To sketch the graph we have to solve the function with each value of x to get the coordinates.
f(x) = x² − 4x − 5
−2 ≤ x ≤ 6
This inequality represents the domain for x. Therefore x is greater than equal to -2 but less than equal to 6.
The range of x is as follows:
x = -2, -1, 0, 1, 2, 3, 4, 5, 6
We already have the values for x therefore, we must substitute the values of x into the function f(x) = x² − 4x − 5 to find the y values.
Solutions:
For x = -2
f(x) = x² − 4x − 5
= -2² − 4(-2) - 5
= 4 + 8 - 5
= 7
Point = (-2,7)
For x = -1
f(x) = x² − 4x − 5
= -1² - 4(-1) - 5
= 1 + 4 - 5
= 0
Point = (-1,0)
For x = 0
f(x) = x² − 4x − 5
= 0² - 4(0) - 5
= 0 - 0 - 5
= -5
Point = (0,-5)
For x = 1
f(x) = x² − 4x − 5
= 1² - 4(1) - 5
= 1 - 4 - 5
= -8
Point = (1,-8)
For x = 2
f(x) = x² − 4x − 5
= 2² - 4(2) - 5
= 4 - 8 - 5
= -9
Point = (2,-9)
For = 3
f(x) = x² − 4x − 5
= 3² - 4(3) - 5
= 9 - 12 - 5
= -8
Point = (3,-8)
For x = 4
f(x) = x² − 4x − 5
= 4² - 4(4) - 5
= 16 - 16 - 5
= -5
Point = (4,-5)
For x = 5
f(x) = x² − 4x − 5
= 5² - 4(5) - 5
= 25 - 20 - 5
= 0
Point = (5,0)
For x = 6
f(x) = x² − 4x − 5
= 6² - 4(6) - 5
= 36 - 24 - 5
= 7
Point = (6,7)
Coordinates for graph = (-2,7) , (-1,0) , (0,-5) , (1,-8) , (2,-9) , (3,-8) , (4,-5) , (5,0) , (6,7)
These are the points to sketch the quadratic graph.
A college with a graduating class of 4000 students in the year 2010 predicts that its graduating class will grow 5% per year.
Using an exponential function to model the number of students y in the graduating class t years after 2010 to predict the number
of students in 2017?
Hello,
[tex]u_0=4000\\u_1=4000*1.05 (for\ year\ 2011)\\\\u_n=4000*1.05^n\\So:\\year\ 2017: u_7=4000*1.05^7=5628,401690625\ \approx{5628}[/tex]
Using an exponential function, the number of students y in the graduating class 7 years after 2010 i.e. in 2017 will be 5628.4
What is an exponential function?y = abˣ, where a is the initial population, b is the rate, and x is the time, is the standard exponential function.
How to solve this problem?Here initial student population = 4000.
Rate = 5% = (100 + 5)/100 = 1.05
Time = 7 years.
Now, in 2017, the population will be y = 4000 * (1.05)⁷ = 5628.401691 ≅ 5628.4.
Therefore, using an exponential function, the number of students y in the graduating class 7 years after 2010 i.e. in 2017 will be 5628.4
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4.OA.2: The Turner family uses 548 liters of water per day. The Hill family uses 3 times as much water per day. How much more water does the Hill family use per day?
Answer:
1096 more water
Step-by-step explanation:
Let;
x = the water used in general
but used 3 times of the original = 3x
3*(548) = 1644 water a day
How much more water =New - original
where:
new = 1644
original= 548
1644 - 548
=1096 more water
10. The sum of the digits of a two digit number is 7. The number obtained by interchanging the digits exceeds the original number by 27 . find the number
Answer:
Step-by-step explanation:
Let "ab" represent the digits of the number. The value of "ab" is 10a+b.
a+b = 7
The value of "ba" is 10b+a
(10b+a) - (10a+b) = 9b-9a = 27
b-a = 3
a+b = 7
b-a = 3
------------
2b = 10
b = 5
a = 2
The number is 25.
Simplify
[tex]\frac{1}{1}+\frac{1}{1+2}+\frac{1}{1+2+3} +...+\frac{1}{1+2+3+...+99}[/tex]
Answer:
65/264 or 0.2462
Step-by-step explanation:
The given series is
(1/1.2.3) + (1/2.3.4) + (1/3.4.5) + ………………
If we denote the series by
u(1) + u(2) + u(3) + u(4) +……………..u(n),
where u(n) is the nth term, then
u(n) = 1/[n(n+1)(n+2)] , n = 1,2,3,4,………n.
which can be written as
u(n) = (1/2) [1/n(n+1) - 1/(n+1)(n+2)] ………………………(1)
In the question, the number of terms n =10, thereby restricting us only to first 10 terms of the series and we have to find the sum for this truncated series. Let S(10) denote the required sum. We have then from (1),
u(1) = (1/2) (1/1.2 - 1/2.3)
u(2) = (1/2) (1/2.3 - 1/3.4)
u(3) = (1/2) (1/3.4 - 1/4.5)
u(4) = (1/2) (1/4.5 - 1/5.6)
u(5) = (1/2) (1/5.6 - 1/6.7)
u(6) = (1/2) (1/6.7 - 1/7.8)
u(7) = (1/2) (1/7.8 - 1/8.9)
u(8) = (1/2) (1/8.9 - 1/9.10)
u(9) = (1/2) (1/9.10 - 1/10.11)
u(10) = (1/2) (1/10.11 - 1/11.12)
Let us now add the terms on LHS and the terms on RHS independently. The sum of LHS is nothing but the sum S(10) of the series up to 10 terms. On the RHS, alternate terms cancel and we are left with only the first and the last term. Therefore,
S(10) = (1/2) (1/1.2 - 1/11.12) = (1/2) (66–1)/132 = [65/(132.2)]
= 65/264
= 0.2462 (correct to four decimal places)
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Need help with these 3 problems!
Answer:
1. 25
2. 44
3. 9
Step-by-step explanation:
Answer:
25 students44 cents9 eggsStep-by-step explanation:
If there are 3 cookies for each student and 75 cookies in total, then the equation would be 75 ÷ 3. that equals 2588 total for 2 cans. Divide 88 by 2 for the unit price. That makes 44 cents. 45 eggs total, 5 layers. Divide 45 by 5. That makes 9 eggs per layer.Given that the expression 2x^3 + mx^2 + nx + c leaves the same remainder when divided by x -2 or by x+1 I prove that m+n =-6
Given:
The expression is:
[tex]2x^3+mx^2+nx+c[/tex]
It leaves the same remainder when divided by x -2 or by x+1.
To prove:
[tex]m+n=-6[/tex]
Solution:
Remainder theorem: If a polynomial P(x) is divided by (x-c), thent he remainder is P(c).
Let the given polynomial is:
[tex]P(x)=2x^3+mx^2+nx+c[/tex]
It leaves the same remainder when divided by x -2 or by x+1. By using remainder theorem, we can say that
[tex]P(2)=P(-1)[/tex] ...(i)
Substituting [tex]x=-1[/tex] in the given polynomial.
[tex]P(-1)=2(-1)^3+m(-1)^2+n(-1)+c[/tex]
[tex]P(-1)=-2+m-n+c[/tex]
Substituting [tex]x=2[/tex] in the given polynomial.
[tex]P(2)=2(2)^3+m(2)^2+n(2)+c[/tex]
[tex]P(2)=2(8)+m(4)+2n+c[/tex]
[tex]P(2)=16+4m+2n+c[/tex]
Now, substitute the values of P(2) and P(-1) in (i), we get
[tex]16+4m+2n+c=-2+m-n+c[/tex]
[tex]16+4m+2n+c+2-m+n-c=0[/tex]
[tex]18+3m+3n=0[/tex]
[tex]3m+3n=-18[/tex]
Divide both sides by 3.
[tex]\dfrac{3m+3n}{3}=\dfrac{-18}{3}[/tex]
[tex]m+n=-6[/tex]
Hence proved.
What are the zeroes of f(x) = x^2 + 5x + 6? (4 points)
A) x = -2, -3
B) x = 2,3
C) x= -2,3
D) x = 2, -3
Answer:
the answer is A, if you need explanation comment
Step-by-step explanation:
Find the value of a and b
Answer:
a = 133 degrees
b = 78 degrees
Step-by-step explanation:
the top and bottom lines are parallel.
the two sidelines are lines that intercept the top and bottom lines.
as they intercept parallel lines, they actually must have the same angles with them.
so, the 47 degrees inner angle at the bottom line, must be also somewhere at the interception point with the top line. and right, it must be now mirrored the outward angle at the top line. and that means a (the inward angle at the top line) is also the outward angle at the bottom line.
the sum of inward and outward angles at a point must always be 180 degrees.
so, the outward angle of 47 = the inward angle a =
= 180 - 47 = 133 degrees.
similar in the other side.
102 is the inward angle.
the outward angle of that is 180 - 102 = 78 degrees.
and that is also the inward angle b.
b = 78 degrees
20 Points- Which of the following is true for f of x equals the quotient of the quantity x squared plus 9 and the quantity x minus 3?
There is a removable discontinuity at x = 3.
There is a non-removable discontinuity at x = 3.
The function is continuous for all real numbers.
Answer:
There is a non-removable discontinuity at x = 3
Step-by-step explanation:
We are given that
[tex]f(x)=\frac{x^2+9}{x-3}[/tex]
We have to find true statement about given function.
[tex]\lim_{x\rightarrow 3}f(x)=\lim_{x\rightarrow 3}\frac{x^2+9}{x-3}[/tex]
=[tex]\infty[/tex]
It is not removable discontinuity.
x-3=0
x=3
The function f(x) is not define at x=3. Therefore, the function f(x) is continuous for all real numbers except x=3.
Therefore, x=3 is non- removable discontinuity of function f(x).
Hence, option B is correct.
GIVING BRAINLIEST ANSWER PLZ ';CCC
Answer:
slope= difference in y ÷difference in x
=y-y1÷x-x1
=-3-(-1)÷-3-1
=-3+1÷-3-1
=-2÷-4
=1/2
Step-by-step explanation:
hope this is helpful
Y2 -Y1 ÷ X2-X1
-1 - 1 ÷ -3 - -3= 0.5 or 1/2
Instructions: Problem 2 ! Find the missing angle in the image below. Do not include spaces in your answers !! PLEASE HELP ME
Answer:
Below.
Step-by-step explanation:
Ok so since 71 +25 = 96. A line segment is 180 so 180-96= 84. Hope this is right little hard to see.
Points R, L, and S are
A. non-collinear and non-coplanar
B. coplanar and collinear
C. non-collinear and coplanar
D. collinear and collinear
Answer:
C. non collinear and coplanar
Option (C) non-collinear and co planar is the correct answer about the points R, L, and S.
What is coplanar?A set of points in space are co planar, if there exists a geometric plane that contains them all.
What is non-collinear?Non-collinear points are points that do not lie on one straight line. The points are not collinear, when they are joined with each other, they form a triangle, which is a three-sided polygon.
For the given situation,
The diagram shows the plane M and the triangle.
In the diagram, all the points are lie on the same plane but the points are not lie on the same line.
Three points are always co planar, and if the points are distinct and non-collinear, the plane they determine is unique.
Hence we can conclude that option (C) non-collinear and co planar is the correct answer about the points R, L, and S.
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2 thirds divided by 4
help please (ignore my answer i just put whatever)
Answer:the awnser would b 2
Step-by-step explanation: it’s telling you if you look at the triangle from ABC it’s 54 degrees, but if you look at it from BAC it’s 30 degrees so you can only draw 2 triangles because no other combination is given the only other information we know is the line connecting A and B is 5 in some length which is a line not a triangle it would be a triangle thou if lines BC and AC were given. Long story short it’s B) 2
Solve: 4(x + 3) ≤ 44
x ≥ 16
x ≤ 16
x ≤ 8
x ≥ 8
Please help
Answer:
C
Step-by-step explanation:
[tex]4(x + 3) \leqslant 44 \\ \\ 4x + 12 \leqslant 44 \\ 4x \leqslant 44 - 12 \\ 4x \leqslant 32 \\ 4x \div 4 \leqslant 32 \div 4 \\ x \leqslant 8[/tex]
PLEASE HELP! Solve the system of equations by graphing on your own paper. What is the x-coordinate of the solution?
Answer:
x = 4
Step-by-step explanation:
steps are in the pic above.
7z+15+27, z, plus, 15, plus, 2
Answer:
[tex]7z + 15 + 27 \\ 7z + 42 \\ z = 42 \div 7 \\ z = 6[/tex]
What is the slope of the graph shown below
Answer:
B=-5
Step-by-step explanation:
Slope=rise/run
The line passes in
P1(-1,3)
and
P2(0,-2)
So slope=(3-(-2))/(-1-0)=5/-1=-5
(15pts) Given the diagram: what is the area of the shaded sector corresponding to AB, rounded to two decimal places?
Answer:
Area of a Sector of Circle = (θ/360º) × πr²
θ = angle subtended at the center r = radius of the circle[tex]area \: = \: \frac{70}{360} \times \frac{22}{7} \times 10 {}^{2} \\ = 61.11[/tex]
on rounding off to two decimal places:-
61 Sq. unitsPorfavor necesito ayuda en esto.
Es para hoy :(
Answer:
17
Step-by-step explanation:
Which equation describes the summer for two vectors plotted below?
Answer:
B
Step-by-step explanation:
Expansion (2x-3y+4z)^2
Answer:
Step-by-step explanation:
(a+b+c)²=a²+b²+c²+2ab+2bc+2ca
(2x-3y+4z)²=(2x)²+(-3y)²+(4z)²+2(2x)(-3y)+2(-3y)(4z)+2(4z)(2x)
=4x²+9y²+16z²-12xy-24yz+16zx
We know that,
→ (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
Now Putting 2x = a, -3y = b and 4z = c , we get
→ (2x - 3y + 4z)²
→ (2x)² + (- 3y)² + (4z)² + 2 × 2x × (- 3y) + 2 × (- 3y) × 4z + 2 × 4z × 2x
→ 4x² + 9y² + 16z² - 12xy - 24yz + 16zx
Arranging according to the like terms, we get
→ 4x² - 12xy + 16zx + 9y² - 24yz + 16z²
▬▬▬▬▬▬▬▬▬▬▬▬Can someone help me with this question
Use the integer tiles to evaluate the following expressions. 6 + 3 = 6 + (–4) = 6 + (–6) =
Given:
The expressions are:
[tex]6+3[/tex]
[tex]6+(-4)[/tex]
[tex]6+(-6)[/tex]
To find:
The value of given expression by using integer tiles.
Solution:
We have,
[tex]6+3[/tex]
Here, both number are positive. When we add 6 and 3 positive integer tiles, we get 9 positive integer tiles as shown in the below figure. So,
[tex]6+3=9[/tex]
Similarly,
[tex]6+(-4)[/tex]
Here, 6 is positive and -4 is negative. It means we have 6 positive integer tiles and 4 negative integer tiles.
When we cancel the positive and negative integer tiles, we get 2 positive integer tiles as shown in the below figure. So,
[tex]6+(-4)=2[/tex]
[tex]6+(-6)[/tex]
Here, 6 is positive and -6 is negative. It means we have 6 positive integer tiles and 6 negative integer tiles.
When we cancel the positive and negative integer tiles, we get 0 integer tiles as shown in the below figure. So,
[tex]6+(-6)=0[/tex]
Therefore, [tex]6+3=9, 6+(-4)=2,6+(-6)=0[/tex].
Answer:
1=9
2=2
3=0
Step-by-step explanation:
(a) Expand and simplify (4 + root3)(4 – root3).
Step-by-step explanation:
just use (a+b)(a-b) = [tex]a^{2} - b^{2}[/tex][tex](4+\sqrt{3}) (4-\sqrt{3)} = 4^{2} - (\sqrt{3} )^{2} = 16 - 3 = 13[/tex]
answer is 13
On the unit circle, which of the following angles has the terminal point
coordinates.
A. 45
B. 135
C. 225
D. 315
Answer: C. 225
Step-by-step explanation:
Directions: Given the point and slope, write the equation of the line.
(4, 2); slope = 36
Answer:
y - 2 = 36(x - 4)
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Here m = 36 and (a, b ) = (4, 2 ) , then
y - 2 = 36(x - 4) ← equation of line
What type of health screening would this patient most likely receive?
Sue is a 45-year-old woman with a family history of breast cancer. Her healthcare professional will most likely recommend that she receive a
Answer:
she would need annual breast cancer screening with mammograms.
Step-by-step explanation:
hope this helps! hope you have a nice day.
The two
triangles are similar.
What is the value of x?
Enter your answer in the box:
Answer:
x = 5
Step-by-step explanation:
Sides of large triangle: 4x and 15
Corresponding sides of small triangle: 3x + 1 and 12
[tex] \dfrac{4x}{15} = \dfrac{3x + 1}{12} [/tex]
[tex] 60 \times \dfrac{4x}{15} = 60 \times \dfrac{3x + 1}{12} [/tex]
[tex] 16x = 15x + 5 [/tex]
[tex] x = 5 [/tex]
Solve the following simultaneous equations : 5m - 3n = 19; m - 6 = -7
Answer:
m = -1
n= -8
Step-by-step explanation:
5m -3n = 19
m - 6 = -7
solve for m:
m = -7+6
m = -1
plug in m
5(-1) - 3n = 19
-5 - 3n = 19
-3n = 24
n = -8