Express the graphed inequality in interval notation:012345678910-1-2-3-4-5-6-7-8-9-10x∈ (Enter your answer in INTERVAL notation, using U to indicate a union of intervals; or enter DNE if no solution exists; use "oo" to express ∞ )
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We have a filled circle in -5 so we will use [ because we touch the -5 and an unfilled circle in 2 therefore we will use ) because we did not touch the 2, therefore, our interval will be
[tex]-5\le\: x<\: 2[/tex]In interval notation
[tex]\: \lbrack-5,\: 2)[/tex]Related Questions
Order following numbers from least to greates0. 480.4460.480.480.44 8<0. 460.460.55:
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okay so the first thing we can look at is the tenths place
all of them except one start with a 4
so we can now assume that 0.5 is the greatest value
next, we look at the hundredth value
with me so far?
so do you know what the bar on top of the number means?
no worries
so the bar on top of the number means that the number is repeating
so for example
0.48 with a bar would mean 0.484848484848
got it?
okay great so now lets write all of the numbers in that format to make it easier to understand
0.48484848
0.44666666
0.48
0.4888888
0.44888888
0.46
What is the scale factor of the dilation (with center at the origin) shown below?A) 1/2B) -2C.)2D) -1/2
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The graph is shown having two triangle with different coordinates.
The one triangle is of larger size and othe triangle is of smaller size.
To determine the scale factor of the dilation we need to find the coordinates of the triangle.
The larger triangle coordinate are,
[tex]A^{\prime}=(-4,-4)\text{ ,B'}=(-2,4)\text{ , C'}=(4,2)[/tex]The smaller triangle coordinates are,
[tex]A=(-2,-2),B=(-1,2),C=(2,1)[/tex]The coordinate A is formed by multiply with
[tex]\frac{1}{2}[/tex]in A' coordinate.
Similarly other coordinates is also determined by multiply with 1/2 in the corrdinates with B' and C'.
Therefore, the scale factor for dilation obtained is,
[tex]\frac{1}{2}[/tex]Hence the correct option is A.
if x= 2y-4 and x=6y+16 find the value for both x and y
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In order to find the values of x and y, let's compare both values of x given:
[tex]\begin{gathered} x=2y-4 \\ x=6y+16 \\ \\ 2y-4=6y+16 \\ 6y-2y=-4-16 \\ 4y=-20 \\ y=-\frac{20}{4} \\ y=-5 \\ \\ x=2y-4 \\ x=2\cdot(-5)-4 \\ x=-10-4 \\ x=-14 \end{gathered}[/tex]So we have that x = -14 and y = -5.
Helppppppppppppppppppp
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If the y value of the coordinate was flipped, then the opposite axis would be where it was flipped over. Think of it on a coordinate plane; (8,-7) is below the x-axis, while (8,7) is above the x-axis. If the point went from below the x-axis to above the x-axis, then the x axis is what it was reflected over.
The sum of one-fifth of a number and three is equal to half of the number. What is the number?
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Answer:
Step-by-step explanation:
(1/5)(x)+3=(1/2)(x)
3=(1/2)x-(1/5)x
3=(5/10)x-(2/10)x
3=(3/10)x
3=0.3x
30=3x
x=30/3
x=10
there are 20, 000 owls in the wild. Every year the owl population decrease 8%.identify the state. the starting amount the rate change this growth or decay justify .write the equation that represents the owl population after a number of years. how many owls will there be after six years
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Given:
Number of owls in the wils is 20,000.
The rate of decrease is 8%.
From the given data the starting amount of owls is 20000.
The rate of change is -8%.
The general exponential equation of population growth is,
[tex]P=P_0(1+\frac{r}{100})^t[/tex]Here t represents the number of years.
Substitute the given values in the above equation,
[tex]\begin{gathered} P=20000(1+(-\frac{8}{100}))^t \\ P=20000(1+(-0.08))^t \\ P=20000(1-0.08)^t \\ P=20000(0.92)^t \end{gathered}[/tex]Hence, the required equation that represents the owl population after a number of years is obtained.
The number of owls after 6 years can be calculated by substituting t = 6 in the above equation.
[tex]\begin{gathered} P=20000(0.92)^6 \\ P=20000(0.606355) \\ P=12127 \end{gathered}[/tex]Hence, the population of owls in the wild is 12,127 after 6 years. And the population is decreasing.
I would like somebody to verify my solution for this particular problem!
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Step 1
Given;
[tex]\begin{gathered} x(t)=t-2 \\ y(t)=2t^2+4 \\ t\text{ is on the interval \lbrack-3,1\rbrack} \end{gathered}[/tex]Required; To write in standard form.
Step 2
[tex]\begin{gathered} x=t-2 \\ t=x+2 \end{gathered}[/tex][tex]\begin{gathered} y(t)=2(x+2)^2+4 \\ y(t)=2x^2+8x+12 \\ \end{gathered}[/tex]The answer will be;
[tex]y=2x^2+8x+12\text{ where x is on the interval \lbrack}[/tex]Which of the following are true of bar graphs? 1.Bars must be in order from least to greatest. 2.Data is displayed in intervals. 3. Specific data is shown. 4. There are gaps between bars.
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1.Bars must be in order from least to greatest. → correct
2.Data is displayed in intervals. → not necesarly, this depends on wether the variable is discrete or continuous
3. Specific data is shown. → No, the observed frequency for the determined range of the variable is observed.
4. There are gaps between bars. →No, only if there are no observations for a determined value of the variable.
How many per ounces and which circle do I need to choose
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We are asked to determine the unit price of two different packages. The unit price is determined by dividing the price of an item over the quantity used to measure that item at the given price. In this case, the unit of measure is "ounce", therefore, we need to determine the price per ounce. The first unit price is determined by dividing the price of $3.19 for 11.5 ounces, like this:
[tex]P_1=\frac{3.19\text{ dollars}}{11.5\text{ ounces}}=0.28\text{ dollar/ounce}[/tex]Since we are told to round to the nearest cent we take the first two digits after the decimal point and we add 1 to the second digit if the third digit is equal to or greater than 5.
Now we use the same procedure to determine the second unit price:
[tex]P_2=\frac{7.98\text{ dollars}}{30.6\text{ ounces}}=0.26\text{ dollar/ounce}[/tex]Since the unit price for the 30.6 ounces package is less than the price for the 11.5 ounces package this means that the second package is a better buy.
If she pays $10.00 to join, she will get 10% off on all the grocerie must she buy before her savings equal her membership fee?
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Answer:
rat
Step-by-step explanation:
rewrite an equivalent expression for 84+96
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Answer:
90 + 90
Step-by-step explanation:
Consider the function f(θ)=4sin(2θ)+2.What is the amplitude of f?What is the period of f?Graph of the function f below.
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Given data:
The given function is f(θ)=4sin(2θ)+2.
Amplitude is the maximum vertical distance, amplitude of the given function is,
A=6
The period of the given function is,
[tex]\begin{gathered} P=\frac{2\pi}{2} \\ =\pi \end{gathered}[/tex]The graph of the given function is shown below.
Thus, amplitude of the function is 6, and period is π.
Which of the following expressions can be used to find PQ?
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Answer:
C
[tex]\frac{30}{\cos25}[/tex]Explanation:
Given the image of the right angle, to find PQ, we have to take the cosine of angle 25 degrees as shown below;
[tex]\cos 25=\frac{30}{PQ}[/tex]Let's go ahead and make PQ the subject of formula;
[tex]\begin{gathered} PQ\cos 25=30 \\ PQ=\frac{30}{\cos25} \end{gathered}[/tex]what is 11/12 ÷ 1/3 0 2 1/4 0 2 3/40 3 1/3 0 3 2/3
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Identify the terminal point for a 45° angle in a unit circle.O A. (24)O B. (1.)Oc. (1,1)O D. (2,3)
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(x, y) = ( cos 45, sin 45) =
[tex]=\text{ (}\frac{\sqrt[]{2}}{2}\text{ , }\frac{\sqrt[]{2}}{2}\text{ )}[/tex]The correct option is A
I need help with this question please. Ignore the wording below. Fyi this is a part of a homework practice
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So,
Given that the zeros of our polynomial function are:
[tex]3i,2,-4[/tex]We know that there are 2 real zeros, and 2 complex zeros. (3i and -3i).
So, what we're going to do to find the equation of this polynomial, is to multiply all zeros together, such that we obtain an expression that we can simplify. Like this:
[tex](x-2)(x+4)(x-3i)(x+3i)[/tex]Now, we're going to multiply and distribute:
[tex]\begin{gathered} (x^2+2x-8)(x^2+3xi-3xi-9i^2) \\ \to(x^2+2x-8)(x^2-9i^2) \end{gathered}[/tex]Remember that:
[tex]i=\sqrt[]{-1}\to i^2=-1[/tex]So, we can rewrite:
[tex](x^2+2x-8)(x^2+9)[/tex]Multiplying these terms, we got that:
[tex]\begin{gathered} (x^2+2x-8)(x^2+9) \\ \to x^4+9x^2+2x^3+18x-8x^2-72 \\ \to x^4+2x^3+x^2+18x-72 \end{gathered}[/tex]Therefore,
[tex]P(x)=x^4+2x^3+x^2+18x-72[/tex]The average cost (in dollars) per mile for riding x miles in a cab is c(x)=2.5+2x/x. As x gets larger and larger, what does the end behavior of the function tell you about the situation?
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ANSWER:
The average cost per mile decreases
STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]C\mleft(x\mright)=\frac{2.5+2x}{x}[/tex]If we give value to x, we obtain the following:
[tex]\begin{gathered} c(10)=\frac{2.5+2\cdot10}{10}=2.25 \\ c(50)=\frac{2.5+2\cdot50}{50}=2.05 \\ c(100)=\frac{2.5+2\cdot100}{100}=2.025 \\ c(200)=\frac{2.5+2\cdot200}{200}=2.0125 \end{gathered}[/tex]We can see that it is evident that as x increases, c (x) decreases. Depending on the situation, if we travel more miles, the average cost per mile decreases.
Please HELP me on my ASSESSMENT practice its URGENT Find the ZEROS of each quadratic function by factoring
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13.
[tex]x^2+x-20=(x+5)(x-4)[/tex]Then, the zeros are x=-5 and x=4.
14.
[tex]x^2-4x-60=(x+6)(x-10)[/tex]Then, the zeros are x=-6 and x=10.
15.
[tex]x^2-15x+50=(x-5)(x-10)[/tex]Then the zeros are x=5 and x=10.
16.
[tex]x^2-x-72=(x+8)(x-7)[/tex]Then the zeros are x=-8 and x=7.
17.
[tex]x^2+2x-48=(x+8)(x-6)[/tex]Then the zeros are x=-8 and x=6.
18.
[tex]x^2-12x+36=(x-6)^2[/tex]Then there is only one zero at x=6.
19.
[tex]x^2+32x+60=(x+30)(x+2)[/tex]Then the zeros are x=-30 and x=-2.
20.
[tex]x^2-21x-100=(x+4)(x-25)[/tex]Then the zeros are x=-4 and x=25.
AB, CD and EF are straight lines
AB is parallel to CD
work out the size of angle y
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The required value of y is 117°
Given AB and CD are parallel lines;
and EF is the transversal
Thus 2x + 16 = 3x - 12 { because they are corresponding angles }
On solving the above mentioned linear equation
we get,
x = 25
Thus the required angles are 2x + 16 = 50 + 16 = 66 degrees
and 3x - 12 = 75 - 12 = 63 degrees
And to find the value of y
we can use linear pair property
Thus y + 63 = 180
y = 180 - 63
y = 117 °
To know more about parallel lines ; you may visit the link which is mentioned below ;
https://brainly.com/question/13352230
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Rewrite the following polynomial in standard form.1+ 10x − 2x³ + x5-x^2-9
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Hello!
We have the following polynomial:
[tex]1+10x-2x^3+x^5-x^2-9[/tex]To put it in the standard form, we have to start with the highest exponent on the left and then write in decreasing order. Look:
[tex]\begin{gathered} x^5-2x^3-x^2+10x-9+1 \\ \end{gathered}[/tex]We can simplify it by solving -9 +1, look:
[tex]x^5-2x^3-x^2+10x-8[/tex]Write an equation that passes through (5,-1) and is perpendicular to y=5/2x-5
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Answer:
[tex]y=-\frac{2}{5}x+1[/tex]Step-by-step explanation:
The equation of a line is represented by the following equation:
[tex]\begin{gathered} y=mx+b \\ \text{where,} \\ m=\text{ slope} \\ b=y-\text{intercept} \end{gathered}[/tex]If the given line is perpendicular to the one we want to find, the slope of the missing line would be the negative reciprocal of the given slope:
[tex]\begin{gathered} m=-(\frac{2}{5}) \\ m=-\frac{2}{5} \end{gathered}[/tex]Use the slope-point form of the line equation to determine the equation in slope-intercept form:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-1)=-\frac{2}{5}(x-5) \\ y+1=-\frac{2}{5}x+2 \\ y=-\frac{2}{5}x+2-1 \\ y=-\frac{2}{5}x+1 \end{gathered}[/tex]Sandwiches cost $5, French friescost $3, and drinks cost $2. Theexpression 5n + 3n + 2n gives the totalfor cost, in dollars, for buying a sandwich,French fries, and a drink for n people.Which is another way to write thisexpression?A. 10nB. 10nC. 30nD. 30n3
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Given 5n+3n+2n, we need to combine like terms
By combining like terms, we get 5n+3n+2n=1
Pythagorean Theorem:a? + b2 = c2 Re-write the formula solving for b?.
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The Pythagorean Theorem states the following:
[tex]a^2+b^2=c^2[/tex]Where "c" represents the hypotenuse of the Right triangle (which is a triangle that has an angle that measures 90 degrees), and "b" and "c" are the legs of the triangle.
To rewrite the formula solving for "b", you can follow the steps shown below:
1. Apply the Subtraction property of Equality by subtracting a^2 from both sides of the equation:
[tex]\begin{gathered} a^2+b^2-(a^2)=c^2-(a^2) \\ b^2=c^2-a^2 \end{gathered}[/tex]2. Now you must apply square root to both sides of the equation:
[tex]\begin{gathered} \sqrt[]{b^2}=\sqrt[]{c^2-a^2} \\ b=\sqrt[]{c^2-a^2} \end{gathered}[/tex]Because remember that:
[tex]\sqrt[n]{m}^n=m[/tex]Therefore, the formula solved for "b", is:
[tex]b=\sqrt[]{c^2-a^2}[/tex]In ARST, the measure of ZT=90°, the measure of ZR=6°, and RS = 3.6 feet. Find thelength of ST to the nearest tenth of a foot.S3.6XN60T70
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we have taht
sin(R)=ST/SR -----> by opposite side divided by the hypotenuse
substitute given values
sin(6)=x/3.6
solve for x
x=3.6*sin(6)
x=0.4 ftNeed help with question 8 Only Part B C and D
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Answer:
Explanation:
Given:
[tex]g(x)=3x^2+12x+9[/tex]B.)
To find the vertex, we use the following formula:
[tex]\begin{gathered} x=-\frac{b}{2a} \\ \text{From the Form:} \\ y=ax^2+bx+c \end{gathered}[/tex]So based on the given equation, the values of a and b are:
a=3
b=12
We plug in what we know:
[tex]\begin{gathered} x=-\frac{b}{2a} \\ =-\frac{12}{2(3)} \\ x=-2 \end{gathered}[/tex]Next, we plug in x=-2 into g(x)=3x^2+12x+9:
[tex]\begin{gathered} g(x)=3x^2+12x+9 \\ =3(-2)^2+12(-2)+9 \\ \text{Calculate} \\ g(x)=-3 \end{gathered}[/tex]Therefore, the vertex is (-2,-3).
C.
Now, to find the axis of symmetry, we also use the formula x=-b/2a since it is the vertical line that goes through the vertex.
Therefore, the Axis of Symmetry for the given equation is x = -2.
D.
We let g(x)=0 to find the x-intercept:
[tex]\begin{gathered} 3x^2+12x+9=0 \\ \text{Simplify} \\ =3(x^2+4x+3) \\ =3(x+1)(x+3) \end{gathered}[/tex]Based on the factors, the values for x are:
x=-1
x=-3
Therefore, the x intercept points are:
(-1,0),(-3,0)
To get the y-intercept, we let x=0 and plug in into g(x)=3x^2+12x+9. So,
[tex]\begin{gathered} g(x)=3x^2+12x+9 \\ g(0)=3(0)^2+12(0)+9 \\ g(0)=9 \end{gathered}[/tex]Therefore, the y intercept point is (0,9).
Find (and classify) the critical points of the following function and determine if they are local max, local min, or neither: f(x) =x^4 - 2x^2
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Solution:
Given:
[tex]f(x)=x^4-2x^2[/tex]To get the local maximum and minimum point, we differentiate the function twice.
