Solve by completing the square:
x^2 + 2x - 3 =0
a. - 3 or 1
b. X-3 or -1
C. - 3 or -1
d. 2-3 or 1
Please select the best answer from the choices provided
Answers
Answer:
a
Step-by-step explanation:
Given
x² + 2x - 3 = 0 ( add 3 to both sides )
x² + 2x = 3
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(1)x + 1 = 3 + 1
(x + 1)² = 4 ( take the square root of both sides )
x + 1 = ± \(\sqrt{4}\) = ± 2 ( subtract 1 from both sides )
x = - 1 ± 2
Thus
x = - 1 - 2 = - 3
x = - 1 + 2 = 1
Related Questions
what is the equation of y=x^3 with the given transformations
Answers
Each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.
1. Horizontal Shift (c):
If there is a horizontal shift, the equation becomes y = (x - c)^3.
For example, if there is a shift of 2 units to the right, the equation would be y = (x - 2)^3.
2. Vertical Shift (d):
If there is a vertical shift, the equation becomes y = x^3 + d.
For example, if there is a shift of 3 units upwards, the equation would be y = x^3 + 3.
3. Vertical Stretch (a):
If there is a vertical stretch or compression, the equation becomes y = a * x^3.
For example, if there is a vertical stretch by a factor of 2, the equation would be y = 2 * x^3.
4. Reflection (along the x-axis):
If there is a reflection along the x-axis, the equation becomes y = -x^3.
This flips the graph of the original function upside down.
5. Reflection (along the y-axis):
If there is a reflection along the y-axis, the equation becomes y = (-x)^3.
This mirrors the graph of the original function.
6. Combined Transformations:
If there are multiple transformations, we can apply them in the order they are given. For example, if there is a vertical stretch by a factor of 2 and a horizontal shift of 3 units to the right, the equation would be y = 2 * (x - 3)^3.
Remember, each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.
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Write the quotient as a mixed number.
94 divided by 7 = 13 R3
Answers
Answer:
13 3/7
Step-by-step explanation:
94÷7=13 r3
13 and 3 over 7
what happens when the sampling distribution is altered (e.g. filtering out all values below the mean) and how does it effect type 1 errors.
Answers
In other words, altering the sampling distribution in this way increases the likelihood of making a type 1 error.
What is mean?The arithmetic mean, arithmetic average, or simply the mean or average, is the sum of a collection of numbers divided by the number of numbers in the collection in mathematics and statistics. The collection is frequently a collection of results from an experiment, observational research, or survey.
Here,
The sampling distribution is a distribution of the values of a statistic (such as the mean or median) calculated from a set of sample data. It gives us information about how the statistic is likely to vary from sample to sample, and it is used in hypothesis testing to calculate the probability of observing certain results if the null hypothesis is true.
Filtering out all values below the mean has the effect of changing the shape, location, and spread of the sampling distribution. For example, if the original sampling distribution is normally distributed with a mean of 0 and a standard deviation of 1, filtering out all values below the mean would result in a new sampling distribution with a mean greater than 0 and a standard deviation smaller than 1.
When the sampling distribution is altered, for example by filtering out all values below the mean, it can have an effect on type 1 errors. Type 1 errors occur when we reject the null hypothesis when it is actually true.
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Evaluate 9 ÷ 3[(18 − 6) − 2^2]. Answers A.0.188 B.0.375 C.24 D.48
Answers
Answer:
C. 24
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
9 ÷ 3[12 - 4]
3[8] = 24
Calculate
H
ˉ
0
(2000 K)−
H
ˉ
0
(0 K) for H(g)
Answers
The value of ΔH°(2000 K) - ΔH°(0 K) for H(g) is the enthalpy change of formation of H(g) at 2000 K minus the enthalpy change of formation of H(g) at 0 K.
What is the enthalpy change of formation of H(g) at 2000 K?The enthalpy change of formation (ΔH°f) is the heat energy released or absorbed when one mole of a substance is formed from its elements in their standard states. To calculate ΔH°(2000 K) for H(g), we need to find the enthalpy change of formation of H(g) at 2000 K.
At 2000 K, H(g) is in a gaseous state. To determine its enthalpy change of formation, we compare it to the elements in their standard states. The standard state of hydrogen is H₂(g) at 298 K and 1 atm. Thus, we need to consider the energy required to convert H₂(g) at 298 K and 1 atm to H(g) at 2000 K.
The enthalpy change of formation at a specific temperature can be calculated using the equation:
ΔH°(T₂) = ΔH°(T₁) + ∫Cp(T)dT
Where ΔH°(T₂) is the enthalpy change of formation at temperature T₂, ΔH°(T₁) is the enthalpy change of formation at temperature T₁ (in this case, 298 K), Cp(T) is the heat capacity of the substance as a function of temperature, and the integral is taken over the temperature range from T₁ to T₂.
To obtain an accurate calculation, we would need the specific heat capacity data for H(g) over the temperature range from 298 K to 2000 K. Unfortunately, without this data, we cannot provide a precise value for ΔH°(2000 K) for H(g).
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What is
100 ?
OA) 1000
OB 100
O. 10,000
OD. 10
Answers
Answer:
D 10
Step-by-step explanation:
10 x 10 = 100
100/10 = 10
10 is a perfect square
A researcher wants to test the null hypothesis that the population proportion of people who believe wearing a face mask in public is an important public health measure is at least 0.6, against the alternative hypothesis that it is less. A 5% level of significance will be used. The researcher plans to poll a random sample of 2,000 adults. What is the population? Letter (see multiple choices in the instructions) Group of answer choices
Answers
In this scenario, the population consists of the multiple choices provided in the instructions. These choices represent the various categories or options that the respondents can select when expressing their beliefs about wearing face masks in public as an important public health measure.
The researcher plans to poll a random sample of 2,000 adults from this population in order to gather data and test the null hypothesis against the alternative hypothesis.
By examining the responses of this sample, the researcher aims to make inferences about the larger population and draw conclusions regarding the proportion of people who believe in the importance of wearing face masks in public.
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1 yard is equal to 3 feet or 36 inches. How many inches are in 2
yards, 3 feet?
Answers
Answer:84 because 36 x 2 =72 and then 1/3 of 36 is 12 and 12+72=84
Step-by-step explanation:
The average age of undergraduate students at grand canyon university is 44. if the standard deviation is 4, what percentage of undergraduate students are between 36 and 52 years old?
Answers
75% is percentage of undergraduate students are between 36 and 52 years old.
What is percentage and example?
A percentage is a ratio or fraction where the full value is always 100. For example, if Sam received 30% marks in his math test, it signifies that he scored 30 marks out of 100. In ratio form, it is expressed as 30:100 and in fraction form as 30/100.The percentage is used to determine “how much” or “how many.” A percentage number aids in calculating the exact amount or figure that is being discussed. Fractions are compared.This would be true if k=3, but k=2
because (36-44)/4 = -2 and (52-44)/4 = 2
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Find the slope m of the line passing through the given pair of points. (If an answer is undefined, write UNDEFINED.) (23,28) and (16,−14)
Answers
The slope of the line passing through the points (23,28) and (16,-14) is 6.
To find the slope of a line passing through two points, we use the slope formula:
m = (y2 - y1)/(x2 - x1)
where (x1,y1) and (x2,y2) are the coordinates of the given points.
In this case, the given points are (23,28) and (16,-14), so we substitute these values into the formula:
m = (-14 - 28)/(16 - 23)
Simplifying the expression in the numerator and denominator, we get:
m = (-42)/(-7)
Dividing both numerator and denominator by -7, we get:
m = 6
Therefore, the slope of the line passing through the points (23,28) and (16,-14) is 6. This means that for every 1 unit increase in the x-coordinate (from 16 to 23), the y-coordinate increases by 6 units (from -14 to 28).
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The buyer for a chain of stores purchased tables in bulk, paying $200 each. The stores will sell each table for $338. What percentage is the mark-up?
Answers
The percentage mark-up of the goods is 69 percent.
How to find the percentage mark-up?The mark-up percentage is calculated by subtracting the unit cost from the selling price, dividing by the unit cost and multiplying times 100.
Therefore, the buyer for a chain of stores purchased tables in bulk, paying $200 each. The stores will sell each table for $338.
Hence, the percentage mark-up can be calculated as follows:
percentage mark-up = 338 - 200 / 200 × 100
percentage mark-up = 138 × 100 / 200
percentage mark-up = 13800 / 200
percentage mark-up = 138 / 2
percentage mark-up = 69 %
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A parallelogram has a height of 2 units. One side of the parallelogram is AB¯¯¯¯¯. The paralleogram has no right angles.
Draw the parallelogram using the Polygon tool.
Each segment on the grid represents 1 unit.
Keyboard Instructions
Initial graph state
The horizontal axis goes from 1.5 to 6.5 with ticks spaced every 1 unit(s).
The vertical axis goes from 1.5 to 6.5 with ticks spaced every 1 unit(s).
Point with coordinates (2, 3) labelled: A.
Point with coordinates (5, 3) labelled: B.
Answers
It is a unique variety of quadrilateral called a parallelogram that has both pairs of opposite sides parallel and equal.
What is quadrilateral?A polygon with has four sides, four angles, and four vertices is called a quadrilateral. The Latin words 'Quadri', which denotes four, and latus, which means side, were combined to form the English word quadrilateral.
Given, Height of the Parallelogram = 2 units
Each segment on the grid is represented as = 1 unit.
So, One side of the Parallelogram = 3 units
Properties of Parallelogram
a. Opposite sides are equal.
b. Opposite sides are parallel.
c. Diagonals Bisect each other.
Also, Every Rectangle is a Parallelogram.
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When 3 times a number is added to the square of the number, the result is 40. Determine the number
Answers
Answer:
5 or -8
Step-by-step explanation:
\((3 \times x) + x {}^{2} = 40\)
\(3x + {x}^{2} = 40\)
\( {x}^{2} + 3x - 40 = 0\)
using factorization method
\(( {x}^{2} + 8x) ( - 5x - 40) = 0\)
\(x(x + 8) - 5(x + 8) = 0\)
\((x - 5)(x + 8) = 0\)
\(x - 5 = 0\)
or
\(x + 8 = 0\)
\(x = 5\)
or
\(x = - 8\)
Find the percent change. State whether it is an increase or decrease. Round to the nearest tenth of a percent.
From 68 to 63
Answers
The percentage increase is 7.9 %.
The given numbers are 68 and 63.
What is the percent change?Percentage change is the difference coming after subtracting the old value from the new value and then divide by the old value and the final answer will be multiplied by 100 to show it as a percentage.
Here, old value = 63 and new value = 68
Difference = 68-63 =5
Percentage increase = Difference of old value and new value ÷ old value
= 5/63 × 100
= 0.0793 × 100
= 7.93 %
≈ 7.9 %
Therefore, the percentage increase is 7.9 %.
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Graph the following three equations on your own device and answer the questions below.
1: f(x)=5x+7
2: f(x)=x^2+6
3: f(x)=2^x+3
a. what is f(10)
b. what is f(100)
c. what is f(1000)
d. Which function has the highest value at each value of x?
e. Use your answers to decide which type of function will increase the fastest?
f. At what point did this function exceed the other two?
g. Do you think this would work for any function of this type? Why?
h. If these 3 equations represent the growth of mucus in a membrane, describe and state the domain and range for each function.
Answers
Due to length restrictions, we kindly invite to read the explanation of this question for further details on functions.
What are the characteristics of each of the three functions?
a) In this part we must evaluate each of the three functions at the given value of x:
Case 1
f(10) = 5 · 10 + 7
f(10) = 57
Case 2
f(10) = 10² + 6
f(10) = 106
Case 3
f(10) = 2¹⁰ + 3
f(10) = 1027
b) In this part we must evaluate each of the three functions at the given value of x:
Case 1
f(100) = 5 · 100 + 7
f(100) = 507
Case 2
f(100) = 100² + 6
f(100) = 10006
Case 3
f(100) = 2¹⁰⁰ + 3
f(100) = 1.267 × 10³⁰ + 3
c) In this part we must evaluate each of the three functions at the given value of x:
Case 1
f(1000) = 5 · 1000 + 7
f(1000) = 5007
Case 2
f(1000) = 1000² + 6
f(1000) = 1000006
Case 3
f(1000) = 2¹⁰⁰⁰ + 3
f(1000) = (1.268 × 10³⁰)¹⁰ + 3
f(1000) = 10.744 × 10³⁰⁰ + 3
f(1000) = 1.074 × 10³⁰¹ + 3
e) The third function increases the fastest.
f) In this part we need to compare the third function with respect to the first and second functions:
5 · x + 7 = 2ˣ + 3
2ˣ - 5 · x = 4
The solutions of the equation are x = - 0.675 and x = 4.81. The function will exceed the other first function at x = 4.81.
x² + 6 = 2ˣ + 3
2ˣ - x² = 3
The solution of the equation is x = 4.588. The function will exceed the other second function at x = 4.588.
g) Yes, exponential functions with bases greater than 1 will surpass polynomic function at any point x such that x > 0.
h) The domain represents the set of x-values of a function and the range represents the set of y-values of a function. Then, the domain and range of each function is:
Case 1
Domain - All real numbers.
