Answer:
V=904.78 in^3
Step-by-step explanation:
V=4/3pir^3=4/3.pi.6^3=904.77868in^3
How do you factor f(x) = x^3 – 3x^2 – 10x + 24 ?
Answer:
f(x) = x³ – 3x² – 10x + 24 = (x + 3)(x – 2)(x – 4)Step-by-step explanation:
I would use the Horner method.
f(x) = x³ – 3x² – 10x + 24
f(2) = 2³ - 3·2² - 10·2 +24 = 0 ⇒ x=2 is the root of function
So:
| 1 | -3 | -10 | 24 |
2 | 1 | -1 | -12 | 0 |
therefore:
f(x) = x³ – 3x² – 10x + 24 = (x – 2)(x² – x – 12)
For x² – x – 12:
[tex]x=\dfrac{1\pm\sqrt{(-1)^2-4\cdot1\cdot(-12)}}{2\cdot1}=\dfrac{1\pm\sqrt{1+48}}{2}=\dfrac{1\pm7}{2}\\\\x_1=\dfrac{1+7}{2}=4\ ,\qquad x_2=\dfrac{1-7}{2}=-3[/tex]
It means:
f(x) = x³ – 3x² – 10x + 24 = (x – 2)(x – 4)(x + 3)
Identify the domain and range of y = 3x - 7.
(1+sinA-cosA)/1+sinA+cosA=(1+sinA+cosA)/1+sinA-cosA=2cosecA
Answer:
Hi,
LHS = sinA-cosA+1/sinA+cosA-1
divide both numerator and denominator by cosA
LHS=(tanA−1+secA)/(tanA+1−secA)LHS=(tanA−1+secA)/(tanA+1−secA)
Now
sec2A=1+tan2Asec2A=1+tan2A
sec2A−tan2A=1sec2A−tan2A=1
Using above relation at denominator of LHS
LHS=(tanA−1+secA)/(tanA−secA+sec2A−tan2A)LHS=(tanA−1+secA)/(tanA−secA+sec2A−tan2A)
LHS=(tanA−1+secA)/((secA−tanA)(−1+secA+tanA))LHS=(tanA−1+secA)/((secA−tanA)(−1+secA+tanA))
LHS=1/(secA−tanA)LHS=1/(secA−tanA)
LHS=RHSLHS=RHS
Hence Proved.
I think above proof will clear your doubt,
All the best.
CAN SOMEONE HELP ME FAST
Find the distance between the two points in simplest radical form.
(-5, 8) (-3, 1)
Answer:
6.40312423 hope that helps
Answer:
[tex]\sqrt{53}[/tex]
Step-by-step explanation:
Calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (- 5, 8) and (x₂, y₂ ) = (- 3, 1)
d = [tex]\sqrt{(-3+5)^2+(1-8)^2}[/tex]
= [tex]\sqrt{2^2+(-7)^2}[/tex]
= [tex]\sqrt{4+49}[/tex]
= [tex]\sqrt{53}[/tex]
Which ordered pair can be removed so that the resulting graph represents a function?
(–2, 2)
(1, 3)
(5, –4)
(–4, –4)
Answer:
(1, 3)
Step-by-step explanation:
Answer: B. 1, 3
Step-by-step explanation: On Edge!!!!
A number is called flippy if its digits alternate between two distinct digits. For example, 2020 and 37373 are flippy, but 3883 and 123123 are not. How many five-digit flippy numbers are divisible by 15?
A 3
B 4
C 5
D 6
E 8
Answer:
A
Step-by-step explanation:
The number of five-digit flippy numbers are divisible by 15 is;
Option B; 4 Numbers
We want 5 digit flippy numbers that are divisible by 15.For a number to be divisible 15, it has to be divisible by 3 and 5.
Also, for a number to be divisible by 5, it's last digit has to be 0 or 5.
Since it is a flippy digit and 0 cannot start it as it is a five digit number, then the first and last digits must be 5. Also, the center digit must be 0 or 5 to fulfill both conditions.Thus, the format of the number should be;5N5N5
For it to be divisible by 3, since 5 + 5 + 5 = 15 is divisible by 3, the N + N can be equal to 0, 6, 12, or 18 since N is identical.
Thus, possible numbers are; 50505, 53535, 56565, 59595.Read more at; https://brainly.com/question/19238760
Esteban stands on a dock 1.25 yd above the water. A fish swims below Esteban at -4.61 yd from the surface of the water. How many yards apart are Esteban and the fish?
Answer: 5.86yd
Step-by-step explanation:
From the question, we are informed that Esteban stands on a dock 1.25 yd above the water and that a fish swims below Esteban at -4.61 yd from the surface of the water.
The distance between Esteban and the fish can be calculated by subtracting -4.61 yd from 1.25 yd. This will be:
= 1.25 yd - (-4.61 yd)
= 1.25 yd + 4.61 yd
= 5.86 yd
There are 12 pencils and 24 map colors to be boxed. Each box must contain only one type of item, and every item must be boxed. What is the most that can be placed in a box so that each box has the same number of items?
Answer:
the answer is 2
Step-by-step explanation:
The way I no this is because I used division and got two for each box. 24 divided by 12 = 2 for every box
write this equation in word form.
x3 + 1
Answer:
X cubed plus one
Step-by-step explanation:
x + 2x + 12y + 4 Using the expression shown, add like terms and produce an equivalent expression.
Answer: 3x+12y+4
Step-by-step explanation:
The only like terms are the x+2x so we add them to get the simplfied answer
Answer:
3x + 12y + 4
I dont really know how to explain but since there is an X at the and of the 2, you can add X + 2x to get 3x. Since 3x, 12y, and 4 are not alike, this is the simplest form.
Charlie bought 2 3/4 pounds of pears for $.76 per pound and 2 3/4 pounds of grapes for $1.40 per pound how much money in dollars and cents did Charlie pay for the pears and grapes
Answer:
$5.94
Step-by-step explanation:
Multiply 2.75 by $0.76 to get $2.09
Multiply 2.75 by $1.40 to get $3.85
Add $3.85 and $2.09 to get $5.94
Answer:
$5.94
Step-by-step explanation:
For the following exercises, determine whether the relation is a function
a) {(5.2),(6,1),(6,2),(4,8)}
Factor the polynomial.
5x4 + 10x3 + 15x2
Answer:
5x^2(x^2 + 2x + 3)
Step-by-step explanation:
All the terms can be factored by 5 and x^2, so we get:
5x^2(x^2 + 2x + 3)
there are no more common terms so this is the answer
julissa gave out an equal number of oranges to each of the 6 apartments on her floor. if she gave each apartment 5 oranges how many oranges did julissa give out in all
What is the radius of a circle that has a circumference of 3.14 meters?
Answer:
r≈0.5m
Step-by-step explanation:
she was right
Answer:
r≈0.5m
Step-by-step explanation:
Please help me the picture is above, I’ll mark as brainliest.
Using the slope, state whether the lines are parallel, perpendicular, or neither.
Y= 2x-3
y=-1/2x+2
Answer:
Parralel lines have the exact same slope.
in the equation y=mx+b m is the slope
Both of these equations are in slope intercept form (y=mx+b) meaning that the coefficient in both equations is the slope.
Parralel lines have the same slope and perpendicular lines have the inverse opposite slope. For example if a line had a slope of 2 or 2/1 then the perpendicular line to it would have a slope of -1/2.
With that knowledge we can easily see that the lines are perpendicular since their slopes (represented by the coefficient) are the inverse opposite.
Perpendicular is your answer
Step-by-step explanation:
3) Where do planes M and NJF intersect?
A. KJH
B. FG
C. JFG
D.GN
Answer:
C) JFG BECAUSE THAT IS WERE IT CROSSES AT
Answer:
the origen is where they all start
Use the law of exponents to rewrite (4x2)^9
What is the solution 8x-3(2x-4)=3(x-6)
Answer:
x = 30
General Formulas and Concepts:
Pre-Alg
Order of Operations: BPEMDASEquality PropertiesStep-by-step explanation:
Step 1: Define equation
8x - 3(2x - 4) = 3(x - 6)
Step 2: Solve for x
Distribute: 8x - 6x + 12 = 3x - 18Combine like terms: 2x + 12 = 3x - 18Subtract 2x on both sides: 12 = x - 18Add 18 to both sides: 30 = xRewrite: x = 30Step 3: Check
Plug in x to verify it's a solution.
Substitute: 8(30) - 3(2(30) - 4) = 3(30 - 6)Multiply: 240 - 3(60 - 4) = 3(30 - 6)Subtract: 240 - 3(56) = 3(24)Multiply: 240 - 168 = 72Subtract: 72 = 72What is 2x(3+x2) when x = −2?
it would be -4 i think
come back and tell me if im wrong
Can someone please check to see if I selected the right answer... Please
What is the first step in solving this equation?
3(2x+6) -4 = 2(5x-2) +6
Answer:
Distrubutative property
Step-by-step explanation:
how do I work this out, I've tried
[tex] \frac{6}{4} = \frac{k \times - 4}{ - 4} [/tex]
and that gave me
[tex] \frac{1}{ - 1.5} x[/tex]
Answer:
The required answer is [tex]y=-\mathbf{\frac{3}{2}}x\\[/tex]
Step-by-step explanation:
We are given that value of x and y vary directly so , if two values vary directly we can write
y∝x
y=kx
Now, we are given x=-4 and y=6 and we have to fill in the blank. We actually have to find value of k i.e y=____x . Yhe blanks must be filled by value of k because y=kx
Using values of x and y i.e x=-4 and y=6 to find value of k
[tex]y=kx\\6=k(-4)\\Divide \ both \ sides \ with \ -4\\\frac{6}{-4}= \frac{k(-4)}{-4} \\k=\frac{-3}{2}[/tex]
The value of k is [tex]\mathbf{\frac{-3}{2}}[/tex]
So, the required answer is [tex]y=-\mathbf{\frac{3}{2}}x\\[/tex]
Y=-2(x-1)^2+8 a) Determine the coordinates of its turning point and state whether it is a Maximum or minimum B) Determine the y-intercept C)Determine the coordinates of the x-intercepts(if any)
Answer:
(a) The coordinates of the inflection point are (1; 8) and, being the value of a less than zero, then these coordinates indicate the maximum of the function.
(b) The y-intercept has a value of 6
(c) The coordinates of the x-intercepts have a value of x=3 and x=-1
Step-by-step explanation:
You know y= -2*(x-1)² + 8
(a) Every quadratic function can be expressed by the canonical form:
f(x)=y= a*( x- h)² + k
where a is the principal coefficient and the ordered pair (h; k) are the coordinates of the vertex of the parabola.
The quadratic function will have a maximum or minimum value at the vertex. If a> 0, the parabola is concave, that is, it will have its branches upwards, therefore the vertex will indicate the minimum of the function. But if a <0 the parabola is convex and the vertex will indicate the maximum of the function.
Comparing the given equation with the canonical form of a quadratic function you can see that:
a=-2h=1k=8Then, the coordinates of the inflection point are (1; 8) and, being the value of a less than zero, then these coordinates indicate the maximum of the function.
(b) The y-intercept arises from evaluating the function at x = 0. So, in this case:
y= -2*(0-1)² + 8
Solving:
y= -2*(-1)² + 8
y= -2*1 + 8
y= -2+8
y= 6
The y-intercept has a value of 6
(c) The roots or coordinates of the x-intercepts arise from evaluating the function at y = 0. So, in this case:
0= -2*(x-1)² + 8
Solving:
-8= -2*(x-1)²
[tex]\frac{-8}{-2} =(x-1)^{2}[/tex]
4= (x-1)²
√4= |x-1|
⇒ 2=x-1 → 2+1=x → 3=x
⇒ -2=x-1 → -2+1=x → -1=x
The coordinates of the x-intercepts have a value of x=3 and x=-1
An office uses paper drinking cups in the shape of a cone, with dimensions as shown. To the nearest tenth of a cubic inch, what is the value of each drinking cup?
*see attachment for the dimensions of the cone given.
Answer:
7.9 in³
Step-by-step explanation:
Given:
Height of cone = 4 in.
Diameter of cone = 2¾ in
Radius (r) = ½ of 2¾ = 1.375 in
Required:
Volume of the cup
Solution:
Volume of the cup = volume of a cone
Volume of a cone = ⅓πr²h
Plug in the values of π, r and h into the formula.
Volume = ⅓*3.14*1.375²*4 = 7.9 in³ (approximated to the nearest tenth)
what is the slope to y=−3x+7
Answer: slope= -3
Step-by-step explanation: use the slope intercept form to find slope
Micah's Family ate some of the two pies that he baked. which number represents the amount of pies that is left
Answer:
The answer is 6/8
Step-by-step explanation:
6/8 is the only logical answer because you need to have an answer that is less than one, 8/6 evens out to 1 1/3, 6/2 evens out to 3, and 8/4 evens out to 2. 6/8 is the only fraction that is less than one.
Answer:
its 6/8
Step-by-step explanation:
A volleyball has a mass of 4 kg Calculate the potential energy of a volleyball that is in the air at a height of 15 m. (g = 9.8 m/s
Gravitational Potential Energy = mass x acceleration due to gravity x height
GPE = mgh
ОА
147J
B
588 J
O C60
O
D
360 J
A sequence has the recursive definition f(1)= 2/3, f(n)= f(n-1)•
3/2 for n > 2
Write the first 5 terms of the sequence. Keep the answers as fractions.