use substitution to solve the following system of equations.
4x+4y=16 AND y=x+2
( [?], [?])

There are 10 different ways to choose three products out of five.

What are permutation and combination?

Permutation and combination are mathematical concepts used to study the arrangements and selections of items.

Permutation: An arrangement of items, where order matters.

Combination: A selection of items, where order does not matter.

In this case, the manager has to choose three products out of five possibilities, which is a combination problem. To find the number of different ways to choose three products out of five, we can use the formula: nCr = n! / (r! (n - r)!).

n = 5 (number of items)

r = 3 (number of items to be chosen)

nCr = 5! / (3! (5 - 3)!) = 5! / (3! 2!) = (5 x 4) / (2 x 1) = 10.

Hence, there are 10 different ways to choose three products out of five.

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The vertex form of the equation of the parabola is the quadratic equation y - 3 = - 3 · (x + 4)².

Parabolae are represented by quadratic equations, there are two forms for such equations: (i) standard form, (ii) vertex form. The vertex form of the equation of the parabola is shown below (please notice that parabola is parallel to y-axis when axis of symmetry is a vertical line):

y - k = C · (x - h)²

Where:

If we know that h = - 4, k = 3 and (x, y) = (- 3, 0), then the equation of the parabola in vertex form is:

C = (y - k) / (x - h)²

C = (0 - 3) / [(- 3) + 4]²

C = - 3 / 1²

C = - 3

The equation of the parabola in vertex form is the quadratic equation y - 3 = - 3 · (x + 4)².

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i) The absolute change of the CPI from 2009 to 2014 is given as follows: 22,199.

ii) The absolute change of the Tuition from 2009 to 2014 is given as follows: $26.5.

iii) The relative change of the CPI from 2009 to 2014 is given as follows: 10.35%.

iv) The relative change of the Tuition from 2009 to 2014 is given as follows: 26.59%.

Tuition has increased more in this time period.

The absolute change between two amounts is given by the absolute value of the difference of these two amounts.

Hence for the CPI from 2009 to 2014 is given as follows:

236736 - 214537 = 22,199

For the Tuition, it is given as follows:

126.15 - 99.65 = $26.5.

The relative change is given by the absolute change divided by the initial value and multiplied by 100%, hence:

Due to the higher relative change, the Tuition increased more in this time period.

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Water and ocean are two closely related words, as the ocean is the largest source of water on the planet.

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Answer:

---------------------------------

Real distance is 4.4 miles and on the map it is 8 inches.

The scale is:

or

The perimeter of Triangle ABC, given the triangle in drawn in the graph, would be 40 .54 units .

To find the perimeter of the triangle , you first need to find the lengths of the sides of the triangle .

The lengths would be the distance between the points A , B , and C .

The vertices are : A ( - 1 , - 8) , B ( -4 , 6 ) and C ( 4 , 9 ) .

The distance between the points can be found by the formula:

= √(( x₂  – x₁ )² + ( y₂ – y₁) ²)

The distance between AB is 14.3 units

The distance between BC is 8. 54 units.

The distance between AC is 17.7 units.

The perimeter is:

= 14.3 + 8. 54 + 17. 7

= 40 .54 units

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Answer: -2a+b-2

Step-by-step explanation:

Luke save $10 after buying 5 boxes.

What is a function?

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

Here, we have

Given: Luke buys a certain brand of cereal that costs $11 per box. Luke changes to a super-saving brand of the same size.

The function of the first cereal is

y = 11x

Now, another cereal that Luke decides to buy is $9 per box, which is expressed

y = 9x

Now, the difference between the costs is $2, because 11-9=2.

So, the original brand costs $2 more than the super-saving brand.

Now, if Luke buys 5 cereal boxes per month, the cost in each case would be

y = 11(5) = 55

y = 9(5) = 45

Luke is saving per month 55 - 45 = $10

Hence, Luke save $10 after buying 5 boxes.

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Answer:

C

Step-by-step explanation:

kilograms x pounds of dog food = ?

2.2 x 25 = 55

process of elimination;;;

A- correct answer, wrong setup

B- wrong answer, correct setup

C- correct answer, correct setup. makes the most sense

D- wrong answer, wrong setup

The outer perimeter of the rectangular base will be 34 meters.

Let W be the rectangle's width and L its length.

The perimeter of the rectangle will be defined as the total length of all of its sides. So the rectangle's perimeter will be

Perimeter of the rectangle = 2(L + W) units

The outer dimension of the base will be given as,

L = 8 + 1 + 1

L = 10 m

W = 5 + 1 + 1

W = 7 m

The outer perimeter of the rectangular base will be given as,

P = 2(7 + 10)

P = 2 x 17

P = 34 m

The outer perimeter of the rectangular base will be 34 meters.

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An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

When exponents, constants, and variables are combined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable).

The sum of terms with the notation kxn, where k is any number and n is a positive integer, is referred to as a polynomial.

Using a binomial and a trinomial as a product, one can factor the sum or difference of two cubes. It follows that x3+y3=(x+y)(x2+xy+y2) and x3+y3=(xy)(x2+xy+y2).

If an expression can be thought of as the difference of two perfect squares, then a3 - b3 = (a - b)(a2 + ab + b2). To prevent issues, use parentheses. The trinomial phrase should be free of inner parenthesis.

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Answer:

His son is 13 years old now.

Step-by-step explanation:

Since the man was 26 years old when his son was born, his age is 26 more than his son's age, or mathematically speaking, x + 26 if the age of his son is x.

26 + x - dad's age

x - son's age

3 x son's age = dad's age

3x = 26 + x

2x = 26

x = 13

His son is 13 years old.

The system of inequalities that defines how many of each you can take is: C≥12,E≥6,C+E≤26. Option A

The questions says that you must take at least 12 core credits

let core courses be = C

This tells us that C has to be greater than or equal to 12

C ≥ 12

Then it says that you must take at least 6 electives as well. This would be represented in the same way.

E = elective

E ≥ 6

Lastly, it says that you can take no more than a total of 26 credits

Hence your credit has to be 26 in number or less.

This would be written as C + E ≤ 26

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Complete question

To graduate you must take at least 12 core credits and 6 electives credits and you can take no more than a total of 26 credits. Write a system of inequalities that defines how many of each you can take.

C≥12,E≥6,C+E≤26

C+E≥18,C+E≤26

C+E≥18,C+E<26

C≤12,E≤6,C+E≤26

Answer:

This is a sequence of numbers that can be expressed as a linear function. The linear function would be of the form y = mx + b, where m is the slope of the line and b is the y-intercept. In this case, m = 3 and b = 7, so the linear equation for this sequence is y = 3x + 7.

Pls mark as brainliest :) ty

[tex]area = \frac{1}{2} \times base \times height \\ 9 = \frac{1}{2} \times 4.5 \times h \\ 9 = 2.25h \\ \frac{9}{2.25} = \: \frac{2.25h}{9} \\ 4 = height[/tex]

Answer:

Step-by-step explanation:

First, we need to convert the area of 15 feet by 10 feet to square feet. That is 15*10 = 150 sq ft.

We know that 22 people fit comfortably in a 150 sq ft area, so we can estimate the number of people that can fit in a given area by dividing the area by the number of square feet per person.

So if we have an area of 10 feet deep on one side of the street along a 1-mile section of a parade route, we can estimate the number of people that can fit in that area by using the following equation:

(Area of crowd) / (Square feet per person) = Number of people

We know that 1 mile = 5280 feet, so the area of the crowd is 10*5280 = 52,800 sq ft.

Now we can estimate the number of people that can fit in that area by dividing the area by the number of square feet per person:

52,800 sq ft / 150 sq ft/person = 352 people

So, we can estimate that around 352 people can fit comfortably in a crowd that is 10 feet deep on one side of the street along a 1-mile section of a parade route.

Customers who purchase items with discount of  credit has 30 days to repay the balance. However, if clients pay for their products within 10 days,

A trade discount, often referred to as a functional reduction, can be applied as a fixed percentage or flat rate deduction from the a seller's initial catalogues list price, in which case the trading discount amount is calculated by multiplying the list price by the percentage difference. Calculating the trade discount requires knowledge of both the item's original list price and the trade discount percentage. The list price is multiplied with the trade discount % in decimal form to arrive at the trade discount.

Here,

they will receive a 2% discount. Customers need only pay $9,800

if they buy $10,000 from Group A underneath the terms 2/10 gross 30 and pay within ten days ($10,000 x 0.98 = $9,800).

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Total thingamajigs made by Karen, Sue and Peter = 48 and same as the number of widgets.

Multiply means enlarge or increase. Adding equal number of groups is termed as multiply. Multiply 4 by 4 means 4 is added to 4 in 4 times.

given, Karen can make 1 widget in 1 hour.

In a 1-hour time period Sue can make 1 widget

Peter can make 4 widgets in 1 hour.

If they all work 8 hours in a day, then total number of widgets made by them will be

= 1 × 8 + 1×8 + 4×8 =48

They together can make 48 widgets in a day.

similarly, Karen can make 4 thingamajigs in 1 hour.

Sue can make 1 thingamajig in 1 hour.

Peter can make 1 thingamajig in 1 hour.

In total 8 hours period they together can make (4×8 + 1×8 +1×8)

48 thingamajigs.

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The estimation number of death from measles occured in developing countries in 2019 is 1.9 million deaths.

To estimate the number of deaths from measles in developing countries, we can use the following calculation:

Deaths = (Total number of cases in developing countries) × (Fatality rate in developing countries)

According to the World Health Organization, 75% of measles cases occurred in developing countries in 2019. Assuming a total of 10 million cases worldwide, 7.5 million cases would have occurred in developing countries.

The fatality rate in developing countries is approximately 25%, so:

Deaths = (7.5 million cases) × (0.25) = 1.875 million deaths.

Deaths = 1.875 million deaths ≈ 1.9 million deaths

So, 1.9 million deaths from measles are likely to have resulted in developing countries in 2019.

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Answer:

To determine the amount of the investment after 7 years, we can use the formula:

A = P(1 + r/n)^(nt)

Where:

A = the future value of the investment (the amount after 7 years)

P = the initial principal or investment amount ($2750)

r = the annual interest rate (3.5%)

n = the number of times the interest is compounded per year (quarterly)

t = the number of years the investment is held (7)

First, we convert the annual interest rate to a decimal: 3.5% = 0.035

Then we convert the interest rate to a quarterly rate by dividing by the number of times it is compounded per year: 0.035 / 4 = 0.00875

We can now substitute these values into the formula:

A = $2750(1 + 0.00875)^(4*7)

A = $2750(1.00875)^28

A = $2750(1.3471)

A = $3710.82

So, the amount of the investment after 7 years is $3710.82, rounded to the nearest hundredth.

The multiplier would be used to increase a number by 15% is, 1.15

The multiplicative rate of change is a number by which we get another number from the previous number, to get the value of this number , we have to divide the other number from the previous number.

Suppose

first number = X

second number = Y

second number is 15% more than first number

So, Y = X + 15% of X

Y = X + 0.15X

Y = 1.15 X

for multiplicative rate of change we have to apply divide operation,

⇒  P = Y/X

⇒  P = 1.15X/X

⇒  P = 1.15

Hence, the result is 1.15

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Answer:

-6/5

Step-by-step explanation:

Perpendicular definition is that two gradients multiplying each others must equal to -1. This can be written in the form of [tex]\displaystyle{m_1m_2=-1}[/tex] where m stands for gradient or slope.

First, we know that the gradient of a line is 5/6, we'd have to find another gradient that is perpendicular to each other. Hence, substitute in the equation:

[tex]\displaystyle{\dfrac{5}{6}m_2=-1}[/tex]

Solve for [tex]m_2[/tex], multiply both sides by 6 first:

[tex]\displaystyle{\dfrac{5}{6}m_2 \times 6=-1 \times 6}\\\\\displaystyle{5m_2=-6}[/tex]

Divide both sides by 5:

[tex]\displaystyle{\dfrac{5m_2}{5}=\dfrac{-6}{5}}\\\\\displaystyle{m_2=-\dfrac{6}{5}}[/tex]

Therefore, the gradient that is perpendicular to 5/6 is -6/5

The gradient of a line perpendicular to a line with a gradient of ⅚​ is -5/6.

We have,

A line perpendicular to a line with a gradient of ⅚​ will have a gradient that is the negative reciprocal of ⅚​.

The negative reciprocal of ⅚​ can be found by taking the reciprocal of ⅚​ (which is 6/5) and then negating the result.

So the gradient of the perpendicular line is:

-1/(6/5) = -5/6

Therefore,

The gradient of a line perpendicular to a line with a gradient of ⅚​ is -5/6.

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Answer:

Step-by-step explanation:

It has to be option D by looking at the question.

It says, that it is $5.50 per hour for kids.

If x is the hours, then total cost spent just for the kid will be $5.50x

It also says there is a flat $3 admission. So just add that to the equation.

$5.50x + 3 ≤ 20.

20 ( given)

Thanks

An integer which can be used to represent a diver's elevation if the diver is 40 feet below sea level is -40.

In Mathematics, an integer can be defined as a whole number that may either be positive, negative, or zero (0). This ultimately implies that, a positive integer simply refers to a whole number that is greater than or equal to one (1).

On the other hand (conversely), a negative integer simply refers to a whole number that is less than zero (0), but do not include decimals or fractions.

In this context, we can reasonably infer and logically deduce that an integer which can be used for representing a diver's elevation when he or she is 40 feet below sea level would be the negative integer -40.

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Answer: find zero on the number line then put a dot on -7/5 (-1 2/5) then do the same on positive 7/5 (1 2/5

Step-by-step explanation:

find zero on the number line then put a dot on -7/5 (-1 2/5) then do the same on positive 7/5 (1 2/5 . I think that is correct sorry if it isnt.

Step-by-step explanation:

Answer:

x = 17

Step-by-step explanation:

The sum of the interior angles of a triangle is 180

x + 17 + 4x - 34 + 6x + 10 = 180  Combine like terms

11x -7 = 180  Add 7 to both sides

11x - 7 + 7 = 180 + 7

11x = 187  Divide both sides by 11

[tex]\frac{11x}{11}[/tex] = [tex]\frac{187}{11}[/tex]

x = 17

Answer:

the answer is x=17 because the triangle is isosceles

The relationship between the trigonometric ratios of the non-right angles in a triangle and the measures of the angles are;

1.) c.) They are reciprocals

2.) a.) They are equal

3. b.) They are complementary

The non-right angles in a right triangle are he two acute angles in the right triangle.

1) Complementary angles are angles that have a sum of 90°

Let A and B be two complementary angles, we get;

m∠A + m∠B = 90°

Let a and b represent the lengths of the opposite sides to the complementary angles ∠A and ∠B

Let side a represent the side opposite to the angle ∠A and let side b  represent the side opposite to the angle ∠B, we get

tan(A) = a/b tan B = b/a

Therefore, tan(B) is the reciprocal of tan(A)

The correct option is c,) They are reciprocals

2) Let r represent the length of the hypotenuse of the right triangle, we get;

sin(A) = a/r

cos(A) = b/r

sin(B) = b/r

cos(B) = a/r

The values, sin(A) = cos(B), and sin(B) = cos(A), therefore;

3) The sum of angles in the right triangle is 180°, therefore;

m∠A + m∠B + 90° = 180°

m∠A + m∠B = 180° - 90° = 90°

m∠A + m∠B = 90°

The sum of the two non-right angles in a triangle is 90°,  therefore, the two non-right angles re complementary.

The correct option is therefore; b.) They are complementary

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Answer:

Step-by-step explanation:

will make a purchase is dependent on a variety of factors. These include the product or service being offered, the price point, the customer's needs and wants, the customer's current financial situation, and the salesperson's ability to effectively communicate the value of the product or service. Many businesses will use analytics and data to track customer purchasing habits and trends, as well as the effectiveness of their marketing and sales strategies. This allows them to better determine the probability of a sale. Additionally, a salesperson's past performance, customer relationships, and other factors all influence the probability of a sale. Ultimately, the probability of any given sale is unique to each customer and situation.

it would take 12 weeks to save and buy the iphone.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

Johny is saving money to buy an Iphone X which cost $1000.

He started saving money $300 he receieved for a birthday gift.

He saved allowance of $60 per week.

We need to find how long will it take for him to save and the Iphone X.

1000=300+60x

Subtract 300 from both sides

700=60x

Divide both sides by 60

700/60=x

11.66=x

Hence, it would take 12 weeks to save and buy the iphone.

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