Priya’s Pet Store never has more than a combined total of 20 cats and dogs and never more than 8 cats. This is represented by the inequalities x+y≤20
and x≤8
. Represent the number of cats and dogs that can be at the store on a graph. Solve the system of inequalities by graphing.
Need help graphing it and finding where the two inequalities meet.

The number of different outfits cory can make is 270 ways.

Each of the different groups or selections can be formed by taking some or all of a number of objects, irrespective of their arrangements is called a combination. The various ways in which objects from a set may be selected, generally without replacement to form subsets is known as combination.

Given;

He has 5 pairs of pants to pick from, 18 shirts , and 3 pairs of shoes

Now, the combination;

=5*18*3

=270

Therefore, the combinations will be 270.

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Answer:

The system of equations are solved by eliminating a variable and solving for the remaining variable. Add the two equations together to eliminate the y, then solve for x.

Answer:

- 3cos²Θ

Step-by-step explanation:

using the identity

sin²Θ + cos²Θ = 1 , then

sin²Θ = 1 - cos²Θ

given

3sin²Θ - 3

= 3(1 - cos²Θ) - 3

= 3 - 3cos²Θ - 3

= - 3cos²Θ

He had a taxable income of $-748.01 last year, which means he did not owe any federal income tax for the period.

What is simple interest?

The simple interest method, which always adds interest to the starting principal amount at the same rate for each time cycle, is a quick and easy way to calculate interest on money. Any bank where we deposit money will return our investment with interest. Simple interest is one of the several forms of interest that banks charge. Now, before going into any detail on the concept of fundamental curiosity,

The formula for simple interest is:

S = p*t*r/100

The part-time receptionist's taxable income would be calculated by deducting their exemptions and standard deduction from their gross income. The person's gross income was $9101.99. A $3650 exemption was requested by the person. They also qualified for a $5700 standard deduction.

We can figure out their taxable income by deducting the exemption and standard deduction from their gross income. $9101.99 - $3650 - $5700 = $-748.01 would be used to compute the taxable income.

Hence He had a taxable income of $-748.01 last year, which means he did not owe any federal income tax for the period.

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If a rock needs to weigh 2,000 lb in order not to be shifted by waves, the volume of this basalt rock is equal to 0.625 in³.

In Science, the density of a chemical substance such as lead can be calculated by using this formula:

Density = M/V

Where:

Making volume the subject of formula, we have the following:

Volume = Mass/Density

Volume = 2,000/3,200

Volume = 0.625 in³.

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Answer:

12

Step-by-step explanation:

45 total

2/3 * 45 = 30 gave speeches

so 15 remaining

1/5 *15 = 3 gave speeches

remaining 12 didn't

The distances of the following places are:

Camp → waterfall = 2.25 km

waterfall → meadow = 4.5 km

meadow → camp = 9 km

Speed is the ratio of distance and time.

It shows how fast an object is moving at a given time.

We have,

Places traveled:

Camp → waterfall → meadow → camp.

We are assuming the time taken as follows:

Camp → waterfall = 30 minutes = 0.5 hour

waterfall → meadow = 1 hour

meadow → camp = 2 hours.

Now,

Speed = 4.5 km per hour.

Speed = Distance / Time

So,

The distance between camp → waterfall.

= 4.5 x 0.5

= 2.25 km

The distance between the waterfall → meadow.

= 4.5  x 1

= 4.5 km

The distance between the meadow → camp.

= 4.5 x 2

= 9 km.

Thus,

The distances are:

Camp → waterfall = 2.25 km

waterfall → meadow = 4.5 km

meadow → camp = 9 km

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The rate of the westbound train is 85miles per hiur

Velocity is the rate of change of displacement with time. It is measured in meter per second. It is a vector quantity.

Since the two trains move at the same time and in opposite directions, then the total displacement (d) = d1 - d2

900 = (vt)1 - (Vt)2

if v1 is the eastbound train velocity and v2 is the westbound train velocity

v1 = v2+10

they have thesame time of 5hours

therefore;

900 = (v2+10-(-v2)(5)

900 =( 2v2+10)5

divide both sides by 5

180 = 2v2 +10

2v2 = 170

v2 = 170/2

v2 = 85

therefore the rate of the westbound train is 85 miles per hour

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Answer:

f(-4) = -18

Step-by-step explanation:

So we have f(x) and we have f(-4). The X is where the -4 is so that means x = -4.

