The areas of the squares are calculated from the Pythagoras relation of right angled triangle and it is 40 ft², 55 ft², 95 ft²
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the right angle triangle be represented as ΔABC
Now , the measure of side AB = √40 feet
The measure of side BC = √55 feet
The measure of side AC = √95 feet
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
Substituting the values in the equation , we get
AC² = AB² + BC²
( √95 )² = ( √40 )² + ( √55 )²
On simplifying the equation , we get
95 = 40 + 55
95 = 95
Therefore , the area of squares formed is 40 ft², 55 ft², 95 ft²
Hence , the triangle is having sides √40 feet , √55 feet and √95 feet
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for
6. Tami multiplies two fractions. The first fraction is greater than -1 but less than 0. The
notei
second fraction is greater than 0 but less than 1.
Which statement describes the product of the two fractions Tami multiplied?
The product of the two fractions Tami multiplied will be a negative number between 0 and -1.
How to find the product of the multiplicationSince the first fraction is negative greater than -1 but less than 0
and the second fraction is positive, greater than 0 but less than 1, their product will be negative.
This is because when a negative number multiplies a positive number the product is a negative number
Moreover, since both numbers are in fraction and less than whole their multiplication will also be a reduction tending towards zero
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What’s 10 more than triple P
The value of mathematical expression is,
⇒ 10 + 3P
What is Mathematical expression?Mathematical expression is defined as the collection or combination of the numbers, variables and functions by using operations like as addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 10 more than triple P.
Now, We can simplify mathematical expression as;
Triple P = 3P
Hence, We get the expression as;
⇒ 10 more than triple P.
⇒ 10 + 3 × P
⇒ 10 + 3P
Therefore, We get;
The value of mathematical expression is,
⇒ 10 + 3P
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Use the Fundamental Counting Principle to find the total number of possible outcomes.
The number of possible outcomes is given as follows:
18 outcomes.
What is the Fundamental Counting Theorem?The Fundamental Counting Theorem states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the total number of outcomes is calculated by the multiplication of the number of outcomes for each trial as presented as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
For this problem, we have that:
There are 3 options for the location.There are 6 options for the activity.Hence the number of outcomes is given as follows:
3 x 6 = 18 outcomes.
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Amplitude is ______.
the maximum displacement of a function on a graph
the minimum displacement of a function on a graph
Amplitude is the maximum displacement of a function on a graph.
What is amplitude?
Amplitude is the maximum displacement of a function on a graph. It refers to the maximum height or distance from the baseline of a wave or oscillation.
It is often used in physics and engineering to describe the strength or size of a signal, vibration, or wave. In simple terms, it can be thought of as the "peak-to-peak" distance of a waveform, or the height of the waveform above and below the baseline.
But the minimum displacement of a function on a graph would typically be referred to as the minimum value or the "valley" of the function.
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Evaluate 2x + 3y if x =2 and y = 8
Figure order is a rectangle what are the coordinates of point Q
The coordinates of point Q in the rectangle named QRST is (5, 5).
What are Coordinates?A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
Given:
We have the Graph having coordinate T(5, 2).
and, length of QT = 3 unit
As, the vertical distance shows the y coordinate then the y coordinate of Q is 3.
and, the x coordinate is same as T.
Then, the Coordinate of Q is (5, 2+3) or (5, 5).
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Levels of Measurement!
What type of measure scale is being used? Nominal, Ordinal, interval or Ratio.
1. A satisfaction survey of a social website by number:
1 = very satisfied, 2 = somewhat satisfied, 3 = not satisfied.
2. The colors of crayons in a 24-crayon box.
3. Baking temperatures for various main dishes: 350, 400, 325, 250, 300
4. The distance in miles to the closest grocery store.
5. High school men soccer players classified by their athletic ability:
Superior, Average, Above average.
1) A satisfaction survey of a social website by number is Ordinal.
2) The colors of crayons in a 24-crayon box are nominal.
3) The baking temperatures for various main dishes are interval.
4) The distance in miles to the closest grocery store is Ratio
5) High school men soccer players classified by their athletic ability are Ordinal.
