Answer:
k = ab/ ( a^2 - b^2)
Step-by-step explanation:
a/b=b/a+1/k
Multiply each side by abk to get rid of the fractions
abk *a/b=abk(b/a+1/k)
a^2k = b^2k + ab
Subtract b^2k from each side
a^2k - b^2k = b^2k - b^2k + ab
a^2 k - b^2 k = ab
Factor out k
k( a^2 - b^2) = ab
Divide each side by ( a^2 - b^2)
k( a^2 - b^2)/ ( a^2 - b^2) = ab/ ( a^2 - b^2)
k = ab/ ( a^2 - b^2)
Answer: K= ab/(a+b)(a-b)
what is the sign of -a^4/3 when a is less than zero
A positive
B negative
C zero
Reasoning:
'a' is less than 0, so we write a < 0
Since a < 0, this means a^4 > 0. Raising a negative to an even exponent will make the result positive. Example: (-2)^4 = 16
Applying the cube root to some positive number leads to some other positive number.
So far we see that the expression a^(4/3) is positive
The final result however is negative because the negative out front flips things from positive to negative.
It turns out it doesn't matter if 'a' is positive or negative. As long as 'a' is nonzero, then -a^(4/3) is negative. If a = 0, then the whole thing is 0.
The length of a rectangle is 2 units greater than the width. The area of the rectangle is 24 square units. What is it's width?
Answer:
4 units
Step-by-step explanation:
Length would be 6 units and width would be 4 units
6*4 = 24 proving my claim to be true
Answer:
Width = 4 units
Step-by-step explanation:
Let us pose the width as w, and the length as l. If the length is 2 units greater than the width, consider the following;
[tex]l = 2 + w,\\\\w = width,\\l = length[/tex]
The area of this rectangle can be determined through length * width / l * w, and is given to be 24 square units. We can say l = 2 + w instead, solving for the width ( w );
[tex]( 2 + w ) * w = 24,\\2w+w^2=24,\\\left(w-4\right)\left(w+6\right)=0,\\w = 4, w = - 6\\\\Solution - width = 4 units[/tex]
As the width couldn't be a negative value, we had to take the positive of 4 and - 6, which was 4 units.
Solve the equation. 5 = –z – 3
Answer:
-8
Step-by-step explanation:
Answer:
Let's do this step by step
Step-by-step explanation:
I hope this helps
Which expression is equivalent to x5 • x2?
Answer:
[tex]x^{7}[/tex]
Step-by-step explanation:
= [tex]x^{5} * x^{2}[/tex]
When bases are same, powers are to be added
= [tex]x^{5+2}[/tex]
= [tex]x^{7}[/tex]
Please help with this question !
Answer:
to solve an equation you do PEMDAS in reverse.
Step-by-step explanation:
Add 1 to both sides.
multiply both sides by 4
square root both sides
now solve what's inside the parentheses by subtracting 5 from both sides.
Answer:
see below
Step-by-step explanation:
Add 1 to both sides
multiply both sides by 4
take the square root of both sides
subtract 5 from both sides
Given that ∠ABC ≅ ∠DBE, which statement must be true?
∠ABC ≅ ∠ABD
∠ABD ≅ ∠CBE
∠CBD ≅ ∠DBE
∠CBD ≅ ∠ABC
Answer:
∠ABD ≅ ∠CBE
Step-by-step explanation:
So we know that ∠ABC ≅ ∠DBE. Those angles equal the same thing. Let's represent that with x.
So does ABD = CBE?
Well we can model that with our xs.
ABD = ABC + CBD
so ABD = x + CBD
CBE = DBE + CBD
so CBE = x + CBD
Look at what we have!
x + CBD = x + CBD.
You can tell that ∠ABD ≅ ∠CBE because those given angles are equal to each other.
Or for an easier (but lazier) method, you can just look at the diagram, which is actually drawn to a reasonable scale. You can tell right off the bat that none of the other options work.
Solve tan^2 theta + 1 = -2 tan theta on the interval 0° ≤ θ ≤ 360°.
Answer:
Step-by-step explanation:
[tex]tan^2 \theta+1=-2 \tan \theta \\tan^2 \theta +2 tan \theta +1=0\\(tan \theta+1)^2=0\\tan \theta=-1=-tan 45=tan (360-45)=tan 315\\\theta =315 ^\circ[/tex]
PLZ HELP IM TIMED!!! Which correctly describes a cross section of the right rectangular prism if the base is a rectangle measuring 15 inches by 8 inches? Select three options.. A right rectangular prism with length 15 inches, width of 8 inches, and height of 6 inches. A cross section parallel to the base is a rectangle measuring 15 inches by 8 inches. A cross section parallel to the base is a rectangle measuring 15 inches by 6 inches. A cross section perpendicular to the base through the midpoints of the 8-inch sides is a rectangle measuring 6 inches by 15 inches.
Answer:
The correct options are (1), (2) and (4).
Step-by-step explanation:
If the cross-section of a right rectangular prism parallel to its base then the cross section is a rectangle.
If the cross section of a right rectangular prism perpendicular to its base then the cross section is a rectangle.
It is provided that a right rectangular prism has a rectangular base measuring 15 inches by 8 inches.
Then the right rectangular prism could have:
Dimensions: Length = 15 inches, Width = 8 inches and Height = 6 inches. A cross section parallel to the base which is a rectangle measuring 15 inches by 8 inches. A cross section perpendicular to the base through the midpoints of the 8-inch sides is a rectangle measuring 6 inches by 15 inches.Thus, the correct options are (1), (2) and (4).
What is the solution to y = x² + 5x – 2
y = 3x - 2
Answer:
(0,-2)(-2,-8)
Step-by-step explanation:
Answer:
(0,-2) (-2,-8)
Hope this helps
Consider the reduction of the complex figure with a scale factor of what is the area of the reduced figure?
42 mm
6 mm
28 mm Area = 1225 mm2
4 mm
mm
49
175
196
Intro
Done
For anyone here who comes from edge.
Consider the reduction of the complex figure with a scale factor of 1 /7 . What is the area of the reduced figure?
The answer is A ; 25 mm2. I got it right on edge
Gordon Ramsey made a stew that contained shrimp and potatoes. Shrimp was expensive, so he used three times the amount of potatoes as he did shrimp. If the stew had 5 lbs. Total shrimp and potatoes, how many pounds of potatoes did he buy?
Answer:
He bough 1.25 lbs of shrimp and 3.75 lbs of potato.
Step-by-step explanation:
Since the stew is composed of shrimps and potatoes, then the sum of the weighs of these ingredients must be equal to the weigh of the stew, so we have:
[tex]shrimp + potato = 5[/tex]
We also know that he bought three times more potatoes than shrimps, therefore:
[tex]potato = 3*shrimp[/tex]
Using the second equation on the first one, we have:
[tex]shrimp + 3*shrimp = 5\\4*shrimp = 5\\shrimp = \frac{5}{4} = 1.25[/tex]
[tex]potato = 3*shrimp = 3*1.25 = 3.75[/tex]
He bough 1.25 lbs of shrimp and 3.75 lbs of potato.
Write the equation of the line with a slope of 3 that passes through the point (4, 1).
Answer:
Step-by-step explanation:
y - 1 = 3(x - 4)
y - 1 = 3x - 12
y = 3x - 11
Answer:c
Step-by-step explanation:
f function g has the factors (x − 7) and (x + 6), what are the zeros of function g?
A.
-7 and 6
B.
-6 and 7
C.
6 and 7
D.
-7 and -6
Answer:
B
Step-by-step explanation:
Can someone help me with these
Answer:
Problem 2) : the gradient is "-2", and the y-intercept is "3"
Problem 3)
A is [tex]y=2x+2[/tex]
B is [tex]y=x+2[/tex]
Step-by-step explanation:
Problem 2)
In the line given by the equation: [tex]y=-2x+3[/tex]
the "gradient" (also known as "slope") is the numerical coefficient that multiplies the variable "x". So in this case the gradient is "-2"
the y-intercept is the numerical term "+3" because that is the y-value result of evaluating the expression for x = 0
[tex]y=-2x+3\\y=-2\,(0)+3\\y=3[/tex]
Problem 3)
Consider the two lines :
[tex]y=x+2[/tex] and [tex]y=2x+2[/tex]
notice that both have the same y-intercept (that is the numerical term "2" at the end of both expressions. That means that both lines cross the y-axis at the point y=2.
Now notice that the gradient of one of them is "1" (for [tex]y=x+2[/tex] ) that is the coefficient that multiplies the variable "x". While for the other line ( [tex]y=2x+2[/tex]) the gradient is "2" and therefore steeper than the previous one.
Then, the line identified as "A" which is the one with steeper gradient, corresponds to the equation [tex]y=2x+2[/tex], and the line identified with "B" is the one with smaller gradient [tex]y=x+2[/tex] .
Find the value of n (-2/3)^4 ÷ (-2/3)^3 = (-3/2)^n
Answer:
Left side simplifies to (-2/3)^1 and the right side simplifies to (-2/3)^(-n) which means 1 = -n so n = -1.
Joseph is eating his favorite kind of cookie.The cookie is part of 9/10 cm thick. The frosting is 33/100 cm thick.What expression can be used to find the total thickness of the cookie and the frosting
Answer:
The expression is: [tex]\text{total thickness} = \text{cookie thickness} + \text{frosting thickness}[/tex]
The thickness of the cookie is: [tex]\frac{123}{100}[/tex] cm
Step-by-step explanation:
The cookie is formed by two layers, the cookie and the frosting. So if we want to know the total thickness of the cookie and frosting we need to sum the thickness of each layer as shown below:
[tex]\text{total thickness} = \text{cookie thickness} + \text{frosting thickness}\\\text{total thickness} = \frac{9}{10} + \frac{33}{100}\\\\\text{total thickness} = \frac{10*9 + 33}{100}\\\\\text{total thickness} = \frac{123}{100} \text{ cm}[/tex]
The expression is: [tex]\text{total thickness} = \text{cookie thickness} + \text{frosting thickness}[/tex]
The thickness of the cookie is: [tex]\frac{123}{100}[/tex] cm
What is the rate of change between (6,12) and (8,20)
Step-by-step explanation:
It might be easier thinking of "rate of change" as the slope. Since you'll be finding a slope, then, use the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] and substitute the values.
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\m=\frac{20-12}{8-6}\\m=\frac{8}{2} \\m=4[/tex]
Answer:
[tex]m=\frac{4}{1}[/tex] or [tex]m=4[/tex]
Please help! Correct answer only please! I need to finish this assignment by today.
Sweet Dreams Bakery recently sold 4 brownies and 14 other desserts. What is the experimental probability that the next dessert sold will be a brownie?
Simplify your answer and write it as a fraction or whole number.
P(brownie) =
Answer:
2/9
Step-by-step explanation:
If the bakery sold 4 brownies and 14 other desserts, then they sold a total of +14=18 desserts. This means that the experimental probability that the next dessert is a brownie is 4/18=2/9. Hope this helps!
The numbers 1,6,8,13,15,20 can be placed in the circle below, each exactly once, so that the sum of each pair of numbers adjacent in the circle is a multiple of seven
in fact, there is more than one way to arrange the numbers in such a way in the circle. Determine all different arrangments. Note that we will consider two arrangments to be the same if one can be obtained from the other by a series of reflections and rotations
Answer:
[tex]\fbox{\begin{minipage}{4em}36 ways\end{minipage}}[/tex]
Step-by-step explanation:
Step 1: Re-state the problem in an easier way to set up a permutation problem
"The numbers 1,6,8,13,15,20 can be placed in the circle below, each exactly once, so that the sum of each pair of numbers adjacent in the circle is a multiple of seven"
The series above can be represented again, in form of:
7a + 1, 7b - 1, 7c + 1, 7d - 1, 7e + 1, 7f - 1
with a, b, c, d, e, f are non-negative integers.
=> 3 numbers are multiply of 7 plus 1
=> 3 numbers are multiple of 7 minus 1
Step 2: Perform the counting:
For the 1st number, there are 6 ways to select
To satisfy that each pair of numbers creates a multiple of 7, then:
For the 2nd number, there are 3 ways left to select
For the 3rd number, there are 2 ways left to select
For the 4rd number, there are 2 ways left to select
For the 5th number, there are 1 way left to select
For the 6th number, there are 1 way left to select
=> In total, the number of possible ways to select:
N = 6 x 3 x 2 x 2 x 1 x 1 = 72
However, these numbers are located around a circle, each option is counted twice.
=> The final number of possible ways:
N = 72/2 = 36
Hope this helps!
:)
A baker needs a total of cups of flour to make four batches of cookies. How much flour, in cups, does she need for each batch of cookies? Write and solve an equation to find the answer.
Answer:
She needs cups of flour for each batch of cookies.
Step-by-step explanation:
Step-by-step explanation:
A baker needs a total cups of flour to make four batches of cookies.
We have to calculate how much flour she needs for each batch of cookies.
Let the flour needed for one batch be f, so the expression would be
f × 4 =
First we convert mixed fraction to proper fraction.
f × 4 =
f =
= × =
Now we convert this proper fraction to mixed fraction.
=
She needs cups of flour for each batch of cookies.
Answer:
she needs 3 1/3 of a cup
Step-by-step explanation:
I have finished the test
EDGE 2021
Can anyone help me solve this equation? 4b+11=39
(-4,-1),(-3,-1),(-2,-3),(-1,0),(-3,2 )IS IT AN FUNCTION OR NOT
Answer:
No it isn't a function one of the x values, -3, repeats
Step-by-step explanation:
i am thinking of a fraction. The sum of the numerator and denominator is 19. When I add
8 to the denominator, the fraction becomes 1/2 What is the fraction I am thinking of?
Answer:
[tex]\frac{9}{10}[/tex]
Step-by-step explanation:
Let the fraction be [tex]\frac{x}{y}[/tex].
That would mean:
(1) x+y = 19
&
(2) y+8 = 2x or 2x = y+8
In order to use substitution, we multiply equation by 2:
(3) 2x+2y = 38
Then we substitute equation (2) into (3):
y+8 + 2y = 38
3y + 8 = 38
3y = 30
y = 10
Substitute this into equation (1)
x + 10 = 19
x = 9
Therefore the fraction would be:
[tex]\frac{9}{10}[/tex]
Answer:
9/10
Step-by-step explanation:
let the fraction be x/y.
x+y=19
x/y+8=1/2
solve simultaneously
y=2x-8
y=19-x
2x-8=19-x
3x=27
x=9
y=10
What is the answer ?????????????????
Answer:
The answer is :
[tex] \cos(51) = 0.63[/tex]
[tex] \sin(63) = 0.89[/tex]
[tex] \tan(12) = 0.21[/tex]
Help me
Verified and certified by me
-ayyyyyyy
Answer:
c. 412.5 cm^2
Step-by-step explanation:
first triangle: 5 x 15 = 75
75/2 = 37.5
rectangle: 15 x 19 = 285
triangle 2: 15 x 12 = 180
180/2 = 90
37.5 + 285 + 90 = 412.5
Write a rule for the linear function in the graph
(0, 1) , (5, 3)
Answer: x = 5, y = 2
Step-by-step explanation
x = 0, x = 5
5 - 0 = 5
y = 1, y = 3
3 - 1 = 2
Four lines are drawn on a coordinate plane to form trapezoid WXYZ. A coordinate grid with 4 lines. Line X W is drawn with point W at (negative 4, 1) and passes through (0, 2) with and (3, 3). Line Y X is drawn with point Y at (3, 0) and passes through (0, 3). Line Z W is drawn with point Z at (0, negative 3) and point W at (negative 4, 1). LIne Z Y is drawn with point Y at (3, 0) and point Z at (0, negative 3). Which statements are true about the lines? Select three options. Line WZ has the same slope as line XY. Line YX has a greater slope than line ZY. Line XW has a lesser slope than line YZ. Line ZW has the same y-intercept as line YZ. Line XY has a lesser y-intercept than line XW.
Answer:
A,C,D
or
Line WZ has the same slope as line XY.
Line XW has a lesser slope than line YZ.
Line ZW has the same y-intercept as line YZ.
Step-by-step explanation:
did it on edge 2020
Answer:
A C D
Step-by-step explanation:
BOYYYYYYYYYYYYYYYYYY
A car was bought a year ago for £2375. It is now worth £1729. What percentage of the cost of the car is the car worth now?
Answer:
72.8%
Step-by-step explanation:
1729 / 2375 = 0.728 -> 72.8%
Answer:
72.8 %
Step-by-step explanation:
£2375 ............ 100%
£1729 ...................x%
x = £1729×100%/£2375 = £172900/£2375 = 72.8 %
al3xis
Which describes the intersection of line M and line N
Answer: A point
Step-by-step explanation:
To find the point of intersection algebraically, solve each equation for y, set the two expressions for y equal to each other, solve for x, and plug the value of x into either of the original equations to find the corresponding y-value. The values of x and y are the x- and y-values of the point of intersection.
GEOMETRY HELP WILL MARK BRAINLIEST
Answer: the answer is 77 degrees
Step-by-step explanation: a triangle's angles all add up to 180, so all you need to do is 180-(59+44)