Answer:
IbI
Step-by-step explanation:
The square root of [tex]\( b^2 \)[/tex] is [tex]\( b \),[/tex] as the square root of any positive number is its positive root.
The square root of [tex]\( b^2 \)[/tex] can be calculated step by step as follows:
Step 1:
Understand the concept.
The square root of a number is a value that, when multiplied by itself, gives the original number. For any real number [tex]\( b \), \( b^2 \)[/tex] represents [tex]\( b \)[/tex]multiplied by itself.
Step 2:
Apply the square root property.
The square root of [tex]\( b^2 \)[/tex] is [tex]\( b \)[/tex] because [tex]\( b \times b = b^2 \).[/tex] The square root of any positive number is its positive root.
Step 3:
Interpret the result.
Since the square root of [tex]\( b^2 \)[/tex] is [tex]\( b \),[/tex] regardless of the value of \( b \), the square root of [tex]\( b^2 \)[/tex] is simply [tex]\( b \)[/tex] . This property holds true for any real number [tex]\( b \).[/tex]
So, the square root of [tex]\( b^2 \)[/tex] is [tex]\( b \).[/tex]
The graph shows the location of Point A and Point B. Point A is on the y-axis and has the same y-
coordinate as Point B. Point C is graphed at (n, -3). The distance from Point B to Point C is equal to the
distance from Point B to Point A. What is the distance from Point B to Point C? What is the value of n?
The value of n and the distance from Point B to Point C cannot be determined without specific coordinates for these points. Given that B is the midpoint between points A and C, the x-coordinate for Point B should be n/2. The distance between the points would be calculated using the distance formula derived from the Pythagorean Theorem.
Explanation:To calculate the distance between points in a graph, we typically use the distance formula, which is derived from the Pythagorean Theorem. From our given information, Point A lies on the y-axis and has the same y-coordinate as Point B. Point C is graphed at (n, -3). Given that the distance is the same from Point B to both points A and C, this implies that Point B is the midpoint between Points A and C. The coordinates of the midpoint are obtained by averaging the x and y coordinates of the two points. Therefore, the x-coordinate of Point B must be n/2.
The distance from Point B to Point C (or similarly to Point A) can be obtained using the distance formula: sqrt((x2−x1)² + (y2−y1)²), where x1, y1 are the coordinates of one point and x2, y2 are the coordinates of the other point.
However, without concrete values for some of these points in the given equation, we cannot provide a specific numerical value for the distance or n. This calculation depends specifically on the placement of the points on the graph.
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Please help i only have 5 minutes left
Find the volume of a cylinder, we need to follow the formula:
Volume = πr2h
Following the formula, we substitute for:
π×82×10
π=3.14, so we multiply it:
= 640π
= 2010.6192982975 feet3
Which geometric figures are drawn on the diagram?
Check all that apply.
To identify geometric figures in a diagram, know the definitions and characteristics of each shape like a circle, triangle, and rectangle. By recognizing these characteristics, you can determine which shapes are in the diagram.
Explanation:In order to identify which geometric figures are drawn in a diagram, you need to know the basic definitions and characteristics of geometric shapes. For instance, a circle is a figure in which all points are equidistant from a single point in the center. A triangle is a figure formed by three straight lines. A rectangle has four sides and all the angles are right angles. A square is a special type of rectangle where all four sides are equal. By identifying these various characteristics, you can determine which geometric shapes are represented in the diagram.
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On a piece of paper graph y=x+2 then determine which answer choice matches the graph you drew use the graph to find the zero of the function select the answer choice that shows the correct graph and correct zero
Answer:
The correct option is B) zero x = -2.
Step-by-step explanation:
Consider the provided graph y = x + 2
The zeros of a function are the point on which graph intersects the x axis or we can say the value of x when y = 0.
Substitute y = 0 in the provided equation.
0 = x + 2
x = -2
The coordinate is (-2,0). Also the zero of the graph is at x = -2 because it follows the definition of zeros.
Now substitute x = 0 in the provided equation.
y = 0 + 2
y = 2
The coordinate is (0,2).
Now, draw a line passing through the point (-2,0) and (0,2).
The required line is shown in figure 1.
Now consider the provided options only option A and B have the same graph.
But the correct option is B as the zero of the option B is x = -2.
Hence, the correct option is B) zero x = -2.
Explanation of graphing y=x+2 and finding its zero. Find the correct graph and x-intercept.
Graph: First, graph the equation y = x + 2. This is a straight line with a slope of 1 (rise of 1, run of 1) and y-intercept at 2.
Zero of the function: To find the zero of the function (where y = 0), set x + 2 = 0 and solve for x. In this case, x = -2.
Which of the following equations represents the axis of symmetry for the parabola shown?
Y = 10x
X = 10
X = y + 10
Y = x + 10
Answer:
x = 10
Step-by-step explanation:
The axis of symmetry is the vertical line that passes through the vertex. We can readily see that the x-coordinate of the vertex is 10.
Therefore, the axis of symmetry here is x = 10.
Which is the scale factor proportion for the enlargement shown?
Answer:
A. 1/x = 2/6
Step-by-step explanation:
Given the sides of the smaller parallelogram:
1 in and 2 in
Given the sides of the bigger parallelogram:
x in and 6 in
By Comparison of similar sides
I.e. the slant sides (1in and x in) and the base (2in and 6in) of both parallelogram.
1/x = 2/6
Hence, the scale factor proportion for the enlargement is 1/x = 2/6.
Solving further to get the value of x
Simplify both sides
1/x = ⅓
Multiply both sides by x
1/x * x = ⅓ * x
1 = ⅓x
Multiply both sides by 3
1 * 3 = ⅓x * 3
3 = x
So x = 3 in
Answer:
A. 1/x = 2/6
Step-by-step explanation:
Seema is now 9 years older than Beena. In 10 years
Seema will be twice as old as Beena was
10 years ago Find their present ages.
Answer:
Beena = 19 years old
Seema = 28 years old
Step-by-step explanation:
Beena = x
Seema = x + 9
x + 9 + 10 = 2x
19 + x = 2x
2x - x = 19
x = 19
The solution to a system of two linear equations in two variables corresponds to the ____
The answer can be stated as "The solution to a system of two linear equations in two variables corresponds to the intersection of straight lines represented by them."
How to represent a straight line on a graph?To represent a straight line on a graph consider two points namely x and y intercepts of the line. To find x-intercept put y = 0 and for y-intercept put x = 0. Then draw a line passing through these two points.
A system of linear equation in two variables can be written as,
a₁x + b₁y + c₁ = 0
a₂x + b₂y + c₂= 0
In order to find their solution these equations are solved either by substitution or elimination.
A linear equation in two variable represents a straight line.
Thus, the solution to these equations are the coordinates of the intersection point of these two lines.
Hence, the solution to a system of linear equation in two variables indicate the coordinate of their intersection.
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Which values of m and b will create a system of equations with no solution? Check all that apply.
y = mx + b
y = –2x +
m = –3 and b =
m = –2 and b =
m = 2 and b =
m = – and b =
m = –2 and b =
m = 3 and b =
Mark this and return
Answer:
y = -2x + 1
Step-by-step explanation:
Then any equation of the form y = -2x + b, b≠1 will create a system with no solution. Hence the values of m and b are m = -2, b ≠ 1.
hope i helped
Answer:
Option B and E
Step-by-step explanation:
As we know a system of two parallel lines has no solution.
In other words two lines having same slope will have no solution.
In this question equation of one line is
y = -2x + b
So another line having same slope (-2) will have no solution.
Option B and E are the correct options.
State the value of the discriminant of the equation. Then determine the number of real solutions of the equation.
8n^2-4n+2=5n
[tex]\bf 8n^2-4n+2=5n\implies 8n^2-4n-5n+2=0\implies 8n^2-9n+2=0 \\\\[-0.35em] ~\dotfill\\\\ \qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{a}{\downarrow }}{8}n^2\stackrel{\stackrel{b}{\downarrow }}{-9}n\stackrel{\stackrel{c}{\downarrow }}{+2}=0 ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{\underline{two solutions}}\\ negative&\textit{no solution} \end{cases} \\\\\\ (-9)^2-4(8)(2)\implies 81-64\implies 17[/tex]
Answer:
2 real distinct roots.
