[tex] \sf \looparrowright \: 8 \frac{1}{6} - 5 \frac{5}{6} [/tex]
Convert the mixed fractions to improper fractions
Denominator × Integer + Numerator = Improper fractionThe Denominator remains the same as before[tex] \underbrace {8\frac{1}{6} = \frac{6 \times 8 + 1}{6} = \frac{49}{6} }[/tex]
[tex] \underbrace {5\frac{5}{6} = \frac{6 \times 5 + 5}{6} = \frac{35}{6} }[/tex]
Now,[tex] \sf \looparrowright \: \frac{49}{6} - \frac{35}{6} [/tex]
Write the numerators above the common Denominator 6
[tex] \sf \looparrowright \: \frac{49 - 35}{6} [/tex]
Calculate the difference
[tex] \sf \looparrowright \: \frac{14}{6} [/tex]
Reduce the fraction with 2
[tex] \sf \looparrowright \frac{7}{3} [/tex]
someone please give a step by step way on how to solve this problem
Answer:
10
Step-by-step explanation:
There are several ways to solve this problem which I’ll demonstrate these ways and see which method is way easier to understand.
First Method
This method is to convert the fractional expression to a single exponent expression using a law of exponent.
[tex]\displaystyle \large{\frac{m^a}{m^b} = m^{a-b}}[/tex]
In words, it means if both divisor (denominator) and dividend (numerator) have same values or are same, we can subtract the exponent from dividend (numerator) with divisor (denominator).
The dividend (numerator) exponent is unknown, let’s say it’s got ‘x’ as an exponent and this ‘x’ is what we are going to find since we don’t know its value.
Now we have the equation:
[tex]\displaystyle \large{\frac{m^x}{m^7} = m^3}[/tex]
Apply the exponent rules above.
[tex]\displaystyle \large{m^{x-7} = m^3}[/tex]
Solve an exponential equation - If both sides of equation have same base, we can solve the exponents.
Since LHS (Left-Handed Side) and RHS (Right-Handed Side) both have same base which is ‘m’ therefore, solve exponents.
[tex]\displaystyle \large{x-7=3}\\\displaystyle \large{x=7+3}\\\displaystyle \large{x=10}[/tex]
Therefore, the missing exponent is 10.
Additional Info
You can also use logarithm to solve an exponential equation.
[tex]\displaystyle \large{m^{x-7} = m^3}[/tex]
Take a logarithm of base ‘m’ both sides so we can apply other properties.
[tex]\displaystyle \large{\log_m m^{x-7} = \log_m m^3}[/tex]
From the property [tex]\displaystyle \large{\log_a b^n = n \log_a b}[/tex]
[tex]\displaystyle \large{(x-7) \log_m m = 3 \log_m m}[/tex]
From the property [tex]\displaystyle \large{\log_a a = 1}[/tex]
[tex]\displaystyle \large{(x-7)1 = 3 \cdot 1}\\\displaystyle \large{x-7=3}\\\displaystyle \large{x=10}[/tex]
______________________________
Second Method
This method is to isolate the term with missing exponent.
[tex]\displaystyle \large{\frac{m^x}{m^7} = m^3}[/tex]
Transport m^7 to multiply with m^3 via transportation property.
[tex]\displaystyle \large{m^x = m^3 \cdot m^7}[/tex]
We also have to apply another law of exponent as well.
[tex]\displaystyle \large{m^a \cdot m^b = m^{a+b}}[/tex]
Similar to the one with division (fraction), this one, when same bases multiply each other, we have to add both exponents while the other one subtracts exponents.
[tex]\displaystyle \large{m^x = m^{3+7}}\\\displaystyle \large{m^x = m^{10}}[/tex]
In the first method, we know that when solving an exponential equation, if two bases from left and right sides are same, we solve the exponent.
Therefore, [tex]\displaystyle \large{m^x = m^{10} \to \boxed{x=10}}[/tex]
______________________________
Summary
Laws of Exponent
[tex]\displaystyle \large{a^m \cdot a^n = a^{m+n}}\\\displaystyle \large{\frac{a^m}{a^n} = a^m \div a^n = a^{m-n}}\\[/tex]
For what I demonstrate in my explanation only.
Exponential Equation
When two bases from left side and right side are same, we can solve through exponents.
Examples:
[tex]\displaystyle \large{2^{x-3} = 2^{4}}\\\displaystyle \large{x-3=4}\\\displaystyle \large{x=4+3}\\\displaystyle \large{x=7}[/tex]
You can also substitute x-value in an equation to see if both sides are equal or not.
[tex]\displaystyle \large{2^{x-4} =2^3}[/tex]
Substitute x = 7 for check.
[tex]\displaystyle \large{2^{7-4} = 2^3}\\\displaystyle \large{2^3 = 2^3 \ \ \checkmark}[/tex]
Logarithm
This is not necessary used in this question. This is mostly used for converting to exponential and more advanced mathematics.
[tex]\displaystyle \large{\log_a b^n = n\log_a b}\\\displaystyle \large{\log_a a = 1}[/tex]
Only from what I demonstrate in my explanation.
______________________________
If you are still stuck or need clarification regarding my answer and explanation, you may ask in comment below.
Hope this helps! And wish you luck in your assignment.
The sum of the second and third terms of a geometric sequence is 280 and the sum of the fifth and the sixth terms is 4375. Determine the common ratio and the first term
Step-by-step explanation:
I'll do it on my laptop.......
first answer = brainliest
In the data set {(0,−1);(−2,4);(−4,−8);(−1,5);(1,−3);(2,1);(3,−2);(−1,2)}, which point is a possible outlier?
(−4,−8)open paren negative 4 comma negative 8 close paren
(2,1)open paren 2 comma 1 close paren
(−1,5)open paren negative 1 comma 5 close paren
(3,−2)
From the coordinate points, we can see that the data point that differs significantly is (−4,−8)
What is an outlier?An outlier in statistics is a data point that differs significantly from other observations in the given data
This may be due to variability in the measurement or it may indicate an experimental error.
From the coordinate points, we can see that the data point that differs significantly is (−4,−8). This gives the possible outlier of the given coordinate
Learn more on outlier here: https://brainly.com/question/3631910
Answer:
It's would be -4,-8 Have a great day
Estimate 5/8 - 1/10
A. 0
B. 1/2
C. 1
D. 1 1/2
Solution:
Make the denominators equivalent and solve.
=> 5/8 - 1/10=> 25/40 - 4/40=> 21/40 ≈ 1/2Hoped this helped!
hi can anyone help with this? 15 points.
Step-by-step explanation:
that a picture of what you need. Go through it and get back to me.
Leticia spends $18. 45 on a shirt. She spends at least $3. 00 more than Humberto spends. If h represents the amount Humberto spends, which symbol can be used to complete the inequality below to represent this situation? 18. 45 blank 3 h > < Greater-than-or-equal-to Less-than-or-equal-to.
Inequality is the comparison of mathematical expressions which are not strictly equal. The needed inequality is: 18.45 ≥ 3 + h
How to form mathematical expression from the given description?You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
For the given case, we've got:
Amount spent by Leticia = $18.45
Amount spent by Humberto = h dollars
Since amount spent by Leticia is at least $3. 00 more than what Humberto spends, thus:
18.45 is at least h + 3 (all in dollars)
(we usually skip stuffs like currency sign or units in equations or inequalities, to keep things as minimized as possible. It is known from the context what unit or currency or such thing is being discussed).
At least can be thought of as equal to that quantity or greater than that quantity but not less than that quantity.
This more than or equal to is written as ≥
Thus, the inequality we get is:
18.45 ≥ 3 + h
Learn more about inequalities here:
https://brainly.com/question/11901702
Use 3.14 as an approximation for π. Round your answer to the nearest tenth.
Answer:
7
Step-by-step explanation:
1.5 x 1.5 = 2.25
2.25 x 3.14 = 7.065
[tex]Area \: = \pi {r}^{2} = 3.14 \times {1.5cm}^{2} \\ = 7.065 \: \: {cm}^{2} [/tex]
= 7 cm^2
a rectangular poster is 17 inches by 54 inches long. write and solve an equation to estimate the area of the rectangle poster. what is the actual area of the rectangular poster
It should be noted that the area of the rectangle given will be 918 inches².
How to calculate area of a rectangleFrom the information given, it was stated that a rectangular poster is 17 inches by 54 inches long.
The area of the rectangle will be:
Area = Length × Width
Area = 17 × 54
Area = 918 inches²
Learn more about area on:
https://brainly.com/question/25292087
PLEASE ANSWER QUICKLY!
Transversal d intersects lines e and f to form 8 angles. The angles formed with line e, clockwise from top left, are blank, 112 degrees, blank, 3. The angles formed with line f, clockwise from top left are 1, 2, blank, 49 degrees.
Use the diagram to find the indicated angle measures.
m∠1 =
degrees
m∠2 =
degrees
m∠3 =
degrees
Answer:
mz4=
V57
degrees
m5=
V 123
degrees
m26=
35
degrees
Answer: The answer should bemz 4=
V57
degrees
m5=
V 123
degrees
m26=
35
degrees
Step-by-step explanation:
I dont know why this was wrong ?? anyone know
Answer:
= f(x) = x²+16
is correct.
Step-by-step explanation:
I hope this helps!![tex] \dashrightarrow f( \rm x) = (x - 4)(x - 4)[/tex]
[tex] \\ \\ [/tex]
[tex] \dashrightarrow f( \rm x) = \: {x}^{2} - 4x - 4x + 16[/tex]
[tex] \\ \\ [/tex]
[tex] \dashrightarrow f( \rm x) = \: {x}^{2} - 8x + 16[/tex]
what is the unit rate for 4 gallons
Answer:
completing the division operation: numerator divided by denominator.
Step-by-step explanation:
If you have a rate, such as price per some number of items, and the quantity in the denominator is not 1, you can calculate unit rate or price per unit by completing the division operation: numerator divided by denominator.
If 2 miles is equal to 3,218.7meters, how many meters are there in 7 miles
2p-q=7 and 3p+2q=7 solve using simultaneous equation
Answer:
q = -1 and p = 3
Step-by-step explanation:
make q the subject of the formula
q = 2p - 7
Let use the other equation to manipulate data
3p + 2q = 7
:3p + 2 (2p - 7) = 7
:3p + 4p - 14 = 7
:3p + 4p = 7 + 14
:7p = 21
7. 7
like terms cancel each other
thus
p = 3
ANDwe the first equation to find the value of q
q = 2p - 7
since we have find p as 3, let's substitute
q = 2 (3) - 7
q = 6 - 7
q = -1
Item 4
A member of the sales team earns 30% commission on any sales. A salesperson sold $450 worth of merchandise.
How much was the salesperson's commission on the sale?
$30
$135
$180
$315
Answer:
its 135
Step-by-step explanation:
50 POINTS!!!! HELP ASAP!!!
20
I'm sorry but I rea
Step-by-step explanation:
65 *x =1300
1300÷65= x
X=20
Answer:
I wish you help you more but I can only go this far.
Step-by-step explanation:
question 1:
1,300÷65=20
salesman A has to make 20 sales to reach his maximum sales for the week.
question 2:
1. x÷2+4 = -1
x= -10.
-10÷2 = -5
-5 +4= -1
2. x+3÷5=-2
x= (5×-2)+3
x= -13
3. nil
4. x-5×2=14
x=-2
5. x × 4 - 5 = -8
(please calculate it)
I hope I helped a little.
10 pounds of
strawberries cost
$20. 7 pounds of
strawberries cost
$14. What is the
cost per pound?
In a bag containing 4 yellow balls and 3 blue balls. 2 balls are drawn in a succession without replacement. Find The values of random variables. B where B represents the number of blue balls drawn
The above pic is your answer mate.
Two punches are made from steel bar stock 9 7/16 inches long. If one punch is 4 1/64 inches long and the other is 4 3/32 inches long, how many inches of stock are wasted?
a. 1 1/16 inches
b. 1 5/16 inches
c. 1 15/64 inches
d. 1 21/64 inches
Answer:
d. 1 21/64 inches
Step-by-step explanation:
Add the lengths of the two punches.
4 1/64 + 4 3/32 = 4 1/64 + 4 6/64 = 8 7/64
Subtract the sum from the length of the bar stock.
9 7/16 - 8 7/64 = 9 28/64 - 8 7/64 = 1 21/64
Answer: d. 1 21/64 inches
The 1 15/64 inches of stock are wasted (option c).
To find out how much stock is wasted, we need to subtract the sum of the lengths of the two punches from the original length of the steel bar.
Original length of the steel bar = 9 7/16 inches
Length of the first punch = 4 1/64 inches = 4 + 1/64 inches
Length of the second punch = 4 3/32 inches = 4 + 3/32 inches
Total length of the two punches = (4 + 1/64) + (4 + 3/32) inches
Now, add the lengths of the two punches:
Total length of punches = 8 + 1/64 + 3/32 inches
Convert the fractions to a common denominator (64):
Total length of punches = 8 + 1/64 + 6/64 inches
Total length of punches = 8 + 7/64 inches
Now, subtract the total length of punches from the original length of the steel bar:
Wasted stock = 9 7/16 - (8 + 7/64) inches
Convert 9 7/16 to an improper fraction:
Original length of the steel bar = 9 * 16/16 + 7/16 = 151/16
Now, subtract the total length of punches:
Wasted stock = 151/16 - (8 * 16/16 + 7/64)
Wasted stock = 151/16 - (128/16 + 7/64)
Wasted stock = 151/16 - 130/16 - 7/64
Wasted stock = 21/16 - 7/64
Wasted stock = (21 * 4)/(16 * 4) - 7/64
Wasted stock = 84/64 - 7/64
Wasted stock = 77/64 inches
Now, let's simplify 77/64:
77/64 = 64/64 + 13/64 = 1 + 15/64 inches
To know more about subtract:
https://brainly.com/question/13619104
#SPJ3
Which equation represents this statement?
3.1 less a number is 1.76.
n−3.1=1.76
3.1=1.76−n
3.1−n=1.76
3.1=n−1.76
The statement 3.1 less a number is 17.6=3.1-n=1.76
Answer:
Helps you in comprehending the methodology to solve sum of first terms of an arithmetic progression
Makes you memorise the important formulas and methodologies
Assists you in scoring all the questions on arithmetic progression accurately
Step-by-step explanation:
Find the area. PLEASE HELP!!!!
Answer:
623 mm²
Step-by-step explanation:
I am going to split this shape into a 15mm x 19mm rectangle and a 26mm x 13mm rectangle. (the 19mm comes from 32mm at the bottom minus 13mm at the top to find how long the first rectangle is)
Rectangle 1: 15mm • 19mm = 285mm²
Rectangle 2: 26mm • 13mm = 338mm²
Total Area: 285mm² + 338mm² = 623mm²
Which expression is equivalent to 10-3(4x=8)
a.-12x-14
b 12x +14
c 14-12x
d -14+12x
SHOW ME ALL YOUR STEPS
Answer: c
Step-by-step explanation:
The factory pays 7 cents per kWh for energy. Find the cost for each bulb type at 0 hours of
and at 10,000 hours of use. Show your work. (4 points: 1 point for each of the four costs)
Cost at 0 hours ($)
Cost at 10,000 hours ($)
CFL bulb
$
LED bulb
$
Answer:
$46.27¢
Step-by-step explanation:
Good thing I was a teacher
What is the value of x?
Enter your answer as a decimal in the box.
Answer:
[tex]x = 22.5[/tex]
Explanation:
Given Sides:
HB = 6HD = 6+15 = 21HM = 9HT = 9 + x-----------------------------
using all these sides, create similarities equation:
[tex]\frac{HB}{HD} = \frac{HM}{HT}[/tex]
[tex]\frac{6}{21} = \frac{9}{9+x}[/tex]
[tex]6(9+x) = 9(21)[/tex]
[tex]54 + 6x = 189[/tex]
[tex]6x = 189 - 54[/tex]
[tex]6x = 135[/tex]
[tex]x = \frac{135}{6}[/tex]
[tex]x = 22.5[/tex]
fil in the balnk for what makes the equation true 10* =5
Answer:
1/2 or 0.5
Step-by-step explanation
1/2 of 10 = 5
We can write 1/2 as a decimal.
Do you need a decimal or fraction as the answer?
Still stuck? Get 1-on-1 help from an expert tutor now.
Given the function f(x)=3x^2+4x−4
find the following.
(a) the average rate of change of f on [−4,0].
(b) the average rate of change of f on [x,x+ℎ].
Answer:
(a) -8
(b) 6x +4 +3h
Step-by-step explanation:
Sometimes, it works well to find the general solution first, then use that to solve the specific problem. That's what we'll do here.
(b)The average rate of change on the interval [x, x+h] is defined as ...
m = (f(x+h) -f(x))/h
For the given f(x), this is ...
[tex]m=\dfrac{((3(x+h)^2+4(x+h)-4)-(3x^2+4x-4)}{h}\\\\m=\dfrac{3x^2 +6xh+3h^2+4x+4h-4-3x^2-4x+4}{h}\\\\m=\dfrac{6xh+3h^2+4h}{h}\\\\\boxed{m=6x+4+3h}\qquad\text{average rate of change on $[x,x+h]$}[/tex]
__
(a)Using the above result for the interval [-4. 0], we have x=-4 and h=4. The average rate of change on that interval is ...
m = 6(-4) +4 +3(4) = -24 +4 +12 = -8
The average rate of change on [-4, 0] is -8.
_____
Additional comment
In the above, we worked the generic problem first. That way, we only needed to expand f(x+h)-f(x) once. If you're not terribly comfortable with doing algebra on literal expressions, sometimes it is more comfortable to work the numerical problem--as this question would have you do. This lets you get an idea of the kinds of operations that are involved and the way terms combine.
We note that the average rate of change is the instantaneous rate of change (derivative of the function) at the midpoint of the interval. That derivative is the value of m when h=0: 6x+4. The midpoint of the interval [-4,0] is x=-2, and the derivative there is 6(-2)+4 = -8, as above.
Ben and Landon took turns driving on a 820 mile road trip. Ben averaged 60 miles per hour and Landon averaged 56 miles per hour. The trip took them 14 hours. How many hours did Landon drive?
Answer:
See below!
Explanation:
distance = speed * timespeed = distance/timetime = distance/speedequation for distance:
Lets Ben hours be x and Landon hours be y,
60x + 56y = 820 .........equation 1
equation for time:
[tex]\frac{60x}{60}+ \frac{56x}{56} =14[/tex]
x + y = 14 .........equation 2
Make x the subject:
60x + 56y = 820
x = (820 - 56y)/60 ..........equation 3
x + y = 14
x = 14 - y ........equation 4
Solve equation 3 and 4 simultaneously:
14 - y = (820 - 56y)/6060(14 - y) = 820 - 56y840 - 60y = 820 -56y840 - 820 = -56y + 60y20 = 4yy = 5[ Therefore Landon drove 5 hours ]
Extra's further investigated:
if y = 5
x = 14 - yx = 14 - 5x = 9[ Therefore Ben drove 9 hours ]
Answer:
Landon drove 5 hours (and Ben drove 9 hours)
Step-by-step explanation:
Let B = number of miles Ben drove
Let L = number of miles Landon drove
Given The trip took them 14 hours
⇒ B + L = 14
Given, Ben averaged 60 miles per hour and Landon averaged 56 miles per hour. Ben and Landon took turns driving on a 820 mile road trip:
⇒ 60B + 56L = 820
Rewrite B + L = 14 to make B the subject, substitute into 60B + 56L = 820, and solve for L:
⇒ B = 14 - L
⇒ 60(14 - L) + 56L = 820
⇒ 840 - 60L + 56L = 820
⇒ 20 = 4L
⇒ L = 5
Therefore, Landon drove for 5 hours
Which relationship is proportional?
A. Bob scored 24 points in 4 games and Joe scored 48 points in 10 games.
B. At one store it costs $18 for 3 necklaces and at another it's $30 for 5 necklaces
C. Casey worked 4 hours for $32 and Allie worked 7 hours for $28.
Somebody please help me I am struggling very much
Answer:
B
Step-by-step explanation:
We will divide 18 by 3 and 30 by 5, and if the results are the same, then this relationship is proportional.
18/3 = 6
30/5 = 6
The two answers are the same, so this relationship is proportional.
Stop & Shop is having a sale on paper towels: 5 rolls for $3. How much will 8 roll(s) cost?
Divide using long division
pls show work
9x^3+18x^2-4x+8/3x-2
Answer:Quotient =3x^2 +8x +4
Remainder=16
Step-by-step explanation: