Answers
The values for the parabola are found as-
Focus, a = 4x axis vertex; h = 5y-axis vertex; k = 8What is meant by the parabola?A parabola is a curve equation in which a point on a curve is equidistant out of a fixed point and a fixed line. The fixed point is known as the parabola's focus, and also the fixed line is known as the parabola's directrix. It is also worth noting that the fixed point does not lie just on fixed line.The focus of the parabola is the point (a, 0).The parabola's directrix is the line sketched parallel to a y-axis and passing through point (-a, 0). The directrix is perpendicular to a parabola's axis.For the given question.
The total horizontal distance covered by water is 10 feet.
The maximum height attained by nozzle of water is 8 feet.
Thus, the vertex of parabola (h, k) = (5, 8)
The nozzle was 4 foot above the ground, a = 4.
The equation of parabola becomes;
y = a(x - h)² + k
y = 4(x - 5)² + 8
Thus, the equation of parabola becomes; y = 4(x - 5)² + 8.
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Related Questions
look and solve this:
Answers
a) fractions; 15.3/3
b) yes, it is a rational number
solution to this inequality 15+x<24
Answers
Answer: x < 9
Step-by-step explanation:
Move all terms not containing x to the right side of the inequality.
John held a garage sale. He priced all the items at a dime or a quarter. His sales totaled
less than $5. Write an linear inequality that describes this situation.
Answers
John held a garage sale. He priced all the items at a dime or a quarter, his sales totaled less than $5, the solution is shaded region in quadrant I.
What is a slope?In mathematics, line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. The letter m is frequently used to represent the slope; reason for this usage is unclear, but it can be found in O'Brien's (1844) and Todhunter's (1888) formulations of equation for a straight line as "y = mx + b" and "y = mx + c," respectively.
He priced all items at a dime or a quarter. His sales totaled less than $5
Since dime =$ 0.10=$0.10 and the quarter =$0.25=$0.25
Let x=x= the number of the items sold for a dime
Let y=y= the number of the items sold for a quarter
0.10x+0.25y<5
0.10x+0.25y<5
Inequality in the slope-intercept form
0.10x+0.25y Subtract 0.10x from both sides
0.25y<-0.10x+5 Divide both sides by 0.25
Subtract 0.10x from both sides
[tex]y= -\frac{2}{5}x+20\\[/tex]
The slope is, [tex]-\frac{2}{5}[/tex] and the y- intercept is 20
Since inequality sign is << so, draw a dashed line
Test point (0,0)(0,0)
Substituting the values 0 for x and 0 for y,
[tex]y < -\frac{2}{5}x+20\\\\0 < -\frac{2}{5}(0)+20\\\\0 < +20[/tex]
Since inequality is true
So, (0,0)(0,0) is solution of the inequality
Shade region containing (0,0)(0,0).
The graph below shows all possible solutions
Since boundary line is dashed and the number of items is always positive
The solution is shaded region in quadrant I
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a farmer is building a fence to enclose a rectangular area consisting of 2 separate regions. the 4 walls and one additional vertical segment to separate the regions are made up of fencing. if the farmer has 648 feet of fencing what are the dimensions of the region which enclose the maximum area?
Answers
The dimensions of the region which enclose the maximum area is a side of 162 feet and vertical segment of 108 feet
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the side parallel to the vertical segment and y represent the other side. If the farmer has 648 feet of fencing, hence:
x + x + y + y + x = 648
3x + 2y = 648
y = 324 - 1.5x
Area (A) = xy
A = xy
A = x(324 - 1.5x)
A = 324x - 1.5x²
The maximum area is at A' = 0, hence:
A' = 324 - 3x
324 - 3x = 0
3x = 324
x = 108 feet
y = 324 - 1.5(108) = 162 feet
x = 108 feet, y = 162 feet
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find the domain of each function
f(x)=(x+5)/x
Answers
FOR THE GIVEN FUNCTION WE WILL HAVE TO CHECK DENOMINATOR PART BECAUSE IT IS THE ONE WITH THE GREATER EFFECT ON MAKING THE FUNCTION UNDEFINED.
THE FUNCTION WILL BE UNDEFINED ONLY IF x=0
THIS BRINGS US TO A CONCLUSION OF SAYING THE DOMAIN IS ALL REAL NUMBERS BUT X IS NOT EQUAL TO 0
2) What is the equation for the below function? Show your work!
Answers
The equation for the given function passing through (0,5) and (4,0) is equal to y = (-5 /4)x +5.
As given in the question,
As shown in the graph drawn we have
( x₁ , y₁ )=(0, 5)
( x₂ , y₂ )=( 4, 0)
Equation for the given function passing through ( x₁ , y₁ ) = (0, 5) and
( x₂ , y₂ )=( 4, 0) is given by :
( y - y₁ )/ (x -x₁ )=( y₂ - y₁ )/( x₂ - x₁ )
⇒( y -5) / (x -0)=( 0 -5)/( 4 -0)
⇒( y - 5) /x=-5/4
⇒y -5=(-5/4)x
⇒y=(-5/4)x + 5
Therefore, the equation for the given function passing through (0,5) and (4,0) is equal to y=(-5 /4)x +5.
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b) A different pattern is made using 20 straight lines
and 14 arcs.
The straight lines and arcs are made from metal.
20 straight lines cost £12
cost of one straight line: cost of one arc = 2:3
Work out the total cost of metal in the pattern.
26.4
Answers
total cost of metal in the pattern is £24.6
What is ratio and proportion ?To compare two values is to use a ratio. A proportion is formed when two ratios have the same value. Choose whether the ratio is part-to-part or part-to-whole before you write it.
Calculation20 straight line cost £12
12 ÷ 20 = 0.6 per straight line
straight line : cost of one arc = 2:3
arc = 0.6 x (3/2) = 0.9
total = 12 + 14 x 0.9
= 12 + 12.6
= 24.6
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Please help me my mom is very upset and I’m grounded
Answers
Which transformation
of y = f(x) moves the graph
7 units to the left and 3 units down?
1) y=(x+7)-3
2) y=f(x+7)+3
3) y=f(x-7)-3
4) y=f(x-7)+3
Answers
7 units left would be (x-7)
And 3 units down would be (y-7)
can someone tell me how to solve this
Answers
Answer:
See below
Step-by-step explanation:
If there are no other forces on the body. the NET force is the result of the two forces acting to the left and total 5 N Left
Answer: The correct answer is Net Force = 5, Direction = N
Step-by-step explanation: Net force in the same direction is cumulative and simply added together, where opposing forces are subtracted. In this case, they are in the same direction or to the left.
City carpet advertises that they can instal 1,200 square feet of carpet in 2 1/2 hours They charge $40 per hour for a special install of 1,920 squares free how much will they charge
Answers
Total charge for 1,920 squares feet is $160.
What is basic algebra ?The area of mathematics known as algebra aids in the representation of circumstances or problems as mathematical expressions. To create a meaningful mathematical expression, it takes variables like x, y, and z together with mathematical operations like addition, subtraction, multiplication, and division. Algebra is used in all areas of mathematics, including trigonometry, calculus, and coordinate geometry. 2x + 4 = 8 is a straightforward algebraic expression.In algebra, symbols are used, and operators are used to connect the symbols to one another. It is more than just a mathematical idea; it is a skill that we all utilize on a regular basis without even being aware of it.
Given that :City carpet advertises that they can instal 1,200 square feet of carpet in 2 1/2 hours They charge $40 per hour.
City carpet can install 1,200 square feet of carpet in 2.5 hours
In 1 hour they can install [tex]\frac{1200}{2.5} =480 squares feet[/tex]
In 4 hour they can install 1920 squares feet carpet
They charge $40 per hour
So total charges for 1920 square feet will be 4 ×40
= $160
Total charge for 1,920 squares feet is $160.
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tell wheter the lines through the given points are parallel, perpendicular or neither.
a. Line 1: (2,-3), (-4, -6)
Line 2: (-3, 2), (2, -8)
b. Line 1: (-4, -5), (4, 1)
Line 2: ( 6, 10), (-3, -2)
c. Line 1: (0, -4), (-2, -8)
Line 2: (-1, 5), (1, 9)
Help I need this by tomorrow :c
Answers
Answer:
a. Perpendicular
Make sure to read the step-by-step explanation to figure out how to do the other 2.
Step-by-step explanation:
I will not be providing answers to all three, but I will answer the first one (this is, so you don't depend on people to solve this for you).
Parallel lines have one thing in common, their slope. Two lines that have the same slope never intersect because they are both facing the same direction and moving the same distance. So, you can find the slope of two lines by using the slope formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m_1=\frac{-6-(-3)}{-4-2}=\frac{-3}{-6}=\frac{1}{2}\\m_2=\frac{-8-2}{2-(-3)}=\frac{-10}{5}=-2[/tex]
This is evidence that the two lines are not parallel. But, by finding the slope, we can conclude that it is perpendicular.
This brings me to how to identify perpendicular lines. The slope of perpendicular lines is negative reciprocals. A reciprocal is just a fraction that is flipped, and it's negative. For example, [tex]\frac{-2}{3}[/tex]'s negative reciprocal would be [tex]\frac{3}{2}[/tex]. The negative of -2/3 is a positive, and the reciprocal of 2/3 is 3/2. So, the negative reciprocal is 3/2.
How does this apply to what I said earlier?Well, [tex]-2[/tex] is the negative reciprocal of [tex]\frac{1}{2}[/tex]. The reciprocal of [tex]\frac{1}{2}[/tex] is 2, and the negative of 2 is -2. So, simply, lines 1 and 2 are perpendicular.
Use this method to solve the other questions. If they don't have the same slope and aren't negative reciprocals, then they are neither.
Answer:
Step-by-step explanation:
To solve this problem, we use the following formula:
[tex]\displaystyle\\\boxed {\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} }[/tex]
a) (2,-3) (-4,-6)
[tex]x_1=2\ \ \ \ x_2=-4\ \ \ \ y_1=-3\ \ \ \ y_2=-6[/tex]
[tex]\displaystyle\\\frac{x-2}{-4-2} =\frac{y-(-3)}{-6-(-3)} \\\\\frac{x-2}{-6}=\frac{y+3}{-6+3} \\\\\frac{x-2}{-6} =\frac{y+3}{-3}[/tex]
Multiply both parts of the equation by -3:
[tex]\displaystyle\\\frac{x-2}{2}=y+3\\\\0.5x-1=y+3\\\\0.5x-1-3=y+3-3\\\\0.5x-4=y\\[/tex]
⇔ Line 1: y=0.5x-4 m₁=0.5
(-3,2) (2,-8)
[tex]\displaystyle\\\frac{x-(-3)}{2-(-3)}=\frac{y-2}{-8-2} \\\\\frac{x+3}{2+3} =\frac{y-2}{-10} \\\\\frac{x+3}{5} =\frac{y-2}{-10} \\\\[/tex]
Multiply both parts of the equation by -10:
[tex]-2(x+3)=y-2\\-2x-6=y-2\\-2x-6+2=y-2+2\\-2x-4=y[/tex]
⇔ Line:y=-2x-4 m₂=-2
[tex]\displaystyle\\m_1=-\frac{1}{m_2}[/tex]
⇒ The given lines are perpendicular
b)
(-4,-5) (4,1)
[tex]\displaystyle\\\frac{x-(-4)}{4-(-4)}=\frac{y-(-5)}{1-(-5)} \\\\\frac{x+4}{4+4}=\frac{y+5}{1+5} \\\\\frac{x+4}{8} =\frac{y+5}{6} \\[/tex]
Multiply both parts of the equation by 6:
[tex]\displaystyle\\\frac{6(x+4)}{8} =y+5\\\\\frac{3}{4} x+3=y+5\\\\\frac{3}{4} x+3-5=y+5-5\\\\\frac{3}{4} x-2=y\\[/tex]
⇔ Line 1: y=(3/4)x-2 m=3/4
(6,10) (-3,-2)
[tex]\displaystyle\\\frac{x-6}{-3-6} =\frac{y-10}{-2-10} \\\\\frac{x-6}{-9} =\frac{y-10}{-12} \\\\[/tex]
Multiply both parts of the equation by -12:
[tex]\displaystyle\\\frac{-12(x-6)}{-9} =y-10\\\\\frac{4}{3}x-8=y-10 \\\\\frac{4}{3}x-8+10=y-10+10\\\\\frac{4}{3}x+2=y[/tex]
⇔ Line 2: y=(4/3)x+2 m=4/3
⇒ The given lines are neither perpendicular and neither parallel
c)
(0,-4) (-2,-8)
[tex]\displaystyle\\\frac{x-0}{-2-0} =\frac{y-(-4)}{-8-(-4)} \\\frac{x}{-2}=\frac{y+4}{-8+4} \\\\\frac{x}{-2}=\frac{y+4}{-4}[/tex]
Multiply both parts of the equation by -4:
[tex]2x=y+4\\2x-4=y+4-4\\2x-4=y[/tex]
⇔ Line 1: y=2x-4 m₁=2
(-1,5) (1,9)
[tex]\displaystyle\\\frac{x-(-1)}{1-(-1)} =\frac{y-5}{9-5} \\\\\frac{x+1}{1+1} =\frac{y-5}{4}\\\\\frac{x+1}{2} } =\frac{y-5}{4} \\[/tex]
Multiply both parts of the equation by 4:
[tex]2(x+1)=y-5\\2x+2=y-5\\2x+2+5=y-5+5\\2x+7=y[/tex]
⇔ Line 2: y=2x+7 m₂=2
m₁=m₂
⇒ The given lines are parallel
Use the digits 1, 2, 3 and 4 to fill in each rectangle in order to
create the sum closest to 50. Each digit may only be used once.
+
Manewering the Middle 110
Answers
The sum will be 46 which is the nearest combinational value that could be deduced from the digits 1, 2, 3, and 4.
Let's check all the combinations which can be possibly used,
34 + 21 = 46, which is 4 numbers less than 50 so far the nearest.
43 + 12 = 55, which is 5 numbers more than 50.
32 + 41 = 73, which is 23 numbers more than 50.
32 + 14 = 46, which is 4 numbers less than 50 so far the nearest.
23 + 41 = 64, which is 14 numbers more than 50.
So the two combinations are deduced after permutation and a combination of numbers that are 3 and 4 + 2 and 1 and another is 3 and 2 + 1 and 4.
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What is the slope-intercept form of the equation of the line that contains the points (1, 4)and (0, 1)?
Answers
Answer:
3
Step-by-step explanation:
m=y2-y1÷x2-x1
4-1÷1-0=3÷1=3
Cual es elvalor absoluto del opuesto de 2,5 ?
Answers
Answer:|2.5|
Step-by-step explanation:
En este caso el valor absoluto de 0 a |2.5| es 2.5. Esto se debe a que ya sea que cambies la ecuación o no para que sea igual a otro número, la respuesta SIEMPRE será 2.5. ¡Espero que esto haya ayudado! :D
Grayce has three diamonds that weigh 0.275 g each. Morgan has two diamonds that weigh 0.412 g each. Who has more grams of diamonds?
Answers
Grayce has 0.825 g of diamonds and Morgan has 0.824 g of diamonds. Grayce has more grams of diamonds
Calculating weightsFrom the question, we are to determine the person that has more grams of diamonds
From the given information,
"Grayce has three diamonds that weigh 0.275 g each"
and
"Morgan has two diamonds that weigh 0.412 g each"
Thus,
The total mass of Grayce's diamonds is 3 × 0.275 g
3 × 0.275 g = 0.825 g
Also,
The total mass of Morgan's diamonds is 2 × 0.412 g
2 × 0.412 g = 0.824 g
Since 0.825 is greater than 0.824,
Then,
Grayce has more grams of diamonds.
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The integer 6 makes which of the following equations false?
−6(t − 8) = 12
5m + 3 = 3m
t + 5 = 11
9 = 2x − 3
Answers
Answer:
5m+3 =3m
Step-by-step explanation:
−6(t − 8) = 12
-6((6) -8) =12
5m+3=3m
5m-3m=3
2m=3
2(6)≠3
t + 5 = 11
(6) + 5 = 11
9 = 2x − 3
2x = 9+3
2(6) = 12
Amari bought three chicken wings for $4.80 if Morris spent $27.20 how many chicken wings did she buy
Answers
Answer:
24 wings
Step-by-step explanation:
Answer:
17 wings
Step-by-step explanation:
1. first we multiply 3 by 27.20 you get 81.6
2. then we divide 81.6 by 4.80 and we get 17
17 wings
Work out the values of a, b, c and d.
Justify each of your answers.
W
Z
33%
aº
16°
45°
d°
80°
22%
X
Y
Not drawn accurately
Answers
Answer69
Step-by-step explanation:
Kaj needs to order some new supplies for the restaurant where she works. The restaurant needs at least 736 knives. There are currently 155 knives. If each set on sale contains 12 knives, what is the minimum number of sets of knives Kaj should buy?
Answers
The minimum number of sets of knives Kaj should buy if the restaurant needs at least 736 knives is 48. 4 sets of knives
How to find the minimum number of sets of knives Kaj should buy?Number of knives needed by the restaurant = at least 736 knivesNumber of knives currently available at the restaurant = 155 knivesEach set of knives = 12Number of sets of knives needed to buy = x155 + 12x ≥ 736
substract 155 from both sides12x ≥ 736 - 155
12x ≥ 581
divide both sides by 12x ≥ 581 / 12
x ≥ 48.41666666666666
Approximately,
x ≥ 48. 4 sets of knives
In conclusion, the sets of knives kaj needs to buy more is 48. 4 sets of knives
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use the given domain to find the range of function. help please
Answers
The range for the given domain D = {2, -3, 0} of the function f(x) = 2x² + 7 is; R = {7, 15, 25}
What is the Range of the Function?We are given the function as;
f(x) = 2x² + 7
We are given the domain set as;
D = {2, -3, 0}
Now, the range will simply be gotten by plugging in each domain value into the given function to get the output. Thus;
Range when x = 0 is;
y = 2(0)² + 7
y = 7
Range when x = 2 is;
y = 2(2)² + 7
y = 15
Range when x = -3 is;
y = 2(-3)² + 7
y = 25
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a 100 gram chocolate bar is shared equally between 5 students while a separate 100 gram chocolate bar is shared equally between 20 students. which group of students receives the larger amount of chocolate per student?
Answers
Answer:
The 5 students receive the larger amount.
100:5= 20 gram per student
100÷20= 5 gram per student
Step-by-step explanation:
prove me wrong
a shorter solution that probably will get full pts :
Because each group has the same mass of the chocolate bar, whichever group has less students will get a larger amount of chocolate per student (as there are less people receiving)
and here's if you think it is kinda not too detailed :
The first group has each student receiving 100 : 5 = 20 grams of chocolate per student
The second group has each student receiving 100 : 20 = 5 grams of chocolate per student
Both solutions give us a conclusion of : The group with 5 students have each of the receiving a larger amount of chocolate.
y’all pls help smakhwhwhdhdj
Answers
Answer:
x = 22° (alternate angles, M//N)
Part 1 pls help with this
Answers
Answer:
Below.
Step-by-step explanation:
1) Alternate exterior angles
2) Alternate interior angles
3) Alternate exterior angles
4) Alternate exterior angles
5) Alternate interior angles
6) Corresponding angles
7)Alternate exterior angles
8) Alternate interior angles
9) Corresponding angles
10) Corresponding angles
When two parallel lines are intersected by a transversal 8 angles are formed.
Alternate exterior angles: These angles are located outside the parallel lines but on the opposite side of the transversal.
Alternate interior angles:
These angles are located inside the parallel lines but on the opposite side of the transversal.
Corresponding angles: These angles are located at the same relative position on the same side of the transversal.
Which of the following are rational numbers?
5.48
78.541
97
42.111...
Answers
Answer:
5.48, 78.541 and 97
Step-by-step explanation:
A rational number by definition refers to a number that is in the form of k/m and in which k and m are integers and m is not equal to 0.
Let me give you some examples:
1/32/41/59/3From our question,
5.48 = 137/25 hence rational number78.541 = 78541/1000; rational 97 = 97/1; rational 42.111..... = 4211111*/100000: irrational number. It is recurring hence not a rational number.Therefore 5.48, 78.541 and 97 are rational numbers
Select the correct answer.
Which inequality is represented by the number line?
Answers
Answer:
I think C. Correct me if I am wrong.
Step-by-step explanation:
Hope it helps! =D
Answer: The answer is C.
Step-by-step explanation: Because I use a graphing calculator
Name the property used in the given expression −33/ 57 × −7/ 28 = −7/ 28 × −33/ 57 . With steps and solution pls
Answers
Step-by-step explanation:
as the other answer said, if is the commutative property of multiplication (the same as for addition, as multiplication is just a shortcut form of special additions) :
a × b = b × a
you need a solution ? you mean, you need this multiplication done and simplified, right ?
you know that
a/b × c/d = (a×c)/(b×d)
so,
-33/57 × -7/28 = -33/57 × -7/(4×7) =
= -33/57 × -1/4 = (-33×-1)/(57×4) =
= 33/228
Show your work. Please help I really need!
Answers
a. Expression for length L in terms of x is L = 1040 - 2x
b. Expression for the area of the pasture in terms of L and x, A = Lx
c. Expression for the area of the pasture in terms of x only = x (1040 - 2x)
d. The area of the pasture will enclose greater than or equal to 60 square feet
How to find the area in terms of the given dimensionsGiven data
length of fence = 1040 ft
length if the pasture = L
width of the pasture = x
Expression for length L in terms of x
from the figure we can see that the fenced part is 3 sides which include 2 widths and 1 length. So we represent this with the expression below
L + x + x = 1040
L + 2x = 1040
L = 1040 - 2x
Expression for the area of the pasture in terms of L and x
Area of the pasture, A = L * x
A = Lx
Expression for the area of the pasture in terms of x only
= L * x
and L = 1040 - 2x
= x (1040 - 2x)
A sentence that makes the area to enclose at least 60 000 square feet.
from A = Lx
we have
A = Lx ≥ 60
The area of the pasture will enclose greater than or equal to 60 square feet
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i need your helppppppp
Answers
The result of the function n(x)= [tex]-1-\frac{1}{3}x+1\frac{2}{3}[/tex] when x = -2,0 and 5
n(-2) = 4/3
n(0) = 2/3
n(5) = -1
The function is n(x)= [tex]-1-\frac{1}{3}x+1\frac{2}{3}[/tex]
The function is an equation which expression the relationship between one variable and another variable. If one variable is independent variable then another variable will be dependent variable.
The function is n(x)= [tex]-1-\frac{1}{3}x+1\frac{2}{3}[/tex] when x= -2,0 and 5
Here we have to substitute the value of x in the given function
n(-2) = -1-(1/3)(-2)+5/3
= -1+(2/3)+5/3
= 4/3
n(0) = -1-(1/3)(0)+5/3
= -1+(5/3)
= 2/3
n(5) = -1-(1/3)(5)+5/3
= -1-(5/3)+(5/3)
= -1
Hence, the result of the function n(x)= [tex]-1-\frac{1}{3}x+1\frac{2}{3}[/tex] when x = -2,0 and 5
n(-2) = 4/3
n(0) = 2/3
n(5) = -1
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f (x) = 2x-1 and g (x) = x+2. Find f(g(x))
Answers
Answer:2x^2+3x-2
Step-by-step explanation:
2x-1*x+2=2x^2+3x-2
Answer:
2x+3
Step-by-step explanation:
so first you plug in g(x) in for x in f(x). this is how it will look like
2(x+2)-1
then you distribute the 2 in both terms in the parenthesis.
2(x)+2(2)-1
after that, you multiply them and you will get this
2x+4-1
subtract 4 and 1 and this is your answer
2x+3