Given:
[tex]\left(-\dfrac{2}{3}\right)\times \left(-\dfrac{2}{3}\right)^3[/tex]
To find:
The value of given expression by using the Laws of Exponents.
Solution:
We have,
[tex]\left(-\dfrac{2}{3}\right)\times \left(-\dfrac{2}{3}\right)^3[/tex]
Using the Laws of Exponents, we get
[tex]=\left(-\dfrac{2}{3}\right)^{1+3}[/tex] [tex][\because a^ma^n=a^{m+n}][/tex]
[tex]=\left(\dfrac{-2}{3}\right)^{4}[/tex]
[tex]=\dfrac{(-2)^4}{(3)^4}[/tex] [tex][\because \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}][/tex]
[tex]=\dfrac{(-2)\times (-2)\times (-2)\times (-2)}{(3)\times (3)\times (3)\times (3)}[/tex]
[tex]=\dfrac{16}{81}[/tex]
Therefore, the value of given expression is [tex]\dfrac{16}{81}[/tex].
Please explain step by step on how to solve this.
Find the second and fifth terms of each sequence. A(n) = 22 + (n – 1)11
Answer:
A(2) = 33
A(5) = 77
Step-by-step explanation:
n is the counter of the terms.
A(n) is the nth term.
A(1) is the first term.
A(2) is the second term.
etc
To find the 2nd term, let n = 2. Then you have
A(2) = 22 + (2 - 1)11
A(2) = 22 + (1)11
A(2) = 22 + 11
A(2) = 33
To find the 5th term, let n = 5. Then you have
A(5) = 22 + (5 - 1)11
A(5) = 22 + (5)11
A(5) = 22 + 55
A(5) = 77
Answer:
A(2) = 33
A(5) = 77
Math question help please
Answer: The answer is B
Step-by-step explanation:
Answer:b
Step-by-step explanation:
Given h (x) = 5 x + 1, find h(2)
Answer:
h(2) = 5.2 + 1 = 10 + 1 = 11
What is a fraction equivalent to -6/1
Answer:
-18/3
Step-by-step explanation:
Multiply the denominator and numerator by the same whole number.
Andre works as a waiter at a restaurant, where he earns $6 an hour plus tips. After 5 hours of work he has earned $60.20. Write the equation to represents his total earnings for his hours worked.
Answer:
Step-by-step explanation: $6 dollars times 5 equals 30.00 dollars. So Andre made 30.00 dollars from work, and 30.20 dollars.
5. What's the sum of 3/8 and 1/16
Answer:
7/16
Step-by-step explanation:
3/8=6/16
6/16 + 1/16 = 7/16
can anyone PLEASE HELP ME with this question i really need help
Answer:
x = 49°
Step-by-step explanation:
180 = 90 + 41 + x
x = 180 - 131
x = 49
PLEASE HELP! 100 POINTS
Answer:
(-2, 4.111)
(-1, 4.333...)
(0,5)
(1, 7)
Step-by-step explanation:
So for this, you just substitute x with a cero to obtain the x-axis.
So, (0,5)
Then, you do the same with other numbers (replace x) and get the points to later graph it.
Also, you can use desmos, it really helps
Answer:
A.
R.T.
Step-by-step explanation:
Dhte&mfjdcxxbfesfb
Type the correct answer in each box. Use numerals instead of words.
Micah is keeping track of how much he spends this month on gas. In the first week, he bought x gallons of gas at $2.39 per gallon. In
the second week, he bought 3 fewer gallons of gas than the first week at $2.49 per gallon. So far this month, he has spent a total
$46.21 on gas.
In the first week, Micah bought
gallons of gas
in the second week, Micah bought
gallons of gas
Answer:
Micah bought 11 gallons of gas in the first week and 8 gallons of gas in the second week
Step-by-step explanation:
Answer:
Step-by-step explanation:
Micah bought 11 gallons of gas in the first week and 8 gallons of gas in the second week
What is the slope of the line that passes through the points (−3,−3) and (−9,5)?
Express as a percentage.
10
Answer:
10% is ur answer
Step-by-step explanation:
I really need help with this question asap!
Answer:
the answer is C
Step-by-step explanation:
The expression 6.4d - 2 gives the number of Indian rupees you receive when you exchange $d at the local currency exchange. How many Indian rupees do you receive when you exchange $10?
Answer:
62 Indian ruppes
Step-by-step explanation:
We were told in the question that:
The expression 6.4d - 2 gives the number of Indian rupees you receive when you exchange $d at the local currency exchange.
The amount of Indian rupees you receive when you exchange $10 is calculated as:
6.4d - 2
d = $10
Hence:
Amount of Indian rupees = (6.4 × 10) - 2
= 64 - 2
= 62 Indian ruppes
Solve for x.
3x2+8x = 6
(show your work)
look at previous questions for context
Answer:
y = 1/2x - 6
Step-by-step explanation:
Here, we want to get the equation of the line that passes through the given points
Mathematically we can write the equation of a line as;
y = mx + b
where m is slope and b is the y-intercept
We start by getting the slope
m = (y2-y1)/(x2-x1)
m = (-1+5)/(10-2) = 4/8 = 1/2
So we have the equation partially as;
y = 1/2x + b
to get c, we use any of the two points and substitute the individual x and y values
-1 = 1/2(10) + b
-1 = 5 + b
b = -1-5 = -6
so the equation is;
y = 1/2x - 6
How many roots are there for the polynomial that factors into
f(x) = (x^2-1)(x+2)(x-1)^2?
Answer:
3 roots
tho using the fundamental theorem of algebra there should be more, if you use Desmos,there are 5
Step-by-step explanation:
GUITAR Lydia wants to purchase guitar
lessons. She sees a sign that gives the prices
for 7 guitar lessons and 11 guitar lessons.
Write a linear equation to find the total
cost for a lessons.
The answer would be C=10d+12
Hope this helps
Have a great day/night
The total cost for the guitar lessons includes an initial cost fee which is
added to the unit cost.
Where the cost of 7 lessons is a and the cost of 11 lessons is b, we have
The total cost of lessons is; [tex]\displaystyle y = \mathbf{ \frac{1}{4} \cdot ((b - a) \cdot x + 11 \cdot a - 7 \cdot b)}[/tex]Where the cost for 7 lessons is $82, and the cost of 11 lessons is $122, we have;
The total cost of lessons is; f(x) = y = 10·x + 12 and one lesson costs $22Reasons:
The general equation for the total cost of lessons is;
Let a represent the cost of 7 guitar lessons, and let b represent the cost of
9 guitar lessons, given that the cost increases linearly with the number of
lessons, we have;
The cost increase per lesson = The slope of the linear function representing the total cost of a guitar lesson
Therefore;
[tex]\displaystyle Slope = \frac{b - a}{11 - 7} = \mathbf{\frac{b - a}{4}}[/tex]
Expressing the equation in the slope and intercept form, we have;
[tex]\displaystyle (y - a) = \frac{b - a}{4} \cdot (x - 7)[/tex]
[tex]\displaystyle y = \frac{b - a}{4} \cdot x - 7 \times\frac{b - a}{4} + a = \frac{b - a}{4} \cdot x+ \frac{11\cdot a - 7 \cdot b}{4}[/tex]
[tex]\displaystyle y = \frac{b - a}{4} \cdot x+ \frac{11\cdot a - 7 \cdot b}{4} = \mathbf{\frac{1}{4} \cdot ((b - a) \cdot x + 11 \cdot a - 7 \cdot b)}[/tex]
The total cost is; [tex]\displaystyle \underline{y = \frac{1}{4} \cdot ((b - a) \cdot x + 11 \cdot a - 7 \cdot b)}[/tex]Where, in a similar question, a = $82, b = $122, we have;
[tex]\displaystyle y = \frac{1}{4} \cdot(122 - 82) \cdot x+ \frac{1}{4} \cdot (11\times 82 - 7 \times 122)= 10 \cdot x + 12[/tex]
y = 10·x + 12
The total cost of x lessons is; f(x) = y = 10·x + 12
The total cost of a lessons is; y = 10 × 1 + 12 = 22
The cost of a lesson, f(1) = $22Learn more about linear relationships here:
https://brainly.com/question/2154877
Can someone please help me on this question?
108.9 divided by 19.8=
WILL GIVE BRAINLIST
−7x − 13 = −48 Some one pls answer this
Answer:
-7x -13= -48 (add 13 to both sides)
-7x = -35 (divide both sides by -7)
x= 5 (is your answer)
Answer:
x = 5
Step-by-step explanation:
-7x - 13 = -48
+13 +13
-7x = -48 + 13
-7x = -35
Divide both sides by -7
x = -35/-7
x = 5
I hope this was helpful!
Could I get brainliest?
Plz tell me the answer
Answer:
first is correct
second should be
4a² + 5a
Write a linear function $f$ with the values $f(0)=8$ and $\ f(4)=20$ .
Answer:
f(x) = 3x + 8 is the required linear function.
Step-by-step explanation:
We know that the slope-intercept form of linear equation is
y = mx+b
here
m is the slope of the line, and b is the y-interceptGiven initial value
f(0) = 8
Meaning at x = 0, y = 8Thus, the y-intercept = b = 8
Also given
at x = 4, f(4) = 20
Meaning at x=4, y = 20so
substituting the point (4, 20) and y-intercept b=8 in the slope-intercept form to determine the slope
y = mx+b
20 = m(4) + 8
20 = 4m + 8
4m = 20-8
4m = 12
Dividing both sides by 4
m = 3
Thus, the slope = m = 3
Now, substituting m = 3 and b = 8 in the slope-intercept of linear function
y = mx+b
y = 3x + 8
or
f(x) = 3x + 8
Thus,
f(x) = 3x + 8 is the required linear function.
VERIFICATION:
Given the linear function
f(x) = 3x + 8
plug in x = 0
f(0) = 3(0) + 8
f(0) = 8
plug in x = 4
f(x) = 3x + 8
f(4) = 3(4) + 8
f(4) = 12+8
f(4) = 20
simplify this expression
x⁵×x²
Answer:
Step-by-step explanation:
=x7
true or false The angle of depression is the angle formed above the horizontal line
Answer:
False
Step-by-step explanation:
Trust me
False statement the angle of depression is the angle formed is not above the horizontal line.
What is the angle of depression?The angle of depression is defined as the angle obtained by any object below the horizontal line which is used as the reference line.
Here in the question, they are asking The angle of depression is the angle formed above the horizontal line this statement is true or false.
If you will follow the above definition of the angle of depression you will see that the given statement is false.
To know more about the angle of depression follow
https://brainly.com/question/10217662
#SPJ2
Fill in the box with x + - Nd divide
Answer:
[tex]3 \boxed{ + }12 \boxed{ \div }4 = 3 + \frac{12}{4} = 3 + 3 = 6[/tex]
hope this helps.
Which of the following is the midpoint of the segment with endpoints (9,4) and (-3, 2)
Answer:
The midpoint is (3,3)
Step-by-step explanation:
Solve the equation 3x^2
10x + 5 = 0 to the nearest tenth.
A triangle is rotated 90° about the origin. Which rule describes the transformation? (x, y) -(-x, -y) (x, y) - (-y, x) (x, y) - (-4, -x) (x, y) (y, -x)
Answer:
(x, y) arrow (-y, x)
Step-by-step explanation:
Therefore rule of counter is (x,y) arrow (-y,x) ...we have given a triangle is rotated 90'
Pls help 10 points. ac+b=
A=3
B=5
C=1
Answer:
The answer should be 3×1+5=8
Step-by-step explanation:
prove me wrong
Answer:
8
Step-by-step explanation:
AC means 3 times 1 which is 3. B equals to 5. 3 plus 5 equals to 8.
A school buys games for 6 classrooms. It buys 3 board games, 4 puzzles, and 1 video for each classroom. How many games dose the school buy?
Answer:
42
Step-by-step explanation:
4+3=7
7x6 = 42