Final answer:
To find the quotient of 3 ÷ 2 1/3, convert the mixed number to an improper fraction (7/3), find the reciprocal (3/7), and multiply it by 3 to get 9/7, which is the answer in lowest terms.
Explanation:
The quotient of 3 ÷ 2 1/3 can be found by first converting the mixed number 2 1/3 to an improper fraction. The mixed number 2 1/3 is equal to ⅔, which when summed (2 * 3 + 1), gives us 7/3. To divide by a fraction, you multiply by its reciprocal. Thus, we have 3 × ⅓ (which is 3/7). Multiplying these we get 9/7, which cannot be further simplified. Therefore, the quotient in lowest terms is 9/7.
The quotient of 3 ÷ 2 1/3 is found by converting 2 1/3 to an improper fraction (7/3), taking the reciprocal (3/7), and multiplying it with 3. The result is the fraction 9/7, which is already in lowest terms.
Explanation:To find the quotient of 3 ÷ 2 1/3, we first convert the mixed number to an improper fraction. The mixed number 2 1/3 is equivalent to 7/3 (because 2 × 3 + 1 = 7). To divide by a fraction, we multiply by its reciprocal. Therefore, we need to multiply 3 by the reciprocal of 7/3, which is 3/7.
The multiplication is straightforward: 3 × 3/7. We multiply the numerators (3 × 3) to get 9, and the denominators (1 × 7) to get 7, so we have 9/7. Since 9 and 7 have no common factors other than 1, 9/7 is already in its lowest terms. Thus, the quotient is 9/7 or 1 2/7 when expressed as a mixed number.
What are the real and complex solutions of 0=x^4+3x^2-4
Answer:
(2i,0) (-2i,0)
(1,0) (-1,0).
Step-by-step explanation:
The graph below shows that there are only 2 real solutions at x = 1 and x = - 1
Expressed as points, these two are (1,0) and (-1,0). However that is not the complete answer. There are 2 complex points.
y = x^4 + 3x^2 - 4
y = (x^2 - 1)(x^2 + 4)
These two binomials can be equated to 0
x^2 - 1 = 0x^2 = 1sqrt(x^2) = sqrt(1)x = +/- 1Expressed as points (1,0)(-1,0)================
x^2 + 4 = 0x^2 = - 4sqrt(x^2) = sqrt(-4)x = +/- 2 iExpressed as "points" these two can be written as (2i,0) (-2i,0)Can someone help me
Answer:
The scale factor used was 1/2
hope this helped
Step-by-step explanation:
What is the product 4n/4n-4 n-1/n+1
Jeremy is driving on the interstate highway, and he just saw a sign that said Montpelier was 52 miles away. If he's driving at 65 miles per hour, how many minutes will it take him to get to Montpelier?
Answer:
48 min
Step-by-step explanation:
1 h = 60 min
It takes 60 min to go 65 mi.
Time = 52 × 60/65
Time = 48 min
Answer:
48min
Step-by-step explanation:
I used this question and got it right on my test. :)
find three consecutive even integer with the sum of -84
Caroline wants to give 8 equal size packets of flower seed to her friends .She has ½ pound of flowers seeds. How much will each packet of seeds weigh?
Answer:
16
Step-by-step explanation:
We want to divide 1/2 pound in 8 equal parts
1/2 dividend by 8/1 is the same as
1/2 multiplied by 1/8 =1•1/2•8=1/16
Each package will weigh 1/16 of a pound
Or 1 ounce since 1 pound = 16 oz
480 divided by 8 long division
Answer:
60
Step-by-step explanation:
The required result is 60 when 480 is divided by 8, with no remainder.
What is the long division?In mathematics, divides left-hand operands into right-hand operands in the division operation.
To divide 21,900 by 25, we can perform long division as follows:
8 ) 480 ( 60
- 480
________
0
When we divide the first digit of 480 (which is 4) by the divisor 8, which gives us 60 with a remainder of 0.
