The line passing through Po = (7,-1, 1) and perpendicular to the plane 11x + 10y – 9z = 12 is given by the parametric equations x = 7 + 110t, y = -t, z = t, where t is a parameter.
Write a statement, how to find parametric equations for a line through a point that is perpendicular to a given plane?To find the parametric equations for the line, we need to determine a direction vector for the line. Since the line is perpendicular to the plane 11x + 10y – 9z = 12, its direction vector will be orthogonal to the normal vector of the plane.
The normal vector of the plane is (11, 10, -9).
To find a direction vector for the line, we can take any vector that is orthogonal to the normal vector. One such vector is (10, -11, 0). We can obtain this vector by setting x = y = 1 and solving for z in the equation 11x + 10y – 9z = 0.
So, the parametric equations for the line are:
x = 7 + 10ty = -1 - 11tz = twhere t is a parameter.
Note that we can verify that the direction vector (10, -11, 0) is indeed orthogonal to the normal vector (11, 10, -9) of the plane by taking their dot product:
11(10) + 10(-11) + (-9)(0) = 0
Therefore, the line is perpendicular to the plane as required.
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What’s question a? PLEASE HELLPPPP!!!
By using the given formula and solving we get, the original value of the vase is 5000 pounds.
What is percentage?A percentage is a way to express a number as a fraction of 100. It is often denoted by the symbol "%". For example, 25% means 25/100 or 0.25. Percentages are often used to express rates of change or proportions.
What is rate?A rate is a ratio that compares two quantities of different units, such as distance and time, or weight and volume. It is often represented as a fraction or a decimal and can be converted to a percentage by multiplying by 100.
The given formula tells us how the value of the vase changes over time, with the value increasing by a factor of 1.28 (28% increase) every year.
To find the original value of the vase, we need to know the value of the vase when n = 0.
Substituting n = 0 into the formula, we get:
value in pounds = 5000*1.28^0
When n = 0, 1.28^0 = 1, so the original value of the vase is:
value in pounds = 5000*1 = 5000 pounds
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-3/7 is greater than -2/5
Answer: False
Step-by-step explanation:
-3/7 roughly equals -0.428
-2/5 equals -0.4
-0.4>-0.428
-2/5>-3/7
If you have a 30% increase, what percentage of the original amount do you have?
The original amount is (100%) if you have an increased by 30%
What is percentage increase?
Percentage increase is the difference between the final value and the initial value, expressed in the form of a percentage.
In the given question, the percentage increase can be calculated with the help of the percentage increase formula,
Percentage Increase = [(Final Value - Initial Value)/Initial Value] × 100
To get the original amount,
Just add the percentage increase to 100, divide 100 by it, then multiple by the final number to get the original number.
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What is the value of −7 + (−12) + 81?
−100
−76
62
86
How many years will it take for an investment to double if the rate is 6.75% and it is compounded monthly?
By solving an exponential equation, we can see that the investment will be doubled after 10.6 years.
How many years will it take for the investment to double?The investment can be modeled by the exponential equation:
P(x) = A*(1 + 6.75%/100%)^x
Where A is the initial value of the investment (the amount invested).
We can simplify this to get:
P(x) = A*(1 + 0.0675)^x
The investment will be doubled when:
2*A = A*(1 + 0.0675)^x
We want to solve this for x.
2 = (1 + 0.0675)^x
2 = (1.0675)^x
If we apply the natural logarithm in both sides:
ln(2) = ln((1.0675)^x)
ln(2) = x*ln(1.0675)
ln(2)/ln(1.0675) = x
10.6 = x
The investment will be doubled after 10.6 years.
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x^2+x=3 then what is x^3-4x
By algebra properties, the values of algebraic expression x³ - 4 · x are - 3 and 0 for x² + x = 3.
How to derive the result associated to an algebraic expression
In this question we must derive the value of algebraic expression x³ - 4 · x based on the fact that x² + x = 3. First, determine the value of x by algebra properties:
x² + x = 3
x² + x - 3 = 0
x² + (2 - 1) · x + 2 · (- 1) = 0
x² + 2 · x - x - 2 = 0
x · (x + 2) - (x + 2) = 0
(x - 1) · (x + 2) = 0
x = 1 or x = - 2
The roots of x² + x = 3 are 1 and - 2.
