Answers
Given two sets of real numbers:
[tex]\begin{gathered} D=\mleft\lbrace w\mright|w\ge4\} \\ E=\mleft\lbrace w\mright|w<8\} \end{gathered}[/tex]we will write the given sets as intervals
so,
[tex]\begin{gathered} D=\lbrack4,\infty) \\ E=(-\infty,8) \end{gathered}[/tex]The intersections and the union of the sets will be as follows:
[tex]\begin{gathered} D\cap E=\lbrack4,8) \\ \\ D\cup E=(-\infty,\infty) \end{gathered}[/tex]Related Questions
solve the following equation y^4+7y^2-44=0
Answers
Answer:
y = 2, y = -2, y = i √11, y = - i √ 11
Explanation:
To solve the equation for y, we first make the substitution x = y^2. Doing this we write
[tex]x^2+7x-44=0[/tex]The above can be written as
[tex](x-4)(x+11)=0[/tex]Which gives two equations
[tex]\begin{gathered} x-4=0 \\ x+11=0 \end{gathered}[/tex]Substituting back x = y^2 gives
[tex]\begin{gathered} y^2-4=0\rightarrow y=-2,y=2 \\ x^2+11=0\rightarrow y=i\sqrt[]{11},y=-i\sqrt[]{11} \end{gathered}[/tex]Hence, to summarize, the solution to the equation is
[tex]\begin{gathered} y=-2,y=2 \\ y=i\sqrt[]{11},y=-i\sqrt[]{11} \end{gathered}[/tex]Given vector v equals open angled bracket negative 11 comma negative 5 close angled bracket comma what are the magnitude and direction of v? Round the magnitude to the thousandths place and the direction to the nearest degree.
Answers
We will begin by finding the magnitude of a vector, denoted |v|.
The formula we can use is
[tex]|v|=\sqrt{a^2+b^2}[/tex]where a and b represent the vector components. Since we are given the vector <-11,-5>, we will let a be -11 and b is -5.
Substituting those values, we have
[tex]\begin{gathered} |<-11,-1>|=\sqrt{(-11)^2+(-5)^2} \\ \sqrt{121+25} \\ \sqrt{146} \\ \approx12.083 \end{gathered}[/tex]So far, your answer is either the first option or the second option.
Next, we want to find the direction of the vector. We can use another helpful formula:
[tex]\tan\theta=\frac{b}{a}[/tex]Substituting our original values for a and b, we have:
[tex]\tan\theta=\frac{-5}{-11}[/tex]Be careful here! Since the both the a-value and b-value are negative, we are going to be in the third quadrant. After finding our angle (which will be in quadrant 1), we will need to add 180 degrees.
Take the inverse tangent of both sides to get the angle:
[tex]\begin{gathered} \theta=\tan^{-1}(\frac{-5}{-11}) \\ \theta\approx24^{\circ} \end{gathered}[/tex]We'll add 180 degrees to get our final angle:
[tex]24+180=204[/tex]Since our final angle is 204 degrees, the correct answer is the second option.
Answer:
12.083; 24°
explanation:
Magnitude of v = sqrt((-11)^2 + (-5)^2)
Direction of v = atan(-5 / -11)
Calculating these values:
Magnitude of v = sqrt(121 + 25) ≈ 12.083 (rounded to the thousandths place)
Direction of v = atan(-5 / -11) ≈ 0.435 radians
Converting radians to degrees:
The direction of v ≈ 0.435 * (180 / π) ≈ 24.881° ≈ 24° (rounded to the nearest degree)
Therefore, the correct answer is 12.083; 24°.
A straight line passes through points (1, 15) and(5, 3) What isthe equation of the line?Select one:A) y = - 3x + 18B) y = – 7x + 18C) y = 2x + 18D) y = 3x + 18
Answers
Points (1,15) and (5,3)
Find the slope (m)
[tex]m=\frac{y2-y1}{x2-x1}[/tex]where:
(x1,y1) = (1,15)
(x2,y2) = (5,3)
Replacing:
[tex]m=\frac{3-15}{5-1}=\frac{-12}{4}=-3[/tex]the function has a slope m= -3
slope intercept form:
y=mx+b
Where
m= slope
so, the correct function is
y=-3x+18 (A)
Graph the parabola.y=-4x² +5Plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. Then click on the graph-a-function button
Answers
This is the basic parabola shifted 5 units up.
