Write a system of equations to describe the situation below, solve using substitution, and fill
in the blanks.
Aunt Emily is pricing cakes for a baby shower she is throwing. She wants one large cake
shaped like a duckling and also some cupcakes in pastel colors. Clarksville Bakery charges $3
for each cupcake, plus $50 for the large cake. Sebastian's Sweet Shoppe charges $34 for the
large cake and $4 for each cupcake. If Aunt Emily orders a certain number of cupcakes, the
cost will be the same at either bakery. How many cupcakes would that include? What would
the total cost be?
If Aunt Emily orders
cupcakes, it will cost s
at either shop.

Answer:

Answer: 200x + 25y <= 6000

Step-by-step explanation:

The food will be needed to feed all the cub for one year is 1825 kg.

Given :

A lion ha 4 cubs that weigh 1. 7 kg, 2. 1 kg, 3 kg, and 2. 7 kg. Each cub eat 1. 25 kg of food a day.

one cub eats food = 1.25 kg

4 cubs eats food = 1.25 kg * 4

= 125 / 100 * 4 kg

= 500 / 100 kg

= 5 kg

5 kg for one day.

cub eats food for one year = 365 * 5 kg

= 1825 kg.

Therefore the food will be needed to feed all the cub for one year is 1825 kg.

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The required factors of the given polynomial is (r^4 + rs^5)(t^8 - (rs^5t^4) + r^2s^10).

A factor  is a number that partitions another number, leaving no remainder portion.  if multiplying two whole number gives us an item, the numbers we are increasing are variables of the item since they are separable by the item.

We have given,

t^12 - r^3(s)^15

By using formula

(a³ - b³) = ( a+ b)( a² -ab + b²)

Then,

(r^4)^3 - (rs^5)^3

(r^4 + rs^5)((t^4)^2 - rs^5t^4 + (r^5)^2)

(r^4 + rs^5)(t^8 - (rs^5t^4) + r^2s^10)

Thus, required answer is (r^4 + rs^5)(t^8 - (rs^5t^4) + r^2s^10), So option (D) is correct.

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Answer:

the slope is -1/9

Step-by-step explanation:

The first thing to do is use the slope formula y^1 - y^2 over x^1 - x^2. You substitute each value into these variables and solve, which will then give you a negative slope of -1/9.

hope this helps!! :3

Answer:

1.03% of 0.054=0.0005562

Number of square feet of wall painted in 1 hour is 243 square feet. Therefore, option C is the correct answer.

Given that, it takes Zach 10 minutes to paint [tex]40\frac{1}{2}[/tex] square feet of his bedroom wall.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Here,  square feet = 40.5 square feet

Rate at which he paints the wall =40.5/10

= 4.05 square feet per minute

As we know 1 hour =60 minutes

Now, number of square feet

= 4.05×60

= 243 square feet

Number of square feet of wall painted in 1 hour is 243 square feet. Therefore, option C is the correct answer.

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The actual quotient and the estimated quotient of 78,070÷37 is 2110 , so the difference between them is 0.

On dividing 78,070 by 37 ,

we get

78,070 /37

=2110

Since , the number gets divided completely

therefore the estimated quotient and the actual quotient will be 2110.

We first round the dividend and the divisor to the closest tens, hundreds, or thousands, and then divide the rounded figures to approximate the quotient. When the divisor in a division sum has two or more digits, it is helpful to first estimate the quotient before attempting to discover the exact number.

The outcome of dividing two numbers is known as the quotient. Divided divisor = quotient + remainder is the formula for expressing the terms of division.

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Answer:

A/ $4 for 1 gallon

B/ $48

Step-by-step explanation:

Take 24 divided by 6 = $4 per gallon

Then take 4 times 12 = $48 for 12 gallons

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In linear equation, Sofia will order 7 more rolls of sushi (84 pieces) and pay $56.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                  Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

They need at least 100 pieces of sushi

Sofia had ordered and paid for 24 pieces of sushi already

Sushi comes in rolls

Each roll=12 pieces at $8

R=additional rolls that Sofia orders

Additional sushi= Needed sushi - ordered sushi

=100-24

=76 pieces of sushi

Each roll has 12 pieces

76/12=6.33

Sofia has to order in rolls

So, she will order 7 more rolls of sushi of 12 pieces each

12*7=84 pieces

Recall, that they needed at least 100 pieces, so the number of pieces could be more than 100

If Sofia orders 84 pieces + the already ordered 24 pieces

Total pieces=108 pieces

She has paid for 24 pieces (3 rolls) at $8 per roll

7 rolls=$8*7

=$56

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Answer: 36.72 G

Step-by-step explanation:

I sell

As per the given equation, the resulting conversion is written as,

13.6g/cm³ x 1kg/1000 x 10⁶cm³/m³ = 13600kg/m³

Equation:

An equation consist the value of the variable, numbers and the constants.

