Answer:
F(x) = (x + 3)^2 -87
Step-by-step explanation:
Here, we want to rewrite the function by completing the square.
Firstly, we move the c term(-78) to the right hand side of the equation and that becomes
x^2 + 6x = 78
Then, we can complete the square on the right hand side here, to be
Let’s add 9 to both sides
That would be;
x^2 + 6x + 9 = 78 + 9
x^2 + 6x + 9 = 87
(x+3)^2 = 87
or simply
(x+3)^2 -87 = 0
So our F(x) becomes
F(x) = (x + 3)^2 -87
Answer:
The expression after completing the square is:
[tex]f(x) = (x+3)^{2} -87[/tex]
Step-by-step explanation:
The function is rewritten after making algebraic manipulation:
[tex]f(x) = x^{2} + 6\cdot x +9 - 9 - 78[/tex]
The expression after completing the square is:
[tex]f(x) = (x+3)^{2} -87[/tex]
Triangle ABC is represented by the drawing below.
What are the measures of the interior angles of ABC?
Step-by-step explanation:
Therefore,
(x+20) + (x-10) + (2x-30) = 180° (Sum of interior angles of a triangle)
Or, x+x+2x+20-10-30 = 180°
Or, 4x-20 = 180°
Or, 4x= 180+20
Or, 4x= 200°
Or, x= 200°/4
Therefore, x= 50°
So,
(x+20)
= 50+20
=70°
(x-10)
= 50-10
40°
(2x-30)
= 2×50-30
=100-30
=70°
Hope it helped, If it did, please mark it as the brainliest answer :)
Choose all that give the correct explicit and recursive formula for the sequence.
Answer: not clear
Step-by-step explanation:
Which of the following exponential functions represents the graph below?
O A Rx) = 1 • 3*
O B. f(x) = 10
O c.
C. 12-23
OD. f(x) = 3.1
The exponential function represented on the graph is f(x) = (1/3)[tex].^x[/tex]. The correct option is B.
What is an exponential function?The mathematical expression f(x)=exp or e^x denotes the exponential function. The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, though it can be extended to complex numbers or adapted to other mathematical objects like matrices or Lie algebras.
A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
The given graph is representing the exponential function f(x) = (1/3)[tex].^x[/tex] The graph is attached with the answer below. The graph is showing the inverse fraction of ( 1/3).
Therefore, the exponential function represented on the graph is f(x) = (1/3)[tex].^x[/tex]. The correct option is B.
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Rafael ha comprado 185,8 kg. de manzanas y 300,2 kg. de naranjas. ¿Cuánto más pesan las naranjas que las manzanas? ¿Cuánto pesa su compra?
Answer:
a.114.4kg
b. 486kg
Step-by-step explanation:
Firstly , we want to know the value with which the apples weigh more than the oranges
To calculate this, we simply subtract the weight of the oranges from that of the apple
Mathematically, that would be ;
300.2-185.8 = 114.4kg
The total weight of the things bought is calculated by adding both weights together
That would be 185.8 + 300.2 = 486 kg
An object’s weight on Earth varies directly to its weight on the Moon. If a man weighs 180 kg on Earth, then he will weigh 30 kg on the Moon. Set up an algebraic equation that expresses the weight on Earth in terms of the weight on the Moon and use it to determine the weight of a woman on the Moon if she weighs 120 kg on Earth.
Answer:
The gravity of the Moon is about one sixth that of the Earth. For example, an astronaut weighing 180 pounds on the Earth would weigh about 30 pounds on the Moon.
What is the maximum number of possible extreme values for the function,
f(x) = x4+-7x2-x+6?
A. 3
B. 4
C. 2
D. 5
Answer:3
Step-by-step explanation:
Which choice is equivalent to the product below when x>0?
Answer: 1/3
Step-by-step explanation: Using Radical Properties, Whenever we have two or more radical terms which are multiplied with same index, then we can put only one radical and multiply the terms inside the radical.
[tex]\sqrt{ \frac{5}{x^2} }\times \sqrt{ \frac{x^2}{45} }=\sqrt{ \frac{5x^2}{45x^2} }=\sqrt{ \frac{1}{9} }=\frac{1}{3}[/tex]
The expression √(5/x²).√(x²/45) is equivalent to 1/3.
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is √(5/x²).√(x²/45)
Square root of five by x square times square root of x square by forty five
√(5/x²).√(x²/45)
√(5x²/45x²)
Cancel out the x² in the numerator and denominator
√(5/45)
Divide numerator and denominator by 5
√(1/9)
1/3
Hence, the expression √(5/x²).√(x²/45) is equivalent to 1/3.
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Add
(2x^2 - 2x) + (6x - 4)
Answer:
2x^2 +4x -4
Step-by-step explanation:
(2x^2 - 2x) + (6x - 4)
Combine like terms
2x^2 +6x-2x -4
2x^2 +4x -4
(PLEASE HURRY I NEED IT TODAY)
The triangle ABC goes through a series of transformations, resulting in the triangle A’B’C’. The three transformations are listed below. Reflection in the x- axis. Followed by a rotation of 1800 clockwise about the origin Followed by a translation 3 units down and 4 units to the right For triangle ABC, the vertex A is originally located at (-2, 3). Show the new coordinates of A after each of the three transformations above.
Answer:
1) Reflection in the x-axis
A' = (-2, -3)
2) Rotation of 180° clockwise about the origin
A'' = (2, 3)
3) Translation of 3 units down and 4 units to the right
A''' = (6, 0)
Step-by-step explanation:
The transformations are as follows;
1) Reflection in the x-axis
Here the x-coordinate is the same and the y-coordinate changes sign.
Therefore, we have;
A (-2, 3)
After reflection in the x-axis becomes A' = (-2, -3)
2) Rotation of 180° clockwise about the origin
When, a point (x, y) is rotated 180° clockwise about the origin, it becomes (-x, -y)
Therefore, we have;
A' = (-2, -3) becomes A'' = (2, 3)
3) Translation of 3 units down and 4 units to the right
Translation of 3 units down and 4 units to the right = [tex]T_{(4, -3)[/tex]
Which gives
A''' = (2 + 4, 3 - 3) = (6, 0).
1) En el siguiente enunciado, identifica la variable estadística y su tipo: Se quiere lanzar al mercado un nuevo producto y la empresa que lo crea estudia el tiempo de publicidad, en segundos, que otras empresas han utilizado para promocionar un producto de similar calidad. ) Calidad del producto - Cualitativa ordinal b) Tiempo de publicidad - Cuantitativa continua c) Calidad de productos - Cualitativa nominal d) Tiempo de publicidad - Cuantitativa discreta
Answer:
Step-by-step explanation:
Hola!
Las variables aleatorias pueden Cualitativas o cuantitativas.
Las variables aleatorias cualitativas son aquellas que se refieren a atributos o características de los individuos o unidades de interés que no son cuantificables. Dentro de estas variables se pueden identificar dos tipos:
Ordinales: estas variables representan cierto tipo de cualidad que tiene un orden natural, por ejemplo: Opinión de una persona sobre una película de estreno, calificada en "muy buena", "buena", "regular", "mala", "muy mala"
Estas calificaciones son claramente cualidades, pero tienen un orden, todo el mundo sabe que una calificación "regular" es mejor que una "muy mala" y a su vez peor que una calificación "buena"
Nominales: Son aquellas que indican atributos no cuantificables que no tienen un orden natural. Por ejemplo, color de cabello, raza, sexo.
Las variables aleatorias cuantitativas son aquellas que registran valores numéricos, dicho de manera coloquial: "cuentan cosas". Estas variables siempre toman valores dentro de un rango o intervalo de definición, teniendo esto en cuenta podemos definir dos tipos de variables aleatorias cuantitativas:
Continuas: pueden tomar cualquier valor dentro del intervalo de definición de la variable, por ejemplo, la estatura, el peso, la temperatura, entre un valor y otro existen infinita cantidad de valores que la variable puede tomar. En muchos casos, esto está restringido a la precisión de los métodos utilizados para tomar las mediciones.
Por ejemplo, una balanza puede tomar pesos de kilogramo a kilogramo, ej: 20kg, 21kg, 22kg mientras que una más precisa puede tomar pesos intermedios de los mismos objetos, ej: 20.1kg, 21.5kg, 22.9kg y otra más precisa puede indicar mediciones más exactas, ej: 20.142kg, 21.538kg, 22.973kg es decir que, cuanto más precisa la balanza que usemos para obtener las mediciones, mayor será la gama de valores que puede tomar la variable.
Discretas: solo pueden tomar ciertos valores dentro del intervalo de definición de la variable aleatoria, a diferencia de las variables continuas, entre los valores posibles que pueden tomar estas variables, no se encuentra nada, es decir que "saltan" de valor en valor. Por esto también se las llama variables discontinuas.
Uno de los ejemplos más comunes de variable discreta es hacer rodar un dado de 6 caras, la variable puede tomar valores 1, 2, 3, 4, 5, 6 pero no puede tomar valores entre esos valores, es decir, el dado nunca va a mostrar valores intermedios como "2.5" o "3.3".
Dicho esto pasemos a identificar el tipo de cada ejemplo:
a) y c) Calidad del producto
Esta es algo engañosa, porque todo depende de la escala determinada para medir la calidad.
Es decir, si la escala de medición de la calidad de un objeto es de 0 a 10, siendo cero lo peor y 10 lo mejor, entonces la variable es cuantitativa discreta.
Sin embargo, si la escala es nominal, por ejemplo: Alto, medio, bajo, entonces la variable es cualitativa y como las categorías tienen un orden natural, no solo es cualitativa, sino que también es ordinal.
b) y d) Tiempo de publicidad
Esta variable aleatoria "cuenta el tiempo", toma valores numéricos con lo cual es cuantitativa y, además, puede tomar cualquier valor dentro del intervalo de definición, todo depende de la precisión del reloj utilizado lo que la califica como variable continua.
Espero que tengas un buen días!
Kent is cutting a long tree into pieces. He cut the trunk into 3 pieces. Then he cut each of those pieces into 3 smaller pieces. Finally he cut each of those smaller pieces into 3 still smaller pieces. How many pieces did they have then?
Answer:
27
Step-by-step explanation:
he started by cutting one log into 3
1×3=3
then cutting each of those into 3
3×3=9
then again
9×3=27
Which percent is equivalent to One-half? edgeunity
Answer:50%
Step-by-step explanation:
Answer:
The answer is 50%
Step-by-step explanation:
The answer for this should be 50 but I don’t know how could someone tell me why it’s $50?
Answer:
50
Step-by-step explanation:
So say the bill is x.
18% of x = 0.18x
0.18x = 9
x = 50
Answer:
it is 50
Step-by-step explanation:
you have to do 9 x 10/18
Please answer correctly !!!! Will mark brainliest !!!!!!!!!!
Answer:
[tex]2x^2-x+3[/tex]
Step-by-step explanation:
So just divide the areas by the length:
[tex]2x^2-x+3[/tex]
And that is your width.
Answer:
iddk
Step-by-step explanation:
PLEASE HELP MEEE ITS VERY URGENT
Answer:
[tex]C=31.42[/tex]
[tex]A=78.55[/tex]
Step-by-step explanation:
[tex]C=2\pi r[/tex]
[tex]C=2 \times 3.142 \times 5[/tex]
[tex]C=31.42[/tex]
[tex]A=\pi r^{2}[/tex]
[tex]A=3.142 \times 5^{2}[/tex]
[tex]A=3.142 \times 25[/tex]
[tex]A=78.55[/tex]
A book sold 32100 copies in its first month of release. Suppose this represents 6.2% of the number of copies sold to date. How many copies have sold to date.
