The answer is D. octagon.
Therefore, the only shapes that can be formed by slicing a square prism with a plane from the given options are a rectangle, a triangle, and an octagon. A hexagon is not possible, making option C the correct answer.
The correct answer is C. A hexagon is not possible when slicing a square prism with a plane.
When slicing a square prism with a plane, the resulting cross section can take on various shapes depending on the angle and position of the cutting plane. Here are the possible cross sections:
- If the plane is parallel to one of the faces of the prism and intersects the prism, the cross section will be a rectangle (Option A).
- If the plane intersects two adjacent edges of the prism, the cross section will be a triangle (Option B).
- If the plane passes through the prism in such a way that it intersects all four edges of one face of the prism, the cross section will be an octagon (Option D), provided that the plane does not intersect the prism at the corners of the square base.
However, a hexagon (Option C) is not a possible cross section when slicing a square prism with a plane. This is because to create a hexagon, the plane would need to intersect three non-adjacent edges of the prism's base, which is geometrically impossible given the right angles of the square base. A hexagon has six sides, and a square prism's base has only four edges, which cannot be divided into three pairs of non-adjacent edges that a plane could intersect to form a hexagon.
At the football game, 4 hamburgers and 6 soft drinks cost $34, and 4 hamburgers and 3 soft drinks cost $25. Which two equations can be used to determine the price of a hamburger and the price of a soft drink? Let x represent the cost of a hamburger and y represent the cost of a soft drink.
Answer:
[tex]4x+6y=34\\\\4x+3y=25[/tex]
Step-by-step explanation:
Let be "x" the cost in dollars of a hamburger and "y" the cost in dollars of a soft drink.
The cost of 4 hamburguers can be represented with this expression:
[tex]4x[/tex]
And the cost of 6 soft drinks can be represented with this expression:
[tex]6y[/tex]
Since the total cost for 4 hamburgers and 6 soft drinks is $34, you can write the following equation:
[tex]4x+6y=34[/tex] [Equation 1]
The following expression represents the the cost of 3 soft drinks:
[tex]3y[/tex]
According to the information given in the exercise, the total cost for 4 hamburgers and 3 soft drinks is $25. Then, the equation that represents this is:
[tex]4x+3y=25[/tex] [Equation 2]
Therefore, the Equation 1 and the Equation 2 can be used to determine the price of a hamburger and the price of a soft drink
I WILL GIVE BRAINLIEST
Answer:
[tex] - 10 \div 9 = \frac{ - 10}{9} [/tex]
[tex]10 \div ( - 9) = \frac{10}{ - 9} [/tex]
[tex] - ( - 10 \div ( - 9)) = - (10 \div 9) = - \frac{10}{9} [/tex]
[tex] - \frac{10}{9} = \frac{10}{ - 9} = - \frac{10}{9} [/tex]
A and B are the correct choices.
A flock of geese landed landed in a dog park. All the dogs ran to investigate. Alex counted
22 animals 64 legs. How many many geese and how many dogs did he count?
Answer:
12 geese
10 dogs
Step-by-step explanation:
We are given;
Total number of animals (dogs and geese) is 22 Total number of legs of animals is 64We are required to determine the number of geese and dogs that Alex counted;
We need to know that;
a dog has 4 legs while, a geese has 2 legs Therefore;Assuming he counted x number of geese and y number of dogs;
Then;
x + y = 22, and
2x + 4y = 64
Thus, solving the equation simultaneously;
we can multiply the first equation by 2, to get
2x + 2y = 44
2x + 4y = 64
Eliminating x (by subtracting the second eqn from the first eqn), we get;
-2y = -20
y = 10
Solving for x;
x = 22 - y
= 22 - 10
x = 12
Therefore; he counted 12 geese and 10 dogs
For the function f defined by f(x)=3x2−2x+5 find f(−x),−f(x) , and −f(−x).
Step-by-step explanation:
[tex]f(x)=3x^2-2x+5\\\\f(-x)=\text{substitute (-x) instead x in f(x)}\\\\f(-x)=3(-x)^2-2(-x)+5=3x^2+2x+5\\\\-f(x)=-(3x^2-2x+5)=-3x^2-(-2x)-5=-3x^2+2x-5\\\\-f(-x)=-(3x^2+2x+5)=-3x^2-2x-5[/tex]
The answers are:
[tex]\begin{aligned}& f(-x)=3 x^2+2 x+5 \\& -f(x)=-3 x^2+2 x-5 \\& -f(-x)=-3 x^2-2 x-5\end{aligned}[/tex]
Let's find f(−x), −f(x), and −f(−x) for the given function [tex]f(x)=3 x^2-2 x+5[/tex].
f(−x):
Replace x with −x in the function:
[tex]f(-x)=3(-x)^2-2(-x)+5[/tex]
Simplify this expression:
[tex]f(-x)=3 x^2+2 x+5[/tex]
−f(x):
Multiply the entire function f(x) by −1:
[tex]-f(x)=-\left(3 x^2-2 x+5\right)[/tex]
Distribute the negative sign:
[tex]-f(x)=-3 x^2+2 x-5[/tex]
−f(−x):
Replace x with −x in the function f(x) and then multiply the whole expression by −1:
[tex]-f(-x)=-\left(3(-x)^2-2(-x)+5\right)[/tex]
Simplify this expression:
[tex]-f(-x)=-\left(3 x^2+2 x+5\right)[/tex]
Distribute the negative sign:
[tex]-f(-x)=-3 x^2-2 x-5[/tex]
Question:
For the function f defined by [tex]f(x)=3 x^2-2 x+5[/tex] find f(−x),−f(x) , and −f(−x).
Louis wants to carpet the rectangular floor of his basement.The basement has a area 432 square feet,The width of the basement is 1/3 its length.What's the length of Louis's basement.
Answer:
36 ft
Step-by-step explanation:
Let L represent the length of Louis's basement. The area is the product of length and width, so is ...
A = L(L/3)
432 = L²/3 . . . . . fill in area value
1296 = L² . . . . . . multiply by 3
36 = L . . . . . . . . . take the square root
The length of Louis's basement is 36 feet.
What is 967 divided by 60 equals???
Answer:
16.11(6)
Step-by-step explanation:
967/60=16 7/60
OK it has 5 g Of sugar per serving. A banana has 15 g of sugar per serving.
1/3 banana hgfdsedcrtvfybgunhimjnyhtbgvfdcvfbgnhmij,omhnbvdcrmjytgvg
How do I find the area
Answer:
For the smaller rectangle: 9 x 19.8 = 178.2
For the bigger rectangle: 27 x 10.8 = 291.6
Which point is on the line y = -2x + 3?
(-2,-1)
(3, -3)
(3, 3)
(-3,-9)
Answer:
Hence (3, -3) is on the given line y = -2x + 3
Step-by-step explanation:
For a point on the Line, It must Satisfy the Equation of a line
Therefore for
[tex]y=-2x+3[/tex]
For (-2,-1)
Substitute x = - 2 and y = -1 in above equation
Left Hand Side = y
= -1
Right Hand Side = -2 × (-2) +3
= 4 +3
= 7
Left Hand Side ≠ Right Hand Side
Not Satisfied
Hence (-2,-1) is NOT on the given line
For (3, -3)
Substitute x = 3 and y = -3 in above equation
Left Hand Side = y
= -3
Right Hand Side = -2 × (3) +3
= -6 +3
= -3
Left Hand Side = Right Hand Side
Satisfied
Hence (3, -3) is on the given line y = -2x + 3
For (3, 3)
Substitute x = 3 and y = 3 in above equation
Left Hand Side = y
= 3
Right Hand Side = -2 × (3) +3
= -6 +3
= -3
Left Hand Side ≠ Right Hand Side
Not Satisfied
Hence (3,3) is NOT on the given line
For (-3,-9)
Substitute x = -3 and y = -9 in above equation
Left Hand Side = y
= -9
Right Hand Side = -2 × (-3) +3
= 6 +3
= 9
Left Hand Side ≠ Right Hand Side
Not Satisfied
Hence (-3,-9) is NOT on the given line
Only the point (3, -3) lies on the line y = -2x + 3. None of the other points satisfy the equation.
To determine which point lies on the line y = -2x + 3, we need to substitute the coordinates of each point into the equation:
(-2, -1): Substitute x = -2 into y = -2x + 3:
y = -2(-2) + 3 = 4 + 3 = 7. Since y = -1, this point does not lie on the line.
(3, -3): Substitute x = 3 into y = -2x + 3:
y = -2(3) + 3 = -6 + 3 = -3. Since y = -3, this point lies on the line.
(3, 3): Substitute x = 3 into y = -2x + 3:
y = -2(3) + 3 = -6 + 3 = -3. Since y = 3, this point does not lie on the line.
(-3, -9): Substitute x = -3 into y = -2x + 3:
y = -2(-3) + 3 = 6 + 3 = 9. Since y = -9, this point does not lie on the line.
The only point that satisfies the equation is (3, -3).
Complete question:
Which point is on the line y = -2x + 3?
A. (-2,-1)
B. (3, -3)
C. (3, 3)
D. (-3,-9)
(3-20i)-(14+6i)-(8-2i)
Because there are parentheses we distribute the negative signs:
3 - 20i + (-14) - 6i + (-8) + 2i
Next combine like terms:
3 + (-14) + (-8) and -20i - 6i + 2i
-19 -24i
NEED HELP ASPA PLS HELP WITH THIS
SEE IMAGE FOR A, B, C, D REFERENCE
A- 3
B- 3
C- 6
D- 3x+6
On the board you should have 6 of the orange + tiles and 3 of the orange x tiles.
Square root of one hundred and twenty three
7x + 3x + 5 - 2x + 7. Select all that are equivalent.
a. 2x + 6
b. 10X + 12 - 2x
c. 12x + 12
d. 8x + 12
Answer:
d 8x+12
Step-by-step explanation:
7x+3x+5-2x+7
combine 7x+3x-2x=8x
and 5+7=12
8x+12
Answer:
Step-by-step explanation:
7x+3x-2x=8x
5+7=12
8x+12
The cube root of 0.000004913 is
Answer:
[tex]\sqrt[3]{0.000004913}=0.017[/tex]
Step-by-step explanation:
Cubic Root
The cubic root of a number N is M, if
[tex]M^3=N[/tex]
It's usually tedious to manually compute cubic roots, but if we use some basic algebra concepts, the job is easily done.
Let's compute
[tex]M=\sqrt[3]{0.000004913}[/tex]
The argument can be expressed in scientific notation as
[tex]0.000004913= 4913\ 10^{-9}[/tex]
The power of 10 has an exact cubic root since the exponent is a multiple of 3. To find the cubic root of the mantissa, we note it's the triple product of 17, i.e.
[tex]4913=17*17*17=17^3[/tex]
Thus our number is
[tex]M=\sqrt[3]{17^3\ 10^{-9}}=17\ 10^{-3}=0.017[/tex]
We have then
[tex]\boxed{\sqrt[3]{0.000004913}=0.017}[/tex]
1 9/10, 1 7/10, blank, 1 3/10, 1 1/10 what is the blank
Answer:15/10
Step-by-step explanation:
You subtract the top of the fraction by 2
Answer:
1 5/10 or 1 1/2
Step-by-step explanation:
You seem to have an arithmetic sequence, with each term 2/10 less than the one before.
2/10 less than 1 7/10 is 1 5/10. The fraction can be reduced to 1 1/2, but you may not want to.
what conclution can be drawn about lines AB and CD?
Answer:
Step-by-step explanation:
they are both equal
Answer: They are not parallel because the two given alternate interior angles are not congruent
Step-by-step explanation:
Convert to scientific notation
Answer:
5.7* 10 to the power of 4
Answer:
57,000 = 5.7 × 10⁴Step-by-step explanation:
[tex]\text{The scientific notation}:\\\\a\times10^k\\\\\text{where}\\\\1\leq a<10,\ k\in\mathbb{Z}\\\\================================[/tex]
[tex]57,000=5.7\times10000=5.7\times10^4\\\\-----------------------\\\\57000=5\underbrace{7000}_{\leftarrow4}=5\times10^4[/tex]
What is the measure of AC?
Answer:
AC = 52.8
Step-by-step explanation:
33/20 = 1.65
12*1.65 = 19.8
BA = 19.8
CB + BA = AC
33 + 19.8 = 52.8
Answer:
AC = 52.8
Step-by-step explanation:
Since BE is parallel to CD and intersects the 2 sides of the triangle then it divides those sides proportionally, that is
[tex]\frac{BC}{AB}[/tex] = [tex]\frac{DE}{AE}[/tex], substituting values
[tex]\frac{33}{AB }[/tex] = [tex]\frac{20}{12}[/tex] ( cross- multiply )
20AB = 396 ( divide both sides by 20 )
AB = 19.8
Thus
AC = AB + BC = 19.8 + 33 = 52.8
Lucas says his twin baby brothers have a total weight of 15 and one eighth pounds. jackson 6 and one fourth pounds and jeremy weighs 8 and seven eighths pounds. explain how you can use estemation to tell if the total weight is reasonable
By rounding each brother's weight to the nearest whole number and adding these, we get an estimate of 15 pounds. The actual total weight, 15 and one eighth pounds, is close to this estimate, indicating that Lucas' claim about his brothers' weight is reasonable. This demonstrates how estimation can be used to quickly verify the validity of a claim.
Explanation:Estimation is a valuable mathematical tool that can be used to assess the reasonableness of a solution. In the case of Lucas' twin baby brothers' weight, you can use rounding to estimate their total weight. Let's start by rounding each brother's weight to the nearest whole number. In this scenario, Jackson, who weighs 6 and one fourth pounds could be estimated to weigh 6 pounds, and Jeremy, who weighs 8 and seven-eighths pounds, could be estimated to weigh roughly 9 pounds.
Adding these together gives a total of 15 pounds. The actual weight of the twins, 15 and one eighth pounds, is very close to this estimation, indicating that Lucas' claim about his brothers' weight is reasonable. This approach makes effective use of estimation as a means to quickly and simply verify a given claim's feasibility.
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Which of the following functions has the same horizontal asymptote as the function graphed below?
f(x)=-3^x+2 +2
f(x)=2^x-3
f(x)=3^x+2 -2
f(x)=2^x+2 -3
Answer:
The functions which has the same horizontal asymptote y = -3 as given in the graph are,
f(x) = [tex]2^{x} - 3[/tex] and
f(x) = [tex]2^{(x+2)} -3[/tex]
Step-by-step explanation:
The function that is graphed has horizontal asymptote as y = -3 .
As x → -∞ f(x) → - 3 for the second and fourth function. Hence the functions which has the same horizontal asymptote y = -3 as given in the graph are,
f(x) = [tex]2^{x} - 3[/tex] and
f(x) = [tex]2^{(x+2)} -3[/tex]
2x-7 divided by 6x squared -37x+56
Answer:
the 6.192# melebulated by 59 and devide it by 597 your answere is 64
Step-by-step explanation:
Substitution for {2x-3y=11 and -x + 2y = -6
Step-by-step explanation:
-x+2y=-6
x-2y=6
x=2y+6
substitute in 2x-3y=11 gives us 2(2y+6)-3y=11
4y+12-3y=11
y=-1
-x+2(-1)=-6
-x=-4
x=4
Passes through (3,-7), m=-2
If you are trying to find the equation of a line:
The equation of a line is y = mx + b [m is the slope, b is the y-intercept or the y value when x = 0 ---> (0, y) or the point where the line crosses through the y-axis]
Since you have m = -2, plug it into the equation
y = mx + b
y = -2x + b To find b, plug in the point they gave you (3, -7)
-7 = -2(3) + b
-7 = -6 + b Add 6 on both sides
-1 = b Now that you have b, plug it into the equation
y = -2x - 1
what is the quotient of m^6/5 divided by 5/m^2
Answer:
[tex]\large\boxed{\dfrac{m^8}{25}}[/tex]
Step-by-step explanation:
[tex]\dfrac{m^6}{5}\div\dfrac{5}{m^2}\\\\\text{Divide by a fraction is the same as multiply by its reciprocal}\\\\=\dfrac{m^6}{5}\times\dfrac{m^2}{5}=\dfrac{m^6\times m^2}{5\times5}\\\\\text{use}\ a^n\times a^m=a^{n+m}\\\\=\dfrac{m^{6+2}}{25}=\dfrac{m^8}{25}[/tex]
9 cm
3 cm
AB is parallel to DC.
AD = 9 cm, DC = 3 cm. Angle BCD = 35°
Angle ABD = 90°
Calculate the size of angle BAD.
Give your answer correct to one decimal place.
Answer:
∴ ∠BAD = [tex]sin^{-1}[/tex](0.2044) = 11.8°
Step-by-step explanation:
i) AD = 9 cm
ii) DC = 3 cm
iii) ∠BCD = 35°
iv) Since AB is parallel to DC and ∠ABD = 90° then we can conclude that ∠BDC = 90°.
v) [tex]\frac{BD}{DC} = \frac{BD}{3\hspace{0.1cm}cm} = tan(35)[/tex] = 0.6128 ∴ BD = 3 [tex]\times[/tex] 0.6128 = 1.84 cm
vi) ∴ sin(∠ BAD ) = [tex]\frac{BD}{AD}[/tex] ⇒ sin(∠ BAD ) = [tex]\frac{1.84}{9}[/tex] = 0.2044
∴ ∠BAD = [tex]sin^{-1}[/tex](0.2044) = 11.8°
Answer:
Step-by-step explanation:
Input the expression x +9/2
Answer:um where is the constant
Step-by-step explanation:
The expression 'x + 9/2' involves adding a variable 'x' to the fraction 9/2. In an example situation, if you substitute x with the number 5, the result would be 9.5. Remember, x can represent any number.
Explanation:The expression you provided is x + 9/2. In mathematics, this is an algebraic expression which comprises of a variable x and a fraction 9/2. It means that you're adding the x variable to the fraction 9/2. For example, if you were to substitute x with a number, let's say 5, the answer would then be 5 + 9/2 = 9.5. It's important to remember that variables can represent any number, and in this case, the variable is x.
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In Connecticut, there is a tax charge of $0.84 on a $14 dinner bill. Find the tax rate in
Connecticut. (Tax rates are based on cents per one dollar.)
What is the equation to solve this?
Explanation: Calculation of the general sales taxes of Connecticut State for 2019 ... combined rates mentioned above are the results of Connecticut state rate (6.35%). There is no county sale tax for Connecticut. There is no city sale tax for the Connecticut cities. ... The Connecticut's tax rate may change depending of the type of purchase.
Answer:
0.84+1.00=1.84 +14=15.
If there are 12 people sitting at a round table how many different pairs of people can have conversations assuming they can all talk to each other?
Answer: 6
Step-by-step explanation: 12/2 because a pair is 2 people and there are 12 people in total.!
The number of different pairs of people who can have conversations at a round table with 12 people is 66. This is calculated using the combination formula C(n, 2).
The student asks about the number of different pairs of people who can have conversations at a round table with 12 people, assuming that everyone can talk to each other. The problem is a combinatorial one and can be solved by using the formula for combinations. The formula for the number of combinations of pairs from a set of n items is [tex]C(n, 2) = \frac{n! }{2! * (n - 2)!}[/tex], where n! (n factorial) is the product of all positive integers up to n, and C denotes the combination.
To find how many different pairs can have conversations, we plug in n = 12 into the combination formula:
[tex]C(12, 2) = \frac{12! }{2! * (12 - 2)!} = \frac{12 * 11}{2 * 1} = 66[/tex]
So, there are 66 different pairs of people that can have conversations at a round table with 12 people.
W
13. one-third the sum of eleven and p
We can model the statement "one-third the sum of eleven and [p]" as y = (1/3)(11 + p)
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have one-third the sum of eleven and [p].
We can model the given question as -
y = (1/3)(11 + p)
Therefore, we can model the statement "one-third the sum of eleven and [p]" as y = (1/3)(11 + p)
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Find the product. Simplify your answer.
(4z–1)(z–3)
Answer: 4z (to the 2 power) - 13z + 3
Step-by-step explanation: