Answer:
n = - 1 , n = 3
Step-by-step explanation:
n² - 2n - 3 = 0 ( add 3 to both sides )
n² - 2n = 3
to complete the square
add ( half the coefficient of the x- term)² to bpth sides
n² + 2(- 1)n + 1 = 3 + 1
(n - 1)² = 4 ( take square root of both sides )
n - 1 = ± [tex]\sqrt{4}[/tex] = ± 2 ( add 1 to both sides )
n = 1 ± 2
Then
n = 1 - 2 = - 1
n = 1 + 2 = 3
Z is a standard normal random variable. The P(Z > 2.11) equals
0.4821
0.9821
0.5000
0.0174
lines are and s are parallel. what is m1
Answer:
30 degrees
Step-by-step explanation:
Solve&Share-
The store sells boxes of adhesive
bandages. The boxes have: 12, 15, 18, 20, 25, 36, 40, 45,
50, 64, 75, or 100 bandages per box.
Which boxes have bandages that can be separated
into 2 first-aid kits with no leftover bandages?
Which boxes have bandages that can be separated into
5 first-aid kits with no leftover bandages?
Which boxes have bandages that can be separated into
10 first-aid kits with no leftover bandages?
Therefore, there are 12 bandages in 2 boxes, which is the answer to the unitary method presented problem.
What is a unitary method?The term "unitary" refers to a single or separate unit or variable . As a result, this strategy's objective is to establish values in terms of a single unit. For instance, if a car travels 44 kilometres on two litres of gas, the unitary technique can be used to determine how many kilometers it will drive on one.
Here,
Given: Each box of bandages has three packs, with two bandages in each pack.
Now, determine how many bandages there are in two boxes.
Therefore, we solve using the unitary method:
One pack contains two bandages.
In 3 packs, there are therefore = 2*2 = 6 bandages.
One box contains three packs as stated.
Consequently, we multiply 2 by 6 to obtain the bandages in 2 boxes:
=> 2 * 6 = 12
Therefore, there are 12 bandages in 2 boxes, which is the answer to the unitary method's presented problem.
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What is 5c−3d−12c+d−6 written in simplest form?
To simplify the expression 5c−3d−12c+d−6, we can combine like terms:
5c − 12c + d − d − 6 = (-12c + d) + (-6)
Therefore, the expression 5c−3d−12c+d−6 can be simplified to -12c + d - 6.
These tables correspond to inputs and outputs. Which of these input and output tables could represent a function rule, and which ones could not?
Table A is a function.
Table B is not a function.
Table C is a function.
Table D is not a function.
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
We know a relation is a function if it is one-to-one or many-to-one.
But a relation is not a function if it is one to many.
Table A is a function and it is a many-to-one function.
Table B is not a function as input 1 leads to two different outputs 1, - 1.
Table C is a function and it is a one-to-many function.
Table D is not a function as one input leads to 3 different outputs.
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What is number 3 on the plot diagram?
Answer:
Kumain ka Ng pansit para ka Maka sagot
Step-by-step explanation:
follow pleas helpme
How do you explain 2 3?
This is a coordinate pair of a point. 2 and 3 denotes X and Y coordinate respectively.
What is coordinate system?The system that is used to represent the location of points in the space is termed as coordinate system. There are two types of coordinate system such as polar and cartesian. In case system there are two reference axes which are perpendicular to each other.
In the cartesian system points are represented with respect to a vertical axis named Y axis and a horizontal axis named X axis.
How do we explain 2 3?We stated earlier that in the cartesian system a location of a point is identified by a pair of numerical terms.
So, 2, 3 indicates a pair of numerical terms. 2 denotes the X coordinate of the point and 3 denotes the Y coordinate of that point.
In the next, the distance of the point from X axis is 3 unit and distance from Y axis is 2 unit.
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Complete question is: In the point (2,3) which point denotes the y-coordinate.
May I know the answer and steps, thank you.
(3-i/1+i)³
An imaginary number is produced when we square a negative number.
The value of I is -1.
What is the Value of i?This article's introduction included a proposition. The specific measure or value of what I stands for was the subject of the statement. It is discussed in this section of the article along with an explanation of its value.
Iota is the term used to describe the imaginary portion of a complex number. The symbol "iota" or I is used to represent an imaginary number's value. An imaginary number is produced when we square a negative number.
The value of I is -1.
The concept of complex numbers is understood using this value of i.
x2 plus 1 equals zero in a quadratic equation.
x2 = -1
x = √-1
The imaginary portion is shown as -1.
I = √-1
i2 = -1
An imaginary number can be squared to get a negative value, as was previously discussed.
I = √-1
both sides being square
i2 = -1
An imaginary number plus a real number are combined to get any complex number. Iota, sometimes known as I stands for all non-real quantities.
Real numbers include 10, -20, 3, and other like values.
The integers 2i, -5, -i, etc. are examples of imaginary numbers.
Complex numbers take the form of a + ib, where I denotes the imaginary component. In addition, the number zero is complicated. Only the imaginary component of a complex number can be added to or subtracted from the imaginary part, and vice versa for the real part of the complex number.
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does the point (2, 8) satisfy the equation y = 4x?
The point satisfies the equation ! 8 = 4 × (2)
Answer:
Yes
Step-by-step explanation:
If you plug in the numbers to the equation, you should get:
8 = 4(2)
Then,
8 = 8
therefore, (2,8) does satisfy the equation y = 4x.
I want to solve the math problem
Answer:
Here are a few of the factor pairs. The rest you can find in the pdf below.
Work out the area of this shape. Give your answer
in cm².
3 cm
4 cm
10 cm
The area of the given shape is 46 cm²
Formulas used:
Area of the triangle = (1/2) × Base × Height
Area of rectangle = Base × Width
Here we have
The composite figure with a right-angled triangle and a rectangle
In a right-angled triangle,
The base of the triangle = 3 cm
Height of the triangle = 4 cm
Area of the triangle
= (1/2) × base × height
= (1/2) × 3 × 4
= (1) × 3 cm × 2 cm
= 6 cm²
In rectangle,
Length of the rectangle = 10 cm
Width of the rectangle = 4 cm
Area of the rectangle
= Length × Width
= 10 cm × 4 cm
= 40 cm²
By the above calculations,
Area of the given figure = Area of triangle + Area of rectangle
= 6 cm² + 40 cm² = 46 cm²
Therefore,
The area of the given shape is 46 cm²
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Nachelle just accepted a job at a new company where she will make an annual salary of $57000. Nachelle was told that for each year she stays with the company, she will be given a salary raise of $4000. How much would Nachelle make as a salary after 4 years working for the company? What would be her salary after tt years?
a) Using the slope-intercept equation, after 4 years of working at the new company, Nachelle's salary will be $73,000 per annum.
b) After t years of working at the new company, Nachelle's salary will be $57,000 + $4,000(t).
What is the slope-intercept equation?The slope-intercept equation is in the form of y = mx + b.
The slope intercept describes the equation of a straight line, where m is the slope of the line, y and x are the y and x coordinates, and b is its y-intercept.
Initial starting salary per year = $57,000
Annual raise in salary = $4,000
Period = 4 years
Salary after 4 years = $73,000 [$57,000 + $4,000(4)]
Salary after t years = $57,000 + $4,000(t)
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How is the graphed system of equations classified?
Drag and drop words into the boxes to correctly complete the statements.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
A Response area system has at least one solution. A Response area system has an infinite number of solutions.
A system that has no solution is classified as inconsistent.
A system that has one and only one solution is classified as independent
The system of equation graphed is consistent and independent.
How to interpret the graph of linear equations?The equations given by the graph are expressed as;
3x - 4y = 32
3x + 5y = 24
Now, if we subtract eq 1 from eq 2, we will get;
5y - (-4y) = 24 - 32
9y = -8
y = -8/9
Put 8/9 for y in eq 2 to get;
3x + 5(8/9) = 24
3x = 24 - 40/9
3x = 176/9
x = 176/27
Now, to classify solution to equations, we say that;
1) When there is no solution, it is inconsistent.
2) When there is one and only one solution, it is independent
Since we have a solution and only one solution, then we can say that the system of equation graphed is consistent and independent.
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An experiment was conducted to evaluate the success of an Ebola virus vaccine. The subjects were unaware of the treatment they were given. What is this type of blinding used to prevent? Grounds for malpractice suits Subjects assigned randomly to treatments A possible source of bias Injury to the subjects The placebo effect
This type of blinding is used to prevent a potential source of bias in the experiment. By keeping the subjects unaware of the treatment they are receiving, the researchers can eliminate the possibility of any psychological effects influencing the outcome of the study. This is particularly important in cases where a treatment is being evaluated for subjective outcomes such as pain, anxiety, or depression, as the subjects' expectations and beliefs can influence their perception of the treatment's effectiveness. By keeping the subjects blinded to their treatment, researchers can ensure that the results of the study are as unbiased as possible.
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50x4-(3 divided by 2)
198.5 is the answer
50X4-(3÷2)=198.5
Answer: 198.5
Step-by-step explanation:
= 50x4-(3 divided by 2)
= 50x4-(3/2)
= (50 x 4) - ( 3/2 )
= (200) - (3/2)
= 200 - 1.5
= 198.5
10.)The charge for electricity consumption, E,
is partly constant and partly varies as the
number N of units used. The charge for 163
units is N453.80 while the charge for 42 units
is #139.20.
a Calculate the charge per unit of
electricity.
b Obtain a formula for E in terms of N.
On solving the provided question, we can say that - the charge for 42 units = is $139.20; so, charge per unit is 139.20/42 = $3.3142857143
What is unitary method ?The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
here,
the charge for 42 units = is $139.20.
so, charge per unit is 139.20/42 = $3.3142857143
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A hotel is offering two weekend specials. The first special is 3 nights and 4 meals for $233. The second
special is 3 nights and 3 meals for $226.50.
Part A: Write a system of equations to represent cost per night x and cost per meal y.
Part B: What is the cost per night and the cost per meal?
Answer: Part A:
To represent the cost per night x and cost per meal y in a system of equations, we can use the information provided in the question:
First Special:
3x + 4y = 233
Second Special:
3x + 3y = 226.50
Where x is the cost per night and y is the cost per meal.
Part B:
To find the cost per night and the cost per meal, we can use the information provided in the question and system of equations.
We can solve this system of equations using several methods: substitution or elimination method.
One common method to find the solution is by substitution method, where we find the value of x in terms of y from one of the equations and then substitute it into the other equation to solve for y.
x = (233 - 4y)/3
then substitute it into the other equation:
3(233 - 4y) + 3y = 226.50
now solve for y:
699 - 12y + 3y = 226.50
-9y = -472.50
y = 52.50
and we can substitute it back into the first equation:
3x + 4(52.50) = 233
3x = 80.50
x = 26.83
So the cost per night is $26.83 and the cost per meal is $52.50
Step-by-step explanation:
Machines at a factory produce circular washers with a specified diameter. The quality control manager at the factory periodically tests a random sample of washers to be sure that greater than 90 percent of the washers are produced with the specified diameter. The null hypothesis of the test is that the proportion of all washers produced with the specified diameter is equal to 90 percent. The alternative hypothesis is that the proportion of all washers produced with the specified diameter is greater than 90 percent. Which of the following describes a Type I error that could result from the test
Proportion is the ratio of the two equal fractions. It compares the part of a whole to another part of another whole. Option c is the correct option which is, The test provides convincing evidence the proportion is greater than 90% but the actual proportion is equal to the 90%.
What is proportion?
proportion is the ratio of the two equal fraction. It compare the part of a whole to other part of of the another whole.
Given
Options for the following question are,
A) The test does not provide convincing evidence that the proportion is greater then 90 percent but the actual proportion is greater then 90 percent.
B) The test does not provide convincing evidence the proportion is greater than 90% but the actual proportion is equal to the 90%.
C)The test provides convincing evidence the the proportion is greater than 90% but the actual proportion is equal to the 90%.
D)The test provides convincing evidence that the proportion is greater then 90 percent but the actual proportion is greater then 90 percent.
E) All type 1 error is not possible for this hypothesis test.
The Null Hypothesis for the given question is,
The proportion of all washers produced with the specified diameter is equal to 90 percent. The Null Hypothesis for the given case is true and actual proportion is equal to 90 percent.
Hence, option c is the correct option which is, The test provides convincing evidence tha the proportion is greater than 90% but the actual proportion is equal to the 90%.
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Factor Completely:
-3x² + 15x - 12
Answer:
-3 (x - 4) (x - 1)
Step-by-step explanation:
What is m∠B?
A. 67
B. 54
C. 57
D. 150
The measure of angle B is, 67°.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
Interior angles are,
⇒ ∠ C = 83°
⇒ ∠ B = 6x + 7
An exterior angle is,
⇒ ∠ A = 15x
Now, We know that;
The sum of two interior angles in a triangle is equal to the exterior angle in a triangle.
⇒ 83° + 6x + 7 = 15x
⇒ 90 = 15x - 6x
⇒ 90 = 9x
⇒ x = 10
Thus, The measure of B is,
⇒ m ∠B = 6x + 7
= 6×10 + 7
= 60 + 7
= 67
⇒ m ∠B = 67
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At Memorial High School, 60 of the 240 freshmen students are on an athletic team sponsored by the school. If the ratio is the same for the sophomore class, how many of the 220 sophomores are NOT athletes
Answer:
165 students or the sophomore class of 220 are not athletic.
Step-by-step explanation:
60/240 = .25 This means that 25% of the class is athletic. That would mean and .75 or 75% are not athletic.
220 x .75 = 165
Help please!! I would appreciate it
The behavior of the graph at the intervals are as follows
(0, 4} = increasing
(0, 2} = negative
{-2, 0) = decreasing
(-4, -1) = positive
How to determine the behavior of the function in the intervalsThe intervals represents some numbers and the numbers within the interval depends on the type bracket
(0, 4} = integer values from 1 2 3 4 at this interval the curve is going up hence increasing
(0, 2} = integer values from 1 2 at this interval the curve is on the negative side
{-2, 0) = integer values from -2 -1 at this interval the curve is on the decreasing
(-4, -1) = integer values from -3 -2 -1 at this interval the curve is on the on the positive side
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What is the difference 19√5 - 3√5 A.16 B.22 C.16√5 D.25
Answer:
C - 16√5
Step-by-step explanation:
Simply subtract 19 and 3 while keeping √5 the same.
19√5 - 3√5 = 16√5
a rectangular prism has dimensions of 8cm by 9cm by 10cm what is its volume?
A rectangular prism has dimensions of 8cm by 9cm by 10cm therefore the volume is 720cm³.
What is Volume?This is referred to as the measure of the space occupied within the boundaries of any three-dimensional solid.
Volume of rectangular prism = l × w × h where l is length, w is width and h is height.
Volume = 8cm × 9cm × 10cm = 720cm³.
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Y=6 and x=-1 parallel or perpendicular line
By plot in graph, we get Y=6 and x=-1 is perpendicular lines.
What is parallel line?Parallel lines are lines in a plane that are always the same distance apart and never intersect. They are coplanar lines that do not intersect each other, and they have the same slope.
What is perpendicular line?Perpendicular lines are lines that intersect at a right angle (90 degrees). In other words, they are lines that are at a 90-degree angle to each other. The slope of perpendicular lines are opposite reciprocals of each other, meaning that if one line has a slope of m, the other line will have a slope of -1/m.
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Tell whether the rate form a proportion. 4. 8 lap every 8 minute; 3. 6 lap every 6 minute
Yes, the rate 4.8 laps every 8 minutes; 3.6 laps every 6-minute form a proportion.
A proportion is an equation that sets two ratios at the same value. For instance, you might express the ratio as follows:
1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls. 0.25 are male (by dividing 1 by 4)
4.8 lap every 8 minutes will be equal to (4.8/8) = 0.6 lap a minute.
3.6 lap every 6 minutes will be equal to (3.6/6) = 0.6 lap in a minute.
Here, as the value of the ratio of both the quantities are same so the given values are said to be in Proportion.
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Find the area of the semi-circle with the radius of 4. 1mm. Round to the nearest tenth
The area of the semi-circle with the radius of 4.1 mm, round to the nearest tenth is 52.8 mm²
The area of the semi-circle will be calculated by the formula -
Area = 1/2πr², where r is the radius of the circle.
Keep the values in formula to find the value.of area of semi circle
Area = 1/2×3.14×4.1²
Performing multiplication on Right Hand Side of the equation to find the area of the semi-circle
Area = 52.78 mm²
Round off the nearest tenth
Area = 52.8 mm²
Thus, the area of semi-circle with mentioned radius is 52.8 mm².
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Sandy ate 1/6 of the candy bar John ate 3/4 of it how much more of the candy bar did John eat then Sandy
Answer: 7/12
Step-by-step explanation:
Based on the given conditions, formulate: 3/4 - 1/4
Find the common denominator and write the numerators above the common denominator: 9/12 - 2/12
Calculate the product or quotient:
Write the numerators over the common denominator: 9-2
12
Calculate the sum or difference: 7/12
Answer: 7/12
Given the function p(x)=6x+2, compare and contrast p(-2) and p(4). Choose the statement that is true concerning these two values.
(A) The value of p(-2) is larger then the value of p(4).
(B) The value of p(-2) is smaller then the value of p(4).
(C) The value of p(-2) is the same as the value of p(4).
(D) The values of p(-2) and p(4) cannot be compared.
Given the function p(x)=6x+2, p(-2) is -10 while p(4) is 26, this shows that value of p(-2) is smaller than the value of p(4). The correct option is B.
What is a function?A function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). It is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. Let A & B be any two non-empty sets; mapping from A to B will be a function only when every element in set A has one end, only one image in set B.
p(x)=6x+2
for p(-2)
p(-2) = 6(-2) + 2
p(-2) = -12 + 2
p(-2) = -10
for p(4)
p(4) = 6(4) + 2
p(4) = 24 + 2
p(4) = 26
p(-2) < p(4)
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Answer:
(B) "The value of p(-2) is smaller then the value of p(4)" is True
Step-by-step explanation:
p(x)=6x+2
p(-2) = 6*(-2)+2
p(-2) = -12+2
p(-2) = -10
p(4) = 6*(4)+2
p(4) = 26
====
p(-2) = -10
p(4) = 26
===
(A) The value of p(-2) is larger then the value of p(4). False
(B) The value of p(-2) is smaller then the value of p(4). True
(C) The value of p(-2) is the same as the value of p(4). False
(D) The values of p(-2) and p(4) cannot be compared. False
In a certain year, 31% of adults in a certain country viewed college education as essential for success. For the following ten-year period, this percentage increased by approximately 2. 6 each year.
The percentage of adults from this country who viewed a college education as essential for success x years after the first year can be represented by __
The percentage of adults from this country who viewed a college education as essential for success x years after the first year can be represented by the function P(x) = 31 + 2.6x.
What is the percentage function?
To determine the percentage, we have to divide the value by the total value and then multiply the resultant by 100. Percentage formula = (Value/Total value) × 100. Example: 2/5 × 100 = 0.4 × 100 = 40 per cent.
The percentage of adults from this country who viewed a college education as essential for success x years after the first year can be represented by the function:
P(x) = 31 + 2.6x
Where P(x) is the percentage of adults who viewed college education as essential for success x years after the first year, and x is the number of years after the first year.
The function shows that the percentage increase by 2.6 every year for x years after the first year, and the initial percentage is 31%.
This function is representing a linear trend since the coefficient of x is constant.
Hence, The percentage of adults from this country who viewed a college education as essential for success x years after the first year can be represented by the function P(x) = 31 + 2.6x.
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