Answer:
a) 483.6cm²b) 850.1 cm³Step-by-step explanation:
Given the slant height 's' and its radius 'r' to be 15cm and 8cm respectively.
the total surface of the cone A = πrs+πr² and the volume is expressed as
V = 1/3πr²h
For the surface area of the cone;
Given parameters
radius = 8 cm and slant height s = 15 cm
Total surface area A = π(8)(15) + π(8)²
A = 90π+64π
A = 154π
If π = 3.14
A = 154(3.14)
A = 483.56cm²
A = 483.6cm²
Hence the total surface area of the cone to the nearest tenth is 483.6cm²
For the volume of the cone;
V = 1/3πr²h
Using pythagoras theorem to get the height of the cone;
l² = h²+r²
h² = l²-r²
h² = 15²-8²
h² = 225-64
h² = 161
h = √161
h = 12.69cm
V = 1/3π* (8)² * 12.69
V = 1/3π* 64 * 12.69
V = 1/3*3.14* 64 * 12.69
V = 2550.1824/3
V = 850.06 cm³
V = 850.1 cm³
Hence, the volume of the cone is 850.1 cm³ to the nearest tenth.
if the first step of the equation -x + 6 = 5 - 3x is "subtract 5" then what should the next step be
Answer:
The next step is add x to each side
Step-by-step explanation:
-x + 6 = 5 - 3x
Subtract 5 from each side
-x + 6-5 = 5-5 - 3x
-x+1 = -3x
Add x to each side
-x+1 = -3x+x
1 = -2x
Answer:
Step-by-step explanation:
all you need to do is solve for x right? so in that case when you subtract 5 from both sides you get -x+1=-3x
then you will add x on each side
you should now have 1=-2x
divide each side by -2 and then you will have
-1/2=x
Desmond is 2 inches taller than Niki. If we let w represent Nikis height in inches, write an algebraic expression for Desmonds height. Enter your answer as an expression. Example: 3x^2+1
Answer:
w + 2
Step-by-step explanation:
Niki's height = w in
Desmond height = w + 2
Answer:
w+2
Step-by-step explanation:
Since Desmonds is 2 inches taller than Niki, w+2 would make the most sense.
what is .7 of a mile
Answer:
1232 yards or 3696 feet or 44352 inches or 0.7 of a mile
Step-by-step explanation:
Not every straight line will pass the vertical line test. What is the only type
of straight line that would fail the vertical line test? *
A-horizontal line
B-vertical line
C-Option 3
A vertical line has all points with the same x coordinate, but infinitely many different y coordinates. It inherently fails the vertical line test because we can pass a single straight line through more than one point on the function curve.
Put another way, the input is a single value but there's infinitely many outputs. A function must have each input produce exactly one output. This is of course only when the input is in the domain.
Answer:
c
Step-by-step explanation:
a ladder 7.5m long is leaning against a wall if the foot of the ladder is 3m from the wall how far up the wall does the ladder reach to reach the nearest metres
Answer:
7 m
Step-by-step explanation:
Use the pythagorean theorem.
a^2+b^2=c^2
7.5 is your hypotenuse and 3 is one of your legs.
7.5^2 - 3^2 = 47.25
the sqrt of 47.25 is 6.873863542, therefore the nearest meter it reaches is 7.
Bart opens a bank account and deposits $10 each week. If he has $90 in his account, how many weeks has he been depositing money?
The number of weeks Bart has been depositing money is 9 weeks according to investment and time.
The number of weeks of money depositing will be given by the formula -
Number of weeks = total amount deposited each week/total number of weeks × 100
Keep the values in formula to find the number of weeks of money deposit
Number of weeks = 90/10
Perform division that will include cancelling zeroes
Number of weeks = 9
Hence, Bart deposited the money for 9 weeks.
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The mean of 5 numbers is 11. The numbers are in the ratio 1 : 1 : 2 : 3 : 4. Find the numbers.
Answer:
5, 5, 10, 15, 20
Step-by-step explanation:
Since the mean of the 5 numbers is 11, we know that the sum of the 5 numbers is 5 * 11 = 55. If we call the numbers x, x, 2x, 3x and 4x respectively based off of the ratio, we can write:
x + x + 2x + 3x + 4x = 55
11x = 55
x = 5 so 2x = 2 * 5 = 10, 3x = 3 * 5 = 15 and 4x = 4 * 5 = 20, therefore, the numbers are 5, 5, 10, 15, and 20.
Given that
Numbers are in ratio 1:1:2:3:4 Mean of these numbers is 11 .To Find.
We have to find these five numbers.Solution .
→ Let's assume these numbers as
→ x , x , 2x , 3x and 4x
→ Mean of any observations is = Sum of observations/ Number of observations.
→ Sum of observations = x+x+2x+3x+4x
→ 11x
→ Number of observations = 5
→ Mean = 11
→ 11 = 11x/5
→ 11 (5) = 11x
→ 11(5)/11 = x
→ value of x = 5
Putting the value of x for finding all numbers .
→ 1st number = x → 5
→ 2nd number = x → 5
→ 3rd number = 2x → 10
→ 4th number = 3x → 15
→ 5th number = 4x → 20
Please answer this question now
Answer:
396 yd^2
Step-by-step explanation:
8X12=96
(96/2)*2=9
10*10=100
100*3=300
300+96=396
Answer:
416 yd^2
Step-by-step explanation:
The formula for the surface area of a triangular prism is
[tex]A=2\sqrt{\frac{a+b+c}{2}(\frac{a+b+c}{2}-a)(\frac{a+b+c}{2}-b)(\frac{a+b+c}{2}-c)}+(a+b+c)h[/tex]
where h is the height (10), and a, b and c are the base sides (10, 10, 12).
Where r is the radius of the cylinder and h is the height of the cylinder. Find the surface area when r is 3 inches and h is 5 inches. A. 50π in² B. 112π in² C. 48π in² D. 80π in²
Answer:
C
Step-by-step explanation:
The surface area of a cylinder is given by this formula:
● Sa = 2×r^2× PI + 2r×Pi×h
r is 3 inches and h is 5 inches.
● Sa = 2×3^2 × Pi + 2×3×Pi×5
● Sa = 48 × Pi in^2
If 1 pound of grass seed costs 25x cents, represent in terms of x the cost of 7 pounds of seed? In polynomial simplest form
Answer:
175 cents
Step-by-step explanation:
25x=
25 • 7
25 • 7 = 175
Therefore the cost of 7 pounds of seed is 175 cents.
solve this equation -2x+9=-5x-15
Answer:
x = -8
I hope this helps!
Name a real world context to describe the sums of rational numbers.
Step-by-step explanation:
when you are cooking you need to measure fractions of ingredients
Does The TI-Nspire works just like the TI-84 ?
Answer:
TI-Nspire models automatically detect most points of interest such as x and y-intercepts, maximum values, and minimum values when you are in trace mode. TI-84 Plus models require you to use a series of left and right bounds and guesses to find those same values.
Please answer this question now
Answer:
113 degrees
Step-by-step explanation:
Measure of arc ADCB = 58+108+60 = 226 degrees
Measure of angle B = 226/2 = 113 degrees
Answer:50
Step-by-step explanation:
4x- 3y = -13 -x + 6y = -44
Answer:
3x and 9y and -31 is the correct answer if you are bloviating.
Step-by-step explanation:
bloviate the factors of x and y.
evaluate 1 whole number 2/5 + 3/4 and give your answer to one significant figure
Answer:
The answer is
2 to 1 significant figureStep-by-step explanation:
[tex]1 \frac{2}{5} + \frac{3}{4} [/tex]
To solve the question first convert the mixed fraction to an improper fraction
That's
[tex]1 \frac{2}{5} = \frac{7}{5} [/tex]
So we have
[tex] \frac{7}{5} + \frac{3}{4} [/tex]
Find the LCM of the fractions
The LCM of 5 and 4 is 20
That's
[tex] \frac{7}{5} + \frac{3}{4} = \frac{7(4) + 3(5)}{20} = \frac{28 + 15}{20} [/tex]
[tex] = \frac{43}{20} [/tex]
= 2.15
We have the final answer as
2 to 1 significant figureHope this helps you
The scale for a drawing is 1 centimeter to 5 meters. If the actual object is 35 meters, the drawing is _____ centimeters long.
A. 30
B. 17
C. 7
D. 40
Answer:
its c.7
Step-by-step explanation:
I took the quiz
Answer:
c. 7
Step-by-step explanation:
i had this quiz also
when simplifying the expression y=(2x(x-3)(x-3))/(x-1)(x-3) do all of the x-3 s get cancelled or just one in the numerator and one in the denominator?
Answer:
x-3 is cancelled and just one remains in numerator.
Answer it answer it answer it.
Answer:
Option C. P = 3/q
Step-by-step explanation:
To know the the correct answer to the question, do the following:
Let us assume a certain number for P say 2 and 3, and then, find the corresponding value for q in each case to see which will give a decreased value for q.
Option A
When P = 2, q =.?
P = 3q
2 = 3q
Divide both side by 3
q = 2/3
When P = 3, q =.?
P = 3q
3 = 3q
Divide both side 3
q = 3/3
q = 1
From the above illustration, we can see that as P increase, q also increase.
Option B
When P = 2, q =.?
P – 3 = q
2 – 3 = q
q = – 1
When P = 3, q =.?
P – 3 = q
3 – 3 = q
q = 0
From the above illustration, we can see that as P increase, q also increase.
Option C
When P = 2, q =.?
P = 3/q
2 = 3/q
Cross multiply
2 × q = 3
Divide both side by 2
q = 3/2
q = 1.5
When P = 3, q =.?
P = 3/q
3 = 3/q
Cross multiply
3 × q = 3
Divide both side by 3
q = 3/3
q = 1
From the above illustration, we can see that as P increase, q decreases.
Option D.
When P = 2, q =.?
1/p = 3/q
1/2 = 3/q
Cross multiply
1 × q = 2 × 3
q = 6
When P = 3, q =.?
1/p = 3/q
1/3 = 3/q
Cross multiply
1 × q = 3 × 3
q = 9
From the above illustration, we can see that as P increase, q also increase.
Now, haven done the above, only option C gives a decreased value for q as the value of P increases.
c
this before
Step-by-step explanation:
Counting from 1 to 46, how many 4s will you encounter? 8 10 11 12 14
Answer:
11
Step-by-step explanation:
4=1
14=2
24=3
34=4
40=5
41=6
42=7
43=8
44=9
45=10
46=11
You will encounter 11 4s.
Which two complex numbers when subtracted from each other equal another complex number from the table? A -3 − 4i B -7 − 6i C 13 + i D -9 + 6i E 8 − 8i F -15 + 9i G 2 + 12i H 6 − 10i
Answer:
if you have a ti-84 plus, input ur problem into the calculator
Step-by-step explanation: you may use calculator for answers
Answer:
The difference of A and D equals the complex number in row H in the table (6 − 10i):
A − D
=
-3 − 4i − (-9 + 6i)
=
-3 − 4i + 9 − 6i
=
-3 + 9 − 4i − 6i
=
(-3 + 9) + (-4 − 6)i
= 6 − 10i
Step-by-step explanation:
Which property can you apply to Hayley's expression to show that it is equivalent to Gretchens expression?
Answer: Distributive property of the multiplication.
Step-by-step explanation:
You did not post Gretchen's expression, but i gues that it is 3*(x + y)
I guess that it is the distributive property of the multiplication.
For 3 numbers, A, B and C, we have that:
A*(B + C) = A*B + A*C
here we have:
3*x + 3*y
We can do the inverse process to the distributive property, and get:
3*x + 3*y = 3*(x + y)
which i guess is Gretchen's expression.
Answer:
the other person is right it is Distributive property of the multiplication.
The value of y varies directly with x, where LaTeX: y=50y = 50 when LaTeX: x=40x = 40. Find the value of x when y is 10.
Group of answer choices
LaTeX: x=8 x = 8 x = 8 x = 8 x = 8 x = 8 x = 8 x = 8
LaTeX: x=12.5 x = 12.5 x = 12.5 x = 12.5 x = 12.5 x = 12.5 x = 12.5 x = 12.5
LaTeX: x=1.25 x = 1.25 x = 1.25 x = 1.25 x = 1.25 x = 1.25 x = 1.25 x = 1.25
LaTeX: x=0
Answer:
x= 8
Step-by-step explanation:
The equation of direct variation is
y = kx
When y = 50 when x = 40
50 = k* 40
Divide each side by 40
50/40 = k
5/4 = k
The equation is
y = 5/4x
Let y = 10
10 = 5/4x
Multiply each side by 4/5
4/5 * 10 = 5/4 x * 4/5
8 = x
MATH QUESTION: When 8668/25 + 4141/9 - 5533/25 is computed and written as a mixed number in simplest form, what is the fractional part of that mixed number?
Answer:
23/45
Step-by-step explanation:
8668/25 + 4141/9 - 5533/25
= 26348/45
= 585(23/45)
=23/45
Suppose y varies jointly as x & z. If y = -180 when z = 15and x = -3,then find y when x = 7 and z = -5. 1 point
Answer:
y = - 140
Step-by-step explanation:
The statement
y varies jointly as x & z is written as
y = kxzto find y when x = 7 and z = -5 we must first find the relationship between the variables
when y = - 180
z = 15
x = - 3
- 180 = k(15)(-3)
-180 = - 45k
Divide both sides by - 45
k = 4
The formula for the variation is
y = 4xzwhen
x = 7
z = -5
y = 4(7)(-5)
y = 4(-35)
y = - 140Hope this helps you
Find the vertex of f(x)= x^2+ 6x + 36
Pls help soon
Answer:
vertex(-3,27)
Step-by-step explanation:
f(x)= x^2+ 6x + 36 ( a=1,b=6,c=36)
V(h,k)
h=-b/2a=-6/2=-3
k=f(-3)=3²+6(-3)+36
f(-3)=9-18+36=27
vertex(-3,27)
I need this answer ASAP pls someone help ASAP work shown
Worth 10 pts
Answer:
5c² + 4c - 4
Step-by-step explanation:
Subtract the shaded area from the area of the outer rectangle, that is
(2c + 3)(3c - 2) - (c + 2)(c - 1) ← expand both pairs of factors using FOIL
= 6c² + 5c - 6 - (c² + c - 2) ← distribute parenthesis by - 1
= 6c² + 5c - 6 - c² - c + 2 ← collect like terms
= 5c² + 4c - 4
Which of the following is most likely the next step in the series?
A.
B.
C.
D.
Answer:
C
Step-by-step explanation:
The amount of sides on the shape are increasing, like 4, 5, 6, so the best answer should be 7 sides for the next shape, however there is no shape that is 7, so C which has 8 sides is the next best answer.
Most likely the next step in the series is hectogon. Therefore, option A is the correct answer.
What is the pattern?A pattern in mathematics is an arrangement of numbers, shapes, colours and other elements that repeat. This arrangement can be related to any event or object. When a group of numbers is organised in a certain way, it is referred to as a pattern. Patterns can also be referred to as a series.
The given series has square, pentagon and hexagon.
We know that, square has 4 sides, pentagon has 5 sides and hexagon has 6 sides.
So, the next figure in the series must have 7 sides.
Thus, 7 sided figure is called has hectogon and septagon.
Therefore, option A is the correct answer.
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Find the LCM of
[tex]14 {a}^{3} {b}^{2} [/tex]
and
[tex]20 {a}^{4} {b}^{2} [/tex]
Answer:
Hi,
I hope you are searching for this answer.
The lcm of an expression is calculated by taking the common factor and multiply the common factor with the remaining one, alright.
or, simply the lcm of an expression is calculated by the product of common factors and the factors which are not common.
Hope it helps...
solve the equation: sin(2x)= sin x
Answer:
Below
Step-by-step explanation:
sin(2x) = 2 ×cos(x)× sin(x)
● sin(x) = 2 × cos(x) × sin(x)
● 2 × cos(x) = 1
● cos (x) = 1/2
So we can deduce that:
● x = Pi/3 + 2*k*Pi
● or x = -Pi/3 + 2*k*Pi
K is an integer
The Solution of x:
x = π/3 + 2πn, where n is an integer.
x = 2π/3 + 2πn, where n is an integer.
In degrees:
x = 60° + 360°n, where n is an integer.
x = 120° + 360°n, where n is an integer.
To solve the equation sin(2x) = sin(x), we can use the properties of trigonometric functions.
First, let's simplify the equation using the double angle identity for sine:
sin(2x) = 2sin(x)cos(x).
Now we can rewrite the equation as:
2sin(x)cos(x) = sin(x).
2cos(x) = 1.
Dividing both sides of the equation by cos(x), we get:
2 = 1/cos(x).
Now, we can find the value of cos(x) by taking the reciprocal of both sides:
cos(x) = 1/2.
From the unit circle or trigonometric values,
we know that cos(x) = 1/2 corresponds to angles of π/3 or 2π/3 (in radians) or 60° or 120° .
So, the solutions for x are:
x = π/3 + 2πn, where n is an integer.
or
x = 2π/3 + 2πn, where n is an integer.
In degrees:
x = 60° + 360°n, where n is an integer.
or
x = 120° + 360°n, where n is an integer.
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