So, the vertex is at::
(0, 5)
Now, to get 2 points to the left, we take x = -1 and x = -2 and find corresponding y value.
To get 2 points to the right, we take x = 1 and x = 2 and find corresponding y values.
Thus,
When x = -1,
y = -4(-1)^2 + 5
y = 1
When x = -2,
y = -4(-2)^2 + 5
y = -11
When x = 1,
y = -4(1)^2 + 5
y = 1
When x = 2,
y = -4(2)^2 + 5
y = -11
Plotting these 5 points, we connect a smooth curve.
Shown below:
the dealer in a card game draws three cards from a deck of 52 cards and places them face-up on the table select all the correct probabilities
Answers
Explanation:
nCx give us the number of ways in which we can select x cards from a group of n cards.
So, the number of ways in which we can select 3 cards from 52 is:
52C3.
On the other hand, the number of ways to select 3 cards but none of them are kings is 48C3 because there are 48 cards that aren't kings. So:
[tex]P(no\text{ Kings)=}\frac{_{48}C_3}{_{52}C_3}[/tex]The number of ways to draw 2 fives is: 4C2*48C1
Because the dealer needs to draw 2 cards from the 4 that are fives and 1 card from the other 48 cards. So, P(2 fives) is:
[tex]P(\text{ 2 fives)=}\frac{_4C_2\times_{48}C_1}{_{52}C_3}[/tex]The number of ways to draw 1 heart and 2 spades is: 13C1*13C2
Because there are 13 heart cards and 13 spades cards. So, P(1 heart and 2 spades) is:
[tex]P(1\text{ Heart and 2 spades) = }\frac{_{13}C_1\times_{13}C_2_{}}{_{52}C_3}[/tex]Finally, the number of ways to select 4 aces and 1 ten is
A dilation from the origin with scale factor of 3 will map the point (5,4) to (8,7) explain why or why not this statement is correct
Answers
This statement is false because if the factor of dilatation is 3, the new coordinates should be 3 times the original ones. So the new point shoud be (15,12)
How to solve Use completing the square to find the vertex of the following parabolas
Answers
To use completing the square to find the vertex of the given parabola, we proceed as follows:
[tex]g(x)=x^2-5x+14[/tex]- we divide the coefficient of x by 2 and add and subtract the square of the result, as follows:
[tex]g(x)=x^2-5x+(\frac{5}{2})^2-(\frac{5}{2})^2+14[/tex]- simplify the expression as follows:
[tex]\begin{gathered} g(x)=(x^2-5x+(\frac{5}{2})^2)-(\frac{5}{2})^2+14 \\ \end{gathered}[/tex][tex]g(x)=(x^{}-\frac{5}{2})^2-(\frac{5}{2})^2+14[/tex][tex]g(x)=(x^{}-\frac{5}{2})^2-\frac{25}{4}^{}+14[/tex][tex]g(x)=(x^{}-\frac{5}{2})^2-\frac{25}{4}^{}+\frac{56}{4}[/tex][tex]g(x)=(x^{}-\frac{5}{2})^2+\frac{-25+56}{4}^{}[/tex][tex]g(x)=(x^{}-\frac{5}{2})^2+\frac{31}{4}^{}[/tex]From the general vertex equation, given as:
[tex]g(x)=a(x-h)^2+k[/tex]The coordinate of the vertex is taken as: (h, k)
Therefore, given:
[tex]g(x)=(x^{}-\frac{5}{2})^2+\frac{31}{4}^{}[/tex]We have the vertex to be:
[tex](\frac{5}{2},\frac{31}{4})\text{ or (2.5, 7.75)}[/tex]1. The diagram below, not drawn to scale, shows a flexible piece of paper in the shape of a sector of a circle with centre 0 and radius 15 cm. 22 Use . B А 126 0 15 cm C (a) Show that the perimeter of the paper is 63 cm. [3] (b) Calculate the area of the paper OABC. 121 (c) The paper is bent and the edges OA and OC are taped together so that the paper forms the curved surface of a cone with a circular base, ABC. (1) Draw a diagram of the cone formed, showing clearly the measurement 15 cm, the perpendicular height, h, and the radius, r, of the base of the cone. [1] (ii) Calculate the radius of the circular base of the cone. 121 (iii) Using Pythagoras' Theorem, or otherwise, determine the perpendicular height of the resulting cone. 121
Answers
Given
Circle of radius 15 cm and angle at the centre equal to 126 degree.