Answer:
1900 copies sold to date
Step-by-step explanation:
you need to find the value of 6.2% of 32100
To do this:
6.2 ÷ 100
= 0.062
0.062 x 32100
= 1990.2
However, it's not possible to have .2 of a copy, so your round down
The answer is 1900 copies.
Hope it helped :)
A certain television is advertised as a 17-inch TV (the diagonal length). If the width of
the TV is 8 inches, how many inches tall is the TV?
Answer:
15 inches
Step-by-step explanation:
We can solve this problem using the Pythagorean theorem. The formula is:
[tex]a^{2} + b^{2} = c^{2}[/tex]
where 'c' is the hypotenuse (the longest side) and 'a' and 'b' are the legs (the other sides).
First, draw a diagram for the problem. (See the photo attached below)
We know the other leg is 8 and the hypotenuse is 17. 'a' is the missing side.
a = ?
b = 8
c = 17
Substitute the values into the equation.
[tex]a^{2} + b^{2} = c^{2}[/tex]
[tex]a^{2} + 8^{2} = 17^{2}[/tex]
Rearrange to isolate 'a'
[tex]a^{2} = 17^{2} - 8^{2}\\[/tex] Square root both sides
[tex]a = \sqrt{17^{2} - 8^{2}}[/tex] Square each number
[tex]a = \sqrt{289-64}[/tex] Subtract under the root
[tex]a = \sqrt{225}[/tex] Find the square root
[tex]a =15[/tex] Final answer
Therefore, the TV is 15 inches tall.
Working together, Shawn and Hector can install a tile floor in 6 hours. It would take Shawn 9 hours to do the job alone.
Calvin was told he should drink 2 liters of water
everyday. If he did this, how much water would
he drink in I week (7 days) ?
Answer:
14
Step-by-step explanation:
Its pretty simple. You just have to multiply 7 and 2 to get the product of 14. Hopw this helps
Answer:
14 liters every week.
Step-by-step explanation:
There are 7 days in a week.
If he drank 2 liter every day, you could solve this the following ways...
2+2+2+2+2+2+2=14 because 2 liter every day for 7 days
7 x 2 because there are 7 days in a week, and he drank 2 liters a day, so 7 x 2 would work.
7 + 7 would also work.
Your welcome.
I really hope I helped.
Can I plz have brainliest please?
Find the
15x^2 and 18
Answer:
I couldn't understand your question, please send once more
Answer: GCF = 3
~~~~~~~~~~~~
Hope this helps!
PLEASE SEE PIC BELOW
Answer:
They have the same domain and range
Step-by-step explanation:
Although they are different equations, they both have a domain of
[0,∞)
and a range of
[0,∞)
Help fasttt!
What is the value of x?
Answer:
14
Step-by-step explanation:
5x = 70
x = 14
Answer:
The answer is option 1.
Step-by-step explanation:
Given that total angles in a quadrilateral is 360°. So in order to find x, you have to substract the remaining angles from 360° :
[tex]5x + 110 + 110 + 70 = 360[/tex]
[tex]5x + 290 = 360[/tex]
[tex]5x = 360 - 290[/tex]
[tex]5x = 70[/tex]
[tex]x = 70 \div 5[/tex]
[tex]x = 14[/tex]
SOMEBODY PLEASE HELP:)
Answer:
A =12.92 cm^2
Step-by-step explanation:
The area of a triangle is given by
A = 1/2 bh where b is the base and h is the height
A = 1/2 ( 7.6) ( 3.4)
A =12.92 cm^2
Answer:
[tex] = 12.92 {cm}^{2} [/tex]
Step-by-step explanation:
[tex]area = \frac{1}{2} \times b \times h \\ = \frac{1}{2} \times 7.6 \times 3.4 \\ = \frac{25.84}{2} \\ = 12.92 {cm}^{2} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
A room is 20 feet by 25 feet with a 10-foot ceiling. If Mickey paints the walls and the ceiling, how much surface area will he cover? Think, What area ISN'T Micky covering and subtract out that area...
Answer:
1400ft²
Step-by-step explanation:
Given
Room Dimension: 20 ft by 25 ft by 10 ft
Where Length = 20 ft
Width = 25 ft
Height = 10 ft
Required
Surface area of painted walls and ceiling
We'll assume that the room is rectangular in shape and all 4 sides are covered.
This means that Mickey will paint 4 walls and 1 ceiling.
The dimension of the 2 of the 4 walls is as follows;
20ft by 10ft, 25ft by 10ft,
Because opposite sides of a rectangle are equal, the dimension of the remaining 2 walls is: 20ft by 10ft, 25ft by 10ft
Calculating the area of the 4 walls;
[tex]Area = 20ft * 10ft + 25ft * 10ft + 20ft * 10ft + 25ft * 10ft[/tex]
[tex]Area = 200ft^2 + 250ft^2 + 200ft^2 + 250ft^2[/tex]
[tex]Area = 900ft^2[/tex]
The dimension of the ceiling is as follows:
20ft by 25ft
Calculating the area of the ceiling
[tex]Area = 20ft * 25ft[/tex]
[tex]Area = 500ft^2[/tex]
So, the area Micky will cover = Area of 4 walls + Area of ceiling
Total Surface Area [tex]= 900ft^2 +500ft^2[/tex]
Total Surface Area = [tex]1400ft^2[/tex]
Hence, Micky will cover 1400ft²
Teena and Adil have a total of 560 counters. Adil has 2/5 of the number of counters that Teena has. How many more counters does Teena have then Adil?
A) 240
B) 336
C) 400
D) 224
ANSWER:
:2/5 * 560 = D) 224
Which of the x values are solutions to the inequality 4(2 – x) > –2x – 3(4x + 1)?
Answer:
x > - 1.1
All values that are more than - 1.1.
Step-by-step explanation:
4(2 – x) > –2x – 3(4x + 1)
8 - 4x > - 2x - 12x - 3
8 - 4x > - 14x - 3
8 - 4x + 14x > - 14x+ 14x - 3
8- 8 + 10x > - 3 - 8
10x > - 11
x > - 1.1
All values that are more than - 1.1.
Answer:
1.1
Step-by-step explanation:
A triangle on a coordinate plane is translated according
the rule T-3, 5(x, y). Which is another way to write this rule?
OOO
(x,y) → (X-3, y + 5)
(x, y) → (X-3, y-5)
(x,y) → (X + 3, y-5)
(x, y) - (x + 3, y + 5)
Answer:
(x,y) ---> (x - 3, y + 5).
Step-by-step explanation:
The x coordinates are moved 3 to the left (negative) and the y coordinates are moved 5 units up (positive y).
it's A) (x,y) → (X-3, y + 5) on edge 2020
Please answer my question
Answer:
25 percent
Step-by-step explanation:
Total months: 12
Months read more than three books: 3
3/12=25 percent
Answer:
1/4 = 25%.
Step-by-step explanation:
To figure out the percent of months in which she read more than 3 books, we need to figure out how many times she read more than 3 books.
According to the table, she read more than 3 books exactly 3 times: 4, 5, 5.
We also know that there is a total of 12 months. Out of the 12 total months, she read more than 3 books 3 times. So we can say that:
3/12 = 1/4 = 25% of the months she read more than 3 books.
I hope this helps!
(y+3)(x^2–3y+9) What is the product?
Answer:
yx
2
−3y
2
+3x
2
+27
Step-by-step explanation:
En el videojuego "City Sweet" hay una ciudad sitiada en la que hay víveres para 2000 personas durante 15 días, un grupo de 500 habitantes decide rendirse. ¿Cuántos días podrán resistir los demás, si los que se rinden no se llevan víveres?
Answer:
20 days.
Step-by-step explanation:
In this case we must make an inverse proportionality rule, it is inverse because the fewer people there are, the more days must survive. In other words, we know that 2000 people can resist for 15 days, now, if there are no longer 2000 people, but 500 less, that is, 1500 (2000 - 500) how many days can they resist.
people days
2000 15
1500 x
x = 2000 * 15/1500
x = 20
That is, they could last 20 days.
