define the solution to a system of linear inequalities.

Answer: 30/250 and 45/375 would be two equivalent fractions.

Answer:

5 is the greatest number of cups we can make.

Step-by-step explanation:

Given: 50 red bears, 25 blue bears and 35 green bears.

Now, finding the greatest number of cups we can make with same number of each colour in cups.

∴ we will be using greatest common factor (GCF) to know the number of cups.

[tex]50= 5\times 5\times 2\\\\25= 5\times 5\\\\35= 5\times 7[/tex]

∴ [tex]GCF= 5[/tex]

5 is the greatest number of cups we can make with same number of each colour.

Answer:

12) x = 10 or x = -10

13) b = 3 or b = -3.

14) r = 6 or r = -2

15)  n = 0 or -2

Step-by-step explanation:

12) Given, 4|x| + 3 = 43

Now, for x ≥ 0, |x| = x and for x < 0, |x| = -x

So, for x ≥ 0, the equation becomes 4x + 3 = 43

⇒ 4x = 40

⇒ x = 10

Again, for x < 0, we have - 4x + 3 = 43

⇒ - 4x = 40

⇒ x = - 10

Therefore, the solution of the equation is x = 10 or x = -10. (Answer)

13) Given, 3|b| + 5 = 14

Now, for b ≥ 0, |b| = b and for b < 0, |b| = -b

So, for b ≥ 0, the equation becomes 3b + 5 = 14

⇒ 3b = 9

⇒ b = 3

Again, for b < 0, we have - 3b + 5 = 14

⇒ - 3b = 9

⇒ b = - 3

Therefore, the solution of the equation is b = 3 or b = -3. (Answer)

14) 9|2r - 4| + 1 = 73

Now, for 2r - 4 ≥0 i.e. r ≥ 2, then

9(2r - 4) + 1 = 73

⇒ 2r - 4 = 8

⇒ 2r = 12

⇒ r = 6

Again, for (2r - 4) < 0 i.e. r < 2, then

9(4 - 2r) + 1 = 73

⇒ 4 - 2r = 8

⇒ 2r = - 4

⇒ r = -2

Hence, the solutions are r = 6 and r = -2  (Answer)

15) For, 10n + 10 ≥ 0 i.e. n ≥ -1, then

1 + 4(10n + 10) = 41

⇒ 10n + 10 =10

⇒ 10n = 0

⇒ n = 0

Again, for 10n + 10 < 0 i.e. n < -1, then

1 - 4(10n + 10) = 41

⇒ 10n + 10 = - 10

⇒ 10n = -20

⇒ n = -2  

Hence, the solution is n = 0 or -2 (Answer)

Symmetry is when an image or being is halved into two, and both sides are the exact same to each other.

Final answer:

Symmetry in mathematics refers to an object's balanced or invariant properties under transformations like reflection, rotation, or translation. It is significant in physics for understanding conservation laws and is observed in various aspects of nature and art, providing balance and stability.

Explanation:

Symmetry is a fundamental concept in mathematics, physics, and the natural world. It implies that an object or system possesses a form of invariance or balance under certain transformations, such as reflection, rotation, or translation. In mathematical terms, symmetry refers to a situation where a figure can be manipulated in various ways, such as being flipped over a mirror plane (reflective symmetry), rotated around a central point (rotational symmetry), or shifted along a direction without changing its appearance (translational symmetry).

An example of symmetry in nature is bilateral symmetry, where an object can be divided into two symmetrical parts across a unique plane. This type of symmetry is easily observed in some living organisms, like humans, who have a left and right side that are mirror images of each other. In the realm of physics, symmetry plays an impactful role, especially in the study of sub-atomic particles through the use of particle accelerators like the Large Hadron Collider at CERN. Emmy Noether's work highlighted the deep connection between symmetries and conservation laws, illustrating the significance of symmetry in understanding the foundational principles of our universe.

In art, symmetry is associated with balance and harmony. Symmetrical balance is visually stable, often featuring compositions that are identical, or nearly so, on either side of a central axis. Optical devices, such as mirrors and lenses, also exploit principles of symmetry, with their function heavily dependent on a specific optical axis to guide light appropriately.

