Answer: No Solution
Step-by-step explanation:
||3x - 1| + 5| <1 ⇒
[tex]\left \{ {{|3x - 1| + 5 < 1} \atop {|3x - 1| + 5 > -1 }} \right.[/tex] ⇒
[tex]\left \{ {{|3x - 1| < -4} \atop {|3x - 1| > -6} \right.[/tex] ⇒
The first equation does not make sense because absolute value and as it is a system of equations, the whole system does not have a solution.
Design a pseudocode and the corresponding flow chart for calculating; the area of a circle,the perimeter of a rectangle, the perimeter of a square
See below for the pseudocode and the flowchart is added as an attachment
What is a pseudocode and a flowchart?Flowcharts and pseudocodes are used as prototypes of actual programs.
Flowcharts are in graphical form, while pseudocodes are in the form of texts.The flowchart and pseudocode do not conform to programming syntaxHow to design the pseudocode and the flowchart?Area of circle
The pseudocode is as follows:
StartInput radius, rCalculate Area, A = pi * r^2Display AreaStopPerimeter of rectangle
The pseudocode is as follows:
StartInput dimensions, l and bCalculate Perimeter, P = 2 * (l + b)Display PerimeterStopPerimeter of square
The pseudocode is as follows:
StartInput dimensions, lCalculate Perimeter, P = 4 * lDisplay PerimeterStopSee attachment for the flowcharts
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If you go to a restaurant and there are 4 choices for main dishes, 5 choices for sides, and 6 choices for drinks, how many possible meals can you order if you do or don't get one of each item?
Answer:
4 * 5 * 6 = 120 possible meals can we order.
Step-by-step explanation:
given that-
If you go to a restaurant and there are 4 choices for main dishes, 5 choices for sides, and 6 choices for drinks
4 * 5 * 6 = 120 combinations or Ways to Order
we can order the main dish in 4 different ways. Then, we can choices for sides in 5 different ways and the drinks in 6 different ways.
(The outcome of the selection of the first does not influence the second or third)
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what is the value of m in the figure below? if necessary, round your answer to the nearest tenth of a unit.
The value of m in the right triangle to the nearest tenth is 7.2 units.
How to find the side of a right triangle?The figure above is a right triangle.
The right triangles are similar.
Therefore, right triangle ABC is similar to right triangle BDC.
Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.
Therefore, let's find the value of m using the similar triangle principle,
m / 13 = 4 / m
cross multiply
m × m = 13 × 4
m² = 52
square root both sides
√m² = √52
m = 7.21110255093
Therefore,
m = 7.2 units.
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There are 2 different maps of North Carolina. The scale on the first map is 1 cm to 2 km. The distance from Durham to Cary is 15 cm. The scale of the second map is 1 cm to 5 km. What is the distance from Durham to Cary on the second map
The distance from Durham to Cary on the second map is 75 km
The scale of the first map:
1 cm = 2 km
The scale of the second map:
1 cm = 5 km
Map scale: A distance on a map and its corresponding distance on the planet are related by a scale. The equivalent of a map scale can be expressed, typically using different units. or visually, using a bar scale.
Distance from Durham to Cary = 15 cm
Distance from Durham to Cary on the second map = Scale of the second map * Distance from Durham to Cary
= 5*15
= 75 km
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how many whole numbers are there between 121and176
TO KNOW HOW MANY WHOLE NUMBERS THERE ARE BETWEEN 121 AMD 176 WE CAN SIMPLY GET THEIR DIFFERENCE.
THE DIFFERENCE IS THE NUMBER OF WHOLE NUMBERS INBETWEEN 121 AND 176.
[tex] = 176 - 121 \\ = 55[/tex]
THERE ARE 55 WHOLE NUMBERS BETWEEN 121 AND 176.
Answer:
54
Step-by-step explanation:
Whole numbers are 0,1,2,3,... Following that pattern forever.
Take a simpler example. How many whole numbers between 2 and 5? It would be just 3 numbers; 3 and 4.
We could subtract 5-2 to get 3 and then subtract 1 more to get the answer of 3
What if I wanted to know the number of whole numbers between 3 and 7?
The numbers would be 4,5,6.
7-3 = 4 and then subtract 1 more to get the answer that there are 3 whole numbers between 3 and 7.
176 - 121 = 55 take one more away to get 54
Write an algebraic expression to represent each statement
50 added to half of a number, c
The expression represented by 50 added to half of a number, c is 50 + c/2
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to translate the algebraic expression?The expression is given as
50 added to half of a number, c
half of a number, c means divide c by 2
So, we have
50 added to half of a number, c => 50 added to c/2
Added to means +
So, we have
50 added to half of a number, c => 50 + c/2
Hence, the expression represented by the statement is 50 + c/2
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HELP ASAP, ITS DUE TODAY AT MIDNIGHT!!!!! 92 POINTS!!!!!!!!!!!
The relationship is that number sense can be used to solve area models or partial products.
What is number sense?Number sense refers to a set of important numerical skills. It includes the capacity to comprehend numbers and concepts such as more and less. Some people have a better sense of numbers than others.
Number sense is a set of abilities that enable humans to work with numbers. These abilities are essential for performing math as well as many other jobs.
In this case, partial products model of multiplication. This is a model which breaks numbers down into their factors. or place values in order to make multiplication easier. This depicts number sense.
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what is the value of x-y if y=4 and 3/5 / 1/2 = x/10
like
3/5
___
1/2
F.) 4
G.) 8
H.) 10
J.) 12
K.) 16
pls show work
f(x)=x-7; vertical stretch of 3 g(x)
The function that represents the vertical stretch by a factor of 3 of f(x) is given as follows:
g(x) = 3x - 21.
How are vertical stretches and compression applied to the graph of a function f(x)?Vertical stretches or compression to the graph of a function f(x) are applied by the multiplication of a constant a to the function, as follows:
g(x) = a x f(x).
Then the value of the constant determines if it is an stretch or a compression.
If the absolute value of the constant a is greater than 1, it is a stretch. If the absolute value of the constant a is less than 1, it is a compression.For this problem, we want a vertical stretch with a factor of 3, then the constant is given as follows:
a = 3.
Then the definition of function g(x) is given by:
g(x) = 3f(x)
g(x) = 3(x - 7)
g(x) = 3x - 21.
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7,5,2,1,.......
tell the common difference of this sequence
There are 2 numbers between 7 and 5 and 3 numbers between 5 and 2
. TEST SCORES Benjamin's test scores for the quarter so far are 78, 82, 95, and 88. What does he need to score on the fifth test of the quarter in order to have an average test score of 87?
3) Margaret invests $3,500 in a savings account that offers 5% simple interest per
annum. How much interest will she get after 8 years?
Margaret invests $3,500 in a savings account that offers 5% simple interest per annum. So interest she will get after 8 years is
What is simple interest ?Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.
Given that : Margaret invests $3,500 in a savings account that offers 5% simple interest per annum.
S.I = [tex]\frac{(P)(R)(T)}{100}[/tex]
P = $3,500
R=5%
T=8 years
S.I = [tex]\frac{(P)(R)(T)}{100}[/tex]
S.I = [tex]\frac{(3500)(5)(8)}{100}[/tex]
S.I = 1400
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Which table of ordered pairs represents a proportional relationship?
need this answer ASAP
Answer:
It's the 3rd one
Step-by-step explanation:
2x7=14 7x4=28 7x6=42
Answer:
The third table, since x/y = 7.
A rock is dropped from a height of 10 feet. The height of the rock is modeled by the graph shown.Part AWhat is the height of the rock 0.5 seconds after being dropped? The height of the rock 0.5 seconds after being dropped is ........... feet Part BTo the nearest tenth of a second, how many seconds after being dropped does the rock hit the ground? The rock hits the ground approximately ...............................seconds after being dropped.
SOLUTION:
Step 1:
In this question, we have the following question:
A rock is dropped from a height of 10 feet. The height of the rock is modeled by the graph shown.
Part A
What is the height of the rock 0.5 seconds after being dropped? The height of the rock 0.5 seconds after being dropped is ........... feet
6 .
Step 2:
Part B
To the nearest tenth of a second, how many seconds after being dropped does the rock hit the ground?The rock hits the ground approximately ...............................seconds after being dropped.
0.8
How many integer solutions are there to the equation x³ + 2x² -41x-25-17 on the interval 0≤x≤10?
The solution in the given interval is x =6
What is inequalities?A "equal to" symbol on both sides of an equation is not necessarily necessary for it to be balanced. It may also refer to a connection when two things are "not equal to," i.e., where one is better or worse than the other. Any relationship between two numbers or other mathematical expressions that leads to an unfair comparison is referred to in mathematics as an inequality. Certain algebraic mathematical expressions are known as inequalities.
Equation is :
[tex]x^{3} +2x^{2} -41x -25 =17\\x^{3} +2x^{2} -41x -42\\Put x =-1\\-1^{3} -2(-1)^{2} -41(-1) -42=0\\So, (-1) is the solution of the given equation and (x+1) must divide the equation so,\\\frac{x^{3} +2x^{2} -41x -42}{(x+1)} =x^{2} +x-42\\So we can write \\(x+1)(x^{2} +x-42)=0\\(x+1)(x^{2} +7x-6x-42)=0\\(x+1)(x-6)(x+7)=0\\So the solution of the equation are\\x_{1} =-1\\x_{2} =+6\\x_{3} =-7\\[/tex]
We need to find the integer solution in the interval 0≤x≤10
So total no. of solution in the given interval is 1
The solution in the given interval is x =6
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the probability that a randomly chosen student in a statistics class submits his/her homework on time is 0.06. each student does homework independently. in a statistics class of 50 students, what is the probability that at least 5 will do their homework on time?
the probability that at least 5 will do their homework on time in a class of 50 students is 0.1
How do you calculate probability?
Probability is calculated by dividing the number of ways the event can occur by the total number of outcomes. Probability and odds are different concepts. Odds are the probability that something happens divided by the probability that it doesn't happen.
the probability that a randomly chosen student in a statistics class submits his/her homework on time is 0.06.
each student does homework independently.
in a statistics class of 50 students, what is the probability that at least 5 will do their homework on time?
probability = event occur/ total number of outcomes
= 5/50= 1/10=0.1
thus the probability becomes 0.1
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Justin runs at a constant rate, traveling 17 km in 2 hours.
Write an equation that shows the relationship between d, the distance he runs in kilometers, and h, the time he spends running in hours.
The relationship between the distance that Justin runs, in kilometers, and the running time, in hours, is equal to d = (17 / 2) · t.
How to define the model to describe the distance travelled by Justin at a constant rate
In this problem we find that the distance that Justin runs (d), in kilometers, is directly proportional to the running time (t), in hours. That is:
d ∝ t
d = k · t
Where:
d - Distance, in kilometers.t - Time, in hoursk - Speed, in kilometers per hour.If we know that d = 17 km and t = 2 h, then the relationship between distance and time is described below:
k = 17 km / 2 h
k = 17 / 2 km / h
d = (17 / 2) · t
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In one year, a school uses 11,280 pieces of white paper, 3,580 fewer pieces of blue paper than white paper, and 3,600 fewer pieces of yellow paper than blue paper. how many pieces of paper does the school use in all?
The school uses a total of 23,080 pieces of paper in one year.
To calculate the total number of pieces of paper used by the school we use addition. We also use subtraction to find the pieces of blue paper and yellow paper.
As the pieces of blue paper are 3580 fewer than white paper, we find the pieces of blue paper by subtracting 3580 from 11,280.
blue paper = 11280 - 3580 = 7700
As the pieces of yellow paper are 3600 fewer than blue paper, we subtract 3600 from the total number of pieces of blue paper.
