The left boundary of the confidence interval in question 1 depends on the specific data and confidence level used to calculate it. In general, the left boundary represents the lower limit of the range of values within which we can be confident that the true population parameter falls. The confidence interval is calculated by taking the point estimate of the parameter, such as the sample mean or proportion, and adding and subtracting a margin of error based on the standard error and the desired level of confidence. The left boundary will be further from the point estimate than the right boundary and will decrease as the level of confidence increases.
A confidence interval is a range of values within which we can be reasonably confident that the true population parameter falls. The interval is calculated using a point estimate of the parameter, such as the sample mean or proportion, and a margin of error based on the standard error and desired level of confidence. The left boundary of the confidence interval represents the lower limit of this range of values and will be further from the point estimate than the right boundary.
In summary, the left boundary of the confidence interval depends on the specific data and confidence level used to calculate it. It represents the lower limit of the range of values within which we can be confident that the true population parameter falls. The left boundary will be further from the point estimate than the right boundary and will decrease as the level of confidence increases.
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y=x^2+6x+8 solve by completing the square.
On solving the quadratic function x²+6x+8, the solutions x = -4 and x = -2 are obtained.
What is a quadratic function?
A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.
The given quadratic function is - x²+6x+8
To solve the function first multiply - 8 × x² = 8x²
Take the LCM of 8x².
8x² = 2 × 2x × 2x
Now, we need to form such two numbers that if added or subtracted gives 6x and when multiplied gives 8x².
8x² = 4x × 2x
6x = 4x + 2x
Factorize the equation using the numbers obtained -
= x²+6x+8
= x²+ 4x + 2x + 8
= x(x + 4) +2(x + 4)
= (x + 4)(x + 2)
This gives the value as x = -4 and x = -2.
Therefore, the solution points are x = -4 and x = -2.
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y=(x-2)^2+4 standard form
The standard form of the equation Y=(x-2)² + 4 is written as y=x²-4x+6.
Definition of standard formA standard form serves as a gauge for how widely scattered the data is in comparison to the mean.
The data are grouped around the mean when the standard deviation is low.
A parabola with the point at its vertex represents this equation (2,4). On a coordinate plane, the equation can be graphed, revealing a parabola that extends upwards and has a minimum value of 4 at the point (2,4).
The factored version of the equation
Y=(x-2)² + 4 is y = (x-2) (x-2) + 4
This representation of the equation demonstrates that it is the result of two binomials. When the common element is eliminated, the equation can be made simpler (x-2).
The equation is now more easily expressed as
y = (x-2) (x-2) + 4 = (x-2)² + 4.
Expanded form of the equation
Y=(x-2)² + 4 is expressed as y = x² - 4x + 6.
This representation of the equation demonstrates that it is the outcome of expanding (x-2)².
You may use this equation to determine the vertex of the parabola, which is (2,4). The vertex is the location where the parabola's value is at its lowest.
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What is the exponential form of 72?
The exponential form of 72 can be written as [tex]2^{3}[/tex] . [tex]3^{2}[/tex] . It can be written using the prime factorization of the number.
The exponential form is an easier way of writing repeated multiplication involving base and exponents. To write the exponential form we have to write the prime factorization of that number. Prime factorization of the number is that number written as a product of prime numbers or as a product of powers of prime numbers. A basic exponential function from its definition is of the form f(x) = b x, where 'b' is a constant and 'x' is a variable. generally it refers to the positive valued function of a real variable. We can find the prime factorization of a number using factor trees, which are tools used to repeatedly break a number into products until all of the factors are prime numbers.
72 = 2 × 2 × 2 × 3 × 3 = [tex]2^{3}[/tex] . [tex]3^{2}[/tex]
Therefore, the exponential form of 72 can be expressed as [tex]2^{3}[/tex] . [tex]3^{2}[/tex] .
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An investor invested a total of $1,600 in two mutual funds. One fund earned a 9% profit while the other earned a 4% profit. If the investor's total profit was $84, how much was invested in each mutual fund?
The amount invested in each mutual fund is $400 and $1200 respectively
What is Simultaneous equation?Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 10 and 8x − 4y = 2
Let represent the amount the first fund get by x and the amount the second fund get by y.
