Answer:
y = -4x² + 4x -3
Step-by-step explanation:
The standard form of quadratic equation is:
y = ax² + bx + c
We need to use the points given to find the value of a, b and c
We are given point (-1,-11) where x =-1 and y=-11 putting values in the above equation
y = ax² + bx + c
-11 = a(-1)² + b(-1) +c
-11 = a -b+c eq(1)
Now putting the point(0, -3) where x =0 and y =-3
y = ax² + bx + c
-3 = a(0)² + b(0) + c
-3 = 0 + 0 + c
=> c = -3
Now Putting the point (3, -27) where x =3 and y = -27
y = ax² + bx + c
-27 = a(3)² +b(3) + c
-27 = 9a + 3b + c eq(2)
Putting value of c= -3 in eq(2)
-27 = 9a + 3b -3
-27 +3 = 9a +3b
-24 = 9a + 3b
=> 3(3a+b) = -24
3a + b = -24/3
3a + b = -8 eq(3)
Putting value of c= -3 in eq(1)
-11 = a -b+c
-11 = a -b -3
-11 + 3 = a - b
-8 = a - b
=> a - b = -8 eq(4)
Now adding eq(3) and eq(4)
3a + b = -8
a - b = -8
__________
4a = -16
a = -16/4
a = -4
Putting value of a in equation 4
a - b = -8
-4 -b = -8
-b = -8+4
-b = -4
=> b = 4
The values of a , b and c are a= -4, b =4 and c= -3
Putting these values in standard quadratic equation
y = ax² + bx + c
y = -4x² + 4x -3
You have a normal distribution of hours per week that music students practice. The mean of the values is 8 and the standard deviation of the values is 4. According to the normal distribution, half of the music students practice between 5.3 to 10.7 hours each week. What percentage of the students study less than 5.3 hours each week? 12.5% 20% 25% 50%
Answer:
25%
Step-by-step explanation:
Since Normal Distribution is symmetrical Distribution and 5.3 and 10.7 are both 2.7 below and 2.7 above the mean respectively.
So, % of students less than 5.3 hours per week is 25%
Which is an equivalent form of the compound inequality −44 > −2x − 8 ≥ −8?
Answer:
22 and 0
Step-by-step explanation:
−44 > −2x − 8 ≥ −8?
/-2 - 44 > -2x / . -2 -8 ≥ -8
= 22 +8 =0
Answer:
An equivalent form of the compound inequality is the pair of single inequalities:
-2x - 8 < - 44, and −2x − 8 ≥ −8Explanation:
You can split the compound inequality into two equivalent inequalities by taking each side from the variable.
The compound inequality −44 > −2x − 8 ≥ −8 means that two conditions must be satisfied:
1. From the left side: - 44 > - 2x - 8
2. From the right side: −2x − 8 ≥ −8
Then, as a first approach you can tell that an equivalent form of the compound inequality is the pair of single inequalities:
-44 > -2x - 8, and −2x − 8 ≥ −8You should put the variable on the left sides, which will yield the best form of an equivalent pair of inequalitis.
- 2x - 8 < -44, and- 2x - 8 ≥ - 8That is the best choice of an equivalent form, and from there you can solve the inequalities which will permit to obtain the solution. Of course, you can manipulate the variable and find many other equivalent forms.
Notice, that both inequalities must be satisfied simultaneously.
This is how you solve that system
- 2x - 8 < -44nAdd 8 to both sides: - 2x < -36
Divide both sides by - 2 (you have to change the sign): x > 18
- 2x - 8 ≥ - 8-
Add 8 to both sides: - 2x ≥ 0
Divide by - 2 (again, you must change the sign): x ≤ 0
Then, the solution set is:
x > 18 and x ≤ 0 and that is an empty set, since x cannot be at the same time greater than 18 and less or equal to 0.This is, you conclude that the compound inequality is false, because there is not a value of x which is a solution.
graph the linear equation. find three points that solve the equation, then plot on the graph. -x-3y=-6
Answer:
The equation can be written as
x+3y=6
To graph, you need to create a table for values of x with corresponding values of y that satisfy the equation
Sample points that solve the equation could be;
(-3,3),(3,1) and (-9,5)
From the graph attached, the three points are;
(-6,4)(0,2)(6,0)Someone please help
Evaluate the formula
V= Bh/3 for B= 15in ^2
And
H=28in
Answer:
[tex]\large\boxed{V=140\ in^3}[/tex]
Step-by-step explanation:
[tex]V=\dfrac{Bh}{3}\to\text{it's a formula of a volume of a pyramid or a cone}\\\\B-base\ area\\h-height\\\\\text{We have}\ B=15\ in^2\ \text{and}\ h=28\ in.\\\\\text{Put the given values to the formula of a volume:}\\\\V=\dfrac{(15)(28)}{3}=(5)(28)=140\ in^3[/tex]
Y=f(x)=1/16^x Find the f(x) when x=1/4 Express as a decimal rounding to the nearest thousandth
Answer:
0.500.
Step-by-step explanation:
f(x) = 1/16 ^ 1/4
Now 16 ^1/4 = ⁴√16
= 2
so f(x) = 1/2
= 0.500.
d/dx(1+x^4+x^6/x^2+x+1)
A)2x+1
B)2x-1
C)2
D)0
\frac{d}{dx}\left(\frac{1+x^4+x^6}{x^2+x+1}\right)=\frac{4x^7+5x^6+8x^5+3x^4+4x^3-2x-1}{\left(x^2+x+1\right)^2}
copy and paste that into a URL
How is finding the fourth vertex of a parallelogram that is not a rectangle or a square the same as it is for a rectangle or square? How is it different?
well, the only difference from a parallelogram that is a square or a rectangle and one that isn't, is that the interior angles are 90° in the square and rectangle, however for other ones, like the one in the picture below, they are not 90°.
however, getting to any vertex, is just a matter of moving horizontally and vertically the same distances, as you see those arrows on the picture, since both pair of sides are parallel, one moves the same distance horizontall and vertically to get to the next vertex, so on that, is the same as for a square or rectangle as well.
is only different in that you're not moving alongside the segment, in a rectangle or a square, the lines are only vertical or horizontal, so you simply move straight to get the next vertex, on other parallelograms like the one below, you do move the same but is not alongside the segments.
What is the interquartile range of this day at set?
Answer: 49
Step-by-step explanation
Am god
Use the figure and flowchart proof to answer the question.
Which Property of equality accurately completes Reason B?
A). Addition Property of Equality
B). Divison Property of Equality
C). Substitution Property of Equality
D). Subtraction Property of Equality
Answer:
D Subtraction Property of Equality
Step-by-step explanation:
Whenever we subtract the same number of expression from both sides of the equation, the equality remains the same.
Reason A. - Consecutive Interior Angles
Reason B. - Substitution Property of Equality
Reason C. - Subtraction Property of Equality
The Property of equality that accurately completes Reason B in the figure and flowchart proof is the Addition Property of Equality (A).
Explanation:The property of equality that accurately completes Reason B in the figure and flowchart proof is the Addition Property of Equality (A).
The Addition Property of Equality states that if you add the same number to both sides of an equation, the equality is still preserved. In other words, if A + B = B + A, you can add the same number to both sides to obtain A + B + C = B + A + C, where C is any number.
In the given figure and flowchart proof, the equation A + B = B + A represents the Addition Property of Equality, and by applying this property, we can conclude that Reason B should be completed with the Addition Property of Equality (A).
What is the 47th term of the arithmetic sequence with this explicit formula?
an= -11 + (n - 1)(-3)
Answer:
-149
Step-by-step explanation:
Just plug in 47
-11+(47-1)(-3)
-11+46(-3)
-11+-138
- 149
Answer:
= -149
Step-by-step explanation:
an= -11 + (n - 1)(-3)
The 47th term means n = 47
a47 = -11 + (47-1) (-3)
= -11 + 46 (-3)
= -11 -138
= -149
PLEASE HELP! SEE ATTACHMENT
Answer:
-24 - 4ε
Step-by-step explanation:
100000000000 = 10¹¹ [One hundred billion]
You multiply this by -5 to get -500000000000. Now, "⁻²" means you will be taking the Multiplicative Inverse of whatever this result is, and since it is a long answer, I decided to give it to you in Calculus [Calculator] Notation.
Answer:the answer is ten to the eleventh minus five and then minus itself twice times ten
Step-by-step explanation:
the price of one share of XYZ inc's stock drop by $0.02 on Monday. On Tuesday the price goes back up by $0.05.
Write an expression with three terms to show the change in price of XYZ stock.
_____________________________________________________________
If one share of XYZ stock cost $34.18 at the start of business on Monday morning, what is the price of the one share of XYZ stock at the close of business on Tuesday evening?
Answer:
1. $(x+0.03) - $x
2. $ 34.21
Step-by-step explanation:
Let the price of XYZ inc's share to be = $ x
On Monday, the price drops by $ 0.02 = $ x- $ 0.02 = $ (x-0.02)
New price of shares on Monday is = $ (x- 0.02)
On Tuesday the price goes up by $0.05 = $ (x-0.02) + $ 0.05 = $(x-0.02+0.05)
New price on Tuesday = $( x+ 0.03)..............................................(a)
Change in price of one share of XYZ's stock= Price on Tuesday - price of share
= $(x+0.03) - $x..........................................(b)
2. Give that x= $34.18 solve equation (a) above
Price on Tuesday at close of business= $ (x+0.03)
= $ (34.18+0.03)
= $ 34.21
What is the solution of 2x+4 = 16?
Answer:
x=6
Step-by-step explanation:
2x+4=16
-4 -4
2x+4-4=16-4
2x=12
/2 /2
2x/2=12/2
x=6
Answer:
x=6
Step-by-step explanation:
2x+4 = 16
Subtract 4 on each side
2x+4-4 = 16-4
2x = 12
Divide each side by 2
2x/2 = 12/2
x = 6
Which of the following represents a region of a circle?
A. Sector
B. Arc
C. Tangent
D. Circumference
Answer:
A. Sector
Step-by-step explanation:
A Sector represents a region of a circle.
Answer:
The one that represents a region of a circle is A: Sector.
Step-by-step explanation:
It is a slice, a piece-slice part of a circle the area between two radiuses and the connecting arc of a circle. The segment of a circle is the region bounded by a chord and the arc subtended by the chord. It differs from the segment because the segment is the region bounded by a chord and the arc subtended by the chord.
Which term describes a function in which the yvalues form a geometric
sequence?
O
A. Linear increase
O
B. Exponential growth
O
C. Linear function
O
D. Exponential function
Answer:
C. Third option
Step-by-step explanation:
C is the correct answer, because linear function describes a function in which the y values form a geometric sequence.
Hope this helps!
Use the diagram and given information to answer the questions and prove the statement.
Re-draw the diagram of the overlapping triangles so that the two triangles are separated.
What additional information would be necessary to prove that the two triangles, XBY and ZAY, are congruent? What congruency theorem would be applied?
Prove AZ ≅ BX using a flow chart proof.
Answer:
See explanation
Step-by-step explanation:
ASA Postulate (Angle-Side-Angle):
If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.
Consider triangles XYB and ZYA. In these triangles
∠X≅∠Z (given)XY≅ZY (given)∠Y is common angleBy ASA Postulate, triangles XYB and ZYA are congruent. Congruent triangles have congruent corresponding sides, so
BX≅AZ
[tex]\rm \overline{AZ} \cong \overline{BX}[/tex]
Please refer the below solution.
Step-by-step explanation:
Given :
[tex]\rm \angle X \cong \angle Z[/tex][tex]\rm \angle Y \;is\;common[/tex]
[tex]\rm \overline{XY} \cong \overline{ZY}[/tex]
Solution :
According to ASA (Angle Side Angle) postulate:
If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then both the triangles are congruent.
Now, consider triangle XBY and ZAY
[tex]\rm \angle X \cong \angle Z[/tex]
[tex]\rm \overline{XY} \cong \overline{ZY}[/tex]
[tex]\rm \angle Y \; is \; common[/tex]
According to ASA postulate triangle XBY and ZAY are congruent. And congruent triangles have congruent corresponding sides, therefore
[tex]\rm \overline{AZ} \cong \overline{BX}[/tex]
For more information, refer to the link given below
https://brainly.com/question/10629211?referrer=searchResults
Find y: 5 + y = -15
Answer:
y = -20
Step-by-step explanation:
5 + y = -15
Subtract 5 from both sides to isolate y.
y = -15 - 5
y = -20
Hello!
Answer:
[tex]\boxed{y=-20}\checkmark[/tex]
The answer should have a negative sign.
Step-by-step explanation:
First, you switch sides.
[tex]y+5=-15[/tex]
Then, you subtract by 5 both sides.
[tex]y+5-5=-15-5[/tex]
Finally, you simplify.
[tex]-15-5=-20[/tex]
[tex]y=-20[/tex], which is our answer.
Hope this helps!
Thanks!
Have a nice day! :)
-Charlie
The cross-sectional area parallel to the bases of the two figures above is the same at every level. Find the volume of the cone, to the nearest tenth.
A.
26.5 cm3
B.
44.2 cm3
C.
79.5 cm3
D.
132.5 cm3
Answer:
B. 44.2 cm3
Step-by-step explanation:
we know that
If the cross-sectional area parallel to the bases of the two figures above is the same at every level
then
the area of the base of the triangular pyramid is the same that the area of the base of the cone
step 1
Find the area of the base of the pyramid
[tex]A=(1/2)[6*4.8]=14.4\ cm^{2}[/tex]
step 2
Find the volume of the cone
The volume of the cone is equal to
[tex]V=\frac{1}{3}Bh[/tex]
we have
[tex]B=14.4\ cm^{2}[/tex]
[tex]h=9.2\ cm[/tex]
substitute
[tex]V=\frac{1}{3}(14.4)(9.2)[/tex]
[tex]V=44.2\ cm^{3}[/tex]
john played his xbox 180 times over a 12 week period. if john played the same number of times each week, how many times did john played in one week?
Answer:
15
Explanation:
180 times / 12 weeks = 15 times in one week
Find the probability of selecting a class that runs between 51.25 and 51.75 minutes
Answer:
0.05
Step-by-step explanation:
This question is on probability
A uniform distribution means there is equal probability density for every number.
This graph will be distributed to form a rectangle with area 1 unit square.
The base/range = 58-48 =10
Height of rectangle should be such that the area is 1 square unit. i.e 1/10 units
The probability will be found by calculating the area under the graph;
P( 51.25≤ x ≤ 51.75) , Area = (51.75-51.25)×1/10
0.5/10 =0.05
If f(x) = 7 + 4x and g(x) = 2x, what is the value of 8 (5)?
A)11/2
B)27/10
C)160
D)270
If the functions f(x) = 7 + 4x and g(x) =1/2x then the value of (f/g)(5) is 270, option D is correct.
What is a function?A relation is a function if it has only One y-value for each x-value.
The given functions are f(x) = 7 + 4x and g(x) =1/2x
We have to find the value of (f/g)(5)
We know that from properties of functions
(f/g)(a)=f(a)/g(a)
So let us find f(5) and g(5)
f(5)=27
g(5)=1/10
(f/g)(5)=27/(1/10)
=27×10
=270
Hence, if the functions f(x) = 7 + 4x and g(x) =1/2x then the value of (f/g)(5) is 270, option D is correct.
To learn more on Functions click:
https://brainly.com/question/30721594
#SPJ5
Basketball court has a perimeter of 278 feet the basketball court is 38 feet longer than it is wide find the length and the width of the garden justify your answer
ANSWER
[tex]w = 50.5[/tex]
[tex]l = 88.5[/tex]
EXPLANATION
The basketball court has a rectangular shape.
The perimeter of this court is calculated using the formula
[tex]P=2(l + w)[/tex]
It is given that,the court has a perimeter of 278ft. Let the width of the court be 'w' units, then the length is "w+38"
The perimeter then becomes:
[tex]2(w + 38+ w) = 278[/tex]
[tex]2w + 38= 139[/tex]
[tex]2w = 139 - 38[/tex]
[tex]2w = 101[/tex]
[tex]w = 50.5[/tex]
[tex]l = 50.5 + 38 = 88.5[/tex]
Check
[tex]P = 2(88.5 + 50.5)[/tex]
[tex]P = 2(139) = 278[/tex]
Which expression is equivalent to 12*12*12*12*12*12*12*12*12*12*12
Answer:
33?
Step-by-step explanation:
Answer:
Step-by-step explanation:
solve the equation for all real solutions 20p^2+33p+16=6
First you must bring 6 to the other side of the equation so it equals zero. To do this subtract 6 to both sides
20p^2+33p+16 - 6=6 - 6
20p^2+33p+10=0
Use the quadratic equation to solve this (image of the quadratic equation is below)
Remember that quadratic functions are set up like so:
[tex]ax^{2} +bx +c = 0[/tex]
That means that in this equation...
a = 20
b = 33
c = 10
^^^Plug these numbers into the quadratic equation and solve...
[tex]\frac{-33+/-\sqrt{(33)^{2}-4(20)(10)}}{2(20)}[/tex]
[tex]\frac{-33 +/-\sqrt{1089-800}}{40}[/tex]
[tex]\frac{-33+/-\sqrt{289} }{40}[/tex]
[tex]\frac{-33+/-17}{40}[/tex]
Keep in mind that +/- is ±
[tex]\frac{-33+17}{40}[/tex] ---> -2/5 ---> -0.4
[tex]\frac{-33-17}{40}[/tex] ---> -5/4 ---> - 1.25
Hope this helped!
~Just a girl in love with Shawn Mendes
Bill will rent a car for the weekend. He can choose one of two plans. The first plan has no
initial fee but costs $0.70 per mile driven. The second plan has an initial fee of $50 and
costs an additional $0.50 per mile driven. How many miles would Bill need to drive for the
two plans to cost the same?
Clear
Undo Help
Answer:
250 miles
Step-by-step explanation:
Let number of mile driven be x
plan 1: Cost = 0.7x
plan 2: Cost = 50 + 0.5x
for both plans to cost the same,
Plan 1 Cost = Plan 2 Cost
0.7x = 50 + 0.5x (solve for x)
0.7x - 0.5x = 50
0.2x = 50
x = 250 miles
Who can help me?
please
Thank you
The sum of the interior triangles in a triangle is 180, so if we add all the angle measures together, we should get 180. Therefore, we can make an equation like this,
[tex]110-2x+x+50+5x-40=180[/tex]
Simplify this.
[tex]4x+120=180[/tex]
[tex]4x=60[/tex]
[tex]x=15[/tex]
Now we can find each angle measure.
[tex]110-2x[/tex]
[tex]110-2(15)[/tex]
[tex]110-30[/tex]
[tex]80[/tex]
[tex]x+50[/tex]
[tex]15+50[/tex]
[tex]65[/tex]
[tex]5x-40[/tex]
[tex]5(15)-40[/tex]
[tex]75-40[/tex]
[tex]35[/tex]
So the angle labeled [tex]110-2x[/tex] is the largest angle in the triangle.
Answer:
x=15
biggest angle is 110-2x
Step-by-step explanation:
The surface area of a rectangular prism is increased by a factor of 16.
By what factor is the volume of the figure increased?
Answer:
The factor of the volume of the figure increased is 64
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared and the ratio of its volumes is equal to the scale factor elevated to the cube
step 1
Find the scale factor
Let
z ----> the scale factor
z²=16
z=4 -----> scale factor
so
z³=4³=64
The factor of the volume of the figure increased is 64
Answer:
The volume of the rectangular prism will increase by a factor of 64.
Step-by-step explanation:
Surface area = [tex]length\times length[/tex]
or [tex]\sqrt{surface area} =length[/tex]
Therefore, the increase in the length of the sides will be = [tex]\sqrt{16}=4[/tex]
We know the volume is =[tex]length\times width\times height[/tex]
When there is increase in length of sides by 4 times, then volume will increase by [tex]4^{3}[/tex]
And [tex]4^{3}[/tex] = [tex]4\times4\times4=64[/tex]
Hence, the volume of the rectangular prism will increase by a factor of 64.
PLZ HELP ME RIGHT NOW!
Type the correct answer in each box.
Answer:
fragrance A $26
fragrance B $24
Fragrance A has the greater unit rate
Step-by-step explanation:
To find the price of fragrance A , take the price and divide by the number of bottle
$78/3 bottles = $26 per bottle
To find the price of fragrance A , we can look at the graph and find the price for 1 bottle on the x axis and go up until we hit the red line. The value of y is 24 dollars
Which is a reasonable first step that can be used to solve the equation
Answer:
Use distributive property:
2x + 12 = 3x - 12 + 5
Step-by-step explanation:
This can allow for combining like terms later on, and eventually isolating x as a variable.
For this case we have the following equation:
[tex]2 (x + 6) = 3 (x-4) +5[/tex]
The first step we must follow to solve the equation is to apply distributive property to the terms within the parenthesis:
[tex]a (b + c) = ab + ac[/tex]
Then, the equation is:
[tex]2x + 12 = 3x-12 + 5[/tex]
Answer:
The first step is to apply distributive property to the terms within parentheses.
m[tex]m^{2} -5m+mn-5n[/tex] equals what?