Step-by-step explanation:
8n^2 - 4n + 2 = 5n
Rearranging to standard form:
8n^2 - 9n + 2 = 0
The discriminant = b^2 - 4ac
= (-9)^2 - 4 * 8 * 2
= 17.
So there will be 2 real distinct roots.
The length of a rectangular garden ABCD is 9 feet more than its width. It is surrounded by a brick walkway 4 feet wide as shown below. Suppose the total area of the walkway is 400 square feet. What are the dimensions of the garden?
PLEASE HELP I KEEP TRYING TO DO IT BUT IT DOESN'T WORK.
Answer:
The dimensions of the garden are
Length [tex]25.5\ ft[/tex] and Width [tex]16.5\ ft[/tex]
Step-by-step explanation:
Let
x----> the length of the rectangular garden
y ---> the width of the rectangular garden
Aw ----> the area of the walkway
we know that
[tex]x=y+9[/tex] ----> equation A
[tex]Aw=(x+8)(y+8)-xy[/tex]
[tex]Aw=400\ ft^{2}[/tex]
so
[tex]400=(x+8)(y+8)-xy\\400=xy+8x+8y+64-xy[/tex]
[tex]400=8x+8y+64[/tex] ----> equation B
Substitute equation A in equation B
[tex]400=8(y+9)+8y+64[/tex]
[tex]400=8y+72+8y+64[/tex]
[tex]400=16y+136[/tex]
[tex]16y=400-136[/tex]
[tex]y=16.5\ ft[/tex]
Find the value of x
[tex]x=16.5+9=25.5\ ft[/tex]
therefore
The dimensions of the garden are
Length [tex]25.5\ ft[/tex]
Width [tex]16.5\ ft[/tex]
Evaluate the expression when a=3 and b=4
[tex]2a^{2} +b=[/tex]
Answer:
The answer to this problem is 22.
Step-by-step explanation:
To solve this problem, we simply need to plug in the values given for a and b into the expression given and simplify.
We are given that a=3 and b=4, thus, these are the numbers we will plug in before we simplify.
2a^2 + b =
2(3)^2 + 4
Next, we should follow the rules of PEMDAS. This tells us that we should solve the parentheses first, but since there are no parentheses, we can move onto exponents.
If we simplify, we get:
2(9) + 4
Next, we should perform the multiplication.
18 + 4
Finally, we can add together the remaining terms.
18 + 4 = 22
Therefore, your answer is 22.
Hope this helps!
2[tex]a^{2} + b[/tex]
First you must substitute a and b for the corresponding values:
a = 3
b = 4
so...
2*[tex]3^{2}[/tex] + 4
Now you must evaluate using the rules of PEMDAS (Parentheses, Exponent, Multiply, Divide, Add, Subtract)
There are no parentheses so skip that step and go on to the next one, exponent, which is [tex]3^{2}[/tex]
[tex]3^{2}[/tex] = 3*3
9
^^^Replace [tex]3^{2}[/tex] with 9
2 * 9 + 4
The next step is multiply 2 and 9
2*9 = 18
^^^Replace 2*9 with 18
18 + 4
Now add 18 and 4 together
22
Hope this helped!
~Just a girl in love with Shawn Mendes
Amanda is placing an order for running shoes and leather boots for her footwear boutique. She needs a total of 48 pairs of shoes and twice as many pairs of running shoes as leather boots.
Set up the two equations that can be used to find the number of each type of shoe that Amanda needs to order.
Let the equation that represents the total number of pairs of shoes be referred to as constraint 1.
Let constraint 2 refer to the equation that describes the ratio of the number of running shoes to leather boots.
Only constraint _ would be met if 18 pairs of leather boots and 36 pairs of running
shoes were ordered.
Only constraint _ would be met if 12 pairs of leather boots and 36 pairs of running shoes were ordered.
1. Only constraint 2 would be met if 18 pairs of leather boots and 36 pairs of running shoes were ordered.
Constraint 2 is satisfied because 18 pairs of leather boots equals 1/2 of the running shoes.
2. Only constraint 1 would be met if 12 pairs of leather boots and 36 pairs of running shoes were ordered.
Constraint 1 is satisfied because 12 pairs of leather boots 36 pairs of the running shoes equal 48 pairs (12 + 36).Data and Calculations:
Total pairs of shoes required = 48 pairs
Running shoes required (r) = 2 of leather boots
Leather boots required (b)= 1/2 of running shoes
Constraint 1:
The total pairs of different shoes required:
Running shoes = 32r
Leather boots = 16b
Total pairs = 32r + 16b = 48
Constraint 2:
Ratio equation:
Running shoes = 2r
Leather boots = b
Equation = 2r + b = 48
Thus, Constraint 2 satisfies the first order, while Constraint 1 satisfies the second order. The two constraints do not satisfy the two orders.
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Amanda needs 48 pairs of shoes total, with twice as many running shoes as leather boots. Constraint 1 is x + y = 48, and constraint 2 is y = 2x. An order of 18 boots and 36 running shoes meets only constraint 2, while 12 boots and 36 running shoes meet both constraints.
Amanda needs to order a total of 48 pairs of shoes, with twice as many pairs of running shoes as leather boots. To set up the equations, let x represent the number of pairs of leather boots and y represent the number of pairs of running shoes.
Constraint 1:
The total number of pairs of shoes:
x + y = 48
Constraint 2:
The ratio of the number of running shoes to leather boots:
y = 2x
To check which constraints are met by given orders:
1. For 18 pairs of leather boots (x = 18) and 36 pairs of running shoes (y = 36):
Using constraint 1: 18 + 36 = 54. This does not meet constraint 1.
Using constraint 2: 36 = 2(18). This meets constraint 2.
2. For 12 pairs of leather boots (x = 12) and 36 pairs of running shoes (y = 36):
Using constraint 1: 12 + 36 = 48. This meets constraint 1.
Using constraint 2: 36 = 2(12). This meets constraint 2.
Simplify. x^2-3x-18/x+3
x - 3
x - 6 where x -3
x - 6 where x 6
1/x+3 where x -3
Simplify x-2/x^2+4x-12
1/x+6 where x -6
1/x+6 where x -6,2
1/x+2 where x -2
x+2
Simplify 5x^3/7 x^3+x^4
5/7+x where c 0,-7
5/7+x where x -7
5/7x where x 0
5/7
Simplify x/6x-x^2
1/6-x where x 0,6
1/6-x where x 6
1/6x where x 0
1/6
Answer:
1. Option C is correct
2. Option A is correct
3. Option C is correct
4. Option B is correct
5. Option D is correct
Step-by-step explanation:
1. x^2-3x-18/x+3
Factorize the numerator
x^2-6x+3x-18/x+3
x(x-6)+3(x-6)/x+3
(x+3)(x-6)/x+3
x-6
x-6 where x≠6
Option C is correct.
2. x-2/x^2+4x-12
Factorizing the denominator
x-2/x^2+6x-2x-12
x-2/x(x+6)-2(x+6)
x-2/(x-2)(x+6)
1/x+6
1/x+6 where x≠-6
Option A is correct.
3. 5x^3/7 x^3+x^4
5x^3/7x^3+x^4
5x^3/x^3(7+x)
5/7+x
Option C is correct
5/7+x where x≠-7
4. Simplify x/6x-x^2
x/6x-x^2
x/x(6-x)
1/6-x
Option B is correct
1/6-x where x≠6
5. 2/3a * 2/a^2
Multiplying both terms
4/3a^3
Option D is correct.
4/3a^3 where a≠0
which is the graph of y=^3√x+1-2
Answer: Bottom Graph
Step-by-step explanation: An easy way to eliminate answers is to plug in 0 for x and see if the y-intercept is accurate. If we plug in 0 for x we get -1, which is the y-int for the bottom graph, but not the top graph, therefore the bottom graph is correct.
The graph of (x + 1)^(1/3) - 2 is option B.
What is a function?A function is a mathematical expression, rule, or law that specifies the relationship between one variable (the dependent variable) and another variable (the independent variable).
Function given in the question = (x + 1)^(1/3) - 2
Initial function for this is f(x) = x^(1/3)
The changes done in the question is f(x + 1) - 2
Hence the graph of x^(1/3) will go one unit to the left on the X-axis and two units down on the Y-axis.
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what is 140 squared pleas help me i am dumb
Answer:
19600
Step-by-step explanation:
140 squared = 140 x 140 = 19600
Use the properties of exponents to rewrite the expression
(m^4 n^3)^6
[tex]m^{24}n^{18}[/tex]
Explanation:We can distribute the terms using the distributive property first. [tex](m^4)^6 * (n^3)^6[/tex]
Then, use the power of a power property to multiply the powers. [tex]m^{4*6} * n^{3*6} = m^{24}n^{18}[/tex]
A student performed row operations on a matrix as shown below.
Which operations did the student perform?
Answer:
Option A is correct i.e 2R2+R3 -> R3
Step-by-step explanation:
The given matrix is:
[tex]\left[\begin{array}{ccc}-4&1&2&4\\0&-1&3&1\\3&2&4&5\end{array}\right][/tex]
If we perform the operation 2R2 + R3 we get the result given i.e
[tex]\left[\begin{array}{cccc}-4&1&2&4\\0&-1&3&1\\3&0&10&7\end{array}\right][/tex]
The operations performed are:
2R2 i.e. we multiply the row 2 with 2
we get 0 -2 6 2
now add it with row 3
0 -2 6 2
3 2 4 5
___________
3 0 10 7
So, Option A is correct i.e 2R2+R3 -> R3
what is the sum of one gross, a quarter of a dozen and two scores
Final answer:
To find the sum of one gross, a quarter of a dozen, and two scores, you add 144 (one gross), 3 (a quarter of a dozen), and 40 (two scores) to get a total of 187.
Explanation:
The sum of one gross, a quarter of a dozen, and two scores can be calculated as follows:
One gross = 144
A quarter of a dozen = 3
Two scores = 40
Therefore, the sum = 144 + 3 + 40 = 187
Answer: 187
Step-by-step explanation:
First, we need to define what these words mean numerically.
One gross = 144
A quarter of a dozen = 12/4 = 3
Two scores = 2 * 20 = 40
Now, we can find the sum of one gross, a quarter of a dozen, and two scores. Sum means addition.
144 + 3 + 40 = 187
What is the domain function of f(x)=x^2-9x-15
Answer:
ALL REAL NUMBERS
Step-by-step explanation:
Any quadratic function is ALWAYS R.
Express the distance traveled as a function of the number of hours at the average speed. The morris family is traveling from providence to Fredericksburg. Given city traffic they will average 45 mph
Answer:
Dist = 45 m/h * x h
Step-by-step explanation:
We know a speed is a measure of distance over time: speed = dist / time
In this case, we are looking for a distance expressed in terms of time.
So, we only need to modify the formula a bit: dist = speed * time
We don't know the time (which will be a variable), but we know their speed. So, the formula becomes:
Dist = 45 m/h * x h
Enter the number of hours in the formula and that will give you an approximation of the distance traveled within that time (approximation since our result will be rely on an average).
Which number is an integer?
A. -3/4
B. 0
C. 2.3
D. π (pi)
please don’t respond if you don’t FOR SURE know the answer
Answer:
0
Step-by-step explanation:
Integers are counting numbers, opposite of counting numbers, and 0.
if the sum of 9 and a half a number equals 35 translation?
9+1/2x=35
x=52
hope this helps
Which statement best describes a line in slope-intercept form when the coefficient of the x-term is positive
Answer:
The line will be going 'uphill' from left to right
Step-by-step explanation:
we know that
The equation of the line into slope intercept form is equal to
y=mx+b
where m is the slope
b is the y-intercept
If the coefficient of the x-term is positive
then
the slope is positive
therefore
If the values of x increases, the values of y increases
If the values of x decreases, the values of y decreases
The line will be going 'uphill' from left to right
Answer: the line slants up
Step-by-step explanation:
X being positive will cause a “ rise “ in the positive x,y plane.
Find the values of the six trigonometric functions of an angle in standard position if the point with coordinates (40, 9) lies on its terminal side.
Answer:
See below in bold.
Step-by-step explanation:
The 40 is the adjacent side of the triangle that can be drawn and the 9 is the opposite side.
The hypotenuse = sqrt (40^2 + 9^2) = 41.
sine = opp/hyp = 9/41 = 0.2195.
cosine = 40/41 = 0.9756.
tangent = 9/40 =0.2250.
cosec = 1/ sine = 41/9 = 4.5556.
secant = 1 / cosine = 41/40 = 1.0250.
cotangent = 1 / tangent = 40/9 = 4.4444.
The decimal forms are correct to the nearest ten thousandth.
The values of the six trigonometric functions are:
sin θ = 9/41, cos θ = 40/41, tan θ = 9/40, cot θ = 40/9, sec θ = 41/40, cosec θ = 41/9.
What are trigonometric functions?The values of all trigonometric functions dependent on the value of the ratio of sides of a right-angled triangle are known as trigonometric ratios. The trigonometric ratios of a right-angled triangle's sides with regard to any of its acute angles are known as that angle's trigonometric ratios.
The three sides of the right-angled triangle are:
Hypotenuse (the longest side)
Perpendicular (opposite side to the angle)
Base (Adjacent side to the angle)
The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
The trigonometry ratios for a specific angle ‘θ’ is given below:
Trigonometric Ratios:
Sin θ = Perpendicular/Hypotenuse
Cos θ = Base/Hypotenuse
Tan θ = Perpendicular/Base or Sin θ/Cos θ
Cot θ = Base/Perpendicular or 1/tan θ
Sec θ = Hypotenuse/Base or 1/cos θ
Cosec θ = Hypotenuse/Perpendicular or 1/sin θ
What is Pythagoras theorem?According to the Pythagoras theorem, we can say that in a right-angled triangle:
Hypotenuese² = Base² + Perpendicular²
How do we solve the given question?We have to find the six trigonometric functions of an angle in standard position if the point with coordinates (40, 9) lies on its terminal side.
With the angle being θ, we have drawn a figure of the case. (attached)
In the right-angled triangle AOB, with respect to angle θ,
Hypotenuse: AO, Perpendicular: AB, and Base: BO
First we derive the value of AO, using the Pythagoras theorem,
AO² = AB² + BO² = 9² + 40² = 81 + 1600 = 1681 = 41²
∴ AO = 41 units.
Now we find the value of the six trigonometric functions, with respect to the angle θ.
sin θ = Perpendicular/Hypotenuse = AB/AO = 9/41
cos θ = Base/Hypotenuse = BO/AO = 40/41
tan θ = sin θ/cos θ = (9/41)/(40/41) = 9/40
cot θ = 1/tan θ = 1/(9/40) = 40/9
sec θ = 1/cos θ = 1/(40/41) = 41/40
cosec θ = 1/sin θ = 1/(9/40) = 40/9.
∴ The values of the six trigonometric functions are:
sin θ = 9/41, cos θ = 40/41, tan θ = 9/40, cot θ = 40/9, sec θ = 41/40, cosec θ = 41/9.
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find the axis of symmerty for x y=x squared -4x-8
Answer:
x=2
Step-by-step explanation:
y = x^2 -4x-8
This is in the form y = ax^2 + bx +c
The axis of symmetry, h is found by h=-b/2a
We know a = 1, b=-4
h = -(-4)/ (2*1)
=4/2
=2
The axis of symmetry is x=2
Calculate
19.25tons=___lbs.
Answer:
19.25 tons = 38500 lbs
Step-by-step explanation:
We are to convert the following given amount of tons in pounds.
We know that, 1 ton = 2000 pounds. So using the ration method, we can convert 19.25 tons into pounds.
[tex]\frac{1 ton}{19.25 tons} =\frac{2000 lbs}{x}[/tex]
[tex] x = 2 0 0 0 \times 1 9 . 2 5 [/tex]
[tex] x = 3 8 5 0 0 lbs[/tex]
Therefore, 19.25 tons = 38500 lbs.
Answer: [tex]38,500\ lbs[/tex]
Step-by-step explanation:
In order to answer the question, it is necessary to make the corresponding conversion from 19.29 tons (t) to pounds (lbs).
Then, for this conversion it is important to remember that:
[tex]1\ t=2,000\ lbs[/tex]
Finally, knowing this, you can make the conversion:
[tex](19.25\ t)(\frac{2,000\ lbs}{1\ t})=38,500\ lbs[/tex]
Therefore, you get this result:
[tex]19.25\ t=38,500\ lbs[/tex]
Determine which polynomial is a perfect square trinomial. 4x2 − 12x + 9 16x2 + 24x − 9 4a2 − 10a + 25 36b2 − 24b − 16
Answer:
4x^2 - 12x + 9
Step-by-step explanation:
Please use " ^ " to denote exponentiation: 4x^2 - 12x + 9.
This 4x^2 - 12x + 9 factors into (2x - 3)^2, and is thus a perfect square trinomial.
The polynomial [tex]4x^2-12x + 9[/tex] is a perfect square trinomial. It has a binomial factor (2x - 3).
What is a perfect square trinomial?The product of a binomial by itself gives the perfect square trinomial.
A trinomial is a polynomial that has only three terms and A binomial is a polynomial that has only two terms.
Factorizing the given trinomials:A. Trinomial [tex]4x^2-12x+9[/tex]
⇒ [tex](2x)^2-2(2x)(3)+(3)^2[/tex]
This is in the form of [tex]a^2-2ab+b^2[/tex] . So, we can write [tex](a - b)^2[/tex]
⇒ [tex](2x - 3)^2[/tex] or (2x - 3)(2x - 3)
Thus, this is a perfect square trinomial.
B. Trinomial [tex]16x^2+24x-9[/tex]
⇒ [tex](4x)^2+2(4x)(3)-(3)^2[/tex]
Since it cannot split into a binomial square, this trinomial is not a perfect square trinomial.
C. Trinomial [tex]4a^2-10a+25[/tex]
⇒ (2a)^2-2(5a)+(5)^2
This cannot be split into a binomial square, this is not a perfect square trinomial.
D. Trinomial [tex]36b^2-24b-16[/tex]
⇒ [tex](6b)^2-2(6b)(2)-(4)^2[/tex]
So, this is not a perfect square trinomial.
Therefore, the trinomial at option A is a perfect square trinomial.
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If f(x) = 1/2x – 10, then f^-1(x) =
Answer:
f^-1 (x) = 2x+20
Step-by-step explanation:
f(x) = 1/2x – 10
To find the inverse, replace f(x) with y
y = 1/2 x -10
Exchange x and y
x = 1/2 y- 10
Solve for y
Add 10 to each side
x+10 = 1/2 y-10+10
x+10 = 1/2 y
Multiply by 2
2(x+10) = 1/2y *2
2x+20 = y
The inverse is
f^-1 (x) = 2x+20
What is the area of triangle ABC if a = 8, b = 11, and c = 15?
Final answer:
To calculate the area of triangle ABC with sides measuring 8, 11, and 15 units, Heron's formula is used. The semiperimeter s is 17 units, which leads to an area of the square root of 1836 or approximately 42.8 square units.
Explanation:
To find the area of triangle ABC with sides a = 8, b = 11, and c = 15, we can use Heron's formula, which is a method of finding the area of a triangle when you know the lengths of all three sides. The formula states that the area of a triangle is the square root of s(s-a)(s-b)(s-c) where s is the semiperimeter of the triangle, or half of the triangle's perimeter. First, we calculate the semiperimeter: s = (a + b + c) / 2. Then, we substitute the values of a, b, and c into the formula to find the area.
The semiperimeter s is (8 + 11 + 15) / 2 which equals 17. Using Heron's formula, the area is the square root of 17(17-8)(17-11)(17-15). Therefore, the area of triangle ABC is equal to the square root of 17 imes 9 imes 6 imes 2, which simplifies to the square root of 1836, resulting in an area of 42.8 square units.