The second side of a triangular deck is 6 feet longer than the shortest side and a third side that is 6 feet shorter than twice the length of the shortest side. If the perimeter of the deck is 68 ​feet, what are the lengths of the three​ sides?

Using the elimination method, the given system of equations leads to a solution of x = -1, y = 1, and z = -2.

https://brainly.com/question/13877817

#SPJ3

The other two angles are 23 degrees and 67 degrees.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given,

Given a right angled triangle with one angle 90 degrees.

We need to find the other two angle measures of a right triangle with side lengths 5, 12, and 13

The relations in a right triangle are given as follows:

The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.

The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.

The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.

In this problem, the hypotenuse is the largest size of 13.

The angle opposite to the side of length 5 is found as follows:

sinθ=5/13

θ=sin⁻¹5/13

θ=23

By angle sum of 3 angles is of 180º, the other angle is of 67º.

Hence, the other two angles are 23 degrees and 67 degrees.

To learn more on trigonometry click:

https://brainly.com/question/25122835

#SPJ6

the six to the left is worth more than the six in the hundredths

hope

i helped

Answer:

The expanded form of 310 is:

310 = 300 + 10.

Joe will write two numbers to form 310.

Step-by-step explanation:

The expanded form is used to write numbers and see the math value of individual digits. So, the numbers are separated into individual place values and decimal places and form a mathematical expression.

310 in expanded form is 300 + 10 = 310.

Answer:

Option C is correct

Yes, the set of ordered pairs {(–5, –5), (–1, –2), (0, –2), (3, 7), (8, 9)}  represents the function.

because every x-value corresponds to exactly one y-value.

Step-by-step explanation:

A function states that it is a relation in which every domain value is paired with exactly one element of range.

Given the set of ordered pair:

{(–5, –5), (–1, –2), (0, –2), (3, 7), (8, 9)}

Domain is all the x-values, and range is all the y-values.

Domain: {-5, -1, 0, 3, 8}

Range:  {-5, -2, -2, 7, 9}

By definition:

each input value (i.e x values) is paired with exactly one element of y-value.

therefore,the set of ordered pairs {(–5, –5), (–1, –2), (0, –2), (3, 7), (8, 9)}  represents the function.

Answer:

midpoint is (0,0)

Step-by-step explanation:

the midpoint of the x-intercepts of

[tex]f(x) = (x - 4)(x + 4)[/tex]

To find the midpoint of x intercepts, we need to find the x intercepts first

we find x intercepts by replacing f(x) with 0

[tex]0 = (x - 4)(x + 4)[/tex]

Set each factor =0 and solve for x

[tex]x-4=0 , x=4[/tex]

[tex]x+4=0, x=-4[/tex]

X intercepts are -4  and 4

Midpoint of -4 and 4 is [tex]\frac{-4+4}{2} =0[/tex]

X intercepts lies on x axis . So midpoint is (0,0)

If the total debt is near $1.8 × 10¹³, then every person has to pay $60,000.

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 mentioned data in the question,

Total debt in the United States = $1.8 × 10¹³

Total number of people in the United States = 3 × 10⁸

If  every person paid their share, then each person has to pay,

= ($1.8 × 10¹³)/(3 × 10⁸)

= $6 × 10⁴ or,

It can be written as $60,000.

To know more about arithmetic operations:

https://brainly.com/question/13585407

#SPJ5

In 2013, there were approximately 4.509 McDonald's restaurants per 100,000 people in the US.

To calculate the number of McDonald's restaurants per capita in the US in 2013, we divide the total number of McDonald's locations (14267) by the population of the US (316,500,000).

[tex]\[ \text{McDonald's per capita} = \frac{14267}{316500000} \][/tex]

Performing the division, we get [tex]\( 4.509 \times 10^{-5} \)[/tex].

This means there were approximately 4.509 McDonald's restaurants per 100,000 people in the US in 2013.

So, the number of McDonald's restaurants per capita in the US in 2013 is [tex]\( 4.509 \times 10^{-5} \) or \( 4.509 \times 10^{-5} \)[/tex] McDonald's per person.

By converting the total trip time to minutes, using the formula for speed (distance/time), and using a system of equations representing the total trip speed when the boat is moving downstream and upstream, we can find the average speed of the boat relative to the water.

To solve this problem, we first need to convert the total trip time to minutes to make calculations easier. Given in the problem, 3 hours 20 minutes equates to 200 minutes. Next, we should use the formula for speed, which is distance divided by time. We know that the total distance traveled by the boat is 80 miles downstream and 80 miles back, totaling 160 miles.

When moving downstream, the speed of the boat and the speed of the current both aid in the boat’s motion. Thus we have speed of the boat = speed of the boat in still water + speed of the current.  However, when the boat is moving upstream, the speed of the current works against the boat's motion. Thus we have speed of the boat = speed of the boat in still water - speed of the current.

By using the system of these equations and the fact that total time equals total distance divided by the speed of the boat, we can find the speed of the boat in still water, which represents the average speed of the boat relative to the water.

https://brainly.com/question/680492

#SPJ2

Answer: I wrote the rate, with $5.95 in the numerator and 3 loaves in the denominator. I needed to find an equivalent rate expressed as a fraction with the denominator of 1. I noticed 3 loaves divided by 3 gave a denominator of 1, so I divided $5.94 by 3 to find that each loaf costs $1.98.

Just did it on Edge 2021

Btw Can you mark me brainlest pls

The equivalent rate of the bread is $1.98.

Since the store advertises a sale for 3 loaves of bread for $5.94, in order to find the equivalent rate, the person has to divide $5.94 by 3. This will be:

= $5.94/3

= $1.98

Therefore, the equivalent rate of the loaves of bread will be $1.98

Read related link on:

https://brainly.com/question/10884356

Final answer:

The number 21,070 is already in standard form. Standard form is a straightforward expression of a number as commonly written, without the need for scientific notation for simple numbers like this one.

Explanation:

The number 21,070 written in standard form is simply 21,070 itself. In mathematics, standard form refers to the way a number is commonly written. This number is already in standard form because it is expressed in a direct and straightforward manner. There is no need for further simplification or conversion. When numbers are very large or very small, they can be cumbersome to write out in full, which is why scientists and mathematicians may use scientific notation to express them.

For instance, if we had a larger number like 77,123,450, we could write it in scientific notation as 7.712345 × 10⁷, emphasizing that it is 7.712345 times ten to the seventh power.

For the provided number 21,070, no such conversion is necessary, and it remains 21,070 in standard notation.

Answer:

Angle x =  63 °.

Step-by-step explanation:

Given  : A circle larger arc angle 184° and smaller arc angle 58°.

To find: What is the value of x.

Solution : We have given that  larger arc angle 184°

Smaller arc angle 58°.

Angle formed by tangent and chord = x

m∠x = [tex]\frac{1}{2}( 184 - 58 )[/tex].

m∠x =   [tex]\frac{1}{2}( 126)[/tex].

m∠x =  63 °.

Therefore, Angle x =  63 °.

Answer: 3.1

Step-by-step explanation:

The mean of the frequency distribution is 3.1. Which is the correct answer would be an option (B)

Arithmetic mean is defined as the ratio of the sum of observations to the total number of observations. It can be referred to as the average of a specific set of data or the arithmetic mean. One of the basic methods used to acquire a result, the term "Mean" is commonly used in the field of statistics.

The formula for the mean of a given set of data is as follows:

Mean = Sum of Observations/Total number of observations

Given the frequency distribution as :

Household size (x)         Frequency (f)                    fx      

           1                                   2                            1 × 2 = 2

           2                                   4                           2 × 4 = 8

           3                                   6                           3 × 6 = 18

           4                                   5                          4 × 5 = 20

           5                                   2                           5 × 2 = 10

Summation of fx = (Σfx) = 2 + 8 + 18 + 20 + 10 = 58

Total frequency = (Σf) = 2 + 4 + 6 + 5 + 2 = 19

⇒ Mean = Σfx/Σf

⇒ 58/ 19

⇒ 3.1

Thus, the mean of the frequency distribution is 3.1.

Learn more about the Arithmetic means here:

brainly.com/question/13000783

#SPJ2

Answer:

$2.50

Step-by-step explanation

Answer:

On Odyssey ware it is -c/a

Step-by-step explanation:

The x-intercept and the y-intercept of a line can be found by setting y and x to zero in the line equation respectively. The x-intercept is -c/a and the y-intercept is -c/b.

To find the x and y-intercepts of the given line equation L = ax + by + c = 0, we must set one variable to zero and solve for the other.

To find the x-intercept of a line, we can set y to zero (as this is the case when the line crosses the x-axis), we get:

L = ax + b(0) + c = 0 or x = -c/a

Therefore the getX-intercept of the line is -c/a.

Similarly to find the y-intercept of the line equation, we can set x to zero (as this is the case when the line crosses the y-axis), we get:

L = a(0) + by + c = 0 or y = -c/b

Hence, the y-intercept of the line is -c/b.

https://brainly.com/question/33234142

#SPJ2

Answer:

g(x) has greatest y-intercept.

Step-by-step explanation:

We are given a table of values for function f(x) as:

x   y=f(x)

−3 −14  

−2  −6

−1     −2  

0       3  

1        5  

2       6

We know that the y-intercept of a function is a point where the x-value is zero.

i.e. the input value is zero.

Hence, after looking at the table of values of the function f(x) we have the y-intercept of the function f(x) is:

y=3

Also we are given function g(x) as:

g(x) = 3 cos(2x) + 1

Hence, we calculate the y-intercept of the function g(x) by taking x=0

on taking x=0 we have:

g(0)=3 cos(0)+1

g(0)=3+1=4

Hence, the y-intercept of function g(x) is 4.

Hence, g(x) has the greatest y-intercept.