MATHEMATICS HIGH SCHOOL

Which of the following best describes the base of a pyramid?A. It can be any polygon.
B. It is a circle.
C. It must be a square.
D. It is a triangle.

Answers

Answer 1

Answer:

Answer:

A. It can be any polygon.

Step-by-step explanation:

A pyramid is a polyhedron with a base, which can be any polygon, but is most often a square.

When the base is a triangle, the pyramid has a total of four faces.

The famous Egyptian pyramids have square bases and four triangular faces. As the number of sides increases in a pyramid, it begins to look like a cone.

So, we can say A and C are both correct. But we will go with A as a square will also be considered in it.

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1. Solve the following equation using the quadratic formula: 3x2 + 6x + 8 = 6.2. Is the quadratic formula the most efficient way to solve this equation? Why or why not?

Answers

Answer:

1. $x=-(3+√(3))/(3)\text{ (or) }x=(-3+√(3))/(3)$

2. Quadratic formula is the most efficient way to solve this equation.

Step-by-step explanation:

We have been given an equation $3x^2+6x+8 = 6$ . We are asked to solve our given equation using quadratic formula.

$x=(-b\pm√(b^2-4ac))/(2a)$ , where,

b = Coefficient of x term,

c = Constant,

a = Coefficient of $x^2$ term.

$3x^2+6x+8-6=6-6$

$3x^2+6x+2=0$

Upon substituting our given values, we will get:

$x=(-6\pm√(6^2-4(3)(2)))/(2(3))$

$x=(-6\pm√(36-24))/(6)$

$x=(-6\pm√(12))/(6)$

$x=(-6\pm √(4\cdot 3))/(6)$

$x=(-6\pm 2√(3))/(6)$

$x=(-6-2√(3))/(6)\text{ (or) }x=(-6+2√(3))/(6)$

$x=(-2(3+√(3)))/(2*3)\text{ (or) }x=(2(-3+√(3)))/(2*3)$

$x=-(3+√(3))/(3)\text{ (or) }x=(-3+√(3))/(3)$

Therefore, the solutions for our given equation are $x=-(3+√(3))/(3)\text{ (or) }x=(-3+√(3))/(3)$ .

2. We cannot factor our given equation by splitting the middle term because there are no such numbers which add up-to 6 and whose product is 6.

Therefore, the quadratic formula is the most efficient way to solve this equation.

Hannah has a biased coin.She is going to throw the coin once.
The probability of getting heads is 0.7
Work out the probability of getting tails.

Answers

There is a 90% chance of getting tails so yea 0.99

Student take an average of 45 minutes and standard deviation of 8 minutes to complete a certain statistics test. If a student is selected at random, what is the probability that the student takes more than 56 minutes to compete the test?

Answers

A standard normal table can be used to estimate what part of a normal distribution will fall within a certain range, given the number of standard deviations (or Z-Score) from the mean. 56 minutes is 11 minutes from 45, and the standard deviation is 8, so the Z-Score is 11/8 = 1.375. The lookup table gives 8.5% complementary probability (greater than the given number of standard deviations) for 1.37 and 8.4% for 1.38. Checking a graph, the part of the curve above 1.375 standard deviations should be somewhere between 5 and 10%, so this seems reasonable.

Which sequence of transformations produces an image that is not congruent to the original figure?A. A translation of 3 units to the left followed by a reflection across the x-axis
B. A rotation of 90 clockwise followed by a translation of 6 units to the left
C. A translation of 5 units to the left followed by a dilation of a factor of 2
D. A reflection across the y-axis followed by a rotation of 180counterclockwise

Answers

Answer:

Option C

Step-by-step explanation:

Whenever transformation is done we have either reflection on a given line, or rotation about a fixed point or a dilation by a scale factor

Whenever transformations are reflections over a line, the original figure size will not be altered and hence we have congruent figures.

Similarly for rotations also original figures will not be altered

But whenever a dilaton by a scale factor other than 1 is done, we have either shrink or dilation of original figure.

So there is a chance of getting similar figure but not congruent figure.

So here we find option C is right answer

Option C.

All the other options deal with transformatios that just move the figure without modifying their dimmenssions.

When you dilate a figure you increase the dimmenssions, so the result is a different figure.

The sixth graders at jenna's school got to visit either the science museum or the history museum. 32 students picked the science museum and 16 picked the history museum. What is the ratio of the number of sixth graders who visited the history museum to the number of sixth graders who visited the science museum?

Answers

The ratio of the number of sixth graders who visited the history museum to the number of sixth graders who visited the science museum is 2 : 1.

What are ratio and proportion?

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given, The sixth graders at Jenna's school got to visit either the science museum or the history museum. 32 students picked the science museum and 16 picked the history museum.

∴ The ratio of the number of sixth graders who visited the history museum to the number of sixth graders who visited the science museum

History museum : Science museum = 32 : 16.

History museum : Science museum = 2 : 1.

For every 2 students go to the science museum, 1 student goes to the history museum.

learn more about proportion here :

brainly.com/question/7096655

#SPJ5

Answer:

The ratio is 16:32 or 1:2. this is because 16 times 2 is 32.

Hope this helped! Please mark me brainliest if I am correct! Thank you and have a great day!

Step-by-step explanation:

Base 5
3213
3444
+ 3323

Answers

Answer:

21040

Step-by-step explanation:

As with base-10 addition, when the sum is equal to the base or more, a "carry" is generated into the next place value column. Useful equivalents here are ...

5₁₀ = 10₅

6₁₀ = 11₅

7₁₀ = 12₅

9₁₀ = 14₅

10₁₀ = 20₅

The addition is shown in the attachment. The sum is 21040₅.

_____

The equivalent decimal addition problem is 433+499+463=1395.

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