[tex]\bf \textit{lateral area of a cone}\\\\ LA=\pi r\sqrt{r^2+h^2}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=3 \end{cases}\implies LA=\pi (3)\sqrt{3^2+3^2} \\\\\\ LA=3\pi \sqrt{2(3^2)}\implies \boxed{LA=9\pi \sqrt{2}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \textit{total surface area of a cone}\\\\ SA=\pi r\sqrt{r^2+h^2}+\pi r^2~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=3 \end{cases}\implies SA=\boxed{9\pi \sqrt{2}}+\pi 3^2 \\\\\\ SA=9\pi \sqrt{2}+9\pi \implies SA\approx 68.26[/tex]
Determine which ordered pair is a solution for the system of equations.
Y=5/2x-3
y=-x+3
(12/7, 9/7)
Since y = -x + 3, substitute it into the first equation.
-x + 3 = 5/2x - 3
Now add x and subtract 3 from both sides.
0 = 7/2x - 6
Now add 6 on both sides.
6 = 7/2x
Now divide by 7/2 on both sides.
12/7 = x
Now, just substitute x into the second equation.
y = -12/7 + 3
y = -12/7 + 21/7
y = 9/7
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show your work and answer choice in the comments
Answer: D. 2550 cm³
Step-by-step explanation:
Volume of one box = Length x width x height
Volume of 6 boxes = 6(L x w x h)
= 6(14 x 6 x 5)
= 6(14 x 30)
= 6(420)
= 2520
a school art teacher needs 200 sticks of clay. An art shop donates 9 small boxes and 6 large boxes of clay. the small boxes have 7 sticks of clay and the large has 10. how many more sticks of clay are needed?
Write an equation of the line passing through the point (5,3) with slope m = -4
Answer:
Step-by-step explanation:
For this problem, point slope form would be the easiest.
Point Slope Form- y-y1 = m(x-x1)
In this case, y1 is 3, x1 is 5, and m would be the slope which is -4.
y-3=-4(x-5)
This is how to write an equation for the problem.
Answer:
[tex]\large{\boxed{y-3=-4(x-5)-\text{point-slope form}}\\\boxed{y=-4x+23}}[/tex]
Step-by-step explanation:
The equation of a line in point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - point
We have the slope m = -4 and the point (5, 3). Substitute:
[tex]y-3=-4(x-5)[/tex] use distributive property
[tex]y-3=-4x+(-4)(-5)[/tex]
[tex]y-3=-4x+20[/tex] add 3 to both sides
[tex]y=-4x+23[/tex]
please help on #15 thank you !!
Answer: A. $3
Step-by-step explanation:
Price: $ 60.00
Sales Tax (5%): $ 3.00
Total: $ 63.00
OR, an easier way to do it is:
60 × 0.05 = 3
* Hopefully this helps:)!!!Mark me the brainliest:)!!
∞ 234483279c20∞
Answer:
The Answer is $3
Step-by-step explanation:
5% of 60= $3
1) Step I
5%=0.05
2) there asking for the amount of the tax So its 5%of 60
Which is solve like This
0.05 x 60 = 3
Hopes this helps you!
Solve the equation for x by graphing -2^x+3=-3^(- x)-2
Answer: =2.35
Step-by-step explanation:
What is the inverse of the following statement? If it is night, the street lights will come on. Select the best answer from the choices provided. A. If the street lights come on, then it is night. B. The street lights will come on if it is night. C. If it is not night, then the street lights will not come on. D. If the street lights do not come on, then it is not night.
ANSWER
C. If it is not night, then the street lights will not come on.
EXPLANATION
The given statement is
"If it is night, then the street lights will come on"
Given the statement,
"If p, then q",
then the inverse of this statement is
"If it is not night,then the street lights will not come on"
"If not p, then not q"
The correct choice is C.
The inverse of a conditional statement is created by negating both the hypothesis and the conclusion. Thus, the inverse of the statement 'If it is night, the street lights will come on.' is 'If it is not night, then the street lights will not come on.'
Explanation:The question is asking for the inverse of a given statement. In logic, the inverse of a conditional statement is created by negating both the hypothesis and the conclusion. The original statement: 'If it is night, the street lights will come on.' becomes 'If it is not night, then the street lights will not come on.' in its inverse form. So, the correct answer is C. If it is not night, then the street lights will not come on.
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Which equations correctly represent a line that has a slope of -2/3 and passes through the points (–2, 8) and (1, 6)?
Answer:
2x + 3y = 20
Step-by-step explanation:
Slope of the line is -2/3 . We can use any of the given points to find the equation of the line. Lets use (1, 6)
The general point-slope form of a line is:
[tex]y-y_{1} =m(x-x_{1} )[/tex]
Here m is the slope which is -2/3
x1 and y1 are the coordinates of the point. So x1 = 1 and y1 = 6
Using these values, we get:
[tex]y-6=-\frac{2}{3} (x-1)\\\\ 3(y-6)=-2(x-1)\\\\ 3y-18=-2x+2\\\\ 2x+3y=20[/tex]
Answer:
2x + 3y = 20
Step-by-step explanation:
We are given two points: (–2, 8) and (1, 6) and the slope (m) of the line and we are to find the equation of this line.
We know that the standard equation of a line is:
[tex]y=mx+c[/tex]
So we will plug in the given values in the above equation to find the y intercept.
[tex]6=-\frac{2}{3} (1)+c[/tex]
[tex]c=\frac{20}{3}[/tex]
So the equation of this line will be:
[tex]y=-\frac{2}{3} x+\frac{20}{3}[/tex]
or
2x + 3y = 20
What is the interquartile range for the data set??
Answer:
65
Step-by-step explanation:
First, order the numbers in order. Then find the "middle numbers" and omit them after you have divided the number set into two equals parts. Then find the median of those number sets and then subtract.
You should get 71-6 at the end which is 65.
Type the correct answer in each box. If necessary, use / for the fraction bar(s). Given: AB || CD . If the coordinates of point A are (8 , 0) and the coordinates of point B are (3 , 7), the y-intercept of AB is _____ . If the coordinates of point D are (5 , 5), the equation of line CD is y = ___ x + ___ .
Answer:
Im not sure about the other 2 but the last box is 12, the answer above is incorrect for PLATO. I just took the test.
The y-intercept of line AB is 0, and the equation of line CD is y = 5.
Explanation:The y-intercept of a line is the point where it intersects the y-axis. In this case, we are given the coordinates of point A as (8, 0). Since the y-coordinate of point A is 0, the y-intercept of line AB is 0.
The equation of a line can be determined using the slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept. The slope of line CD can be found by finding the difference in y-coordinates divided by the difference in x-coordinates between points C and D. In this case, the slope is (5 - 5) / (5 - 5) = 0. Therefore, the equation of line CD is y = 0x + b, where b is the y-intercept. Since point D has coordinates (5, 5), the y-intercept is 5. Therefore, the equation of line CD is y = 0x + 5, or simply y = 5.
Solve each system by adding or subtracting -2x-y=-5,3x+y=-1
Answer:
(-6,17)
Step-by-step explanation:
-2x-y=-5,
3x+y=-1
Add the two equations together to eliminate t
-2x-y=-5
3x+y=-1
-------------------
x = -6
Now that we know x, we can substitute it into one equation to find y
3x+y = 1
3(-6) +y = 1
-18 +y = -1
Add 18 to each side
-18+18 +y = -1+18
y = 17
(-6,17)
A web-site asks users to create a 5-symbol PIN code where first and second symbols are any letters from the English alphabet and next 3 symbols are any digits. How many different PIN codes can be created?
What is the product of 7x-4 and 8x+5
➷ (7x - 4)(8x + 5) ==> 56x^2 + 35x - 32x - 20
This can be simplified to 56x^2 + 3x - 20
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The product of the polynomials 7x - 4 and 8x + 5 is 56x^2 + 3x - 20, attained by applying the FOIL method.
Explanation:The given question asks to find the
product
of two polynomials: 7x - 4 and 8x + 5. The product of two polynomials can be found using the distributive property, also known as the FOIL (First, Outer, Inner, Last) method. So, start by multiplying the first terms of each polynomial: 7x * 8x = 56x^2. Then, multiply the outer terms: 7x * 5 = 35x. Next, the inner terms: -4 * 8x = -32x. And finally, the last term: -4 * 5 = -20. Summing all these gives the final answer: 56x^2 + 3x - 20.
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Can you help me out on this one
Answer:
I think the answer is C if I'm wrong sorry its been two years since i last learnt this
Step-by-step explanation:
Please solve this. I'm very confused
Answer:
244.56
Step-by-step explanation:
Alice starts with x amount of money, and then spends 41.52 of it. This means that x-41.52 is equal to the amount of money Alice has left because spending 41.52 means that it is subtracted from the bank account. Thus, x-41.52=203.04 .
Using the additive property of equality, we can add 41.52 to both sides, resulting in x=244.56
If F(x)=2^x +5x and g(x)=3x-5 find (f+g)(x)
Final answer:
The sum of the functions [tex]F(x) = 2^x + 5x[/tex] and g(x) = 3x - 5 is [tex](f+g)(x) = 2^x + 8x - 5[/tex], which is obtained by adding the corresponding elements of each function and combining like terms.
Explanation:
The question asks for the sum of two functions, F(x) and g(x). In mathematical terms, (f+g)(x) means we have to add the functions F(x) and g(x) together. This is done by adding the corresponding elements of each function.
Here are the given functions:
F(x) = 2x + 5x
g(x) = 3x - 5
To find (f+g)(x), we combine them like this:
(f+g)(x) = F(x) + g(x) = (2x + 5x) + (3x - 5)
Now, we simply combine like terms:
(f+g)(x) = 2x + 5x + 3x - 5
(f+g)(x) = 2x + 8x - 5
This is the simplified form of the sum of the functions F(x) and g(x).
Final answer:
To find (f+g)(x) where f(x)=2ˣ + 5x and g(x)=3x-5, you simply add the functions together to get (f+g)(x) = 2ˣ + 8x - 5.
Explanation:
The student has asked to find (f+g)(x) where f(x) = 2ˣ + 5x and g(x) = 3x - 5.
To find (f+g)(x), we add the two functions together:
f(x) = 2ˣ + 5xg(x) = 3x - 5So, (f+g)(x) is:
(f+g)(x) = (2ˣ + 5x) + (3x - 5)
Combine like terms:
(f+g)(x) = 2ˣ + 5x + 3x - 5
(f+g)(x) = 2ˣ + 8x - 5
That is the simplified form of the function (f+g)(x).
Nina earns $2.00 for each Enjoy the Citybook she sells. Each time she sells a book she also gets a five-dollar tip. Does the following scenario model the equation y= 2x + 5
Answer:
yes
Step-by-step explanation:
Nina earns $2.00 for each Enjoy the Citybook she sells. = 2x
the word each gives a clue to multiplication
Each time she sells a book she also gets a five-dollar tip = +5
each refers to the sentence before and gets gives a clue to addition.
so, y=2x+5 is correct
plz give brainliestttt
the base of a triangle and a parallelogram are the same length there Heights are also the same if the area of the parallelogram is 48 m 2 what is the area of the triangle
Answer:
24
Step-by-step explanation:
The area of a parallelogram is A = b*h. The area of a triangle is A = 1/2 b*h. This means if the area of the parallelogram is 48 square meters then the area of the triangle is 24 square meters.
Answer:
24 m^2
Step-by-step explanation:
help please thanks will mark brainliest
Answer:
A
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
To find x subtract the sum of the 2 given angles from 180, that is
x = 180° - (32 + 52)° = 180° - 84° = 96°
-------------------------------------------------------
x and y form a straight angle, hence
y = 180 - x = 180° - 96° = 84°
------------------------------------------------------
To find z subtract the sum of the 2 angles from 180
z = 180° - (55 + y)° = 180° - (55 + 84)° = 180° - 139° = 41°
--------------------------------------------------------
x = 96°, y = 84°, z = 41° → A
What is the distance between two points located at (–6, 2) and (–6, 8) on a coordinate plane?"
Answer:
4 units
Step-by-step explanation:
X coordinate never changed so you just need to subtract 2 from 8 to see the unit difference.
The distance between the two points (-6, 2) and (-6, 8) on a coordinate plane is 6 units, as they share the same x-coordinate, and the distance can be found by the absolute value of the difference in y-coordinates.
The distance between two points on a coordinate plane can be determined by finding the absolute difference between their x-coordinates if they share the same x-coordinates or their y-coordinates if they share the same y-coordinates. Since the points (-6, 2) and (-6, 8) share the same x-coordinate, we can subtract the y-coordinates to find the distance:
Distance = |y2 - y1|
= |8 - 2|
= |6|
= 6 units
Therefore, the distance between the two points located at (-6, 2) and (-6, 8) on a coordinate plane is 6 units.
brett has been studying a type of bacteria that doubles every month. Originally, there were 5 bacterial cells. He wants to know how many there will be after 42 months?
Answer:
Step-by-step explanation:
Originally, there were only five bacterial cells. After one month, the amount of bacteria is doubled with ten bacteria. The growth is represented by the formula:
a42 = 5 x 2^1
After 42 months, the growth can be solved using this formula:
a42 = 5 x 2^42 just so you know my cuz help me shes good in this
Answer:
[tex]N=2.1990232556 \times 10^{13}[/tex]
Step-by-step explanation:
Given : Brett has been studying a type of bacteria that doubles every month. Originally, there were 5 bacterial cells.
To Find: He wants to know how many there will be after 42 months?
Solution:
Since we are given that initially there were 5 bacterial cells.
Bacteria doubles every month
Let n denotes the number of months .
Function becomes : [tex]N=N_0(2)^n[/tex]
[tex]N_0[/tex] = initial amount
N = amount after n months
So, [tex]N=5(2)^n[/tex]
Substitute n = 42
[tex]N=5(2)^{42}[/tex]
[tex]N=2.1990232556 \times 10^{13}[/tex]
Thus there will be [tex]2.1990232556 \times 10^{13}[/tex] bacteria after 42 months.
6! = 3! • 2! = =
Evaluate each expression
Answer:
120
Step-by-step explanation:
! means 3*2*1
so 6*1=6*5*4*3*2*1
6=720
720/6=120
factorial of n is given as
n! = n × (n-1) × (n-2)× . . . . . × 1
so lets solve it
6! = 6 × (6-1) × (6-2) × ( 6-3)×(6-4)×(6-5)
= 6×5×4×3×2×1
=720
similarly
3! = 3×2×1 =6
2!= 2×1= 2
3! × 2! = 6×2= 12
To watch the high school play, theatre goers must buy a ticket at the door. The cost of an adult ticket is $10.00, and the cost of a student ticket is $7.50. If the number of adult tickets sold is represented by a, and the number of student tickets sold is represented by s, which expression represents the amount of money collected at the door from the ticket sales? A. 7.50as B. 7.50(a + s) C. (10.00a)(7.50s) D. 10.00a + 7.50s
Answer: Option 'D' is correct.
Step-by-step explanation:
Let the number of adult tickets sold be 'a'.
Let the number of students tickets sold be 's'.
Cost of an adult ticket = $10.00
Cost of a student ticket = $7.50
According to question, it becomes,
[tex]10.00a+7.50s[/tex]
Hence, option 'D' is correct.
The expression that represents the amount of money collected at the door from the ticket sales is $10a + $7.50s
The total amount collected at the door is the sum of the total cost of adult tickets and children tickets
Total cost of adults ticket = cost per ticket x total number of adults tickets sold
$10 x a = $10a
Total cost of children's ticket = cost per ticket x total number of children tickets sold
$7.50 x s = $7.50s
The total amount collected at the door = $10a + $7.50s
A similar question was solved here: https://brainly.com/question/18977332?referrer=searchResults
need help anyone know the answer
Answer:
5 and 6
Step-by-step explanation:
5 and 6
use the table of values to write the exponential function
Answer:
[tex]\frac{1}{2}(\frac{1}{4}^x)[/tex]
Step-by-step explanation:
To find the function, compare the y values. Notice that each y value decreases by being divided by 4. This means the base of the exponential is 1/4.
To find the initial value, consider the point (0,0.5). When 1/4 is raised to the 0 power, the value is 1. This leaves that the initial value is 1/2 since 1/2*1 = 0.5.
The function is [tex]\frac{1}{2}(\frac{1}{4}^x)[/tex].
Answer:
The required function is [tex]f(x)=\frac{1}{2}\left(\frac{1}{4}\right)^x[/tex].
Step-by-step explanation:
The general exponential function is
[tex]f(x)=ab^x[/tex] .... (1)
where, a is the initial value and b is growth factor.
