Answer:
Step-by-step explanation:
Because of the nature of the information we are given, we have no choice but to use the equation
[tex]y=a(x-h)^2+k[/tex]
and solve for a.
We know by the info that the vertex is (0, 84). We also know that if the vertex is at the origin, and that the base is 42 feet wide, it spans 21 feet to the right of the origin and 21 feet to the left of the origin. That means that we have 2 coordinates from which we need to pick one for our x and y in the equation. I don't like negatives, so I am going to choose the coordinate (21, 0) as x and y. Because this parabola opens upside down, as archways of door openings do, our "a" value better come out algebraically as a negative. Let's see...From the vertex we have that h = 0 and k = 84. So filling in:
[tex]0=a(21-0)^2+84[/tex] and simplifying a bit:
0 = 441a + 84 and
-84 = 441a so
[tex]a=-\frac{84}{441}=-\frac{4}{21}[/tex] Good, a is negative. Your equation is, then:
[tex]y=-\frac{4}{21}x^2+84[/tex]
Answer:
x² = -21y
Step-by-step explanation:
THIS IS THE RIGHT ANSWER I TOOK THE TEST
Polygon ABCD is defined by the points A(-4, 2), B(-2, 4), C(1, 3), and D(2, 2). Match the coordinates of the points of the transformed polygons to their correct values. the coordinates of D′ if polygon ABCD rotates 90° counterclockwise to create A′B′C′D′ (-2, 2) the coordinates of C″ if polygon ABCD rotates 90° clockwise to create A″B″C″D″ (4, -2) the coordinates of A′′′ if polygon ABCD rotates 180° clockwise to create A′′′B′′′C′′′D′′′ (3, -1) the coordinates of B″ if polygon ABCD rotates 270° counterclockwise to create A″B″C″D″ (4, 2)
Answer:
The coordinates of D′ if polygon ABCD rotates 90° counterclockwise to create A′B′C′D′ is at (-2, 2)
The coordinates of C″ if polygon ABCD rotates 90° clockwise to create A″B″C″D″ is at (3, -1)
The coordinates of A′′′ if polygon ABCD rotates 180° clockwise to create A′′′B′′′C′′′D′′′ is at (4, -2)
The coordinates of B″ if polygon ABCD rotates 270° counterclockwise to create A″B″C″D″ is at (4, 2)
Step-by-step explanation:
A transformation is the movement of a point from its initial position to a new position. If a shape is transformed, all its points are also transformed. Types of transformation are reflection, rotation, dilation and translation.
Given Polygon ABCD is defined by the points A(-4, 2), B(-2, 4), C(1, 3), and D(2, 2).
If a point X(x, y) is rotated 90° counterclockwise, the new location X' is at (-y, x)
If a point X(x, y) is rotated 90° clockwise, the new location X' is at (y, -x)
If a point X(x, y) is rotated 180° clockwise, the new location X' is at (-x, -y)
If a point X(x, y) is rotated 270° counterclockwise, the new location X' is at (y, -x)
The coordinates of D′ if polygon ABCD rotates 90° counterclockwise to create A′B′C′D′ is at (-2, 2)
The coordinates of C″ if polygon ABCD rotates 90° clockwise to create A″B″C″D″ is at (3, -1)
The coordinates of A′′′ if polygon ABCD rotates 180° clockwise to create A′′′B′′′C′′′D′′′ is at (4, -2)
The coordinates of B″ if polygon ABCD rotates 270° counterclockwise to create A″B″C″D″ is at (4, 2)
Answer:
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
If a point A(x, y) is rotated 90° counterclockwise, the new point is at A'(-y, x).
If a point A(x, y) is rotated 90° clockwise, the new point is at A'(y, -x). If a point A(x, y) is rotated 180° counterclockwise, the new point is at A'(-x, -y).
If a point A(x, y) is rotated 270° counterclockwise, the new point is at A'(y, -x).
Polygon ABCD is defined by the points A(-4, 2), B(-2, 4), C(1, 3), and D(2, 2).
The coordinates of D′ if polygon ABCD rotates 90° counterclockwise to create A′B′C′D′ is D'(-2, 2)
The coordinates of C″ if polygon ABCD rotates 90° clockwise to create A″B″C″D″ is C"(3, -1).
The coordinates of A′′′ if polygon ABCD rotates 180° clockwise to create A′′′B′′′C′′′D′′′ is A''"(4, -2)
The coordinates of B″ if polygon ABCD rotates 270° counterclockwise to create A″B″C″D″ is B"(4, 2)
A 250.0 kg rock falls off a 40.0 m cliff. What is the kinetic energy of the rock just before it hits the ground (hint: conservation of energy)?
Answer:
kinetic energy body when it hits the ground is 98000 joule
1000joule = 1 kilojoule
, kinetic energy body when it hits the ground is 98 kilo-joule
Step-by-step explanation:
conservation of energy states that total energy of a system remains constant.
Potential energy of body = mgh
m = mass
g = gravitational pull = 9/8 m/s^2
h = height
kinetic energy = 1/2 mv^2
where v is the velocity of body
________________________________________
Total energy for this at any point is sum of potential energy and kinetic energy
total energy at height h
v= 0
PE = 250*9.8*40= 98,000
KE = 1/2 m0^2 = 0
total energy at when ball hits the ground
h=0
PE = 250*9.8*0 =
KE = 1/2 mv^2
_______________________________________\
Applying conservation of energy
Total energy at height h = total energy at ground
98000 = KE
Thus, kinetic energy body when it hits the ground is 98000 joule
1000joule = 1 kilojoule
, kinetic energy body when it hits the ground is 98 kilo-joule
if the gradient of the line joining the points [4,-9]and [-3,h]is -3, find the value of H
Answer:
h = 12Step-by-step explanation:
To find the value of h use the formula for finding the slope of a line
That's
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]
Where ( x1, y1) and (x2 ,y2) are the points
From the question
slope = - 3
The points are [4,-9] and [-3,h]
Substitute these values into the equation
We have
[tex] - 3 = \frac{h + 9}{ - 3 - 4} [/tex]
[tex] - 3 = \frac{h + 9}{ - 7} [/tex]
Cross multiply
That's
- 3(-7) = h + 9
21 = h + 9
h = 21 - 9
We have the final answer as
h = 12Hope this helps you
multiplying polinomiyal(5x+2)(3x+4)
Answer:
(5x+2) (3x+4)
= 15x²+20x+6x+8
= 15 x²+ 26x+8
Hope this helps ^_^
Answer:
Step-by-step explanation:
Use FOIL method
(5x + 2)(3x + 4) = 5x * 3x + 5x *4 + 2*3x +2*4
= 15x² + 20x + 6x + 8 { now add like terms}
= 15x² + 26x + 8
A school system is reducing the amount of dumpster loads of trash removed each week. In week 5, there were 40 dumpster loads of waste removed. In week 10, there were 30 dumpster loads removed. Assume that the reduction in the amount of waste each week is linear. Write an equation in function form to show the amount of trash removed each week. A f(x) = −2x + 40. B f(x) = 2x + 40 C f(x) = −2x + 50 D f(x) = 2x + 50
Answer:
The answer is A f(x) = -2x + 40
Step-by-step explanation:
it has a negative 2 because the dumps are decreasing by 2 every week and x is the amount of weeks and + 40 because that is the amount you started with.
Could you help with maths please? All shown on the picture :)
Answer:
4 is tenths (a) and 5 is hundredths (b)
Step-by-step explanation:
Now, 0.45
0 indicates the ones place (it comes before the decimal)
0.45 can also be written as:
0.4+0.05
= 4/10+5/100
what can we conclude from this?
we can say that 4 is in the tenths whilst 5 is in the hundredths.
therefore, a is 4 and b is 5.
Hope this helps you! :)
Point B is on line segment AC. Given BC=9 and AB=11, determine the length AC.
Answer:
20
Step-by-step explanation:
If point B is on line segment AC, then we know for sure AB + BC = AC.
