Answer:
Step-by-step explanation:
[tex]5 ^{2x} = 3(2^{x} )[/tex]
[tex]x=\frac{\ln \left(3\right)}{2\ln \left(5\right)-\ln \left(2\right)}\quad \mathrm{ }:\quad x=0.43496 \right)[/tex]
(2x+y)^2- (y-2x)^2
pleaseee help me
The midpoint of the line segment connecting the points (0,0) and (5, -6) is:
(5, -6)
(2.5,-3)
(25, 36)
(0,0)
Answer:
(2.5,-3)
Step-by-step explanation:
midpoint = (x', y')
x' = (x1 + x2)/2
y' = (y1 + y2)/2
x1=0
x2=5
y1=0
y2=-6
solution
(0+5)/2 =2.5---->x'
(0+(-6))/2 = -3--->y'
Solve by completing the square.
[tex]6 {b}^{2} + 12b - 14 = 0[/tex]
Please show all work!
Answer:
b = - 1 ± [tex]\sqrt{\frac{10}{3} }[/tex]
Step-by-step explanation:
Given
6b² + 12b - 14 = 0 ( add 14 to both sides )
6b² + 12b = 14
To complete the square the coefficient of the b² term must be 1
Factor out 6 from the 2 terms on the left side
6(b² + 2b) = 14
To complete the square
add/subtract ( half the coefficient of the b- term)² to b² + 2b
6(b² + 2(1)b + 1 - 1) = 14
6(b + 1)² + 6(- 1) = 14
6(b + 1)² - 6 = 14 ( add 6 to both sides )
6(b + 1)² = 20 ( divide both sides by 6 )
(b + 1)² = [tex]\frac{20}{6}[/tex] = [tex]\frac{10}{3}[/tex] ( take the square root of both sides )
b + 1 = ± [tex]\sqrt{\frac{10}{3} }[/tex] ( subtract 1 from both sides )
b = - 1 ± [tex]\sqrt{\frac{10}{3} }[/tex] ← exact solution
Answer:
x = -1 ± √(10/3) = (-3 ± √30)/3
Step-by-step explanation:
Steps to complete this process:
ax² + bx + c = 0
Divide by the co-efficient of x² i.e. 'a'=> (ax² + bx + c)/a = 0/a
=> x² + (b/a)x + (c/a) = 0
=> x² + 2x(b/2a) + (c/a) = 0
Now it seems somewhat like a square (x² + 2x(b/2a), in order to complete:
Add (b/2a)² to both sides=> x² + 2(b/2a) + (b/2a)² + (c/a) = (b/2a)²
=> (x + b/2a)² + (c/a) = b²/4a²
=> (x + b/2a)² = (b² - 4ac)/4a²
So on & you can derive quadratic formula.
In the given question:
=> 6b² + 12b - 14 = 0
=> (6b² + 12b - 14)/6 = 0/6
=> b² + 2b - 7/3 = 0
=> b² + 2(1)b + 1² - (7/3) = 1²
=> (b + 1)² - (7/3) = 1
=> (b + 1)² = 10/3 or 30/9
=> b + 1 = ±√(30/9)
=> b = -1 ± √(30)/3
=> b = (-3 ± √30)/3
*this is the rationalized form(rational-denominator), exact answer:
=> (b + 1)² - (7/3) = 1
=> (b + 1) = ± √(10/3)
=> b = -1 ± √(10/3)
You can take LCM, and even rationalize it to (-3 ± √30)/3.
Divide. Write your answer in simplest form. −8/9÷(−8/9)=
Answer:
[tex] - \frac{8}{9} \div ( - \frac{8}{9} ) \\ - \frac{8}{9} \times ( - \frac{9}{8} ) \\ = 1[/tex]
I hope I helped you^_^
solve this please
please
Answer:
Step-by-step explanation:
cos(2a) = cos^2(a) - sin^2(a)
cos(2a) = 2cos^(a) - 1
cos(2a) = 11/25
11/25 = 2 cos^(a) - 1 Add 1 to both sides
1 + 11/25 = 2 cos^2
25/25 + 11/25 = 2 cos^2(a)
36/25 = 2 cos^2 (a) Divide by 2
36/50 = cos^2 (a) Take the square root of both sides.
6/5*sqrt(2) = cos(a)
One is given the following:
[tex]cos(2A)=\frac{11}{25}[/tex]One is asked to prove the following:
[tex]cos(A)=\frac{6}{5\sqrt{2}}[/tex]In order to prove the statement above, one will need to use a trigonometric identity. In this case, the following identity is the most relevant in the proof.
[tex]cos(2a)=2cos^2(A)-1[/tex]
One can manipulate this identity to suit the needs of the given problem:
[tex]cos(2a)=2cos^2(A)-1[/tex]
[tex]cos(2a)+1=2cos^2(A)[/tex]
[tex]\frac{cos(2a)+1}{2}=cos^2(A)[/tex]
[tex]\sqrt{\frac{cos(2a)+1}{2}}=cos(A)[/tex]
Now substitute the given information into this identity,
[tex]cos(2A)=\frac{11}{25}[/tex]
[tex]\sqrt{\frac{cos(2a)+1}{2}}=cos(A)[/tex]
Substitute,
[tex]\sqrt{\frac{\frac{11}{25}+1}{2}}=cos(A)[/tex]
Simplify, remember, any number over itself equals (1) and, in order to add two fractions, they must have the same denominator.
[tex]\sqrt{\frac{\frac{11}{25}+1}{2}}=cos(A)[/tex]
[tex]\sqrt{\frac{\frac{11}{25}+\frac{25}{25}}{2}}=cos(A)[/tex]
[tex]\sqrt{\frac{\frac{36}{25}}{2}}=cos(A)[/tex]
[tex]\sqrt{\frac{18}{25}}=cos(A)[/tex]
[tex]\frac{3\sqrt{2}}{5}=cos(A)[/tex]
Manipulate so that it resembles the given information; remember, any number over itself is (1), multiplying an equation by (1) doesn't change it,
[tex]\frac{3\sqrt{2}}{5}=cos(A)[/tex]
[tex]\frac{3\sqrt{2}}{5}*\frac{\sqrt{2}}{\sqrt{2}}=cos(A)[/tex]
[tex]\frac{3\sqrt{2*2}}{5*\sqrt{2}}=cos(A)[/tex]
[tex]\frac{6}{5\sqrt{2}}=cos(A)[/tex]
what is 6x^2+2x ?
please help will mark brainliest
Answer:
38x
Step-by-step explanation:
[tex]6x^{2}+2x\\=\\36x+2x\\=\\38x[/tex]
Chow,...!
Write six different numbers between 365.89 and 365.91
Answer:
365.891, 365.892, 365.893, 365.894, 365.895, 365.896
Step-by-step explanation:
Since we want 6 numbers between 365.89 and 365.91, we can add the ten-thousandths digit and count up from there.
HELP WITH B, C, & D PLS: g(x) = 2x2 + 5x + 1, find: -3g(3)
Find the indicated length
4x + 4 = 14 + 14
4x + 4 = 28
4x = 24
x = 6
Verification : 3×6 - 4 = 14
4×6+4 = 28
.........
A lumberjack can cut a log into 5 pieces in 20 minutes. How long does it take to cut a log of the same size and shape into 7 pieces? If you dont have the correct answer please dont comment
Answer:
28minutes
Step-by-step explanation:
Use this simple trick, it can be used almost everywhere
Time taken pieces
20mins 5
? 7
An x shape is always multiply and straight line is divide
So (7 x 20) ÷5
If u still don't understand, just comment again
Answer:
Step-by-step explanation:
No that is incorrect 28 is not the answer:
1. 4 cuts every 20 mins it would take one cut every 5 mins. You only need one more cut because 6 cuts make 7 pieces. If you draw it.
1/5= 6/30 so 30 mins!
ALGEBRA 1 MATH PLEASE HELP !!
Answer:
|x| - 5
Step-by-step explanation:
Subtracting on the outside translates vertically (down).
Identify whether or not the following features are represented in the above diagram for each feature that is represented write the name(s) denoted it in the diagram
The geometric features of objects are the objects features that are constructed by the aid of elements of geometry
The definition of the geometrical features are as follows
A ray is a line having a single starting point and a straight extension, having no end pointA vertex is the meeting point of two or more linesAn angle is formed by two rays that have a common vertexParallel lines are two lines that are always the same distance from each otherParallel planes are two planes that have equal distance from each otherCoplanar points are points on the same planeCollinear points are points on the same lineSegment addition postulate states that segment AC can include a third point B, when AB + BC = ACPerpendicular lines are two lines that intersect at 90°
Based on the above definitions, the values in the table are as follows;
[tex]\begin{array}{lcl} \mathbf{Feature}&& \mathbf{Denoted \ in \ diagram (s)}\\ \\Ray&&\\\\Vertex&&\\\\Angle&&\\\\Parallel \ lines &&\\\\Parallel \ planes &&\\\\Coplanar \ points&&\mathbf{C, \ F, A, N, B}\\\\Collinear \ points&&\mathbf{A, N, B}\\\\Segment \ addition \ postulate&&\mathbf{AN + NB} = AB\\\\Perpendicular \ lines&&\end{array}\right][/tex]
The features in the diagram are;
Coplanar points: C, F, A, N, B
Collinear points: A, N, B
Segment addition postulate: AN + NB = AB
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DECIDE !!!!!!!!!!!!!
Answer:
55Step-by-step explanation:
Use the identity for the sum of squares of n natural numbers:
Sₙ² = n(n + 1)(2n + 1)/6Since we have the sum, 56980:
n(n + 1)(2n + 1)/6 = 56980(n² + n)(2n + 1) = 56980*62n³ + 3n² + n - 341880 = 0Solve the equation graphically to get a natural solution of n = 55
Jonathon can jog 2 2/7 miles in 2/8 hour. Find his average speed of miles per hour.
Answer:
9.14 miles an hour
Step-by-step explanation:
How many times greater is the value of the 7 in 70,048 than the value of 7 in 17,992?
Answer:
10 times
Step-by-step explanation:
The value of the 7 in 70,048 is 70,000
The value of the 7 in 17,992 is 7,000.
If you divide 70,000 by 7,000, you get 10.
The first 7 is 10 times greater than the 2nd.
I hope this helps!
pls ❤ and mark brainliest pls!
Answer:10 times
Step-by-step explanation:
The value of 7 in 70,048 stands for 7 Ten thousand which is equal to 70,000
Also 7 in 17,992 stands for 7 thousand which is equal to 7,000
So we divide to know how much the lesser value is in the grater vale giving us
70,000/7,000 =10
Therefore, the value of 7 in 70,048 is 10 times than the value of 7 in 17,992
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x²-2xy+y² when x=3 and y=2
Answer:
1
Step-by-step explanation:
First plug in x and y:
(3)^2 - 2(3)(2) + (2)^2
Use order of operations (PEMDAS). First, evaluate the exponents:
9 - 2(3)(2) + 4
Then multiplication:
9 - 12 + 4
Then addition and subtraction, which is done from left to right:
-3 + 4
1
Answer:
[tex] {x}^{2} - 2xy + {y}^{2} \\ x = 3 \\ y = 2 \\ then \: we \: can \: written \: as \\ {3}^{2} - 2 \times 3 \times 2 + {2}^{2} \\ = 9 - 12 + 4 \\ = - 3 + 4 \\ = 1 \\ or \: in \: another \: way \\ this \: is \: the \: expansion \: of \: {(x - y)}^{2} \\ so \: put \: x = 3and \: = 2in {(x - y)}^{2} \\ then \: {(3 - 2)}^{2} \\ = {1}^{2} = 1 \\ thank \: you[/tex]
Jessica spent half of her allowance going to the movies. She washed the family
car and earned 9 dollars. What is her weekly allowance if she ended with
17 dollars ?
Answer:
16 dollars.
Step-by-step explanation:
She ended with 17 dollars after earning 9 dollars, so her amount of money before earning this was 17 - 9 = 8 dollars. This is half of her weekly allowance, so her weekly allowance is double this or 16 dollars.
How would I graph y = 5/3 x -9
PLEASE HELP :( WORTH 20 PIONTS I WILL MARK BRAINLIEST please answer honestly :)
here is the table of values for y = f(x)
x -2 , -1 , 0, 1, 2 , 3, 4 , 5, 6
f(x) 5, 6, 7, 8, 9, 10, 11, 12, 13
mark the statements that are true
A. f (-1) =6
B. f (5) = - 2
C. The domain for (x) is the set (-2, -1, 0, 1 , 2, 3, 4, 5, 6
D. the range for f(x) is all real numbers
[tex]Hello[/tex] [tex]There![/tex]
The answer is...
A. f (-1) = 6.
C. The domain for (x) is the set (-2, -1, 0, 1, 2, 3, 4, 5, 6).
Hopefully, this helps you!!
[tex]JesusLoveMeAlways[/tex]
:)
Help plzzzzzzz…………..
Answer:
-7 + 5 = -2
Step-by-step explanation:
-7 + 5 = -2 is the correct equation as you can see it ended on -2 so in this equation also it's -2
Julie wants to draw square that has an area of 17 in.² what is the exact length of a square with this area
Answer:
√17
Step-by-step explanation:
Since it's a square, the area will simply be the side length squared. Therefore, we can take the square root of 17 to get the exact length. Since 17 is a prime number, it cannot be simplified any further.
Factorise: (Using Algebraic Identities)
64x^3-(4x-3y)^3
Answer:
9y(16x2−12xy+3y2)
Step-by-step explanation:
Factor 64x3−(4x−3y)3
144x2y−108xy2+27y3
=9y(16x2−12xy+3y2)
Answer:
9y(16x2−12xy+3y2)
Which number is NOT plotted correctly on the number line?
For each line, determine whether the slope is positive, negative, zero, or undefined.
Line 1
Line 2
Line 3
Line 4
O Positive
O Negative
Zero
Undefined
Positive
O Negative
O Zero
O Undefined
O Positive
O Negative
O Zero
O Undefined
O Positive
O Negative
O Zero
O Undefined
For line 1 slope is negative, for line 2 slope is undefined, for line 3 slope is positive and for line 4 slope is zero.
What is the Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
The slope of a line is a measure of its steepness and direction. To determine the sign of the slope, we need to look at the direction of the line:
If the line is slanting upwards from left to right, the slope is positive.If the line is slanting downwards from left to right, the slope is negative.If the line is vertical, the slope is undefined (since the denominator of the slope formula, which is the difference in x-coordinates, is zero).If the line is horizontal, the slope is zero (since the numerator of the slope formula, which is the difference in y-coordinates, is zero).Therefore, Lines 1, 2, and 4 have negative slopes, undefinable slopes for lines 2 and 3, and positive slopes for lines 3 and zero for lines 4.
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If two functions, f(x) and g(x), are inverse functions, what must the composition of f(g(x)) and g(f(x)) both equal?
A. 0
B. 1
C. f(x) = g(x)
D. x
==========================================================
Explanation:
The composition of the original function with its inverse will cancel out the operations to yield the input as the output.
Consider the example functions shown below
f(x) = x+5g(x) = x-5The first function adds 5 while the second function does the complete opposite and subtract 5. The two functions are inverses of each other.
We see that,
f(x) = x+5
f(g(x)) = g(x)+5
f(g(x)) = x-5+5
f(g(x)) = x
and you should find that g(f(x)) = x for similar steps.
No matter what the x input is, the output will be identical to the input.
For instance, if we plug in x = 7, then adding 5 to it gets us 12. Then undoing that operation to subtract 5 gets us back to 7 again. This is one example showing why both f(g(x)) and g(f(x)) both equal x, where f and g are inverses of each other.
02:23:02
A rectangle with an area of x2 - 4x - 12 square units is
represented by the model
What side lengths should be used to model the
rectangle?
O(x + 2) and (x-6)
0 (x + 6) and (x - 2)
0 (x + 2) and (x – 10)
o (x + 10) and (x - 2)
XX
-
-
X
Save and Exit
Next
Submit
Answer:
[tex](x + 2) \: \: and \: \: (x-6)[/tex]
Step-by-step explanation:
[tex] {x}^{2} −14−12 \\ = {x}^{2} + 2x - 6x - 12 \\ = x(x + 2) - 6(x + 2) \\ = (x + 2)(x - 6)[/tex]
Hope it is helpful....(x + 2) and (x-6) are the side lengths which should be used to model the rectangle.
What is Area of Rectangle?The area of Rectangle is length times of width.
Given that rectangle with an area of x² - 4x - 12 square units.
We have to find the side lengths which should be used to model the
rectangle.
x² - 4x - 12
x square minus four times of x minus twelve.
x² -6x+2x-12
Now factorize the given expression.
x(x-6)+2(x-6)
(x+2)(x-6)
Hence, (x + 2) and (x-6) are the side lengths which should be used to model the rectangle.
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multiply (x+8) (x-5)
Step-by-step explanation:
(x+8) (x-5)
multiply
x×x=x
8×-5=-40
What is the interest rate when you borrow $600 for 1 year and pay $45.00 interest?
Answer:
Im not certain but I think 7.5% If you get another answer which is different trust them not me if u get one which is the same it should be correct
The interest rate was 7.5% when borrowing $600 for one year and paying $45.00 interest.
What is the simple interest?Simple interest is defined as interest paid on the original principal and calculated with the following formula:
S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100.
We have been given data as:
Principal (P) = $600
Time (T) = 1 year
Simple interest = $45.00
⇒ Simple interest = P × R × T
Substitute the value of P, and T in the above formula, and solve for R
⇒ 45.00 = 600 × R × 1
⇒ 45.00 = 600R
⇒ R = 45.00/600
⇒ R = 0.075
⇒ R = 7.5/100
⇒ R = 7.5%
Therefore, the interest rate was 7.5%.
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A Rohmbus has an area of 40 cm^2 and adjacent angles of 50 degree amd 130 degree. Find the length of a side of rohmbus
Answer:
7.2 cm
Step-by-step explanation:
The adjacent interior angles of a rhombus must be supplementary.
Let ABCD be the rhombus whose area is 40 cm².
Let the diagonals AC and BD intersect at O.
If s is the side, one-half diagonal = s× sin(25) and the other is s× sin(65) = s × cos(25)
Area of a rhombus = ½× (a×b)²× sin(ø)]
side length, a = b
Area of rhombus = ½× s² × sin(25)cos(25)
40 cm² = ½ × s² × sin(25)cos(25)
sin(a)cos(b) = 2[sin(x+y)+sin(x-y)]
sin(a)cos(b) = 2[sin(x+y)+sin(x-y)] Since x = y = 25°
sin(a)cos(b) = 2[sin(x+y)+sin(x-y)] Since x = y = 25°sin(a)cos(b) = 2[sin(x+y)]
》40 cm² = ½ × s² × 2sin(50)
》40 cm² = s² × sin(50)
[tex] {s}^{2} = \frac{40}{ \sin(50) } \\ s = \sqrt{ \frac{40}{ \sin(50) } } [/tex]
s = 7.2260841106 cm
Therefore, the length of the side of a rhombus, s is 7.2 cm
3. Determine the value of x if:
3.1. 75x -15 =5x + 125
3.2. 6(3x - 2) = 7(x + 3) +2
3.3.10/x-3= 8
3.4. x + 7 = 5x - 13
3.5. 20x +4 =4x - 46
Step-by-step explanation:
3.1.
your question
75x-25=5x+125
collect like terms
70x=150
Divide both side by the coefficient of x
70x/70=150/70
70 ti cancel 70 on x side to leave x alone
:. x=150/70 or 2.14
3.2.
6×(3x-2)=7×(x+3)
multiply by the bracket
18x-12=7x+21
collect like terms
18x+7x=21+12
25x=33
divide by the coefficient of x
25x/25=33/25
x=33/25 or 1.32
3.3.
10/x-3=8
cross multiply(know that 8 is /1)
x‐3×8=10×1
8x-24=10
8x=10+24
8x=34
divide both sides by coefficient of x
8x/8=34/8
8x=34/8 or 4.25
3.4.
x+7=5x-13
collect like terms
7+13=5x-x
20=4x
divide both sides by the coefficient of x
20/4=4x/4
5=x
:.x=5
3.5.
20x+4=4x-46
collect like terms
20x-4x=-46-4
16x=-52
divide both sides by the coefficient of x
16x/16=-52/16
:.x=52/16 or 3.25