Answer:
Step-by-step explanation:
It seems that the question was cut off before it was completed. To provide an answer related to the domain in mathematical terms, the domain is an essential component of a function. Let me explain it in detail:
In mathematics, when we talk about a function, f(x), the domain of the function represents the set of all possible input values (x-values) for which the function is defined. It's essentially the set of "allowable" values that we can plug into our function to get an output.
To determine the domain of a given function, we have to consider the nature of the function itself and any mathematical rules or constraints that apply. Here are several examples that can come up:
1. **For a polynomial function**, such as f(x) = x^2 - 3x + 2, there's no restriction on the x-values. So the domain is all real numbers, often written as (-∞, ∞).
2. **For a rational function** (a ratio of two polynomials), like f(x) = (2x + 1) / (x - 3), we must exclude x-values that would make the denominator equal to zero, since division by zero is undefined. In this case, the domain is all real numbers except x = 3, or in interval notation: (-∞, 3) U (3, ∞).
3. **For a square root function**, such as f(x) = √(x - 4), the expression inside the square root must be non-negative, since we're typically considering real-valued functions. So the domain of this function is x ≥ 4, or in interval notation, [4, ∞).
4. **For a logarithmic function**, like f(x) = log(x), the argument of the logarithm must be positive. Therefore, the domain is x > 0, or in interval notation, (0, ∞).
5. **For trigonometric functions**, such as f(x) = sin(x), since there are no restrictions on the input of sine function in terms of real numbers, the domain is all real numbers.
In conclusion, to define the domain of a particular function, we need to consider the mathematical constraints such as not dividing by zero, keeping the radicand of square roots non-negative, and ensuring the arguments of logarithms positive, among others. Once these conditions are taken into account, we can specify the domain of the function, which is often expressed as an interval or a set of intervals on the real number line.
Find the center, vertices, and foci of the ellipse. Simplify your answers as much as possible.
Answer:
1)center =(-2,3)
2) Vertices = (8,3) and (-12,3)
3) foci =(4,3) and (-8,3)
Step-by-step explanation:
As the general equation of ellipse with center at (h,k) is given by:
(x-h)^2/a^2 +(y-k)^2/b^2 = 1
where a=radius of the ellipse along the x-axis
b=radius of the ellipse along the y-axis
h, k= the x and y coordinates of the center of the ellipse.
Given equation of ellipse:
(x+2)^2/100 + (y-3)^2/64 = 1
1)
Finding center:
comparing with the general formula
h=-2 and k=3
Center of given ellipse is at (-2,3)
2)
Finding vertices:
comparing given equation of ellipse with the general formula:
a^2= 100 and b^2=64
then a = 10 and b=8
As a>b, it means the ellipse is parallel to x-axis
hence vertices along the x-axis are a = 10 units to either side of the center i.e (8,3) and (-12,3)
The co-vertices along the y-axis are b=8 units above and below the center i.e (-2,11) and (-2,-5)
3)
Finding Foci, c:
From equations of general ellipse we have a^2 - c^2=b^2
Putting values of a^2=100 and b^2=64 in above
100-c^2=64
c^2=100-64
= 36
taking square root on both sides
c=6
foci of given ellipse is either side of the center (-2,3) that is (4,3) and (-8,3)!
Translate the word phrase into a math expression: nine more than the quotient of a number and five
Answer: [tex]\frac{x}{5}+9[/tex]
Step-by-step explanation:
Let be "x" the number mentioned in the given phrase.
"...the quotient of a number and five" indicates a division. In other words, the number "x" is divided by 5. This can represented as:
[tex]\frac{x}{5}[/tex]
Now, "Nine more than the quotient of a number and five" indicates that you need to add 9 to the quotient of a number and five ( [tex]\frac{x}{5}[/tex]).
Knowing this, you can conclude that the translation of "Nine more than the quotient of a number and five" into a math expression is:
[tex]\frac{x}{5}+9[/tex]
Final answer:
The word phrase 'nine more than the quotient of a number and five' translates to the math expression '(x/5) + 9', where 'x' represents the number.
