Answer: triangleDEF - 3 units down
triangleGHI - 5 units left
triangleJKL - 4 units left and 5 units down
Step-by-step explanation:
Please Help! 30 POINTS! Given the following three points, find by hand the quadratic function they represent. (−1,−8), (0,−1),(1,2) A. f(x)=−3x2+4x−1 B. f(x)=−2x2+5x−1 C. f(x)=−3x2+10x−1 D. f(x)=−5x2+8x−1 Determine if the following set of ordered pairs represents a quadratic function. Explain. (5, 7), (7, 11), (9, 14), (11, 18) A. The y-values go up by the square of the x-value (22=4). Therefore, the ordered pairs represent a quadratic equation. B. The y-values go up by the square of the x-value (22=4). Therefore, the ordered pairs do not represent a quadratic equation. C. Since the differences between the x-values is 2 and the differences between the y-values is 4, that means that the differences between the differences of the y-values are all zero. Therefore, the ordered pairs represent a quadratic equation. D. Since the differences between the differences of the y-values is not consistent, the ordered pairs do not represent a quadratic equation.
Answer:
(1) B
(2) D
Step-by-step explanation:
(1)
Let the quadratic function be:
[tex]y = ax^{2} + bx + c[/tex]
For the point, (0,-1),
[tex]y = ax^{2} + bx + c[/tex]
[tex]-1=(a\times0)+(b\times0}+c\\-1=c\\c=-1[/tex]
Then the equation is:
[tex]y = ax^{2} + bx -1[/tex]
For the point (-1, -8) ,
[tex]y = ax^{2} + bx -1[/tex]
[tex]-8=(a\times (-1)^{2})+(b\times -1)-1\\-8=a-b-1\\a-b=-7...(i)[/tex]
For the point (1, 2) ,
[tex]y = ax^{2} + bx -1[/tex]
[tex]2=(a\times (1)^{2})+(b\times 1)-1\\2=a+b-1\\a+b=3...(ii)[/tex]
Add the two equations and solve for a as follows:
[tex]a-b=-7\\a+b=3\\\_\_\_\_\_\_\_\_\_\_\_\_\_\_\\2a = -4\\a = -2[/tex]
Substitute a = -2 in (i) and solve for b as follows:
[tex]a-b=-7\\-2-b=-7\\b=5[/tex]
Thus, the quadratic function is:
[tex]f(x)=-2x^{2}+5x-1[/tex]
The correct option is (b).
(2)
The ordered pairs are:
(5, 7), (7, 11), (9, 14), (11, 18)
Represent them in an XY table as follows:
X : 5 | 7 | 9 | 11
Y : 7 | 11 | 14 | 18
Compute the difference between the Y values as follows:
Diff = 11 - 7 = 4
Diff = 14 - 11 = 3
Diff = 18 - 14 = 4
Now compute the difference between the Diff values:
d = 3 - 4 = -1
d = 4 - 3 = 1
Since the differences between the differences of the y-values is not consistent, the ordered pairs do not represent a quadratic equation.
The correct option is D.
Let f (x) = |2). Write a function g whose graph is a vertical shrink by a factor of
followed by a translation 2 units up of the graph of f.
Answer:
This is poorly written, so i will answer it as it was:
"Let f (x) = |2). Write a function g(x) whose graph is a vertical shrink by a factor of A, followed by a translation 2 units up of the graph of f."
I don't really know what you do mean by I2), so i will answer it in a general way.
First, we do a vertical shrink of factor A.
A must be a number smaller than one and larger than zero., then if g(x) is a vertical shrink of factor A of the graph of f(x), we have that:
g(x) = A*f(x)
As 0 < A < 1
We will have that the graph of g(x) is a vertical compression of the graph of f(x)
Now we do a vertical shift of 2 units up.
A general vertical shift of N units up is written as:
g(x) = f(x) + N
Where N is a positive number.
So in our case, we have:
g(x) = A*f(x) + 2.
Where you will need to replace the values of A and f(x) depending on what the actual question says,
please help!!!!!!!!!!!!! Select ALL the correct answers. Choose the statements that are true about a cube with side length 1 unit.
Answer:
i think it is 2
Step-by-step explanation:
The reciprocal of 1 is *
Answer:
[tex]\boxed{1}[/tex]
Step-by-step explanation:
When finding the reciprocal of a value, it flips the denominator with the numerator and vice versa.
The number 1 can be represented as the fraction 1/1 and 1 divided by 1 is still equivalent to 1.
Therefore, the reciprocal of 1 will always be 1.
Sophie is making a copy of an angle. The original angle will be labeled G and the new angle will be labeled B. She has just finished using a compass, with the point on G, to draw an arc that intersects both rays of angle G. Which of the following should she do next
Answer:
The next step is;
Label the two intersection points
Step-by-step explanation:
To make a copy of an angle, the steps are;
1) Draw the rays of the original angle passing through the point B
2) Open the compass slightly and place the compass point on the vertices G where the two rays meet to draw an arc that intersect both rays
3) Label the point of intersection of both rays points C and D
4) With the compass still opened to the same width, move the compass to the point B on the line the angle is to be copied and draw a similar arc intersecting the ray at J
5) Open the compass to the width of C and D on the original angle and place the compass at point J to mark the arc on the copied angle location at M
6) Draw a line from B passing through M to complete the second ay of the copied angle.
two years ago a woman wad 7 times as old as her daughter, but in 3 years time she would be x times as old as the girl. how old are they now?
Answer:
The present age of the woman is 37 years and her daughter is 7 years
Step-by-step explanation:
two years ago a woman was 7 times old as her daughter, but in 3 years time she would be 4 times old as the girl. how old are they now
Two years ago a woman wad 7 times as old as her daughter
Let her daughter=x-2
The woman=y-2
x-2
7(y-2)=7y-14
x-2=7y-14
x-7y=-14+2
x-7y= -12 (1)
but in 3 years time she would be 4 times as old as the girl.
x+3
y+3
x+3
4(y+3)=4y+12
x+3=4y+12
x-4y=12-3
x-4y=9. (2)
x-7y= -12 (1)
x-4y=9. (2)
Subtract (1) from (2)
4y-(-7y)=9-(-12)
-4y+7y=9+12
3y=21
y=21/3
y=7
Substitute
y=7 into (1)
x-7y= -12
x-7(7)=-12
x-49=-12
x= -12+49
=37
The present age of the woman is 37 years and her daughter is 7 years
Helppppp!!!! Thank you
Greetings from Brasil...
In a triangle the sum of the internal angles is 180 °.... Thus,
Ô = 180 - 30
Ô = 60
The desired area is the area of the rectangle triangle, minus the area of the circular sector whose angle 60
A1 = area of the rectangle triangle
TG B = OA/AB
AB = OA / TG B
AB = 6 / TG 30
AB = 6√3
A1 = (AB . OA)/2
A1 = (6√3 . 6)/2
A1 = 18√3A2 = area of the circular sector
(rule of 3)
º area
360 ------------ πR²
60 ------------ X
X = 60πR²/360
X = 6π
So,
A2 = 6πThen the area shaded is:
A = A1 - A2
A = 18√3 - 6πThe projected worth (in millions of dollars) of a large company is modeled by the equation w = 206(1.1) t. The variable t represents the number of years since 2000. What is the projected annual percent of growth, and what should the company be worth in 2011? A. 10%; $534.31 million B. 11%; $646.52 million C. 10%; $587.74 million D. 11%; $226.60 million
Answer:
Hey There!! The Correct answer is: The equation is w = 241(1.06)t
And here variable t represents the number of years since 2000.
In 2001 means t=2001 -2000 = 1
So we plug 1 for t in the given expression , that is w = 241(1.06)1 = 241 * 1.06 = 255.46
Therefore in 2001, it should be worth to 255.46.
And in the given expression 1.06=1 +0.06, where 0.06 is the annual percent of growth that is 6 % .
Hope It Helped!~ ♡
ItsNobody~ ☆
The projected annual percent of growth is 10% and the company worth in 2011 will be $587.74 millions. Then the correct option is C.
What is an exponent?Consider the function:
y = a (1 ± r) ˣ
Where x is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.
If there is a plus sign, then there is exponential growth happening by r fraction or 100r %.
If there is a minus sign, then there is exponential decay happening by r fraction or 100r %.
The projected worth (in millions of dollars) of a large company is modeled by the equation is given as,
[tex]\rm w = 206\times (1.10)^t\\\\w = 206\times (1+0.10)^t[/tex]
Then the projected annual percent of growth is 10%.
The variable t represents the number of years since 2000.
Then the company worth in 2011 will be
w = 206 × 1.1¹¹
w = $587.74 millions
The projected annual percent of growth is 10% and the company worth in 2011 will be $587.74 millions.
Then the correct option is C.
More about the exponent link is given below.
https://brainly.com/question/5497425
#SPJ2
PLEASE help me solve this question! No nonsense answers please!
Answer:
[tex]\boxed{\sf Option \ 1}[/tex]
Step-by-step explanation:
The profit is revenue (R ) - costs (C ).
Subtract the expression of costs (C ) from revenue (R ).
[tex]10x-0.01x^2-(2x+100)[/tex]
Distribute negative sign.
[tex]10x-0.01x^2-2x-100[/tex]
Combine like terms.
[tex]8x-0.01x^2-100[/tex]
The first option has a positive 100, which is wrong.
The rest options are right, when we expand brackets the result is same.
How many solutions does the system have?
Answer:
B. no solutionsStep-by-step explanation:
Left sides of both equations are the same sum (8x+2y), so the right sides also has to be the same. They are not so there is no solutions.
{If they are the same then system has infinitely many solutions.}
What is the divisor of 5.2 and 0.052
Answer:
5.2/0.052 is 100, and 100 is 10^2, so the missing divisor is 10^2
Answer:
100
Step-by-step explanation:
5.2/x = 0.052
Since the decimal place moves 2 places to the left from 5.2 to 0.052, the divisor is 100.
5.2/100 = 0.052
Find the constant of proportionality (r) in the equation y = r x
Answer:
r = 11Step-by-step explanation:
y = r x
r is the constant of proportionality
To find r pick any values of x and y provided and substitute it into the above formula and solve for r.
That's
using
x = 2
y = 22
We have
22 = 2r
Divide both sides by 2
r = 11Therefore the constant of proportionality is 11
Hope this helps you
PLEASE help me with this question!!! REALLY URGENT!
Answer:
The third table is the correct answer
Step-by-step explanation:
Here in this question, we are concerned with determine which of the tables correctly represents what an exponential function is.
An exponential function is a function of the form;
y = x^n
where the independent variable x in this case is raised to a certain exponent so as to give the results on the dependent variable axis (y-axis)
In the table, we can see that we have 2 segments, one that contains digits 1,2 and so on while the other contains purely the powers of 10.
Now, let’s set up an exponential outlook;
y = 10^x
So we have;
1 = 10^0
10 = 10^1
1/10 = 10^-1
1000 = 10^3
1/100 = 10^-2
We can clearly see here that we have an increase in the value of y, depending on the value of the exponent.
However it is only this table that responds to this successive correctness as the other tables in the answer do have a point where they fail.
For example;
10^-2 is not 10 which makes the fourth table wrong
10^4 is not 100 which makes the first table wrong
we have same error on second table too
Point M is on line segment LN. Given LM=7 and MN=10, determine the length LN.
Answer:
[tex]\huge \boxed{17}[/tex]
Step-by-step explanation:
Point M is on the line segment LN.
LM = 7
MN = 10
LN = LM + MN
LN = 7 + 10 = 17
The value of the line segment LN is 17.
What is a line segment?A line segment in geometry is a section of a line that has two clearly defined endpoints and contains every point on the line that lies within its confines.
Given that point, M is the online segment LN. Given LM=7 and MN=10,
The value of the line segment will be calculated as:-
Point M is on the line segment LN.
LM = 7
MN = 10
LN = LM + MN
LN = 7 + 10 = 17
Therefore, the value of the line segment LN is 17.
To know more about line segments follow
brainly.com/question/3573606
#SPJ5
The pH of 0.0001 M solution of Ca(OH)2 is
Step-by-step explanation:
Since Ca(OH)2 is Basic, we need to find pOH:
pOH = - log [OH-]
pOH = - log(0.0001)
pOH = - ( - 4)
pOH = 4
Since, pH + pOH = 14
Therefore,
pH of 0.0001M sol. of Ca(OH)2 = 10
In a naval engagement, one-third of the fleet was captured, one-sixth was sunk, and two ships were destroyed by fire. One-seventh of the surviving ships were lost in a storm after the battle. Finally, the twenty-four remaining ships sailed home. How many ships were in the fleet before the engagement?
Answer:
60 ships.
Step-by-step explanation:
Let the total number of ships in the naval fleet be represented by x
One-third of the fleet was captured = 1/3x
One-sixth was sunk = 1/6x
Two ships were destroyed by fire = 2
Let surviving ships be represented by y
One-seventh of the surviving ships were lost in a storm after the battle = 1/7y
Finally, the twenty-four remaining ships sailed home
The 24 remaining ships that sailed home =
y - 1/7y = 6/7y of the surviving fleet sailed home.
Hence
24 = 6/7y
24 = 6y/7
24 × 7/ 6
y = 168/6
y = 28
Therefore, total number of ships that survived is 28.
Surviving ships lost in the storm = 1/7y = 1/7 × 28 = 4
Total number of ships in the fleet(x) =
x = 1/3x + 1/6x + 2 + 28
Collect like terms
x - (1/3x + 1/6x) = 30
x - (1/2x) = 30
1/2x = 30
x = 30 ÷ 1/2
x = 30 × 2
x = 60
Therefore, ships that were in the fleet before the engagement were 60 ships.
Astrid is in charge of building a new fleet of ships. Each ship requires 40 tons of wood, and accommodates 300 sailors. She receives a delivery of 4 tons of wood each day. The deliveries can continue for 100 days at most, afterwards the weather is too bad to allow them. Overall, she wants to build enough ships to accommodate at least 2100 sailors. How much wood does Astrid need to accommodate 2100 sailors?
Answer: 280 tons
Step-by-step explanation: divide all at tons/pound which accumulated to 280 tons
Answer: 10 ships
Step-by-step explanation:
Write the equation of a circle with a center at (12, 6) and a radius of 6.
Answer:
(x-12)² + (y-6)² = 36 (Option C)
Step-by-step explanation:
use circle formula
(x-h)² + (y-k)²= r²
h= 12 and k= 6 and r= 6
(x-12)² + (y-6)² = 6²
6 squared = 36 (6·6)
(x-12)² + (y-6)² = 36
suppose we want to choose 6 letters without replacement from 13 distinct letters. A) how many ways can this be done if order does not matter? B) how many ways can this be done if order of choices matters
Answer: A) 1716 B) 1235520
Step-by-step explanation:
If order doesn't matter , then we use combinations, where the number of combinations of selecting r things from n is given by :-[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
If order matters , then we use permutations, where the number of permutations of selecting r things from n is given by :-[tex]^nP_r=\dfrac{n!}{(n-r)!}[/tex]
Given, Total distinct letters = 13
To choose = 6 letters
A) Number of ways to choose (if order does not matter)=[tex]^{13}C_6[/tex]
[tex]=\dfrac{13!}{6!7!}=\dfrac{13\times12\times11\times10\times9\times8\times7!}{(720)\times 7!}\\\\= $$1716[/tex]
B) Number of ways to choose (if order matters)=[tex]^{13}P_6[/tex]
[tex]=\dfrac{13!}{7!}=\dfrac{13\times12\times11\times10\times9\times8\times7!} 7!}\\\\= $$1235520[/tex]
Hence, A) 1716 B) 1235520
An empty row in a frequency table is a mistake True or false
Answer:
False I think
Step-by-step explanation:
10) Find the least number that must be subtracted from the following numbers to make them perfect squares. a) 1098 b) 4498
Answer:
a. 9
b. 9.
Step-by-step explanation:
a) √1098 = 33.136
33^3 = 1089
So the answer is 1098 - 1089
= 9.
b) √4498 = 67.067
67^2 = 4489
Answer = 9.
Answer:
a). 9
b). 9
Step-by-step explanation:
a) If you try to subtract 1 to 8 from 1098, it won't make a perfect square. But if you subtract 9 from 1098 (that will make it 1089), it will make a perfect square.
√1089 = 33
33² = 33 × 33 = 1089
So the answer is 9.
b). If you try to subtract 1 to 8 from 4498, it won't make a perfect square. But if you subtract 9 from 4498 (that will make it 4489), it will make a perfect square.
√4489 = 67
67² = 67 × 67 = 4489
So the answer is 9.
Hope you understand ◉‿◉ (◠‿◕)
Find the height of the triangle by applying formulas for the area of a triangle and your knowledge about
triangles.
9 in
9 in.
Xin
6 in
Answer:
8.5
Step-by-step explanation:
Applying pythagora's theorem,
hypotenuse^2 = opposite^2 + adjacent^2
but, hypotenuse = 9
opposite = X
adjacent = 1/2(base of triangle)= 1/2(6)
adjacent = 3
9^2 = X^2 + 3^2
X^2 = 81 - 9
X^2 = 72
X = 8.5
A rectangle with sides 13 cm and 7 cm has the same diagonal as a square. What is the length of the side of the square. Give your answer as a surd.
Answer:
Step-by-step explanation:
The diagonal ^2= 13^2+7^2
=169+49=218
diagonal = V218
the lengh of the square=l
l^2+l^2= 218
2l^2=218
l^2= 218/2= 109
l= ✓109
what is mean absolute deviation (MAD) and how do I find it?
Steps to find MAD:
Step 1. Calculate mean([tex]\overline{x}[/tex]) of the data using formula: [tex]\overline{x}=\dfrac{\sum x}{n}[/tex] , where x denotes data points and n is the number of data points.
Step 2. Calculate distance of each data point from mean :
Distance = [tex]|x-\overline{x}|[/tex]
Step 3. Divide distance of each data point from mean by n:
MAD = [tex]\dfrac{\sum |x-\overline{x}|}{n}[/tex] , which is the final computation to find MAD.
Simplify (5x3y) (2xy4)
Answer: 10x^4y^5
Step-by-step explanation:
5x^3y^1•2x^1y^4
5•2=10
x^3•x^1=x^4
y^1•y^4=y^5
10x^4y^5
How do we solve 56x + 79 if x = 23? (30 points!) GIVE A GOOD EXPLANATION, NOT JUST AN ANSWER, WHO EVER DOES IT FIRST GETS BRAINLIEST.
Hello friend!
The answer is: 1367
First, since x = 23, we rewrite the problem.
56(23) + 79 = ?
Now we need to figure out 56 time 23
56 times 23 = 1288
Now we have 1288 + 79.
1288 + 79 = 1367
Answer:
1,367
Explanation:
Step 1 - Input the value of x in the given expression
56x + 79
56(23) + 9
Step 2 - Multiply fifty six by twenty three
56(23) + 79
56 × 23 + 79
1,288 + 79
Step 3 - Add
1,288 + 79
1,297
Therefore, the answer to the given expression is 1,367.
use the formula S = 40,000 (1.06)t to calculate your salary after 4 years. Round your answer to the nearest dollar.
a. $42,400
b. $44,944
c. $47,641
d. $50,499
Answer:
d. $50,499
Step-by-step explanation:
Given:
S = 40,000 (1.06)^t
Where,
t=4 years
S=40,000(1.06)^4
=40,000(1.26247696)
=50,499.0784
To the nearest dollar
S=$50,499
The answer is d. $50,499
If BH = 66, find DE. Round your answer to two decimal places if necessary.
Answer:
BH= 66
DE= ...?
We know that
BH is 1 to 6 = 66
DE is only take one space of that--> 3 to 4
so 66/6 = 11
1 space = 11 = DE
Hope it helps ^_^
What is the value of x in the equation 3x-4y =65, when y = 4? i will gift brainliest
Answer:
3x-4y=65
3x=65+4y
x=(65+4y)/3, when y=4
x=(65+4*4)/3
x=(65+16)/3
x=81/3
x=27
Answer:
x = 27
Step-by-step explanation:
3x - 4y = 65
Let y= 4
3x - 4(4) = 65
3x -16 = 65
Add 16 to each side
3x-16+16 = 65+16
3x = 81
Divide by 3
3x/3 =81/3
x=27
solve the equation below[tex]\sqrt[5]{27(x-2)}=3[/tex]
Answer:
x = 11
Step-by-step explanation:
Raising both sides to the fifth power, we get:
27(x - 2) = 3⁵
x - 2 = 3⁵ / 27
x - 2 = 3⁵ / 3³
x - 2 = 3⁽⁵⁻³⁾ = 3² = 9
x = 11