Second, determine the values associated with the two roots found in previous step:
x = 1
y = x³ - 4 · x
y = 1³ - 4 · 1
y = 1 - 4
y = - 3
x = - 2
y = x³ - 4 · x
y = (- 2)³ - 4 · (- 2)
y = - 8 + 8
y = 0
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A traw i placed inide a rectangular box that i 6 inche by 6 inche by 1 inche, a hown. If the traw fit exactly into the box diagonally from the bottom left corner to the top right back corner, how long i the traw? Leave your anwer in implet radical form
The length of the straw placed inside the rectangular box is [tex]\sqrt{73}[/tex] inches.
A quadrilateral with parallel sides equal to one another and four equivalent vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason.
Rectangles can also be referred to as parallelograms since their opposite sides are equal and parallel. The area of a rectangle is given as the product of the length and breadth of the rectangle.
The given parameters are:
Length (l) = 6 inchesWidth (w) = 6 inchesHeight (h) = 1 inchesThe straw is said to fit into the box diagonally from the bottom.
So, the length (s) of the straw is calculated as:
[tex]s=\sqrt{l^{2}+w^{2}+h^{2} }\\[/tex]
The equation becomes:
[tex]s=\sqrt{6^{2}+6^{2}+1^{2} }\\[/tex]
Evaluate the exponents:
[tex]s=\sqrt{73}[/tex] inches
=> s≈8.544 inches
Hence, the length of the straw is 8.544 inches.
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Each week, the price of oranges at the farmer's market increases by `20\%`.
Select all the equations that represent the relationship between the price of oranges last week, `x`, and the price of oranges this week, `y`.
The equation of the relationship between the price of oranges last week and this week is y = 1.2x
How to determine the equation that represent the relationship?From the question, we have the following parameters that can be used in our computation:
Price last week = x
Rate of increment = 20%
Price this week = y
Using the above as a guide, we have the following:
Price this week = Price last week * (1 + Rate of increment)
Substitute the known values in the above equation, so, we have the following representation
y = x * (1 + 20%)
Express as decimal
y = x * (1 + 0.2)
Evaluate the sum
y = x * 1.2
So, we have
y = 1.2x
Hence, the equation is y = 1.2x
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Is 0 an exponential function?
0 is not an exponential function.
We know that the general form of exponential function f with base b is defined as:
f(x) = b^x
where b > 0 and b is not equal to 1
and x is any real number.
If it is negative b < 0, the function is undefined for -1 < x < 1.
If in an exponential function the base is less than zero, then it would make the function values complex for certain fractional values.
If the base of exponential function is 0 then function would create a graph which violates the properties / definition of exponential functions.
Also, we can not write 0 in exponential function form.
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Function or not a function?
c + –4c + 10 + –10
an
Answer:
-3c
Step-by-step explanation:
During photosynthesis, what is the path or flow of energy among biotic and abiotic parts of an ecosystem?
Answer:
-3c
Step-by-step explanation:
c+-4c+10+-10= c+-4c= -3c
Solve:
[tex]sin^2(2x+3)+cos^2(2x+3)=2x+3[/tex]
The solution of the trigonometric equation sin^2(2x+3)+cos^2(2x+3)=2x+3 is x = -1.
How to solve a trigonometric equation?Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles
sin²(2x+3) + cos²(2x+3) = 2x + 3
Remember, the trigonometric identity, sin²θ + cos²θ = 1.
Thus, we can say sin²(2x+3) + cos²(2x+3) = 1. We now have:
sin²(2x+3) + cos²(2x+3) = 2x + 3
1 = 2x + 3
2x = 1-3
2x = -2
x = -2/2
x = -1
Therefore, the solution of the equation is x = -1
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Which statement best explains if the graph correctly represents the proportional relationship y = 0.5x? (4 points) A coordinate plane is shown. Points are graphed at 1 comma 0.5 and 4 comma 2. The points are joined by a line.
The correct statement is (A) the points on the line would indeed be a part of the equation y = 0.5x.
What are proportional relationships?Relationships between two variables that are proportional occur when their ratios are equal.
Another way to consider them is that in a proportionate relationship, one variable is consistently equal to the other's constant value.
The "constant of proportionality" is the name of this constant.
Observing the graph, the line traverses (0, 0). We obtain y=0.5(0)=0 if x=0.
Since this is the point's y-coordinate, it passes through this.
Y=mx+b, where m is the slope and b is the y-intercept, is the slope-intercept form equation for this line.
m=0.5 and b=0 in this equation.
This indicates that the slope is 0.5 or 1/2; as slope = rise/run, this indicates that the line rises one for every increase in the horizontal dimension of two.
This implies that starting from (0, 0), we would climb 1 and cross 2 to make the spot (2, 1).
When examining the graph, the line passes through this location.
We would then ascend 1 and cross over 2 once more to (4, 2). Once more, the line passes through this spot.
Therefore, the correct statement is (A) the points on the line would indeed be a part of the equation y = 0.5x.
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Complete question:
Which statement best explains if the graph correctly represents the proportional relationship y = 0.5x?
A. Yes, the points shown on the line would be part of y = 0.5x
B. Yes, all proportions can be shown on a graph of this line
C. No, the points shown would not be part of y = 0.5x
D. No, proportions cannot be represented on a graph
PLEASE HELP ME I NEED THIS DONE AS SOON AS POSIBLE
a. Liam wants to know how the function would need to change to reflect the amount of money the business will take in. Use this function to model a function for gross sales. (Gross sales are the total amount of money the flowers sell for.)
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b. Liam knows that his cost (c) in terms of the units of mums sold (x) can be modeled by the function Replace the variable x in this function with the function that gives the number of units sold (x) in terms of price p. What does this turn the function c into?
Type your response here:
c. Liam wants to calculate the profit his shop would earn from the sale of mums. He knows that it can be done by deducting the costs from the money that the store makes selling mums. Now that he has the functions for the cost and gross sales, can he subtract the function for cost from the function representing the gross sales to arrive at a function for profit? Why?
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d. Find the store’s profit function for selling mums by subtracting the function for cost from the function for gross sales. Consider pr(p) as the profit function.
Type your response here:
e. Is the profit function linear or quadratic?
Type your response here:
f. Liam wants to use the profit function to determine the range of prices at which he can sell mums and make a profit. How can he determine the price range?
Type your response here:
g. Use the quadratic formula to find the factors of the profit function you wrote.
Type your response here:
h. Using the factors you found in part g, find the zeros of the quadratic profit function.
Type your response here:
i. Liam needs to find the range of prices at which he can sell mums and make a profit. Based on the equation, what are the points between which he will earn a profit on his mums?
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j. Liam wants to determine the most profitable price point for the mums. Use the completing the square technique to find this price.
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k. Liam is interested in determining the maximum profit possible for the mums. Find the maximum profit corresponding to the most profitable price point.
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Task 2: A Boat Ride
Jake went on a riverboat tour. After returning from the tour, he was curious to know the speed at which the boat was going. During the tour, he was told that he would travel 10 miles upstream and then 10 miles downstream. He also knows that the river was flowing at a rate of 3 miles/hour and that the tour took about three hours.
The boat moved at a constant speed for the whole journey, although its actual speed varied with the current.
a. Jake wants to know the boat’s actual speed going upstream and actual speed coming downstream. If the boat was moving at a constant speed of x miles per hour, determine the boat’s relative speed in each direction.
Type your response here:
b. Was the time it took the boat to go upstream the same as the time it took to come downstream?
Type your response here:
c. Jake first reasoned that because the boat ride took 3 hours, it must have taken 1.5 hours to go upstream and 1.5 hours to go downstream. Thinking about it further, however, he realized that the ride upstream had to take longer than the trip downstream. What is the reason it took longer to travel one direction than the other?
Type your response here:
d. The time it took the boat to go upstream is U, and the time it took to come downstream is D. What is U + D?
Type your response here:
e. Jake knows that the relationship between distance (d), velocity (v), and time taken (t) is given by d = vt. Rewrite this equation for t.
Type your response here:
f. Using the equation you rewrote in part e, write an equation for the time taken for the upstream trip.
Type your response here:
g. Now construct an equation for the time taken for the downstream trip.
Type your response here:
h. Jake already has the equation U + D = 3, which represents the total time taken for the whole journey. Now that he has individual equations for U and D, he needs to combine these three equations to get a single equation. Construct a combined equation for U + D in terms of x, the constant speed at which the boat was going.
Type your response here:
i. Jake now has an equation with x as the only unknown variable. He needs to solve for x. Transform the equation you found in part h into a quadratic equation, and find the value of x, the constant speed at which the boat traveled.
Type your response here:
Answer::b.
Step-by-step explanation:
8x−5y=−11 determine the intercepts
The x and y-intercepts of the given equation of line 8x - 5y = -11 are (-11/8,0) and (0,11/5) respectively.
What are the x and y-intercepts of the given equation of line?Given the equation of line in the question;
8x - 5y = -11
To find the x-intercept, substitute in 0 for y and solve for x.
8x - 5y = -11
8x - 5(0) = -11
8x - 0 = -11
8x = -11
x = -11/8
Hence, the x-intercept is (-11/8,0)
To find the y-intercept, substitute in 0 for x and solve for y.
8(0) - 5y = -11
0 - 5y = -11
-5y = -11
y = -11 / -5
y = 11/5
Hence, the y-intercept is (0,11/5).
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Help please! Triangle Proofs are so hard!
The required two-column proof that the triangles are congruent is explained below.
Properties of a congruent triangles.A triangle is a three sided plane shape whose the sum of internal angles is 180^o. Thus two or more triangles are said to be congruent when their corresponding sides and measure of internal angles are equal.
When two triangles are congruent, it can be proven in all respect that they are thus equal (considering their corresponding length of sides and measure of internal angles).
The two-column proof required in the question is given below:
STATEMENT JUSTIFICATION
1. <WXZ ≅ <YXZ Property of an angle bisector.
2. <XZW ≅ <XZY Definition of a perpendicular bisector.
3. WX ≅ YX Congruent sides of a triangle.
4. WZ ≅ YZ Definition of a midpoint.
Therefore,
ΔWXZ ≅ ΔYXZ Angle-Angle-Side theorem
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What are the explicit equation and domain for an arithmetic sequence with a first term of 3 and a second term of 5?
Group of answer choices
an = 3 + 2(n − 1); all integers where n ≥ 0
an = 3 + 6(n − 1); all integers where n ≥ 1
an = 3 + 6(n − 1); all integers where n ≥ 0
an = 3 + 2(n − 1); all integers where n ≥ 1
Note that the explicit equation and domain for an arithmetic sequence with a first term of 3 and a second term of 5 is n = 3 + 2(n − 1); all integers where n ≥ 1 (Option D)
What is an arithmetic sequence?Arithmetic progression or arithmetic sequence is a numerical series in which the difference between subsequent terms is constant. For example, the sequence 5, 7, 9, 11, 13, 15..
The first term of the arithmetic sequence is 3, followed by 5. Thus, the common difference is, 5-3 = 2. You use these values to the derived formulas for arithmetic progression. One of these formulas is
An = A1 + (n-1)d
where
An is the nth term in the sequence
A1 is the first term of the sequence
n is the total number of terms within the sequence
d is a common difference.
In this problem, A1 = 5 and d=2. Substituting to the equation,
An = 3 + (2)(n-1)
An = 3 + 2(n-1), where n should be more than 1. In order for it to become a sequence, it should contain more than one term.
Therefore, it is correct to appropriate an explicit equation and domain for an arithmetic sequence with a first term of 3 and a second term of 5 to be: n = 3 + 2(n − 1); all integers where n ≥ 1
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Which of the following are solutions to the equation below?
Check all that apply.
4x²2²-12x+9=5
□ A. x= √5-3
□ B. x= -√4-3
C. x=--√5 + 3
□ D. x = √5 +
□ Ex= √4-3
□ F. x= -√5-3
Equation 4x222-12x+9=5 has a solution of x= -√4-3. It is said to be linear when an equation has the form y=mx+b .
what is equation ?In algebra, a linear equation is one with the form y=mx+b. B is the slope, and m is the y-intercept. Because y and x are variables, the previous sentence is frequently referred to as a "linear equation with two variables." Bivariate linear equations are those with two variables. There are various examples of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation has the formula y=mx+b, where m denotes the slope and b the y-intercept, it is referred to as being linear. It is said to be linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.
given
4x²2²-12x+9=5
8x2 - 12x +4 = 0
8x2 - 6x - 6x +4 = 0
2x(4x - 3) - 2(3x +2) = 0
Equation 4x222-12x+9=5 has a solution of x= -√4-3 . It is said to be linear when an equation has the form y=mx+b .
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A cylinder has a height of 19 millimeters and a radius of 7 millimeters. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth.
Step-by-step explanation:
[tex]volume \: of \: cylinder = \pi \: {r}^{2} h \\ volume = 3.14 \times {7}^{2} \times 19 \\ = 2923.34 \: millimetres[/tex]
What value(s) of b will cause 2x2 + bx + 128 = 0 to have one real solution? Select all that apply. A. b = 32 B. b = −50 C. b = −20 D. b = –32
The value of b can be -32 or +32 to ensure that the equation has only one true solution.
What is discriminant of the equation?The discriminant is the quadratic formula section behind the square root symbol: b2-4ac. The discriminant indicates whether there are two solutions, one solution, or none at all. The "discriminant" is the argument (that is, the contents) of the square root, which is the equation b2 4ac, because by utilizing its value, you may "discriminate" between (that is, determine the difference between) the various solution types.
Here,
The discriminant of the equation is ...
d = b² -4ac
d = b² -4(2)(128)
d = b² -1024
In order for there to be one real solution, we must have d=0. So ...
0 = b² -1024
1024 = b²
±√1024 = ±32 = b
The value of b can be -32 or +32 to cause the equation to have one real solution.
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Please please please help! 20+ points! Thank you :)
Answer:
CD = 27
Step-by-step explanation:
2(4x - 1) + 2(3x + 3) = 116
8x - 2 + 6x + 6 = 116
14x + 4 = 116
14x = 112
x = 8
3(8) + 3
= 24 + 3
= 27
Arvin is training for a race. He wants to bike:
between 35 and 41 miles a week,
either 3 or 4 days a week, and
the same number of miles each day.
What are two possible ways Arvin can complete his training plan?
Answer:
Two possible ways Arvin can complete his training plan are:
Biking 35 miles a week, 3 days a week, biking 11.67 miles per day.
Biking 41 miles a week, 4 days a week, biking 10.25 miles per day.
In the first option, Arvin bikes 35 miles a week, 3 days a week, which means he bikes 11.67 miles per day to achieve his goal.
In the second option, Arvin bikes 41 miles a week, 4 days a week, which means he bikes 10.25 miles per day to achieve his goal.
It is important to note that these are just examples, and there could be other options that Arvin can consider, as long as it meets his requirement of biking between 35 and 41 miles a week, either 3 or 4 days a week, and the same number of miles each day.
Step-by-step explanation:
help me cause its due today
The value of x is equal to 9 for the two-variable equation -2x - 7y = 17 when y is equal to -5.
Two variable equationA two-variable equation is an equation that has 2 variables, typically x and y
For the two-variable equation;
-2x - 7y = 17
we shall evaluate for the value of x when y = -5 as follows:
-2x - 7(-5) = 17
-2x + 35 = 17
subtract 35 from both sides of the equation
-2x = 17 - 35
-2x = -18
divide through by -2
x = -18/-2
x = 9
Therefore, 9 is the value of x when y is equal to -5 for the two-variable equation -2x - 7(-5) = 17.
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50 POINTS!
INDUCTIVE/DEDUCTIVE ARGUMENT
Since the United States' Declaration of Independence was signed in the year 1776, it follows that the United States is over 200 years old.
Argument A is deductive and Argument B is inductive.
What is deductive and inductive argument ?Deductive reasoning uses broad premises to arrive at specific conclusions, while inductive reasoning starts with specific premises and draws general conclusions.
If the premises are valid, deductive reasoning's conclusions cannot be false. This is so because there is nothing in the conclusion that isn't already there in the premises. Yet, an inductively drawn conclusion goes beyond the information in the premises, unlike deductive reasoning.
Argument A is deductive because from the premise it is saying that the Grand Canyon was carved out by aliens from Jupiter, which is not sure.
Argument B is inductive because from the premise it is saying that Since the United States' Declaration of Independence was signed in the year 1776, it follows that the United States is over 200 years old, which is true.
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The complete question is:
INDUCTIVE /DEDUCTIVE ARGUMENT
Argument A: The Grand Canyon could not have been made by humans, so it follows that the Grand Canyon was carved out by aliens from Jupiter.
Argument B: Since the United States' Declaration of Independence was signed in the year 1776, it follows that the United States is over 200 years old.
A textbook store sold a combined total of history and math textbooks in a week. The number of history textbooks sold was three times the number of math textbooks sold. How many textbooks of each type were sold?
Answer:
not enough info
Step-by-step explanation:
Let h = number of history books.
Let m = number of math books.
"The number of history textbooks sold was three times the number of math textbooks sold."
h = 3m
"A textbook store sold a combined total of history and math textbooks in a week."
h + m = t
t = total number of books sold.
We have a system of equations:
h = 3m
h + m = t
Since we do not have a value for t, and we have a system of 2 equations in 3 variables, we cannot find the numbers of history or math books sold.
What is the exponential form of 3?
Answer:The 3 in 103 is called the exponent. The expression 103 is called the exponential expression. base → 103 ←exponent
Step-by-step explanation:
How do you get the answer on answering the multiplication of integers?
Get each number's absolute value first. Next, multiply the absolute values or calculate their product. Lastly, ascertain the final response's sign. According to the rule, the outcome will be negative if the signs of the two integers are different.
What is an integer ?All whole numbers and negative numbers are considered integers.
This means that if we combine negative numbers with whole numbers, a collection of integers results.
An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion. Integers include things like -5, 0, 1, 5, 8, 97, and 3,043. Z is a representation of a collection of integers.
A straight line of numbers is shown visually as a number line.
This line is used to compare integers that are spaced equally apart on an infinite line that extends horizontally on both sides.
The collection of integers can be shown on a number line much like other sets of numbers..
Hence, Get each number's absolute value first. Next, multiply the absolute values or calculate their product. Lastly, ascertain the final response's sign. According to the rule, the outcome will be negative if the signs of the two integers are different.
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40-32 dived by 8+5-2
39
40-32÷8+5-2
40-4+3
40-1
39
2(3b+6) =78 : Answer is 11
-2(6c-3) = -72 : Answer is 6.5
Check left Side of both equations
The left side of the first equation is 2(3b+6) and the left side of the second equation is -2(6c-3). Both sides of the equations are products of a constant and a variable or a sum/difference of variables.
Answer:
2(3b+6) =78 : b=11
-2(6c-3) = -72 : c=6.5
Step-by-step explanation:
They are correct
The quadratic number pattern: 4; p; 11; q; 22; ... 4.1 Show that p = 7 and q = 16.
The quadratic pattern with value of p and q has been proved.
Why is quadratic referred to as quadratic?A quadratic in mathematics is a particular kind of problem that involves squaring, or multiplying a variable by itself. This terminology comes from the fact that a square's area equals the product of its side length and itself. Quadratum, the Latin word for square, is where the word "quadratic" originates.
Here,
Given : 1st difference
p−4;
11−p;
q−11;
22−q;
2nd difference−2p+15;
q+p−22;
33−2q−2p+15=1−2p=−14p
=733−2q
=1q+p−22
=1−2q=−32or/of
q+7−22=1
q=16
Therefore , the solution of the given problem of quadratic comes out to be q =16
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