For zeroes i.e for value(s) of q and s, the given equations must be equal to 0, so let's start with first equation and then 2nd equation ;
[tex]{:\implies \quad \sf 6q^{2}-17q+12=0}[/tex]
[tex]{:\implies \quad \sf 6q^{2}-9q-8q+12=0}[/tex]
[tex]{:\implies \quad \sf 3q(2q-3)-4(2q-3)=0}[/tex]
[tex]{:\implies \quad \sf (3q-4)(2q-3)=0}[/tex]
[tex]{:\implies \quad \sf Either\:\:3q-4=0\:\:\:or\:\:\: 2q-3=0}[/tex]
[tex]{:\implies \quad \sf Either\:\:3q=4\:\:\:or\:\:\:2q=3}[/tex]
[tex]{:\implies \quad \bf q=\dfrac{3}{2},\dfrac43}[/tex]
Now, turning to the second equation ;
[tex]{:\implies \quad \sf 8s^{2}+2s-15=0}[/tex]
[tex]{:\implies \quad \sf 8s^{2}+12s-10s-15=0}[/tex]
[tex]{:\implies \quad \sf 4s(2s+3)-5(2s+3)=0}[/tex]
[tex]{:\implies \quad \sf (4s-5)(2s+3)=0}[/tex]
[tex]{:\implies \quad \sf Either\:\:4s-5=0\:\:\:or\:\:\: 2s+3=0}[/tex]
[tex]{:\implies \quad \sf Either\:\:4s=5\:\:\:or\:\:\:2s=-3}[/tex]
[tex]{:\implies \quad \bf s=\dfrac{5}{4},-\dfrac32}[/tex]
Answer:
Below in bold.
Step-by-step explanation:
I am assuming you want to factor these expressions.
6q^2 - 17q + 12
We need 2 numbers whose product is (6*12) = 72 and whose sum is -17.
Theses are -9 and -8 so we write:
= 6q^2 - 9q - 8q + 12
= 3q(2q - 3) - 4(2q - 3)
= (3q - 4)(2q - 3)
If you want the solution of this expression = zero they are q = 4/3, 3/2.
8s^2 + 2s - 15
8 * -15 = -120. -120 = -2 * 2 * 2 * 3 * 5 = +12 * -10 ( to give the +2s)
= 8s^2 + 12s - 10s - 15
= 4s(2s + 3) - 5(2s + 3)
= (4s - 5)(2s + 3)
If you want the solution of this expression = zero they are s = 5/4, -3/2.
Mai earns a salary of $200 per week plus an additional 5% commission on her sales. If
Mai's weekly salary increases by $25 and her commission increases to 6%, how much will
she earn if her weekly sales are $2,500?
so Mai had booming sales of $2500, now her commission used to be 5%, but since she rules it went up to 6%, how much is her commission on that?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{6\% of 2500}}{\left( \cfrac{6}{100} \right)2500}\implies 150[/tex]
since her salary which used to be $200 but is now 200 + 25 = $225, so for that week she earned 225 + commission or 225 + 150 = 375.
help me pls pls bro pls
six times three added to seven
pa answerr-,-
Answer:
25 :) hope this helps you
:v
help again thank you .
Answer:
Left 2, up 1
Step-by-step explanation:
If you use slope, remember rise/run. You go up then left.
Answer: left 2 up 1
Step-by-step explanation: I did it by using the rule rise over run so it goes up then left . Hope it helps
Find the decimal approximations for these give your answers to 1 decimal place.
a)square root of 3
b)square root of 21
c)square root of 62
Answer:
A) 1.7
B) 4.5
C) 7.8
Mika’s gym allows her to bring 3 guests for free. After the first three, she must pay $7 per guest. How many guests, g, can she bring to the gym if she pays $42?
Answer:
9 guests
Step-by-step explanation:
the first 3 guests are free and anyone after is 7 per guest
well if we divide 42/7 we get 6
and we add the 3 we get 9 guests.
This makes sense due to the fact that the first 3 guests are free and we are paying for everyone else after them. So it's 7 dollars a student therefore, 9 guests.
Rewrite 4 as a fraction.
4/4
4/1
1/4
Answer:
4/1
Step-by-step explanation:
when you divide 4 by 1 you will get 4 which is your original answer.
Plese help me.....
GOD WILL BLESS YOU
4 11
8 22
16 n
8 x n = 22 x 16
n = 44
A polynomial p(x) has 3, 2-i, and √3 as its roots and goes through (0,-90), find p(x)
Answer:
p(x) = -2x⁵ +14x⁴ -28x³ -12x² +102x -90
Step-by-step explanation:
Assuming the desired polynomial has real and rational coefficients, each of the complex and irrational roots has a corresponding conjugate. That is, the roots of p(x) must include ...
{3, 2 -i, 2 +i, √3, -√3}
Each of these roots corresponds to a linear factor. Root p corresponds to factor (x -p), for example.
__
Factored formThen the factored p(x) will be ...
p(x) = k(x -3)(x -(2 -i))(x -(2 +i))(x -√3)(x +√3) . . . . for some scale factor k
Simplifying a bit, we have ...
p(x) = k(x -3)((x -2)² +1)(x² -3) = k(x -3)(x² -4x +5)(x² -3)
__
Scale factorAt x=0, this evaluates to ...
p(0) = k(0 -3)(0² -4·0 +5)(0² -3) = 45k
We want p(0) = -90, so we require ...
45k = -90
k = -2
__
Then the function p(x) factored to integers is ...
p(x) = -2(x -3)(x² -4x +5)(x² -3)
When we multiply this out, we find the standard form equation is ...
p(x) = -2x⁵ +14x⁴ -28x³ -12x² +102x -90
Find the equation of the exponential function represented by the table below,
X.Y
0 4
1 8
2 16
3 32
Answer:
Graph the exponential function.
[tex]y=-3(8)^{x}[/tex]
Step-by-step explanation:
to make a sketch of this graph. We're gonna make a table of values. I think that's probably our best route. So we'll do a couple negative values, but I'm gonna actually start at 08 to 0. Power zero. And I'm sorry. 80 parts one and one times negative. Three is negative. Three eight to the first. Power is eight and eight times negative. Three is negative. 24 8 X squared is 64 64 times negative. Three is on negative. 192. Okay, I think that's plenty. E to the negative. First power is 18 and 1/8 times negative. Three is negative. 3/8 and eight to the negative. To power is 1 64th times negative. Three is negative. 3 60 force. Okay, I think we can see where that's going. Is getting really close to zero. So as faras my graph here, I'm gonna focus on the fourth quadrant, I think. All right. So we got our X and y axis here. We're starting at 01 and to and we'll also do negative one. And negative two aren't horizontally, vertically. I do. I want to scale this whole the way to 1 92 I guess I will. Um, so whatever it is scaled by, maybe twenties. Yeah, let's do that. 20 40 60 8120 40 60 8200. So there's negative. 200? Um, negative. 1 80 Negative 1 60? Nope. That's not right. Because I scaled by twenties didn't. So this is actually negative. 1 60 This one's negative. 1 20 This one's negative. 80. And this is negative. 40. There we go. All right now a plot. These points to negative 1 92 is practically to 200 one. Negative. 24 is all the way over here. Zero negative three is practically on the X axis The way I have this, and same with those fractional values. They're practically on the X axis. So let's start almost parallel to the X axis because it's never actually touch step than its we don't ever. Slowly and then it starts going down rapidly, decreasing in value to the point where it's almost vertical, but it never will get vertical, so there's a decent sketch of y equals negative three times eight to the power of acts
please help me answer this?
Answer:
$102
Step-by-step explanation:
The pay for the day of work is the total of morning hours worked and afternoon hours worked. In each case, the hours worked is the difference between the "Out" time and the "In" time.
morning hours = 12:15 -8:15 = 4:00
afternoon hours = 17:30 -13:00 = 4:30
total hours worked = morning hours + afternoon hours
total hours worked = 4:00 +4:30 = 8:30
This notation tells you (hours):(minutes). You know that 30 minutes is 1/2 hour, so the total time worked is 8 1/2 hours.
The pay is the product of the hours worked and the pay per hour:
pay = (8 1/2 hours) × ($12 /hour) = $102
What is 3x + 2y = 12 (show your work)
Answer:
y = (-3/2)x + 6
Step-by-step explanation:
3x + 2y = 12
2y = -3x + 12
÷2 ÷2 ÷2
y = (-3/2)x + 6
Slope: (-3/2)
Y-intercept: (0,6)
I hope this helps!
Solve the equation 3x = 9 Show and justify each step you take to solve the equation
Hello!
This is a one-step equation, meaning that we can solve it in just 1 step.
This is the step:
Divide both sides by 33x=9
x=3
That's the answer; we can easily check it:
3*3=9
Hope everything is clear.
Let me know if you have any questions!
Always Remember: Knowledge Is Power!
Isaiah decides to launch a model rocket to demonstrate parabolic motion. Given x stands for time and y stands for height in feet, find the equation for his rocket if it launches at 5 seconds, lands at 11 seconds, and is at 80 feet after 10 seconds. Explain in one sentence how you created your equation.
The parabolic motion is an illustration of a quadratic function
The equation that models that path of the rocket is y = -16/31x^2 + 256/31x - 880/31
How to model the function?Given that:
x stands for time and y stands for height in feet
So, we have the following coordinate points
(x,y) = (5,0), (11,0) and (10,80)
A parabolic motion is represented as:
y =ax^2 + bx + c
At (5,0), we have:
25a + 5b + c = 0
c= -25a - 5b
At (11,0), we have:
121a + 11b + c = 0
Substitute c= -25a - 5b
121a + 11b -25a - 5b = 0
Simpify
96a + 6b = 0
At (10,80), we have:
100a + 10b + c = 80
Substitute c= -25a - 5b
100a + 10b - 25a -5b = 80
75a -5b = 80
Divide through by 5
15a -b = 16
Make b the subject
b = 15a + 16
Substitute b = 15a + 16 in 96a + 6b = 0
96a + 6(15a + 16) = 0
Expand
96a + 90a + 96 = 0
This gives
186a = -96
Solve for a
a = -16/31
Recall that:
b = 15a + 16
So, we have:
b = -15 * 16/31 + 16
b =-240/31 + 16
Take LCM
b =(-240 + 31 * 16)/31
[tex]b =256/31
Also, we have:
c= -25a - 5b
This gives
c= 25*16/31 - 5 * 256/31
Take LCM
c= -880/31
Recall that:
y =ax^2 + bx + c
This gives
y = -16/31x^2 + 256/31x - 880/31
Hence, the equation that models that path of the rocket is y = -16/31x^2 + 256/31x - 880/31
Read more about parabolic motion at:
https://brainly.com/question/1130127
Main Factoring Special Case Quadratics
[tex]81c {}^{2} - 4 = (9c - 2)(9c + 2)[/tex]
since it is in the form of:
[tex]x {}^{2} - y {}^{2} = (x - y)(x + y)[/tex]
2)
[tex]75x {}^{2} - 27y {}^{2} = (5 \sqrt{3} x - 3 \sqrt{3} y)(5 \sqrt{3} x + 3 \sqrt{3} y)[/tex]
3)
[tex]z {}^{2} + 12z + 36[/tex]
[tex]z {}^{2} + 6z + 6z + 36[/tex]
[tex]z(z + 6) + 6(z + 6)[/tex]
[tex](z + 6)(z + 6)[/tex]
[tex](z + 6) {}^{2} [/tex]
4)
[tex]4f {}^{2} + 18f + 18f + 81[/tex]
[tex]2f(2f + 9) + 9(2f + 9)[/tex]
[tex](2f + 9)(2f + 9)[/tex]
[tex](2f + 9) {}^{2} [/tex]
5)
[tex]49a {}^{2} - 14a + 1[/tex]
[tex](7a - 1) {}^{2} [/tex]
6)
[tex]x {}^{4} - 16[/tex]
[tex](x {}^{2} - 4)(x {}^{2} + 4)[/tex]
Please help I will give brainliest.
Answer:
The first two
Step-by-step explanation:
graph the parabola to see
In the figure diameter DE is drawn with the midpoint of the circle at C(-3; 2).
EA is a tangent to the circle at E (1,3).
Answer:
4
Step-by-step explanation:
[tex]gradient = \frac{y2 - y1}{x2 - x1} [/tex]
[tex]y2 = - 3 \\ y1 = 3 \\ x2 = 2 \\ x1 = 3[/tex]
[tex] \frac{ - 3 - 1}{2 - 3} = \frac{ - 4}{ - 1} = 4[/tex]
explain what operation should be used to solve the equation 3.5n= 10.5 what is the value of n?
Answer: n = 3
Step-by-step explanation:
divide 3.5n by 3.5n then divide 10.5 by 3.5 which is
n = 3
Answer:
[tex]\boxed{\sf{n=3}}[/tex]
Step-by-step explanation:
To find the value of n, you have to isolate it on one side of the equation.
3.5n=10.5
First, multiply by 10 from both sides.
[tex]\sf{3.5n*10=10.5*10}[/tex]
Solve.
35n=105
Divide by 35 from both sides.
35n/35=105/35
Solve.
105/35=3
n=3
Therefore, the final answer is n=3.I hope this helps you! Let me know if my answer is wrong or not.
Ms. James class is making bracelets. A bracelet I made out of 3 pieces of string that are each 6 inches long. How many YARDS of string does the class need to make 84 bracelets?
Answer:
42 yards.
Step-by-step explanation:
3 x 6 is 18. 18 x 84 is 1512. 1512 divided by 12 is 126. 126 divided by 3 is 42.
7^-6/7^-2 rewrite it using a singular positive exponent
Answer:
1/7^4
Step-by-step explanation:
negative exponents flip to opposite side of the fraction and add to like-base terms.
Help pleazeeeeee! I need this as soon as possible
The concession stand has 18 gallons of punch. If there are a total of 240 students who want to purchase 1 cup of punch each, will there be enough punch for everyone?
Answer:
Yes.
Step-by-step explanation:
18 gal = 288 cups.
(1 gal = 16 cups)
If 240 students purchase 1 cup each, there will be 48 cups left over.
So,yes, there will be enough punch for everyone.
Please mark as brainliest!
Thanks!
Can someone please help me with this?
Answer:
[tex]403.06 cm^2; 100.77cm^2[/tex]
Step-by-step explanation:
Ok, step 1. What's the measure of the internal angle of a dodecagon? After some splitting in triangles you get that's [tex](n-2)\pi = 10\pi[/tex]. That makes each angle measure [tex]\frac{10}{12}\pi[/tex].
That allows us to split the whole figure in 12 isosceles triangles with (congruent) angles of [tex]\frac5{12}\pi[/tex]. Consider just one, red in my picture. The height of that triangle - orange "vertical" line - can be found with some trigonometry as [tex]3tan \frac5{12}\pi \approx 11.2 cm[/tex]
At this point one triangle has area [tex]\frac12 \cdot 6\cdot 11.2 = 33.6 cm^2[/tex] and the whole cookie has area as 12 triangles [tex]403.06 cm^2[/tex].
After her eating spree, you're left with 3 triangles, for a grand total of [tex]100.77 cm^2[/tex]
If there are fifty dimes in a roll of coins, then it is equal to________dollars
Answer:
$5
10 Dimes = $1 so If we have 50 dimes that = 5$
Please mark brainliest trying to level up :)
A zoo measured the height, in feet, of 9 giraffes.
18, 16, 22, 14, 17, 19, 15, 19, 22
What is the median height of the giraffes?
16 ft
17 ft
18 ft
19 ft
Answer:
19 ft because the median is 4.5th item so,the commutative frequency just greater than 4.5 is 6.
so,median=9ft
A school needs 138 5 meters of fencing for a new playground Fencing is
sold in 12-foot sections. How many sections of fencing should be
purchased to fence the playground? PLEASE ANSWER AS QUICKLY AS YOU CAN!!!!
Answer:
12 Sections
Step-by-step explanation:
With 138.5 meters needed and fencing being purchased in 12-foot sections, you would need 12 sections purchased. 138.5/12=11.54, this is rounded up to 12 because of the purchase size.
AB = 18, BC = 9, then AC = __
Answer:
AC=162/B
Step-by-step explanation:
AB= 18
A=18/B
BC=9
C=9/B
AC=18/B * 9/B
AC=162/B
Click all the questions that are considered statistical questions. No links please.
Answer:
The first three are not statistical, the last three are.
A box of 15 cookies costs $9dollar sign, 9. What is the cost for 1 cookie?
what is 6(x+?)= 6x + 30
??????????
Answer:
Let y = '?'
6(x + y) = 6x + 30
6x +6y = 6x + 30
6x + 6y - 6x = 6x + 30 - 6x
6y = 30
6y / 6 = 30 / 6
y = 5