[tex]4 \times {8}^{x + 1} = {2}^{2x} [/tex]
Calculate the value of x
Answer:
[tex] - 2[/tex]
Step-by-step explanation:
2^2×2^3(x+1)=2^2x
same base cancel,you will get
2+3x+3=2x
take same variable then - or + you will get
[tex]x = - 2[/tex]
Answer:
x=-5
Step-by-step explanation:
2^2×2^3(x+1)=2^2xsince they have the same Base we equat the exponents2+3(x+1)=2x2+3x+3=2x group like terms3x-2x=-3-2x=-5In a game show, players play multiple rounds to score points. Each round has 3 times as many points available as the previous round.
Round 0 1 2 3 n
Points 25 75 225 675
Which equation shows the number of points available, p, in round n of the game show?
Answer:
[tex]p = 25(3)^n[/tex]
Step-by-step explanation:
Given
Round 0 1 2 3
Points 25 75 225 675
Required
Determine the equation
Let n = rounds and p = points.
So, we have:
[tex](n_1,p_1) = (0,25)[/tex]
[tex](n_2,p_2) = (1,75)[/tex]
[tex](n_2,p_2) = (3,225)[/tex]
The above shows a geometric progression.
So, we solve using
[tex]p = ab^n[/tex]
In [tex](n_1,p_1) = (0,25)[/tex]
n = 0 and p = 25
Substitute these values in [tex]p = ab^n[/tex]
[tex]25 = ab^0[/tex]
[tex]25 = a*1[/tex]
[tex]25 = a[/tex]
[tex]a = 25[/tex]
In [tex](n_2,p_2) = (1,75)[/tex]
n = 1 and p = 75
Substitute these values in [tex]p = ab^n[/tex]
[tex]75 = ab^1[/tex]
[tex]75 = ab[/tex]
Substitute 25 for a
[tex]75 = 25*b[/tex]
Make b the subject
[tex]b = \frac{75}{25}[/tex]
[tex]b = 3[/tex]
So, we have:
[tex]a = 25[/tex] and [tex]b = 3[/tex]
The equation [tex]p = ab^n[/tex] becomes
[tex]p = 25(3)^n[/tex]
Equation representing the number of points 'P' in 'n' games will be [tex]P=25(3)^{n}[/tex].
Explicit formula of the Geometric sequence:a, ar, ar², ar³........arⁿ
There is a common ratio of 'r' in each successive term to the
previous term.
Therefore, it's a geometric sequence.
Explicit formula of a geometric sequence is given by,[tex]T_n=ar^{n-1}[/tex] (For n ≥ 1)
Here, [tex]a=[/tex] First term
[tex]r=[/tex] Common ratio
[tex]n=[/tex] nth term
Given in the table,
Common ratio (r) of any successive term to the previous term,[tex]r=\frac{75}{25}=3[/tex]
First term of the sequence 'a' = 25Explicit formula of the sequence will be,
[tex]P=25(3)^{n}[/tex] [For n ≥ 0]
Therefore, equation representing the number of points 'P' in 'n' games will be [tex]P=25(3)^{n}[/tex].
Learn more about the geometric sequence here,
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Hi can anyone solve this for me please solve it on a piece of paper please
Answer:
Awsten Knight
Step-by-step explanation:
The sum of twice a number and five is greater than three times the number minus three.
Answer:
x<8
Step-by-step explanation:
2x+5>3x-3
2x+8>3x
8>x
Answer:
n < 8
Step-by-step explanation:
Let n represent the unknown number. Then:
2n + 5 > 3n - 3
Collecting like terms:
8 > n or n < 8
7. QR =
8. Z
P
24x - 2
Q 6x +14 R
102
->
Answer:
7Q ^12
Step-by-step explanation:
Porque se se suman la cuestione y porque solo me estás pagando con cinco puntos
Three vertices of a parallelogram are shown in the figure below. Give the coordinates of the fourth vertex.
Coordinates: (-3,8) (4,5) (2,-5)
Given:
The three vertices of a parallelogram are (-3,8), (4,5), (2,-5).
To find:
The fourth vertex of the parallelogram.
Solution:
Let the vertices of the parallelogram are A(-3,8), B(4,5), C(2,-5) and D(a,b).
We know that, diagonals of a parallelogram bisect each other. It means midpoints of both diagonals are same.
Midpoint formula:
[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]
Two diagonals of ABCD are AC and BD.
Midpoint of AC = Midpoint of BD
[tex]\left(\dfrac{-3+2}{2},\dfrac{8-5}{2}\right)=\left(\dfrac{4+a}{2},\dfrac{5+b}{2}\right)[/tex]
[tex]\left(\dfrac{-1}{2},\dfrac{3}{2}\right)=\left(\dfrac{4+a}{2},\dfrac{5+b}{2}\right)[/tex]
On comparing both sides, we get
[tex]\dfrac{4+a}{2}=\dfrac{-1}{2}[/tex]
[tex]4+a=-1[/tex]
[tex]a=-1-4[/tex]
[tex]a=-5[/tex]
And,
[tex]\dfrac{5+b}{2}=\dfrac{3}{2}[/tex]
[tex]5+b=3[/tex]
[tex]b=3-5[/tex]
[tex]b=-2[/tex]
Therefore, the coordinates of fourth vertex are (-5,-2).
a) The regular price of a T-shirt is $18. What is the discounted price?
b) If the regular price of an item is x dollars, what is the discount price in dollars?
c) The discounted price of a hat is $18. What is the regular (original) price?
help fast!!!
Answer:
B
Step-by-step explanati
the price of the shirt is $18 and lets say x is the discount . X is the discount cause there wasnt a discount provided. so therefore x is unknown. C is talking about a hat and were talking abot a shirt. so whats left.... B
Answer:
the price of the shirt is $18 and lets say x is the discount . X is the discount cause there wasnt a discount provided. so therefore x is unknown. C is talking about a hat and were talking abot a shirt.
Step-by-step explanation:
A circle has its centre at the origin and has a radius of 5.
What is its equation?
Answer:
x²+y²=25
Step-by-step explanation:
(x-h)²+(y-k)²=r²
(x-0)²+(y-0)²=5
x²+y²=25
Line CD contains points A (4, 6) and B (4, 3). The slope of line CD is (2 points)
positive
undefined
negative
zero
Answer:
slope is undefined
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = A(4, 6) and (x₂, y₂ ) = B(4, 3)
m = [tex]\frac{3-6}{4-4}[/tex] = [tex]\frac{-3}{0}[/tex]
Division by zero is undefined thus the slope of CD is undefined
what’s the answer? someone help!!!
In which quadrant does the terminal side of 225° angle in standard position lie
Answer:
4 th quadrant
Step-by-step explanation:
olz make me brainliest
If 2^2x = 2^3, what is the value of x?
Answer:
The value of "X" would be 2.
To solve for x, you'd have to get it by itself. To do so, you'd simplify both sides by solv8ng the exonents of each side (2^2 = 4) and (2^3 = 8). This leaves you with 4x = 8, which you'd then divide both sides by 4. Thus getting 2 as a final answer.
I hope this helps!
(can i plz have brainlist :D hehe)
Step-by-step explanation:
how about this one −p+
5
3
q−
10
1
q+
9
1
−
9
1
p
Answer:
NaNx10^-23
Step-by-step explanation:
Two sisters want to save money to buy a game. The game costs $90. One sister has $36 and the other has $40. How much more money do they need?
y = 3x - 2
y = 4x - 5
Answer:
x = 3
y = 7
Step-by-step explanation:
y=3x-2
y=4x-5
then 3x-2 = 4x-5
reduce
x = 3
y = 7
Answer:
SOLVE FOR Y
y=
2
x+5
SOLVE FOR X
x=2y−5
Step-by-step explanation:
Sarah started with two large dogs and 8 small dogs, write the ratio of large to small dogs. then interpret the ratio with words
Answer:
2:8
Sarah has 2 small dog and 8 big ones
Step-by-step explanation:
Work out the size of angle x
Answer:
angle x=10
Step-by-step explanation:
The system of equations has
options are
1. no solution
2. one solution
3. infinitely many solutions
Answer: no solution
Step-by-step explanation: after simplifying they are parallel which means they have no solutions
Simplify the following expression -24 - 3.r) + (5x - 2)
Answer:
-3 (r+8)
Step-by-step explanation:
-3 (r) -24
-3 (r) - 3 (8)
-3 (r+8)
I’m struggling with this could you help me pls
Step-by-step explanation:
a) x=0, y=6
x=1, y=4
x=2 , y=2
x=3, y=0
x=4, y= -2
y= 6-2x
b) look at the attachment.
c)
6-2x=3
-2x=-3
x=3/2
what is the area of a right triangle with a height of 8.9cm and a base of 14.3cm
4x + 3y = -26
x-3y =-14
Answer:
y = 8 x= -16
Step-by-step explanation:
4x+26x = -6y =14
30x = 14
-6y = 14 x = 14- 30
y+= 14-6
y = 8 x= -16
3s algebraic expression in word form
Answer:
trice the number"s"
Step-by-step explanation:
is this wht u want ? like am i rght? if not pls delete my answer.
Answer:
Thrice a number
Three times the variable "s"
Step-by-step explanation:
Hope it helps!!!
Which of the following best describes AD?
D
А
c
A. Altitude
B. Angle bisector
C. Perpendicular bisector
D. Median
Answer:
it will option A. Altitude hope it helps
The segment AD in the given triangle describes as Altitude.
What is Triangle?A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.
Sum of the interior angles of a triangle is 180 degrees.
Given is a triangle ABC.
Altitude of a triangle is defined as the perpendicular segment drawn from a vertex to the opposite side.
Angle bisector is the line segment drawn from a vertex to the opposite side which bisects the angle at that vertex.
Perpendicular bisector is the perpendicular line segment drawn from a vertex to the opposite side which divides the opposite side to two halves.
Median is the line segment joining the vertex with the mid point of the other side.
Here, it is only given that the drawn line is perpendicular. It does not bisect side or angles.
So it is altitude.
Hence the given segment is altitude.
Learn more about Altitudes of Triangles here :
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Find the equivalent expressions for (x + 7)(x + 1).
x(x + 7+8)
(x +4)^2 - 9
x^2+ 8x + 7
x^2+ 7x + 8
(x+ 4)^2 +9
x(x + 8) +7
Answer:
The answers should be
x^2 + 8x + 7
x(x + 8) +7
Step-by-step explanation:
(x + 7)(x + 1)
x(x) + x(1) + 7(x) + 7(1)
x^2 + x + 7x + 7
x^2 + 8x + 7
Answer:
C d
Step-by-step explanation:
BC has endpoints B(-3,-5) and C(12,12). FInd the coordinates of the midpoint of BC
Answer:
(9/2, 7/2)
Step-by-step explanation:
The easiest way to remember how to do this problem is to average the x-coordinates and average the y-coordinates.
So, in your problem (-3 + 12)/2 = 9/2 and (-5 + 12)/2 = 7/2
The midpoint is (9/2, 7/2)
Which expression represents the quotient of the model shown? -x2 O x + 3 x - 3 lolo o O -X-3 -x + 3
Answer:
-x+3Step-by-step explanation:
Given the expression
-x^2 + x + 3 x - 3
Factorize
(-x^2 + x) + (3 x - 3)
-x(x-1)+3(x-1)
= (x-1)(-x+3)
Hence one of the quotient is -x+3
find the missing angle
Answer:
50°
Step-by-step explanation:
65+65+<z = 180
130+ <z = 180
<z = 50°
y=4x-6
2x-3y=8
if this problem is to be solved bye substitution, which is correct step
Answer:
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
ok
Andrew is starting his own snow plowing business. Andrew has calculated that he needs to earn $500 per week to support his family. If he knows he will only be able to work 50 hours per week, what is the minimum amount of dollars per hour that he will need to charge his customers?
Answer:Ten dollars per hour
Step-by-step explanation:
50 hour =500 dollars
1 hour = ?
Using the criss cross method we multiply one hour by five hundred dollars and divide by fifty dollars.
?=(1 hour×500 dollars)/50 hour
?= 500 dollars/50
?=10 dollars per hour
Answer:
$10
Step-by-step explanation:
$500/50= 10
He needs to earn $10 an hour x the 50 hours = $500