The solution set for all possible side lengths for side L is;
⇒ L < 7
What is Triangle?
A triangle is a three sided polygon , which has three vertices and three angles.
Given that;
The longest side of a triangle must be less than the sum of the other two sides.
Suppose a triangle is made up of lengths 2 inches, 5 inches and L. inches, where, L is the longest side.
Now, By the given condition;
''The longest side of a triangle must be less than the sum of the other two sides.''
We can formulate;
L < 2 + 5
L < 7
So, The solution set for all possible side lengths for side L is;
⇒ L < 7
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Please help with the following question:
Using it's concept, the probabilities are given as follows:
a) Type A die and orange: 1/10 = 0.1.
b) Blue: 23/30
c) Type B, if blue: 8/23.
What is a probability?A probability is calculated as the number of desired outcomes in the experiment divided by the number of total outcomes in the experiment.
For item a, the probability that a type A dice is chosen is:
3/5.
As there are 5 dices, 3 of type A and 2 of type B.
The probability that a type A dice comes up orange is:
1/6.
As it has six faces, one of which is orange.
Then the probability of an orange type A dice being chosen is:
3/5 x 1/6 = 1/10 = 0.1.
For item b, the probability of blue is divided as follows:
5/6 of 3/5 -> type A.4/6 of 2/5 -> type B.Hence the probability of a blue dice is:
p = 5/6 x 3/5 + 4/6 x 2/5 = 23/30
For item c, we apply the conditional probability, hence the probability is given as follows:
p = (4/6 x 2/5)/(23/30) = (8/30)/(23/30) = 8/23.
Dividing the probabilities of type B and blue by the probability of blue.
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Graph the quadratic equation ^^2m² + m +3 = 0
Given -
2m² + m +3 = 0
To Find -
2m² + m +3 = 0
Step-by-Step Explanation -
2m² + m +3 = 0
We will first calculate the roots of the equation:
[tex]\begin{gathered} m\text{ = }\frac{-b\text{ }\pm\sqrt{b^2\text{ - 4ac}}}{2a} \\ \\ Here,\text{ } \\ \\ a\text{ = 2, b = 1, c = 3} \\ \\ On\text{ Putting the values in the equation,} \\ \\ m\text{ = }\frac{-1\pm\sqrt{1^2\text{ - 4}\times2\times3}}{2\times2} \\ \\ m\text{ = }\frac{-1\pm\sqrt{-23}}{4} \end{gathered}[/tex]So, Both the roots are imaginary.
having d = -23
Final Answer:
Graph :
Can you help me with this question
The component form of vector is (-6,8)
What is vector ?Geometrical objects with magnitude and direction are called vectors. A line with an arrow pointing in its direction can be used to represent a vector, and the length of the line corresponds to the vector's magnitude. As a result, vectors are depicted as arrows and have starting and ending points. It took 200 years for the idea of vectors to develop. Physical quantities like displacement, velocity, acceleration, etc. are represented by vectors.Additionally, the development of the field of electromagnetic induction in the late 19th century marked the beginning of the usage of vectors. Here, we'll examine the definition of vectors as well as their characteristics, mathematical formulas, and uses.
The component form of vector is (-6,8)
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is the quotient of two natural numbers is always a rational number a true or false statement
Answer:
True
Step-by-step explanation:
Find the answer to the green box give your answer in simplest form
Apply right triangle proportions:
[tex]\frac{16}{x}=\frac{x}{20}[/tex]20 (16) = x (x)
320 = x^2
√320 = x
x = 8√5
Ax+By=C2y=3x+6 in standard format
The given equation written in standard format is 3x - 2y = -6
Standard form of linear equations with two variablesFrom the question, we are to write the given equation in standard format.
The given equation is
2y = 3x + 6
The standard form of a linear equation with two variables is
Ax + By = C
Where x and y are the variables
A is the coefficient of x
B is the coefficient of y
and C is the constant
Now, we will write the given equation in the format
2y = 3x + 6
Subtract 3x from both sides of the equation
2y - 3x = 3x - 3x + 6
-3x + 2y = 6
Multiply through by -1
3x - 2y = -6
The standard format of the equation is 3x - 2y = -6
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A company sells 1000 packs of cards per day at a price of $5 per pack. With every $0.02 reduction in price, 10 more packs a day are sold. Under these conditions, what is the maximum possible income per day, and what price per pack of cards will produce this income? Include how much extra money is made with this new price structure.
From the statement, we know that:
0. the company sells 1000 packs of cards per day for $5 per pack,
,1. with every $0.02 reduction in price, 10 more packs a day are sold.
To solve this problem, we define the following variables and functions:
• r = # of price reductions,
• n(r) = # of packs sold by the company as a function of r,
,• p(r) = price per pack (in $) as a function of the # of price reductions,
,• I(r) = income (in $) as a function of the # of price reductions.
Using points 1 and 2, we write the following functions: function of # of packs sold n(r) as:
• the i
[tex]n(r)=1000+10*r,[/tex]• the function of the price per pack p(r):
[tex]p(r)=5-0.02*r,[/tex]• the function for the income I(r) is given by the product of the # of packs sold n(r) and the price per pack p(r):
[tex]I(r)=n(r)*p(r)=(1000+10*r)*(5-0.02*r)=-0.2r^2+30r+5000.[/tex](1) To find the maximum income, we must maximize the function I(r) for r. To do that, we compute and make equal to zero its first derivative:
[tex]I^{\prime}(r)=-0.2*2r+30=0.[/tex]Solving for r, we get:
[tex]\begin{gathered} -0.4r+30=0, \\ 0.4r=30, \\ r=\frac{30}{0.4}=75. \end{gathered}[/tex]We have found that the maximum income is achieved when the # of price reductions is equal to r = 75.
(2) s
[tex]I(75)=-0.2*75^2+30*75+5000=6125.[/tex]We have found that the maximum possible income per day is $6125.
(3) s
[tex]p(r)=5-0.02*75=3.5.[/tex]We have found that the price per pack that maximizes the income is $3.5.
(4) s
[tex]1000*\text{ \$}5=\text{ \$}5000.[/tex]With this new price structure, the company wins $6125 s
Answer• The maximum possible income per day is $6125.
,• The price per pack that maximizes the income is $3.5.
,• The company makes $1125 extra with this new price structure.
19. Ciara is saving for a video game. The first week, she puts $2 dollars in an
envelope. Each week after that, she puts twice as much in the envelope as
she did the previous week. How many dollars does she save on the 6th
week? How many dollars does she save in all?
Answer:
On sixth week , she collects 2⁶ = $64.
She saves 2(1+2+4+8+16+32) = $126 in all.
Element X decays radioactively with a half life of 13 minutes. If there are 430 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 6 grams?
Using an exponential function, it is found that it would take 80.12 minutes for the element to decay to 6 grams.
What is an exponential function?An exponential function is defined according to the following rule:
[tex]y = a(b)^{\frac{t}{n}}[/tex]
In which:
a is the initial value of the function.b is the rate of change of the function.n is the time in which the rate of change occurs.Considering the half life of the substance, and the initial amount of 430 grams, the parameters are given as follows:
a = 430, b = 0.5, n = 13.
Then the amount of the substance after t minutes is given by:
[tex]y = 430(0.5)^{\frac{t}{13}}[/tex]
The time it will take for the element to 6 grams is t when y = 6, hence:
[tex]6 = 430(0.5)^{\frac{t}{13}}[/tex]
[tex](0.5)^{\frac{t}{13}} = \frac{6}{430}[/tex]
[tex]\log{((0.5)^{\frac{t}{13}})} = \log{\left(\frac{6}{430\right)}[/tex]
[tex]\frac{t}{13}\log{0.5} = \log{\left(\frac{6}{430\right)}[/tex]
[tex]t = 13\frac{\log{\left(\frac{6}{430}\right)}}{\log{0.5}}[/tex]
t = 80.12 minutes.
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Please help me I was sick today and missed out on class and I don’t understand this question
I hope this is clear enough , although I did not arrive at the same answer using x in both equation .
Use the drawing tool(s) to form the correct answer on the provided graph.
Graph the inverse of the line provided on the graph.
Answer:
(4,8) x=4/y=8
Step-by-step explanation:
the four is the x line and the 8 the y line.
4 laying down line to the right (positive four)
8 straight up line top(positive 8)
Stephen subtracts 3.48 from 154.2 and gets an answer of 119.4. Use estimation to explain how you know Stephen's answer is incorrect. Then, explain a strategy Stephen could use to solve this problem.
1. Using estimation shows that Stephen's answer is incorrect because when the whole number 3 is subtracted from 154, it gives 151 and not 119. The actual result should be between 150 and 151.
2. The strategy that Stephen could use to solve this subtraction problem is an approximation. Approximately, 3.48 is 3.5, but for a quick estimation, the decimals are eliminated or appropriated.
What is estimation?Estimation means a rough calculation or an approximation.
Estimation provides a quick means of arriving at number solutions without going into detailed calculations.
Estimates are used for decision-making when complete information is not required or available.
The minuend = 154.2
The subtrahend = 3.48
The estimated value of the minuend reduces it to 154.
The estimated value of the subtrahend reduces it to 3.
Using estimation, the difference = 151 (154 - 3)
Actual difference = 150.72 (154.2 - 3.48)
The actual difference can be approximated to 151.
Thus, using appropriate estimation, Stephen can easily solve this subtraction problem without difficulty.
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Percent that’s equivalent to 15/50
The percentage that equivalent to 15/50 is 30%
The given term is 15/50
The percentage is defines as a relative value indicating hundredth parts of any number. It is denoted using the percentage symbol "%". We can also say that percentage is a number or ratio expressed as a fraction of 100.
The given term is 15/50
Here the denominator is 50 and numerator is 15
To find the equivalent percentage, first we have to divide 15 by 50, then multiply the result by 100
15/50 = 0.3
Multiply the result by 100
0.3×100 = 30%
Hence, the percent that equivalent to 15/50 is 30%
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if g(x)=2x+x, what is g(7)?
Answer:
g(7) = 21
Explanation:
To calculated g(7), we need to replace x by 7 in g(x) as:
[tex]\begin{gathered} g(x)=2x+x \\ g(7)=2(7)+7 \\ g(7)=14+7 \\ g(7)=21 \end{gathered}[/tex]Therefore, g(7) is equal to 21
What is the explicit formula for this geometric sequence?
8, 4, 2, 1,...
The explicit formula of the given geometric sequence is a(n) = 8(1/2)ⁿ⁻¹.
What is a geometric sequence ?Every term in a geometric series is obtained by multiplying the term before it by the same number aₙ= aₙ₋₁ + d is the general phrase for it. The common ratio is denoted by the number r. Any term in the sequence can be used to find it by dividing it by the word before it.
Any number series in which the ratio of succeeding terms is constant is referred to as a geometric sequence. where r is the proportion shared by all following terms. For instance, "2,6,18,54,162,486,1458,...
We have a sequence: 8, 4, 2, 1
The above sequence represents the geometric sequence with common ratio:
r = 4/8 = 1/2
First term a = 8
nth term:
a(n) = 8(1/2)ⁿ⁻¹
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Apply the distributive property to the expression 5(2 + y) to produce an equivalent expression.
Answer:
10+5y
Step-by-step explanation:
5(2+y)
distribute
=5(2)+5(y)
simplify
=10+5y
Find the x intercepts of the graph of the function.
g(x)=-1(x-4)(x+2). Hint x intercepts happen when g(x)=0.
(Show Work)
The X- intercept of the graph of the function at x =>-4 and x = 2.
The provided function is g(x)=-1(x-4)(x+2).
The x intercept of the function means, that point at which the graph of function will have the y coordinate as zero.
So, the x intercept of the function will be at the point where the function g(x) will be equal to zero.
g(x) = 0
-1(x-4)(x+2) = 0
(4-x)(x+2) = 0
Here,
We will get two values of x at which g(x) will be zero,
X = 4 and -2.
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what determines the type of feedback?
answer asap for brainlist
Answer:
A
Step-by-step explanation:
if you feel cold your body will tell your brain or give feedback to make you think or say its cold
Which equation is in the point slope-form and is depicted by this graph
Explanation
iven the points (-1,-4) and t(3,2). The points slope form of the equation can be found using the formula
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \\ where\text{ x}_1,y_1=-1,-4 \\ x_2,y_2=3,2 \end{gathered}[/tex]We would then substitute the value into the formula;
[tex]\begin{gathered} y-(-4)=\frac{2-(-4)}{3-(-1)}(x-(-1)) \\ y+4=\frac{6}{4}(x+1) \\ y+4=\frac{3}{2}(x+1) \end{gathered}[/tex]Answer: Option 3
at what rate is the amount of water in the tank changing? Use a signed number, and include the unit of measurement in your answer.
Part A) The tank's water level is changing at a rate of -[tex]\frac{2}{3}[/tex] gallons per minute.
Part B) The tank will finish draining in 7.5 minutes.
Part C) Jada arrived 4.5 minutes before the water tank was empty.
What is rate of change?The rate of change (ROC) measures how quickly a variable alters over a predetermined amount of time.
Given Data
Up to 10 gallons can be stored in a water tank.
A drain continuously drains water from the tank when it is operational.
When Jade first noticed the tank, there were 7 liters of water inside.
3 minutes later, there were 5 gallons of water remaining.
Part A: How quickly is the tank's water level changing?
In three minutes, the gallons were reduced from seven to five. It indicates that 2 gallons were lost in three minutes.
Thus, gallons Change in gallons per minute would be -[tex]\frac{2}{3}[/tex]. As a result, the tank's water level is changing at a rate of -[tex]\frac{2}{3}[/tex] gallons per minute.
Note that a negative sign means there are less gallons of water available.
Part B) How long will it take for the tank to entirely drain?
The amount of time it will take the tank to entirely empty is denoted by the letter "m."
As,
2.3 gallons per second (5 gallons) in (m minutes).
So,
m = 5 ([tex]\frac{3}{2}[/tex])
= [tex]\frac{15}{2}[/tex]
= 7.5 min.
As a result, the tank will finish draining in 7.5 minutes.
Part C: How long did it take the water tank to fill up entirely before Jada arrived?
When there are 10 gallons of water, r is complete. This means that there are now 7 gallons more of water than there were when Jada arrived, an increase of 3 gallons.
Let 'm' be the time in minutes when the water tank was full and before Jada arrived.
So,
([tex]\frac{2}{3}[/tex]) (m) = 3
m = 3([tex]\frac{3}{2}[/tex]) = [tex]\frac{9}{2}[/tex]
= 4.5 min.
The water tank was thus full before to Jada's arrival by 4.5 minutes.
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Which two lines are parallel?
The point (10, y) also lies on line A.
What number does y stand for?
The point (x, 21) also lies on line B.
What number does x stand for?
a. The slopes of lines C and B are the same, therefore, they are parallel.
b. y = 30
c. x = 11
How to Find the Slope of a Line?The slope of a line (m) = change in y/change in x.
Two lines having the same slope (m) value means they are parallel to each other.
a. Slope of line A = change in y/change in x = (9 - 0)/(3 - 0) = 9/3
Slope of line A = 3
Slope of line B = (15 - 1)/(8 - 1) = 14/7
Slope of line B = 2
Slope of line C = (21 - 3)/(12 - 3) = 18/9
Slope of line C = 2
Slope of line D = change in y/change in x = (14 - 2)/(9 - 1) = 12/8
Slope of line D = 3/2
Lines C and B have the same slope, therefore they are parallel.
b. 3 = (9 - y)/(3 - 10)
3 = (9 - y)/-7
-21 = 9 - y
-21 - 9 = -y
-30 = -y
y = 30
c. 2 = (15 - 21)/(8 - x)
2 = -6/(8 - x)
2(8 - x) = -6
16 - 2x = -6
-2x = -6 - 16
-2x = -22
x = 11
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A solar panel has an area of x2 + 13x + 42. Find the possible dimensions of the solar panel.
Answer: x+6 and x+7
Step-by-step explanation:
[tex]x^{2} +13x + 42 = 0\\D = b^{2} - 4ac = 169 - 4*42 = 169 - 168 = 1\\x_{1} = (-13 + 1)/2 = -6\\x_{2} = (-13 -1)/2 = -7\\\\So, x^{2} + 13x + 42 = (x+6)(x+7) \\\\\\[/tex]
Hence, the possible dimensions are x+6 and x+7.
Answer: (x + 6) and (x + 7)
Step-by-step explanation: Determine if the polynomial terms contain a common factor. In this case, there's no common factor. Next, find two numbers whose product is 42 and whose sum is 13. The only pair of numbers that satisfies these conditions is 6 and 7. Finally, write the polynomial in factored form as (x + 6)(x + 7). Therefore, the possible dimensions of the rectangle are (x + 6) by (x + 7).
If DZ = 6, ZR = 2, and EZ= 8, what is IR?
Answer:
8/6*(8)=32/3 or 10.66666.... or 10.7 rounded
Step-by-step explanation:
They are similar triangles
so we cam compare the size of the big triangle DIR to the smaller triangle DEZ
More specifically
EZ:DZ=IR:DR
8:6=IR:(6+2)
4:3=IR:8
the to solve for IR
we multiply by 8 each side
4/3*8=32/3
is the median and mean equal? if not which is greater, explain your reasoning
Answer: The median and mean of height of students is not equal, the median is greater.
Step-by-step explanation:
Definition of Median:
Median is the middle value in the picture. To find the median, order the numbers and see which one is in the middle value of the list.
in this picture, first, we order the numbers in numerical order:
1,1,1,2,2,3,3,5,6,6
Find the middle number:
1,1,1,2,2,3,3,5,6,6
As above, 3 is the middle number, then we find which bar represents the median of height of students:
1+1+1+2+2+3 = 10 students
Referring back to the chart, if we add the first 2 bars together, we will get 6+2 = 8 students, but the median number is 10 students, that means the median will be at the third bar, median of height of students = 62-64.
Definition of Mean:
Mean is the sum of the numbers divided by the number of numbers.
In this picture, the Mean will be
(2+6+5+6+3+3+2+1+1+1) / 10
= 3 students
which means the mean height of students = 60-62.
I need help ASAP, thanks
ANSWER
x = 4 or x = -9
STEP-BY-STEP EXPLANATION:
As you can see from the question provided, you were given the following logarithms equation
[tex]\log _6x+log_6(x\text{ + 5) = 2}[/tex]Recall that,
[tex]\text{Log}_xA+log_xB=Log_x(A\text{ x B)}[/tex][tex]\begin{gathered} \text{Let} \\ \log _xA=log_6x \\ \log _xB=log_6(x\text{ + 5)} \end{gathered}[/tex]The next thing is to replace the values and simplify
[tex]\begin{gathered} \log _6x(x\text{ + 5) = 2} \\ x(x+5)=6^2 \\ \text{Open the parenthesis} \\ x^2\text{ + 5x = 36} \\ x^2\text{ + 5x - 36 = 0} \end{gathered}[/tex]As you can see from the last process, the logarithms function resulted in a quadratic equation.
The next thing is to solve the equation using the factorization method.
Note that, the general quadratic function is given below as
[tex]ax^2\text{ + bx + c = 0}[/tex]Relating the two equations, you will have the following data
• a = 1
,• b = 5
,• c = -36
The next thing is to find the value of ac
[tex]\begin{gathered} ac\text{ = 1 }\cdot\text{(-36)} \\ ac\text{ = -36} \end{gathered}[/tex][tex]\begin{gathered} x^2\text{ -4x + 9x - 36 = 0} \\ x(x\text{ - 4) + 9(x - 4) = 0} \\ (x\text{ - 4) (x + 9) = 0} \\ (x\text{ - 4) = 0 or (x + 9) = 0} \\ x\text{ - 4 = 0 or x + 9 = 0} \\ x\text{ = 0 + 4 or x - 9 = 0} \\ x\text{ = 4 or x =-9} \end{gathered}[/tex]Hence, the values of x are 4 and -9
Given f(x) = x³ + kx + 13, and the remainder when f(x) is divided by x + 1 is
22, then what is the value of k
The value of k = -10 in f(x).
What is polynomial?Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables.
What is remainder?The amount "left over" after a calculation is the remainder. The integer that remains after multiplying one integer by another to create an integer quotient is known as the remnant in mathematics.
Given that,
f(x) = x³ + kx + 13
The remainder when f(x) is divided by x + 1 is 22,
Here, the f(x) is divided by x+1
Hence, x = -1
Substitute x = -1 in f(x)
22 = f(x) = x³ + kx + 13
22 = f(-1) = (-1)³ + k(-1) + 13
22 = -1 –k +13
22 = -k +12
K = -10
Therefore, the value of k = -10 in f(x).
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Please answer I give brainliest
Answer:
x= 12
Step-by-step explanation:
8/4 = 2
2x6 = 12
please help me with my homework
Answer:
a. Using a graphing calculator: 4.486089611
b. To 2 decimal places: 4.49
Can you please help me with this question please
Given model is
[tex]A=8000+8000(0.045t)[/tex]Substitute A=12981 to find the value of t, we get
[tex]12981=8000+8000(0.045t)[/tex]Subtracting 8000 from both sides, we get
[tex]12981-8000=8000+8000(0.045t)-8000[/tex][tex]4981=8000(0.045t)[/tex]Multiplying 8000 and 0.045, we get
[tex]4981=360t[/tex]Dividing both sides by 360, we get
[tex]\frac{4981}{360}=\frac{360t}{360}[/tex][tex]t=13.8361[/tex]Round off nearest tenth, we get
[tex]t=13.8\text{ years}[/tex]Hence it would take 13. 8 years for the loan amount to $ 12981.
I have to determine whether the equation 3(4g+6) = 2 (6g+9) has one solution, no solution, infinitely many solutions. the equation has a: one solution b: no solution c: infinitely many solutions g=
Answer
Option C is correct.
The equation has infinitely many solutions.
Explanation
To know the nature of the solutions, we need to solve the given equation
3 (4g + 6) = 2 (6g + 9)
12g + 18 = 12g + 18
12g - 12g = 18 - 18
0 = 0
Any equation that results in 0 = 0, is known to have infinitely many solutions because any number will fit in for g and still work for the given equation.
Hope this Helps!!!