Draw a line for the axis of symmetry of function f. Also mark the x-intercept(s), y-Intercept, and vertex of the function.
f(x)= x^2- 4x-5
+
10-
Line
8
6
4
2-
-10
-8
Answers
Answer:
1) Please find attached the graph sowing the line of symmetry
The symmetry line is a vertical line passing through (2, -9)
2) The x-intercept are (5, 0) and (-1, 0)
The y-intercept is (0, -5)
The vertex is (2, -9)
Step-by-step explanation:
The given function is;
f(x) = x² - 4·x - 5
The data values are generated as follows;
x, f(x)
-1, 0
-0.8, -1.16
-0.6, -2.24
-0.4, -3.24
-0.2, -4.16
0, -5
0.2, -5.76
0.4, -6.44
0.6, -7.04
0.8, -7.56
1, -8
1.2, -8.36
1.4, -8.64
1.6, -8.84
1.8, -8.96
2, -9
2.2, -8.96
2.4, -8.84
2.6, -8.64
2.8, -8.36
3, -8
3.2, -7.56
3.4, -7.04
3.6, 6.44
3.8, -5.76
4, -5
4.2, -4.16
4.4, -3.24
4.6, -2.24
4.8, -1.16
5, 0
The minimum is found from differentiating the function, f(x), with respect to x and looking for the zeros of the result as follows;
f'(x) = 2·x -4
f'(x) = 0 = 2·x -4
x = 2
The y-coordinate gives; f(2) = 2² - 4×2 - 5 = -9
Therefore, the symmetry line is a vertical line passing through (2, -9)
The x-intercept is the point at which y = 0, therefore, from f(x) = x² - 4·x - 5, we have;
0 = x² - 4·x - 5 = (x - 5)·(x + 1)
Therefore, the x-intercept are x = 5 or -1
The x-intercept are (5, 0) and (-1, 0)
The y-intercept occur at the point where the x value = 0, therefore, we have;
The y-intercept occur at y = f(0) = 0² - 4·0 - 5 = -5
The y-intercept is (0, -5)
Re-writing the equation in vertex form y = a(x - h)² + k gives;
f(x) = x² - 4·x - 5 = 1·(x - 2)² - 9
Therefore, the vertex is (2, -9)
Answer:
see attached graph
The x-intercept are (5, 0) and (-1, 0)
The y-intercept is (0, -5)
The vertex is (2, -9)
Step-by-step explanation:
Related Questions
Please answer this question now
Answers
Answer:
m∠C = 102°
Step-by-step explanation:
This is a quadrilateral inscribed in a circle
The sum of opposite angles in a cyclic quadrilateral is equal to 180°
m∠D + m∠B = 180°
m∠B = 180° - m∠D
m∠B = 180° - 80°
m∠B = 100°
We know what m∠B
We have external angles outside the circle.
m∠CDA is opposite m∠B
m∠CDA = 2 × m∠B
m∠CDA = 2 × 100°
m∠CDA = 200°
m∠CDA is the sum of m∠CD and m∠DA
m∠CDA = m∠CD + m∠DA
m∠DA = m∠CDA - m∠CD
m∠DA = 200° - 116°
m∠DA = 84°
m∠DAB is an exterior angle also, hence,
m∠DAB is the sum of m∠DA and m∠AB
m∠DAB = m∠DA + m∠AB
m∠DAB = 84° + 120°
m∠DAB = 204°
Finally we can solve for m∠C
m∠DAB is Opposite m∠C
So, m∠C = 1/2 × m∠DAB
m∠C = 1/2 × 204
m∠C = 102°
problem that would represent
an elevator starts at street
level (main lobby) goes up 6
floors and then back down 8
floors to the parking garage.
1 + 7 - 8 = 0
0 + 8 + (-2) = 6
1 + 6 + (-8) = -1
0 + 6 + (-8) = -2
Answers
[tex]\\ \sf \longmapsto 1+6+(-8)[/tex]
Downward motion noted as negative and upward is positive.Lobby will be 1[tex]\\ \sf \longmapsto 1+6+(-8)[/tex]
[tex]\\ \sf \longmapsto 1+6-8[/tex]
[tex]\\ \sf \longmapsto 7-8[/tex]
[tex]\\ \sf \longmapsto -1[/tex]
option c is correct
A 51-foot wire running from the top of a tent pole to the ground makes an angle of 58° with the ground. If the length of the tent pole is 44 feet, how far is it from the bottom of the tent pole to the point where the wire is fastened to the ground? (The tent pole is not necessarily perpendicular to the ground.)
Answers
Answer:
35.11 ft
Step-by-step explanation:
This given situation can be thought of as triangle [tex]\triangle PQR[/tex] where PQ is the length of pole.
PR is the length of rope.
and QR is the distance of bottom of pole to the point of fastening of rope to the ground.
And [tex]\angle Q \neq 90^\circ[/tex]
Given that:
PQ = 44 ft
PR = 51 ft
[tex]\angle R = 58^\circ[/tex]
To find:
Side QR = ?
Solution:
We can apply Sine Rule here to find the unknown side.
Sine Rule:
[tex]\dfrac{a}{sinA} = \dfrac{b}{sinB} = \dfrac{c}{sinC}[/tex]
Where
a is the side opposite to [tex]\angle A[/tex]
b is the side opposite to [tex]\angle B[/tex]
c is the side opposite to [tex]\angle C[/tex]
[tex]\dfrac{PR}{sinQ}=\dfrac{PQ}{sinR}\\\Rightarrow sin Q =\dfrac{PR}{PQ}\times sinR\\\Rightarrow sin Q =\dfrac{51}{44}\times sin58^\circ\\\Rightarrow \angle Q =79.41^\circ[/tex]
Now,
[tex]\angle P +\angle Q +\angle R =180^\circ\\\Rightarrow \angle P +58^\circ+79.41^\circ=180^\circ\\\Rightarrow \angle P = 42.59^\circ[/tex]
Let us use the Sine rule again:
[tex]\dfrac{QR}{sinP}=\dfrac{PQ}{sinR}\\\Rightarrow QR =\dfrac{sinP}{sinR}\times PQ\\\Rightarrow QR =\dfrac{sin42.59}{sin58}\times 44\\\Rightarrow QR = 35.11\ ft[/tex]
So, the answer is 35.11 ft.
Which equation can be used to solve for x in the following diagram? Choose 1 answer. 2x° degrees, 4x° degrees, 150° degrees
Answers
Answer:
The answer is option D.
Step-by-step explanation:
Hi, there!!!
Here, if you closely look this figure, you will find that AB and CD are interested at a point O.
now, OP is just a line constructed from point "O".
now, 2x°+4x°=150°.....is equation.
{Because, They are vertically opposite angle}
When two st. line intersects at a point then the abgle formed oppositely are equal.
Hope it helps..
WILL MARK BRAINLIEST!!!!20 POINTS!!!!URGENT!!!
Answers
Answer:
the firsts third and last one
Step-by-step explanation:
hope this helped
Solving Inequalities and graphing them.
Answers
Answer:
I used to know this not anymore sry g
Help pls
You add the same amount of money to your savings each week. At week 5 you have $45. At week 12 you have $80. How much money do you have at week 20?
Answers
Answer: $120
First, create a function
x = number of weeky = amount of money in savingsa = amount of money added each weekb = the amount of money in savings at week 0[tex]\left \{ {{5a+b=45} \atop {12a+b=80}} \right.\\\\(5-12)a+(1-1)b=45-80\\\\-7a=-35\\\\a=\frac{-35}{-7} =5\\\\5a+b=45\\\\5(5)+b=45\\\\b=45-25=20[/tex]
Therefore, the function is y = 5x + 20
To find the amount of money at week 20, set x = 20 and solve:
[tex]y=5(20)+20=100+20=120[/tex]
Therefore, the answer is $120.
The two-way frequency table below shows data on years working with the company and college degree status for Tom's coworkers. Complete the following two-way table of row relative frequencies. (If necessary, round your answers to the nearest hundredth.)
Answers
Answer:
Lets start with the top row.
First, add the two values.
5+14=19
Now, divide each value by the total.
5/19=0.26315789473
Round the decimal to the nearest hundredth.
5/19=0.26
14/19=0.73684210526
Round it to the nearest hundredth.
14/19=0.74
Now, The second row.
Add the two values.
16+7=23
Divide the first value by the total.
16/23=0.69565217391
Round it to the nearest hundredth.
16/23=0.70
Divide the second value by the total.
7/23=0.30434782608
Round to the nearest hundredth.
7/23=0.30
Done!
Answer:
Row 1: 0.26 0.74
Row 2: 0.70 0.30
Step-by-step explanation:
Khan
Angie has 18 oatmeal cookies.She splits them evenly among b bags.Choose the expression that shows how many cookies are in each bag. 1.B-18 2.18/b 3.18 4.B
Answers
Answer:
2, 18/b
Step-by-step explanation:
if you divide by the number of bags you will get the number of cookies in each bag.
Answer:2,18/b
Step-by-step explanation:If you multiply the cookies in a bag by b, you will get 18
(1,-2),(-2,-5) find the slope and show me how u got it please
Answers
Answer:
where m= slope m= -7/3
Step-by-step explanation:
Solve: XC - XV. Show your answer as a Roman Numeral. Standard Number 1 5 10 50 100 500 1,000 Roman Numeral 1 V X Х L с D M A) V B) VI C) VIL
Answers
Answer: A
Step-by-step explanation:
I need domain and range
Answers
Answer:
Domain: all real numbers/ (-inf,inf)/ -inf<x<inf
Range: all real numbers greater than -4/ [-4,inf)/ -4≤y<inf
Step-by-step explanation:
the graphs/equations of ALL quadratics (parabolas) have a domain of all real numbers
The vertex of the parabola is at y=-4 so the range cannot be any less than that, and then both ends point up, so they will continue on for infinity.
Hope i could help!
Find the value of x for which pll q.
Answers
Answer:
D) 9
Step-by-step explanation:
These angles are equal to each other because they’re alternate interior angles so:
9x + 8 = 15x - 46
9x - 15x = -46 - 8
-6x = -54
x = 9
The average of four different positive integers is 9. What is the greatest value for one of the integers?
Answers
From the given information; Let the unknown different positive integers be (a, b, c and d).
An integer is a set of element that are infinite and numeric in nature, these numbers do not contain fractions.
Suppose we make an assumption that (a) should be the greatest value of this integer.
Then, the other three positive integers (b, c and d) can be 1, 2 and 3 respectively in order to make (a) the greatest value of the integer.
Therefore, the average of this integers = 9
Mathematically;
[tex]\mathbf{\dfrac{(a+b+c+d)}{4} =9}[/tex]
[tex]\mathbf{\dfrac{(a+1+2+3)}{4} =9}[/tex]
[tex]\mathbf{\dfrac{(6+a)}{4} =9}[/tex]
By cross multiplying;
6+a = 9 × 4
6+a = 36
a = 36 - 6
a = 30
Therefore, we can conclude that from the average of four positive integers which is equal to 9, the greatest value for one of the selected integers is equal to 30.
Learn more about integers here:
https://brainly.com/question/15276410?referrer=searchResults
The greatest value for one of the four positive integers is 30.
To find the largest positive integer, you have to minimize the other three positive integers.
The least three different positive integers available = 1, 2, 3let the largest positive integer = ythe sum of the four different positive integers = 1 + 2 + 3 + y = 6 + yFind the average of the four positive integers and equate it to the given value of the average.
[tex]\frac{6 + y}{4} = 9\\\\6+ y = 36\\\\y = 36-6\\\\y = 30[/tex]
Thus, the greatest value for one of the positive integers is 30
learn more here: https://brainly.com/question/20118982
The length of the major axis of the ellipse below is 10 What is the sum of the lengths of the red and blue line segments? A. 10 B. 5 C. 15 D. 20
Answers
Answer:
A. 10
Step-by-step explanation:
As we know that
The length of the major axis of the ellipse is 10
i.e
2 a = 10
Also, the ellipse is the curve that consists of 2 focal points in order that the total of the distance to the 2 focal points would remain constant for each and every point displayed in the curve
Now we assume that P is the curve point
So,
PF1 + PF2
i.e
2 a (blue line) + (red line)
2 a = 10
Therefore the sum of the length is 10
Answer:
10
Step-by-step explanation:
What are the solutions to the equation f(x)=g(x)?
A) x= -3, 4
B) x= -4, 2.5
C) x= -0.8, 2.5
D) x= 8, -8
Answers
Answer:
B
Step-by-step explanation:
The points where f(x) intersects g(x) are - 4 and 2.5. These points are the solution of the equation f(x)=g(x)
Answer:
(-4,8) and ( 2.5, -8)
Step-by-step explanation:
The solutions are where the two graphs intersect
They intersect at x = -4 and y = 8 and at x = 2.5 and y = -8
(-4,8) and ( 2.5, -8)
Meguel does not understand which digit is in the tenths location in the number 514.196 Where would it be located at
Answers
Answer:
first number after the decimal point
Step-by-step explanation:
after the decimal point is the tenths, hundredths, and thousandths place.
0.1 - tenths
0.09 - hundredths
0.006 - thousandths
SOMEBODY HELP PLEASE! ACME Hardware is introducing a new product called Greener Cleaner. Complete the table by finding the cost per milliliter for each size based on the sales price. One liter is 1,000 milliliters. (Answer the questions too, please!)
Answers
Answer:
Kindly check explanation
Step-by-step explanation:
SMALL SIZE :
AMOUNT OF LIQUID = 250 milliliters
Sales price = $4.50
Cost per milliliter :
Sales price / amount of liquid
$4.50 / 250 = $0.018
MEDIUM SIZE :
AMOUNT OF LIQUID = 500 milliliters
Sales price = $9.95
Cost per milliliter :
Sales price / amount of liquid
$9.95 / 500 = $0.0199
= $0.020 ( 3 decimal places)
LARGE SIZE :
AMOUNT OF LIQUID = 1 LITRE = 1000 milliliters
Sales price = $16.95
Cost per milliliter :
Sales price / amount of liquid
$16.95 / 500 = $0.0199
= $0.01695
= $0.017 ( 3 decimal places)
A) LARGE < SMALL < MEDIUM
B) LEAST EXPENSIVE WAY TO BUY 1500 milliliters of green cleaner :
1 large size + 2 small sizes
$16.95 + 2($4.50)
$16.95 + $9.00
= $25.95
C.) MOST EXPENSIVE WAY TO BUY 1500 milliliters of green cleaner :
3 medium sizes
3 * ($9.95)
$29.85
Question. 1 The product of a monomial and a binomial is a (a) monomial (b) binomial (c) trinomial (d) None of these
Answers
Answer:
The answer to this question is (D)
The hypotenuse of a right triangle measures nem and one of its legs measures o em.
Mnd the measure of the other leg. If necessary, round to the nearest tenth.
Sun
attempt to
Answers
Using Pythagorean theorem
[tex]\\ \sf\longmapsto P^2=H^2-B^2[/tex]
[tex]\\ \sf\longmapsto P^2=11^2-9^2[/tex]
[tex]\\ \sf\longmapsto P^2=121-81[/tex]
[tex]\\ \sf\longmapsto P^2=40[/tex]
[tex]\\ \sf\longmapsto P=\sqrt{40}[/tex]
[tex]\\ \sf\longmapsto P=6.2cm[/tex]
Step-by-step explanation:
Given,
Hypotenuse = 11 cm
Base (One of the given leg) = 9 cm
Therefore,
According to Pythagoras Theorem,
[tex] {base}^{2} + {height}^{2} = {hypotenuse}^{2} [/tex]
[tex] = > {(9)}^{2} + {height}^{2} = {(11)}^{2} [/tex]
[tex] = > {height}^{2} = {(11)}^{2} - {(9)}^{2} [/tex]
[tex] = > {height}^{2} = 121 - 81[/tex]
[tex] = > {height}^{2} = 4 0[/tex]
[tex] = > height = \sqrt{40} [/tex]
=> height = 6.3245553203
When rounded to nearest tenth,
=> height = 6.3
Hence,
Required length of other leg is 6.3 (Ans)
+
If the
sides of a triangles are
6, 8 and n. how
many integer values of n
could be the
measure of the
third side of the triangle?
Answers
Answer:
11
Step-by-step explanation:
The sum of the shortest two sides must be greater than the longest side.
If n is the longest side:
6 + 8 > n
14 > n
If 8 is the longest side:
6 + n > 8
n > 2
So n must be an integer greater than 2 and less than 14.
n can be 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, or 13.
There are 11 possible integers.
[tex] \LARGE{ \boxed{ \rm{ \purple{Answer}}}}[/tex]
We know,
Sum of two sides of a triangle > Third side
Then,
⇛ 6 + 8 > n
⇛ 14 > n
Nextly,
Difference of two sides of a triangle < Third side
Then,
⇛ 8 - 6 < n
⇛ 2 < n
Then, Range of third side:
☃️ 2 < n < 14
Possible measures of 3rd sides = 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 or 13.
There are 11 possible values of 3rd side. Out of them, any measure is the length of 3rd side.
━━━━━━━━━━━━━━━━━━━━
Which expression gives the length of the transverse axis of the hyperbola
shown below?
X
У
Focus
Focus
O AY
O B. X-y
O c. xt
O D. X+ y
Answers
Answer:
Option (B)
Step-by-step explanation:
From the picture attached,
F1 and F2 are the focii of the hyperbola.
Point P(x, y) is x units distant from F1 and y units distant from the other focus F2.
By the definition of a hyperbola,
"Difference between the distances of a point from the focii is always constant and equals to the measure of transverse axis."
Difference in the distances of point P from focii F1 and F2 = (x - y) units
This distance is equal to the length of the transverse axis = (x - y) units
Therefore, Option (B) will be the answer.
Answer:
x-y
Step-by-step explanation:
The length of one side of a rhombus is 20 m.Find its perimeter.
Answers
Answer:
80 m
Step-by-step explanation:
Given :-
One side of rhombus = 20 m.
[ as one of the property of rhombus = all sides are equal ]
So, perimeter of rhombus = sum of all sides
= 20+20+20+20 = 80 m
...........................OR............................
Perimeter of rhombus = 4 × side
= 4 × 20 = 80 m
Hence, the perimeter of the rhombus is 80m.
Answer:
The perimeter is 80 meters
Step-by-step explanation:
The geometric characteristic of a rhombus is that it has 4 equal sides, then if one side measures 20 m, then each of the other sides measure also 20 m.Then its perimeter (addition of all the sides must render: 4 * 20 m = 80 m
What am I supposed to do when parentheses are side by side like this?
Answers
Answer:
Evaluate each expression inside both grouping symbols, then multiply the result.
Step-by-step explanation:
[tex]\displaystyle (3 - 1)(4 + 2) = (2)(6) = 12[/tex]
G - Grouping Symbols
E - Exponents
M\D - Division & Multiplication [left to right]
S\A - Subtraction & Addition [right to left OR vice versa]
I am joyous to assist you at any time.
15 points! I will give Brainliest and heart! Answer ASAP but with DETAIL, I need step - by - step, clear words, correct grammar. A pair of equations is shown below: y = 3x − 5 y = 6x − 8 Part A: Explain how you will solve the pair of equations by substitution or elimination. Show all the steps and write the solution. (5 points) Part B: If the two equations are graphed, at what point will the lines representing the two equations intersect? Explain your answer. (5 points)
Answers
Hey there! I'm happy to help!
PART A
Let's look at our two equations.
y=3x-5
y=6x-8
We will solve this with substitution because we have two different values for y, so it will be be very easy to substitute.
We know that y is equal to 6x-8. This means that we can replace the y in the first equation with 6x-8 and then solve for x.
6x-8=3x-5
We add 8 to both sides.
6x=3x+3
We subtract 3x from both sides.
3x=3
We divide both sides by 3.
x=1
We can plug this x-value into either of our equations to figure out what y is.
y=6(1)-8
y=6-8
y=-2
Therefore, our solution is x=1 and y= -2.
PART B
When graphing the two equations in a systems of equation, the point where they intersect is the solution. We already have our solution, so now we will just write it as a point, which is (1,-2).
Have a wonderful day! :D
Answer:
see below
Step-by-step explanation:
y = 3x − 5
y = 6x − 8
I will use substitution by substituting for y in the first equation
y = 3x − 5
6x -8 = 3x-5
Subtract 3x from each side
6x-3x -8 = 3x-5-3x
3x-8 = -5
Add 8 to each side
3x-8+8 = -5+8
3x =3
Divide by 3
3x/3= 3/3
x =1
Now find y
y = 3x − 5
= 3(1) -5
=3-5
= -2
( 1,-2)
The two lines will intersect at ( 1,-2)
The solution to the two equations is where the lines intersect.
A truck costs $8,000 with a residual value of $1,000. It has an estimated useful life of 7 years. If the truck was bought on July 9 what would be the book value at the end of year 1?
Answers
Answer:
$7520.55
Step-by-step explanation:
Cost of truck = $8000
Residual value = $1000
Estimated useful life = 7 years
Depreciation = (cost of asset - salvage value) / useful life
Depreciation = (8000 - 1000) / 7
Depreciation = 7000 / 7
Depreciation = $1000
Truck was purchased on July 9, Therefore, Depreciation by the end of year one will be;
Number of days between July 9 and year end = 175 days
Daily Depreciation = $1000 / 365 = $2.739
Total Depreciation by year end = (daily Depreciation * 175 days) = $479.45.
Book value at the end of year 1 = (8000 - 479.45)
= $7520.55
Answer:
The answer is "$7,500".
Step-by-step explanation:
Formula:
In the month of July-December the depreciation:
[tex]\frac{\text{Cost-Residual}}{\text{Useful life}}\times \frac{6}{12} \\[/tex]
Cost-Residual= costs -residual value
Given:
Cost-Residual = $8, 000 - $ 1,00
= $7,000
Useful life= 7 years
Put the value in the above-given formula:
[tex]=\frac{7 000}{7}\times \frac{6}{12}\\\\= 1 000\times \frac{1}{2}\\\\= 5 00\\[/tex]
Therefore, the book value on point at the end of one year is:
= $8,000 -$ 500
= $7,500
Correct answer gets brainliest and 5 stars
Answers
Answer:
Does the answer help you?
what are the roots of the quadratic equation below 2x^2+8x+7=0
Answers
Answer:
x = -1.29 and -2.71
Step-by-step explanation:
Use the quadratic formula, which is [tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex] and [tex]x=\frac{-b-\sqrt{b^2-4ac} }{2a}[/tex]
[tex]\frac{-8+\sqrt{8^2-4(2)(7)} }{2(2)}[/tex] and [tex]\frac{-8-\sqrt{8^2-4(2)(7)} }{2(2)}[/tex]
[tex]\frac{-8+\sqrt{8} }{4}[/tex] and [tex]\frac{-8-\sqrt{8} }{4}[/tex]
Further reduced down to:
[tex]\frac{-8+2\sqrt{2} }{4}[/tex] and [tex]\frac{-8-2\sqrt{2} }{4}[/tex]
In decimal form, to the hundredths place, both of these are:
-1.29 and -2.71
ILL MARK BRAINIEST IF U DO THIS RIGHT!!!
Answers
Answer:
D because even though the flat fee is 150 paying 5$ a hour it will cost less
Mike wants to buy a used car for $3200. He has$400 in savings and can save another $250 each month. How many months will it take him to be able to buy this car?
Answers
Answer:
12 months
Step-by-step explanation:
mental math