The cross section of the satellite dish is an illustration of a quadratic function
The quadratic function that models the cross-section is y = 1/6(x^2 - 9)
How to determie the equation of the cross-section?The given parameters are:
Width = 6 feet
Depth = 1.5 feet
Express the width the sum of two equal numbers
Width = 3 + 3
The above means that, the equation of the cross section passes through the x-axis at:
x = -3 and 3
So, we have:
y = a(x - 3) * (x + 3)
Express as the difference of two squares
y = a(x^2 - 9)
The depth is 1.5.
This is represented as: (x,y) =(0,-1.5)
So, we have:
-1.5 = a(0^2 - 9)
Evaluate the exponent
-1.5 = -9a
Divide both sides by -9
a = 1/6
Substitute 1/6 for a in y = a(x^2 - 9)
y = 1/6(x^2 - 9)
Hence, the quadratic function that models the cross-section is y = 1/6(x^2 - 9)
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Evaluate the function graphically.
Find f(3)
In the Lincoln Grade School, 200 students are in the first grade, 150 are in the second grade, 300 in the third grade, 250 in the fourth grade, 200 in the fifth grade, and 275 in the sixth grade. Construct a bar graph that represents the number of students per grade at Lincoln Grade School. Label the bar graph with a title and the correct, consistent scale.
Answer:
In image
Step-by-step explanation:
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How many times more is 2 ^ 10 than 2^ 6
Answer choices
8
16
12
Answer:
16
Step-by-step explanation:
2^10 = 1,024
2^6 = 64
1,024/64 = 16
Hope that helps!
Find the solution of the system of equations shown on the graph
The solution of the system of the equations shown is where the equations intersect
--> (-7, 1)
Hope that helps!
Answer:
(-7, 1),
Step-by-step explanation:
The solution is the coordinates of the point of intersection.
At this point x = -7 and y = 1.
Find the next three terms in the sequence. 24,20,16,12…. (If you could explain it that would be great too. It’s a bit confusing)
Answer:
the next three numbers should be 8, 4, 0
Step-by-step explanation:
it reduces by 4 each time
24 - 4 = 20
20 - 4 = 16
16 - 4 = 12
12 - 4 = 8
8 - 4 = 4
4 - 4 = 0
First term =a=24
common difference=d=20-24=-4
Formula
a_n=24-4(n-1)a_5
24-4(4)8a_6
24-5(4)4a_7
24-6(4)0Simplify and write in scientific notation (5.6 * 10 ^ 5)/(1.4 * 10 ^ - 2)
Answer:
4.0x10^7
Step-by-step explanation:
5.6÷1.4=4
10^(5-(-2))
=10^7
=4.0x10^7
What is the rule and how do you find n? 100 points to answer!
Answer:
n = 17
Rule: y = 2x + 1
Step-by-step explanation:
By inspection of the first two ordered pairs in the given table, it appears that for each 1 unit increase in x, y increases by 2 units.
To check this, write the ordered pairs with 5 ≤ x ≤ 10 using this rule:
(5, 11) (6,13) (7, 15) (8, 17) (9, 19) (10, 21)
As the ordered pair (10, 21) appears in the table, then we can confirm that this is the rule and that it is a linear function.
If y increases by 2 units for every 1 unit increase of x, then the slope of the linear function will be 2.
Using the point-slope form of a linear function: [tex]\sf{y-y_1=m(x-x_1)}[/tex]
(where m is the slope and [tex]\sf(x_1,y_1)[/tex] is a point on the line)
Given:
m = 2[tex]\sf(x_1,y_1)=(5,11)[/tex]Substituting these values into the formula:
[tex]\implies \sf{y-11=2(x-5)}[/tex]
[tex]\implies \sf y=2x+1[/tex]
Therefore, the rule is [tex]\sf y=2x+1[/tex]
To find n, simply substitute x = 8 and y = n into the equation:
[tex]\implies \sf n=2(8)+1=17[/tex]
Therefore, n = 17
Take 2 points and form equation
(5,11)(6,13)Slope:-
m=13-11/6-5=2Equation in point slope form
y-11=2(x-5)y-11=2x-10y=2x+1So
for n
n=2(8)+1n=16+1n=17Find the x-intercept and y-intercept of the line.
=+6x3y−6
Kurt drove to his college after summer break
The graph shows the distance he traveled during his drive,
Distance Kurt
Traveled
100
y
(1.5,75)
75+
Use the drop-down menus to complete the statements based on the graph.
Distance (miles)
50+
25+
0
Time (hours)
CLEAR
The labeled point means in
hours, Kurt traveled
miles.
In 1 hour, Kurt traveled
miles.
His distance changed at a unit rate of
miles per hour, so Kurt's speed was
miles per hour.
If Kurt had driven more slowly, the slope of the graph would be
Answer:
1.5 hours; 75 miles50 miles50 miles per hour; 50 miles per hourless/decreased/reduced/smallerStep-by-step explanation:
The labels on the axes of the graph tell you the meaning of the coordinates of a point on the graph. The ordered pair lists the horizontal coordinate first. The horizontal axis is labeled hours, and the vertical axis is labeled miles.
The point (hours, miles) = (1.5, 75) means Kurt drove 75 miles in 1.5 hours.
__
You can find the miles driven in 1 hour by reading the graph at the horizontal coordinate 1 hour. You find that is 50 miles. The 1 represents 1 unit, so the "unit rate" is 50 miles in 1 hour. Such a rate is also called a "speed" of 50 miles per hour.
If Kurt had driven fewer miles in an hour, the points on the graph would all have smaller vertical coordinates. The unit rate (slope) would be less than 50 miles per hour.
Sonia has only dimes and nickels in her coin jar; they are in a ratio of 3 to 5. IF she had 120 coins in the jar, how many are dimes? PLEASE HELP
Answer:
45 dimes and 75 nickels
Step-by-step explanation:
3 ÷ 8 × 120 = 45
you divide the three by both ratios summed up (8) and then you multiply that by the coins
doing so will you can get 45
and to get the amount of nickels you just subtract 45 from 120 and you get 75
i need help with 7 and 8 explanations and show work for solving?
Answer:
ang ganda noh
Step-by-step explanation:
sorry di ko po alam yung sagot
If you had a coupon for $0.50 off the price for one of your items, would this change your answer for which is a better buy? Give an example
Answer: yes it would change my answer for what is a better buy
Step-by-step explanation: if you buy a $1.98 large soda for 50¢ off you’ll have a $1.48 soda that is only 30¢ more but the size is significantly larger
2/5 10+36-6 ................... HELP PLEASE
Answer:
if it is just the 10+36-6 then that is 40 but then if it is 2/5 10+36-6 then that would be 16
Step-by-step explanation:
add 10 and 36 which is 46 then subtract 6 which is 40 then get the 2/5 which would be 16 hope this helps you
need help will give the brainlest
Answer:
should be 4L
Step-by-step explanation:
there is 4 cups with 1L of water in them so you add them up to get the total amount .
Answer:
4 Liters
Step-by-step explanation:
1. Create Equation
1L+1L+1L+1L
2. Solve
1L+1L+1L+1L
1+1+1+1
2+1+1
2+2
4
3. Check
1+1+1+1=4
2+2=4
4=4
Correct
4. Answer
4L
I would really like help with A & B
Check the picture below.
Make sure your calculator is in Degree mode.
Do I subtract the fractions or divide or do something else with them please help
Answer:
7/6
Step-by-step explanation:
in order to find the answer you have to -5/6 by 1/3 and then you get 7/6 so technically you have to minus it
40 points please help
IJKL is a rectangle, so opposite sides have the same length:
• IJ = KL ⇒ 6y - 6 = 2x + 20
• JK = IL ⇒ 3x + 21 = 6y
Substitute the second equation into the first and solve for x :
6y - 6 = 2x + 20
(3x + 21) - 6 = 2x + 20
3x + 15 = 2x + 20
x = 5
Solve for y :
3x + 21 = 6y
15 + 21 = 6y
36 = 6y
y = 6
Use+the+following+data+to+compute+the+relative+market+share+of+each+brand+and+its+position+on+the+growth-share+matrix+if+the+market+growth+rate+is+13. 4%. +which+of+the+following+is+correct?
Market share is simply the percentage of the total revenue or sales in a market which a particular business makes.
What is a market share?
Your information is incomplete. Therefore, an overview of the market share will be given. Market share is a measure of consumers' or businesses' preference for a product over other similar products.
A higher market share means greater sales and less effort is needed to sell more and a strong barrier to entry for other competitors.
For example, if there are 50,000 units sold per year in an industry, a company that has sales of 5,000 of those units would then have a 10 percent share in that market.
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A rectangular field is 120 meters long and 85 meters wide.
Give the length and width of another rectangular field that has the same perimeter but a smaller area.
Answer:
Length: 200
Width: 5
Step-by-step explanation:
The perimeter of 120 and 85 is 410
The perimeter of 200 and 5 is 410
The area of 200 and 5 is 200 times 5 which is 1000
The area of 120 and 85 is 120 times 85 is 10200
-I hope this helps
If gas costs $3.58 a gal.how many gallons for $15.00
Answer:
Simple, Just divide 15.00 by 3.58 to get the answer of 4.19
Step-by-step explanation:
15.00 ÷ 3.58 = 4.19
a small movie theater sells children's tickets for $4 each and adult tickets for $10 each for an animated movie. The theater sells a total of $338 in ticket sales.
(c) show that after multiplying both sides of the equation in (a) by 2, c=52 and a=18 is still a solution to this equation.
Equation: 4c+10a=388
Answer:
Proved below!
Step-by-step explanation:
Start by multiplying both sides by 2 (as said in the question):
[tex]\implies 4c + 10a = 388[/tex]
[tex]\implies 2(4c + 10a) = 2(388)[/tex]
[tex]\implies 8c + 20a = 776[/tex]
Substitute the solution(s) in the equation:
[tex]\implies 8(52) + 20(18) = 776[/tex] (c = 52; a = 18)
[tex]\implies 416 + 360 = 776[/tex]
[tex]\implies \bold{776 = 776 \ \ \ (Proved)}[/tex]
Answer:
Let c = number of children's tickets sold
Let a = number of adults tickets sold
Given:
Cost of child ticket = $4Cost of adult ticket = $10Total ticket sales = $388⇒ 4c + 10a = 388
Multiply both sides of the equation by 2:
⇒ 2(4c + 10a) = 2 × 388
⇒ 8c + 20a = 776
If c = 52 and a = 18, substitute these values into the equation and solve:
⇒ 8(52) + 20(18)
⇒ 416 + 260
⇒ 776
As 776 = 776, this proves that c = 52 and a = 18 is a solution to this equation.
4. Is (x + 2)a factor of (x + 5x 3 2 - 4x – 20)? -
Answer:
yes
Step-by-step explanation:
if (x + 2) is a factor of the polynomial , then if x = - 2 gives the polynomial a value of zero it is a factor
(- 2)³ + 5(- 2)² - 4(- 2) - 20
= - 8 + 5(4) + 8 - 20
= - 8 + 20 + 8 - 20
= 0
since polynomial = 0 then (x + 2) is a factor
Reflect the shape A in the line x=1
What are the coordinates of the vertices of the image?
anyone who is amazing at maths please help!!!!!!!!!!!!!!!!!!!!
i am running out of time
Answer:
reflected image shown in red on attached diagram
Step-by-step explanation:
When reflecting an object in the line x = a:
reflected x-values: 2a - xreflected y-values are the same as the original y-valuesSo when reflecting in the line x = 1
given x-value = 2, so reflected x-value = 2(1) - 2 = 0given x-value = 4, so reflected x-value = 2(1) - 4 = -2(2, 7) → (0, 7)
(2, 4) → (0, 4)
(4, 4) → (-2, 4)
|x-b|=c, only one solution is -3
Answer:
x-b=-3
Step-by-step explanation:
1. Simplify
|x-b|=c
x-b=c
If c=-3 then,
Answer= x-b=-3
what numbers can you make ?
Answer:
196
Step-by-step explanation:
Given a circle with a radius of 7 inches and a central angle of 140°, find the area of the sector.
Answer: 343pi/18
Step-by-step explanation:
Find the sum or product two different ways. 5+6+7+8
Determine the ratio of the note B to middle C.
a. 1.8877
b. 1.7983
C. 1.9348
d. 1.3654
Answer:
To determine the ratio of the note B to middle C, we need to find the frequency of note B and then divide it by the frequency of middle C.
The frequency of note B is 493.9 Hz, and the frequency of middle C is 261.6 Hz.
Therefore, the ratio of the frequency of note B to middle C is:
493.9 / 261.6 = 1.8877
So the answer is (A) 1.8877
please help!!!! thanks
what is a pair lines that are parallel
Answer:
The pairs of lines that do not intersect or meet at any point are called parallel lines. These lines lie on the same plane but do not intersect. The line segments or rays that lie on the same plane but do not intersect are also parallel.
Step-by-step explanation:
Answer
A parallel line is a position of two lines on a plane that does not have a point of intersection even though the two lines are extended.Geometrically, parallel lines will never meet each other because they have the same slope (gradient). Parallel lines do not have to be the same length