Therefore, 480 divided by 8 is 60, with no remainder.
To learn more about the division operation click here :
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The complete question would be as:
What is the result when 480 is divided by 8 long division?
ANSWER QUICK PLEASE
If f(x) = |x – 5| + 3, find f(2).
Answer:
SO if f(x)= |x-5|+3 then F(2)= 6
Step-by-step explanation:
These signs | | mean that it is an absolute value equation. SO that means any negative will automatically change to positive values and positive values will stay at positive values. You are supposed to substitute 2 in for x and if you do 2-5 then that is negative 3 but it changes to positive 3 and add three and then f(2)= 6
what is the value of the sum? Drag and drop the answer into the box to match the sum with its value. -3/8 + 5/16. Answer Choices----------- -11/16, -1/16, 1/16, 1/4, 11/16.
Kate had 50 50 tickets to use for rides at the fair. She lost some of them. Her dad doubled the tickets she had left. Kate wrote the expression 2(50−t) 2 ( 50 - t ) to find the number of tickets she has now, where t t is the number of tickets she lost. Jack correctly wrote another expression, 100−2t 100 - 2 t , to find the number of tickets Kate has now. Use the drop-down menus to explain what each part of Kate's and Jack's expressions mean.
Answer: Kate expression: 2(50-t)
2 : represents twice,
50 : represents Initial number of tickets Kate has,
t : The lost tickets
50-t : represents Number of ticket Kate has After loosing t tickets
Jack expression: 100 - 2t
100 : Twice of initial ticket Kate has,
t : The lost tickets
2t : represents twice of the lost tickets,
100-2t : represents Final number of ticket Kate has.
Step-by-step explanation:
Since, According to the question,
Initially Kate has 50 tickets.
She lost tickets = t
And, after losing t ticket she has tickets = 50 - t
But, His father doubled the amount, Thus she has final tickets = 2(50-t)= 2×50 -2× t = 100 - 2t
Final answer:
Kate's expression, 2(50−t), represents the number of tickets she has now by doubling the tickets she had left after losing some. Jack's expression, 100−2t, represents the number of tickets Kate has now by subtracting twice the number of tickets she lost from the total number of tickets she initially had.
Explanation:
Kate wrote the expression 2(50−t) to find the number of tickets she has now. In this expression, t represents the number of tickets she lost. The expression is simplified as follows: multiply 2 by the quantity (50−t). This means that Kate's dad doubled the tickets she had left after losing some tickets.
Jack's expression, 100−2t, also determines the number of tickets Kate has now. In this expression, t represents the number of tickets she lost. The expression is simplified as follows: subtract 2 times the quantity t from 100. This means that Jack found the number of tickets Kate has by subtracting twice the number of tickets she lost from the total number of tickets she initially had.
A line has a Y-intercept of 6 and a slope of 8. What is its equation in slope-intercept form?
Answer:
y = 8x + 6
Step-by-step explanation:
The slope intercept form is: y = mx + c
where m ⇒ slope
c ⇒ y-intercept
(x,y) is a point on the graph the satisfy the equation representing that graph. x is the x-coordinate of a point on the line and y is the y-coordinate of a point on the line.
m = 8
Y-intercept = 6
y = mx + c ⇒ y = 8x + 6
On a piece of paper, graph y≤ -2x.Then determine which answer matches the graph you drew.
A.(-2,4) (3,-6)
B.(-2,4) (1,2)
C.(-2,-6) (1,3)
D.(-2,-6) (1,3)
Answer:
The correct option is A.
Step-by-step explanation:
The given inequality is
[tex]y\leq -2x[/tex]
The sign of inequality is ≤, it means the points on relation line lie in the solution set.
The related equation of the inequality is
[tex]y=-2x[/tex]
At x=0,
[tex]y=-2(0)=0[/tex]
At x=1,
[tex]y=-2(1)=-2[/tex]
Plot the points (0,0) and (1,-2) on a coordinate plane.
The sign of inequality is ≤, it means we have shade below the line.
The point (-2,4) and (3,-6) are in solution set because,
[tex]4\leq -2(2)\Rightarrow 4\leq 4[/tex] (True)
[tex]-6\leq -2(3)\Rightarrow -6\leq -6[/tex] (True)
Therefore option A is correct.
The points (1,2) and (1,3) are not in the solution set because,
[tex]2\leq -2(1)\Rightarrow 2\leq -2[/tex] (False)
[tex]3\leq -2(1)\Rightarrow 3\leq -2[/tex] (False)
Therefore options B,C and D are incorrect.
Answer: (1,2) (-2,-4)
Step-by-step explanation:
If x= -5+6i and y= 3-2x, then which of the following is the value of the expression 4x-y
[tex]y=3-2x\\\\4x-y=4x-(3-2x)=4x-3+2x=6x-3\\\\\text{Put}\ x=-5+6i\ \text{to the expression}\ 6x-3:\\\\6(-5+6i)-3\qquad\text{use distributive property}\\\\=(6)(-5)+(6)(6i)\\\\=-30+36i\\\\Answer:\ \boxed{4x-y=-30+36i}[/tex]
Adeline types 150 words in 2 minutes. Enter the number of words Adeline types in 6 minutes at this rate
Answer:
450
Step-by-step explanation:
what is the range if the function in this table?
The range of a function is the set of y-values the function contains. Thus, in this case, the range would be the set of values under the y column, as this represents the y-values the function produces.
We see "2, 3, 4, 2" under the y column. Since we are establishing a set of values, we are going include all the values under the column, which includes 2, 3, and 4. We are not going to repeat the second 2 because it isn't necessary, as 2 is already in the set thus.
Thus, the final set for the range of the function is {2, 3, 4}, or Choice A.
ASAP what is the value of a number raised to the power of 1?
Final answer:
The value of any number raised to the power of 1 is the number itself, as it implies a single multiplication of the number by 1.
Explanation:
The value of a number raised to the power of 1 is always the number itself. This is because an exponent represents how many times to multiply the number by itself. When the exponent is 1, you are simply multiplying the number by 1, which does not change its value.
For example:
51 = 5101 = 10-31 = -3tell whether the ratio is in simplest form, if not, then write it in simplest form 1)8:6 2)48/28 3)7 to 9
8/6= 1 1/3
48/28= 1 4/7
7/9 is in simplest form
3m+5=8 help plz on math
Answer:
m = 1
Step-by-step explanation:
Given -> 3m + 5 = 8
Subtraction -> 3m = 3
Division -> m = 1
Answer:
m= 1
Step-by-step explanation:
3m +5 = 8 Substract 5 to both sides
3m = 3 Divide 3 in both sides
m = 1
Find the slope of the line represented by the table of values.
A) 1/2
B) 2
C) −1/2
D) −2
Answer:
D) -2
Step-by-step explanation:
Answer:
D- -2
Hope this helps :)
Which sequence is geometric and has `1/4` as its fifth term and `1/2` as the common ratio?
Answer:
4, 2, 1, [tex]\frac{1}{2}[/tex], [tex]\frac{1}{4}[/tex], .....
