triangle
Step-by-step explanation:
Triangle area = (base*heigth)/2
Consider randomly selecting a student at a large university, and let A be the event that the selected student has a Visa card and B be the analogous event for MasterCard. Suppose that P(A) = 0.6 and P(B) = 0.4.
a. Could it be the case that P(A ∩ B) = 0.5? Why or why not?
b. From now on, suppose that P(A ∩ B) = 0.3. What is the probability that the selected student has at least one of these two types of cards?
c. What is the probability that the selected student has neither type of card?
d. Describe, in terms of A and B, the event that the selected student has a Visa card but not a MasterCard, and then calculate the probability of this event.
e. Calculate the probability that the selected student has exactly one of these two types of cards
Answer:
A)P(A ∩ B) cannot be equal to 0.5.
B)P(A ⋃ B) = 0.7
C)P[(A ∪ B)'] = 0.3
D)P(A ∩ B') = 0.3
E)probability that the selected student has exactly one of these two types of cards = 0.4
Step-by-step explanation:
A) We want to find out if P(A ∩ B) = 0.5
Now, this value is not possible because the probability of intersection of two events can not be greater than the probability of each individual event.
We are told that P(A) = 0.6 and P(B) = 0.4.
Due to the fact that the probability of B is less than 0.4 which is less than 0.5, It means that the intersection of A and B can't be greater than 0.4.
Thus, P(A ∩ B) cannot be equal to 0.5.
B) Now, P(A ∩ B) = 0.3
The probability that the selected student has at least one of these two types of cards would be P(A ⋃ B)
Now, this is expressed as;
P(A ⋃ B) = P(A) + P(B) − P(A ∩ B)
Thus,
P(A ⋃ B) = 0.6 + 0.4 - 0.3
P(A ⋃ B) = 0.7
C) Probability that the selected student has neither type of card would be expressed as; P[(A ∪ B) ' ]
Thus is further expressed as;
P[(A ∪ B) ' ] = 1 − P(A ∪ B)
P[(A ∪ B)'] = 1 - 0.7
P[(A ∪ B)'] = 0.3
D) We want to describe in terms of A and B, the event that the selected student has a Visa card but not a MasterCard.
This is simply an intersection of event A and compliment of event B. Thus, it implies that we we will remove the events when student has both types of cards from the events of A. This probability is expressed as P(A ∩ B')
Thus gives;
P(A ∩ B') = P(A) - P(A ∩ B)
P(A ∩ B') = 0.6 - 0.3
P(A ∩ B') = 0.3
E) Now, we want to find the probability that the selected student has exactly one of these two types of cards.
This is simply the addition of intersection of event A with compliment of event B and intersection of event B with compliment of event A . The probability is given by:
P(A ∩ B') + P(A' ∩ B)
Expanding this gives;
P(A ∩ B') + P(B) - P(A ∩ B)
Plugging in the relevant values gives;
0.3 + 0.4 - 0.3 = 0.4
On the number line, a point was moved from -7 to -3. Which of the following problems describes this move?
0-7-4=-3
0-7+3=-4
-7 - 3 = -10
-7 +4= -3
Answer:
-7 + 4 = -3
Step-by-step explanation:
So you start at -7 and if you add a positive number to a negative number you basically subtract from the negative number, so you would do -7 + 4 which equals -3
Please answer the second conversion. Convert 25 ML to L
Answer:
0.025 l
Hope it helped u if yes mark me BRAINLIEST
i cant understand any of these if you guys can help that’d be great!
Answer:
1. -9/20
2. 1 7/12
3. -4 1/3
Step-by-step explanation:
When adding and subtracting fractions with unlike denominators, you must first make them like denominators. To do this we must:
1. Find the Least Common Multiple of the denominators (which is called the Least Common Denominator).
2. Change each fraction (using equivalent fractions) to make their denominators the same as the least common denominator.
3. Then add (or subtract) the fractions, as we wish!
The easiest way to this is by multiplying the denominators. Remember that whatever you do to the bottom, you also do to the top
1. -5/4 +4/5
if we multiply 4 and 5, we get 20. Our denominator will be 20 before we simplify.
our new equation is going to be -25/20 + 16/20. Now we can add these together to get an answer of -9/20. Which is in the simplist form.
One more thing: to make a mixed number an improper fraction, you multiply the whole number by the denominator, and add the numerator.
1X4=4
4+1=5
The improper fraction is 5/4.
To make a Whole number a fraction, multiply the number by the denominator
-5x3=15
The improper is -15/3.
To go from an improper to a mixed, divide the numerator by the denominator. The remainders are going to be the fraction attached.
on a function map, the values for the domain of the function appear on the ______ and the values for the range appear on the _______
Answer:
domain is x
range is y
Step-by-step explanation:
The values for the domain of the function appear on the x-axis and the values for the range appear on the y-axis.
What is the range and domain of a function?A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.
The domain is for the independent variable while the range is for the dependent variable.
For example f(x) = x²
Now if we put x = 1 then it is called as domain variable while the value of function at x = 1 its that f(1) = 1 called range variable.
The range is the interval where the function f(x) is defined whereas the domain is the input interval of the independent variable (x).
For example f(x) = x²
Now if we put x = 1 then it is called as domain variable while the value of function at x = 1 its that f(1) = 1 called range variable.
Hence "The values for the domain of the function appear on the x-axis and the values for the range appear on the y-axis".
For more details about the range and domain of the function,
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1.81 repeating as a fraction
Answer: 1 73/90 if the decimal is 1.81 and the one is repeating
If the .81 is repeating then 1 9/11
Step-by-step explanation:
Answer:
20/11
Step-by-step explanation:
let 0.(81) = x
--> 100x = 81.(81)
--> 100x - x = 81.(81) - 0.(81)
--> 99x = 81
--> x = 81/99 = 9/11
1.(81) = 1 + 0.(81) = 1 + x = 1 + 9/11 = 20/11
Determine the volume of fluid in the graduated cylinder shown.
which expression is equivalent to -14-6
Kira owes Mark $5, and Mark owes Kira $7. Which statement means the same thing?
Answer:
mark owes Kira $2
I think
simplify the following
3³×6-³×2^5
Answer:
4
Step-by-step explanation:
3³=27
6-³=1/216
2^5=32
27X1/216x32
=4
Two consecutive numbers have a sum of 27. What is the smaller number?
Answer:
13
Step-by-step explanation:
The value halfway between them is their average: 27/2 = 13.5.
The smaller number is 13.
__
The larger number is 14.
negative thirty-one less than s is greater than 93
Answer:
s > 62
Step-by-step explanation:
Write it out: s - (-31) > 93Simplify: s + 31 > 93Subtract 31 from each side, so it now looks like this: s > 62I hope this helps!
The inequality which represents the given statement is given by s > 62.
What are inequalities ?
When two values are compared , an inequality represents whether one is greater than, less than, or not equal to the other.
The given statement is "negative thirty-one less than s is greater than 93". This statement must be transformed into form of an inequality.
We know that an inequality comes when a number is greater than or less than another number . Here the variable is the unknown number 's'. This meant the expression can be written as :
s - (-31) > 93
Simplifying this inequality we get :
s + 31 > 93
s > 93 - 31
s > 62
Therefore , the inequality which represents the given statement is given by s > 62.
Learn more about inequalities here :
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A package of fish weighs 2.5 pounds. The price is $3.50 per pound. What is the price of this package?
Answer:
$8.75
Step-by-step explanation:
If you do
$3.50 x 2.5 you get
$8.75
Carmen has 1/6 of a loaf pumpkin bread. She cuts the loaf into six equal pieces and gives one piece to each of her six friends. How much of the whole loaf of bread does each of the six friends get?
Answer:
each friend gets 1/36 of the loaf of pumpkin bread
Step-by-step explanation:
1/6 of a loaf
1/6 divided by 6
turn 6 into a fraction → 6/1
1/6 ÷6/1
to divide multiply the reciprocal 6/1 → 1/6
1/6 x 1/6 = 1/36
each friend get 1/36
OR
6/x = 1/6
x= 36
6/36
Billy has some nickels and dimes worth $3.25. He has 3 times as many nickels as dimes. How many nickels does he have?
[tex]3d=n[/tex]
[tex]10d+5n=325[/tex]
[tex]10d+15d=325[/tex]
[tex]25d=325[/tex]
[tex]d=13[/tex]
[tex]n=39[/tex]
Hope this helps.
頑張って!
1. Which of the following is a true statement? *
To square a number, multiply the number by 2.
The inverse of squaring a number is to divide the number by 2.
To square a number, multiply the number by itself.
O A perfect square is a number whose square root is an even number.
Answer:
To square a number, multiply the number by itself.
Step-by-step explanation:
If CE= 7x+4
x+3 + 8x-9 = 7x+4
WILL GIVE BRAINLIEST: If the graph of 2x+3y − 6=0 is perpendicular to the graph of ax − 3y=5. What is the value of a?
Answer:
a = [tex]\frac{9}{2}[/tex]
Step-by-step explanation:
To find the value of a, find the Slope of both the equations.
For lines to be perpendicular to each other [tex]m_{1}m_{2} = - 1[/tex]
For line 1:
2x + 3y − 6 = 0 represent the line in y=mx +c form
3y = -2x + 6
y = [tex]\frac{-2}{3} x[/tex] + [tex]\frac{6}{3}[/tex]
y = [tex]\frac{-2}{3} x[/tex] + 2
[tex]m_{1}[/tex] = [tex]\frac{-2}{3}[/tex]
For line 2:
ax - 3y = 5
ax = 5 + 3y
ax - 5 = 3y
y = [tex]\frac{ax}{3} - \frac{5}{3}[/tex]
[tex]m_{2}[/tex] = [tex]\frac{a}{3}[/tex]
Apply the condition of perpendicularity:
[tex]\frac{-2}{3}[/tex] * [tex]\frac{a}{3}[/tex] = - 1
[tex]\frac{2a}{9} = 1[/tex]
a = [tex]\frac{9}{2}[/tex]
In March 1999, Bertrand Piccard and Brian Jones attempted to become the first people
to fly around the world in a hot air balloon. Based on the average sped of 97.8
kilometers per hour, the distance that they traveled in kilometers, d, can be modeled by
d(t) = 97.8t, where t is the time in hours. They traveled a total of 478 hours.
What is the domain of this function?
Answer:
Distance traveled= 41968.4 km
The domain of the function is t
t(h)= 478
h = hours
Step-by-step explanation:
the distance that they traveled in kilometers, d, can be modeled by
d(t) = 97.8t
where t is the time in hours
They traveled a total of 478 hours.
Distance traveled d(t)
d(t) = 87.8(478)
d(t) = 41968.4
Distance traveled= 41968.4 km
The domain of the function is t
t(h)= 478
Between which two integers is the positive value of the square root of 75?
Answer:
8 and 7
Step-by-step explanation:
the square root of 75 is approximately 8.66025 or 5√3 in radical form