Range - All real numbers
Case 2
Domain - All real numbers.
Range - [6, +∞)
Case 3
Domain - All real numbers.
Range - (3, +∞)
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What would the area be for a circle with the diameter of 7
Answers
Answer:
The answer is 38.48
Step-by-step explanation:
Picture with explanation provided below.
. Multiply (3x+2)(4x-7)
Answers
Answer:
12\(x^{2}\) + 29x - 14
Step-by-step explanation:
(3x+2)(4x-7)
Multiply out 3x first then 2
(3x * 4x) - (3x * -7) + (2 * 4x) + (2 * -7)
12\(x^{2}\) - (- 21x) + 8x + ( -14)
12\(x^{2}\) + 21x + 8x - 14 Combine like terms
12\(x^{2}\) + 29x - 14
Answer:
\( \boxed{ \bold{ \boxed{ \sf{12 {x}^{2} - 13x - 14}}}}\)
Step-by-step explanation:
\( \sf{(3x + 2)(4x - 7)}\)
Use the distributive property to multiply each term of the first binomial by each term of the second binomial
\( \longrightarrow{ \sf{3x(4x - 7) + 2(4x - 7)}}\)
\( \dashrightarrow{ \sf{12 {x}^{2} - 21x + 8x - 14}}\)
Collect like terms
\( \longrightarrow{ \sf{12 {x}^{2} - 13x - 14}}\)
Hope I helped!
Best regards! :D
Math help: Variables
I need help solving these two questions, explanations would be greatly appreciated.
Answers
Answer:
1. h = 11 cm
2. d = 220 km
Step-by-step explanation:
1. A = 1/2bh
Where,
A = 66 cm²
b = 12 cm
A = 1/2bh
66 = 1/2 * 12 * h
66 = 6h
h = 66/6
h = 11 cm
2. s = d/t
Where,
s = 110 km/h
t = 2h
s = d/t
110 = d/2
Cross multiply
110 * 2 = d
d = 220 km
Which property is demonstrated? (7 × 25) × 9 = 7 × (25 × 9)
Answers
Answer:
Associativity.
Step-by-step explanation:
Which of the following is NOT a component of a linear programming model? O Constraints O Objective Function O Feasible Region O Decision variables Which of the following refers to the collection of all points that satisfy each constraint in an LP problem? O Decision variables O Objective function O Feasible Region O Constraints
Answers
The component of a linear programming model that is NOT listed is "Decision variables."
A linear programming model consists of several components that work together to optimize a given objective while considering various constraints. The components of a linear programming model include:
Constraints: These are the limitations or restrictions that define the feasible set of solutions. Constraints restrict the values that decision variables can take.
Objective Function: This function represents the goal or objective of the linear programming problem. It is either minimized or maximized based on specific criteria.
Feasible Region: Also known as the feasible set or feasible solution space, this refers to the collection of all points that satisfy each constraint in the linear programming problem. It represents the set of possible solutions that meet all the given constraints.
However, "Decision variables" is not a component of a linear programming model but rather the unknowns or variables that we want to determine in order to optimize the objective function.
Decision variables are not a component of a linear programming model. The components of a linear programming model include constraints, objective function, and feasible region. The feasible region refers to the collection of all points that satisfy each constraint in the linear programming problem.
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Can somebody answer this
Answers
12345679×18 por favorissssss
Answers
Answer: 222,222,222
Step-by-step explanation: that’s the anwser
What is 3 divided by 80?
