Answer:
7^4
Step-by-step explanation:
The equivalent expression 7^8 x 7^-4 using a single exponent is 7^4
How to write the expression using a single exponent.From the question, we have the following parameters that can be used in our computation:
7 ^ 8 x 7 ^ -4
This means that
7^8 x 7^-4
Apply the law of indices
So, we have
7^8 x 7^-4 = 7^(8 - 4)
This gives
7^8 x 7^-4 = 7^4
Hence, the solution is 7^8 x 7^-4 = 7^4
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simplify and factor if necessary
Hello there today we will solve your problem, we will need to factorize btw...
[tex]{\huge{\boxed{\mathfrak{Equation}}}[/tex]
[tex]{\big{\boxed{\frac{x^2-5x+4}{x^2-4x}}}}[/tex]
First we will factor [tex]x^2-5x+4[/tex], which gives us [tex]\left(x-1\right)\left(x-4\right)[/tex]
[tex]\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\left(x-1\right)\left(x-4\right)}{x^2-4x}\\[/tex]
factorize [tex]x^2-4x[/tex] giving us [tex]x\left(x-4\right)[/tex]
[tex]\frac{\left(x-1\right)\left(x-4\right)}{x\left(x-4\right)}[/tex]
cancel the common factor [tex]x-4[/tex]
and we get [tex]\frac{x-1}{x}[/tex]
Which sequence shows the numbers in order from least to
greatest?
1
2
-3
4
3
-3
OA) 2 3
} }
OB) Ź. *.
oc) * * Ź
OD) * *
4
Answer:
-3 1 2 3 4
Step-by-step explanation:
Answer:
-3 1 2 3 4
Step-by-step explanation:
X/2 = Y/3 = Z/4. prove that :2X-Y+5Z / 3Y-X =3. note :: (/) is for a fraction aka divide. help pls I've been stuck on it for a few days
The given equation
x/2 = y/3 = z/4
can be broken into three separate equations which I'll call equations (A), (B) and (C)
x/2 = y/3 ..... equation (A)y/3 = z/4 .... equation (B)x/2 = z/4 .... equation (C)We'll start off solving for z in equation (C)
x/2 = z/4
4x = 2z ... cross multiply
2z = 4x
z = 4x/2 ... divide both sides by 2
z = 2x
Now let's solve for y in equation (A)
x/2 = y/3
3x = 2y
2y = 3x
y = 3x/2
y = (3/2)x
y = 1.5x
The results of z = 2x and y = 1.5x both have the right hand sides in terms of x. This will allow us to replace the variables y and z with something in terms of x, which means we'll have some overall expression with x only. The idea is that expression should simplify to 3 if we played our cards right.
We won't be using equation (B) at all.
---------------------
The key takeaway from the last section is that
z = 2xy = 1.5xLet's plug those items into the expression (2x-y+5z)/(3y-x) to get the following:
(2x-y+5z)/(3y-x)
(2x-y+5(2x))/(3y-x) ..... plug in z = 2x
(2x-y+10x)/(3y-x)
(12x-y)/(3y-x)
(12x-1.5x)/(3(1.5x)-x) .... plug in y = 1.5x
(12x-1.5x)/(4.5x-x)
(10.5x)/(3.5x)
(10.5)/(3.5)
3
We've shown that plugging z = 2x and y = 1.5x into the expression above simplifies to 3. Therefore, the equation (2x-y+5z)/(3y-x) = 3 is true when x/2 = y/3 = z/4. This concludes the proof.
Find the equation of the line.
the line go through 2 points ( -4 ; -5 ) and ( 6 ; 4 )
ANSWER: [tex]y=\frac{9}{10}x -\frac{7}{5}[/tex]
ok done. Thank to me :>
PLEASE HELP QUESTION IN PICTURE.
Answer:
D
Step-by-step explanation:
Answer:
12 square units
Step-by-step explanation:
once you plot the triangle on a graph, you'll see that the height is 4 sq inches, while the base is 6. multiply those two and you get 24, and divide that by 2. thats 12
In the figure below, a tangent and a secant are drawn to a circle from exterior point E.
Suppose that EG = 13 and ED=26. Find CD.
Answer:
19.5 = CD
Step-by-step explanation:
The square of the tangent = (length of the secant)(the length of the outside part of the secant)
EG² = (ED)(EC)
13² = (26)(EC)
169 = 26EC
169/26 = EC
6.5 = EC
Now ED = EC + CD
26 = 6.5 + CD
19.5 = CD
The value of the segment CD will be equal to 19.5.
What is secant and tangent?The relationship between the line segments produced by a secant and a tangent line and the corresponding circle is described by the tangent-secant theorem.
The square of the tangent = (length of the secant)(the length of the outside part of the secant)
It is given that In the figure below, a tangent and a secant are drawn to a circle from exterior point E. Suppose that EG = 13 and ED=26.
The value of the segment CD will be calculated as below:-
EG² = (ED)(EC)
13² = (26)(EC)
169 = 26EC
169/26 = EC
6.5 = EC
Calculate CD.
ED = EC + CD
26 = 6.5 + CD
19.5 = CD
Therefore, the value of the segment CD will be equal to 19.5.
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What are the steps to convert a number from standard notation to scientific notation?
Answer:
Step-by-step explanation:
The goal in scientific notation is to express a value in terms of a number that contains a single unit before the decimal point.
Examples:
10000: 1.0 x 10^4
23456: 2.3456x10^4
In both cases, the x10^4 is telling us to multiply the first number by 10,000. 10^4 is the same as 10x10x10x10 = 10,000
The justification for scientific notation is that is makes expression large and small numbers much easier, as well as reduces errors due to an incorrectly placed decimal.
An example: Divide 2500000000 by 5000. That would normally require setting up a long-hand division problem that not only wastes paper and pencil, but is also prone to decimal point errors.
Do the same problem with scientific notation:
Count the places you want to move the decimal point backwards to just beyond the 5 in 2500000000. It takes nine steps to move the decimal point to between the 2 and 5: 2.5 followed by 8 zeros. That's a total of next steps to go in front of the 5. This is written 2.5 x 10^9
5000 is represented by 5.0x10^4
Now when we divide the same numbers, but in scientific format, it is easier to see the answer:
(2.5x10^9)/(5.0x10^4)
2.5/5 = 0.5
10^9/10^4 = 10^5 [The exponents are subtracted when dividing with exponents: 9-4 = 5]
Put them together to find the final answer: 0.5x10^5
Then move the decimal point one spot to the right and reduce the exponent by 1:
5.0x10^4
------
Add exponents when multiplying: 10^3 x 10^5 = 10^8 (3+5=8)
Subtract when dividing: 10^7/10^2 = 10^5 (7-2=5)
Multiply when there is an exponent raised to another exponent: (10^4)^3 = 10^12 (4x3 = 12)
-X + 2y= -3 and -8x — 3y= -5
Answer:
x=1, y=-1. (1, -1).
Step-by-step explanation:
-x+2y=-3
-8x-3y=-5
----------------
-8(-x+2y)=-8(-3)
-8x-3y=-5
------------------------
8x-16y=24
-8x-3y=-5
-----------------
-19y=19
y=19/-19
y=-1
-x+2(-1)=-3
-x-2=-3
-x=-3+2
-x=-1
x=1
(1, -1)
Answer:
x = 1, y = -1
or as an ordered pair, (1, -1).
Step-by-step explanation:
-x + 2y = -3
-8x — 3y = -5
Multiply first equation by -8:
8x - 16y = 24
Add this equation to the second equation:
-19y = 19
y = -1.
Plug y = -1 into the second equation:
-8x - 3(-1) = -5
-8x + 3 = -5
-8x = -8
x = 1.
quotient of 2 2/3 and 3 1/2
Answer:
16/21
Step-by-step explanation:
find the inverse function f(x)=1/2x+2
Answer:
y=2x-4
Step-by-step explanation:
f(x)=1/2x+2
y=1/2x+2
-----------------
x=1/2y+2
1/2y=x-2
y=2(x-2)
y=2x-4
please keep it simple.
Answer:
[tex]z^{2} +\frac{1}{2} +11z[/tex]
Step-by-step explanation:
→ Minus the z² terms
[tex]1\frac{1}{2} z^{2} -\frac{1}{2} z^{2}=1 z^{2}[/tex]
→ Minus the whole numbers
[tex]3\frac{1}{2} -3=\frac{1}{2}[/tex]
→ Add the z terms
11z
PLS HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
R=11cm, r=3cm
Step-by-step explanation:
π(R²-r²) = π(121-9) = 112π cm² = 35.63cm².
hope this helps you.
A rectangle has a width of 9 units and a length of 40 units. What is the length of a diagonal? 0 34 units 0 39 units 0 41 units o 49 units Mark ihis and return Save and Exit
Answer:
41
Step-by-step explanation:
a² + b² = c²
9² + 40² = c²
81 + 1,600 = c²
√1681 = √c²
41 = c
In his pocket, Hamid has $2.95 in dimes and quarters. If there are 16 coins in total, which system represents the number of dimes and quarters that Hamid has?
A. x + y = 16. 0.10 x + 0.25 y = 2.95.
B. x + y = 16. 0.05 x + 0.25 y = 2.95.
C. x + y = 2.95. 0.10 x + 0.25 y = 16.
D. x + y = 16. 0.01 x + 0.25 y = 2.95.
Answer:
A. x + y = 16; 0.10x + 0.25y = 2.95Step-by-step explanation:
Given:
Dime is $0.10, number of dimes is x, total of dimes = 0.10xQuarter is $0.25, number of quarters is y, total of quarters is 0.25yNumber of coins is 16:
x + y = 16Total amount is $2.95:
0.10x + 0.25y = 2.95Correct choice is A
I need help eeeeeeeee
Answer:
one left so they all shift by 1
pleeeeeeeease help meeeee
Answer:
45
Step-by-step explanation:
First, we have to find the Nth term of this sequence. Since this is linear we can just find the difference to get the n. For example, we can do 3-2 which is one and we can also do 5-4 which is also 1 which confirms that the n is 1. So in other words, 1n However, we don't write the 1 in front of the n because the n itself represents 1n. Next, we have to take away 1 from the first term, which also gives us 1. This is the adjustment to the 1n. So our answer is n+1, which is the nth term for this linear sequence. So now we just substitute 44 into the equation. 44+1=45, which is the 44th term.
The table shows the relationship between the two variables. Which selection describes the relationship?
The table and options are below!
Answer:
D.
Step-by-step explanation:
It's not linear but it is decreasing.
Answer: Firstly, we take a look at the Y numbers to figure out if we're increasing or decreasing. Obviously, the numbers are going into the negatives so we know it's decreasing. After plotting the graph you'll see it's constant and in a straight line making it linear. So, your answer would be decreasing; linear.
A piece of timber is
x
cm long.
How long would 3 pieces of timber be put together in a line?
Answer:
3x cm long.
Step-by-step explanation:
If one piece is x cm
and there are 3 together, presumeabley the same length
then you'd just need to multiply the length 3 times, therefore 3x respresents multiplying x 3 times.
Have a good day!
Answer:
3x cm long
Step-by-step explanation:
3 times x is 3x
Problem 1
Jayden has $11 and begins saving $5 each week
towards buying a new phone. At the same time that
Jayden begins saving, Aditi has $60 and begins
spending $2 per week on supplies for her art class.
Is there a week when they have the same amount of
money?
Yes
No
Answer:
I'm thinking its a no because the money is odd every time Jayden adds $5
Step-by-step explanation:
Jayden has [tex]\$11[/tex] and begins saving [tex]\$5[/tex] per week.
Aditi has [tex]\$60[/tex] and begins spending [tex]\$2[/tex] per week.
Have x denote the number of weeks and y indicate the quantity each person has. Therefore, according to the stated conditions, the maximum amount Jayden will have after x weeks will be,
[tex]\to y = 11+5x[/tex]
Aditi will have [tex]y= 60-2x[/tex] after x weeks. Therefore, the number of weeks in which they will each have the same amount will be calculated as,
[tex]11+5x=60-2x\\\\5x+2x=60-11\\\\7x=49\\\\x=\frac{49}{7}\\\\x=7[/tex]
As a result, after 7 weeks, Lin and Diego will have the same amount, which is [tex]\$46[/tex].
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When you purchase a car in the future, what are at least 3 things
you will have to think about first?
Answer:
How much it cost!? Will it fly?! How far will it fly?!
Step-by-step explanation:
Jorge has 2% + 1 saved in his piggy bank. Lou Ellen has X-2 saved in the bank. What is
the minimum amount Jorge will have in savings for them to have $163 together. Letj
represent Jorge,
Answer:
yeyeyeeyeyeeyeey
Step-by-step explanation:
The angle measures of an isosceles triangle are shown. Find the value of w.
Answer:
[tex]w=7[/tex]
Step-by-step explanation:
Using the Angle Sum Theorem which states that all the interior angles in a triangle add up to 180 degrees you can use that to solve for w with the following:
[tex]62 +9w-1+8w=180[/tex] First combine like terms
[tex](62-1)+(9w+8w)=180[/tex]
[tex]61+17w=180[/tex] Then subtract 61 from both sides.
[tex]17w=180-61[/tex]
[tex]17w=119[/tex] Now divide by 17
[tex]w=119/17[/tex]
[tex]w=7[/tex]
Autumn wants to invest $1000. The table below shows the value of her investment under two different options for three different years:
Number of years 1 2 3
Option 1 (amount in dollars) 1100 1200 1300
Option 2 (amount in dollars) 1100 1210 1331
Part A: What type of function, linear or exponential, can be used to describe the value of the investment after a fixed number of years using option 1 and option 2? Explain your reasoning. (4 points)
Part B: Autumn wants to invest in an option that would help to increase her investment value by the greatest amount in 7 years. Will there be any significant difference in the value of Autumn's investment after 7 years if she uses option 2 over option 1? Explain your answer, and show the investment value after 7 years for each option if the equation for option 1 is f(x)=100x + 1000 and the equation for option 2 is g(d) = 1000(1.1)d
Answer:
See belowStep-by-step explanation:
Part AAccording the table, the yearly amount increases by 100 dollars in option 1 and 1.1 times in option 2.
It means the function is linear in option 1 and exponential in option 2.
Part BCalculate the amount of total value in each case substituting x or d by 7 and compare the amounts:
f(7) = 100*7 + 1000 = $1700g(7) = 1000*(1.1)^7 = $1948.72 (rounded)As we see the option 2 is better choice and the difference is:
$1948.72 - $1700 = $248.721. Reduce the ratio to the simplest form:
a)5:10=_____.
b)60:54=____.
Answer:
1:2 by division of 5
10:9 by division of 6
juliana wrote the terms below. –8, –4, 0, 4, 8, 12 what do these terms represent? an arithmetic series an arithmetic sequence a geometric series a geometric sequence
Answer:
B. an arithmetic sequence
Step-by-step explanation:
hope this helps :)
If a new car is valued at $26,000 and 10 years later it is valued at $7000, then what is the average rate of change
of its value during those 10 years?
Answer:
The change in value is 19,000 altogether and 1900/year
Step-by-step explanation:
Change in value:
initial value - final value
= $26,000 - $7000
= $19,000
Change in value/year:
change in value/time
= $19,000/10
= $1900/year
The distance between two cities on a map is 6cm. If the scale one the map is 2 cm=50 miles, how many miles apart are the two cities
Work Shown:
2 cm : 50 miles
3*(2 cm) : 3*(50 miles)
6 cm : 150 miles
Two plans for reaching a goal are given below. Plan A: Save $450 over the next 8 weeks by working 9 hours per week at $7. 20 per hour. Plan B: Save $450 over the next 6 weeks by working 15 hours per week at $6. 50 per hour. Which of the following is a true statement? a. Only plan A will work for achieving the goal. B. Only plan B will work for achieving the goal. C. Both plans will work for achieving the goal. D. Neither plan will work for achieving the goal.
Answer:
C, both plans will work for achieving the goal.
Step-by-step explanation:
For plan A, you must multiply 7.20 by 9, then multiply the product by 8. The answer is 526.4 This means that plan A will work, and more than the original goal will be saved up.
For plan B, you must multiply 6.50 by 15, then multiply the product by 6. The answer is 585. This is more than the original goal, so plan B would work as well.
This means that C is correct, because both plans will work for achieving the goal.
Answer:
C
Step-by-step explanation:
Edged 2022
Will give thank,brainly and 5 stars!
The second and last one.
The second one multiplies the cost of each type of ticket by two, therefore saying that you wanted to buy two of each type of ticket.
The last one multiplies the cost of a single ticket of all three types and multiplies it by 2.
Answer:
The second and last one
Step-by-step explanation:
Hope this helps and have a good day!
Select all the equations that have {7} as its solution set. 65−2x=6x+9 9−x=14x 3+4x=5x−4 x2+1=8x−5
Answer:
the answer is this hope it helps im not sure if its all right good luck.
Step-by-step explanation:
A. 65-2x=6x+9
B. 9-x=14x
C. 3+4x=5x-4
d is wrong
The first and third equations have {7} as their solution set.
What is an equation?It is a mathematical statement that is made up of two expressions connected by an equal sign.
The first equation is
65−2x=6x+9
Rearranging the above equation gives
8x = 65-9 = 56
i.e x = 7
Consider the second equation,
9−x=14x
i.e x = 9 / 15 = 0.6
The third equation is:
3+4x = 5x−4
i.e x = 7
The last equation is
x^2+1 = 8x−5
Its solution is not equal to 7.
As a result of the preceding equations, we can conclude that only the first and third equations have "7" as their solution set.
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