Answer:
Step-by-step explanation:
the answer is 4
Find the value of k such that the system of linear equations is inconsistent.
6x-12y = -7
2x + ky = 14
For the given system of linear equations 6x-12y = -7 and 2x + ky = 14 the value of k for which linear equations are inconsistent is k= -4.
As given in the question,
Given system of linear equations are as follow:
6x-12y = -7 ____(1)
2x + ky = 14 _____(2)
Form equation (1) we have,
6x -12y = -7
⇒3 ( 2x -4y) = -7
⇒ 2x - 4y = -7 /3 ____(3)
From equation (2) and (3) we have,
2x + ky = 14
2x - 4y = - 7/3
Value of k so that the given system of equations are inconsistent is given by:
k = -4
For inconsistent there is no solution.
Therefore, for the given system of linear equations 6x-12y = -7 and 2x + ky = 14 the value of k for which linear equations are inconsistent is k= -4.
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Allison has 2 aquariums. In each aquarium she has 2 families of guppies and 3 tetras. Leigh has 1
16
aquarium with 10 tetras and 3 families of guppies. Allison and Leigh have the same number of
fish and their guppy families each have the same number of members. How many guppies are in
each family?
PLEASE HELP URGENT
By solving a linear equation, it can be calculated that
There are 4 guppies in each family
What is a linear equation?
At first it is important to know about equation.
An equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sigh
A one degree equation is known as linear equation.
Here a linear equation needs to be solved
Let the number of guppies in each family be x
Allison has 2 aquariums.
In each aquarium she has 2 families of guppies and 3 tetras.
Total number of fishes Allison have = 2(2x + 3) = 4x + 6
Leigh has 1 aquarium with 10 tetras and 3 families of guppies.
Total number of fishes Leigh have = 3x + 10
By the problem,
4x + 6 = 3x + 10
4x - 3x = 10 - 6
x = 4
There are 4 guppies in each family
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A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 72 feet per second. The height $h$, in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=-16 t²+72 t+7. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at ? second(s) after launch.
(Simplify your answer.)
The maximum height reached by the object is ? feet.
(Simplify your answer.)
The time taken for the rocket to reach its maximum height is; 2.25 seconds.
The maximum height reached by the toy rocket is; 88 feet.
What is the maximum height reached by the rocket?It follows from the task content that the maximum height reached by the rocket is to be determined.
The given function is; h (t) = -16 t² + 72t + 7.
Since it follows from evaluation that; at maximum height, the rate of change of height to time is equal to 0.
Therefore; at maximum height;
h'(t) = 0
h'(t) = -32t + 72 = 0
-32t = -72
t = -72/-32
t = 2.25 seconds.
Therefore, the time taken for the rocket to reach its maximum height is; 2.25 seconds.
Also, the maximum height reached by the rocket is at; h (2.25);
h(2.25) = -16(2.25)² + 72 (2.25) + 7
= -81 + 162 + 7
= 88.
The maximum height reached is; 88 feet.
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Select answers from the drop-down menus to correctly complete the statements. A scale factor of Choose... was applied to the first triangle to the get the resulting image. This scale factor is Choose... .
((Image: An isosceles triangle with a side length of 3.4. An arrow points to a smaller isosceles triangle with a side length of 1.7)
Answer: A scale factor of 1/2 was applied to the first triangle to get the resulting image.
Step-by-step explanation: The initial side length of 3.4 is twice as long as 1.7, the initial triangle was reduced to half of the initial size.
Answer:
The triangle is still an equilateral triangle as before, and the only difference is that the side length is halved from 3.4 to 1.7 (3.4/2=1.7). Therefore, the scale factor is 1.7/3.4=0.5. A scale factor <1 means that the original shape is reduced. The scale factor would be a reduction.
Step-by-step explanation:
The image would be of a triangle.
Hope this helps! :))
1,1,2,3,4,5,7,9,
Find the common value
Find all intervals on which the function f(x) = (e^(2x^2+5)/-6x is decreasing.
The function f(x) is decreasing on the interval x∈(1/2,∞) and all the real values.
What is meant by a function?A function from a set X to a set Y in mathematics assigns to each element of X exactly one element of Y. The domain of the function is the set X, and the codomain of the function is the set Y.
The first known approximation to the concept of function is attributed to the Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were originally idealistic representations of how one variable quantity depended on another. The location of a planet, for example, changes throughout time. Historically, the concept was formed with infinitesimal calculus near the end of the 17th century, and the functions that were analyzed were differentiable until the 19th century.
Given function,
f(x)=[tex]e^{2 x^{2} +5}[/tex]/-6x
f'(x)=-1/6x([tex]e^{2 x^{2} +5}[/tex])(4x)+[tex]e^{2 x^{2} +5}[/tex](1/6x²)
=[tex]e^{2 x^{2} +5}[/tex]/6x((1/x)-4x)
f'(x)=0
((1/x)-4x)=0
1-4x²=0
4x²=1
x=±1/4
Given that, f(x) is decreasing function then,
f'(x)<0
((1/x)-4x)<0
(1-4x²)/x<0
1-4x²<0
1<4x²
1/4<4x²
x²>1/4
x>1/2
x∈(1/2,∞)
Hence, f(x) is decreasing on the interval x∈(1/2,∞)
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What is the average hourly pay of someone making 45,000 per year? Assume a 40 hour workweek and a 52 week year.
The average hourly pay of person making 4500 per year is 21.63 per hour.
Given that,
we have to find what does a person making $45,000 a year make per hour on average, Assume a 52-week year and a 40-hour workweek.
To calculate this
The ratio of the sum of the values in a given set to all the values in the set is the mean value, which is the definition of the average.
We have to multiply 52-week year and a 40-hour work week.
40×52
2080
Now, divide 45000 by 2080
45000/2080
21.63
Therefore, The average hourly pay of person making 4500 per year is 21.63 per hour.
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Find m<1, m<2 and m<3 86 degree 12 and 3
The angle measures are <1 = 86 degrees, <2 = 94 degrees and <3 = 86 degrees
How to determine the measure of each angle?The possible diagram that completes the question is added as an attachment
From the attached diagram, we have the following representation
<1 + <2 = 180 degrees --- by the theorem of supplementary angles
Also, we have the following angle measure
Given that
<1 = 86 degrees
Substitute the known values in the above equation
So, we have the following equation
86 + <2 = 180
Evaluate the like terms
<2 = 94
Also, we have
<3 = <1 --- by the theorem of vertical angles
Substitute the known values in the above equation
<3 = 86
This is so because <1 = 86 degrees
Hence, the measures of the angles are <1 = 86 degrees, <2 = 94 degrees and <3 = 86 degrees
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Write an equation in standard form of the line that passes through
(–9, 4) and has a slope of –2/3.
(Add explanation please )
Also, Write the standard form of the equation y + 4 = – ⅗ (x – 8).
Answer:
2x + 3y = - 63x + 5y = 4-------------------------------
Standard form of a lineax + by = cGivenPoint on the line (-9, 4) and a slope m = - 2/3Use point- slope form and convert to standardy - y₁ = m(x - x₁), where (x₁, y₁) is the point on the liney - 4 = - 2/3(x - (-9))y - 4 = - 2/3(x + 9)3(y - 4) = - 2(x + 9)3y - 12 = - 2x - 182x + 3y = 12 - 182x + 3y = - 6Standard of the line y + 4 = - 3/5(x - 8)y + 4 = - 3/5(x - 8)5(y + 4) = - 3(x - 8)5y + 20 = - 3x + 243x + 5y = 24 - 203x + 5y = 4Please help me verify. I am stuck.
The trigonometric identity presented in this problem is proved trough the answer, reaching an answer 1 = 1.
Proving the identityThe identity is presented as follows:
[tex]\csc{\beta} + 1 = \frac{\cot{\beta}}{\sec{\beta} - \tan{\beta}}[/tex]
Then we take the right side of the denominator, and apply the subtraction of perfect squares to the denominator, as follows:
[tex]\frac{\cot{\beta}}{\sec{\beta} - \tan{\beta}} \times \frac{\sec{\beta} + \tan{\beta}}{\sec{\beta} + \tan{\beta}} = \frac{\cot{\beta}(\sec{\beta} + \tan{\beta})}{\sec^{2}{\beta} - \tan^2{\beta}}[/tex]
The following identity relates the square of the secant and of the tangent:
[tex]\tan^2{\beta} + 1 = \sec^2{\beta}[/tex]
Hence:
[tex]\sec^2{\beta} - \tan^2{\beta} = 1[/tex]
Thus the remaining expression is:
[tex]\frac{\cot{\beta}(\sec{\beta} + \tan{\beta})}{\sec^{2}{\beta} - \tan^2{\beta}} = \cot{\beta}(\sec{\beta} + \tan{\beta})[/tex]
The equations of the cotangent, secant and tangent are given as follows:
Cotangent: cosine/sine.Secant: 1/cosine.Tangent: sine/cosine.Hence:
[tex]\cot{\beta}(\sec{\beta} + \tan{\beta}) = \frac{\cos{\beta}}{\sin{\beta}}\left(\frac{1}{\cos{\beta}} + \frac{\sin{\beta}}{\cos{\beta}}\right) = \frac{1}{\sin{\beta}} + 1[/tex]
One divided by the sine is the cosecant, as follows:
[tex]\frac{1}{\sin{\beta}} = \csc{\beta}[/tex]
Hence the simplified expression is:
[tex]\csc{\beta} + 1[/tex]
Which is equivalent to the right side of the expression, hence an identity of the format 1 = 1 is reached and the identity is proven.
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One hundred eight Americans were surveyed to determine the number of hours they spend watching television each month. It was revealed that they watched an average of 151 hours each month with a standard deviation of 32 hours. Assume that the underlying population distribution is normal.
Which distribution should you use for this problem? (Enter your answer in the form z or tdf where df is the degrees of freedom.)
The Z distribution also referred to as the standard normal distribution is the distribution that we would have to use here.
What is the z distribution?A unique type of normal distribution with a mean of 0 and a standard deviation of 1 is known as the standard normal distribution, or z-distribution.
By transforming the values of any normal distribution into z-scores, it is possible to standardize it. Z-scores indicate the number of standard deviations from the mean that each value falls within.
This is the z distribution given that the value of n is more than 30.
We have to make use of z when n which is the number of samples is greater than 30.
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Hey can someone please help me out? Thank you so much!
Answer:
Step-by-step explanation:
area=10×5+[(15-5)+7]/2×(10-6)
=50+(17)/2×4
=50+34
=?
What is the probability of drawing an event number then drawing a diamond out of a deck?
Probability is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
The probability of drawing an even number from a deck of cards is 5/13.
The probability of drawing an even number and then drawing a diamond out of a deck is 1/8.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
The number of even numbers in a deck of cards.
= 5 x 4
= 20
The number of diamonds in a deck of cards.
= 4
Now,
The probability of drawing an even number from a deck of cards.
= 20 / 52
= 10/26
= 5/13
Now,
The remaining cards.
= 52 - 20
= 32
The probability of drawing diamonds after drawing the even numbers.
= Number of diamonds / remaining cards
= 4 / 32
= 1/8
Thus,
The probability of drawing an even number from a deck of cards is 5/13.
The probability of drawing an even number and then drawing a diamond out of a deck is 1/8.
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I need the answer:’)
Answer:
its D
Step-by-step explanation:
calculator
The following data represent the number of people aged 25 to 64 years covered by health insurance (private or government) in 2018. Approximate the mean and standard deviation for age.
Age: 25-34 35-44 45-54 55-64
Number: 24.3 36.1 36.7 20.9
(Millions)
The mean age is:
The standard deviation is:
The mean age is equal to: 44.09.
The standard deviation is equal to: 10.07.
How to determine the mean age and standard deviation?First of all, we would determine the median of each class interval as follows:
Median 1 = (25 + 34)/2 = 29.5
Median 2 = (35 + 44)/2 = 39.5
Median 1 = (45 + 54)/2 = 49.5
Median 1 = (55 + 64)/2 = 59.5
Next, we would calculate the mean age by using this mathematical expression:
Mean age = ∑fx/∑f
Substituting the given parameters into the formula, we have;
Mean age = [(24.3 × 29.5) + (36.1 × 39.5) + (36.7 × 49.5) + (20.9 × 59.5)]/(24.3 + 36.1 + 36.7 + 20.9)
Mean age = [716.85 + 1,425.95 + 1,816.65 + 1,243.55]/118
Mean age = [5,203]/118
Mean age = 44.09.
Now, we can calculate the standard deviation as follows:
Standard deviation, S = √((∑f(xi - μ)²/∑f)
Standard deviation, S = √((24.3 × (29.5 - 44.09)² + (36.1 × (39.5 - 44.09)² + (36.7 × (49.5 - 44.09)² + (20.9 × (59.5 - 44.09)²)/(24.3 + 36.1 + 36.7 + 20.9))
Standard deviation, S = √((5172.70 + 760.56 + 1,074.14 + 4,963.08)/118)
Standard deviation, S = √(11,970.48/118)
Standard deviation, S = √101.5
Standard deviation, S = 10.07.
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NO LINKS!! Please help me with this one
Answer:
The letter a in an ellipse equation is:
Half of the major axis if a > b and the ellipse is horizontal, orHalf of the minor axis if b > a and the ellipse is vertical.Step-by-step explanation:
General equation of an ellipse
[tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex]
where:
center = (h, k)Vertices = (h±a, k) and (h, k±b)Foci = (h±c, k) or (h, k±c) where c²=a²−b²If a > b the ellipse is horizontal, a is the major radius, and b is the minor radius.
If b > a the ellipse is vertical, b is the major radius, and a is the minor radius.
The major axis is the longest diameter of an ellipse, so the major radius is one half of the major axis.
The minor axis is the shortest diameter of an ellipse, so the minor radius is one half of the minor axis.
Therefore the letter a in an ellipse equation is:
The major radius (half of the major axis) if a > b and the ellipse is horizontal, orThe minor radius (half of the minor axis) if b > a and the ellipse is vertical.Name a plane in the image.
A
•C
B
Answer:
ABCStep-by-step explanation:
A is a point
AB is a line
ABC is a plane
Therefore, ABC is a plane.
__________________
Hope this helps!
Have a great day!
Lea sold half of her comic books and then
bought seven more. She now has 29.
With how many did she begin?
A pet store has 7 cats. Here are their weights (in pounds).
14, 11, 10, 10, 6, 8, 14
Send data to calculator
Find the mean weight of these cats.
If necessary, round your answer to the nearest tenth.
pounds
To find the arithmetic mean (average) of a group of numbers add the numbers and divide by the total number of items we added.
(12+16+10+8+14+15)/6
= 75/6
= 12.5 (answer is already rounded to nearest tenth)
will reward brainliest please help!!!
Dianelys accepted a new job at a company with a contract guaranteeing annual raises. In the first year, Dianelys' salary will be $40000, and she will get a raise of $2500 every year. Make a table of values and then write an equation for S,S, in terms of n,n, representing Dianelys' salary after working nn years for the company.
1. Dianely's salary can be represented with the following table of values for 5 years as follows:
Year Salary
1 $40,000
2 $42,500
3 $45,000
4 $47,500
5 $50,000
2. The equation to model Dianely's salary after n years is S = 40,000 + 2,500n.
What is an equation?An equation is a mathematical statement equating two or more mathematical expressions.
Equations use variables, numbers, mathematical operands, and the equation symbol (=).
Dianely's initial salary = $40,000
Salary raise per year = $2,500
Dianely's salary after n years in equation form, S = 40,000 + 2,500n.
Table of Values for Dianely's Salary:Year Salary
1 $40,000
2 $42,500 (40,000 + 2,500)
3 $45,000 (42,500 + 2,500)
4 $47,500 (45,000 + 2,500)
5 $50,000 ($47,500 + 2,500)
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Suppose the government has a balanced budget and wants to increase spending without changing tax rates. The government enters the loanable funds market to borrow $150 billion for economic stimulus spending. How much money is available for private investment after this action has shifted the demand curve as shown in the figure?
The money available for private investment is $250 billion dollar
What is demand curve ?
The demand curve is a graphical representation of the connection between the cost of a commodity or service and the amount that is demanded over time. The price will often be shown on the left vertical axis in a representation, and the amount needed will typically be shown on the horizontal axis.
Refer to the attachment for graph:
Once investments and government borrowing are added together, the total is = $400
if borrowing from the government is= $150
private investment
=( investment and and government borrowing) - (government borrowing )
= $400 - $150 = $250
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what is -112 = -7(v + 4) ?
Answer:
Step-by-step explanation:
1.) -112*-7=784
784=v+4
2.)784-4=780
v=780
Answer:
v = 12
Step-by-step explanation:
-112 = -7v -28
7v = 112 - 28
7v = 84
7/7 v = 84/7
v = 12
Can you write 6 x 10^5 x 0.08 in scientific notation.
Please.
4.8 × 10^4
Step-by-step explanation:= 4.8 × 10^4 {scientific notation}= 4.8e4 {scientific e notation}= 48 × 103 {engineering notation - thousand; prefix kilo- (k)}= 4.8 × 104 {standard form}4 {Order of Magnitude - for scientific and standard forms}= 48000 {real number}= forty-eight thousand {word form}Anika earns $5 a week for doing all of her chores around the house. Which graph below represents this relationship between x, the number of weeks she has been doing chores, and y, the amount of money she has earned?
The graph of the linear equation can be seen in the image at the end.
Which graph represents the amount of money Anika has?We start by defining the variables we will use:
x = number of weeks.
y = money that Anika has.
We assume that Anika starts with $0, and then she wins $5 each week, so after x weeks she has:
y = $5*x
To graph this linear equation we need to find two points on the line, if x = 0 we get:
y = $5*0 = $0
So we have the point (0, 0)
if x = 1
y = $5*1 = $5
So we have the point (1, 5)
Now we can graph these two points and connect them with a line, the graph can be seen below.
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Select the correct answer.
Which set of absolute values is compared correctly?
A. -71 <181<|9|<1-10|
B.1-41 <1-3/<13<|4|
C. 1211-51> |-7|>1-81
D. 1-41>19> |-31 >|-10|
Answer: A
Step-by-step explanation:
The absolute value of a number is its relative distance from zero, so it doesn't matter if it is negative. For example, -3 and 3 are both 3 units away from zero on the number line.
An amusement park has two types of season passes. Plan 1 charges a one-time fee of $145.00 for admission
plus $5.00 every trip for parking. Plan 2 charges a one-time fee of $40.00 for parking plus $12.00 every trip for
admission. For what number of trips is the cost of these plans the same?
The number of trips after the cost of the plan A and plan B is 16.
According to the question,
We have the following information:
Plan 1 charges a one-time fee of $145.00 for admission plus $5.00 every trip for parking. Plan 2 charges a one-time fee of $40.00 for parking plus $12.00 every trip for admission.
So, this will make an arithmetic progression.
The formula to find nth term of an A.P:
an = a+(n-1)d where a is the first term
Now, on left hand side, we have nth term for plan A and on the right hand side, we have the nth term for plan B because their nth term will be equal.
145+(n-1)5 = 40+(n-1)12
145+5n-5 = 40+12n-12
5n+140 = 12n+28
140-28 = 12n-5n
7n = 112
n = 112/7
n = 16
Hence, the number of trips after the cost of the plan A and plan B is 16.
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Find a number that is 6 times as large as 9 minus 3
The required number is 1 which represents "6 times as large as 9 minus 3".
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is reasoning.
We have to determine the number that is "6 times as large as 9 minus 3".
Let the required number would be x
Translate the phrase "6 times as large as 9 minus 3" into the algebraic form :
⇒ 6 × x = 9 - 3
⇒ 6x = 6
⇒ x = 6 / 6
⇒ x = 1
Thus, the required number is 1 which represents "6 times as large as 9 minus 3".
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The ratio of teachers to students on a field trip is 2:13. If there are 132 more students than adults on the field trip, how many adults are there and how many students are there?
There are 284 number of students and 152 number of adults.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
The ratio of teachers to students on a field trip is 2:13
Let x be the number of adults
If there are 132 more students than adults on the field trip, then 132+x
To find the number of adults and number of students formulate a equation as below
2/13=(x+132)/x
Apply cross multiplication
2x=13(x+132)
Apply distributive law on RHS
2x=13x+1716
11x=1716
Divide both sides by 11
x=152
x+132=152+132=284
Hence there are 284 number of students and 152 number of adults.
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what percent is 25 of 100
Answer:
25 percent.
Step-by-step explanation:
25 divided by 100 is equal to 0.25. You then multiply that by 100 to get percent, which is 25 percent.
Hope it helps.
The blood types of 200 people are collected at a doctor’s office. The table shows the breakdown of patients by blood type.
If a person from this group is selected at random, what is the probability that this person has type AB blood? Express your answer as a fraction in lowest terms or as a decimal rounded to the nearest millionth (if necessary).
Blood Type Survey Results
Blood Type Number of Patients
A 45
B 65
O 75
AB 15
Answer:
[tex]\frac{3}{40}=0.075[/tex]
Step-by-step explanation:
The probability of a person selected at random from this group having type AB blood is 15 out of 200 total people. Therefore:
[tex]\frac{15}{200}=\frac{3}{40}=0.075=7.5\%[/tex]
