Find the domain. Then use the drop down menu to select the correct symbols to indicate your answer in interval notation. If a number is not an integer then round it to the nearest hundredth. To indicate positive infinifty ( \infty ) type the three letters "inf". To indicate negative infinity(-\infty ) type "-inf" with no spaces between characters. \frac{ \sqrt[]{x-4} }{\sqrt[]{x-6}} AnswerAnswer,AnswerAnswer
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The domain of a function is all values of x the function can have.
Since this function has radicals, and the value inside a radical needs to be positive or zero, and also the denominator of a fraction can't be zero, we have the following conditions:
[tex]\begin{gathered} x-4\ge0 \\ x\ge4 \\ \\ x-6>0 \\ x>6 \end{gathered}[/tex]Since the first condition contains the second, so the domain set is represented by the second condition:
[tex](6,\text{inf)}[/tex]Related Questions
when a graph is a smooth curve it means that there is not a definite law connecting the two quantities which are plotted true or false
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Question:
When a graph is a smooth curve it means that there is not a definite law connecting the two quantities which are plotted.
Solution:
a smooth curve is by definition a function, so by definition of a function, we have that there is a definite law connecting the two variables (quantities).
Answer: false.
Lashonda deposits $500 into an account that pays simple interest at a rate of 6% per year. How much interest will she be paid in the first 3 years?
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Answer:
The amount of interest she will be paid in the first 3 years is;
[tex]\text{ \$90}[/tex]Explanation:
Given that Lashonda deposits $500 into an account that pays simple interest at a rate of 6% per year. for the first 3 years;
[tex]\begin{gathered} \text{ Principal P = \$500} \\ \text{rate r = 6\% = 0.06} \\ \text{time t = 3 years} \end{gathered}[/tex]Recall the simple interest formula;
[tex]i=P\times r\times t[/tex]substituting the given values;
[tex]\begin{gathered} i=500\times0.06\times3 \\ i=\text{ \$90} \end{gathered}[/tex]Therefore, the amount of interest she will be paid in the first 3 years is;
[tex]\text{ \$90}[/tex]Use the formula for n^P_r to evaluate the following expression.
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Use the following formula:
[tex]_nP_r=\frac{n!}{(n-r)!}[/tex]Then, for 11P6:
[tex]\begin{gathered} _{11}P_6=\frac{11!}{(11-6)!}=\frac{11!}{5!}=\frac{5!\cdot6\cdot7\cdot8\cdot9\cdot10\cdot11}{5!} \\ _{11}P_6=6\cdot7\cdot8\cdot9\cdot10\cdot11=332640 \end{gathered}[/tex]Hence, the result is 332640
231231312312312312311
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Answer: 3456765432345
Step-by-step explanation:
2345676543456
Using this formula and other formulas, find Q1,Q2, Q3 the midquartile, and the interquartile range for the data set.51, 62, 73, 92, 97, 100, 104
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Given:
The given set of data is 51, 62, 73, 92, 97, 100, 104.
The objective is to find Q1,Q2, Q3 the midquartile, and the interquartile range.
Explanation:
The given set of data is already arranged in increasing oder.
To find Q2:
The quartile Q2 represents the middle term of the set of data arranged in increasing order.
The number of terms in the set of data is N = 7.
Then, the middle term of the set of data is 92, which is Q2.
To find Q1:
The quartile 1 represents the middle term of the left side of the Q2.
The left side of Q2 contains 51, 62, 73.
Thus, the middle term of the left side of Q2 is 62, which is Q1.
To find Q3:
The quartile 3 represents the middle temr of the right side of the Q2.
The right side of Q2 contains 97, 100, 104.
Thus, the middle term of the right side of Q2 is 100, which is Q3.
To find midquartile:
The midquartile is termed as the average of highest and lowest value of the set of data.
The highest value in the given set of data is 104 and the lowest value in the given set of data is 51.
Then, the midquartile can be calculated as,
[tex]\begin{gathered} \text{Midquartile}=\frac{104+51}{2} \\ =77.5 \end{gathered}[/tex]To find interquartile:
The
Find the exact value of the expression. No decimal answers. Show all work.Hint: Use an identity to expand the expression.
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Given the expression:
[tex]\cos (\frac{\pi}{4}+\frac{\pi}{6})[/tex]You can expand it by using the following Identity:
[tex]\cos \mleft(A+B\mright)\equiv cos(A)cos(B)-sin(A)sin(B)[/tex]You can identify that, in this case:
[tex]\begin{gathered} A=\frac{\pi}{4} \\ \\ B=\frac{\pi}{6} \end{gathered}[/tex]Then, you can expand it as follows:
[tex]\cos (\frac{\pi}{4}+\frac{\pi}{6})=cos(\frac{\pi}{4})cos(\frac{\pi}{6})-sin(\frac{\pi}{4})sin(\frac{\pi}{6})[/tex]By definition:
[tex]\cos (\frac{\pi}{4})=\frac{\sqrt[]{2}}{2}[/tex][tex]\cos (\frac{\pi}{6})=\frac{\sqrt[]{3}}{2}[/tex][tex]\sin (\frac{\pi}{4})=\frac{\sqrt[]{2}}{2}[/tex][tex]\sin (\frac{\pi}{6})=\frac{1}{2}[/tex]Then, you can substitute values:
[tex]=(\frac{\sqrt[]{2}}{2})(\frac{\sqrt[]{3}}{2})-(\frac{\sqrt[]{2}}{2})(\frac{1}{2})[/tex]Simplifying, you get:
[tex]\begin{gathered} =(\frac{\sqrt[]{2}}{2})(\frac{\sqrt[]{3}}{2})-(\frac{\sqrt[]{2}}{2})(\frac{1}{2}) \\ \\ =\frac{\sqrt[]{6}}{4}-\frac{\sqrt[]{2}}{4} \end{gathered}[/tex][tex]=\frac{\sqrt[]{6}-\sqrt[]{2}}{4}[/tex]Hence, the answer is:
[tex]\frac{\sqrt[]{6}-\sqrt[]{2}}{4}[/tex]what is 40+56 in GCF
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The GCF stands for greatest common factor. To represent a sum by its GCF we need to use the distributive property and we need to first find the GCF of the numbers. Let's break each number by its factors:
[tex]\begin{gathered} 40=2\cdot2\cdot2\cdot5 \\ 56=2\cdot2\cdot2\cdot7 \end{gathered}[/tex]We now multiply the numbers that appear on both.
[tex]\text{GCF}=2\cdot2\cdot2=8[/tex]We now apply the distributive property:
[tex]8\cdot(5+7)[/tex]During Thanksgiving Break, 68% of a school's students ate green bean casserole. Out of 650 students, how many ate green bean casserole?
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650 --- total
650*.68=442
442 students ate green bean casserole
.68 represents the percentage
so for example, if they asked me for 50% of 1000
we need to multiply 1000*0.5
if they asked for 60% we will multiply 1000*0.6
what is 9932.8 rounded to the nearest integer
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ANSWER
9933
EXPLANATION
We have the number 9932.8.
We want to round it to the nearest integer.
An integer is a number that can be written without decimal or fraction.
To do that, we follow the following steps:
1. Identify the number after the decimal
2. If the number is greater than or equal to 5, round up to 1 and add to the number before the decimal.
3. If the number is less than 5, round down to 0.
Since the number after the decimal is 8, we therefore have that:
[tex]9932.8\text{ }\approx\text{ 9933}[/tex]Calculate the slope of the given line using either the slope formula m = y 2 − y 1 x 2 − x 1 or by counting r i s e r u n . Simplify your answer. You can choose your method.
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The slope of the line that passes through points (x1, y1) and (x2, y2) is computed as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Replacing with the points (-8, 3) and (0,1) we get:
[tex]m=\frac{1-3}{0-_{}(-8)}=\frac{-2}{8}=-\frac{1}{4}[/tex]White the standard form of the equation of the line through the given point with the given slope.
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The standard form equation of a line is expressed as
Ax + By = C
where
A, B and C are real numbers and A and B are not both zero. From the information given,
the line passes through(- 2, 5) and slope = - 4
We would find the y intercept of the line, c by substituting slope, m = - 4, x = - 2 and y = 5 into the slope intercept equation which is expressed as
y = mx + c
Thus, we have
5 = - 4 * - 2 + c
5 = 8 + c
c = 5 - 8 = - 3
Thus, the equation of the line in the slope intercept form is
y = - 4x - 3
We would convert it to standard form. Thus, we have
y + 4x = - 3
4x + y = - 3
Thus, the equation in standard form is
4x + y = - 3
Find y if the line through (1, y) and (8, 2) has a slope of 3.
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[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{y})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{y}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{1}}} ~~ = ~~\stackrel{\stackrel{m}{\downarrow }}{3}\implies \cfrac{2-y}{7}=3 \\\\\\ 2-y=21\implies -y=19\implies y=\cfrac{19}{-1}\implies y=-19[/tex]
What is the probability that a randomly chosen marble is red or small?
