Do the data in the table you made support the notion the arch is not a parabola? Explain why.
Answers
The parabola that has the height and width similar to the Gateway arc, gives;
(a) The quadratic equation of the parabola is presented as follows;
[tex] f(x) = -6.991 \times 10^{-3} \cdot x^2 + 4.181 \cdot [/tex]
(b) The completed table is presented as follows;
Width. Height
567. 63.12
478. 225.67
308. 459.2
What is the shape of the graph of a quadratic function?The shape of a quadratic function is a parabola, which is either upward facing or downward facing
(a) The given dimensions of the arc are;
Height = 625
Width at the base = 598
The points on the parabola are therefore;
(0, 0), (598÷2, 625) = (299, 625), (598, 0)
The equation of the parabola is of the form;
f(x) = a•x² + b•x + c, which gives;
f(0) = 0 = a×0² + b×0 + c = c
c = 0
f(299) = 625 = a×299² + b×299 + 0...(1)
f(598) = 0 = a×598² + b×598...(2
(a×598² + b×598) - 2×(a×299² + b×299) = 0 - 2×625
a•178802 = -2×625
a = -2×625 ÷ 178802
a ≈ -6.991 × 10^(-3)
b ≈ 4.181.
The equation is therefore;
[tex] f(x) = -6.991 \times 10^{-3} \cdot x^2 + 4.181 \cdot [/tex]
(b)
The table of values is completed as follows;
When the width is 567 feet, x = 299 - 567÷2 = 15.5
[tex] \displaystyle{f(15.5) = -6.991 × 10^{-3} \times 15.5² + 4.181 \times 15.5 approx 63.12} [/tex]
When the width is 478 feet, x = 299 - 478÷2 = 60
[tex] \displaystyle{f(60) = -6.991 × 10^{-3} \times 60² + 4.181 \times 60 approx 225.67} [/tex]
When the width is 308 feet, x = 299 - 308÷2 = 145
[tex] \displaystyle{f(145) = -6.991 × 10^{-3} \times 145² + 4.181 \times 145 approx 459.2} [/tex]
The table is therefore presented as follows;
Width. Height
567. 63.12
478. 225.67
308. 459.2
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Related Questions
A linear function contains the following points.What are the slope and y-intercept of this function?
Answers
Answer: The slope is 4/5 and the y-intercept is (0,-1)
Step-by-step explanation:
What is equation of straight line in slope-intercept form?
The formula for equation of straight line in slope-intercept form is y = mx +c
where m = slope and c = y-intercept
Analysis
y2-y1/x2-x1
3-(-1)/5-(-0)
=4/5
The slope of the linear function is 4/5
The y-intercept is (0.-1)
Find the missing quantity with the information given. Round rates to the nearest whole percent and dollar amounts to the nearest cent.Original Price = $6.50$ Markdown = $1.30Reduced Price = ?
Answers
Since we have a markdown of $1.30 we just need to substract this amount to the original price, then we have:
[tex]6.50-1.30=5.20[/tex]Therefore the reduced price is $5.20
can you help me with number 2? I am confused
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
The equation of a circle is given as :
[tex](x-a)^2+(y-b)^2=r^2[/tex]comparing with the given equation:
[tex]\text{( x+5)}^2+(y-4)^2=9[/tex]we have that:
[tex]\begin{gathered} \text{Centre ( a, b ) = ( -5, 4)} \\ and\text{ } \\ \text{Radius = }\sqrt[]{9}=\text{ 3} \end{gathered}[/tex]CONCLUSION:
From the detailed explanation, we can see that the correct answer is:
[tex](-5,\text{ 4); r = 3 ( OPTION }C)[/tex]2. Two of your classmates are arguing over the solution to a problem. Rhonda believes that the only method to solving the following theequation below is by using the quadratic equation. Max believes that you can use the quadratic formula but you can also factor theequation. Explain if Rhonda or Max is correct.2x^2-5x=88Some words/phrases to consider using in your response would be:factorFOIL MethodZero-Product PropertyStandard Formquadratic expressionquadratic equationscoefficientperfect square
Answers
Given data:
The given expression is x^2 -6x-7=0.
The given expression can be written as,
[tex]\begin{gathered} x^2-6x=7 \\ x^2-6x+(\frac{6}{2})^2=7+(\frac{6}{2})^2 \\ x^2-2(x)(3)+3^2=7+3^2 \\ (x-3)^2=16 \end{gathered}[/tex]Thus, the number 9 is added on both sides to complete square.
Fill in the reason that justifies the step to solve for x in the diagram Given: QS = 42 X + 3 + 2x = 42 o R A. Substitution PropertyB. Segment Addition Postulate C. Simplify.
Answers
With the Segment Addition Postulate you have that:
[tex]QS=QR+RS[/tex]As you have that 42 is equal to QS, and 42 is equal to X + 3 + 2, you use
write each phrase as an algebraic expression:1) n times 72) 4 minus y3) 13 added to x
Answers
1) n times 7
times means multiplication
7n
A 128 ounce container of hand lotion is separated into 4 ounce sample packs. How many sample packs are created from the large
container?
Please help will give brainlest!!
Answers
Answer:
32
Step-by-step explanation:
Solution
If the total amount of hand lotion is available, then you have 128 ounces of hand lotion.
If 128 oz is put into a number of smaller containers (each one 4 oz) then you have
128/4 containers.
128 / 4 = 32.
You can make 32 containers each one holding 4 ounces. The question uses division to solve.
Find any domain restrictions on the given rational equation:
X+2
-25
+1=
8x
2x-10
Select all that apply.
A. x = 5
127
B. x = -2
C. X = -5
D. x = 0
Answers
The domain restrictions on the rational equation
[tex]\frac{x +2}{x^{2} -25 }+1 =\frac{8x}{2x-10}[/tex] are Options A and C. x = 5 and x = - 5 .
What are domain restrictions?A domain restriction is a prescription or criterion that limits the range of possible values for a function. A domain in mathematics is the collection of all values for which a function produces a result. Domain constraints allow us to create functions defined over numbers that meet our needs.Functions defined in pieces are made up of various functions with distinct domain restrictions. Some functions are not allowed to accept values that would make them undefined.How to find the domain restrictions?
The numbers that makes the denominators zero and the entire expression infinite or undefined are the domain restrictions.
Consider the denominators,
[tex]x^{2}[/tex] - 25 ≠ 0 --(1)
[tex]x^{2}[/tex] ≠ 25
x ≠ 5 and x ≠ -5
2x - 10 ≠ 0 ---(2)
2x ≠ 10
x ≠ 10/2
x ≠ 5
The domain restrictions on the rational equation [tex]\frac{x +2}{x^{2} -25 }+1 =\frac{8x}{2x-10}[/tex] are
x ≠ 5 and x ≠ -5 .
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Angie added a stone border 2 feet in width on all sides of her garden making her harder 12 by 6 feet. What is the area, in square feet, of the portion of the garden that excludes the border?
A. 4
B. 16
C. 40
D. 56
E. 72
Answers
The area, in square feet, of the portion of the garden that excludes the border is 40.
What is the area of the rectangle?The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
We have been given that Angie added a stone border of 2 feet in width on all sides of her garden making her harder 12 by 6 feet.
Length = 12 ft
Width = 6 ft
The dimension of the garden that excludes the border of 2 feet are;
Length = 12 ft- 2 = 10 ft
Width = 6 ft - 2= 4 ft
Thus, Area = length × Width
Area = 10 x 4
Area = 40 square feet
Hence, the area, in square feet, of the portion of the garden that excludes the border is 40.
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An item is regularly priced at $65. Lena bought it on sale for 60% off the regular price. How much did Lena pay?
Answers
The regular price of an item is $65
Lena bought it on sale for 60% off the regular price.
Then it means that she paid only (100% - 60% = 40%) of the price.
Let us find the 40% of $65
[tex]\frac{40}{100}\times\$65=\$26[/tex]Therefore, Lena paid only $26 for the item.
Draw a sketch of f(x) = (x-4)^2+5. Plot the point for the vertex, label the coordinates as a maximum or minimum, draw and write the equation for the axis of symmetry
Answers
Given the function:
[tex]f(x)=(x-4)^2+5[/tex]the given function is a quadratic function
The graph of the function is as shown in the following picture
As shown the function has a minimum point at ( 4, 5 )
So, vertex = ( 4, 5 )
And Axis of symmetry: x = 4
2. What is an algebraic expression for each phrase?a. the product of 9 and a number tb. the difference of a number x and 1/2c. the sum of a number m and 7.1 d. the quotient of 207 and a number n
Answers
The algebraic expression for each phrase would be the following:
a. the product of 9 and a number t would be expressed as:
9*t
b. the difference of a number x and 1/2 would be expressed as:
x - 1/2
c. the sum of a number m and 7.1 would be expressed as:
m + 7.1
d. the quotient of 207 and a number n would be expressed as:
207 / n
Using the formula C =5/9(F −32), find C when F is −58∘.? C∘
Answers
ANSWER
C = -50 degree Celcius
STEP-BY-STEP EXPLANATION:
What to find? The value of C in degree Celcius
Given Parameters
F = -58 degree Fahrenheit
The formula is given below
[tex]C=\text{ }\frac{5}{9}(F\text{ - 32)}[/tex]Substitute the value of into the equation
[tex]\begin{gathered} C\text{ = }\frac{5}{9}(-58\text{ - 32)} \\ \text{Solve the expression inside the parenthesis first} \\ C\text{ = }\frac{5}{9}(-90) \\ C\text{ = }\frac{-5\cdot\text{ 90}}{9} \\ C\text{ = }\frac{-450}{9} \\ C=-50^oC \end{gathered}[/tex]Hence, the value of C is -50 degrees
At an all-you-can-eat barbeque fundraiser, adults pay $6 for a dinner and children pay $4 for a dinner. 212 people attend and you raise $1,128. What is the total number of adults and the total number of children attending? A)140 adults and 72 children B)72 adults and 140 children C)142 adults and 70 children D)70 adults and 142 children
Answers
A)140 adults and 72 children
Explanation
Step 1
Let x represents the number of childrend attending
Let y represents the number of adults attending
then
total cost for the children=4x
total cost for the adults=6y
if you raise 1128,
[tex]4x+6y=1128\text{ Equation(1)}[/tex]Now, 212 people attend,Hence
[tex]x+y=\text{212 Equation(2)}[/tex]Step 2
solve for x and y
a)isolate x in equation (2), then replace in equation (1)
[tex]\begin{gathered} x+y=212 \\ x=212-y \\ \text{now, replace} \\ 4x+6y=1128 \\ 4(212-y)+6y=1128 \\ 848-4y+6y=1128 \\ 2y+848=1128 \\ \text{subtract 848 in both sides} \\ 2y+848-848=1128-848 \\ 2y=280 \\ d\text{ivide boths ides by 2} \\ \frac{2y}{2}=\frac{280}{2} \\ y=140 \end{gathered}[/tex]it means 140 adults are attending
b)replace y=140 in equatin (2) to find x
[tex]\begin{gathered} x+y=212 \\ x+140=212 \\ \text{subtract 140 in both sides} \\ x+140-140=212-140 \\ x=72 \end{gathered}[/tex]so, the number of children is 72 and 72 children
Given parallelogram JKLM, what could the expression 180 - (3x + 8) represents? Explain.
Answers
Based on the given figure, you can conclude:
The expression 180 - (3x + 8) represents a supplementary angle to the angle (3x + 8). This angle would be an angles subtended from side KL to a line that is a prolongation of line JK.
in a triangle one angle is three times the smallest angle and the third angle is 45 more than twice the smallest angle. find the measure of all 3 angles. Hint: the angles of a triangle add up to 180.
Please show me full steps. I need help.
Answers
The angles are 22.5°, 67.5° and 90°.
How to calculate the angle?Let the smallest angle = x
Total angles in a triangle = 180°
One angle is three times the smallest angle. This will be 3x.
The third angle is 45 more than twice the smallest angle. This will be:
= (2 × x) + 45
= 2x + 45
The angles will be:
x + 2x + 45 + 3x = 180
6x + 45 = 180
Collect like terms
6x = 180 - 45
6x = 135
Divide
x = 135 / 6
x = 22.5°
Smallest angle = 22.5°
The other angles will be calculated by substitutibg 22.5° for x. This will be:
3x = 3 × 22.5 = 67.5°
Also, 2x + 45 = 2(22.5) + 45 = 90°
This illustrates the concept for angles in a triangle.
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for the polyhedron, find the missing numberneed a whole number of faces
Answers
The Euler's polyhedron formula states that, for a polyhedron with F faces, E edges and V vertices, we have:
F + V - E = 2
For E = 12 and V = 6, then we have:
F + 6 - 12 = 2
F = 2 + 12 - 6
F = 8
y=-2x+6x+8 how do i find the vertex
Answers
Then the vertex is (3/2, 25/2)
A general equation of a parabola is:
[tex]y=ax^2\text{ + bx + c; the vertex of a parabola is the point (h,k) where h = -b/2a}[/tex]This way you find the value of h
Since h is a value of x, you can find the corresponing value of y by using the original equation:
[tex]y=ah^2\text{ + bh + c}[/tex]and this will be the value of K
Find the coordinates P (-9, 10.5) after translating it 3 units left and 11 units up.
Answers
ANSWER
P'(-12, 21.5)
EXPLANATION
We are given the cordinates of P as:
P(-9, 10.5)
Cordinate points are given as A(x, y)
We want to translate it 3 units left and 11 units up.
That means that we are moving it 3 units towards the negative side of the x axis and 11 units towards the positive side of the y axis.
Therefore, we will subtract 3 from the x cordinate and add 11 to the y cordinate.
Therefore, the translation is:
P(-9, 10.5) => P'(-9 - 3, 10.5 + 11)
=> P'(-12, 21.5)
The cordinates of P have been translated.
The Entertainment Center accumulates the following cost and net realizable value (NRV) data at December 31.
Inventory
Cost
Categories Data
Camera
Camcorders
DVDs
$11,600 $10,100
8,500
8,000
Market
Data
13,500
12,900
What is the lower-of-cost-or-net-realizable-value of the inventory?
Lower-of-cost-or-net-realizable-value $
Answers
The lower-of-cost-or-net-realizable-value of the inventory is $31000.
Define net-realizable-value.An asset's worth is often assessed using the net realizable value (NRV) approach for inventory accounting. It is discovered by calculating the difference between the asset's anticipated selling price and all of the expenses related to the asset's eventual sale. The cash sum that a corporation anticipates receiving is known as net realizable value (NRV). Consequently, net realizable value is also known as cash realizable value. The terms "net realizable value" and "current assets" are frequently used in relation to inventory and accounts receivable.
Given,
Camera
Cost = 11600
Market value = 10100
(Market value is less. so 10100.)
Camcorders
Cost = 8500
Market value = 8000
( Market value is less so 8000)
DVD
Cost = 13500
Market value = 12900
(Market value is less, so 12900)
the lower-of-cost-or-net-realizable-value of the inventory:
= 10100 + 8000 + 12900
= 31000
The lower-of-cost-or-net-realizable-value of the inventory is $31000.
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True or False? When the first coordinate is positive, that point is located to theright of the x-axis.TrueFalse
Answers
True
Explanations:Note that when you have the position of a point as (x, y), the first coordinate is the x - axis while the second is the y - axis.
Also note that, to the right of the x axis, you have positive numbers while you have negative numbers to the left.
We can then conclude that When the first coordinate is positive, that point is located to the right of the x-axis
What is the y-intercept of f(x) =(3/5)^x?
Answers
Answer:
the y intercept is -1.
Step-by-step explanation:
the y intercept is -1 because it goes through the point (0,-1)
I need help with this statistics question please!
Answers
The margin of error of a z-confidence interval is given by: [tex]$M=z \frac{\sigma}{\sqrt{n}}$$[/tex]
The margin of error of a z-confidence interval is 142.945936.
How to estimate the margin of error?The margin of error of a z-confidence interval exists given by:
[tex]$M=z \frac{\sigma}{\sqrt{n}}$$[/tex]
Where, z is the critical value.
[tex]$\sigma$[/tex] be the population standard deviation.
n is the sample size.
The first step is finding the critical value, which exists z with a p-value of [tex]$\frac{1+\alpha}{2}$[/tex] in which [tex]$\alpha$[/tex] is the confidence level.
In this problem, [tex]$\alpha[/tex] = 0.95, therefore, z with a p-value of 1 + 0.95 / 2 = 0.975, which means that it is z = 1.96.
The population standard deviation exists of 12.2 meters, thus [tex]$\sigma[/tex] = 12.2.
We want a width of 5 , thus a margin of error of M = 2. Therefore, we have to simplify the equation for the margin of error for n.
Let the equation be [tex]$M=z \frac{\sigma}{\sqrt{n}}$$[/tex]
substitute the values in the above equation, we get
[tex]$2=1.96 \frac{12.2}{\sqrt{n}}$[/tex]
[tex]$2 \sqrt{n}=1.96(12.2)$[/tex]
simplifying the above equation, we get
[tex]$\sqrt{n}=\frac{1.96(12.2)}{2}$[/tex]
[tex]$(\sqrt{n})^2=\left(\frac{1.96(12.2)}{2}\right)^2$[/tex]
n = 142.945936
Therefore, the value of n = 142.945936.
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Study the diagram, where AB and C'D are chords that intersect inside of the circle at point P, which is not the center.
Answers
Answer:
answer of the given question
Rewrite the equation by completing the square. x^2 + 4x − 21 = 0
( x + _ )^2 = _
Answers
[tex] {x}^{2} + 4x + ( \frac{4}{2} )^{2} - 21 = 0 + ( \frac{4}{2} )^{2} \\ {x }^{2} + 4x + 4 = 4 + 21 \\ (x + 2)(x + 2) = 25 \\ {(x + 2)}^{2} = 25[/tex]
ATTACHED IS THE SOLUTION
I would like to learn the long multiplication so I can teach my fifth grader this math problem
352x20=
Answers
Answer: 7040
Step-by-step explanation:
1
352
x20
——-
000
7040
+
———
7040
i will drop a picture
Answers
B) y= -1/2x -4
1) Let's start by picking two points from that line: (0,3) and (-2,-1). Now we can plug them into the slope formula and find out the slope of that line:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\Rightarrow m=\frac{-1-3}{-2-0}=\frac{-4}{-2}=2[/tex]2) Examining that graph we can see that when x=0 y=3, so the linear coefficient b is 3. Therefore we can write the equation as y= 2x-3.
2.2) Since the question wants a perpendicular line, then the slope of this perpendicular line must be reciprocal and opposite to m=2, so:
[tex]m\perp=-\frac{1}{2}[/tex]So, plugging the given point (6,-7) we can find out the linear coefficient of that perpendicular line:
y=mx +b
-7 = 6(-1/2) +b
-7 =-3 +b
-7+3 = b
b=-4
3) Hence, the answer is y= -1/2x -4
what is the geometric sequence of 2 4
Answers
an = ar^ (n- 1)
for n = 3 (3rd term)
r = common ratio = 4/ 2 = 2
a3 = 2 (2) ^ (3-1)
a3 = 2 (2)^2
a3 = 2 (4)
a3 = 8
n= 4 (4th term)
a4 = 2 (2)^(4-1)
a4 = 2 (2)^3
a4 = 2 (8)
a4 = 16
2, 4 , 8 , 16
Systems of 2 Equations Word Problems
Answers
Let x and y be the two numbers
x + y = 72 ------------------------------(1)
x - y = 4 ----------------------------------(2)
Add equation (1) and equation (2)
2x = 76
Divide both-side of the equation by 2
x = 38
substitute x = 38 into equation (1) and then solve for y
38 + y = 72
subtract 38 from both-side of the equation
y = 72 - 38
y = 34
The two numbers are 34 and 38
2.Find the range of thisquadratic function.1-3-2-11y = x2 + 2x-27А-1 < y< ooB- < y < oo
Answers
Okay, here we have this:
Considering that the range of a function is the complete set of all possible resulting values of the dependent variable (y), we can see in the graph of the function that:
The values of the variable "y" go from -1 to plus infinity, this mean that the range is:
-1≤y<∞
Finally we obtain that the correct option is the first option.