Answers
a domain for a rational is any values of "x" that are safe, namely will not make the denominator undefined, there are a few other constraints, but this is the only one in this case.
so, what values "x" cannot take on safely? well, we can find out what makes the denominator to 0, by simply, yeap, you guessed it, zeroing it out, let's do so,
[tex]\bf 5x+2=0\implies 5x=-2\implies x=-\cfrac{2}{5}[/tex]
so, if ever "x" becomes -2/5, our handy dandy fraction will go poof.
so the domain is all real numbers for "x", EXCEPT -2/5, or in Set Builder notation, {x | x ∈ ℝ; x ≠ -⅖}
Related Questions
A total of 705 tickets were sold for the school play. they were either adult tickets or student tickets. there were 55 more student tickets sold than adult tickets. how many adult tickets were sold?
Answers
Adults = 325
use the following system of equations:
x - y = 55
x + y = 705
There were 380 student tickets and 325 adult tickets were sold for the school play.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Let the number of student tickets would be x and the number of adult tickets would be y
As per the given question, the following system of equations:
x - y = 55 ....(i)
x + y = 705 ....(ii)
Add both equations,
x - y + x + y = 55 + 705
2x = 760
x = 760 / 2
x = 380
Substitute the value of x = 380 in equation (ii),
x + y = 705
380 + y = 705
y = 705 - 380
y = 325
Hence, there were 380 student tickets and 325 adult tickets were sold for the school play.
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If x varies directly as y, and x = 48 when y = 16, find x when y = 5.
A) 5/3
B) 153.6
C) 15
Answers
1. You have the following information given in the problem above: x varies directly as y. When x is 48, y is 16.
2. Keeping the information above on mind, you have:
y=x/k
Where k is the constant of variation
3. Then, the value of k is:
k=x/y
k=48/16
k=3
4. Therefore, when when y=5, the value of x is:
y=x/3
x=(5)(3)
x=15
5. Then, as you can see, the correct answer is the last option (Option C), which is:
C. 15
Is this function one-to-one? Explain how you determine your answer
Answers
Find the 86th term of the arithmetic sequence 21, 15, 9, ...21,15,9,...
Answers
The 86th term of the arithmetic sequence is [tex]\(-489\).[/tex]
To find the 86th term of the arithmetic sequence, we can use the formula for the nth term of an arithmetic sequence:
[tex]\[ a_n = a_1 + (n - 1) \cdot d \][/tex]
where:
- [tex]\( a_n \)[/tex] is the nth term,
- [tex]\( a_1 \)[/tex] is the first term,
- ( n ) is the term number,
- ( d ) is the common difference.
In this sequence:
- [tex]\( a_1 = 21 \),[/tex]
- [tex]\( d = 15 - 21 = -6 \).[/tex]
Now, we can plug these values into the formula to find the 86th term:
[tex]\[ a_{86} = 21 + (86 - 1) \cdot (-6) \][/tex]
[tex]\[ a_{86} = 21 + 85 \cdot (-6) \][/tex]
[tex]\[ a_{86} = 21 - 510 \][/tex]
[tex]\[ a_{86} = -489 \][/tex]
So, the 86th term of the arithmetic sequence is [tex]\(-489\).[/tex]
A movie theater is 3 blocks due north of a supermarket and a beauty parlor is 4 blocks due east of the movie theater. how many blocks long is the nearest street that runs directly from the supermarket to the beauty parlor?
Answers
The legs of the triangle are 3 blocks and 4 blocks.
The question is about finding the hypotenuse.
Therefore,
Hypotenuse = Sqrt (3^2+4^2) = 5 blocks. The street is 5 blocks long.
Can someone help me find the area of the following figure
Answers
Like you drew, there is an imaginary triangle missing. We can find the dimensions of it by subtracting from the given information. The shorter leg of it is 21 - 12 = 9, the longer leg is 28 - 14 = 14.
Now we find the area of the triangle. Area of a triangle is 1/2 * base * height. So 1/2 * 9 * 14 = 1/2 * 126 = 63.
Now we do the full area of 588 minus the area of the missing triangle piece.
588 - 63 = 525 ft²
2. Do the area of the rectangle and then this time add on the area of the triangle. 7 * 15 = 105. Area of the triangle = 1/2 * 2 * 7 = 1/2 * 14 = 7.
105 + 7 = 112 in²
If you work 52 weeks/year and 40 hours/week, how many hours would you work in one year?
Answers
Today, 32 customers at Tasha's Juice Emporium bought a total of 512 ounces of juice. How much juice did each customer buy on average?
Answers
The amount of juice did each customer buy on average is,
⇒ 16 ounces
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
Today, 32 customers at Tasha's Juice Emporium bought a total of 512 ounces of juice.