Explanation:
To translate the word phrase 'nine more than the quotient of a number and five' into a math expression, we first identify the quotient of a number and five, which is denoted as ‘x ÷ 5’ or ‘x/5’ where x represents the number. Next, we address the phrase 'nine more than', which indicates that we need to add nine to that quotient. So, the phrase translates to the algebraic expression ‘(x/5) + 9’.
Therefore, as per the above explaination, the correct answer is (x/5) + 9
The transformation (x,y) -> (x + 4,y – 3) is performed on the line segment AB.
The image is the line segment A' B' where point A' = (3, -3) and point B' = (5,-3).
What are the coordinates of A and B in line segment AB?
A. A=(-1,6), B = (1,-6)
B. A= (-1,0), B = (1,0)
C. A = (7,6), B = (9,–6)
D. A = (7,0), B = (9,0)
It’s either d or A but I’m sure it’s A
Help please (10 points)
Answer:
A = 13 cm^2
Step-by-step explanation:
The area of a triangle is
A = 1/2 bh where b is the length of the base and h is the height
A = 1/2 (6.5) * 4
A = 13 cm^2
can anyone solve this for me pleaee ??
Let Poly = X
Andy gets twice as much as Poly so Andy = 2X
Pheobe gets three times as much as Andy, so she is 3(2x) = 6X
Now add them together to equal 270:
X + 2X + 6X = 270
Simplify:
9X = 270
Divide both sides by 9:
X = 270 /9
X = 30
Poly = X = 30
Andy = 2X = 2(30) = 60
Pheobe = 6X = 6(30) = 180
2. What is the experimental probability of rolling a 4
3. Getting at least one tail
Experimental and theoretical
Answer:
1. 40%
2. The theoretical probability is 3% greater than the experimental probability.
Step-by-step explanation:
We are informed that a number cube is rolled 20 times and the number 4 is rolled 8 times. The experimental probability of rolling a 4 is;
(the number of times a 4 was rolled)/(total number of rolls)
8/20 = 0.4
0.4*100 = 40%
The experimental probability of obtaining at least one tails, one or more tails, is represented in mathematical notation as;
P(HT or TH or TT)
The above events are mutually exclusive, thus;
P(HT or TH or TT) = P(HT) + P(TH) + P( TT)
= (22+34+16)/(28+22+34+16)
= 0.72 = 72%
On the other hand, the theoretical probability of obtaining at least one tails,
P(HT or TH or TT) = 3/4
= 75%
This is because there is at least one tail in 3 out of 4 possible outcomes.
Therefore, it is true to say that the theoretical probability is 3% greater than the experimental probability.
Answer:
1. 40%
2. The theoretical probability is 3% greater than the experimental probability.
Step-by-step explanation:
1. Lets define experimental probability first.
Experimental probability is the probability of an event's occurrence when the experiment was conducted.
The number cube is rolled 20 times, so our sample space is 20.
And the number 4 came in result 8 times, so the the event space is 8.
So,
Experimental Probability = 8/20
=> 0.4
Converting into percentage will give:
=> 40%
So the first option is correct.
2. First we have to find the theoretical probability of getting at least one tail when two coins are tossed
The sample space is {HH, HT, TH, TT}
3 out of these 4 outcomes contain at least one tail
So the theoretical probability of getting at least one tail is: 3/4
=> 0.75 or 75%
Now for the experimental probability,
The total sample space is 28+22+34+16 = 100
The number of favorable outcomes are(Which contain at least one tail):
22+34+16 = 72
So, experimental probability of getting at least one tail = 72/100
=> 0.72 or 72%
We can see that the theoretical probability is 3% greater than the experimental probability. So second option is correct..
how much is 5/9 of -3/5
a.1/2
b.-1/3
c.1/7
d.-25/27
Answer:
b.-1/3
Step-by-step explanation:
Is means equals and of means multiply
W =5/9 * (-3/5)
W = -3/9
W = -1/3
10. A cliff on the seashore is eroding at the rate of 17 centimeters per year. Write and solve an equation to find the number of
years in which the cliff will erode 85 centimeters.
Answer: 17x = 85
Step-by-step explanation:
X is the number in which you'd multiply 17 by to equal 85, therefore x = the number of years.
Answer: Equation would be,
17x = 85
Where, x represents the number of year.
Step-by-step explanation:
Let x represents the number of year after which the cliff erodes 85 centimeters,
Since, the cliff on the seashore is eroding at the rate of 17 centimeters per year,
So, the total eroding of cliff after x years = 17x
[tex]\implies 17x = 85[/tex]
Which is the required equation..
why is the answer actually 1 not 0
-2^2÷ -2^2=1
(-2)(-2)÷ (-2)(-2)=1
4 ÷4=1
Answer is 1
Answer:
Any number divided by itself is 1.
Step-by-step explanation:
One of the nice parts about algebra is that -- if a number appears more than once -- you can make things a lot cleaner looking by throwing them in a variable. Let's let x = -2² . Our equation then becomes x ÷ x = 1, and it's much clearer here that, since we're dividing x by itself, the answer should clearly be one.
Simplify the given expression.
Answer:
C. [tex]\frac{32g^2}{3h^4}[/tex]
Step-by-step explanation:
Answer:
Option C is correct
Step-by-step explanation:
[tex]\frac{\frac{h}{3g^2}}{\frac{h^5}{32g^7}}[/tex]
We need to simplify the above expression.
We can write the above expression as:
[tex]\frac{h}{3g^2}\div\frac{h^5}{32g^7}[/tex]
Changing division sign into multiplication and reciprocating the second term we get,
[tex]\frac{h}{3g^2}*\frac{32g^7}{h^5}[/tex]
Applying the power rule: a^m/a^n = a^{m-n}
Solving:
[tex]\frac{h*32g^7}{3g^2*h^5}\\\\\frac{32g^{7-2}}{3h^{5-1}}\\\frac{32g^5}{3h^4}[/tex]
So, Option C is correct.
Different groups of 100 graduates of a business school were asked the starting annual salary for their first job after graduation, and the sampling variability was low. If the average salary of one of the groups was $96,000, which of these is least likely to be the average salary of another of the groups?
Given the low sampling variability, the average annual salary for the other group of the business school graduates is most likely to be close to $96,000. Thus, extreme values, significant higher or lower than $96,000, are less likely.
Explanation:In the domain of statistics, when the sampling variability is low, it means that most of the samples drawn from a population will have averages (means) that are close to the population mean. The data from the samples will be clustered around a single value.
In this context, given that the average salary of one group was $96,000, the salaries of the other groups are also likely to be around this value given the low sampling variability. Therefore, an average annual salary that is significantly higher or lower than $96,000 for another group would be least likely.
By using the concept of sampling variability, we could reasonably predict that extremes, such as $40,000 or $150,000, would be highly unlikely as average salaries for the other groups if the business school graduates' salaries are distributed normally and the sampling variability is indeed low.
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slope of the line 4x−8y=20
Answer:
y=1/2x-2.5
Step-by-step explanation:
4x-8y=20
Subtract 4x from both sides to get the 8y on on side.
-8y=-4x+20
divide -8 from both sides to get the y by itself.
y=1/2x-2.5
idk the equation is
[tex]\bf \textit{area of a square}\\\\ A=s^2~~ \begin{cases} s=&sides'\\ &length\\ \cline{1-2} A=&150 \end{cases}\implies 150=s^2\implies \sqrt{150}=s~~ \begin{cases} 150=&2\cdot 3\cdot 5\cdot 5\\ &2\cdot 3\cdot 5^2 \end{cases} \\\\\\ \sqrt{2\cdot 3\cdot 5^2}=s\implies 5\sqrt{2\cdot 3}=s\implies 5\sqrt{2}\cdot \sqrt{3}=s[/tex]
well then, we have a couple of known fellows, √2 and √3.
now, let's bear in mind that 2 and 3 are both prime numbers, a prime number is not divisible by anything but itself or 1, so we will never find two same-values that will give us either 2 or 3, namely, there's no exact root for √2 or √3, which means they're both irrationals, and therefore since they're factors of the answer, the answer is irrational.
Which transformations will produce similar, but not congruent, figure
Rotations, translations and reflections are transformations that preserve areas, so they always produce congruent figures.
So, the only way you have to produce a similar but not congruent figure is to use dilation with a scale different than 1.
A painter leans a 13ft ladder against a house. The base of the ladder is 5ft from the house. How high on the house does the ladder reach?
Answer:
13,92838827718412ft
Step-by-step explanation:
a² + b² = c²
a = 13ft
b = 5ft
169 + 25 = 194
c = √194
c = 13,92838827718412ft
Keisha is solving the equation 7 to the power of x equals 9. Which equation shows the first step she should take?
Question 4 options:
log 7 to the power of x equals log 9
log 7 to the power of x equals 9
7 x equals log 9
log 7 to the power of x equals ln 9
Mary is solving the equation 2 to the power of n end power minus 3 equals 83. Her first three steps are shown:
Step 1: 2 to the power of n end power minus 3 equals 83
Step 2: 2 to the power of n equals 86
Step 3: ln 2 to the power of n end power equals ln 86
Which equation could be Step 4?
Question 5 options:
n equals ln 86 minus ln 2
ln 2 equals n ln 86
n plus ln 2 equals ln 86
n ln 2 equals ln 86
What is the exact solution of 2 e to the power of x equals 14?
Question 6 options:
ln 7
ln 12
2 ln 14
2 ln 7
Answer:
The correct answers are:
Question 4: the first step Keisha should take is: log to the power of x equals log 9.
Question 5: step 4 could be n ln 2 equals ln 86
Question 6: the exact solution is x=ln(7)
Step-by-step explanation:
Ok,
Question 4: the equation that shows the first step Keisha should take is:
[tex]7^{x}=9[/tex]
[tex]log(7^{x} )=log(9)[/tex]
[tex]x(log(7))=log(9)[/tex] (applying the properties of logarithms)
[tex]x=\frac{log(9)}{log(7)} =1.129[/tex]
Solution: the first step Keisha should take is: log to the power of x equals log 9.
Question 5: Her first three steps are:
[tex]2^{n}-3=83[/tex]
[tex]2^{n}-3+3=83+3[/tex] (adding 3 to both sides)
[tex]2^{n}=86[/tex]
[tex]2^{n}-3+3=83+3[/tex]
[tex]nln(2)=ln(86)[/tex]
Solution: step 4 is: [tex]nln(2)=ln(86)[/tex] (applying the properties of logarithms)
Question 6: The exact solution of 2 e to the power of x equals 14 is:
[tex]2e^{x}=14[/tex]
[tex]\frac{2e^{x} }{2} =\frac{14}{2}[/tex] (dividing both sides by 2)
[tex]e^{x}=7[/tex]
[tex]xln(e)=ln7[/tex] (ln(e)=1)
[tex]x=ln(7)[/tex]
Solution: [tex]x=ln(7)[/tex]
For Keisha's equation, the first step involves taking the logarithm of both sides, and for Mary's equation, the fourth step involves taking the natural logarithm. The exact solution for the third equation is x = ln 7.
Question 4:
Keisha is solving the equation [tex]\(7^x = 9\)[/tex]. The correct first step is:
[tex]\[ \log(7^x) = \log(9) \][/tex]
So the correct option is:
[tex]\[ \text{log } 7^x = \text{log } 9 \][/tex]
Question 5:
For Mary's equation [tex]\(2^n - 3 = 83\)[/tex], Step 4 involves taking the natural logarithm:
[tex]\[ n \ln 2 = \ln 86 \][/tex]
So the correct option is:
[tex]\[ n \ln 2 = \ln 86 \][/tex]
Question 6:
The equation [tex]\(2e^x = 14\)[/tex] can be solved by taking the natural logarithm:
[tex]\[ x = \ln \left(\frac{14}{2}\right) \][/tex]
Simplifying this gives:
[tex]\[ x = \ln 7 \][/tex]
So the correct option is:
[tex]\[ \ln 7 \][/tex]
Which system of equations has no solutions?
Answer:
A
Step-by-step explanation:the lines do not cross therefor the two equations do not share a solution.
Answer:
A
Step-by-step explanation:
Please answer and explain!
multiply and simplify -3x^2y^2 * y^4x3
a. -3x^5y^6
b. -3x^6y^2
c. 9x^5y^2
d. -3x ^5y^2
Answer:
a. [tex]-3x^{5}y^{6}[/tex]
Step-by-step explanation:
We want to multiply and simplify:
[tex]-3x^2y^2\times y^4x^3[/tex]
We rearrange the product to obtain:
[tex]-3x^2\times x^3\times y^2\times y^4[/tex]
Recall that:
[tex]a^m\times a^n=a^{m+n}[/tex]
We apply this property to obtain:
[tex]-3x^{2+3}y^{2+4}[/tex]
We simplify to obtain:
[tex]-3x^{5}y^{6}[/tex]
Misha wrote the quadratic equation 0=-x2+4x-7 in standard form. what is the value of c in her equation
Answer:
Final answer is c=-7.
Step-by-step explanation:
Given equation is [tex]0=-x^2+4x-7[/tex].
Now question says that Misha wrote the quadratic equation 0=-x2+4x-7 in standard form. Now we need to find about what is the value of c in her equation.
We know that standard form of quadratic equation is given by [tex]ax^2+bx+c=0[/tex].
compare given equation with the standard form, we find that -7 is written in place of +c
so that means +c=-7
or c=-7
Hence final answer is c=-7.
Which is the standard form of the equation of a parabola with a focus of (0, –3) and its vertex at the origin?
Answer:
A : x^2 = -12y
Step-by-step explanation:
TO ALL MY EDGE PEOPLE
Answer:
a) x^2=-12y
Step-by-step explanation:
each leg of a 45-45-90 triangle measures 14 cm what is the length of the hypotenuse
ANSWER
The hypotenuse is 14√2 units.
EXPLANATION
Let the hypotenuse be x, then we can use the Pythagoras Theorem to find the length of the hypotenuse.
We have from the question that, each leg of the 45-45-90 triangle measures 14 cm.
Then, the Pythagorean Theorem, gives:
[tex] {x}^{2} = {14}^{2} + {14}^{2} [/tex]
[tex] {x}^{2} = 2 \times {14}^{2} [/tex]
Take positive square root to obtain;
[tex]x = \sqrt{ {14}^{2} \times 2} [/tex]
This simplifies to
[tex]x = 14 \sqrt{2} [/tex]
The length of the hypotenuse of the 45-45-90 triangle is 19.796 cm.
In a 45-45-90 triangle, the two legs are congruent (they have the same length) and the length of the hypotenuse is equal to the length of the legs multiplied by the square root of 2.
Given that each leg of the triangle measures 14 cm, the length of the hypotenuse can be calculated as follows:
Length of hypotenuse = Length of leg × √2
Length of hypotenuse = 14 cm × √2
Using a calculator or approximating the square root of 2 to 1.414, we can find:
Length of hypotenuse ≈ 14 cm × 1.414
Length of hypotenuse ≈ 19.796 cm (rounded to three decimal places)
Therefore, the length of the hypotenuse of the 45-45-90 triangle is approximately 19.796 cm.
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Need Help On This Problem PLZ :-)
Answer:
y = 9 + 19x
Step-by-step explanation:
To find the equation matching a set of data, you simply try a few values for x and see if by solving that side of the equation you get the value of y. If you do, you found your equation.
You have a big advantage here... since you have the value of y when x = 0.
When x = 0, y = 9, that's a very important data to have to simplify your research.
Let's try the value of 0 for x in each of the given equations:
y = 18 + 10 (0) = 18 --- NO
y = 9 + 19 (0) = 9 --- YES! We can confirm with another value of x:
y = 9 + 19 (1) = 28 --- YES! Confirmed!
y = 9 + 19x is your answer!
what ratio is the same as 2/3?
The ratios 4/6 and 8/12 are equivalent ratio of 2/3 which we obtain by multiplying or dividing both numerator and denominator by same number.
To find a ratio that is the same as 2/3, we can multiply or divide both the numerator and the denominator by the same non-zero number.
This will result in an equivalent ratio.
If we multiply both the numerator and denominator of 2/3 by 2, we get:
(2 × 2) / (3 × 2)
= 4/6
Therefore, the ratio 4/6 is the same as 2/3.
Similarly, if we multiply both the numerator and denominator of 2/3 by 2, we get:
8/12
So, the ratio 8/12 is also the same as 2/3.
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A group of 40 students went on a field trip. Exactly 8 students wore blue shirts. What percent of the students on the field trip wore a blue shirt?
20% of the students wore blue shirts
40 x 0.08 = 3.2
3.2% out of the 40 students wore blue shirts.
Please help I’m very confused
Hello! The interquartile range would be 5°
You must subtract Quartile one from quartile 3 to find iqr
Solve the following inequality. Then place the correct number in the box provided. 3x < 18
For this case we must solve the following inequality:
[tex]3x <18[/tex]
Dividing between 3 on both sides of the inequality we have:
[tex]x <\frac {18} {3}\\x <6[/tex]
Thus, the solution of the variable "x" is given by all the numbers smaller than 6.
Answer:
All values of "x" less than 6.
(-∞, 6)
The population of a specific strain of bacteria in a culture medium is given by f(x) = x + 3 where f(x)is the population in millions and x
is the time in hours. Find the piecewise function that matches this absolute value function. Then, graph the function using a graphing calculator
and describe what you see.
Answer:
Step-by-step explanation:
f(x) = { 0, x<0; 0 <= x, (x +3) * 1000000 }
(Note the graph ought to flatten to zero for x < 0)
ANSWER:
You need to write it’s piecewise function if
x < -3, the term x+3 becomes negative. So , for all values of x < -3 , the term becomes -(x+3)
Piecewise will be
F(x) = square root of (x+3) when x is greater than or equal to -3
F(x) = square root of -(x+3) when x less than or equal to -3
Solve please I need help
Answer:
28
Step-by-step explanation:
We can see that all the angles are inside of a triangle and the sum of the interior angle of the triangle is 180 degrees.
Knowing this, we know that the sum of all the angles present is 180 degrees.
1st angle can be seen as 90 degrees, 2nd angle is x+6 and the 3rd is 2x.
The sum can be written as ( 90 + x + 6 + 2x ) and this equals to 180 degrees.
90 + x + 6 + 2x = 180
96 + 3x = 180
( subtract 96 on both sides )
3x = 180 - 96
3x = 84
( divide by 3 on both sides )
x = 84 / 3
x = 28
Answer:
x = 28
Step-by-step explanation:
Consider the lower right triangle
The 2 given angles sum to 90° ( sum of angles in a triangle = 180° )
Hence
x + 6 + 2x = 90
3x + 6 = 90 ( subtract 6 from both sides )
3x = 84 ( divide both sides by 3 )
x = 28
2{[11(a-2)+12]-[2(5a-3)+a)}. Help me solve this please
Let's simplify step-by-step.
2(11(a−2)+12)−(2(5a−3)+a)
Distribute the Negative Sign:
=2(11(a−2)+12)+−1(2(5a−3)+a)
=2(11(a−2)+12)+−1(2(5a−3))+−1a
=2(11(a−2)+12)+−10a+6+−a
Distribute:
=(2)(11(a−2))+(2)(12)+−10a+6+−a
=22a+−44+24+−10a+6+−a
Combine Like Terms:
=22a+−44+24+−10a+6+−a
=(22a+−10a+−a)+(−44+24+6)
=11a+−14
Answer:
=11a−14
Which two cloud numbers round to 8 7.66 7.19 9.47
Answer:
It would be 7.66 and 7.19 because you can not round downward although I am a little confused on how 7.19 is able to round upwards But I am positive 7.66 rounds up to 8
Step-by-step explanation: