Find the point on the line 4x+4y+5=0 which is closest to the point (−2,−3).
Answers
The point on the line 4x+4y+5=0 which is closest to the point (−2,−3) will be located on the line perpendicular to the given line and will go through the given point
step 1
the slopes of two perpendicular lines
are
m1*m2=-1
given line
4x+4y+5=0------> 4y=-4x-5----> y=-x-1.25
m1=-1
so
m2=1
step 2
find the equation of the line with m2=1 and point (−2,−3)
y-y1=m*(x-x1)-----> y+3=(1)*(x+2)----> y=x+2-3-----> y=x-1
step 3
The point on the line 4x+4y+5=0 which is closest to the point (−2,−3) is the intersection of the line y=-x-1.25 and the line y=x-1
using a graph tool
see the attached figure
the solution is the point (-0.125,-1.125)
Related Questions
. Convert 5π/3 to degrees
Answers
Convert [tex] \pi [/tex] to 180 to get the following fraction:
[tex] \frac{5 * 180}{3} [/tex]
Multiply 5 and 180 together to get the following fraction:
[tex] \frac{900}{3} [/tex]
Simplify the fraction.
[tex] \frac{900}{3} [/tex] = 300
The answer is 300 degrees.
so 5π / 3 radians = 180 / π * 5 π / 3 = 900 / 3 = 300 degrees Answer
A game involves rolling a fair six-sided die. If the number facing upward on the die is a whole number multiple of three, the player wins an amount equal to the number on the die times $20. If the number is not a multiple of three, the player gets nothing. What is the expected value of a player's winnings on each roll?
Answers
Answer:
$30
Step-by-step explanation:
To find the expected value, first we find the outcomes for the sample space.
Rolling a 6-sided die, we have
1, 2, 3, 4, 5, 6
There are 2 values that are whole number multiples of 3: 3 and 6.
There is a 1/6 chance of rolling a 3 and a 1/6 chance of rolling a 6.
There is a 1/6 chance of rolling a 1, 1/6 chance of rolling a 2, 1/6 chance of rolling a 4, and 1/6 chance of rolling a 5.
Next we multiply the value won or lost by each probability.
If the player rolls a 3, they win 3(20) = 60. Multiplying it by its probability, we have
1/6(60) = 60/6 = 10
If the player rolls a 6, they win 6(20) = 120. Multiplying it by its probability, we have
1/6(120) = 120/6 = 20.
If the player rolls a 1, 2, 4 or 5, they win nothing. 0 times all of these will be 0.
Lastly, we add together these products:
10+20+0+0+0+0 = 30
Michelle will be 72 years old in eighteen years. How old is Michelle now?
Answers
72-18=54
what is 4.6 repeating as a fraction???
please help!! :'(
Answers
Let
x=4.66¯6
Then 10x=46.66¯6
So 10x−x=46.66¯6
4.66¯6.−−−−−−−− subtract
9x=42
Divide both sides by 9
x=429=423
What is the area of a circle with a radius of 13 millimeters?
(Use 3.14 for Pi.)
Answers
The area of a circle with a radius of 13 millimeters is calculated using the formula πr², which equals 530.66 mm².
Explanation:The area of a circle is calculated using the formula πr², where 'r' represents the radius of the circle and 'π' (Pi) is a mathematical constant approximately equal to 3.14. When you have a circle with a radius of 13 millimeters, you would substitute 13 into the formula in place of 'r'.
So, the calculation for this circle's area becomes π*(13)² = 3.14 * 169. When you calculate this, you get 530.66 mm². Therefore, the area of a circle with a radius of 13 millimeters is 530.66 mm².
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A 90% confidence interval for the mean percentage of airline reservations being canceled on the day of the flight is (1.1%, 3.2%). what is the point estimator of the mean percentage of reservations that are canceled on the day of the flight?
Answers
If p is the point estimator;
Then,
Minimum range = p - Error
Maximum range = p + Error
Solving one of the two expressions,
0.011 = p - 0.0105 => p = 0.011+0.0105 = 0.0215 = 2.15%
Answer:
Read more on Brainly.com - https://brainly.com/question/9975138#read more Error = 1/2(Maximum range - Minimum range) = 1/2(3.2-1.1) = % = 0.0105If p is the point estimator; Then, Minimum range = p - Error Maximum range = p + Error Solving one of the two expressions,0.011 = p - 0.0105 => p = 0.011+0.0105 = 0.0215 = 2.15%
Step-by-step explanation:
A mirror frame in the shape of an oval is shown below. The ends of the frame form semicircles:
An oval is formed by a rectangle with semicircles at each end. The length of the rectangle is 62 inches. The width of the rectangle is 27 inches.
Which of the following is the perimeter of the inner edge of the frame?
(π = 3.14)
146.78 inches
208.78 inches
293.56 inches
347.56 inches
Answers
1. You have that:
- An oval is formed by a rectangle with semicircles at each end.
- The length of the rectangle is 62 inches. The width of the rectangle is 27 inches.
2. Then, the perimeter is:
P=((3.14)(diameter)/2)(2)+(Lenght of the rectangle)(2)
P=((3.14)(27 inches)/2)(2)+(62 inches)(2)
P=208.78 in
Answer: P=208.78 in
i took the test on flvs its right
I WILL MARK BRAINLIEST
Answers
You can use the Pythagorean Theorem
[tex]a^{2} + b^{2} = c^{2} [/tex]
c is the hypotenuse which is the side across the right angle
a and b are the other sides
Put in the values you know
[tex] a^{2} + 5^{2} = 12^{2} [/tex]
Square the numbers
[tex]a^{2} + 25 = 144[/tex]
Subtract 25 from both sides
[tex] a^{2} = 119[/tex]
Take the square root of both sides
a = 10.9
The answer is D) 10.9 centimeters
Hope this helps!
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prestonshelton
Expert
1.1K answers
231K people helped
Hello!
You can use the Pythagorean Theorem
c is the hypotenuse which is the side across the right angle
a and b are the other sides
Put in the values you know
Square the numbers
Subtract 25 from both sides
Take the square root of both sides
a = 10.9
The answer is D) 10.9 centimeters
Hope this helps!
What is the length of AB?
Answers
Let the center be O. So OB is the radius = 14.5
We can draw a triangle as shown in the image below. We have a right angled triangle. We know the hypotenuse and the base, we need to find the perpendicular side. This can be done using the Pythagorean theorem.
So, we can write:
[tex](14.5)^{2}=10^{2}+OA^{2} \\ \\ OA^{2}=110.25 \\ \\ OA=10.5 [/tex]
Thus, the measure of OA = 10.5
OB = OA + AB
14.5 = 10.5 + AB
⇒
AB = 4
form a right triangle with the 10 as 1st side and r as the hypotenuse.
get the length of the other side using pythagorean.
c = sqrt(14.5^2 - 10^2) = 10.5
The length from the center to point A = c = 10.5
AB = r - c = 14.5 - 10.5 = 4
length AB = 4
Mr bartley is taking the theater club on a field trip he wrote the the folowing function for the school treasure 52(25+2)
Answers
Answer:
The answer is 1,404
Step-by-step explanation:
To do this operation, you should be aware of the order of operations. PEMDAS is a good way to remember the order of operations:
1. Parenthesis
2. Exponents
3. Multiplication
4. Division
5. Addition
6. Substraction
Therefore, the first thing we have to do is the parenthesis.
(25+2) = 27
And now, we can do the multiplication
52*27 = 1,404.
Using the rate of $8 for every 2 pounds of rice, how much would a 1/2 pound of rice cost
Answers
8/4=2
It would be 2$
1 pound = $8 ÷ 2 = $4
1/2 pound = $4 ÷ 2 = $2
Answer: $2
Simplify the expression 1 + 2a - 3(4+5a) + 6(7-8a)
Answers
Answer:
31 - 61a
Step-by-step explanation:
We distribute, being especially careful with the negative signs:
1 + 2a - 3(4 + 5a) + 6(7 - 8a)
1 + 2a - 3 * 4 - 3 * 5a + 6 * 7 - 6 * 8a
1 + 2a - 12 - 15a + 42 - 48a
31 - 61a
The required simplified expression of the given expression is 31 - 61a.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
As mentioned in the quesiton, to simplify the expression 1 + 2a - 3(4+5a) + 6(7-8a),
⇒ 1 + 2a - 3(4+5a) + 6(7-8a),
⇒ 1 + 2a - 12 - 15a + 42 - 48a
Adding alike terms,
⇒ 31 - 61a
Thus, the required simplified expression of the given expression is 31 - 61a.
Learn more about simplification here:
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what is the value of this expression 3*[(7+8)*2+6] A.64 B.87 C.96 D.108
Answers
thats the answer
[tex]=3*36[/tex]
[tex]=108[/tex]
Hope this helps :)
(evaluating expressions) what is the value of the expression 2½x + 3⅔y if x = 4 and y = 3? * 21
Answers
10 + 11 = 21
ms blankenship had 80 dollars to purchase school supplies for her class.she bought 32 glue sticks and 32 boxes of crayons.each glue stick cost 1.40 and each box of crayons vost 0.59 .how much money did ms blankenship have left after these purchases
Answers
Together 32 box of crayons cost $ 18.88.
$44.80 + $18.88 = $63.68
$80 - $63.68 = $16.32
So Ms. Blankenship had $16.32 left after buying school supplies.
Hope this Helps!!
What formula would I use to find A?
Answers
a ^ 2 = (6.3) ^ 2 + (15.10) ^ 2 - 2 * (6.3) * (15.10) cos (70)
Clearing a we have:
a = root ((6.3) ^ 2 + (15.10) ^ 2 - 2 * (6.3) * (15.10) cos (70))
Answer:
A formula to find A is:
a = root ((6.3) ^ 2 + (15.10) ^ 2 - 2 * (6.3) * (15.10) cos (70))
The volume of a right rectangular prism is 573.3 cm³. The length of the right rectangular prism is 7.35 cm and the height is 16.25 cm. What is the width of the right rectangular prism? Enter your answer in the box.
Answers
Answer:
4.8
Step-by-step explanation:
Which of the following are exterior angles ? Check all that Apply NEED ASAP
Answers
Answer:
∠2 , ∠3 , ∠5 ,∠6 are exterior angles
Step-by-step explanation:
Given : Figure.
To find : Which of the following are exterior angles.
Solution : We have given a figure with angle 1 ,2, 3,4,5,6.
Exterior angle : An angle which lies outside the closed figure.
We can see ∠1 and ∠4 area lies in closed figure.
But all other angle ∠2 , ∠3 , ∠5 ,∠6 are lies outside so, these are the exterior angles.
Therefore, ∠2 , ∠3 , ∠5 ,∠6 are exterior angles
Answer:
5. 6. and 2
Step-by-step explanation:
All exterior ANGLES that are still connected to the triangle. 3 Is not an angle on Triangle 1. It is its own triangle, as well as a point.
Anyone know the answer?
Answers
Reduce the fraction to lowest terms. 38x^2yz^2/ -19 yz^2z^3
Answers
On a recent trip, sarah's car traveled 20 mph faster on the first 110 miles than it did on the remaining 80 miles. the total time for the trip was 4 hr. find the speed of sarah's car on the first part of the trip.
Answers
Speed = (x-20) mph
Time, t = Distance/Speed
On 110 miles, t1 = 110/x hrs
On 80 miles, t2 = 80/(x-20) hrs
Total time = 4 hrs = t1+t2 = 110/x + 80/(x-20)
Solving for x;
4 = [110(x-20) + 80(x)]/x(x-20)
4(x)(x-20) = 110x -2200 + 80x
4x^2 - 80x = 110x - 2200 + 80x
4x^2 -80x -110x - 80x +2200 = 0
4x^2 -270x +2200 = 0
Solving the quadratic equation;
x = [-(-270)+/- Sqrt ((-270)^2 -4(4)(2200)]/2*4 = 33.75+/- 24.27 = 9.48 mph or 58.02 mph
Ignore the value smaller than 20 as this would yield a negative value of second speed which is not practical.
Therefore, speed in the first 110 miles is 58.02 mph
If there is a ratio of 3 to 2, than how many are there in the first number if there is a total of 80?
Answers
Answer:
48
Step-by-step explanation:
The total number of "ratio units" is 3+2 = 5, so each stands for 80/5 = 16 items. Then 3 ratio units stand for 3×16 = 48 items.
3 : 2 = 48 : 32
The first number is 48.
Miguel’s teacher asked him to color 4/8 of his grid. He must use 3 colors: red, blue, and green. There must be more green sections than red sections. how can Miguel color the sections of his grid to follow all the rules.
Answers
2x-14y= -16 solve for x ..
Answers
2x = -16 + 14y
Now divide both sides of the equation by 2.
x = -8 + 7y
Since we cannot simplify this equation any further,, the correct answer will be that x = -8 + 7y.
Let me know if you have any further questions.
:)
2x - 14y = -16
Move all the terms without the variable on the other side of the equation. Add 14y to both sides of the equation.
2x = -16 + 14y
Divide both sides by 2.
x = -8 + 7y is your answer.
The angle of elevation from point A to the top of a cliff is 38 degrees. If point A is 80 feet from the base of the cliff, how high is the cliff?
A.
60.50 ft.
B.
62.50 ft.
C.
63.50 ft.
D.
61.50 ft.
Answers
h = 80 tan 38 = 62.50 ft
Its B
What is the surface area of this square pyramid?
Round your answer to the nearest tenth.
Answers
This pyramid encloses a volume V, so it has five surfaces, namely:
*One square base.
*four triangular surfaces.
1. Surface area of the square base:
All four sides are equal, so:
As = LxL = (8.4yd)(8.4yd) = 70.56[tex]yd^2[/tex]
2. Area of triangular surfaces:
Given that the angle β=60°, we have four equilateral triangles which have three equal sides each, therefore:
At = [tex] 4(\frac{base.height}{2}) [/tex] = [tex]2L.Ap[/tex]
Now we need to calculate the apothem Ap.
Using trigonometry, we can calculate Ap using the sine function:
sinβ = [tex] \frac{opposite}{hypotenuse} [/tex] = [tex] \frac{Ap}{a} [/tex]
Given that the triangles are equilateral, then a = L
∴ Ap = (a)(sinβ) = 8.4sin(60°) = (8.4)([tex] \frac{ \sqrt{3} }{2} [/tex]) = 7.275yd
So:
[tex]At = 2(8.4)(7.275) = 122.22 yd^{2}[/tex]
Therefore, the surface area of the pyramid is:
A = As + At = 70.56 + 122.22 = 192.78 [tex] yd^{2} [/tex]
The answer is 192.8 yd²
A flower vase has 5 white lilies, 4 pink roses, and 6 yellow carnations. one flower is chosen at random and given to a woman. another flower is then chosen at random and given to a different woman. what is the probability that both flowers are pink roses?
Answers
Answer:
Step-by-step explanation:
The probability that the first flower is a pink rose is 4 /15.
The probability that the second flower is a pink rose is 3 /14 .
Therefore, the probability that both flowers are pink roses is
4 /15 · 3 /14 = 0.057
please please please someone help me no one on this site will help me. i so confused. please help.
PLEASE SOMEONE HELP ME!!!!! ILL GIVE BRAINLIEST
1. A model rocket is launched from a roof into a large field. The path of the rocket can be modeled by the equation y = –0.04x2 + 8.3x + 4.3, where x is the horizontal distance, in meters, from the starting point on the roof and y is the height, in meters, of the rocket above the ground. How far horizontally from its starting point will the rocket land?
A. 208.02 m
B. 416.30 m
C. 0.52 m
D. 208.19 m
2. A catapult launches a boulder with an upward velocity of 184 ft/s. The height of the boulder (h) in feet after t seconds is given by the function h= -16t^2 + 184t + 20. How long does it take the boulder to reach its maximum height? What is the boulder's maximum height.
A. Reaches a maximum height of 11.6 feet after 5.75 seconded.
B. Reaches a maximum height of 549 feet after 11.5 seconds.
C. Reaches a maximum height of 549 feet after 5.75 seconds.
D. Reaches a maximum height of 23.2 feet after 11.6 seconds.
3. A ball is thrown into the air with an upward velocity of 32 ft/s. Its height (h) in feet after t seconds is given by the function h= -16t^2 + 32t + 6. How long does it take the ball to reach its maximum height? What is the ball’s maximum height? Round to the nearest hundredth, if necessary.
A. Reaches a maximum height of 22 feet after 1.00 second.
B. Reaches a maximum height of 22 feet after 2.00 seconds.
C. Reaches a maximum height of 44 feet after 2.17 seconds.
D. Reaches a maximum height of 11 feet after 2.17 seconds.
Answers
The rocket will hit ground level when y = 0. The plan is is to set y =0 and solve the quadratic. Be careful how you go about to this. It is an odd way to represent this kind of problem. The question does say that y defines how far off the ground the rocket is at the beginning. Therefore the height of the building does not matter (or shouldn't). All that matters is that y is ground level when y = 0.
a = - 0.04
b = 8.3
c = 4.3
[tex]\text{x = }\dfrac{ -b \pm \sqrt{b^{2} - 4ac } }{2a} [/tex]
[tex]\text{x = }\dfrac{ -8.3 \pm \sqrt{8.3^{2} - 4*(-0.04)*(4.3) } }{2(-0.04)}[/tex]
From here you should be able to calculate the answer. One of them is -0.52 which is not the one you use. Minus heights do not matter in these problems yet. The other root is your answer.
Problem Two
Problem two is the usual way to express what happens to a projectile in the air. It again is going to be solved by the quadratic equation.
There are two ways to do this problem. If you know physics, you can solve it using the projectile formulas. If you don't , then you can use the trick in the previous problem. You can calculate how long it takes to hit the ground (h will then be zero).
This problem is rather nasty for someone who has not taken physics. There is another trick. You have to divide the time you get from the previous step by 2. When you solve the quadratic for h = 0, you get 11.6 seconds. But that is the time it takes to hit the ground. Half time is when the boulder will be at it's highest point. t = 11.6 / 2 = 5.8 (which your answers record as 5.75).
h = 0
a= -16
b = 184
c = 20
[tex]\text{x = }\dfrac{ -b \pm \sqrt{b^{2} - 4ac } }{2a} [/tex]
[tex]\text{x = }\dfrac{ -184 \pm \sqrt{184^{2} - 4*(-16)*(20) } }{2*(-16)} [/tex]
The answer from this equation is t = 11.6
The time you want is t = 5.75. You can calculate the maximum height by putting 5.75 in for t.
Problem 3
Problem 3 is done exactly the same way as problem two. You just have different numbers. When h = 0 the time taken to reach zero = 2.17 seconds. Therefore the time you want to put into the original equation for the maximum height is 1/2 of 2.17 seconds. From there you can find the maximum height.
Note: there is a lot of math in here. I have gotten you past the physics. I have also alluded to the answers. I think you should be able to carry out the rest.
Maria is ordering copy paper for her office. The office is low on white paper and on blue paper. She will pay $3.50 per realm of white paper and $3.75 per realm of blue paper. If the purchase order is for $36.00 and she ordered 10 realms of paper, how many realms of white paper will she receive
Answers
x: the number of reams of white paper purchased
y:the number of reams of blue paper purchased
Then, you have the following system of equations:
x+y=10
3.50x+3.75y=36
When you solve the system shown above, you obtain:
x=6
y=4
The answer is: 6 reams of white paper
1>>> a+b=10
2>>> 3.50a+3.75b=36
a=6
b=4
There will be 6 realms of white paper that Maria will receive
WILL MARK BRAINLIEST! PLEASE HELP
In triangle PQR, mP= 43, PQ=7.5 and PR= 8.4. What is mR to the nearest degree?
A. 64
B. 52
C. 41
D. 60
In triangle ABC mA=43, mB=62 and BC=22 in. What is AB to the nearest tenth of an inch?
A. 28.5
B. 15.6
C. 14.1
D.31.2
thank you.
Answers
we know that
the law of cosines establishes that
c²=a²+b²-2*a*b*cos C
in this problem
c=QR
a=PQ=7.5
b=PR=8.4
C=angle P=43°
c²=a²+b²-2*a*b*cos C----> c²=7.5²+8.4²-2*7.5*8.4*cos 43°
c²=34.66--------> c=5.89
QR=5.9
applying the law of sines
7.5/sin R=5.9/sin 43-----> 7.5*sin 43=5.9*sin R---> sin R=7.5*sin 43/5.9
sin R=0.8669---------> R=arc sin (0.8669)----> R=60.11°----> R=60°
the answer Part 1) is the option
D. 60
Part 2) In triangle ABC mA=43, mB=62 and BC=22 in. What is AB to the nearest tenth of an inch?
we know that
∠C=180-(62+43)-----> ∠C=75°
Applying the law of sines
22/sin 43=AB/sin 75------> AB=22*sin 75/ sin 43-----> AB=31.16 in
AB=31.2 in
the answer Part 2) is
D.31.2