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]
Write each as a percent. Use proportions.
7/25
2/3
3/8
What number should be subtracted from -3/4 to get 5/6?
Answer:
Let that rational number to be subtracted be x.Given,-5/6 - x = 4/9= - x = 4/9+5/6= - x = 23/18x = - 23/18.
Step-by-step explanation:
What is the product?
La potencia que se obtiene de elevar a un mismo exponente un numero racional y su opuesto es la misma verdadero o falso?
Answer:
Falso.
Step-by-step explanation:
Sea [tex]d = \frac{a}{b}[/tex] un número racional, donde [tex]a, b \in \mathbb{R}[/tex] y [tex]b \neq 0[/tex], su opuesto es un número real [tex]c = -\left(\frac{a}{b} \right)[/tex]. En el caso de elevarse a un exponente dado, hay que comprobar cinco casos:
(a) El exponente es cero.
(b) El exponente es un negativo impar.
(c) El exponente es un negativo par.
(d) El exponente es un positivo impar.
(e) El exponente es un positivo par.
(a) El exponente es cero:
Toda potencia elevada a la cero es igual a uno. En consecuencia, [tex]c = d = 1[/tex]. La proposición es verdadera.
(b) El exponente es un negativo impar:
Considérese las siguientes expresiones:
[tex]d' = d^{-n}[/tex] y [tex]c' = c^{-n}[/tex]
Al aplicar las definiciones anteriores y las operaciones del Álgebra de los números reales tenemos el siguiente desarrollo:
[tex]d' = \left(\frac{a}{b} \right)^{-n}[/tex] y [tex]c' = \left[-\left(\frac{a}{b} \right)\right]^{-n}[/tex]
[tex]d' = \left(\frac{a}{b} \right)^{(-1)\cdot n}[/tex] y [tex]c' = \left[(-1)\cdot \left(\frac{a}{b} \right)\right]^{(-1)\cdot n}[/tex]
[tex]d' = \left[\left(\frac{a}{b} \right)^{-1}\right]^{n}[/tex]y [tex]c' = \left[(-1)^{-1}\cdot \left(\frac{a}{b} \right)^{-1}\right]^{n}[/tex]
[tex]d' = \left(\frac{b}{a} \right)^{n}[/tex] y [tex]c = (-1)^{n}\cdot \left(\frac{b}{a} \right)^{n}[/tex]
[tex]d' = \left(\frac{b}{a} \right)^{n}[/tex] y [tex]c' = \left[(-1)\cdot \left(\frac{b}{a} \right)\right]^{n}[/tex]
[tex]d' = \left(\frac{b}{a} \right)^{n}[/tex] y [tex]c' = \left[-\left(\frac{b}{a} \right)\right]^{n}[/tex]
Si [tex]n[/tex] es impar, entonces:
[tex]d' = \left(\frac{b}{a} \right)^{n}[/tex] y [tex]c' = - \left(\frac{b}{a} \right)^{n}[/tex]
Puesto que [tex]d' \neq c'[/tex], la proposición es falsa.
(c) El exponente es un negativo par.
Si [tex]n[/tex] es par, entonces:
[tex]d' = \left(\frac{b}{a} \right)^{n}[/tex] y [tex]c' = \left(\frac{b}{a} \right)^{n}[/tex]
Puesto que [tex]d' = c'[/tex], la proposición es verdadera.
(d) El exponente es un positivo impar.
Considérese las siguientes expresiones:
[tex]d' = d^{n}[/tex] y [tex]c' = c^{n}[/tex]
[tex]d' = \left(\frac{a}{b}\right)^{n}[/tex] y [tex]c' = \left[-\left(\frac{a}{b} \right)\right]^{n}[/tex]
[tex]d' = \left(\frac{a}{b} \right)^{n}[/tex] y [tex]c' = \left[(-1)\cdot \left(\frac{a}{b} \right)\right]^{n}[/tex]
[tex]d' = \left(\frac{a}{b} \right)^{n}[/tex] y [tex]c' = (-1)^{n}\cdot \left(\frac{a}{b} \right)^{n}[/tex]
Si [tex]n[/tex] es impar, entonces:
[tex]d' = \left(\frac{a}{b} \right)^{n}[/tex] y [tex]c' = - \left(\frac{a}{b} \right)^{n}[/tex]
(e) El exponente es un positivo par.
Considérese las siguientes expresiones:
[tex]d' = \left(\frac{a}{b} \right)^{n}[/tex] y [tex]c' = \left(\frac{a}{b} \right)^{n}[/tex]
Si [tex]n[/tex] es par, entonces [tex]d' = c'[/tex] y la proposición es verdadera.
