Exo math 30 page 229

1. The expression of each ratio as a fraction in the simplest form is as follows:

2. Writing the ratio of red to yellow pots of flowers three different ways are as follows:

3. Expressing each rate as a unit rate is as follows:

A ratio is the unit rate, which is the quotient of one value compared to another.

The quotient of the value is the division of one quantity by another.

a)  26:169 = 26/169 = 2/13

b. 36 to 78 = 36/78 = 12/26 = 6/13

The number of houses with a pot of red flowers = 32

The number of houses with a pot of yellow flowers = 24

The ratios of red to yellow pots of flowers in three different ways = 32: 24

The sum of ratios = 56 (32 + 24)

a) 32:24 = 4:3 = 1.75:1

b) 32:24 = 57% (32/56 x 100)

c) 32:24 = 0.57 (32/56)

a. 32 teams in 4 divisions = 8 team per division (32/4)

b. $2.70 for 15 ounces = $0.15 ($2.70/15)

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Answer: The answer is 14mm

Step-by-step explanation: Area of A= 4mm times 2mm= 8mm

                                             Area of B= 3mm times 2mm= 6mm

8mm + 6mm= 14mm

How I got Area A or Area of A Is I divided the shape into two with an imaginary line

Answer:

See below.

Step-by-step explanation:

We are asked to find the area of the figure.

Let's first break the figure into 2 parts, where there is 2 rectangles.

Rectangle A has the dimensions of 4 mm to 2 mm.

Rectangle B has the dimensions of 3 mm to 2 mm.

For clarification what rectangle is which, Rectangle A is on its smallest side, and Rectangle B is on its longest side.

To find the area of the 2 rectangles we multiply the 2 dimensions given to us, then add their areas together.

[tex]A = L \times W[/tex]

Substitute:

[tex]8 = 4 \times 2 \ (Rectangle \ A)[/tex]

[tex]6 = 3 \times 2 \ (Rectangle \ B)[/tex]

Add:

[tex]6+8=14 \ (A \ and \ B)[/tex]

The area of the figure is 14 mm².

Answer:

The given expression is:

p^2 + 4q^2 + 9 + 36 + pq + 3 + 4q + 6p

Rearranging the terms, we get:

p^2 + 6p + 4q^2 + pq + 4q + 48

Now, we can group the first three terms and the last three terms together as follows:

(p^2 + 6p + 9) + (4q^2 + pq + 4q + 39)

The first group can be factorized as a perfect square trinomial:

(p + 3)^2

The second group can be factorized by grouping the first two terms and the last two terms:

(pq + 4q) + (4q^2 + 39)

We can factor out q from the first two terms, and 4 from the last two terms:

q(p + 4) + 4( q^2 + 9)

Now, we can factor the second group as a sum of squares:

q(p + 4) + 4(q + 3)(q - 3)

Therefore, the fully factorized form of the expression is:

(p + 3)^2 + q(p + 4) + 4(q + 3)(q - 3) + 48

Note that this expression cannot be simplified further.

Answer: B, a counterclockwise rotation of 270 degrees about the origin.

The cost of one dinner without any sides is $2, and the cost of 6 dinners without any sides is 6 times that amount, which is $12. Answer: $12.

An equation is a statement that asserts the equality of two expressions. Equations typically contain one or more variables, which are quantities that can take on different values. The goal of solving an equation is to find the values of the variables that make the equation true.Equations can take many different forms, but some common types include linear equations, quadratic equations, polynomial equations, and exponential equations.

An expression is a combination of numbers, variables, and mathematical operations that represents a value. Expressions can contain constants, variables, and operators, such as addition, subtraction, multiplication, and division.

In the given question,

There are different ways to approach this problem, but one possible method is to use ratios. Let's assume that the cost of a dinner without any sides is x dollars. Then, the cost of a dinner with salad is x plus some additional amount for the salad, which we don't know yet. Let's call this additional amount y dollars. Therefore, the cost of a dinner with salad is x + y dollars.

According to the problem, Russell can buy 6 dinners with salads for $114. This means that the total cost of 6 dinners with salads is $114. We can write this as an equation: 6(x + y) = 114

Simplifying this equation, we get: 6x + 6y = 114

Dividing both sides by 6, we obtain: x + y = 19

Now we need to find the cost of 6 dinners without any sides, which is 6 times the cost of a dinner without any sides. We already know that the cost of one dinner without any sides is x dollars, so the cost of 6 dinners without any sides is 6x dollars.

To find x, we can use the fact that x + y = 19, which we derived from the given information. We don't know y, but we can express it in terms of x by using the fraction of the salad price to the total price of a dinner with salad. From the long division, we have:

2x - 3

x + 1

This means that y is equal to the remainder of the division, which is -3/(x+1). Therefore, we have: y = -3/(x+1)

Now we can substitute this expression for y into the equation x + y = 19:

x - 3/(x+1) = 19

Multiplying both sides by x+1, we get: x(x+1) - 3 = 19(x+1)

Expanding the products and simplifying, we obtain a quadratic equation:

x^2 + 18x - 22 = 0

We can solve this equation by using the quadratic formula:

x = (-18 ± √(18^2 + 4122)) / (2*1)

x = (-18 ± √(400)) / 2

x = (-18 ± 20) / 2

x = -9 or x = 2

Since we are interested in the cost of a dinner without any sides, which should be a positive number, we discard the negative solution and take x = 2. Therefore, the cost of one dinner without any sides is $2, and the cost of 6 dinners without any sides is 6 times that amount, which is $12. Answer: $12.

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There are initially 150 pharaoh ants in Southeast Asia, and every year the population increases by 950,000 ants.

The rate of change of a function refers to how much the output of the function changes with respect to changes in its input, typically expressed as the derivative of the function.

The initial value of a function refers to the value of the function at a specific point in its domain, often denoted as f(0) or f(x_0) for some value x_0 in the domain. It is called "initial" because it is usually the starting point for analyzing the behavior of the function over a range of inputs.

The given function is y=-150x+950,000, where x represents time in years and y represents the total population of pharaoh ants in Southeast Asia.

The initial value of the function is the y-intercept, which is 950,000. This means that at the beginning of the observation period (when x=0), there are 950,000 pharaoh ants in Southeast Asia.

The rate of change of the function is the coefficient of x, which is -150. This means that every year, the population decreases by 150,000 ants. Therefore, option A is correct because it states that the population decreases every year by 150,000 ants, which is the same as -150 multiplied by 1,000.

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Answer:

Step-by-step explanation:

A curriculum is said to as "integrated" when it simultaneously targets learning objectives across different topic areas.

Children can pursue learning holistically with an integrated curriculum, free from the limitations frequently imposed by topic boundaries.

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Answer:

10 2/3 kg

8 X 1 1/3 kg = 10 2/3 kg

Hence, in response to the provided question, we can say that Hence, the solutions to the equation [tex]Ax^2 - 3x = 0 are x = 0 and x = 3/A.[/tex]

An algebraic equation is a method of connecting two quotes by using the equals symbol (=) to express equality. In algebra, an explanation is a definitive expression that verifies the equivalency of two formula. For example, the identical character divides the numbers 3x + 5 and 14. A linear equation might be used to recognize the connection that existing between the texts written on separate sides of a letter. The product and application both frequently the same. 2x - 4 equals 2, for example.

We can factor out x to get the answer to the equation Ax2 - 3x = 0.

x(Ax - 3) = 0

We can set each factor to zero and solve for x because the product of two factors is zero if and only if one or both of the factors are zero.

x = 0 or Ax - 3 = 0

If A is greater than zero, we can solve the second equation for x by adding 3 to both sides and dividing by A:

[tex]Ax-3 = 0 Ax-3 = 3 x = 3/A[/tex]

Hence, the solutions to the equation[tex]Ax^2 - 3x = 0 are x = 0 and x = 3/A.[/tex]

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The solution for the equation ax² - 3x = 0 are x = 0 and x = 3/a.

The equals sign (=), which expresses equality, is a way to join two quotes in an algebraic equation. An explanation in algebra is a conclusive phrase that confirms the similarity of two formulas. The same letter, for instance, divides the integers 3x + 5 and 14.

The relationship between the texts written on the different sides of a letter can be determined using a linear equation. Products and applications are usually interchangeable. In this case, 2x - 4 equals 2.

From the question,

We can factor out x to get the answer to the equation ax² - 3x = 0.

x (ax - 3) = 0

The product of two factors is zero if and only if one or both of the factors are zero, thus we can set each element to zero and find x.

x = 0 or ax - 3 = 0

By adding 3 to both sides and dividing by a, we may solve the second equation for x if a is greater zero:

ax = 3

⇒ x = 3/a

Therefore, the solutions of the equation are x = 0 and x = 3/a.

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Answer:

B. F(x)=x^5

Step-by-step explanation:

Answer:60

Step-by-step explanation:

Answer: Your welcome!

Step-by-step explanation:

The equivalent fractions for 3/10 and 1/7 using the least common denominator are 6/20 and 3/20. The least common denominator of 3/10 and 1/7 is 20, so the fractions must be multiplied by the same number to reach the denominator of 20. 3/10 multiplied by 2/2 is 6/20, and 1/7 multiplied by 3/3 is 3/20.

The box and whiskers plot is made up of five points: the minimum, the first quartile (Q1), the median (Med), the third quartile (Q3), and the maximum. The minimum is the lowest value in the dataset and the maximum is the highest value in the dataset.

Median is the middle number in a set of numbers when the numbers are arranged in order from least to greatest. It is a type of measure of central tendency, which provides an indication of the “middle” value in a set of numbers. It is often used to measure the average of a set of numbers, particularly when there are extremely large or small values in the set.

The box and whiskers plot for this set of data is a visual representation of the data that makes it easier to interpret. The first quartile is the value that is 25% of the way through the dataset and the third quartile is the value that is 75% of the way through the dataset. The median is the middle value in the dataset.

To create a box and whiskers plot for this set of data, the minimum is 2, the first quartile is 4, the median is 5, the third quartile is 10, and the maximum is 14. The box and whiskers plot would then be represented by the following graph:

|                                 |

| 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |

|    |    |    |    |    |    |    |    |    |    |

|  2 |  4 |  5 | 10 | 14 |

The box and whiskers plot graphically illustrates the spread of the data and allows us to easily compare the data to other datasets. It is also useful for identifying outliers in the dataset, as any value outside of the box and whiskers plot is considered an outlier.

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Answer:

the answer is C.

Step-by-step explanation:

Put both equations in the slope intercept form of the line and then graph to estimate where the lines cross.

y = mx + b

7x - y = 7   The 7x is on the wrong side of the equal sign, so subtract 7x from both sides of the equation

7x - 7x -y = -7x + 7

-y = -7x + 7  We want the equation to start y = , not -y =. so divide all the way through by -1

[tex]\frac{-1y}{-1}[/tex] = [tex]\frac{-7x}{-1}[/tex]  + [tex]\frac{7}{-1}[/tex]

y = 7x - 7

x + 2y = 6   The x is on the wrong side of the equal sign.  Subtract x from both sides

x -x + 2y = -x + 6

2y = -x + 6  Divide all the way through by 2

[tex]\frac{2y}{2}[/tex] = [tex]\frac{-1}{2}[/tex]x + [tex]\frac{6}{2}[/tex]

y = [tex]\frac{-1}{2}[/tex] x + 3

You can see from the graph attached where the lines cross.  

Helping in the name of Jesus.

The congruency statement of the line congruent to VU is: VU ≅ VY

An isosceles triangle is defined as a triangle that has two sides of equal length and its corresponding angles are equal in measure .

When two straight lines are cut by a transversal, then the angles formed on the opposite side of the transversal with respect to both the lines are called alternate angles.

Thus:

∠TWU ≅ ∠YUW

By inspection, ΔTUW is an isosceles triangle and as such UT ≅ UW.

Since ∠TWU ≅ ∠YUW, then UY is parallel to TX. Thus:

UW ≅ YX and VU ≅ VY

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Answer:

Step-by-step explanation:

To find the constant of proportionality, we can use the formula for a proportional relationship: y = kx, where y is the total cost, x is the number of songs, and k is the constant of proportionality.

Using the table, we can find two pairs of values for y and x:

When x = 6, y = $1.80

When x = 12, y = $3.60

We can set up a proportion:

y1 / x1 = y2 / x2

$1.80 / 6 = $3.60 / 12

Simplifying, we get:

$0.30 = $0.30

This tells us that the constant of proportionality is $0.30.

We can check this by using another pair of values:

When x = 20, y = $6

Using the formula y = kx, we get:

$6 = ($0.30)(20)

Simplifying, we get:

$6 = $6

This checks out, so we can be confident that the constant of proportionality is $0.30.

The y-intercept is (0, 9), and the parabola has no x-intercepts.

An intercept in mathematics is a location on the y-axis through which the line's slope passes. It is a place on the y-axis where a straight line or a curve crosses. This is reflected in the equation for a line, which is written as y = mx+c, where m denotes slope and c denotes the y-intercept.

X-intercept and Y-intercept are the two main intercepts. The line's x-intercept and y-intercept are located where the line crosses the x and y axes, respectively.

To find the y-intercept of the parabola, we set x = 0 and solve for y:

y = 3x² - 9x + 9

y = 3(0)² - 9(0) + 9

y = 9

Therefore, the y-intercept is (0, 9).

To find the x-intercepts, we set y = 0 and solve for x:

0 = 3x² - 9x + 9

0 = x² - 3x + 3

Using the quadratic formula, we get:

x = [3 ± √((-3)² - 4(1)(3))]/(2(1))

x = [3 ± √(9 - 12)]/2

x = [3 ± √(-3)]/2

The square root of a negative number is not a real number.

The parabola does not intersect the x-axis, and therefore, there are no x-intercepts.

Therefore, the y-intercept is (0, 9), and the parabola has no x-intercepts.

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[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{-6}~,~\stackrel{y_2}{4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{2}}}{\underset{\textit{\large run}} {\underset{x_2}{-6}-\underset{x_1}{4}}} \implies \cfrac{ 2 }{ -10 } \implies - \cfrac{ 1 }{ 5 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{- \cfrac{ 1 }{ 5 }}(x-\stackrel{x_1}{4}) \\\\\\ y-2=- \cfrac{ 1 }{ 5 }x+\cfrac{4}{5}\implies y=- \cfrac{ 1 }{ 5 }x+\cfrac{4}{5}+2\implies {\Large \begin{array}{llll} y=- \cfrac{ 1 }{ 5 }x+\cfrac{14}{5} \end{array}}[/tex]

The different circumferences to go from the start to the finish are 21.98, 31.4, 37.68, and 65.94.

One of the ways of calculating the circumference is using the diameter of a circle (distance from one side to the next one) and applying the formula circumference = diameter x [tex]\pi[/tex]. Now, let's calculate the circumference.

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The net worth of the landscaping company is given by:

$187.205.

How to calculate the net worth?

The net worth of a company or of a person is given by the sum of all assets of the person subtracted by the sum of all debts of the person.

In the context of this problem, the assets, and it's values, of the company are given as follows:

Owned Inventory: $48,760.

Cash: $126,790.

Savings account: $32,436.

Owned equipment: $20,700.

Accounts receivable: $15,640.

Property value: $225,678.

Hence the sum of the assets is given by:

Assets = 48760 + 126790 + 32426 + 20700 + 15640 + 225678 = $469,994.

The debts of the company, with it's values, are given as follows:

Small Business Loan: $76,400.

Building Mortgage: $189,429.

Other debt: $16,970.

Hence the sum of the debts is given by:

Debts = 76400 + 189429 + 16970 = $282,799.

Then the net worth of the company is:

Net worth = Assets - Debt = 469,994 - 282,799 = $187,205.

Answer:

a. 13n

Step-by-step explanation:

product signifies multiplication and 13n=13xn

a. 13

Answer:

6

Step-by-step explanation:

This is a right triangle, so the point is C(-2, -2), so 2+4=6

Answer:

3m=24

m=8

12m=96

24m=192

48m=384

96m=768

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Answer: I believe the answer would be 130°

Step-by-step explanation:

Answer:

The angle A will remain the same irrespective of their rotation so it will be 130°.

Step-by-step explanation:

Answer:  1863[tex]\pi[/tex] cm^3  (option C)

Step-by-step explanation:

The volume is given by the equation

[tex]V=\pi r^2h[/tex]
Just placing the values:
[tex]V=\pi (9)^2(23)[/tex]
Notice the pi is left over, so just get the 9^2*23=1863
So the answer for the volume is 1863[tex]\pi[/tex] in cm^3

So your answer is just fine, 5849. Just notice the pi is not in it.

There are 3/8 more white paint on the palette of the highest than the least

A line plot is a type of graph or simple data visualization tool that uses dots to represent individual data points along a numerical axis.

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

The line plot

On the line plot, we have

Most white paint = 3/4

Least white paint = 3/8

Calculate the difference between both so, we have

Amount = 3/4 - 3/8

Evaluate

Amount = 3/8

Hence, the amount is 3/8

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