Answers
Answer:
Hello,
Step-by-step explanation:
a)
\(x^2-2x-6=x^2-2x+1-1-6\\\\=(x-1)^2-7\\\)
b)
\(x^2-2x-6=(x-1)^2-7\\\\=(x-1-\sqrt{7} )(x-1+\sqrt{7} )\\\\\\\boxed{x=1-\sqrt{7} \ or\ x=1+\sqrt{7} }\\\)
Related Questions
If the the price of a pair of shoes is 35$ before tax and the tax is 20% what will the final price of the shoes be
Answers
Answer:
$42
Step-by-step explanation:
You want the price with tax of a $35 pair of shoes subject to a 20% tax.
Price with taxThe tax is the cost of the shoes multiplied by the tax rate. The final price is the sum of the cost of the shoes and the tax:
final price = price + price × tax rate
final price = price × (1 + tax rate) = $35 × 1.20 = $42
The final price of the shoes is $42.
Answer:
42$
Step-by-step explanation:
tax increase will be
20% of 35$
= 20/100 × 35
= 7$
Final price = Old price + Tax
= 35 + 7
= 42$
WILL GIVE BRAINLIEST
Answers
Answer:
C) 2x10²
Step-by-step explanation:
1400000/7000=
1400/7=
200=
2x10²
consider the following probability distribution: 1 2 3 4 5 0.1 0.15 0.40 0.25 0.10 find (write it up to second decimal place).
Answers
The mean value is 1.19
x p(x) x*p(x) X^2p(x)
1 0.1 0.1 0.1
2 0.15 0.3 0.6
3 0.4 1.2 3.6
4 0.25 1 4
5 0.1 0.5 2.5
Sum 1 3.1 10.8
Mean =Σx * p(x)
u=3.1
Variance=σ^2
=Σx*p(x)-u^2
=10.8-(3.1)^2 =1 .19
A probability distribution is a frequency distribution that has been idealised. A frequency distribution is a description of a particular sample or dataset. It is the number of times each possible variable value appears in the dataset.
The probability of occurrence determines how many times a value appears in a sample. Probability is a number between 0 and 1 that indicates the likelihood of an event occurring:
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will mark brainleist pls help
Answers
Answer:
x = 31°
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180° , that is
x + 54° + 95° = 180°
x + 149° = 180° ( subtract 149° from both sides )
x = 31°
Five angels of a hexagon are 123,124,118,130’110. Calculate the six angle
Answers
Answer:
The sixth angle is 115°.
Step-by-step explanation:
Number of sides in a hexagon = n =6
Sum of interior angles = (n−2)180°
= (6−2)180 ∘
= 720
∴ Let the six angle of hexagon be x.
⇒ x + 123 + 124 + 118 + 130 + 110 = 720°
⇒ x + 605 = 720°
⇒ x = 720 - 605
⇒ x = 115
Drag and drop the relationships below to classify them as being a function or not a function?
Answers
A relation that has more than one output of each input. That is not a function. A function only has one output of each input. Function a and function b are linear functions. Function a is represented by the table values. function b is represented by the equation y=3x+4.
Determine the domain of a piece wise function?Domain, is a term that is used to measure the independent variable’s values. Also known as the “x” values. It tells you what values of “x” are applicable in the function. What values will satisfy the function.
Determine the range of a piece wise function?Range, is a term used to measure the dependent variable’s values. Also known as the “y” values. It tells you what values of why does the graph of the function extends till.
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Someone please help answer !
Choose the number that is closest to the mean of the distribution
Answers
The mean of the distribution is 3
What is arithmetic mean?Arithmetic mean is defined as the ratio of the sum of observations to the total number of observations. It can be referred to as the average of a specific set of data or the arithmetic mean. One of the basic methods used to acquire a result, the term "Mean" is commonly used in the field of statistics.
The formula for the mean of a given set of data is as follows:
Mean = Sum of Observations/Total number of observations
According to the first graph,
Given the bar of observations as :
0, 5, 6, 3, 1, 1, 3, 6, 4, 1
Here the Sum of Observations = 30
And the total number of observations = 10
The mean of the distribution = 30/10
The mean of the distribution = 3
According to the second graph,
Given the bar of observations as :
0, 1, 3, 3, 9, 0, 9, 4, 4, 1
Here the Sum of Observations = 34
And the total number of observations = 10
The mean of the distribution = 34/10
The mean of the distribution = 3.4
The mean of the distribution = 4 (closest)
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2√x + 5 + 5y³ for x = 20 and y = -2
Answers
Solution
Step 1
Write the expression:
\(2\sqrt{x+5}\text{ + 5y}^3\text{ }\)Step 2
Next, substitute x = 20 and y = -2 into the expression:
\(\begin{gathered} 2\sqrt{x+5}\text{ + 5y}^3 \\ \\ 2\sqrt{25}\text{ + 5}\times(-2)^3 \\ \\ 2\times5\text{ + 5}\times(\text{ -8\rparen} \\ \\ 10\text{ - 40} \\ \\ -30 \end{gathered}\)Final answer
-30
Solve the system of equations using the substitution or elimination method.
y = 4x - 7
4x + 2y = -2
.
Show your work
Correct x and y
Answers
The solution to the system of equations is x = 1 and y = -3.
To solve the system of equations using the substitution or elimination method, let's start with the substitution method.
Given equations:
y = 4x - 7
4x + 2y = -2
We'll solve equation 1) for y and substitute it into equation 2):
Substituting y from equation 1) into equation 2):
4x + 2(4x - 7) = -2
4x + 8x - 14 = -2
12x - 14 = -2
Now, we'll solve this equation for x:
12x = -2 + 14
12x = 12
x = 12/12
x = 1
Now that we have the value of x, we can substitute it back into equation 1) to find y:
y = 4(1) - 7
y = 4 - 7
y = -3
Therefore, the solution to the system of equations is x = 1 and y = -3.
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(12sin(pi/2x)*lnx)/((x³+5)(x-1))
lim as x approaches 1
Answers
The limit of the given function as x approaches 1 is 0.
To find the limit of the given function as x approaches 1, we need to evaluate the expression by substituting x = 1. Let's break it down step by step:
1. Begin by substituting x = 1 into the numerator:
\(\[12\sin\left(\frac{\pi}{2}\cdot 1\right)\ln(1) = 12\sin\left(\frac{\pi}{2}\right)\ln(1) = 12(1)\cdot 0 = 0\]\)
2. Now, substitute x = 1 into the denominator:
(1³ + 5)(1 - 1) = 6(0) = 0
3. Finally, divide the numerator by the denominator:
0/0
The result is an indeterminate form of 0/0, which means further analysis is required to determine the limit. To evaluate this limit, we can apply L'Hôpital's rule, which states that if we have an indeterminate form 0/0, we can take the derivative of the numerator and denominator and then evaluate the limit again. Applying L'Hôpital's rule:
4. Take the derivative of the numerator:
\(\[\frac{d}{dx}\left(12\sin\left(\frac{\pi}{2}x\right)\ln(x)\right) = 12\left(\cos\left(\frac{\pi}{2}x\right) \cdot \left(\frac{\pi}{2}\right) \cdot \frac{-1}{x} + \frac{\sin\left(\frac{\pi}{2}x\right)\ln(x)}{x}\right)\]\)
5. Take the derivative of the denominator:
\(\[\frac{d}{dx}\left((x^3 + 5)(x - 1)\right) = \frac{d}{dx}\left(x^4 - x^3 + 5x - 5\right) = 4x^3 - 3x^2 + 5\]\)
6. Substitute x = 1 into the derivatives:
Numerator: \(\[12\left(\cos\left(\frac{\pi}{2}\right) \cdot \left(\frac{\pi}{2}\right) \cdot \frac{-1}{1} + \sin\left(\frac{\pi}{2}\right) \cdot \frac{\ln(1)}{1}\right) = 0\]\)
Denominator: 4(1)³ - 3(1)² + 5 = 4 - 3 + 5 = 6
7. Now, reevaluate the limit using the derivatives:
lim as x approaches 1 of \(\[\frac{{12\left(\cos\left(\frac{\pi}{2}x\right) \cdot \left(\frac{\pi}{2}\right) \cdot \frac{{-1}}{{x}} + \sin\left(\frac{\pi}{2}x\right) \cdot \frac{{\ln(x)}}{{x}}\right)}}{{4x^3 - 3x^2 + 5}}\]\)
= 0 / 6
= 0
Therefore, the limit of the given function as x approaches 1 is 0.
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Israel started to solve a radical equation in this way:
square root of x plus 6 − 4 = x
square root of x plus 6 − 4 + 4 = x + 4
square root of x plus 6 = x + 4
(square root of x plus 6)2 = (x + 4)2
x + 6 = x2 + 8x + 16
x + 6 − 6 = x2 + 8x + 16 − 6
x = x2 + 8x + 10
x − x = x2 + 8x + 10 − x
0 = x2 + 7x + 10
0 = (x + 2)(x + 5)
x + 2 = 0 x + 5 = 0
x + 2 − 2 = 0 − 2 x + 5 − 5 = 0 − 5
x = −2 x = −5
Solutions = −2, −5
What error did Israel make?