Yellow paper = 7700 - 3600 = 4100
Now, the total number of pieces can be found by the addition of white, blue, and yellow pieces of paper.
Total pieces = White papers + Blue papers + Yellow papers
Total pieces = 11,280 + 7700 + 4100
Total pieces = 23,080
Therefore, 23,080 pieces of paper were used by the school in one year.
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y is inversely proportional to a³
When a = 2, y = 10
a is directly proportional to x
When x = 4, a = 20
Find a formula for y in terms of x.
Give your answer in its simplest form.
The formula for y in terms of x is y = [tex]\frac{16}{25} x^{3}[/tex]
What is proportionality?Any relationship that has a constant ratio is said to be proportionate. For instance, the ratio of proportionality is the average number of apples per tree, and the amount of apples in a crop is proportional to the number of trees in the orchard.
Given that,
Y is inversely proportional to a³ When a = 2, y = 10
A is directly proportional to x when x = 4, a = 20
If y is inversely proportional to a³
[tex]\frac{y}{x^{3} }[/tex]∝1
y = [tex]\frac{k}{a^{3} }[/tex], where k is the proportionality constant
Given, a=2, y=10, then 10 = [tex]\frac{k}{2^{3} }[/tex]
k = 10 × 2³
k = 80
Substituting k = 80 back into the formula;
y = [tex]\frac{80}{a^{3} }[/tex]............. 1
Similarly, if a is directly proportional to x, then a ∝ x i.e a = kx
If x=4, a=20 then;
20 = 4k
k = [tex]\frac{20}{4}[/tex]
k = 5
Substituting k = 5 back into the formula;
a = 5x ....... 2
Substitute equation 2 into 1;
y = [tex]\frac{80}{a^{3} }[/tex]
y = [tex]\frac{80}{5x^{3} }[/tex]
y = [tex]\frac{80}{125x^{3} }[/tex]
y = [tex]\frac{16}{25x^{3} }[/tex]
Therefore, the formula for y in terms of x is y = [tex]\frac{16}{25} x^{3}[/tex]
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Determine whether the graph is linear or non linear and explain
The given graph represents a non-linear function.
What are linear and non-linear functions?When a function is plotted on a graph, a linear function produces a straight line, whereas a nonlinear function does not (it is curved in some way). While the slope of a nonlinear function is continuously changing, the slope of a linear function is constant.Take two points in the graph and calculate the slope:
Slope of (-2,1) and (0,2) = (2-1)/(0-(-2) = 1/2
Slope of (2,1) and (0,2) = (2-1)/(0-2) = 1/(-2)
As the slope of the given graph is variable, it is a non-linear function.
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Simplify.
16-8+5x-3x
08+8x
O 10 x
08+2x
O 16+ 2 x
Help please
Step-by-step explanation:
The answer is 8+2x . This is the correct answer .
9(4)^2 + 24(4) + 20 = 4
Answer:
Step-by-step explanation:
Use the following information to find x: AB = 4x + 5; BC = 13; and B is the midpoint of AC
The numerical value of x is 2 as segment AB equals segment BC.
What is the numerical value of x ?A midpoint is simply a point that divides a line segment into two equal halves.
Given the data in the question;
B is the midpoint of ACSegment AB = 4x + 5Segment BC = 13Given that B is the midpoint of segment AC, this means that segment AB is equal to segment BC.
Hence
Segment AB = Segment BC
4x + 5 = 13
Solve for x
Subtract 5 from both sides
4x + 5 - 5 = 13 -5
4x = 8
Divide both sides by 4
4x/4 = 8/4
x = 8/4
x = 2
Therefore, the value of x is 2.
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A rock is dropped into a pond, creating a circular ripple. The radius of the ripple increases steadily at 6 cm/s. A toy boat is floating on the pond, 2.00 m east and 1.00 m north of the spot where the rock is dropped. How long does the ripple take to reach the boat?
Answer: 28.87 seconds
Step-by-step explanation:
Check attached image for explaination
To enroll in lessons to learn about pottery wheel throwing, you must pay an rollment of $20 for each lesson. The pottery studio also charges you $2.99 pe pound for the amount of clay used.To enroll in lessons to learn about pottery wheel throwing, you must pay an enrollment of $20 for each lesson. The pottery studio also charges you $2.99 per pound for the amount of clay used. Write an expression for the total cost of a person using c pounds of clay during a lesson. Use the expression to calculate the cost of a lesson where Sam uses 3.5 pounds of clay.
Answer:
cost per day = 2.99(c)+20
sam's lessons cost $30.47 per day
Step-by-step explanation:
2.99 (price of clay used per pound) * c (pounds of clay used) + 20 (cost of lesson)
2.99(c)+20
since sam uses 3.5 pounds of clay per lesson that's 2.99(3.5)+20, which is equal to 30.47
Keith has a shirt company that charges a delivery fee. The total charges are include the following
• $10 per short sleeve shirt
. $15 per long sleeve shirt
• The total of the charges must be at least $500 to get a discount.
Which inequality models the situation where x is the number of short sleeve shirts and y is the number of long sleeve shirts.
A
15x+10y≤ 500
B 15x+10y 2 500
C
10x + 15y ≤ 500
D 10x+15y 2 500
2x+3y=13
4x-y=-2
Find x and y
Answer:
x = 1/2, y = 4
Step-by-step explanation:
2x + 3y = 13----------> 2x + 3y = 13
4x - y = -2------------> 12x - 3y = -6
-----------------
14x = 7
x = 1/2, y = 4
Please help!!!
Create an equivalent expression for 18^-7 • 18^5
1. -18^2
2. 18^2
3. 1/18^-2
3. 1/18^2
For an equivalent expression for [tex]18^{-7}\\[/tex] * [tex]18^5\\[/tex] it is option 4 that is correct that means the equivalent expression can be seen as [tex]\frac{1}{18} ^{2}[/tex].
What analogous expressions are there?Expressions that can be considered are equivalent do the same thing even when they have distinct appearances. When we get to enter the same value(s) for the same variable, two algebraic expressions that are equivalent have the same value (s).
Calculating the equivalent expression,
[tex]18^{-7}\\[/tex] * [tex]18^5\\[/tex]
= [tex]18^{-7+5}[/tex]
=[tex]18^{-2}[/tex]
= [tex]\frac{1}{18} ^{2}[/tex]
What is a good example of an equivalent expression?An expression that can be considered equivalent to another phrase but then differs in appearance is the one that has the same value or worth. In algebra, we can say 2(2x – 3y + 6) is equal to 4x -6y + 12 as an example of an equivalent expression.
Which two expressions are interchangeable?When two expressions can be reduced to a single thread expression or when one of the expressions can be written in the same way as the other, they are said to be equivalent. You can also determine whether two expressions are equivalent.
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Please explain!!!
A clock face has a radius of 8 inches. What is the area of the clock face. Round your number to nearest hundredth.
Answer:
200.96 square inches
Step-by-step explanation:
it's asking for the area of a circle
we know that the radius is 8, so we can just plug it into the circle area formula which is
area = (pi) r^2
you plug in 8 for r (r stands for radius)
8^2 is 64
64 times pi is 200.96 (because pi=3.14)
Rewrite 7x + 49 using a common factor.
Here are some options it gave me.
(A) . 7(x + 7)
(B). 7(x + 49)
(C). 7x(x + 7)
(D). 7x(x + 49)
7x + 49 rewritten using common factor is 7(x + 7)
How to find common factors?A common factor is a whole number which is a factor of two or more numbers.
In other words, common factors of two or more numbers are a number which divides each of the given numbers exactly.
For example the common factor of 24 and 36 are 1, 2, 3, 4, 6 and 12.
Therefore,
rewriting 7x + 49 using common factors is as follows:
7x + 49 = 7(x + 7 )
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