Answer:
volume ≈ 930 cm³ (nearest cubic cm)
Step-by-step explanation:
The base of the prism which is a pentagon is regular. The apothem which is a line drawn from the center to any side of the pentagon is 4 cm. The height of the prism is 16 cm.
The volume of a prism = Bh
where
B = base area
h = height of the prism
The base of the prism can be divided into 5 congruent triangles.But the base of the triangles is unknown.
The sum of interior angle of a pentagon is 540°. That means each angle is 108° . The triangle divide the angle into 2. Making the 2 base angle as 54° each. The last angle of the triangle at the center is 72°(remember sum of angle in a triangle is 180° which is 54° + 54° + 72° = 180°) .
The angle form the center can be divided by the line of height of the triangles. The angle will then be 36°. Using tangential ratio half of the length of the base of the triangle can be known. Therefore,
tan 36° = opposite/adjacent
tan 36° = opposite/4
opposite = 4 tan 36°
The full base of the triangles = 2(4 tan 36°)
area of each triangle = 1/2 × 2(4 tan 36°) × 4 = 16 tan 36°
Base area of the prism(pentagon) = 5 × 16 tan 36° = 80 tan 36°
Volume of the prism = Bh
where
h = 16 cm
B = 80 tan 36°
volume = 80 tan 36° × 16 = 1280 tan 36° = 1280 × 0.726542528
volume = 929.974435847 cm³
volume ≈ 930 cm³ (nearest cubic cm)
Answer choices for both of them are
A) linear
B) exponential
C) quadratic
Answer:
#16 is linear but idk what 17 is
PLEASE HELP ME I BEG
Answer:
x = 3
Step-by-step explanation:
Applying Pythagoras' identity to the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
x² + x² = ([tex]\sqrt{18}[/tex] )², that is
2x² = 18 ( divide both sides by 2 )
x² = 9 ( take the square root of both sides )
x = [tex]\sqrt{9}[/tex] = 3
I will give brainliest to the first person who answers.
Answer:
the answer is [tex]\sqrt{5\\}[/tex] , and - [tex]\sqrt{5\\}[/tex] which is C.
Step-by-step explanation:
well I got that answer by doing this
we have [tex]x^{2}[/tex]= 5
For [tex]x^{2}[/tex]= f (a) the solutions are x = [tex]\sqrt{f(a)\\}[/tex] , - [tex]\sqrt{f(a)\\}[/tex]
so in this case the solutions are [tex]\sqrt{5\\}[/tex], and - [tex]\sqrt{5\\}[/tex]
HOPE THIS HELPS :)
Doug believes that the function y=6 is linear, while Olga believes that it is not linear. Who is right, and why?
A
Doug is right, because the function cannot be written in the form y = mx + b.
B
Doug is right, because the function can be written in the form y = mx + b, with m = 0.
С
Olga is right, because the function cannot be written in the form y = mx + b
D
Olga is right, because the function can be written in the form y = mx + b. with m = 0
Answer:
A
Step-by-step explanation:
A linear equation is an equation of a straight line, which means that the degree of a linear equation must be 0 or 1 for each of its variables. In this case, the degree of variable y is 1 .
Sara has x dollars and Dina has 15 dollars less than Sara . Together the number
of dollars they have is?
Answer:
2x-15
Step-by-step explanation:
Sara has x dollars
dina has 15 less which is
x-15
together it will be
x+x-15
=2x-15
Doing a test and timed so please help1
Answer:
20
Step-by-step explanation:
The hypotenuse is always the largest number and side length in a right triangle. We know the answer is 20 because it is the largest number.
'Ello there! 20 points and brainliest!!! FOR JOHAN!!
List 3 expressions that equal the number 12
List 2 expressions that equal the number 2
Wow this question is literally the hardest thing I have ever seen PLEASE HELP MEEE!!!
Answer:
for twelve: 4 x 3, 9 + 3, 24 / 2.
for two: 1 x 2, 1 + 1.
Step-by-step explanation:
4 x 3 = 12, 9 + 3 = 12, 24 / 2 = 12
1 x 2 = 2, 1 + 1 = 2.
plz help!!! Drag the tiles to the correct boxes to complete the pairs.
Match each point of intersection with the system of equations whose solution is at that point. (look at image)
Answer:
Step-by-step explanation:
Each point of intersection with the system of equations was matched.
what is a linear equation?Any equation in the form [tex]ax+by+c=0[/tex] is called a linear equation where a,b,c∈R.
In the given diagram, to find the intersection of two lines, solve the equations of two lines.
1)[tex]\left \{ {{y=-2x-3} \atop {y=2x-1}} \right.[/tex]
The solution of the given system of equations comes to be x=-1/2 and y=-2.
So they will intersect at (-1/2, -2) i.e. same as the graph.
2)[tex]\left \{ {{y=x+4} \atop {y=-x+2}} \right.[/tex]
The solution of the given system of equations comes to be x=-1 and y=3.
So they will intersect at (-1,3)
Similarly, the other two systems of equations will intersect at (-7/3,5/3) and (-1,1) respectively.
Hence, each point of intersection with the system of equations was matched.
To get more about equations visit:
https://brainly.com/question/14323743
Please give me the answer
Answer:
5.3
Step-by-step explanation:
Which expressions can never result in a negative real number when evaluated for any value of x? Select all that apply.
1) x^1/2
2)x^2/3
3)x^-3/5
4)x^-1/2
5)x^1/3
The expressions that can never result in a negative real number when evaluated for any value of x are x^1/2, x^2/3 and x^1/3
1) x^1/2
find the square root
[tex]= √x^1/2
[/tex]
[tex]= x^1[/tex]
= x
2) x^2/3
[tex]= 3√x^2/3[/tex]
= x²
3) x^-3/5
[tex]= 5√x^-3/5[/tex]
[tex]= x^-3[/tex]
[tex]= 1/x^3[/tex]
4) x^-1/2
[tex]= √x^-1/2[/tex]
,
[tex]= x ^-1[/tex]
[tex]= 1/x[/tex]
5) x^1/3
[tex]= 3√x^1/3[/tex]
[tex]= x^1[/tex]
= x
Therefore, the expressions that can never result in a negative real number when evaluated for any value of x are x^1/2, x^2/3 and x^1/3
Read more:
https://brainly.com/question/19045022
Use the values log 48 congruant to 1.68 and log 3 congruant to 0.48 to find the approximate value of log3 48.
Answer:log(48) = 1.68124
Step-by-step explanation:
After checking for the values of log 48 and log 3, then the approximate value will be 1.08.
What is an arithmetic operation?The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers.
Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.
As per the given information in the question,
log(48) = 1.68
log(3) = 0.48
Then, the approximate value of log 3 and log 48 will be: 1.08
To know more about arithmetic operations:
https://brainly.com/question/13585407
#SPJ2
What is the average rate of change of g over the interval -8≤t≤2? Give an exact number.
Per the plot, looks like g(-8) = 1 and g(2) = -4. Then the average rate of change of g over [-8, 2] is
(g(2) - g(-8)) / (2 - (-8)) = (-3 - 1)/10 = -2/5
Consider the equation -2x+3y=6.
Write the equation in slope-intercept form.
Identify the y-intercept.
Identify the slope.
Answer:
y=2/3x+2
Step-by-step explanation:
PLS ANSWER ASAP 12 POINTS
Answer:
2/9
Step-by-step explanation:
its in the range to be 2/9
Function A is represented by the equation
y=1/3x+5. Function B is represented by the graph. Which function has a greater rate of change? explain.
Answer:
They have the same rate of change.
Step-by-step explanation:
Well the graph of Function B is y = 1 / 3x + 2
So they have the same rate of change, since they have the same slope.
Identify the points corresponding to P and Q.
Answer:
the first one( even though it has an error : P is (-2,1) ) and because the Q is correct there too.
2. Making sure your calculator is in DEGREE MODE, evaluate each of the following an
verify that they either match or are close to the ratios you found in #1.
(a) sin( 67 ) =
(b) cos(67 ) =
(c) tan (67") =
Answer:
a. 0.921
b. 0.391
c. 2.356
Enter the quotient.
6532 ÷ 23 =
Answer:
284
Step-by-step explanation:
Below are the average incomes for different education levels. How does the outlier affect the mean?mm
Answer:
It affects the Mean by how many different numbers.
Step-by-step explanation:
Find the medianDetermine all of your answers. and Figure out if the mean and the outlier are similiar.HURRY!! WILL MARK BRAINLIEST!!!
whixhxh two points on the number line are opposites? !!HURRY WILL CASHAPP 10 BUCKS.
Answer:
points a and d because point a is -1 and 2/3 and point d is 1 and 2/3 so they are opposites
The diameter of a circle measures 8 cm. What is the circumference of the circle?
Use 3.14 for it, and do not round your answer. Be sure to include the correct unit in your answer.
Answer:
16π or 50.266
Step-by-step explanation:
Circumference formula is just 2πr ,and the radius is 8, so just sub into the formula
Answer: 25.12 cm
Step-by-step explanation:
The formula for the circumference of a circle is [tex]2\pi r[/tex], when r = the radius.
Diameter = 2 x radius = 8 cm. Therefore, the radius = 4 cm.
Plug r = 4 cm in to the circumference formula: [tex]2\pi (4)[/tex] = 8 x 3.14 = 25.12 cm.
Given: m arc AB = 4x, m arc BC = 3x
m arc CD = 2x, m arc DA = 3x
Find: m∠APB
Answer:
a > m/bp
Step-by-step explanation:
flip the equation
abp > m
divide both sides with bp
abp/bp > m/bp
a > m/bp
Answer:
m<APB = 30 degrees
Step-by-step explanation:
The sum of angles in a circle is 360 degrees. Add up all the arcs to get the equation : 4x+3x+2x+3x=360 degrees.
x is equal to 30 degrees
m arc AB = 4x = 120 degrees
m arc DC = 2x = 60 degrees
By secants exterior angles, m<APB = 1/2(m arc AB - m arc DC) = 1/2(120-60) = 30 degrees.
The answer is m<APB = 30 degrees
pls help will mark as brainliest
Answer:
The measure of the hypotenuse is 25.
Step-by-step explanation:
To solve, we can use the Pythagorean theorem a² + b² = c² where,
a = 7
b = 24
(7)² + (24)² = 625
We have to take the square root of 625 to get our answer.
[tex]\sqrt{625} = 25[/tex]
Answer:
25
Step-by-step explanation:
This is a right triangle. This is because of the little square in the corner that indicates a right angle. Therefore, we can use the Pythagorean Theorem.
a^2+b^2=c^2
where a and b are the legs, and c is the hypotenuse.
We know that 7 and 24 are the legs, because they make up the right angle. We know c is the hypotenuse because it is opposite the right angle.
7^2+24^2=c^2
Evaluate the exponents on the left side.
49+576=c^2
Add 49 and 576
625=c^2
Since c is being squared, take the square root of both sides. This will cancel out the exponent, and leave c by itself.
√625= √c^2
√625=c
25=c
The measure of the hypotenuse is 25
DUE NOW PLZ HELP
6, 9, 3, 7, 8, 7, 5
minimum:
maximum:
Answer:
minimum is 3 and maximum is 9
Step-by-step explanation:
PLZ HELP I NEED IT ASAP!
Answer:
4
Step-by-step explanation:
Since it is going up four and over one you would just simplify 4/1 to just being 4.
Please help due in 20 minutes!
Answer:
x =12
Step-by-step explanation:
We use the Pythagorean theorem
a^2 + b^2 =c^2 where a and b are the legs and c is the hypotenuse
x^2 + 5^2 = 13^2
x^2 +25 =169
Subtract 25 from each side
x^2 +25-25=169-25
x^2 = 144
Take the square root of each side
sqrt(x^2) = sqrt(144)
x = 12
10 over 13 as a decimal rounded to the nearest tenth
Answer:
0.7
Step-by-step explanation:
If you divide 10 by 13 you get 0.76923 which rounded to the nearest tenth is 0.7
Hope this helped!
Answer:
0.8
Step-by-step explanation:
To find the decimal form of [tex]\frac{10}{13}[/tex] you'll need to divide 10 by 13.
10 ÷ 13 = 0.76923076923
The tenths decimal place is one to the right of the decimal: 0.1
Because the number after the tenths place is greater than or equal to 5, we will round the 0.7 up to a 0.8
convert the mixed number to an improper fraction. enter your answer below using the slash mark ( / ) as the fraction bar.
4/frac{1}{8}
What is y=2(x+1)^2 in standard form
Answer:
[tex]y=2x^2+4x+2[/tex]
Step-by-step explanation:
[tex]y=2(x+1)^2[/tex]
[tex]y=2(x^2+2x+1)[/tex]
[tex]y=2x^2+4x+2[/tex]
Need Help On This
simplify:
9a(-4a^3 b^5)(-2a^4 bc^6)
Answer:
72a^8b^6c^6
Step-by-step explanation: