b. Does a12 x a4 = a8 x a8 for all values of a? Explain.
Answers
Answer:
We can use the Laws of Exponent to rewrite both sides of the equation:
Let a¹² x a⁴ = a⁸ x a⁸
⇒ a¹²⁺⁴ = a⁸⁺⁸
a¹⁶ = a¹⁶ ✅
⇒ a¹² x a⁴ = a⁸ x a⁸ is true for all values of a.
Explanation:
The equation a¹² x a⁴ = a⁸ x a⁸ is true because, on both the RHS and LHS of the equation, both terms in 'a' have exponents that when added (Law of Multiplication of Exponents) are equal to each other, i.e. 12+4 = 8 + 8.
Related Questions
in a scholl there are 720 boys and 640 girls find the % of girls
Answers
Answer:
47%
Step-by-step explanation:
720+640=
1360. 640/1360 = 47
can anyone help me please I need the answer to this fast
Answers
Answer:
y = 4/7x - 22/7Step-by-step explanation:
Take 2 points:
(-5, -6) and (2, -2)Find the slope:
m = (- 2 + 6)/(2 + 5) = 4/7Find the y- intercept:
-6 = 4/7(-5) + b-6 = - 20/7 + bb = - 6 + 20/7b = - 22/7The line is:
y = 4/7x - 22/7Prove that:
[tex] \cos( \frac{3\pi}{2} + \theta) \cos(2\pi + \theta) [ \cot( \frac{3\pi}{2} - \theta) + \cot(2\pi + \theta) ] = 1 [/tex]
Please solve this problem because tomorrow is my maths exam.
Answers
Explanation:
On taking LHS
Cos[(3π/2)+θ]Cos(2π+θ)[Cot{(3π/2)-θ}+Cot(2π+θ)]
We know that
π = 180°
2π = 2×180° = 360°
3π/2 = (3×180°)/2 = 540°/2 = 270°
Now
LHS becomes
Cos(270°+θ)Cos(360°+θ)[Cot(270°-θ)+Cot(360°+θ)]
We know that
Cos (270°+θ) = Sin θ
Cos (360°+θ) = Cos θ
Cot (270°-θ) = Tan θ
Cot (360°+θ) = Cot θ
→ Sin θ Cos θ [Tan θ + Cot θ]
→ Sinθ Cosθ[(Sinθ/Cosθ)+(Cosθ/Sinθ)]
→ Sinθ Cosθ[(Sin²θ+Cos²θ)/(SinθCosθ)]
→ Sin θ Cos θ [1/(Sin θ Cos θ)]
Since Sin²θ+Cos²θ = 1
→ (Sin θ Cos θ)/(Sin θ Cos θ)
→ 1
→ RHS
→ LHS = RHS
Hence, Proved.
Here are the formulae that I have used:
→ π = 180°
→ Cos (270°+θ) = Sin θ
→ Cos (360°+θ) = Cos θ
→ Cot (270°-θ) = Tan θ
→ Cot (360°+θ) = Cot θ
Here are the Trigonometric Identities that I have used:
→ Sin²θ+Cos²θ = 1
Write an equation of the line passing through point P(2, 3) that is perpendicular to the line y-4=-2(x+3) .
Answers
Answer:
y - 3 = 1/2(x - 2)Step-by-step explanation:
The given line has a slope of -2.
The perpendicular line will have a negative-reciprocal slope:
m = 1/2Use same point-slope form and the point P(2, 3):
y - y₁ = m(x - x₁)y - 3 = 1/2(x - 2)[tex]\\ \sf\longmapsto y-4=-2(x+3)[/tex]
Here slope is -2
The perpendicular line have additive and multiplicative inverse slopem=1/2
Put co-ordinates of P in equation
[tex]\\ \sf\longmapsto y-3=\dfrac{1}{2}(x+2)[/tex]
6 exponent 2-4 for b=5
Answers
Answer
6 exponent 2 is 36
6 exponent 4 is 1296
Both added is 1332
Step-by-step explanation:
1. 6x6=36
2. 6X6X6X6= 1296
3 1296+36=1332
f(x)=5x-1; find f (-2), f (0), and f (x+1)
Answers
Answer:
f(-2) = -11
f(0) = -1
f(x+1)= f (x+1)=5x+4
Step-by-step explanation:
The graph shows the height of a plant over time. What is the unit rate?
Answers
What value of x is in the solution set of 2(3x - 1) = 4x - 6?
О -10
0-5
-3
ОО
О-1
Answers
Answer:
-1
Step-by-step explanation:
Step-by-step explanation:
Given by your question
2(3x-1)≥4x-6
Distributive property to take off the parentheses
2×3x-2×1≥4x-6
6x-2≥4x-6
Subtract 4x on both sides (Subtractive property of equality)
6x-2-4x≥4x-6-4x
2x-2≥-6
Add 2 on both sides (Addition property of equality)
2x-2+2≥-6+2
2x≥-4
Divide 2 on both sides (Division property of equality)
2/2 x≥-4/2
x≥-2
----------------------------------------------------------------------------
Looking at the options you've provided.
-10 INCORRECT, it is not greater or equal to -2
-5 INCORRECT, it is not greater or equal to -2
-3 INCORRECT, it is not greater or equal to -2
-1 CORRECT, it is greater than -2
Answer:
2(3x -1) = 4x - 6
6x - 2 = 4x - 6
6x -2+2 = 4x -6 + 2
6x - 4x = 4x - 4x -6 + 2
6x - 4x = -6 + 2
2x = -4
2 2
x = -2
A girl received $100 for her birthday. At the store she can buy 1 video game and 3 DVDs for $100. She could ask buy 2 video games and 1 DVD for $100. Write and solve a system of equations to determine the cost of a video and the cost of a dvd
Answers
Answer:
Step-by-step explanation:
I NEED HELP ASAP WILL GIVE BRAINLIEST
Answers
Step-by-step explanation:
length of missing side = sqrt(5^2 + 12^2) = sqrt(169) = 13
distance = sqrt(50^2 +25^2) =sqrt(3125)= 55.90metres
Factor completely: 8x^2-4x-4
Answers
Answer:
4(2x+1)(x−1)
Step-by-step explanation:
8x2−4x−4
8x2−4x−4
=4(2x+1)(x−1)
HELPP AND SHOW YOUR WORK!!!
4. −10(x − 3)
A) −15x + 30
B) −10x + 30
C) −15x + 35
D) −15x + 37
Answers
Answer:
B) [tex]-10x+30[/tex]
Step-by-step explanation:
You distribute:
-10 times X minus 3 ( -10*x-3)
Which gives you:
Answer: -10x+30
Hope this helps!
Answer:
-10x+30Step-by-step explanation:
[tex]\sf -10(x -3)[/tex]
[tex]\sf -10x-\left(-10\right)\times \:3[/tex]
[tex]\sf -10x+30[/tex]
What is the graph of the function f(x) = the quantity of x squared minus 7 x plus 12, all over x minus 3 ? (1 point);
Answers
Answer:
pic is answer
Step-by-step explanation:
what fraction of an hour is 5 minutes in its simplest form
Answers
Answer:
1 / 12
Step-by-step explanation:
one hour = 60 minutes
so
5 / 60
= 1 / 12
Answer:
[tex]\frac{1}{12}[/tex]
Step-by-step explanation:
There are 60 minutes in 1 hour , then 5 minutes as a fraction of an hour is
[tex]\frac{5}{60}[/tex] = [tex]\frac{1}{12}[/tex] ← in simplest form
what is 3.26% of 1298
Answers
Answer:
42.3148
Step-by-step explanation:
3.26% of 1298
3.26/100*1298
42.3148
Let f(t) represent the temperature of a turkey baking in an oven as a function of time (t) in the oven (in minutes). This means time is the independent variable and temperature of the turkey f(t) is the dependent variable. The turkey was in the oven for 360 minutes and then removed. Note that when something is baked in an oven, the temperature of the oven stays constant.
1. Describe the rate of change pattern over each interval of the graph listed below:
a) 0 < t < 345
b) 345 < t < 360
c) t > 360
2. Explain what is happening in each interval of your graph in terms of the turkey and its temperature, using complete sentences.
3. Let's say that the turkey sat on the counter for an additional hour (beyond the 390 minutes) and its temperature cooled to 80 degrees. Write that value in function notation.
Answers
solution:
1. A carnival charges $2.50 per
ride
after an entrance fee. You paid a total
of $22.50 after 6 rides and the initial
entrance fee.
a. Write an equation that gives the
total cost as a function of the number
of rides.
1
b. Find the total cost for 10 rides.
Answers
Answer:
a. 2.50(6) + X = 22.50
b. $25.00
Step-by-step explanation:
A.
a ride = $2.50
total spent = $22.50
2.50(6) + X = 22.50
15.00 + X = 22.50
X = 22.50 - 15.00
X = 7.50
entrance fee = $7.50
B.
10*2.50= $25.00
Answer:
$22.50
Step-by-step explanation:
:)
Help like rn. Like rn please I will mark brainiest but pls help.
Answers
Answer:
90
and
20
i think so ye
Step-by-step explanation:
Answer:
Nvm
Step-by-step explanation:
U don’t need help anymore?
HELPPPPP PLEASEEEEEEEEEEE
Answers
Answer:
60 students are divided into equal groups of 5 student each.
Groups of 5 students per group totaled up to 60 students.
The quotient in both expression is 60:5 = 12 students per group.
Step-by-step explanation:
The ratio expression is a way of expressing the division of numerator by a denominator.
Here,
The total number of students is the numerator = 60
The denominator is the number of students per group = 5
Hence, the quotient is the value of the divison obtained which is (60/2) = 12
Therefore, there are 12 groups of 5 students.
i need help please with this
Answers
Answer:
Thus, width is 6 and length is 25.
Step-by-step explanation:
Let us assume the width is x, then, the length is (4x+1).
Therefore, 2x + 2(4x+1) = 62
Or, 2x + 8x + 2 =62
Or, 10x = 60
Or, x = 6
Answer:
27 units.
Step-by-step explanation:
The perimeter is equal to 2 x length + 2 x width.
If the width is 4 then:
62 = 2 x length + 2 x 4
62 = 2 x length + 8
Then, we can subtract 8 from both sides.
54 = 2 x length
Next, divide both sides by 2
27 = length
so,
The length is 27 units.
Complete the conjecture based on the pattern you observe in the examples below:
Conjecture: The sum of any two odd numbers is ___
1 + 1 = 2 9 + 11 = 20
1 + 5 = 6 13 + 21 = 34
7 + 9 = 16 101 + 103 = 204
Conjecture: The product of any two numbers is ___
1 . 1 = 1 9 . 11 = 99
1 . 3 = 3 13 . 11 = 143
3 . 7 = 21 101 . 103 = 10,403
Conjecture: The product of a number (x-1) and the number (x+1) is always equal to ___
3 . 5 = 4² - 1 7 . 9 = 8² - 1
4 . 6 = 5² - 1 6 . 8 = 7² - 1
5 . 7 = 6² - 1 8 . 10 = 9² - 1
Answers
Step-by-step explanation:
the writing and spacing of the problem description is difficult to understand.
but there is no mystery. look at the examples.
all of them
3×5 = 15 = 16 - 1 = 4² - 1
4×6 = 24 = 25 - 1 = 5² - 1
5×7 = 35 = 36 - 1 = 6² - 1
6×8 = 48 = 49 - 1 = 7² - 1
7×9 = 63 = 64 - 1 = 8² - 1
8×10 = 80 = 81 - 1 = 9² - 1
so, what does this look like ?
(x-1)×(x+1) is always equal to (x² - 1)
mike wants to buy the same number of balloons for 2 of his friends. her has $59, and each balloon costs $7. What is the largest number of balloons that mike buys for each friend
Answers
Answer:
4
Step-by-step explanation:
7x8=56 wich is the highest number it can go to
so 8/2=4
Help plsssss! I need this done
Answers
Answer:
B)p=20
Step-by-step explanation:
25=5p/4
25×4=5p
100=5p
p=100/5
p=20
Find the slope of the line through each pair of points.
(−13, −19), (13, 3)
Find the slope of each line.
y = 2x − 1
Answers
The question gives us two points, (−13, −19) & (13, 3), from which we can find the slope and later the equation of the line.
Finding the Slope
The slope of the line (m) = (y₂ - y₁) ÷ (x₂ - x₁)
= ((3 - (-19)) ÷ (13 - (-13))
= 22 ÷ 26
= ¹¹/₁₃
Checking my answer:
We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line. If the line passes through both of the points then we calculated the slope correctly.
⇒ y + 19 = ¹¹/₁₃ (x + 13)
I have included a Desmos Graph that I graphed using the information equation (including the slope) and the points given.
If 10% is RS 1500 then find 90%.
Answers
Answer:
10%=1500
so 100% = 15000
90%= 100% - 10%
15000-1500=13500
90%=13500
A package of 5 pairs of insulated gloves costs $33.45. What is the unit price of the pairs of gloves?
The unit price is $
per pair of gloves.
Answers
Answer:
$6.69
Step-by-step explanation:
Since we know the total cost of 5 pairs of gloves, all we have to do to find the unit price is divide the total cost by how many gloves were are being sold:
33.45 / 5 = 6.69
Therefore, one pair of gloves costs $6.69
Hope this helps :)
please help im the worst at algebra 2
Answers
Answer:
Option AStep-by-step explanation:
According to the matrix, the system is:
3x + 2y -z = 40x + 3y + 7z = 8 ⇒ 3y + 7z = 8x - 3y + 4z = 7Correct match is A
The following graph shows how many gallons of water leaves a bucket every hour.
- right the slope intercept equation. Find the constant rate of change and the vertical intercept of the line. Explain how they are related to this situation
Answers
Answer:
thanks for your points and the time
p + 7 /8 = 18/ 12 what does p equal
Answers
Answer:
P = 5/8 or 15/24
Step-by-step explanation:
p = 18/12 - 7/8
p = 36/24 - 21/24
p = 15/24 ( Simplify )
p = 5/8
Answer:
Step-by-step explanation:
[tex]p+\dfrac{7}{8}=\dfrac{18}{12}\\\\p=\dfrac{18}{12}-\dfrac{7}{8}\\\\\\LCM \ of 8 \ and \ 12 \ is \ 24\\\\p=\dfrac{18*2}{12*2}-\dfrac{7*3}{8*3}\\\\p=\dfrac{36}{24}-\dfrac{21}{24}\\\\p=\dfrac{15}{24}[/tex]
[tex]p=\dfrac{5}{8}[/tex]
Work out the value of 3^2+2^3
Answers
Answer:
Step-by-step explanation:
3^2=9
2^3=8
9+8=17
Answer:
17
Step-by-step explanation:
3²+2³
= (3×3)+(2×2×2)
= 9+8
= 17