The vertex of the given parabola [tex]$x^{2}=8 \mathrm{y}$[/tex] exists (0, 0).
What is the vertex of a parabola?The vertex of a parabola exists as the point at the intersection of the parabola and its line of symmetry. The vertex of the parabola exists as the minimum point on the graph for a positive right-handed parabola.
Given the equation of parabola exists [tex]$x^{2}=8 y$[/tex].
[tex]$\mathrm{y}=x^{2} / 8[/tex]
General vertex form for any given parabola exists [tex]$\mathrm{y}=\mathrm{a}(x-a)^{2}+\mathrm{b}$[/tex]
where (a, b) exists the coordinates of the vertex.
For this function it exists [tex]$\mathrm{y}=1 / 8(x-0)^{2}+0$[/tex]
The vertex of the given parabola exists at (0, 0).
Therefore, the vertex of the given parabola [tex]$x^{2}=8 \mathrm{y}$[/tex] exists (0, 0).
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Using the image, find the midpoint of the line segment. Reduce all fractions and enter using a forward slash (i.e. "/").
Find the surface area of the prism
The surface area of the prism is 256in².
Given that the sides of the prism is 5in, 12in and 4in.
The total area occupied by the surfaces of an object is called the area.
Here, l=12in, b=5in and h=4in
Firstly, we will find the area of the base, we get
B=l×b
B=12×5
B=60in²
Now, we will find the perimeter of the base, we get
P=2(l+b)
P=2(12+5)
P=2×17
P=34in
Further, we will find the surface area of the prism by using the formula SA=2B+Ph.
Here, we will substitute the values from above, we get
SA=2×60in²+34in×4in
SA=120in²+136in²
SA=256in²
Hence, the surface area of the prism where the sides of the prism is 5in, 12in and 4in is 256in².
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A spaceship is traveling at a steady rate. The table shows the distance the spaceship travels in a given period of time. Find the distance the spaceship travels in 4 minutes.
Ty.
The distance of the spaceship in discuss as in the task content given can be evaluated as; 800miles.
What is the distance the spaceship travels in 4 minutes?The distance travelled by the spaceship in discuss can be evaluated by means of the slope of the linear relationship as follows;
Hence it follows from ratios that by observation, the linear relationship has a slope of 200mi/min.
Consequently, we can evaluate the distance travelled after 4 minutes as;
Distance = 200 × 4 = 800mi.
Ultimately, the distance travelled per minute by the spaceship is; 800mi.
Remarks:
600 miles
520 miles
800 miles
1,080 miles
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Ron works at the local bookstore for an hour every day. He earns $5 daily from this job. If he adds this amount to his daily allowance, he has $70 at the end of each week. The amount of money Ron receives each week is represented by the equation 7(x + 5) = 70, where x is the amount of Ron's daily allowance. Plug the numbers from the set {5, 10, 15, 20} into the equation to find x, the amount of Ron's daily allowance.
please help with math
Answer:
2nd option, x > 1.10
Step-by-step explanation:
[tex]7e^{2x}-5 > 58[/tex]
Add 5 to both sides,
[tex]7e^{2x}-5+5 > 58 +5\\7e^{2x} > 63[/tex]
Divided both sides by 7,
[tex]\frac{7e^{2x}}{7} > \frac{63}{7}[/tex]
[tex]e^{2x} > 9[/tex]
Apply Exponent Rule,
[tex]2x > 2ln(3)[/tex]
[tex]\frac{2x}{2} > \frac{2ln(3)}{2}[/tex]
x > ln(3) or x > 1.09861
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If two marbles are selected at random with replacing between draws, what is the probability that the outcome is red then yellow? (round your answer to four decimal places. )
The probability that the outcome is red then yellow is 0.036.
Given that in a jar there are 8 red marbles, 1 yellow marble and 6 green marbles.
We are required to find the probability of obtaining a red then yelow marble if two marbles are drawn and replacement is used.
Probability is the calculation of finding the chance of happening a event among all the events possible. It lies between 0 and 1.
Probability=Number of items/ Total items.
Number of red marbles=8
Number of yellow marble=1
Number of green marbles=6
Total marbles=15
Probability of obtaining red marble=8/15
Probability of obtaining yellow marble=1/15 (Because replacing is there so the number of total marbles do not decrease)
Required probability=8/15*1/15
=8/225
=0.035555
After rounding off we will get 0.036.
Hence the probability that the outcome is red then yellow is 0.036.
Question is incomplete. The following line should be included in question:
A jar contains 8 red marbles , a yellow marble and 6 green marbles.
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Find the general solution of the given system of odes. { dx/dt =2x 2y,dy/dt =x 3y}
The general solution of the given system of odes is
m=1 ; m=4 (real roots)
In arithmetic, a system of odes equations is a finite set of differential equations. Any such device may be either linear or non-linear. Also, such a machine can be both a machine of normal differential equations or a system of partial differential equations.
the compatibility conditions of an overdetermined system of odes equations may be succinctly stated in terms of differential forms (i.e., a shape to be specific, it needs to be closed). See integrability situations for differential systems for more.
It is an elaborately based poem praising or glorifying an event or character, describing nature intellectually as well as emotionally. A traditional ode is dependent on three essential parts: the strophe, the antistrophe, and the epode. Distinct forms together with the homostrophic ode and the abnormal ode also enter.
dx/dt = 2x+2y = x^1 = 2x+2y 1
dy/dt = x+3y = y^1 = x+ 3y 2
differentiating 1 with respect to 't'
x^11 = 2x^1+ 2y^1
y^1 = x+3y
x^11 = 2x^1= 2(x+3y)
x^11 = 2x^1+ 2x+ 6y
x^11 = 2x^1+ 2x+ 6(x^1-2x/2)
x^11 = 2x^1+ 2x+ 3x^1- 6x
x^11 = 5x^1 - 4x
x^11 -5x^1 - 4x
x^11 - 5x^1 -4x =0
Auxillary equation is m^5- 5m+4=0
m^2 - m - 4m + 4 = 0
m(m-1) -4 (m-1) =0
(m-1) (m-4) = 0
m=1 ; m=4 (real roots)
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Question
In the xy-plane, what is the y-intercept of the graph of the equation y = 6 (x − 1/2) (x+3)?
-9
-1/2
-1/2
3
9
Answer:
-9
Step-by-step explanation:
To find the y intercept, substitute 0 in for x.
So, the equation looks like this:
[tex]y=6(0-\frac{1}{2} )(0+3)[/tex]
Now, just solve for y and you will get y = -9
The y-intercept of the graph of the equation is y = -9 which is the correct answer that would be an option (A).
What is the equation of a line?The general equation of a line is y = mx + c
where m is the slope of the line and c is the intercept.
A linear equation is defined as an equation in which the highest power of the variable is always one.
Given equation as:
y = 6 (x - 1/2)(x+3)
To determine the y-intercept of the graph of the equation
Substitute the value x = 0 in the equation,
y = 6 (0 - 1/2)(0+3)
Apply the arithmetic operation and solve for y
y = -9
Hence, the y-intercept of the graph of the equation is y = -9.
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30. A man walks diagonally from one corner of a
rectangular lot to the opposite corner. If he
walks at the rate of 5 feet a second, and the lot is
50 feet by 120 feet, how many seconds will he
save by walking diagonally instead of walking
along the perimeter of the lot?
(A)8
(B) 10
(C) 17
(D) 34
The time he saves when walking diagonally is 8 seconds
How to find diagonal and side of a rectangle?A rectangle has opposite sides equal to each other.
The angles are equal.
Therefore,
perimeter of a rectangle = 2l + 2w
where
l = lengthw = widthTherefore,
distance of the diagonal =√ 50² + 120²
distance of the diagonal = √2500 + 14400
distance of the diagonal = √16900
distance of the diagonal = 130 feet
distance if he follows the length of the rectangle = 50 + 120 = 170 feet
Hence,
Time spent diagonally
5 = 130 / t
t = 130 / 5
t = 26 seconds
Time spent along the perimeter
5 = 170 / t
t = 170 / 5
t = 34 secods
Therefore,
Time he will save by walking diagonally = 34 - 26 = 8 seconds
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Write the equation for a circle centered at the origin with x-intercepts of (-9,0) and (9,0).use ^2 for squared, ^3 for cubed,
The equation of the circle can be shown as, x² + y² = 9², or, x² + y² = 81.
The equation of a circle, with the center at the origin and the radius r units, is given as x² + y² = r².
In the question, we are asked to write the equation for a circle centered at the origin with x-intercepts of (-9, 0) and (9, 0).
We can find the radius of the circle using the distance formula,
D = √((x₂ - x₁)² + (y₂ - y₁)²), where (x₁, y₁) and (x₂, y₂) are the endpoints of a line segment.
Radius is the distance between the center and any point on the circle.
Thus, taking (x₁, y₁) as (0, 0), the origin, for the center, and (x₂, y₂) as (9, 0), for any point on the circle, we get the radius as:
r = √((9 - 0)² + (0 - 0)²),
or, r = √(9² + 0²),
or, r = √9² = 9.
Thus, the radius of the circle is r = 9 units.
Thus, the equation of the circle can be shown as, x² + y² = 9², or, x² + y² = 81.
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Which graph shows the solution to this system of inequalities y < - 1/3 x + 1
Answer:
See attached image.
Step-by-step explanation:
The image does not show the graph options. The attachment sjhhows the graph of y < - 1/3 x + 1.
Complete the equation of the line through (-10,-7)(−10,−7)left parenthesis, minus, 10, comma, minus, 7, right parenthesis and (-5,-9)(−5,−9)left parenthesis, minus, 5, comma, minus, 9, right parenthesis. Use exact numbers. y=y=
[tex](\stackrel{x_1}{-10}~,~\stackrel{y_1}{-7})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{-9}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-9}-\stackrel{y1}{(-7)}}}{\underset{run} {\underset{x_2}{-5}-\underset{x_1}{(-10)}}} \implies \cfrac{-9 +7}{-5 +10} \implies \cfrac{ -2 }{ 5 }\implies -\cfrac{2}{5}[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-7)}=\stackrel{m}{-\cfrac{2}{5}}(x-\stackrel{x_1}{(-10)}) \\\\\\ y+7=-\cfrac{2}{5}(x+10)\implies y+7=-\cfrac{2}{5}x-4\implies y=-\cfrac{2}{5}x-11[/tex]
Help me pls i very need your answer
[tex]x = \frac{\sqrt{5} + 1}{2} \approx 1.618033989[/tex]
Vectors u and v are shown in the graph. What is -3(u•v)?
[tex]\mathbf{u} =\langle -6, -10 \rangle \\ \\ \mathbf{v}=\langle 7,8 \rangle \\ \\ \mathbf{u} \cdot \mathbf{v}=(-6)(7)+(-10)(8)=-122 \\ \\ \therefore -3(\mathbf{u} \cdot \mathbf{v})=-3(-122)=\boxed{366}[/tex]
The value of -3(u•v) is 366 when vector u= -6i - 10j and vector v=-6i - 10j is given.
What is dot product ?The dot product of two vectors is the sum of the products of their corresponding components.
Here, u= -6i - 10j, from the figure as u goes 6 coordinate left to the y axis and and 10 coordinates below the x axis.
v= 7i + 8j, from the figure as v corrdinates right to the y axis and 8 coordinats upwards to the x axis.
Therefore u.v= (-6i - 10j).(7i + 8j)
= -42 - 80
= -122
So, -3(u.v)= (-3)×(-122)
=366
Hence, the value of -3(u•v) is 366
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What is the volume of the pyramid
Answer:
Option A - 32 cm³
Step-by-step explanation:
Volume of a pyramid is given by the formula :
V = [tex]\frac{lwh}{3}[/tex]
Substituting values given gives us :
V = (4)(4)(6)/3
V = (16)(6)/3
V = 96/3
V = 32
Units will be cm³ as this is volume
Hope this helped and have a good day
Answer:
A. 32 cm³
Step-by-step explanation:
V = (1/3)(area of base)(height)
The base is a square of side 4 cm.
area of base = side × side
V = (1/3)(4 cm × 4 cm)(6 cm)
V = 32 cm³
Complete the equation.
2 x 4 =
x 2
2x4=8
8x2=16
the answer is 16
The black graph is the graph of y =f(x). Choose the equation for the red graph. A. y - 1 = f() B. y + 1 = f() C. = f(x - 1) D. f(x)
Answer: C
Step-by-step explanation:
The red graph is the result of reflecting the graph of y=f(x) across the x-axis and then translating 1 unit to the right.
The motion of an object was recorded by measuring the velocity of the object in meters per second at various times, as shown in the table. The scatterplot below was graphed from the data in the table, where t represents the time, and v represents the velocity. Based on the scatterplot, which equation BEST represents the relationship between velocity and time?
Based on the scatterplot, the equation that BEST represents the relationship between velocity and time is y = 2.2x + 6
How to determine the line of best fit?The line of best fit is the line that best represents the relationship between 2 variables. The equation of a line in slope-intercept form is expressed as:
y = mx + b
where
m is the slope
b is the intercept
Using the coordinate points on the plane (0, 6) and (10, 28)
Determine the slope
Slope = 28-6/10-0
Slope = 22/10
Slope = 2.2
Determine the y-intercept
6 = 2.2(0) + b
b = 6
Determine the equation of aline of best fit.
y = 2.2x + 6
Hence based on the scatterplot, the equation that BEST represents the relationship between velocity and time is y = 2.2x + 6
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HELPPP SIMPLE QUESTION‼️‼️‼️‼️‼️
Four less than a number x is twice another number y.
write in an equation
Answer:
x - 4 = 2y
Step-by-step explanation:
"four less than a number x" therefore; x - 4
"is twice another number y" therefore; 2y
Bruce went to sleep at 9:00 pm and set old-shchool analog alarm clock to ring when he wanted to wake up the next morning: at 10:00. HHow many hours will Bruce sleep?
PLEASE HELP IN STUCK
14. Suppose the diameter of circle B were 18 inches instead of 8 inches. What is the
total cost of the glass for your window now?
The total cost of the glass for your window now $174.8
How to determine the total cost of the glass for your window now?The complete question is added as an attachment
From the attached figure, we have the following parameters:
Square of side length 24 inchesCircle B of diameter 20 inchesCircle A of diameter 18 inchesThe area of region 1 is calculated using:
Region 1 = Area of square - Area of circle B
This is calculated as
Region 1 = L^2 - π(d/2)^2
So, we have:
Region 1 = 24^2 - 3.14 * (20/2)^2
Evaluate the quotient
Region 1 = 24^2 - 3.14 * 10^2
Evaluate the exponent
Region 1 = 576 - 3.14 * 100
Evaluate the product
Region 1 = 576 - 314
Evaluate the difference
Region 1 = 262
The cost per square inch of this region is $0.10.
So, we have:
Total cost of region 1 = 262 * $0.10
Total cost of region 1 = $26.10
The area of region 2 is calculated using:
Region 2 = Area of circle B - Area of circle A
This is calculated as
Region 2 = π(D/2)^2 - π(d/2)^2
So, we have:
Region 2 = 3.14 * (20/2)^2 - 3.14 * (18/2)^2
Evaluate the quotient
Region 2 = 3.14 * 10^2 - 3.14 * 9^2
Evaluate the exponent
Region 2 = 3.14 * 100 - 3.14 * 81
Evaluate the product
Region 2 = 314 - 254.34
Evaluate the difference
Region 2 = $59.66
The cost per square inch of this region is $0.15.
So, we have:
Total cost of region 2 = 59.66 * $0.15
Total cost of region 2 = $8.949
The circle B is divided into sectors.
And the angles of the sectors are 90 and 270 degrees
The area of each sector is
Area = ∅/360 * π(d/2)^2
So, we have:
Circle B = ∅/360 * π(d/2)^2 + ⊕/360 * π(d/2)^2
So, we have:
Circle B = 90/360 * 3.14 * (18/2)^2 + 270/360 * 3.14 * (18/2)^2
Evaluate the quotient
Circle B = 0.25 * 3.14 * 9^2 + 0.75 * 3.14 * 9^2
Evaluate the exponent
Circle B = 0.25 * 3.14 * 81 + 0.75 * 3.14 * 81
Evaluate the product
Circle B = 63.585 + 190.755
The cost per square inch of this region is $0.80 for 1 sector and $0.20 for the rest
So, we have:
Total cost of circle B = 63.585 * 0.80 + 190.755 * 0.20
Total cost of circle B = 89.019
Add the total costs
Total cost of the glass for your window = Region 1 + Region 2 + Circle B
Total cost of the glass for your window = $26.10 + $59.66 + $89.019
Evaluate the sum
Total cost of the glass for your window = $174.779
Approximate
Total cost of the glass for your window = $174.8
Hence, the total cost of the glass for your window now $174.8
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Cory saw 27 animals in the woods. two-thirds of them were insects. one-third of the insects were ants. the rest of the insects were flies. cory saw two times as many squirrels as rabbits. cory also saw a family of deer: a buck, a fawn, and a doe. how many of each animal did cory see?
Number of ants = 6
Number of flies = 12
Number of buck = 1
Number of fawn = 1
Number of doe = 1
Number of squirrels = 3
Number of rabbit = 6
What is the number system?
A system of writing numbers is known as a number system. It is the mathematical notation for consistently employing digits or other symbols to represent the numbers in a particular set. It represents the arithmetic and algebraic structure of the numbers and gives each number a distinct representation.
A system for representing numbers is called a number system. It also defines a set of numbers to represent a quantity and is referred to as the system of numeration.
Given,
Total number of animals Cory saw = 27
Number of insects = [tex]27 \times \frac{2}{3}[/tex]
[tex]= 18[/tex]
Remaining number of animals = [tex]27-18[/tex]
= [tex]9[/tex]
From the insects-
Number of ants = [tex]18 \times \frac{1}{3}[/tex]
[tex]=6[/tex]
Number of flies = [tex]18-6[/tex]
= [tex]12[/tex]
Number of buck = 1
Number of fawn = 1
Number of doe = 1
Let the number of squirrels be [tex]x[/tex]
Then, the number of rabbits = [tex]2x[/tex]
Remaining animals = [tex]2x+x[/tex]
⇒ [tex]9=3x[/tex]
⇒ [tex]x= 3[/tex]
Therefore,
Number of squirrels = 3
Number of rabbits = [tex]2x[/tex]
= 6
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3. According to the diagram above, what is 2xº?
(A) 18⁰
(B) 27°
(C) 36°
(D) 54
A sheet of glass has a density of 2.5 8 What is the density of the glass in k8 ? mi.
Based on the density and the given parameters, the density of the sheet of glass in kg per m cubed is 2500 kg/m cubed
How to determine the density of the sheet of glass in kg per m cubed?The density of the sheet of glass is given as
Density = 2.5g/cm cubed
Start by converting grams (g) to kilogram (kg)
This is done by dividing 2.5 by 1000
So, we have:
Density = 2.5/1000 kg/cm cubed
Evaluate the quotient
Density = 0.0025 kg/cm cubed
Next, we then convert cm cubed (cm^3) to meter cubed (m^3)
This is done by dividing the volume by 1000000
So, we have:
Density = 0.0025 kg/(1/1000000) m cubed
Express as product
Density = 1000000 * 0.0025 kg/m cubed
Evaluate the product
Density = 2500 kg/m cubed
Based on the density and the given parameters, the density of the sheet of glass in kg per m cubed is 2500 kg/m cubed
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Answer:
See below
Step-by-step explanation:
Are you wanting to convert density of gm/ cm^3 to kg/m^3 ??
there are 100 x 100 x 100 cm^3 = 1,000,000 cm^3/ m^3
2.5 gm / cm^3 * 1 000 000 cm^3 / m^3 = 2, 500 000 gm / m^3
now 1 kg is 1000 gm
2, 500 000 gm / m^3 * 1 kg / 1000 gm = 2500 kg / m^3
Express each fraction as a decimal:
- 2 4/100
PLEASE HELP IM STUCK
Step-by-step explanation:
what is the problem ?
the solution of such a system of 2 equations is the point, where they cross.
this point has the same coordinates for both equations, and that is called the solution.
and we can clearly see that point in the graph :
(-1, 1)
formally we can solve that way
y = 2x + 3
y = -x
therefore,
2x + 3 = -x
3x + 3 = 0
3x = -3
x = -1
y = -x = - -1 = 1
so, we get
(-1, 1) as solution.
find the slope given the following information
(3,7) and (-4,10)
Answer:
m=-3/7
Step-by-step explanation:
m=rise/run=Δy/Δx
m=y2−y1/x2−x1
m=10−7/−4−3
m=3/−7
m=−3/7
y = 3x + 15
3x + 3y = 9
Answer:
[tex]\Large\boxed{x=-3}[/tex][tex]\Large\boxed{y=6}[/tex]
Step-by-step explanation:
Given the system of equations
[tex]1)~y=3x+15[/tex]
[tex]2)~3x+3y=9[/tex]
Divide 3 on both sides of the 2) equation
[tex]3x+3y=9[/tex]
[tex]3x\div3+3y\div3=9\div3[/tex]
[tex]x+y=3[/tex]
Current system
[tex]1)~y=3x+15[/tex]
[tex]2)~x+y=3[/tex]
Substitute 1) equation into the 2) equation
[tex]x+(3x+15)=3[/tex]
Combine like terms
[tex]x+3x+15=3[/tex]
[tex]4x+15=3[/tex]
Subtract 15 on both sides
[tex]4x+15-15=3-15[/tex]
[tex]4x=-12[/tex]
Divide 4 on both sides
[tex]4x\div4=-12\div4[/tex]
[tex]\Large\boxed{x=-3}[/tex]
Substitute the x value into one of the equations to find the y value
[tex]y=3x+15[/tex]
[tex]y=3(-3)+15[/tex]
[tex]y=-9+15[/tex]
[tex]\Large\boxed{y=6}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
30 POINTS FOR THIS QUESTION
Answer:
Perimeter is 4a - 10
Area is a^2 - 5a
Step-by-step explanation:
Two sides of the rectangle are "a" and two sides of the rectangle are "a-5" add all four sides and you get a+a+a-5+a-5 Combine the like terms and you get 4a - 10.
The area is when you multiple the two sides together
A = lw
A - a(a-5) = a^2 - 5a
