The value of the inequality when the sum of two consecutive integers is less than -9 is x < - 5.
How to calculate the value?It is vital to note that an inequality simply shows that the expressions aren't equal.
In this case, the sum of two consecutive integers is less than -9.
Let the integers be x and x + 1.
Therefore, x + x + 1 < -9
2x + 1 < -9
Collect like terms
2x < -9 - 1
2x < -10
Divide
x < - 10 / 2
x < - 5
The value is x < - 5.
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the wheels on Kiran's bike are 64 inches in circumference. How many times doo the wheels rotate if Kiran rides 300 yards ?
Answer:
169 times
Step-by-step explanation:
We know that the circumference of Kiran's bike wheel is 64 inKiran rides total distance of 300 yardsTo find number of rotations made by wheel...
Know that 1 yard = 36 in
300 yards = 36 x 300 = 10800 in
Number of rotation = Total distance covered by wheel ÷ Circumference of wheel
Number of rotations = 10800 ÷ 64 = 168.75 ≅ 169
Therefor, the wheel rotates = 169 times
Hope this helps! :)
x^3=x^2-1 find all the real zeros
Answer:
ask this braslate which matirias
An investor has $100,000 to invest in three types of bonds: short-term, intermediate, and long term. how much should he invest in each type to satisfy conditions?
short-term pay 4% annually, intermediate pays 6% and long term pays 8%. The investor wishes to have a return of $6700 on his investment, with equal amounts invested in intermediate and long term bonds.
I know it will be an x+y+z system. I don't know how to set it up. x+y+z=100,000; .04x+.06y+.08z=6700 and ? or is it something else?
The equation used to solve this problem is x + y + z = 100000, 0.04x + 0.06y + 0.08z = 6700 and y = z
What is an equation?An equation is an expression showing the relationship between two or more numbers and variables.
Let x represent the amount of money invested at 4% (short term), y represent the amount of money invested at 6% (intermediate term) and z represent the amount of money invested at 8% (long term)
Since an investor has $100,000 to invest, hence:
x + y + z = 100000 (1)
Also, the investor wishes to have a return of $6700, hence:
0.04x + 0.06y + 0.08z = 6700 (2)
Equal amounts invested in intermediate and long term bonds. This gives:
y = z (3)
The third equation used to solve this problem is y = z
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The probability of tails of a weighted coin is 0. 65. The number of tails is noted each of the 15 times the coin is tossed. If this procedure is repeated 100 times, what type of distribution is simulated?
A. A sampling distribution of the sample proportion with n=15 and p=0. 65
B. A sampling distribution of the sample proportion with n=100 and p= 0. 65
C. A binomial distribution with n=15 and p= 0. 65
D. A binomial distribution with n=2 and p= 0. 65
E. There is not enough information to determine the type of distribution
A sampling distribution of the sample proportion with n=15 and p=0. 65 is stimulated here when The probability of tails of a weighted coin is 0. 65. The number of tails is noted each of the 15 times the coin is tossed.
What is probability?Probability is simply the likelihood of something occurring. When we are uncertain about the result of an event, we might discuss the probabilities of several outcomes—how likely they are. Statistics is the study of occurrences guided by probability. Probability is synonymous with possibility. It is a mathematical discipline that deals with the occurrence of a random event. The value ranges from zero to one. Probability has been introduced in mathematics to predict the likelihood of occurrences occurring. The probability is a measure of the possibility that an event will occur. It assesses the event's certainty. P(E) = Number of Favourable Outcomes/Number of Total Outcomes is the probability formula.
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Besa brings 2 boxes of chocolates. Each box has a painting on the front. The picture in the 320 g box has the shape of a rectangle with dimensions 102mm by 170mm. The painting on the 480g box is sized 140mm by 226mm. Show that the two rectangles are not congruent similarly.
The short side of one box divided by the short side of the other box must equal the long side of one box divided by the long side of the other box. If the results are the same, they are proportional, if not, they are not proportional
[tex]\frac{102}{140} = 0.72 \\\\\frac{170}{226} = 0.75[/tex]
If the sum of the first 3n positive integers is 150 more than the sum of the first n positive integers, then what is the sum of the first 4n positive integers?
Answer: 300
Step-by-step explanation:
[tex]\sum^{3n}_{k=1} k=\frac{3n(3n+1)}{2}\\\\\sum^{n}_{k=1} k=\frac{n(n+1)}{2}\\\\\therefore \frac{3n(3n+1)}{2}-150=\frac{n(n+1)}{2}\\\\3n(3n+1)-300=n(n+1)\\\\9n^2 +3n-300=n^2 +n\\\\8n^2 +2n-300=0\\\\4n^2 +n-150=0\\\\(n-6)(4n+25)=0\\\\n > 0 \implies n=6\\\\\therefore 4n=24\\\\\implies \sum^{4n}_{k=1} k=\sum^{24}_{k=1} k=\frac{24(25)}{2}=300[/tex]
The graph shows y as a function of x. Suppose a point is added to this graph. Which choice gives a point that preserves the function? Responses
A (9, −1)(9, −1)
B (3, 5)(3, 5)
C (2, −4)(2, −4)
D (0, 9)
The point that preserves the function is (0, 9), so the correct option is D.
Which option preserves the function?A function is a relationship that maps elements from a set (domain) into another set (range).
Such that each element in the domain is mapped into only one element of the range.
In the graph of the function we can see the points:
(-7, 4)
(-3, -3)
(2, 9)
(3, -8)
(5, 7)
(9, 3)
So the inputs {-7, -3, 2, 3, 5, 9} are already used and we can't use them anymore, the correct option then is:
D (0, 9)
Which has the only input that is not already graphed on the function's graph.
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Translate the sentence into an inequality. The sum of a number times 3 and 23 is greater than 25.
Translation of the given sentence with variable y into inequality is given by 3y + 23 > 25.
As given in the question,
Given sentence is :
Let the number be represented by y.
The sum of y times of 3 and 23 is greater than 25.
Translation of the given sentence into inequality is given by :
y times 3 is represented by 3y
Sum of y times 3 and 23 is given by 3y + 23
Sum is greater than 25
3y + 23 > 25
Simplify the inequality we get,
3y > 25 -23
⇒3y > 2
⇒y > 2/3
Therefore, translation of the given sentence with variable y into inequality is given by 3y + 23 > 25.
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What is the domain of y equals two divided by the quantity x minus three squared all minus one ?
All real numbers less than 3
All real numbers except 3
All real numbers greater than 1
All real numbers greater than 3
All real numbers
The domain of y equals two divided by the quantity x minus three squared all minus one [y = (2)/(x - 3)² - 1] is: all real numbers.
What is a domain?In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined.
This ultimately implies that, a domain is the set of all possible input numerical values or numbers (x-values) to a function and the domain of a graph comprises all the input numerical values which are located on the x-coordinate.
Translating the word problem into an algebraic equation, we have;
y = (2)/(x - 3)² - 1
When x = 3, we have:
y = (2)/(3 - 3)² - 1
y = 2/-1 = -2
When x = 1, we have:
y = (2)/(1 - 3)² - 1
y = 2/3
In conclusion, the domain of this function is all real numbers.
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point A is located at (-2,-6) on the coordinate plane. Point A is reflected over the y-axis to create point A’. What ordered pair describes the location of A’?
The ordered pair coordinates of A' are (2, -6) if A is reflected over the y-axis.
What are transformations?The transformation, or f: X → X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the picture X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation. A function can be moved in one way or another using translation, rotation, reflection, and dilation. A function can also be scaled using rotation around a point.
The coordinates of A are (-2, -6).
Point A is reflected over the y- axis to create point A'
(x, y) → (-x,y)
A (-2, -6) → A' (- (-2), -6))
So, the coordinates of A' are (2, -6).
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Explain how to find the distance between -2 and 3
on a number line.
The distance between -2 and 3 on a number line is 5 units.
What is a number line?
A horizontal line with evenly spaced numerical increments is referred to as a number line. The number on the line depends on how the number is contained.
The Distance Between Two Points on a number line.
The secret to finding the distance between two points is to remember that the geometric definition of subtraction is the distance between the two integers if we subtract the smaller number from the larger one.
