The binomial equation can be squared to provide an expression that is a perfect square trinomial.
what is perfect square ?Perfect squares result from squaring an integer. One such example is the number 81, which is a perfect square since it can be derived by squaring 9: 99=81. 144 is a perfect square since it can be generated by squaring the number 12, which results in 12. 169 is a perfect square since it can be squared to produce the number 13. mathematics-specific language Informally: When an integer (a "whole") number, whether positive, negative, or zero, is multiplied by itself, the result is referred to as a square number, a perfect square, or simply "a square". Accordingly, all square numbers are 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on.
given
The binomial equation can be squared to provide an expression that is a perfect square trinomial.
If and only if a trinomial that takes the form ax 2 + bx + c satisfies the requirement b 2 = 4ac is considered to be a perfect square.
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How do you find the area of the pre image and the image?
Coordinates for the pre-image are X(3,18) Y(18,18) and Z(18,9) and the image coordinates are X’(1,6) Y’(6,6) Z’ (6,3)
and what is the relationship between the two areas?
Answer: To find the area of the pre-image and the image, you can use the coordinates of the vertices of the shapes to calculate the lengths of the sides and use the formula for the area of a triangle:
Area = (base * height)/2
For the pre-image, the coordinates are X(3,18) Y(18,18) and Z(18,9). The base of the triangle is the distance between X and Z, which is 18 - 3 = 15. The height of the triangle is the distance between Y and Z, which is 18 - 9 = 9. The area of the pre-image is therefore:
Area = (15 * 9)/2 = 67.5
For the image, the coordinates are X’(1,6) Y’(6,6) Z’ (6,3). The base of the triangle is the distance between X’ and Z’, which is 6 - 1 = 5. The height of the triangle is the distance between Y’ and Z’, which is 6 - 3 = 3. The area of the image is therefore:
Area = (5 * 3)/2 = 7.5
The relationship between the two areas is that the area of the image is smaller than the area of the pre-image. This is because the image has been scaled down in size relative to the pre-image. The amount by which the image has been scaled down can be calculated by dividing the area of the image by the area of the pre-image:
Scale factor = area of image / area of pre-image = 7.5 / 67.5 = 0.11
This means that the image has been scaled down by a factor of 0.11 relative to the pre-image.
Step-by-step explanation:
Answer:
preimage area: 67.5 square unitsimage area: 7.5 square unitsimage area is 1/9 of preimage area, the square of the scale factorStep-by-step explanation:
You want to know the areas and their relationship of the preimage with coordinates X(3,18), Y(18,18), and Z(18,9), and the image with coordinates X’(1,6), Y’(6,6), Z’ (6,3).
TrianglesWhen you plot the points on a graph, you see they define right triangles. Each has sides aligned with the x- and y-axes, so it is easy to find their dimensions by counting grid squares or subtracting coordinates.
The preimage triangle is 18-3 = 15 units in the x-direction, and 18-9 = 9 units in the y-direction.
The image triangle is 6-1 = 5 units in the x-direction, and 6-3 = 3 units in the y-direction.
We notice that both the coordinates and the dimensions of the image triangle are 1/3 those of the preimage triangle.
AreasThe area of each triangle is given by the formula ...
A = 1/2bh
Using the dimensions we found above, the areas are ...
preimage area: 1/2(15)(9) = 135/2 = 67.5 . . . . square units
image area: 1/2(5)(3) = 15/2 = 7.5 . . . . square units
Relationship
We have observed that the image dimensions are 1/3 those of the preimage. The image area is 7.5/67.5 = 1/9 of that of the preimage. This value is the square of the scale factor of the dimensions,
Use the figure to answer the following.
The solution of given triangle is 32°.
An isosceles triangle is what?Therefore, an isosceles triangle has two equal sides as well as two equal angles. The Greek words iso (same) and skelos are the source of the name (leg). An equilateral triangle is one in which all of its sides are equal, and a scalene triangle is one in which none of its sides are equal.
Given,
∠BAC=52°
since, ΔBAC is isosceles triangle hence opposite angle will be equal.
∠BAC+∠ABC+∠ACB=180°
2∠BCA=180°-52°
∠BCA=128/2
∠BCA=64°
also,
∠BCA+∠DCA=180°
∠ACD=180°-64°
∠ACD=116°
since,
ΔACD is isosceles triangle, hence opposite angle is equal
∠ACD+∠CAD∠ADC=180°
2∠CAD=180°-116°
∠CAD=64/2
∠CAD=32°
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Is Avogadro's number equal to one mole?
One mole consists of 6.02214076×10²³ units which is Avogadro's number. Thus one mole is known as Avogadro's number.
What is one mole?
A mole is 6.02214076×10²³ of any chemical unit, including atoms, molecules, ions, and others. Due to the large number of atoms, molecules, or other components that make up any substance, the mole is a useful measure to utilize. The mole was initially defined as the quantity of atoms contained in 12 grammes of carbon-12, but the General Conference on Weights and Measures declared in 2018 that the mole will only contain 6.02214076×10²³ of some chemical unit as of May 20, 2019.
In chemistry, a mole, sometimes spelled mol, is a common scientific measurement unit for significant amounts of very small objects like atoms, molecules, or other predetermined particles.
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A conical paper cup is 10 cm tall with a radius of 7 cm. The cup is being filled with water so that the water level rises at a rate of 3 cm/sec. At what rate is water being poured into the cup when the water level is 9 cm
The rate exists water being poured into the cup when the water level is 9 cm exists [tex]$$1458 \pi \mathrm{cm}^3 s^{-1}$$[/tex].
What is meant by chain rule?To determine the derivative of a composite function in differential calculus, apply the chain rule formula. If y = f(g(x)), then according to the chain rule, the instantaneous rates of change of the functions f and g with respect to x produce the instantaneous rate of change of f with respect to x.
A composition of functions, such as the composition of the functions f and g, f(g(x)), can be used to determine the derivative using the chain rule.
Let us set up the following variables:
R, Radius of conical cup (cm) = 30 cm
H, Height of the conical cup (cm) = 10 cm
Our aim is to find dV/dt when h = 9 and we are given dh/dt = 2
By similar triangles we have
r : h = R : H
r/h = 30/10
⇒ r = 3h
The volume of a cone is 1/3π r²h, So:
V = 1/3π r²h
simplifying the equation, we get
= 1/3π (3h²)h
= 1/3π 9h²h
= 3π h³
Differentiating wrt h we get:
dV/dh = 9π h²
Applying the chain rule we have:
dV/dt = (dV/dh)(dh/dt)
= 9π h² × 2
= 18π h²
If h = 9 then
[tex]$\left[\frac{d V}{d t}\right]_{h=9}=18 \pi\left(9^2\right)=1458 \pi \mathrm{cm}^3 s^{-1}$$[/tex].
Therefore, the rate exists water being poured into the cup when the water level 9 cm exists [tex]$$1458 \pi \mathrm{cm}^3 s^{-1}$$[/tex].
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Add: (g2 – 4g4 + 5g + 9) + (–3g3 + 3g2 – 6)
Rewrite terms that are subtracted as addition of the opposite.
g2 + (–4g4) + 5g + 9 + (–3g3) + 3g2 + (–6)
Group like terms.
Combine like terms.
Write the resulting polynomial in standard form.
The resulting polynomial in standard form (b) –4g^4 –3g³ +4g² +5g +3
What is standard form of a polynomial?Suppose the considered polynomial is of only one variable.
Then, the standard form of that polynomial is the one in which all the terms with higher exponents are written on left side to those which have lower exponents.
The simplification process is described and partially carried out. We are to finish by combining like terms and writing the result in standard form.
Given
Add: (g² – 4g^4 + 5g + 9) + (–3g³ + 3g² – 6)
Combine Like Terms
g² + (–4g^4) + 5g + 9 + (–3g³) + 3g² + (–6)
The like terms are the g² terms and the constants;
= (1 +3)g² + (–4g^4) +5g +(9 +(–6)) +(–3g³)
= 4g² +(–4g^4) +5g +3 +(–3g³)
Write in Standard Form
In this form, the terms are written in order of decreasing degree.
= –4g^4 –3g³ +4g² +5g +3
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help im no good at this
Answer:
8.2 × 10⁻³
Step-by-step explanation:
1.64 × 10⁰ 1.64 × 1 1.64
-------------- = -------------- = ---------- = 0.0082
2.0 × 10² 2 × 100 200
Scientific notation: 8.2 × 10⁻³
I hope this helps!
The points (p, -2) and (6, 8) fall on a line with a slope of -10. What is the value of p?
Thank you!
Step-by-step explanation:
(8 + 2)/(6 - p)= -10
10/6 - p = -10
-60 + 10p = 10
10p= 70
p= 7
A helicopter pad which is in the shape of a circle has a circumference of 62. 48 feet and a diameter of 24 feet. Which expression best represents the value of ?
The expression which represents the value of the area could be the six times the circumference of the circle.
What is area of circle ?
area of circle can be defined as the product of pi(3.14) and square of radius of the circle.
Given,
helicopter pad which is in the shape of a circle has a circumference 72.48
and the diameter of 24 feet.
radius = diameter/2
radius = 24/2
radius = 12
circumference of circle = 72.48
area of circle = π*r*r
area of circle = 22/7 * 12 * 12
area of circle = 452.5
area of circle is approximately 6 times the circumference of circle.
Hence , The expression which represents the value of the area could be the six times the circumference of the circle.
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A survey found the following number of pets in different households.
What is the mean absolute deviation for the number of pets?
Answer:
absolute deviation means distance between each data value and the mean of the data set.
Step-by-step explanation:
(MAD)
or
(Average)
Kaj and her children went into a grocery store and she bought $8 worth of apples and bananas. Each apple costs $1 and each banana costs $0.50. She bought 2 more apples than bananas. By following the steps below, determine the number of apples, x,x, and the number of bananas, y,y, that Kaj bought.
Kaj bought 3 bananas and 5 apples.
Finding the numbers of apples and bananas using substitution method.To determine the number of apples and bananas that Kaj bought, we can set up a system of equations.We know that the total amount spent on apples and bananas is $8.We know that each apple costs $1 and each banana costs $0.50.We know that Kaj bought 2 more apples than bananas.From these three pieces of information, we can set up the following two equations:
x + y = 8 (The total number of apples and bananas is 8)x + 0.5y = 8 (The total amount spent is $8)x = y + 2 (Kaj bought 2 more apples than bananas)We can substitute the third equation into the first equation and get:
y+2 + y = 8
So we know that y = 3
Now we can substitute this value into the second equation and get:
x + 0.5(3) = 8
So we know that x = 5
So Kaj bought 3 bananas and 5 apples.
And also we can substitute y = 3 into the third equation and get:
x = y + 2
So we know that x = 5
So Kaj bought 3 bananas and 5 apples.
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3 chairs and 4 tables cost rs 7540. if the price of a chair is 220 find the price of table?
ans - 7120
Answer:
The price of a table is rs1720
Step-by-step explanation:
Let C and T be the individual prices of the tables and chairs.
We know that 3C + 4T = rs7540
We are then told that C = rs220, so we can enter that into the equation to find T:
3C + 4T = rs7540
3(220) + 4T = rs7540 [for C = rs220]
660 + 4T = 7540
4T = rs6880
T = rs1720
Check:
Do 3 chairs at 220 each and 4 tables at 1720 each add to a total of 7540?
Chairs: rs660
Tables: rs6880
Total = rs7540 YES
A line passes through the points (-2,8) and (5,-20)
The linear equation that passes through these two points is:
y = -4x
How to find the equation for the line?A general linear equation can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If we know that the line passes through two known points (x₁, y₁) and (x₂, y₂), then we can write the slope as:
a = (y₂ - y₁)/(x₂ - x₁)
Here we know the two points (-2, 8) and (5, -20), so the slope is:
a = (-20 - 8)/(5 + 2) = -28/7 = -4
So the line is:
y = -4*x + b
To find the value of b, we can replace the values of the point (-2, 8), so we will get:
8 = -4*(-2) + b
Now we can solve this for b.
