Answer:
a = - [tex]\frac{9}{2}[/tex] , b = - [tex]\frac{25}{4}[/tex]
Step-by-step explanation:
To obtain the required form use the method of completing the square
add/ subtract ( half the coefficient of the x- term)² to x² - 9x
y = x² + 2(- [tex]\frac{9}{2}[/tex] )x + [tex]\frac{81}{4}[/tex] - [tex]\frac{81}{4}[/tex] + 14
= (x - [tex]\frac{9}{2}[/tex] )² - [tex]\frac{81}{4}[/tex] + [tex]\frac{56}{4}[/tex]
= (x - [tex]\frac{9}{2}[/tex] )²- [tex]\frac{25}{4}[/tex] ← in the form (x + a)² + b
with a = - [tex]\frac{9}{2}[/tex] and b = - [tex]\frac{25}{4}[/tex]
Answer:
a = 4.5
b = -6.25
Step-by-step explanation:
The given equation to us is ,
[tex]\implies y = x {}^{2} - 9x + 14[/tex]
And its given that it can we written in the form of ,
[tex]\implies (x + a) {}^{2} + b[/tex]
Where ,
a and b are constants .Therefore ,
[tex]\implies y = x^2 -9x + 14 [/tex]
Multiplying 9x by 2/2 ,we have ,
[tex]\implies y = x^2 -\dfrac{2}{2}\times 9 x + 14 [/tex]
Adding and subtracting (9/2)² ,
[tex]\implies y = \bigg\{ x^2 -\dfrac{2}{2}\times 9 x + \bigg(\dfrac{9}{2}\bigg)^2 \bigg\} +14 -\bigg(\dfrac{9}{2}\bigg)^2[/tex]
Therefore , we can write it as ,
[tex]\implies y = \bigg( x + \dfrac{9}{2}\bigg)^2 + 14 - 20.25 \\\\\implies \underline{\underline{ y = \bigg( x + \dfrac{9}{2}\bigg)^2 - 6.25 }}[/tex]
Hence the value of a is 9/2 and b is -6.25 .
The 9th term of an arithmetic progression is 3+3p and the sum of the first four terms is 2p-10, where p is constant. Given that the common difference is 2, find the value of p.
Answer:
3
Step-by-step explanation:
Let's find the first term in terms of p.
So an arithmetic sequence is a linear relation.
That means it will have the same slope no matter the pair of points used. We are given the slope, the common difference, is 2. We are going to use point (9, 3+3p) and (1, t(1)) along with m=2 to find t(1).
[t(1)-(3+3p)]/[1-9]=2
Simplify denominator
[t(1)-(3+3p)]/[-8]=2
Multiply both sides by -8
t(1)-(3+3p)=-16
Add (3+3p) on both sides
t(1)=-16+3+3p
Combine like terms
t(1)=-13+3p
This means we can find the next term by adding 2 this.
t(2)=-11+3p
Let's find the next term by adding 2 this.
t(3)=-9+3p
Finally we can find the 4th term by adding 2 to this
t(4)=-7+3p
We are given the sum of the first 4 terms is 2p-10. So we can write:
-13+3p+-11+3p+-9+3p+-7+3p=2p-10
Combine like terms on left
12p-40=2p-10
Subtract 2p on both sides
10p-40=-10
Add 40 on both sides
10p=30
Divide both sides by 10
p=3.
-----------------
Checking:
t(1)=-13+3p=-13+3(3)=-13+9=-4
t(2)=-11+3p=-11+3(3)=-11+9=-2
t(3)=-9+3p=-9+3(3)=-9+9=0
t(4)=-7+3p=-7+3(3)=-7+9=2
----sum of the first 4 is -4
And 2p-10 at p=3 gives 2(3)-10=6-10=-4
So this part checks out
In general, the pattern that those 4 terms I wrote out follow t(n)=(-13-2)+2n+3p. I know this because the 0th term would have been (-13-2)+3p and this part goes up by 2 each time. The plus 3p part doesn't change.
Anyways t(9)=(-13-2)+2(9)+3p=-15+18+3p=3+3p. And this part looks good too.
the lines given by the equations y=6x and y=6x+2 are ____
They are parallel, as shown by the graph.
The interior angle of a polygon is 3degrees greater than the exterior angle.find the sum of the angles of the polygon
Step-by-step explanation:
We know that the sum of angle around a point is 180° . Therefore let the first angle be x then second will be x + 3 .
According to the Question ,
> x + x + 3 = 360°
> 2x = 357=
> x = 357°/2
> x = 178.5°
6. Don Juan compro un terreno con las dimensiones que se muestran en la figura el cual se va acondicionar para realizar eventos sociales, por lo que desea instalar césped en la region sombreada. ¿Cuantos metros cuadrados de césped requiere? Considera rt=3.14 16 m O 50 24 m2 0 205 76 m2 256 00 m2 0 5504 m2
Answer:
Not sure but I think it might be A
Step-by-step explanation:
Took the test
Marc puts 28 liters of water into a tub and 6 liters of water into a bucket. Then, he pours both containers into a tank.
Answer:
34
Step-by-step explanation:
Joanne earns $150 per week plus a 5% commission on her sales. If she made $355 last week, what were her sales for this week?
Answer:
150 + (.05x) = 355
.05x = 205
x = $4100
Step-by-step explanation:
Subtract to find amount of commission made:
355 - 150 = 205
She made $205 in commissions
Divide the amount she made in commission by the percentage she gets:
205 / 0.05 = 4,100
Her sales was $4,100
A u B u C A=(a,b,c,d,e) B=(d,e,f,g,h,i) C=(a,e,i,o,u) help class 8
Answer:
If U = { a, b, c, d, e, f, g, h} , find the complements of the following sets:(i) A = {a, b, c} (ii) B = {d, e, f, g} (iii) C = {a, c, e, g} (iv) D = { f, g, h, a}
Answer:
if;A= { a,b,c,d,e}
B= {d,e,f,g,h,i}
C= {a,e,i,o,u}
AuBuC = {a,b,c,d,e,f,g,h,i,o,u}
HAVE A NİCE DAY
Step-by-step explanation:
GREETİNGS FROM TURKEY ¯ツ
Help me with this problem
Answer:
The answer is 180 - 65
Step-by-step explanation:
We got 180, because that is the number of degree's in a line
so 180 - 65 is 115 degrees, that's your answer :)
How much would $500 invested at 5% interest compounded continuously be worth after 4 years? Round your answer to the nearest cent
Answer:
$610.70
Step-by-step explanation:
[tex]a = pe^{rt}[/tex]
a = 500 [tex]e^{.05 * 4}[/tex]
a = $610.70
If f(x) is an exponential function where f(-1.5)=26 and f(5.5)=7 then find the value of f(10), to the nearest hundredth
Answer:
5.0956537e-46
Step-by-step explanation:
^ means root
* means multiply
f(x) = ab^x
f(-1.5)=26 = ab^-1.5
f(5.5)=7 = ab^5.5
f(5.5)/f(-1.5) = 26/7 = ab^5.5/ab^-1.5
3.714 = b^7
b = 3.714^-7
f(-1.5)=26 = ab^-1.5
26 = ab^-1.5
26 = a * 3.714^-7
a = 3.714^-7 / 26
a = 0.00000394578
f(10) = ab^10
f(10) = 0.00000394578 * (3.714^-7)^10
f(10) = 5.0956537e-46
solve the equation x + 5 = 12
Answer:
x = 7
Step-by-step explanation:
x + 5 = 12
Subtract 5 from both sides
5 - 5 cancels out
12 - 5 = 7
We're left with x = 7
1. Write down the gradient of the line joining the points (2m, n) and (3, -4).
2.Find the value of n if the line is parallel to the X-axis
3.Find the value of m if the line is parallel to the Y-axis.
Answer:
Step-by-step explanation:
1 . ( n + 4 ) / ( 2m - 3 )
The gradient (slope) is
= ( change in y direction ) / ( change in x direction )
= ( n - (-4) ) / ( 2m - 3 )
= ( n + 4 ) / ( 2m - 3 )
2.
A line parallel to the x-axis will always have the equation of y = #. This is because all along that line, every value of x, y will still equal the same number. For example, a line parallel to the x-axis that crosses the y-axis at 2, will be y = 2. If it is in the negative range, it's the same concept, for example if it crossed the y-axis at -4, the equation would be y = -4.
Example - Computational Knowledge Engine
3.
To understand the slope of a line parallel to y axis, let us consider the figure given below.
1 . The gradient (slope) is ( n + 4 ) / ( 2m - 3 )
2. n = -4
3. m is not defined.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
points (2m, n) and (3, -4).
1 . The gradient (slope) is
= ( change in y direction ) / ( change in x direction )
= ( n - (-4) ) / ( 2m - 3 )
= ( n + 4 ) / ( 2m - 3 )
2. A line parallel to the x-axis will always have the equation of y = x.
The line is therefore horizontal so gradient = 0
(n+4) / (2m-3)= 0
n = -4
(iii) Find the value of m if the line is parallel to the y-axis
(n+4) / (2m-3)= gradient
(n+4) / (2m-3)= 1
We know n = -4 from part (ii) then
(-4+4) /(2m-3)= 1
0/(2m-3) = 1
0 = 1 The 'm' vanishes
Hence, m is not defined.
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P=(2,3,5,7) Express it in description method and in rule method.
Answer:
prime number between 1 to7
The description of set P is the set of prime numbers less than or equal to 7 and the rule is {x | x is a prime number less than or equal to 7}
How to describe the set of P?The set P is given as:
P = {2,3,5,7}
Note that the numbers are prime numbers.
This means that the description of set P is the set of prime numbers less than or equal to 7
The rule form of the set would be:
P = {x | x is a prime number less than or equal to 7}
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The number 6 is a solution to which of the following inequalities?
X - 13 > 7
6x < -12
6x > 32
21 + x < 28
Answer
6x<-12
Step-by-step explanation:
Answer:
There would be 2 answers in this case:
C. 6x > 32
and
D. 21 + x < 28
Step-by-step explanation:
A. Incorrect
6-13 = -7, and -7 is NOT greater than 7
B. Incorrect
6(6) = 36, and 36 is NOT less than -12.
C. Correct
6*6 = 36, which is greater than 32.
D. Correct
21+6 = 27, which is less than 28.
given circle o, what are the values of x and y?
Answer:
x = 38°
y = 90°
Step-by-step explanation:
x is an inscribed angle, so, 78/2=39
y is an inscribed angle of which connects two endpoints of the diameter, so y = 90°
Answered by GAUTHMATH
Solve the following equa
8 (2v + 8) = 96
оа
v = 2
ii need help
Answer:
1
Step-by-step explanation:
64+32 =96 that'd how I got the answer
Answer:
[tex]{ \tt{8(2v + 8) = 96}} \\ { \tt{2v + 8 = 12}} \\ { \tt{2v = 4}} \\ { \bf{v = 2}}[/tex]
4. In the quadratic function y = 232 + ba + c, the
affects the width of the parabola.
Answer:
d am
Step-by-step explanation:
In ΔTUV, the measure of ∠V=90°, UT = 65, VU = 56, and TV = 33. What ratio represents the cosine of ∠T?
Answer: [tex]\frac{33}{65}[/tex]
Step-by-step explanation:
cosine of ∠T = [tex]\frac{adjacent}{hypotenuse}[/tex]
For ∠T,
Adjacent side = 33Hypotenuse = 65cosine of ∠T = [tex]\frac{33}{65}[/tex]
The value of the trigonometric relation cos ∠T = 0.507
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the triangle be represented as ΔTUV
where the measure of ∠UVT = 90°
And , the measure of side UT = 65 units
The measure of VU = 56 units
And , the measure of TV = 33 units
From the trigonometric relations ,
cos θ = adjacent / hypotenuse
On simplifying , we get
cos ∠T = TV / UT
cos ∠T = 33 / 65
cos ∠T = 0.50769
Hence , the trigonometric relation is solved
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I do not understand any of this
Answer:
to get the slope. take the change of y axis value divide by the change of x axis value
Mark had 3/2 cans of paint and used 1/2 cans for his room. What fraction of the paint did he use
Help I’m slowww
Answer:
1/3 fraction of whole paint is used by mark
Step-by-step explanation:
Mark used 1/2 out of 3/2 cans.
[tex]\frac{1}{2}[/tex] ÷ [tex]\frac{3}{2} = \frac{1}{2}*\frac{2}{3}=\frac{1}{3}[/tex]
Which number line model represents the expression -2+(-7)
Answer:
B
Step-by-step explanation:
Start at zero.
Go 2 units left to -2.
Then go another 7 units left to add -7.
Answer: B
Someone tell me where everyone is going right please !!
Answer:
1min = 0.25miles
5.25miles / 0.25miles = 25 = 25minutes
Step-by-step explanation:
Hope this is right I'm not the best at worded time/distance math questions.
9514 1404 393
Answer:
0 ≤ t < 52.5 minutes
Step-by-step explanation:
Riko will be behind Yuto until her distance traveled matches his. That is, she will be behind for ...
0.35t < 5.25 +0.25t
0.10t < 5.25
t < 52.5
Riko will be behind Yuto on the interval 0 ≤ t < 52.5 minutes.
_____
Additional comment
distance = speed × time
Here, time is measured from when Riko starts riding. In addition to the 5.25 miles that Yuto has already gone, his distance will be the product of his speed (0.25 mi/min) and the travel time (t min). Then Yuto's total distance is 5.25+0.25t miles. The speed×time product is also used to find Riko's distance traveled. In her case, it is 0.35t miles.
What are the zeros of the polynomial function f(x) = x(x + 5)(x – 8)?
–5, 8
0, –5, 8
5, –8
0, 5, –8
Answer:
Option B is answer.
Step-by-step explanation:
Hey there!
Given;
f(X) = X(X+5)(x-8)
According to the factor theorem, f(X) = 0;
Or, X(X+5)(x-8) = 0
Either;
x = 0
Or;
(x+5)= 0
X = -5
Or;
(x-8)= 0
x = 8.
Therefore, the zeros of the polynomial are: 0,-5,8.
Hope it helps!
pLZ HELPPPPPPPPPPPPPPPPPPPPPPPPP.
Answer:
x^4+4x^3+6x^2+7x+2
What is the coefficient of x^3 in the expansion of (2x−3)^5?
Help please!!
Answer:
1....................
Answer:
1Step-by-step explanation:
COEFFICIENT....
justbrainlyuser
factor completely 8y2 + 6y + 1
Answer:
Step-by-step explanation:
8y²+6y+1
=8y²+4y+2y+1
=4y(2y+1)+1(2y+1)
=(2y+1)(8y+1)
what is the solution to 4 1/5 x (1 1/9 x 3)
Answer:
14
Step-by-step explanation:
[tex]4 \frac{1}{5} \times (1 \frac{1}{9} \times 3) \\\\= \frac{21}{5} \times ( \frac{10}{9} \times 3)\\\\=\frac{21}{5} \times( \frac{10}{3})\\\\= \frac{21 \times 10}{ 5 \times 3}\\\\=7 \times 2 \\\\= 14[/tex]
Find the TWO integers whos product is -12 and whose sum is 1
m
Answer:
[tex] \rm Numbers = 4 \ and \ -3.[/tex]
Step-by-step explanation:
Given :-
The sum of two numbers is 1 .
The product of the nos . is 12 .
And we need to find out the numbers. So let us take ,
First number be x
Second number be 1-x .
According to first condition :-
[tex]\rm\implies 1st \ number * 2nd \ number= -12\\\\\rm\implies x(1-x)=-12\\\\\rm\implies x - x^2=-12\\\\\rm\implies x^2-x-12=0\\\\\rm\implies x^2-4x+3x-12=0\\\\\rm\implies x(x-4)+3(x-4)=0\\\\\rm\implies (x-4)(x+3)=0\\\\\rm\implies\boxed{\red{\rm x = 4 , -3 }}[/tex]
Hence the numbers are 4 and -3.
Answer:
-3,4 are the TWO integers whos product is -12 and whose sum is 1.
Step-by-step explanation:
-3×4=12
-3+4=1
Using trial and improvement, find the solution between 5 and 6 for the following equation:
x
2
=
27
Give your answer rounded to 1 DP.
Answer:
2
Step-by-step explanation:
that is √ 14 which is 27 ×>44.2177
What is the radius of the circle: x^2+y^2=4
1. (0, -4)
2. (0, 4)
3. (2, -4)
4. (0, 0)
Answer:
radius = 2
Step-by-step explanation:
The equation of a circle centred at the origin is
x² + y² = r² ( where r is the radius )
x² + y² = 4 ← is in this form
with r² = 4 ⇒ r = [tex]\sqrt{4}[/tex] = 2
centre (0, 0 ) and radius = 2
