A certain triangle has longest side three times it’s shortest side, the middle side is three less than the longest side. The perimeter of the triangle is 32 cm. What is the length of the shortest side?

In 2021 a 30-second commercial during the Super Bowl cost $5.6 million and the CPI was approximately 271.4. Assuming that price changes are simply due to inflation, when the CPI was 33.4 the estimated cost of a 30-second commercial during the first Super Bowl in 1967 would be approximately $68,900.

To calculate the cost of the 30-second commercial during the first Super Bowl in 1967, we can use the concept of inflation and the Consumer Price Index (CPI).

The CPI measures the average price change of a basket of goods and services over time. By comparing the CPI values of two different years, we can estimate the relative increase in prices due to inflation.

Given data:

Cost of a 30-second commercial in 2021 = $5.6 million

CPI in 2021 = 271.4

CPI in 1967 = 33.4

To calculate the cost in 1967, we need to adjust the 2021 cost for inflation using the CPI ratio:

Cost in 1967 = (Cost in 2021) * (CPI in 1967 / CPI in 2021)

Cost in 1967 = ($5.6 million) * (33.4 / 271.4)

Cost in 1967 ≈ $0.689 million

To round the cost to the nearest hundred dollars, we can multiply the cost by 100 and round it to the nearest whole number:

Cost in 1967 ≈ $68,900

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Answer:

B = (5,4), C = (-5, -4), D = (5, -4), A = (-5, 4)

Step-by-step explanation:

look at x axis first (horizontal), then y axis (vertical)

The coordinates of the points are:

Remember that for a point (x, y), we need to count x units on the horizontal axis, and y units on the vertical axis.

With that in mind, we can see that:

Now, answering the questions:

Which point has coordinates (5, 4)?

Point B

Which point has coordinates (-5, -4)?

Point C

Which point has coordinates (5, -4)?

Point D

Which point has coordinates (-5, 4)?

Point A.

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Simplifying this equation, we get:

8 + 4k + 4k + 6 = 30

8k + 14 = 30

8k = 16

k = 2

Therefore, the value of k is 1.

In mathematics, a polynomial is an expression consisting of variables (usually represented by x), coefficients, and non-negative integer exponents, which are combined using the operations of addition, subtraction, and multiplication. For example,

\(3x^2 + 2x - 1\)

is a polynomial with three terms, or a "trinomial," where the variable x is raised to the powers of 2 and 1, and the coefficients are 3, 2, and -1.

The degree of a polynomial is the highest power of the variable in the expression. For example, the polynomial above has a degree of 2, since the highest power of x is 2.

Polynomials are used in many areas of mathematics, including algebra, calculus, and geometry, and are used to model many real-world phenomena.

We can use the remainder theorem, which states that if a polynomial f(x) is divided by (x - a), then the remainder is equal to f(a). In this case, we know that when the polynomial\(l x^3 + kx^2 + 2kx\) + 6 is divided by (x - 2), the remainder is 30. So, we can set up the following equation:

\(x^3 + kx^2 + 2kx + 6 = (x - 2)q(x) + 30\)

where q(x) is the quotient when. \(x^3 + kx^2 + 2kx + 6\) is divided by (x - 2). We don't need to know what q(x) is, since we're only interested in finding k.

Now, let's substitute x = 2 into the equation above:

\(2^3 + k(2^2) + 2k(2) + 6 = (2 - 2)q(2) + 30\)

Simplifying the left-hand side, we get:

\(8 + 4k + 4k + 6 = 30\)

\(16k = 16\)

\(k = 1\)

OR

8 + 4k + 4k + 6 = 30

8k + 14 = 30

8k = 16

k = 2

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Could be -24 if you are raising the -30 by 6.

Answer: 2a < 2b

Step-by-step explanation:

We are given a statement:

a < b and b < c, then 2a ____ 2b

We can use simple numbers that make the statement true.

Where,

a = 2

b = 3

c = 4

Now lets plug it in.

2 < 3 and 3 < 4, then 2(2) ____ 2(3)

and lets simplify:

2 < 3 and 3 < 4, then 4 ____ 6

We can see that 4 is less than 6,

so as a is less than b, 2a is less than 2b.

The only thing changing is the coefficient being multiplied by the variables a and b.

in the given image

m it is given that m

120 = 3x - 5 + 2x

120 = 5x - 5

5x = 120 + 5

x = 125/5

x = 25

so the value of x is 25

So, mm

m = 3 (25) - 5

= 75 - 5

mso, m

the, sum of the angles

so,

120 + mmm

Answer:

This is your answer ☺️☺️☺️

Answer:

13

Step-by-step explanation:

Answer:

The point-slope form of the equation of the parallel line is y - 3 =  \(\frac{3}{4}\) (x - 4)

Step-by-step explanation:

Parallel lines have the same slopes and different y-intercepts

The slope-intercept form of the linear equation is y = m x + b, where

The point-slope form is of the linear equation is y - y1 = m(x - x1), where

∵ The equation of the given line is y = \(\frac{3}{4}\) x - 3

→ Compare it with the first form of the equation above

∴ m =  \(\frac{3}{4}\)

∴ The slope of it is  \(\frac{3}{4}\)

∵ Parallel lines have the same slopes

∴ The slope of the parallel line is  \(\frac{3}{4}\)

∵ The point-slope form is y - y1 = m(x - x1)

→ Substitute the value of the slope in the form of the equation above

∴ y - y1 =  \(\frac{3}{4}\) (x - x1)

∵ The line passes through the point (4, 3)

∴ x1 = 4 and y1 = 3

→ Substitute them in the equation above

∴ y - 3 =  \(\frac{3}{4}\) (x - 4)

∴ The point-slope form of the equation of the parallel line is

    y - 3 =  \(\frac{3}{4}\) (x - 4)

Answer:

Step-by-step explanation:

Given the equation j – 16 = 7, If Nolan is using substitution to determine if 23 is a solution to the equation, then Nolan need to make j the subject of the formula from the equation. The following statements must therefore be made by Nolan.

First, Nolan must substitute for the value of j in the equation.

To simplify, Nolan must subtract the value of  7 from both sides to have;

j – 16 - 7= 7 - 7

j – 23 = 0

Then Nolan must add 23 to both sides of the equation to get the value of j as shown;

j – 23 + 23 = 0+23

j = 23

23 is therefore a solution to the equation

Answer:First, Nolan must substitute 23 for j.To simplify, Nolan must subtract 16 from 23. 23 is a solution of the equation.

Step-by-step explanation:

I got it right on Edge

Answer:

Step-by-step explanation:

T1 = 20

Tn = T(n-1)*3

Given geometric sequence is,

20, 60, .......

Recursive formula of the geometric sequence is given by,

a₁ = First term of the sequence

\(T_n=T_(n-1)\times r\)

\(T_n=\) Successive term of the sequence

\(T_{n-1}=\) Previous term of the sequence

r = common ratio

Here, \(r=\frac{\text{2nd term}}{\text{1st term}}=\frac{60}{20}\)

r = 3

Therefore, \(T_n=T{(n-1)}\times 3\)

Therefore, recursive formula of the sequence is,

\(a_1=20\)

\(T_n=3(T_{n-1})\)

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Answer: 2048

Step-by-step explanation: 1. Write the exponential growth model.

The population of the town doubles every year, so the growth factor is 2. The initial population is 112, so the equation is: P(t) = 112(2)^t where P(t) is the population in year t and t is the number of years since 2014.

2. Estimate the population of the town in 2023. To estimate the population of the town in 2023, we can set t=9, since 2023 is 9 years after 2014. Plugging this into the equation, we get: P(9) = 112(2)^9 = 2048

Therefore, the estimated population of the town in 2023 is 2048.

Answer:

A = 228 tickets

Step-by-step explanation:

We need to set up a system of equation to find the number of adult tickets sold, where A represents the adult tickets and S represents the student tickets.

Because the number of adult and student tickets together equals 506, we have A + S = 506.

Because there are 56 more student tickets than adult tickets we have A + 56 = S

And the way the system is already set up allows us to use substitution.

Thus, we have:

\(A + S=506\\A+56 = S\\\\A+A+56 =506\\2A+56=506\\2A=456\\\\A=228\\228+56=S\\278=S\)

The number of student tickets was not necessary to find in this problem, but I found anyway just in case you wanted check the work or wanted to prove the validity of the values.

The solution set of the inequalities y ≤ x² – 3 and y > –x² + 2 is the darker region shown in the graph.

An equation is an expression that shows the relationship between two or more variables and numbers.

Inequality is an expression that shows the non equal comparison of two or more numbers and variables

The solution set of the inequalities y ≤ x² – 3 and y > –x² + 2 is the darker region shown in the graph.

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The graphs of f(x) and g(x) are transformed function from the function y = x^2 and the solution of the set of inequalities is (±1.581, -0.5)

The complete question is in the attached image (the first graph)

From the graph, we have:

f(x) = x^2 - 3 and g(x) = -x^2 + 2

To derive y ≤  x^2 - 3, we simply change the equality sign in the function f(x) to less than or equal to.

To derive y > -x^2 + 2, we simply change the equality sign in the function g(x) to greater than

The inequalities of the graphs become

y ≤ x^2 - 3 and y > -x^2 + 2

From the graph of the above inequalities (see attachment 2), we can see that the curves of the inequalities intersect at (±1.581, -0.5)

Hence, the solution of the set of inequalities is (±1.581, -0.5)

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Answer:

Step-by-step explanation:

Option 1: 1000 + 2000 + 1238

Option 2: 1500 + 1700 + 2038

The area of glass used to make the window is 3200 sq. cm.

A kite is a member of quadrilateral which has two diagonals. The area of a kite can be determined by;

area of a kite = (length of diagonal 1 * length of diagonal 2) / 2

Therefore to determine the square meter of glass used to make the window in the given question, we have;

length of diagonal 1 = 40 + 40

                                 = 80 cm

length of diagonal 2 = 35 + 45

                                  = 80 cm

area of the window = (80*80)/2

                                 = 6400/2

area of the window = 3200 sq. cm.

Therefore, 3200 sq. m. of glass was used to make the window.

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The steps for bisecting a line segment are to place the reflective device, draw the line of reflection, place the reflective device on point B, move the reflective device around, place the reflective device on point A and repeat the process.

This process implies creating a new line that is perpendicular to the original line, which means the new line will cross the original one. The steps for this are:

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Answer:

22 46 15

Step-by-step explanation:

i looked it up because i was even confused. but i think this is right. hope this helps.

Answer:

its b4 + 7b3 + 4b2 + b5 + 7b4+ 4b3= b5+8b4+11b3+4b2

Answer:

When multiplying, add the exponents, (example) remember if there is "7b" the exponent is one.

Multiply b^2 * b^3 = b^5  (add the exponent 2 + 3 = 5)

Multiply 7b * b^3 = 7b^4 (the exponent of 7b is one, add 1 + 3 for the exponent to become 4)

Multiply 4 * b^3 = 4b^3 (4 doesn't have a variable, the exponent will be 3)

b^2 * b*2 = b^4 (add exponents)

7b * b^2 = 7b^3 (add the exponents 1 + 2)

4 * b^2 = 4b^2

              b^2             +               7b             +        4

b^3           b^5              +           7b^4            +   4b^3

+                                                                                      

b^2           b^4             +           7b^3            + 4b^2

b^5 + 7b^4 + 4b^3 + b^4 + 7b^3 + 4b^2

\(b^5 + 7b^4 + 4b^3 + b^4 + 7b^3 + 4b^2\)

Answer: 120

Step-by-step explanation: I got it right, hope this helps ✨

Answer:

he has I20 different ways to put the books

Step-by-step explanation:

to solve this you would multiply 5x4x3x2 this is how many different combinations he can but the note book on the shelf. 5x4x3x2 is equal to 120

According to the definition of the median of the trapezoid: B. The length of the median is half the sum of the lengths of the bases.

The median of a trapezoid is the line segment that connects the two legs of a trapezoid and is parallel to each of the base of the trapezoid. Also, the length equals half of the sum of the two base lengths of the trapezoid.

Thus, based on the definition of the median of a trapezoid, the true statement is: B. The length of the median is half the sum of the lengths of the bases.

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The pivot positions of the matrix are 1, 3, 5, and 7.

A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

In this case, all the given options (A, B, C, and D) contain the same numbers and have the same structure, so we can examine any one of them to determine the pivot positions.

The pivot positions in the given matrix can be found as follows:

The first pivot position is in the first row, first column (1).

The second pivot position is in the second row, second column (3).

The third pivot position is in the third row, third column (5).

The fourth pivot position is in the fourth row, fourth column (7).

So, the pivot positions in the matrix are 1, 3, 5, and 7. These are the bold values in the matrix and indicate the leading entries after row operations have been performed.

Complete Question:

Identify the pivot positions in the original matrix. The pivot positions are indicated by bold values. Choose the correct answer below.

A.1 2 3 4 3 4 5 6 5 6 7 8

B.1 2 3 4 3 4 5 6 5 6 7 8

C.1 2 3 4 3 4 5 6 5 6 7 8

D.1 2 3 4 3 4 5 6 5 6 7 8

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Answer:

The greatest number of arrangements that he can make if every balloon is used is 8.

Step-by-step explanation:

The greatest number of arrangements will be the greatest common factor between 24 and 32.

GCF of 24 and 32:

We keep factoring both numbers by prime factors, while they can both be divided by the same number. So

24 - 32|2

12 - 16|2

6 - 8|2

3 - 4

There is no factor for which we can divide both 3 and 4. So the GCF is 2*2*2 = 8.

This means that the greatest number of arrangements that he can make if every balloon is used is 8.

Therefore, linear equation  Boeing 747-8 Global Aircraft will not be able to fly nonstop for 16 hours between Los Angeles and Melbourne using the information provided.

A linear regression model is one that uses the equation y=mx+b. The inclination is B, and the y-intercept is m. Even though y and y are separate parts, the preceding phrase is commonly referred to as a "mathematical equation with two variables." The only factors in bivariate linear equations are two. There are never any answers to the application areas of linear equations. Y=mx+b.

Here,

We must first establish the amount of fuel usage in order to apply a linear equation to predict how much jet fuel will be left after eighteen hours of flight.

The graph shows that the fuel is consumed at a pace of about 4,000 gallons every hour.

Using this rate, we can forecast how much fuel the aircraft will have left over after 18 hours of flight:

Gasoline left over: 63,500 - (4,000 x 18)

Gasoline left: 63,500 to 72,000

Gasoline left over: -8,500

But we are aware that the fuel that is still present cannot be bad. This indicates that the aircraft will require refuelling before finishing its 18-hour journey.

The Boeing 747-8 Global Aircraft will not be able to fly nonstop for 16 hours between Los Angeles and Melbourne using the information provided.

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Answer:

3 cm cube: 27

6 cm cube: 216

Step-by-step explanation:

First, you would need to find the volume of the 3 cm cube: 3*3*3=27

To build this cube you would need 27 1 cm cubes

For the 6 cm side cube you would need to do 6*6*6=216

So you would need 216 1 cm cubes

Hope this helps!

The fourth term a₄ of the sequence is 29933

From the question, we have the following definition of the function that can be used in our computation:

a₁= 3

aₙ = (aₙ₋₁)² + 4

The above definitions imply that we simply square the previous term and then add 4 to the squared result to get the current term

Using the above as a guide,

so, we have the following representation

a₂ = (3)² + 4

a₂ = 13

Also, we have

a₃ = (13)² + 4

a₃ = 173

Lastly, we have

a₄ = (173)² + 4

Evaluate the equation

a₄ = 29933

Hence, the value of a₄ is 29933

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Answer:

One side - 15 feet

Second side - 4 feet

Third side - 13 feet

Step-by-step explanation:

Let's call the sides A B and C, respectively.

We know that:

A = B + 11

C = B + 9

and that

A + B + C = 32

Please note that we have 3 equations and 3 unknowns. We can solve this, we'll use substitution.

A + B + C = (B + 11) + B + (B + 9) = 32

3B + 20 = 32

3B = 12

B = 4

The sides have lengths of 4+11 = 15, 4 and 4+9 = 13. This is in fact a proper triangle (because the shorter sides add up to more than the longer side).