Here, we have
the distance between -2 and 0 is 2 units
the distance between 0 and 3 is 3 units
2+3 = 5
OR
3- (-2) =
3+2 = 5
5 units
Hence, the distance between -2 and 3 on a number line is 5 units.
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Solve the inequality statement:
-5ω < 15
---
w >3
wς 3
w< -10
The simplified form of the given inequality is w > -3.
What is inequality?
When two values are compared, an inequality reveals whether one is bigger than, less than, or simply not equal to the other. The term "inequality" in mathematics refers to a relationship between two expressions or values that is not equal to one another. The occurrence of an unfair distribution of opportunities and resources among individuals of a certain society is referred to as inequality. To different people and in various contexts, the term "inequality" may mean different things.
Here the given inequality is ,
=> -5w<15
=> -5 *w < 15
=> w>15/-5
=> w > -3.
Hence the correct simplified form of the inequality is w >-3.
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50 points
Please help
Graph -8+x=4y-16
Equation of the line - 8 + x = 4y - 16
In order to graph the line, find its x- and y- intercepts, then connect the two pointsx- intercept, at y = 0:
- 8 + x = 0 - 16x = - 16 + 8x = - 8y- intercept, at x = 0:
- 8 = 4y - 164y = 16 - 84y = 8y = 2The points are (0, 2) and (- 8, 0), plot them and connect to get the graph.
The graph that connects points (-8,0) and (02) is shown below
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given equation is,
-8+x=4y-16
x- intercept, at y = 0:
- 8 + x = 4(0) - 16
x = - 16 + 8
x = - 8
y- intercept, at x = 0:
- 8 + 0 = 4y - 16
4y = 16 - 8
4y = 8
y = 2
The points are (-8,0) and (02)
So, the graph that connects points (-8,0) and (02) is shown below
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Two-thirds of a number subtracted from nine is seven. Find the number.
Answer:
3
Step-by-step explanation:
9-2/3x=7
We know that 9-2=7 so 2/3x must be 2
2/3x=2
You have to multiply each side by 3/2
x=3
The number is 3
CAN someone help me with DIS
The area of the triangle below is 224 inches squared.
How to find the area of a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.
The area of a triangle an be described as follows:
area of a triangle = 1 / 2 bh
where
b = baseh = heightTherefore, the area of the triangle can be found as follows:
b = 4t = 4(4) = 16 inches
h = 7(t) = 7(4) = 28 inches
Therefore,
are of the triangle = 1 / 2 × 16 × 28
are of the triangle = 8 × 28
Therefore,
are of the triangle = 224 inches²
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Answer:
224 inches squared.
Step-by-step explanation:
have great day
The lengths in the diagram are in centimetres. The square (2x,2x) and the rectangle (10, x+8) have perimeters of the same length.
a. Write an equation to show this.
b. Solve the equation.
c. Find the length of the rectangle.
(a) Equation is 8x - 2x = 36
(b) By solving equation we get the value of x = 6
(c) The length of the rectangle is 14
Given,
In the question:
A square and a rectangle have same perimeter.
The square (2x,2x) and the rectangle (10, x+8) have perimeters of the same length.
Now, According to the question:
We know that the formula of Perimeter of rectangle and square.
Perimeter of square = 4 x side
Perimeter of rectangle = 2(length + breadth)
Perimeter of a square = 4(2x) = 8x
Perimeter of rectangle = 2(x + 8) + 20
Now,
8x = 2x + 16 + 20
6x = 36
x = 6
Hence, (a) Equation is 8x - 2x = 36
(b) By solving equation we get the value of x = 6
(c) The length of the rectangle is 14 .
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9,4,23,7,18,16,14.Work out the range of the numbers in the list.
Step-by-step explanation:
Range = Highest number - Lowest number
= 23 - 4
= 19
The variable y has a proportional relationship with x as suggested by the graph. Use the graph to find the constant of proportionality.
The relationship has a constant of proportionality of 37
How to determine the constant of proportionality?From the graph, we have the following points
x = 1 and y = 37
These points can be represented:
x = 1
y = 37
The above parameters can be represented as the following points
(x, y) = (1, 37)
The constant of proportionality of the points is then calculated as
k = y/x
Substitute the known values in the above equation
So, we have the following equation
k = 37/1
Evaluate the quotient
So, we have
k = 37
Hence, the constant of proportionality is 37
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7(x+4)-2[x-3(5+x)]=2/3(x-6)
Hope this helps! Bye, have a nice day!
1. the following two points are located on a line (-12, 6). and (4,6), find the slope of the line.
2. Solve for the value of x : 2/8 = 3/x+2
thank you! this assignment is graded on accuracy so please try your hardest!!
The slope of the linear equation is 0, and the solution of the second equation is x = 10.
How to find the slope of the line?A general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If the line passes through two points (x1, y1) and (x2, y2), then the slope is:
slope = (y2 - y1)/(x2 - x1)
So if the line passes through (-12, 6) and (4, 6), the slope is:
slope = (6 - 6)/(4 + 12) = 0
The slope is 0.
2) How to solve the equation for x?
Here we have the equation:
2/8 = 3/(x + 2)
If we move the denominators we get:
2*(x + 2) = 3*8
2x + 4 = 24
2x = 24 - 4
2x = 20
x = 20/2 = 10
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graph y =-x+7
pls help i was gone when we did this
the slop is -1 and the y-intercept is (0,7)
What is vertex?An element of a line is a line segment.A line segment that can be extended endlessly is known as a ray.An angle is created when two line segments or rays cross one another.A vertex is created by definition whenever two lines come together to produce an angle.Thus, we can state that a vertex is formed when two line segments or rays intersect.acc to our question-
plot a point on the y- axis line at 7. Then go right 7 units and down 7 unitsHence,the slop is -1 and the y-intercept is (0,7)
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Solve by factorisation
2x2 + 3x - 20 = 0
Ms. Rumble's history class conducted interviews with their grandparents for a class project. The grandparents older than 89 years old knew that Amelia Earhart was the first woman to fly solo across the Atlantic Ocean.
Determine the graph to represent this scenario.
number line with open circle on the number 89 and line shaded to the right
number line with closed circle on the number 89 and line shaded to the right
number line with closed circle on the number 89 and line shaded to the left
number line with open circle on the number 89 and line shaded to the left
A graph to represent this scenario is number line with open circle on the number 89 and line shaded to the right
The rules for writing an inequality.In Mathematics, the following rules are generally used for writing and interpreting an inequality on a number line:
The circle on a number line should be shaded (closed) when the inequality symbol is (≥ or ≤).When the arrow points to the left on a number line, the inequality is either (≤ or <).The circle on a number line should not be shaded (open) when the inequality symbol is (> or <).When the arrow points to the right on a number line, the inequality is either (≥ or >).Let the age of the grandparents be x. Therefore, an inequality which represents the situation described above is given by:
x > 89
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Niecy has Nine-fourteenths of a cup of pears and Three-fourteenths of a cup of mangos. She combines the fruit in one container.
How many cups of fruit does Niecy have in the container?
Three-fourteenths
Six-fourteenths
StartFraction 12 over 14 EndFraction
StartFraction 27 over 14 EndFraction
When Niecy combines the fruit she will have a total of Start Fraction 12 over 14 End Fraction
How to calculate sum of fruits Niecy will haveinformation form the question
Niecy has Nine-fourteenths of a cup of pears
Three-fourteenths of a cup of mangos
The problem is faced with addition of fractions
writing out the fractions in figures gives
Niecy has Nine-fourteenths of a cup of pears = 9 / 14
Three-fourteenths of a cup of mangos = 3 / 14
Addition of the fraction is done as follows
= 9 / 14 + 3 / 14
= (9 + 3) / 14
= 12 / 14
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Someone has the answer?
Find the value of x so that the function has the given value. j(x) = 3-x;j(x) = -5
The input value x in the function j(x) = 3-x as j(x) equals -5 is 8.
What is the value of x in the given function?A function is simply a relationship that maps one input to one output.
Given the function in the question;
j( x ) = 3 - xj( x ) = -5x = ?To determine the value x or input value, equate the function to -5 and solve for x.
j( x ) = 3 - x
j( x ) = -5
-5 = 3 - x
Add 5 to both sides
-5 + 5 = 3 + 5 - x
0 = 8 - x
Add x to both sides
0 + x = 8 - x + x
x = 8 - x + x
x = 8
Therefore, the value of x is 8.
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On a photograph an ant is enlarged at a scale 25:1. In the photo, the ants leg is 15 cm. What is the actual length of the ants leg?
Answer:
0.6cm
Step-by-step explanation:
25 : 1
1 : 0.04
15 : 0.6
plsssssssshelpppppppppp
a) The correct equation to represent the given condition is;
⇒ 4 (x + $3) = $36
Where, x represents the amount Pablo parents added in each day.
b) The amount to added by his parents in his account = $6
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
For 4 days, Pablo put $3 into his account.
And, His parent also add the some money to his saving account.
In the end, there was a total $36 in his account.
Now,
Let the amount Pablo parents added in each day = x
So, We can formulate;
⇒ 4 (x + $3) = $36
Solve for x as;
⇒ 4x + $12 = $36
⇒ 4 x = $36 - $12
⇒ 4x = $24
Divide by 4 both side, we get;
⇒ x = $6
Thus,
a) The correct equation to represent the given condition is;
⇒ 4 (x + $3) = $36
Where, x represents the amount Pablo parents added in each day.
b) The amount to added by his parents in his account = $6
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What else must you know to prove the triangles congruent by SAS?
D
B
OA AB CD
OB. AD AC
O CAB DC
OD AD BC
As per the reference attachment attached thereby along with the question statement, to prove the triangles ABC and ADC are congruent by SAS property, proving either of (AB ≅ CD), (AB ≅ DC) or (AD ≅ BC) will suffice.
In the reference attachment attached thereby along with the question statement, we are provided with two triangles, (ADC and ABC),
And as per the question statement, we are required to determine the relation between the corresponding sides or angles of the concerned triangles which we will need to prove over the information already provided in the figure, to ascertain that triangles ABC and ADC are congruent by SAS property.
Now, for two triangles to be congruent by SAS property, they will need to have two pairs of equal corresponding sides, and one set of equal corresponding angles.
Among our concerned triangles, ΔABC and ΔADC, already given that,
(∠DAC = ∠BCA), i.e., one set of equal corresponding angles,
And, (AC) is a common side to both ΔABC and ΔADC, i.e., one set of equal corresponding sides.
At this point, for ΔABC and ΔADC to be congruent, we will need to prove another set of corresponding sides to be equal, to complete SAS property.
Therefore, proving either of (AB ≅ CD), (AB ≅ DC) or (AD ≅ BC) will complete the second set of corresponding sides being equal, and (ΔABC and ΔADC) can be proved to be congruent triangles.
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X
Work out the mean for the data set
below:
6.8, 5.7, 0.8, 4.7, 1.3
Give your answer as a decimal.
a group of 350 people includes 187 play the flute, 172 play the clarinet, and 47 both the flute and the clarinet. a person is selected at random. 1. what is the probability that he/she plays the clarinet but not the flute? a. 0.4213 b. 0.3571 c. 0.7812 d. 0.4587 e. 0.2743 2. what is the probability that he/she plays exactly one of these types of instruments? a. 0.7821 b. 0.2457 c. 0.5057 d. 0.7571 e. 0.3645 3. what is the probability that he/she plays at most one of these instruments? a. 0.7514 b. 0.9245 c. 0.5151 d. 0.2486 e. 0.8657
Using probability concepts, we calculated that the likelihood that the person plays the clarinet but not the flute is 0.2743.
What is conditional probability?The possibility of an event or outcome occurring based on the existence of a prior event or outcome is known as conditional probability. It is calculated by dividing the likelihood of the previous event by the likelihood of the subsequent, or contingent, event.
Here,
Finding people who can play the clarinet but not the flute is necessary. There are 172 people who can play the clarinet.
There are 47 people who can play both the clarinet and the flute.
As a result, 172-47=125 represents the number of people who can only play the clarinet and not the flute.
Probability(P),
P=( 125 / 350)
P=0.2743.
Therefore, the probability that a single person chosen at random can play clarinet but not flute is 0.2743.
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