c. 6.8m-7.2+8.7k
[tex](2.4k-7.4)+(6.3k-2.2)+(6.8m+2.4)[/tex] combine like terms
[tex]2.4k+6.3k+6.8m-7.4-2.2+2.4\\9.7k+6.8m-9.6+2.4\\9.7k+6.8m-7.2[/tex]
Please someone help me, youvmust find the value of:
Answer:
1
Step-by-step explanation:
Using the sum to product formulae and the exact values
sin x + sin y = 2sin([tex]\frac{x+y}{2}[/tex] )cos([tex]\frac{x-y}{2}[/tex] )
cos x + cos y = 2cos([tex]\frac{x+y}{2}[/tex] )cos([tex]\frac{x-y}{2}[/tex] )
sin45° = cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] , cos30° = [tex]\frac{\sqrt{3} }{2}[/tex]
Given
[tex]\frac{sin75+sin15}{cos75+cos15}[/tex]
= [tex]\frac{2sin(\frac{75+15}{2})cos(\frac{75-15}{2}) }{2cos(\frac{75+15}{2})cos(\frac{75-15}{2}) }[/tex]
= [tex]\frac{2si45cos30}{2cos45cos30}[/tex]
= (2 × [tex]\frac{1}{\sqrt{2} }[/tex] × [tex]\frac{\sqrt{3} }{2}[/tex] ) ÷ (2 × [tex]\frac{1}{\sqrt{2} }[/tex] × [tex]\frac{\sqrt{3} }{2}[/tex] )
= 1
Answer: 1
Step-by-step explanation:
sin 75 = sin(30 + 45) = sin30 · cos45 + cos30 · sin45
[tex]=\dfrac{1}{2}\cdot \dfrac{\sqrt2}{2}+\dfrac{\sqrt3}{2}\cdot\dfrac{\sqrt2}{2}\qquad =\dfrac{\sqrt2+\sqrt6}{4}[/tex]
sin 15 = sin(45 - 30) = sin45 · cos30 - cos45 · sin30
[tex]=\dfrac{\sqrt2}{2}\cdot \dfrac{\sqrt3}{2}-\dfrac{\sqrt2}{2}\cdot\dfrac{1}{2}\qquad =\dfrac{\sqrt6+\sqrt2}{4}[/tex]
cos 75 = cos(30 + 45) = cos30 · cos45 - sin30 · sin45
[tex]=\dfrac{\sqrt3}{2}\cdot \dfrac{\sqrt2}{2}-\dfrac{1}{2}\cdot\dfrac{\sqrt2}{2}\qquad =\dfrac{\sqrt6-\sqrt2}{4}[/tex]
cos 15 = cos(45 - 30) = cos45 · cos30 + sin45 · sin30
[tex]=\dfrac{\sqrt2}{2}\cdot \dfrac{\sqrt3}{2}+\dfrac{\sqrt2}{2}\cdot\dfrac{1}{2}\qquad =\dfrac{\sqrt6+\sqrt2}{4}[/tex]
[tex]\dfrac{\sin 75+\sin 15}{\cos 75+\cos 15}[/tex]
[tex]=\dfrac{\frac{\sqrt2+\sqrt6}{4}+\frac{\sqrt6-\sqrt2}{4}}{\frac{\sqrt6-\sqrt2}{4}+\frac{\sqrt6+\sqrt2}{4}}\\\\\\=\dfrac{\frac{\sqrt6}{2}}{\frac{\sqrt6}{2}}\\\\\\=1[/tex]
Rationalize the denominator of $\frac{\sqrt{32}}{\sqrt{16}-\sqrt{2}}$. The answer can be written as $\frac{A\sqrt{B}+C}{D}$, where $A$, $B$, $C$, and $D$ are integers, $D$ is positive, and $B$ is not divisible by the square of any prime. Find the minimum possible value of $A+B+C+D$.
Rationalizing the denominator involves exploiting the well-known difference of squares formula,
[tex]a^2-b^2=(a-b)(a+b)[/tex]
We have
[tex](\sqrt{16}-\sqrt2)(\sqrt{16}+\sqrt2)=(\sqrt{16})^2-(\sqrt2)^2=16-2=14[/tex]
so that
[tex]\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{\sqrt{32}(\sqrt{16}+\sqrt2)}{14}[/tex]
Rewrite 16 and 32 as powers of 2, then simplify:
[tex]\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{\sqrt{2^5}(\sqrt{2^4}+\sqrt2)}{14}[/tex]
[tex]\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{2^2\sqrt2(2^2+\sqrt2)}{14}[/tex]
[tex]\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{4\sqrt2(4+\sqrt2)}{14}[/tex]
[tex]\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{16\sqrt2+4(\sqrt2)^2}{14}[/tex]
[tex]\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{16\sqrt2+8}{14}[/tex]
[tex]\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{8\sqrt2+4}7[/tex]
So we have A = 8, B = 2, C = 4, and D = 7, and thus A + B + C + D = 21.
The rationalized form of the given surd is [tex]\frac{8\sqrt{2}+4}{7}[/tex], and the minimum possible value of A + B + C + D = 8 + 2 + 4 + 7 = 21
Rationalizing SurdsFrom the question, we are to rationalize the denominator of the given surd.
We are to write the answer in the form
[tex]\frac{A\sqrt{B}+C}{D}[/tex]
and find the minimum possible value of A + B + C + D
The given surd is
[tex]\frac{\sqrt{32}}{\sqrt{16}-\sqrt{2}}[/tex]
To rationalize the surd, we will multiply the numerator and denominator by the conjugate of the denominator
The conjugate of the denominator is [tex]\sqrt{16}+\sqrt{2}[/tex]
Therefore,
[tex]\frac{\sqrt{32}}{\sqrt{16}-\sqrt{2}} \times \frac{\sqrt{16}+\sqrt{2}}{\sqrt{16}+\sqrt{2}}[/tex]
[tex]= \frac{\sqrt{32}(\sqrt{16}+\sqrt{2})}{(\sqrt{16}-\sqrt{2})(\sqrt{16}+\sqrt{2})}[/tex]
[tex]= \frac{\sqrt{512}+\sqrt{64})}{(\sqrt{16})^{2} -(\sqrt{2})^{2} }[/tex]
[tex]= \frac{16\sqrt{2}+8}{16-2}[/tex]
[tex]= \frac{16\sqrt{2}+8}{14}[/tex]
[tex]= \frac{2(8\sqrt{2}+4)}{2(7)}[/tex]
By comparing with, [tex]\frac{A\sqrt{B}+C}{D}[/tex]
A = 8, B = 2, C = 4, and D = 7
Then, the minimum possible value of A + B + C + D = 8 + 2 + 4 + 7 = 21
Hence, the rationalized form of the given surd is [tex]\frac{8\sqrt{2}+4}{7}[/tex], and the minimum possible value of A + B + C + D = 8 + 2 + 4 + 7 = 21
Learn more on Rationalizing surds here: https://brainly.com/question/9547165
3-12=
please help i do not understand this
Unfortunately, I do not go to Harvard Business School so I am unable to solve this complex equation.
Answer: -9
Step-by-step explanation: you want to take away 12 from 3, which will leave you in the negatives
The Yellow Cab Company charges just $0.25 a mile, but it costs $5 to get in the cab. Express
Cab charges no fee to get in the cab, but $1.50 a mile for the ride.
a) If you are going 7 miles, which cab company should you call?
b)
If you are going 3 miles, which cab company should you call?
c)
For what length of drive is the cost equal?
Answer:
For 7 miles call they Yellow Cab and for 3 miles call Express Cab
In 4 miles it cost $6.00 for both
Step-by-step explanation:
Express Cab= $4.50 for 3 miles, and for 7 miles it cost $10.50
Yellow Cab = $5.75 for 3 miles, and for 7 miles it cost $6.75
add 1.50 to 4.50 and is 6 dollars in 4 miles and add 0.25 to 5.75 and it also makes it 4 miles
find the inverse of the function f(x)=6x^2+3
Answer:
The answer is
[tex]{f}^{ - 1} (x) = \sqrt{ \frac{x - 3}{6} } [/tex]Step-by-step explanation:
f(x) = 6x² + 3
To find the inverse of the function above equate it to y
That's
f(x) = y
So we have
y = 6x² + 3
Next interchange the variables that's x becomes y and y becomes x.
x = 6y² + 3
Next make y the subject
Subtract 3 from both sides
That's
6y² + 3 - 3 = x - 3
6y² = x - 3
Divide both sides by 6
That's
[tex] {y}^{2} = \frac{x - 3}{6} [/tex]Next find the square root of both sides
[tex]y = \sqrt{ \frac{x - 3}{6} } [/tex]We have the final answer as
[tex] {f}^{ - 1} (x) = \sqrt{ \frac{x - 3}{6} } [/tex]Hope this helps you
what is 4 1/2 * 2 1/7 as a mixed number in simplest form?
Answer:
9 9/14
Step-by-step explanation:
[tex]4\frac{1}{2}\times\:2\frac{1}{7}\\\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 4\frac{1}{2}=\frac{9}{2}\\\\\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 2\frac{1}{7}=\frac{15}{7}\\\frac{9}{2}\times\frac{15}{7}\\\\\mathrm{Multiply\:fractions}:\\\quad \frac{a}{b}\times\frac{c}{d}=\frac{a\:\times\:c}{b\:\times\:d}\\\\=\frac{9\times\:15}{2\times\:7}\\\\=\frac{135}{14}\\\\[/tex]
[tex]\mathrm{Convert\:improper\:fractions\:to\:mixed\:numbers}:\quad \frac{135}{14}\\=9\frac{9}{14}[/tex]
HELP PLEASE
Will give brainliest
Answer:
[tex]=7x^2+8x-2[/tex]
Step-by-step explanation:
So, on Monday, Tuesday, and Wednesday, he mowed:
[tex](4x^2+3x-4),(5x-8),(3x^2+10)[/tex]
yards, respectively.
To determine how many yards he mowed in the three days, simply add the three expressions. Thus:
[tex](4x^2+3x-4)+(5x-8)+(3x^2+10)[/tex]
Combine like terms:
[tex]=(4x^2+3x^2)+(3x+5x)+(-4-8+10)[/tex]
Add or subtract:
[tex]=7x^2+8x-2[/tex]
And it cannot be simplified further :)
Give an example of a function with both a removable and a non-removable discontinuity.
Answer:
(x+5) (x=3)
(X+5) (x+1)
Step-by-step explanation:
A removeable discontinuity is always found in the denominator of a rational function and is one that can be reduced away with an identical term in the numerator. It is still, however, a problem because it causes the denominator to equal 0 if filled in with the necessary value of x. In my function above, the terms (x + 5) in the numerator and denominator can cancel each other out, leaving a hole in your graph at -5 since x doesn't exist at -5, but the x + 1 doesn't have anything to cancel out with, so this will present as a vertical asymptote in your graph at x = -1, a nonremoveable discontinuity.
what is the differnece in meaning between f and f(x)
Answer:f(x) indicates applying the function to the value x and can also represent the actual value obtained by applying the function to x
Step-by-step explanation:
Answer:
f(x) means y
Step-by-step explanation:
You use f(x) when it is representing y in a function
Find the difference. 15 5/12 - 11 1/8
Answer:
4 7/24
Step-by-step explanation:
Answer:
103/24 or 4.29 or 4 7/24
Step-by-step explanation:
15 5/12 - 11 1/8
185/12 - 89/8
370/24 - 267/24 = 103/24
or
15 10/24 - 11 3/24 = 4 7/24
Please help me with math.
Answer:
Step-by-step explanation:
1=
option b= 4
2.
option b=60miles per hour
Hope it helps
If segment AB is 4 units, segment AD is 23 units, and segment CD is 12 units, what is the length of segment BC?
23
A
9 units
B.
6 units
C
7 units
D
8 units
Answer:
C . 7 unitsStep-by-step explanation:
The question is lacking appropriate diagram. Find the diagram to the question attached.
From the diagram, it can be seen that AD = AB+BC+CD
Given the following
AD = 23units
AB = 4units
CD = 12units
To get C=BC, we will substitute the given segments into the expression above as shown;
23 = 4+BC+12
23 = BC + 4 + 12
23 = BC+16
Subtract 16 from both sides
23-16 = BC+16-16
7 = BC
Hence the length of segment BC is 7units.
What is "the sum of twice a number and six is the same as three subtracted from the number itself"?
Answer:
x=-1
Step-by-step explanation:
2x+6=3-x
Step 1: Simplify both sides of the equation.
2x+6=3−x
2x+6=3+(−x)
2x+6=−x+3
Step 2: Add x to both sides.
2x+6+x=−x+3+x
3x+6=3
Step 3: Subtract 6 from both sides.
3x+6−6=3−6
3x=−3
Step 4: Divide both sides by 3.
3x/3=−3/3
x=−1
Answer:
x=−1
Max spent $15 on bowling. This included a $5 charge for shoe rental and a $2.50 charge per game. If g represents the number of games, which equation can be solved to find the number of games that Max bowled?
Answer:
Step-by-step explanation:
$2.50g + $5 = $15
$2.50g = 10
g = 4 games
The equation that is used to find the number of games that Max bowled is [tex]5+2.50x=15.[/tex]
Charge for shoe rental [tex]=[/tex] $[tex]5[/tex].
Charge per game [tex]=[/tex] $[tex]2.50[/tex].
Let [tex]g[/tex] represents the number of games.
The total charge is the sum of shoe rental charge and charge per game times the number of games.
Total money spent [tex]=[/tex] $[tex]15[/tex].
[tex]5+2.50x=15[/tex]
This is the equation that is used to find the number of games that Max bowled.
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Apply each transformation described to Figure A. If you get stuck, try using tracing paper. A figure A with a point P, a line l and a point P prime on a triangular grid. A translation which takes LaTeX: PP to LaTeX: P'P ′ A counterclockwise rotation of A, using center LaTeX: PP, of 60 degrees A reflection of A across line LaTeX: \ellℓ HTML EditorKeyboard Shortcuts
Answer:
p
Step-by-step explanation:
find the value. 2⅔×2¹/7
Answer: 40/7, if you need, the mixed fraction is 5 5/7
Step-by-step explanation:
First of all, convert all the mixed fraction into improper fraction.
2 2/3=8/3
2 1/7=15/7
Then do the multiplication.
8/3 × 15/7=120/21=40/7 (You can directly simplify it to 40/7 since you can use 15 divided by 3 to get 5 left in the numerator)
Hope this helps!! :)
Please let me know if you have any question
Answer:
5.71
Step-by-step explanation:
two two by three × two one by seven
=8/3×15/7
=8×5/7 as 15 and three will divide and 15 will change to 5
=40/7
=5.71
The chart shows the cost of tuition at a certain state university. Model the data in the chart with a linear function, using the points (1,9941) and (3,11242). Predict the cost of college tuition in 2007-2008.
What is the linear model for the data?
Y=?
Answer:
The cost in 2007 - 2008 = $15,795.5
The linear model for the data is y = $650.5·x + $9290.5
Step-by-step explanation:
The given data can be presented as follows;
College year, x, Estimated tuition, y
1997-1998, 0, $9412
1998-1999, 1, $9941
1999-2000, 2, $10561
2000-2001, 3, $11242
2001-2002, 4, $11965
2002-2003, 5,
2003-2004, 6,
2004-2005, 7,
2005-2006, 8,
2006-2007, 9,
2007-2008, 10,
With points (1, 9941) and (3, 11242), we have the slope given by the equation;
[tex]m = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
Which gives;
[tex]m = \dfrac{11242 - 9941}{3 - 1}= 650.5[/tex]
Therefore;
y - 11242 = 650.5 × (x - 3)
y= 650.5·x - 650.5 ×3 + 11242
y = 650.5·x + 9290.5
Therefore from the above table at 2007 - 2008, the value of x should be 10, we therefore have;
y = 650.5×10 + 9290.5 = $15,795.5
The cost (estimated tuition) in 2007 - 2008 = $15,795.5
The linear model for the data is y = 650.5·x + 9290.5.
The linear model for the data is y = 650.5x + 9290.5 and The cost of college tuition in 2007-2008 is $15795.5
Linear equationA linear equation is in the form:
y = mx + b
where y, x are variables, m is the rate of change and b is the initial value of y.
Let y represent the cost of tuition of battery after x years.
From the table using the points (1, 9941) and (3, 11242):
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\ \\ y-9941=\frac{11242-9941}{3-1}(x-1)\\ \\ y=650.5x+9290.5[/tex]
The linear model for the data is y = 650.5x + 9290.5
At 2007-2008 (x = 10:
y = 650.5(10) + 9290.5 = 15795.5
The cost of college tuition in 2007-2008 is $15795.5
Find out more on linear equation at: https://brainly.com/question/14323743
Is two to the fourth power equal to 2×4
Answer:
No
Step-by-step explanation:
2 to the fourth power is equal to 16.
On the other hand, 2 times 4 is equal to 8.
So, they are not equivalent because 16 [tex]\neq[/tex] 8
4² is the same as the question 4 x 4 which is 16
perimeter help please quick !
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{x = 4.4}}}}}[/tex]
Step-by-step explanation:
Given,
Length of the rectangle ( l ) = 3x + 5
Breadth of the rectangle ( b ) = 2x - 1
Perimeter of the rectangle ( P ) = 52
Finding the value of x
[tex] \boxed{ \sf{perimeter \: of \: rectangle = 2(l + b)}}[/tex]
⇒[tex] \sf{52 = 2(3x + 5 + 2x - 1)}[/tex]
⇒[tex] \sf{52 = 2(5x + 4)}[/tex]
⇒[tex] \sf{52 = 10x + 8}[/tex]
⇒[tex] \sf{10x + 8 = 52}[/tex]
⇒[tex] \sf{10x = 52 - 8}[/tex]
⇒[tex] \sf{10x = 44}[/tex]
⇒[tex] \sf{ \frac{10x}{10} = \frac{44}{10} }[/tex]
⇒[tex] \sf{x = 4.4 \: }[/tex]
Hope I helped!
Best regards!! :D
PLZ HELP!!!
At the band’s peak of popularity, a signed Black Diamond poster sold for $500. Three years later, the band was almost forgotten, and the poster was worth only $10. Write a function that will allow you to calculate how much the poster is worth after x years. State the meaning of each part of the equation in the context of the problem.
The annual depreciation rate is 72.86%
Answer:
The annual depreciation rate is 72.86%.
Step-by-step explanation:
The information provided are:
At the band’s peak of popularity, a signed Black Diamond poster sold for $500.Three years later, the band was almost forgotten, and the poster was worth only $10.From the above data we know that the band's popularity depreciated.
The initial cost of a signed Black Diamond poster was, a = $500.
After three years the cost of a signed Black Diamond poster was, y = $10.
It can be seen that the value of a signed Black Diamond poster is decreasing exponentially over the years.
The formula for exponential decay or depreciation is:
[tex]y=a(1-r)^{x}[/tex]
Here,
y = final value
a = initial value
r = rate of depreciation
x = time
Compute the annual depreciation rate as follows:
[tex]y=a(1-r)^{x}[/tex]
[tex]10=500\times (1 -r)^{3}[/tex]
[tex](1-r)^{3}=\frac{10}{500}[/tex]
[tex](1-r)=\sqrt[3]{\frac{1}{50}}[/tex]
[tex]1-r=0.2714[/tex]
[tex]r=1-0.2714\\\\r=0.7286[/tex]
Thus, the annual depreciation rate is 72.86%.
Please help me!! I can't do this...
Answer:
focus and belive on your self
Step-by-step explanation:
How can you prove that a conjecture if false?
Answer:
To show that a conjecture is false, you have to find only one example in which the conjecture is not true. So an example could be a drawing, a statement, or a number.
Laura is the fund-raising manager for a local charity. She is ordering caps for an upcoming charity walk. The company that makes the caps charges $6 per cap plus a $25 shipping fee. Laura has a budget of $1,000. What is the greatest number of caps she can buy? A.162 A. 162 B.163 B. 163 C.166 C. 166 D.167 D. 167
Answer:
Option B, 163 caps.
Step-by-step explanation:
The price of caps are = $6 per cap.
Shipping charge = $25
The total budget of the Laura = $1000
Since the $25 is shipping charge so subtract it from the budget = 1000 – 25 = $975
Here $975 will be used to buy the caps at the price of $6 per cap.
Thus, the number of caps = budget after subtracting the shipping fee / per cap price
Total caps = $975 / 6
Total caps = 162.5 or 163 caps.
Do the ratios 20/10 and 1/2 form a proportion?
Answer:
Yes . Divide by 10 for 10/20 to get 1/2.
10/10= 1
20/10= 2
10/20= 1/2
On a coordinate plane, point M is plotted (-3,-1) and point N is plotted (4,5). What is the distance between points M and N? square root of 117 square root of 85 5 square root of 17 85
Answer:
The square root of 85
Step-by-step explanation:
The formula to find out the distance between the points is shown below:
The Distance is
[tex]= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
where,
x_1 = -3
y_1 = -1
x_2 = 4
And, the y_2 = 5
Now place these values to the above formula
So, the distance is
[tex]= \sqrt{(4+3)^2 + (5+1)^2} \\\\= \sqrt{49 + 36} \\\\= \sqrt{85}[/tex]
= 9.22 units
Hence, the distance between points M and N is 9.22 units or the square root of 85
Hence, the second option is correct
14, the difference of 4 times a and b
Plz help ASAP!!!! WILL MARK YOU BRAINLIST IF YOUR ANSWER IS CORRECT!! Question # 7 last question
Answer:
the last one
Step-by-step explanation:
i took the test
If you plug x = 3 into choice A, then you dont have any division by zero errors or square roots of negative values.
Choice B in contrast has x-9 = 3-9 = -6 under the square root, so this leads to an imaginary/complex result. Choice D is similar.
Choice C will have zero in the denominator after plugging in x = 3 since x^2-9 = 3^2-9 = 9-9 = 0.
On Saturday, a local hamburger shop sold a combined total of 404 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Saturday
Answer:134.7
Step-by-step explanation:
Does 21, 10, and 9 be the measures of the sides of a triangle
Answer:
no
Step-by-step explanation:
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
9+10 > 21
19 >21
This is not true so it cannot make a triangle
Find the solutions to the equation below.
Check all that apply.
6x2 + 5x - 4 = 0
A. X=
-IN
B. X=
C. x =
1 D. x = -2
E. x=-5
F. X= 4
Answer:
X=1/2. X=4/3
Step-by-step explanation:
6x2+5X-4=0
6X2+8X-3X-4=0
2x(3x+4) - 1(3x+4)=0
2x-1) (3X-4)
X=1/2. X=4/3
The Solution of Equation is x = -4/3 or x= 2.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
We have the Equation:
6x² + 5x - 4 = 0
Solving the Quadratic equation
6x² + 5x - 4 = 0
6x² -3x + 8x - 4 = 0
3x( x- 2) +4 (x-2)= 0
(3x + 4) (x-2) = 0
3x +4 = 0 or x-2 = 0
x = -4/3 or x= 2
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