Answers
Answer:
[tex] A(\triangle ABC) = 7.2\: units^2 [/tex]
Step-by-step explanation:
C = (0, 7)
Since, point A lies on y-axis, so it's x coordinate will be zero. Line y = 2x + 1 passes through point A.
Therefore, plug x = 0 in y = 2x +1, we find:
y = 2*0 + 1 = 0 + 1 = 1
Hence, coordinates of point A are (0, 1).
Now, by distance formula:
[tex] AC= \sqrt{(0-0)^2 +(7-1)^2} [/tex]
[tex] AC= \sqrt{(0)^2 +(6)^2 }[/tex]
[tex] AC= \sqrt{0 +36 }[/tex]
[tex] AC= \sqrt{36 }[/tex]
[tex] AC= 6\: units[/tex]
Length of perpendicular CB dropped from point C (0, 7) to line y = 2x + 1 or 2x - y + 1 = 0 can be obtained as given below:
[tex] CB =\frac{|2\times 0+(-1)\times 7+1|}{\sqrt {2^2 +(-1)^2} } [/tex]
[tex] CB =\frac{|0-7+1|}{\sqrt {4 +1} } [/tex]
[tex] CB =\frac{|-6|}{\sqrt {5} } [/tex]
[tex] CB =\frac{6}{2.24} [/tex]
[tex] CB =2.68\: units [/tex]
By Pythagoras Theorem:
[tex] AB=\sqrt{AC^2 - CB^2} [/tex]
[tex] AB=\sqrt{6^2 - (2.68)^2} [/tex]
[tex] AB=\sqrt{36 - 7.18} [/tex]
[tex] AB=\sqrt{28.82} [/tex]
[tex] AB=5.36842621\: units [/tex]
[tex] AB\approx 5.37\: units [/tex]
[tex] A(\triangle ABC) = \frac{1}{2} \times AB\times CB[/tex]
[tex] A(\triangle ABC) = \frac{1}{2} \times 5.37\times 2.68[/tex]
[tex] A(\triangle ABC) = \frac{1}{2} \times 14.3916[/tex]
[tex] A(\triangle ABC) = 7.1958[/tex]
[tex] A(\triangle ABC) = 7.2\: units^2 [/tex]
Related Questions
Please Please Please Help me with this math problem
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Answer:
y=10(3/4)^x
10 and 3/4
Step-by-step explanation:
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Answer:
The answer is C
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
if you see where the red line ends on the right side it is at 170 on the protractor
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Answer:
C. 3
Step-by-step explanation:
A^2+B^2=C^2
A^2+4^2=5^2
A^2+16=25
A^2=9
A=3
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I NEED HELP!!
In the figure below, vertices D and F of
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Answers
Answer:
D 108
Step-by-step explanation:
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Which of the following is the midpoint of segment
AB
given that
A(−5,12) and B(3,−8)
Answers
Answer:
(-1, 2)
Step-by-step explanation:
Finding the midpoint of a line, having been given two points, is like finding the average coordinate of those two points.
To find the average x coodinate (and hence the midpoint's x coordinate), you have to sum the x coordinates and divide by 2 - like finding the mean.
To find the y coordinate, sum the y coordinates and divide by two.
[tex](x,y) = (\frac{-5+3}{2} , \frac{12+-8}{2} )[/tex]
Answer:
Step-by-step explanation:
(12 - 8)/2 = 4/2 = 2
(-5 + 3)/2 = -2/2= -1
(-1, 2) midpoint
Calculate the vapor pressure (in torr) of a solution containing 0.2 moles of solute dissolved in 10 moles of water at 25°C. Vapor pressure of pure water at 25°C is 23.8 torr. Enter text here Enter 2021 Acellus Corporation. All Rights Reserved. C
Answers
Answer:
the vapor pressure of a solution at 25°C that contains 76.6 g of glucose (180.2 g/mole) in 250.0 mL of water. The vapor pressure of pure water at 25°C
Step-by-step explanation:
your answer is: 22.9 torr at 25°C
Explanation:
When a non volatile solute is added to a pure solvent, the vapour pressure of the mixture decrease regard to the pure solvent following the equation
Where vapour pressure of the pure solvent (Water) is 23.8torr at 25°C.
Mole fraction of water is the ratio between moles of water and total moles in solution. The solution has a mole fraction of water of:
Replacing in Raoult's law:
Vapor pressure of the solution is 22.9 torr at 25°C
hope this helps!
Christina is having a Super Bowl party with 7 of her celebrity friends. Kobe lives 32 miles from Christina. Will Smith has to drive 32 miles to get to Christina’s. Kim Kardashian will drive 15 miles to get there. Wiz Khalifa is going to ride his bike 2 miles to get there. Andre 3000 is going to run 3 miles to get to Christina’s, and Lebron lives 32 miles from Christina’s house as well. Cardi B lives 45 miles from Christina. What is the median, mode, and mean of distance that they can travel? Complete the table below.
Answers
Answer:
Median: 32
Mode: 32
Mean of Distance: 22.60
Step-by-step explanation:
2, 3, 12, 32, 32, 32, 45
kobe 32 miles away
will smith 32 miles away
kim 12 miles away
wiz 2 miles away
andre 3 miles
lebron 32 miles
cardi b 45 miles
GURRY FOR BRAINLEIST PLS HURRY
Answers
Answer:
C= 10.6
Step-by-step explanation:
AB^2=AC^2+CB^2
C^2=7^2+8^2
C^2= 113
√113=10.630
1. 36.19 to the nearest tenths
Answers
Answer:
36.2
Step-by-step explanation:
Answer:
36.20
Step-by-step explanation:
it's basiclaly another word for 1 decimal place. 9 is bigger than 5 so it rounds 1 to 2.
Find the surface area of the prism.
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what is (p−5)−(4p−7)?
Answers
Answer:
the answer is − 3 + 2
1. Which of the following descriptive statistics is
LEAST affected by extreme values?
A. Mean
B. Median
C. Standard deviation
D. Range
Answers
Solve 0 = x2 + 6x + 13 by completing the square.
A. x = 5 and x = 1
B. x = 3 + i22−−√ and x = 3 − i22−−√
C. x = −1 and x = 1
D. x = −3 + 2i and x = −3 − 2i
Answers
Answer:
x = -3 - 2i and x = -3 + 2i
Step-by-step explanation:
I was too lazy to complete the square but solved it on WolframAlpha
what is (h - 5)(h - 8)
Answers
multiply h with both numbers on other side
h times h, h times -8
multiply -5 with both numbers on other side
-5 times h, -5 times -8
h^2-8h-5h+40
h^2-13h+40
Answer:
h^2-13h+40
Step-by-step explanation:
(h-5)(h-8)
h^2-5h-8h+40
h^2-13h+40
Find the slope of the line. Write your answer in simplest form.
Answers
What is decimal and percent for 3/1000
Answers
Answer:
.003 .03%
Step-by-step explanation:
3/1000 ———> 0.3%
ill mark brainliest please help
Answers
Answer:
56 cups
Step-by-step explanation:
56 cups=3.5 gallons
What is the equation of a line that passes through the points 0,5 and 4,8 in slope intercept form
Answers
Answer:
y = 3/4 + b
Step-by-step explanation:
To get slope intercept form you need to have the y = then you need to find the slope which is y2 - y1 and x2 - x1, find the answer whether it be a fraction or a whole number. And since you don't know the y-intercept you mark the last integer as b, since you don't the answer. So it comes out to y = 3/4 + b
y = (3/4)x + 5
Using the two coordinates, you can find slope and y-intercept
y-intercept is 5, from the point (0,5)
slope is 3/4, from rise/run, and that 0 to 4 is 4, while 5 to 8 is 3.
Combine slope and y-intercept for slope intercept form
y = (3/4)x + 5
are 3:6 and 6:3 equivalent?
Answers
Answer:
No
Step-by-step explanation:
3:6 is a ratio saying for every 3, there's 6, or just convert them into fractions, like 3:6 is 3/6 and 6:3 is 6/3,
so is 3/6 = 6/3, no so they aren't equivalent
Compare and Contrast: Two equations are listed below. Solve each equation and compare the solutions. Choose the statement that is true
about both solutions. (2 points)
Equation 1 Equation 2
5x - 61 = -41 17x + 131 = 27
оа
Equation 1 has more solutions than equation 2.
Ob
Equation 1 and Equation 2 have the same number of solutions.
ос
Equation 2 has more solutions than Equation 1.
Od
The number of solutions cannot be determined.
Answers
Answer:
equation 2
Step-by-step explanation:
what does 6 × 9 + 6 + 9 equal? :)
Answers
Explanation:
(6x9)+6+9
=54+6+9
=69
Can I get an answer to these? I feel asleep during a zoom class and I didn't hear what he said and now I'm confused.
Answers
I need help with this
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Answer:
its d
Step-by-step explanation:
the slope is -20 because for every 30 seconds the altitude gets smaller by 600 feet. 600/30=20 so its going down 20 feet per second.
Round to the nearest thousand. 8,643
Answers
Answer:9,000
Step-by-step explanation:
The 6 rounds the 8 up to a 9
(Sorry if wrong havent learned in a while)
that’s the answer when the number before the one your doing is a 5 or higher it goes up to the next one if it’s lower it goes to a 0
Find the area 3/4 circle with the radius of 4.
THXXXXX
Answers
Step-by-step explanation:
If you were asking what is the 3/4 the area of circle with radius 4 I can answer this.
The area of a circle with radius 4 is π4 ^2=16π
3/4*16π= 12π, thus your answer.
Find the inverse of the matrix (if it exists). (If the answer does not exist, enter DNE in any cell of the matrix.)
Answers
Answer:
[tex]\begin{pmatrix}-15&-28\\ -8&-15\end{pmatrix}[/tex]
Step-by-step explanation:
[tex]\begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}^{-1}=\frac{1}{\det \begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}}\begin{pmatrix}d\:&\:-b\:\\ -c\:&\:a\:\end{pmatrix}[/tex]
This is the formula we will use. Accordingly:
[tex]=>\frac{1}{\det \begin{pmatrix}-15&28\\ 8&-15\end{pmatrix}}\begin{pmatrix}-15&-28\\ -8&-15\end{pmatrix}[/tex]
det represents the determinant
if the determinant is 0 then only the inverse matrix will not exist. So let's find the determinant.
[tex]\det = \left(-15\right)\left(-15\right)-28\cdot \:8\\ = 1[/tex]
Now we multiply the following matrix by 1/1:
[tex]\frac{1}{1}\begin{pmatrix}-15&-28\\ -8&-15\end{pmatrix} = \begin{pmatrix}-15&-28\\ -8&-15\end{pmatrix}[/tex]
Help me cuz yah gurl gotta test UwU
Answers
Answer:
got u
Step-by-step explanation:
Amelia bought a violin that was on sale for 15% off. If the original price was
$220 what is the sale price? *
O $15
O $33
O $187
O $253
Answers
If 20% of a number is 28 and 25% of the same number is 35, find 45% of that
number.
Answers
Explanation: The sum of the two percentages is 45%. Thus the sum of the 28 and 35 (63) is equal to 45% of the number.
If you needed to check your work, you could work out the number to be 140 and simply multiply by 0.45.