Since we know that, we plug it into the equation. Everywhere we see an X

So instead of 5(x) + 2, it will be 5(-4)+2.

5 times -4 is -20, which makes it -20 + 2

-20 + 2 = -18. Giving us our answer

Answer:

[tex]-18[/tex]

Step-by-step explanation:

f is a function of x. f depends on x. For every value of x, a certain value of f(x) is obtained.

This question requires us to determine the value of f(x) for x = [tex]-4[/tex]:

Substitute x = [tex]-4[/tex] into the provided function:

[tex]f(-4) = 5(-4) +2[/tex]

         = [tex]-20 + 2[/tex]

         = [tex]-18[/tex]

Answer:

Step-by-step explanation:

We can set up a proportion to solve for the unknown amount of gasoline needed:

distance traveled / amount of gasoline = constant

Let x be the amount of gasoline needed to travel 155 miles. Using the given information, we can set up the following proportion:

713 miles / 23 gallons = 155 miles / x

Simplifying, we get:

x = (155 miles * 23 gallons) / 713 miles

x = 5 gallons (rounded to the nearest gallon)

Therefore, the car needs 5 gallons of gasoline to travel 155 miles.

The dimension of rectangular dining room measures length 24.3 and breadth  1.73 metres.

In mathematics, dimensions refer to the length or width of an area, region, or space in one direction. It is just the measurement of something's length, width, and height. Length, breadth, and height are common ways to describe dimensions.

Our world has three dimensions.

Height, length, and width are the three dimensions that define everything around us, including the homes we live in and the everyday items we use.

Length, breadth, and height are the common three dimensions that can be described in three distinct ways.

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To get 4 pairs of blue socks, on average, you would need to choose 16 pairs of socks at random.

The number of socks chosen at random will be denoted by the letter "n." Given by: The anticipated number of blue socks in "n" pairs

Expected number of blue socks = n * 1/4

In order for there to be four blue socks as expected, we need to determine the value of "n." Thus, we can construct the equation:

n * 1/4 = 4

And solving for n:

n = 4 / (1/4) = 4 * 4 = 16

So, To get 4 pairs of blue socks, on average, you would need to choose 16 pairs of socks at random.

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Divergence and curl are two important concepts in vector calculus. They are used to describe the behaviour of vector fields, which are functions that assign a vector to each point in space.

Divergence is a scalar function that describes the extent to which a vector field is spreading or contracting at a given point. If the vector field is spreading, the divergence at that point is positive; if it is contracting, the divergence is negative.

If the vector field is unchanged in size, the divergence is zero. The formula for the divergence of a vector field is given by the dot product of the gradient of the field with the unit normal vector at a point.

Curl, on the other hand, is a vector function that describes the rotational aspect of a vector field. It is defined as the cross-product of the del operator and the field. Curl measures the rate at which the vectors in a field are rotating about a point. If the curl is zero, the field is said to be irrotational. If the curl is non-zero, the field is said to be rotational.

Divergence and curl cannot be defined for a scalar function because a scalar function assigns a single scalar value to each point in space, while divergence and curl describe the behaviour of vector fields.

A scalar function has no direction or rotational component, so there is no way to describe the spreading or contracting behaviour or the rotational behaviour of the function.

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The required probability is 0.112 × [tex]10^-^1^3[/tex]

In the combination, ordering of items does not consider important when we need to determine the number of ways to select the _k_ items from the total _m_ items. There will be two cases in selecting the items- one in which repetition allowed, and the other is repetition not allowed.

Total Number of US senators (n) =100

Number of politicians to be chosen (r) = 50

Total number of ways in which 50 politicians can be chosen from 100 senators is:

[tex]C^n_r = C^1^0^0_5_0[/tex]

Number of senators in each US state = 2.

The number of ways in which senator can be chosen such that each state is represented = [tex]2_C_1[/tex]

Thus, the number of ways in which senator can be chosen for 50 states is:

[tex](2_C_1)^5^0[/tex]

Let A be an event that a politician is chosen such that each state is represented.

P(A) = [tex]\frac{2^5^0}{100_C_5_0}[/tex]

By solving, we get:

P(A) = 0.112 × [tex]10^-^1^3[/tex]

Hence, the required probability is 0.112 × [tex]10^-^1^3[/tex]

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The segment [P3, P4] satisfies the minimum requirements, and the minimal price value is $840.

Let X be the amount of mix A (in pounds), and Y be the amount of mix B.

The constraints are

20X + 10Y >= 400

10X + 30Y >= 960

5X + 10Y >= 210

X >= 0,  Y >= 10.

The objective function to minimize is  F(X, Y) = 20X+40Y.

In the equivalent form, the constraints are

2X + 1Y >= 40

X+ Y >= 33

X+2Y >= 42

The feasibility area is the infinite area in the first quadrant which lies ABOVE each of the following straight lines :

A red   (which represents the constraint (1'));

The green (which represents the constraint (2')),

A blue  (which represents the constraint (3')).

Plot 2X + 1Y = 40 (const. (1'), red);  

X+Y = 33 (const. (2'), green)

X+2Y = 42 (const. (3'), blue)

The four corner points of the area are:

P1 = (0,40), P2 = (7,26), P3 = (24,9), P4 = (42,0)

As per the Linear Programming method, we can calculate and compare the values at these 4 points.

These values of P1, P2, P3,P4 are:

P1: F(0,40) = 0 + 40*40 = 1600

P2: F(7,26) = 20*7+40*26 = 1180

P3: F(24,9) = 20*24+40*9 = 840

P4: F(42,0) = 20*42+0 = 840.

By comparing the numbers, any value of (X, Y) that lies on the segment [P3, P4] satisfies the minimum requirements.

The segment [P3, P4] satisfies the minimum requirements, and the minimal price value is $840.

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The value of x of the parallelogram is x = 38

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The four types are parallelograms, squares, rectangles, and rhombuses

Properties of Parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent.

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

Given data ,

Let the parallelogram be represented as ABCD

Now , the diagonals of the parallelogram are AC and BD

The measure of DE = 31

The measure of EB = x - 7

Now , Each diagonal of a parallelogram separates it into two congruent triangles where the measure of AC = BD

So , substituting the values in the equation , we get

BD = BE + DE and BE = DE

On simplifying the equation , we get

31 = x - 7

Adding 7 on both sides of the equation , we get

x = 31 + 7

x = 38

Hence , the measure of x of parallelogram is 38

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Answer:

1+(2×m)

Step-by-step explanation:

We can break the problem down and find the keywords.

1 plus the product of 2 and m

plus=+

product=×

1+(2×m)

Answer:

she can buy 2 outfits

Step-by-step explanation:

Gabriel would have $45,985.67 more than Ava in his account. This is because Gabriel's account is compounded daily, meaning that his interest would be compounded 365 times a year, while Ava's account is compounded continuously,

Compounding is the process of combining two or more elements to create a new, more complex product. In finance, compounding refers to the interest earned on an investment that is reinvested and earns additional interest. This cycle continues, allowing the principal to grow exponentially over time. The effective rate of return is greater than the stated interest rate.

The calculation for Gabriel's account is: 23,000 * (1.11^(365*8)) = $69,985.67. The calculation for Ava's account is: 23,000 * e^(0*8) = $24,000. The difference between the two is $45,985.67.

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Answer:997

Step-by-step explanation:

The cost of Nadine's order was found by multiplying the number of t - shirts she ordered, by their individual cost, and then deducting the value of the coupon.

The order was that Nadine bough4 t - shirts for her class club from a website.

Each of these shirts cost $ 10. 95. But, Nadine gets a coupon of $ 12. 50 to be deducted from the total order.

To find the cost therefore, we can multiply the cost of the shirts and the number of shirt and then deduct the value of the coupon as shown in the formula :

= ( Cost of shirt x Number of shirts ) - coupon

= ( 10. 95 x 4 ) - 12. 50

= $ 31. 30

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The full question is:

Nadine ordered 4 t-shirts for her class club form a website. Each shirt is $10.95 and Nadine has a coupon for $12.50 off her total order. Write a sentence to describe how you calculated the cost of Nadine's order.

Difference of (-x² + 9xy) and  (x² + 6xy - 8y²) is - 2x² + 3xy + 8y².

Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.

Given expression,

(-x² + 9xy) - (x² + 6xy - 8y²)

Distributing negative sign

-x² + 9xy - x² - 6xy + 8y²

Adding like terms

- 2x² + 3xy + 8y²

Hence, - 2x² + 3xy + 8y² is the difference of (-x² + 9xy) and (x² + 6xy - 8y²).

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The triangle that's created has angles of 90°, 45° and 45°.

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane.

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.

The triangle is attached.

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Answer:

288/720 or simplified to its lowest is 2/5

Here are three different equations that relate C and B:

1. B = (2/7) * C

2. B/C = 2/5

3. 5C = 2B

1. B = (2/7) * C

Since the ratio of cocoa to cocoa butter is 5:2, we can write 5 + 2 = 7, which represents the total number of parts. Dividing 2 by 7, we get 2/7, which represents the fraction of cocoa butter in the mixture. To find the number of grams of cocoa butter needed for C grams of cocoa, we multiply C by 2/7.

2. B/C = 2/5

Dividing the number of grams of cocoa butter (B) by the number of grams of cocoa (C), we get the ratio of cocoa butter to cocoa, which is 2/5.

3. 5C = 2B

Since the ratio of cocoa to cocoa butter is 5:2, we can write the equation 5 * C = 2 * B, which represents the number of parts of cocoa to the number of parts of cocoa butter. Solving for B in terms of C, we get B = (2/5) * C.

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Answer:

D) (such a situation is not possible as with 2 points, there will be 4 tangents to the circle)

Addition And Subtraction

1.) -27+68-56+61= 46

2 ) 4.17-9.42+0.2= -5. 05

3 ) 3.1+(-4.72)+(-8.12)-(-0.96)=-8.78

4 ) -18.31-6.27+(-8.44)-(-31.67)=-1. 35

5 ) 6 5/12 - (-4 2/3)8 + (-2 3/4)= 5/12

6 ) 4 1/8 - 6 2/9+ (-3 1/6) - (-5 3/4)= -49/72

1.) -27+68-56+61=

Because in this arithmetic operation there is only addition and subtraction, it can be calculated starting from anywhere.

2 ) 4.17-9.42+0.2= -5. 05

Because in this arithmetic operation there is only addition and subtraction, it can be calculated starting from anywhere.

3 ) 3.1+(-4.72)+(-8.12)-(-0.96)=-8.78

Because in this arithmetic operation there is only addition and subtraction, it can be calculated starting from anywhere.

But it should be noted that before the number (-0.96) there is a negative sign (-) so you need to multiply the sign with the number in brackets. In this case the result is . positive.

4 ) -18.31-6.27+(-8.44)-(-31.67)=-1. 35

Because in this arithmetic operation there is only addition and subtraction, it can be calculated starting from anywhere.

But it should be noted that before the numbers (-8.44) and (-31.67) there is a negative sign (-) so you need to multiply the sign with the number in brackets. In this case the result is positive.

5 ) 6 5/12 - (-4 2/3) + (-2 3/4)= 5/12

In question number 5, it involves mixed fractions. To do this, you can change mixed fractions to improper fractions.

6 ) 4 1/8 - 6 2/9+ (-3 1/6) - (-5 3/4)= -49/72

In question number 6, it involves mixed fractions. To do this, you can change mixed fractions to improper fractions.

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The angles m∠w and m∠y are supplementary angles and their measures are 50° and 130° respectively.

If two angles add up to 180°, they are considered supplementary angles, we can observe that the positions of the angles formed by the transversal cutting the parallel lines makes the two angles on a straight line which are supplementary so;

4x + 6 + 12x - 2 = 180

16x + 4 = 180°

16x = 180 - 4 {subtract 4 from both sides}

16x = 176

x = 176/16 {divide through by 16}

x = 11.

m∠w = 4(11) + 6 = 50°

m∠y = 12(11) - 2 = 130°

Therefore, the supplementary angles m∠w and m∠y have their measures as 50° and 130° respectively.

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The size of the population after 15 hours is 6400 bacteria.

The size of the population after 15 hours can be found using the exponential growth formula. The formula for exponential growth is P = P₀ × 2^(t/k), where P₀ is the initial population, t is the time elapsed, k is the time it takes for the population to double, and 2^(t/k) is the exponential growth factor.

In this case, the initial population is 200, the time elapsed is 15 hours, and the time it takes for the population to double is 3 hours. Putting these values in the formula, we get:

P = 200 × 2^(15/3)

P = 200 × 2⁵

P = 200 × 32

P = 6400

So, the size of the population after 15 hours is 6400 bacteria.

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