Solving a System of Linear Equations - Applications - Item 35812
A sandwich shop only sells sandwiches and homemade soup.
The table shows the number of sandwiches and bowls of soup purchased in the past
2 hours.
The total earnings for hours 1 and 2 are given.
Each sandwich costs the same price, and each bowl of soup costs the same price.
The system of equations can be used to represent the situation.
Use the drop-down menus to complete each statement.

We can use substitution to solve this system of equations. We can solve the first equation for y and get:

y = (2x + 12)/3

We can then substitute this expression for y into the second equation:

(2x + 12)/3 + 3x = -7

Multiplying both sides of this equation by 3 to eliminate the denominator, we get:

2x + 12 + 9x = -21

Simplifying this equation gives:

11x = -33

Dividing both sides by 11, we get:

x = -3

We can then substitute this value of x back into either of the two original equations to find y. Using the first equation, we get:

3y = 2(-3) + 12

3y = 6

y = 2

Therefore, the solution to the system of equations is x = -3 and y = 2.

To check the solution, we substitute these values back into both equations:

3y = 2x + 12 3(2) = 2(-3) + 12 6 = 6

This equation is true, so the solution (x = -3, y = 2) checks out.

Answer:

a) Distance is 40m b)0 c)2.5m/min

Step-by-step explanation:

a)8*5=40 b)He went from A to A c)16 min s=d/t 40/16

Answer: x= 24 and y= 73

Step-by-step explanation:

we know

The opposite interior angles are equal and

The angles on the same side of the transversal are supplementary, that means they add up to 180 degrees.
the sum of the interior angles of a parallelogram is 360 degrees.

So 107 + y = 180

180 - 107 = 73

Y = 73

y is equal to its opposite angle so

X can be found by 73 = 3x + 1

Subtract 1 from both sides

73 - 1 = 3x +1 -1

Simplify

72 = 3x

Divide both sides by 3 to solve for x

72/3 = 3/3x

x=24

Check your work by adding the 4 angles together to equal 360

107 + 107 + 73 + 73 = 360

360 = 360

They equal so your solution is correct

The volume integral for f(x,y,z) = 1 over the region E : x² + y² + z² ≤ 4,

1) In spherical coordinates system is

[tex]V = {\int_{0}^{2π} \int_{0}^{π} \int}_{0}^{2} \rho^{2} \sin( \phi) \: d\rho d\phi d\theta[/tex]

2) In cylinderical coordinates system is

[tex]V = \int_{0}^{2π} \int_{0}^{2} (\int_{-\sqrt {4 - x² - y²}}^{\sqrt{ 4 - x² - y²}} dz) rdr d \theta \\ [/tex]

3) In rectangular coordinates syatm is

[tex]V = \int_{0}^{2}\int_{-\sqrt {4 - x²}}^{\sqrt{4 - x²}} \int_{ - \sqrt{ 4 - x² - y²}}^{ \sqrt{4 - {x}^{2} - {y}^{2} } } \: dz dy dx \\ [/tex]

We pick a region E : x² + y² + z² ≤ 4 and determine volume over the region E for function, f(x,y,z ) = 1 .

[tex]V = {\int \int \int}_{E} f(x,y,z) dV[/tex]

In spherical coordinates system we plug,

[tex]x = \rho sin \phi cos \theta[/tex]

[tex]y = \rho sin \phi sin \theta[/tex]

[tex]z = \rho cos \phi [/tex]

[tex]dV = dx dy dz = |J| d\rho d\phi d\theta [/tex]

where, [tex]|J| = \rho² sin \phi[/tex]

=> [tex]dx dy dz = \rho² sin \rho d\rho d\phi d\theta[/tex]

So, [tex]V = {\int \int \int}_{x² + y² + z² ≤ 4} 1 \: dxdy dz[/tex]

Now, [tex]V = {\int_{0}^{2π} \int_{0}^{π} \int}_{0}^{2} \rho^{2} \sin( \phi) \: d\rho d\phi d\theta[/tex]

Region , E : x² + y² + z² ≤ 4

=> z² ≤ 4 - x² - y²

=> z ≤ ± √4 - x² - y²

[tex]V = {\int \int_{ x² + y² ≤ 4} \int}_{ - \sqrt{ 4 - x² - y²}}^{ \sqrt{4 - {x}^{2} - {y}^{2} } } 1 \: dz dx dy \\ [/tex]

here, r∈[0, 2], θ∈[0,2π]

[tex]V = \int_{0}^{2π} \int_{0}^{2} (\int_{-\sqrt {4 - x² - y²}}^{\sqrt{ 4 - x² - y²}} dz) rdr d \theta \\ [/tex]

[tex]V = {\int \int \int}_{E} f(x,y,z) dV[/tex]

[tex]V = {\int \int_{ x² + y² ≤ 4} \int}_{ - \sqrt{ 4 - x² - y²}}^{ \sqrt{4 - {x}^{2} - {y}^{2} } } 1 \: dz dx dy \\ [/tex]

Here, y² ≤ 4 - x²

=> y = ± √4 - x² and x∈ [0,2], So,

[tex]V = \int_{0}^{2}\int_{ -\sqrt {4 - x²}}^{\sqrt{4 - x²}} \int_{ - \sqrt{ 4 - x² - y²}}^{ \sqrt{4 - {x}^{2} - {y}^{2} } } \: dz dy dx \\ [/tex]

Hence, in above we determined the volume integral for region, E in all three coordinates systems.

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Answer:

x = 24

Step-by-step explanation:

by the similarity theorem

the ratios of corresponding sides are in proportion , that is

[tex]\frac{x}{9}[/tex] = [tex]\frac{16}{6}[/tex] ( cross- multiply )

6x = 9 × 16 = 144 ( divide both sides by 6 )

x = 24

Answer:

Delia's hair grew less since her last haircut

Step-by-step explanation:

2.45 centimeters is a higher number then 2.03, making Delia's hair shorter than Carolyn's.

Answer:

Delia's hair grew less.

Step-by-step explanation:

2.45 - 2.03 = 0.42

Deila's hair is 0.42 less than Carolyn's hair.

Angle Y measures 125 degrees and angle Z measures 63 degrees.

what is a circle?

A circle is a geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center. It can also be defined as the set of points that are a fixed distance (called the radius) away from the center point. The distance around the circle is called its circumference, and the distance across the circle passing through the center is called its diameter.

Since quadrilateral WXYZ is inscribed in a circle, we know that opposite angles add up to 180 degrees. Therefore:

m∠Y + m∠W = 180 degrees ...(1)

m∠Z + m∠X = 180 degrees ...(2)

We are given that m∠W = 55 degrees and m∠X = 117 degrees, so we can substitute those values into equations (1) and (2):

m∠Y + 55 = 180 ...(1)

m∠Z + 117 = 180 ...(2)

Solving for m∠Y and m∠Z, we get:

m∠Y = 125 degrees

m∠Z = 63 degrees

Therefore, angle Y measures 125 degrees and angle Z measures 63 degrees.

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The number is 300, as stated in the sentence. A histogram:

One common plotting instrument is the histogram. It is employed to present interval-scaled summaries of discontinuous or continuous data. It is commonly applied to easily represent the key features of the information's distribution.

To create a histogram of the weights of the miniature poodles, we would first divide the weight range into a series of intervals, or bins. The bin width should be chosen so that each bin has a similar number of observations.

According to the histogram and table: the height of a cell represents 10 15 ≤ x < 20: 120 ÷ 12=10

28 ≤ x <30 has 30 cells, so the frequency is 30 × 10=300

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Using the circumference formula the number of full revolutions the wheels need to make to travel 220 feet is obtained as 35.

What is circumference?

The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The region a circle occupies is determined by its area.

The distance traveled by the car in one full revolution of the wheel is equal to the circumference of the wheel.

The circumference of a circle is given by the formula -

C = 2πr

where C is the circumference, π is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.

Since the diameter of the wheel is 2 feet, the radius is half of that, or 1 foot.

Therefore, the circumference of the wheel is -

C = 2π(1 foot) = 2π feet

To find how many full revolutions the wheel needs to make to travel 220 feet, we can divide the distance traveled by the circumference of the wheel -

Number of revolutions = distance traveled / circumference of the wheel

Number of revolutions = 220 feet / (2π feet) ≈ 35.03

Therefore, the wheels need to make 35 full revolutions to travel 220 feet.

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let's firstly convert the mixed fractions to improper fractions.

[tex]\stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}}~\hfill \stackrel{mixed}{1\frac{1}{4}} \implies \cfrac{1\cdot 4+1}{4} \implies \stackrel{improper}{\cfrac{5}{4}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{~~ \frac{ 7}{ 2} ~~}{\frac{5}{4}}\implies \cfrac{7}{2}\cdot \cfrac{4}{5}\implies \cfrac{7}{5}\cdot \cfrac{4}{2}\implies \cfrac{7}{5}\cdot 2\implies \cfrac{14}{5}\implies 2\frac{4}{5}\implies 2.8[/tex]

10: Missing length, x = 16 cm

area of the composite figure = 240 cm²

perimeter = 72 cm

11: Missing length, x = 37 mm

area of the composite figure = 240 mm²

perimeter = 90 mm

To find the area and perimeter of a composite figure, you can break it down into simpler shapes such as triangles, rectangles, circles, etc. and then find the area of each individual shape and add them together.

No. 10

You will notice that the triangle is sharing one side with the square. And the length of the side is 12 cm. Thus:

x = √(20² - 12²)    (Pythagoras)

x = 16 cm

area of the figure = area of square + area of triangle

area of the figure =  L²  + (1/2 * base * height)

area of the figure =  12²  + (1/2 * 16 * 12)

area of the figure = 240 cm²

perimeter = 12 + 12 + 12 + 20 + 16 = 72 cm

No. 11

You will notice that the small triangle is sharing one side with the big triangle. And the length of the side is unknown. Let's call it y. Thus:

y = √(13² - 5²)    (Pythagoras)

y =  12 mm

x = √(35² + 12²)    (Pythagoras)

x = 37 mm

area of the figure = area of small triangle + area of big triangle

area of the figure =  (1/2 * base * height)   + (1/2 * base * height)

area of the figure =  (1/2 * 5 * 12) + (1/2 *  35 * 12)  

area of the figure = 240 mm²

perimeter = 5 + 13  + 37 + 35 = 90 mm

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The "loading" of the die makes P(1)=112, P(6)=312, and the following four outcomes equally likely. A roll with an even number larger than two has a 50% probability of occurring.

The probability of rolling an even number is 1/2 since there are three even numbers (2, 4, 6) and six possible outcomes in total.

The probability of rolling a number greater than two is 5/6 since there are five outcomes (3, 4, 5, 6) greater than two and six possible outcomes in total.

To find the probability that the number rolled is both even and greater than two, we need to find the probability of rolling a 4 or a 6 since these are even numbers that are greater than two.

The probability of rolling a 4 is P(4) = 1/12 + 1/6 = 1/4 since the die is loaded to favour a 6 over the other numbers, but all other outcomes are equally likely.

The probability of rolling a 6 is P(6) = 3/12 = 1/4 since the probability of rolling a 6 is given as 3/12.

Therefore, the probability of rolling an even number that is greater than two is:

P(even and greater than two) = P(4 or 6) = P(4) + P(6) = 1/4 + 1/4 = 1/2.

So the probability of rolling an even number that is greater than two is 1/2.

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Answer: √698 or 26.42 (2 d.p.)

Step-by-step explanation:

Pythagoras' Threorem is a² + b² = c²

Substitute 13 for a and 23 for b

13² + 23² = x²

169 + 529 = x²

698 = x²

x = √698 = 26.42 (2 d.p.)

Answer:

12.5

Step-by-step explanation:

9.6² + 2.8² = 10²

10² + 7.5² = 12.5²

Answer: 2(x-6) < -3(x-1) is x < 3.

