Answer: B. 10A + 7B
Step-by-step explanation:
To find the correct binomial, we will factor the given expression. I assume that by "-498²" you mean "-49B²".
This is a difference of squares:
(10A + 7B)(10A - 7B)
The binomial 10A + 7B is an answer option, so our answer is:
B. 10A + 7B
When you are performing multiple transformations it is called?
When you are performing multiple transformations it is called a composite transformation.
A number of transformations or sequence of transformations that can be combined into a single transformation is called as composition. The resulting matrix is known as composite matrix. The process of combining is known as concatenation.
A composite transformation (or a composition of transformations) refers to the two or more transformations performed one after the other. For example: a translation followed by a reflection which is again followed by a rotation. Another example can be: a rotation followed by a translation or a rotation followed by a reflection.
Therefore, when you are performing multiple transformations it is called a composite transformation.
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Solve an equation based on the following description: “11 less than three times a number, n, is the same as 75 less than the product of -1 and the number”
The solution to the equation based on the description given is: n = -16.
How to Solve an Equation?First, we need to translate each given statement into algebraic expressions.
"11 less than 3 times n" can be translated as: 3 × n - 11 = 3n - 11
"75 less than the product of -1 and n" would be translated as: (-1)(n) - 75 = -n - 75.
It is stated that both statements or description are the same. This means, they are equal to each other. Therefore, the equation that would be formed is:
3n - 11 = -n - 75
Solve for n
3n - 11 + n = -n - 75 + n [addition property of equality]
4n - 11 = - 75
4n - 11 + 11 = - 75 + 11 [subtraction property of equality]
4n = -64
Divide both sides by 4
4n/4 = -64/4 [division property of equality]
n = -16
Therefore, the solution to the equation based on the description given is: n = -16.
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A tire swing hangs 12 feet above the water. A swimmer is 40 feet away from the swing (horizontally). What is the angle of elevation from the swimmer to the tire swing?
Draw a picture!
You get a right triangle with hypotenuse = 20 ft and horizontal leg = 12 ft
Use the Pythagorean Theorem to find the length of the vertical leg:
vertical leg = √(20²-12²) = √256 = 16 ft
Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
The system of equations has exactly one solution.
How to calculate the value?Based on the information given, the equation is illustrated as:
2x - 3y = -4
-3x - 3y = 3
Add both equations
5x = -1
Divide
x = -1/5
Since 2x - 3y = -4
2(-1/5) - 3y = 4
-2/5 - 3y = 4
3y = -2/5 - 4
3y = - 4 2/5.
Divide
y = -4 2/5 ÷ 3
y = 1 7/15
Therefore, the system of equations has exactly one solution as the value of x and y are gotten.
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Which one of these are Rational Numbers?
A) -7.9898...
B) 4.9832
C) 6.329...
D) 7
Answer:
D) 7
Step-by-step explanation:
The answer is D because A, B, and C are not considered numbers that are natural, whole, integers, or fractional. Irrational numbers are numbers that cannot be quantified any other way, do not have repeating decimals, and never end. A good example of this is π or 3.14159265.... you get the picture.
Hope this helps!
Side ______ is missing, which is a ______
.
Side height is missing, which is a 6[tex]\sqrt{30}[/tex].
For the right angle triangle we have a formula:
[tex]hypotenuse^{2}[/tex] = [tex]height^{2}[/tex] + [tex]base^{2}[/tex]
Here Hypotenuse and the base are given, we have to find the height of the triangle.
Hypotenuse = 37
Base = 17
To find the height of the triangle we have:
[tex]height^{2}[/tex] = [tex]Hypotenuse^{2}[/tex] - [tex]base^{2}[/tex]
= [tex]37^{2}[/tex] - [tex]17^{2}[/tex]
= 1369 - 289
= 1080
Height =[tex]\sqrt{1080}[/tex]
= 6√30
Therefore the height of the triangle is 6√30.
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two triangles represent 100 percent. one is fully filled and the other is half filled. what is the percentage
Answer:
75% filled
Step-by-step explanation:
Each triangle is 50%.
Half of 50% is 25%.
One full triangle, 50%, plus one half triangle, 25%, add up to 75% percent of the two triangles being filled.
Each ordered pair is from an inverse variation. Find the constant of variation. (0.9,4)
The constant of variation is 3.6
What is Inverse variation ?The inverse variation property states that , whenever the product of values of two quantities is a constant value then there is opposite variation between these two corresponding values. Or we can also say that if the productive nature of two corresponding values is constant, then one quantity is inversely varies with second quantity. That means, we can say that if one values will increase then other will automatically decrease and vice versa.
Let say if x and y are two values and k is a constant value, then
According to inverse variation
k = xy or y = k/x
In the given question,
Take the order pair (0.9,4)
As it is an inverse variation, we can substitute it
y=k/x
Now find the constant of variation
4=k/0.9
K=3.6
Therefore, constant of variation is 3.6
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The quotient of 4 and the difference of 7 and a number.
Answer:
10
Step-by-step explanation:
(x + 4)/7=10
The number is -28.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them. Variables are the name given to these symbols because they lack set values. We frequently observe constant change in specific values in our day-to-day situations. But the need to depict these shifting values is ongoing. These values are frequently represented in algebra by symbols such as x, y, z, p, or q, and these symbols are known as variables. In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
quotient of a number and 4 is -7
let the number be x
So, n/4 = -7
n= 4 x (-7)
n= -28
Hence, the number is -28.
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Which graph correctly shows the system of equations {x−2y=4y=2x+4?
Which graph correctly shows the system of equations [tex]\left \{ {{x-2y=4} \atop {y=2x+4}} \right.[/tex] ?
Correct graph for the system of equations is 3rd graph.
We graph the collection of ordered pairs that make up the equation's solution when graphing a system of equations in two variables.
The universal equation for any straight line is y=mx+c. m is the line's slope, and c is the y-intercept.
First, we take the equations as x-2y=4 as equation (1) and y=2x+4 as equation (2).
Now solve the equation (1)
x-2y=4
The equation is not in the form of y=mx+c.
So, we write as y= [tex]\frac{1}{2}[/tex]x-2
Here, slope m=[tex]\frac{1}{2}[/tex] and y-intercept is (0,-2).
If we take x=2 we get y=-1.
y= [tex]\frac{1}{2}[/tex](2)-2
y=1-2
y=-1
Now we have 2 solution for the equation (1) that are (0,-2) and (2,-1).
If we see the third graph in the given options.
There is a blue straight line and that is the line for equation (1) there we can see the points (0,-2) and (2,-1).
Now solve the equation (2)
y=2x+4
The equation is in the form of y=mx+c.
Here, slope m=2 and y-intercept is (0,4).
If we take x=1 we get y=6.
y= 2(1)+4
y=2+4
y=6
Now we have 2 solution for the equation (2) that are (0,4) and (1,6).
If we see the third graph in the given options.
There is a green straight line and that is the line for equation (2) there we can see the points (0,4) and (1,6).
Therefore, the correct graph for the given system of the equation[tex]\left \{ {{x-2y=4} \atop {y=2x+4}} \right.[/tex] is the third graph.
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Flying Home A bird flies from the bottom of a canyon that is 57 1/5 feet below sea level to a nest that is
664 7/10 feet above sea level. What is the difference in elevation between the bottom of the canyon and
the bird's nest?
Answer:
Exact Form:
1215 / 2
Decimal Form:
607.5
Mixed Number Form:
607 1/2
The ratio of the number of adults to the number of students at the prom has to be 1:10. Last year there were
477 more students than adults at the prom. If the school is expecting the same attendance this year, how many
adults have to attend the prom?
The number of adults who have to attend the prom are 53
According to the question we have been given the ratio of number of adults to the number of students attending the prom which is :
[tex]\frac{x}{y} = \frac{1}{10}[/tex] (1)
where, x = number of adults
and y = number of students attending the prom
Now equation (1) can be written as
y = 10x (2)
That is number of students that attend the prom will be 10times the number of adults.
Now we have been given that there were 477 more students
y = x + 477
Now putting the value of y from equation (2) we get
10x = x+477
9x = 477
x = 53
Thus if the school is expecting the same attendance this year, then total 53 adults have to attend the prom.
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Which is true about the graph of y < x^2 + 2x - 6
A. The parabola opens down
B. The vertex is located at (-1,-7)
C. The shading is inside the parabola
D. The parabola is a solid line
The true statement about the graph of the parabola inequality given as y < x^2 + 2x - 6 is (b) the vertex is located at (-1,-7)
What are parabola equations?Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
How to determine the true statement about the graph?The parabola inequality is given as
y < x^2 + 2x - 6
Next, we plot the graph of the parabola inequality
To plot this graph, we simply enter the inequality y < x^2 + 2x - 6 in a graphing calculator
From the attached graph, we can see that the vertex of the parabola inequality is at (-1, -7)
Hence, the true statement about the graph of the parabola inequality given as y < x^2 + 2x - 6 is (b) the vertex is located at (-1,-7)
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Use the distributive property to find the product of 4 (3z+5+2y^2-2x-1). Write your answer in standard form.
The product using the distributive property is 12z+8y²-8x+16 in the standard form.
The distributive law, which states that a × (b + c)=(a × b)+(a × c), is generalized by the distributive property of binary operations.
In every scenario, the distributive property can be summed up as follows:
Each summand (or minuend and subtrahend) is multiplied by this factor, and the resulting products are added, to multiply a sum (or difference) by a factor (or subtracted).
This concept states that multiplying the sum of two addends by a number will produce the same outcome as multiplying each addend separately by the number and then adding the results.
Given product: 4×(3z+5+2y²-2x-1)
Using the distributive property we can write it as:
= (4×3z)+(4×5)+(4×2y²)-(4×2x)-(4×1)
= 12z+20+8y²-8x-4
= 12z+8y²-8x+16
So the product using the distributive property is 12z+8y²-8x+16 in the standard form.
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6. Which biconditional is not a good definition?
A. Two angles are supplementary if and only if the sum of their angles measures 180 degrees.
B. Two angles are vertical angles if and only if they are nonadjacent and are formed by two intersecting lines.
C. Two angles form a linear pair if and only if the angles are adjacent.
D. The sum of two angles is 90 degrees if and only if they are complementary.
------------------------------------------
11. Use the Law of Syllogism to determine whether a valid conclusion can be reached from the set of statements/ If a valid conclusion is not possible, choose "not possible."
If you are 18 years old, then you are in college.
If you are in college, then you are not done learning.
A. You are at least 18 years old.
B. If you are 18 years old, then you are not done learning.
C. You are no more than 18 years old.
D. not possible
-------------------------------------------------
12. Write the converse of the following true conditional statement. If the converse is false, write a counterexample.
If you are 18 years old, then you may be eligible to join the U.S. military.
A. if you are eligible to join the U.S. military, then you are 18 years old; true.
B. If you are not 18 years old, then you are not eligible to join the U.S. military; true
C. If you are eligible to join the U.S. military, then you are 18 years old; false.
counterexample: You are eligible to join the U.S. military and you are not 18; you are 19.
D. if you are not 18 years old, then you are not eligible to join the U.S military; false.
counterexample: You are eligible to join the U.S. military and you are not 18; you are 19.
----------------------------------------
Best answer will get brainliest.
The correct response is [C]: If and only if the angles are nearby, two angles form [a] linear pair.
Think about the response option shown in "Answer choice: [C]":
If and only if the angles are contiguous, two angles constitute a linear pair.
Then, think about the next:
1) "Two additional angles make a linear pair."
Is this a fact? Of course, but not always. (In other words, "sometimes") By definition, a "linear pair" of angles IS supplementary, but not all supplementary pairs of angles are linear pairs. In order for supplementary angles to also be "linear angles," they MUST ALSO BE ADJACENT.
2) "Two vertical angles are next to each other." Is this a fact? It's not true; it never is.
In light of the fact that this biconditional is NOT an acceptable definition, answer choice "C" is the one that is appropriate. This can be determined by looking at all the other options.
Think about the other response options:
The maxim "Two angles are supplementary if and only if the total of their angles measures 180" is the correct response.
is WRONG despite being a nice definition:
1) The total of the measurements of two additional angles is 180 degrees.
2) Two angles are supplementary if the total of their measurements equals 180 degrees.
"Two angles are vertical angles only if they are not close to one other and are produced by two intersecting lines," is the correct response (option B);
is WRONG despite being a nice definition:
1) Nonadjacent angles are those created by two crossing lines when two angles are vertical.
2) Two angles are vertical angles if they are nonadjacent angles created by two intersecting lines.
The sum of two angles equals 90 if and only if both angles are complementary (answer option [D]);
is WRONG despite being a nice definition:
1) The total of two complimentary angles' measurements equals 90 degrees.
2) Two angles are complimentary if the total of their [measured] is 90 degrees.
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5. Find the lowest number which is exactly divisible by 14 and 16.
Answer:
112
Step-by-step explanation:
Find the lowest common multiple of 14 and 16.
To find the lowest common multiple:
1) Break the numbers down into their prime factors.
14 = [tex]2^{1}[/tex] x [tex]7^{1}[/tex]
16 = 2 x 8 = 2 x 2 x 4 = 2 x 2 x 2 x 2 = [tex]2^{4}[/tex]
2) Multiply the highest power of each prime number.
We have three numbers, but only two are unique: [tex]2^{1}[/tex] , [tex]7^{1}[/tex] and [tex]2^{4}[/tex]
[tex]2^{4}[/tex] > [tex]2^{1}[/tex] , so we will use [tex]2^{4}[/tex]
[tex]7^{1}[/tex] x [tex]2^{4}[/tex] = 7 x 16 = 112
Mikel was on a diving trip. He dove down 108 feet below sea level 6 minutes. How many feet per minute did Mikel travel on his dive?
Answer:
Gemma, a scuba diver, begins a dive on the side of a boat 4 feet above sea level. She descends 28 feet.
Step-by-step explanation:
√35 +5 rational or irrational
Answer: Yes √35 +5 is a rational number
Step-by-step explanation:
A rational number is any number that is a fraction, decimal, repeating decimal, or negative decimal.
given that the mass of the sun is approximately 1.9 ×10 to the 30 power kg , how many Venuses and Earth's would it take to equal the mass of the sun
Given that,
Mass of earth = 5.9 × 10²⁴ kg
Mass of = 4.9 × 10²⁴ kg
a) Combined mass of earth and
5.9 × 10²⁴ + 4.9 × 10²⁴ = 10.8 × 10²⁴
b) If the mass of the sun = 1.9 × 10³⁰
Let's say the total gain of earth and combined x
so it will equal the mass.
Then,
10.8 × 10²⁴ + x = 1.9 × 10³⁰
x = 18989.2 kg
Hence "Combined mass of earth and venues is 10.8 × 10²⁴ and there are a total of 18989.2 kg taking earth and venue to equal to the sun.
Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Summation = addition of two or more numbers or variable
For example = 2 + 8 + 9
Subtraction = Minus of any two or more numbers with each other called subtraction.
For example = 4 - 8
Division = divide any two numbers or variable called division.
For example 4/8
Multiplication = to multiply any two or more numbers or variables called multiplication.
For example 5 × 7.
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adding and subtracting polynomials
Answer:
2. 7x^2 + 4x + 2x
4. -x - 6
6. 4x^2
8. 7x - 2
10. 10x^2 + 5
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The points K(6,-4) L(6,3), M(-2,6) and N(-2,-1) form parallelogram KLMN. Plot the points then click the "Graph Quadrilateral" button. Then find the perimeter of the parallelogram. Round your answer to the nearest tenth if necessary.
Answer:
31 units
Step-by-step explanation:
Use the Change of Base Formula to rewrite each expression using common logarithms. log₃ 16
The logarithmic expression log₃ 16 changed by the base rule is 2.52.
What is represent as logarithmic expression?The inverse about an exponential function is a logarithmic or log function. To find an exponent, we could use a log function.
To analyze earthquake magnitudes or compare the magnitudes of 2 distinct earthquakes, we must be able to transform among logarithmic and exponential forms.
Let's use this data to create our log. The logarithmic function is as follows:
Quotient Rule: ㏒(A/B) = ㏒A - ㏒BProduct Rule : ㏒A + ㏒B = ㏒(AB)Power Rule: n㏒A = ㏒AⁿBase Rule = ㏒ₐb = ㏒ₓb/㏒ₓaExponent Rule = e∧lnx = xNow, for the stated conditions;
= log₃ 16
Using the Base Rule of log functions, the above expression can be written as,
= ㏒ₓ16/㏒ₓ3
If the base is taken as 10. Then the expression will become.
= ㏒₁₀16 /㏒₁₀3
= 1.204/0.477
= 2.52
Therefore, the value of the given log expression log₃ 16 is obtained as 2.52.
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What is the horizontal asymptote for the rational function?
b. y=x-1/x²+4 x+4
For the given rational number, y=x-1/x²+4 x+4
Vertical Asymptotes: x= - 2
Horizontal Asymptotes: y = 0
What are the asymptotes?
A line that, in analytical geometry, is an asymptote of a curve is one where, when one or both of the x or y coordinates go to infinity, the distance between the curve and the line approaches zero. An asymptote of a curve is a line that is tangent to the curve at a point at infinity in projective geometry and similar settings.
Given,
y=x-1/x²+4 x+4
y = x-1 / (x+2)²
x = -2, x = 0
So the horizontal asymptote will be 0.
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Solve this Equation ASAP
1.) 7z(2a³+5)
2.) 5p(3s-4t)
The values of the equation will be:
7z(2a³+5) = 14a³z + 35z
2.) 5p(3s-4t) = 15ps - 20pt
How to illustrate the information?It should be noted that an equation is used to express the relationship between the variables.
Therefore, the equation will be solved by simply opening the brackets and multiplying them. This will be:
7z(2a³+5) = 14a³z + 35z
5p(3s-4t) = 15ps - 20pt
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Work out the size of one exterior angle of a regular hexagon.
Answer:60 degrees
Step-by-step explanation: hexagon is 360 degrees. has 6 sides. 360 divided by 6= 60 degrees
(02.01 MC) Given g(x) = 3x + 6, identify the domain, range, and x-intercept of the function. Domain: 3 < x < 6; Range: −6 < y < ∞; x-intercept (2, 0) Domain: 3 < x < 6; Range: −∞ < y < 6; x-intercept (−2, 0) Domain: −∞ < x < ∞; Range: −∞ < y < ∞; x-intercept (2, 0) Domain: −∞ < x < ∞; Range: −∞ < y < ∞; x-intercept (−2, 0)
The domain and the range are −∞ < x < ∞ and −∞ < y < ∞ while the intercept is (2, 0)
What is the domain of a function?The domain of the function is the set of input values of the graph
What is the range of a function?The range of the function is the set of input values of the graph
How to determine the domain and the range of the function?The function is given as
g(x) = 3x + 6
The above function is a linear function
This means that the domain and the range of the function are the set of all real values
i.e. −∞ < x < ∞ and −∞ < y < ∞
Calculate x when g(x) = 0 to determine the x-intercept
So, we have
3x + 6 = 0
Divide through by 3
x + 2 = 0
This gives
x = -2
Hence, the domain and the range are −∞ < x < ∞ and −∞ < y < ∞ while the intercept is (2, 0)
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Hi can someone please help me with this!!!!!!
Answer:
The larger figures are 3 times the size of the smaller figures.
Scale factor = 3?
Step-by-step explanation:
Answer:
The scale factor is 3 :)
Step-by-step explanation:
The smaller figure multiplied by 3 is the larger figure.
3(4x—8)=36
I need help ASAPP
Answer:
x=5
Step-by-step explanation:
STEP
1
:
STEP
2
:
Pulling out like terms
2.1 Pull out like factors :
4x - 8 = 4 • (x - 2)
Equation at the end of step
2
:
(0 - 12 • (x - 2)) - -36 = 0
STEP
3
:
STEP
4
:
Pulling out like terms
4.1 Pull out like factors :
60 - 12x = -12 • (x - 5)
Equation at the end of step
4
:
-12 • (x - 5) = 0
STEP
5
:
Equations which are never true:
5.1 Solve : -12 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation:
5.2 Solve : x-5 = 0
Add 5 to both sides of the equation :
x = 5
Mrs linesman deposits 500 dollars into a bank account that earns 4 percent simple interest per year what is the total amount in her account after 1 year
she has $520 after 1 year.
Step-by-step explanation:
principal= 500dollars
rate= 4%
time=1 year
simple interest=principal x rate x time
100
simple interest= 500 x 4 x 1 = 2000/100 = 20
100
To find total amount money in the account
= simple interest + principal
= 20 + 500
= 520dollars
Using the number 12,345.6789 to round to the nearest whole number
Answer: 12346
Step-by-step explanation:
Firstly, to round the decimal number 12345.6789 to its nearest whole number we will look at the tenth place. the digit to the immediate right of the decimal point.
Here in the given example 12345.6789, the tenth digit is 6.
If the tenth place digit is equal to or more than 5 we will round up and if it is less than 5 we will round down.
If the hundredth digit of the decimal number is equal to or more than 5, then round up.
Since the tenth digit 6 is >= 5 we will round up i.e. ( ones place digit + 1 ) and the remaining all digits next to the decimal point are removed.
Therefore, the number 12345.6789 rounded to the nearest whole number is 12346. if this is wrong im sorry but i think this is how i even double checked.