If x-2 is one of the factors of x^4-kx^2+4, find the value of k.
Step-by-step explanation:
Given expression is x⁴-kx²+4 =0
x−2 is a factor of the given expression.
So, x=2
Substitute in the equation, we get
2⁴-k(2)²+4
⇒16+4k+4=0
⇒4k=−20
⇒k=−5
for f(x) =4x+1 g(x)=x²-5, find (f•g)(x)
Answer:
(f · g)(x) = 4x³ + x² - 20x - 5
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Combining Like TermsExpand by FOIL (First Outside Inside Last)Step-by-step explanation:
Step 1: Define
f(x) = 4x + 1
g(x) = x² - 5
(f · g)(x) is f(x)g(x)
Step 2: Find (f · g)(x)
Substitute: (f · g)(x) = (4x + 1)(x² - 5)Expand [FOIL]: (f · g)(x) = 4x³ - 20x + x² - 5Combine like terms: (f · g)(x) = 4x³ + x² - 20x - 5We know that,
[tex] \Large \underline{\boxed{\sf{ (f . g)(x) = f(x) \times g(x) }}}[/tex]
By substituting values :
[tex] \sf : \implies (f . g)(x) = (4x+1) \times (x^{2} -5)[/tex]
[tex] \sf : \implies (f . g)(x) = 4x(x^{2} -5) +1(x^{2} -5)[/tex]
[tex] \sf : \implies (f . g)(x) = 4x^{3} - 20x + x^{2} -5[/tex]
[tex] \sf : \implies (f . g)(x) = 4x^{3} + x^{2} - 20x -5[/tex]
Hence, answer is :
[tex]\underline{\boxed{\sf{(f . g)(x) = 4x^{3} + x^{2} - 20x - 5}}}[/tex]
Four students simplified the expression.
410
45
Camilla added the exponents: 410 + 5 = 415
Bentley divided the exponents: 410 + 5 = 42
Mira multiplied the exponents: 410.5 = 450
Regan subtracted the exponents: 410 - 5 = 45
Which student correctly simplified the expression?
Answer:
camilaaaaaaaaaaaaaaa
Answer:
Regan subtracted the exponents: 410 − 5 = 45
Can you please help due at 1130
Answer:
y-8 = 5(x+3)
Answer:
y+3=-5(x-8)
Step-by-step explanation:
Select the table representing a linear function (Graph them if necessary.)
Answer:
B
Step-by-step explanation:
In order for a function to be linear, It must be a straight line. Letter B is the only table that, when graphed, creates a straight line.
Answer: B
Step-by-step explanation: I just answered this question on the a p e x semester exam
You go shopping and spend $264 on shirts and shorts. You purchase a total of 9 items. Each shirt costs $24 and each pair of shorts cost $32. How many of each did you buy?
Answer:
3 shirts, 6 shorts
Step-by-step explanation:
A total of $264 is spent during shopping on shirts and shorts
Each shirt costs $24
Each shorts cost $32
Therefore the quantity of shirts and shorts bought can be calculated as follows
24× 3= 72
32×6= 192
192+72= 264
Hence 3 shirts and 6 shorts were bought
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Answer:
y = 0.35x + 2.5
Step-by-step explanation:
The triangles formed by a man, a pole, and a point on the ground between them, are similar. What is the height of the pole?
Emma is making two different kinds of cookies for a cookie party she will be attending. She needs 2 and 2/3 cups of sugar for the first recipe and 1 and 1/4 cups of sugar for the second recipe. Emma thinks she will have enough sugar but she isn't quite sure. She knows that her full 2 pound bag of sugar says it contains 4 and 1/2 cups of sugar. Determine the exact difference between the amount of sugar Emma has and the amount of sugar she needs for the recipes.) Emma's mom brought home another 2 pound bag of sugar (4 and 1/2 cups) and wants to make fudge to take to work. Her mom will need 2 and 1/6 cups of sugar. Write a numerical expression that could be used to determine exactly how much sugar will be left over from the two bags of sugar after Emma bakes cookies and her mom makes fudge
Answer:
Step-by-step explanation:
Emma is making two different kinds of cookies for a cookie party she will be attending. She needs 2 and 2/3 cups of sugar for the first recipe and 1 and 1/4 cups of sugar for the second recipe. Emma thinks she will have enough sugar but she isn't quite sure. She knows that her full 2 pound bag of sugar says it contains 4 and 1/2 cups of sugar. Determine the exact difference between the amount of sugar Emma has and the amount of sugar she needs for the recipes.) Emma's mom brought home another 2 pound bag of sugar (4 and 1/2 cups) and wants to make fudge to take to work. Her mom will need 2 and 1/6 cups of sugar. Write a numerical expression that could be used to determine exactly how much sugar will be left over from the two bags of sugar after Emma bakes cookies and her mom makes fudge
Determining Points on a Line Given a Direct Variation
y
x
y
What other points are on the line of direct variation through
(5, 12)? Check all that apply.
(0,0)
(2.5, 6)
36
32
28
24
(3, 10)
(7.5, 18)
20
18
(12.5, 24)
12
00
(15, 36)
x
Draw
8
12
10
Click or tap the graph to plot a point.
Tone
Answer:
Step-by-step explanationAl final de esta lección, debes ser capaz de:
Reconocer una relación de variación directa
Encontrar la fórmula de una relación de variación directa
Resolver problemas verbales asociados con variaciones directas
Introducción
x = Horas Trabajadas 0 1 2 3 4
y = Dólares Ganados 0 3 6 9 12
La tabla anterior muestra la relación entre las horas trabajadas y el dinero en dólares, que obtuvo Juan trabajando a razón de $3.00 por hora. En esta tabla, podemos ver que el dinero ganado es igual al producto de las horas trabajadas por 3. Otra manera de decir eso es que la constante de variación o proporción es igual o 3. También se puede observar que cada vez que x aumenta en un 1, la variable y aumenta en 3. Otra manera de decir eso es que la razón de cambio es igual a 3.
En la aplicación de abajo, mueve el botón de la barra “constante de variación” a 3. Observa que los puntos de la gráfica coinciden con los valores en la tabla, y que con cada aumento de 1 en x, la variable y aumenta 3 y que la relación entre las variables es y = 3 × x .
Lo sentimos, pero la GeoGebra Applet no se pudo iniciar. Por favor, asegzrese de que Java 1.4.2 (o posterior) esta instalado y activo en su navegador ( Haga clic aqum para instalar Java ahora )
Cajas de Leche 0 1 2 3 4
Botellas de Leche 0 4 8 12 16
Si cada caja de leche contiene 4 botellas, la tabla anterior muestra la relación entre el número de cajas de leche y el número de botellas que contienen. En esta tabla, podemos ver que el número de botellas de leche se obtiene multiplicando el número de cajas de leche por 4.
En la aplicación de arriba, mueve el botón de la barra constante de variación a 4. Observa que los puntos de la gráfica coinciden con los valores en la tabla, y que con cada aumento de 1 en x, y aumenta 4 y que la relación entre las variables es y = 4 × x.
.
Cantidad de dólares 0 1 2 3 4
Cantidad de galletas que se puede comprar 0 2 4 6 8
Si una galleta cuesta 50 centavos, la tabla anterior muestra la relación entre la cantidad de dólares y la cantidad de galletas que se puede comprar. En esta tabla, podemos ver que la cantidad de galletas se obtiene multiplicando la cantidad de dólares por 2.
En la aplicación de arriba, mueve el botón de la barra constante de variación a 2. Observa que los puntos de la gráfica coinciden con los valores en la tabla, y que con cada aumento de 1 en x, la variable y aumenta en 2 y que la relación entre las variables es y = 2 × x
.
En todas estas relaciones de los ejemplos anteriores, una variable es igual a otra variable multiplicada por una constante distinta de cero. Estas relaciones se conocen como proporciones directas o variaciones directas.
Definición
Dadas dos variables x y y, los enunciados:
y varía directamente como x,
y es directamente proporcional a x y
y es proporcional a x
todos significan que y = kx, para algún número real fijo k.