To understand this better, draw a line segment, then put a point anywhere on the line segment. There are two line segment divided by that point. If you combine those two line segments then you have your original figure.
So 11 + 9 = 20.
I need help answering these two questions
Answer:
Step-by-step explanation:
1. Area=3b*b=300 inches^2
3b^2=300
:3 :3
b^2=100
b=V100inches ^2
b=10 inches
2. Area=4b*3b
so 12b^2=4800
:12 :12
b^2=400
b=V400
b=20 inches
Use the least common denominator of 10 and 15 to solve 2/10+7/15 .
Answer: 2/3
Step-by-step explanation: As you can see, the denominators are different so we need to find a common denominator to add these 2 fractions.
We find the common denominator by finding
the common multiple for these 2 denominators.
Multiples of 10
1 x 10 = 10
2 x 10 = 20
3 x 10 = 30
Multiples of 15
1 x 15 = 15
2 x 15 = 30
As you can see, we have a common multiple of 30.
To get 30 in the denominator of 2/10, multiply top and bottom by 3.
To get 30 in the denominator of 7/15, multiply top and bottom by 2.
So we have 6/30 + 14/30 which is 20/30.
20/30 can be reduced to 2/3.
A trader buys tea for $1200 and sells it for $1500. Per sack of tea he makes a profit of $50. How many sacks of tea did he have?
Answer:
6 sacks
Step-by-step explanation:
Buying Price = $1200
Selling Price = $1500
Total profit = Selling price - Buying Price
= $1500 - $1200
= $300
Given that the profit on each sack of tea is $50
Number of Sacks of Tea = Total Profit ÷ profit per sack
= $300 ÷ 50
= 6 sacks
The number of sacks of tea he has is 6.
The first step is to determine the total profit earned by the trader. Profit is the selling price less the cost price.
Profit = selling price - cost price
$1500 - $1200 = $300
The second step is to divide the total profit by the profit made per sack of tea.
Number of sacks = $300 / $50 = 6
To learn more about division, please check: https://brainly.com/question/194007
If P = (3,4), Find: Rx=1 (P)
Answer:
-1, 4
Step-by-step explanation:
Answer:
Step-by-step explanation:
answer is (-1,4)
30 PTS!! Can someone PLEASE rephrase this? The compass and straightedge is more important in constructing geometric structures than other drawing tools such as rulers and protractors. Because steps taken with a compass and straightedge cannot be seen at first glance and this situation become a problem for students.
Answer:
Step-by-step explanation:
This study investigated three mathematics teachers' construction process of geometric structures using compass and straightedge. The teacher-student-tool interaction was analysed. The study consists of the use of a compass and straightedge by the teachers, the ideas of the teachers about their use, and the observations regarding the learning process during the construction of the geometric structures. A semi-structured interview was conducted with the teachers about the importance of the use of a compass and straightedge to construct geometric structures. It was found that teachers taught compass and straightedge constructions in a rote manner where learning is little more than steps in a process. The study concludes with some suggestions for the use of a compass and straightedge in mathematics classes based on the research results. SUMMARY Purpose and significance: For more than 2,000 years, the way in which geometric structures could be constructed with the help of compasses and straightedges has caught the attention of mathematicians. Nowadays, mathematics curriculums place an emphasis on the use of the compass and straightedge. The compass and straightedge is more important in constructing geometric structures than other drawing tools such as rulers and protractors. Because steps taken with a compass and straightedge cannot be seen at first glance and this situation become a problem for students. However, 'doing compass and straightedge construction early in the course helps students to understand properties of figures'
10 points to the person who answers this question.
Answer:
your answer is
2 X l+b
2 X 6x + 3x
8x + 10...
Bob has taken out a loan of $15,000 for a term of 48 months (4 years) at an interest rate of 6.5%. Using the amortization table provided, what will be his total finance
charge over the course of his loan?
Monthly Payment per $1,000 of Principal
Rate 1 Year 2 Years 3 Years 4 Years 5 Years
6.5% $86.30 $44.55 $30.65 $23.71 $19.57
7.0% $86.53 $44.77
$30.88
$23.95
$19.80
7.5% $86.76 $45.00
$31.11
$24.18
$20.04
8.0% $86.99 $45.23
$31.34
$24.41
$20.28
8.5% $87.22 $45.46
$24.65
$24.65
$20.52
9.0% $87.45 $45.68
$31.80
$24.89
$20.76
A.
$355.65
O
B.
$975.00
C.
$1,682.40
D.
$2,071.20
E. $17,071.20
Reset
Next
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Answer:
D. $2071.20
Step-by-step explanation:
The table tells you that Bob's monthly payment on a 4-year loan at 6.5% will be $23.71 per thousand borrowed. The sum of those 48 payments is ...
48 × $23.71 = $1138.08
That means, Bob pays $138.08 in total finance charge for each $1000 he borrows. He is borrowing 15 times $1000, so his total finance charge will be ...
finance charge = 15 × $138.08 = $2071.20 . . . matches choice D
What is the 6th row of Pascal's triangle?
Answer:
1, 6, 15, 20, 15, 6, 1
Plz help me with this problem guys
If 2x3 – 4x2 + kx + 10 is divided by (x + 2), the remainder is 4. Find the value of k using remainder theorem. Please help :)
The polynomial remainder theorem states that the remainder of the division of a polynomial [tex]P(x)[/tex] by [tex]x-a[/tex] is equal to [tex]P(a)[/tex].
Therefore
[tex]P(-2)=4\\2\cdot(-2)^3 - 4\cdot(-2)^2 + k\cdot(-2) + 10=4\\-16-16-2k=-6\\-2k=26\\k=-13[/tex]
Solving Inequalities and graphing them.
Answer:
I used to know this not anymore sry g
I don’t really understand this
Answer
pretty sure its a or c, sorry I cant be more specific
Step-by-step explanation:
Find the slope and the y-intercept of the line.
- 8x+4y=-4
Write your answers in simplest form.
slope:
.
08
Undefined
X
$
?
y-intercept: 1
Answer:
slope - (2x)
y-intercept - (-1)
Step-by-step explanation:
-8x + 4y = - 4
4y = 8x - 4
y = 2x - 1
HELP HELP HELP Sally can paint a room in 4 hours. Joe can paint a room in 6 hours. How
long will it take if they paint the room together? I’m not sure if it’s 1.4
Answer:
2 hrs, 24 min
Step-by-step explanation:
Sally: in one hour, she can paint 1/4 of the room.
Joe: in one our, he can paint 1/6 of the room
Hour one: 1/4+1/6=3/12+2/12=5/12
1÷5/12=1*12/5=12/5
12/5= 2 & 2/5 hours, or 2.4 hours, or 2 hrs 24 minutes
Answer: 2.4 hours
Step-by-step explanation:
1/4 1/6
LCM
3/12+2/12=5/12 repricical 12/5 =2.4
A man traveled to his country home, a distance of 150 miles and then back. His average rate of speed going was 50 miles an hour and his average return speed was 30 miles per hour. His average rate of speed for the entire trip was Need help will mark brainlist
Answer:
37.5 mi/h
Step-by-step explanation:
time = distance / speed
On the trip 'going', the time was (150 mi)/(50 mi/h) = 3 h.
On the return trip, the time was (150 mi)/(30 mi/h) = 5 h.
__
speed = distance / time
The average speed for the whole trip was ...
speed = (150 mi +150 mi)/(3 h +5 h) = (300 mi)/(8 h) = 37.5 mi/h
His average rate of speed was 37.5 miles per hour.
4x + 5 = x + 26 need help
Answer:
x = 7
Step-by-step explanation:
4x + 5 = x + 26
4x - x = 26 - 5
3x = 21
x = 21/3
x = 7
Check:
4*7 + 5 = 7 + 26
28 + 5 = 33
6) By which least number should each of the following numbers be divided to make them perfect squares?
a) 3920
3920|2
1960|2
980|2
490|2
245|5
49|7
7|7
1
[tex]3920=2^4\cdot5\cdot7^2=(2^2)^2\cdot5\cdot7^2[/tex]
It's 5
The product of 2 rational numbers is -16/9 . If one of the numbers is -4/3 find the other plz fast
Answer:
4/3
Step-by-step explanation:
let the other number be x.
