Jessica has a sack of vegetables.
There are 3 carrots for every 4 potatoes
in the sack.
If there are 12 carrots in the sack, how
many potatoes are there?

Since AB || CD and m∠2 = 35° in Quadrilateral ABCD, the measure of angle 5 (m∠5) is equal to 35°.

In Mathematics, the Alternate Interior Angles Theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent.

Additionally, these angles are generally referred to as alternate interior angles. In this scenario, we can logically deduce the following information and parameters from Quadrilateral ABCD:

Therefore, we can logically deduce and conclude that m∠5 in Quadrilateral ABCD is equal to 35 degrees in accordance with the Alternate Interior Angles Theorem.

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The data that is shown in a frequency table can be displayed in:

There are several types of graphs that can be used to display data from frequency tables, including bar graphs, line graphs, and histograms. Bar graphs are a type of graph that use bars to represent different categories or groups of data, with the height of the bars representing the frequency of each category.

Line graphs are a type of graph that use a series of connected points to show trends or changes in data over time, with the height of the points representing the frequency of the data.

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Step-by-step explanation:

To model this situation, we can set up two equations: one for the bird and one for the leaf.

For the bird, we can let t be the time in seconds and h be the height of the bird in feet. We know that the bird flies up at a rate of 4 feet per second, so we can write the equation:

h = 4t

This equation represents the height of the bird at any given time t.

For the leaf, we can also let t be the time in seconds and h be the height of the leaf in feet. We know that the leaf drops from a height of 21 feet and floats to the ground at a rate of 3 feet per second, so we can write the equation:

h = 21 - 3t

This equation represents the height of the leaf at any given time t.

Together, these two equations form a system of equations that can be used to model the situation.

A) If the original cost of the car was $90000 and it now costs 34% more, the price has increased by 0.34*90000 = $30600. Therefore, the price today is 90000+30600 = $120600.

B) During the sale, the price of the bicycle dropped from $160 to $125, a difference of 160-125 = $35. This represents a decrease in price of 35/160 = 21.875%. Therefore, the percentage decrease in price is approximately 22%.

Jim's and Susan's lawn care businesses charge different rates for a 10-hour shift; the difference is $40.

The groupings of numbers include ones, tens, scores, tens, millions, and so forth. Ones, tens, or hundreds are the three subgroups that make up each group. When printing or reading a huge number, start with both the largest group on the left and work your way right.

work done = force × distance. W = F s. When the amount of work (W) is expressed in joules.

It will be Susan's Charge for ten hours.

= 168 + 72 $

= 240 $

while Jim Charges was for 10 hours

= 120 + 80 $

= 200$

The rates Susan and Jim charge during 10 hours of labor in their respective lawn care businesses are as follows:

= 240 - 200 $

= 40$

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The solutions of the linear equation is

x      y

-8    9

-6    8

-4    7

-2    6

0     5

2      4

4      3

6      2

8      1

10     0

the graph is a straight-line graph

The solutions of the linear equation is the found by substituting an x value and solve for y

the given equation 1/2x + y = 5, rearranging the equation gives

y = 5 - 1/2 x

For x = -8,  y = 5 - 1/2 * -8 = 9

For x = -6,  y = 5 - 1/2 * -6 = 8

For x = -4,  y = 5 - 1/2 * -4 = 7

For x = -2,  y = 5 - 1/2 * -2 = 6

For x = 0,  y = 5 - 1/2 * 0 = 5

For x = 2,  y = 5 - 1/2 * 2 = 4

For x = 4,  y = 5 - 1/2 * 4 = 3

For x = 6,  y = 5 - 1/2 * 6 = 2

For x = 8,  y = 5 - 1/2 * 8 = 1

For x = 10,  y = 5 - 1/2 * 10 = 0

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The percentage he has chopped is 25%

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

Total number of tomatoes = 60

Total number of chopped tomatoes = 15

The percentage he has chopped is then calculated as

Percentage = Total number of chopped tomatoes/Total number of tomatoes * 100%

Substitute the known values in the above equation, so, we have the following representation

Percentage = 15/60 * 100%

Evaluate

Percentage = 25%

Hence, the percentage is 25%

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Answer: One-third of a gallon divided by 3 gallons equals one-ninth.

Step-by-step explanation:  1/3 / 3/1  = 1/3 x 1/3 = 1/9

Using the addition method to solve the given system of equations, It can't be solved because these are the set of parallel lines.

An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A collection of one or more linear equations containing the same variables is known as a system of linear equations in mathematics. A set of two or more linear equations with two or more variables each constitutes a system of linear equations, all of which are taken into account simultaneously. Finding a numerical value for each variable in the system that will simultaneously satisfy all of the system's equations is necessary to identify the one and only solution to a system of linear equations.

There are three ways to solve systems of linear equations :

take first equation multiply it by 2 and subtract second equation from it,

We can't solve for any values,

This is because our equations are parallel in nature.

They never intersect each other.

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The probability to know of it is a fair game depends on how the spinner is designed.

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events.

It depends on how the spinner is designed and the probability of landing on each number. If the spinner is fair and each number is equally likely to be spun, then the probability of winning is 1/2, or 50%.

This means that over the long run, you would be expected to win half of the games you play. If you and your friend agree that these are the rules of the game and you both understand the probability of winning, then the game could be considered fair.

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The ratio of total points scored to games played for each player are  Kiara 7:1,  Cecilia = 6:1, and Kayleigh= 7:1. (b) The ratios of Kiara and Kayleigh are proportional

You should know that two ratios are proportional to each other if they are equal.  also, you should be aware that ratios show the number of times a number appears in another number when divided.

The parameters that will guide us to get these ratios are

Players             Number of games     Total points             Ratios

Kiara                               25                      175                         1:7

cecilia                             20                       120                       1:6

Kayleigh                          15                        105                       1:7

Therefore from the table shown above, the ratios of Kiara and Kayleigh are proportional with 1:7 respective.

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The percentage of the marks scored by Ravi is 72%.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that Ravi scored 18 marks out of 25 in a maths unit test. The percentage of the marks will be calculated as,

Percentage = ( Marks obtained / total marks ) x 100

Percentage = ( 18 / 25 ) x 100

Percentage = 0.72 x 100

Percentage = 72%

Hence, the percentage will be 72%.

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Answer:

9:37

Step-by-step explanation:

right!

Answer:

8:19

Step-by-step explanation:

Answer:

$50

Step-by-step explanation:

900 - 350 - 500

50

The volume of the top section of the figure is 16 cm³.

Given is the solid cuboidal figure as shown in the image.

The volume of the top cuboidal figure will be -

V = L x B x H

V = 2 x 2 x 4

V = 4 x 4

V = 16 cm³

Therefore, the volume of the top section of the figure is 16 cm³.

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The maximum area for each stall can be achieved when the width and length are equal, so the dimensions must be any value greater than 0.

a) Let x = width of each stall, y = length of each stall

b) Area of each stall = xy

c) Domain: x > 0, y > 0

Range: all real numbers

d) To maximize the area of each stall, we must maximize the product of x and y. Taking the derivative of xy with respect to both x and y, we get y = x. Therefore, the maximum area will be achieved when the width = length = x. Therefore, the dimensions that will produce the maximum area for each stall is x = x = any value greater than 0 so the dimensions must be any value greater than 0.

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The complete question is

pat has of feneing to enclose three identical stalls behind the barn. as shown. what dimensions will produce a maximum area for each stall? a) label correctly the given diagram at the side with chosen variables that must be identified. use let statements. b) express the area of the stalls as a function of its width. c) determine the domain and range of this area function. show your work. domain: range: d) determine the dimensions thst would produce a maximum area for each stall.

The equation that can be used to find the number of peaches Muriel has is; 2 + 3·x = 17

A mathematical equation is a statement that has two expressions, joined by the equals to, '=' sign.

The number of peaches Frances has = 17

Let x represent the number of peaches Muriel has

Therefore;

The number of peaches Frances has = 2 + 3·x

Which indicates through substitution property, that we get;

17 = 2 + 3·x

The equation that can be used to find the number of peaches Muriel has, x is; 17 = 2 + 3·x

Solving for x in the above equation, we get;

17 = 2 + 3·x

3·x = 17 - 2 = 15

x = 15 ÷ 3 = 5

The number of peaches Muriel has, x = 5 peaches

The 17 peaches Frances has and the indication that Frances has 2 more than 3 times the number of peaches Muriel has, indicates that the equation that could be used to find the the number of peaches Muriel has is; 17 = 2 + 3·x

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m+n = 8. The probability that Kathy will be happy is 3/8. This can be seen by counting the total number of possible arrangements of red and green cards that would make her happy (6). There are a total of 8 arrangements, so the probability is 3/8.

There are 6 possible arrangements of red and green cards that would make Kathy happy:

RRRRR, GGGGG, RRGGG, GGRRR, GRRRG, and RGGGR.

There are a total of 10 cards and 5 of them are laid out in a row, so the total number of arrangements is

10C5 = 10!/5!(10-5)!

= 10*9*8*7*6/5*4*3*2*1

= 10*9*8/5*4*3

= 8*9

= 72.

The probability that Kathy will be happy is the number of arrangements that make her happy (6) divided by the total number of arrangements (72). Therefore, the probability is

6/72

= 3/8.

Therefore, m+n = 8.

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Answer:

x = -5

Step-by-step explanation:

6(x+2) = (5x+7)

6x + 12 = 5x + 7

x = -5

Senior Math Online Content Active ical Models with Applications - MA4072 A Click to read the online material. when an element is removed from the RHS or LHS.

Think about a single-variable equation 2 x+5=4 x+3

If a variable is not dropped from either the LHS or the RHS, we obtain a different solution.

Put the variable on one side and the constant on the other.

[tex]$$\begin{aligned}& \rightarrow 4 x-2 x=5-3 \\& 2 x=2\end{aligned}$$[/tex]

on both sides, divide by two.

x=1

We will now only have constants, which may or may not be equal, if we remove the variables from both sides.

Now, suppose LHS if we drop inequality from one side.

4 x+3=5

4 x=5-3

[tex]$$\begin{aligned}& 4 \mathrm{x}=2 \\& x=\frac{2}{4} \\& =\frac{1}{2}\end{aligned}$$[/tex]

We eliminate inequity from the opposite side, or RHS.

[tex]$$\begin{aligned}& 5+2 x=3 \\& 2 x=3-5 \\& 2 x=-2\end{aligned}$$[/tex]

By dividing by 2, x equals -1 on both sides. As a result, we have three different solutions when no variable is dropped from any side; and when a variable is dropped from either the LHS or the RHS.

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There will be approximately 1.9 billion rabbits after 30 days. It will take approximately 9.8 days for the population of rabbits to reach 10,000.

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

a) To find the number of rabbits after 30 days, we can substitute 30 for t in the equation [tex]P(t) = 18(2)^t[/tex]:

[tex]P(30) = 18(2)^{30}[/tex]

= 18 × 1073741824

= 1934917632

So there will be approximately 1.9 billion rabbits after 30 days.

b) To find the time it takes for the population to reach 10,000 rabbits, we need to solve the equation P(t) = 10,000 for t. We can do this by first dividing both sides of the equation by 18 to get:

(1/18)P(t) = (1/18)(10,000)

[tex](2)^t = (10,000/18)[/tex]

We can then take the logarithm of both sides of the equation with base 2:

t = log₂((10,000/18))

= log₂(555.56)

= 9.8

Therefore, tt will take around 9.8 days for the rabbit population to reach 10,000.

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According to the given statement  if Divisor = 5,  Dividend = 3075 then The quotient is 615.

Division is an arithmetic operation that is the inverse of multiplication. It is used to determine how many times one number, called the divisor, is contained within another number, called the dividend. The result of the division is called the quotient.The three most widely discussed are the Commutative, Associative, and Distributive Laws.

The quotient is 615.

You can find this by dividing the dividend (3075) by the divisor (5) using long division or by using the formula: Quotient = Dividend / Divisor

In this case, 3075 / 5 = 615

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The fee is 50$

Step-by-step explanation: The way I got this is by checking the differences between each month and finding out that each one is 30 and then I subtracted it from 80 and got 50$

Refer to the image uploaded, all the steps included

Step-by-step explanation:

-13 x 4 = -52

-52 x 0.5 = -25

-2 x 0.5 = -1

-1 + -25 = -26

Step-by-step explanation:

p and q are parallel.

let's first only look at a and it's intersections with p and q.

based on the rules of intersecting lines (the angles of intersecting lines are the same in both sides of any of the lines, they are only left-right mirrored) and then parallel lines at that (the intersecting angles of a line with parallel lines are the same with every parallel line, otherwise they are not parallel).

angle 2 = angle 5 = angle 10 = angle 13

therefore,

8x + 14 = 10x - 10

14 = 2x - 10

24 = 2x

x = 24/2 = 12

angle 2 = 8×11 + 14 = 88 + 14 = 102°

because of the same rules of intersecting lines and parallel lines. it is also clear that

angle 4 = angle 7 = angle 12 = angle 15

therefore,

13y + 19 = 15y + 5

19 = 2y + 5

14 = 2y

y = 14/2 = 7

angle 4 = 13y + 19 = 13×7 + 19 = 91 + 19 = 110°

if a and b would be parallel too, then the principle of the same angles would be true not only top-down (as for the pervious 2 problems) but also left-right.

and then angle 2 would be equal to angle 4.

but they are not.

although the difference is small, it means a and b will intersect somewhere.

and they are therefore not parallel.

The polynomial in the standard form is 4m³ - 9m² - m + 25. Then the polynomial is a cubic polynomial.

A polynomial expression is an algebraic expression with variables and coefficients. Unknown variables are what they're termed. We can use addition, subtraction, and other mathematical operations. However, a variable is not divisible.

The polynomial is given below.

⇒ 25 - 9m² - m + 4m³

Convert the polynomial into its standard form. Then we have

⇒ 25 - 9m² - m + 4m³

⇒ 4m³ - 9m² - m + 25

The degree of the polynomial is 3. Then the polynomial is a cubic polynomial.

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A pair of alternate interior angles given that g || h include the following: D. <5 and <7.

In Mathematics, parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.

The Alternate Interior Angles Theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent. Additionally, these angles are generally referred to as alternate interior angles.

In this scenario, we can logically conclude that angle 5 and angle 7 forms a pair of alternate interior angles because line g is parallel to line h.

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After the discount and the tax is applied, the final cost of the shoes is $42.21

Remember that if the original price is P, and we have a discount of X, the new price will be:

P' = P*(1 - X/100%)

If instead we have an increase, like a tax, the new price will be:

P' = P*(1 - x/100%)

Here the original price is $67, first we apply a discount of 40% so we get:

P' = $67*(1 - 40%/100%)

P' = $67*(1 - 0.4)

P' = $67*(0.6)

And now we apply a tax of 5%, then the final price will be:

P'' = $67*(0.6)*(1 + 5%/100%)

P'' = $67*(0.6)*(1.05) = $42.21

The final cost of the shoes is $42.21

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