Step-by-step explanation:
64/(1+1+2)
= 64/4
= 16
1 : 1 : 2
mark = 1×16 = 16
dave = 1×16 = 16
ralph = 2×16 = 32
Step-by-step explanation:
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What ordered pairs are the solutions of the system of equations shown in the graph below?
The ordered pairs which give the solutions of the system of equations are (-4, 1) and (-8, 9)
How to determine what ordered pairs are the solutions of the system of equations?In order to determine the ordered pairs which give the solutions of the system of equations in a linear-quadratic graph, you need to find the points of intersection of the line and curve from the graph.
Then trace to the x and y-axes to find the ordered pairs values (Check the image attached)
Thus, the ordered pairs are (-4, 1) and (-8, 9)
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Which of the following expressions are polynomials ? (i) x^3−5x+2(ii) y^2+√2y–√5(iii) 2√x+7(iv) −6(v) 4t^2+1/6t+2√3(vi) z^2+5/z^2+1(vii) 1/3x(viii) 1−√5x(ix) 1/14x^−2+3x+5(x) 6√x+x^3/2/√x
In the given expression, expression [tex]x^3[/tex]−5x+2 is a polynomial expression. So the option (i) is correct.
In the given question we have to find which of the following expression are polynomials.
As we know that,
The Greek words "polynomial" and "nominal" are the origins of the word polynomial, which is translated as "many phrases" when combined. There is no limit to the number of terms that a polynomial can have.
Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an equation made up of variables, constants, and exponents. The expression is categorized as monomial, binomial, or trinomial depending on how many terms are present in it.
So if we see on the given expression then we can see that the option (i) [tex]x^3[/tex]−5x+2 have the degree 3 so [tex]x^3[/tex]−5x+2 is a polynomial expression.
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1. Which of the following is a true statement? a. The measure of angle A is 53°. b. The measure of angle B is 117°. c. The measure of angle C is 53°. d. All of the above are true.
Answer: B
Step-by-step explanation:
Since they are all on one line, 27 + 90 + A = 180
Using this, we can get the value of A, which is 63 degrees.
Therefore, A is false.
C is equal to A since they are vertical angles.
Therefore, C is also false.
At this point, two statements are already wrong, so D is obviously false.
The correct statement is B, which we can test by subtracting 63 from 180. And sure enough, it's correct.
What is class inequality?
Class inequality refers to the unequal distribution of wealth, income, and social status among different groups within a society. This means that some individuals or groups have more resources, such as money, property, and access to education and job opportunities, while others have less.
Economic inequality is one of the main forms of class inequality, where a small group of individuals or families own a disproportionate amount of wealth and control the majority of resources, such as land, businesses, and investments. This can lead to a lack of economic mobility for those in lower classes, making it difficult for them to improve their economic situation.
Another form of class inequality is educational inequality, where individuals from lower socio-economic backgrounds have less access to quality education, which in turn limits their opportunities for higher-paying jobs and career advancement. This can also lead to a lack of social mobility, as education is often seen as a key factor in upward mobility.
Healthcare inequality also plays a role in class inequality, as those from lower socio-economic backgrounds often have less access to quality healthcare, leading to poorer health outcomes and increased health disparities.
These forms of class inequality can perpetuate a cycle of poverty and disadvantage for those in lower classes, while those in higher classes have greater access to resources and opportunities, leading to a widening gap between the rich and the poor.
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Darion picks 16 grapefruits off a tree in his backyard. he puts 4 grapefruits in each bag. How many bags dose he need?
Answer:
4
Step-by-step explanation:
What is the additive inverse of 3 /- 11?
11/3 is the additive inverse of 3/-11.. This means that the two numbers have an equal but opposite value. They have the same absolute value but opposite signs.
The additive inverse of a number is the number that when added to the original number, the sum is equal to zero. To find the additive inverse of 3/-11, we need to find the number that when added to 3/-11 will equal zero.
To begin, we need to know the signs of each number. The first number, 3, is a positive number, and the second number, -11, is a negative number. Because the signs of the two numbers are different, we will need to switch the signs in order to find the additive inverse.
11/3 is the additive inverse of 3/-11.. This means that the two numbers have an equal but opposite value. They have the same absolute value but opposite signs. To verify this, we can add 3/-11 and 11/3. When we do this, we find that the sum is zero. Therefore, 11/3 is the additive inverse of 3/-11.
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Are all numbers multiples of primes?
Yes, all the numbers are multiples of prime numbers is a true statement as it get proved by prime factorization theorem.
As given in the question,
Given statement is written as:
All the numbers are representing multiples of prime numbers.
In the field of mathematics,
Using prime factorization theorem also known as fundamental theorem of arithmetic states that:
All the integers which are greater than one are represented as a multiple of prime numbers:
Example of the above stated theorem:
2 = 2×1
3 = 3 × 1
6 = 2 × 3
14 = 2 × 7 ( 2 and 7 both are prime numbers )
98 = 7 × 7 ×2 ..... and so on.
Therefore, all the numbers represents as a multiple of prime numbers is a true statement.
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Kevin runs a legal services company. He charges a registration fee of $150 when a new client is registered. He will then meet with the client to discuss their legal needs and bills they $200 per hour. Write an linear equation that models this relationship.
Fill in the table using the linear equation that models this relationship
x y
0
1
3
4
7
The linear equation modeling the given relationship is y = 150 + 200x, where y is the fees and x is the time in hours.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Given that,
Registration fee for a new client = $150
There is also a fees of $200 per hour.
If x represents the hours, then the additional fees for x hours is 200x.
Total fees, y = 150 + 200x
If x = 0 hours, then y = $150
If x = 1 hour, y = 150 + (200 × 1) = $350
If x = 3 hours, y = 150 + (200 × 3) = $750
If x = 4 hours, y = 150 + (200 × 4) = $950
If x = 7 hours, y = 150 + (200 × 7) = $1550
Hence the linear equation modeling the situation is y = 150 + 200x.
If x = 0, 1, 3, 4 and 7, the values of y are 150, 350, 750, 950 and 1550.
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A block on the end of a spring is pulled to position x=a and released from rest. In one full cycle of its motion, through what total distance does it travel?.
The total distance it travels during one full cycle of motion is 4A. Hence, the correct answer is D.
When a block on the end of a spring is pulled to position x = A and released from rest, it begins to oscillate. The block will oscillate back and forth along the x-axis between the position x = A and the position x = -A.
In one full cycle of its motion, the block will travel from position x = A to position x = -A and back to position x = A. The total distance traveled by the block in one full cycle of its motion is the sum of the distance traveled in each direction.
The distance traveled by the block in one direction is A, and the distance traveled in the other direction is A. So, the total distance traveled by the block in one full cycle of its motion is:
A + A = 2A.It's important to note that the amplitude of the oscillation is equal to the distance from the equilibrium position to the position x = A. This means that the total distance the block moves in one full cycle is equal to twice the amplitude of the oscillation.
Therefore, the total distance traveled by the block in one full cycle of its motion is:
2.A = 4AHence, the correct answer is D, 4A.
This question should be provided with answer choices, which are:
A. A/2B. AC. 2AD. 4AThe correct answer is D.
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A man takes a walk 6 miles south and 9 miles east from his house. What is the shortest distance he must walk to return to his house?
Instead of taking 6 miles south and 9 miles east to the house the shortest distance is 10.82 miles
How to find the shortest distanceThe distance described 6 miles south and 9 miles east represents a right triangle with
opposite = 6 miles
adjacent = 9 miles
hypotenuse is the shortest distance
Using Pythagoras theorem given by the the formula
hypotenuse² = opposite² + adjacent²
plugging the values as in the problem
let x be the required distance
x² = 9² + 6²
x² = 81 + 36
x² = 117
x = √117
x = 10.82
the shortest distance is 10.82 miles
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What is the solution of the system?
4g + h = -4
12g + 2h = -4
Enter the coordinate pair in the boxes in alphabetical order (_, _)
what numbers,x,for which x<7 and x>-2 is true
Answer: -1,0,1,2,3,4,5,6
Step-by-step explanation:
x<7
x>-2
Write that in one equation and you get
-2<x<7
The values of x that satisfy this inequality are
-1,0,1,2,3,4,5,6
Algebraic expression for "half as many points as George"
Divide (36z^2y^6-12z^6y^6) divided by (4z^5y^2)
The simplification of the equation is 9y⁴/z³ - 3zy⁴.
What is simplification?Simplifying procedures is one way to achieve uniformity in work efforts, expenses, and time. It reduces diversity and variety that is pointless, harmful, or unnecessary.
Solving a math problem is the same thing as simplifying an expression. You basically strive to write an expression as simply as you can when you simplify it. In conclusion, there shouldn't be any more multiplying, dividing, adding, or removing to do.
Here, we have
Given: (36z²y⁶-12z⁶y⁶)/(4z⁵y²)
We have to simplify this equation.
= (36z²y⁶-12z⁶y⁶)/(4z⁵y²)
= 36z²y⁶/4z⁵y² - 12z⁶y⁶/4z⁵y²
= 9y⁴/z³ - 3zy⁴
Hence, the simplification of the equation is 9y⁴/z³ - 3zy⁴.
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How do you do 10th grade inequalities?
You do inequalities by familiarizing yourself with inequalities.
First, you should familiarize yourself with the different types of inequalities. Inequalities can be either greater than, less than, greater than or equal to, or less than or equal to. Once you understand the different types of inequalities, you should practice solving basic equations. Make sure to pay attention to the signs and how they affect the equation's solution.
Next, you should start solving inequalities with two terms. Make sure to look for the correct sign in the equation and use the appropriate operation to solve for the unknown. Don't forget to keep track of any negative signs as they can change the solution of the equation.
Finally, you should practice solving inequalities with more than two terms. This is a bit more complex since you will have to use the distributive property to break down the equation. Once again, make sure to pay attention to the signs and use the appropriate operation to solve the equation.
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Given m
||n, find the value of x and y
dy.
(4y-7)°
(2x+3)°
(6x+9)⁰
m
n
The value of x is 21° and y is 13°. The solution is obtained using the properties of parallel lines.
What are Parallel lines?
When two lines in a plane do not cross at any point, they are said to be parallel. In other words, lines that never cross paths with one another and do not have a common junction point are said to be parallel.
The characteristics of parallel lines with respect to transversal are listed below:
Angles that coincide are equal.Angles that are vertically opposite or vertically angled are equal.Interior angles that alternate are equal.Exterior angles that alternate are equal.On the same side of the transversal, a pair of interior angles are supplementary.As shown in the figure, angles (2x+3)° and (6x+9)° denote the interior angles on the same side of the transversal.
Therefore, both the angles add upto 180°
So, (2x+3) + (6x+9)=180
8x+12=180
8x= 168
x= 21°
Also, angles (4y-7)° and (6x+9)° form a linear pair.
Therefore, both the angles add upto 180° and we know that x= 21°
So, (4y-7)+((6×21)+9)=180
4y+128=180
4y=52
y=13°
Hence, the value of x is 21° and y is 13°.
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How do you find a function from a table of values?
Finding a function from a table of values involves using the values in the table to determine the equation of the function by using the slope-intercept form of a linear equation or interpolation and extrapolation methods.
One way to do this is by using the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.
To find the slope, you can use the formula: m = (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are two points on the table. Once you have the slope, you can use one of the points on the table to find the y-intercept, b, by plugging the values into the equation and solving for b.
Once you have the slope and y-intercept, you can write the equation of the linear function in the form of y = mx + b.
Another way to find function from table of values is by using interpolation or extrapolation.
Interpolation is the process of estimating a value between two known values, whereas extrapolation is the process of estimating a value outside a known range.
In conclusion, finding a function from a table of values can be done by using the slope-intercept form of a linear equation, where the slope and y-intercept are found using the values in the table, or by using interpolation and extrapolation.
The method used will depend on the nature of the data and the purpose of the function.
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What are the 4 most common graphs?
Line graphs, bar graphs, pie charts, scatter plots, and histograms are examples of common graph types.
Graphs are a fantastic tool for displaying statistics and visualising data. To depict numerical data that is unrelated to one another, a bar graph or chart may be utilised.
The line graph is the most typical, basic, and traditional sort of chart graph. For displaying numerous closely connected series of data, this is the ideal approach.
Data that is readily apparent. appropriate unit-specific labelling for each axis. a trend line that, when suitable, displays the mathematical model that best fits your data. If there is more than one sort of information, there should be a legend.
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Use the drop-down menus to complete the equation that represents the data in the table.
d
1
2
3
4
5
t
9
13
17
21
25
t =
Choose...
d +
Choose...
The equation that represents the linear equation is t = 4d + 5.
What is linear equation?Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.
Given:
The table is given in the attached image.
To find the equation:
First, find the common difference.