He subtracted 6 before subtracting x.
He added 4 before squaring both sides.
He factored x2 + 7x + 10 incorrectly.
He did not check for extraneous solutions.
Answers
Answer:
He did not check for extraneous solutions.
Step-by-step explanation:
He solved the equation correctly and obtained solutions -2 and -5, but there is one final step he did not do.
Every time you square both sides of an equation to solve it, you must check for extraneous solutions. If he did, he would have eliminated x = -5.
Answer: He did not check for extraneous solutions.
can some help me figure this out
Answers
Answer:
e
Step-by-step explanation:
e
A worker is pouring milk for students lunches. She knows that 3 quarts of milk contain 12 cups. How many cups can she pour with 7 quarts of milk?
Answers
Answer:
7 quarts = 28 cups 10 cups = 2.5 quarts
Answer:
28 cups
Step-by-step explanation:
Find the zeros of g(x) = x3 + x2 – 9x – 9
Answers
Answer: The zeros are -1,-3, and 3
Hope this helps
Answer:
let g[x]=0
then0=x3−x2-9x+9
rewrite it as x3−x2−9x+9=0
by factorising it becomes
(x−1)(x+3)(x−3)=0
therefore
either x-1=0 OR x+3=0 OR x-3=0
which becomes
x=1 OR x=-ve3 OR x=3
are the zeroes of the polynomial
hope this helps
Which of the following is used to represent complex numbers?
A.
x2 + y
B
C.
bi + 2
D.
a + bi
Answers
Answer: D) a+bi
Where both a and b are real numbers.
In your textbook, you might see \(a,b \in \mathbb{R}\) to indicate that they are real numbers.
An example would be 7+13i, where a = 7 and b = 13.
How many gallons of a 50% antifreeze solution must be mixed with 70 gallons of 10% antifreeze to get a mixture that is 40% antifreeze?
Answers
Answer: 180 gallons needed
Step-by-step explanation:
Zykeith,
Assume x gallons of 50% antifreeze is needed
Final mixture is x + 60 gallons
Amount of antifreeze in mixture is 0.4*(x+60)
Amount of antifreeze added is .5x + .1*60 = .5x + 6
so .5x + 6 = .4(x + 60)
.5x -.4x = 24 -6
.1x = 18
x = 180
Let x be the number of gallons of the 50% antifreeze solution needed. We know that the resulting mixture will be 70 + x gallons. To get a 40% antifreeze mixture, we can set up the following equation:
\({\implies 0.5x + 0.1(70) = 0.4(70 + x)}\)
Simplifying the equation:
\(\qquad\implies 0.5x + 7 = 28 + 0.4x\)
\(\qquad\quad\implies 0.1x = 21\)
\(\qquad\qquad\implies \bold{x = 210}\)
\(\therefore\) We need 210 gallons of the 50% antifreeze solution to mix with 70 gallons of 10% antifreeze to get a mixture that is 40% antifreeze.
\(\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}\)
what is the integer of 14,000 feet above sea level
Answers
Answer:
it's 14,000
Step-by-step explanation:
(sea level means 0)
12
A paratrooper falls to the ground along a diagonal line. His fall begins 5 330 meters above the ground, and the line he follows has a slope
of 6.5. That is, he falls 6.5 meters vertically for every 1 meter he moves across horizontally. How far horizontally across the ground does
he land from his initial position in the sky?
meters
Answers
Answer:
820
Step-by-step explanation:
Using the given values you can form the equation f(x)=-6.5x+5330 to model this example. All you need to do is look to where the x intercept is and there is you answer.
On a flight from Chicago, Illinois, to Denver, Colorado,
the typical cruising altitude of a passenger jet is approximately
38,000 feet. As the flight departs from O'Hare International Airport,
the jet begins to ascend. At 4.3 miles away from the airport, the jet
is at an altitude of 4200 feet. The jet reaches an altitude of 36,700
feet at 167.5 miles away from the airport.
Determine the slope of ascent of the flight given that 5280 feet = 1 mile.
Round your answer to the nearest thousandth.
Answers
The slope of ascent of the flight is 0.04
How to calculate the slope of ascent?From the question, we have the following parameters that can be used in our computation:
Typical cruising altitude = 38,000 feetInitial point of ascend = 4.3 miles at 4,200 feetAnother point of ascend = 167.5 miles at 36,700 feetThe above parameters can be represented as
(x, y) = (4.3, 4200) and (167.5, 36,700)
The slope is then calculated as
Slope = (y₂ - y₁)/(x₂ - x₁)
Where x and y are defined above
So, we have
Slope = (36700 - 4200)/(167.5 - 4.3)
Evaluate
Slope = 199.14 feet per mile
Recall that 5280 feet = 1 mile.
