Answer:
Step-by-step explanation:
Here's the game plan. In order to find a point on the x-axis that makes AC = BC, we need to find the midpoint of AB and the slope of AB. From there, we can find the equation of the line that is perpendicular to AB so we can then fit a 0 in for y and solve for x. This final coordinate will be the answer you're looking for. First and foremost, the midpoint of AB:
and
Now for the slope of AB:
and
So if the slope of AB is 1/3, then the slope of a line perpendicular to that line is -3. What we are finding now is the equation of the line perpendicular to AB and going through (0, 3):
and filling in:
y - 3 = -3(x - 0) and
y - 3 = -3x + 0 and
y - 3 = -3x so
y = -3x + 3. Filling in a 0 for y will give us the coordinate we want for the x-intercept (the point where this line goes through the x-axis):
0 = -3x + 3 and
-3 = -3x so
x = 1
The coordinate on the x-axis such that AC = BC is (1, 0)
What should you substitute for y in the bottom equation to solve the system by the substitution method?
A. y=3x+15
B. y =-x-5
C. y=x+5
D. y=-3-15
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
f equals to 2 f - 20
Answer:
20
Step-by-step explanation:
f = 2f - 20
f - 2f = - 20
- f = - 20
f = 20
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
Jesse spends 1/2 of his pocket money on Monday.
On Tuesday, he spends 2/3 of what is left.
On Wednesday, he spends 1/4 of what remains.
What fraction of the pocket money does he have left? Choose the most
reasonable answer
Answer:
The fraction of the pocket money she left is 1/8.
Step-by-step explanation:
Let the total pocket money is p.
Spent on Monday = p/2
Amount left = p - p/2 = p/2
Spent on Tuesday = 2/3 of p/2 = p/3
Amount left = p/2 - p/3 = p/6
Spent on Wednesday = 1/4 of p/6 = p/24
Amount left = p/6 - p/24 = p/8
So, the fraction of the pocket money she left is 1/8.
What conversion ratio was skipped in this multiple-step conversion?
Answer:
B
Step-by-step explanation:
B was missed. You have to convert this from hours into minutes before you can deal with seconds.
You are given the exponential function g(x)=3^x. Which ootion below gives the formula for the new function h created by stretching g by a factor of 3 along the y-axis?
Answer:
h(x) = 3^(x + 1)
Step-by-step explanation:
The exponential function is;
g(x) = 3^(x)
Now, in transformation of exponential functions of say f(x) = b^(x), when the new function g(x) is created by stretching by a factor of say c along the y-axis, we have;
g(x) = c•b^(x)
In this question, we are told it is stretched by a factor of 3 along the y-axis.
Thus, new function h is;
h(x) = 3 × 3^(x)
Using law of indices, we have;
h(x) = 3^(x + 1)
Need help ASAP !!!!!!
answer:
to test whether agraph is linear
Find the values of x and y from the following equal ordered pairs. a) (x,-2) = (4,y) b) (3x, 4) = (6, 2y) c) (2x-1, y + 2) = (-1,2) d) (2x + 4, y + 5) = (3x + 3,6) e) (x + y,y + 3) = (6, 2y) f) (x + y, x - y) - (8,0)
Answer:
a)
x=4, y=-2
b)
x=2, y=2
c)
x=0, y=0
d)
x=1, y=1
e)
x=3, y=3
f)
x=4, y=4
Step-by-step explanation:
a) (x,-2) = (4,y)
x=4
y=-2
b) (3x, 4) = (6, 2y)
3x=6 => x=2
2y=4 => y=2
c) (2x-1, y + 2) = (-1,2)
2x-1 =-1 => x=0
y+2 = 2 => y=0
d) (2x + 4, y + 5) = (3x + 3,6)
2x+4 = 3x+3 => x=1
y+5 = 6 => y=1
e) (x + y,y + 3) = (6, 2y)
x+y = 6 => x+3 = 6 => x=3
y+3 = 2y => y=3
f) (x + y, x - y) - (8,0)
x+y = 8 => 2x=8 => x=4
x-y = 0 => x=y => y=4
Six liters of paint will cover 50 square meters. How many square meters will nine liters cover?
Answer:
75 m²Step-by-step explanation:
Six liters of paint will cover 50 square meters.
6L ⇒ 50m²
then,
1L ⇒ 50/6 m²
9L ⇒ 50 × [tex]\frac{9}{6}[/tex] m²
⇒ 75 m²
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.
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!
can anyone help me here asapp,, I am in this question for nearly an hour
Answer:
See below
Step-by-step explanation:
Let side AB equal x. Since triangle ABC is equilateral, sides AB, BC, and Ac are all the same length, x. In any isosceles triangle(equilateral is a type of isosceles triangle) the median is the same as the altitude and angle bisector. This means we can say that AD is also a median. A median splits a side into two equal sections, so we can say BD = DC = x / 2. We are given that DC = CE, so we can also say CE = DC = x / 2. Now, we can use the pythagorean theorem to find the length of AD. So we get the equation:
AB^2 - BD^2 = AD^2
We have the values of AB and BD, so we can substitute them and solve for AD:
x^2 - (x/2)^2 = AD^2
x^2 - x^2 / 4 = AD^2
AD^2 = 3x^2 / 4
AD = x√3 / 2
DE is equal to the sum of DC and CE because of segment addition postulate, so we can say DE = DC + CE = x / 2 + x/ 2 = x. We can again use the pythagorean theorem to find the length of AE:
AD^2 + DE^2 = AE^2
(x√3 / 2)^2 + x^2 = AE^2
3x^2 / 4 + x^2 = AE^2
AE^2 = 7x^2 / 4
AE = x√7 / 2
Now, we know(from before) that AE squared is 7x^2 / 4. We can say EC squared is x^2 / 4 because EC is x / 2 and x / 2 squared is x^2 / 4. We can also notice that AE squared is 7 times EC squared because 7x^2 / 4 = 7 * x^2 / 4
Therefore, we can come to the conclusion AE^2 = 7 EC^2
There is money to send four of nine city council members to a conference in Honolulu. All want to go, so they decide to choose the members to go to the conference by a random process. How many different combinations of four council members can be selected from the nine who want to go to the conference
Answer:
126
Step-by-step explanation:
There are 9 city council members.
We have to choose 4 of them.
We have to use the combination as :
[tex]$^9C_4$[/tex]
where, 9 is the population size
4 is the sample size.
Therefore, the total number of possible samples without replacement is given as :
[tex]$^9C_4=\frac{9!}{4!(9-4)!}$[/tex]
[tex]$=\frac{9!}{5! \ 4!}$[/tex]
[tex]$=\frac{9 \times 8 \times 7 \times 6}{4 \times 3 \times 2 \times 1}$[/tex]
= 126
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.
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:
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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
When Zero added to any integer, what is the result?
Answer:
answer will be the integer only which was added to zero
Please help I don’t understand
Answer:
8/15
Step-by-step explanation:
The ratio of perpendicular to base is tan B .
Here ,
=> tan B = 8 ft/ 15ft
=> tan B = 8/15
5 + 3bc =
9a + b =
cd + bc =
Answer:
You can't answer these questons
sorry
Hope This Helps!!!
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 (●'◡'●)
The daily listening audience of an AM radio station is five times as large as that of its FM sister station. If 144,000 people listen to these two radio stations, how many listeners does the FM station have?
Answer:
The number of FM listereners are 24000.
Step-by-step explanation:
Let the listeners of FM are p and thus the istereners of AM are 5p.
According to the question,
p + 5 p = 144000
6 p = 144000
p = 24000
The number of FM listereners are 24000.
The table shows information about water used in a household.
The value for April is missing.
The mean monthly water used for the six months is 18 m
Work out the value for April.
Answer:
is there is no value of April
Step-by-step explanation:
so the value of the month April is zero
Solve the inequality.
–13.4 ≥ 6.7 + 4.3 + w
–24.4 ≥ w
24.4 ≥ w
23.4 ≥ w
–23.4 ≥ w
Answer:
-24.4 ≥ w
Step-by-step explanation:
-13.4 ≥ 6.7 + 4.3 + w
-13.4 - 6.7 - 4.3 ≥ w
-24.4 ≥ w
PLEASE HELP ME SOMEONE I NEEDDDDDDD HELP PLEASE QUICK!!!!!!!!
Answer:
2/60 = 1/30 = 3.3%
Step-by-step explanation:
Find the quotient: 63/-9
Answer:
-7
Step-by-step explanation:
63/9 but there is an odd number of negative numbers so negative answer
What is the value of x in the equation 0.7x – 1.4 = –3.5?
1. -7
2. -3
3. 7
4. 3
Answer:
the answer is -3
Step-by-step explanation:
0.7x - 1.4 = -3.5
add 1.4 to both sides of the equation
you're left with 0.7x = -2.1
then divide both sides by 0.7
you're left with your answer of -3
The polygons are similar, but not necessarily drawn to scale. Find the value of x. PLEASE HELPPPP
Answer:
x = 27.5.
Step-by-step explanation:
There are given numbers on each side. If the figures are similar, then they have a set ratio for each value.
So, 55:8 and x:4. If you want to, you can flip it, so that it is 8:55 and 4:x.
With that in mind, it is easy to see what the ratio is. Because 4 is half of 8, x is half of 55. 55 divided by 2 is 27.5.
Therefore, x = 27.5.
someone help me please with this algebra problem
Answer:
D.
Step-by-step explanation:
She cannot buy a negative number of notebooks. She can buy 0 notebooks, or 1 notebook, or 2, or 3, etc. The number of notebooks she buys must be a non-negative integer.
Answer: D.
If a = 5, b = 4, and c = 7, find the value for 3(b + a) = c.
10
15
34
20
Answer:
20
Step-by-step explanation:
3 (b + a) = c
3 (4 + 5) = 7
12 + 15 = 7
27 = 7
27 - 7
20
[tex]\huge\boxed{ \sf{Answer}} [/tex]
Given,
[tex]a = 5 \\ b = 4 \\ c = 7[/tex]
And the equation we need to solve is,
[tex]3(b + a) = c[/tex]
To find the answer, you need to substitute the values of a, b & c in the equation.
[tex]3(b + a) = c \\ 3b + 3a = c \\ ( 3 \times 4) +( 3 \times 5) = 7 \\ 12 + 15 = 7 \\ 12 + 15 - 7 = 0 \\ = 27 - 7 \\ = 20[/tex]
↦ The answer is 20.
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