Answer:
d) The equation of the standard parabola
x² = 6 y
Step-by-step explanation:
The given directrix is y= -31.5
The equation of the parabola is of the form x² =4 a y
Given focus (0,1.5) , Here a= 1.5
The equation of the standard parabola
x² = 4 a y
x² = 4 (1.5)y
x² = 6 y
Conclusion:-
The equation of the standard parabola
x² = 6 y
The equation that represents the parabola shown on the graph is x∧2 = 6 y
What is a parabola?
A parabola is known as a plane curve that starts from a point and moves such that its distance from a fixed point is equal to its distance from a fixed line.
The graph shows a vertical parabola opened upwards with the vertex at the origin.
How to determine the equation
The equation of the parabola from the graph is;
x∧2 = 4ay
The equation of the directrix;
y = -a = -1. 5
Thus, the value of a = 1.5
Then, substitute the value of a = 1.5 in the equation deduced from the graph
x∧2 = 4 × (1.5) × y
x∧2 = 6 y
Therefore, the equation that represents the parabola shown on the graph is x∧2 = 6 y
Learn more on parabola here:
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Carter has 143 songs pn a playlist. He's categorized them in the following manner: 7 classical, 19 rock, 29 hip hop, 16 gospel, 13 pop, 24
country, and 35 jazz. If Carter begins listening to his playlist on shuffle, what is the probability that the first song played is a rock song?
Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Plssss help
Answer:
19/ 143
Step-by-step explanation:
There are 19 rock songs out of 143 total
P(rock) = number of rock songs/ total
= 19/ 143
A plumber charges $70 per hour plus $40 for the call. What does he charge for 4 hours of work? Use x to represent the hours of work.
Answer:
Step-by-step explanation:
70x4 is 280 plus 40 is 320.
Answer:
$320
Step-by-step explanation:
(4 x $70) + $40 is the equation
$280 + $40 = $320
$320
Constructing a Circle through Three Points Not on a Line
Construct a circle through points
X, Y, and z.
Answer:
the circle has one point even if it is a concentric circle it will have one central point or it needs more collections of the circle at equidistance
Answer:
The circle would look like the image attached
Step-by-step explanation:
Please answer correctly !!!!!!!!! Will mark brainliest answer !!!!!!!!!!!!
Answer:
So it will take the stone 1 (one) second to reach its maximum height.
Step-by-step explanation:
Notice that the mathematical quadratic expression given is that of a parabola with branches pointing down. This means that the maximum value for that parabola is at the vertex. Your expression is also given in vertex form:
[tex]f(x)=a\,(x-x_v)^2+y_v[/tex]
where the pair of coordinates [tex](x_v,y_v)[/tex] are the x coordinate of the vertex and the y coordinate of the vertex.
Since x in your case is the time the stone is on the air, then the maximum (vertex) is at the point (1, 45) where "1" is the time in seconds and 45 is the height of the stone in meters.
So it will take the stone 1 (one) second to reach its maximum height.
Please please please answer this if you do this i will give you brain list I’ll give a thank you and I’ll rate you five star. It’s due soon so pls answer FAST!!
Answer:
b) 30^2 + b^2 = 40^2
Step-by-step explanation:
This is cuz the diagonal is the hypotenuse of the diagonal formed so it'll be c^ 2
c ^ 2 always is on the right hand side of the equation.
In this case since 40^2 is c^2 is should be on the right side of the equation.
A baker is folding up open-topped boxes to package up her baked goods. She has
flat, rectangular pieces of cardboard that are 10 inches by 6 inches. She wants to
maximize the volume of the box. What size squares should she cut from the corners
of the cardboard?
Answer:
She should cut 1.21 inches (or a square of area 1.46 inch²) from 4 corners to get the maximum volume
Step-by-step explanation:
Length = L = 10 inches
Width = W = 6 inches
Suppose x is cut from the 4 corners to make a box.
Dimensions of the Box:
L= 10 - 2x
W = 6 - 2x
H = x
Volume of the Box:
V = (L)(W)(H)
V = (10-2x)(6-2x)(x)
V = 4x³ - 32x² + 60x
For Maximum value:
[tex]\frac{dV}{dx}=0[/tex]
[tex]\frac{dV}{dx}=\frac{d}{dx}(4x^3-32x+60x)\\\frac{dV}{dx}=12x^2-64x+60\\12x^2-64x+60 = 0[/tex]
The values of x found are:
x= 4.12 , x = 1.21
If we put x= 4.12 in W= 6-2x , the value of width becomes negative, so that is not possible.
We discard 4.12. Now x=1.21
So,
If 1.21 inches are cut from 4 corners, or a square of 1.21*1.21 = 1.46 inch² is cut from 4 corners, we get the maximum value of V
please help me with this question!
A cone-shaped vase has height 28 cm and radius 9 cm. An artist wants to fill the vase with colored sand. The sand comes in small packages, each of which is a cube with side length 3 cm. At most, how many packages of sand can the artist use without making the vase overflow?
Answer:
87 packages
Step-by-step explanation:
First we need to find the volume of the cone-shaped vase.
The volume of a cone is given by:
V_cone = (1/3) * pi * radius^2 * height
With a radius of 9 cm and a height of 28 cm, we have:
V_cone = (1/3) * pi * 9^2 * 28 = 2375.044 cm3
Each package of sand is a cube with side length of 3 cm, so its volume is:
V_cube = 3^3 = 27 cm3
Now, to know how many packages the artist can use without making the vase overflow, we just need to divide the volume of the cone by the volume of the cube:
V_cone / V_cube = 2375.044 / 27 = 87.9646 packages
So we can use 87 packages (if we use 88 cubes, the vase would overflow)
Answer:
87.97 packsStep-by-step explanation:
This problem bothers on the mensuration of solid shapes, a cone
the expression for the volume of a cone is
[tex]v=\frac{1}{3} \pi r^2h[/tex]
Given data
height h= 28cM
radius r= 9cm
substituting the data the data into the expression for the volume we can solve for the volume
[tex]v=\frac{1}{3} *3.142*9^2*28\\\v= \frac{7126.056}{3}\ \\v= 2375.35cm^3\\\\[/tex]
we know that a pack contains a cube, we then need to calculate the volume of a cube in a pack, given that the length of a cube is 3cm
the volume is = [tex]l^3= 3^3= 27cm^3\\[/tex]
now the volume of a pack is [tex]27cm^3[/tex], hence the amount of packs needed to fill the cone is calculated as,
[tex]=\frac{2375.35}{27}\\ = 87.97 packs[/tex]
help please thank you
[tex]answer \\ 187 \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps[/tex]
Zachary can't believe how bad London's traffic is today. In the past 10 minutes, his cab has barely moved 500 meters! He wonders if walking would have been faster. If Zachary walks at an average speed of 5 kilometers per hour, how many minutes would it take him to walk 500 meters?
Answer:
6 min
Step-by-step explanation:
5 kilometers = 5,000 meters
500/5,000 = 1/10 meaning it would take him 1/10 of an hour or 6 minutes to cover this distance.
Analyze the set below and answer the question that follows. (KUM) n (KUL) Which Venn diagram has shading that represents the given set?
Answer:
Choice A. The shading in the Venn Diagram shown in the first attachment represents the set [tex](K \cup M) \; \cap \; (K \cup L)[/tex].
Step-by-step explanation:
Let [tex]A[/tex], [tex]B[/tex], and [tex]C[/tex] be sets. By the distributive law of sets, [tex]A \cup (B \cap C)[/tex] and [tex](A \cup B) \cap (A \cup C)[/tex] refer to the same set.
Apply this property to simplify the given expression:
[tex]\begin{aligned}(K \cup M) \; \cap\; (K \cap L) = K\cup (M \cap L)\end{aligned}[/tex]
[tex]M \cap L[/tex] refers to the intersection between the two lower circles. The union of that intersection with set [tex]K[/tex] (the upper circle) would be the shaded region seen in choice A.
For which table would 70 be the missing value,x?
It is C
The Stone and Pounds
Answer:
c
Step-by-step explanation:
Please help!
Does this represent a linear function, non-linear function, or no function?
Answer: It would represent a linear function.
Step-by-step explanation:
Every time, the amount of blocks increase by 3, which would be the slope of it were on a graph, and it is constant. It’s not a quadratic nor an exponential function because it is not divided or multiplied at a certain factor, but it just adds by 3 each time.
An employee at a homemade wooden toy store earned $860 over the past week. The employee needs to pay 14% for Federal Income Tax and 3% for State Income Tax, both on the initial amount he earned. How much will the employee earn after paying both taxes?
Answer:
$713.8
Step-by-step explanation:
14%of 860 = 120.4
3% of 860 = 25.8
so, subtract the sum of the above 2 values from 860.
860 - (120.4+25.8) = 860-146.2 = 713.8
Hope this helps
Answer:
$713.008
Step-by-step explanation:
P= $450 r=6% t= 3 what is I ?
Answer:
535.96 (rounded up)
Step-by-step explanation:
Y= a ( 1 + r )^t
What’s the sum of -30 and 29
Answer:
The answer of -1.
Step-by-step explanation:
You have to add both numbers together :
[tex] - 30 + 29 \\ = - 1[/tex]
[tex] - 30 + 29 \\ = - 1 \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]
pleasee help marking brainlest
Answer:
See below in bold.
Step-by-step explanation:
The cost of what he wants to buy = 4.25 + 0.89 + 10.99
= $16.13
a) He does have enough to buy everything.
b) He has 20 - 16.13 = $3.87 left over.
if g(x)= -3 +1, Find x if g(x)= 16
Answer:
X= -5
Step-by-step explanation:
Replace the g(x) with 16.
16= -3x +1
Move -3x on other side.
3x+16=1
Subtract one from both sides.
3x= -15
Divide both sides by 3 to get x by itself.
x= -5
Here are two similar rectangles. Work out the area of the larger rectangle
Answer:
take the picture please or give the measurements of the rectangles
Answer:
see attachment for measurements
Step-by-step explanation:
2 3 x = − 1 2 x + 5 what is x?
Answer: 1/7
Step-by-step explanation:
23x = -12x + 5
23x + 12x = 5
35x = 5
x = 1/7
!!WILL MARK BRAINLIEST!! Write in slope-intercept form an equation of the line that passes through the given points.
Answer:
y = 1/4x
Step-by-step explanation:
First find the slope
m = (y2-y1)/(x2-x1)
= (2-1)/(8-4)
= 1/4
The slope intercept form of a line is
y = mx+b
where m is the slope and b is the y intercept
y = 1/4x +b
Substitute a point into the equation
1 = 1/4(4) +b
1 = 1+b
b= 0
y = 1/4x
The 6 in 61 represents how many times the value of the 6 in 69?
What is the value of m in the equation 1/2 m - 3/4 n equals 16 when n equals 8
Answer:
m =44
Step-by-step explanation:
1/2 m -3/4 n = 16
Let n =8
1/2 m - 3/4(8) = 16
1/2 m - 6 = 16
Add 6 to each side
1/2 m -6+6 = 16+6
1/2 m = 22
Multiply each side by 2
m = 22*2
m = 44
Answer:c
Step-by-step explanation:
John would like to go on a ski trip with his friends. In order to go on the trip, John needs to save more
than $350 dollars. Write an inequality that describes, M, the money that John needs to save.
Answer:
$350 < M
Step-by-step explanation:
Which one the following is a polynomial?
A. x^3-4x^2+√x-5
B. √2x^3-2x^2+3x-1
Answer:
B
Step-by-step explanation:
A has a sqrt(x) as a term, which makes it not a polynomial
The development of technology _____________.
a. has no effect on the environment
b. depends on people’s needs
c. depends only on our imagination
d. depends on what is learned in school
Answer:
B
Step-by-step explanation:
show the relationship between the number of miles and the number of hours in the ratio 12 to 1
Answer:
The person has a speed of 12 miles per hour.
Step-by-step explanation:
The ratio is 12 miles to 1 hour.
This means, that in every hour, the person can move 12 miles and has a speed of 12 miles per hour.
Which formula gives the zeros of y = sin(x)?
O pi for any positive integer k
0 pi for any integer k
Kpi
2 for any positive integer k
O
kpi
2 for any integer k
Pls mark brainliest,thankyou.
Answer:
b
Step-by-step explanation:
Find the surface area of the triangular prism. The base of the prism is an isosceles triangle.
Answer:
[tex]A=2\times25\times 44+14\times44+2\times\frac{14\times24}{2} =3152\; cm^2[/tex]
The surface area of the triangular prism is 3152 square cm if the base of the prism is an isosceles triangle.
What is a triangular prism?When a triangle is, stretch it out to produce a stack of triangles, one on top of the other. A triangular prism is the name given to this novel 3D object.
We have a triangular prism, is showing in the picture:
Here a = 25
b = 25
c = 14
h = 44
The surface area of the triangular prism is given by:
[tex]\rm A=ah+bh+ch+\dfrac{1}{2}\sqrt{-a^4+2(ab)^2+2(ac)^2-b^4+2(bc)^2-c^4][/tex]
Plug all the values in the formula we get:
A = 3152 square cm
Thus, the surface area of the triangular prism is 3152 square cm if the base of the prism is an isosceles triangle.
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Which expession is equivalent to 4-(-7)
Answer:
4 + 7 = 11
Step-by-step explanation:
Subtracting a negative means adding.
To subtract a number, add its opposite. The opposite of -7 is 7, so to subtract -7, add 7.
4 - (-7) = 4 + 7 = 11
Answer:
4+7
Step-by-step explanation:
Find the perimeter of the figure. If you need to use Pi in your computation, approximate its value as 3.14. Rectangle topped by a semicircle A rectangle topped by a semicircle. The rectangle has length of 6 meters and width of 5 meters. The circle has diameter 5 meters. a. 29.85 m b. 18.57 m c. 32.70 m d. 24.85 m
Answer:
l think the answer is C
32.70m
Step-by-step explanation:
we all know that perimeter is the distance round the shape.
so the first step is adding 6 +6 because the other side of the shape is also 6 then add 5 and this equals to 17.
After that we find the area of the circle
which is 3.14*5= 15,7
After getting this value we add it to 17
then we get 32.70m
Answer:C
Step-by-step explanation:
