Step-by-step explanation:
The two equation will intersect each other at the point which will be the solution of the given two equations , and the given equations are ,
[tex]\implies 2x -y +6=0\\\\\implies 2x + 3y -6=0[/tex]
On subtracting the given equations we have,
[tex]\implies -y - 3y +6 -(-6) = 0 \\\\\implies -4y = -12 \\\\\implies y = -12/-4\\\\\implies y = 3 [/tex]
Put this value in any equation , we have ,
[tex]\implies 2x -3 +6 =0\\\\\implies 2x = -3 \\\\\implies x =\dfrac{-3}{2} \\\\\implies x =-1.5 [/tex]
Hence the lines will Intersect at ,
[tex]\implies\underline{\underline{ Point=(-1.5, 3)}}[/tex]
for the first one x = 1/2 y-3" and y = 2 x + 6 and for the other one is x = − 3 /2 y+ 3 and y= − 2 /3 x + 2
how i did this Step 1: Add -3y to both sides.
Step 2: Add 6 to both sides.
Step 3: Divide both sides by 2.
prime factor of 8 and prime factor of 12
Answer:
2
Step-by-step explanation:
a prime factor is a factor that is a prime number
a prime number is a number that will have a fraction in the quotient if it's divided by any number other than itself
2 is the only prime factor shared between 8 and 12
The number 6 is a solution to which of the following inequalities?
X - 13 > 7
6x < -12
6x > 32
21 + x < 28
Answer
6x<-12
Step-by-step explanation:
Answer:
There would be 2 answers in this case:
C. 6x > 32
and
D. 21 + x < 28
Step-by-step explanation:
A. Incorrect
6-13 = -7, and -7 is NOT greater than 7
B. Incorrect
6(6) = 36, and 36 is NOT less than -12.
C. Correct
6*6 = 36, which is greater than 32.
D. Correct
21+6 = 27, which is less than 28.
Your vacation cabin on the lake has three rooms. The bathroom is 12' X 6', the bedroom is 14' X 18' and the great room is 20' X 30'. The ceiling height is 10'. What is the total volume of your cabin? Group of answer choices 9420 Cubic Feet 9240 Cubic Feet 9240 Square Feet 9420 Square Feet
Answer: [tex]9240\ ft^3[/tex]
Step-by-step explanation:
Given
Dimension of the bathroom is [tex]12'\times 16'[/tex]
Dimension of the bedroom is [tex]14'\times 18[/tex]
Dimension of the great room is [tex]20'\times 30'[/tex]
Height of the ceiling is [tex]h=10'[/tex]
Total area of the cabin
[tex]\Rightarrow A=12\times6+14\times 18+20\times 30\\\Rightarrow A=72+252+600\\\Rightarrow A=924\ ft^2[/tex]
Volume of the cabin is [tex]V=A\times h[/tex]
[tex]\Rightarrow V=924\times 10\\\Rightarrow V=9240\ ft^3[/tex]
PLEASE HELP ASAP!!!!
Use the graph of ƒ to find x if ƒ(x) = 2.
x = –0.5
x = –8
(–∞, –0.5)
x = 0.5
Answer:
[tex]{ \tt{f(x) = 2}} \\ when \: y = 2 \\ { \bf{x = - 0.5}}[/tex]
A bus leaves Riverside for Springfield and averages only 48 mph. Ten minutes later Smith leaves Riverside for Springfield traveling 64 mph in his car. How long before he overtakes the bus?
Answer:
pls give brainliest even if u dont want to. it will make u better person. when u give brainliest it makes u 3 times smarter
Step-by-step explanation:
Smith overtakes the bus at (2/3)×60=40 minutes
What is speed?
A body is said to have speed v if he travels v distance in unit time.
How to solve it?Suppose that Smith overtakes the bus at a time 't'. Then the distance traveled by bus is 48×t m and that by Smith is 64×(t-1/6).
Smith needs t-1/6 hours to reach the same position that the bus is in.
Since Smith leaves ten minutes later hence it takes t-1/6 hours for him to overtake the bus.
Because 10 minutes is equal to 10/60=1/6 hour.
So,
48×t=64×(t-1/6)
⇒t=2/3
Hence, Smith overtakes the bus at (2/3)×60=40 minutes
Learn more about speed and distance here-
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I really need some help with this question also.
A) 2/5
B) 3/5
C) 11/25
D) 14/25
Suppose you had been in charge of designing the study. What sample size would be needed to construct a margin of error of 2% with 95% confidence
Answer:
A sample size of 2401 is needed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
What sample size would be needed to construct a margin of error of 2% with 95% confidence?
This is M for which n = 0.02.
Supposing we have no estimate for the true proportion, we use [tex]\pi = 0.5[/tex].
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.02 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.02\sqrt{n} = 1.96*0.5[/tex]
[tex]\sqrt{n} = \frac{1.96*0.5}{0.02}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*0.5}{0.02})^2[/tex]
[tex]n = 2401[/tex]
A sample size of 2401 is needed.
hi i need help with this
Evaluate 4(3-1)^2
Hey there!
4(3 - 1)^2
3 - 1 = 2
= 4(2^2)
2^2
= 2 * 2
= 4
4(4)
= 16
Answer: 16
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Answer:
4(3-1)^2= 16
Step-by-step explanation:
4(3-1)^2
=4×(2)^2
=4×4
=16 ........
HOPE THIS HELPS YOU....
Help me with this problem
Answer:
Angle A is F Angle A = 57. 52+71=123. 180-123=57
A retailer allows 15% discount on the Marked price of an electric fan. If a customer pays Rs 2244 with 10% VAT,find the Marked Price of the fan
Answer:
2400
Step-by-step explanation:
2244 is the final price. it includes the VAT based on the actual sale price. and that is then actually 15% lower than the originally marked price.
so, let's calculate backwards :
2244 = 100% sale price + 10% VAT = 110%
1% = 2244 / 110 = 20.40
100% (actual sale price) = 20.40×100 = 2040
now, because of the 15% discount, these 2040 are only 85% of the originally marked price.
2040 = 85%
1% = 2040 / 85 = 24.00
100% (the original marked price) = 24×100 = 2400
Find the volume of this cylinder. Use 3 for .
V = 7r2h
14 cm
2
V = T[?]?
28 cm
Hint: Plug in the value of the
radius for r. The radius is shown
directly in the diagram.
Step-by-step explanation:
V = πr²h
V = 3 × 14² × 28
v = 16464cm³
4x2 -28x-32 fully factored
GCF=4
4(4x^2/4+-28x/4+-32f/4)
=4(x^2-7x-8f)
Hello,
[tex]4x^2-28x-32\\\\=4(x^2-7x-8)\\\\=4(x^2-8x+x-8)\\\\=4[x(x-8)+1(x-8)]\\\\=4(x-8)(x+1)\\[/tex]
3x-4y=-24
Identify the x- and y-intercept of the graph of each question
Answer:
x = -8 and y = 6
Step-by-step explanation:
3x - 4y = -24
Solve for y - intercept
3x - 4y = -24
To find y intercept , substitute x = 0
3 × 0 - 4y = -24
Any expression multiplied by 0 equals 0.
0 - 4y = -24
-4y = -24
Divide both sides by -4
-4y / -4 = -24/-4
y = 6
Similarly, Solve for x-intercept
3x - 4y = -24
To find x- intercept , susbtitute y = 0
3x - 4 × 0 = -24
Any expression multiplied by 0 equals 0.
3x - 0 = -24
3x = -24
Divide both sides by 3
3x / 3 = -24 / 3
x = -8
Therefore, y = 6 and x = -8
HELP HELP HELPPPP PLEASEEE
Directions: Determine if segments AB and CD are parallel, perpendicular, or neither.
AB formed by (-2, 13) and (0, 3)
CD formed by (-5, 0) and (10, 3)
Given:
AB formed by (-2,13) and (0,3).
CD formed by (-5,0) and (10,3).
To find:
Whether the segments AB and CD are parallel, perpendicular, or neither.
Solution:
Slope formula:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
AB formed by (-2,13) and (0,3). So, the slope of AB is:
[tex]m_1=\dfrac{3-13}{0-(-2)}[/tex]
[tex]m_1=\dfrac{-10}{2}[/tex]
[tex]m_1=-5[/tex]
CD formed by (-5,0) and (10,3). So, slope of CD is:
[tex]m_2=\dfrac{3-0}{10-(-5)}[/tex]
[tex]m_2=\dfrac{3}{10+5}[/tex]
[tex]m_2=\dfrac{3}{15}[/tex]
[tex]m_2=\dfrac{1}{5}[/tex]
Since [tex]m_1\neq m_2[/tex], therefore the segments AB and CD are not parallel.
[tex]m_1\times m_2=-5\times \dfrac{1}{5}[/tex]
[tex]m_1\times m_2=-1[/tex]
Since [tex]m_1\times m_2=-1[/tex], therefore the segments AB and CD are perpendicular because product of slopes of two perpendicular lines is always -1.
Hence, the segments AB and CD are perpendicular.
Answer:
AB is perpendicular to CD.
Step-by-step explanation:
AB formed by (-2, 13) and (0, 3)
CD formed by (-5, 0) and (10, 3)
Slope of a line passing through two points is
[tex]m= \frac{y''-y'}{x''- x'}[/tex]
The slope of line AB is
[tex]m= \frac{3- 13}{0+2} = -5[/tex]
The slope of line CD is
[tex]m'= \frac{3 -0 }{10+5} = \frac{1}{5}[/tex]
As the product of m and m' is -1 so the lines AB and CD are perpendicular to each other.
$975, and there is 7 percent sales tax on the purchase.
How much is the sales tax?
Answer:
$68.25
Step-by-step explanation:
To get the sales tax, you must notice that the sales tax is 7% of 975.
That is equal to:
975 × 0.07
0.07 is equal to 7%, or [tex]\frac{7}{100}[/tex].
The answer to the equation is 68.25.
How do I write
(28/4) - (x+7) in written form?
Answer: The quotient of 28 and 4 minus the sum of a number and 7
Step-by-step explanation:
What are the coordinates of R?
Answer: y,0
Step-by-step explanation:
Find the Value of x.
Answer:
x = 91
Step-by-step explanation:
Opposite angles of an inscribed quadrilateral are supplementary.
x + 89 = 180
x = 91
number of ways you can wear 10 outfits to school each day in a 5 day week
Answer:
1 day=10outfits
5days=10outfits×5
=50outfits
Step-by-step explanation:
hope this is helpful
Based on the calculation, you can wear the 10 outfits in 50 different ways throughout the week.
How to calculate the number of waysTo calculate the number of ways you can wear 10 outfits to school each day in a 5-day week, you need to consider the total number of outfits across all days. Since there are 10 outfits and 5 days, the total number of outfit combinations can be calculated by multiplying the number of outfits per day by the number of days:
10 outfits/day × 5 days = 50 outfit combinations
Therefore, you can wear the 10 outfits in 50 different ways throughout the week.
Learn more about permutations
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A(3,4) and B(-3,2) are pointd on a coordinate plane. find the coordinate of a points C on the x axis such that AC=BC
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)
Please help, I also need an explanation.
If Q is the midpoint of PR, find the coordinates of R if P(11,-2) and Q(4,3).
Answer:
R = (-3, 8).
Step-by-step explanation:
Recall the midpoint formula:
[tex]\displaystyle M=\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)[/tex]
Where M is the midpoint, (x₁, y₁) is one point and (x₂, y₂) is another.
We are given that Q is the midpoint of PR, where P = (11, -2) and Q = (4, 3) and we want to find the coordinates of R.
Substitute Q for M and let P(11, -2) be (x₁, y₁). Hence:
[tex]\displaystyle (4, 3)=\left(\frac{11+x_2}{2}, \frac{-2+y_2}{2}\right)[/tex]
Split into two separate equations:
[tex]\displaystyle \frac{11+x_2}{2}=4\text{ and } \frac{-2+y_2}{2}=3[/tex]
Solve for each case:
[tex]\displaystyle 11+x_2=8\Rightarrow x_2=-3[/tex]
[tex]\displaystyle -2+y_2=6\Rightarrow y_2=8[/tex]
Therefore, our second point (x₂, y₂) is (-3, 8).
Hence, R = (-3, 8).
Answer:
(15/2),(1/2)
Step-by-step explanation:
(x1 + x2 / 2) , (y1 + y2) / 2)
(11 + 4 / 2) , (-2 + 3 / 2)
(15/2) , (1/2)
What is the length of the dotted line in the diagram below? Leave your answer in simplest radical form. HELP PLEASE
Answer:
11.7…?
Step-by-step explanation:
Small triangle and other triangle are similar based on sas theorem (I think) so find scale factor — 2— then do Pythagorean theorem
hhhhhhhhhheeeeeeeeeeeeeeeeellllllllllllllllllllllppppppppppppp
Answer:
40°
Step-by-step explanation:
As sum of angles of the triangle is 180°
therefore the third angle will be 180 -( 75 + 65)=40°
x=40°= vertically opposite angle
Answer:
x = 40°
Step-by-step explanation:
a + 65 + 75 = 180 {Angle sum property}
a + 140 = 180
a = 180 - 140
a = 40
x = a {Vertically opposite angles}
x = 40°
Christina cycles 2 kilometers during each trip to work. Write an equation that shows the relationship between the number of trips to work x and the total distance cycled y.
Answer:
y=2x
Step-by-step explanation:
Help me to do this question plz plz plz
Answer:
area of parallelogram=base *height
Answer:
area =36cm²
Step-by-step explanation:
area of parallelogram= b×h
9×436cm²hope it helps stay safe healthy and happy..Find the surface area or volume of each rectangular prism. (Show work pls)
Answer:
496 in.²
346 mm²
880 in.²
168 cm³
960 m³
420 yd³
Step-by-step explanation:
SA = 2(wl + hl + hw)
SA = 2 · (8 · 16 + 5 · 16 + 5 · 8)
SA = 496
SA = 2(wl + hl + hw)
SA = 2 · (5 · 13 + 6 · 13 + 6 · 5)
SA = 346
SA = 2(wl + hl + hw)
SA = 2 · (4 · 20 + 15 · 20 + 15 · 4)
SA = 880
V = whl
V = 4 · 7 · 6
V = 168
V = whl
V = 10 · 8 · 12
V = 960
V = whl
V = 14 · 3 · 10
V = 420
Using appropriate properties find 2/3 x (– 3/5) + 1/5 x 4/3 + 2/3 x ( – 3/2)=
Answer:
- [tex]\frac{17}{15}[/tex] -1 [tex]\frac{2}{15}[/tex] , 1.13
Step-by-step explanation:
if f(x)=2x/x-5 find f^-1(x)
Answer:
[tex]f^{-1}[/tex] (x) = [tex]\frac{5x}{x-2}[/tex]
Step-by-step explanation:
let y = f(x) and rearrange making x the subject
y = [tex]\frac{2x}{x-5}[/tex] ( multiply both sides by x - 5 )
y(x - 5) = 2x ← distribute left side
xy - 5y = 2x ( subtract 2x from both sides )
xy - 2x - 5y = 0 ( add 5y to both sides )
xy - 2x = 5y ← factor out x from each term on the left side )
x(y - 2) - 5y ← divide both sides by y - 2
x = [tex]\frac{5y}{y-2}[/tex]
Change y back into terms of x with x = [tex]f^{-1}[/tex] (x) , then
[tex]f^{-1}[/tex] (x) = [tex]\frac{5x}{x-2}[/tex]
Look into the image. I hope it helps❤
#CarryOnLearningCan like someone help me I'm lost-
Answer:
the first graph
Answer:
1st option
Step-by-step explanation:
If the rate of change is constant, then it's always a straight line, so the 1st option, and if you see the graph, you'll see the line is going down at a rate of 1/4, so the slope is 1/4. So the answer to your question will be the 1st option.
Answered by GAUTHMATH