Answer:

x=510/7

Step-by-step explanation:

51/70=x/100

cross product

70*x=51*100

70x=5100

x=5100/70

x=510/7

x =72.86. This means that 51 out of 70 is equivalent to 72.86%.

51/70 = x/100.

51 * 100 = 70 * x.

5100 = 70 x

5100 / 70 = x.

The result is x = 72.86.

So, x = 72.86.

This means 51 out of 70 is equivalent to 72.86 out of 100 as a percentage.

Final answer:

To determine the number of classes at which the total cost for both options is the same, we can set up an equation. When attending 6 classes in a month, the total cost for both options will be the same, which is $60.

Explanation:

To determine the number of classes at which the total cost for both options is the same, we can set up an equation. Let x be the number of classes attended in a month.

For the membership option, the total cost is $60 per month.

For the walk-in option, the total cost is $10 multiplied by the number of classes attended.

Setting up the equation, we have:

60 = 10x

Dividing both sides by 10, we find:

x = 6 classes

So, when attending 6 classes in a month, the total cost for both options will be the same.

Using this value of x, we can find the total amount. For the membership option, it would be $60. For the walk-in option, the total amount is $10 multiplied by 6 classes, which is $60 as well.

the answer would be 750

Answer:

When x=5, y=22. And when x=3, y=6.

Step-by-step explanation:

y=x^2-3

8x-y=18

-------------

y=8x-18

x^2-3=8x-18

x^2-8x-3=-18

x^2-8x-3-(-18)=0

x^2-8x-3+18=0

x^2-8x+15=0

factor out the trinomial,

(x-5)(x-3)=0,

zero property

x-5=0, x-3=0,

x=0+5=5

x=0+3=3

-------------------------

y=5^2-3=25-3=22

y=3^2-3=9-3=6

Answer:D) No, because for some x's there are more than one y's.

Step-by-step explanation:The definition of a function states that for every x there is only one y. If you look at the data table for an x- value of 8 there are 2

different y-values 7 and 9. Therefore the correct answer is No, because for some x's there are more than one y's.

Answer:

the answer is D

Step-by-step explanation:

Answer:

2.25 seconds

87 feet

[6, 87]

Step-by-step explanation:

The height of a projectile is:

h(t) = -16t² + vt + s

where v is the initial vertical velocity and s is the initial height.

Here, v = 72 and s = 6.

h(t) = -16t² + 72t + 6

This is a downwards parabola.  The maximum is at the vertex.

t = -b / (2a)

t = -72 / (2×-16)

t = 2.25

h(2.25) = 87

It takes 2.25 seconds to reach the maximum height of 87 feet.

The range is from the lowest height (6 feet) to the maximum height (87 feet).  In interval notation:

[6, 87]

Final answer:

This response explains the time to reach maximum height, calculates the maximum height, and determines the range function for the projectile motion of the T-shirt launched by a slingshot during halftime at a football game.

Explanation:

Maximum Height Calculation:

Time to Reach Maximum Height: 2.25 seconds

Maximum Height: 81 feet

Range Function: The range function (horizontal distance) can be determined using the formula: R = V₀t, where V₀ is the initial velocity and t is the time taken to reach the maximum height.

Answer:

Answer:

The value of  (f-g)(x)=4^x-5x-14

Step-by-step explanation:

Given : If f(x) = 4^x-8 and g(x)=5x+6

To find : The value of  (f - g)(x)?

Solution :

f(x) = 4^x-8

g(x)=5x+6

We can write, (f-g)(x)=f(x)-g(x)

Substitute the value of f(x) and g(x)

(f-g)(x)=4^x-8-(5x+6)

(f-g)(x)=4^x-8-5x-6

(f-g)(x)=4^x-5x-14

Therefore, The value of  (f-g)(x)=4^x-5x-14

Plz mark brainliest

Answer:

25x+300=y

Step-by-step explanation:

The equation represents Tonya's profit, y, for working x for hours is

y = 25x - 300

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

Tonya's profit will depend on how many hours she works and how much she earns from tutoring.

Let's assume she works x hours, then she earns 25x dollars from tutoring.

However, she also has to pay the monthly rent of $300 regardless of how many hours she works.

Therefore, her profit y can be calculated as follows:

y = 25x - 300

This equation takes into account both her revenue (25x) and her expenses (the fixed cost of $300 for rent), and gives us her profit as the difference between the two.

Thus,

The equation represents Tonya's profit, y, for working x for hours is

y = 25x - 300

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Answer:

The area of the rectangular playroom is 260 feet² .

Step-by-step explanation:

Given:

The perimeter of the rectangular playroom is 72 feet and it's width is 10 feet.

Now, to find its area we need the length .

So, putting the formula of perimeter we get it's length:

Let the length be l .

Perimeter = 2( length + width)

[tex]72=2(l+10)[/tex]

[tex]72=2l+20[/tex]

subtracting both sides from 20:

[tex]72-20=2l+20-20[/tex]

[tex]52=2l[/tex]

Dividing both sides by 2:

[tex]52\div2=2l\div2[/tex]

[tex]26=l[/tex]

Length is 26 feet.

And, to get the area we put the formula of finding the area:

[tex]Area=length\times width[/tex]

[tex]Area=26\times 10[/tex]

[tex]Area=260[/tex]

Therefore, the area of the rectangular playroom is 260 feet² .

Final answer:

To determine the area of the rectangular playroom at Miss Pittypat's Day Care, we calculate the length using the perimeter and width provided, then multiply the length by the width. The playroom's area is found to be 260 square feet.

Explanation:

The question involves calculating the area of a rectangle when given the perimeter and the width. To find the length, we first use the perimeter formula P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. Since the perimeter is given as 72 feet and the width is 10 feet, we can solve for the length:

72 = 2l + 2(10)

72 = 2l + 20

52 = 2l

l = 26 feet

Once we have the length, we calculate the area by multiplying the length by the width:

Area = l × w

Area = 26 ft × 10 ft

Area = 260 square feet

Therefore, the area of the rectangular playroom is 260 square feet.

The range of function is { 0, -6, -9}

Given that the function is:

[tex]f(x) = \frac{-3}{4}x - 6[/tex]

Also given its domain is (-8, 0, 4)

To find: Range of the function

Domain of the function is possible input of the function that is "x" and range of the function is possible output of the function that is f(x)  

As there are only three input values for "x" that are (-8, 0, 4) we can determine the range by calculating value of f(x) for each of the x

For x = 8:

[tex]f(-8)=\frac{-3}{4} \times(-8)-6=6-6=0[/tex]

[tex]f(-8)=0[/tex]

For x = 0:

[tex]\begin{array}{l}{f(0)=\frac{-3}{4} \times(0)-6=-6} \\\\ {f(0)=-6}\end{array}[/tex]

For x = 4:

[tex]\begin{array}{l}{f(4)=\frac{-3}{4} \times(4)-6=-3-6=-9} \\\\ {f(4)=-9}\end{array}[/tex]

Thus the range of function is { 0, -6, -9}

Answer:

Sqrt50

Step-by-step explanation:

In order to solve for the diagonal, we use the Pythagorean Theorem.

5^2+5^2=c^2

25+25=c^2

50=c^2

sqrt50=c

Answer:

a = [tex]\frac{w + 4 - 3b}{6}[/tex]

Step-by-step explanation:

Given

w = 3(2a + b) - 4 ( add 4 to both sides )

w + 4 = 3(2a + b) ← distribute parenthesis

w + 4 = 6a + 3b ( subtract 3b from both sides )

w + 4 - 3b = 6a ( divide both sides by 6 )

[tex]\frac{w+4-3b}{6}[/tex] = a

Han's mixture has a higher concentration of orange juice concentrate, it is likely to taste stronger compared to Clare's mixture.

To determine whose orange juice mixture tastes stronger, we can compare the concentration of orange juice in each mixture. The concentration of orange juice can be measured by the ratio of orange juice concentrate to the total liquid volume.

Let's calculate the concentration for each mixture:

For Clare's mixture:

- Water: [tex]\(2\frac{1}{2}\)[/tex] cups

- Orange juice concentrate: [tex]\(\frac{1}{3}\)[/tex] cup

Total liquid volume: [tex]\(2\frac{1}{2} + \frac{1}{3} = \frac{7}{2} + \frac{1}{3} = \frac{21}{6} + \frac{2}{6} = \frac{23}{6}\) cups[/tex]

Concentration of orange juice concentrate in Clare's mixture: [tex]\(\frac{\frac{1}{3}}{\frac{23}{6}} = \frac{1}{3} \times \frac{6}{23} = \frac{2}{23}\) (ratio)[/tex]

For Han's mixture:

- Water: [tex]\(1\frac{2}{3}\)[/tex] cups

- Orange juice concentrate: [tex]\(\frac{1}{4}\)[/tex] cup

Total liquid volume: [tex]\(1\frac{2}{3} + \frac{1}{4} = \frac{5}{3} + \frac{1}{4} = \frac{20}{12} + \frac{3}{12} = \frac{23}{12}\) cups[/tex]

Concentration of orange juice concentrate in Han's mixture: [tex]\(\frac{\frac{1}{4}}{\frac{23}{12}} = \frac{1}{4} \times \frac{12}{23} = \frac{3}{23}\) (ratio)[/tex]

Comparing the concentrations:

- Clare's mixture has a concentration of [tex]\(\frac{2}{23}\)[/tex] orange juice concentrate.

- Han's mixture has a concentration of [tex]\(\frac{3}{23}\)[/tex] orange juice concentrate.

Since Han's mixture has a higher concentration of orange juice concentrate, it is likely to taste stronger compared to Clare's mixture.

The probable question maybe:

Clare mixes 2(1)/(2) cups of water with (1)/(3) cup of orange juice concentrate. Han mixes 1(2)/(3) cups of water with (1)/(4) cup of orange juice concentrate. Whose orange juice mixture tastes stronger? Explain or show your reasoning.

Option a. 11 is the right answer

Step-by-step explanation:

To find the value of a function on particular input, the value is put in the function in place of variable

Given function is:

[tex]f(x) = \left \{ {{3x-7\ \ \ x>0} \atop {2x+3\ \ \  x<0}} \right.[/tex]

As we have to find f(6) and x>0 the part of function 3x-7 will be used

so,

[tex]f(6) = 3(6)-7\\= 18-7\\=11[/tex]

Hence,

Option a. 11 is the right answer

Keywords: Functions, Variables

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Answer:

(x+1)

Step-by-step explanation:

(x^2-x-2)/(x-2)=(x+1)

Because (x-2)(x+1)=x^2-2x+x-2=x^2-x-2.

Answer:

x + 1

Step-by-step explanation:

(x² − x − 2) / (x − 2)

Factor the numerator.  Using the AC method:

ac = (1)(-2) = -2

Factors of -2 that add up to -1 are -2 and 1

Divide by a and reduce: -2/1 and 1/1

The factors are (x − 2) and (x + 1)

(x − 2) (x + 1) / (x − 2)

Divide:

x + 1

Answer:

The answer is pi and 3pi

Step-by-step explanation:

Answer:

pi and 3 pi

Step-by-step explanation:

the second one is: (B) x=pi/2 and (D) x=3pi/2

:)

Number of text messages Keisha sent: 16

Number of text messages Miguel sent: 21

Number of text messages Pablo sent: 32

Step-by-step explanation:

Total messages sent = 69

Let,

Messages sent by Keisha = x

Messages sent by Miguel = y

Messages sent by Pablo = z

According to given statement;

x+y+z=69    Eqn 1

y=x+5    Eqn 2

z=2x    Eqn 3

Putting Eqn 2 and 3 in Eqn 1

[tex]x+(x+5)+2x=69\\x+x+5+2x=69\\4x=69-5\\4x=64[/tex]

Dividing both sides by 4;

[tex]\frac{4x}{4}=\frac{64}{4}\\x=16[/tex]

Putting x=16 in Eqn 2

[tex]y=16+5=21[/tex]

Putting x=16 in Eqn 3

[tex]z=2(16)=32\\[/tex]

Number of text messages Keisha sent: 16

Number of text messages Miguel sent: 21

Number of text messages Pablo sent: 32

Keywords: addition, linear equation

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Answer:

[tex]V=400\ mm^3[/tex]

Step-by-step explanation:

we know that

The volume of the triangular prism is equal to

[tex]V=BL[/tex]

where

B is the area of the triangular base

L is the length of the triangular prism (also is called the height of the prism) is the perpendicular distance between the triangular bases

we have

[tex]B=25\ mm^2[/tex]

[tex]L=16\ mm[/tex]

substitute

[tex]V=25(16)[/tex]

[tex]V=400\ mm^3[/tex]

Answer:

The volume of the triangular prism is [tex]400mm^3[/tex]

Explanation :

Area of the triangle = 25 sqmm

Height of the triangle prism = 16mm

Suppose height of the prism is h and breadth is b and length is l

Area= A

Since the formula of volume of prism is

Volume= Area ×height of the prism

= A × h

Substituting the values

= 25×16

=400mm3

The volume of the triangular prism is [tex]400mm^3[/tex]

The percent error in the meteorologist's forecast for Monday is 5.26316 %

Given that Monday's high temperature would be 76°F

On Monday,  the temperature reached 80°F

To find:  percent error in the meteorologist's forecast for Monday

Percent error is the difference between a measured and known value, divided by the known value, multiplied by 100%

The percent error is given as:

[tex]\text {percent error }=\frac{\text {observed - standard}}{\text { standard value}} \times 100[/tex]

Here standard value = 76 and observed value on monday = 80

[tex]\text { percent error }=\frac{80-76}{76} \times 100[/tex]

[tex]\text { percent error }=\frac{4}{76} \times 100=5.26316 \%[/tex]

Thus percent error in the meteorologist's forecast for Monday is 5.26316 %

Answer:

5%

Step-by-step explanation:

i got it right

3 batches can be made with 5 tablespoons of drink mix and 36 ounces of water

We have been given that a sports drink recipe calls for 5/3 tablespoons of powered drink mix for every 12 ounces of water.

We need to find out how many batches can be made with 5 tablespoons of drink mix and 36 ounces of water.

So, from the given information we see that to make 1 batch of sports drink we need 5/3 tablespoons of powdered drink mix for every 12 ounces of water.

So, we have 36 ounces of water. But we know that for 1 batch of sports drink we need to 12 ounces. So with 36 ounces of water we can make

[tex]=\frac{36}{12}[/tex]

= 3 batches

Therefore, we can make 3 batches of sports drink from 5 tablespoons of powdered drink mix and 36 ounces of water.

We can make 3 batches of the sports drink with 5 tablespoons of mix and 36 ounces of water, based on the recipe's ratio.

The subject of this question is mathematics, specifically a type of word problem involving ratios. In this case, the ratio is between the amount of powdered drink mix and the amount of water. The recipe stipulates a ratio of 5/3 tablespoons of mix for every 12 ounces of water. To find how many batches we can make with 5 tablespoons of mix and 36 ounces of water, we need to divide the quantities we have by the quantities needed for a single batch.

First, let's find how many batches we can make with the drink mix we have:

Then, we do the same with the water:

So, based on the quantities of both the mix and water, we can make 3 batches of the drink.

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Answer:

3.8m+4.25n=23250

Step-by-step explanation:

To express the total sales of gasoline and diesel fuel worth $23,250, the equation is: 3.80m + 4.25n = 23,250, where m is the gallons of gasoline sold and n is the gallons of diesel sold.

The question asks for an equation that represents the total sales of fuel worth $23,250, where m gallons of gasoline are sold at $3.80 per gallon and n gallons of diesel fuel are sold at $4.25 per gallon. To find this equation, we can multiply the number of gallons of each fuel type by its respective price per gallon and set the sum equal to the total sales value.

Therefore, the equation is: 3.80m + 4.25n = 23,250.

This equation signifies that the revenue generated from selling m gallons of gasoline at $3.80 per gallon plus the revenue from selling n gallons of diesel at $4.25 per gallon equals $23,250.

Answer:

A) x=3

Step-by-step explanation:

x+2y=11

x+2(4)=11

x+8=11

x=11-8

x=3

Answer:

6

Step-by-step explanation:

(3/4)/(1/8)=(3/4)(8/1)=3*2/1=6/1=6