Answers
Answer:
A) (-8, -16)
B) (0, 48)
C) (-4, 0), (-12, 0)
Step-by-step explanation:
A) the vertex is the minimum y value.
extremes of a function we get by using the first derivation and solving it for y' = 0.
y = x² + 16x + 48
y' = 2x + 16 = 0
2x = -16
x = -8
so, the vertex is at x=-8.
the y value is (-8)² + 16(-8) + 48 = 64 - 128 + 48 = -16
B) is totally simple. it is f(0) or x=0. so, y is 48.
C) is the solution of the equation for y = 0.
the solution for such a quadratic equation is
x = (-b ± sqrt(b² - 4ac)) / (2a)
in our case here
a=1
b=16
c=48
x = (-16 ± sqrt(16² - 4×48)) / 2 = (-16 ± sqrt(256-192)) / 2 =
= (-16 ± sqrt(64)) / 2 = (-16 ± 8) / 2 = (-8 ± 4)
x1 = -8 + 4 = -4
x2 = -8 - 4 = -12
so the x- intercepts are (-4, 0), (-12, 0)
Related Questions
How many kilograms of coffee worth 40/kg must be mixed with coffee worth $11/kg to give 12kg of coffee worth $9.50/kg
Answers
Answer:
0.62kg
Step-by-step explanation:
Let
x = 40/kg coffee
y = 11/kg coffee
two equations can be derived from the question
x + y = 12 equation 1
40x + 11y = 114 (9.5 x 12) equation 2
multiply equation 1 by 11
11x + 11y = 132 equation 3
subtract eqn 3 from eqn 2
29x = 18
divide both sides of the equation by 29
x = 0.62kg
Please solve fast. It's really easy!
Answers
Answer:
j = 10.1
Step-by-step explanation:
The difference between 9.5 and 11.3 is
11.3 - 9.5 = 1.8
This is split into 3 divisions, that is
1.8 ÷ 3 = 0.6
Then
j = 9.5 + 0.6 = 10.1
The topic= Direct and Inverse Proportions
It is given that y is directly proportional to x and y=36 and when x=12
(a)
An equation connecting to x and y
(b)
That value of y when x=5
(c)
The value of x when y=12
Please help me answer my hw, thank you!
Answers
Answer:
A) 3
B)60
C)4
Step-by-step explanation:
y = kx
36 = 12k
A)k=3
~~~~~~~~~~
b) 60
12*5
c) 4
12/3
CAN SOMEBODY PLEASE HELP ME
Answers
Answer: AS = 46
Step-by-step explanation:
Since we know that a circumcenter is equidistant from all three vertices, we know that segment BS is congruent to segment CS which is congruent to segment AS. By the definition of congruent segments, BS = AS. Since BS is 46, we know that AS will also be 46.
find the measure of the missing angles in the kite
Answers
Answer: 360 - 44 - 80 = 236
236 ÷ 2 = 118
both angle equal to 118
Step-by-step explanation:
The measure of angle 1 is 118 degrees and the measure of angle 2 is 118 degrees.
What is quadrilateral?It is defined as the four-sided polygon in geometry having four edges and four corners.
We know that kite is quadrilateral, having :
It has one pair of opposite congruent angles.
One diagonal is bisected.
The top and bottom angles are bisected but
As we know from the kite properties it has one pair of opposite congruent angles
From the properties of the quadrilateral the sum of the interior angles is 360 degrees
44 + angle 1 + angle 2 + 80 = 360
Angle 1 = angle 2 = x(say)
44 + x + x + 80 = 360
2x + 124 = 360
2x = 236
x = 118 degrees
Angle 1 = angle 2 = 118 degrees
Thus, the measure of angle 1 is 118 degrees and the measure of angle 2 is 118 degrees or m∠1 = 118° and m∠2 = 118°.
Learn more about the quadrilateral here:
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I really need help……
Answers
Answer:
Option C
Step-by-step explanation:
A function's input is assigned to exactly one output. Any input must not repeat.
Option A's not a function because the input of 3 repeats.
Option B's not a function because the input of -4 repeats.
Option C's a function because no inputs repeat.
Option D's not a function because the input of 5 repeats.
Hope this helps.
HELPPPPP ASAP!!!! Thx!! and NOOO FILESSSS!!
Answers
Answer:
[tex]x=32[/tex]°
Step-by-step explanation:
The law of sines is a property of all triangles that relates the sides and angles of a triangle. This property states the following:
[tex]\frac{sin(a)}{A}=\frac{sin(b)}{B}=\frac{sin(c)}{C}[/tex]
Where side (A) is the side opposite angle (<a), side (B) is the side opposite angle (<b), and side (C) is the property opposite angle (<c).
Substitute each of the sides and respective angles into the formula, and solve for the unknown angle (<x). Please note that a triangle with two congruent sides (referred to as an isosceles triangle) has a property called the base angles theorem. This states that the angles opposite the congruent sides in an isosceles triangle are congruent. Therefore, there can be two (<x)'s in this triangle.
[tex]\frac{sin(a)}{A}=\frac{sin(b)}{B}=\frac{sin(c)}{C}[/tex]
[tex]\frac{sin(x)}{10}=\frac{sin(116)}{17}=\frac{sin(x)}{10}[/tex]
One can shorten the equation so it only holds the parts that will play a role in solving this equation,
[tex]\frac{sin(x)}{10}=\frac{sin(116)}{17}[/tex]
Now take the cross product in this equation to simplify it further,
[tex]\frac{sin(x)}{10}=\frac{sin(116)}{17}[/tex]
[tex]17(sin(x))=10(sin(116))[/tex]
Inverse operations, solve this equation for (x),
[tex]17(sin(x))=10(sin(116))[/tex]
[tex]sin(x)=\frac{10(sin(116))}{17}[/tex]
[tex]x=sin^-^1(\frac{10(sin(116))}{17})[/tex]
[tex]x=31.91782...[/tex]
[tex]x\approx32[/tex]
Answer:
hello,
Step-by-step explanation:
the triangle is isocele,
x+x+116=180
x=(180-116)/2
x= 32° (thirty-two , trente-deux in french)
What do you know about the slope when X2 - X1 = 0 ?
A. The slope is undefined.
B. The slope is zero.
C. The slope is positive.
D. The slope is negative.
Answers
Answer:
B
Step-by-step explanation:
The slope is zero is the answer
The radius of the base of this right circular cone is 10 centimeters and the slant height of the cone is 25 centimeters. What is its surface area? Leave your answer in terms of
OA) 100 cm OC) 350 cm? OB) 250 cm OD) 6257 cm
Answers
Answer:
C.) [tex]350\pi[/tex] [tex]cm^{2}[/tex]
Step-by-step explanation:
Since we are given the radius of the cone's base and the slant height, we can use the following equation to solve for surface area:
[tex]A = \pi r^{2} + \pi rl[/tex]
Now we just plug in the given information and solve:
[tex]A = \pi (10cm)^2 + (\pi) (10cm)(25cm)\\A = 100\pi cm^2 + 250\pi cm^2\\A = 350\pi cm^2[/tex]
answer the question
Answers
(v^3)(w^-3) / (-v^-6)(w^3)
(-v^9)(w^-3) / (w^3)
(-v^9)(w^-6)
ANSWER: Option 4
Hope this helps!
Theodore recently hired a contractor to do some necessary work. On the final bill, Theodore was charged a total of $715. $315 was listed for parts and the rest for labor. If the hourly rate for labor was $50, how many hours of labor was needed to complete the job?
Answers
Answer:
Hours of labor needed = 8 hour
Step-by-step explanation:
Given:
Amount total charged = $715
Listed amount = $315
Hourly rate for labor = $50
Find:
Hours of labor needed
Computation:
Total amount of labour = Amount total charged - Listed amount
Total amount of labour = 715 - 315
Total amount of labour = $400
Hours of labor needed = Total amount of labour / Hourly rate for labor
Hours of labor needed = 400 / 50
Hours of labor needed = 8 hour
find the surface area of this cylinder??
Answers
Answer:
4
Step-by-step explanation:
A=ch
then,
2ft×2ft
4ft
If area of circle is 210cm ,find the value of radius
Answers
Answer:
8.18
Step-by-step explanation:
r = square root of A/ pi
R = square root 210/ 3.14
I hope the formula helped!
3. Arcadia, decides to offer two different options for payment.
Option 1
No admission fee
$15 admission fee
and
Option 2
$5 / game
$6/game
a. Write an equation to represent the total cost of a day spent gaming at Arcadia for Option 2.
the total cost of the day would be
Answers
Answer:
[tex]Total = 15 + 6 x[/tex]
Step-by-step explanation:
Given
Option 1
[tex]Admission = 0[/tex]
[tex]Rate = \$5/game[/tex]
Option 2
[tex]Admission = 15[/tex]
[tex]Rate = \$6/game[/tex]
Required
The total cost for option 2
This is calculated as:
[tex]Total = Admission + Rate * x[/tex]
Where:
[tex]x \to[/tex] games
So, we have:
[tex]Total = 15 + 6 * x[/tex]
[tex]Total = 15 + 6 x[/tex]
Help anyone can help me do this question,I will mark brainlest.
Answers
Answer:
but what to do in do I have to find the area of the particular Region or a length of that
You have to post this question again with full explanation!
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan. Click the trashcan to clear all your answers.
Indicate the equation of the line through (2, -4) and having slope of 3/5.
Answers
Answer:
The equation of the line is [tex]y = \frac{3}{5}\cdot x -\frac{26}{5}[/tex].
Step-by-step explanation:
Given the values of the slope and a point of the line, we can derive the equation of the line by means of this formula:
[tex]y-y_{1} = m\cdot (x-x_{1})[/tex] (1)
Where:
[tex]x[/tex] - Independent variable.
[tex]y[/tex] - Dependent variable.
[tex]m[/tex] - Slope.
[tex](x_{1}, y_{1})[/tex] - Coordinates of the given point.
If we know that [tex]m = \frac{3}{5}[/tex] and [tex](x_{1},y_{1}) = (2, -4)[/tex], then the equation of the line is:
[tex]y+4 = \frac{3}{5}\cdot (x-2)[/tex]
[tex]y + 4 = \frac{3}{5}\cdot x -\frac{6}{5}[/tex]
[tex]y = \frac{3}{5}\cdot x -\frac{26}{5}[/tex]
The equation of the line is [tex]y = \frac{3}{5}\cdot x -\frac{26}{5}[/tex].
9. Find the remainder when the polynomial: p(x) = x⁴ + 2x³- 3x² + x - 1 is divided by (x - 2)
pls it's urgent
Answers
Answer:
answer is 21..............
Explanation:
p(x) = x⁴ + 2x³- 3x² + x - 1
Factor of p(x)
x-2=0
x=2
Then by using synthetic division
1/4 Luke's marbles are white,
3/8 are blue,
and the rest are 30 yellow marbles.
How many of the marbles are white?
Answers
Answer:
i dont know the total sum of marbles
Step-by-step explanation:
A fraction is written in the form of a numerator and a denominator
where the denominator is greater than the numerator.
1/4 of 80 is 20.
The number of white marbles is 20.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.
Example: 1/2, 1/3 is a fraction.
We have,
Total marbles = x
The number of white marbles = 1/4x
The number of blue marbles = 3/8x
The number of yellow marbles = 30
Total marbles.
x = (1/4)x + (3/8)x + 30
x - (1/4)x - (3/8)x = 30
(8x - 2x - 3x) / 8 = 30
3x/8 = 30
3x = 30 x 8
3x = 240
x = 80
The number of white marbles.
= (1/4)x
= (1/4) x 80
= 20 marbles.
Thus,
The number of white marbles is 20.
Learn more about fractions here:
https://brainly.com/question/24370499
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An equation parallel to y = – 3x + 2 through (2,3)
Answers
Answer:
y = -3x+9
Step-by-step explanation:
Parallel lines have the same slope
y = -3x+2
This is in slope intercept form where y =mx+b where m is the slope
The slope is -3
y = -3x+b
Using the point (2,3)
3 = -3(2)+b
3 = -6+b
Add 6 to each side
3+6 = b
9=b
y = -3x+9
Answer:
slope (m) = -3
3= -3(2)+b
b = 9
y=mx+b → y= -3x+9
OAmalOHopeO
Which shapes have the greatest area?
(Select all that apply.)
Answers
Answer:
the trapiezium
Step-by-step explanation:
It has a area of 4 which is the highest
Can someone please help me with this
Answers
Answer:
Step-by-step explanation:
Answered by Gauthmath
Find an explicit rule for the nth term of the sequence.
-1, -5, -25, -125, ...
Answers
Answer:
-(5^N)
Step-by-step explanation:
The sequence is a negated 5 to the N power
ex.) -(5^0) = -1
-(5^1) = -5
-(5^2) = -25
-(5^3) =125
help I cant do this 1-(a-b)²
Answers
Instructions: Find the measure of the missing angles in the kite
Answers
Answer:
m∠1 = 90º
m∠2 = 25º
Step-by-step explanation:
m∠1
diagonals of a kite are perpendicular by definition
m∠2
the 65º angle, the angle to the right of ∠1, and ∠2 form a triangle
we know that triangles are 180º
65º + 90º + m∠2 = 180º
m∠2 = 25º
Also called regrouping this is when adding numbers results in more than two digits and one digit is placed in the colum to the left
Answers
Answer:
Carrying forward.
Step-by-step explanation:
When regrouping is done to add the numbers where results in a more than 2 digit and one digit is placed to left Colum is called as carrying forward. As regrouping refers to carrying the place values in order to perform operations like addition or subtraction.NEED HELP ASAP, find the value of X
Answers
Answer:
C
Step-by-step explanation:
Given 2 intersecting chords in a circle, then
The product of the parts of one chord is equal to the product of the parts of the other chord, that is
DK × KB = AK × KC , substitute values
12(4x + 1) = 14(3 + 3x) ← distribute parenthesis on both sides )
48x + 12 = 42 + 42x ( subtract 42x from both sides )
6x + 12 = 42 ( subtract 12 from both sides )
6x = 30 ( divide both sides by 6 )
x = 5 → C
(3 1/3) (6) What is the answer?
Answers
Answer:
20
Step-by-step explanation:
(6x3=18) (6x1/3=2) (18+2=20)
First things first!
Multiply 6 by 3 (18).
Mulitply 6 by 1/3 (2).
Add 18 and 2, and ... *drum roll*, the final answer is 20!
Hope this helps :)
Find the value of x.
Answers
Answer:
x=8
Step-by-step explanation:
(3x-8)/1=4x/2. 3x-8=2x, x=8
How long would it take a garden snail at his top speed of 0.01 m/s to travel 1 mile? Use 1 mile = 1609 meters. Round to the nearest whole hour.
Answers
Answer:
45 hours
Step-by-step explanation:
1 mile * 1609 meters * 1 s = 160900 sec
1 mile .01 meters
160900 sec / 60 /60 = 44.7 = 45 hours
Step-by-step explanation:
This is a cute question lol.
So this lil snail is trying to go 1609 meters, at a speed of 0.01 m/s (meters per second). Lets see how long that takes.
The way I like to do conversion problems is by starting with the value that doesn't have something on the bottom (1609 m) then multiplying to get rid of that variable.
I'll show you what I mean:
[tex]\frac{1609 m}{1} *\frac{1 s}{0.01 m} *\frac{1 min}{60s} *\frac{1 hr}{60 min}[/tex]
Then, we just multiply everything.
[tex]\frac{1609 *1*1}{1*0.01*60*60}hr[/tex]
Simplify.
[tex]\frac{1609}{36}hr[/tex]
Divide.
[tex]44.694444444...hr[/tex]
Round to the nearest whole hour.
[tex]45 hr[/tex]
Answer:
45 hours
Lydia has half of her investment in stock paying a 7% dividend and the other half in a stock paying 13% interest. If her total annual interest is $410, how much does she have invested?
Answers
Answer:
$4,100
Step-by-step explanation:
Interest = principal * rate * time
Let entire principal = amount invested = p
Investment A :
Rate, r = 7%, principal = p/2, time, = 1
Investment B :
Rate, r = 13%, principal = p/2, time = 1
Total interest = $4.10
(p/2 * 0.07 * 1) + (p/2 * 0.13 * 1) = 410
0.035p + 0.065p = 410
0.1p = 410
p = 410 / 0.1
p = $4100
