Answers
The theorems or postulates for the given pair of angles are as follows:
2. ∠2 ≅ ∠8 → Alternate exterior angles are congruent;
3. ∠2 ≅ ∠4 → Vertically opposite angles are congruent;
4. ∠3 ≅ ∠5 → Alternate interior angles are congruent;
5. ∠3 is supplementary to ∠6 → Consecutive interior angles are supplementary;
6. ∠4 ≅ ∠8 → Corresponding angles are congruent;
What are the types of pairs of angles?Consider two lines m and n are parallel. A transversal t is intersecting the lines m and n.
So, it forms 8 angles with the lines m and n. They are ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7, and ∠8.
Based on their position, they are paired into different categories. Such as:
Interior angles: ∠3, ∠4, ∠5, ∠6
Exterior angles: ∠1, ∠2, ∠7, ∠8
'Alternate interior angles' are the pair of interior angles on the opposite side of the transversal 't'. I.e., (∠3, ∠5), (∠4, ∠6) are congruent.'Alternate exterior angles' are the pair of exterior angles which are on the opposite side of the transversal 't'. I.e., (∠2, ∠8), (∠1, ∠7) are congruent.'Consecutive interior angles' are the pair of interior angles which are on the same side of the transversal 't'. I.e., (∠3, ∠6), (∠4, ∠5). These are also called "Supplementary angles" which mean they add up to 180°.'Consecutive exterior angles' are the pair of exterior angles on the same side of the transversal 't'. I.e., (∠2, ∠7), (∠1, ∠8). These are also called "Supplementary angles" which mean they add up to 180°.'Vertically opposite angles' are the pair of angles that are opposite to each other at the point of intersection. I.e., (∠1, ∠3), (∠2, ∠4), (∠5, ∠7), (∠6, ∠8)'Corresponding angles' are the pair of consecutive angles in which one of the angles is exterior and the other is interior. I.e., (∠1, ∠5), (∠2, ∠6), (∠4, ∠8), (∠3, ∠7)Theorems or postulates for the given pair of angles:Classifying the given pair of angles and their corresponding theorems:
2. ∠2 ≅ ∠8 → These angles belong to pair of Alternate exterior angles.
Theorem - "The alternate exterior angles are congruent"
3. ∠2 ≅ ∠4 → These belong to pair of vertically opposite angles.
Theorem - "The verticle angles are congruent"
4. ∠3 ≅ ∠5 → These belong to pair of alternate interior angles.
Theorem - "The alternate interior angles are congruent"
5. ∠3 is supplementary to ∠6 → These angles belong to pair of consecutive interior angles. Thus, they are supplementary.
Theorem - " The supplementary angles add up to 180°"
6. ∠4 ≅ ∠8 → These angles belong to pair of corresponding angles.
Theorem - " The corresponding angles are congruent".
Learn more about the pair of angles here:
https://brainly.com/question/18772057
#SPJ1
Related Questions
Find the next two terms in the sequence 3, 6, 12, 24, 48, ...
Answers
Answer:
96 and 192
Step-by-step explanation:
This is a geometric sequence with a common ratio of 2 :
3 × 2 = 6
6 × 2 = 12
12 × 2 = 24
24 × 2 = 48
48 × 2 = 96
96 × 2 = 192
Therefore our final answers are 96 and 192
Hope this helped and have a good day
What is the name for the threshold p-value that determines when the null hypothesis is rejected?.
Answers
Alpha level. the minimum P-value at which we reject the null hypothesis
What is Null hypothesis ?That two options are identical is the null hypothesis. According to the null hypothesis, the observed difference is solely the result of chance. The probability that the null hypothesis is correct can be determined via statistical testing.
What is alpha level?The "significance level," often known as the alpha level, must be established before performing any statistical test. The likelihood of rejecting the null hypothesis when it is true is what is meant by the term "alpha level" in statistics. The likelihood of making a poor decision is what this phrase means.
To know more about Null hypothesis visit:
https://brainly.com/question/28098932
#SPJ4
The diameter of a circle is 8mm. What is the circumference of the circle?
Answers
Answer: 8π mm (in terms of π)
Step-by-step explanation:
1) The formulas for solving the circumference of a circle is πd (π times diameter).
2) 8 times π equals 8π mm.
Hopes this helps!
Answer:
12.56 [tex]mm^{2}[/tex]
Step-by-step explanation:
c = 2[tex]\pi[/tex]r
or c =[tex]\pi[/tex]D
The diameter is the measure of a line segment going from one side the circle to the other and going through the middle of the circle. A radius is a line 1/2 a diameter. It is a line segment that goes from the center of a circle to a point on the edge of the circle.
C = (3.14)(4)
C = 12.56
The formula for __________________________ is x = t e or raw score (x) equals the true score (t) plus error (e).
Answers
The formula for Observed Score is; Observed score (X) = True score (T) + measurement error (e)
What is the observed score formula?The formula for Observed Score is;
Observed score (X) = True score (T) + measurement error (e)
1) True score is the score that would be obtained if an individual took a test an infinite amount of times and those test scores were averaged. The concept of true score is theoretical because you can't give someone something an infinite number of times.
2) Standard error of measurement is the standard deviation of multiple test scores (how far the sample mean of the data is likely to be from the true population mean).
The less random error (e) in the measure, the more the observed score X approximates the true score T.
Thus;
Observed score = True Score + Error
Read more about Observed Score at; https://brainly.com/question/13700221
#SPJ1
Does x^-2 equal 2/x?
Answers
Answer:
No,
Step-by-step explanation:
X^-2 is equal to 1/X^2. so any number or letter to negative power, is the same as 1 divided by that number or letter to the positive power..(power remains with denominator
Suppose the six people consist of three mar- ried couples and each couple wants to sit together with the older partner on the left. how many ways can the six be seated together in the row?
Answers
6 possible ways to order 3 couples in a row
Given,
We have three married couples. that is six persons in total.
a, b, c, d, e, f may taken as the six persons.
Considering the statement:
Elder partner on the left, assume a, c and e as elders.
Then we have, (a, b) ------ ( 1)
(c, d) ------ (2)
(e, f) ------ (3)
There is no change in position between the couples.
So, we get three persons in total.
Possible ways to order these three persons will be like this: 3! = 3×2×1
= 6
Learn more about seating arrangement here ; https://brainly.com/question/10702719
#SPJ4
Assume thst y varies directly with x then solve if y=4 when x=12 find y when x=-24
Answers
Answer:
-8
Step-by-step explanation:
y=(1/3)x
4 = (1/3)12
y=(1/3)(-24)
y= -8
Adrian has a bag full of pebbles that all look about the same. he weighs some of the pebbles and finds that their weights are normally distributed, with a mean of 2.6 grams and a standard deviation of 0.4 grams. what percentage of the pebbles weigh more than 2.1 grams? round to the nearest whole percent.
Answers
89% of pebbles weigh more than 2.1 grams.
What is a percentage?
Percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity. percentage.Given,
Mean = 2.6
SD = 0.4
As we have to find the percentage of pebbles weighing more than 2.1, we have to find the z-score for 2.1 first.
[tex]z = \frac{x- mean}{SD}[/tex]
[tex]z = \frac{2.1 - 2.6}{0.4}[/tex]
[tex]z = -1.25[/tex]
Now we have to use the z-score table to find the percentage of pebbles weighing less than 2.1
So,
[tex]P ( x < 1.25 ) = 0.10565[/tex]
This gives us the probability of P(z<-1.25) or P(x<2.1)
To find the probability of pebbles weighing more than 2.1
[tex]P ( x > 2.1 ) = 1 - P( x < 2.1 ) = 1 - 0.10565 = 0.89435[/tex]
Converting into percentage
0.89435 × 100 = 89.435 %
Rounding off to nearest percent =89%
Therefore, 89% of pebbles weigh more than 2.1 grams.
Learn more about percent
brainly.com/question/4546769
#SPJ4
Find the value of x if a, b, and c are collinear points and b is between a and c. ab=x 6,bc=3x−5,ac=36−x
Answers
The value of x if a, b, and c are collinear points and b is between a and c : 7
What is collinear points?Collinear points are those that are situated on the same line of sight or within a single line. In Euclidean geometry, two or more points are said to be collinear if they are located on a line either close to or far from one another.
According to the given information:
if A, B, and C are col-linear points and B is between A and C
then
AB+BC=AC
AB=x+6
BC=3x-5
AC=36-x
substituting value:(x+6)+(3x-5)=36-x
(x+3x)+(6-5)=36-x
4x+1=36-x
4x+x=36-1
5x=35
x=35/5
x=7
The value of x is 7
To know more about collinear points visit:
https://brainly.com/question/1593959
#SPJ4
Consider the expressions below. for each expression below, select the letter that corresponds to the equivalent expression given above. is equivalent to expression . is equivalent to expression . is equivalent to expression . is equivalent to expression .
Answers
The considerations of expressions for each expressions are shown below.
What is an expression?An expression in mathematics is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division, etc.) Expressions and phrases are similar in structure. In English, a phrase may involve action on its own, but it does not constitute a whole sentence.To consider the expressions:
Part 1:
(x²+15x+65)+(2x-5)*(3x+8)(x²+15x+65)+(6x²+16x-15x-40)(7x²+16x+25)The answer to Part 1 is the letter B,
(7x²+16x+25)
Part 2:
(4x+1)*(3x-4)-(5x²-10x-12)(4x+1)*(3x-4)-(5x²-10x-12)(12x²-16x+3x-4)-(5x²-10x-12)(7x²-3x+8)The answer to Part 2 is the letter D,
(7x²-3x+8)
Part 3:
(8x²+19x+4)+(3x+2)*(x-5)(8x²+19x+4)+(3x²-15x+2x-10)(11x²+6x-6)The answer to part 3 is the letter A,
(11x²+6x-6)
Part 4:
(6x+1)*(3x-7)-(7x²-34x-20)(18x²-42x+3x-7)-(7x²-34x-20)(11x²-5x+13)The answer to part 4 is the letter C,
(11x²-5x+13)
Therefore, the considerations of expressions for each expression are shown.
Know more about expressions here:
https://brainly.com/question/24734894
#SPJ4
The complete question is given below:
For each expression below, select the letter that corresponds to the equivalent expression given above.
The following are the distances (in miles) to the nearest airport for 11 families. 9, 11, 11, 16, 16, 24, 28, 30, 34, 42, 45 Notice that the numbers are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set.
Answers
Here is the five-number summary, range and interquartile range:
Minimum: 9
Lower quartile: 11
Median: 24
Upper quartile: 34
Maximum: 45
Interquartile range: 23
What is the five-number summary?The minimum number is the smallest number in the data. The minimum number is 9. The maximum number is the biggest number in the dataset. The maximum number is 45.
The first quartile, third quartile and the interquartile range are used to measure dispersion.
The first quartile : 1/4(n + 1)
1/4 x (12) = 3rd term = 11
The third quartile : 3/4 x (n + 1)
3/4 x (12) = 9th term = 34
Interquartile range = third quartile - first quartile
34 - 11 = 23
Median can be described as the number that is at the center of the dataset when the number is arranged in either ascending or descending order.
Median = 25
To learn more about median, please check: https://brainly.com/question/14746682
#SPJ1
What's the perimeter or how do you find it?
Answers
The perimeter of inside of the track is 536.44m
Perimeter of a circle and rectangleThe perimeter of a circle is also known as the circumference of the circle. The formula for calculating the circumference is expressed as:
C = 2πr
where
r is the radius
From the given diagram
r = 46/2 = 23m
C = 2(3.14)(23)
C = 144.44m
Find the perimeter of the rectangle
P = 2(l+w)
p = 2(46+150)
P = 2(196)
P =392m
The perimeter of the inside track = 144.44 + 392
The perimeter of the inside track = 536.44m
Hence the perimeter of inside of the track is 536.44m
Learn more on perimeter of composite shape here: https://brainly.com/question/16247505
#SPJ1
nvm no need liao
The curve y = ax^n, where a and n are constants, passes through the points (2.25, 27), (4, 64) and (6.25, p). Without using logarithms, calculate the value of a, of n and of p.
Answers
a. The value of n is 3/2
b. The value of a is 8.
c. The value of p is 125
The curve is an exponential function
What is an exponential function?An exponential function is a function of the form y = axⁿ where a and n are constants
a. How to find the value of n?
Since y = axⁿ where a and n are constants, passes through the points (2.25, 27), (4, 64) and (6.25, p), substituting these points into the equation, we have
y = axⁿ
27 = a(2.25)ⁿ (1)
64 = a(4)ⁿ (2)
P = a(6.25)ⁿ (3)
Dividing (2) by (1), we have
64/27 = a(4)ⁿ/a(2.25)ⁿ
4³/3³ = (4 ÷ 2¹/₄)ⁿ
4³/3³ = (4 ÷ ⁹/₄)ⁿ
4³/3³ = (4 × 4/9)ⁿ
4³/3³ = (16/9)ⁿ
4³/3³ = (4²/3²)ⁿ
(4/3)³ = (4/3)²ⁿ
Equating exponents, we have
2n = 3
n = 3/2
The value of n is 3/2
b. What is the value of a?Using equation (2)
64 = a(4)ⁿ
a = 64/(4)ⁿ
substituting n = 3/2 into the equation, we have
[tex]a = \frac{64}{4^{\frac{3}{2} } } \\= \frac{64}{(\sqrt{4 } )^{3} } \\= \frac{64}{2^{3} } \\= \frac{64}{8} \\= 8[/tex]
So, the value of a is 8.
c. What is the value of p.Using equation (3), we have
P = a(6.25)ⁿ (3)
substituting the values of a and n into the equation,we have
[tex]P = 8(6.25)^{\frac{3}{2} } \\= 8(\sqrt{6.25}) ^{3} \\= 8(2.5}) ^{3} \\= 8(15.625})\\= 125[/tex]
The value of p is 125
Learn more about exponential function here:
https://brainly.com/question/12940982
#SPJ1
Work out the circumference of this circle.
Take it to be 3. 142 and give your answer to 1 decimal place.
4 cm
Answers
The circumference of the given circle is 25.1 cm.
According to the statement
we have given that the the radius of circle which is 4cm.
And we have to find the circumference of the circle.
So, For this purpose
The circumference is the length of any great circle, the intersection of the sphere with any plane passing through its center.To calculate the circumference of a circle, multiply the diameter of the circle with π (pi).
The formula to calculate it is
C = 2(pi)r
So, substitute the values in it then
Here use pi value is 3.14
C = 2 *3.14*4
C = 25.12.
The circumference of the given circle is according to one decimal place is 25.12 cm.
So, The circumference of the given circle is 25.1 cm.
Learn more about circumference here
https://brainly.com/question/4233129
#SPJ1
Complete the square to transform the expression x2 − 2x − 2 into the form a(x − h)2 k.
Answers
The given expression is equivalent to the expression (B) [tex](x-1)^{2} -3[/tex].
What is an equivalent function?Two functions are equivalent if they share the same domain and codomain and have the same values for all domain components.To complete the square to transform the expression:
The given expression is [tex]x^{2} -2x-2[/tex].Then the expression can be written as, add and subtract one.Then we have:[tex]x^{2} -2x+1-1-2\\x^{2} -2x+1-3\\(x-1)^{2} -3[/tex]Therefore, the given expression is equivalent to the expression (B) [tex](x-1)^{2} -3[/tex].
Know more about equivalent function here:
https://brainly.com/question/2972832
#SPJ4
The correct question is shown below:
Complete the square to transform the expression x^2− 2x − 2 into the form a(x − h)^2+ k.
(A) (x − 1)2 + 3
(B) (x − 1)2 − 3
(C) (x − 2)2 − 3
(D) (x − 2)2 + 3
A man bought a car for 8500 and sold it for 9500. find his percentage gain
Answers
Answer:
11.7647%
Hope this helps!
Choose the expression that represents a quadratic expression. 9x − 2 5x2 9x − 1 −2x3 8x2 − 7x 1 x4 − 12x3 8x2 − 7x 1
Answers
5x² + 9x - 1 is the expression that represents a quadratic expression.
What is quadratic expression?
Quadratic expression is an expression with the variable with the highest power of 2. The word quadratic is derived from the word quad which means square. The expression should have the power of two and not higher or lower.A quadratic expression is of the form
ax² + bx +c = 0 where a ≠ 0
The give options are-
9x - 2
5x² + 9x - 1
-2x³ + 8x² - 7x +1
[tex]x^{4} - 12 x^{3} + 8x^{2} - 7x +1[/tex]
From the given options, the only expression which is quadratic is
5x² + 9x - 1
wChoose the expression that represents a quadratic expression. 9x − 2 5x2 9x − 1 −2x3 8x2 − 7x 1 x4 − 12x3 8x2 −here a =5, b=9 and c=-1
Therefore, 5x² + 9x - 1 is the expression that represents a quadratic expression.
Learn more about quadratic expression.
brainly.com/question/24108537
#SPJ4
given that sinθ=-3/4 in quadrant 4 find cosθ
Answers
Step-by-step explanation:
sin∅=-3/4 in 4 quadrant which sine is negative there
using soh cah toa
sin=opp/hyp
where our opp=-3 and our hyp=4
using pythagoras theorem
hyp²=opp²+adj²
(4)²=(-3)²+adj²
16=9+adj²
16-9=adj²
adj²=7
adj=√7
from soh cah toa
cos∅=adj/hyp
cos∅=√7/4
I'm not sure how to do both of them
Answers
The total surface area of the shape is 10053 cm²
Calculating Surface areaFrom the question, we are to determine the surface area of the shape
The surface area of the shape = Surface area of hemispherical part + Surface are of the cylindrical part
∴ Surface area of the shape = 2πr² + 2πrh + πr²
Where r is the radius
and h is the height of the cylindrical part
From the given information.
r = 20
h = 50
Putting the parameters into the equation, we get
Surface area of the shape = 2π(20)² + 2π(20)(50) + π(20)²
Surface area of the shape = 2π×400+ 2π×1000 + π×400
Surface area of the shape = 800π+ 2000π + 400π
Surface area of the shape = 3200π cm²
Surface area of the shape = 10053.096 cm²
Surface area of the shape ≈ 10053 cm²
Hence, the total surface area of the shape is 10053 cm²
Learn more on Calculating surface area here: https://brainly.com/question/27812847
#SPJ1
Find the surface area of the cylinder and round to the nearest tenth. (Use the π button on your calculator)
Answers
The surface area of the cylinder with the given height and radius is 835.2 square inches
How to determine the surface area?The given parameters are
Height, h = 12 inches; this is represented by the distance between the curved surfaces of the cylinderRadius, r = 7 inches; this is represented by the distance between the center of the circle to its circumferenceThe surface area is then calculated using the following formula
A = 2πr² + 2πrh
Substitute the given values in the above equation
So, we have:
A = 2 * 3.14 * 7^2 + 2 * 3.14 * 7 * 12
Evaluate the exponents
A = 2 * 3.14 * 49 + 2 * 3.14 * 7 * 12
Evaluate the products
A = 307.72 + 527.52
Evaluate the sum
A = 835.2
Hence, the surface area of the cylinder with the given height and radius is 835.2 square inches
Read more about surface area at:
https://brainly.com/question/2835293
#SPJ1
List the sides in order from the smallest to the largest.
L
K
27°
OA. LJ, KL, JK
OB. LJ, JK, KL
OC. KL, LJ, JK
D. JK, LJ, KL
Reset Selection
78°
75°
Answers
Answer:
A
Step-by-step explanation:
the side opposite of the angle is related to the size of this angle. Smaller angles have less space for the line to "spread out," so it will be shorter. Vice versa, bigger angles will have opposite sides longer because of more space.
Find the surface area of the prism
Answers
The surface area of the prism is 256in².
Given that the sides of the prism is 5in, 12in and 4in.
The total area occupied by the surfaces of an object is called the area.
Here, l=12in, b=5in and h=4in
Firstly, we will find the area of the base, we get
B=l×b
B=12×5
B=60in²
Now, we will find the perimeter of the base, we get
P=2(l+b)
P=2(12+5)
P=2×17
P=34in
Further, we will find the surface area of the prism by using the formula SA=2B+Ph.
Here, we will substitute the values from above, we get
SA=2×60in²+34in×4in
SA=120in²+136in²
SA=256in²
Hence, the surface area of the prism where the sides of the prism is 5in, 12in and 4in is 256in².
Learn more about surface area of prism from here brainly.com/question/1581706
#SPJ1
Write down the coordinates of the image of the point (2-3) under reflecting about the line joining the points (3, 5) and (3,7)
Answers
Answer:
(4 , -3)
Step-by-step explanation:
the points (3 , 5) and (3 , 7) have the same x-coordinates 3
then ,the line D joining them has the equation
D : x = 3
the image of the point A(2 , -3) under reflecting about The line D ,
lie on the line ∆ perpendicular to D and passes through A.
∆ perpendicular to D then the equation of ∆ is :
∆ : y = a ,where a is a real number.
Calculating ‘a’ :
∆ passes through A
Then
-3 = a
Therefore
the final equation of ∆ is :
∆ : y = -3
Obviously, the lines D and ∆ intersect at the point M(3 , -3)
FINAL STEP :
Calculating the coordinates of the point B(x , y) image of the point A(2 , -3)
M is the midpoint of the line segment AB :
Then
3 = (2 + x)/2 and -3 = (-3 + y)/2
Then
x = 4 and y = -3.
How many solutions does the equation −3y 3y 4 = 4 have? none infinitely many one four
Answers
A given linear equation has infinitely many solutions.
What is a linear equation?There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that make a linear equation true and plot those values on a coordinate grid.As much as possible, reduce the equation to y = mx + b. Verify the exponents in your equation. It is nonlinear if it has exponents. Your equation is linear if there are no exponents in it.The definition of a linear equation is an equation with a maximum degree of one.Given: −3y 3y 4 = 4
3y+4=3y+4
The given linear equation satisfies any value of 'y'.
So, A given linear equation has infinitely many solutions.
To learn more about linear equations, refer to:
brainly.com/question/875464
#SPJ4
In the power function f(x) = -2x, what is the end behavior of f(x) =-2x^3 as x goes to [infinity]?
Answers
The end behavior of a polynomial function is as x tends to infinity, f(x) tends to negative infinity.
In this question,
The power function is f(x) =-2x^3
The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.
The degree and the leading coefficient of a polynomial function determine the end behavior of the graph.
The graph below shows the behavior of the function f(x).
The above equation has the degree of 3, which is odd and the leading coefficient has the negative coefficient.
Then the end behavior is
As x -> ∞,
[tex]\lim_{x \to \infty} f(x)[/tex]
⇒ [tex]\lim_{x \to \infty} -2x^{3}[/tex]
⇒ [tex]-2(\infty)^3[/tex]
⇒ - ∞
Hence we can conclude that the end behavior of a polynomial function is as x tends to infinity, f(x) tends to negative infinity.
Learn more about end behavior of a polynomial function here
https://brainly.com/question/22443880
#SPJ4
The functions f(x) = −(x − 1)2 5 and g(x) = (x 2)2 − 3 have been rewritten using the completing-the-square method. apply your knowledge of functions in vertex form to determine if the vertex for each function is a minimum or a maximum and explain your reasoning.
Answers
The vertex of the function f(x) exists (1, 5), the vertex of the function g(x) exists (-2, -3), and the vertex of the function f(x) exists maximum and the vertex of the function g(x) exists minimum.
How to determine the vertex for each function is a minimum or a maximum?Given:
[tex]$\mathrm{f}(\mathrm{x})=-(\mathrm{x}-1)^{2}+5$[/tex] and
[tex]$\mathrm{g}(\mathrm{x})=(\mathrm{x}-2)^{2}-3$[/tex]
The generalized equation of a parabola in the vertex form exists
[tex]$y=a(x-h)^{2}+k[/tex]
Vertex of the function f(x) exists (1, 5).