[tex]\begin{gathered} f^{\prime}(x)=4x^3-4x \\ \\ To\text{ get the critical points, f'(x)=0} \\ 4x^3-4x=0 \\ \text{Factorizing,} \\ 4x(x^2-1)=0 \\ \text{Thus,} \\ (4x)(x-1)(x+1)=0 \\ \text{Hence, the critical points are;} \\ x=0,x=1,x=-1 \end{gathered}[/tex]To get the maximum and minimum points, we differentiate further,
[tex]\begin{gathered} f^{\prime}(x)=4x^3-4x \\ f^{\doubleprime}(x)=12x^2-4 \\ \\ \text{Inputting the critical points into f''(x),} \\ \text{when x = -1,} \\ f^{\doubleprime}(-1)=12(-1)^2-4=12-4=8 \\ S\text{ ince f''(x)>0, then this is a minimum point.} \\ x=-1\text{ is a minimum} \\ \\ \\ \text{when x = 1,} \\ f^{\doubleprime}(1)=12(1^2)-4=12-4=8 \\ S\text{ ince f''(x)>0, then this is a minimum point.} \\ x=1\text{ is a minimum} \\ \\ \text{when x = 0,} \\ f^{\doubleprime}(0)=12(0^2)-4=0-4=-4 \\ S\text{ ince f''(x)<0, then this is a maximum point.} \\ x=0\text{ is a maximum} \end{gathered}[/tex]Thus,
[tex]\begin{gathered} At\text{ x = 0,} \\ f(x)=x^4-2x^2 \\ f(0)=0^4-2(0^2)=0-0=0 \\ \\ \text{Hence, (0,0) is a local maximum} \\ \\ \\ At\text{ x = -1,} \\ f(x)=x^4-2x^2 \\ f(-1)=(-1)^4-2(-1)^2=1-2=-1 \\ \\ \text{Hence, (-1,-1) is a local minimum} \\ \\ \\ At\text{ x = 1,} \\ f(x)=x^4-2x^2 \\ f(1)=1^4-2(1^2) \\ f(1)=1-2=-1 \\ \\ \text{Hence, (1,-1) is a local minimum} \end{gathered}[/tex]The graph is as shown below;
Therefore,
The local minimum occurs at (-1,-1) and (1,-1)
The local maximum occurs at (0,0)
what is -35/-7 in simplest form
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-35/-7 can be simplified computing the division, that is, (-35) ÷ (-7) = 5
Given vectors u =<4, -1> and v= <-5, 11>find the followingto 1 decimal):||u||=
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Answer:
[tex]\lvert u\rvert=17[/tex]Step-by-step explanation:
Given the vector, u =<4, -1>, determine the magnitude.
The magnitude of a vector is represented as:
[tex]\begin{gathered} \lvert{v}\rvert=\sqrt{v1^2+v2^2} \\ where, \\ v=\langle v1,v2\rangle \end{gathered}[/tex]Therefore, for the given vector:
[tex]\begin{gathered} \lvert{u}\rvert=\sqrt{4^2+(-1)^2} \\ \lvert{u}\rvert=\sqrt{16+1} \\ \lvert{u}\rvert=\sqrt{17} \end{gathered}[/tex]Find the mean, median, mode, mid range, and then answer the given question.
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First, let's arrange the given data in order from lowest to highest.
[tex]\lbrace2,4,5,6,7,7,8,8,8,8,9,9,12,15\rbrace[/tex]
Let's now calculate the mean. Add all the data and divide the answer by the total number of data which is 14.
[tex]2+4+5+6+7+7+8+8+8+8+9+9+12+15=108[/tex][tex]108\div14=7.71428\approx8[/tex]The mean or the average number of Atlantic Hurricanes that occurred each year starting from the year 2000 is approximately 8 hurricanes per year.
To find the median, since there are 14 values, the median would be the middle value and that is between the 7th and 8th data. Based on the arranged data, the 7th data is 8 and the 8th data is also 8. Hence, the median value is 8.
On the other hand, the mode is the data with the highest frequency. Based on the data that we have, 8 is the data that has the highest frequency because there are 4 8's in the data. Therefore, our mode is also 8.
Lastly, the midrange is 1/2 the difference between the maximum data and the minimum data.
[tex]Midrange=\frac{max-min}{2}=\frac{15-2}{2}=\frac{13}{2}=6.5\approx7[/tex]The mid-range of the given data is approximately 7.
Since the data is about the occurrence of Atlantic Hurricanes each year starting from 2000, the important feature of the data that is not revealed by any of the measures of the center is the pattern of the number of occurrences of the hurricanes over time. It is important to know the pattern so that emergency measures are prepared when hurricanes occur.
Which equation shows the distributive property? A 4(3+6)=12+24 B (4+3)+6=6+(4+3) C (12+4)+0=12+4 (12+4)+6=12+(4+6) D
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To “distribute” means to divide something or give a share or part of something. According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
so the correct answer is A.
A 4(3+6)=12+24
B (4+3)+6=6+(4+3)
C (12+4)+0=12+4
D (12+4)+6=12+(4+6)