Al número k se le llama la constante de variación o constante de proporcionalidad. El valor de k también representa la razón de cambio de la relación. Es decir, cada aumento de 1 en x va a corresponder a un aumento de k en y.
Pasos para hallar la Fórmula para Relaciones de Variación Directa
Las relaciones de variación directa tienen la forma y = kx donde x y y son variables y k es una constante distinta de cero. La fórmula para una relación de variación directa se puede hallar mediante los siguientes pasos:
Paso 1: Traducir el enunciado a una fórmula de variación directa.
y es directamente proporcional a x significa
y =k·x
Paso 2: Sustituir las variables conocidas para encontrar k.
Paso 3: Sustituir k y escribir la fórmula.
Ejemplos
Ejemplo 1
u es proporcional a v. Si u = 16 cuando v = 4, escribe la fórmula para la relación entre u y v.
Paso 1: Traducir el enunciado a una fórmula de variación directa.
u es proporcional a v significa
u =k·v
Paso 2: Sustituir valores conocidos para encontrar k.
16 = k· 4
k=164=4
Paso 3: Sustituir k y escribir la fórmula.
u =4v
Conclusión: la fórmula para expresar la relación entre u y v es u =4v
Ejemplo 2
p varía directamente como z. Si p = 210 cuando z = 200, escribe la fórmula para expresar la relación entre p y z .
Paso 1: Traducir el enunciado a una fórmula de variación directa.
p varía directamente como z significa
p = k·z
Paso 2: Sustituir valores conocidos para encontrar k.
210 = k· 200
k=210200=1.05
Paso 3: Sustituir k y escribir la fórmula.
p =1.05z:
Answer:
A, B, D, F On edge!
Step-by-step explanation:
Have a good day! :3
given that f(x)=2x/3 evaluate f^-1(6)
Answer:
9
Step-by-step explanation:
we know by definition that
[tex]f^{-1}(f(x))=x\\\\f^{-1}(\frac{2x}{3})=x\\\\f^{-1}(x)=ax\\\\f^{-1}(\frac{2x}{3})=a(\frac{2x}{3})=x\\\\f^{-1}(x)=\frac{3x}{2}[/tex]
so now we evaluate
[tex]f^{-1}(6)=\frac{3*6}{2}\\\\=3*3\\\\f^{-1}(6)=9[/tex]
and if we want to do an extra step
[tex]f^{-1}(f(6))=6\\\\f^{-1}(\frac{2*6}{3})=f^{-1}(4)=\frac{3*4}{2}=6[/tex]
which works.
the sum of three consecutive integers is 261 , which equation could be used to find the integer .
Answer:
You got it wrong, its the first option
Step-by-step explanation:
Since its not asking for a consectuive EVEN or ODD integer its not
X + X+2 + X+4...
Instead its just the normal way
X + X+1 + X+2 + X+3....
SO thats the correct answer.
A water tank already contains 55 gallons of water when John begins to fillet water flows into the tank at a rate of 8 gallons per minute write a linear equation to model the situation find the volume of the water tank in 25 minutes after John begins filling the tank.
Answer:
y= 8x + 55
After 25 minutes the tank will have 255 gallons
Step-by-step explanation:
Given g(x) = 2x – 1, solve for x when g(x) = 3.
Answer:
x = 2
Step-by-step explanation:
g(x) = 2x - 1
g(x) = 3
2x - 1 = 3
Add 1 to both sides;
2x = 4
Divide both sides by 2;
x = 2
Which expression has the same value as 37.4 - 54.9?
Answer:
The answer is D.
Step-by-step explanation:
Hope this helps and I hope u have an Amazing day!!
4 × (3 + 7) = (4 ×[]) + (4 ×[])
Answer:
4 × (3 + 7) = (4 ×7) + (4 × 3)
Step-by-step explanation:
If you go by the order of PEMDAS you would do the parentheses first. 3 + 7 =10. 10 × 4 = 40. Then you would just use the distributive property and do (4× 7) + (4 × 3)
4 × 7 = 28 and 4 × 3 = 12 28 +12 =40
helppp me plzzzzzz ahh
When Luis was 4 years old, his parents put $6,500 into a college fund account that earned 3.5% interest. What is the total amount in the account when Luis starts college at 18 years old? (there are no answer choices)
Answer: LOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOL FAT NECK AHH BOY
Helpppppplpppo! Hurry hurry
Answer:
I hurried wat
Step-by-step explanation:
wAT
Find the measure of each exterior angle of the regular polygon. (Please answer correctly!)
what is the y = mx + b form of x - 3y = 6
Step-by-step explanation:
x - 3y = 6
3y = x - 6
y = 1/3 x - 2.
Here m is 1/3 and b is -2.
Mrs . Smith has 4 tables for her students. Each table can seat 5 students,
How many students can sit at all the tables?
A. 8
B. 9
C. 16
D. 20
E. 25
Answer:
D.20
Step-by-step explanation:
4*5=20
Which expression is equivalent to the one below? minus 1 over 2 open parentheses 10 plus 1 over 4 close parentheses
Answer:
300
Step-by-step explanation:
Please help me???? Transition math
Which ratio forms a proportion with 1442? Bruh I will give y’all points and brainlesst
Answer:
7/21
Step-by-step explanation:
14/42 is 7/21 in another form
A sheet of 28 stickers has star and heart stickers. There are 16 heart stickers. How many heart stickers does a pack of 140 stickers have? Choose equivalent ratios to show your reasoning. __ heart stickers; __ = __ fractions and numbers to drag: 60, 80, 12/28, 60/140, 80/140, 16/28, and 12
Answer:
80 heart stickers does a pack of 140 stickers
Step-by-step explanation:
The number of heart stickers in a pack of 140 stickers is 60.
Given that, a sheet of 28 stickers has star and heart stickers.
What is the ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Here, the number of star stickers in a sheet
= 28-16 =12
The ratio of star and heart stickers
= 12:16
= 3:4
Now, 3+4=7
Number of heart stickers = 3/7 ×140
= 60
Therefore, the number of heart stickers in a pack of 140 stickers is 60.
To learn more about the ratio visit:
brainly.com/question/13419413.
#SPJ5
A linear function is a function in which the dependent variable changes at a constant rate relative to the independent variable. Based on this assumption, determine whether each relationship below can be modeled by a linear function. Select Yes or No for each situation. Yes No The total number of tires, T, on c cars. C The cost, C. in dollars, of p pounds of tangerines 0 O The temperature, F, after m minutes of a pie taken out of the oven. The value, V, in dollars, of a bank account eaming compound interest after t years. OO
yes
no
no
yes
hope it help!!!
Yes, no, no, yes I believe
PLS HELP WILL GIVE BRANLIEST
Answer:
she took 13 classes that were worth 3 credits
Step-by-step explanation:
well we know that some of the classes are worth 3 and some are worth 4 and that all of these together = 59 so your first equation would be
3x+4y=59
x would be the number of classes worth 3 credits and y would be the number of classes worth 4 credits.
then it says the total number of classes that they took was 18 so we know that
x + y =18.
you want to solve for the number of 3 credit classes so lets go ahead and get rid of the y values. SO you need you multiply the x+y equation by 4
4x+4y=72
then subtract 4x+4y=72 from 3x+4y=59 to get
-x = -13
and then x is a negative so you need to divide -1 from both sides and you get that she took 13 classes that were worth 3 credits.
pov you scrolling through brainly looking for a bots post
smh
Answer:
HoW diD yOu KnOw ?? :/
Step-by-step explanation:
:D have a blessed day <3
Answer:
no just trying to see who I can help
does anyone know how to tell the difference between rational and irrational numbers?
Answer:
Rational numbers refers to a number that can be expressed in a ratio of two integers. An irrational number is one which can't be written as a ratio of two integers. Expressed in fraction, where denominator ≠ 0. Cannot be expressed in fraction.
Step-by-step explanation:
done