The equation of the parabola that has its x-intercepts at (-1.6, 0) and (-3.2, 0) and its y-intercept at (0, 25.6) is 5x² + 8x - 25.6
How to write the equation of the parabola with the x intercepts at (-1.6, 0) and (-3.2, 0)The x intercept refers to the value of x when y = 0 this otherwise known as the roots of the polynomial equation.
The intercept form of parabolic equation is
y = a(x - p)(x - q)
where
p and q are roots
a = constant
writing the equation at (-1.6, 0), (-3.2, 0)
y = a( x + 1.6 ) ( x + 3.2 )
passing through point (0, 25.6)
25.6 = a( 0 + 1.6 ) ( 0 + 3.2 )
25.6 = 5.12a
a = 5
substituting into the equating gives
y = a(x - p)(x - q)
y = 5( x + 1.6 ) ( x + 3.2 )
expanding the equation gives
= 5(x² + 3.2x - 1.6x - 5.12)
= 5(x² + 1.6x - 5.12)
= 5x² + 8x - 25.6
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Determine which of the following statements is true concerning the values described in column #1 and column #2.
Column #1
Column #2
The x-coordinate of the vertex of the equation The x-coordinate of the vertex of the equation y=2x²-4x+12
y=4x²+8x+3
The value found in column #1 is greater than the value found in column #2
The value found in column #1 is less than the value found in column #2.
The value found in column #1 is equivalent to the value found in column #2.
The relationship between column #1 and column #2 cannot be determined by the information given.
The value of the vertex for the x-coordinate is less in column 1 as compared to the value of the vertex of x -the coordinate for column 2.
What are the coordinates and vertex of an equation?
When a graph crosses its symmetry axes, the vertex formula in mathematics may be used to get the vertex coordinate of a parabola. The vertex point is often represented by (h, k). We are aware that a parabola's conventional equation is y=a[tex]x^{2}[/tex]+bx+c. The vertex in this case should be near the base of the U-shaped curve if the coefficient [tex]x^{2}[/tex] is positive. The apex of the U-shaped curve should be at the top of the coefficient [tex]x^{2}[/tex] is negative.
In the given question, It is given:
The two equations are:
[tex]y=2x^{2}-4x+12[/tex]
and,
[tex]y=4x^{2}+8x+3[/tex]
We have to find the vertex of the x-coordinate.
So, for the equation: [tex]y=2x^{2}-4x+12[/tex]
In Column 1:
[tex]\begin{aligned}y &=-2 x^2-4 x+12 \\&=-2\left(x^2+2 x-6\right) \\&=-2\left((x+1)^2-7\right)\end{aligned}[/tex]
So, By comparing the equation, we can say that the x-coordinate of the vertex in the column is -1.
So, for the equation:[tex]y=4x^{2}+8x+3[/tex]
In Column 2:
[tex]\begin{aligned}y &=x^2-4 x+3 \\&=(x-2)^2+(-1)\end{aligned}[/tex]
So, By comparing the equation, we can say that the x-coordinate of the vertex in the column is 2.
So, Option b is correct.
Hence, The value of the vertex for the x-coordinate is less in column 1 as compared to the value of the vertex of x -coordinate for column 2.
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Quetion
Enrique plan to ell hi car and place a 6-line ad. Hi paper charge $42 for the firt two line and$6. 75 per extra line, to run the ad for one week. What will Enrique' ad cot to run for three week?
The cost of running the ad for three weeks by Enrique will be $207.
To estimate the overall cost for three weeks, we need the amount for one week. Further, we need the cost for six lines advertisement. So, performing calculation for the cost of advertisement of six lines in one week.
Total cost in one week = charge for first two lines + number of additional lines × cost of each additional line
Keep the values in formula. Out of six lines, the additional will be 4 as (6-2=4).
Total cost in one week = 42 + 4×6.75
Performing multiplication
Total cost in one week = 42 + 27
Performing addition
Total cost in one week = $69
Cost for three weeks = 69×3
Performing multiplication
Cost for three weeks = $207
Thus, Enrique will pay $207 for three weeks.
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A6-Sequences and Series
Q1. Below are the first few terms of some important mathematical sequences. State the 7th term
of each sequence:
a) 2, 4, 6, 8, .......
b) 1, 4, 9, 16, ....
c) 1, 8, 27, 64, ....
d) 2, 3, 5, 7, 11, ....
7th term is.
7th term
7th term is .............. (1)
7th term is ........…….…….. (1)
(Total 4 marks)
Answer:
Step-by-step explanation:
7th term of the first sequence is 14
first we need to find out the nth term so,
tn=Ti+(n-1)d
2(n-1)2
2+2n-2
2n+2-2
2n+0
Now we need to find out the 7th term
n=7
2(7)-0
14-0=0
Second sequences 7th term is 33
first we need to find the nth term
1(n-1)3
1+3n-3
3n+1-3
3n-2
so now we need to find 7th term
3(7)-2
35-3
33
the 4th sequence 7th term is 20
Jonas is a runner. He ran m miles last week. His goal this week was to run one mile more than twice the miles he ran last week. If he tripled his goal, write an expression in simplest form to show how many more miles he ran this week compared to last.
Expression for the miles jonas ran this week is 6m + 3 where m is the miles ran in the last week.
Given that jonas ran 'm' miles in last week.
acc. to statement he run one mile more than twice the miles he ran last week, so the equation will now become:
2m + 1 = miles in this week.
Again if he tripled his goal then the equation would become :
3(2m + 1 ) = new goal
6m + 3 = new goal
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In the two functions f and g, f∘g and g∘f are both equivalent to x. Which of the following statements must be TRUE?
A) The two functions are translations of each other.
B) The two functions are inverses of each other.
C) The two functions are reciprocals of each other.
D) The two functions are reflections of each other.
Two functions f and g, f∘g and g∘f are both equivalent to x, then two functions are inverses of each other.
What is a function?A relation is a function if it has only One y-value for each x-value.
A function is a relation in which each element of the domain has a unique image in the co-domain.
Composition of functions refers to the combining of two or more functions such that the output of one function becomes the input for the next function.
Two functions f(x) and g(x) are inverse functions if (ƒ ∘ g)(x) = (g ∘ ƒ)(x) = x.
Hence two functions f and g, f∘g and g∘f are both equivalent to x, then two functions are inverses of each other.
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Find the area of the sas triangle with side lengths 29 and 36 and included angle 62 degrees.
To find the Area of the sas triangle with side lengths 29 and 36 and included angle 62 degrees is 459.36.
A triangle's feature known as SAS, or "Side, Angle, Side," has two sides and an angle that are both known.
The space occupied between the sides of the SAS triangle in a plane can thus be calculated with the use of the SAS triangle area formula.
The formula to find area of SAS triangle is:
Area = ½ ab Sin C = ½ × 29 × 36 × sin 62
Thus, Area = 522 × sin 62 = 522 × 0.88 = 459.36
Hence, Area of SAS triangle with side lengths 29 and 36 and included angle 62 degrees is 459.36.
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find the 7th term of 3,9,27
Answer:
2187
Step-by-step explanation:
1. 3
2. 9
3. 27
4. 81
5. 243
6. 729
7. 2187
If 5p² = 20, what is a possible value of p + 5 ?
Answer:
Okay let's start out with checking what p even equals.
Let's start with using 2 as a possible amount for p
5 x 2 to the 2nd power = 20.
2 is correct. So, p + 5 has a chance of equaling 7.
Step-by-step explanation:
Answer:
p=2
p+5=7
Step-by-step explanation:
5p^2=20
/5. /5
p^2=4
Square root both sides
p=2
Now fill in p into p+5
2+5
7
Hopes this helps please mark brainliest
a cone-shaped paper drinking cup is to be made to hold 27cm3 of water. find the height and radius of the cup that will use the smallest amount of paper.
The height and radius of the cone-shaped cup that will use the smallest amount of paper, that is the maximum volume is 3.72 and 2.632 respectively.
Formula used in the solution is
Volume of the cone= (1/3)π(r^2)h
Area of the cone= πr√(l^2 + r^2)
Given, the volume of the cone is 27 cm^3.
(1/3)π(r^2)h =27
Simplifying the equation to get the value of r.
π(r^2)=81/h
r^2=81/hπ
[tex]r=\sqrt{\frac{81}{\pi h} }[/tex]
Substituting the value of r in area, we get
[tex]A=\pi \sqrt{\frac{81}{\pi h} } \sqrt{h^{2} + \frac{81}{\pi h} }[/tex]
[tex]\frac{dA}{dh} =\pi \sqrt{\frac{81}{\pi h} } \sqrt{h^{2} + \frac{81}{\pi h} }[/tex]
dA/dh=√81 × (π - 162/[tex]h^{3}[/tex]) × 1/√(πh + 81/[tex]h^{2}[/tex])
At dA/dh=0, we will get,
√81 × (π - 162/[tex]h^{3}[/tex]) × 1/√(πh + 81/[tex]h^{2}[/tex])=0
√81 × (π - 162/[tex]h^{3}[/tex])=0
[tex]\pi - \frac{162}{h^{3} }=0[/tex]
Thus, [tex]\pi h^{3} -162=0[/tex]
[tex]\pi h^{3} =162[/tex]
[tex]h^{3} =\frac{162}{\pi}[/tex]
h^3= 51.5662015618
h= 3.7221
Now, substitute h in radius,
[tex]r=\sqrt{\frac{81}{\pi \times 3.7221} }[/tex]
r=2.632
Hence, the height of the cone shaped cup is 3.7221 and the radius is 2.632.
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In 7 hours the depth of the water in Leah's pool increased 28 inches.
The water in Glados's pool had an initial depth of 11 inches. After one
hour the depth increased to 13 inches. After two hours, the depth was
19 inches. Which comparison of the two rates of change is correct?
Answer:
in the first one the water changed by 4 inch every hour and the second one has an increasing 1 to 3 to 5 inches
Step-by-step explanation:
through: (-4, 3), perp. to y = -2x+5
Answer:
y = [tex]\frac{1}{2}[/tex] x + 5
Step-by-step explanation:
Perp means perpendicular?
Perpendicular slopes are the opposite reciprocals of each other. So the slope would be [tex]\frac{1}{2}[/tex]
Use -4 for x and 3 for y and the slope of [tex]\frac{1}{2}[/tex] to find the y intercept
y=mx +b
3 = [tex]\frac{1}{2}[/tex](-4) + b
3 = -2 + b Add 2 to both sides
5 = b
y = mx +b We know the slope (m) is [tex]\frac{1}{2}[/tex] and the y intercept (b) is 5.
y=mx+ b
y = [tex]\frac{1}{2}[/tex] x + 5
X=1 x=-8 Are the two linear equations parallel, perpendicular, or neither?
The two linear equations are parallel lines
What are parallel lines?parallel lines are straight line that never intersects or meet each other.
some features of parallel lines include
the lines will not meetthe slope of the lines are equalthe lines are equal distance apartIn the problem, x = 1 and x = -8 are both vertical lines. In a cartesian coordinate x = 1 is in the positive coordinate and x = -8 is in the negative coordinate
The slope of both lines are zero
The equal distance apart is calculated as
| -8 - 1 | = 9 units
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Use the Pythagorean Theorem to calculate the value of to 1 decimal place
Answer:
19.9
Step-by-step explanation:
As 21 is opposite the right angle this side must be the hypotenuse :
Pythagoras Theorem says :
a² + b² = c²
Where c is the hypotenuse.
Substituting values in gives us (a and b do not matter) :
x² + (√43)² = 21²
Now we simplify :
Using the surd law:
√a ×√a = a
(√43)² = √43×√43 = 43
21² = 441
x² + 43 = 441
Subtract 43 from both sides :
x² + 43 - 43 = 441 - 43
x² = 398
Square root both sides :
x = √398
√398 = 19.9 to 1 d.p.
Hope this helped and have a good day
Camilla visited her parents in Belmont and took them out to dinner. Their dinner cost $112, and the sales tax in Belmont is 9%. If Camilla left an 18% tip on the $112, how much in total did she pay?
Answer:
$366.24
Step-by-step explanation:
Camilla visited her parents in Belmont and took them out to dinner. Their dinner cost $112, and the sales tax in Belmont is 9%. If Camilla left an 18% tip on the $112, how much in total did she pay?
dinner cost $112
sales tax: $112 * 1.09 = $122.08
tip: $112 * 1.18 = $132.16
total: 112 + 122.08 + 132.16 = $366.24
help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Based on the compound interest, Erica owes a total of $10865 after 5 years
How to determine the amount Erica needs to pay?The given variables can be represented as:
Loan amount P = $5300Rate of interest, R = 8%Time to pay back the loan, t = 6 yearsThe compound interest formula is given as
A = P(1 + r/n)^nt
Also from the question, we have
n = 12
This is so because the loan is compounded 12 times in a year as a result of being compounded monthly
Solving further, we replace the variables with their values in the above equation
A = 5300 * (1 + (8%/12))^(6*12)
Evaluate the expression
A = 10865
Hence, the amount owed is $10865
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Kelly is knitting a scarf for her brother. It took her 13 hour to knit 38 foot of the scarf. How fast is kelly's knitting speed, in feet per hour?.
Ariana invested $400 in an account paying an interest rate of 3.8% compounded
monthly. Assuming no deposits or withdrawals are made, how much money, to the
nearest ten dollars, would be in the account after 11 years?
The amount to be in the account after 11 years, assuming no deposits or withdrawals is $602.880
Given,
Ariana invested $400 in an account paying an interest rate of 3.8% compounded monthly.
What is the formula for the future value on compound interest?
A = P(1+r)ⁿ
P = $400
r = 3.8%
Amount after 11 years.
r = 3.8/100
= 0.38
= 400 (1+3.8/100)¹¹
= $602.880
Therefore the amount after 11 years the amount will be $602.880.
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20000(4)^6 as a deceimal
Answer:8.192x10^7
Step-by-step explanation:
Answer:
81,920,000
Step-by-step explanation:
20000(4096)
81920000
Hopes this helps please mark brainliest
Savio leaves his home at 07 30 to drive to work.
He drives a distance of 50 miles.
Savio thinks he drives at an average speed of 40 miles per hour,
(a) If Savio is correct, at what time will he arrive at work?
Csecond chancel Review your Carter and Naomi are stood on opposite sides of a phone mast. The phone mast is 130 m tall. The angle of elevation from Carter to the top of the mast is 73°. The angle of elevation from Naomi to the top of the mast is 41°. Work out the distance between Carter and Naomi. Give your answer to the nearest metre.
If from a 130 m tall phone mast the angle of elevation are 73° and 41° then the distance between Carter and Naomi is nearly 189 meters.
What is angle of elevation?
The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.
According to the given question:
Let the distance of Carter and Naomi from from 130m tall phone mast be x and y respectively.
Angle of elevation from Carter to top is 73°
tan 73° = 130/x
Similarly angle of elevation from Naomi to top 41°
tan 41° = 130/y
Now, total distance between Carter and Naomi is x + y
∴ x + y = 130[ 1/tan 73° + 1/tan 41°]
= 130[ 1/3.27 + 1/0.87]
= 130 [ 4.14/2.8449]
≈ 189 meters
Hence the distance between Carter and Naomi is 189 meters.
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(input-output values) that fit with this function rule: f(x)=2x−1
Input-output values that fit with this function rule: f(x)=2x−1 is (0,-1),(1,1),(2,3) and (3,5).
Given function:
f(x) = 2x - 1.
if x = 0
y = 2(0) - 1
= 0 - 1
= -1
(0,-1)
if x = 1
y = 2(1) - 1
= 2 - 1
= 1
(1,1)
if x = 2
y = 2(2) -1
= 4 - 1
= 3
(2,3).
if x = 3
y = 2*3 - 1
= 6 - 1
= 5
(3,5).
Therefore Input-output values that fit with this function rule: f(x)=2x−1 is (0,-1),(1,1),(2,3) and (3,5).
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What is SAS SSS and SAS?.
SSS, SAS, ASA, AAS, and HL, or Hypotenuse Leg for right triangles only, stand for Side Side Side, Side Angle Side, Angle Side, and Angle Angle Side, respectively.
What is SAS?According to the SAS rule, two triangles are said to be congruent if any two sides and any angle between the sides of one triangle are equal to the corresponding two sides and angle between the sides of the second triangle.
What is SSS?According to the SSS rule, two triangles are said to be congruent if all three sides of one triangle are equal to the corresponding three sides of the second triangle.
What is ASA?According to the ASA rule, two triangles are said to be congruent if any two angles and the side included between the angles of one triangle are equal to the corresponding two angles and side included between the angles of the second triangle.
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3) Which equation correctly matches the graph below?
answer option:
y=5/3x +5
y= -3/5 +5
y= 5/3x +5
y=5/3x-5
Which of the following shows the line with a slope of -1/2 through the point (-3, 2) graphed correctly?
The linear equation is written as:
y = (-1/2)*(x + 3) + 2
And its graph can be seen in the image at the end.
Which one is the graph of the line?Here we don't have the options, so I will post the graph of the line.
A linear equation with a slope a and a known poing (h, k) is written as:
y = a*(x - h) + k
Here we know that the slope is -1/2 and the point is (-3, 2), then the linear equation is:
y = (-1/2)*(x + 3) + 2
To graph the linear equation we just need to find two points on the line and connect them with a line, we already know one, so let's find another.
If we use x = 1, then:
y = (-1/2)*(1 + 3) + 2
y = (-1/2)*4 + 2
y = -4/2 + 2 = -2 + 2 = 0
y = 0
The other point is (1, 0)
With these two we can draw the graph you can see below.
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Two cars leave at the same time but travel at different speeds. car a travels 20 miles per hour faster than car b. in the time it takes car a to travel 350 miles, car b travels 250 miles. find the speed of car a.
Two cars leave at the same time but travel at different speeds. Car a travels 20 miles per hour faster than car b. In the time it takes car a to travel 350 miles, car b travels 250 miles.
The number of hours needed for Car B to overtake Car A is greater then 5 hours, Car A = 60km/h; Car B= 75km/h.
After h hours, the number of kilometers covered by Car A is 60*h
After h hours, the number of kilometers covered by Car B is 75(h-1)… since Car B started one hour later.
For Car B to overtake Car A,
75(h-1) > 60h
75h- 75 > 60h
75h - 60h > 75
15h > 75
h > 75/15
h > 5 hours
Hence the answer is, the number of hours needed for Car B to overtake Car A is greater then 5 hours, Car A = 60km/h; Car B= 75km/h.
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Torie, Lara and Dalia collect shells on a beach.
They decide to share the shells between them in the ratio
3:5:2.
If Lara and Dalia have 70 shells between them, how many
shells does Torie have?
Torie will have 30 shells.
What is ratio?The relationship in quantity, amount, or size between two or more things.
Given that, Torie, Lara and Dalia collect shells on a beach. They decide to share the shells between them in the ratio 3:5:2. Lara and Dalia have 70 shells between them,
Let them have each 3x, 5x and 2x shells.
5x+2x = 70
7x = 70
x = 10
Then, Torie = 3*10 = 30
Hence, Torie will have 30 shells.
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there is a four-stage hypothesis about the origin of life. what are the stages in the correct order?
3) What is the difference between the sum of all the even numbers between 305 and 609 and the sum of all the odd numbers between 304 and 608?
PLEASE HELP
The difference between the sum of the numbers is 0.
3) What is the difference between the sum of all the even numbers between 305 and 609 and the sum of all the odd numbers between 304 and 608?To find the sum of even number between 305 and 609, and the sum of all the odd numbers between 304 and 608, we use the sum of an arithmetic progression.
Note that there are 103 even numbers between 305 and 609. The even numbers start from 306 and end at 608.
Also, there are 103 odd numbers between 304 and 608. The odd numbers start from 305 and end at 607.
Using the sum of an arithmetic progression S = n/2(a + T) where
n = number of terms of AP, a = first term and T = last term.Now, for the sum of even numbers between 305 and 609, we have
n = 103a = 304 and T = 608So, S = n/2(a + T)
= 103/2(304 + 608)
= 103(912)/2
= 103(456)
= 46968
Also, for the sum of odd numbers between 304 and 608, we have
n = 103a = 305 and T = 607So, S' = n/2(a + T)
= 103/2(305 + 607)
= 103(912)/2
= 103(456)
= 46968
So, the difference between S and S' is d = S - S'
= 46968 - 46968
= 0
So, the difference is 0.
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Nathan took his car in for service and repairs. He had a coupon for 15% off. Original Prices • Labor $299.88 • Parts $307.54 • Other $74.71 Which amount is closest to Nathan's total costs after the 15% discount and including 6% sales tax? [Assume tax is applied after the discount is applied.]
The amount that is closest to Nathan's total costs after the 15% discount and including 6% sales tax, assuming tax is applied after the discount is applied would be $624. That is option A.
What is discount on sales?The discount on sales is the amount of money that is being deducted from the original price of an item by a seller to their customers.
The original price for labor= $299.88
The original price for parts = $ 307.54
The original price for others = $ 74.71
The total original price = $682.13
The discount of on the total price = 15%.
That is;
= 15/100 × 682.13
= 10,232.95/100
= $102.32
When discount is removed from the original price;
= 682.13 - 102.32
= $579.81
When the tax is acted on the discount total sales;
= 6/100 × 579.81
= $3,478.86/100
= $34.79.
The total cost after discount and tax would be;
= 579.81 + 34.79
= $614.59
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What is the change to the graph of y = - 3x - 2 when the slope is changed to - 1/3?
Answer:
The change will be that of run over run.
Step-by-step explanation:
In the equation, y= -3x - 2 it moves 3 spaces down directly on the y-axis and 1 space to the right from there in the direction of the x-axis. Although, if you were to change the slope from -3 to -1/3 it will move 1 space down directly on the y-axis and 3 spaces to the right from there in the direction of the x-axis.
Image in green is the equation of: y= -3x - 2
Image in red is the equation of: y= -1/3x - 2