Therefore x+y = 1600 equation 1
and 9/100 × x + 4/100 × y = 84
9x/100 + 4x/100 = 84
multiply through by 100
9x + 4x = 8400 equation 2
using elimination method
9x+ 9y = 14400 equation 3
9x + 4y = 8400 equation 4
subtract equation 4 from 3
5y = 6000
divide both sides by 5
y = 6000/5
y = $1200
substitute 1200 for y in equation 1
1200+x = 1600
x = 1600-1200
x = 400
Therefore the first fund will get $400 and the second fund will get $1200
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Rectangle is similar to rectangle . Which proportion can be used to find the value of x?
If rectangle is similarity to rectangle, to find the value of x we use proportion (c) 5/12 = 2/x.
What is called similarity of shapes?When applying a scale factor, similar shapes are enlarged versions of one another.
All of the matching angles and lengths in related shapes are equal and in the same ratio.
If two figures share the same shape, congruent corresponding angles (which means the angles in the same places of each shape are the same), and identical scale factors, they are said to be "similar figures."
Given that rectangle EFGH is similar to rectangle JKLM, it means the corresponding sides of both rectangles are similar, and as such the ratios if the corresponding sides of rectangle EFGH and rectangle JKLM would be equal.
Thus, EF/JK = FG/KL
Since, EF = 5; JK = 12; FG = 2; and KL= x, therefore, the proportion to use in finding x would be:
5/12= 2/x
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Simplify the expression below
2(4.4x + 7.6) + 2(24x + 12)
Answer:
56.8x+39.2 Welcome :D
Step-by-step explanation:
Answer:
[tex]56.8x+39.2[/tex]
Step-by-step explanation:
First, you must distribute the 2's to the expressions:
2(4.4x+7.6) = 2(4.4x) + 2(7.6) which is equal to 8.8x + 15.2 and;
2(24x+12) = 2(24x) + 2(12) = 48x + 24
Now add both: 8.8x + 48x + 24 + 15.2 ; combine like terms.
56.8x + 39.2 is what you get from doing that.
This cannot be simplified any further, and therefore is your answer:
56.8x + 39.2
Darla is able to drive her car 37.5 miles per gallon of gasoline. Write an inequality that could be used to determine the minimum number of gallons, g, of gasoline Darla would need to drive 120 miles to her brother’s house.
i need help
The inequality can be written as g * 37.5 >= 120.
What is linear inequality?
A linear inequality is a mathematical statement that describes a relationship between two or more variables that form a half-plane when graphed. The equation of a linear inequality is in the form of "ax + by < c" or "ax + by > c" or "ax + by <= c" or "ax + by >= c", where x and y are variables, and a, b and c are constants.
An inequality that could be used to determine the minimum number of gallons, g, of gasoline Darla would need to drive 120 miles to her brother's house is:
g >= 120/37.5
This inequality states that the number of gallons, g, must be greater than or equal to the number of miles Darla needs to drive, 120, divided by the number of miles per gallon her car gets, 37.5. This is because Darla wants to ensure that she has enough gasoline to make the trip, and she may not want to risk running out of gas on the way.
Another way to write this inequality is
g * 37.5 >= 120
This inequality represents the same meaning as before, we multiply g by the number of miles per gallon the car gets, 37.5 and it should be greater than or equal to the distance she needs to travel which is 120 miles.
Hence, the inequality can be written as g * 37.5 >= 120.
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The assets and liabilities of a salesperson are listed below.
Home Value $264,500
Retirement Portfolio $473,906
Credit Card Balances $58,236
Bank Loan $35,275
Mortgage $187,632
Car Value $22,750
Investments $139,664
Home Furnishings $23,100
What is the value of the liquid assets?
$139,664
$264,500
$473,906
$613,570
If the salesperson has the given the assets and liabilities. The value of the liquid assets is: D. $613,570.
What is liquid assets?Liquid assets can be defined as those assets that can be turn into cash with a short period of time.
Now let find the liquid asset using this formula
Liquid assets = Retirement Portfolio + Investment
Where:
Retirement Portfolio = $473,906
Investments = $139,664
Let plug in the formula
Liquid assets = $473,906 + $139,664
Liquid assets = $613,570
Therefore we can conclude that the correct option is D.
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Write a conjecture that describes the pattern in the sequence, and then use the conjecture to find the next term in the sequence.
2, 8, 32, 128
The next term in the geometric sequence will be 512.
What is a geometric sequence?A series of non-zero integers where every term after the first is obtained by increasing the one before it by a constant, non-zero value known as the scale factor.
Let a₁ be the first term and r be the common ratio.
Then the nth term of the geometric sequence is given as,
aₙ = a₁ · (r)ⁿ⁻¹
The sequence is given below.
2, 8, 32, 128
The first term is 2 and the common ratio is calculated as,
r = 8 / 2
r = 4
Then the next term in the sequence will be given as,
a₅ = 2 · (4)⁵⁻¹
a₅ = 2 · (4)⁴
a₅ = 2 · 256
a₅ = 512
The next term in the geometric sequence will be 512.
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The next term of the sequence is 512.
What is Geometric Sequence?A geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio, r.
Given:
Sequence :2,8, 32, 128,...
As, the sequence is a geometric progression which can be expressed as
[tex]Tn = ar^{n-1[/tex]
Here, a is the first term = 2
n is the number of terms = 5 (next term is the 5th term)
r is the common ratio = 8/2 = 32/8 = 4
So, [tex]Tn = ar^{n-1[/tex]
[tex]T_5[/tex] = 2[tex](4)^{5-1[/tex]
[tex]T_5[/tex] = 2 x [tex]4^4[/tex]
[tex]T_5[/tex]= 2 x 256
[tex]T_5[/tex]= 512
Hence, the next term is 512
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Han is traveling at a speed of -12 miles per hour. If he starts at a position of zero, what will his position be after 3 hours?
Answer:
-36
Step-by-step explanation:
3*-12=-36
Answer: -36
Step-by-step explanation:
Can the length 4.5 cm 3.5 cm 6.4 cm be the dimensions of a triangle?
It is possible to construct a triangle whose sides are 4.5 cm 3.5 cm and 6.4 cm because the sum of two sides are greater than the third sides.
In the given question, we have to check that it is possible to construct a triangle whose sides are 4.5 cm 3.5 cm and 6.4 cm.
To check whether the given sides can make a triangle or not, we have to check that the sum of two sides always greater than the third side.
To check this we firstly add the 4.5 and 3.5
4.5 + 3.5 > 6.4
8 > 6.4
Now we add 4.5 and 6.4
4.5 + 6.4 > 3.5
10.9 > 3.5
Now we add 3.5 and 6.4
3.5 + 6.4 > 4.5
9.9 > 4.5
It is possible to construct a triangle whose sides are 4.5 cm 3.5 cm and 6.4 cm because the sum of two sides are greater than the third sides.
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Choose an equivalent expression for three fourths raised to the fourth power times three fourths raised to the third power all raised to the second power.
The correct statement is three fourths raised to the fourteenth power.
What are the 10 rules of exponents?
The Power rule for exponents: (am)n = am*n. To raise a number with an exponent to a power, multiply the exponent times the power. Negative exponent rule: x–n = 1/xn. Invert the base to change a negative exponent into a positive.
The important laws of exponents are :
am×an = a. m+nam/an = a. m-n(am)n = a. mnan/bn = (a/b) na0 = 1.a-m = 1/a. ma 1 n = a n.Given:
(((3/4)^4 * (3/4)^3)^2
Now,
((3/4)^ ( 4+3))^2
=((3/4)^7)^2
=(3/4) ^(7*2)
=(3/4)^14
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The option are:
nine sixteenths raised to the twenty fourth power
nine sixteenths raised to the fourteenth power
three fourths raised to the twenty fourth power
three fourths raised to the fourteenth power
How to find the formula of an exponential function from a table?
To find the formula of an exponential function from a table, you need to identify two points that fall on the exponential curve, and then use them to find the function's base.
The first step is to identify two points that fall on the exponential curve. Look for two pairs of x and y values that are not too far apart. For example, (1, 2) and (2, 4) are good choices.
Next, you use these two points to find the base of the function, which is the number b in the equation y = b^x. To do this, you take the ratio of the y-values and the logarithm of that ratio with base b. The logarithm of the ratio is equal to the difference of the x-values.
For example, if you have (1, 2) and (2, 4) you can find the base by taking log2(4/2)=log2(2)=1, which means that the base of the function is 2.
Now you have the base you can write the formula of the exponential function as y = 2^x.
It is important to note that you can use the same process with other bases, such as base 10 or base e, depending on the problem and the logarithm function you have available.
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what is the value of x in the equation - 5.4 = 4x - 1.8
Answer:
x = - 0.9
Step-by-step explanation:
- 5.4 = 4x - 1.8 ( add 1.8 to both sides )
- 3.6 = 4x ( isolate x by dividing both sides by 4 )
[tex]\frac{-3.6}{4}[/tex] = x , that is
x = - 0.9
Answer: 0.9 Step-by-step explanation:
is there a proportional relationship between the original price of an item and it’s sale price?
Answer:
It seems that your question is missing something, it looks like a question to a previous question. Please add all info when making a question. Also you can comment underneath my reply with that additional info.
Elizabeth is putting cupcakes into boxes. Each box will hold 4 cupcakes. Elizabeth has 48 cupcakes.
Which TWO number sentences could be used to find the total number of boxes Elizabeth will need?
Responses
(24÷4)+(20÷4)
(40÷4)+(8÷4)
(40×4)+(8×4)
(24÷4)+(24÷4)
48 x 4
Answer:
(40÷4)+(8÷4)
(24÷4)+(24÷4)
Step-by-step explanation:
1 box holds —> 4 cup cakes
x boxes holds —> 48 cup cakes
cross multiply
48 × 1 = 4 × x
48 = 4x
[tex] \frac{ \\ 48}{4} = \frac{4x}{4} [/tex]
x = 12
since the number of boxes needed to hold 48 cup cakes are 12 we need to look for an expression that is equivalent with our figure.
lets try
(24 ÷ 4) + (20 ÷ 4)
= 6 + 5
= 11 (Not correct)
(40 ÷ 4) + ( 8 ÷ 4)
= 10 + 2
= 12 ( correct)
(40 × 4) + ( 8 × 4)
= 160 + 32
= 192(Not correct)
(24 ÷ 4) + (24 ÷ 4)
= 6 + 6
= 12(correct)
48 × 4
= 192(Not correct)
i hope i helped
Read the scenario and select a correct option for Part 1-3 questions.
Afnan has 24 coins in his pocket. They are all quarters and dimes and their total value is $4.65.
Part 1: What is the system of equations that represents this situation?
Part 2: How many dimes does he have?
Part 3: How many quarters does he have?
The system of equations that represents this situation is D + Q =24 and 10D + 25Q = 465 with 15 and 9 quarters and dimes respectively.
What are dimes?The dime is a ten-cent coin that is one-tenth of a dollar and is officially known as "one dime" in American use. The Coinage Act of 1792 initially allowed this denomination.The dime is the smallest and thinnest denomination now in circulation in the United States.Its obverse has President Franklin D. Roosevelt's profile, while its reverse features, from left to right, an olive branch, a torch, and an oak branch.The dime is the only currency in general circulation in the United States that is not valued in terms of dollars or cents. The cost to make a dime in 2011 was 5.65 cents.Given that
let the quarter be represented by Q and dimes with D
D + Q =24 (multiply this by 10)
10D + 10Q = 240
10D + 25Q = 465
Subtracting both the equations:
15Q =225
Q = 225/15 = 15 quarters
Now putting this value in equation 1st we get
D = 24-15 = 9 dimes
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How to solve linear equations in two variables by substitution?
The procedure of solving linear equations in two variables by substitution includes selecting one eqn and solving it for one variable, substituting the result in another equation, solving the new eqn, and finally substituting the value into any of the eqns and solving for another variable.
An equation is a linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b (≠ 0).
To solve systems using substitution, follow these steps:
Step 1. Select one equation and solve it for one of its variables.
Step 2. In the other equation, substitute the value get from step 1.
Step 3. Solve the new equation.
Step 4. Substitute the value found into any equation involving both variables and solve for the other variable.
Step 5. Check the solution in both original equations.
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What are the types of line of best fit?
An examination of two or more independent variables using simple linear regression will provide a straight line. Sometimes a curved line is generated by a multiple regression incorporating a number of related variables.
What does analysis of linear regression entail?
When predicting a variable's value based on the value of another variable, linear regression analysis is utilized. The dependent variable is the one you want to be able to forecast.
The independent variable is the one that you are utilizing to forecast the value of the other variable.
Why do we use linear regression analysis?
It is crucial to comprehend linear regression since it offers a method for calculating and forecasting future events. Finding predictions and evaluating them can aid many firms and people by enabling them to operate more efficiently and produce thorough research materials.
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Solve for X and find the measure of the angle indicated in bold.
for the ones that doesn't have a number then the first one is 25, 27
Also please help. I need to get this done by tomorrow. please also explain how you got the answers two for everyone of the problems, thanks!
Due to the corresponding angle property, which requires that the sum of neighboring opposite angles be 180, the angles are 90 and 79.8.
what is angle ?In Euclidean geometry, an angle is a shape that is made up of two rays, known as the angle's sides, that meet at a point in the middle known as the angle's vertex. Two rays may combine to form an angle in the plane where they are positioned. When two planes collide, an angle is also created. They are referred to as dihedral angles. An angle in plane geometry is the possible configuration of two rays or lines that share a termination. The origin of the English term "angle" is the Latin word "angulus," which meaning "horn." The vertex is the point where the two rays, also known as the sides of the angle, converge.
given
Due to the property of matching angles,
the angles are 90 and 21x + 8
90 + 21x + 18 = 180
= 108 + 21x = 180
= 21x = 72
x = 3.42
Due to the corresponding angle property, which requires that the sum of neighboring opposite angles be 180, the angles are 90 and 79.8.
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How many factor are there for 36 Write them What do you notice about the number of factor of 36 and the number of array Courtney can make with the photo?
There are number of factors of 36 are 9 and number of array Courtney can make with the photo is 9.
factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder. For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly. The other factors of 12 are 1, 2, 4, and 12.
In math, an array refers to a set of numbers or objects that will follow a specific pattern.
the arrays can Courtney make with the 36 photos are,
1 by 36,
36 by 1,
2 by 18,
18by 2,
3 by 12,
12 by 3,
4 by 9,
9 by 4,
6 by 6.
the factors of 36 are,
1, 2, 3, 4, 6, 9, 12, 18, 36
∴ 9 ( factors ) = 9 ( arrays )
Therefore, there are number of factors of 36 are 9 and number of array Courtney can make with the photo is 9.
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What fraction of 3 3/4 is 22 1/2
30 points
fractions are a way of expressing the part of a whole.
What is the fraction?To answer this question, we need to first convert both fractions into the same denominator. The fraction 3 3/4 can be converted to 15/4, and 22 1/2 can be converted to 45/2.Once both fractions are in the same denominator, we can divide the numerators by the denominators to get the solution. When we divide 15/4 by 45/2, the answer is 1/3. Therefore, 22 1/2 is one third of 3 3/4. To explain this in more depth, In the fraction 3 3/4, the numerator 3 is the number of parts of the whole, and the denominator 4 is the number of equal parts that make up the whole.Therefore, 3 3/4 can be expressed as 3 parts out of 4 parts, or 3 out of every 4. Similarly, 22 1/2 can be expressed as 22 parts out of 2 parts, or 22 out of every 2. When we divide 15/4 by 45/2, we are essentially asking what fraction of 3 3/4 is 22 1/2. To get the answer, we divide 15, the numerator of 3 3/4, by 45, the numerator of 22 1/2. This gives us the answer of 1/3. In other words, 22 1/2 is one third of 3 3/4.3 3/4 = 15/4
22 1/2 = 90/4
90/4 ÷ 15/4 = 6
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Which number is greater than the number at point P?
The correct answer is -60
Why did we choose -60 not -70?When you look at -70 it looks like it would be higher then -60 but -60 is actually higher then -70 because it has a negative line.
Therefore, the correct answer is -60
Can the length 4.5 cm 3.5 cm 6.4 cm be the dimensions of a triangle?
The length 4.5 cm 3.5 cm 6.4 cm can be the dimensions of a triangle according to rule.
Considering the dimensions of triangle, the one side of the triangle should be less than the sum of other two sides. Based on the rule, let us say that 4.5, 3.5 and 6.4 cm is side a, b and c.
Keep the values to compare the sides
Side a + side b > side c
4.3 + 3.5 > 6.4
Add the digits
7.8 > 6.4
Side b + side c > side a
3.5 + 6.4 > 4.5
Add the digits
9.9 > 4.5
side c + side a > side b
6.4 + 4.5 > 3.5
Add the digits
10.9 > 3.5
All the sides follow the rule. Therefore, the mentioned lengths are possible for a triangle.
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What is 2/3 as an exponent?
The expression " [tex]\frac{2}{3}[/tex] to the exponent of 3" is represented as , [tex](\frac{2}{3} )^{3}[/tex] , and the value of [tex]\frac{2}{3}[/tex] to the exponent of 3 is [tex]\frac{8}{27}[/tex] .
What are Exponents ?
The Exponents are defined as the representation of a number that is multiplied by several to itself .
For Example : 8 multiplied by two times to itself , can be represented in exponential form as 8² .
We have to find the value of " [tex]\frac{2}{3}[/tex] to the exponent of 3" ;
the given exponential expression can be solved further as :
⇒ [tex](\frac{2}{3} )^{3} = \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3}[/tex]
On simplifying ,
we get ;
⇒ [tex]\frac{2\times 2 \times 2}{3 \times 3\times 3}[/tex]
⇒ [tex]\frac{8}{27}[/tex] .
Therefore , the value of " [tex]\frac{2}{3}[/tex] to the exponent of 3" is [tex]\frac{8}{27}[/tex] .
The given question is incomplete , the complete question is
What is [tex]\frac{2}{3}[/tex] to the exponent of 3 ?
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Evaluate the iterated integral. The first integral is 0 to 2 and the second integral is 2 to 3. xy^2 dx dy. Please show step by step with detail. integral 0 to 2 xy^2 dxdy
The value of the evaluated iterated integral is 6.667.
As per the given data the iterated integral is [tex]$\int_2^3 \int_0^2 x y^2 d x d y$[/tex]
Here we have to evaluate the given iterated integral to find the value of [tex]$\int_2^3 \int_0^2 x y^2 d x d y$[/tex] .
The definite integral of a real-valued function f(x) with respect to a real variable x on an interval (a, b) is expressed as
[tex]$\int_a^b f(x) d x=\mathrm{F}(\mathrm{b})-\mathrm{F}(\mathrm{a})$[/tex]
Here,
[tex]$\int=$[/tex] Integration symbol
a - Lower limit
b - Upper limit
f(x) - Integrand
dx - Integrating agent
Thus, [tex]$\int a b f(x) d x$[/tex] is read as the definite integral of f(x) with respect to dx from a to b.
Indefinite integrals are implemented when the boundaries of the integrand are not specified.
[tex]& \int_2^3 \int_0^2 x y^2 d x d y \\[/tex]
Integrate the given iterated integral.
We get:
[tex]& \int_2^3 x d x \int_0^2 y^2 d y \\[/tex]
[tex]& =\int_2^3 x d x\left(\left.\frac{y^3}{3} \right|_0 ^2\right) \\[/tex]
Substitute the limits in y.
[tex]& =\int_2^3 \frac{8}{3} x d x \\[/tex]
[tex]& =\left.\frac{8}{3\times2} x^2\right|_2 ^3 \\[/tex]
[tex]& =\left.\frac{4}{3} x^2\right|_2 ^3 \\[/tex]
Substitute the limits in x.
[tex]& =\frac{4}{3} \times 9-\frac{4}{3} \times 4 \\[/tex]
[tex]& =\frac{20}{3}[/tex]
= 6.667.
Therefore answer is 6.667.
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A triangle has sides with lengths of 32 kilometers, 60 kilometers, and 68 kilometers. Is it a right triangle?
Answer:
yes
Step-by-step explanation:
a^2 + b^2 = c^2
so
32^2 + 60^2 = 68^2
1024 + 3600 = 4624
help please thanks no guessing tho
The answer to each of the absolute functions is given below.
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
Given is are the absolute function equations.
{1} -|5 + m| < 13
5 + m < 13 and 5 + m < - 13
[a] - and
{2} -4|y + 6| ≥ 3
|y + 6| ≥ 3/4
y + 6 ≥ 3/4 or y + 6 ≥ -3/4
[b] - or
{3} -|g - 3| = - 2
we can write -
g - 3 = - 2
g = 1
and
g - 3 = - (-2)
g - 3 = 2
g = 5
Therefore, the answer to each part is given above.
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The parent function f(x) = x2 is reflected across the x-axis, vertically stretched by a factor of 5, and translated 3 units down to create g. Identify g in vertex form.
The function g in vertex form is g (x) = –5x^2 – 3.
In this case, the parent function is:
f (x) = x^2
First, after the reflection across the x-axis, we will get:
f (x) = –f (x)
And, the function will be:
g (x) = –x^2
Then, vertically stretched by a factor of 5, we will get:
g (x) = –5x^2
Last, translated 3 units down, we will get:
g (x) = –5x^2 – 3
Thus, the vertex form of the function g will be:
g (x) = –5x^2 – 3
What is translation?In mathematics, a translation is a transformation which occurs when a figure is moved from one location to another location without changing its size or shape.
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How do you know if an ordered pair is an exponential function?
To determine if the set of ordered pairs satisfies an exponential function, x -coordinates must have a constant increment.
We know that generally exponential function is written in the form function can be written in the form y = ab^x ,
where a and b are real numbers such that, a ≠ 0 , b > 0 , and b ≠ 1
a is called the initial value of function
and b is the constant ratio
We know that as x increases by a constant value, the value of y increases by a common ratio. This is characteristic of all exponential functions.
To determine whether the set of ordered pairs satisfies an exponential function, the condition that 'The x -coordinates must have a constant increment' must be satisfied.
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