Answer:
[tex](f+g)(1)=0[/tex]
Step-by-step explanation:
We are given that:
[tex]\displaystyle f=\left\{(-2, -5), (3, -1), (1, -1)\right\}\text{ and } \\ \\ g = \left\{(1, 1), (-1, -2), (-4, 1), (-3, -1)\right\}[/tex]
And we want to find the value of (f + g)(1).
Recall that this is equivalent to:
[tex]=f(1)+g(1)[/tex]
According to the set, f(1) = -1 and g(1) = 1. Hence:
[tex]=(-1)+(1)=0[/tex]
A wooden board 27 ft long is cut into two pieces so that the longer piece is 8
times as long as the shorter piece. Find the lengths of the two pieces.
Answer:
3ft and 24 ft.
Step-by-step explanation:
Let the length of the shorter piece be xThe longer piece is 8 times as long as shorter piece
therefore,
Length of longer piece = 8xTotal length of the wooden board = 27 ft.
27 = longer length + shorter length
27 = x + 8x
27 = 9x
dividing both sided by 9
3 = x
since x was the length of the shorter piece
shorter piece is 3 ft. long
and the longer piece was equal to 8x
longer piece is 24 ft. long
Which of the following is ordered pair for point C?
Answer:
B. (4,2)
Step-by-step explanation:
Answer:
B(4,2)
Step-by-step explanation:
as you can see that if want to find coordinates u should know that the position of x and y is (x,y). So u can that c on the x is lower than 5 so that u can say it is 4 and y is too far away from 5 also u it will be 2.
Find all possible values of α+
β+γ when tanα+tanβ+tanγ = tanαtanβtanγ (-π/2<α<π/2 , -π/2<β<π/2 , -π/2<γ<π/2)
Show your work too. Thank you!
Answer:
[tex]\rm\displaystyle 0,\pm\pi [/tex]
Step-by-step explanation:
please note that to find but α+β+γ in other words the sum of α,β and γ not α,β and γ individually so it's not an equation
===========================
we want to find all possible values of α+β+γ when tanα+tanβ+tanγ = tanαtanβtanγ to do so we can use algebra and trigonometric skills first
cancel tanγ from both sides which yields:
[tex] \rm\displaystyle \tan( \alpha ) + \tan( \beta ) = \tan( \alpha ) \tan( \beta ) \tan( \gamma ) - \tan( \gamma ) [/tex]
factor out tanγ:
[tex]\rm\displaystyle \tan( \alpha ) + \tan( \beta ) = \tan( \gamma ) (\tan( \alpha ) \tan( \beta ) - 1)[/tex]
divide both sides by tanαtanβ-1 and that yields:
[tex]\rm\displaystyle \tan( \gamma ) = \frac{ \tan( \alpha ) + \tan( \beta ) }{ \tan( \alpha ) \tan( \beta ) - 1}[/tex]
multiply both numerator and denominator by-1 which yields:
[tex]\rm\displaystyle \tan( \gamma ) = - \bigg(\frac{ \tan( \alpha ) + \tan( \beta ) }{ 1 - \tan( \alpha ) \tan( \beta ) } \bigg)[/tex]
recall angle sum indentity of tan:
[tex]\rm\displaystyle \tan( \gamma ) = - \tan( \alpha + \beta ) [/tex]
let α+β be t and transform:
[tex]\rm\displaystyle \tan( \gamma ) = - \tan( t) [/tex]
remember that tan(t)=tan(t±kπ) so
[tex]\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta\pm k\pi ) [/tex]
therefore when k is 1 we obtain:
[tex]\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta\pm \pi ) [/tex]
remember Opposite Angle identity of tan function i.e -tan(x)=tan(-x) thus
[tex]\rm\displaystyle \tan( \gamma ) = \tan( -\alpha -\beta\pm \pi ) [/tex]
recall that if we have common trigonometric function in both sides then the angle must equal which yields:
[tex]\rm\displaystyle \gamma = - \alpha - \beta \pm \pi [/tex]
isolate -α-β to left hand side and change its sign:
[tex]\rm\displaystyle \alpha + \beta + \gamma = \boxed{ \pm \pi }[/tex]
when is 0:
[tex]\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta \pm 0 ) [/tex]
likewise by Opposite Angle Identity we obtain:
[tex]\rm\displaystyle \tan( \gamma ) = \tan( -\alpha -\beta\pm 0 ) [/tex]
recall that if we have common trigonometric function in both sides then the angle must equal therefore:
[tex]\rm\displaystyle \gamma = - \alpha - \beta \pm 0 [/tex]
isolate -α-β to left hand side and change its sign:
[tex]\rm\displaystyle \alpha + \beta + \gamma = \boxed{ 0 }[/tex]
and we're done!
Answer:
-π, 0, and π
Step-by-step explanation:
You can solve for tan y :
tan y (tan a + tan B - 1) = tan a + tan y
Assuming tan a + tan B ≠ 1, we obtain
[tex]tan/y/=-\frac{tan/a/+tan/B/}{1-tan/a/tan/B/} =-tan(a+B)[/tex]
which implies that
y = -a - B + kπ
for some integer k. Thus
a + B + y = kπ
With the stated limitations, we can only have k = 0, k = 1 or k = -1. All cases are possible: we get k = 0 for a = B = y = 0; we get k = 1 when a, B, y are the angles of an acute triangle; and k = - 1 by taking the negatives of the previous cases.
It remains to analyze the case when "tan "a" tan B = 1, which is the same as saying that tan B = cot a = tan(π/2 - a), so
[tex]B=\frac{\pi }{2} - a + k\pi[/tex]
but with the given limitation we must have k = 0, because 0 < π/2 - a < π.
On the other hand we also need "tan "a" + tan B = 0, so B = - a + kπ, but again
k = 0, so we obtain
[tex]\frac{\pi }{2} - a=-a[/tex]
a contradiction.
If z varies jointly as x and y and inversely as w^2?, and
z = 72 when x = 80, y = 30 and
w=5, then find z when x = 20, y = 60 and w=9.
Answer:
Step-by-step explanation:
z = (k*x*y) / w²
Where,
k = constant of proportionality
z = 72 when x = 80, y = 30 and w = 5
z = (k*x*y) / w²
72 = (k * 80 * 30) / 5²
72 = 2400k / 25
Cross product
72 * 25 = 2400k
1800 = 2,400k
k = 2,400/1800
k = 24/18
= 4/3
k = 1 1/3
k = 1.33
find z when x = 20, y = 60 and w=9
z = (k*x*y) / w²
z = (1.33 * 20 * 60) / 9²
z = (1596) / 81
Cross product
81z = 1596
z = 1596/81
z = 19.703703703703
Approximately,
z = 19.7
What is 8 x 3 + 10 - 13 x 2? Show your work.
Will give first answer brainliest
Hello!
8 × 3 + 10 - 13 × 2 =
= 24 + 10 - 13 × 2 =
= 24 + 10 - 26 =
= 34 - 26 =
= 8
Good luck! :)
Answer:
8
Step-by-step explanation:
According to bdmas rule
First multiply 8 and 3 or 13 and 2
Then, there will be 24 + 10 - 26
Then add 24 + 10, there will be 34
and again minus by 26
Then finally answer will be 8
P÷✓2=✓t/r+q
express t in the terms of p and q
Given:
Consider the given equation is:
[tex]p\div \sqrt{2}=\sqrt{\dfrac{t}{r+q}}[/tex]
To find:
The value of t in terms of p, q and r.
Solution:
We have,
[tex]p\div \sqrt{2}=\sqrt{\dfrac{t}{r+q}}[/tex]
It can be written as:
[tex]\dfrac{p}{\sqrt{2}}=\sqrt{\dfrac{t}{r+q}}[/tex]
Taking square on both sides, we get
[tex]\dfrac{p^2}{2}=\dfrac{t}{r+q}[/tex]
Multiply both sides by (r+q).
[tex]\dfrac{p^2(r+q)}{2}=t[/tex]
Therefore, the required solution is [tex]t=\dfrac{p^2(r+q)}{2}[/tex].
Graph: Y - 3 = 1/2 (x+2)
Answer:
see graph
Step-by-step explanation:
Personally I put into slope intercept form before graphing
y - 3 = 1/2 (x+2)
y -3 = 1/2x + 1
y = 1/2x + 4
4 is y-intercept
1/2 is slope. [tex]\frac{Rise= 1}{Run= 2}[/tex]
HELP! how do I find the degrees for this problem
Answer:
90°
Step-by-step explanation:
m∠x+m∠y+m∠z=180°
m∠x+m∠y+90=180
m∠x+m∠y=180-90=90°
Maya collected data about the number of ice cubes and milliliters of juice in several glasses of juice and organized the data into this table.
Ice Cubes 4 2 3 5 5 3 1
Juice (milliliters) 177 234 202 140 155 210 265
She used a graphing tool to display the data in a scatter plot, with x representing the number of ice cubes and y representing the milliliters of juice. Then she used the graphing tool to find the equation of the line of best fit:
y = -29.202x + 293.5.
Based on the line of best fit, approximately how many milliliters of juice will be in a glass with 7 ice cubes?
A.
10
B.
89
C.
118
D.
208
Answer:
Maya collected data about the number of ice cubes and milliliters of juice in several glasses of juice and organized the data into this table.
Ice Cubes 4 2 3 5 5 3 1
Juice (milliliters) 177 234 202 140 155 210 265
She used a graphing tool to display the data in a scatter plot, with x representing the number of ice cubes and y representing the milliliters of juice. Then she used the graphing tool to find the equation of the line of best fit:
y = -29.202x + 293.5.
Based on the line of best fit, approximately how many milliliters of juice will be in a glass with 7 ice
Step-by-step explanation:
Based on the line of best fit, approximately how many milliliters of juice will be in a glass with 7 ice.
Maya collected data about the number of ice cubes and milliliters of juice in several glasses of juice and organized the data into this table.
Ice Cubes 4 2 3 5 5 3 1
Juice (milliliters) 177 234 202 140 155 210 265
She used a graphing tool to display the data in a scatter plot, with x representing the number of ice cubes and y representing the milliliters of juice. Then she used the graphing tool to find the equation of the line of best fit:
y = -29.202x + 293.5.
What is the line of best fit?
A line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points. Statisticians typically use the least-squares method to arrive at the geometric equation for the line, either through manual calculations or regression analysis software.
Based on the line of best fit, approximately how many milliliters of juice will be in a glass with 7 ice.
To learn more about the data visit:
https://brainly.com/question/19243813
#SPJ2
When Zero added to any integer, what is the result?
Answer:
answer will be the integer only which was added to zero
What is the solution to the equation One-fourth x + 2 = negative StartFraction 5 Over 8 EndFraction x minus 5?
x = negative 8
x = negative 7
pls hurry
x = 7
x = 8
Answer:
c = 24
Step-by-step explanation:
please help me for 5 points
Answer:
275 adults
130 children
Step-by-step explanation:
Answer:
275 adults, 130 children
Step-by-step explanation:
HELP ME PLEASEEEEEE. !!!
Answer:
107,100
Step-by-step explanation:
[tex]h(t) = 9 {t}^{2} + 900t \\ \\ plug \: t = 70 \\ \\ h(70) = 9 {(70)}^{2} + 900(70) \\ = 9 \times 4900 + 63000 \\ = 44100 + 63000 \\ = 107,100 \: cm[/tex]
Two friends enter a contest. Kelsey scored 200 more points than Jake. Together,
they collected a total of 1250 points. How many points did they each score?
Subtract the amount Kelsey got more than Jake from the total:
1250 - 200 = 1050
Divide by 2:
1050/2 = 525
Jake got 525
Kelsey got 525 + 200 = 725
The diagram shows a cylinder of diameter 6 cm and height 20 cm what is the volume in cm3
Answer:
565.2cm³
Step-by-step explanation:
the radius= 6/2= 3 cm
the height= 20cm
the volume= 3.14× 3²×20
= 3.14×180= 565.2 cm³
Check the picture below.
Someone please help me with this math problem?
Answer:
(C) 0.3(10 + 4h) = 0.25(6h)
Step-by-step explanation:
Here's what we know about Fernando's fees:
$10 is the initial fee
$4 is the hourly fee (h)
Saves 30% (also written as 0.3) of the total cost (includes initial and hourly fee)
Here's what we know about Brenna's fees:
No initial fee
$6 is the hourly fee (h)
Saves 25% (also written as 0.25) of the total cost (just the hourly fee because she doesn't have an initial fee)
We want to find which hour Fernando and Brenna will have saved the same amount of money.
To do this, let's first set up an equation for Fernando and Brenna separately:
Fernando's equation:
0.3(10 + 4h) = how much money he saves from the total cost
Brenna's equation:
0.25(6h) = how much money she saves from the total cost
Now we set them equal to each other:
0.3(10 + 4h) = 0.25(6h)
There's your answer!
Hope it helps (●'◡'●)
Instructions: Problem 2 ! Find the missing angle in the image below. Do not include spaces in your answers
Step-by-step explanation:
since angles in a triangle add up to 180
<vuw=180-(71+23)
=86°
since angles in a straight line add up to 180
<vuf=180-86
=94
280L of water consumed my 7 people. water consumed by 50 people =___L
Step-by-step explanation:
7 people = 280 liters
1 p = 40 liters
50 p = 40 x 50
50 p = 2000 liters
hope it helps.
Also, I think that Brainly is an awesome app, but there's an app which is doing great work for me in maths, named Gauthmath. I will suggest it. Video concepts and answers from real tutors.
f(x) = 2x^2 Find f (-6)
Answer:
[tex]72[/tex]
Step-by-step explanation:
[tex]f(x)=2x^2[/tex]
replace x with -6
[tex]f(-6)=2(-6)^2[/tex]
exponent
[tex]f(-6)=2(36)[/tex]
multiply
[tex]f(-6)=72[/tex]
Consider the equation: x^2 - 4x + 4 = 2x
Rewrite the equation by completing the square:
Your equation should look like (x+a)^2 = b or (x-c)^2 = d
______
What are the solutions to the equation? (1 right answer!)
Answer:
(x+3)^2=5
Step-by-step explanation:
x^2-4x+4=2x
x^2-6x+4=0
x^2-6x+9-5=0
(x-3)^2-5=0
(x-3)^2=5
Please hurry I will mark you brainliest
Answer:
D. -1/7
Step-by-step explanation:
Substitute and solve
Answer:
[tex]-\frac{1}{7}[/tex]
Step-by-step explanation:
When given the following expression,
[tex]\frac{a+c}{a^2-c^2}[/tex]
With the information that the values (a = -2) and (c = 5), one is asked to evaluate the expression. One's first instinct is probably to substitute the values into the expression and solve, however, a faster approach is to simplify the expression. The denominator is the difference of squares, thus one can rewrite it as the product of two linear expressions. Then one can simplify it by canceling out like terms in the denominator and the numerator. Finally, one can then substitute the values of the (a) and (c) into the simplified expression and solve.
[tex]\frac{a+c}{a^2-c^2}[/tex]
[tex]=\frac{a+c}{(a+c)(a-c)}[/tex]
Cross out like terms in the numerator and denominator,
[tex]=\frac{a+c}{(a+c)(a-c)}[/tex]
[tex]=\frac{1}{a-c}[/tex]
Now substitute the values of (a) and (c) into the expression and simplify to evaluate,
[tex]=\frac{1}{a-c}[/tex]
[tex]=\frac{1}{(-2)-(5)}\\\\=\frac{1}{-2-5}\\\\=-\frac{1}{7}[/tex]
to move a function, you need to___it.
Answer:
shift
Step-by-step explanation:
shift
Need help ASAP !!!!!!
answer:
to test whether agraph is linear
Which set of ordered pairs does not represent a function? \{(5, -9), (6, -6), (-3, 8), (9, -6)\}{(5,−9),(6,−6),(−3,8),(9,−6)} \{(-6, -4), (4, -8), (-6, 9), (1, -3)\}{(−6,−4),(4,−8),(−6,9),(1,−3)} \{(1, -1), (-5, 7), (4, -9), (-9, 7)\}{(1,−1),(−5,7),(4,−9),(−9,7)} \{(8, -9), (-3, -6), (-4, 4), (1, -5)\}{(8,−9),(−3,−6),(−4,4),(1,−5)}
Answer:
[tex]\{(-6, -4), (4, -8), (-6, 9), (1, -3)\}[/tex]
Step-by-step explanation:
Given
[tex]\{(5, -9), (6, -6), (-3, 8), (9, -6)\}[/tex]
[tex]\{(-6, -4), (4, -8), (-6, 9), (1, -3)\}[/tex]
[tex]\{(1, -1), (-5, 7), (4, -9), (-9, 7)\}[/tex]
[tex]\{(8, -9), (-3, -6), (-4, 4), (1, -5)\}[/tex]
Required
Which is not a function
An ordered pair is represented as:
[tex]\{(x_1,y_1),(x_2,y_2),(x_3,y_3),..........,(x_n,y_n)\}[/tex]
However, for the ordered pair to be a function; all the x values must be unique (i.e. not repeated)
From options (a) to (d), option (b) has -6 repeated twice. Hence, it is not a function.
help me pls beestar is not fun
Answer:
C. 3/9
Step-by-step explanation:
First, you need to understand what the tree diagram means.
You spin a three-color spinner once. You can get one of three results:
green, blue, or yellow. This is shown in the figure under "1st spin."
Now you spin the spinner a second time. This second spin can also have three outcomes, green, blue, or yellow. For each of the three outcomes of the first spin, you can have 3 different outcomes of the second spin. That is shown under the "2nd spin."
That means there are 9 possible outcomes (numbered from 1 to 9 below):
1. green, green
2. green, blue
3. green, yellow
4. blue, green
5. blue, blue
6. blue, yellow
7. yellow, green
8. yellow, blue
9. yellow, yellow
Each of the 9 outcomes above shows the outcome of the first spin followed by the outcome of the second spin. As you can see there are 9 different outcomes of the two spins.
Now count the number of outcomes that have the same color for the first and second spin. They are shown in bold below.
1. green, green
2. green, blue
3. green, yellow
4. blue, green
5. blue, blue
6. blue, yellow
7. yellow, green
8. yellow, blue
9. yellow, yellow
3 out of 9 outcomes are the same color twice.
Answer: C. 3/9
5 + 3bc =
9a + b =
cd + bc =
Answer:
You can't answer these questons
sorry
Hope This Helps!!!
2. Resolve into factors.
a) 8x3 + y3
Answer:
(2x + y)(4x² - 2xy + y²)
Step-by-step explanation:
8x³ + y³ ← is a sum of cubes and factors in general as
a³ + b³ = (a + b)(a² - ab + b²) , then
8x³ + y³
= (2x)³ + y³
= (2x + y)((2x)² - 2xy + y²) , that is
(2x + y)(4x² - 2xy + y²)
How to find the domain
f equals to 2 f - 20
Answer:
20
Step-by-step explanation:
f = 2f - 20
f - 2f = - 20
- f = - 20
f = 20
using quadratic equation:
help me solve it
[tex]10x - \frac{1}{x } = 3[/tex]
Answer:
[tex]10x - \frac{1}{x} = 3 \\ 10x = 3 + \frac{1}{x} \\ 10x = \frac{3x + 1}{x} \\ 10x \times x = 3x + 1 \\ 10 {x}^{2} = 3x + 1 \\ 10 {x}^{2} - 3x - 1 = 0 \\ 10 {x}^{2} - 5x + 2x - 1 = 0 \\ 5x(2x - 1) + 1(2x - 1) = 0 \\ (5x + 1)(2x - 1) = 0 \\ \\ 5x + 1 = 0 \\ 5x = - 1 \\ x = \frac{ - 1}{5} \\ \\ 2x - 1 = 0 \\ 2x = 1 \\ x = \frac{1}{2} [/tex]
hope this helps you.
Have a nice day!