Given,

Here we have the density of mercury is 13.6 grams per cubic centimeter.

Now, we have to convert this one into kg/m3.

Here the process of conversion of  13.6 g/cm3 to kg/m3

We know that, 1 Kg of weight is equal to 1000 grams of weight

Then it can be written as

=> 1 g = 1 kg/1000

Then the first blank (numerator) will be filled with 1 Kg

Similarly, 1 meter is equal to 100 centimeter

So, for cubic unit it can be written as,

=> 1 cm³ = 1m³/100³

It can be simplified as,

=> 1 cm³ = 1m³/10⁶

Now, the second blank (numerator) will be filled with 10⁶

Finally, the third blank (denominator) will be filled with 1m³

Therefore, the last blank will be 13600

Hence, we have find the all the values on the blanks.

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The value of f(-7) is -29.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

f(x)=-x² + 2x + 6

So, to find f(-7) put x= -7

f(-7) =  -(7)² + 2(7) + 6

f(-7) =  -49 + 14 + 6

f(-7) =  -29

Hence, the value of f(-7) is -29.

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Rounding to the nearest tenth, we get that the length of KN is approximately 21.8.

What is a Pythagoras theorem?

The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This relationship is often expressed in the form of the equation:

a² + b² = c²

To find the length of KN in this right triangle, you can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the hypotenuse is KL, and the other two sides are KM and KN. The theorem can be written as:

KL² = KM² + KN²

Substituting the given values, we get:

24² = 10² + KN²

Solving for KN, we get:

KN² = 24² - 10²

= 576 - 100

= 476

KN = √476

= 21.84

Hence, rounding to the nearest tenth, we get that the length of KN is approximately 21.8.

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Rounding to the nearest tenth, we get that the length of KN is approximately 21.8.

What is a Pythagoras theorem?

The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This relationship is often expressed in the form of the equation:

a² + b² = c²

To find the length of KN in this right triangle, you can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the hypotenuse is KL, and the other two sides are KM and KN. The theorem can be written as:

KL² = KM² + KN²

Substituting the given values, we get:

24² = 10² + KN²

Solving for KN, we get:

KN² = 24² - 10²

= 576 - 100

= 476

KN = √476

= 21.84

Hence, rounding to the nearest tenth, we get that the length of KN is approximately 21.8.

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Answer:

s = 3

Step-by-step explanation:

We model the proportion with the equation:

[tex]s =\frac{k}{t}[/tex]

We have s and t, but we need to find the k (i.e., the constant of proportionality) by plugging in the s and t we already have:

[tex]0.9=\frac{k}{2}\\ 1.8=k\\s=\frac{1.8}{t}[/tex]

To find s when t = 0.6, we simply plug in 0.6 for t in last equation we found with k:

[tex]s=\frac{1.8}{0.6}\\ s=3[/tex]

Figure D was reflected over the y axis and translated 4 units upwards to form figure E

What is transformation?

Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.

Rigid transformation preserves the shape and size of the figure. Reflection, translation, rotation are rigid transformations.

According to the given question:

On translating the figure D over y-axis, the figure E will be 4 units above.

Therefore,  Figure D was reflected over the y axis and translated 4 units upwards to form figure E.

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you will be on floor no. -8 and your friend will be in floor no. 5 if you and your friend started at floor no. 0

YOU CAN ALSO VISUALISE THIS WAY

Answer:

23.5 degrees north

Step-by-step explanation:

The percent of increase is 4.761 %

Given :

A laptop computer originally priced at $2100 now and sell for $2,200.

Percentage :

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100.

If we have to calculate percent of a number, divide the number by the whole and multiply by 100.

Difference = sell price - original price

= 2200 - 2100

= 100

Percent of increase = 100 * 100 / 2100

= 100 * 1 / 21

= 100 / 21

= 4.761 %

Therefore 4.761 % increase in percent.

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Answer: I believe it is reflected over the y-axis.

Step-by-step explanation:

Always look for the dum (I know it is spelled wrong but Brainly won't let me type it) and dummer answer choices. The other two choices aren't even a type of transformation. Think about it. If you are reflecting over the y-axis, the y-values stay the same and the x-values change.

The range of the function f(x) = 3x - 4, having domain x ≥ 1 is x ≥ -1 and the graph is attached below so, option D is correct.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

Given:

The function, f(x) = 3x - 4,

Domain = x ≥ 1

When domain = 1,

Range = 3 × 1 - 4 = -1

When domain = 2

Range = 3 × 2 - 4 = 2

Thus, you can conclude the range of the function as x [-1, ∞) or x ≥ -1

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Answer:

A

Step-by-step explanation:

s must be a number greater than 7

The required state income tax owed on a $90,000 per year salary is $4950.

Given that,
A table shows the income tax owed by the state on the particularar salary,
Income Range ($)      Tax Rate

0 - 10,000                     3%
10,001 - 50,000             5%
50,001 - 100,000           5.5%

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
on $90,000
Tax owed = 5.5% of 90000, because this salary lies in the segment 50,001 - 100,000.
Tax owed = 0.055[90000] = $4950

Thus, the required state income tax owed on a $90,000 per year salary is $4950.

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Answer:

56

Step-by-step explanation:

divide 7 into 28 which is 4.

Then substitute 4 for M so 4 times 14 which is 56.

The calculated value of the rocket's greatest height is 196 feet

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

height function,  h(t) =-16t² + 80t + 96

So, we have

h(t) =-16t² + 80t + 96

The maximum value of t is calculated as

t = -b/2a

So, we have

t = -80/(2 * -16)

Evaluate

t = 2.5

The rocket's greatest height is at t = 2.5

So, we have

h(2.5) =-16(2.5)² + 80(2.5) + 96

Evaluate

h(2.5) = 196

Hence, the rocket's greatest height is 196 feet

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5 children can share all parts of the bread if each child takes 0.2 parts.

Fraction are numbers of the form [tex]\frac{a}{b}[/tex] where a and b are real numbers. It is represented as a portion or part of a whole.

The number on the top is called numerator and the number on the bottom is called denominator.

There are 10 equal parts of bread and each child takes 0.2 part.

Total parts of the bread = 10

Part each child takes = 0.2 = [tex]\frac{2}{10}[/tex]

2 parts out of 10 are taken by each child.

Remaining are  [tex]\frac{8}{10}[/tex] parts.

[tex]\frac{2}{10}[/tex] × 4 =  [tex]\frac{8}{10}[/tex]

Remaining parts can be shared by 4 children.

Hence number of children who can share the bread if each takes 0.2 parts = 5

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There were 1080 seats in the theater.

In this question, we have been given that the 6th grade students went on a field trip to see a ballet.

The students filled 702 seats leaving 35% vacant.

We need to find the total seats in the theater.

Let there were n seats in the theater.

Given that 35 percent of total seats were vacant.

So, we get an equation,

702 + (35% of n) = n

702 + 0.35n = n

(1 - 0.35)n = 702

0.65n = 702

n = 1080

Therefore, the total seats in the theater = 1080

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The domain of f(x) = 2x² + 2x + 4  is (-∞, ∞).  

A quadratic equation, or quadratics, is a polynomial equation with a maximum degree of two. It will be in the form of ax² + bx + c = 0.

When a quadratic function is represented in a graph on the x and y grid, It will represent a parabola. Either it will open upwards or downwards.

The domain of a parabola is the entire set of real numbers [ Without any restrictions ]

Here we have

Ethan uses the function, f(x) = 2x² + 2x + 4

As we know all quadratic functions are parabolas

And its domain is the set of real numbers

Therefore,

The domain of f(x) = 2x² + 2x + 4  is (-∞, ∞).

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Answer:

$1,018.39

Step-by-step explanation:

Interest formula is I = Prt/100

where P = principal

r = interest rate (in percent)

t = number of time periods

Here we have P = 740

interest = 0.66% per day

t = 57 days

I = 740 x 0.66 x 57 /100 = 278.39 (rounded)

Total amount to pay back = 740 + 278.39 = $1,018.39

Answer:

1/8

Step-by-step explanation:

9/72 = 1/8