Answer:
Vertex: (3,5)
Focus: (3,8)
Directrix: y = 2
Step-by-step explanation:
Get y by itself by adding 5 over to the other side. The equation is now y = 1/12(x-3)^2 + 5.
The value inside of the parentheses is -3. Since it's within the parentheses, switch the signs for the x value of the vertex. The "+ 5" represents the y value. Therefore the vertex is (3,5).
The value "a" on the parabola is 1/12. To find the distance from the vertex to the focus/directrix, use the equation a = 1/4p. 1/12 = 1/4p. p = 3. This parabola opens up, so "p" must be added onto the y value of the vertex for the focus. The focus is therefore (3,8).
For the directrix, subtract "p" from the y value of the vertex. The directrix is a horizontal line at y = 2.
3. Find the probability that a point chosen randomly inside the rectangle is in each given shape. Round to
the nearest hundredth.
Answer:
20% probability
Step-by-step explanation:
First, we need to calculate the area of all the figures inside the rectangle.
Area of triangle= 1/2 BH
So, 3x2=(6)
Area of Square= L^2
3x3=(9)
Area of rectangle= LxW
=60.
60+9+6= 75.
75 is the total area.
Now, lets find the added area of only the triangle and square.
9+6= 15
The probability will be 15/75=
Convert into percent form
= 20%
Hope this helps and please mark me brainliest :)
Answer:
20% probability
Step-by-step explanation:
20% probability
20% probability
20% probability
20% probability
PLEASE HELP I WILL GIVE 40 pts
Answer:
option C is the answer
Step-by-step explanation:
I think it will help you
A caterpillar moves at a constant speed of 1/2 inches per second. Let x represent the time travel in seconds and y represent the distant travel in inches. I Really need help with this!
Step-by-step explanation:
Expression = 1/2x = y
Easy algebraic expression
~Done~
what is 34x50^2+89-89 divided by 89
Answer:
(34×(50^2))+89-(89÷89)=8,5088
Step-by-step explanation:
hope this helps if not let me know have a great day
50 points please help
The ceiling of Stacy's living room is a square that is 22 ft long on each side. Stacy knows the diagonal of the ceiling from corner to corner must be longer than 22 ft, but she doesn't know how long it is.
Solve for the length of the diagonal of Stacy's ceiling in two ways:
(a) Using the Pythagorean Theorem.
(b) Using trigonometry.
Round each answer to the nearest whole number and make sure to show all your work. (Hint: the answers should be the same!)
#a
H²=P²+B²P and B are sides of square
H²=22²+22²H²=484+484H²=968H≈22√2ftH≈31ft#b
Apply cosines
cos45=22/H1/√2=22/HH=22√2ft=31ftLet assume "M" is the midpoint of the segment AB. Find AM. AM= x+7 MB=2x A. 7 B. 14 C. 12 D. 9
The length of the line segment AM, which is a part of line segment AB when it is divided into two equal parts by Midpoint M is 14 units.
What is midpoint?For a line segment, mid-point is the middle point of it which divides the line segment into the two equal parts.
Let assume "M" is the midpoint of the segment AB. The value of has to be found out. It is given that,
[tex]AM= x+7 \\MB=2x[/tex]
In this line segment AB, M is midpoint. Thus, it divide the line segment into two equal parts of AM and MB. Thus,
[tex]x+7=2x\\2x-x=7\\x=7[/tex]
Put the value of x in AM,
[tex]AM=x+7\\AM=7+7\\AM=14\rm\; units[/tex]
Thus, the length of the line segment AM, which is a part of line segment AB when it is divided into two equal parts by Midpoint M is 14 units.
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Find the determinant of this matrix:
[tex]\left[\begin{array}{ccc}0&1\\1&0\end{array}\right][/tex]
Answer:
-1
Step-by-step explanation:
Formula to the determinant is:
[tex]\left[\begin{array}{ccc}a&b\\c&d\end{array}\right] = ad-bc[/tex]
0(0)–1(1)
0-1
-1
Answer:
-1
Step-by-step explanation:
Formula: ad-bc
0(0) - 1(1)
0-1
-1
Larry owns an automobile dealership. Last week, he received a shipment of 160 automobiles.
He now has 938 automobiles for sale. How many automobiles did Larry have before the
shipment?
Larry had 778 automobiles before he had the shipment.
Given: r(x) = x3 - 7, k(x) = 5 ln (2x) Find: (k ○ r) (x)
The value of (k ○ r) (x) from the given parameters in the task content is; 5 ln(2x³ -14)
What is (k ○ r) (x) from the task content?If follows from the task content that;
r(x) = x³ - 7 and k(x) = 5 ln (2x)It therefore follows that;
(k ○ r) (x) = k(r(x)) = 5 ln (2(x³-7)).
On this note, the expression which represents (k ○ r) (x) is; 5 ln(2x³ -14).
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Which of the following scenarios MUST represent two independent events?
P(blue) = 20%, P(green) = 60%, P(blue and green) = 13%
P(blue) = 40%, P(green) = 30%, P(blue and green) = 13%
P(blue) = 70%, P(green) = 30%, P(blue and green) = 21%
P(blue) = 80%, P(green) = 20%, P(blue and green) = 18%
Answer: C) P(blue) = 70%, P(green) = 30%, P(blue and green) = 21%
Step-by-step explanation:
Given probabilities P(A) AND P(B) are independent, the probability that both events to occur is given by:
P(A)∩P(B)
thus from the example, independent events will be:
P(blue)=70%, P(green)=30%, P(blue and green)=21%
Because:
P(blue)∩P(green)=0.7×0.3=0.21=21%
dan makes pizza. he puts 6 pepperoni on each pizza. he makes 7 pizzas.
how many pepperonis does he use?
if he has 6 pepperoni and he puts them on 7 pizzas
6x7=42
The first to answer first will brainliest
Answer:
[tex]\sf \left(-\dfrac{1}{2},-\dfrac{1}{8}\right)[/tex]
See the graph below.
Equation: y = x³
Only (-0.5, -0.125) lies on the graph of the equation y = x³
option D is correct.Triangle PQR has ZP = 63.5° and ZQ = 51.2° and r = 6.3 cm. Find the other two sides and unknown angle. Options :
A R = 65.3°, p = 6.21 cm and q = 5.40 cm
B R = 65.3°, p = 5.21 cm and q = 5.40 cm
C R = 65.3°, p = 6.21 cm and q =4.40 cm
D R = 65.3°, p = 3.21 cm and q = 4.40 cm and q = 4.40 cm
Answer:
ben told it was 78
Step-by-step explanation:
ben said that
Use the diagram to write an equation that describes the position and the radius of ⊙P.
(x – 4)2 + (y + 2)2 = 16
(x + 4)2 + (y – 2)2 = 16
(x + 4)2 + (y – 2)2 = 4
(x – 4)2 + (y + 2)2 = 4
The equation of circle p with center at (-4, 2) and a radius of 4 units is (x + 4)² + (y - 2)² = 16
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The circle p has center at (-4, 2) with a radius of 4 units, hence, the equation is:
(x - (-4))² + (y - 2)² = 4²
(x + 4)² + (y - 2)² = 16
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50 points each question (visit profile for more). Please help. How do I solve?
Answer:
Check the image of solution
combine the like terms to create an equivalent expression
-3z - z
Answer:
Coefficient 1.2. Exponent 1.3. Variable or Base
Step-by-step explanation:
you build a two-person tent, as shown. How many square feet of material is needed to make the tent, assuming the tent has a floor?
The material is needed to make the tent, assuming the tent has a floor would be equal to 36/√3.
What is a triangular prism?Connect three rectangles edge to edge. Now close their triangular mouths from both ends. That shape is called a triangular prism.
Let the tent width be w and the given Length is 6 feet.
[tex]tan\theta = \dfrac{opposite }{adjecent} \\\\tan60 = \dfrac{h}{w/2} \\\\\sqrt{3} = \dfrac{6}{w/2} \\\\\sqrt{3} = \dfrac{12}{w} \\\\w = \dfrac{12}{\sqrt{3} }[/tex]
[tex]sin60 = \dfrac{opposite }{hypotenuse} \\\\sin60 = \dfrac{6}{x}\\\\x = \dfrac{6}{\sqrt{3}/2 }\\\\x = \dfrac{12}{\sqrt{3} }[/tex]
The area of the front tent =
[tex]\dfrac{1}{2} \times base \times height\\\\\dfrac{1}{2} \times w\times h\\\\\\\dfrac{1}{2} \times 12/\sqrt{3} \times 6\\\\\dfrac{36}{\sqrt{3} }[/tex]
The area of the back tent is also the same.
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Find the surface area of this rectangular prism. Be sure to include the correct unit in your answer.
Answer:
the answer is in the picture
BRAINLIEST +STARSS!!!
Question 1 (6 points) Retake question ✓ Saved
Anthony's sink is shaped like a half-sphere, and it has a volume of 512n cubic inches.
It is completely full of water, and he has two different cylindrical cups he can use to
scoop it out.
The blue cup has a diameter of 4 in. and a height of 8 in., and the green cup has a
diameter of 8 in. and a height of 8 in.. How many cupfuls of water will it take for him
to empty his sink using each cup?
In your answer, give the number of cupfuls it will take to empty the sink using each
cup, and then explain how you calculated it.
Answer:
The green would take 4 and the blue would take 16 times respectivly. I did it by finding the volumes of the cups in terms of pi, then dividing it by the volume of the sink.
Step-by-step explanation:
So the volume of the whole half sphere is 512pi.
Now we have to find the volumes of the cup.
Equation: [tex]\pi r^2h[/tex]
Blue cup:
[tex]\pi 2^2(8)\\\pi 4(8)\\\pi 32[/tex]
It would take 16 times to drain it completly.
Green cup:
[tex]\pi 4^2(8)\\\pi 16(8)\\\pi 128[/tex]
It would take 4 times to drain it completly.
A cone has a height of 6 inches and a radius of 7 inches. What is the volume? Keep your answer in terms of pi.
Answer:
V≈307.88in³
Step-by-step explanation:
V=πr2h
3=π·72·6
3≈307.87608in³
Answer:
[tex]98\pi[/tex]
Step-by-step explanation:
The formula of the volume of a cone is given by [tex]V=\frac{\pi r^2h}{3}[/tex], which, applying the values yields [tex]V=\frac{\pi 7^26}{3} = 98\pi[/tex]
Which graph represents an exponential function?
Answer:
The first one
Step-by-step explanation:
As x increases, the value of y approaches infinity. As x decreases, the value of y approaches 0.
Hope it helps
What is the total of all 3 tickets below. use the menu to solve
Answer:
$103.14
Step-by-step explanation:
The calculation of slips are amounted to a total of $103.14
Each member of a 5-member cross-country team runs a course. Their individual times are as follows:
2 hours 17 minutes
2 hours 48 minutes
1 hour 53 minutes
2 hours 19 minutes
1 hour 38 minutes
The team’s overall score is the average number of minutes it takes for its members to complete the course. What is this team’s score?
Step-by-step explanation:
the average is the sum of all data points divided by the number of data points (5).
2 hours 17 minutes
2 hours 48 minutes
1 hour 53 minutes
2 hours 19 minutes
1 hour 38 minutes
------------------------------
8 hours 175 minutes
175 minutes = 2 hours 55 minutes
so, we need to add this to the 8 hours and get
10 hours 55 minutes
this we need to divide by 5 for the average time
(10 hours 55 minutes) / 5 = 2 hours 11 minutes =
= 2×60 + 11 = 120 + 11 = 131 minutes.
so, their score is 131.
help me please what is 5y – 4n
Answer:
8
Step-by-step explanation:
y = 4 and n = 3
5y - 4n = 5(4) - 4(3)
= 12
Answer:
−4n+5y
Step-by-step explanation:
A two-variable inequality is shown in the graph.
Which point is not included in the solution set for the inequality?
(–1, 3)
(0, 4)
(1, 5)
(2, 4)
The point which is not included in the solution set for the inequality of the two-variable inequality shown in the graph is (-1,3).
How to graph the inequality?Inequality of a graph is represented with the greater then(<), less then(>) or with the other inequity signs. The inequality line on the graph is represented with the dotted lines.
A two-variable inequality is shown in the graph. It is a parabola. The vertex form of parabola is the equation form of quadratic equation which is used to find the coordinate of vertex points at which the parabola crosses its symmetry.
The standard equation of the vertex form of parabola is given as,
[tex]y=a(x-h)^2+k[/tex]
Here, (h, k) is the vertex point. In the graph, vertex points are (1,2). Thus, the equation become,
[tex]y=a(x-1)^2+2\\[/tex]
By the point of graph (0,3), find the value of a,
[tex]3=a(0-1)^2+2\\3=a+2\\a=3-2\\a=1[/tex]
Thus, the equation become,
[tex]y=1(x-1)^2+2\\y=x^2-2x+1+2\\y=x^2-2x+3\\[/tex]
The graph of this line is attached below. In this graph only point (-1,3), does not fall hence, does not satisfy the equation.
Thus, the point which is not included in the solution set for the inequality of the two-variable inequality shown in the graph is (-1,3).
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Answer:
Its (-1,3)
Step-by-step explanation:
Please Help!!!!
Using the slope formula, find the slope of the line through the given points. (12,0) and (2,-5)
Answer: The slope is 1/2
Step-by-step explanation:
Calculate the rise (change in y-component) divided by the run (change in x-component).
rise = 0 - (-5) = 5
run = 12 - 2 = 10
slope = 5/10 = 1/2
Help Me On This!!
[tex] \\ \\ \\ [/tex]
Answer:
First Find the Radius of Cake by dividing 40/2
Now Find Area of the cake of Bottom
And Then Use the Formula to calculate volume of Circle
Cross Section Area=π Square
Bole of Circle 4/3π× radius cube
Answer:
24,727.5 cm³
Step-by-step explanation:
Information to keep in mind
r₁ = 20 cm (bottom layer)r₂ = 20/2 = 10 cm (middle layer)r₃ = 10/2 = 5 cm (top layer)h (of each layer) = 15 cmFormula of a cylinder
V = πr²hVolume (total)
V = πr₁²h + πr₂²h + πr₃²hV = πh (r₁² + r₂² + r₃²)V = 3.14 x 15 ([20]² + [10]² + [5]²)V = 47.1 (400 + 100 + 25)V = 47.1 (525)V = 24,727.5 cm³Find the surface area of this triangular prism. Be sure to include the correct unit in your answer.
Answer:
984
Step-by-step explanation:
Solve for the base: 14 x 10
Solve for the sides: 2(1/2(10 x 24))
Solve for the backside: 10 x 24
Solve for the slanted plane or front: 14 x 26
Answer:
the answer is in the picture
What is the following product?
3 StartRoot 2 EndRoot (5 StartRoot 6 EndRoot minus 7 StartRoot 3 EndRoot
= $3500
= $4750
What is the value of each?
Answer:
The boat is 2000 and the bird is 750.
Step-by-step explanation:
1. 750+750=1500
1500+2000=3500
2. 2000+2000=4000
4000+750=4750