Aina builds a cube model out of manila cards. If the volume of the constructed cube is (2+3p) ³ cm³, find the total surface area of the cube in terms of p.
HELPPPP
Given:
The volume of a cube = [tex](2+3p)^3\ \text{cm}^3[/tex]
To find:
The total surface area of the cube in terms of p.
Solution:
Volume of a cube is:
[tex]V=a^3[/tex] ...(i)
Where, a is the side length.
It is given that,
[tex]V=(2+3p)^3\ \text{cm}^3[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]a=2+3p\text{ cm}[/tex]
Now, the total surface area of a cube is:
[tex]A=6a^2[/tex]
Where, a is the side length.
Putting [tex]a=2+3p[/tex], we get
[tex]A=6(2+3p)^2[/tex]
Therefore, the total surface area of the cube in terms of p is [tex]6(2+3p)^2\ \text{cm}^2[/tex].
In the rectangle below, EI = 2x+6, FI = 5x-6, and m ZIFE = 49º.
Find E G and m ZIGF.
E
F
m ZIG
H
G
Answer:
gdfhddfdhgbg
Step-by-step explanation:
A triangular prism whose total surface area = 64 cm2, and its lateral area = 40 cm2, find the area of its base?
Answer:
Area of its base = 12cm²
Step-by-step explanation:
The Area of its base = 1/2 of its surface area - 1/2 of its lateral area
Its surface area = 64, then 1/2 X 64 = 32cm²
Its lateral area = 40, then 1/2 X 40 = 20cm²
So, Area of its base = 32 - 20 = 12cm²
if bought 15 caterpillars for $3.00, how much was each caterpillar (find the unit rate for price per caterpillar)
Answer:
20 cents
Step-by-step explanation:
Divide 3 dollars by 15 caterpillars.
3/15 = 0.2
20 cents
If the equation 2x2+bx+5=0 has no real solutions, which of the following must be true?
Answer:
There are no choices but in order to qudratic equation not to have real roots the discriminant must be negative.
d = b² - 2*2*5 = b² - 20If d < 0, we get:
b² - 20 < 0b² < 20b < |√20|- √20 < b < √20or
-2√5 < b < 2√5or
b = (-2√5, 2√5)Two turtles race. The speed of the first is 4 1/ 2 inches per minute and the speed of the other is 5 inches per minute How far apart the be in 3 minutes 5 minutes? 10 minutes?
Answer:
(a) 1.5 inches
(b) 2.5 inches
(c) 5 inches
Step-by-step explanation:
speed of first turtle = 4 1/2 inches per minute = 9/2 inches per minute
speed of the second turtle = 5inches per minute
distance = speed x time
(a) Distance traveled by first turtle in 3 minutes
s = 9/2 x 3 = 13.5 inches
distance traveled by second turtle in 3 minutes
s' = 5 x 3 = 15 inches
So, the gap is
s'- s = 15 - 13.5 = 1.5 inches
(b) Distance traveled by first turtle in 5 minutes
s = 9/2 x 5 = 22.5 inches
distance traveled by second turtle in 5 minutes
s' = 5 x 5 = 25 inches
So, the gap is
s'- s = 25 - 22.5 = 2.5 inches
(c) Distance traveled by first turtle in 10 minutes
s = 9/2 x 10 = 45 inches
distance traveled by second turtle in 10 minutes
s' = 5 x 10 = 50 inches
So, the gap is
s'- s = 50 - 45 = 5 inches
4n+11−2n what is the solution for this equation.
Answer:
2n +11
Step-by-step explanation:
4n+11−2n
Combine like terms
4n -2n +11
2n +11
Answer:
2n+11
Step-by-step explanation:
14.
Solve x2 + 2 = 6 by graphing the related function.
A. There are no real number solutions.
B. There are two solutions: ±[tex]\sqrt{8}[/tex].
C. There are two solutions: 2 and –2.
D. There is one solution: 2
Answer:
C. There are two solutions: 2 and –2.
Step-by-step explanation:
Answer:
Step-by-step explanation:
we have
we know that
The solution of the function is equivalent to solve the following system of equations
------> equation A
------> equation B
The x-coordinate of the intersection point both graphs is the solution of the given function
Using a graphing tool
see the attached figure
The intersection points are and
therefore
The solution of the given function are
Solve x2 + 2 = 6 by graphing the related function. x^2 + 2 is a parabola with a vertex at the point (0, 2). When x = -1 or x = 1, then x^2 + 2 = 3, so we should put the points (-1,3) and (1,3) on the graph. When x = -2 or x = 2, then x^2 + 2 = 6, so we should put the points (-2,6) and (2,6) on the graph. We could continue adding points to the graph if we want, but we already have our two solutions. x^2 + 2 = 6 when x = -2 or x = 2. Therefore, x = -2, and x = 2 are the two solutions to this equation.