So,
13 - 9 = 4
17 - 13 = 4
21 - 17 = 4
25 - 21 = 4
Here, the first difference 4 is common.
That means, the equation is a linear equation.
And the general form of the linear equation is,
t = md + c
Here, m = 4
So,
t = 4d + c
To find C:
Substitute the value of t = 9 and d = 1,
So, c = 5
So, the linear equation is t = 4d + 5.
Therefore, t = 4d + 5 is the linear equation.
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Using the recursive rule, f (n) = f ( n - 1) + 8; f (1) = -10. Type of sequence : Common ratio or difference : Explicit equation : Recursive equation :
The given equation f (n) = f ( n - 1) + 8; f (1) = -10; is a form of Recursive equation.
Define the term Recursive equation?A recursive formula is one that specifies each term in a sequence by reference to the one before it (s).
The following parameters are defined using the recursive formulas:
The first phrase in the series.Getting any term out of its prior term is the pattern rule.The following is the recursive formula for calculating the nth term in an arithmetic sequence:
n2: a = an-1 + d
where,
The common difference is d, and an is really the nth term of an A.P.For the given equation:
f (n) = f ( n - 1) + 8 and f (1) = -10 are the form of recursive formula.
As, the common difference is added to the function as 8.
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2|-5| - 3(-5•4)
what do i do
Answer:
70
See explanation below
Step-by-step explanation:
The absolute value of a number is always its positive value
|-5| means absolute value of -5 which is 5
2|-5| becomes 2 · 5 = 10
- 5 · 4 = -20
-3(-5 · 4) becomes - 3 ( - 20 ) = + 60
So
2|-5| - 3(-5•4) = 10 + 60 = 70
PLEASE HELP!!
A box holds 12 cans. The dimensions of the box are shown. Calculate the total volume of the twelve
Answer:
49875 cm^3
Step-by-step explanation:
We use the formula, "V = bh" to find the volume of one cylinder (can), where "b" is the area of the circle base of the cylinder, and "h" is the height.
First, we can find the volume of one cylinder.
The base would be calculated by "πr^2", where "r" is the radius. To find the radius, we can use the information given in the diagram: four cans in a row have a length of 84 cm. Thus, if we divide 84 by 4, we get the diameter of one can. If we divide that diameter by 2, we get the radius of one can: 84/4/2 = 10.5 = r
πr^2 --> π10.5^2 = 110.25π
The height is shown in the diagram: one can fits perfectly inside the box, so the height dimension of the box is the same as the can's height dimension.
h = 12
Now, we can calculate the volume of one can: V = 12 * 110.25π = 1323π
As the problem calls for the volume of 12 cans, we can multiply the volume of one can by 12 to find the volume of 12 cans:
12 * 1323π = 15876π = 49875 cm^3
Answer:
Step-by-step explanation:
Firstly we have to find the dimensions of the can.
Height of can - 12 cm
Diameter of can - 21 cm
The radius of can - 21/2 = 10.5 cm
Volume of can - [tex]\pi r^2[/tex] * h ( height )
[tex]3.14 * 10.5^2[/tex] * 12
3.14* 110.25 *12
346.185 *12
4154.22
Volume of 12 cans - 4154.22 *12
Answer - [tex]49850.64cm^3\\[/tex]
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.
Determine each segment length in right triangle XYZ.
Y
60°
Z 5 W
20
30°
10√/2
X
10√3
5
5√/2
XW
XY
15
5√3
The lengths of segments XY, XW, and YW in right triangle XYZ are given by:
XY = (1/2) * XZ
XW = (√3/2) * XZ
YW = (1 - √3/2) * XZ
Explanation:
To determine the lengths of segments XY, XW, and YW in right triangle XYZ, we can use the trigonometric ratios for the angles Y = 60° and Z = 30°.
Let's start with segment XY. The side opposite the 30° angle is half the length of the hypotenuse. Therefore, XY = (1/2) * XZ.
Next, let's find the length of segment XW. The side opposite the 60° angle is √3 times the length of the side opposite the 30° angle. Therefore, XW = √3 * XY = √3 * (1/2) * XZ = (√3/2) * XZ.
Finally, let's determine the length of segment YW. YW is the difference between XY and XW. Therefore, YW = XY - XW = (1/2) * XZ - (√3/2) * XZ = (1 - √3/2) * XZ.
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A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 447gram setting. Based on a 24 bag sample where the mean is 444 grams and the standard deviation is 10, is there sufficient evidence at the 0.1 level that the bags are underfilled or overfilled? Assume the population distribution is approximately normal.
Step 4 of 5: Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.
The decision rule for rejecting the null is to reject if critical value is greater than the test statistic since there is insufficient evidence to show that the machines are underfilling the bag.
How to carry out the hypothesis testFirst we have to solve for the test statistic
The formula is given as:
t = x - u / s /√n
where x = 444
u = 447
n = 24
s = 10
we would have:
444 - 447 / 10 / √24
-3 / 2.0412
= -1.4697
at 0.1 significance level, we would have: n - 1 = 24 - 1 = 23
the critical value is -1.3194.
Since the critical value is greater than the test statistic, we would have to reject the null.
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Drag and drop each angle measure into the correct box to find the measure of each angle.
The measure of angles are,
m ∠K = 50°
m ∠L = 90°
m ∠M = 40°
m ∠LMN = 140°
What is triangle?
A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.
Let the triangle KLM is given.
We have to find the measure of each angle of triangle.
Since the measure of three angles of triangle is 180 degree.
⇒ m ∠K + m ∠L + m ∠M = 180°
5x + 9x + 4x = 180°
18x = 180°
x = 10°
⇒ m ∠K = 5x = 5(10°) = 50°
m ∠L = 9x = 9(10°) = 90°
m ∠M = 4x = 4(10°) = 40°
m ∠LMN = m ∠L + m ∠K
= 90° + 50°
m ∠LMN = 140°
Hence,
m ∠K = 50°
m ∠L = 90°
m ∠M = 40°
m ∠LMN = 140°
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Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right.
Answer:
A number line from -5 to 5 in increments of 1. An open circle is at 3 and a bold line starts from 3 and is pointing to the right
Graph the following equations.
y=-2x+1
The graph of the given equation will be a straight line.
What is the equation of a line?The equation of a straight line is y = m x + c m is the gradient and c is the height at which the line crosses the y-axis, also known as the y -intercept.
Given is an equation, y = -2x+1, we are asked to plot a graph for the same,
To plot the graph, we will firstly find the coordinates,
Therefore, the equation is y = -2x+1,
Put x = 0,
y = 1
The first coordinates = (0, 1)
Put y = 0
x = 1/2
The second coordinates = (1/2, 0)
Now, plot this points on the graph, and connect them, since the equation is linear, we will get a straight line, passing through these points, that will be the line of the equation given, (refer to graph attached)
Hence, the graph of the given equation will be a straight line.
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How is 13 a prime number?
13 is considered as a prime number as there are only two factors of 13 which are equals to 1 and 13 itself.
As given in the question,
Given number is equal to 13,
Prime numbers are those numbers which has only two factors : one and the number itself.
Here is not divisible by any other number.
Factors of 13 are equals to :
1 and 13 itself.
There are only two factors of thirteen which are equals to one and number 13 itself.
Therefore, 13 is considered as a prime number because there are only two factors of 13.
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I WILL MARK AS BRAINLIEST HELP!!
Answer:
(a) = $640
(b) = $8640.
Step-by-step explanation:
(a) To calculate the total interest Teresa will have to pay, use the formula:
Interest = Principal x Rate x Time
In this case, the principal is $8000, the rate is 4% (expressed as a decimal), and the time is 2 years.
So, Interest = $8000 x 0.04 x 2 = $640
(b) To find the total repayment amount, add the interest to the original principal.
In this case, the total repayment amount = $8000 + $640 = $8640.
How do you find the shortest distance between two lines in 3D vectors?
The shortest distance between two lines in 3D represented by vectors can be found by using the dot product of the vector joining the two lines with the cross product of the direction vectors of the lines, divided by the length of the cross product vector.
To find the shortest distance between two lines in 3D space represented by vectors, you can use the following method:
Write the parametric equations of the two lines: Line 1: X = X1 + tv and Line 2: X = X2 + sv, where X1, X2 are the position vectors of the two lines, and v, s are the direction vectors of the two lines, respectively.Find the vector joining the two lines: X2 - X1Find the cross product of the direction vectors of the two lines, this is the vector that is perpendicular to both lines.Take the dot product of the vector joining the two lines and the cross product of the direction vectors, and divide by the length of the cross product vector.The absolute value of the result obtained in step 4 is the shortest distance between the two lines.To learn more about 3D vectors at
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