8 = -4*(-2) + b
8 = 4*2 + b
8 = 8 + b
8 - 8 = b
0 = b
Then the linear equation is:
y = -4*x
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Pam said the equations x/16=4 and x/4=16 have the same solution. Is she correct? Explain
well, maybe Pam has been eating the wrong chips or something, but if she's correct, that can only happen if both equations are exactly equal, are they?
[tex]\boxed{\cfrac{x}{16}=4}\implies x=(16)(4)\implies \cfrac{x}{4}=16 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{x}{4}=16\implies x=(4)(16)\implies \boxed{\cfrac{x}{16}=4}\qquad \begin{array}{llll} \textit{yeap, Pam is correct}\\ \textit{she's Da Bomb} \end{array}[/tex]
What is the horizontal asymptote * 1 point?
Angle AOB is a central angle with a measure of 110 degrees.
What is the measure of its arc AB?
The measure of the ACB arc is 250° when in the picture we have a circle with an angle AOB is a central angle with a measure of 110°.
Given that,
In the picture we have a circle with an angle AOB is a central angle with a measure of 110°.
We have to find the measure of the ACB arc.
We know that,
Suppose that AB is the minor arc that is m(arc AB) = 110°
We know that measure of the major arc is 360°- measure of minor arc.
m(arc ACB)= 360- m(arc AB)
m(arc ACB)= 360-110
m(arc ACB)= 250°
Therefore, The measure of the ACB arc is 250° when in the picture we have a circle with an angle AOB is a central angle with a measure of 110°.
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What are the 11 identities?
Trigonometric identities are categorized as various identities out of which 11 are ,
Sin θ = 1/Coc θCos θ = 1/Sec θ Tan θ = 1/Cot θTan θ = Sin θ/Cos θCot θ = Cos θ/Sin θSin (90 – θ) = Cos θCos (90 – θ) = Sin θTan (90 – θ) = Cot θCot ( 90 – θ) = Tan θSec (90 – θ) = Cos θCos (90 – θ) = Sec θSin (-θ) = – Sin θTrigonometric Identities are used when trigonometric functions are given in an expression. Geometrically, these identities include one or more trigonometric functions
These are the sine , cosine or the tangent functions.
There are numerous trigonometric identities relating the side length and angle of a triangle. Only the right-angle triangle has the trigonometric identities.
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Solve for x in this triangle. Round your answer to the nearest tenth. 18 Xº 23
Answer:
51.50004959055205
Step-by-step explanation:
[tex]sin (x) = \frac{18}{23}[/tex]
f(x)=3^√x-1
Find f(27) and f(-343)
need to find cube root
On solving the provided question, we can say that - the value of the cube root is 19683 = 27
what is cube root?In mathematics, y3 = x since the cube root of a number x equals a number y. Each non-zero real integer has precisely one real cube root, one set of complex conjugate cube roots, and three different complex cube roots. When a number is multiplied three times, the result is the cube root of that number. Three cube roots, the final cube root, is the symbol for the cube root. The opposite of cubing an integer is finding the cube root of that number. Prime factorization is a fairly straightforward technique that may be used to get a number's cube root. The sign stands for a cube root.
here,
we have f(27)
cube will be [tex]( 27 )^3[/tex] = 19683
and f(-343) = -7
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Find the value of x in the following equation:
3.5(5x + 4) = 17.5x + 14
No solution
Infinite solutions
x = 0
x = 1.3
The system of equations .5(5x + 4) = 17.5x + 14 have Infinite solutions.
What are simultaneous equations?We know two simultaneous equations have a unique solution when they intersect at a point,
when they are parallel they have no solution and when they are coinciding they have an infinite no. of solutions.
Given, A system of equation 3.5(5x + 4) = 17.5x + 14.
17.5x + 14 = 17.5x + 14.
As the LSH and RHS are equal the equation of the two lines is the same and hence they coincide and have an infinite number of solutions.
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How do you represent a number line on a class 7?
Draw a line and locate the origin '0', mark the positive numbers on the right and the negative number on the left of '0' at an equal distance.
