Answer:
[tex]\large\boxed{2^{4x}=2^{3x-9}}[/tex]
Step-by-step explanation:
[tex]8=2^3\to 8^{x-3}=(2^3)^{x-3}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=2^{3(x-3)}\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\=2^{(3)(x)+(3)(-3)}=2^{3x-9}[/tex]
If you want a solution of this equation:
[tex]2^{4x}=8^{x-3}\\\\2^{4x}=2^{3x-9}\iff4x=x-3\qquad\text{subtract}\ x\ \text{from both sides}\\\\3x=-3\qquad\text{divide both sides by 3}\\\\x=-1[/tex]
Answer: the correct option is
(D) [tex]2^{4x}=2^{3x-9}.[/tex]
Step-by-step explanation: We are given to select the correct equation that is equivalent to the following equation :
[tex]2^{4x}=8^{x-3}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
Equivalent equations means two equations that can be obtained from one another using some properties of formula.
We will be using the following formula :
[tex](a^b)^c=a^{b\times c}.[/tex]
From equation (i), we have
[tex]2^{4x}=8^{x-3}\\\\\Rightarrow 2^{4x}=(2^3)^{x-3}\\\\\Rightarrow 2^{4x}=2^{3\times(x-3)}\\\\\Rightarrow 2^{4x}=2^{3x-9}.[/tex]
Thus, the required equivalent equation is [tex]2^{4x}=2^{3x-9}.[/tex]
Option (D) is CORRECT.
Can someone help me plz
Step-by-step explanation:
m∠3 + m∠4 = 180°
TRUE - they are supplementary angles
m∠2 + m∠4 + m∠6 = 180°
TRUE - measureas of angles in a triangle add up to 180°
m∠2 + m∠4 = m∠5
TRUE, because
m∠2 + m∠4 + m∠6 = 180° and m∠6 + m∠5 = 180°
therefore m∠2 + m∠4 + m∠6 = m∠6 + m∠5 subtract m∠6 from both sides
m∠2 + m∠4 = m∠5
m∠1 + m∠2 = 90°
FALSE, because m∠1 + m∠2 = 180°
m∠4 + m∠6 = m∠2
FALSE, because
m∠4 + m∠6 + m∠2 = 180° subtract m∠2 from both sides
m∠4 + m∠6 = 180° - m∠2
m∠2 + m∠6 = m∠5
FALSE, because
m∠5 + m∠6 = 180° subtract m∠5 from both sides
m∠6 = 180° - m∠5 add m∠2 to both sides
m∠2 + m∠6 = 180° - m∠5 + m∠2
PLEASE ANSWER FIRST GETS BRAINLIEST
Both equations start with y =
Set both equations equal to each other and solve for x first:
1/3x-4 = -7/3x +4
Add 7/3x to both sides:
8/3x - 4 = 4
Add 4 to each side:
8/3x = 8
Divide both sides by 8/3
x = 3
Now you have the value of x, replace x in the equation to solve for y:
y = 1/3(3) -4 = 1-4 = -3
y = -7/3(3) +4 = -7+4 = -3
y = -3
X = 3 and y = -3
Question 5 (1 point)
Chandler employees 30 people and plans to increase the number of seasonal
workers by 5% each week. Select the correct equation that represents this scenario.
a) Linear: f (x) = 30 + 1.05x
b) Exponential: f (x) = 30(1:05)?
c) Exponential: f (x) = 30(0.05)
d) Linear: f (x) = 30 + 0.05x
Answer:a) Linear: f (x) = 30 + 1.05x
Step-by-step explanation:
Linear: f (x) = 30 + 1.05x is the correct equation.
The answer is option A.
What's an equation example?An equation is a mathematical statement this is made up of expressions related with the aid of the same signal. for instance, 3x – five = 16 is an equation. Solving this equation, we get the price of the variable x as x = 7.
A one-step equation is an algebraic equation you may resolve in the most effective one step. You've got solved the equation when you get the variable through itself, and not using numbers in the front of it, on one side of the same signal.
Learn more about the equation here: https://brainly.com/question/1214333
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A patrolman spends 25% every day completing paperwork. The patrolmans shift each day is 8 hours. How much of his time does he spend doing paperwork each day
Answer:
2 hours.
Step-by-step explanation:
8 hours x 25 / 100 = 2 hours
Answer:
2 hours.
Step-by-step explanation:
Let the number of hours taken doing paperwork be x.
Shift of each day=8 hours
According to question
x=25%of 8 hours
x=25×8/100
x=2 hours
Thus, answer is 2 hours.
A baker has 2,000 grams of flour he uses 425 grams of it what is the mass of the flour left
Answer:
1575 grams
Step-by-step explanation:
If a baker has 2,000 grams of flour and uses 425 grams of it, the mass will become 1575 grams.
2000 - 425 = 1575
Answer:
1575 grams of flour
Step-by-step explanation:
If he had 2000 grams of flour and used 425 grams of it, you have to subtract 2,000 by 425, which would equal 1,575 grams of flour left.
Algebra 2 help? will give brainliest
(Free points)
Factorise x³ + 216y³ + 8z³ - 36xyz
Answer:
[x+6y+2z][x²+(6y)²+(2z)²-6xy-12yz-2xz]
Step-by-step explanation:
x³+216y³+8z³-36xyz
x³+(6y)³+(2z)³-3×6×2×xyz
As we know
a³+b³+c³-3abc=(a+b+c)(a²+b²+c²-ab-bc-ca)
Let a=x
b=6y
c=2z
Now.
[x+6y+2z][(x²+(6y)²+(2z)²-x×6y-6y×2z-x×2z]
[x+6y+2z][x²+(6y)²+(2z)²-6xy-12yz-2xz]
Answer:
have a good day
Step-by-step explanation:
you deserve it
What are the coordinates of the image of vertex F after a
reflection across the line y=-X?
(-1,-3)
(3,-1)
(1,3)
(-3,1)
G(-2. -3)
F(1.-3)
E -1, -5
H(2-5)
This takes too long to do. I will provide the steps.
For each point given, plug into the equation y = - x.
Point 1:
(-1, -3)
y = -x
y = -(-1)
y = 1
The first point reflected across the line y = - x is (-1, 1).
Do the same with the remaining points.
Which of the following describe an angle with a vertex at Y?
Check all that apply.
A. XYZ
B. ZXY
C. XZY
D. ZYX
Answer:
A and D
Step-by-step explanation:
See I cannot explain you by diagram as I cannot make it here but the short trick is that the angle with the vertex you are looking for should be in the centre.
Here, it is XYZ and ZYX
Factor this trinomial completely.
-6x2 + 26x+ 20
Answer:
−2(3x+2)(x−5)
Step-by-step explanation:
−6x2+26x+20=
=−2(3x+2)(x−5)
Which best describes the transformation that occurs from
the graph of f(x) = x2 to g(x) = (x - 2)2 + 3?
right 2, up 3
left 2, down 3
right 2, down 3
left 2, up 3
Answer:
A. right 2, up 3
Step-by-step explanation:
We are asked to find the transformation that occurs from the graph of [tex]f(x)=x^2[/tex] to [tex]f(x)=(x-2)^2+3[/tex].
Let us recall transformation rules:
[tex]f(x)\rightarrow f(x+a)=\text{Graph shifted to left by a units}[/tex]
[tex]f(x)\rightarrow f(x-a)=\text{Graph shifted to right by a units}[/tex]
[tex]f(x)\rightarrow f(x)-a=\text{Graph shifted downwards by a units}[/tex]
[tex]f(x)\rightarrow f(x)+a=\text{Graph shifted upwards by a units}[/tex]
Upon looking at our given functions, we can see that graph of [tex]f(x)=x^2[/tex] is shifted to right by 2 units as 2 is inside parenthesis. The graph is shifted upwards by 3 units as we have positive 3 outside parenthesis.
Therefore, option A is the correct choice.
Which equations and/or functions represent the graphed
line? Select four options.
Answer with explanation:
The equation of line having X intercept (-4,0) and Y intercept (0,2) is given by the formula
[tex]\rightarrow \frac{x}{a}+\frac{y}{b}=1\\\\ \rightarrow \frac{x}{-4}+\frac{y}{2}=1\\\\ \rightarrow x -2 y= -4\\\\ x -2 y+4=0[/tex]
Bethany wrote the equation x+(x+2)+(x+4)=91 when she was told that the sum of three consecutive odd integers had a sum of 91. Which statement about her equation is true?
A) Bethany is correct because consecutive odd integers will each have a difference of two.
B) Bethany is correct because there are three xs in the equation and three is an odd number so it represents the sum of odd numbers.
C) Bethany is incorrect because 2 and 4 are even numbers, she should use 1 and 3 in their place.
D) Bethany is incorrect because consecutive integers always increase by 1 each time, not by 2.
Answer:
Bethany is correct because consecutive odd integers will each have a difference of two.
For example: [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21...] All those are odd numbers, and have a difference of two.
So every time time we make 'x' an odd number in Bethany's equation, we will get three consecutive numbers.
For example, if 'x' equals '1', then we will get the three consecutive numbers 1, 3 and 5.
If 'x' equals 7, then we will get the three consecutive numbers 7, 9 and 11.
Answer:
A.) Bethany is correct because consecutive odd integers will each have a difference of two
Step-by-step explanation:
The sum of 3 consecutive odd integers is 91. Let the first odd integer is x. The next odd integer will be obtained by adding 2 in x i.e. (x + 2). The third odd integer will be obtained by adding 2 in the second odd integer i.e. (x + 2) + 2 = x + 4
After the information stated we can conclude that:
The 3 odd integers will be:
x , (x+2) and (x+4)
Their sum is given to be 91. So we can write:
x + (x+2) + (x+4) = 91
Hence, we can conclude that: Bethany is correct because consecutive odd integers will each have a difference of two.
What is Y=3/4+2 graphed
Answer:
I don't possess a graph so I'll teach it to you.
Step-by-step explanation:
In a coordinate plane with 4 quadrants, the formula for this equation is SLOPE. This is fairly a very easy topic to learn about. The formula is y = mx + b.
So I assume you forgot to put the "x" after the 3/4.
Anyway, to answer this the "2" in bthe equation is the y-intercept. So the X-coordinate will ALWAYS be ZERO! O basically you plot at (0,2).
Next, you grab the slope. To get it you must use the RISE OVER RUN technique. You rise 3 UP and since it's a POSITIVE SLOPE, 3/4, NOT -3/4, you RUN 4 units to the RIGHT, which gives you (5,4), I believe. And you keep doing that until the graph is finished. And if you want to go backwards from (0,2), you make the RISE AND RUN, NEGATIVE. It's very simple. In the end you should get a line like "/" on your graph which means it's a POSITIVE SLOPE. If it's "\", IT'S A NEGATIVE SLOPE.
I hope this helps and PLEASE FOLLOW ME! I JUST STARTED BRAINLY!
6x-5y=5
3x+5y=4
The x-coordinate of the solution to this system of equation is
Answer:
x=1
Step-by-step explanation:
1) 6x-5y=5
2) 3x+5y=4
ets perform the following operation
1) +2), This leads to the following equation:
6x+3x-5y+5y=5+4
From where we obtain the solution for x
9x=9
x=1
HELP FAST WILL MARK BRAINLIEST
How much money would you have to invest in order to get $20,000 after 25 years in a 11% annual interest account that is compounded weekly?
Answer:
[tex]\$1,282.28[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=25\ years\\ A=\$20,000\\ r=0.11\\n=52[/tex]
substitute in the formula above
[tex]20,000=P(1+\frac{0.11}{52})^{52*25}[/tex]
[tex]20,000=P(1.0021)^{1,300}[/tex]
[tex]P=20,000/(1.0021)^{1,300}[/tex]
[tex]P=\$1,282.28[/tex]
Which number line represents the solution set for the inequality -4(x+3) ≤ -2 - 2x?
Answer:
d
Step-by-step explanation:
u got the answer right
The ratio of the number of boys in a school play to the number of students in the play is 7/10. What is the ratio of the number of girls in the play to the number of boys in a play
Answer:
3/7
Step-by-step explanation:
The total number of students in the play is 10.
The number of boys in the play is 7.
The remaining students in the play must be girls, so 10-7=3.
There are 3 girls in the play.
The ratio of girls in the play to boys in the play would be:
girls/boys= 3/7.
Answer:
Step-by-step explanation:
The no of girls is 3/10
Girls : boys
3/10 : 7/10
3 : 7
Koalas absorb only 25% of the fiber they eat. A koala absorbed 10.5 ounces of fiber in one day. How many ounces of fiber did he eat that day?
[tex]\huge{\boxed{\text{42 ounces}}}[/tex]
25% is equal to [tex]\frac{1}{4}[/tex], so multiplying it by 4 gets 100%. This means we can multiply 10.5 by 4 to get 100% of the fiber the koala ate that day.
[tex]10.5*4=\boxed{42}[/tex]
Answer:
42 ounces
Step-by-step explanation:
So a koala absorbs 25% of fiber they eat.
A koala absorbed 10.5 ounces in a day.
Let x be the amount of ounces of fiber the source(s) actually contained that day.
So we have 25% of x is 10.5
As an equation that is .25x=10.5 or 1/4 *x=10.5.
.25x=10.5
To solve this equation you can divide both sides by .25 giving you
x=10.5/.25=42.
If you chose the other equation which is an equivalent equation you would multiply both sides by 4.
1/4 *x=10.5
x=4(10.5)
x=42
Which of the following mixed numberd is represented by the letter A in number line shown?
Answer:
A
Step-by-step explanation:
The line is divided into 9 parts between 1 and 2
A is situated 6 parts of the way between 1 and 2, that is
[tex]\frac{6}{9}[/tex] = [tex]\frac{2}{3}[/tex] ← cancelling by 3
Hence
A = 1 + [tex]\frac{2}{3}[/tex] = 1 [tex]\frac{2}{3}[/tex] → A
Multiplying monomials and binomials
Answer:
The product of 28w(w-17) is 28w^2 - 476w
Step-by-step explanation:
Given
28w(w-17)
We have to find the product of the monomial and binomial polynomials
The term 28w will be distributed to w-17
So,
= (28w)(w) - (28w)(17)
= 28w^2 - 476w
Therefore, the product of 28w(w-17) is 28w^2 - 476w ..
Final answer:
When multiplying monomials and binomials, you can follow certain rules. Multiply the numerical coefficients, add the exponents of the variables, and then combine like terms if possible.
Explanation:
When multiplying monomials and binomials, you can follow a few rules. For monomials, you simply multiply the numerical coefficients and add the exponents of the variables. For binomials, you can use the distributive property to multiply each term of one binomial by each term of the other binomial. Then, combine like terms if possible.
For example, let's say we have (2x^2)(3x^3). We would multiply the coefficients (2 * 3 = 6) and add the exponents of the variable x (2 + 3 = 5). So the resulting expression is 6x^5.
Darrin can skateboard 2 miles against a 4 mph wind in the same amount of time he skateboards 6 miles with a 4 mph wind. Find the speed Darrin skateboards with no wind.
Answer:
Speed = 8mph
Step-by-step explanation:
Speed of wind = 4mph
Let speed of Darrin with no wind be "x" mph
then resultant speed of Darrin, travelling in direction of wind = (x + 4) mph
Using a result, Time = Distance travelled / Net speed
Time taken by Darrin to travel 6miles in direction of wind = 6 / (x + 4)
When Darrin travel in opposite direction of wind, then its net speed = (x - 4)mph
Darrin travel 2 miles against the wind in 6/(x + 4) hr
then Distance = speed × time
2 = ( x- 4 ) × ( 6/x + 4)
2x + 8 = 6x - 24
4x = 32
x = 8 mph
Therefore speed of Darrin skateboard with no wind = 8mph
Answer:
Speed without wind will be 8 mph
Step-by-step explanation:
Now by revising basic formula here
Velocity = Distance/Time. . . . (A)
Assume speed without wind is 'x'
When Darrin is moving against wind to cover 2 miles;
net speed will be x-4
When Darrin is moving along with the wind to cover 6 miles;
net speed will be x+4
Please note that the time for covering distance of 2 miles and 6 miles is same,
So, from equation (A)
Time = Distance/Velocity,
Time for 2 miles will be
Time = 2/(x-4)
Time for 6 miles will be
Time = 6/(x+4)
Since, the time for both distances is same, here we can equate,
2/(x-4) = 6/(x+4)
by cross multiply
2(x+4) = 6(x-4)
2x+8 = 6x-24
4x = 32
x = 8
So, 8 miles per hour is the speed of Darrin if there is no wind.
Can someone please do 41 and 45???? Thanks!!!
Answer:
Part 41) The solution of the compound inequality is equal to the interval [-1.5,-0.5)
Part 45) The solution of the compound inequality is equal to the interval
(-∞, -0.5] ∪ [1,∞)
Step-by-step explanation:
Part 41) we have
[tex]-4\leq 2+4x < 0[/tex]
Divide the compound inequality into two inequalities
[tex]-4\leq 2+4x [/tex] -----> inequality A
Solve for x
Subtract 2 both sides
[tex]-4-2\leq 4x [/tex]
[tex]-6\leq 4x [/tex]
Divide by 4 both sides
[tex]-1.5\leq x [/tex]
Rewrite
[tex]x\geq -1.5[/tex]
The solution of the inequality A is the interval -----> [-1.5,∞)
[tex] 2+4x < 0[/tex] -----> inequality B
Solve for x
Subtract 2 both sides
[tex]4x < -2[/tex]
Divide by 4 both sides
[tex]x < -0.5[/tex]
The solution of the inequality B is the interval ------> (-∞, -0.5)
The solution of the inequality A and the Inequality B is equal to
[-1.5,∞)∩ (-∞, -0.5)------> [-1.5,-0.5)
see the attached figure N 1
Part 45) we have
[tex]2x-3\leq -4[/tex] or [tex]3x+1\geq 4[/tex]
Solve the inequality A
[tex]2x-3\leq -4[/tex]
Adds 3 both sides
[tex]2x\leq -4+3[/tex]
[tex]2x\leq -1[/tex]
Divide by 2 both sides
[tex]x\leq -0.5[/tex]
The solution of the inequality A is the interval ------> (-∞, -0.5]
Solve the inequality B
[tex]3x+1\geq 4[/tex]
Subtract 1 both sides
[tex]3x\geq 4-1[/tex]
[tex]3x\geq 3[/tex]
Divide by 3 both sides
[tex]x\geq 1[/tex]
The solution of the inequality B is the interval -----> [1,∞)
The solution of the compound inequality is equal to
(-∞, -0.5] ∪ [1,∞)
see the attached figure N 2
If x is in west of y and y is in north of z, towards which direction of x is z?
Answer: southeast
Step-by-step explanation:
Draw a picture showing x to the left of y and z below y:
x y
z
This results in z being south and east from x
If x is in west of y and y is in north of z, direction of x with respect to z is South-east .
What is direction of x with respect to z ?Given that x is in west of y and y is in north of z.
To obtain the direction of a respective person with respect to a given person, we draw the given image as mentioned in the question.
Drawing the required direction as per given in question -
x y
z
Thus, we can clearly see that z is South-east direction of x.
Therefore, if x is in west of y and y is in north of z, direction of x with respect to z is South-east .
To learn more about direction, refer -
https://brainly.com/question/13696986
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Which will result in a difference of squares?
(-7x+4)(-7x+4)
(-7x+4)(4-7%)
0 (-7x+4)(-78-4)
(-7x+4)(7x-4)
Answer:
The expression which will result in difference of two squares is:
(–7x + 4)·(–7x – 4)
Step-by-step explanation:
We know that the formula of the type:
(a-b)(a+b)=a²-b²
i.e. it is a difference of two square quantities. (a^2 and b^2)
since,
a= -7x , b=4
(-7x+4)(-7x-4)= (-7x)² - (4)²
=(7x)² - 4²
So the expression is a difference of two square quantities:
(7x)² and (4)²
Hence the answer is (–7x + 4)·(–7x – 4)....
please help this is mainly on fuctions
Answer:
B and C
Step-by-step explanation:
We are going to look at each choice:
Let's look at choice A.
f(5)=1
f(5) means look at function f and then see which piece contains x=5.
5>1 so we are looking at [tex]x^2[/tex] for x=5 which gives you [tex]5^2=25[/tex], this is not 1.
The answer is not A.
Let's look at choice B.
f(2)=4
f(2) means look at function f and then see which piece contains x=2.
2>1 so we are looking at [tex]x^2[/tex] for x=2 which gives you [tex]2^2=4[/tex], so this is true that f(2)=4.
Let's look at choice C.
f(1)=5
f(1) means look at function f and then see which piece contains x=1.
1=1 which means we are using [tex]5[/tex] for x=1, so f(1)=5 which is what choice C says so choice C is true.
Let's look at choice D.
f(-2)=4
f(-2) means look at function f and then see which piece contains x=-2
-2<1 so we use [tex]2x[/tex] for x=-2, so we get 2(-2)=-4 which is not 4 so f(-2)=4 is not true.
The midsegment of ABC IS IM. What is the length of MC if BC is 18 inches
long?
A. 36 inches
B. 18 inches
C.27 inches
D. 9 inches
Answer:
D. 9 inches
Step-by-step explanation:
By using proportionality theorem,
Triangle BLM ~ Triangle BAC
[tex] \frac{bm}{bc} = \frac{bl}{ba} [/tex]
as ba = bl + la and as bl = la
Therefore, bl + la = 2bl
[tex] \frac{bm}{bc} = \frac{bl}{2bl} [/tex]
Now, we get,
[tex] \frac{bm}{18} = \frac{1}{2} [/tex]
as bc = 18
Hence,
[tex]bm = 9 \: inches[/tex]
Answer: D. 9 inches
Step-by-step explanation:
Given : The midsegment of Δ ABC is line segment IM.
Such that for side BC , BM=MC [ Show in the picture ] (1)
and BC= BM+MC (2)
The length of BC = 18 inches (3)
From (1) and (2), we have
[tex]BC=MC+MC\\\\\Rightarrow\ BC=2MC[/tex]
Using (3), we have
[tex]2MC=18\text{ inches}\\\\\Rightarrow\ MC=\dfrac{18}{2}=9\text{ inches}[/tex]
Therefore, the length of MC = 9 inches.
Hence, D is the correct option.
Find the measure of HG¯¯¯¯¯¯¯¯.
A. 12
B. 16
C. 14
D. 7
HG^2 = FG * (FG + EF)
Fill in the values:
(x+3)^2 = x * (7+x)
Simplify the right side:
(x+3)^2 = 7x +x^2
Rewrite the left side using the FOIL method
x^2 + 6x + 9 = 7x +x^2
Subtract x^2 from both sides:
6x +9 = 7x
Subtract 6x from both sides:
x = 9
Now you have x solve for HG
HG = x +3 = 9+3 = 12
The answer is A.
Please help me with this question
Answer:
-2 degrees
Step-by-step explanation:
If you work backwards you will eventually get -2
For example: -3 + 3 = 0, then 0 - 2 = -2, so on...........
If f(x) = 3x? - 4 and g(x) = x+2, find (f - g)(x).
O
O
O
O
A. 3x2 - *-6
B. 3x2 - x-2
C. 3x -8
D. *- 3x - 2
Answer:
The answer is A, (3x2-x-6)
Step-by-step explanation:
f(x)=3x2 -4
g(x)=x+2
f(x)-g(x)= 3x2-4 -x-2= 3x2-x-6
Final answer:
The expression (f - g)(x) is found by subtracting g(x) from f(x) and simplifying, which results in 3x² - x - 6, corresponding to option A.
Explanation:
To find (f - g)(x) when f(x) = 3x² - 4 and g(x) = x + 2, we need to subtract the function g(x) from f(x). The operation looks like this:
(f - g)(x) = f(x) - g(x) = (3x² - 4) - (x + 2)
Let's perform the subtraction step by step:
Distribute the negative sign to both terms in g(x):
(3x²- 4) - x - 2
Combine like terms:
3x² - x - 4 - 2
Final simplification:
3x² - x - 6
Therefore, the correct answer is 3x² - x - 6, which matches option A from the provided choices.