Answer: option C.
Step-by-step explanation:
Given a quadratic function of the form , if the coefficient a is less than zero, then the function is opened upward.
The options A is not opened upwards, then it is not the answer.
Then the given equation can be written as:
This function is equal to the parent function, shifted 4 units down.
Therefore, the graph that you are looking for must be a parabola that is opened upwards and has its vertex in the point (0,-4).
Then, the correct option is C. And the solution is:
Nicole paint a circle table that has a diameter of 37 in what is the area of the table
Answer:
A≈1075.21
d Diameter
37
d
r
r
r
d
d
C
A
Using the formulas
A=
π
r
2
d=
2
r
Solving forA
A=
1
4
π
d
2
=
1
4
π
37
2
≈
1075.21009
Step-by-step explanation:
A geometric sequence starts with 12,.
...,27,..., 60.75,...
where 12 is the first term, 27 is the third term and 60.75 the fifth term.
Work out the common ratio of the sequence.
What’s the answer?
Answer:
b
Step-by-step explanation:
it's right cause I took the quix
If ∝ and β are the roots of the quadratic equation x² – x – 2 = 0 then ∝² + β² is equal to
Answer:
α² + β² = 5
Step-by-step explanation:
Given a quadratic equation in standard form
ax² + bx + c = 0 ( a≠ 0 ) , then
sum of roots = - [tex]\frac{b}{a}[/tex]
product of roots = [tex]\frac{c}{a}[/tex]
x² - x - 2 = 0 ← is in standard form
with a = 1, b = - 1, c = - 2 , then
α + β = - [tex]\frac{-1}{1}[/tex] = 1
αβ = [tex]\frac{-2}{1}[/tex] = - 2
Using the identity
(α + β)² = α² + β² + 2αβ , then
α² + β² = (α + β)² - 2αβ = 1² - 2(- 2) = 1 + 4 = 5
[tex] \large \boxed{ \boxed{\mathrm{ \alpha }^{2} + { \beta }^{2} = 5}}[/tex]
Given : [tex] \alpha + \beta = 1[/tex][tex] \alpha \times \beta = - 2[/tex]let's solve for :
[tex] { \alpha }^{2} + { \beta }^{2} [/tex][tex] { \alpha }^{2} + { \beta }^{2} + 2 \alpha \beta - 2 \alpha \beta [/tex][tex]( \alpha + \beta ) {}^{2} - 2 \alpha \beta [/tex]let's plug the values,
[tex](1) {}^{2} -2 \times ( - 2)[/tex][tex]1 + 4[/tex][tex]5[/tex][tex] \mathfrak{best \: \: of \: \: luck \: \: for \: \: your \: \: assignment}[/tex]
A(n) ___ expression is an expression that contains a radical symbol.
A.exponential
B.constant
C.polynomial
D.variable
F.radical
Answer:
radical
Step-by-step explanation:
Please help Ill give brainlest
Answer: D
Step-by-step explanation:
I NEED HELP ASAP PLEASE ILL GIVE YOU MORE POINTS HELPPP!:(
Answer:
1st one is 9
2nd one is 6
3rd one is 2
Step-by-step explanation:
PLEASE HELP WITH THESE 2 QUESTIONS I WILL GIVE BRAINLIEST
Answer:
For the first one it is 8, and the second one is 19
Step-by-step explanation:
Find the distance between the two points in simplest radical form.
(7,-1) and (9,-9)
Answer:
[tex]\sqrt{68}[/tex]
Step-by-step explanation:
(7 , -1) = (x1 , y1)
(9 , -9) = (x2 , y2)
distance formula = [tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2}[/tex]
=[tex]\sqrt{(9 - 7)^2 + (-9 - (-1))^2}[/tex]
=[tex]\sqrt{2^2 + (-9 + 1)^2}[/tex]
=[tex]\sqrt{4 + (-8)^2}[/tex]
=[tex]\sqrt{4 + 64}[/tex]
=[tex]\sqrt{68}[/tex]
Answer:
[tex]Distance = \sqrt{ 68 } \\\\or \\\\Distance =2 \sqrt{17}[/tex]
Step-by-step explanation:
[tex]Let \ (x_1 , y_1) = ( 7 , - 1 ) \ and \ (x_2, y _ 2 ) = ( 9 , - 9 )\\\\\\Distance = \sqrt{(x_2 - x_ 1)^2 + (y_ 2 - y_ 1)^2}\\\\[/tex]
[tex]= \sqrt{(9 - 7)^2 + ( -9 --1)^2} \\\\=\sqrt{2^2 + ( -9 + 1)^2 }\\\\=\sqrt {4 + (-8)^2 }\\\\=\sqrt{ 4 + 64 }\\\\=\sqrt{68}\\\\= \sqrt { 4 \times 17}\\\\=\sqrt{2^2 \times 17}\\\\=2 \sqrt{17}[/tex]
The thickness of 12 sheets of paper is 3.16mm. Find the thickness of 1 sheet
Answer:
79/300 mm
Step-by-step explanation:
We can use Ratio and Proportion to answer this question,
We know,
12 sheets of paper = 3.16mm
So,
1 = 3.16/12 mm
So, the thickness of 1 sheet of paper is => 3.16 / 12
=> 79/300
Hope it helps :)
Answer:
Step-by-step explanation:
Thickness of 1 sheet = thickness of 12 sheets ÷ number of sheets
= 3.16 ÷ 12
= 0.26 mm
Un frutero ha comprado 165kg de manzanas a 2 € el kilo; se le han estropeado 15 kg y el resto los vende a 4 € el kilo. ¿ Cuánto ha ganado? ( 1,25p)
Answer:
€270
Step-by-step explanation:
If a fruit vendor has bought 165kg of apples at € 2 per kilo, the total amount spent is expressed as;
Cost price = 165 * 2 = €330
If 15kg spoilt, the amount of fruit remaining will be 165 - 15 = 150kg
If he rests he sells for € 4 per kilo, then;
Selling price = 150 * 4 = €600
Amount earned = €600 - €330
Amount earned = €270
Please help fast! Calculate the mean and explain the mean that would signify the entire population of fish by using this sample
Pls help me with this
Answer:
12
Step-by-step explanation:
f(-7) = 5-(-7)=5+7=12
solve number 2 please
Answer:
a) 6x² + 2x + 4
b) 32 cm
Step-by-step explanation:
a) In terms of x ,
Perimeter of the figure =
[tex](x+2) + (x^2) + (x^2) + (x+2) + (4x^2)[/tex]
[tex]= 6x^2+2x+4[/tex]
b) If x = 2cm ,
Perimeter of the figure [tex]= 6 \times (2)^2+2 \times (2)+4[/tex]
[tex]= 24 + 4 + 4[/tex]
[tex]= 32\;cm[/tex]
A triangle has sides with lengths of 40 yards, 75 yards, and 85 yards. Is it a right triangle?
Answer:
Yes
Step-by-step explanation:
To check, the squared values of the two smaller lengths must equal the squared value of the biggest length (Pythagorean Theorem)
40² + 75² = 85²
1600 + 5625 = or ≠ 7225
7225 = 7225
It is equivalent so it is correct.
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
How to solve this? I have no clue and also teach me on how to solve this! Thank you!!! thank you for your time!!!! :)
====================================================
Explanation:
Plot the two points on the same xy grid (refer to the diagram below). Once this is done, the answer probably will become apparent. We should move point B 11 units to the right so that we move directly over top point B'. Count out the spaces to see why this is the case, or you can subtract the x coordinates and apply absolute value
|x1-x2| = |-5 - 6| = 11
Then we need to move 3 units down to finally arrive at point B'
---------------------------
A non-visual or non-graph approach could look like this:
B is at (-5,-2) while B' is at (6,-5)
Focus on the x coordinates for now. Like before, we subtract the x coordinates and apply absolute value to get |x1-x2| = |-5 - 6| = 11. This is the "11 units to the right" motion.
Do the same for the y coordinates to get |y1-y2| = |-2-(-5)| = 3. We move down because the y coordinate of B' is further away from 0 compared to the y coordinate of B.
In short, we apply the translation rule [tex](x,y) \to (x+11, y-3)[/tex] to describe the motion of right 11, down 3.
Help Pleasee
Reflect shape A in the line x = -2
Answer: Check out the diagram below
The reflected image is shown in red.
=================================================
Explanation:
Draw a vertical line through -2 on the x axis. This is the mirror line.
Now focus on the upper right corner of the figure, which is at (-3, -1). Notice how the horizontal distance from this corner point to the mirror line is exactly 1 unit. If we move another 1 unit to the right, then we'll arrive at (-1,-1) which is where the reflected point lands or ends up.
In short, the upper right corner point (-3,-1) reflects over x = -2 to land on (-1,-1)
----------------------
As another example, the upper left corner point (-5, -1) will move exactly 4 spaces to the right to get to the mirror line. Then we move another 4 spaces to the right to get to (2,-1).
So the upper left corner (-5,-1) will ultimately move to (2,-1) after the reflection over x = -2.
Apply these steps to the other corner points and you'll end up with what is shown below.
Take note that a point like A(-5,-1) moves to A'(1,-1), and similar to the other points as well. Also, notice that when going from A to B to C, etc we are moving clockwise. We move counterclockwise when going from A' to B' to C' etc. Reflections always swap the orientation.
Transformation involves changing the position of a shape.
The coordinates of the image are:
[tex]\mathbf{A '= (1,1)}[/tex] [tex]\mathbf{B' = (-1,-1)}[/tex] [tex]\mathbf{C' = (-1,-4)}[/tex] [tex]\mathbf{D' = (0,-4)}[/tex]
[tex]\mathbf{E' = (0,-3)}[/tex] [tex]\mathbf{F = (1,-3)}[/tex]
The vertices of the shape are:
[tex]\mathbf{A = (-5,-1)}[/tex]
[tex]\mathbf{B = (-3,-1)}[/tex]
[tex]\mathbf{C = (-3,-4)}[/tex]
[tex]\mathbf{D = (-4,-4)}[/tex]
[tex]\mathbf{E = (-4,-3)}[/tex]
[tex]\mathbf{F = (-5,-3)}[/tex]
The rule of reflection across line x =-2 is:
[tex]\mathbf{(x,y)=(-x -4,y)}[/tex]
So, we have:
[tex]\mathbf{A '= (5 - 4,-1) = (1,-1)}[/tex]
[tex]\mathbf{B' = (3-4,-1) = (-1,-1)}[/tex]
[tex]\mathbf{C' = (3-4,-4) = (-1,-4)}[/tex]
[tex]\mathbf{D' = (4-4,-4) = (0,-4)}[/tex]
[tex]\mathbf{E' = (4-4,-3) = (0,-3)}[/tex]
[tex]\mathbf{F = (5-4,-3) = (1,-3)}[/tex]
So, the coordinates of the image are:
[tex]\mathbf{A '= (1,-1)}[/tex]
[tex]\mathbf{B' = (-1,-1)}[/tex]
[tex]\mathbf{C' = (-1,-4)}[/tex]
[tex]\mathbf{D' = (0,-4)}[/tex]
[tex]\mathbf{E' = (0,-3)}[/tex]
[tex]\mathbf{F = (1,-3)}[/tex]
See attachment for the image of the transformations
Read more about transformations at:
https://brainly.com/question/11709244
Find the equation of the line parallel to y = 2/3-7 (2 over 3)
passing through A(6,-1).
Answer:
y = 2/3x - 5
Step-by-step explanation:
y = 2/3x + b
-1 = 2/3(6) + b
-1 = 4 + b
-5 = b
Question # 2: A circle has a radius of 12 feet. What is the area of the circle? Use 3.14 for Pi.
Answer:
452.16 ft²
Step-by-step explanation:
Use the circle area formula, A = [tex]\pi[/tex]r²
Plug in 3.14 as pi and 12 as the radius, then solve:
A = (3.14)(12)²
A = (3.14)(144)
A = 452.16
So, the area of the circle is 452.16 ft²
Complete the equation describing how x and y are related.
Answer: The "?" would equal 1.
Step-by-step explanation: This is simply a line with a slope of 1 and a y-intercept of zero.
El sueldo bruto de un trabajador de la educación es de 900.000 pesos, si el descuento total que le harán corresponde al 20% de su sueldo ¿Cuánto será su sueldo líquido?
Answer:
Sueldo neto= $160.000
Step-by-step explanation:
Dada la siguiente información:
Sueldo bruto= $200.000
Descuento total= 20%
Para calcular el sueldo neto, debemos usar la siguiente formula:
Sueldo neto= sueldo bruto* (1 - porcentaje de descuento)
Sueldo neto= 200.000*( 1 - 0.2)
Sueldo neto= $160.000
$262 to the markup rate of 30% what is the final price?
Answer:
the final price is $ 163 can be wrong
Profit: $78.60
Revenue: $340.60
Un cable guía de 600 pies esta sujeto a la parte superior de una torre de comunicaciones. Si el cable forma un ángulo de 65° con la Tierra. ¿Cuál es la altura de la torre de comunicaciones?
Answer:
La torre tiene 543.78 pies de altura.
Step-by-step explanation:
Podemos pensar en esta situación como si fuera un triángulo rectángulo, donde el cable es la hipotenusa y la torre es uno de los catetos. (Abajo se puede ver un dibujo de esta situación).
Nosotros queremos encontrar el valor de H, que es el cateto opuesto al ángulo conocido de 65°.
Entonces simplemente podemos usar la relación:
Sin(θ) = (cateto opuesto)/(hipotenusa)
donde:
cateto opuesto = H
θ = 65°
hipotenusa = 600 ft
sin(65°) = H/600ft
sin(65°)*600ft = H = 543.78 ft
La torre tiene 543.78 pies de altura.