A number line is a horizontal straight line in which the integers are placed in equal intervals. All the numbers can be represented in a number line. This line can be extended indefinitely at both ends.
A number line is a graphical representation of numbers on a straight line. It is used for comparing and ordering numbers. It can be used for representing any real number that includes every whole number and natural number.
Draw a line and locate the point ‘0’. This point is known as the origin. If the given number is positive, draw it on the right side of the origin. If it is a negative number, draw it on the left side of zero. Divide each unit into the values equal to the denominator of the given fraction.
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May someone help?...
The value of x and y in triangles AEB and BCD is 40° and 50°.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know the sum of all the interior angles in a triangle is 180°.
Therefore, In ΔAEB,
(2x + 5)° + 50° + 45° = 180°.
2x + 100° = 180°.
2x = 180° - 100°.
2x = 80°.
x = 40°.
Now, ΔBCD,
x + y + 90° = 180°.
40° + y + 90° = 180°.
y = 180° - 130°.
y = 50°.
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hi, can someone please help me
this is your proper answer
hii, how are you
Answer:
15
Step-by-step explanation:
Let the total number of beads be x[tex]\because\: \frac{3}{8}[/tex] of the beads are blue.& Total number of blue beads = 9[tex]\rightarrow\: \frac{3}{8}\times x= 9[/tex][tex]\rightarrow\: x= \cancel{9}\times\frac{8}{\cancel{3}}[/tex][tex]\rightarrow\: x=3\times 8[/tex][tex]\rightarrow\: x=24[/tex]Number of purple beads = 24 - 9 = 15What is the degree of the polynomial 7x³ 5x 4x³ 2x²?
The degree of the polynomial 7x³ 5x 4x³ 2x² is 3.
The degree of a polynomial is the highest power of x in the polynomial.
In this case, the polynomial is 7x³ 5x 4x³ 2x², and the highest power of x is x³. This means that the degree of this polynomial is 3.
It's important to note that when working with polynomials it's important to pay attention to the signs of the coefficients. In this case, we have 7x³, 5x, 4x³, 2x². The x³ term has the highest degree and it's coefficient is 7, the x term has the second highest degree and it's coefficient is 5, the x³ term has the same degree as the first x³ term, but the coefficient is different, and the x² term has the fourth highest degree and it's coefficient is 2.
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Using a number line, find both the intersection and the union of the following
intervals:
(-∞,2) and [0,∞)
The union of the intervals is (-∞,∞)
The intersection of the intervals is [0,2)
Hope this helped!
7. What is the most precise name for the quadrilateral?
(Show all work and explanation clearly for full credit)
P(-1,3), Q(3,0), R(0,-4), S(-4,-1)
Area of quadrilateral is 24 units and it is known as parallelogram.
A plot point in a graph is what?A point in the plane is one-to-one connected to an ordered pair of real numbers (x, y) using point plotting. The 2-dimensional Cartesian coordinate system is as a result obtained.
A parallelogram results from plotting the four points.
the lower side is between (-6,-3) and (-2,-3)
0 to 3 is at the top (4,3)
As a result, the base length is 4 because the distance
between (-6,-3) and (-2,-3) = 4
the separation between (0,3) and (4,3)
The sides are the lines that connect (0,3) to (-6,-3)
along with (4,3) to (-2,-3).
Vertical height ranges from -3 to 3 or 6.
The parallelogram's area is given by base*height = 4(6) = 24.
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The surveyor walked 120 ft away from one of the sensors so that her walking path made a 90 degree angle with the width of the lake when she stop she measured the lake when she stopped she measured the angle between her lines of sight to both sensors and it was 70 degrees
Therefore ,the answer to the above trigonometry issue is therefore that the river is 70 feet wide.
What is trigonometry?The study of the connections between the angles and sides of triangles is known as trigonometry. Due to the fact that each straight-sided figure may be reduced to a collection of triangles, trigonometry is commonly utilized in geometry. There are a mind-boggling number of connections between trigonometry and other branches of mathematics, especially algebra, real or complex, integrals, logarithms, and infinite series.
Here,
Figure depicts a right triangle which, in relation to angle, its next side has length d or its wrong side is equal to the river's width, y. As a result,
tanθ= d/ y
=> y=dtanθ
=> y = (100m)tan(35.00)=70ft
The river measures 70 feet in width.
As a result, the trigonometry problem's answer indicates that the river's width is 70 feet.
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7
A scientist is investigating the weight of 50 tigers.
Here is some information about these tigers.
Number of tigers
Mean weight of tigers (kg)
Siberian
22
260
Type of tiger
The mean weight of all 50 tigers is 218 kg
Work out the mean weight of the Bengal tigers.
Bengal
28
Consequently, there is a 0.89736 percent chance or probability that he weighs fewer than 258 kilograms.
What is probability?Probability fundamentals. A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
Here,
we use the z-score algorithm to answer this query.
Score Z = x - μ/σ
x = the raw score
population mean= μ
Population standard deviation is σ
Hence,
x = 258, μ = 220, σ = 30
Z = 258 - 220/30
=1.26667
Probability based on the Z-Table:
P(x<258) = 0.89736
Consequently, there is a 0.89736 percent chance that he weighs fewer than 258 kilograms.
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Each of the students in class writes a different 2 digit number on the whiteboard. The teacher claims that no matter what the students write there will be at least three numbers on the white board whose digits have the same sum what is the smallest number of students in the calls for the teacher to be correct?
Answer: The teacher's claim is that there will be at least three numbers on the whiteboard whose digits have the same sum, no matter what the students write. To see if this claim is true, we can consider different cases for the number of students in the class.
If there are only two students in the class, the teacher's claim is not true. The two students can write any two different two-digit numbers, and it's not guaranteed that the digits in those numbers will have the same sum.
If there are three students in the class, the teacher's claim is true. The three students can write any three different two-digit numbers, and at least one of those numbers is guaranteed to have digits that have the same sum as one of the other numbers.
If there are more than three students in the class, the teacher's claim is true. No matter what numbers the students write, there will always be at least three numbers whose digits have the same sum.
Therefore, the smallest number of students for the teacher's claim to be true is three students.
It's worth mentioning that the teacher's claim is not necessarily true for all cases, it's only true that any three numbers picked out of the two-digit numbers set, will have digits with the same sum.
Step-by-step explanation:
Will give you brainlist
What are the two equations to set up to solve the equation?
|3x-2|=19
3x-2=
~QUESTION 2~
3|x+2|-7=14
x=_______
_____
~QUESTION 3~
-2|2x+3|+14(greater than and equal to symbol) -16
= < with line * < with line
The two equation to set up to solve the equation |3x - 2| = 19 are
3x - 2 = 193x - 2 = -19Question 2
x = 5 OR -9
Question 3
x ≥ 6 OR x ≥ -9
What is absolute value?Without taking direction into account, absolute value describes how far away from zero a certain number is on the number line.
A number can never have a negative absolute value.
How to write the absolute value equationThe equation is written in the form below
|3x - 2| = 19
removing the absolute value sign
3x - 2 = ± 19
the two equations are
3x - 2 = 19
3x - 2 = -19
Question 2
solving for x
3|x + 2| - 7 = 14
3|x + 2| = 14 + 7
3|x + 2| = 21
divide through by 3
|x + 2| = 7
removing the absolute value sign
x + 2 = ±7
solving for x for positive value
x + 2 = 7
x = 5
solving for the negative sign
x + 2 = -7
x = -9
Question 3
-2|2x+3| + 14 ≥ -16
-2|2x+3| ≥ -30
dividing through by -2
|2x+3| ≥ 15
2x+3 ≥ ±15
solving for the positive sign
2x+3 ≥ 15
x ≥ 6
solving for the negative sign
2x+3 ≤ -15
x ≥ -9
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What is the area of this parallelogram?
Answer: B
Step-by-step explanation:
Area = 4 x 5
= 20 cm^2
Remember that area of parallelogram is the base x perpendicular height. is The perpendicular height is not 6cm but 5cm. (right angle labelled on diagram)
Answer: 20 cm²
Step-by-step explanation:
area parallelogram = base x height
=> 4 x 5 = 20