Find the domain of f(x) = -√√²-4.
Ox≥ 2 orx≤ - 2
Ο x >2
0x2 -2 or x ≤ 2
O all real numbers
The domain of the given function is x≤-2
What are functions?Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given here: The function f(x)=-√(√-4x)²
Simplifying the expression we get
f(x)=-√(√-4x)²
f(x)= -√-4x
Case 1) If the domain of x is greater than 2 then we have
f(3)=-√-12 which is a complex number and thus is not possible.
Case2 id x≤-2
then we have
f(-2)=-√8 which is not complex
Thus the feasible domain of the function is given by x≤-2
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Triangle RST is shown in the coordinate plane. What are the coordinates of R'S'T' if the figure is reflected over the x-axis and translated down two units? Responses (1, 2), (1, 5), (6, 5) (1, 2), (1, 5), (6, 5), (1, -6), (1, -9), (6, -9) (1, -6), (1, -9), (6, -9) , (3, 2), (3, 5), (8, 5) (3, 2), (3, 5), (8, 5) ,(3, 4), (3, 7), (8, 7) (3, 4), (3, 7), (8, 7) ,
The reflected and then translated coordinates of the triangle are R'( 3,2), S'(3,5), and T'( 8, 5).
What is reflection?A sort of symmetry known as reflective symmetry occurs when one half of an object mirrors the other half. It also goes by the name "mirror symmetry."
For instance, both the left and right sides of a human face are typically the same. Most butterflies have identical wings on their left and right sides.
The given points of the triangle are R(3,-4), S(3,-7), and T(8,-7).
The reflected points of the triangle will be:-
R(3,-4) = R'( 3, 4)
S(3,-7) = R'(3,7)
T(8,-7) = R(8, 7)
The translated points by 2 units down will be:-
R'( 3, 4) = R''( 3, 2)
R'(3,7) = S''( 3, 5)
R(8, 7) = T''(8,5)
Therefore, the reflected and then translated coordinates of the triangle are R'( 3,2), S'(3,5), and T'( 8, 5).
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Answer:
so the other guy can get brainlyest
Step-by-step explanation:
pls like and rate
A regular polygon has an interior angle of 172°. Find the exterior angle and work out how many sides it has.
Answer:
Hi my dream princess
A regular polygon with an interior angle of 172° has the following characteristics:
Exterior angle: 360° / number of sides - interior angle.
Number of sides: 360° / exterior angle.
Using this information, we can find the exterior angle and the number of sides:
Exterior angle: 360° / number of sides - 172°.
Number of sides: 360° / (360° / number of sides - 172°).
Solving for the number of sides, we have:
Number of sides: 360° / (360° / number of sides - 172°)
= 360° / (360° / number of sides) - 172° / (360° / number of sides)
= number of sides - 172° / (360° / number of sides)
= number of sides (1 - 172° / 360°)
= number of sides * 188° / 360°.
Since we have a fraction involving a fraction, we can simplify:
Number of sides = number of sides * 188° / 360°
= number of sides * 47° / 90°
= number of sides * 47 / 90.
Since 47 and 90 are both divisible by 47, we can simplify further:
Number of sides = number of sides * 47 / 90
= number of sides * 1 / 2.
Therefore, the regular polygon has 2 sides and each exterior angle is 180°. The polygon is an isosceles triangle.
6. RSTU and MNOP are similar. Find the scale factor of RSTU to MNOP. Then find the values of x and y. Show your work.
The scale factor is 1.4
the value of x is 4.2
the value of y is 130
How to find the scale factorThe scale factor is calculated by checking the proportions of the sides
Let the scale factor be k
10k = 14
k = 14/10
k = 1.4
solving for x
15 * k = 5x
15 * 1.4 = 5x
5x = 21
x = 21 / 5
x = 4.2
solving for y
y + 50 = 180
y = 180 - 50
y = 130
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a circle is divided into 4 sectors, the ratio of whose areas is what is the central angle of the largest sector in degrees?
With the ratio of 1 : 2 : 3 : 6, the central angle of the largest sector of the circle is 180°.
A circle is a two-dimensional shape consisting of all points in a plane that are at a given distance from the center. Equivalently, we can define a circle to be the curve traced out by a point that moves in a plane so that its distance from the center (a given point) is constant.
A sector is defined to be a part of a circle that is made of the arc of the circle along with its two radii. The shape of a sector of a circle is identical to the shape of a slice of pie or pizza.
We're given a ratio of 1 : 2 : 3 : 6 of all the 4 sectors of a circle. The largest sector in degrees is indicated by 6 out of 12 (12 being the sum of numbers in the ratio). We know that a circle is divided into 360°. Therefore, the central angle θ of the largest sector is:
θ = 6/12 x 360°
θ = 1/2 x 360°
θ = 180°.
The complete question is "A circle is divided into 4 sectors, and the ratio of whose areas is 1 : 2 : 3 : 6. What is the central angle of the largest sector in degrees?"
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Which two square roots are used to estimate Start Root 47 End Root?
Answer:4
Step-by-step explanation: answer 4
Write a conjecture that describes the pattern in each sequence. Then use your conjecture to find the next item in the sequence. 1, 10, 100, 1000
The conjecture that describes the pattern in each sequence is *10, the next item in the sequence. 1, 10, 100, 1000 is 10000.
What is a geometric sequence and how to find its nth terms?Suppose the initial term of a geometric sequence is a
and the term by which we multiply the previous term to get the next term is r
Then the sequence would look like
[tex]a, ar, ar^2, ar^3, \cdots[/tex]
(till the terms to which it is defined)
Thus, the nth term of such sequence would be T_n = ar^{n-1} (you can easily predict this formula, as for nth term, the multiple r would've multiplied with initial terms n-1 times).
Given;
The following sequence that can be used in our computation:
1,10,100,1000
In the above sequence, we can see that 4 is added to the previous term to get the current term
Using the above as a guide,
Next term = 1000*10
Evaluate
Next term = 10000
Therefore, the next term of sequence will be 10000.
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when constructing a confidence interval for a population proportion, we check that the sample size is less than 10% of the population size. a. why is it necessary to check this condition? b. what happens to the capture rate if this condition is violated?
(a) A reasonable guideline for ensuring that the sample size is small enough to give credible findings is to confirm that the sample size is less than 10% of the population size.
(b) The confidence interval may not correctly reflect the genuine population proportion, resulting in incorrect inferences and actions based on the findings.
(a)
This condition must be checked since the sample size must be much less than the population size to ensure that the sample is representative of the population. A high sample size may not fully represent the population, resulting in biased results.
(b)
If the sample size exceeds 10% of the population size, the "10% criterion" is violated. When this requirement is broken, the capture rate may rise, but the accuracy of the confidence interval may fall. As a result, the confidence interval may grow broader and less reliable in capturing the genuine population percentage.
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The perimeter of a rectangle is 76 inches. Find the length and width if the length is an integer and the width is 2 times the next consecutive integer.
The length and the width of the rectangle are 8. 5 inches and 21 inches
How to determine the value of the sidesIt is important to note the the formula for the perimeter of a rectangle is expressed as;
P = 2(L + W)
Given that;
P is the perimeter of the rectangleL is the length of the rectangleW is the width of the rectangleWe have that;
P = 76 Inches
L = l
W = 2(l + 2)
Substitute the values
76 = 2( l + 2l + 4)
collect like terms
76 = 2(4l + 4)
expand the bracket
76 = 8l + 8
collect like terms
8l = 68
l = 8. 5 inches
Width, w = 21 inches
Hence, the values are 21 inches and 8. 5 inches
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The length and width of the rectangle are 12inches and 26 inches
What is perimeter of a rectangle?The perimeter is the length of the outline of a shape. To find the perimeter of a rectangle or square you have to add the lengths of all the four sides.
Represent the length of the rectangle by x and width by y
y = 2(x+1)
P = 2(l+w)
Represent 2(x+1) for y
P= 2(x + 2( x+1) )
P= 2( x+ 2x +2)
P = 2(3x+2)
P =6x +4
76 = 6x +4
6x = 76 - 4
6x = 72
divide both sides by 6
x = 72/6
x = 12
y = 2( 12+1)
y = 2× 13
y = 26 inches
therefore the length of the rectangle is 12inches and the width is 26inches
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Look at picture below!
The cardinal number of the set , n ( D ) = 1 .
What is the cardinal number of a set ?The natural numbers that are used to determine the cardinality of sets are extended into cardinal numbers . The shortened term "cardinals" is frequently used to describe cardinals. The number of objects contained within a finite set , known as the cardinality , is equal to a natural number .
The cardinal number here would therefore be the number of unique values which is only 1 and that 1 is eight .
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The dog shelter has Labradors, Terriers, and Golden Retrievers available for adoption. If P(terriers) = 15%, interpret the likelihood of randomly selecting a terrier from the shelter.
Likely
Unlikely
Equally likely and unlikely
This value is not possible to represent probability of a chance event
Answer:
likely
Step-by-step explanation:
The value of 15% does not represent the probability of randomly selecting a terrier from the shelter. Probability is a measure of the likelihood that a certain event will occur, and 15% does not provide enough information to calculate a probability.
Wich are the dividers of 25? And 120 and 71 and 24
Answer:
the dividers of 25 are: 1, 5, and 25.
the dividers of 120 are: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.
the dividers of 71 are: 1, 71.
The dividers of 24 are: 1, 2, 3, 4, 6, 8, 12, and 24.
Step-by-step explanation:
given a list of a finishing times at a marathon, which function should you use to rank each runner's place based on these finishing times?
Answer:
Below
Step-by-step explanation:
Rank in order of SHORTEST time to LONGEST time ....
shorter times mean the runner was faster to the finish line.
You are having a conference call with the CEO of a paper company. You have interpreted the number of trees cut down versus profit as the function P(x) = x^3 - 5x^2 − 2x + 24.
A.) how many zeros/roots will we have? Explain how you know. (1 points)
B.) What are the x-intercepts/roots/zeros? Show your work for finding these... (This should take some work to find! We did this in section 4.6) (5 points)
C.) What is the y-intercept of the graph? Explain how you know. (1 points)
D.) Describe the end behavior of this graph (3 points)
a) The number of zeros of the function is given as follows: 3.
b) The x-intercepts of the function are given as follows: x = -2, x = 3 and x = 4.
c) The y-intercept of the graph is given as follows: y = 24.
d) The end behavior of the function is given as follows: As x -> -∞, f(x) -> -∞, and as x -> ∞, f(x) -> ∞.
How to obtain the features of the function?The function is of the third degree, as it has a higher exponent of 3, hence the number of zeros is of 3.
The x-intercepts are the values of x for which the graph of the function crosses the y-axis, hence they are given as follows:
x = -2, x = 3 and x = 4.
The y-intercept is the graph of y when the graph of the function crosses the y-axis, hence it is given as follows:
y = 24.
The end behavior is given as follows:
Decay to left: As x -> -∞, f(x) -> -∞.Increases to right: as x -> ∞, f(x) -> ∞.More can be learned about functions at https://brainly.com/question/24808124
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Generally, which one of the following is the least appropriate measure of central tendency for a data set that contains outliers? a. mean b. median c. 2nd quartile d. 50th percentile An important measure of location for categorical data is the a. mean b. median c. mode d. margirn
mean the least appropriate measure of central tendency for a data set that contains outliers
What is a mean in math?The mean (aka the arithmetic mean, different from the geometric mean) of a dataset is the sum of all values divided by the total number of values. It's the most commonly used measure of central tendency and is often referred to as the “average.The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data setMean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers. Mean = (Sum of all the observations/Total number of observations) Example: What is the mean of 2, 4, 6, 8 and 10To learn more about mean refers to:
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what is the correct solution for the arithmetic expression (2 8)/2*9/3 using the order of operations employed by oracle 12c when solving equations?
The correct solution to the arithmetic expression (2 8)/2*9/3 using the order of operations as employed by Oracle 12c when solving equations is 4.
According to the Order of Operations, the first step is to evaluate expressions inside parentheses, then perform any multiplications or divisions, and finally perform any additions or subtractions. In this expression, the first step would be to evaluate the expression inside the parentheses: (28)/2. This evaluates to 14.
Next, the expression becomes 14 * 9/3. According to the Order of Operations, we need to perform the multiplication first, so 14 * 9 = 126. Finally, we perform the division: 126/3 = 42.
So, the correct solution to the expression (2 8)/2 * 9/3 is 42.
Order of operations is a set of rules used to determine the sequence in which arithmetic operations should be performed in a mathematical expression to obtain the correct result. The rules ensure that operations are performed in a consistent and predictable manner.
The order of operations is typically represented by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
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The line representing the equation part of the constraint 7x1 + 4x2 s 28 goes through the following two points a) (4,0) and (7,0). b) (0, 4) and (7,0). c) (4,0) and (0,7). d) (0, 4) and (0,7). e) none of the above
The required line representing the equation part of the constraint is go through (0, 4) and (7,0).
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
According to question:The line representing the equation 7x1 + 4x2 = 28 is a boundary line that separates the feasible solutions from the infeasible solutions in a linear programming problem.
The line passes through two points, which can be determined by substituting the x1 and x2 values into the equation. By substituting the values (4,0) and (7,0) into the equation, we can see that both points satisfy the constraint.
This means that any point on the line also satisfies the constraint, and any point above or to the right of the line would be infeasible as they would not meet the requirement of the constraint.
Understanding the position and shape of the constraint lines is important in solving linear programming problems and finding the optimal solution.
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HELP PLS !!!!
5. Explain how iteration and using a recursive formula are similar.
1. iteration is similar to using a recursive formula because you use the output from the previous calculation as the input to find the next answer
2. Iteration uses the subsequent value to find the previous value, and recursive formulas require a sequence to work
3. Iteration is similar to using a recursive formula because both processes use the same initial value.
4. Both iteration and recursive formulas generate only arithmetic sequences.
Answer:
1) Iteration is similar to using a recursive formula because you use the output from the previous calculation as the input to find the next answer.
Iteration is similar to using a recursive formula because you use the output from the previous calculation as the input to find the next answer. The correct option is A.
What are iteration and recursive formulas?The process of defining a problem or the solution to a problem in terms of a simpler version of itself is known as recursion. There are two kinds of recursion. The first is direct recursion, and the second is indirect recursion.
As a result, recursion is a method of problem-solving in which the solution is dependent on solutions to smaller instances of the same problem.
Therefore, the correct option is A, which is Iteration is similar to using a recursive formula because you use the output from the previous calculation as the input to find the next answer.
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how many different possible options of combinations are available in binary code using eight bits?
1. 64
2. 16
3. 128
4. 256
There are a total (4) 2⁸ = 256 possible methods to join 8 bits or 8 binary digits.
What are binary codes?A binary code uses a two-symbol system to represent text, computer processor instructions, or any other data.
The binary number system's "0" and "1" are frequently employed as the two symbols in this system.
Each character, command, etc. is given a set of binary digits, often referred to as bits, by the binary code.
A binary string of eight bits (also known as a byte) can, for instance, represent any of 256 possible values and hence a vast range of distinct things.
8 bits, or 8 binary digits, can be combined in 2⁸=256 different ways.
Some of these combinations are shown in the following table.
(The number in parentheses is the equivalent in decimal form.)
Therefore, there are a total (4) 2⁸ = 256 possible methods to join 8 bits or 8 binary digits.
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what information can you gather from the standard deviation, particularly as it pertains to the percentage of normal distribution?
The standard deviation of a data set provides information about the spread or dispersion of the data around the mean.
It helps to determine the percentage of normal distribution in the data. If the standard deviation is small, it indicates that the data is tightly clustered around the mean and a high percentage of the data falls within a few standard deviations of the mean. On the other hand, if the standard deviation is large, it suggests that the data is more spread out and a smaller percentage of the data falls within a few standard deviations of the mean.
In a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. So, the standard deviation provides insight into the proportion of data points that are close to the mean, and therefore, the shape of the distribution.
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A law firm is going to designate associates and partners to a big new case. The daily rate charged to the client for each associate is $600 and the daily rate for each partner is $1200. The law firm assigned a total of 13 lawyers to the case and was able to charge the client $12000 per day for these lawyers' services. Graphically solve a system of equations in order to determine the number of associates assigned to the case, x, and the number partners assigned to the case, y. ( solve by graphing )
The number of associates assigned to the case and the number of partners assigned to the case is 6 and 4.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
Given that,
The daily rate charged to the client for each associate is $600 and the daily rate for each partner is $1100.
The law firm assigned a total of 10 lawyers to the case and was able to charge the client $8000 per day for these lawyers' services.
Here we assume number of associate be x and no of partners be y.
Based on the above information, the calculation is as follows:
x + y = 10
x = 10 - y
Now put the value of x in the below equation
600x + 1100y = 8,000
600 (10 - y) + 1100y = 8000
6000 - 600y + 1100y = 8000
2000 = 500y
y = 4
So x = 10 - 4
= 6
Hence, The number of associates assigned to the case and the number of partners assigned to the case is 6 and 4.
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A survey of 1,000 people was done. 80% of the people surveyed knew all 50 states in alphabetical order. How many of the 1,000 people did not know all 50 states in alphabetical order?
Answer: 200
Becase 80% of 1000 is 800 and 1000- 800 =200
What is the total surface area of the square pyramid below?
The total surface area of the square pyramid is; 336 ft²
How to find the total surface area of the square pyramid?To find the total surface area of the square pyramid, we will first of all calculate the areas of the individual shapes into which it is broken down and then add up to get the total surface area.
Area of a triangle is given by the formula;
A = ¹/₂ * base * height
Thus, area of 4 triangles here is;
A = 4(¹/₂ * 12 * 8)
A = 192 ft²
Area of square = 12 * 12
= 144 ft²
Thus;
Total surface area of square pyramid = 192 + 144
= 336 ft²
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select all answer choices that show a correct comparison A 1/2 < 1/5 B 3/5 > 3/10 C 2/8 < 1/4 D 5/6 > 2/5 E 5/10 > 2/5 HELP WANTED
The true inequalities are:
B) 3/5 > 3/10
D) 5/6 > 2/5
E) 5/10 > 2/5
Which options show a correct compairison?Here we want to see which ones of the given inequalities are true.
Remember that an inequality:
A > B
Is true if the value of A is larger than the one of B.
From the given inequalities, the true ones are:
B) 3/5 > 3/10
That is true because the denominator is smaller on the left side.
D) 5/6 > 2/5
We can rewrite these fractions at:
25/30 > 10/25
E) 5/10 > 2/5
2.5/5 > 2/5
This is also true.
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Are the triangles similar, if so what postulate can you use to prove similarity? *
Answer:
AA postulate
Step-by-step explanation:
We can prove as:
We have vertically opposite angles, which are equal
Also, we have been given two corresponding equal angles, thus we can prove using AA similarity postulate.
Find the equation of the line represented by the graph below.
y = x+
The equation of the line represented by the graph is y = -x/3 + 5.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y are the points.(0,5)(6,3)
Based on the information provided, we can logically deduce the following data points on the line:
Points on x-axis = (0, 6).Points on y-axis = (5, 3).At point (0, 5), a linear equation of this line can be calculated in slope-intercept form as follows:
y - 5 = (3 - 5)/(6 - 0)(x - 0)
y = -2/6(x - 0) + 5
y = -x/3 + 5
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help please will give brainliest no question
Answer:
The penguins swan 2 2/5 miles in one hour
Step-by-step explanation:
A print of a famous painting is 1/3 the size of the original if the original is 9 feet long how long is the print
The print size of the painting is 3 ft long.
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size.
Given that, a print of a famous painting is 1/3 the size of the original, the original is 9 feet long, we need to find the length of the print.
Let the print size of the painting be x ft long,
Since, the scale factor is 1/3
Therefore,
1/3 = 9/x
x = 9/3
x = 3
Hence, the print size of the painting is 3 ft long.
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Consider this expressi
√2³ 7 + |-4|
One way to compute a 15% tip for a bill is to multiply it by 0.15.
A restaurant bill was $42.40.
what do i do ??????
im in middle school
The amount of tip will be $6.36. And the total amount of the restaurant bill with the tip will be $48.76.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
One way to compute a 15% tip for a bill is to multiply it by 0.15. A restaurant bill was $42.40.
Then the amount of tip is given as,
Tip amount = $42.40 x 0.15
Tip amount = $6.36
The total amount is given as,
Total amount = $42.40 + $6.36
Total amount = $48.76
The amount of tip will be $6.36. And the total amount of the restaurant bill with the tip will be $48.76.
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