Answers
Answer: 3/80 = 0.0375
solve the equations. -4x + 7y = 20y= 3x + 15x=y=
Answers
Explanation:
-4x + 7y = 20 ... equation 1
y= 3x + 15 ...equation 2
Rewriting the equations:
7y - 4x = 20
y - 3x = 15
using elimination method:
I want to eliminate y. So, I multiply equation 2 by 7 so both equations can have same coefficient
7y - 4x = 20 ... equation 1
7y - 21x = 105 ...equation 2
subtract equation 1 from 2:
7y - 7y -21x - (-4x) = 105 - 20
-21x + 4x = 85
-17x = 85
divide both sides by -17:
-17x/-17 = 85/-17
x = -5
To get y, we insert the value for x in any of the equation
using equation 1
7y - 4(-5) = 20
7y + 20 = 20
7y = 20-20
7y = 0
y = 0/7
y = 0
x = -5 and y = 0
Find the lowest common denominator (multiple). Type the equivalent fractions. Then, add or subtract. Simplify your answer. 1
2
1
3
Answers
Answer:what
Step-by-step explanation:what does this mean
Show that if m
∗
(A)=0, then m
∗
(AUB)=m
∗
(B)
Answers
A and B have the same elements, the measure of AUB will be equal to the measure of B.
To show that if m*(A) = 0, then m*(AUB) = m*(B), we need to prove the following:
1. If m*(A) = 0, then A is a null set.
2. If A is a null set, then AUB = B.
3. If AUB = B, then m*(AUB) = m*(B).
Let's break down each step:
1. If m*(A) = 0, then A is a null set:
- By definition, a null set has a measure of 0.
- Since m*(A) = 0, it implies that A has no elements or its measure is 0.
- Therefore, A is a null set.
2. If A is a null set, then AUB = B:
- Since A is a null set, it means that it has no elements or its measure is 0.
- In set theory, the union of a null set (A) with any set (B) results in B.
- Therefore, AUB = B.
3. If AUB = B, then m*(AUB) = m*(B):
- Since AUB = B, it implies that both sets have the same elements.
- The measure of a set is defined as the sum of the measures of its individual elements.
- Since A and B have the same elements, the measure of AUB will be equal to the measure of B.
- Therefore, m*(AUB) = m*(B).
By proving these three steps, we have shown that if m*(A) = 0, then m*(AUB) = m*(B).
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plsssssss help me
I will give u 10 points
Answers
Therefore...
The slope is 1/3.
Hope this helps :)
Let me know if there are any mistakes!!
27 x 93* can be written in the form we where k is an expression in terms of x. Find k.
Answers
Answer k = 3 + 6x
note that 27 = 3³ and 9 = 3²
27 ×9 to the power 3x = 3³ × (3²)^3x = 3³ × =
hence k = 3 + 6x
Event A: Spinning violet or yellow on the spinner.
Event B: Rolling an even number on a number cube.
What is P(A and B)?
Answers
Answer:
\(\sf P(A \cap B)=\dfrac{1}{4}\)
Step-by-step explanation:
\(\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}\)
Event A - spinning violet or yellow
Assuming that the spinner has 4 different colors (red, orange, violet and yellow) - see attachment.
\(\implies \sf P(A) = \dfrac{2}{4}=\dfrac{1}{2}\)
Event B - rolling an even number
Assuming the number cube has 6 sides numbered 1, 2, 3, 4, 5 and 6. Therefore, the even numbers are 2, 4 and 6.
\(\implies \sf P(B)=\dfrac{3}{6}=\dfrac{1}{2}\)
Events A and B are independent events as the outcome of one event does not affect the outcome of the other event.
For independent events A and B:
\(\implies \sf P(A \cap B)=P(A)P(B)\)
To find P(A and B), substitute the found values of P(A) and P(B):
\(\implies \sf P(A \cap B)=\dfrac{1}{2} \times \dfrac{1}{2}=\dfrac{1}{4}\)
P(A)
2/41/20.5P(B)
3 even nos are 2,4,6
3/61/20.5P(A\(\cap\))
0.5²0.25 or 1/4A forest fire leaves behind an area of grass burned in an expanding circular pattern. If the radius of the circle of burning grass is increasing with time according
to the formula r(t) = 5t + 2, express the area A burned as a function of time, t (minutes).
Answers
The area A burned as a function of time, t is
A(t)=78.5t²+62.8t+12.56
What is Radius of the circle?A circle's or sphere's radius is any of the line segments that connect the object's center to its perimeter; in more recent usage, it is also their length.
According to the given values ;
r(t)=5t+2
.°. A(t)=πr²=π*(5t+2)²
=π(25t²+20t+4)
= 78.5t²+62.8t+12.56
hence ,the area A burned as a function of time, t is
A(t)=78.5t²+62.8t+12.56
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