Answer:
x=cb-ad/bd
Step-by-step explanation:
The statement which can be used to prove that x must be a rational number is x = (cb - ad) / bd
Prove of rational numberGiven nonzero integers:
a, b, c, d
If a/b is added to xa/b + x
the sum is c/da/b + x = c/d
prove x to be a rational number
a/b + x = c/d
subtract a/b from both sidesa/b + x - a/b = c/d - a/b
x = c/d - a/b
x = (cb - ad) / bd
Therefore, the statement which can be used to prove that x must be a rational number is x = (cb - ad) / bd
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What is the slope intercept for 4x Y =- 5?
The slope of the equation 4x+y = -5 is -4 and the y-intercept is -5.
To find the slope and y-intercept of the equation 4x+y = -5, you can rearrange the equation into slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
To rearrange the equation 4x+y = -5 into slope-intercept form, you can subtract 4x from both sides to get
y = -4x - 5
In this form, the coefficient of x is the slope (m = -4) and the constant term (-5) is the y-intercept (b = -5).
You can graph this equation by plotting the y-intercept at (0, -5) and using the slope to find additional points on the line. For example, if you increase x by 1, the corresponding change in y can be found by using the slope:
y = (-4 * 1) + (-5) = -9.
This means that the point (1, -9) is also on the line. You can repeat this process to plot additional points on the line and connect them to graph the equation.
--The question is incomplete, answering to the question below--
" What is the slope and y-intercept for 4x+y = -5?"
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An architect maps two buildings, which are located on a piece of land, onto a coordinate plane. He wants to build a wall at the diagonal ac to divide the piece of land into two parts. What will be the length of the wall?.
The length of the wall will be 6√5 units.
The measurement or size of something from end to end is referred to as its length. To put it another way, it is the greater of the higher two or three dimensions of a geometric form or object. For instance, the length and width of a rectangle define its dimensions.
The length of the wall = diagonal AC = distance between point A (-6, -2) and point C (6, 4).
Distance formula between two points on a graph (d) = [tex]\sqrt{(x_{2}-x_{1})^{2}+ (y_{2}-y_{1})^{2} }[/tex]
Where,
A(-6,-2) = (x1,y1)
C(6,4) = (x2,y2)
[tex]d=\sqrt{(6-(-6))^{2}+ (4-(-2))^{2} }\\d= \sqrt{(6+6)^{2}+ (4+2)^{2} }\\d=\sqrt{(12)^{2}+ (6)^{2} }\\d= \sqrt{180} \\d= \sqrt{36*5}\\ d=6\sqrt{5}[/tex]
Thus, The length of the wall will be 6√5 units.
Refer to the image attached for the graph missing in the question.
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Consider the inequality 5≤x+12 5 ≤ x + 12
And can you please solve the inequality.
The solution for the inequality 5 ≤ x + 12 is x ≥ -7 or x is greater than or equal to -7.
What is inequality?The relationship between two expressions that are not equal to one another is shown by inequality.
The given inequality is,
5 ≤ x + 12.
Simplify the inequality,
Subtract 5 from both the sides,
5 - 5 ≤ x + 12 - 5
0 ≤ x + 7
Further, subtract 7 from bot the sides,
0 -7 ≤ x + 7 - 7
-7 ≤ x
or x ≥ -7
The simplified form of the inequality is x ≥ -7.
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The advantages of automation include: (1) reduced output variability (II) reduced variable costs. (III) machines don't strike or file grievances. (IV) machines are always less expensive than human labor. Multiple Choice
O I and IV
O II and III
O I, II, and III
O I and il
The advantages of automation include
(III) machines don't strike or file grievances.
(IV) machines are always less expensive than human labor.
What is automation?Automation refers to technological applications where the amount of human input is reduced. This includes personal applications like home automation, business process automation (BPA), and IT automation.
By predetermining decision criteria, subprocess relationships, and related actions, automation refers to a wide range of technologies that minimize human intervention in processes.
Machine has the advantage of not going on strike or filing grievances. It just obey instruction. Strike are human way of showing grievances. With automation, there is no issue of strike or filing for grievance.
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How many terms are there in the expression 7x 2 )+ 5x 5?
The number of terms in the expression is 3.
What is an algebraic expression?An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.
Let's write the algebraic expression
7x² + 5x + 5
As we can see this expression has some addition operations that cannot be solved because they differ from variable, but this helps us in a way to determine the number of terms and these are:
n1 = 7x²n2 = 5xn3 = 5The expression has 3 terms
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the volume of a rectangular prism is 165 cubic inches. the base of the prism has an area of 15 square inches. what is the height of the prism
Answer:
H = 11
Step-by-step explanation:
What is the characteristic of the leading coefficient?
Since the leading coefficient can be any real number, The characteristic of the leading coefficient are the characteristic of a real number.
What do you mean by a polynomial?Sums of terms with the form kxⁿ, where K is any number and N is a positive integer, are known as polynomials.
What do you mean by leading coefficient?The term with the greatest x power is the leading term in a polynomial function. The leading coefficient is the coefficient of the leading phrase.
The characteristics of the leading coefficient are:
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A die is rolled 200 times with the following results. outcome 1 2 3 4 5 6 frequency 32 36 44 20 30 38 what is the theoretical probability of the given event? p (3)
a. one-sixth
b. 0
c. one-half
d. startfraction 5 over 6 endfraction
Answer:
A
Step-by-step explanation:
The sixth-graders at Kendrick's school got to choose between a field trip to a museum and a field trip to a factory. 14 sixth-graders picked the museum. If there are 56 sixth-graders in all at Kendrick's school, what percentage of the sixth-graders picked the museum?
There are 35% sixth-graders at Kendrick's school who picked the museum.
What is percentage?Percentage is a part of the whole number.
When the denominator is 100, percentages are really just fractions. We place the percent symbol (%) beside a number to indicate that it is a percentage.
1 %= 1/100.
Given that,
Total number of sixth-graders at Kendrick's school = 56,
Also,
The number of s sixth-graders that picked the museum = 14.
The percentage of the sixth-graders that picked the museum
= (14/56) x 100
= (1/4) x 100
= 25 %
25 percent of the sixth-graders picked the museum.
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Is a graph a function or not?
A system of equations consists of a line s of the equation y = x – 5 and a line t that passes through the points (0, 2) and (8, –4). answer the questions about line t to write the equation. what is the slope of line t? what is the y-intercept of line t? what is the equation in slope-intercept form of line t?
The slope of line t is -3/4, y-intercept of line t is 2 and the equation of line t in slope-intercept form is y = -3/4x + 2.
To find the slope of line t, we can use the slope formula, which is:
slope = (y2 - y1) / (x2 - x1)
In this case, we know that line t passes through the points (0, 2) and (8, -4), so we can plug in the coordinates to find the slope:
slope = (-4 - 2) / (8 - 0)
= -6 / 8
= -3/4
The slope of line t is -3/4.
To find the y-intercept of line t, we can use the point-slope form of a linear equation, which is:
y - y1 = m(x - x1)
In this case, we know that line t passes through the point (0, 2), and we know the slope of the line is -3/4. We can plug these values into the point-slope form to find the y-intercept:
y - 2 = (-3/4)(x - 0)
y - 2 = -3/4x
y = -3/4x + 2
The y-intercept of line t is 2.
To write the equation of line t in slope-intercept form, we can use the slope and y-intercept we found above:
y = -3/4x + 2
This is the equation of line t in slope-intercept form.
Thus, The slope of line t is -3/4, y-intercept of line t is 2 and the equation of line t in slope-intercept form is y = -3/4x + 2.
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slope = (y2 - y1) / (x2 - x1)
slope = (-4 - 2) / (8 - 0)
= -6 / 8
= -3/4
The slope of line t is -3/4.
y - y1 = m(x - x1)
y - 2 = (-3/4)(x - 0)
y - 2 = -3/4x
y = -3/4x + 2
The y-intercept of line t is 2.
y = -3/4x + 2
This is the equation of line t in slope-intercept form.
Thus, The slope of line t is -3/4, y-intercept of line t is 2 and the equation of line t in slope-intercept form is y = -3/4x + 2.
What is the standard deviation of 95?
Answer:
Step-by-step explanation:
5 is the standard deviation of 95
What is the meaning of x³ in math?
To answer, let's use the exponent rules, here x³ denotes "x multiplied by itself three times,"
What is exponent rule?Exponents, often known as powers, specify how many times the base number must be multiplied.
Exponent rules are principles that are used to simplify expressions using exponents. These principles are also useful in simplifying formulas with exponents that are decimals, fractions, irrational numbers, or negative integers.
Negative exponents Rule: [tex]a^{-m} = 1/a^m[/tex]Product Rule: [tex]a^m * a^n = a^{(m+n)}[/tex]Quotient Rule: [tex]a^m / a^n = a^{(m-n)}[/tex]Power of a Power Rule: [tex](a^m)^n = a^{mn}[/tex]An exponent is just a shortened way to denote repeated multiplication. x³ (or "x to the third power") in algebraic terms denotes "x multiplied by itself three times," or x x x.
Power is a mathematical phrase that denotes the repeated multiplication of a value or number.
As an example, power 6³ explains how three times the number 6 is multiplied.
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The complete question s as follows:
What is the meaning of x³ in math?
please help me with this problem
Answer:
140 cm^2
Step-by-step explanation:
Area of rectangular = L x W
14 times 10 = 140cm^2
When should we submit SSS sickness notification?
After the confinement period begins, the SBA Form must be filed to SSS loan within five (5) calendar days for Home Confinement. SSS must receive the SBA Form for Hospital Confinement within one (1) year of the patient's release from the hospital.
OFW members will begin receiving a 30-day grace time for filing illness benefit applications beginning on August 18, 2015, in addition to the current five-day prescriptive period.
This is done to allay the worry that people's claims for sickness benefits are frequently penalized for late submission because of the distance between their place of employment/residence and the closest SSS international branch. The additional 30-day grace period is only applicable in situations where hospital confinement is not necessary.
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Find the non-extraneous solutions of √x+6-5=x+1. (1 point)
Ox=-2
Ox=-6 and x = -5
Ox=-6 and x = -2
O x = 2
What Z mean in sets?
The capital Latin letter Z denotes a set of integers in mathematics.
Z = {..., -3, -2, -1, 0, 1, 2, 3, ...}
In sets, thus we may use it to describe the elements of a set using Z. For example A is set of integers greater than -5 and less than 0. So it can be expressed as
A = { x : -5<x<0, x∈Z}
This is equivalent to A = { -4, -3, -2, -1}. But when the number of elements is infinite or too large to list out the other method is opted. The ∈ symbol means belong to.
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chris is going to rent a truck for one day. there are two companies he can choose from, and they have the following prices. company a has no initial fee but charges cents for every mile driven. company b charges an initial fee of and an additional cents for every mile driven. for what mileages will company a charge more than company b? use for the number of miles driven, and solve your inequality for .
As a result, after 130 miles Company A charges more than Company B.
Describe equation.A number, a variable, or both together with particular operation symbols make up an expression. An equal sign separates two expressions that make up an equation.
Here,
Company A Cost is equal to 0.80 m
Cost for Company B is 65 + 0.30 m.
In light of this,
A>B is true
when,
0.80 m > 65 + 0.30 m
0.50 m >65
m > (65 / 0.50)
m > 130.
As a result, after 130 kilometers, Company A charges more than Company B.
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Which expression is equivalent to2 3?
4/6, 6/9, 8/12, 10/15 ... are equivalent to 2/3. All those fractions obtained by multiplying both the numerator and denominator of 2/3 by the same number are equivalent to 2/3.
And, The expression is equivalent to 2 divide by 3
Now, According to the question:
All those fractions obtained by multiplying both the numerator and denominator of 2/3 by the same integer are equivalent to 2/3.
2/3 × 2/2 = 4/6
2/3 × 3/3 = 6/9
2/3 × 4/4 = 8/12
2/3 × 5/5 = 10/15 and so on...
4/6, 6/9, 8/12, 10/15 ... are equivalent to 2/3.
Thus, 4/6, 6/9, 8/12, 10/15 ... are equivalent to 2/3.
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How do you draw a linear graph?
An equation that depicts a straight line on a graph is said to be linear line.
What is linear line?Linear refers to a straight line. Straight-line graphs called linear graphs are used to show the relationship between two values. The single straight lines on this graph assist to represent a result. The phrase "linear" refers to a straight line and excludes the usage of curves, dots, bars, etc.
A linear line can include more than one variable. Linear lines with two variables, for example, are those that have two variables in them. 2x - 3 = 0 and 2y = 8 are few examples of linear lines.
Steps to draw a linear graph are described below:
A linear relation's graph can be discovered by graphing at least two points. The intercepts lead to the discovery of two locations that are very helpful for illustrating the graph of a line. A graph's x-value at which it crosses the x-axis is known as the x-intercept. A graph's y-value at where it crosses the y-axis is known as a y-intercept. Since the x-axis has a value of y = 0, an x-intercept may be discovered by setting y in the equation to 0 and figuring out x. Setting x = 0 in the equation and calculating y leads to the discovery of a -y intercept.To know more about linear lines refer to:
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What are the factors of the expression x² 6x 16?
On solving the provided question we can say that, - the factors of the given equations [tex]x^2 +6x - 16\\[/tex] are - x= -4 and x = 2
What is factor?A number that divides another number by itself with no residual is known as a factor. In other words, if multiplying two whole numbers results in the creation of a product, the numbers we are multiplying are factors of the product since the product is divisible by them. Division and multiplication are the two ways to discover factors. A number or other mathematical object is factorized or factored in mathematics by expressing it as the product of numerous factors, often smaller or simpler things of the same sort. One factorization of the polynomial x2 - 4 is 3 5, which is also a factorization of the number 15.
[tex]x^2 +6x - 16\\[/tex]
(x+4)(x-2)
x= -4 and x = 2
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How do you find the area of a contour?
4) One-square foot floor tiles come 26 to a package. Find how many packages are needed to
cover a rectangular floor 17 feet by 26 feet.
A total of 11492 packages are needed to cover a rectangular floor.
What is a rectangle?
Rectangles are four-sided polygons with all internal angles equal to 90 degrees. At each corner or vertex, two sides meet at right angles. The rectangle differs from a square in that its opposite sides are equal in length.
Given, One-square foot floor tiles come in 26 packages.
dimension of rectangular floor = 17 feet by 26 feet
Then, total area = 17*26 = 442 square foot
So, total packages needed = 442*26 = 11492
Hence, a total of 11492 packages is needed to cover a rectangular floor.
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What value of x will make the number 40 35 :: 16 x?
Answer:
Since 40:35 simplifies to 8:7, 16:X = 8:7, implies X = 14. Hope this helps you!
Step-by-step explanation:
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What is an example of a one solution equation?
For example, 2x+3=8 is a linear equation having a single variable in it. Therefore, this equation has only one solution, which is x = 5/2.
What is the definition of an equation?
An equation is basically a statement that equates two expressions.
An equation must contain an "equality" sign.
Which is the best definition of a two step equation?
A two-step equation is an algebraic equation that takes you two steps to solve. You've solved the equation when you get the variable by itself, with no numbers in front of it, on one side of the equal sign.
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The scatter plot shows the number of pumpkins that have been picked on the farm during the month of October:
Part A: Using computer software, a correlation coefficient of r = 0.51 was calculated. Based on the scatter plot, is that an accurate value for this data? Why or why not?