-4/3 x=-16/9
x=-16/9×-3/4=4/3
Please help!
Suppose that [tex]\alpha[/tex] is inversely proportional to [tex]\beta[/tex]. If [tex]\alpha=4[/tex] when [tex]\beta=9[/tex], find [tex]\alpha[/tex] when [tex]\beta=-72[/tex]
Answer:
The answer is
[tex] \alpha = - \frac{1}{2} [/tex]Step-by-step explanation:
From the question
[tex]\alpha[/tex] is inversely proportional to [tex]\beta[/tex] is written as
[tex] \alpha = \frac{k}{ \beta } [/tex]where k is the constant of proportionality
When
[tex]\alpha[/tex] = 4[tex]\beta[/tex] = 9Substituting the values into the formula
we have
[tex]4 = \frac{k}{9} [/tex]
cross multiply
k = 4 × 9
k = 36
So the formula for the variation is
[tex] \alpha = \frac{36}{ \beta } [/tex]
when
[tex]\beta[/tex] = - 72
That's
[tex] \alpha = \frac{36}{ - 72} [/tex]
Simplify
We have the final answer as
[tex] \alpha = - \frac{ 1}{2} [/tex]Hope this helps you
A triangle and the coordinates of its vertices is shown in the coordinate plane below. Enter the area of this triangle in square units, rounded to the nearest tenth. square units
Answer:
22 units²
Step-by-step explanation:
1/2b*h=area
You can either count the units or use the distance formula.
[tex]d = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } [/tex]
b = 4 units
h = 11 units
area = (1/2*4)*11 = 22 units²
Solve for x. 23x +2=15x+48x+6
Answer:
[tex]x = - \frac{1}{10} [/tex]Step-by-step explanation:
23x +2 = 15x+48x+6
To solve for x group like terms
That's
Send the constants to the right side of the equation and those with variables to the left side
We have
23x - 15x - 48x = 6 - 2
Simplify
- 40x = 4
Divide both sides by -40
[tex] \frac{ - 40x}{ - 40} = \frac{4}{ - 40} [/tex]We have the final answer as
[tex]x = - \frac{1}{10} [/tex]Hope this helps you
Solve x∕4 + y∕3 = 1 for x.
Answer:
x = [tex]\frac{12-4y}{3}[/tex]
Step-by-step explanation:
Given
[tex]\frac{x}{4}[/tex] + [tex]\frac{y}{3}[/tex] = 1
Multiply through by 12 to clear the fractions
3x + 4y = 12 ( subtract 4y from both sides )
3x = 12 - 4y ( divide both sides by 3 )
x = [tex]\frac{12-4y}{3}[/tex]
Jonas needs a cell phone. He has a choice between two companies with the following monthly billing policies. Each company’s monthly billing policy has an initial operating fee and charge per text message. Sprint charges $29.95 monthly plus .15 cents per text, AT&T charges $4.95 monthly plus .39 cents per text. Create equations for the two cell phone plans.
Answer:
Since both companies have a different plan, two equations are created to determine which company Jonas should choose with respect to the number of messages sent.
Step-by-step explanation:
- Sprint = $ 29.95 * X (0.15)
- AT & T = $ 4.95 * X (0.39)
One dollar equals 100 cents, so 0.15 cents equals $ 0.0015 dollars.
- Sprint = $ 29.95 * X (0.0015)
- AT & T = $ 4.95 * X (0.0039)
Si Jonas envía 500 mensajes de texto el valor mensual de cada empresa sería de:
- Sprint = $ 29.95 * 500 (0.0015) = 22.46 dollar per month.
- AT & T = $ 4.95 * 500 (0.0039) = 9.65 dollar per month.
The company Jonas should choose is AT&T.
AT&T also charges a little more per number of text messages, but since the phone's value is so low it would take thousands of text messages to compare to Sprint's monthly value.