Step-by-step explanation:
Fifth term (a₅) = [tex]\frac{1}{4}[/tex]
Common ratio (r) = [tex]\frac{1}{2}[/tex]
n = 5
The formula to find the [tex]n^{th}[/tex] term of a geometric sequence is
a₅ = a₁r⁽ⁿ⁻¹⁾
=> [tex]\frac{1}{4}[/tex] = a₁*[tex](\frac{1}{2})^{(5-1)}[/tex]
=> [tex]\frac{1}{4}[/tex] = a₁*[tex](\frac{1}{2})^{(4)}[/tex]
=> [tex]\frac{1}{4}[/tex] = a₁*[tex](\frac{1}{2})*(\frac{1}{2})*(\frac{1}{2})*(\frac{1}{2})[/tex]
=> [tex]\frac{1}{4}[/tex] = a₁* [tex]\frac{1*1*1*1}{2*2*2*2}[/tex]
=> [tex]\frac{1}{4}[/tex] = a₁*[tex](\frac{1}{16})[/tex]
Flip the sides of the equation
a₁*[tex](\frac{1}{16})[/tex] = [tex]\frac{1}{4}[/tex]
Multiply both sides by 16
a₁*[tex](\frac{1}{16})[/tex]*16 = [tex]\frac{1}{4}[/tex]*16
Cancelling out the 16's from the top and bottom of the left side
a₁ = [tex]\frac{16}{4}[/tex]
=> a₁ = 4
So, first term of the geometric sequence is 4.
Common ratio = [tex]\frac{1}{2}[/tex]
Second term = First term * Common ratio
= 4* [tex]\frac{1}{2}[/tex]
= [tex]\frac{4}{2}[/tex]
= 2
Third term = Second Term * Common ratio
= 2 * [tex]\frac{1}{2}[/tex]
= [tex]\frac{2}{2}[/tex]
= 1
Fourth term = Third Term * Common ratio
= 1 * [tex]\frac{1}{2}[/tex]
= [tex]\frac{1}{2}[/tex]
Fifth term (given) = [tex]\frac{1}{4}[/tex]
So, the geometric sequence would be
4, 2, 1, [tex]\frac{1}{2}[/tex], [tex]\frac{1}{4}[/tex], .....
You are helping a classmate edit this story. Your classmate decides to change the point of view and write the story from the third person point of view as if the story happened to a group of friends. What change is necessary? Names of the friends should be included. The pronoun we should be changed to they. The pronoun we should be changed to I. Explain in more detail the lesson the friends learned.
To change the story from first person to third person point of view, first-person pronouns like 'I', 'me', and 'we' should be changed to third-person pronouns such as 'they', 'he', 'she', or the friends' names.
Explanation:To change the point of view of the story from first person to third person, it is necessary to change the pronouns used in the narration. If the original story used first-person pronouns such as I, me, and we, these would need to be changed to third-person pronouns such as they, he, she, or the friends' names to reflect the third person point of view.
For example, a sentence that originally reads "We went to the park after school" would change to "They went to the park after school" in the third person point of view. This shift enables the story to be told as if an outside observer is describing the events that happen to the group of friends, rather than the friends themselves narrating the story.
Given: KLMN is a trapezoid, m∠N=m∠KML, FD=8, LM KN = 3 5 F∈ KL , D∈ MN , ME ⊥ KN KF=FL, MD=DN, ME=3 5 Find: KM
Answer:
The length of side KM is [tex]\sqrt{109}[/tex] units.
Step-by-step explanation:
Given information: KLMN is a trapezoid, ∠N= ∠KML, FD=8, LM:KN=3:5, F∈ KL, D∈ MN , ME ⊥ KN KF=FL, MD=DN, [tex]ME=3\sqrt{5}[/tex].
From the given information it is noticed that the point F and D are midpoints of KL and MN respectively. The height of the trapezoid is [tex]3\sqrt{5}[/tex].
Midsegment is a line segment which connects the midpoints of not parallel sides. The length of midsegment of average of parallel lines.
Since LM:KN=3:5, therefore LM is 3x and KN is 5x.
[tex]\frac{3x+5x}{2}=8[/tex]
[tex]\frac{8x}{2}=8[/tex]
[tex]x=2[/tex]
Therefore the length of LM is 6 and length of KN is 10.
Draw perpendicular on KN form L and M.