So, we have
Slope = 199.14 feet/5280 feet
Evaluate
Slope = 0.04
Hence, the required slope is 0.04
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DQ2 Do all linear transformations have a matrix representation? If so, what theorem establishes this? If not, provide a counter-example
Answers
Not all linear transformations have a matrix representation. A counter-example is a linear transformation that changes the dimension of the vector space.
What is Linear transformation?
The function g(x) is a linear transformation if each term of each component of g(x) is a number times one of the variables.
For example, consider the linear transformation T: R^2 -> R^3 defined by:
T(x, y) = (x, y, 0)
This transformation maps each point in the xy-plane to a point in the x,y,z-space with z-coordinate 0. It is a linear transformation, since it preserves addition and scalar multiplication. However, it cannot be represented by a matrix, since it changes the dimension of the vector space.
The theorem that establishes the existence of a matrix representation for every linear transformation is known as the matrix representation theorem. It states that every linear transformation from a finite-dimensional vector space to another finite-dimensional vector space can be represented by a matrix with respect to suitable bases of the vector spaces. However, it does not apply to linear transformations that change the dimension of the vector space.
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Desperate Need Of Help
Answers
The domain and range of the graph above in interval notation include the following:
Domain = [-6, 3]
Range = [-3, 3]
What is a domain?In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.
In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = [-6, 3] or -6 ≤ x < 3.
Range = [-3, 3] or -3 < y < 3
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can anyone solve this
Answers
Step-by-step explanation:
3x-12x=24-9x-9x=24-9x-9x+9x=240=24It has no solution
A norman window has the shape of a square with a semicircle mounted on it. Find the width of the window if the total area of the square and the semicircle is to be 190 ft squared?
Answers
Answer:
11.68ft or 11.68 feet
Step-by-step explanation:
From the above question, we are told that:
Area of the square and the Area semicircle is to be 190 ft squared.
We are also told in the question that:
The window has the shape of a square with a semicircle mounted on it.
Hence, the Diameter of the semicircle = Width of the Square
Let the Width of the square = x
Area of a square = Width²
= x²
Let the Diameter of the semi circle = x
Radius of the semi circle = Diameter of the semi circle/2 = x/2
Area of a semicircle = πr²/2
Area of a the semi Circle = π ×(x/2)² /2
= (πx²/4)/2
= πx²/8
Therefore,
Area of a square + Area of a semicircle = 190ft²
= x² + πx²/8 = 190
Cross Multiply
x² + πx² = 190
= x² ( 1 + π/8) = 190
x² = (190)/(1 + π/8)
x² = 136.42573798
x = √136.42573798
x = 11.680142892ft
Approximately x ≈ 11.68ft
Therefore, the width of the window = 11.68ft
At a local pet store, there are 5 cats for every 2 dogs. If there are 8 dogs, how many cats are at the pet store? 03 cats O 12 cats o 20 cats O 24 cats
Answers
Answer:
20
Step-by-step explanation:
ok so for every 2 dogs is 5 so 2,5; 4,10; 6,15; 8,20.
WHAT IS 5*5 yeehaw new chaatatattatat
Answers
Answer:
25
Step-by-step explanation:
5 + 5 + 5 + 5 + 5
:)
will give brainliest ! 15 points please help <3
Answers
Answer:
1. C
2. G, H
3. A, H
4. x=-4.5
5. B, D, F, G
Step-by-step explanation:
pls Mark Brainliest
Find the unit price of 2 pounds of flour that costs $1.35?
Answers
Answer:
0.675
Step-by-step explanation:
Find the equation of the line that passes through the following points: (n, m) and (n, m + 1).
Answers
Answer:
1
Step-by-step explanation:
(m+1-m)/(n-n)
answer is 1
Subtract
xyz-4xy+5 from 5xyz+xy+3yz-4
Answers
Answer: 4xyz+5xy+3yz-9
Step-by-step explanation:
(SIGNAL RULES)
+(+) = +
+(-) = -
-(+) = -
-(-) = +
5xyz+xy+3yz-4-(xyz-4xy+5) -> 5xyz+xy+3yz-4-xyz+4xy-5 = 5xyz-xyz+xy+4xy+3yz-4-5 = 4xyz+5xy+3yz-9
Bandhan Bank employee salary after 10 years
Answers
Answer:
- Banking Operations salary in India with less than 1 year of experience to 10 years ranges from ₹ 1.4 Lakhs to ₹ 7 Lakhs with an average annual salary of ₹ 3.1 Lakhs based on 261 latest salaries