The first error in Jan'ai's work in determining the considered function is given by: Option D: She incorrectly determined the x-coordinate of the vertex.
What are the coordinates of vertex for a quadratic function?For a quadratic function of the form [tex]y = ax^2 + bx + c[/tex], its vertex form is obtained as:
[tex]y = ax^2 + bx + c\\y =a(x^2 + bx/a) + c\\y = a(x^2 + 2(b/2a)x + (b/2a)^2 -(b/2a)^2 )+ c\\y = a(x^2 + 2(b/2a)x + (b/2a)^2) -a \times (b/2a)^2 + c\\\\y = a(x+b/2a)^2 - a \times (b/2a)^2 + c[/tex]
For the form [tex]y = a(x-h)^2 + k[/tex], the vertex has coordinates (h, k)
Thus, for the obtained equation [tex]y = a(x+b/2a)^2 - a \times (b/2a)^2 + c[/tex], we get the coordinates of vertex as:
[tex]h = -b/2a[/tex], [tex]k = c - a\times(b/2a)^2[/tex]
Thus, the coordinates of vertex of [tex]y = ax^2 + bx + c[/tex] is:
[tex](h,k) = (-b/2a, c - a \times (b/2a)^2 )[/tex]
The missing steps of work of Jan'ai are:
Begin to write a function in factored form. [tex]f(x) = a(x+1)(x-5)[/tex]Substitute x = 0, y = f(x) = -25 to determine a. [tex]-25 = a(0+1)(0-5)[/tex]Simplify and solve to find a. [tex]a=5[/tex]Rewrite the function. [tex]f(x) = 5(x+1)(x-5)[/tex]Rewrite in standard form. [tex]f(x) = 5x^2-20x-25[/tex]Find the x-coordinate of the vertex. [tex]x = -20/2(5) = -20/10; x = -2[/tex]Find the y-coordinate of the vertex.[tex]y = 5x^2-20x-25[/tex]
[tex]y = 5(-2)^2-20(-2)-25[/tex]
[tex]y = 35[/tex]
so (-2,35) is the coordinate of the vertex, which denotes the minimum.
So, as we see, in the 5th step, Jan'ai had the quadratic function [tex]f(x) = 5x^2-20x-25[/tex],
Comparing this to [tex]f(x) = ax^2 + bx + c[/tex], we get a = 5, b = -20, c = -25
The vertex's x-coordinate will be on -b/2a = -(-20)/ 2(5) = 20/10 = 2
But Jan'ai didn't putted that negative sign before b. in the 6th step.
Thus, the first error in Jan'ai's work in determining the considered function is given by: Option D: She incorrectly determined the x-coordinate of the vertex.
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Answer:
The answer is D on edge
Step-by-step explanation:
Write the equation of the line that is parallel to the line y=3x+7 and passes through the
point (-4,-14).
Answer:
y = 3x - 2
Step-by-step explanation:
If two lines are parallel to each other, they have the same slope slopes.
The first line is y = 3x + 7. Its slope is 3. A line parallel to this one will also have a slope of 3.
Plug this value (3) into your standard point-slope equation of y = mx + b.
y = 3x + b
To find b, we want to plug in a value that we know is on this line: in this case, it is (-4, -14). Plug in the x and y values into the x and y of the standard equation.
-14 = 3(-4) + b
To find b, multiply the slope and the input of x (-4)
-14 = -12 + b
Now, add 12 to both sides to isolate b.
-2 = b
Plug this into your standard equation.
y = 3x - 2
This equation is parallel to your given equation (y = 3x + 7) and contains point (-4, -14)
Hope this helps!
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Use your findings from problem 8-79 to answer the questions below. Recall that the diameter of a circle is a segment with endpoints on the circle that passes through the center. The length of the segment is also called the diameter.
Answer:
See below ↓↓↓↓
Step-by-step explanation:
a) Area of circle with radius 10 units
A = πr²A = 3.14 x (10)²A = 3.14 x 100A = 314 sq. unitsb) Circumference of circle with diameter 7 units
r = d/2 = 7/2 unitsC = 2πrC = 2 x 22/7 x 7/2C = 2 x 11 = 22 unitsc) Diameter of circle with area 121π square units
A = πr²121π = πr²r² = 121r = √121 = 11 unitsd = 2r = 2 x 11 = 22 unitsd) Area of circle with circumference 20π units
C = 2πr20π = 2πrr = 10 unitsA = πr²A = 3.14 x (10)²A = 3.14 x 100A = 314 square unitsArea of circle with radius 10 units is 314 square units,
Circumference of circle with diameter 7 units is 22 square units,
Diameter of circle with area 121π square units is 22 units and
Area of circle with circumference 20π units is 314 square units
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
a) Area of circle with radius 10 units
A = πr²
A = 3.14 x (10)²
A = 3.14 x 100
A = 314 sq. units
b) Circumference of circle with diameter 7 units
C = πd
C = 3.14×7
C = 21.98 units
c) Diameter of circle with area 121π square units
A = πr²
121π = πr²
r = √121 = 11 units
d = 2r = 2 x 11 = 22 units
d) Area of circle with circumference 20π units
C = 2πr
20π = 2πr
r = 10 units
A = πr²
A = 3.14 x (10)²
A = 3.14 x 100
A = 314 square units
Hence, Area of circle with radius 10 units is 314 square units, Circumference of circle with diameter 7 units is 22 square units, Diameter of circle with area 121π square units is 22 units and Area of circle with circumference 20π units is 314 square units
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Jody ships her sculptures in boxes with a length of 2 1/3 ft. a width of 2 ft., and a height of 1 2/3 ft. What is the maximum number of sculptures she can ship one box?
The soccer players were required to run 6 more laps per day than the tennis players for five straight days. If the soccer players ran 45 laps total during these days, how many laps did the tennis players run each day?
Answer:
3 laps per day
Step-by-step explanation:
Divide 45 laps by 5 days to get how many laps they ran per day
45/5 = 9 laps per day
The tennis players run 6 less laps per day than the soccer players so subtract 6 laps from 9 laps to get their daily laps
6-9 = 3 laps per day
Hello! Does anyone know how to do this I already tried some but I got them wrong. Giving brainliest!!
Answer:
The only right angles are between the lines (O,F) and (Q,D)
Step-by-step explanation:
by examination. The tangental line goes through the same point the diameter line goes through so to be tangental it has to be 90 degrees on each side.
the side lengths of a triangle are 10,26 and 24 which one is the hypotenuse
a.24
b.26
c.10
d.50
The hypotenuse is the longer of the 3 sides:
answer: b.26
Answer:
[tex]\huge\boxed{\bf\: b. \: 26 \rightarrow hypotenuse }[/tex]
Step-by-step explanation:
Consider a right angled triangle with sides as 10, 26 & 24 units.
Here, we need to find the hypotenuse of the triangle.
The hyptenuse is the side which is opposite to the right angle (90°) & is also the longest side of the triangle.
Then, among the given values, we can clearly say that 26 > 10, 24.
Therefore, [tex]\boxed{\bf\: 26 \: units }[/tex] is the hypotenuse of the triangle with side lengths as 10, 26, 24 units.
[tex]\rule{150pt}{2pt}[/tex]
there are 90 girls in third year, 25 of whom Study biology what percentage of third year girls study biology
Answer:
27.7% of third year girls study biology
GIVEAWAY!!!
50PTS + BRAINLIEST
4(2x)−8x+4
Answer:
4(2x) - 8x + 4
4 × 2x = 8x
8x - 8x + 4
= 4
Done!
A figure was moved 5 units to the right, then a
mirror image was made. Which transformations were used? Rotation, dilation, reflection, translation
Answer:
Step-by-step explanation:
First a translation then a reflection.
You are filling a 5-L fish tank using a 250-mL container. How many full containers are required to fill the fish tank? PLEASE HELP NOW
Answer:
20 containers
Step-by-step explanation:
5L = 5000ml
so,
5000/250 = 20 containers
I hope my answer helps you.
fill 5L tank using 250 ml container .
to find:how many full containers are required to fill the tank.
solution:1 L= 1000 mL
1000 mL/250mL = 4
1 L= 4 full containers
4 containers x 5 liters = 20 full containers.
so, 20 full containers are required to fill the fish tank.
Brad has a garden with dimensions 12 feet long x 7 feet wide. He wants to enlarge the garden to an area of 119 square feet. How much farther will he need to extend the length of the garden to attain his desired area?
Answer:
5 more feet
Step-by-step explanation:
iff you add 5 more feet to 12 ft., you'll get 17 ft., and you can multiply that by 7 to get 119
Simplify the expression.
3.8m + 7 - 2.8m
(Use the operation symbols in the math palette as needed. Simplify your answer. Use whole numbers or decimals for any numbers in the expression.)
Answer:
m + 7
Step-by-step explanation:
→ Collect like terms
3.8m - 2.8m + 7
→ Simplify
m + 7
find the base of the triangle !
please hurry! Thank you!
Answer:
given
area of triangle = 48
height(h)=12
base(b) =‽
now,
area of triangle(a) =1/2 base×height
48=1/2 b×12
48=b×6
b=8
Can someone help me????
Answer:
x= 3(y+8)/
8
y= 8(x-3)/
3
A hiker travels 6 mph, which is 3/11 the rate of a cyclist. Suppose the cyclist is following behind the hiker. How fast does the distance between them decrease?
How fast the distance between them decrease is 16mph
How to calculate the speed of an object?Given the following parameters
Speed of the hiker = 6mph
If is it 3/11 the rate of a cyclist, then the rate of the cyclist will be:
6 = 3x/11
3x = 66
x = 22mph
Distance between them = 22 - 6
Distance between them = 16mph
Hence how fast the distance between them decreases is 16mph
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Answer: 28 mph
Step-by-step explanation:
Hello people ~
what's the area of a rectangle whose width is 16m and length is 13m?
Answer:
208 m²
Step-by-step explanation:
[tex]16 \: m\times 13 \: m = 208 \: {m}^{2} [/tex]
If andre collects $9.80, how many cups did he sell?
Answer:
we need more information
Plss help will give Brainliest!!!!
Answer:
1/6
Step-by-step explanation:
can somebody help me
Answer:
Area = 202 in^2
Step-by-step explanation:
Divide those into pieces to solve for each area and then add the area together.
Left Rectangle:
13 in * 4 in = 52 in^2
Right Rectangle:
15 in * 10 in = 150 in^2
Total Area = 117 in^2 + 150 in^2 = 202 in^2
Of 500 people, 100 wear glasses.
Write the number of people who do not wear glasses as a fraction of the total number of people
Answer:
400/500 people do not wear glasses.
Step-by-step explanation:
There are a total of 500 people, 100 of those people wear glasses. 500-100=400. Therefore, 400 people do not wear glasses out of the 500 people.
Answer:
500/500-100/500=400/500
I believe it is
What is the surface area?
Answer:
24 ft^2
Step-by-step explanation:
The srface area consisists of 2 triangles and 3 rectangles.
Surface area = 2 * 1/2 *4 * 3 + 1*4 + 1*5 + 1*3
= 12 + 4 + 5 + 3
= 24 ft^2.
Bill can paint a closet in 2 hours. Joe can paint the same in 7 hours. Write equation that can used to find long paint the closet working together. Let represent the number both to complete the job.
Answer:
14/9 hours
Step-by-step explanation: 1/2+1/7=9/14, so 1/(9/14)=14/9
how do you do 35x56 i need help please
Answer:
EASY-
Step-by-step explanation:
First you need to write down the equation into what I call box form.Find n that makes this equation true.
4^4 + 4^4 + 4^4 + 4^4
________________ = 4^n
4^3 + 4^3
Answer:
4^4 + 4^4 + 4^4 + 4^4=20
4^3 + 4^3=128
I can't get the real answer
but what can
Make a number line and mark the points that represent the following
values of x
2x <6
A circular flower bed in a botanical garden has a radius of 4 feet. what is the area of the flower bed? use 3.14 for π . enter your answer to the nearest hundredths place in the box. question 7 options:
The area of the flower bed has a radius of 4 feet is 16π or 50.24 square feet.
What is a circle?It is a locus of a point drawn an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.
A circular flower bed in a botanical garden has a radius of 4 feet.
Then the area of the flower bed will be
Area = π r²
Area = π × 4²
Area = 16π
Area = 16 × 3.14
Area = 50.24 square feet.
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The air quality index, or aqi, measures how polluted the air is in your city and assigns a number based on the quality of the air. over 100 is "unhealthy". the number of days the aqi exceeds 100 in a given year is modeled by the following quadratic regression equation: n = 1.76 t squared minus 13.32 t 41.00 let n represent the number of days the aqi exceeds 100 in a given year. approximately how many days did the aqi exceed 100 in the year 1988? round to the nearest whole day. (let t represent the number of years since 1990. therefore, t = 0 corresponds to the year 1990.) a. 60 days b. 75 days c. 61 days d. 21 days
The number of days in which the air quality index exceed 100 in the year 1988 is 75 days. Then the correct option is B.
What is a function?The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.
The air quality index (AQI) is given by the function.
[tex]\rm n = 1.76t^2-13.32 +41[/tex]
Where n be the number of days the AQI exceeds 100 in a given year.
For [tex]\rm t = -2[/tex], then we have
[tex]\rm n = 1.76(-2)^2-13.32(-2) +41\\\\n = 7.04+26.64+41\\\\n = 74.68 \approx 75[/tex]
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I have 39 test to do and it takes me approximately 5 minutes to do one. How long will it take me to do all of them?
Answer:
3 hrs and 15 minutes :)
Step-by-step explanation:
We can solve this by multiplying :)
39 x 5 = 195 minutes
195/60 = 3 hrs and 15 minutes :)
Have an amazing day!!
Please rate and mark brainliest!!
Answer: 195 minutes or 3 hours and 15 mintues
Step-by-step explanation:
We will multiply the number of tests by the amount of time it takes to do each test.
39 total tests * 5 minutes = 195 minutes
195 minutes or 3 hours and 15 mintues
James earns $418 per week and has one exemption. His office’s payroll software is broken and can only compute the withholding for zero exemptions. What weekly salary with 0 exemptions would give the closest exemption to what James should have?
James should earn a weekly salary of $ 432.76 with 0 exemptions to give the closest exemption.
How to estimate the salary without exemption
In this question, we should estimate the salary earned before one exemption and find the equivalent brute salary with no exemptions. The expected salary is equal to product the brute salary minus the product of the tax rate and brute salary.
According to the table we have the expected salary after one exemption:
[tex]x = 418\cdot \left(1-\frac{19.66}{100} \right)[/tex]
[tex]x = 335.82[/tex]
After a quick inspection to the salary column for zero exemptions, we find that percentage associated to a salary with no exemptions: ([tex]r = 22.40\,\%[/tex])
[tex]C = \frac{335.82}{1-\frac{22.40}{100} }[/tex]
[tex]C = 432.76[/tex]
James should earn a weekly salary of $ 432.76 with 0 exemptions to give the closest exemption. [tex]\blacksquare[/tex]
RemarkThe exemption table is missing. The complete figure is shown below.
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In the figure below all lines intersect at point W what is the value of angle VWX?
Answer: 55
Step-by-step explanation:
Angle VWX and the 55 degree angle are vertical angles.