Find
(a) Perimeter of the paper is 63cm.
(b) Area of the paper OABC
(c) i) Draw a cone
ii) radius of circular base
iii) determine the height
Explanation
(a)
Perimeter of sector = Arc length ABC + AO + OC
Arc Length of ABC =
[tex]\begin{gathered} \frac{\theta}{360}\times2\Pi r \\ \frac{126}{360}\times2\times\frac{22}{7}\times15 \\ 33 \end{gathered}[/tex]so , perimeter = 33 +15 +15 = 63
Hence we proved that perimeter is 63 cm
(b) Area of sector =
[tex]\begin{gathered} \frac{\theta}{360}\times\Pi r^2 \\ \frac{126}{360}\times\frac{22}{7}\times15\times15 \\ 247.5 \end{gathered}[/tex](c) i)
ii) Circumference of base =
[tex]\begin{gathered} 2\Pi r=\text{33} \\ r=\frac{33\times7}{2\times22} \\ r=\frac{21}{4} \end{gathered}[/tex]iii) l = 15 cm, r= 21/7
By pythagoras theorem,
[tex]\begin{gathered} h^2=l^2-r^2 \\ h^2=15^2-(\frac{21}{4})^2 \\ h=\text{ 14.05} \end{gathered}[/tex]Final Answer
(a) 63
(b) 247.5
Find the slope of the line that goes through the points (14,-13) and (2,3).
Answers
Answer
The slope of the line is -4/3
Step-by-step explanation:
Given the following coordinates point
(14, -13) and (2, 3)
Slope = rise / run
rise = y2 - y1
run = x2 - x1
Slope = y2 - y1 / x2 - x1
Let; x1 = 14, y1 = -13, x2 = 2, and y2 = 3
Slope = 3 - (-13) / 2 - 14
Slope = 3 + 13 / - 12
Slope = 16 / -12
Slope = -4/3
Hence, the slope of the line is -4/3
Determine algebraically if f(x)=x^2-8 is a function even, odd, or neither.
Answers
For a function to be even, it has to meet the following condition:
[tex]f(x)=f(-x)[/tex]To check if the given is an even function, evaluate the function at x and -x:
[tex]\begin{gathered} f(x)=x^2-8 \\ f(-x)=(-x)^2-8=x^2-8 \\ f(x)=f(-x) \end{gathered}[/tex]It means that the function is even.
For a function to be odd, it has to meet this condition:
[tex]f(-x)=-f(x)[/tex]We already know the values of f(-x) and f(x) and from this we can state that the function is not odd.
A junk drawer at home contains eight pens four of which work what is the probability that a randomly grab three pens from the drawer and don’t end up with a pen that works express your answer as a fraction in lowest terms or decimal rounded to the nearest million
Answers
Answer:
1/14
Explanation:
The number of ways or combinations in which we can select x objects from a group of n can be calculated as:
[tex]\text{nCx}=\frac{n!}{x!(n-x)!}[/tex]So, if we are going to select 3 pens from the drawer that contains 8 pens, the number of possibilities is:
[tex]8C3=\frac{8!}{3!(8-3)!}=\frac{8!}{3!\cdot5!^{}}=56[/tex]Then, if we didn't end up with a pen that works is because we select the three pens from the 4 that didn't work. In this case, the number of possibilities is:
[tex]4C3=\frac{4!}{3!(4-3)!}=\frac{4!}{3!\cdot1!}=4[/tex]Therefore, the probability required is equal to the ratio of these quantities:
[tex]P=\frac{4}{56}=\frac{1}{14}[/tex]So, the answer is 1/14
Find the area of the region enclosed by y = 7x and y = 8x^2.
Answers
Solution
Hence the area under the region is
[tex]A=\int_0^{0.875}7x-8x^2=\frac{343}{384}unit^2[/tex]. Kelly makes $475 per week as an assistant I the human resource department of a law firm. What is her annual salary?
Answers
Week salary = $475
In a year there are 52 weeks
Use a rule of three to find the answer
1 week --------------------$475
52 weeks ----------------- x
x = (52 x 475) / 1
x = $24700
Her annual salary is $24700
What is 2902 divided by 3
Answers
Answer:
967.333333
Step-by-step explanation:
If you need to round it, it's 967.33
As a fraction, it's 2902/3 or 967 1/3
what would the length of segment BC have to be in order for line BC to be tangent to circle
Answers
Given data:
The first given length is AC=53.
The second given length is AB= 45.
The expression for the Pythagoras theorem is,
[tex]\begin{gathered} AB^2+BC^2=AC^2 \\ (45)^2+BC^2=(53)^2 \\ BC^2=784 \\ BC=28 \end{gathered}[/tex]Here, consider only positive sign of BC length as side cannot negative.
Thus, the BC length is 28.
A bag contains the following marbles: 12 black marbles, 8 blue marbles, 16 brown marbles and 14 green marbles. what is the ratio of black marbles to blue marbles.
Answers
Let:
Nbk = Number of black marbles = 12
Nb = Number of blue marbles = 8
The ratio of black marbles to blue marbles will be given by:
[tex]Nbk\colon Nb=12\colon8=\frac{12}{8}=\frac{3}{2}[/tex]Hey can you help me with my homework also can you tell me the points so I can put them into the graphs
Answers
Step 1
Find the equation of f(x)
[tex]\begin{gathered} The\text{ absolute value function is;} \\ y=a|x-h|+k \end{gathered}[/tex][tex]From\text{ the graph the vertex \lparen h,k\rparen is 3,3}[/tex][tex]\begin{gathered} h=3,k=3 \\ y=1,x=5 \end{gathered}[/tex][tex]1=a|5-3|+3[/tex][tex]\begin{gathered} 1=2a+3 \\ 2a=1-3 \\ 2a=-2 \\ \frac{2a}{2}=-\frac{2}{2} \\ a=-1 \end{gathered}[/tex]Thus f(x) will be;
[tex]y=-1|x-3|+3[/tex]Step 2
Find the equation of y= -f(x) then plot the graph
[tex]\begin{gathered} y=-(-1|x-3|+3) \\ y=1\left|x-3\right|-3 \end{gathered}[/tex]Thus the graph using the points below will look like;
[tex](-4,4),(0,0),(3,-3),(6,0),(8,2)[/tex]give some examples in mathematics for a 4th grader.
Answers
• Equivalent Fractions
Two or more fractions are called equivalent fractions if they keep the same proportion. For example:
[tex]\begin{gathered} \frac{1}{2}=\frac{2}{4}=\frac{3}{6}=\frac{4}{8}=\frac{5}{10} \\ \frac{3}{9}=\frac{6}{18}=\frac{9}{27}=\frac{12}{36} \end{gathered}[/tex]Notice that we multiplied the numerator and the denominator by the same number to produce those equivalent fractions. We did by two on the first line, and by 3 on the 2nd line.
These fractions are equivalent since we can simplify all of them and reduce them to 1/2. Dividing both numerator and denominator by the same number.
• Mixed Fractions and Improper fractions
Whenever we divide the numerator by the denominator and it is greater than or equal to 1. We can use Mixed Numbers.
For example:
[tex]\begin{gathered} \frac{9}{8}\longrightarrow\text{ 9}\colon8=1.125 \\ \frac{9}{8}=\text{ 1 +}\frac{1}{8}=1\text{ }\frac{1}{8} \\ \frac{12}{10}=1.2\text{ = 1 + }\frac{1}{5}\text{ =1}\frac{1}{5} \end{gathered}[/tex]We use mixed numbers for recipes (in daily life), and to better understand fractions.
When we need to operate them we must turn those Mixed Numbers into improper fractions (fractions whose denominator is lesser than its denominator (bottom number).
solve for 18 degreex 29
Answers
The given triangle is a right angle triangle. Considering angle 18 as the reference angle,
x = hypotenuse
29 = adjacent side
We would find the hypotenuse, x by applying the cosine trigonometric ratio which is expressed as
Cos# = adjacent side/hypotenuse
Thus, we have
Cos18 = 29/x
29 = xCos18
x = 29/Cos18 = 29/0.95
x = 30.53
In a poll, 50 residents in Greenville and Fairfield were asked whether they prefer swimming or jogging for exercise. This table shows the relative frequencies from the survey.The graph is in the pictureBased on the data in the table, which statements are true? Select all that apply.