Por tanto, se concluye que es falso que toda potencia que se obtiene de elevar a un mismo exponente un número racional y su opuesto es la misma.
the letter v has an unknown value. If you multiply v by 16, the product is 4.what is the value of v?
Answer:
v = 0.25
Step-by-step explanation:
v = ?
v x 16 = 4 (given)
v = 4/16
v = 0.25
Checking:
[ 0.25 x 16 = 4]
Answer:
1/4 or 0.25 (as a decimal)
Step-by-step explanation:
We know that v has an unknown value.
When it is multiplied by 16, we would get the product.
Turn it into an equation:
16x = 4
Find x:
4 ÷ 16 = 0.25 or 1/4
Now we’ve find x:
16 x 1/4 = 4
Which is a true equation
So x equals 0.25 or 1/4 (as a fraction)
I’d recommend choose fraction bu whatever is up to you!
The height of a cone is two times its base diameter. What is the volume of the cone in terms of its base radius r?
options are on the picture:)
Answer:-
The option B is the right answer.
Solution:-
[tex] \sf h = 2d = 2 \: • \: 2r = 4r[/tex]
[tex] \sf = \frac{1}{3} \pi {r}^{2} h[/tex]
[tex] \sf = \frac{1}{3} \pi {r}^{2} \: • \: 4r[/tex]
[tex] \sf = \frac{4}{3} \pi {r}^{3} \: \green✓ [/tex]
Is the discriminant of f positive, zero, or negative?
Answer:
It might be negative, I'm not sure, but I feel postive about that answer.
Step-by-step explanation:
Answer:
Step-by-step explanation:
The discriminant is zero because the graph of the parabola is on the x axis.
I need help with my math!!!
Answer:
[tex]y = |x+2|+1[/tex]
Step-by-step explanation:
Barbara, a school superintendent, asks the local school board for permission to hire an additional teacher whenever the student enrollment at a certain grade level within a school increases by 35 students beyond capacity. This is an example of which type of decision
Answer:
Programmed
Step-by-step explanation:
Programmed Decisons may be classified as those actions which are routinely carried out or performed based on existing rules and protocol. In programmed decision making, the rules are in place, therefore once the criteria or requirement for which the rule or routine is to be enforced arises, programmed Decisons are made. In the scenario, the superintendent required that a programmed Decison be made in cases or situations where enrollment increases by 35 student beyond capacity, Hence, with this, every time this occurs the additional teachers will be hired.
At the beginning of year 1, Matilda invests $450 at an annual simple interest rate of 5%. She makes no deposits to or withdrawals from the account. Which explicit formula can be used to find the account's balance at the beginning of year 15? What is the balance?
Answer:
$765
Step-by-step explanation:
[tex]interest \: = \frac{prt}{100} \\ = \frac{(450)(5)(14)}{100} \\ = 315 \\ total \: money \: = 315 + 450 \\ = 765[/tex]
A(n) = 450 + (n – 1)(0.05 • 450); $765.00
Find the measure of the missing angle using exterior angle sum theorm
Answer:
35
Step-by-step explanation:
The exterior sum theorem states the exterior angle is equal to the sum of the opposite interior angles
145 = ?+110
145 - 100 = ?
35 = ?
Find the area of circle Q in terms of x
Answer:
The answer is C 100πcm^3
Find the solutions of the equation 3x = x4, rounded to two decimal places. (Enter your answers as a comma-separated list.)
Answer:[tex]-0.802; \ 1.517[/tex]
Step-by-step explanation:
Given
[tex]3^x=x^4[/tex]
Here, two functions are given that is [tex]y=3^x[/tex] and [tex]y=x^4[/tex]
Check for the intersection of the graph of two curves
From the graph, they cut at two different points i.e. [tex]x=-0.802\ \text{and}\ x=1.517[/tex]
Rest two roots are negative.
Plss answer the bottom question
Answer:
200
Step-by-step explanation:
250/100=2.5
2.5*80=200
So the answer is 200
Factor -1.8 out of 3.6b-9
=================================================
Explanation:
Consider something like 2b+6 factoring to 2(b+3). When we distribute that outer 2 back inside the parenthesis, we're multiplying that 2 by everything inside. Factoring goes in reverse of this and we divide each term of 2b+6 by the GCF 2.
The same thing applies to this current problem as well.
Divide each term by the -1.8 we want to factor out.
(3.6b)/(-1.8) = -2b(-9)/(-1.8) = 5The results -2b and 5 will go inside the parenthesis. That's how we end up with -1.8(-2b+5)
You can use distribution to verify this
-1.8(-2b+5)
-1.8*(-2b) - 1.8*(5)
3.6b - 9
what most likely caused the man in the caravan to come to the farmhouse where elisa lived? a.he had lost his dog in the vast,open areas b.he needed to purchase supplies c.the country roads confused him d. he was looking for an adventure
Answer: A. He had lost his dog in the vast, open areas.
Step-by-step explanation:
The Chrysanthemums" is a story about a woman whose name was Elisa Allen. She was frustrated about her present condition as she didn't have a child and her husband didn't find her romantically pleasing.
In the book, the reason why the man in the caravan came to the farmhouse where Elisa stayed was because he had lost his dog in the vast, open areas.
a)if A×B ={(1,2),(2,3),(1,3),(2,2),(3,2),(3,3)} find i) set A ii) set B.i need for exam
Answer:
soln,
set A ={ 1,2,3}
set B ={2,3}
Set up a proportion to solve for x in the following similar triangles.
Answer:
C
Step-by-step explanation:
I took the quiz and it was C! Hope this helps :)
4x+9/y+11=0 and 6/y -3x=8
9514 1404 393
Answer:
(x, y) = (-2 12/17, -51)
Step-by-step explanation:
Here is the answer to ...
[tex]4x+\dfrac{9}{y}+11=0\\\\\dfrac{6}{y}-3x=8[/tex]
If you mean something else, then parentheses are needed.
__
Let z = 1/y. Then the equations in general form are ...
[tex]4x+9z+11=0\\3x-6z+8=0[/tex]
The solution (cross multiplication method) is ...
x = (9·8 -(-6)·11)/(4(-6)-3·9) = 138/-51 = -2 12/17
z = (11·3 -8·4)/-51 = -1/51
y = 1/z = -51
The solution is (x, y) = (-2 12/17, -51).
7x-3=5x+9 solve for x
Given :-
7x - 3 = 5x + 9To Find :-
The value of x.Solution :-
Taking the given equation ,
=> 7x -3 = 5x + 9
=> 7x - 5x = 9 + 3
=> 2x = 12
=> x = 12 ÷ 2
=> x = 6
Hence the required answer is 2 .
Find the perimeter of ΔJKL. Round your answer to the nearest tenth if necessary
Answer:
Step-by-step explanation:
as angles of two triangles are equal, so they are similar.
x/17 =35/14=40/16
x/17=35/14
x=35/14×17=85/2=42.5
perimeter of ΔJKL=40+35+42.5=117.5
URGENTT!!!! help quick please
What is the value of tan 0 in the unit circle below?
Answer:
1 / sqrt(3)
Step-by-step explanation:
tan(o) = sin(o) / cos(o)
sin(o) is the vertical distance from the x-axis. and that is in this basic circle the y-coordinate of the point.
cos(o) is the horizontal distance from the y-axis. that is the x-coordinate of the point.
so,
tan(o) = (1/2) / (sqrt(3)/2) = (2×1) / (2×sqrt(3)) = 1/sqrt(3)
A bag contains 6 apples and 4 oranges. If you select 5 pieces of fruit without
looking, how many ways can you get 5 apples?
Answer:
6 I think
Step-by-step explanation:
identify the equation of the line graphed below
pls help, i have class rn :(
in how many ways can alice distribute 12 apples to 3 children (a child can have no apples)
Complete the similarity statement for the two triangles shown
40 m
15 m
30 m
25 m
>H
Enter your answer in the box
20 m
50 m
S
F
ACHS ~A
Answer:
TFY
Step-by-step explanation:
let's start with the 90 degrees angle.
this is C in the first, and T in the second triangle.
so, C and T must be aligned.
and the we go around.
F ~ H
and then
Y ~ S
A man runs at the speed of 10 km/hr. How much time will he take to cover 2000 meters?
Chang knows one side of a triangle is 13 cm. Which set of two sides is possible for the lengths of the other two
sides of this triangle?
5 cm and 8 cm
6 cm and 7 cm
7 cm and 2 cm
8 cm and 9 cm
Answer:
8 cm and 9 cm
Step-by-step explanation:
Hi there!
The sum of the lengths of two sides of a triangle must always be greater than the length of the third side.
5 cm and 8 cm ⇒ 5+8=13; not greater than 13
6 cm and 7 cm ⇒ 6+7=13; not greater than 13
7 cm and 2 cm ⇒ 7+2=9; not greater than 13
8 cm and 9 cm ⇒ 8+9=17; greater than 13
Therefore, the last set of two sides is possible for the lengths of the the other two sides of this triangle.
I hope this helps!
Explain what you would do first to simplify the expression below. Justify why, and then state the result of performing this step.
