Considering the given focus and directrix, the equation of the parabola is given by:
[tex]y = -2.375x^2[/tex]
What is the equation of a parabola?The equation of a parabola, with a directrix in y, is:
[tex]y - k = a(x - h)^2[/tex]
In which:
The value of a is of 0.25C.The vertex is (h,k).The focus if (h, k+C).The directrix if y = k - C.In this problem, we have that the x-coordinate of the vertex is h = 0.
From the focus and the directrix, we have that:
k+C = -9.5
k - c = 9.5.
Hence k = 0, C = -9.5 = a = 0.25C = -2.375.
Thus the equation of the parabola is given by:
[tex]y = -2.375x^2[/tex]
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It takes 7 hours for Will to paint a house. Judy can paint the same house in 3 hours. How long will it take them to paint the house if they work together?
Answer:
2 hours
Step-by-step explanation:
1/7 + 1/3 = 10/21
21/10= 2.1
A box in the shape of a right rectangular prism has a
height of 15 inches and a square base. If the volume
of the box is 1500 cubic inches, what is the side
length, in inches, of the base?
Step-by-step explanation:
volume = height × square base
1500 = 15 × square base
square base = 100
lenght = 10
URGENT!! HELP PLEASE!!
Linear programming problems can also be solved using a graphing calculator. The following instructions will work for most commonly used graphing calculators, but note that they might vary slightly based on calculator model. Now that you’ve learned how to use a graphing calculator to solve linear programming problems, solve the following problems.
Part A
Consider the given system
{2x+y ≤20
{3x+2y ≤30
{x,y ≥0
Graph the inequalities on your graphing calculator, and find the vertex points of this system
Part B
In part A, you obtained the vertex points of the given system. Test these vertex points in the objective function, f(z)=4x+6y using a graphing calculator. Find the maximum point.
Answer:
A. see below for a graph
B. f(x, y) = f(0, 15) = 90 is the maximum point
Step-by-step explanation:
A. See below for a graph. The vertices are those defined by the second inequality, since it is completely enclosed by the first inequality: (0, 0), (0, 15), (10, 0)
__
B. For f(x, y) = 4x +6y, we have ...
f(0, 0) = 0
f(0, 15) = 6·15 = 90 . . . . . the maximum point
f(10, 0) = 4·10 = 40
_____
Comment on evaluating the objective function
I find it convenient to draw the line f(x, y) = 0 on the graph and then visually choose the vertex point that will put that line as far as possible from the origin. Here, the objective function is less steep than the feasible region boundary, so vertices toward the top of the graph will maximize the objective function.
The vertex points of this system are (0, 0), (0, 15) and (10, 0). And the maximum point of the system is 90.
What are systems of inequalities?At least two linear inequalities in the same variables make up a system of linear inequality in two variables. The graph of a linear inequality is the graph of all solutions to the system, and the solution of a linear inequality is the ordered pair that resolves all inequalities in the system.
The given system:
2x+y ≤20
3x+2y ≤30
x, y ≥0
To find the vertex points,
first, we take inequalities in slope-intercept form.
y = 20 - 2x
And y = -3x/2 + 15
x, y ≥0
From that we interpreted the graph.
And the graph is given in the attached image.
A:
Check out the graph below. Given that the first inequality entirely encloses it, the vertices are those defined by the second inequality: (0, 0), (0, 15), (10, 0).
B:
We have objective function f(z) = 4x + 6y
To find the maximum point:
Substituting (0,0) to the function,
4x + 6y
= 4(0) + 6(0)
= 0
Substituting (0,15) to the function,
4x + 6y
= 4(0) + 6(15)
= 0 + 90
= 90
Substituting (10,0) to the function,
4x + 6y
= 4(10) + 6(0)
= 40 + 0
The maximum point is 90.
Therefore, (0, 0), (0, 15) and (10, 0) are the vertex of the system. And the maximum point is 90.
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( also btw this is isnt a college level question, that was a mistake, its a middle school level question) Can someone please evaluate the following expression:
-8 x (-10) - 7 x 1/-1 = ?
And then explain how you got the answer afterwards?
What is the value of x?
According to the given figures of triangle.. The value of x is 2.
Answer:
x = 3
Step-by-step explanation:
assuming the triangle is right.
using Pythagoras' identity
(x + 2)² = x² + 4²
x² + 4x + 4 = x² + 16 ( subtract x² from both sides )
4x + 4 = 16 ( subtract 4 from both sides )
4x = 12 ( divide both sides by 4 )
x = 3
PLEASE HELP QUICK
Examine the diagram.
15 cm circle
Which is the circumference of the circle? (Use : = 3.14)
A 4.71 cm
B. 18. 14 cm
C 23.55 cm
D. 47.1 cm
E 176,625 cm
Answer:
To get the diameter we need to invert the equation: Cπ=D. If we put in all the numbers now we get that: 153,14=4,777070...
Step-by-step explanation:
A cookie recipe for 60 cookies calls for 4 cups of flours how much flour or s needed to make 90 cookies
Answer:
6 Cups of Flower
Step-by-step explanation:
First form a ratio
Cookies:Flour
60:4
Simplify
15:1
Since we now need to find the amount of cups for 90 cookies we must finds the amount of flower.
90:X
Using our old ratio of 15:1 we must divide 90/15 in order to get a factor to multiply 1 to make 15:1 equivalent to 90:X.
90/15 = 6 | 6 is the factor
15(6):1(6)
90:6
Find the perimeter of the figure.
At 6 a.m. the temperature was -8°C. At noon the temperature was 3°C. What was the change of temperature between 6 a.m. and noon?
Answer:11c
Step-by-step explanation:
If Nembutal is used to anesthetize rabbits at a dosage of .09 mg/g of body weight, and the concentration of the solution is 60 mg/mL, how many mL are needed to anesthetize a 4 lb rabbit?
Answer:
2.72 ml
Step-by-step explanation:
4 lb = 1814.37 gm
1814.37 gm * .09 mg/gm / ( 60 mg/ml) = 2.72 ml
Which scenario could be modeled with an exponential function?
Please select one of this:
The amount of money in a certificate of deposit earns 4.3% interest each year.
The amount of money in Avery's wallet increases and decreases by a different amount each week.
The amount of money in Jaylon's savings account where $125 is deducted each month.
Tim adds $10 to his savings account each week.
The scenario that could be modelled with an exponential function is when Tim adds $10 to his savings account each week.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
As we know that a continuous compounding function is an exponential function. Therefore, we need to find the situation where the principal amount is invested for an infinitely long time.
A.) Since the amount is invested and a certificate of deposit is taken the amount will be invested for a fixed period of time. Thus, this is not a continuous compound function.
B.) The amount put into the account and taken out of the account varies for each term. Thus, this is not a continuous function.
C.) As in Jaylon's account the money is reduced by $125 every month, therefore, at a certain point, it will become zero. Thus, this is not a continuous compound function.
D.) As Tim adds $10 to his saving account every month, and there is no time specified, also the account will be always positive. Thus, this is a continuous compound function.
Hence, the scenario that could be modelled with an exponential function is when Tim adds $10 to his savings account each week.
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PLEASE HELP PLEASE PLEASE HELP
Answer:
c) 5 boxes 4 donuts remain.
pls give brainlyist
Step-by-step explanation:
Answer:
C. 5 boxes with 4 doughnuts left over
Step-by-step explanation:
A baker made 64 doughnuts at his bakery on Monday.
The baker wants to put his doughnuts into boxes. Each box holds 12 doughnuts. What is the total number of boxes the baker can fill, and the total number of doughnuts he will have left over?
Given that the baker has 64 doughnuts and each box holds 12 doughnuts, how many boxes can he fill and how many will he have left over?
To find this, we need to divide 64 by 12 using long division.
*View the attached picture*
Hope this helps!
PLEASE HELP, THIS WORK IS DUE TO 11:59
Answer:
Correct Answer: (-3,4) is located in the G region!!
Step-by-step explanation:
This is simple graphing but using regions.
Each region is on a coordinate.
________________________________________________________
There are 4 Quadrants representing each region.
(x, y) is the Quadrant 1 (Top Right) which has every coordinate positive.
(-x , y) is Quad. 2 (Top left) The X coordinate is negative while the y is positive.
(-x , -y) is Quad. 3 (Bottom Left) Both axis are negatives
(x , -y) is Quad. 4 (Bottom Right) The X-axis is positive but the Y is negative.
________________________________________________________
Your question asks for what region (-3,4) is at.
We know that the location of this coordinate is in Quadrant 2 because the x is negative. (Top Right)
Now, you need to go 3 to the left of the x-axis.
Then, go 4 up the y-axis.
Your region for this coordinate is "G"
Are these points collinear?
Which of these groups of values plugged into the TVM Solver of a graphing
calculator will give the monthly payment for a 25-year loan for $175,000 at
6.7% interest, compounded monthly?
A. N=25; 1% = 6.7; PV=0; PMT=; FV=-175000; P/Y=12; C/Y=12;
PMT:END
B. N=25; 1% = 6.7; PV=-175000; PMT=; FV=0; P/Y=12; C/Y=12;
PMT:END
C. N=300; 1% = 6.7; PV=-175000; PMT=; FV=0; P/Y=12; C/Y=12;
PMT:END
D. N=300; 1% = 6.7; PV=0; PMT=; FV=-175000; P/Y=12; C/Y=12;
PMT:END
Answer:
C. N=300; I%=6.7; PV=-175000; PMT=; FV=0; P/Y=12; C/Y=12; PMT:END
Step-by-step explanation:
To find the payment on a loan, a TVM solver needs the Present Value (PV) to be the loan amount, the Future Value (FV) to be zero, and N to be the actual number of payments (25×12 = 300).
Most solvers will take I% to be the annual interest rate. (An HP-12C financial calculator uses the monthly interest rate.)
The set of values needed for finding the monthly payment on this $175,000 loan at 6.7% are listed in choice C.
__
Additional comment
The sign of the cash flow is usually negative for amounts paid, and positive for amounts received. Here, the answer choices show the loan amount to be negative and the payment amount to be positive. We ordinarily expect to receive the loan amount and pay the payments. By the above criteria, the signs are reversed in this problem from what we usually expect.
Please assist with this question.
Answer:
D. [tex]\frac{-19}{74} +\frac{71}{74} i[/tex]
Step-by-step explanation:
[tex]\frac{-8+3i}{5+7i} (\frac{5-7i}{5-7i} )[/tex]
[tex]\frac{-40+56i+15i-21i^2}{25-35i+35i-49i^2}[/tex]
[tex]\frac{-40+71i-21(-1)}{25-49(-1)}[/tex]
[tex]\frac{-40+21+71i}{25+49}[/tex]
[tex]\frac{-19+71i}{74}[/tex]
[tex]\frac{-19}{74} +\frac{71}{74} i[/tex]
I hope this helps and God bless!
Dwayne bought 12 yards of wrapping paper.
How many inches of wrapping paper did he buy? Helppp
Answer:
432 inchesStep-by-step explanation:
Given:
Dwayne = 12 yardsConversion: 1 yard = 3 feet = 36 inches
Use the unitary method and solve:
[tex]\implies \text{1 yard = 3 feet = 36 inches}[/tex][tex]\implies 1 \times 12 \ \text{yard} = 3 \times 12 \ \text{feet} = 36 \times 12 \ \text{inches}[/tex][tex]\implies 12 \ \text{yards} = 36 \ \text{feet} = 432 \ \text{inches}[/tex]Thus, Dwayne bought 432 inches of wrapping paper.
You work for the National Weather Service and are asked to study the average daily temperatures in Anchorage, Alaska. You calculate the mean of the average daily temperatures for each month. You decide to place the information on a graph in which the date is the input and the temperature is the output. You also decide that January 1950 will correspond to the month 0 as indicated by the dot on the input scale.
On a coordinate plane, quadrants 1, 2, 3, and 4 are labeled. Month is on the x-axis and degrees Fahrenheit is on the y-axis.
Determine the quadrant in which you would plot the points that correspond to the following data:
The average daily temperature for July 1910 was 71 degreesF.
a.
Quadrant III
b.
Quadrant IV
c.
Quadrant II
d.
Quadrant I
Please select the best answer from the choices provided
A
B
C
D
Answer:
IT will lie in the quardant 1
because want you to plot a point for "July 1963 was 63 degrees Fahrenheit" so that's in the positive temp region
so the correct option will be 1 and it is
D
Step-by-step explanation:
hope this helps
Which ratio of tablespoons of raspberries to tablespoons of sugar would make a fruitier jam
Answer:
9 to 6 is the answer to make a fruiter jam
Step-by-step explanation:
The ratio that makes a fruiter jam is 9:6
What is a ratio?The quantitative relation between two amounts shows the number of times one value contains or is contained within the other. for example-"the ratio of computers to students is now 2 to 1"
Given here: Macy's mother uses 6 tablespoon of sugar to 8 tablespoon of raspberries.
Original ratio is 4/3
Clearly only the option 9/6=3/2 is greater than 4/3
Thus 9:6 is the required ratio.
Hence, The ratio that makes a fruiter jam is 9:6
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Your question is incomplete. The complete question :
Macy's aunt makes raspberry jam using 6 tablespoons of sugar and 9 tablespoons of raspberries. Macy wants to make a fruitier tasting jam. # Which ratio of tablespoons of raspberries to tablespoons of sugar would make a fruitier jam?
9 to 10
4 to 10
9 to 6
A figure containing VW X is dilated by a scale factor of to form a new figure which contains ZV'W'X'. ZV'W'X' measures 79º. What is the measure of VW X?
Answer:
Its going to be 79 degrees still because it doesnt change.
Step-by-step explanation:
.
I need help again lol! I appreciate all what i can get!
To find the volume of a rectangular prism:
⇒ must know the formula
[tex]Volume = length * width * tall[/tex]
Let's convert all the known lengths into improper fractions if needed
[tex]2\frac{4}{5} =\frac{14}{5}[/tex]Thus: [tex]Volume = \frac{14}{5} *2*\frac{3}{5} =\frac{84}{25}=3.36yd^3[/tex]
When rounded to the nearest tenth, the volume of the pool is 3.4 [tex]yd^3[/tex]
Hope that helps!
Which shape has one less side and one less vertex than a trapezoid
Answer:
An Isosceles trapezoid
Step-by-step explanation:
The shape is triangle.
What is trapezoid?In Euclidean geometry, a trapezoid is a convex quadrilateral by definition. The bases of the trapezoid are the parallel sides. If the remaining two sides are parallel, they are referred to as the legs (or lateral sides); if not, the trapezoid is a parallelogram, and there are two pairs of bases.
Given a trapezoid,
number of vertex trapezoid have = 4
one less vertex than trapezoid = 4 - 1 = 3
number of sides trapezoid has = 4
one less side than trapezoid = 4 - 1 = 3
the shape which has 3 sides and 3 vertex is triangle.
Hence the new shape is triangle.
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Martin earns $18 dollars an hour. Which of the following inequalities represents the amount of time martin needs to work to earn at least $78 per day? 18 - t > 78 18+ t < 78 18t > 78 18t < 78
Answer:
18t >= 78
Step-by-step explanation:
Not sure if there's an equals sign in the problem that you were given, but there should be. The 18 in the inequality stands for the hourly wage. The t stands for hours worked. 18(wage) x t(hours) has to be greater than or equal to 78 in order for Martin to at LEAST $78 per day. :)
answer? ill mark brainlist
Answer:
Step-by-step explanation:
We need to multiply each dimension by 3.
The base was 3*15 = 45
and the height = 3*9 = 27.
how many people u think be on this app every day 10million or 1million?
find the volume of each prism 2.7ft 3ft 2ft
Answer:
16.2 is the volume i hope i helped u
Amanda simplifies the following expression and shows her work below. What mistake did Amanda make that resulted in an incorrect answer?
34−8÷2 + 3∙4
34−4 + 3∙4
37 – 7 ∙ 4
34−28
6
a
She added before multiplying
b
She multiplied before dividing
c
She subtracted before adding
d
She added before dividing
Answer:
A, She added before multiplying.
Step-by-step explanation:
First, start off by using GEMDAS.
Grouping
Exponents
Multiply
Divide
Add
Subtract
You work from left to right - so you obviously divide first, which Amanda did successfully. Then, you multiply, which is exactly where Amanda went wrong. She was supposed to multiply before adding the 3 with 4.
Not sure if this made sense,
A recipe called for the ratio of sugar to flour to be 10 : 3 if you used 70 ounce of sugar, how many ounces of flour would you need to use?
Answer:
21
Step-by-step explanation:
10*7 = 70
3*7 = 21
If T = 81 in, U = 92 in, V = 69 in, W = 135 in, X = 108 in, Y = 19 in, and Z = 115 in, what is the perimeter of the object?
A.
811 in
B.
465 in
C.
619 in
D.
638 in
Answer:
D. 638 in
Step-by-step explanation:
W+X+U+2Y+Z+V+T = 638
Which of the following Platonic solids is made from squares? Check all that
apply.
A. icosahedron
B. cube
c. tetrahedron
D. octahedron
E, hexahedron
F. dodecahedron
Answer:
B. Cube and E. hexahedron
Step-by-step explanation:
Icosahedron are made of triangles, cubes are made of squares, tetrahedron are made of triangles, octahedron are made of triangles, hexahedron are made of squares, dodecahedron are made of pentagons.
i hope it helps! Have a great day!
Sandra~