Answer:
[tex]V=5,676.16cm^3[/tex]
Step-by-step explanation:
The volume of a triangular prism is defined by the formula:
[tex]V=(area-of-base)*(length)[/tex]
In this case the base is triangular and the area of a triangle is: [tex]A=\frac{1}{2}(base)*(height)[/tex]
Then the volume is:
[tex]V=\frac{1}{2}(base*height*length)[/tex]
Now we have to replace with the given values:
[tex]V=\frac{1}{2}(22.4cm*18.1cm*28cm)\\\\V=\frac{1}{2}(11,352.32cm^3)\\\\V=5,676.16cm^3[/tex]
Then the correct answer is the third option.
[tex]V=5,676.16cm^3[/tex]
Answer:
5,676.16 is your answer 2021 Edge
I got it right
Step-by-step explanation:
Trapezoid CDEF was reflected across the x-axis followed by a 90° rotation about the origin to create the other trapezoid shown on the graph. Which congruency statement applies to the trapezoids? CDEF ≅ NPOM CDEF ≅ MNPO CDEF ≅ NMOP CDEF ≅ MOPN
answer is c on edg
Answer:
Yep the answer is C bro. I very much appreciate your help :D
congruency statement applies to the trapezoids is CDEF ≅ NMOP.
What is congruence?Two geometric figures are said to be congruent, or to be in the relation of congruence, if it is possible to superpose one of them on the other so that they coincide throughout.
Trapezoid CDEF was reflected across the x-axis followed by a 90° rotation about the origin to create the other trapezoid
From question, we have
Points C and NPoints D and MPoints E and OPoints F and PHence, Trapezoid CDEF and trapezoid NMOP are congruent.
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Please can someone help.
Answer:
CD = 12.7 cmStep-by-step explanation:
[tex]\text{Use the Pythagorean theorem to calculate the length of the CB:}\\\\CB^2+BA^2=AC^2\\\\CB^2+6^2=12^2\\\\CB^2+36=144\qquad\text{subtract 36 from both sides}\\\\CB^2=108\to CB=\sqrt{108}\\\\CB=\sqrt{36\cdot3}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\CB=\sqrt{36}\cdot\sqrt3\\\\CB=6\sqrt3[/tex]
[tex]\text{Use sine to calculate the length of CD:}\\\\sin\theta=\dfrac{opposite}{hypotenuse}\\\\\theta=55^o\\opposite=6\sqrt3\\hypotenuse=CD\\\\\sin55^o\approx0.8192\qquad(look\ at\ the\ picture)\\\\\text{Substitute:}\\\\0.8192=\dfrac{6\sqrt3}{CD}\\\\0.8192=\dfrac{10.3923}{CD}\qquad\text{multiply both sides by}\ CD\\\\0.8192CD=10.3923\qquad\text{divide both sides by 0.8192}\\\\CD\approx12.7[/tex]
Which parent function is represented by the table?
Answer:
Step-by-step explanation:
Notice that for each unit increase in x, y increases by 1 unit. Thus, the parent function is y = x.
Answer:
f(x)=x
Step-by-step explanation:
We are given with a table, Lets look at the value of x and y
The value of y is constantly increasing and the value of x is also increasing constantly. So it is a table for a linear equation.
the value of x and y are same, so the equation of the line is
y=x
when x=-2 the value of y=-2
when x=1 the value of y=1
Hence , the parent function is [tex]f(x)=x[/tex]
What is the value of x in the drawings if we know the triangles are similar?
A. 12 ft.
B. 30 ft.
C. 36 ft.
D. 18 ft.
Answer:
Step-by-step explanation:
setup a proportion
Big Triangle Small Triangle
corresponding 15 3
corresponding x 6
so you are trying to solve 15/x=3/6
cross multiply 6(15)=3(x)
last step divide both sides by 3 giving x=30 ft
If the triangles are similar, value of x in the drawings is Option(B) 30 ft.
What are similar triangles ?Similar triangles are triangles that have the same shape, but their sizes may vary. If two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
How to calculate the value of x from similar triangle concept ?The given two triangles are similar .
In the diagram, it is mentioned that one side is 3 and its corresponding other side of the similar triangle is 15 .
Thus the proportion is 15/3 = 5
Therefore if the other side of the same triangle is 6 then its corresponding other side of the similar triangle will be 6*5 = 30
Thus x = 30 ft.
Therefore, if the triangles are similar, value of x in the drawings is Option(B) 30 ft.
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Write out the equation of the line parallel to the line y=3x-11 which goes through the point (0,8)
Answer: y=3x+8
Step-by-step explanation:
The slope will be the same as the original equation, so 3. And to make the line go the points (0,8), you can plug in 0 into the original equation to find what needs to change. Hope this helps!
Remember that the slope intercept formula is:
y = mx + b
m is the slope
b is the y-intercept
If lines are parallel then they have the same slope (m)
This means that the slope of the line will be 3
y = 3x + b
Now we must find b
To do that you must plug in the point the line goes through in the x and y of the equation.
(0, 8)
8 = 3(0) + b
8 = 0 + b
8 = b
y = 3x + 8
Hope this helped!
~Just a girl in love with Shawn Mendes
how long is the arc intersected by a central angle of π/3 radians in a circle with a radius of 6 feet round your answer to the nearest tenth
[tex]\bf \textit{arc's length}\\\\ s=r\theta ~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\ \cline{1-1} r=6\\ \theta =\frac{\pi }{3} \end{cases}\implies s=6\left( \frac{\pi }{3} \right)\implies s=2\pi \implies \stackrel{\textit{rounded up}}{s=6.3}[/tex]
Answer: [tex]arc\ length=6.3\ ft[/tex]
Step-by-step explanation:
You need to use the following formula for calculate the arc lenght:
[tex]arc\ length=r\theta[/tex]
Where "r" is the radius and [tex]\theta[/tex] is the central angle in radians.
You know that the central angle in radians s:
[tex]\theta=\frac{\pi }{3}[/tex]
And the radius is:
[tex]r=6\ ft[/tex]
Therefore, the final step is to substitute the values into the formula. Then you get:
[tex]arc\ length=(6\ ft)(\frac{\pi }{3})[/tex]
[tex]arc\ length=6.3\ ft[/tex]
The length and width of a rectangle are consecutive even integers the area of the rectangle is 120 squares units what are the length and width of the rectangle
Answer:
Length =12
Width= 10
Step-by-step explanation:
The difference between two consecutive integers is 2.
Thus the difference between the length and the width of the rectangle also differ by 2.
width- x
length- x+2
AREA=L×W
120=x(x+2)
x²+2x-120=0
Factorizing:
x² - 10x + 12x - 120=0
x(x-10) + 12( x-10)=0
(x-10)(x+12)=0
either x-10=0 or x+12=0
x=10 0r -12
We consider positive roots only. thus x=10
width = 10
length = 10+2 =12
what is the value of 15i/2i
Answer:
-15/2
Step-by-step explanation:
Which will form a composite function?
Answer:
B.
Step-by-step explanation:
Let's find g(f(x)) for each choice for fun and so you can have more examples:
A) f(x)=3x and g(x)=sqrt(x)+1
so g(f(x))=g(3x)=sqrt(3x)+1
So definitely not this choice
B) f(x)=x+1 and g(x)=sqrt(3x)
so g(f(x))=g(x+1)=sqrt(3(x+1))
So this one works! :)
C) f(x)=sqrt(x)+1 and g(x)=3x
so g(f(x))=g(sqrt(x)+1)=3(sqrt(x)+1)
Not this one!
D) f(x)=sqrt(3x) and g(x)=1
g(f(x))=g(sqrt(3x))=1
Do Xuan nam isgoing to invest $1000 at a simple interest rate of 4% how long will it take for the investment to be worth $1040?
[tex]\bf ~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill&\$1040\\ P=\textit{original amount deposited}\dotfill & \$1000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years \end{cases} \\\\\\ 1040=1000(1+0.04t)\implies \cfrac{1040}{1000}=1+0.04t\implies \cfrac{26}{25}=1+0.04t \\\\\\ \cfrac{26}{25}-1=0.04t\implies \cfrac{~~\frac{26}{25}-1~~}{0.04}=t\implies \cfrac{~~\frac{1}{25}~~}{0.04}=t\implies 1=t[/tex]
Find the volume of a cone with a diameter of 12 m and a height of 7 m
Answer:
263.99 m3 (i tried my best)
Step-by-step explanation:
diameter > radius= 12/2
=6 m
v. of cone: 1/3 x 22/7 x r² x h
1/3 x 22/7 x 6² x 7
=263.99 m3
Answer:84piem^3
Step-by-step explanation:AP3X
if f(x)= -8x+4, then f^-1(x)=
Answer:
[tex]f^{-1}[/tex](x) = [tex]\frac{4-x}{8}[/tex]
Step-by-step explanation:
let y = f(x) and rearrange making x the subject
y = - 8x + 4 ( add 8x to both sides )
8x + y = 4 ( subtract y from both sides )
8x = 4 - y ( divide both sides by 8 )
x = [tex]\frac{4-y}{8}[/tex]
Change y back into terms of x
[tex]f^{-1}[/tex](x) = [tex]\frac{4-x}{8}[/tex]
A. 90 degrees
B. 45 degrees
C. 30 degrees
D. 120 degrees
For this case we have by definition, that each of the four internal angles of a square measure 90 degrees.
If we draw the diagonals of the square then the angles are divided by two, that is:
[tex]\frac {90} {2} = 45[/tex]
Thus, angle 3 measures 45 degrees.
[tex]A3 = 45[/tex]
By definition, the sum of the internal angles of a triangle is 180 degrees.
So:
[tex]A2 + A3 + 90 = 180\\A2 = 180-90-A3\\A2 = 180-90-45\\A2 = 45[/tex]
Thus, angle 2 measures 45 degrees.
Answer:
45 degrees
Rewrite using the distributive property 6(x + 3)
Answer: 6x+18
Step-by-step explanation: Because of the Distributive property, you would multiply the 6 by the’x’ and 3, as they are in the parenthesis.
The distributive property is the ability of one operation to "distribute" over another operation contained inside a set of parenthesis. So, all we (you) need to do is "distribute" the 6 to the x and 3. Observe.
6(x + 3) =
6x + 18 is the rewritten equation using the distributive property.
. What's the common difference of the sequence 0, 5, 10, 15, 20, . . . ?
A. d = –5
B. d = 3
C. d = –2
D. d = 5
Answer:
D. d = 5
Step-by-step explanation:
d = d² - d¹
= 5 - 0
= 5
d = d³ - d⁴
= 10 - 5
= 5
d = dⁿ - dⁿ-¹
The common difference of the given sequence will be 5, i.e. option D.
What is Arithmetic progression?Arithmetic progression is the sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value. The common difference is the value between each successive number in an arithmetic sequence
i.e. Common difference (d) = Successive term - Previous term
We have,
0, 5, 10, 15, 20, . . .
Here,
a₁ = 0
a₂ = 5
a₃ = 10
a₄ = 15
a₅ = 20
Now,
Find the common difference,
i.e.
Common difference (d) = a₂ - a₁ = 5 - 0 = 5,
Now,
Common difference (d) = a₃ - a₂ = 10 - 5 = 5
Now,
Common difference (d) = a₄ - a₃ = 15 - 10 = 5
Now,
Common difference (d) = a₅ - a₄ = 20 - 15 = 5
Now,
The Common difference is same for all i.e. 5.
Hence, we can say that the common difference of the given sequence will be 5, i.e. option D.
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Give two different decimals that round to 5.24 when rounding to the nearest hundredths.
ANSWER
5.2387 and 5.2437
EXPLANATION
To round a decimal to the nearest hundredth means we should round to two decimal places.
To round to two decimal places we consider the third decimal place.
When we round 5.2387 to the nearest hundredth, we obtain 5.24 because the third decimal place is greater than or equal to 5 so we round up.
When we round 5.2437 to the nearest hundredth, we get 5.24 because the third decimal place less than 5 so we round off.
In fact there are infinitely many decimals that will round to 5.24 when rounding to the nearest hundredth.
3 + (5 + 7) = (3 + 5) + 7 what property is shown
Answer:
Properties of Real Numbers ...
Step-by-step explanation:
Commutative Property of Multiplication (Numbers) 2 • 10 = 10 • 2
Associative Property of Addition (Numbers) 5 + (6 + 7) = (5 + 6) + 7
Associative Property of Multiplication (Numbers) 6 • (3 • 2) = (6 • 3) • 2
Additive Identity (Numbers) 6 + 0 = 6
The equation demonstrates the Associative Property of Addition, stating that the grouping of numbers being added does not affect the sum.
Explanation:The property shown in the equation 3 + (5 + 7) = (3 + 5) + 7 is the Associative Property of Addition. According to this property, the grouping of numbers being added does not affect the sum. In other words, when adding three or more numbers, it doesn't matter how they are grouped in parentheses.
In this specific equation, we are adding 5 and 7 first, which gives us 12. Then, adding 3 to 12 gives us a sum of 15. On the other side of the equation, we first add 3 and 5 to get 8, and then add 8 to 7 to get the same sum of 15.
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Jamarcus has twenty-one coins is his piggy bank, all of which are either dimes or quarters. If Jamarcus has $4.20 in total, how many of each coin does he have?
Answer:
16 quarters 2 dimes
Step-by-step explanation:
16 quarters is 4 dollars
2 dimes is 20 cents
Step-by-step explanation:
If D is number of dimes and Q is number of quarters:
D + Q = 21
10D + 25Q = 420
Solve the system of equations through either substitution or elimination.
10D + 25(21 - D) = 420
10D + 525 - 25D = 420
105 = 15D
D = 7
Q = 14
There are 7 dimes and 14 quarters.
plzzzzz answer guys!!!
Answer:
Sorry if its wrong i hope it helps!
The angle of elevation from a buoy in the water to the top of a lighthouse is 68degrees. If a buoy is 300 ft from the base of the lighthouse, from the height of the lighthouse.
Answer:
The height of the lighthouse is [tex]742.5\ ft[/tex]
Step-by-step explanation:
Let
h -----> the height of the lighthouse
we know that
The tangent of angle of 68 degrees is equal to divide the height of the lighthouse by the horizontal distance from the buoy to the base of lighthouse
so
[tex]tan(68\°)=\frac{h}{300}[/tex]
Solve for h
[tex]h=(300)tan(68\°)=742.5\ ft[/tex]
What is a point-slope equation of the line with the slope -13 that goes through the point (5,7)?
Answer:
Equation of line: y=3x-18
Step-by-step explanation:
Point: (5,7) and slope=-13
y-7=-13(x-5)
y=-13x+72
what is the factor of 144-49x"2
Because this expression is a difference of squares, meaning both terms have square roots, the factors would be 12+7x and 12-7x
Answer:12+7x and 12-7x
How do I do this problem?
Answer:
7x+y=37
Step-by-step explanation:
You basically just add the numbers, So you add 5 and 2 and then you subtract 2 from 3 which is 1 and then you add 21 and 16
Graph the solution for the following linear inequality system. Click on the graph until the final result is displayed.
y < 8
y ≥ 3
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]y< 8[/tex]
The solution is the interval -----> (-∞,8)
[tex]y\geq3[/tex]
The solution is the interval -----> [3,∞)
The solution of the system is equal to
[3,∞)∩ (-∞,8)-------> [3,8)
All real numbers greater than or equal to 3 and less than 8
The graph in the attached figure
a restaurant offers a lunch special in which a customer can select from one of the 7 appetizers, one of the 10 entrees, and one of the 6 desserts. How many different lunch specials are possible?
Answer:
420
Step-by-step explanation:
Each of the 7 appetizers can be paired with one of 10 entrees, and each entree can be paired with one of 6 desserts. So the number of combinations is:
7 × 10 × 6 = 420
By combination property, there are a total of 420 different lunch specials that are possible.
What is combination property ?The combination property is defined as the selection of items from a set that has distinct members, such that the order of selection does not matter.
How to calculate the different lunch specials that are possible from the property ?It is given that a restaurant offers a lunch special in which a customer can select from one of the 7 appetizers, one of the 10 entrees, and one of the 6 desserts.
Thus, there are 3 different items which quantities are also mentioned. '
Thus by combination property, the total number of lunch specials that are possible -
7 * 10 * 6 = 420 .
Therefore, by combination property, there are a total of 420 different lunch specials that are possible.
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Sec(pi/2)=csc x-true or false
False.
[tex]\sec{\dfrac{\pi}{2}}=undefined[/tex]
Hope this helps.
r3t40
Answer:
TRUE APEX dont trust the other guy!!!
Step-by-step explanation:
need help with the correct answer
Answer:
B. 9/4 <x <= 4
Step-by-step explanation:
5x - 19 <= 1
5x <= 20
x <= 4
-4x + 3 < - 6
-4x < - 9
x > 9/4
Answer
9/4 <x <= 4
Answer:
x ≤ 4
Step-by-step explanation:
1. 5x - 19 ≤ 1
Add: 5x ≤ 20
Divide: x ≤ 4
2. -4x + 3 > -6
Subtract: -4x > -9
Divide: x < ⁹/₄
3. Or means the union of the two sets, or all values that are in either set.
x ≤ 4 ∪ x < ⁹/₄ is x ≤ 4, since they both inequality signs point left, and 4 is larger than ⁹/₄, so x ≤ 4 also includes x < ⁹/₄.
I see here that x ≤ 4 is not one of the options. I'm not sure what to do then.
Given that ƒ(x) = x² + 5x, evaluate ƒ(-2).
-6
-14
7
f(-2) means replace x in the equation with -2, then solve:
-2^2 +5(-2)
Simplify:
4 + -10
Add:
-6
use log4 3~0.7925 and log 4 = 1 to approximate the value of the expression log4 768
Answer:
Step-by-step explanation:
We need to find the value of log4(768).
768 can be written as 3*256
which further can be simplified to 3*4^4
so using the log property log(AB)=log A+ log B
we can write
log4(768) = log4(3)+log4(4^4)
=0.7925+4log4(4)
=0.7925+4
=4.7925
Amara currently sells televisions for company A at a salary of $17,000 plus a $100 commission for each television she sells. Company B offers her a position with a salary of $29,000 plus a $20 commission for each television she sells. How many televisions would Amara need to sell for the options to be equal?
Answer:
150
Step-by-step explanation:
Given that;
Company A offers;
Salary= $ 17000
commission= $100 per tv set
Company B offers;
Salary= $29000
Commission = $ 20 per tv set
Let the number of tv set sold to be= x
To solve this problem, the amount obtained after selling for A option should be equal to B option
Form equations
[tex]17000 +100 x = 29000 + 20x\\\\\\100x-20x= 29000-17000\\\\\\80x=12000\\\\\\x=12000/80 = 150[/tex]
The number of televisions sold for the options to be equal = 150
Answer:
Amara needs to sell 150 televisions to make both options earnings equal.
Step-by-step explanation:
Let the number of television sold be = x
For company A:
Salary is $17,000 plus a $100 commission for each television she sells.
Equation becomes:
[tex]f(x)=17000+100x[/tex]
For company B :
Salary is $29,000 plus a $20 commission for each television she sells.
Equation becomes:
[tex]f(x)=29000+20x[/tex]
So, to calculate how many televisions would Amara need to sell for the options to be equal, we will equal both the equations.
[tex]17000+100x=29000+20x[/tex]
=> [tex]100x-20x=29000-17000[/tex]
=> [tex]80x=12000[/tex]
x = 150
So, Amara needs to sell 150 televisions to make both options earnings equal.
We can check this :
[tex]17000+100(150)=29000+20(150)[/tex]
=> [tex]17000+15000=29000+3000[/tex]
=> [tex]32000=32000[/tex]