Vertex of the function g(x) exists (-2, -3).
Now, if (a > 0) then the vertex of the function exists minimum, and if (a < 0) then the vertex of the function exists maximum.
The vertex of the function f(x) exists at a maximum and the vertex of the function g(x) exists at a minimum.
To learn more about the vertex of the function refer to:
https://brainly.com/question/11325676
#SPJ4
Answer:
- For the function f(x) = -(x - 1)^2/5, the vertex is a maximum point.
- For the function g(x) = x^4 - 3, the vertex is a minimum point.
Step-by-step explanation:
To determine if the vertex for each function is a minimum or a maximum, we need to analyze the leading coefficient of each function.
Let's start with the function f(x) = -(x - 1)^2/5. This function is already in vertex form, where the vertex is (1, 0).
Since the leading coefficient is negative (-1/5), the graph of f(x) opens downward. In this case, the vertex is a maximum point. You can visualize it as a peak on a graph.
Now, let's move on to the function g(x) = (x^2)^2 - 3. This function can be rewritten in vertex form as g(x) = x^4 - 3.
The leading coefficient is positive (1), so the graph of g(x) opens upward. In this case, the vertex is a minimum point. You can visualize it as a valley on a graph.
In summary:
- For the function f(x) = -(x - 1)^2/5, the vertex is a maximum point.
- For the function g(x) = x^4 - 3, the vertex is a minimum point.
Remember, the sign of the leading coefficient determines whether the vertex is a minimum or maximum point.
What is the surface area of a rectangular prism that has a length of 12 mm, a width of 15 mm, and a height of 16 mm?
Answers
Mark me brainliest
Midpoint of US=
Help me please thanks so much
Answers
Given the point U and point V, the midpoint between of the line segment UV is ( 0, -5/2 ).
What is the midpoint of line UV?
The midpoint formula is used to find the midpoint of a line segment.
It is expressed as;
[ (x₁ + x₂ )/2 , (y₁ + y₂ )/2 ]
Given the data in the graph,
Point U = ( 3, -1 ) and Point V = ( -3, -4 )
x₁ = 3x₂ = -3y₁ = -1y₂ = -4We substitute into the formular above.
[ (x₁ + x₂ )/2 , (y₁ + y₂ )/2 ]
[ (3 + (-3) )/2 , ( (-1) + (-4) )/2 ]
[ 0/2, (-1-4)/2 ]
[ 0/2, -5 /2 ]
( 0, -5/2 )
Given the point U and point V, the midpoint between of the line segment UV is ( 0, -5/2 ).
Learn more about midpoint of line segment here: https://brainly.com/question/13792156
#SPJ1
Given that xy=3/2 and both x and y are nonnegative real numbers, find the minimum value of 10x (3y/5)
Answers
The munimum value is, at x = 3/10, y = 5 and 10x+3y/5 = 6.
What are nonnegative real numbers?Non-negative real numbers are the set of positive real numbers that are bigger than 0 (zero). That is, the true values are either positive or negative. The collection will include numbers such as 0, 1, 2, 3, 4, 5, and so on.To find the minimum value of 10x (3y/5):
Given - y = 3/(2x)
So, we want the bare minimum of,
= 10x + 3/5 × 3/(2x)= 10x + 9/(10x)Take the derivative to obtain:
= 10 - 9/(10x^2)When you set it to zero, you get:
= 100x^2 - 9 = 0= (10x-3)(10x+3) = 0= x = ± 3/10So, at x = 3/10, y = 5 and 10x + 3y/5 = 3 + 3 = 6.
Therefore, the munimum value is, at x = 3/10, y = 5 and 10x+3y/5 = 6.
Know more about nonnegative real numbers here:
https://brainly.com/question/26606859
#SPJ4
PLS HELP>>>>solving functions
Answers
Answer:
The first option:
[tex]x^2-5x+9[/tex]
Step-by-step explanation:
Trust me I am right.
If you need work please ask!
Have a nice day!