Answers
Looking at the relative frequencies of the data in the table, these statements are true - "Greenville residents prefer jogging over swimming", "Fairfield residents prefer swimming over jogging", "People who prefer swimming are more likely to be from Fairfield", "People who prefer jogging are more likely to be from Greenville", "There is an association between the town a person lives in and their exercise preference".
It is given to us that -
50 residents in Greenville and Fairfield were asked whether they prefer swimming or jogging for exercise
The given table shows the relative frequencies from the survey.
We have to find out all the statements that are true about this survey.
Greenville people that like swimming = 0.18Greenville people that like jogging = 0.38=> Most Greenville residents prefer jogging over swimming
Similarly, we can see that
Fairfield residents prefer swimming over jogging (0.24>0.20)It can also be said true about the statements that -
People who prefer swimming are more likely to be from FairfieldPeople who prefer jogging are more likely to be from GreenvilleSince more people from Greenville prefers jogging to swimming and more people people from Fairfield prefers swimming to jogging, therefore "There is an association between the town a person lives in and their exercise preference"
Thus, according to the relative frequencies these statements are true - "Greenville residents prefer jogging over swimming", "Fairfield residents prefer swimming over jogging", "People who prefer swimming are more likely to be from Fairfield", "People who prefer jogging are more likely to be from Greenville", "There is an association between the town a person lives in and their exercise preference".
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identify the beginning of a sample period for the function
Answers
Given:
[tex]f(t)\text{ = 2csc\lparen t + }\frac{\pi}{4})-1\text{ }[/tex]The graph of f(t) is shown below:
From the graph, we can see that
[tex]x=\text{ }\frac{\pi}{4}\text{ is a good start for the period of f\lparen t\rparen}[/tex]Answer: Option D
What are the solution(s) to the quadratic equation 9x² = 4?O x = and x = -- 90x = ² and x = -1/33O= and x = --X=no real solutionM/NK
Answers
Given:
The quadratic equation is:
9x² = 4
Required:
Find the solutions to the given equation.
Explanation:
The given equation is:
[tex]9x²=4[/tex]Divide both sides by 4.
[tex]x^2=\frac{4}{9}[/tex]Take the square root on both sides.
[tex]\begin{gathered} x=\pm\sqrt{\frac{4}{9}} \\ x=\pm\frac{3}{2} \end{gathered}[/tex]the solutions to the equation are
[tex]x=\frac{3}{2}\text{ and x =-}\frac{3}{2}[/tex]Final Answer:
Option third is the correct answer.
how many FULL cases of oil can you get from a 150-gallon oil tank?
Answers
Given
The job is to fill the quart size of bottles, from a full 150 gallon oil tank.
And, the oil is packed into 24 quart's of oil.
To find the number of full cases of oil.
Explanation:
It is given that,
The total amount of oil is 150 gallon.
The number of cases it has to be filled is, 24.
Then, the number of the full cases of oil is,
[tex]\begin{gathered} Number\text{ of full cases of oil}=\frac{150}{24} \\ =\frac{50}{8} \\ =\frac{25}{4} \\ =\frac{24}{4}+\frac{1}{4} \\ =6+\frac{1}{4} \\ =6\frac{1}{4} \end{gathered}[/tex]Hence, the number of full cases of oil is 6.
cit Formula = 18 + 7(58 - 1) 58 CRIBE EN ORACIONES COMPLETAS
Answers
a. As you can see, the sequence starts at -3, and increases by 7 each time, Amanda is wrong because she found the following formula:
an = 18 + 7(n - 1)
For n =1 the result should be -3:
n = 1
a1 = 18 + 7(1 - 1) = 18 + 7(0) = 18 + 0 = 18, she miscalculated the first term, and the whole sequence in general.
b. A possible sequence identification could be:
an = 7n - 10
Let's verify it:
n=1
a1 = 7(1) - 10 = 7 - 10 = -3
n=2
a2 = 7(2) - 10 = 14 - 10 = 4
n=3
a3 = 7(3) - 10 = 21 - 10 = 11
and so on...
Now for n=58
a58 = 7(58) - 10 = 396
-------------------------------------------------------------------------
32 = 2 + 3(n - 1)
Solving for n:
Use distributive property on the right hand side:
32 = 2 + 3n - 3
32 = 3n - 1
Add 1 to both sides:
32 +1 = 3n - 1 + 1
33 = 3n
Divide both sides by 3:
33/3 = 3n/3
11 = n
n = 11
The glass portion of a small window is 12 inches by 24 inches. The framework on each side adds on x inches. Express the area of the entire window as a function of x. 72 + x square inches 36+x square inches x² + 36x + 288 square inches 288 + x² square inches
Answers
The area of the entire window expressed as a function of x is x²+36x+288 square inches
How to express the area of the window as a function of x?
Given that: The glass portion of a small window is 12 inches by 24 inches
The framework on each side adds on x inches
That means (x+12) by (x+24) inches. This is the representation of the area of the entire window as a function of x. Thus:
(x+12)(x+24) = x(x+24) + 12(x+24) (Clear the brackets)
= x²+24x+12x+288 (Add like terms)
= x²+36x+288 in²
Therefore, the area of the entire window as a function of x is x²+36x+288 square inches
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calculate the surface area of a tetrahedron with four faces and a base of 1 square foot and a height of 0.866 foot
Answers
The surface area is given by:
[tex]SA=B+\frac{1}{2}ph[/tex]Where:
B = Area of the base
h = height
p = Perimeter of the base
so:
[tex]\begin{gathered} SA=1+\frac{1}{2}(4)(0.866) \\ SA=2.732ft^2 \end{gathered}[/tex]If _____________, then the graph of the polynomial function is symmetric about the origin.f(x) = -f(-x)f(x) = -f(x)f(x) = f(-x)f(x) = f(x + 1)
Answers
ANSWER:
1st option: f(x) = -f(-x)
STEP-BY-STEP EXPLANATION:
The polynomial function is symmetric about the origin in the odds functions, where the following is true:
[tex]\begin{gathered} f(-x)=-f(x) \\ \\ \text{ Therefore:} \\ \\ f(x)=-f(-x) \end{gathered}[/tex]Then it would be:
If f(x) = -f(-x), then the graph of the polynomial function is symmetric about the origin.
The correct answer is the 1st option: f(x) = -f(-x)
3(x + 10) < 2 (20 – x)
Answers
3(x + 10) < 2 (20 – x)
Distributing multiplication over the addition and the subtraction, we get:
3x + 3*10 < 2*20 - 2x
3x + 30 < 40 - 2x
30 is adding on the left, then it will subtract on the right.
2x is subtracting on the right, then it will add on the left.
3x + 2x < 40 - 30
5x < 10
5 is multiplying x on the left, then it will divide on the right.
x < 10/5
x < 2
Carmelo puts $2,200.00 into savings bonds that pay a simple interest rate of 3.4%. How much money will the bonds be worth at the end of 5.5 years? (Find the total worth of the bonds in 5.5 years)
Answers
Let's begin by listing out the information given to us:
Principal (P) = $2,200, Interest rate (r) = 3.4% = 0.034, Time (t) = 5.5 years
[tex]\begin{gathered} I=P\cdot r\cdot t=2200\cdot0.034\cdot5.5 \\ I=\text{ \$414.40} \end{gathered}[/tex]The bond will be worth the sum of the Principal and the Interest:
[tex]\begin{gathered} P+I=2200+411.40 \\ \Rightarrow\text{ \$}2611.40 \end{gathered}[/tex]a ladder 15 feet long leans against a house and make a angle of 60 degrees with the ground . find the distance from the house to the foot of the ladder .
Answers
We can use the next diagram in order to solve the question
we need to find x, x is the distance from the house to the foot of the ladder, we will use a trigonometric function in order to find x in this case we will use the cosine
[tex]\cos (\theta)=\frac{AS}{H}[/tex]where
θ= 60°
AS=x
H=15 ft
we substitute the values
[tex]\cos (60)=\frac{x}{15}[/tex]we need to isolate the x
[tex]x=\cos (60)(15)=7.5ft[/tex]the distance from the house to the foot of the ladder is 7.5 ft