The satisfaction survey scale is ordinal since the numbers are used to indicate the order of satisfaction (i.e., very satisfied is higher than somewhat satisfied, which is higher than not satisfied), but the difference between each level is not known.
The colors of crayons are nominal since they are categorical and do not have an inherent order or numeric value.
The baking temperatures are interval, as the differences between the values are meaningful, but there is no true zero point (i.e., 0 degrees does not indicate the absence of temperature).
The distance to the closest grocery store is ratio, as it has a true zero point (i.e., 0 miles means no distance), and the differences between distances are meaningful and measurable.
The classification of high school soccer players by athletic ability is ordinal since the categories are ordered, but the differences between them are not known.
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Kendra and Allen Tovsky have a combined income of $142,573. They have 1099 forms which report $650 in dividends. They also have $8,500 in income from rental property. They are able to reduce their income by $12,500. What is their adjusted gross income?
Kendra and Allen Tovsky's adjusted gross income is $139,223.
What is Adjusted Gross Income (AGI)?Adjusted Gross Income (AGI) is defined as an individual's gross income minus various adjustments made to that income, such as trade and business deductions.
To calculate Kendra and Allen Tovsky's adjusted gross income (AGI), we need to start with their total income and subtract any deductions or adjustments they are eligible for.
Their total income is:
Combined income: $142,573
Dividends: $650
Rental income: $8,500
Total income before deductions: $151,723
Next, we need to subtract their eligible deductions. In this case, they are able to reduce their income by $12,500, which could include things like contributions to a retirement account or health savings account, self-employed expenses, or student loan interest payments. Let's assume that the full $12,500 deduction applies to their situation.
Adjusted gross income calculation:
Total income before deductions: $151,723
Minus eligible deductions: $12,500
Adjusted gross income: $139,223
Therefore, Kendra and Allen Tovsky's adjusted gross income is $139,223.
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What is the value of the function at x = -2?
Answer:
f(-2) = 2
Step-by-step explanation:
Value of the function at x = -2.
Go to x=-2 and then read what the y value is at x=-2
y = 2 at x = -2.
f(-2) = 2
Using the graphing tool, write the exponential function that best modes the number of trees infected
The exponential function that best modes the number of trees infected [tex]y = a * e^{bx}[/tex]
what is exponential function ?
An exponential function is a mathematical function of the form [tex]f(x) = a^x[/tex] where "a" is a constant called the base, and "x" is the exponent. The base "a" is usually a positive number greater than 1, although it can be any positive number, including fractions and decimals.
Given by the question:
Assuming that the number of infected trees follows an exponential growth pattern, we can use the following equation:
[tex]y = a * e^{bx}[/tex]
where y is the number of infected trees at a given time, x is the time elapsed, a is the initial number of infected trees, and b is the rate of growth.
To find the values of a and b that best fit the data, we can use regression analysis techniques. We would need to input the data into a statistical software program, such as R or Excel, and run a regression analysis to estimate the values of a and b.
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A random sample of 31 charge sales showed a sample standard deviation o $50. A 90% confidence interval estimate of the population standard deviation is:
A 1715.10 - 4055.68
B 1596.45-4466.73
C 39.96-66.83
D 41.39-63.68
A 90% confidence interval estimate of the population standard deviation is 1596.45-4466.73
We can use the chi-square distribution to construct a confidence interval for the population standard deviation, where the lower and upper limits are given by:
[tex]\sqrt{(n-1)*s^2/chi2(alpha/2,n-1)) }[/tex] and [tex]\sqrt{(n-1)*s^2/chi2(1-alpha/2,n-1)}[/tex]
Standard Deviation is a measure that shows how much variation (such as spread, dispersion, spread,) from the mean exists.
Where n is the sample size, s is the sample standard deviation, alpha is the significance level, and chi2 is the chi-square distribution function.
Substituting the given values, we get:
Lower limit
= [tex]\sqrt{(31-1)*50^2/chi2(0.05/2,31-1)}[/tex]
= 1596.45
Upper limit
= [tex]\sqrt{(31-1)*50^2/chi2(1-0.05/2,31-1)}[/tex]
= 4466.73
Therefore, a 90% confidence interval estimate of the population standard deviation is 1596.45-4466.73.
Hence, the correct answer is B) 1596.45-4466.73
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a water cooler contains 5 gallons of water there are 24 students who drink one cup each from The Jug how many pints of water are left in the cooler
The number of pints of water left in the cooler will be 28 pints
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
A water cooler contains 5 gallons of water there are 24 students who drink one cup each from the Jug.
In 5 gallons of water, there are 40 pints of water. And in 1 cup of water, there are 0.50 pints.
Then the number of pints of water left in the cooler is given as,
⇒ 40 - 24 x 0.5
⇒ 40 - 12
⇒ 28 pints
The number of pints of water left in the cooler will be 28 pints
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suppose we roll two six-sided dice. consider event a as getting an odd number on die 1, event b as getting an even sum for the two dice. are event a and b independent?
The events A and B are dependent. P(A and B) is not equal to 1/4, as it is less than that.
The probability of getting an odd number on the first die is 3/6 = 1/2.The probability of getting an even sum is 18/36 = 1/2.The probability of getting an odd number on the first die and an even sum is 9/36 = 1/4.If A and B were independent, we would expect P(A and B) = P(A)P(B) = 1/2 * 1/2 = 1/4. However, P(A and B) is not equal to 1/4, as it is less than that. Therefore, A and B are dependent events.
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A rectangle has a perimeter of 74 centimeters.The length of the rectangle is 5 centimeters less than twice the width.What is the area of the rectangle,in square centimeters?
The area of the rectangle is 322 square centimeters.
Given data :- The perimeter of a rectangle P =74 meter. If the length is 5 meter less than twice it's width.
The dimensions of the rectangle =?
Let assume that the length of the rectangle L = (2x -5)m
And the width of the rectangle W = x meter
Now Perimeter P = 2(L+W)
74 = [2{x+(2x-5)}]
3x-5=37
3x= 42 , x = (42/3)= 14 meter
So the required width of the Rectangle W = 14 meter
Similarly , L = (2*14 - 5) = 23
Now , area of the rectangle = 14*23
Therefore, area of the rectangle = 322
Hence , the area of the rectangle is 322 square centimeters.
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PLEASE ANSWER ASAP!!!!
Sorry about the random numbers throughout the text. I had to censor some words due to brainly being scared of Macbeth.
Read the excerpt from act 1, scene 7 of The Tragedy of Macbeth.
Macbeth. He’s here in double trust:
First, as I am his k1nsman and his subject,
Strong both against the deed; then, as his host,
Who should against his murd3r3r shut the door,
Not bear the kn1fe myself. Besides, this Duncan
Hath borne his faculties so meek, hath been
So clear in his great office, that his virtues
Will plead like angels trumpet-t0ngu’d against
The deep d4mnation of his taking-off;
And p1ty, like a nak3d new-born babe,
Striding the blast, or heaven’s cherubin, hors’d
Upon the sightless couriers of the air,
Shall blow the horr1d deed in every eye,
That tears shall drown the wind. I have no spur
To pr1ck the sides of my intent, but only
Vaulting ambition, which o’er-leaps itself
And falls on the other.
Which statement best describes why Macbeth’s use of both logic and emotion is appropriate in this scene?
A. The use of logic causes Macbeth to envision himself as king, and the use of emotion leads him to think about those who would mourn Duncan’s death.
B. The use of logic causes Macbeth to reconsider his thoughts of killing the king, and the use of emotion leads him to question his motives.
C. The use of logic causes Macbeth to reevaluate Duncan’s capable leadership, and the use of emotion leads him to realize that his plan is justified.
D. The use of logic causes Macbeth to ponder the consequences of murder, and the use of emotion leads him to recommit to the promise he made to his wife.
The correct answer is: The use of logic causes Macbeth to ponder the consequences of murder, and the use of emotion leads him to recommit to the promise he made to his wife.
What is probability?Probability is a branch of mathematics that deals with the likelihood or chance of an event happening. It is a numerical measure of the uncertainty of an event, represented as a fraction, decimal, or percentage between 0 and 1. An event with a probability of 0 means that it is impossible for the event to occur, while an event with a probability of 1 means that it is certain to occur. In probability theory, events can be independent or dependent. Independent events have no effect on each other, so their probabilities are multiplied to find the probability of both events happening. Dependent events are those in which the outcome of one event affects the outcome of another event, so their probabilities must be multiplied differently to find the probability of both events happening.
Here,
The use of both logic and emotion in this scene highlights Macbeth's internal conflict and the struggle between his moral and immoral desires.
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Expand. Your answer should be a polynomial in standard form. ( � − 3 ) ( � − 4 ) = (x−3)(x−4)=
The polynomial in standard form after expansion is x² - 7x + 12.
What are Polynomials?Polynomials are mathematical expressions which consist of one or more terms involving variables and coefficients connected with operations like multiplication, subtraction, addition and natural number powers of variables.
The given expression is (x - 3) (x - 4).
We have to expand this as a polynomial in standard form.
Standard form of a polynomial with degree n is,
a₀ + a₁ x + a₂ x² + ................. + aₙ₋₁ xⁿ⁻¹ + aₙ xⁿ
(x - 3) (x - 4) = x (x - 4) - 3 (x - 4)
Applying the distributive property,
= x² - 4x - 3x + 12
= x² - 7x + 12
This is a standard form of a second degree polynomial.
Hence x² - 7x + 12 is the expansion of the given expression.
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In 2020, of a random sample of votes cast, 12 out of 25 were cast for Candidate A and 23 out of 50 were cast for Candidate B.
What fraction of ballots were cast for someone other than
Candidate A or Candidate B?
The fraction of ballots that were cast for someone other than Candidate A or Candidate B is given by the equation q = 3/50
What is a Fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
Given data ,
Let the fraction of ballots that were cast for someone other than Candidate A or Candidate B be represented as q
Now , the equation will be
The fraction of ballots cast for Candidate A = 12/25 = 24/50
The fraction of ballots cast for Candidate B = 23/50
So , the total fraction of ballots casts for Candidate A and Candidate B = fraction of ballots cast for Candidate A + fraction of ballots cast for Candidate B
Substituting the values in the equation , we get
The total fraction of ballots casts for Candidate A and Candidate B is given by p = ( 24 + 23 ) / 50
p = 47/50
Now , fraction of ballots that were cast for someone other than Candidate A or Candidate B = 1 - p
The value of q = 1 - p
q = 1 - ( 47/50 )
q = 3/50
Hence , the fraction is 3/50
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when two or more objective function coefficients are changed simultaneously, further analysis is necessary to determine whether the optimal solution will change.
The domain of the function f(x)= -long(5-x)+b is all real numbers except for x = 5.
What is function?Function is the process or state of instruction that text inputs performance is specific task and produce an output functional key components of programming language allowing the quarter to create complex commands with simple instruction for example a function can be used to add two numbers together or to generate a random number function can also be combined to create more complex sequence of instruction.
The range of this function is all real numbers as the long function will never return a negative value. The value of b determines the exact range of the function, as it shifts the graph up or down.
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The complete question is: Will changing two or more objective function coefficients simultaneously affect the optimal solution?
Suppose you surveyed 30 people and asked them whether they are white (W) white (N), and how many traumas (serious accidents, rapes, or crimes) they have enced in the past year. You also asked them to tell you whether they perceive theme as being in the upper, middle, working, or lower class. Your survey resulted in the data presented in the table below: a. Identify the level of measurement for each variable. b. Construct raw frequency tables for race. c. What proportion of the 30 individuals is nonwhite? What percentage is white?
a. The level of measurement for each variable are Race: Nominal, trauma: Ratio, Social Class: Ordinal.
b. Raw frequency tables for race:
Race Frequency
W 21
N 9
c. The proportion of the 30 individuals who are nonwhite is: 9/30 = 0.3
So, 30% of the individuals are nonwhite.
The percentage of individuals who are white is: 21/30 x 100% = 70%
So, 70% of the individuals are white.
Race is a nominal variable because it is a categorical variable that does not have any inherent order or ranking. The two categories are "W" for white and "N" for nonwhite.
Trauma is a ratio variable because it is a quantitative variable that has a meaningful zero point. This means that a value of zero indicates the absence of the thing being measured, and values greater than zero indicate a greater quantity of the thing being measured.
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Assume that the conditions for bucket sort are satisfied. the probability that a particular bucket contains more than 5 is at most 1/16.a. Trueb. False
The statement can be true under certain conditions. The probability that a particular bucket contains more than 5 elements will depend on the size of the bucket and the distribution of the elements.
However, if we assume that the distribution is uniform and the number of elements is much larger than the number of buckets, we can estimate the probability using the following formula:
P(bucket > 5) = 1 - P(bucket <= 5) = 1 - (5/n)
Where n is the number of elements to be sorted, and 5 is the maximum number of elements that can fit in a bucket. If we assume that there are 16 buckets, then the probability that a particular bucket contains more than 5 elements is at most 1/16 if:
1 - (5/n) <= 1/16
Solving for n, we get:
n >= 80
This means that if we have at least 80 elements to be sorted, and we distribute them uniformly among 16 buckets, then the probability that a particular bucket contains more than 5 elements is at most 1/16. Therefore, the statement can be true under certain conditions.
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Which expression is equivalent to √64 a6
Answer:
√64 a⁶
or, √2⁶a⁶
or, √(2a)⁶
or, (2a)³
=8a³
What's the possible values of z when t = 81
( be it real or complex number )
[tex] {z}^{2} = \sqrt{t} [/tex]
So annoying ~
Answer:
[tex]\boxed{\mathrm{z=\pm 3}}[/tex]Step-by-step explanation:
[tex]\mathrm{z^2=\sqrt{t}, \; when, \; t=81}[/tex]
Substitute t with 81:-
[tex]\mathrm{z^2=\sqrt{81}}[/tex]
Since 9*9 =81, square of 81 is 9:-
[tex]\mathrm{z^2=9}[/tex]
Take the square root of both sides.
[tex]\mathrm{z=\pm \sqrt{9} }[/tex]
and since 3*3 = 9 the square root of 9 will be 3.:-
[tex]\mathrm{z=\pm 3}[/tex]
_____________________
Hope this helps!
Determine which of the following transformations are linear transformations
A. The transformation T1
defined by T1(x1,x2,x3)=(x1,0,x3)
B. The transformation T2
defined by T2(x1,x2)=(2x1−3x2,x1+4,5x2)
.
C. The transformation T3
defined by T3(x1,x2,x3)=(x1,x2,−x3)
D. The transformation T4
defined by T4(x1,x2,x3)=(1,x2,x3)
E. The transformation T5
defined by T5(x1,x2)=(4x1−2x2,3|x2|)
.
The transformation T1 defined by T1(x1,x2,x3)=(x1,0,x3) is linear transformation among the five given questions.
A linear transformation satisfies two properties: additivity and homogeneity. That is, for any vectors u and v, and any scalars a and b:
T(u + v) = T(u) + T(v)
T(au) = aT(u)
Using these properties, we can determine which of the given transformations are linear transformations:
A. The transformation T1 defined by T1(x1,x2,x3)=(x1,0,x3)
T1(u+v) = (u1+v1, 0, u3+v3) = (u1, 0, u3) + (v1, 0, v3) = T1(u) + T1(v)
T1(au) = (au1, 0, au3) = a(u1, 0, u3) = a*T1(u)
Therefore, T1 is a linear transformation.
The transformation T2 defined by T2(x1,x2)=(2x1−3x2,x1+4,5x2)
T2(u+v) = (2(u1+v1)−3(u2+v2), u1+v1+4, 5(u2+v2))
= (2u1−3u2, u1+4, 5u2) + (2v1−3v2, v1+4, 5v2) = T2(u) + T2(v)
However, T2 does not satisfy homogeneity property. Consider a = -1 and u = (1, 1):
T2(-u) = (-2, 5, -5)
-1*T2(u) = (-2, -5, -5)
Therefore, T2 is not a linear transformation.
The transformation T3 defined by T3(x1,x2,x3)=(x1,x2,−x3)
T3(u+v) = (u1+v1, u2+v2, -(u3+v3)) = (u1, u2, -u3) + (v1, v2, -v3) = T3(u) + T3(v)
T3(au) = (au1, au2, -au3) = a*(u1, u2, -u3) = a*T3(u)
Therefore, T3 is a linear transformation.
The transformation T4 defined by T4(x1,x2,x3)=(1,x2,x3)
T4(u+v) = (1, u2+v2, u3+v3) ≠ (1, u2, u3) + (1, v2, v3) = T4(u) + T4(v)
T4(au) = (1, au2, au3) ≠ a(1, u2, u3) = a*T4(u)
Therefore, T4 is not a linear transformation.
The transformation T5 defined by T5(x1,x2)=(4x1−2x2,3|x2|)
T5(u+v) = (4(u1+v1)−2(u2+v2), 3|u2+v2|)
= (4u1−2u2, 3|u2|) + (4v1−2v2, 3|v2|) ≠ T5(u) + T5(v)
T5(au) = (4au1−2au2, 3|au2|) ≠ a*T5(u)
Therefore, T5 is not a linear transformation.
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Does Stephanie have enough to cover the property damages
Since Stephanie carries a 100/300/100 liability policy, Stephanie's insurance can cover up to $100,000, therefore Stephanie have enough coverage to cover the property damages.
What is Property Damage?Property damage is any harm or destruction to real or tangible personal property that is brought on by carelessness, intentional obliteration, or a natural disaster.
A more serious form of property damage known as destruction of property involves physical harm to items that are either beyond repair or would be very expensive to replace.
We see that Stephanie has an insurance policy and because she has a 100/300/100 liability policy, she can cover for the damage because it is less than $100,000
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Find the surface area of the composite figure.
5 cm
4 cm
4 cm
Hint: Area of a
Triangle = b.h
SA = [?] cm²
4 cm
If you'd like
The surface area of the figure is 56 square units
What is the surface area of the figure?The complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
Net of right rectangular pyramid
The surface area of the figure is calculated as
Area = sum of individual areas
Using the above as a guide, we have the following:
Area = 4 * 4 + 4 * 1/2 * 4 * 5
Evaluate the expression
Area = 56
Hence, the area is 56 square units
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Re-write the quadratic function below in Standard Form y = 4(x−7)(x+3)
plsssssssss help
The quadratic function y = 4(x−7)(x+3) is re-written in standard form as
4x²- 16x - 84 = 0
How to write the standard formThe general formula for a quadratic function is expressed as;
ax² + bx + c = 0
From the information given, we have;
y = 4(x−7)(x+3)
expand the bracket, we get;
(x−7)(x+3)
x²+ 3x - 7x - 21
add or subtract the like terms
x² - 4x - 21
Multiply by 4, we have;
4(x² - 4x - 21)
4x²- 16x - 84 = 0
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A store manager instructs some new trainees that a measuring tape priced at $3 winds up costing a customer $3.24 once the sales tax is included. What is the sales tax percentage?
Answer: To find the sales tax percentage, we can start by subtracting the cost of the item itself from the total cost with tax included.
In this case, the cost of the item is $3, and the total cost with tax included is $3.24, so:
$3.24 - $3 = $0.24
Next, we can divide the amount of sales tax by the cost of the item, and multiply by 100 to find the percentage:
$0.24 ÷ $3 × 100 = 8%
So the sales tax percentage is 8%.
Step-by-step explanation:
Answer:
Step-by-step explanation:
$3 item
h = 100 * 3.24 - 3/ 3 = 24/3 = 8 1 = 8%
Sales tax percentage is = 8%
please help meee.
step by step please
here is the picture please help me.
The domain of function fog (x) is [-2, 3].
From the case, it was given that:
f(x) = √(6 - x)
g(x) = x² - x
Domain of fog (x) ?
First, we need to find the form of function fog (x):
fog (x) = √(6 - (x² - x)
fog (x) = √(6 - x² + x)
fog (x) ≤ 0 --> to be rational
√(6 - x² + x) ≤ 0
To find the domain of function fog(x), we need to find the value of x where fog (x) equals to zero (0):
√(6 - x² + x) = 0
6 - x² + x = 0
(-x + 3) (x + 2) = 0
x = 3 or x = -2
Next, we need to chose random number above, between, and below 3 and -2 to find the domain of fog (x):
-2 < x < 3; x = 0
fog (0) = √(6 - (0)² + (0))
fog (0) = √6 --> rational
x < -2; x = -3
fog (-3) = √(6 - (-3)² + (-3))
fog (-3) = √(6 - 9 - 3)
fog (-3) = √(-6) --> irrational
x > 3; x = 4
fog (4) = √(6 - (4)² + (4)
fog (4) = √(6 - 16 + 4)
fog (4) = √(-6) --> irrational
Hence, the value of x should be -2 ≤ x ≤ 3 to make fog (x) function rational.
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Explain how the tiles show that 2s + 3s² is not
equivalent
to 5s.
The size of s² blocks is larger than that of blocks of s and this shows that the expressions 2s+3s² is not equivalent to 5s.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
The given expressions are 2s+3s² and 5s.
Here, 2s+3s²≠5s
Substitute s=-1 in 2s+3s²≠5s, we get
2(-1)+3(-1)²≠5(-1)
1≠-5
Substitute s=2 in 2s+3s²≠5s, we get
2(2)+3(2)²≠5(2)
16≠10
Therefore, the size of s² blocks is larger than that of blocks of s and this shows that the expressions 2s+3s² is not equivalent to 5s.
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"Your question is incomplete, probably the complete question/missing part is:"
Is 2s+3s² equivalent to 5s? Use math tiles to model 2s+3s² and 5s.
s+s s²+s²+s² s+s+s+s+s
2s 3s² 5s
The expression 2s+3s² is not equivalent to 5s. Explain how that tiles show that 2s+3s² is not equivalent to 5s.
Use the given points to write a system of two linear equations with the two unknowns being the slope and y-intercept of the line. Solve the system to identify those parameters and write the equation for the line passing through the two points in slope-intercept form.
(2, 5) and (6, 2)
(-1, 3) and (0, -2)
(-2, -4) and (2, 1)
The equation of the line passing through (-2, -4) and (2, 1) in slope-intercept form is y = (5/4)x - 9/4.
Describe Equation?An equation is a mathematical statement that shows that two expressions are equal to each other. It consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). The LHS and RHS can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots.
(2, 5) and (6, 2):
The two points are connected by a line that has the following slope:
m = (y2 - y1) / (x2 - x1)
= (2 - 5) / (6 - 2)
= -3/4
We may write the following using the equation of a line in the point-slope form:
y - y1 = m(x - x1)
Choosing point (2, 5) as (x1, y1), we get:
y - 5 = (-3/4)(x - 2)
Simplifying this equation, we get:
y = (-3/4)x + 11/2
So the equation of the line passing through (2, 5) and (6, 2) in slope-intercept form is y = (-3/4)x + 11/2.
(-1, 3) and (0, -2):
The two points are connected by a line that has the following slope:
m = (y2 - y1) / (x2 - x1)
= (-2 - 3) / (0 - (-1))= -5
We may write the following using the equation of a line in the point-slope form:
y - y1 = m(x - x1)
Choosing point (-1, 3) as (x1, y1), we get:
y - 3 = (-5)(x + 1)
Simplifying this equation, we get:
y = -5x - 2
So the equation of the line passing through (-1, 3) and (0, -2) in slope-intercept form is y = -5x - 2.
(-2, -4) and (2, 1):
The two points are connected by a line that has the following slope:
m = (y2 - y1) / (x2 - x1)
= (1 - (-4)) / (2 - (-2))
= 5/4
We may write the following using the equation of a line in the point-form:slope
y - y1 = m(x - x1)
Choosing point (-2, -4) as (x1, y1), we get:
y + 4 = (5/4)(x + 2)
Simplifying this equation, we get:
y = (5/4)x - 9/4
So the equation of the line passing through (-2, -4) and (2, 1) in slope-intercept form is y = (5/4)x - 9/4.
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