Part B: Instead of comparing the number of pumpkins picked and the day in October, write a scenario that would be a causal relationship for pumpkins picked on the farm.
The number of pumpkins that were harvested on the farm during in the month of October is shown below, in accordance with the correlation concept.
It is, in Part A.
Part B: the quantity of harvested pumpkins and the quantity of fertiliser used.
what is correlation?
Correlation is a statistical measure that evaluates the strength of a relationship between two variables. It can range from -1 to +1, where -1 indicates a perfect negative linear correlation, 0 indicates no linear correlation, and +1 indicates a perfect positive linear correlation. Correlation is used to measure the strength of the relationship between variables, and whether changes in one variable are associated with changes in the other. Correlation analysis can also help to identify patterns and trends in data, and can be used to make predictions about future outcomes.
Part A:
The stronger the correlation between two variables, as well as vice versa, the closer this same correlation coefficient is to 1. Additionally, the correlation coefficient is closer to 1 the closer this same data points are spaced apart on a scatter plot.
The scatter plot depicted shows a correlation between the quantity of pumpkins and the number of days. The data points are, however, somewhat further apart from one another. The two variables have a moderate relationship, as evidenced by this. Consequently, the calculated correlation coefficient, r, of 0.51 can be regarded as accurate because r of 0.51 denotes a moderate relationship between the two variables.
Part B:
Instead of the day in October, the amount of fertiliser used could have an impact on the number of pumpkins harvested. As a result, we can evaluate the quantity of pumpkin harvested and fertiliser used.
Therefore,
Part A: YES, it is.
Part B: the quantity of harvested pumpkins and the quantity of fertiliser used.
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the circle with equation x² + y² + sx + ty + 33 = 0 has center (4,5) what is s/t?
someone help please!
The Value for s/t is 4/5.
What is Equation of Circle?We know that the general equation for a circle is ( x - h )² + ( y - k )² = r², where ( h, k ) is the center and r is the radius.
Given:
x² + y² + sx + ty + 33 = 0
x² + y² + sx + s²x²/4 + ty + t²y² / 4 + 33 = 0
(x² + + sx + s²x²/4) + (y² + ty + t²y²/4 ) + 33 = 0
(x+ sx/2)² + ( y+ ty/2)² + 33 = 0..............(1)
We know that the standard form
(x-a)² + (y- b)² = r²
where (a, b) is the center.
So, We have center (4,5)
(x-4)² + (y- 5)² = r²
Now Comparing above with Equation (1) we get
s/2 = -4 and t/2 = -5
s= -8 and t= -10
Then, s/t= -8/(-10)= 4/5
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What is the median of the following 26 27 28 29 30?
The median of the set of numbers 26, 27, 28, 29, and 30 is 28. This is the middle number in the ordered set, and it is not affected by extreme values or outliers.
The median of a set of numbers is the value that is exactly in the middle of the set when it is ordered from least to greatest. In this case, the set of numbers is 26, 27, 28, 29, 30. When we order this set from least to greatest, we get 26, 27, 28, 29, 30. There are five numbers in this set, so the median is the third number. The third number in this set is 28, so the median is 28.
To find the median, we first need to arrange the numbers in order from least to greatest. If there is an odd number of numbers in the set, the median is the middle number. If there is an even number of numbers in the set, the median is the average of the two middle numbers. In this case, there are five numbers in the set, so the median is the middle number.
In summary, the median of the set of numbers 26, 27, 28, 29, 30 is 28. This is the middle number in the ordered set, and it is not affected by extreme values or outliers.
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In the triangle above, a = 45. What is the value of b ?
We have 10 gallons of gas in the
car. We use 1 gallons each hour.
How many hours of gas do we
have?
Answer: 10 hours
Step-by-step explanation:
If you are using 1 gallon of gas per hour and have 10 gallons of gas you subtract 1 gallon for every hour you use the car.