Answer:
[tex]f(x)=-2x(x+4)[/tex]
Step-by-step explanation:
We want to find the equation of a quadratic function in factored form with zeros at x = -4 and x = 0 that passes through the point (-3, 6).
The factored form of a quadratic is given by:
[tex]f(x)=a(x-p)(x-q)[/tex]
Where p and q are the zeros and a is the leading coefficient.
Since we have zeros at x = -4 and x = 0, let p = -4 and q = 0. Substitute:
[tex]f(x)=a(x-(-4))(x-0)[/tex]
Simplify:
[tex]f(x)=ax(x+4)[/tex]
And since we know that the function passes through the point (-3, 6), f(x) = 6 when x = -3. Thus:
[tex](6)=a(-3)(-3+4)[/tex]
Simplify:
[tex]6=a(-3)(1)[/tex]
Thus:
[tex]-3a=6\Rightarrow a=-2[/tex]
So, our quadratic function is:
[tex]f(x)=-2x(x+4)[/tex]
pls help tysm will give brainliest!!
Answer:
% change in perimeter = 43. 44 %
% change in area = 16 %
Step-by-step explanation:
initial perimeter of the rectangle = 2(2p + p)
= 6p
initial area of the rectangle = 2p × p
= 2p²
25% is equal to 0.4therefore,
new length = 2p + (2p × 0.4)= 2p + 0.8p = 2.8 p
new breadth= p - 0.4p
= 0.6 p
new perimeter = 2 ( 2.8 p + 0.6p)= 3.4 p
new area = 2.8p × 0.6p= 1.68 p²
% change in perimeter
[tex] = \frac{6p - 3.4p}{6p} \times 100 \\ = \frac{2.6p}{6p} \times 100 \\ = 43.33\%[/tex]
% change in area
[tex] \frac{2 {p}^{2} - 1.68 {p}^{2} }{2 {p}^{2} } \times 100 \\ = \frac{0.32}{2} \times 100 \\ = 16\%[/tex]
this is so ez guys cmon
Answer:
there are 6 units
hope this help
Express each of the following negative angles as its equivalent positive angle between 0°and360°
+120°
Answer:
Dilated pupils
Long periods of wakefulness
Loss of appetite
Overconfidence
Over-excitement
Paranoia
Runny nose or frequent sniffles
White powder around nostrils
Legal issues
Missing or being late to work
Financial problems
Mood swings
Irritability
Depression
Complete the equation: 2^2 – 14x + __ = (_)^2
A. –14; 2 + 14
B. -14; 2 – 14
C. 49; 2 +7
D. 49; r - 7
The white triangle drawn on the road sign in the picture has a helght of 8" and a base of 5". The red rim around the edge adds another Inch to each dimension making the base of the larger triangle 12 inches. Ignoring the white edge around the very outside, what is the area of the red border? (Hint: find the area of the whole triangle and subtract the area of the smaller triangle inside it.
Answer:
The answer would be
Step-by-step explanation:
you multiple 8 and 5 then you multiple 12 (inches) then subtract the inch that makes up 12 let me know if you need help
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
The marked price of a fan is Rs 1,620 and selling price is Rs 1,539. Find the discount amount.
Answer:
rs. 81
Step-by-step explanation:
given,
mp. = 1620
sp. = 1539
now,
discount = mp - s.p = 1620 - 1539 = 81
What is the sum and classification of StartFraction 3 Over 20 EndFraction + StartRoot 10 EndRoot?
3.31227766..., irrational
3.31227766..., rational
18.16227766..., irrational
18.16227766..., rational
9514 1404 393
Answer:
3.31227766..., irrational
Step-by-step explanation:
3/20 +√10 = 0.15 + 3.16227766017...
The root of 10 is irrational, so adding that to a rational number will give an irrational sum.
The sum is about 3.31227766017..., an irrational number.
Answer:
A
Step-by-step explanation:
How long is JK?
Choose 1 answer:
A: 3
B: 2 square root 3
C: 3 square root 3
D: 6
E: 9
Answer:
C) 3 times the sq root of 3
Step-by-step explanation:
In a right angle triangle, the COS is definned as the ajacent side over the hypotenuse. So
COS 60 = JK/JL
COS 60 = JK/(6*sq root 3)
.5 = JK/(6*3**1/2)
JK = .5 *(6*3**1/2)
JK = 3*3**1/2
what is the quotient of 3/4 ÷ 5/12
Answer:
1 4/5
Step-by-step explanation:
3/4 ÷ 5 /12
Copy dot flip
3/4 * 12/5
Rewriting
3/5 * 12/4
3/5 * 3
9/5
1 4/5
Solve the equation and enter the value of d below. 6d + 7 d= 39
Answer:
d=3
Step-by-step explanation:
13d=39
d=39/13
d=3
Hello!
6d + 7d = 39 <=>
<=> 13d = 39 <=>
<=> d = 39 : 13 <=>
<=> d = 3 => 6 × 3 + 7 × 3 = 39
Good luck! :)
Answer with explaination every steps
Answer:
y = - 35
Step-by-step explanation:
Expressing as a fraction , that is
[tex]\frac{y}{-7}[/tex] = 5 ( multiply both sides by - 7 to clear the fraction )
y = - 35
Use the image below and find the missing angles
Step-by-step explanation:
w = 34° (alternate interior angles)
x = 34° (vertically opposite angles)
y = 101°
z = 79° (corresponding angles)
What is the answer to this
Answer:
Step-by-step explanation:
An auto transport truck holds 12 cars. A car dealer plans to bring in 1,006 new cars in June and July. If an auto transport truck is filled for each delivery, except for the last one, how many full truckloads are needed and how many cars will be in the last truck?
What is the answer of this question?
Answer:
2 ( Option A )
Step-by-step explanation:
The given integral to us is ,
[tex]\longrightarrow \displaystyle \int_0^1 5x \sqrt{x}\ dx [/tex]
Here 5 is a constant so it can come out . So that,
[tex]\longrightarrow \displaystyle I = 5 \int_0^1 x \sqrt{x}\ dx [/tex]
Now we can write √x as ,
[tex]\longrightarrow I = \displaystyle 5 \int_0^1 x . x^{\frac{1}{2}} \ dx [/tex]
Simplify ,
[tex]\longrightarrow I = 5 \displaystyle \int_0^1 x^{\frac{3}{2}}\ dx [/tex]
By Power rule , the integral of x^3/2 wrt x is , 2/5x^5/2 . Therefore ,
[tex]\longrightarrow I = 5 \bigg( \dfrac{2}{5} x^{\frac{5}{2}} \bigg] ^1_0 \bigg) [/tex]
On simplifying we will get ,
[tex]\longrightarrow \underline{\underline{ I = 2 }}[/tex]
I did 70 jumping jacks in 1 minute.
Which is the dependent variable? Which is the independent variable?
Write an equation that represents the relationship between the time you spent doing the activity and the amount of the activity you completed.
Answer:
in jh ynhtym
hunt ghb JBL iggmmjuu ki ju nu j
solve the logarithmic equation
[tex] log_{6}(2x - 6) + log_{6}x = 2[/tex]
Answer:
[tex]x=6[/tex]
Step-by-step explanation:
We want to solve the equation:
[tex]\displaystyle \log_6(2x-6)+\log_6x=2[/tex]
Recall the property:
[tex]\displaystyle \log_bx+\log_by=\log_b(xy)[/tex]
Hence:
[tex]\log_6(x(2x-6))=2[/tex]
Next, recall that by the definition of logarithms:
[tex]\displaystyle \log_b(a)=c\text{ if and only if } b^c=a[/tex]
Therefore:
[tex]6^2=x(2x-6)[/tex]
Solve for x. Simplify and distribute:
[tex]36=2x^2-6x[/tex]
We can divide both sides by two:
[tex]x^2-3x=18[/tex]
Subtract 18 from both sides:
[tex]x^2-3x-18=0[/tex]
Factor:
[tex](x-6)(x+3)=0[/tex]
Zero Product Property:
[tex]x-6=0\text{ or } x+3=0[/tex]
Solve for each case. Hence:
[tex]x=6\text{ or } x=-3[/tex]
Next, we must check the solutions for extraneous solutions. To do so, we can simply substitute the solutions back into the original equations and examine its validity.
Checking x = 6:
[tex]\displaystyle \begin{aligned} \log_{6}(2(6)-6)+\log_{6}6&\stackrel{?}{=} 2 \\ \\ \log_6(12-6)+(1)&\stackrel{?}{=}2 \\ \\ \log_6(6)+1&\stackrel{?}{=}2 \\ \\ 1+1=2&\stackrel{\checkmark}{=}2\end{aligned}[/tex]
Hence, x = 6 is indeed a solution.
Checking x = -3:
[tex]\displaystyle\begin{aligned} \log_6(2(-3)-6) + \underbrace{\log_6-3}_{\text{und.}} &\stackrel{?}{=} 2\\ \\ \end{aligned}[/tex]
Since the second term is undefined, x = -3 is not a solution.
Therefore, our only solution is x = 6.
Answer:
x = 6
Step-by-step explanation:
The given logarithmic equation is ,
[tex]\implies log_{6}(2x - 6) + log_{6}x = 2[/tex]
We can notice that the bases of both logarithm is same . So we can use a property of log as ,
[tex]\bf \to log_a b + log_a c = log_a {( ac)} [/tex]
So we can simplify the LHS and write it as ,
[tex]\implies log_{6} \{ x ( 2x - 6 )\} = 2 [/tex]
Now simplify out x(2x - 6 ) . We get ,
[tex]\implies log_6 ( 2x^2 - 6x ) = 2 [/tex]
Again , we know that ,
[tex]\bf \to log_a b = c , a^c = b [/tex]
Using this we have ,
[tex]\implies 2x^2 - 6x = 6^2 \\\\\implies 2x^2 - 6x -36 = 0 [/tex]
Now simplify the quadratic equation ,
[tex]\implies x^2 - 3x - 18 = 0 \\\\\implies x^2 -6x + 3x -18=0\\\\\implies x( x -6) +3( x - 6 ) = 0 \\\\\implies (x-6)(x+3) = 0 \\\\\implies x = 6 , -3 [/tex]
Since logarithms are not defined for negative numbers or zero , therefore ,
[tex]\implies 2x - 6 > 0 \\\\\implies x > 3 [/tex]
Therefore the equation is not defined at x = -3 . Hence the possible value of x is 6 .
[tex]\implies \underline{\underline{ x \quad = \quad 6 }}[/tex]
Solve for x. Round to the nearest tenth, if necessary.
Answer:
x = 63.9
Step-by-step explanation:
We have:
[tex]\frac{QR}{sin35}[/tex] = [tex]\frac{78}{sin90}[/tex]
=> QR × sin90 = 78 × sin35
=> QR × sin90 = 44.7
=> QR = 44.7
But, we also have: [tex]x^{2}[/tex] + [tex]QR^{2}[/tex] = [tex]78^{2}[/tex] <=> [tex]x^{2}[/tex] + [tex]44.7^{2}[/tex] = [tex]78^{2}[/tex] <=> [tex]x^{2}[/tex] = 6084 - 1998.09
=> [tex]x^{2}[/tex] = 4085.91
=> x = [tex]\sqrt{4085.91}[/tex] = 63.9211.. = 63.9
<3 Have a nice day!!
Find x from this triangle
Hello,
we are going to use the theorem of the bissectrice. (if this word is good in english)
[tex]\dfrac{KL}{LM} =\dfrac{KN}{NM} \\\\\dfrac{8}{x} =\dfrac{14}{20-x} \\\\8(20-x)=14x\\\\160-8x=14x\\\\22x=160\\\\x=\frac{160}{22} \\\\x=\frac{80}{11} \\\\\\x=7.\overline{27}[/tex]
the question is on the image
Answer:
€3,551.05
Step-by-step explanation:
31*29=899
899*3.65=€3,551.05
the school will get an estimate of €3,551.05
The time spent by Nadia to answer the geography quiz is 30 minutes more than the time spent to answer the history quiz. What is the total time that Nadia took to answer both quizzes?
Answer:
1 hour
Step-by-step explanation:
hope it helps ....
Find the coordinates of P so that P partitions segment AB in the part-to-whole ratio of 1 to 3 with A(6, -10) and B(9, -1).
Answer:
Step-by-step explanation:
Use the formulas that allow us to find the point that divides the segment into a ratio which is
[tex]x=\frac{bx_1+ax_2}{a+b}[/tex] and [tex]y=\frac{by_1+ay_2}{a+b}[/tex] where a is 1 (comes from the ratio) and b is 3 (comes from the ratio as well). Filling in:
[tex]x=\frac{3(9)+1(6)}{1+3}=\frac{27+6}{4}=\frac{33}{4}[/tex] and then y:
[tex]y=\frac{3(-1)+1(-10)}{1+3}=\frac{-3-10}{4}=-\frac{13}{4}[/tex] so the coordinates in question are
[tex](\frac{33}{4},-\frac{13}{4})[/tex]
Answer:
Step-by-step explanation:
the answer would be (7,-7)
Solve for x. Thank you
Answer:
Step-by-step explanation:
B/c the bigger triangle is a copy of the smaller we can say
8[tex]\sqrt{3}[/tex] / 12 = x / 8[tex]\sqrt{3}[/tex]
then, solve for x
8[tex]\sqrt{3}[/tex](8[tex]\sqrt{3}[/tex]/12) = x
(64 *3) 12 = x
192 /12 = x
16 = x
nice, the first answer looks good , then :P
Answer:
16
Step-by-step explanation:
what is the mesure of DBC?
Answer:
41
Step-by-step explanation:
EH is a diameter of D. The measure of ef is (10x+ 8) and the measure of gh is (11x). Determine the values
Answer:
x = 5
arcEF = 58degrees
arcGH = 55degrees
Step-by-step explanation:
Find the diagram attached
The sum of angle on the straight line EH is 180degrees
Hence arcEF+ arcFG + arcGH = 180
10x+8 + 67 + 11x = 180
21x + 75 = 180
21x = 180 - 75
21x = 105
x = 105/21
x = 5
Since EF = 10x+8
arcEF = 10(5) + 8
arcEF = 50+8
arcEF = 58degrees
Also, arcGH = 11x
arcGH = 11(5)
arcGH = 55degrees
Consider the quadratic function f(x) = x2 - 5x + 6.
What are the values of the coefficients and constant in the function?
а
b
c
Answer:
a=1
b=-5
c=6
Step-by-step explanation:
ax^2+bx+c=0
Is the formula used for this question.
The given function is the same as y = 1x^2 + (-5x) + 6
Compare it to the form y = ax^2+bx+c, and we have the following:
a = 1
b = -5
c = 6
Consider the transfer function a. By rewriting Eq. (7.283) in the form find a series realization of as a cascade of two first-order systems. b. Using a partial-fraction expansion of , find a parallel realization of . c. Realize in control canonical form.
Answer:
B
Step-by-step explanation:
plss pa brainliest me thanks
What is the slope of the line shown below?
Answer:
Hello there,
The correct answer to this question would be D 1/6
Step-by-step explanation:
I had took the test and it said it was correct.
Anyways hope this helps
if the answer is correct pls mark Brainliest
thank you, have a nice day
Solve |x - 5| = 7 ......
Answer:
12,-2
Step-by-step explanation:
