4^t × 2^t = 2^what [convert all terms to the same base (2)]
∴ 2^t × 2^t × 2^t = 2^what [use the multiplicat law of exponents]
2^(t+t+t) = 2^what [simplify]
2^3t = 2^what
what = 3t
What is the equation of the line that is perpendicular to -2/5x-7 and passes through (4,-1)?
Step-by-step explanation:
maybe this is not the full expression, as you wrote the line equation in a funny way.
I understand the following :
the line is
y = (-2/5)×x - 7
perpendicular means crossing at a right angle (90 degrees).
the slope of the original line is -2/5.
as in every line equation, the slope is the factor of x. and it expresses the ratio y/x indicating the amount of units y is changing, when x changes a certain amount of units (e.g. when going from one point on the line to another).
the perpendicular slope turns the original y/x ratio upside-down, and also flips the sign.
so, it is 5/2.
the equation for the perpendicular line looks like
y = (5/2)×x + b
now what is b ?
for this we use the specified point on the line : (4, -1)
and we put these values as x and y into the equation :
-1 = (5/2)×4 + b = 5×2 + b = 10 + b
b = -11
and so, the full equation of the perpendicular line is
y = (5/2)×x - 11
The graph of y = x2 + 4x + 3 is shown.
a) What are the coordinates of the turning point?
b) What are the coordinates of the roots of the equation x + 4x + 3 = 0 ?
Answer:
a.(-2,-1)
b.(-3,0) and (-1,0)
Step-by-step explanation:
the roots are 2
The length of a rectangular garden is 5 less than triple
its width. If the perimeter of the garden is 70 feet,
find the dimensions of the garden algebraically.
Answer:
Width = 10 feet, Length = 25 feet
Step-by-step explanation:
the width is x
the length is 3x-5
so, 2(x+(3x-5))=70 is the equation
2(x+3x-5)=70
2x+6x-10=70
8x-10=70
8x=10
x=10.
Width = 10 feet
Length = 25 feet
Write as a decimal: two and three-tenths =
Answer:
2.3 is ur answer
Step-by-step explanation:
Answer:
2.3
Step-by-step explanation:
the interweb said so
The GCF of two numbers is 3 and the LCM is 180. If the one of the number is 45, what is the other number?
Answer:
45
Step-by-step explanation:
45 = 3*3*5
180 = 2*2*3*3*5 <---- so the other number had to contain a factor of 2*2 or 4
also, let the other number has to be of the form 3k and it must contain a factor of 4, how about 12 ?
check: lcf of 12 and 45 is 3,
the lcm of 12 and 45 is ...
12 = 2*2*3
45 = 3*3*5
so we need: 2*2*3*3*5 = 180
Which polynomial has (3x + 2) as a binomial factor?
Answer:
Step-by-step explanation:
If binomial (3x+2) is a factor of some polynomial, then number is this polynomial's root. Check all polynomials:
6x^3+3x^2+4x+2
Answer:
B. [tex]12x^2+15x+8x+10[/tex]
Step-by-step explanation: I did this assignment on edge.
One circle has a circumference of 12 cm. Another circle has a circumference of 32 x cm. What is the ratio of the
radius of the smaller circle to the radius of the larger circle?
3:8
8:3
1:3
3:1
Answer:
8:3
Step-by-step explanation:
Answer:
3:8 or 8:3, im leaning towards 3:8 more but i dunno
Step-by-step explanation:
3
10 points
A vector starts at point (-8,-6) and ends at point (7,-3) what is the horizontal component of the vector?
Type your answer...
(2 x 3) + (3 x 4) =
Answer:
18
Step-by-step explanation:
To answer, you want to follow PEMDAS:
P = parentheses
E = exponents
M = multiplication
D = division
A = addition
S = subtraction
So, the first step is parentheses, therefore we do whatever is inside the parentheses, and that is multiplying:
(2 * 3) + (3 * 4) =
6 + 12
Now, because there are no exponents, we cannot multiply anymore, and we cannot divide, we can add:
6 + 12 =
18
And that is our final answer!
Hope this helps :)
Are the triangles congruent?
-yes by SSS
-yes by SAS
-yes by ASA
-yes by AAS
-yes by HL
Answer:
yes by SAS
it is Side angle Side
i need the answer to the bottom question please help !!!!!!!!!!!!!!
Answer:
y = 9/17 x - 28/17
Step-by-step explanation:
Sixty tickets at $90 each cost
Cost of 1 ticket = $ 90
Cost of 60 tickets = ?
Cost of 60 tickets = 90 × 60 = $ 5400.
Answer:
5,400
Step-by-step explanation:
well, if they're sixty tickets and each cost approx. $90, which means it's 60 x 90, and that gets to 5,400.
x over 32 = 3 over 16
Answer:
7/32 = 3/16
Step-by-step explanation:
Answer:
x=6
Step-by-step explanation:
We simplify the equation to the form, which is simple to understand
x/32=3/16
Simplifying:
+ 0.03125x=3/16
Simplifying:
+ 0.03125x=0.1875
We move all terms containing x to the left and all other terms to the right.
+ 0.03125x=0.1875
We simplify left and right side of the equation.
+ 0.03125x=0.1875
We divide both sides of the equation by 0.03125 to get x
Worth 100 Points!
Help, this is after an test. And I still don't understand it. Could someone please help me understand this question related to inverse functions? Thanks!
You were close, and have the right idea, but I think you did it a bit backwards! You want to "flip" it over the y=x line (picture attached below)
To solve for the inverse, you will find the equation of the original, switch the x and y, then solve for y.
We can (mostly, I think?) tell the equation for f(x) is as follows, so we switch the y and x for the steps following to solve for y:
[f(x)] y = -2x + 2
[switch] x = -2y + 2
[subtract 2 from both sides / flip equation] -2y = x - 2
[divide both sides by -2] y = -2x -4
So our equation for g(x) will be about y = 2x -4
(inverse so the negative is weird)
Photos:
- first is y=x
- second is the general idea of the inverse for what g(x) should look like
- third is kinda what the graph will look like (digitally)
I know this isn't a *perfect* answer, but I hope it explains it some and helps. Good luck! :D
HELPPP PLEASEEE
If θ is 180 degrees and the radius is 4.9 cm, the length should be
A) 10.4 cm
B) 13.6 cm
C) 15.4 cm
D) 16.6 cm
Answer:
15.4 is right ans
Step-by-step explanation:
using this formula θ ×(22÷7÷180)×r
Please please help me with this question please now and show your steps
Answer:
[tex]y = {x}^{2} - 8x + 7 \\ a = 1 \: and \: b = - 8 \\ the \: line \: of \: symmetry \: \\ x = \frac{ - b}{2a} = \frac{8}{2} \\ x = 4(line \: of \: symmetry) \\ y = {4}^{2} - 8(4) + 7 \\ = 16 + 32 + 7 = y = 55 \\ vertix \: is \: (4 ,55) \\ y = {0}^{2} - 8(0) + 7 \\ y = 7 \\ 0 = {x}^{2} - 8x + 7 \\ (x - 7)(x - 1) = 0[/tex]
Can someone Please Help
Answer:
4
Step-by-step explanation:
2 to the power of 4 is the same as 2×2×2×2.
That is also the same as 4×4, which equals 16.
Answer:
4
Step-by-step explanation:
Can someone help me :(( thank you so so much if u do <33:)
Answer:
13
Step-by-step explanation:
8-13=-5
Answer:
13
Step-by-step explanation:
8 - 13 = -5
that is your answer
For w(x)=4x-4 find w(-7) show your work
Answer:
-32
Step-by-step explanation:
To find w(-7) we have to substitute x with -7
w(x)=4x-4
w(x = -7) = 4(-7) -4
w(-7) = -28-4
w(-7) = -32
will mark brainliest
Answer:
148 deger ❤❤❤❤❤❤❤❤❤❤
32 meter
90 entre (7 + 3) x 2
Harry drives a lot as a part of his job, and he notes that an upcoming trip is from the office to a meeting location that is 2 inches away on a map. The map uses a scale of 1 inch = 34 miles. What is the actual distance between the office and the meeting location?
Answer: The actual distance is 68 miles.
Step-by-step explanation:
not sure how to do these. i need help with 13! needing it to be reduced just like y should be 8
Answer:
I'm not sure 710
Step-by-step explanation:
I'm not sure
Answer:
#14
y=5
x=14
Step-by-step explanation:
I did 14 for you
the two expressions with x equal each other since they are on the same side of their line, similar to eachother. Then plug in x into one of those expressions and do 180- your answer to get the angle for one of the y expressions since its on the other side of the line. both angles have to add up to 180.
Perimetre of rectangle is 256cm.it length is 3times as long as its breadth.find breadth or length.
help me pls iam confused
Answer:
z=9.6
Step-by-step explanation:
Because you know 17 is one of the values in the model, you do:
65-17=48
Then, because you have 5 z values, you do:
48/5=9.6
z=9.6
Compare 9/15 and 10/15
Answer: 9/15 < 10/15
Step-by-step explanation: 9/15 < 10/15
If (x+iy)³ = y+vi then show that (y/x + v/y) = 4(x²-y²)
Answer:
Step-by-step explanation:
[tex] \large\underline{\sf{Solution-}}[/tex]
Given that,
[tex]\rm \longmapsto\: {(x + iy)}^{3} = y + iv[/tex]
[tex]\rm \longmapsto\: {x}^{3} + 3 {x}^{2}(iy) + 3x {(iy)}^{2} + {(iy)}^{3} = y + iv[/tex]
[tex]\rm \longmapsto\: {x}^{3} + 3 {x}^{2}yi + 3x {i}^{2} {y}^{2} + {i}^{3} {y}^{3} = y + iv[/tex]
We know,
[tex] \purple{\rm \longmapsto\:\boxed{\tt{ {i}^{2} = - 1 \: \: \: and \: \: \: {i}^{3} = - i }}} \\ [/tex]
So, using this, we get
[tex]\rm :\longmapsto\: {x}^{3} + 3 {x}^{2}yi - 3x{y}^{2} - i{y}^{3} = y + iv[/tex]
[tex]\rm \longmapsto\: ({x}^{3} - 3x {y}^{2}) + i(3{x}^{2}y- {y}^{3})= y + iv[/tex]
On comparing real and Imaginary parts, we get
[tex]\rm \longmapsto\:y = {x}^{3} - 3 {xy}^{2} [/tex]
and
[tex]\rm \longmapsto\:v = {3x}^{2}y - {y}^{3} [/tex]
Now, Consider
[tex]\rm \longmapsto\:\dfrac{y}{x} + \dfrac{v}{y} [/tex]
[tex]\rm \: = \: \dfrac{ {x}^{3} - {3xy}^{2}}{x} + \dfrac{ {3yx}^{2} - {y}^{3} }{y} [/tex]
[tex]\rm \: = \: \dfrac{ x({x}^{2} - {3y}^{2})}{x} + \dfrac{y({3x}^{2} - {y}^{2})}{y} [/tex]
[tex]\rm \: = \: {x}^{2} - {3y}^{2} + {3x}^{2} - {y}^{2} [/tex]
[tex]\rm \: = \: 4{x}^{2} - {4y}^{2}[/tex]
[tex]\rm \: = \: 4({x}^{2} - {y}^{2})[/tex]
Hence, Proved
List the terms in the expression xyz+1
Answer:
see explanation
Step-by-step explanation:
xyz + 1 ← has 2 terms
xyz is one term and the other is the constant term + 1
Hank's pickup can travel 54 miles on 3 gallons of gas. How many gallons will Hank's pickup need to travel 36 miles?
Answer:
2 gallons
Step-by-step explanation:
what is the distance from "-15" to 15 ?
15 , 0, -0 , 30
Answer:
the distance would be 30.
Answer:
30
Step-by-step explanation:
-15 to 0 is 15
0 to 15 is another 15
15+15 = 30
absolute value*