What are the angle measures of the triangle?

A right triangle is shown with the measures of the three sides. One leg measures 6. One leg measures 6 Start Root 3 End Root. The hypotenuse measures 12.
A. 45°, 45°, 90°
B. 60°, 60°, 60°
C. 30°, 60°, 90°
D. They cannot be determined.

Answer:

x = 5

Step-by-step explanation:

26x + 10x = 180°

36x = 180

x = 180/36

x = 5

There are total of 152 students in 5th grade, then the number of pencils altogether will be equal to 2,736 pencils.

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.

They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.

As per the given information in the question,

Total number of students in 5th grade = 152

Amount of pencil each student have = 18

Then, the total number of pencils altogether,

= 152 × 18

= 2,736 pencils.

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The largest area a rectangle can have when inscribed in a semicircle of radius 2 is 4 square units.

The dimensions of this rectangle are 2 units by 2 units. This occurs when the sides of the rectangle are parallel to the diameter of the semicircle, so that each vertex of the rectangle lies on the circumference of the semicircle.

The length of the rectangle is equal to the diameter of the semicircle, or 2 units, and its width is half the diameter, or 2/2 = 1 unit. The area of this rectangle is equal to the length times the width, or 2 * 1 = 2 square units.

Since the rectangle is inscribed in a semicircle, its dimensions must be equal, so the largest area rectangle that can be inscribed in a semicircle of radius 2 has sides of length 2 units and an area of 4 square units.

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The length of the segment A'A is 18 units

The length of the segment B'B is 8 units

From the question, we have the following parameters that can be used in our computation:

The similar triangle

Using the ratio of corresponding sides, we have

(AA' + 12)/20 = 12/8

So, we have

AA' + 12 = 20 * 12/8

AA' + 12 = 30

Evaluate

AA' = 18

Here, we have

(BB' + 6)/20 = 6/8

So, we have

BB' + 6 = 20 * 6/8

BB' + 6 = 15

Evaluate

BB' = 8

Hence, the length is 8 units

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A good half a mile time is totally good, if a half mile is the longest distance you've ever run, try a 3/4 mile run the next time. After a few successful attempts at that distance, increase it to a mile.

In the given question, we have to explain, what is a good half a mile time.

First, some background is required for 5:43 for half a mile. When did you start running? Was that time calculated using a full effort, or was it only the distance covered without walking? Don't worry about if it's good if you're spanking new. Use it as a foundation.

Second, like with most things in life, practise makes perfect, and running performance is no exception. If a half mile is the longest distance you've ever run, try a 3/4 mile run the next time. After a few successful attempts at that distance, increase it to a mile. The goal is to gradually push your boundaries until you consistently cross that threshold and then push your limits even farther.

Your body will be encouraged to adapt to the challenge, grow to it, and become prepared for when the challenge gets harder.

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Answer:

Step-by-step explanation:

Check the picture below.

Answer:

-32 is what i got

Step-by-step explanation:

The range of the function g(x) is given as follows:

[0, ∞).

From the graph of the function given in this problem, y assumes all real non-negative values, hence the interval notation representing the range of the function is given as follows:

[0, ∞).

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Answer:

26.75 unit^2 to the nearest hundredth.

Step-by-step explanation:

Integrating between the 2 limits:

            2                            2

Area =   ∫    e^2x dx     =   [   1/2 e^2x ]

            0                            0

= 1/2( e^4 - e^0]

= 1/2(54.598 - 1)

= 26.749

Answer:

ascending: 1.4%, 0.025, 14/100, 1/4, 0.4

OR

descending: 0.4, 1/4, 14/100, 0.025, 1.4%

(your question did not specify which order)

Step-by-step explanation:

make all the values given constant (either decimal or fraction).

1/4 = 0.25

0.4 = 0.4

1.4% = 0.014

14/100 = 0.14

0.025 = 0.025

now that the numbers are easier to compare, rearrange them in the order the questions requires.

ascending: 1.4%, 0.025, 14/100, 1/4, 0.4

descending: 0.4, 1/4, 14/100, 0.025, 1.4%

Answer:

area of the triangle= 1/2 × base × height

24 = 1/2 × 4 × height

height. = 24/2

= 12 inches

answer is third option

Kelly bought 64 muffins.

Solution: Let's represent the total number of muffins Kelly bought as x.

We are given that Kelly gave 1/8 of the muffins to Mike. Thus, the fraction of muffins that she had left is 7/8.

We can, therefore, say that 7/8x represents the number of muffins that Kelly had left after giving some to Mike.

Also, Kelly gave 6 muffins to Fin. We can say that 7/8x - 6 represents the number of muffins that Kelly had left after giving 6 muffins to Fin

Finally, we are given that Kelly had 15 muffins left. Thus,7/8x - 6 = 15

Adding 6 to both sides gives:7/8x = 21

Multiplying both sides by 8/7 gives:

x = 24

Thus, Kelly bought 64 muffins (x + 1/8x = 64).

Answer: 64

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x = 21/16

Hope I helped

Answer:

21/16=x

Step-by-step explanation:

\(8x+\frac{5}{2} =13\\2(8x+\frac{5}{2} =13)\\16x+5=26\\16x=21\\x=\frac{21}{16}\)

Hope this helps ;D

All members of set S can be expressed as numbers of the form 2ᵃ3ᵇ, where a and b are non-negative integers.

We will prove by structural induction that all members of set S can be expressed as numbers of the form 2ᵃ3ᵇ, where a and b are non-negative integers.

Base Case:

We start with the base case, where n = 1. In this case, 1∈ S, and we can see that 1 can be expressed as 2⁰3⁰, which is of the desired form.

Inductive Step:

Now, assume that for some positive integer k, if n = k, then k∈ S can be expressed as 2ᵃ3ᵇ for non-negative integers a and b.

We will show that if n = k + 1, then k + 1 can also be expressed as 2ᵃ3ᵇ for non-negative integers a and b.

Case 1: If n = 2k, then we know that 2k∈ S. By the induction hypothesis, we can express 2k as 2ᵃ3ᵇ for some non-negative integers a and b. Now, we can observe that 2k+1 = 2(2k) = 2ᵃ₊₁3ᵇ, which is still of the desired form.

Case 2: If n = 3k, then we know that 3k∈ S. By the induction hypothesis, we can express 3k as 2ᵃ3ᵇ for some non-negative integers a and b. Now, we can observe that 3k+1 = 3(3k) = 2ᵃ3ᵇ₊₁, which is still of the desired form.

Since we have shown that if n = k + 1, then k + 1 can be expressed as 2ᵃ3ᵇ, the proof by structural induction is complete.

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Step-by-step explanation:

\(3^x=9^{x+5}\\\\3^x=\left(3^2\right)^{x+5}\qquad|\text{use}\ (a^n)^m=a^{nm}\\\\3^x=3^{2(x+5)}\iff x=2(x+5)\qquad|\text{use the distributive property}\\\\x=2x+10\quad|\text{subtract}\ 2x\ \text{from both sides}\\\\-x=10\qquad|\text{change the signs}\\\\\huge\boxed{x=-10}\)

\(27^{4x}=9^{x+1}\\\\\left(3^3\right)^{4x}=\left(3^2\right)^{x+1}\\\\3^{(3)(4x)}=3^{2(x+1)}\iff(3)(4x)=2(x+1)\\\\12x=2x+2\qquad|\text{subtract}\ 2x\ \text{from both sides}\\\\10x=2\qquad|\text{divide both sides by 10}\\\\x=\dfrac{2}{10}\\\\\huge\boxed{x=0.2}\)

\(5^x=25^{3x+5}\\\\5^x=\left(5^2\right)^{3x+5}\\\\5^x=5^{2(3x+5)}\iff x=2(3x+5)\\\\x=(2)(3x)+(2)(5)\\\\x=6x+10\qquad|\text{subtract}\ 6x\ \text{from both sides}\\\\-5x=10\qquad|\text{divide both sides by (-5)}\\\\\huge\boxed{x=-2}\)

The solution set can be described as the line {(2-4t, -1-t, 3t-2, -5-6t)} in R4.  This line can be defined by a vector (4, 1, 1, -6) and any point on the line (2, -1, 0, -5).

The solution set can be described by the line {(2-4t, -1-t, 3t-2, -5-6t)} in R4. To describe this line, we need a point on the line and a vector. The point on the line can be found by setting t = 0, so the point is (2, -1, 0, -5). The vector can be found by subtracting the point from each of the coordinates of the solution set, so the vector is (4, 1, 1, -6). This vector can be used to describe the line in R4, as any point on the line can be expressed as a multiple of the vector plus the initial point on the line. Therefore, the solution set of the system of equations can be described as the line {(2-4t, -1-t, 3t-2, -5-6t)} in R4, defined by the point (2, -1, 0, -5) and the vector (4, 1, 1, -6).

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The sum height of men and women is 139600 and 161000 inches respectively. Their mean height is 66.8 inches and the average of their mean is 67.1 inches.

Number of women =2500

Mean height of women = 64.4 inches

So, the total height of 2500 women = 64.4*2500 = 161000 inches

Number of men=2000

Mean height of men = 69.8 inches

So, the total height of 2000 men = 69.8*2000 = 139600 inches

Therefore, the sum height of all 4500 people = 161000+139600 =b

So, their mean height = 300600/ 4500 = 66.8 inches

The sum of mean height of men and women = 64.4 + 69.8 = 134.2 inches

Hence, The average of their mean = 134.2/ 2= 67.1 inches.

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Answer:

true

Step-by-step explanation:

The  number of significant digits to report in the answer is always the least number of significant figures that can be found in the question.

The term significant figures refers to the non zero digits in a number . It is those numbers that can be assigned a value in any string of digits. In mathematics, we often carry out operations such as addition, subtraction, division and multiplication.

The  number of significant digits to report in the answer is always the least number of significant figures that can be found in the question.

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The answer is c. because all of the other answers arne tpossible due to where they graphed it

Step-by-step explanation:

Hint : we will check for each option whether it is an experiment or not by using the concepts of probability first we will check then if a coin is tossed then it is an experiment or not ? then we will check that if a dice is rolled is it an experiment or not and then we will repeat the same process for choosing a marble from a jar

complete step by step answer and event is a set of outcomes of an experiment to which probability is assigned as take an example when we and I the possibility of 5 appearing on the die is an event if for tossing a coin we do not know the result when a coin is tossed in can give any result whether it will be a head or tails so this is an example for a random experiment if a six-sided dice will be rolled then we do not know what is about to come there result can be anything from 126 so it is also an example for random experiment choosing a marble from a jar is also an experiment because we are choosing one marble from the jar and experiment is a work in which a result can be anything hence option d is the correct option not probability is how likely something is about to happen when a coin is tossed there are two possibility outcomes heads or tails show the probability of an outcome 1

( number of ways it can happen )÷

( total number of outcomes)

so when a coin is tossed the total number of outcomes are to solve the probability of a current head is 1/2

The expression in product-of-sums is A⋅B + A⋅B + B⋅C.

To convert the expression to product-of-sums form, we need to distribute the AND (∧) operator over the OR (∨) operator.

The given expression is: A⋅B+A⋅B+B⋅C

First, let's apply the distributive property:

A⋅B+A⋅B+B⋅C = (A⋅B + A⋅B) + B⋅C

Next, we can factor out common terms within each grouping:

(A⋅B + A⋅B) + B⋅C = A⋅(B + B) + B⋅C

Simplifying further, we have:

A⋅(B + B) + B⋅C = A⋅B + A⋅B + B⋅C

Now, the expression is in product-of-sums form. It can be written as:

A⋅B + A⋅B + B⋅C

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Answer:

The line would be straight; it could be vertical or horizontal.

I would chose more initial zombies, but a slower growth rate because when they grow stronger, you get stronger so you have a better chance of survival if their development rate is gradual, giving you time to collect weapons and construct a shelter.

Growth rate refers to the percentage increase or decrease in a particular variable over a specific period of time. It is commonly used in finance, economics, and business to describe the rate of change of various economic indicators such as gross domestic product (GDP), population, revenue, profit, and so on.

To calculate the growth rate, you need to divide the difference between the final value and the initial value of the variable by the initial value, and then multiply the result by 100 to express it as a percentage. The formula for growth rate is as follows:

Growth rate = ((Final value - Initial value) / Initial value) x 100

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Lines l and m are parallel; line l will map onto line m with a 90° rotation; line l can map onto line m with a vertical line of reflection.

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Answer:

169

Step-by-Step Explanation:

3.8*10^3 = 3800

6.422*10^5 = 642200

642200/3800 = 169

169 is the answer

Answer:169

Step-by-step explanation:

Answer:

\(x=-\frac{39}{2}\\ y=51\)

Step-by-step explanation:

\(8x+4y=48\\12x+5y=21\)

Let's solve the first equation for x or y. I'll do it for y.

\(8x+4y=48\)

Subtract 8x

\(4y=-8x+48\)

Divide by 4.

\(y=-\frac{8}{4}x+\frac{48}{4}\\\)

Simplify.

\(y=-2x+12\)

Now replace the value of y in the second equation for this.

\(12x+5y=21\\12x+5(-2x+12)=21\)

Distribute 5

\(12x-10x+60=21\)

Subtract 60

\(12x-10x=21-60\)

Combine like terms;

\(2x=-39\)

Divide by 2.

\(x=-\frac{39}{2}\)

Now replace this in any of the equations to find the value of y.

\(8x+4y=48\\8(-\frac{39}{2})+4y=48\\\)

8 and 2 can be simplified.

8/2=4

2/2=1

\(4(-39)+4y=48\)

Distribute 4.

\(-156+4y=48\)

Add 156

\(4y=48+156\\4y=204\)

Divide by 4

\(y=\frac{204}{4}\)

\(y=51\)

Proof:

\(8x+4y=48\\8(-\frac{39}{2} )+4(51)=48\\4(-39)+204=48\\-156+204=48\\48=48\)

Answer:

70.7 degrees

Step-by-step explanation: