Answer:
The surface area of the triangular prism is 468 square centimeters. Therefore the correct option is 4.
Step-by-step explanation:
It is given that the bases are right triangles with perpendicular legs measuring 9 centimeters and 12 centimeters. Using Pythagoras theorem, the third side of the base is
[tex]hypotenuse^2=leg_1^2+leg_2^2[/tex]
[tex]hypotenuse^2=(9)^2+(12)^2[/tex]
[tex]hypotenuse^2=225[/tex]
[tex]hypotenuse=\sqrt{225}[/tex]
[tex]hypotenuse=15[/tex]
The area of a triangle is
[tex]A=\frac{1}{2}\times base \times height[/tex]
Area of the base is
[tex]A_1=\frac{1}{2}\times 9\times 12=54[/tex]
The curved surface area of triangular prism is
[tex]A_2=\text{perimeter of base}\times height[/tex]
[tex]A_2=(9+12+15)\times 10[/tex]
[tex]A_2=9\times 10+12\times 10+15\times 10[/tex]
[tex]A_2=360[/tex]
The surface area of the triangular prism is
[tex]A=2A_1+A_2[/tex]
[tex]A=2(54)+360[/tex]
[tex]A=108+360[/tex]
[tex]A=468[/tex]
The surface area of the triangular prism is 468 square centimeters. Therefore the correct option is 4.
Answer:
468 square centimeters
Step-by-step explanation:
What is the midpoint of the segment shown below?
Answer:
A
Step-by-step explanation:
Calculate the midpoint using the midpoint formula
[ 0.5(x₁ + x₂ ), 0.5(y₁ + y₂ ) ]
with (x₁, y₁ ) = (- 1, 5) and (x₂, y₂ ) = (5, 5)
midpoint = [ 0.5(- 1 + 5), 0.5(5 + 5) ]
= [ 0.5(4), 0.5(10) ] = (2, 5 ) → A
Answer:
The answer would be A 2,5
Step-by-step explanation:
Two tins are geometrically similar. If the ratio of their volume is 27:64 find the ratio of their curved surface area.
Answer:
9 : 16
Step-by-step explanation:
Given 2 similar figures with linear ratio = a : b, then
area ratio = a² : b² and
volume ratio = a³ : b³
Here the volume ratio = 27 : 64, hence
linear ratio = [tex]\sqrt[3]{27}[/tex] : [tex]\sqrt[3]{64}[/tex] = 3 : 4
Hence area ratio = 3² : 4² = 9 : 16
Gas costs $6 per gallon and diesel costs $8 per gallon. You have at most $85 to spend on fuel. You must purchase at least 12 gallons of gas for your car to run for the week. Let x be the amount of gas purchased and y be the amount of diesel purchased. Which of the following is a possible solution?
Answer:
(12,1.625)
Step-by-step explanation:
According to the given statement:
Cost of gas per gallon = $6
Cost of diesel per gallon = $8
Cost of x gallon gas = 6x
Cost of y gallon diesel = 8y
You have at most $85 to spend on fuel
Therefore the equation we get is:
6x+8y≤85
You must purchase at least 12 gallons of gas for your car
x≥12
Plot the graph and you get possible solutions:
(12,1.625)..
When solving -1/5 (x − 25) = 7, what is the correct sequence of operations?
A:Multiply each side by negative one over five , add 25 to each side
B:Multiply each side by 5, subtract 25 from each side
C:Multiply each side by negative one over five , subtract 25 from each side
D;Multiply each side by −5, add 25 to each side
Answer:
It is C. Multiply each side by negative one over five , subtract 25 from each side.
Hope this helped you! :3
Answer:
D;Multiply each side by −5, add 25 to each side
Step-by-step explanation:
-1/5 (x − 25) = 7
To solve this equation, we will first multiply both-side of the equation by -5
-5 × -1/5(x-25) =7 × 5
(At the left-hand side of this equation, the 5 we multiplied will cancel the 5 at the denominator, leaving us with just '1' since negative multiply by negative is positive), Hence our equation becomes;
(x - 25) = 35
x - 25 = 35
Then the next thing to do is to add 25 to both-side of the equation in other to get the value of your x
x -25 + 25 = 35 + 25
x=60
Therefore, option D is the correct sequence of operation to follow to enable you solve the equation.
In a certain card game you draw one card off a standard deck of 52 cards. If you draw a spade you get paid $12, if you draw a red Ace you get paid $20, and if you draw a red Queen you get paid $38. If you draw anything else, you get paid nothing. What should this game cost if it is to be a fair game? Use fractions in your work and then calculate the answer as a decimal rounded to 4 decimal places.
Step-by-step explanation:
In a standard deck of 52 cards, there are 2 red aces, 2 red Queens, and 13 spades. That leaves 35 cards for everything else.
For the game to be fair, the cost must equal the expected value. The expected value is the sum of each outcome times its probability.
C = (12) (13/52) + (20) (2/52) + (38) (2/52) + (0) (35/52)
C = 68/13
C ≈ 5.2308
Here's another coaster that will help you think about the effect of a factor's exponent!
Once again, make the coaster cross at x = 500 after an initial rise and fall.
• This time, make your track more realistic: make the coaster come in smoothly at x = 1000 instead
of just falling and suddenly stopping!
y = Flax(x – 1000)
Answer: y=-ax(x-500)(x-1000)^2
Step-by-step explanation:
The behavior of the x-intercept of a graph is given by the multiplicity of the zero
The required polynomial for the coaster is, y = -a·x·(x - 500)·(x - 1000)²
Reason:
The question relates to the introduction of characteristics to the graph of a polynomial through knowledge of the effect of parameters of a polynomial
Known parameter:
Parent function is, y = a·x·(x - 1000)
The polynomial crosses the x-axis when (x - 500) is a factor of the polynomial, therefore, we have;
y = a·x·(x - 500)·(x - 1000)
Given that the graph is to initially rise, the leading coefficient is negative, therefore, we have;
y = -a·x·(x - 500)·(x - 1000)
For the polynomial to come in smoothly to stop at y = 0, when x = 1,000 we have that a turning point of the polynomial will be located at x = 1,000, this is given by introduction of a bump on the x-axis at x = 1,000 with a factor of (x - 1,000)²
Therefore, the required polynomial is y = -a·x·(x - 500)·(x - 1000)²
The height of the above polynomial is progressively smaller as x tends towards 1,000, given that the factors, (x - 500), and (x - 1,000), becomes smaller.
Learn more about the graph of polynomial functions here:
https://brainly.com/question/11829982
He has 2yards of the string .He cut 5 /8 yards of the string for his project how much left
For this case we must subtract:
[tex]2- \frac {5} {8} =\\\frac {8 * 2-5} {8} =\\\frac {16-5} {8} =\\\frac {11} {8}[/tex]
Thus, you have [tex]\frac {11} {8}[/tex]of string, after you have cut[tex]\frac {5} {8}[/tex] of it.
If we convert to a mixed number we have to:
[tex]\frac {11} {8} = 1 \frac {3} {8}[/tex]
Answer:
He has [tex]1 \frac {3} {8}[/tex] of string.
Which graph represents the solution set of the inequality x+2 greater than or equal to 6
Answer:
4 ≤ x
4
●→
Step-by-step explanation:
There is no illustration, it looks something like this.
Need The Answer Plz And Thank You!! I’m Failing
Angle BCA
Step-by-step explanation:
You can see this due to the angle having the name amount of congruent angle marks.
A group of students and workers entering a metro station
were asked whether they were riding the bus or the
subway. The two-way table shows their answers.
Types of Transportation
Bus
Subway
Students
Workers
Total
166
27 + 42 + 21 + 76 = 166
A triangle has vertex A at (0, 0), vertex B at (2, 5), and vertex C at 1
(4, 5). Which side of the triangle has the greatest slope?
0
Check the picture below.
I would like to check my answer! Have I done this correctly ? :)
Answer:
Yes you are right.
The answer is .45 or 45/100 which reduces to 9/20.
Step-by-step explanation:
[tex]\frac{4x}{15}=\frac{3}{25}[/tex]
Your first step is to cross multiply:
[tex]15(3)=25(4x)[/tex]
Simplify both sides:
[tex]45=100x[/tex] You got this! You go!
Divide both sides by 100:
[tex]\frac{45}{100}=x[/tex]
You wrote 45/100 as .45 which is correct!
Nice.
What is the greatest common factor of 8x and 40y
Answer:
The GCF of both the terms is 8....
Step-by-step explanation:
Given:
What is the greatest common factor of 8x and 40y.
The GCF of 8x and 40y is 8.
We will use the method of prime factorization to find the greatest common factor.
The prime factorization of 8x is:
8x = 2*2*2*x
The prime factorization of 40y is:
40y = 2*2*2*5*y
Therefore the common factors in both the terms are 2*2*2 which becomes 8
Thus the GCF of both the terms is 8....
Answer:
8
Step-by-step explanation:
Find the value of x.
A. 1.1
B. 6.6
C. 8.8
D. 5.5
Answer:
B. 6.6Step-by-step explanation:
AC is a midsegment of the trapezoid DFBE.
The formula of a midsegment of trapezoid is:
[tex]m=\dfrac{a+b}{2}[/tex]
a, b - bases of a triangle
We have
a = x, b = 4.4, m = 5.5
Substitute:
[tex]5.5=\dfrac{x+4.4}{2}[/tex] multiply both sides by 2
[tex]11=x+4.4[/tex] subtract 4.4 from both sides
[tex]6.6=x\to x=6.6[/tex]
I got this question that says to Complete the table for the given rule. and that is y=5x and it says (the chart has only numbers under y so you have to find what number x is)
What number is x for 4 and 2
X Y
0 5
0 4
0 2
Answer:
X Y
1 5
4/5 4
2/5 2
Step-by-step explanation:
y=5x
We we know y we need to solve for x
X Y
5
4
2
Let y =5
5 = 5x
Divide by 5
5/5 =5x/5
1=x
Let y =4
4 = 5x
Divide by 5
4/5 =5x/5
4/5=x
Let y =2
2 = 5x
Divide by 5
2/5 =5x/5
2/5=x
X Y
1 5
4/5 4
2/5 2
Answer:
x=0.8 if y=4, x=0.4 if y=2
Step-by-step explanation:
Rearrange the equation to get:
5x= 4 and
5x= 2
Divide equations by 5 to get:
x=0.8
x=0.4
F(x)=x^2+3x+2 is shifted 2 units left.the result is g(x). What is g(x)?
Answer:
Either A or B.
Step-by-step explanation:
When shifting to the left you are adding to x.
Example: x^2 shifted to the left by 3. (x+3)^2
For this case we have that, by definition of horizontal translation of functions we have to:
We assume h> 0:
To graph[tex]y = f (x-h),[/tex] the graph moves, h units to the right.
To graph[tex]y = f (x + h)[/tex], the graph moves, h units to the left.
If we have the following function:
[tex]f (x) = x ^ 2 + 3x + 2[/tex]and move 2 units to the left, then:
[tex]f (x + 2) = g (x) = (x + 2) ^ 2 + 3 (x + 2) +2[/tex]
ANswer:
Option B
The digits of a two-digit number sum to 8. When the digits are reversed, the resulting number is 18 less than the original
number. What is the original number?
Answer:
It's 53.
Step-by-step explanation:
Let the number be xy so the digits are x and y, so:
x + y = 8...........(1)
Reversing the 2 digits we have the number 10y + x and this equals
10x + y - 18 so we have the equation:-
10x + y - 18 = 10y + x
9x - 9y = 18
x - y = 2...........(2) Adding equations (1) and (2) we have:
2x = 10
x = 5
and y = 8 - 5 = 3.
So the original number is 53.
We can check this as follows
Original number is 53 so the reverse is 35 .
53 - 35 = 18 which checks out.
Solve for f:
_
35
- f = 4
Answer:
f=31
Step-by-step explanation:
35-f=4
-35 -35
-f=-31
*-1 *-1
f=31
[tex]\large \textnormal{F=31}[/tex], is the correct answer.
[tex]\large \textnormal{First, subtract by 35 from both sides of the equation.}[/tex]
[tex]\displaystyle 35-f-35=4-35[/tex]
[tex]\large \textnormal{Solve.}[/tex]
[tex]\displaystyle -f=-31[/tex]
[tex]\large \textnormal{Then you divide by -1 from both sides of the equation.}[/tex]
[tex]\displaystyle \frac{-f}{-1}=\frac{-31}{-1}[/tex]
[tex]\large \textnormal{Solve to find the answer.}[/tex]
[tex]\displaystyle -31\div-1=31[/tex]
[tex]\large \boxed{f=31}\checkmark[/tex]
Hope this helps!
Which one of the following equations could describe the graph above?
Answer: A. y=(1/2)^x+6
Step-by-step explanation: If this is the graph you’re talking about-
When “a” is less than one, the graph increases exponentially to the left. The smaller the value of a, the steeper the slope of the line.
There is a vertical shift up 6 as well
factor: d2 + 16dm + 64m2
Answer:
[tex](d + 8m)^2[/tex]
Step-by-step explanation:
[tex]d^2 + 16dm + 64 m^2 = (d + 8m)^2[/tex]
d^2 + 16dm + 64m^2
64m^2 + 16dm + d^2
Note: This polynomial is already in lowest terms. It cannot be factored. Are you sure that you posted the entire, correct problem?
for the level 3 course, examination hours cost twice as much as workshop hours and workshop hours cost twice as much as lecture hours. how id the lectures cost per hour? Total cost level 3 =$528
Answer:
The lectures cost is $7.33 per hour
Step-by-step explanation:
* Lets explain how to solve the problem
- For the level 3 course the examination hours cost twice as much
as workshop hours
- The workshop hours cost twice as much as lecture hours
- There are examination hours , workshop hours and lecture hours
- There are 3 hr for examination, 24 hr for workshops and 12 hr
for lectures
* Let the cost of the lecture hours is $x per hour
∴ The cost of the lecture hours is x per hour
∵ The cost of workshop hours is twice the cost of lecture hours
∴ The cost of the workshop hours is 2(x) = 2x per hour
∵ The cost of examination hours is twice the cost of workshop hours
∵ The cost of the workshop hours is 2x
∴ The cost of examination hours is 2(2x) = 4x per hour
- The cost of the level 3 is the sum of the costs of the lecture hours,
workshop hours and examination hours
∵ There is 12 hours for lectures
∵ There is 24 hours for workshops
∵ There is 3 hours for examination
∵ The total cost of level 3 = 12(x) + 24(2x) + 3(4x)
∴ The total cost of level 3 = 12 x + 48 x + 12 x
∵ The total cost of level 3 = $528
∴ 12 x + 48 x + 12 x = 528
∴ 72 x = 528 ⇒ divide both sides by 72
∴ x = 7.33
∵ x is the cost of the lecture hours per hour
∴ The lectures cost is $7.33 per hour
Three terms of an arithmetic sequence are shown below. Which recursive formula defines the sequence? f(1) = 6, f(4) = 12, f(7) = 18 f (n + 1) = f(n) + 6 f (n + 1) = 2f(n) f (n + 1) = f(n) + 2 f (n + 1) = 1.5f(n)
Answer:
f(n + 1) = f(n) + 2
Step-by-step explanation:
A recursive formula gives any term in the sequence from the previous term.
the n th term of an arithmetic sequence is
f(n) = f(1) + (n - 1)d ← d is the common difference
Given
f(1) = 6 and
f(4) = 12, then
f(1) + 3d = 12, that is
6 + 3d = 12 ( subtract 6 from both sides )
3d = 6 ( divide both sides by 3 )
d = 2
To obtain a term in the sequence add 2 to the previous term, hence
f(n + 1) = f(n) + 2 ← recursive formula
Answer:
c
Step-by-step explanation:
its c
How to solve this 336+x/5=85
Answer:
x = -1255
Step-by-step explanation:
336+x/5=85
Subtract 336 from each side
336-336 +x/5=85-336
x/5 =-251
Multiply each side by 5
x/5 * 5 = -251 *5
x = -1255
Events A and B are disjointed.
P(A) = 4/11 ; P(B) = 3/11.
Find P(A or B).
*Answer Options*
7/11
4/11
3/11
8/11
Answer:
7/11
Step-by-step explanation:
Two events are disjoint events if they cannot occur at the same time. It is given that A and B are disjointed events, so A and B cannot occur at the same time i.e. the intersection of two disjoint events will be 0.
For two disjoint events A and B:
P(A or B) = P(A) + P(B)
P(A) is given to be 4/11 and P(B) is given to be 3/11. Using these values in the equation, we get:
P(A or B) = [tex]\frac{4}{11}+\frac{3}{11} = \frac{3+4}{11}=\frac{7}{11}[/tex]
HELPPPP WILL NAME BRAINIEST
Answer:
Triangle APB is an isosceles triangle ⇒ 3rd answer
Step-by-step explanation:
* Lets explain the how to solve the problem
- ABCD is a square
∴ AB = BC = CD = AD
∴ m∠A = m∠∠B = m∠C = m∠D = 90°
- DPC is equilateral triangle
∴ DP = PC = DC
∴ m∠DPC = m∠PCD = m∠CDP = 60°
- In the Δs APD , BPC
∵ AD = BC ⇒ sides of the square
∵ PD = PC ⇒ sides of equilateral triangle
∵ m∠ADB = m∠BCP = 30° (90° - 60° = 30) ⇒ including angles
∴ Δs APD , BPC are congregant ⇒ SAS
- From congruent
∴ AP = BP
∴ Triangle APB is an isosceles triangle
One can use two-dimensional objects to build three-dimensional objects?
True or False?
Answer:
TRUE
Step-by-step explanation:
a^3b^-4/a^2b^3a^-5 write without rational notation and move all terms to numerator
[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{a^3b^{-4}}{a^2b^3a^{-5}}\implies \cfrac{a^3}{1}\cdot b^{-4}\cdot \cfrac{1}{a^2}\cdot \cfrac{1}{b^3}\cdot \cfrac{1}{a^{-5}}\implies a^3\cdot b^{-4}\cdot a^{-2}\cdot b^{-3}\cdot a^5 \\\\\\ a^3a^5a^{-2}b^{-4}b^{-3}\implies a^{3+5-2}b^{-4-3}\implies a^6b^{-7}[/tex]
Passing through (-2,1 ) and perpendicular to
4x + 7y + 3 = 0.
Answer:
7x - 4y + 18 = 0Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
========================================
Let
[tex]k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2[/tex]
========================================
We have the equation of a line in a general form (Ax + By + C = 0)
Convert it to the slope-intercept form:
[tex]4x+7y+3=0[/tex] subtract 7y from both sides
[tex]4x+3=-7y[/tex] divide both sides by (-7)
[tex]-\dfrac{4}{7}x-\dfrac{3}{7}=y\to m_1=-\dfrac{4}{7}[/tex]
Therefore
[tex]m_2=-\dfrac{1}{-\frac{4}{7}}=\dfrac{7}{4}[/tex]
We have the equation:
[tex]y=\dfrac{7}{4}x+b[/tex]
Put the coordinates of the point (-2, 1) to the equation, and solve for b :
[tex]1=\dfrac{7}{4}(-2)+b[/tex]
[tex]1=-\dfrac{7}{2}+b[/tex] multiply both sides by 2
[tex]2=-7+2b[/tex] add 7 to both sides
[tex]9=2b[/tex] divide both sides by 2
[te]x\dfrac{9}{2}=b\to b=\dfrac{9}{2}[/tex]
Finally:
[tex]y=\dfrac{7}{4}x+\dfrac{9}{2}[/tex] - slope-intercept form
Convert to the general form:
[tex]y=\dfrac{7}{4}x+\dfrac{9}{2}[/tex] multiply both sides by 4
[tex]4y=7x+18[/tex] subtract 4y from both sides
[tex]0=7x-4y+18[/tex]
How do you do number 1?
Whenever I tried to answer it, I always get fraction. help me.
Answer:
The pairs are (13,15) and (-15,-13).
Step-by-step explanation:
If n is an odd integer, the very next odd integer will be n+2.
n+1 is even (so we aren't using this number)
The sum of the squares of (n) and (n+2) is 394.
This means
(n)^2+(n+2)^2=394
n^2+(n+2)(n+2)=394
n^2+n^2+4n+4=394 since (a+b)(a+b)=a^2+2ab+b^2
Combine like terms:
2n^2+4n+4=394
Subtract 394 on both sides:
2n^2+4n-390=0
Divide both sides by 2:
n^2+2n-195=0
Now we need to find two numbers that multiply to be -195 and add up to be 2.
15 and -13 since 15(-13)=-195 and 15+(-13)=2
So the factored form is
(n+15)(n-13)=0
This means we have n+15=0 and n-13=0 to solve.
n+15=0
Subtract 15 on both sides:
n=-15
n-13=0
Add 13 on both sides:
n=13
So if n=13 , then n+2=15.
If n=-15, then n+2=-13.
Let's check both results
(n,n+2)=(13,15)
13^2+15^2=169+225=394. So (13,15) looks good!
(n,n+2)=(-15,-13)
(-15)^2+(-13)^2=225+169=394. So (-15,-13) looks good!
x - 3(x – 7) = 4(x – 7) – 2x
Answer:
x = 12.25
Step-by-step explanation:
Given
x - 3(x - 7) = 4(x - 7) - 2x ← distribute parenthesis on both sides
x - 3x + 21 = 4x - 28 - 2x ← simplify both sides
- 2x + 21 = 2x - 28 ( subtract 2x from both sides )
- 4x + 21 = - 28 ( subtract 21 from both sides )
- 4x = - 49 ( divide both sides by - 4 )
x = [tex]\frac{49}{4}[/tex] = 12.25
Answer: x=12.25
Step-by-step explanation: First, multiply the numbers into the parentheses. You will get:
X -3x +21 = 4x -28 -2x
Combine like terms.
-2x +21 =2x -28
Isolate x by adding 2x to each side.
21 =4x -28
Add 28 to each side to get x by itself.
49=4x
Divide by 4.
X =12.25