[tex]KN=KA+AE+EN[/tex]
[tex]10=6+2(EN)[/tex] (KA=EN, isosceles trapezoid)
[tex]EN=2[/tex]
[tex]KE=KN-EN=10-2=8[/tex]
Therefore the length of KE is 8.
Use pythagoras theorem is triangle EKM.
[tex]Hypotenuse^2=base^2+perpendicular^2[/tex]
[tex](KM)^2=(KE)^2+(ME)^2[/tex]
[tex](KM)^2=(8)^2+(3\sqrt{5})^2[/tex]
[tex]KM^2=64+9(5)[/tex]
[tex]KM=\sqrt{109}[/tex]
Therefore the length of side KM is [tex]\sqrt{109}[/tex] units.
The answer is [tex]\sqrt{70}[/tex]
A student took a system of equations, multiplied the first equation by and the second equation by , then added the results together. Based on this, she concluded that there were no solutions. Which system of equations could she have started with?
A. -2x+4y=4
-3x+6y=6
B.3x+y=12
-3x+6y=6
C.3x+6y=9
-2x-4y=4
D. 2x-4y=6
-3x+6y=9
Answer:
option A
-2x + 4y = 4
-3x + 6y = 6
Step-by-step explanation:
In option A, if the student multiply the first equation by 3 and the second equation by -2, then the equations become
-6x+12y = 12 and
6x-12y =-12
If she adds both equations, she will get 0 = 0
This means that the system has infinite number of solutions.
Hence, the student could have started with equations -2x + 4y = 4 and -3x + 6y = 6.
A motor running at 4500 RPM, revolutions per minute, is actually revolving at how many revolutions per second?
Answer:
A motor running at 75 revolutions per second.
Step-by-step explanation:
Given statement: A motor running at 4500 RPM, revolutions per minute.
⇒ In one minute , a motor running at 4500 revolutions.
Use conversion:
[tex]1 min = 60 sec[/tex]
We have to calculate how many revolutions per second.
in 60 sec , a motor running at 4500 revolutions
then,
in 1 sec , a motor running at [tex]\frac{4500}{60} = 75[/tex] revolutions.
Therefore, a motor running at 75 RPS, revolution per second.
Answer:
Motor run in 1 second = 75 revolution.
Step-by-step explanation:
Given : A motor running at 4500 RPM, revolutions per minute,
To find : how many revolutions per second.
Solution : We have given
Motor run in minute = 4500 revolution.
1 minute = 60 second .
Then ,
Motor run in 60 second = 4500 revolution.
Motor run in 1 second = [tex]\frac{4500}{60}[/tex] revolution.
Motor run in 1 second = [tex]\frac{450}{6}[/tex] revolution.
Motor run in 1 second = 75 revolution.
Therefore, Motor run in 1 second = 75 revolution.
Geometry, Angle Relationships Theorems question
I'm sure this looks a lot harder than it really is, but any help would be appreciated because I'm stumped. I'm supposed to fill in the green boxes but I can't figure out what to do. Thanks :)
Answer:
Step-by-step explanation:
1. <3 = <4 1 Given
2. <2 <3 are supplementary 2. non common sides in opposite rays
3. <2 + <3 = 180 3. Definition of supplementary angles
4. <2 + < 4 = 180 4 substitution
5. <1 = <4 5 Opposite angles are equal
6 <2 + <1 = 180 6 Substitution
7. <1, <2 are supplementary 7. Definition of supplementary angles
The only word I am not sure of is the last word in 2
A sandwich store charges a delivery fee to bring lunch to an office building. One office pays $33 for 4 turkey sandwiches. Another office pays $61 for 8 turkey sandwiches. How much does each turkey sandwich add to the cost of the delivery? Explain how you know.
Answer:
$7. Based on the assumption that both offices paid the same amount for delivery, the difference in the total cost paid is due to the difference in the number of turkey sandwiches ordered, which is 4. The cost of each sandwich is a quarter of this difference in cost.
Step-by-step explanation:
In mathematical working, the explanation above can be written in the form of equations, where we work to solve the value of a variable. In this case, we are interested to find the value of t.
Define variables:
Let the cost of a turkey sandwich be $t while the delivery fee be $d.
Form 2 equations:
Assuming that the sandwich stores charges the same delivery fee for both offices,
4t + d= 33 -----(1)
8t + d= 61 -----(2)
Solve by elimination:
(2) - (1):
4t= 61 - 33
4t= 28
Divide both sides by 4:
t= 7
Thus, each turkey sandwich adds $7 to the cost of the delivery.
To find out how much each turkey sandwich adds to the cost of delivery, we need to determine the cost of delivery in both cases and subtract it from the total price paid by each office.
Explanation:To find out how much each turkey sandwich adds to the cost of delivery, we need to determine the cost of delivery in both cases and subtract it from the total price paid by each office.
For the first office, they paid $33 for 4 turkey sandwiches. Let's assume the cost of delivery is 'x'. So the equation to represent the total cost is: 4x + 33 = total cost.
Similarly, for the second office, they paid $61 for 8 turkey sandwiches. Let's assume the cost of delivery is 'y'. So the equation to represent the total cost is: 8y + 61 = total cost.
Now we can solve both equations to find the values of 'x' and 'y' which will represent the cost of delivery. Once we have those values, we can calculate how much each turkey sandwich adds to the cost of delivery by dividing the cost of delivery by the number of turkey sandwiches ordered.
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Please answer this as quick as possible. Really need help.
Systems of equations have one solution. (5 points)
Always
Sometimes
Never
Answer:
Sometimes
Step-by-step explanation:
When you deal with a system of equations, there may be no solution; there may be one solution; there any positive integer number of solutions; there may be an infinite number of solutions.
The answer is : sometimes
Answer:
sometimes, I got it right on the quiz I just took :)
Step-by-step explanation:
Anna charges $8.50 per hour to babysit. How much will she earn in 3,3 1/2,4 hours?
Anna earns $8.50 per hour babysitting. For 3, 3.5 and 4 hours of work, she will earn $25.50, $29.75, and $34.00 respectively.
Explanation:Anna earns $8.50 per hour for babysitting. To calculate her earnings, we simply need to multiply the number of hours she worked by her hourly rate.
For 3 hours, she will earn $8.50 * 3 = $25.50. For 3.5 hours, she will earn $8.50 * 3.5 = $29.75. For 4 hours, she will earn $8.50 * 4 = $34.00.Learn more about Hourly Wage Calculation here:
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Solve the system using elimination.
2x + 3y = 17
x + 5y = 19
[tex]\left\{\begin{array}{ccc}2x+3y=17\\x+5y=19&|\text{multiply both sides by (-2)}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}2x+3y=17\\-2x-10y=-38\end{array}\right}\qquad\text{add both sides of equations}\\.\qquad\qquad-7y=-21\qquad\text{divide both sides by (-7)}\\.\qquad\qquad \boxed{y=3}\\\\\\\text{Substitute the value of y to the second equation}\\\\x+5(3)=19\\\\x=15=19\qquad\text{subtract 15 from both sides}\\\\\boxed{x=4}\\\\Answer:\ x=4\ and\ y=3.[/tex]
a train traveled 1/5 of the distance between two cities in 3/4 of an hour ,at this rate what fraction of the distance between two cities can the train travel in one hour
sorry, put the wrong answer and cant delete
Answer:
4/15 distance
Step-by-step explanation:
We can use ratio's to solve this, putting distance over time
1/5 distance x distance
---------------- = ----------------------
3/4 hour 1 hour
Using cross products
1/5 * 1 = 3/4 x
1/5 = 3/4 x
Multiply by 4/3 to isolate x
1/5 * 4/3 = 4/3 * 3/4x
4/15 = x
The train can travel 4/15 of the distance in 1 hour