From the given table it is clear that the function passes through the points (0,0.5) and (-1,2). It means the equation of function must be satisfied by the points (0,0.5) and (-1,2).
Substitute f(x)=0.5 and x=0 in equation (1), to find the value of a.
[tex]0.5=ab^0[/tex]
[tex]0.5=a[/tex]
The value of a is 0.5.
Substitute a=0.5, f(x)=2 and x=-1 in equation (1), to find the value of b.
[tex]2=(0.5)b^(-1)[/tex]
[tex]2=\frac{0.5}{b}[/tex]
[tex]2b=0.5[/tex]
Divide both sides by 2.
[tex]b=\frac{0.5}{2}[/tex]
[tex]b=0.25[/tex]
The value of b is 0.25.
Substitute a=0.5 and b=0.25 in equation (1).
[tex]f(x)=0.5(0.25)^x[/tex]
[tex]f(x)=\frac{1}{2}(\frac{1}{4})^x[/tex]
Therefore the required function is [tex]f(x)=\frac{1}{2}\left(\frac{1}{4}\right)^x[/tex].
Which expression defines the arithmetic series 2.3 + 2.6 + 2.9 + for five terms
Answer:
so a sub n=2.3+(n-1)0.3
That's in an arithmetic sequence
Answer:
Option C is the answer.
Step-by-step explanation:
Given arithmetic series is 2.3 + 2.6 +2.9 + ......... 5 terms
Since this series is an arithmetic series so explicit formula of series will be [tex]\sum_{n=1}^{n}[a+(n-1)d][/tex] where a is the first term, d is the common difference and n is the number of term.
Therefore, we replace the values a = 2.3, and d = (2.6 - 2.3) = (0.3)
expression will be [tex]\sum_{n=1}^{n}[2.3+(n-1)(0.3)][/tex]
[tex]\sum_{n=1}^{n}[2.3+(0.3)n-0.3][/tex]
[tex]\sum_{n=1}^{n}[2+(0.3)n][/tex]
Option C is the answer.
Please help me!
I have problem understanding.
Please give me workings
Answer:
A)7
B)14
C)20
D)18
Step-by-step explanation:
For example 2/5 of 80
2/5 x 80/1 =32 Cross cancel
Tell whether the ordered pair is a solution of the linear system.
(-3,-2)
3x - 2y = -5
4x + 3y = -18
the ordered pair is a solution to the two equations.
Answer:
hello : (-3,-2) is solution
Step-by-step explanation:
put x = - 3 and y = -2 in this system :
3(-3) - 2 (- 2 ) = - 9 + 4 = - 5 .... right
4( - 3 ) +3(-2) = - 12 - 6 = -18 .....right
(-3,-2) is solution of the linear system: 3x - 2y = -5
4x + 3y = -18
what is 12 / 2/3 ? nothing pops up when i search it and i have a module exam!
Answer:
18
Step-by-step explanation:
Yur Welcome
The answer to the question [tex]\( \frac{12}{2/3} \) is \( 18 \).[/tex]
To solve the expression [tex]\( \frac{12}{2/3} \)[/tex], need to divide 12 by [tex]\( \frac{2}{3} \).[/tex] Dividing by a fraction is the same as multiplying by its reciprocal. Therefore, we can rewrite the expression as:
[tex]\[ 12 \times \frac{3}{2} \][/tex]
Now, multiply 12 by \( \frac{3}{2} \):
[tex]\[ 12 \times \frac{3}{2} = \frac{12 \times 3}{2} \][/tex]
[tex]\[ \frac{12 \times 3}{2} = \frac{36}{2} \][/tex]
Finally, divide 36 by 2 to get the result:
[tex]\[ \frac{36}{2} = 18 \][/tex]
So, [tex]\( \frac{12}{2/3} = 18 \)[/tex]. This is the value you would use if this calculation appears on your module exam.
Identify which property off addition could be used to solve the following problem. Solve the problem and justify how using the property makes the problem easier to solve.
(5.9 + 3.2) + 1.8
Answer:
so we use BODMAS
B..bracket
O..oppration
D..division
M..multiplication
A..addition
S..subtraction
so we first simplify the bracket 5.9+3.2=9.10)l8
then ther is no O D M we jump them and add with 1.8
9.1+1.8=10.9
so the answer is 10.9