Answer:
vertex = (- 4, - 18 )
Step-by-step explanation:
Given a parabola in standard form
f(x) = ax² + bx + c ( a ≠ 0 )
The the x- coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
f(x) = x² + 8x - 2 ← is in standard form
with a = 1 and b = 8 , thus
[tex]x_{vertex}[/tex] = - [tex]\frac{8}{2}[/tex] = - 4
Substitute x = - 4 into f(x) for corresponding y- coordinate
f(- 4) = (- 4)² + 8(- 4) - 2 = 16 - 32 - 2 = - 18
vertex = (- 4, - 18 )
The vertex of the parabola is (-4, -18).
Option D is the correct answer.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
To find the vertex of the function f(x) = x² + 8x - 2, we first need to convert the function into vertex form, which is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.
Completing the square.
f(x) = x² + 8x - 2
f(x) = (x + 4)² - 18
Therefore,
The vertex of the parabola is (-4, -18).
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What is the slope?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
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Answer:
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simplify −3x^3(−2x^2+4x−3)
Answer:
Step-by-step explanation:
6x^5 - 12x^4 + 9x^3
(-3x^3*(-2x^2) - 3x^3(4x) - 3x^3(-3)
what is the value of x?
Answer:
60
Step-by-step explanation:
60 times 2 is 120 plus 24 is 144
Purple Taxi has no pick-up fee, but charges $0.25 per mile. ABC Taxi charges $3 for pick-up and $0.15 per mile. Which inequality can be used to find the number of miles, n, for which the cost of a cab ride with Purple Taxi exceeds the cost of a cab ride with ABC Taxi?
gohead ask a teacher or another site
I need the same question to
One cubic centimeter of sand weighs 1.9 grams. Find the amount of sand that the sandcastle bucket can hold.
Answer:
2160
Step-by-step explanation:
1872(volume of the cube)+288(volume of the square pyramid)=
2160
v of cube= lwh
v of square pyramid= a² times h/3
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A jar contains 4 red marbles, 6 blue marbles, 3 yellow marbles, and 5 green marbles. If one marble is randomly selected, what is the probability that it is red or green?
Answer:
1/2
Step-by-step explanation:
4 red marbles, 6 blue marbles, 3 yellow marbles, and 5 green = 18 marbles
P( red or green) = red or green / total
= (4+5) / 18
= 9/18
=1/2
Answer:
50%
Step-by-step explanation:
4 red + 5 green = 9 marbles
total marbles = 18 marbles
9 is 50% of 18
What is the solution to 2x2+8x=x2-16?
Answer:
x = -4
Step-by-step explanation:
1. (2x2 + 8x) - (x2 - 16) = 0
2. Factoring x2+8x+16
The first term is, x2 its coefficient is 1 .
The middle term is, +8x its coefficient is 8 .
The last term, "the constant", is +16
Step-1 : Multiply the coefficient of the first term by the constant 1 • 16 = 16
Step-2 : Find two factors of 16 whose sum equals the coefficient of the middle term, which is 8 .
-16 + -1 = -17
-8 + -2 = -10
-4 + -4 = -8
-2 + -8 = -10
-1 + -16 = -17
1 + 16 = 17
2 + 8 = 10
4 + 4 = 8 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 4 and 4
x2 + 4x + 4x + 16
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x+4)
Add up the last 2 terms, pulling out common factors :
4 • (x+4)
Step-5 : Add up the four terms of step 4 :
(x+4) • (x+4)
Which is the desired factorization
Multiply (x+4) by (x+4)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (x+4) and the exponents are :
1 , as (x+4) is the same number as (x+4)1
and 1 , as (x+4) is the same number as (x+4)1
The product is therefore, (x+4)(1+1) = (x+4)2
(x + 4)2 = 0
3.
Solve : (x+4)2 = 0
(x+4) 2 represents, in effect, a product of 2 terms which is equal to zero
For the product to be zero, at least one of these terms must be zero. Since all these terms are equal to each other, it actually means : x+4 = 0
Subtract 4 from both sides of the equation :
x = -4
Answer:
x = -4
Step-by-step explanation:
=> 2x²+8x = x²-16
=> 2x²- x² + 8x + 16 = 0
=> x² + 8x + 16 = 0
Using mid-term break formula
=> x² + 4x + 4x + 16 = 0
=> x(x+4)+4(x+4) = 0
=> (x+4)(x+4) = 0
=> (x+4)² = 0
Taking square root on both sides
=> x+4 = 0
=> x = -4
A rectangle has a length of 6 inches, and a width
of 4 inches. What is the area of this rectangle
Answer:
length times width so.... 24
Please answer correctly !!!!!! Will mark brainliest !!!!!!!!!!
Answer:
d) none of the above
Step-by-step explanation:
g is increasing in the intervals:
- 4.5<x<-3.5
and
-1<x<3.5
These are not covered in the answer options
options a) and c) are partially correct
Answer: d) none of the above
Horses are measured in units called hands one inch equals 1/4 hands the average Clydesdale is 17 1/5 hands tall what is this height in inches in feet
Answer:
68.8 Inches, 5.73 Ft.
Step-by-step explanation:
To find out how many inches tall the horse is, divide 17 1/5 by 1/4. You will get 68.8 inches. To convert that to feet, divide it by 12. that would be 5.7333... Ft, so you will probably need to round it to just 5.73.
Find the measure of the arc.
146°E
mFD =
Answer:
124
Step-by-step explanation:
A circle is a curve sketched out by a point moving in a plane. The measure of the arc mFD is 124°.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.
As we know that the angle made at the center of the circle is 360°. And it is mentioned that the measure of mFE is 146°, while mED is 90°. Therefore, the sum of all angles can be written as,
[tex]\angle FOE + \angle EOD + \angle FOD = 360^o\\\\146^o + 90^o + \angle FOD = 360^o\\\\236^o +\angle FOD =360^o\\\\\angle FOD = 124^o[/tex]
Thus, the measure of the arc mFD is 124°.
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Anyone good at exterior angles of triangles ? I WILL MARK THE BRAINLIEST ANSWER
Answer:
Answer B and F are correct.
Step-by-step explanation:
[tex] angle \: 3 \: \: and \: \: \: angle \: \\ \: \: 4 \: \: \: \: are \: \: \: the \: \: exterior \\ angles \: \: \: \: in \: this \: \: traingle[/tex]
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The estimated probability of a football player scoring a touchdown during a particular game is 39%. Of several simulations of the foot ball player playing two games were performed, in what percentage of the simulations would the football player be most likely to get a touchdown in each of the two games?
Answer:
The percentage of the simulations of two games that the football player would most likely get a touchdown in each of the two games = 15.21%
Step-by-step explanation:
The probability of scoring a touchdown in one game for the football player = 39% = 0.39
Probability of scoring a touchdown in each of the two consecutive games = (Probability of scoring a touchdown in the first game) × (Probability of scoring a touchdown in the second game)
Since the probability of scoring a touchdown in each game the football player plays in is independent of one another.
Probability of scoring a touchdown in the first game = Probability of scoring a touchdown in the second game = 0.39
Probability of scoring a touchdown in each of the two consecutive games = 0.39 × 0.39 = 0.1521
If 100 simulations of the two games are made, the player scores in each of the two games in 15.21 of them, hence, the percentage of the simulations that the football player would most likely get a touchdown in each of the two games = 15.21%
Hope this Helps!!
Please please please help !!!
Figure ABCD is reflected about the y-axis to obtain figure A′B′C′D′:
A coordinate plane is shown. Figure ABCD has vertices A at 2 comma 5, B at 1 comma 2, C at 3 comma 1, and D at 4 comma 5. Figure A prime B prime C prime D prime has vertices A prime at negative 2 comma 5, B prime at negative 1 comma 2, C prime at negative 3 comma 1, and D prime at negative 4 comma 5.
Which statement best describes the relationship between the two figures? (4 points)
A)Figure ABCD is similar to figure A′B′C′D′.
B)Figure ABCD is bigger than figure A′B′C′D′.
C)The measure of angle D is equal to the measure of angle A′.
D)The measure of angle D is equal to the measure of angle B′.
Answer:
A
Step-by-step explanation:
These shapes are not identical, because the angles and sides are mirrored, but much like a mirrored object, they are similar. Another way to explain it is when you look into a mirror what you are seeing is not what people see when they see you with their eyes, it's a REFLECTION!
The correct option is Option A: figure ABCD is similar to A′B′C′D′.
What is reflection?Reflection is the translation of the figure about an axis or point so that the distance of the reflected figure from the axis is the same as the distance of the original figure from the axis.
When a point of coordinate (x,y) is reflected about the y-axis then the coordinate of the reflected point will be (-x,y).
In quadrilateral ABCD the coordinate of A is (2,5) and the coordinate of A' is (-2,5). Here the coordinate of y is unchanged and the x coordinate is changed negatively. So point A' is the reflection of point A.
In quadrilateral ABCD the coordinate of B is (1,2) and the coordinate of B' is (-1,2). Here the coordinate of y is unchanged and the x coordinate is changed negatively. So point B' is the reflection of point B.
In quadrilateral ABCD the coordinate of C is (3,1) and the coordinate of C' is (-3,1). Here the coordinate of y is unchanged and the x coordinate is changed negatively. So point C' is the reflection of point C.
In quadrilateral ABCD the coordinate of D is (4,5) and the coordinate of D' is (-4,5). Here the coordinate of y is unchanged and the x coordinate is changed negatively. So point D' is the reflection of point D.
So all the points of quadrilateral ABCD are reflected about the y-axis.
As it is a reflection about the y-axis for which the size will not be changed and both the reflected and the original figure will be similar.
Therefore the correct option is Option A: figure ABCD is similar to A′B′C′D′.
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Use the method of completing the square to write the equations of the given parabola in this form: (y-k)=a(x-h)^2 where a =0, (h,k) is the vertex, and x=h is the axis of symmetry. Find the vertex of this parabola: y=-x^2-2x-5
Answer:
Step-by-step explanation:
There are but a few rules we have to follow when completing the square. However, they are very important rules so we have to be careful. First and foremost, the coefficient on the x-squared term HAS to be a positive 1. If it is not, we have to manipulate the function so it is a positive 1. Then we take half the linear term, square it and add it to both sides (and sometimes this can be very tricky. It is tricky here, so pay attention.)
We begin by separating the x terms from the constant by setting the parabola equal to 0 and moving the constant:
[tex]-x^2-2x=5[/tex]
The coefficient on the x-squared is a negative 1, so we factor out the negative:
[tex]-(x^2+2x)=5[/tex]
The linear term is 2. We take half of 2 which is 1, square 1 to get 1 and add it into the left side. BUT don't forget that we have a -1 out front of the ( ) refusing to be ignored. It is a multiplier. That means that we didn't add in a +1, we added in -1(1) which is -1. That is what we add to the right side:
[tex]-(x^2+2x+1)=5-1[/tex] which simplifies to
[tex]-(x^2+2x+1)=4[/tex]
The reason for this process is that by completing the square you create a perfect square binomial on the left. We rewrite the parabola in terms of that perfect square binomial:
[tex]-(x+1)^2=4[/tex] which simplifies to
[tex]-(x+1)^2-4=y[/tex]
From this you can now determine that the vertex of the parabola is (-1, -4)
find the mean deviation of the following set of numbers: 10,12,14,15, 17 and 19
(A). 2.5
(B). 2.6
(C). 2.7
(D). 2.8
Answer:
2.5
Step-by-step explanation:
I'm sorry I don't know how to explain it but I'm pretty sure the answer is a. 2.5
Can someone show me how to get x for both
Answer:
So since the sum of both is 13 because it shows both of the lines connected as a length of lines.
So we add them (14+x)+(x+15) = 13
14+2x+15 = 19+2x = 13
-6=2x
x=
-3
Step-by-step explanation:
2 families go to the theatre. the p family of 2 adults and 3 children pay £46. the l family of 3 adults and 5 children pay £76. work out thecost of an adult ticket and child ticket.
Answer:
child: 14
Adult : 2
Step-by-step explanation:
2A + 3C = 46------------eqn 1
3A + 5C = 76------------eqn 2
eqn 1 x 3 : 6A + 9C = 138----------- eqn 3
eqn 2 x 2: 6A + 10C = 152-----------eqn 4
eqn 4 - eqn 3: 1OC - 9C = 152 - 138
1C = 14
subst 1C = 14 into eqn 1
2A + 3(14) = 46
2A = 46 - 42
2A = 4
1A = 2
pls help plsplsplsplsplsplspspslpssplsplsplspslpslpslsplspsps
Answer:
Option A, Option C, Option E
Step-by-step explanation:
The area of a kite can be identified through 1 / 2 of the multiplication of each diagonal. The first diagonal is equivalent to the addition of 50 cm and 10 cm, while the second is of length 20 cm + 20 cm.
[tex]1 / 2 * ( 50 + 10 ) * ( 20 + 20 ),\\1 / 2 * ( 60 ) * ( 40 ),\\( 30 ) * ( 40 ),\\\\Area of Kite = 1200 square cm[/tex]
Consider the first option. If we take a look at the bit 2 * ( 1 / 2 * 20 * 50 ) the 2 and 1 /2 cancel each other out, leaving you with 20 * 50 = 1000 . Respectively in the expression 2 * ( 1 / 2 * 20 * 10 ) the 2 and 1 / 2 cancel each other out, leaving you with 20 * 10 = 200;
[tex]1000 + 200 = 1200 square cm,\\Option A - Correct![/tex]
The second option considers the expression 2 * ( 1 / 2 * 20 * 60 ). Again, the 2 and 1 / 2 cancel each other out, leaving you with 20 * 60;
[tex]20 * 60 = 1200 square cm,\\Option B - Correct![/tex]
Option C is a similar version of option a, besides the fact that the 1 / 2 doesn't exist. Thus, Option C is incorrect!
Option D is a similar version of option a as well, but as the 2 doesn't exist, it is incorrect!
This last option, option E is taken as 1 / 2 of the multiplication of the diagonals, and thus is correct!
[tex]1 / 2 * ( 40 * 60 ),\\1 / 2 * ( 2400 ),\\1200 square cm\\\\Correct![/tex]
I need help with this please!!
Answer:
The answer is Point A is equal to (8,0) and Point B is (26,-20) and point C would be (16,-16) and point D would be (8,-30)
Step-by-step explanation:
If f(x) = 3x + 5, find f(2).
Answer:
f(2) = 11
hope this helps
Step-by-step explanation:
3(2)+5
6+5
11
Answer:
11
Step-by-step explanation:
3(2)+5=11
Substitution -- :D
The perimeter of a room is 43 ft. The width is 9 1 2ft. What is the length?
[tex]answer = 12 \: ft \\ solution \\ perimeter = 43 ft\\ breadth = 9 \times \frac{1}{2} = \frac{19}{2 } = 9.5 \: ft\\ now \\ perimeter \: of \: \: rectangle = 2(l + b) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: or \: 43= 2(l + 9.5) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: or \: 43 = 2l + 19 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: or \: - 2l = 19 - 43 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: or \: - 2l = - 24 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: or \: l = \frac{ - 24}{ - 2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: l = 12 \: ft \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]
Answer:
[tex]length = 12ft[/tex]
Step-by-step explanation:
Given that,
[tex]width =9 \frac{1}{2} = 9.5[/tex]
Let's find the length
[tex]perimeter \\43 = 2(l + w) \\ 43= 2(l + 9.5) \\ 43 = 2l + 19 \\ 43 - 19 = 2l \\ 24 = 2l \\ \frac{24}{2} = \frac{2l}{2} \\ l = 12[/tex]
hope this helps
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Given the function f(x) = -5|x + 1|+ 3, for what values of x is f(x) = -12?
x = -2, x = -4
x = -2, x = 4
x = 2, x = -4
x = 2, x = 4
Answer:
x =2 x = -4
Step-by-step explanation:
-5|x + 1|+ 3 = -12
Subtract 3 from each side
-5|x + 1|+ 3-3 = -12 -3
-5|x + 1| = -15
Divide each side by -5
-5/-5|x + 1| = -15/-5
|x + 1| = 3
Since this is an absolute value, we have two solutions one positive and one negative
x+1 = 3 x+1 = -3
Subtract 1 from each side
x+1-1 = 3-1 x+1-1 = -3-1
x =2 x = -4
Answer:
the answer is c
Step-by-step explanation:
A prism has a trapezoid as its base whose area is 140 square centimeters. A cylinder with the same height has a radius of 6 centimeters. How much larger, to the nearest cubic centimeter, is the volume of the prism than the volume of the cylinder?
Answer:
difference in volume = 26.96h cm³
Step-by-step explanation:
The volume of a prism is the product of the base area and the height. A trapezoid prism has a trapezium as the base shape. Therefore,
volume of a trapezoid prism = area of a trapezium × height
area of the base(trapezoid) = 140 cm²
Volume = 140h
Volume of a cylinder = πr²h
where
r = radius
h = height
volume = πr²h
volume = π × 6² × h
volume = 3.14 × 36 × h
volume = 113.04h
To know how much larger the volume of the prism is than the volume of the cylinder we have to take the difference of the volume.
Recall the height are the same
difference in volume = 140h - 113.04h
difference in volume = 26.96h cm³
if a car cover a distance of 189km in 4.5 hours, what is it average speed?
Answer: 42 kmh
Step-by-step explanation:
Speed = distance / time
= 189 / 4.5
= 42 kmh
Answer:
Average Speed = 42 km/hr
Step-by-step explanation:
Given:
Distance = 189 km
Time = 4.5 hours
Required:
Average Speed = ?
Formula :
Average Speed = Total Distance Covered/ Total Time Taken
Solution:
Putting the givens
Average Speed = 189/4.5
Average Speed = 42 km/hr
Marcus saved money from her allowance for some books she wanted to buy. To determine how much money she will save, she used the function rule: y = 6x. Find f (7) A. $13 B. $36 C. $42 D. $49
Answer:
$42
Step-by-step explanation:
Substitute:
Y = 6x
F = 7
So, Y = 6 * 7 = 42
Answer: 42
Step-by-step explanation:
Please answer correctly !!!!!!!! Will mark brianliest !!!!!!!!!!!!
Answer:
Step-by-step explanation:
Since length times width = the area, you know that the area divided by the length is the width. This means that 6x^2 + 10 / 2 = the length.
6x^2 / 2 = 3x^2
10/2 = 5
You end up with 3x^2 + 5 as the length.
Answer & Step-by-step explanation:
Since you trying to find the width when you are given the length and the area, then you are going to divide the area by the length to get the width.
(6x² + 10) ÷ 2
We can also put this into a fraction so it will be easier to know what you are dividing.
[tex]\frac{6x^2+10}{2}[/tex]
Divide 6x² by 2 and divide 10 by 2. Keep the exponent because 2 does not have a variable.
So, your width will be 3x² + 5
Need help fast
(X-5)^2+11=20
Answer:
X= 8, 2
Step-by-step explanation:
So, to solve answers like these you have to have to take the root of both sides and then solve. Please let me know if you have any questions or if I did not answer it correctly or misunderstood the question so that I can help correct my mistakes. Hope this helps!!
Answer:
Answer: (x-2) • (x-8)
(X-5)^2+11=20
Step by Step explanation:
1. 1 • 16 = 16
2. Find two factors of 16 which will be -10
-16 + -1 = -17
-8 + -2 = -10
3. x2 - 8x - 2x - 16
4. x • (x-8)
2 • (x-8)
5. (x-2) • (x-8)
(((( Yo Welcome)))
x3 - 2x2 + 1 = 0 is a quadratic equation.
True
False
Answer:
false
Step-by-step explanation:
Answer:
False
Step-by-step explanation:
Quadratic equations have the highest degree on x as 2 (a squared value). The given equation has x^3 (assuming x3 is x^3 and not 3x), meaning that the equation is a cubic equation.