Step-by-step explanation:
2(x-6) < -3(x-1)

Expanding the brackets, we get:

2x - 12 < -3x + 3

Adding 3x to both sides, we get:

5x - 12 < 3

Adding 12 to both sides, we get:

5x < 15

Dividing both sides by 5, we get:

x < 3

Answer:

x>12

Step-by-step explanation:

1/3(x-6)>2

distribute 1/3

1/3x-2>2

add 2 to both sides

1/3x>4

multiply both sides by 3

x>12

Answer:

[tex]y=40\sqrt{\frac{6}{x} }[/tex]

[tex]y=-40\sqrt{\frac{6}{x} } ,x > 0[/tex]

Step-by-step explanation:

pls tell me if wrong have a good night/day

Answer:

$38.40

Step-by-step explanation:

20% = 0.2

32 x 0.2 = $6.40

20% tip = $6.40

How much money should they leave for the bill and a 20% tip?

We take

32 + 6.40 = $38.40

So, they should leave $38.40 for the bill and a 20% tip.

Answer:

False.

Step-by-step explanation:

When using multiple adjectives in a sentence, there is a general order that native English speakers tend to follow: opinion, size, age, shape, color, origin, material, purpose. This is known as the "OSASCOMP" order. However, this order is not always strictly followed, and there can be exceptions depending on the specific context or style of writing.

Answer:

It is False

Step-by-step explanation:

Answer:

The sonar station will not detect the submarine.

Step-by-step explanation:

The area that the sonar station can detect can be modelled as a circle with center (0, 0) and radius 5 km.

The equation of a circle formula is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.

Therefore, the equation of the circle modelling the perimeter of the sonar station detection area is:

[tex]\implies (x-0)^2+(y-0)^2=5^2[/tex]

[tex]\implies x^2+y^2=25[/tex]

To determine whether the sonar station will detect a swiss submarine traveling along a trajectory defined by y = -2/3x + 26/3, substitute the equation of the trajectory into the found equation of the circle.

[tex]\implies x^2+\left(-\dfrac{2}{3}x+\dfrac{26}{3}\right)^2=25[/tex]

Simplify:

[tex]\implies x^2+\dfrac{4}{9}x^2-\dfrac{104}{9}x+\dfrac{676}{9}=25[/tex]

[tex]\implies 9x^2+4x^2-104x+676=225[/tex]

[tex]\implies 13x^2-104x+451=0[/tex]

Solve the equation for x using the quadratic formula:

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]

[tex]\implies x=\dfrac{-(-104) \pm \sqrt{(-104)^2-4(13)(451)}}{2(13)}[/tex]

[tex]\implies x=\dfrac{104 \pm \sqrt{-12636}}{26}[/tex]

[tex]\implies x=\dfrac{104 \pm 18\sqrt{39}\:i}{26}[/tex]

[tex]\implies x=4 \pm \dfrac{9\sqrt{39}}{13}\:i[/tex]

As the solutions are complex numbers, this means that the linear trajectory of the submarine will not intersect the detection area of the sonar station. Therefore, the sonar station will not detect the submarine.

Using equations,

The quotient of 3 times a number and 7: 3n/7

5 less than a number is x:  x = n - 5

The sum of twice a number and 9: 2n + 9

Two times the sum of a number and 9: 2 (n+9)

The product of 3 times a number and 7: (3n) (7)

The difference between 5 and a number is x: 5 - n = x

A mathematical statement that has two expressions with equal values separated by the symbol "equal to" is called an equation. Consider the formula 3x + 5 = 15.

Many types of equations exist, including linear, quadratic, cubic, and others.

The quotient of 3 times a number and 7: 3n/7

5 less than a number is x:  x = n - 5

The sum of twice a number and 9: 2n + 9

Two times the sum of a number and 9: 2 (n+9)

The product of 3 times a number and 7: (3n) (7)

The difference between 5 and a number is x: 5 - n = x

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Answer:y=-x+6

Step-by-step explanation:

The probability of flipping heads is 1/2, and the probability of rolling an even number is 1/2 (since there are three even numbers and three odd numbers on the cube). To find the probability of both events happening (flipping heads and rolling an even number), we multiply the probabilities together:

1/2 x 1/2 = 1/4

So the probability that Olive flipped heads and rolled an even number is 1/4 or 25%.

Answer: 1/4

Step-by-step explanation:

The equation for p is p + 6 = 14, which means that the number of pieces left is equal to the difference between the total number of pieces (14) and the number of pieces served (6).

Ron's mother bakes a pizza and divides it into 14 pieces. After serving 6 pieces to Ron and his friends, she has a certain number of pieces left. To determine this number, we can use the equation p + 6 = 14. This equation states that the number of pieces left (p) is equal to the difference between the total number of pieces (14) and the number of pieces served (6). Therefore, the equation for p is p + 6 = 14. By solving this equation, we can determine that the number of pieces left is 8. This means that Ron's mother has 8 pieces left after serving 6 pieces to Ron and his friends.

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Answer: To find out how many rides take place in 28 minutes, we need to divide the total ride length by the length of one side, and then round down to the nearest whole number.

The length of one ride can be calculated by dividing the total ride length by the number of rides. Since we don't know the number of rides, let's call it "n":

length of one ride = total ride length / n

314 minutes / n

Now we can set up an equation to solve for "n":

28 minutes = length of one ride * number of rides

28 minutes = (314 minutes / n) * number of rides

We can simplify this equation by multiplying both sides by "n":

28 minutes * n = 314 minutes * number of rides

Dividing both sides by 314 minutes, we get:

n = (28 minutes * number of rides) / 314 minutes

Multiplying both sides by 314 minutes and dividing by 28 minutes, we get:

number of rides = (n * 314 minutes) / 28 minutes

number of rides = 11.21

Rounding down to the nearest whole number, we get:

number of rides = 11

Therefore, in 28 minutes, 11 rides take place.

Step-by-step explanation:

The confidence level is the probability that a confidence interval will contain the true population parameter in repeated sampling.

Confidence level is a statistical measure used to indicate the level of certainty or reliability in a statistical inference or estimate. In other words, it represents the success rate of the method used to construct a confidence interval. For example, a 95% confidence level indicates that if we were to repeat the same experiment many times and calculate the confidence interval for each trial, then we would expect 95% of these intervals to contain the true value.

The confidence level is typically chosen by the researcher based on the level of certainty they want to achieve. A higher confidence level corresponds to a wider confidence interval, which increases the likelihood of containing the true value, but reduces the precision of the estimate.

It is important to note that the confidence level does not guarantee that a particular confidence interval contains the true value, but rather it indicates the long-run success rate of the method used to construct the interval. Therefore, it is crucial to understand the underlying assumptions and limitations of the statistical method used to construct the confidence interval.

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The confidence level is a percentage between 0% and 100% that measures the success rate of the method used to construct the confidence interval. If we were to draw many samples and use each one to construct a confidence interval, then in the long run, the percentage of confidence intervals that cover the true value would be equal to the ________?

The probability of selecting a blue or green ball on the first draw is 2/3 or approximately 0.67.

What is probability ?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain to occur. If an event has a probability of 0.5, it means that the event is equally likely to occur or not occur. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Probability is an important concept in mathematics, statistics, and many other fields, as it allows us to make predictions and decisions based on the likelihood of certain outcomes.

According to the question:
The total number of balls in the bag is:

6 blue balls + 5 yellow balls + 4 green balls = 15 balls

The probability of selecting a blue or green ball on the first draw can be found by dividing the number of blue and green balls by the total number of balls:

P(blue or green) = (number of blue balls + number of green balls) / (total number of balls)

P(blue or green) = (6 + 4) / 15

P(blue or green) = 10 / 15

P(blue or green) = 2/3

Therefore, the probability of selecting a blue or green ball on the first draw is 2/3 or approximately 0.67.


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The value of the angle m<C is 27 degrees. Option B

First, we need to know the different trigonometric identities and their ratios.

We have;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

From the information given in the diagram, we have;

Opposite side of angle C = 5

Adjacent side of angle C = 7.5

Hypotenuse side of angle C = 11

Using the sine identity

sin C = 5/11

sin C = 0. 4545

Take sine inverse

C = 27 degrees

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