Hence, The amount of juice did each customer buy on average is,
⇒ 512 / 32
⇒ 16 ounces
Thus, The amount of juice did each customer buy on average is,
⇒ 16 ounces
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The Menswear Department of Nancy‘s Department Store had sales of $191,000, cost of goods sold of $134,000, indirect expenses of $13,550, and direct expenses of $27,800 for the current period. What is the Menswear Department's contribution to overhead as a percent of sales?
Answers
To calculate the overhead contribution, divide the indirect expenses by the total sales, and multiply by 100. The Menswear Department's contribution to overhead as a percent of sales for this period is approximately 7.09%.
Explanation:The student is asking about calculating the overhead contribution rate. Overhead contribution can be calculated by dividing indirect expenses by total sales and multiplying by 100. In this case, total sales for the Menswear Department are $191,000 and indirect expenses are $13,550.
Therefore, the rate is calculated as follows: ($13,550 / $191,000) * 100 = 7.09%. Thus, the Menswear Department's contribution to overhead as a percent of sales is 7.09%.
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What is true about side AB and side AD?
1) The slopes are the same.
2)The slopes are the opposite reciprocal.
Answers
Is (3, 2) a solution to this system of equations?
8x + 7y = 37
2y = 4x - 2
Answers
and 2y = 4x is correct
hope it helps :)
edit i was incorrect about second answer it would be
2y =4x-4
What’s the answer to question 13
Answers
Find the exact values ofcos (3pi/4radians) and sin (3pi/4 Radians)
Answers
[tex]\sin\dfrac{3\pi}{4}=\sin\left(\pi-\dfrac{\pi}{4}\right)=\sin\dfrac{\pi}{4}=\dfrac{\sqrt2}{3}[/tex]
Look at the picture.
[tex]\dfrac{\pi}{2} \ \textless \ \dfrac{3\pi}{4} \ \textless \ \pi\\\\therefoere\\\\\cos\dfrac{3\pi}{4} \ \textless \ 0\ and\ \sin\dfrac{3\pi}{4} \ \textgreater \ 0[/tex]
Which expression is another way to show 9/2
Answers
The expression 9/2 can be equivalently expressed as the mixed number 4 1/2, or by multiplying the numerator and denominator by the same number, such as 18/4.
Explanation:The question asks for an expression that is equivalent to 9/2. One way to express this fraction differently is by converting it into a mixed number. Since 9 divided by 2 is 4 with a remainder of 1, we can express 9/2 as 4 1/2 (four and a half). Another method is to multiply both the numerator and the denominator by the same number, which does not change the value of the fraction.
For example, multiplying both by 2 gives us 18/4, which is equivalent to 9/2. Multiplying or dividing both the numerator and denominator by the same non-zero number is a skill that can provide equivalent fractions.
Find the area of the entire slice of pizza. Since the slice of pizza is part of a whole pie, let’s think of the pizza as a sector of a circle. Calculate the area. Be sure to show all of you work.
Answers
Answer:
The area of the entire slice of pizza = 14.13 square inches
Step-by-step explanation:
From the given figure of pizza.
The radius of the pizza is 6 in.
Central angle = 45°
The pizza is in the shape of the circle. We need to find the entire slice of pizza.
Here we have to use the formula to find the area of sector of a circle.
Area of a sector of a circle = [tex]\frac{Central angle}{360} *\pi *r^2[/tex]
Now plug in central angle = 45, r = 6 in the above formula to find the area of the slice of the pizza.
The area of the entire slice of pizza = [tex]\frac{45}{360} *3.14*6^2[/tex]
The value of π = 3.14
= [tex]\frac{45}{360} *3.14*36[/tex]
Simplifying, we get
= [tex]\frac{45}{10} *3.14[/tex]
= 141.3/10
The area of the entire slice of pizza = 14.13 square inches
Solve x2 + 10x + 12 = 36 for x. x = â12 or x = 2 x = â11 or x = 1 x = â2 or x = 12 x = â1 or x = 11
Answers
57(1.31)^t interpret the meaning of the expression
A. The initial number of bacteria is 57 and the growth rate is 3.1% per hour
B. The initial number of bacteria is 57 and the growth rate is 31% per hour
C.the initial number of bacteria is 131 and the growth rate is 5.7% per hour
D.the initial number of bacteria is 131 and the growth rate is 57% per hour
Answers
y = A * (b) ^ t
Where,
A: initial amount
b: growth rate
t: time
We then have the following equation:
y = 57 (1.31) ^ t
The initial number of bacteria is 57 and the growth rate is 31% per hour.
Answer:
B. The initial number of bacteria is 57 and the growth rate is 31% per hour
B. The initial number of bacteria is 57 and the growth rate is 31% per hour
57 is the initial all by itself and 31 is the growth rate. Don't really know why and how to explain the Percentage application but I got the answer correct on my test so.................................
All of the following represent the same expression except _____.
-8ab
-8(a)(b)
8 - ab
-8 · a · b
Answers
8 - ab
looks like subtraction to me
hope that helps
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The expression that is not the same as the rest of the expressions is
8 - ab.
Option C is the answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example:
2 + 3x + 4y = 7 is an expression.
3x - 5 is an expression.
4x + 4 is an expression.
4 x 5 - 5x is an expression.
We have,
1) -8ab
2) -8 (a) (b)
= -8ab
3) 8 - ab
4) -8.a.b
= -8ab
We see that,
All the expressions are the same except the expression
8 - ab
Thus,
The expression that is not same with the rest of the expression is
8 - ab.
Option C is the answer.
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!!!!WILL MARK BRAINLIEST IF CORRECT AND IF YOU ANSWER ALL PARTS OF QUESTION! SHOW WORK PLEASE!!!!!
2. A cube-shaped aquarium has edges that are 3 ft long. The aquarium is filled with water that has a density of 62 lb/ft^3
(a) Should the aquarium be placed on a table that can support a maximum weight of 200 lb? Explain why or why not.
(b) Would the density of the water change if the aquarium was only half full? Explain.
Answers
The table will support a little over 3 ft³ of water. The volume of the aquarium is (3 ft)³ = 27 ft³, substantially larger. Hence the weight of the filled aquarium is substantially more than the table can support.
(b) NO.
The density of water (mass per volume) at a given temperature is substantially constant. That is, water is regarded as an "incompressible fluid." (Water does compress so that its density increases very slightly at extreme depth, but the effect is not measurable over a depth of 1.5 to 3 feet.) Temperature has a much greater effect on the density of water than does depth.
A basketball is theown upwards. The height F(t), The height in feet, in time, t, in seconds is goven by the following. f(t)= -16t(2) +44+ 12. Which of the following is a reasonable domain of the graphof the function when the basketball falls from ots maximum height to the ground?
Answers
[tex](1.4 \: comma \: 3)[/tex]
those parentheses should be brackets, but their isnt any in the equation feature.
Given the quadratic function : f(x)=x^24x-12
Find the vertex.
Can you show the steps?!?
Answers
Say it with symbols a pool has lenght of 3s and a width of 2s. square tiles that are 1 ft. by 1ft. will be placed around the pool as the a border. write an expression that can be used to determine to create the border for pool size.
Answers
P = 2L + 2W (L represents length, W represents width)
P = 2(3s) + 2(2s)
P = 6s + 4s
P = 10s
Caleb and Emily are standing 100 yards from each other. Caleb looks up at a 45° angle to see a hot air balloon. Emily looks up at a 60° angle to see the same hot air balloon. Approximately how far is the hot air balloon off the ground?
Answers
Answer:
63.39 yards.
Step-by-step explanation:
Refer the attached figure
We are given that Caleb and Emily are standing 100 yards from each other i.e. BC = 100
Let BD = x
So, DC = 100-x
We are given that Caleb looks up at a 45° angle to see a hot air balloon i.e. ∠ABD = 45° and Emily looks up at a 60° angle to see the same hot air balloon i.e. ∠ACD = 60°
Let AD be the height of the balloon denoted by h.
In ΔABD
Using trigonometric ratio
[tex]tan \theta = \frac{Perpendicular}{Base}[/tex]
[tex]tan 45^{\circ} = \frac{AD}{BD}[/tex]
[tex]1= \frac{h}{x}[/tex]
[tex]x=h[/tex] ---1
In ΔACD
Using trigonometric ratio
[tex]tan \theta = \frac{Perpendicular}{Base}[/tex]
[tex]tan 60^{\circ} = \frac{AD}{DC}[/tex]
[tex]\sqrt{3}= \frac{h}{100-x}[/tex]
[tex]\sqrt{3}(100-x)=h[/tex] ---2
So, equating 1 and 2
[tex]\sqrt{3}(100-x)=x[/tex]
[tex]100\sqrt{3}-\sqrt{3}x=x[/tex]
[tex]100\sqrt{3}=x+\sqrt{3}x[/tex]
[tex]100\sqrt{3}=x(1+\sqrt{3})[/tex]
[tex]\frac{100\sqrt{3}}{1+\sqrt{3}}=x[/tex]
[tex]63.39=x[/tex]
Thus the height of the balloon is 63.39 yards.
Answer:
B
Step-by-step explanation:
What is the value of y?
I think the hypotenuse is 8 and if it is, am I supposed to do
C^2 - B^2 = A^2?
Answers
make sure your calculator is in Degree mode.
The angle, 60, is directly opposite with what you're trying to find, y. Also since you have another side of the triangle that is identified, you can figure what trig function to use. The line next to the angle is the adjacent. We have the adjacent and opposite. The trig function that implements both sides is the Tangent. The formula for it is tangent(angle) = opposite/adjacent.
Now substitute the number into the formula.
tan(60) = y / 5
We need to isolate y, so we times 5 and tan(60)
tan(60) x 5 = 8.66
y is now isolated and the answer is 8.66 = y
Which pair of numbers are not opposites? Select one: a. |7| and -7 b. 72 and -72 c. 27 and |-27| d. 27 and -27
Answers
|-27| = 27 which is positive and not negative
Saying "27 and |-27|" is the same as saying "27 and 27". We can replace |-27| with 27 as they are equal. In order for them to be opposites, one has to be negative and the other positive; however, both are positive.
Which graph shows a plot of the complex number i - 2
Answers
i - 2
The first thing you should remember is that in a complex number plane:
The vertical axis represents the imaginary part.
The horizontal axis represents the real part.
Answer:
See attached image.
A classroom of children has 16 boys and 19 girls in which five students are chosen to do presentations. what is the probability that at least four boys are chosen?
Answers
Total number of boys = 16
Total number of girls = 19
Favorable outcomes = BBBBB, BBBBG, BBBGB, BBGBB, BGBBB, GBBBB
P(at least 4 boys) = (16/35)(15/34)(14/33)(13/32)(12/31) + 4 (16/35)(15/34)(14/33)(13/32)(19/31) = 78/5797 + 494/5797 = 52/527
Answer: 52/527
The probability of at least four boys from five selected students depends on the ratio of the favorable outcomes (either four boys and one girl, or all five are boys) to the total combinations of five students from 35, calculated using Combinatorics.
Explanation:The subject of your question is Probability, which falls under Mathematics. The question can be approached through Combinatorics, a branch of Mathematics that deals with combinations of objects belonging to a finite set following certain constraints.
To address your question, we first need to find the total number of ways that five students can be selected from the total 35 (16 boys and 19 girls). This can be calculated using combinations, denoted as C(n, r), where n is the total number of elements and r is the number of elements to choose from the total. In this case, the total combinations would be C(35, 5).
Next, we need to find the combinations where at least four boys are chosen. This could mean either four boys and one girl are chosen, or all five chosen are boys.
For the situation where four boys and one girl are chosen, the possible combinations would be C(16, 4) * C(19, 1). For the situation where all chosen are boys, the possible combinations would be C(16, 5).
So, the total desired combinations would be C(16, 4)*C(19, 1) + C(16, 5).
The probability of choosing at least four boys would be the ratio of desired combinations to the total combinations. Thus, Probability = [C(16, 4)*C(19, 1) + C(16, 5)] / C(35, 5).
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Write the sum using summation notation, assuming the suggested pattern continues.
-8 - 3 + 2 + 7 + ... + 67
Answers
Remark: L = a + (n - 1)d is your starting point. In order to find the sum, you must know the value of n.
Givens: a = - 8; d=5; L = 67
Substitute and solve
67 = - 8 + (n - 1)*5 Add 8 to both sides.
67 + 8 = -8 + 8 + (n - 1)*5
75 = (n - 1)*5 Divide by 5 on both sides.
15 = n - 1 Add one to get the answer.
16 = n
Part Two: Use The summation notation to find the sum. Unfortunately, I don't know how to do this in latex.
Sum (n = 1 to 16) -8 + 5*(n - 1)
The dot product of u with itself is 24. what is the magnitude of u?
Answers
Answer - u = 4.8989
u ^ 2 = 24
u = sqrt (24)
u = 4.8989
Answer:
[tex]2\sqrt6[/tex]
Step-by-step explanation:
We have been given that the dot product if u with itself is 24.
Now, we know that the dot product of vector a and b is given by
[tex]a\cdot b=|a||b|\cos\theta[/tex]
Here, [tex]\theta[/tex] is the angle between the vectors a and b.
We have to find the dot product of u with itself. Hence,
a = u
b = u
[tex]\theta=0[/tex]
Thus, dot product is given by
[tex]u\cdot u=|u||u|\cos0\\\\24=|u||u|\cdot1\\\\|u|^2=24\\\\|u|=2\sqrt6[/tex]
Thus, the magnitude of u is [tex]2\sqrt6[/tex]
Keisha can jog 2 miles in 24 minutes. At the same rate , how many miles can she jog in 60 minute