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We have the next formula
[tex]P\mleft(RorS\mright)=P\mleft(R\mright)+P\mleft(S\mright)-P\mleft(RandS\mright)[/tex]P(R)=0.7
P(S)=0.9
P(RandS)=0.6
The probability that randomly chosen marbñe is red or small is
[tex]\begin{gathered} \\ P(RorS)=0.7+0.9-0.6=1 \end{gathered}[/tex]A wheel is rotating 600 times per minute. Through how many degrees does a point in the edge of the wheel move in 1/2 seconds.
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The wheel is rotating 600 times per minute, find how many times rotate in 1 second:
1 minute = 60 seconds
[tex]600\frac{times}{\min}\cdot\frac{1\min}{60s}=10\frac{times}{s}[/tex]Then, if in 1 second it rotates 10 times in 1/2 seconds it rotates:
[tex]\frac{10\frac{times}{s}}{2}=5\text{times}[/tex]Multiply the number of times it rotates (5 times) by 360 (a wheel has 360º)
[tex]5\text{times}\cdot\frac{360º}{1\text{time}}=1800º[/tex]Then, a point moves 1800º in 1/2 secondsMe.Hoffman has a doorstop in his classroom shaped like a triangular prism shown
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- To determine the perimeter of the base, consider that the length is 5 in and the width is the same as the width of the top face of the prism, that is, 2 in. Then, the perimeters is:
P = 2l + 2w
w = 2 in
l = 5 in
P = 2(5 in) + 2(2 in)
P = 10 in + 4 in
P = 14 in
- The height of the doorstop is 1.2 in
- The area of the base is:
A = wl
A = (2 in)(5 in)
A = 10 in²
Find the length of the third side. If necessary, write in simplest radical form. 9 5 Submit Answer Answer:
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The Pythagorean theorem states:
[tex]c^2=a^2+b^2[/tex]where a and b are the legs and c is the hypotenuse of a right triangle.
Substituting with c = 9 and a = 5, we get:
[tex]\begin{gathered} 9^2=5^2+b^2 \\ 81=25+b^2 \\ 81-25=b^2 \\ 56=b^2 \\ \sqrt[]{56}=b \\ \sqrt[]{4\cdot14}=b \\ \sqrt[]{4}\cdot\sqrt[]{14}=b \\ 2\sqrt[]{14}=b \end{gathered}[/tex]O A. 1376 square inchesO B. 672 square inchesO C. 1562 square inchesO D. 936 square inches
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The seat back cushion is a cuboid. The surafce area can be calculated below
[tex]\begin{gathered} l=26\text{ inches} \\ h=5\text{ inches} \\ w=18\text{ inches} \\ \text{surface area=2(}lw+wh+hl\text{)} \\ \text{surface area=}2(26\times18+18\times5+5\times26) \\ \text{surface area=}2(468+90+130) \\ \text{surface area=}2\times688 \\ \text{surface area}=1376inches^2 \end{gathered}[/tex]
The figure below shows two parallel lines, k and f, cut by a transversal. What is the value of x?
A 25
B 35
C 45
D 65
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Answer:
x=65 0r in other words D
Step-by-step explanation:
110=2x-20
+20 +20
130=2x
/2 /2
65=x
A publisher for promising new novel figures fixed costs at $61,000 and variable cost at $1.50 for each book produced if the book is sold to distributors for $15 each how many must be produced and sold for publisher to break even?
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SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given information
[tex]\begin{gathered} For\text{ the cost price function:} \\ Fixed\text{ cost=\$61,000 = constant} \\ Variable\text{ cost = \$1.50 }\times\text{ number of books} \\ Let\text{ x be the number of books produced} \end{gathered}[/tex]The function for the cost price becomes:
[tex]61000+1.5x[/tex]STEP 2: Get the function for the selling price
The function for the selling price becomes:
[tex]\text{ \$}15x[/tex]STEP 3: Calculate the number of books required to break even
To get the breakeven, the cost price will be equal to selling price. Therefore,
[tex]\begin{gathered} 61000+1.5x=15x \\ Subtract\text{ 1.5x from both sides} \\ 61000+1.5x-1.5x=15x-1.5x \\ 61000=13.5x \\ Divide\text{ both sides by 13.5} \\ \frac{61000}{13.5}=\frac{13.5x}{13.5} \\ 4518.518519=x \\ x\approx4519 \end{gathered}[/tex]Hence, the number of books that must be produced and sold to get a breakeven is approximately 4519
A linear regression model for the revenue data for a company is R=25.9t + 204 where R is total annual revenue and t is time since 1/31/02 in years.
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The linear regression model is
[tex]R=25.9t+204[/tex]Where
R is the total annual revenue (dependant variable)
t is the time, in years, since 1/31/02 (independent variable)
To predict the annual revenue for the period ending 1/31/10, the first step is to determine the value of t. Considering that t=0 is the first recorded year (1/31/02), the value of t corresponding to period 1/31/10 is the number of years passed since, including 2002, which is 9 years.
So you have to calculate R for t=9. Replace the formula with t=9 and calculate the corresponding value of R
[tex]\begin{gathered} R=25.9\cdot9+204 \\ R=437.1 \end{gathered}[/tex]R≈437 billion dollars
Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.C=111.1°a=7.1mb=9.6mOption 1: No triangle satisfies the given conditions.Option 2: c=19.6m, A=26.8°, B=42.1°Option 3: c=16.7m, A=30.8°, B=38.1°Option 4: c=13.8m, A=28.8°, B=40.1°
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Answer: Option 4: c=13.8m, A=28.8°, B=40.1°
Explanation:
From the information given,
the known sides are a = 7.1 and b = 9.6
the known angle is C = 111.1
We would find side c by applying the cosine rule which is expressed as
c^2 = a^2 + b^2 - 2abCosC
By substituting the given values into the formula,
c^2 = 7.1^2 + 9.6^2 - 2 x 7.1 x 9.6Cos111.1
c^2 = 50.41 + 92.16 - 136.32Cos111.1
c^2 = 142.57 - 136.32Cos111.1 = 191.6448
c = √191.6448 = 13.8436
c = 13.8
To find angle A, we would apply the sine rule which is expressed as
a/SinA = c/SinC
Thus,
7.1/SinA = 13.8436/Sin 111.1
By cross multiplying, we have
13.8436SinA = 7.1Sin111.1
SinA = 7.1Sin111.1/13.8436 = 0.4785
Taking the sine inverse of 0.4785,
A = 28.8
Recall, the sum of the angles in a triangle is 180. Thus,
A + B + C = 180
28.8 + B + 111.1 = 180
139.9 + B = 180
B = 180 - 139.9
B = 40.1
Option 4: c=13.8m, A=28.8°, B=40.1°
how many pennies are in a dollar
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Answer: 100
Step-by-step explanation:
$1 =100 pennies
Use the strategy to simplify 4/576Write the prime factorization of the radicand.442834O42/2832O 4./283²O4. 2882
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To simplify the fraction we will need to facto
Which parabola corresponds to the quadratic function y = 2x2 + 4x - 16? D. A. B. C. 10:13 1618 10- 12 =10 10 28 -20
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We can see that the y-intercept would be (0,-16) since this is the result of replacing x=0 in the function.
We can also find the x-intercepts solving the equation 0=2x^2+4x-16. Doing so, we have:
[tex]\begin{gathered} 0=2x^2+4x-16 \\ 0=x^2+2x-8\text{ (Dividing by 2 on both sides of the equation)} \\ 0=(x+4)(x-2)\text{ (Factoring)} \\ \text{ We can see that the solutions of the equation are x=-4 and x=2} \\ \text{Therefore the x-intercepts are (-4,0) and (2,0)} \end{gathered}[/tex]The graph that satisfies the conditions we have found previously is the option A.
In 2009, there were 6.1 million females enrolled in degree granting institutions of higher education. over the next several years this number increased at a rate of 400,000 per year. estimate the number of females enrolled in 2024. y = ______ millionthe equation of the line that models this information is;y = 0.4t + 6.1Determine what year 12.9 million females will be enrolled.
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Notice that
400,000 = 0.4 million
That's why the equation that models that information has the factor 0.4, since it expresses the result in millions of females.
Now, we need to notice that t, in the expression 0.4t + 6.1, is the number of years passed since 2009. So, in the year 2024, we have:
t = 2024 - 2009 = 15
Therefore, the number of females enrolled in 2024 can be estimated to be:
y = (0.4 * 15 + 6.1) million
y = (6 + 6.1) million
y = 12.1 million
Now, to determine the year when 12.9 million females will be enrolled, we first need to find t corresponding to y = 12.9, and then add it to the year 2009.
y = 0.4t + 6.1
12.9 = 0.4t + 6.1
12.9 - 6.1 = 0.4t
6.8 = 0.4t
t = 6.8/0.4
t = 68/4
t = 17
Therefore, the year when it happens will be:
2009 + 17 = 2026
Joan uses the function C(x) = 0.11x + 12 to calculate her monthly cost for electricity.• C(x) is the total cost (in dollars).• x is the amount of electricity used (in kilowatt-hours).Which of these statements are true? Select the three that apply.A. Joan's fixed monthly cost for electricity use is $0.11.B. The cost of electricity use increases $0.11 each month.C. If Joan uses no electricity, her total cost for the month is $12.D. Joan pays $12 for every kilowatt-hour of electricity that she uses.E. The initial value represents the maximum cost per month for electricity.F. A graph of the total cost for x ≥ 0 kilowatt-hours of energy used is a straight line.G. The slope of the function C(x) represents the increase in cost for each kilowatt hour used.
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Answer:
The correct statements are:
C. If Joan uses no electricity, her total cost for the month is $12.
F. A graph of the total cost for x ≥ 0 kilowatt-hours of energy used is a straight line.
G. The slope of the function C(x) represents the increase in cost for each kilowatt hour used.
Step-by-step explanation:
Notice that the given function is the equation of a line in the slope-intercept form:
[tex]C(x)=0.11x+12[/tex]From this interpretation, we'll have that the correct statements are:
C. If Joan uses no electricity, her total cost for the month is $12.
F. A graph of the total cost for x ≥ 0 kilowatt-hours of energy used is a straight line.
G. The slope of the function C(x) represents the increase in cost for each kilowatt hour used.
ranslateSave & Exit CertifyLesson: 10.2 Parabolas11/15Question 9 of 9, Step 1 of 1CorrectFind the equationof the parabola with the following properties. Express your answer in standard form.
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Given
[tex]undefined[/tex]Solution
Standard from of a parabola
[tex](x-H-h)^2=4p(y-k)[/tex]Quadrilateral ABCD is a rhombus.DA АC СBMatch the reasons that justifies the given statements.
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A rhombus is a quadrilateral with 4 congruent sides.
For the Rhombus ABCD given
[tex]\begin{gathered} AB\mleft\Vert DC\text{ }\mright? \\ \\ \text{Opposite sides of a rho}mbus\text{ are parallel} \end{gathered}[/tex]Also,
[tex]\begin{gathered} DA\cong CB \\ \text{Opposite sides of a rhombus are congruent} \end{gathered}[/tex]Also,
[tex]\begin{gathered} <\text{ADC}\cong<\text{ABC} \\ \text{Opposite angles of a rhombus are congruent} \end{gathered}[/tex]the pie chart below shows how the annual budget for general Manufacturers Incorporated is divided by department. use this chart to answer the questions
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You can read a pie chart as follows
Looking at the given pie chart.
The budget for Research is arounf 1/6
The budget for Engineering is around 2/6
The budget for Support is around 1/8
The budget for media and marketing are 1/16 each
The budget for sales is around 3/16
a) The department that has one eight of the budget is Support.
b) The budgets for sales and marketing together add up to
[tex]\frac{3}{16}+\frac{1}{16}=\frac{4}{16}=\frac{1}{4}[/tex]Multiply it by 100 to express it as a percentage
[tex]\frac{1}{4}\cdot100=25[/tex]25% of the budget correpsonds to sales and marketing
c) The budget for media looks around one third the budget for research, to determine the percentage of budget that corresponds to media, divide the budget of research by 3
[tex]\frac{18}{3}=6[/tex]The budget for media is 6%
For each ordered pair, determine whether it is a solution to 4x - 5y = -13.Is it a solution?x$(x, y)YesNo(-7, -3)(3, -4)OO(-2, 1)oO(6, 7)0
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The equation is 4x - 5y = -13.
Substitute -7 for x and -3 for y in the equation to check whether ordered pair is solution of the equation.
[tex]\begin{gathered} 4\cdot(-7)-5\cdot(-3)=-13 \\ -28+15=-13 \\ -13=-13 \end{gathered}[/tex]The ordered pair satisfy the equation so point (-7,-3) is solution of equation.
Substitute 3 for x and -4 for y in the equation to check whether ordered pair is solution of the equation.
[tex]\begin{gathered} 4\cdot3-5\cdot(-4)=-13 \\ 12+20=-13 \\ 32\ne-13 \end{gathered}[/tex]The ordered pair not satisfy the equation. So point (3,-4) is not a solution of the equation.
Substitute -2 for x and 1 for y in the equation to check whether ordered pair is solution of the equation.
[tex]\begin{gathered} 4\cdot(-2)-5\cdot1=-13 \\ -8-5=-13 \\ -13=-13 \end{gathered}[/tex]The ordered pair satisfy the equation. So point (-2,1) is solution of equation.
Substitute 6 for x and 7 for y in the equation to check whether ordered pair is solution of the equation.
[tex]\begin{gathered} 4\cdot6-5\cdot7=-13 \\ 24-35=-13 \\ -11\ne-13 \end{gathered}[/tex]The orderedpair not satisfy the equation. So point (6,7) is not a solution of the equation.
