Answer:
Step-by-step explanation:
If I'm not mistaken, and I very well could be, this is a calculus problem(?). In order to find the distance without calculus you'd need a point on the given line to use to find the distance in the distance formula. But you don't have a point on the given line, so we can find the shortest distance between the point (1, 4) and the given line using the derivative of the polynomial formed when using the distance formula.
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] and we have the x and y for x2 (or x1...it doesn't matter which you choose to fill in):
[tex]d=\sqrt{(1-x)^2+(4-y)^2}[/tex]
but what we find is that we have too many unknowns here, namely, the distance, the x coordinate, and the y coordinate. So we can replace the y coordinate with what y is equal to in terms of the linear equation:
[tex]d=\sqrt{(1-x)^2+(4-\frac{1}{3}x-3)^2 }[/tex] and simplify:
[tex]d=\sqrt{(1-x)^2+(7-\frac{1}{3}x)^2 }[/tex]
. No we'll expand each binomial by squaring:
[tex]d=\sqrt{(1-2x+x^2)+(49-\frac{14}{3}x+\frac{1}{9}x^2) }[/tex]
. Combining like terms gives us
[tex]d=\sqrt{\frac{10}{9}x^2-\frac{20}{3}x+50 }[/tex]
The distance between the point (1, 4) and the given line will be at a minimum when the polynomial above is at a minimum. We find the value of x for which the polynomial is at a minimum by finding its derivative, setting the derivative equal to 0, and then solving for x. The derivative of the polynomial is
[tex]\frac{20}{9}x-\frac{20}{3}[/tex]
Setting equal to 0 and getting rid of the denominators gives us
20x - 60 = 0
Solving for x gives us
20x = 60 and x = 3.
That's the value of x that gives us the shortest distance between (1, 4) and the line y = 1/3x - 3. Sub into the distance formula that x value to find the distance:
[tex]d=\sqrt{(\frac{10}{9})(3)^2-(\frac{20}{3})(3)+50 }[/tex]
which simplifies down, finally, to
x ≈ 6.325 units
what is 5.9736/7.349 reduced to simplest form
Answer:
I think that the answer would be, 0.813
Step-by-step explanation:
5.8736
7.349
equals 0.812845
If you round it you get 0.813
The segment shown below could form a triangle. True or False
9514 1404 393
Answer:
B. False
Step-by-step explanation:
In order for segments to form a triangle, the sum of the shorter two must exceed the length of the longest. Here, that is ...
5 + 6 vs 12
11 vs 12
The short segments are not long enough to form a triangle. The assertion is FALSE.
Triangle MNP is similar to triangle QRS. Which sides have the same slope?
Answer:
The corresponding sides have the same slope so the answer is QR and MN, SR and PN and MP and QS. Hope this helps!
Is this right?!! Please answer
Answer:15
Step-by-step explanation:
You have 2L plus 2w = 40 you know that w = 5. multiply 5 by to because you have 2w. your new equation is 2l + 10 = 40. subtract ten from both sides, your new equation is 2l =30. Divide both sides of the equation by two, get L = 15
A rectangular tank 50 cm long, 20 cm wide, and 33 cm high is filled with water to a depth of 12cm. How many more liters of water need to be added to fill the tank?
Answer:
21 litres
Step-by-step explanation:
1 litre = 1000 cubic cm
The rectangular tank is 50 cm long, 20 cm wide, and 33 cm high.
The tank is in the shape of a rectangular prism.
The volume of a rectangular prism is:
V = l * w * h
where l = length
w = width
h = height
Therefor, its volume is:
V = 50 * 20 * 33 = 33000 cubic cm = 33 litres
The tank is filled to a depth of 12 cm.
The volume of water in the tank is:
V = 50 * 20 * 12 = 12000 cubic cm = 12 litres
Therefore, the number of litres left to fill the tank is:
33 - 12 = 21 litres
The liters of water needed to fill the tank is 21 liters.
Determining the volume of the rectangular tankThe first step is to determine the volume of the tank. The tank has the shape of a cuboid. Thus, the formula for the volume of a cuboid would be used to determine the volume of the tank.
Volume of the tank = length x width x height
50 x 20 x 33 = 33,000
Determination of water needed to fill the tank.1 liter = 1000 cm
33,000 / 1000 = 33
The tank is already filled with 12 liters of water.
Water needed = 33 - 12 = 21 liters
To learn more about volume of a cuboid, please check: https://brainly.com/question/46030
use factoring to solve this x^2-4x-12=0
Answer:
x= 6 x= -2
Step-by-step explanation:
x^2-4x-12=0
What 2 numbers multiply to -12 and add to -4
-6*2 = -12
-6+2 = -4
(x-6)(x+2) = 0
Using the zero product property
x-6 =0 x+2 =0
x= 6 x= -2
Find the number of ways a math test can be made with a 20 question test bank and a 15 question test
Answer: we can make 15,504 different math tests
Step-by-step explanation:
Ok, we have a bank with 20 questions (Q1, Q2........ , Q20)
and we want to make a test with 15 of those 20 questions.
As the order of the questions does not matter in the thest ( is the same if the order is Q1, Q2, ...., Q15 than if the order is Q15, Q14, ....., Q1 )
So we only want the number of combinations.
When we have N elements and we want to create groups of K elements, the total number of combinations is:
[tex]C = \frac{N!}{(N - K)!*K!}[/tex]
Here N = 20 and K = 15
[tex]C = \frac{20!}{5!*15!} = \frac{20*19*18*17*16}{5*4*3*2*1} = 15,504[/tex]
So we can make 15,504 different math tests
What are the coordinates of the center and length of the radius of the circle whose equation is x2 + 6x + y2 – 4y = 23?
Step-by-step explanation:
x2+6x+9-9+y2-4y+4-4=23
(x+3)2-9+(y-2)2-4=23
(x+3)2+(y-2)2=36
center:(-3,2)
r:6
a printing machine prints 70 pages in 8 minutes how many pages could it print in one hour
Answer:
525 pages in one hour.
Step-by-step explanation:
1 hour = 60 minutes
70 pages in 8 minutes
[tex]x[/tex] in 60 minutes
8x=4200
525
Answer:
525 pages in 1 hour
Step-by-step explanation:
Use proportions
70 pages --> 8 mins
? pages --> 60 mins
60/8 = 7.5
That means ?/7.5 = 70, then ? = 70*7.5, ? = 525
If it is recommended that you limit your fat intake to less than 30% of your calories, what is the limit if you consume 2,000 calories a day?
Answer:
30% of 2,000 = 600 calories.
Step-by-step explanation:
A candy jar contains flavoured jelly beans. There are 7 orange, 9 cherry, 3 lemon, 15 licorice, and 6 blueberry. Find the probability of choosing and orange or a lemon jelly bean. PLEASE HELP!!!
Answer:
25%
1/4
Step-by-step explanation:
There are 40 beans in total. Only 10 of those are orange and lemon flavored.
What is the value of x?
20
35
60
70
The required value of the x is 20° for the two intersecting lines.
A figure has shown the intersecting line TW and VS. And opposite angles are given x+40 and 3x. The value of the x is to determine in a manner to find the respective angle.
The angle can be defined as the one line inclined over another line.
alternate angles of two intersecting lines is equal.
x +40 = 3x
3x - x = 40
2x = 40
x = 40/2
x = 20°
required angle x and x+40
x = 20
x + 40 = 20+40
= 60°
Thus, the required value of the x is 20°.
Learn more about Angles here:
https://brainly.com/question/13954458
#SPJ6
What is the slope of the line represented by the equation y=-
5x?
0-5
or w/N wind
5
Answer:
the slope would be -5
Step-by-step explanation:
in linear equations, the slope of the line is the coefficient of x
so in this case, it is -5
Here are two similar cones. The area of the base of the small cone is equal to 36 t cm2. The radius and apothem of the large cone are 9 cm and 15 cm respectively. What is the volume of the small cone? *
( IF YOU CAN DO ALL OF THE STEPS THAT WILL BE VERY HELPFUL)
thx
ASAP 7 POINTS + LINK TO A 50 POINT QUESTION
Which of the following will always represent a function?
1: a table of pairs of numbers
2: an equation in the form y = mx + b
3: a list of ordered pairs
4: a list of numbers
Link to 50 point question: https://brainly.com/question/16753532
Answer: 2: an equation in the form y = mx + b
1. An x/y table may have two entries with the same x; not a function in that case.
2. That's a line with a slope; for each x there's a single y, definitely a function
3. Ordered pairs -- like the table, the same x with different ys is possible, which wouldn't be a function.
4. List of numbers -- a list isn't a function, at least not without more context
What is f(a+2)
A.
B.
Or
C.
Answer:
B
Step-by-step explanation:
f(x) = 3(x + 5) + 4/x
To find f(a + 2) , put a + 2 in place of every x
f(a + 2) = 3 (a + 2 + 5) + 4/(a + 2)
f(a + 2) = 3 (a + 7) + 4/(a + 2)
PLEASE HELPPP !!!!!!!!
Answer:
The answer is D
Step-by-step explanation:
These two matrices cannot be added. To be eligible to add two matrices together, they must have the same dimensions. In this case, they have two different dimensions so the answer is D.
Hope this helps! (Please consider giving brainliest)
The base of the pyramid below is a nonregular heptagon with an area of 30.0 square yards. The height of the pyramid is 6.6 yards. Find the volume of the pyramid. Notice the area of the base is GIVEN
Answer:
Volume of the pyramid is 198 yards^3
Step-by-step explanation:
Here, we are asked to calculate the volume of the pyramid given the area of its base and its height.
Mathematically, the volume of the pyramid can be calculated using the formula below;
Volume of pyramid = Area of heptagonal base * height of pyramid
Volume of pyramid = 30 * 6.6 = 198 yards^3
Can someone plz help with this?
Answer:
A = 20 square units ; Type in 20
Step-by-step explanation:
The simplest way to derive the area of this figure, is to first consider what the shape is itself;
[tex]Criteria of Shape - 2 Bases, 1 pair of Parallel Sides, Composed of two triangles, one square -From this we See that - Shape ; Trapezoid ( neither Right nor Isoceles )[/tex]
Knowing that the shape is a Trapezoid, consider the formula ( Average of Bases ) * Height as to solve for it's area;
[tex]Length Of Base 1 - 3 units,\\Length of Base 2 - 7 units,\\Length of Altitude - 4 units,\\[/tex]
Now let us substitute these values, solving for the Area;
[tex]Area Of Trapezoid - ( ( Base 1 + Base 2 ) / 2 ) * Height,\\ ( ( Base 1 + Base 2 ) / 2 ) * Height = ( ( 3 + 7 ) / 2 ) * 4,\\( 10 ) / 2 * 4 = 5 * 4 = 20 square units,\\\\Conclusion ; Area of Trapezoid = 20 square units[/tex]
Solution; A = 20 square units
Answer:
A=20 (square units)
Step-by-step explanation:
B=XW=8-1=7
b=YZ=5-2=3
h=5-1=4
A=(B+b)*h/2
A=(7+3)*4/2=10*2
A=20 square units
15 POINTS AND WILL MARK BRAINLIEST Help?? Pleasee
The experimental probability is calculated based on the results of the experiment; since the name Ted was chosen 26 times out of 123, the experimental probability is [tex]\boxed{\frac{26}{123}}.[/tex]
Typically, the theoretical probability assumes that events are chosen randomly; since the name Ted is one of the 6 in the hat, the theoretical probability is [tex]\boxed{\frac{1}{6}}.[/tex]
If we increased the number of names in the hat, we would expect both the experimental and theoretical probability to decrease, since there are now more names to choose from. Similarly, if we decreased the number of names in the hat, the experimental and theoretical probability would increase.
Tanzila is selling tickets to the MS127 musical. On the first day of ticket sales she sold 2 adults tickets and 10 child tickets for a total of $78. Then she sold $67 on the second day by selling 8 adults tickets and 5 child tickets. What is the price of one adult ticket and one child ticket?
Answer:
One adult ticket is $4 and one child ticket is $7
Step-by-step explanation:
Make a system of equations
2x + 10y = 78
8x + 5y = 67
Solve by elimination, multiply the 2nd equation by -2
2x +10y = 78
-16x -10y = -134
Add the equations
-14x = -56
x = 4
The price of one adult ticket is $4
Plug 4 in as x to find y
2(4) + 10y = 78
8 + 10y = 78
10y = 70
y = 7
The price of one child ticket is $7
Chen buys 4 tickets to a soccer game. The total cost before taxes is $80. Which equation would you use to determine the price, p, of the ticket? A 4p=80 B 80p=4 C 4+p=80 D p/4=80
Answer:
A. 4p=80
Step-by-step explanation:
Total Cost of 4 tickets=$80
Price=p
Quantity=4
Total cost=price×quantity
80=p×4
80=4p
80=4p is the equation that can be used to determine price
From the equation
80=4p
Divide both sides by 4
80/4=4p/4
20=p
Price is $20 per ticket
Answer:
4p = 80
Step-by-step explanation:
Total cost before tax = $80
Number of tickets purchased = 4
Price 'p' of each ticket
p = total price of ticket / number of tickets purchased
p = 80 / 4
Multiplying both sides by 4
4p = 80
Assume that y varies directly with x . Ify = 18when x = 6 , findywhen x = 5 . Write and solve a direct variation equation to find the answer. y =
Answer:
y = 15
Step-by-step explanation:
It's given in this question that y varies directly with x.
That means, y ∝ x
⇒ y = kx (where k is the proportionality constant)
If y = 18 when x = 6,
⇒ 18 = 6k
⇒ k = 3
Therefore, relation between x and y is,
y = 3x
From this relation, if x = 5
y = 3×5
y = 15
Therefore, for x = 15 value of y will be 15.
two similar figures have an area of 25 in^2 and 4 in^2, what is the ratio of the corresponding sides?
Answer:
5/2
Step-by-step explanation:
ratio of sides=(√25)/(√4)=5/2
The hypotenuse of right triangle ABC is represented by segment AB, as shown on the graph.
On a coordinate plane, line A B has points (negative 3, negative 4) and (5, 3).
At which point could point C be located?
(–3, 3)
(–3, 2)
(5, –5)
(5, –3)
Answer:
(-3,3)
Step-by-step explanation:
just took the test on edg.
Answer:(–3, 3)
Step-by-step explanation:
simplify: -2 1/3 - (-10 1/6)
Answer: 47/6
Step-by-step explanation:
-2 1/3 - (-10 1/6)
= -7/3 + 10 1/6
= -7/3 + 61/6
= 47/6
Step-by-step explanation:
[tex] - \frac{6 + 1}{3} - ( \frac{10 \times 6 + 1}{6} ) \\ - \frac{7}{3} - ( \frac{10 \times 6 + 1}{ 6} \\ - \frac{7}{3} - ( - \frac{61}{6} ) \\ - \frac{7}{ 3} + \frac{61}{6} \\ - \frac{14}{6} + \frac{61}{ 6} = 7.8333333[/tex]
the answer is recurring
measures 19.2cm and 21.6cm to the nearest tenth
Answer:
they are already in tenths place value, so they won't change.
Step-by-step explanation:
Which of the binomials below is a factor of this
trinomial?
x2 - 7x - 44
O A. X-5
O B. X-11
O C. X+ 5
O D. x2 + 11
Answer:
The answer is b
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Given
x² - 7x - 44
Consider the factors of the constant term (- 44) which sum to give the coefficient of the x- term (- 7)
The factors are - 11 and + 4 , since
- 11 × 4 = - 44 and - 11 + 4 = - 7 , thus
x² - 7x - 44 = (x - 11)(x + 4) ← in factored form
with (x - 11) as a factor → B
A farmer picked 600 portugals and oranges in total to be sold to the market. There are 3 times as many oranges as there are portugals. How many portugals are picked by the farmer?
Answer:
450 portugals
Step-by-step explanation:
in this question, we are tasked with calculating the number of portugals which are picked by the farmer
Firstly, let the number of portugals picked be p and the number of oranges picked be r.
Thus;
p + r = 600 ••••••••••(i)
Secondly there are 3 times as many oranges as there are portugals;
That would be;
3 * r = p
3r = p. •••••••••(ii)
substitute ii into i
3r + r = 600
4r = 600
r = 600/4
r = 150
P = 3r
p = 3 * 150 = 450
Frank works in the supply room of a law firm. At the beginning of the month, he had 21 boxes of pens with 13 pens in each box. At the end of the month, there were 45 pens left. How many pens did he give out over the month?