what system of equation represents this situation?

Rory can make 3 additional 1/8-pound meatballs with the remaining 3/8 pounds of beef after making 7 meatballs that use 3/8 pound each.

Rory has initially 3 pounds of ground beef. Since he uses 3/8 pound per meatball to make 7 meatballs, we first need to calculate the total beef used for 7 meatballs by multiplying 7 (the number of meatballs) by 3/8 pound (the amount of beef per meatball).

7 meatballs × 3/8 pound/meatball = 21/8 pounds

Now, to find out the remaining beef, subtract the beef used from the total beef available:

3 pounds - 21/8 pounds = 24/8 pounds - 21/8 pounds = 3/8 pounds remaining.

With the remaining 3/8 pounds of beef, Rory wishes to make 1/8-pound meatballs. To find out how many 1/8-pound meatballs he can make, we divide the remaining beef by 1/8 pound:

3/8 pounds ÷ 1/8 pound/meatball = 3 meatballs.

Rory can make 3 additional meatballs, each weighing 1/8 pound, with the remaining beef.

Time that will be taken at speed of 45 miles/hr is 1.8 hrs

Step-by-step explanation:

Distance = Speed × Time

               = 54 × 1.5 = 81 miles

TIme = Distance/Speed

        = 81/45 = 1.8 hrs

Answer:

(15+0)2

Step-by-step explanation:

Answer:

there are no real solutions

Step-by-step explanation:

The discriminant is (-10)² - 4*6*50 is below zero, hence there are no solutions.

Answer: 37

Step-by-step explanation:

Let X represents the score for the eighth test

Hence ( 29+36+32+38+35+34+39+X ) ÷8 =35

243+X /8 =35

243+X =35×8

243+X=280

X = 280-243

X= 37

Answer:

Step-by-step explanation:

Answer:

See attachment

Step-by-step explanation:

To graph

[tex]y \: < \: \frac{1}{4} x[/tex]

You first graph the boundary line

[tex]y = \frac{1}{4} x[/tex]

This is a dashed line going through the origin with slope 1/4.

We test the point (0,1) to get: 1<0 which is false. So we shade the lower half-plane.

To graph

[tex]y \: < \: - 6x + 6[/tex]

We first graph line

[tex]y = - 6x + 6[/tex]

By plotting (0,6), and (1,0)

We draw a dashed boundary line.

We test the origin:

0<6 which is true so we shade the left half-plane .

The intersection of both shaded regions represent the solution set.

The graph us shown in attachment.

Answer:

The generalization will be biased because people living in cities that are not as big as New York, Los Angeles and rural areas of the country were excluded from the possibility of being included in the sample.

Step-by-step explanation:

The sample is therefore not a true representation of the population.

Final answer:

The generalization would be biased because it only includes opinions from large cities, which aren't representative of the entire population, leading to sampling bias. This results in a biased sample as it overlooks the diversity in lifestyles and circumstances found in different geographic areas.

Explanation:

If a company conducts a survey among people who only live in large cities like New York and Los Angeles, and then makes a generalization from this survey, the generalization will be biased. This is because the perspectives of people living in large cities are not necessarily representative of the entire population, which includes people from smaller towns, rural areas, and different socioeconomic backgrounds. Such a sampling method leads to a sampling bias, since it does not adequately reflect the diversity of the whole population.

For instance, urban populations may have different lifestyles, access to services, and daily challenges compared to those living in suburban or rural areas. Therefore, if a survey's findings from a city population are applied to the general population, it may result in an inaccurate picture of the opinions, behaviors, or characteristics of the entire population. This exemplifies a biased sample, as the sampling method does not capture the full range of variables affecting the population as a whole.

Yo sup??

in the given figure

9y-3=69

9y=72

y=8

now by angle sum property

9y-3+69+5x+2=180

5x=40

x=8

Hope this helps

Answer: [tex]x=8[/tex]

Step-by-step explanation:

So seeing the equation

[tex](9y -3)[/tex] [tex]y=8[/tex] [tex](9(8)-3) =69[/tex]

therefore, 69 +69 =138

and then that only means the secound equation has to equal 42 because all angles has to equal to 180 degrees, therefore:...

[tex](5x +2)=x=8[/tex] [tex](5(8)+2)=42[/tex]

Hope this helps please give brainliest!

Answer:

  the number of cookies ordered

Step-by-step explanation:

When an equation is written in the form ...

  (left variable) = (some expression involving one or more right variables)

we usually describe the "left variable" as the "dependent variable" and the "one or more right variables" as the "independent variable(s)".

Here, the equation is given as ...

  C = 3s + 30

__

This tells you C is the dependent variable, and s is the independent variable. The description also says "C is the number of cookies." Since you know that the dependent variable is the number of cookies, you can answer the question ...

  the dependent quantity is the number of cookies ordered.  (matches the first choice)

Answer:

39x-7

Step-by-step explanation:

The perimeter is all the sides added together so

9x + 8x - 2 + 5x + 1 + 17x - 6

Since you can't solve it you just want to simplify the equation, add the like terms together

9x+8x+5x+17x = 39x

-2+1-6 = -7

Your equation is 39x-7

Answer:

Question 5.

89.10

Question 6.

Yes, Lucy will have enough money.

Step-by-step explanation:

Question 5.

3*4*9=108

108/2=54

54*1.65=89.10

Question 6.

26*5=130

They will make $130 from fundraising. $89.10 are needed to purchase the soil. 130>89.1

The value of the trigonometric equation is cos θ = EF/DF

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the triangle be represented as ΔDEF

Now , the sides of the triangle are

The hypotenuse of triangle is DF

where the measure of ∠DEF = 90°

Now , from the trigonometric relations , we get

cos θ = adjacent / hypotenuse

cos θ = EF/DF

Hence , the trigonometric relation is cos θ = EF/DF

To learn more about trigonometric relations click :

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Answer:

Jalen is 11.18 miles from his starting point.

Step-by-step explanation:

Given:

Jalen jogged 10 miles due north, then turned due west and jogged 5 more miles.

Now, to find miles Jalen jogged from his starting point.

So, below is the figure attached to describe the scene.

Now, to get the distance of Jalen jogged from his starting point we use pythagoras theorem:

[tex]AB^2+BC^2=AC^2\\\\10^2+5^2=AC^2\\\\100+25=AC^2\\\\125=AC^2[/tex]

Using square root on both sides we get:

[tex]11.18=AC\\\\AC=11.18\ miles.[/tex]

Therefore, Jalen is 11.18 miles from his starting point.

Answer:

11.18 miles

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

32

-5

----

27

÷3

----

9

Hope it helped

There are 9 invitations mail that has already been mailed.

A fraction is a quantity that is not a whole number. In maths, a fraction usually has a numerator and a denominator.

Lee is sending out 32 birthday invites she gives 5 to family and a third of the rest,

The number of invitations Leah has already mailed is given by;

Number of invitations mailed = 1/3 x (total invitation - invitation mom delivered)

Number of invitations mailed =1/3 x (32 - 5)

Number of invitations mailed =1/3 x (27)

Number of invitations mailed = 9

Hence, there are 9 invitations mail that has already been mailed.

Learn more about fractions here;

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Answer:

a) 2/3

b)[tex]y = \frac{2}{3} x + 5[/tex]

Step-by-step explanation:

b) From my previous answer...

Since parallel lines have the same gradient,

the gradient of the line is 2/3 too.

Thus, m= 2/3.

y= 2/3x +c

Now substitute a coordinate into the equation to find c, the y-intercept.

When x=6, y=9,

9= (2/3)(6) +c

9= 4 +c

c= 9 -4

c= 5

Thus the equation of the line is y= 2/3x +5.

Its C if you are estimating. But there is no other exact answer.

Answer:

To subtract, first reverse the sign of each term we are subtracting (in other words turn "+" into "-", and "-" into "+"), then add as usual.

To add here is an example not sure if entirely right but here it is.

Start with:2x2 + 6x + 5 + 3x2 − 2x − 1.

Place like terms together:2x2+3x2 + 6x−2x + 5−1.

Which is:(2+3)x2 + (6−2)x + (5−1)

Add the like terms:5x2 + 4x + 4

Final answer:

To add or subtract polynomials, align like terms, add or subtract their coefficients accordingly, and ensure to distribute the negative sign across a polynomial when subtracting. Treat polynomial addition and subtraction like usual arithmetic, applying rules for positive, negative, and opposite signs.

Explanation:

Adding and subtracting polynomials is a straightforward process that involves combining like terms. Here is a step-by-step guide:

When adding polynomials, align terms with the same variable and exponent (like terms) vertically.

Next, add or subtract the coefficients of these like terms while keeping the variable part the same.

When you encounter subtraction, it's helpful to distribute the negative sign across the polynomial that is being subtracted, effectively changing the sign of each term in that polynomial.

After changing signs where necessary, proceed with addition as described above.

Remember that addition and subtraction of polynomials adhere to the usual arithmetic rules:

Adding two positive numbers gives a result with a positive sign.

Adding two negative numbers yields a result with a negative sign.

When adding numbers with opposite signs, subtract the smaller absolute value from the larger one, and the result takes the sign of the larger number.

For subtraction, change the sign of the subtracted number and then add as outlined.

Similar methods apply to vector addition and subtraction, scalar operations, and polynomial graphing. Keep these principles in mind while working through your math problems.

Answer:

x = 2      y=0

Step-by-step explanation:

We can solve using elimination method

8x - 4y  = 16 __________(1)

8x + 4y  =16 ___________(2)

Subtract equation (2) from equation (1)

-8y  =  0

Divide both-side of the equation by -8

-8y/-8  =   0/-8

y = 0

Substitute y=0 into equation (1)

8x - 4y  = 16

8x - 4(0)  = 16

8x  = 16

Divide both-side of the equation by 8

8x/8  = 16/8

(On the left-hand side of the equation, 8 at the numerator will cancel-out 8 at the denominator leaving us with just x while on the right-hand side of the equation  16 will be divided by 8)

x = 16/8

x = 2

Therefore x = 2 and y=0

Answer:

30

Step-by-step explanation:

Exterior angle equals sum of opposite interior angles

3x = 2x + 30

3x - 2x = 30

x = 30

Answer:

x=30

Step-by-step explanation:

all interior angles in a triangle must equal 180 degrees

2x+30+90=180

2x+120=180

2x=60

x=30

you can check by substituting 30:

2(30)+30+90

60+30+90=180

another way to do this:

3x is an exterior angle

however it is a supplementary one as well

that means tht

3x+90=180

3x=90

x=30

you get the same answer either way

HOPE THIS HELPS!

Answer:15.25oz can

Step-by-step explanation:

Answer: it is proportional

Step-by-step explanation:

This is my answer because 7/8x can be written in the form y=mx+b. What does this mean?

Well, y=mx+b is slope intercept form, where m is the slope and b is the y intercept , or where the line first crosses the y axis. you can write 7/8x in slope intercept form as:

y= 7/8x+0

Also, you can see that the y intercept is 0, which means the line passes through the origin, or the point 0,0 on the coordinate plane. Therefore it must be proportional because every line that passes through 0,0 (the "origin") is proportional.

I think the other person is wrong..he/she didnt explain their reasoning..

Answer:

x=3

Step-by-step explanation:

[tex]5^{x} = 125\\5^{x} = 5^{3} \\x=3[/tex]

Answer: 5 raised to power of 3

Step-by-step explanation:

5×5×5=125

Answer:

Step-by-step explanation:

Maria:

No. of cans in a pack = 6

No.of cans in 17 pack = 6 * 17 = 102 cans

No. of cans bought by Heather = 9 cans

Total cans = 102 + 9 = 111 cans

Answer:  D

Step-by-step explanation:

trust me

The approximate volume of the cylinder shown is [tex]3017 cm^3[/tex] and the correct answer is option A.

Let's find the approximate volume of the cylinder shown in the diagram through the following Step-by-step process.

The volume of a cylinder can be calculated using the formula [tex]V=\pi r^2h[/tex], where r is the radius of the base and h is the height of the cylinder.

From the diagram, estimate that the radius is [tex]r=\frac{17}{2} cm[/tex] (since the diameter is 17 cm) and the height is [tex]h=19 cm[/tex].

[tex]V=\pi\times r^2h\\\\=\pi\frac{17}{2} ^2\times19\\\\\approx \frac{5491}{4} \pi[/tex]

[tex]V=3017 cm^3[/tex] (rounded to the nearest integer).

Thus the approximate volume of the cylinder is [tex]3017 cm^3[/tex] corresponding to option A

Note: Since we used an approximation for the radius, the final answer is also an approximation.

The solution is (1,0)

Explanation:

The two equations are [tex]3x+16y=3[/tex] and [tex]3x-16y=3[/tex]

We need to solve the equation using elimination method.

Adding the two equations, we get,

[tex]3x+16y=3\\3x-16y=3\\-------\\6x=6[/tex]

[tex]x=1[/tex]

Thus, the value of x is 1

Substituting [tex]x=1[/tex] in the equation [tex]3x+16y=3[/tex] , we get,

[tex]3(1)+16y=3[/tex]

Simplifying, we get,

[tex]16y=3-3[/tex]

[tex]16y=0[/tex]

   [tex]y=0[/tex]

Thus, the value of y is 0.

The solution is (1,0)

Answer:

In 18 years time, the population of the city is approximately 705,084

Step-by-step explanation:

From the given information, the initial population is

[tex]P_0=200000[/tex]

The growth rate is 7% or r=0.07.

For a population with a continuous growth rate, the equation is that models it is:

[tex]P(t)=P_0 {(e)}^{rt} [/tex]

[tex]P(t)=200000 {(e)}^{0.07t} [/tex]

To find the find the population after 18 years, we substitute t=18 into:

[tex]P(18) = 200000{(e)}^{18\times 0.07} [/tex]

[tex]P(18)=705084.3[/tex]

Answer:

R1,380

Step-by-step explanation:

The price of the iPad without VAT is R1200

We calculate 15% to get;

[tex] = \frac{15}{100} \times 1200[/tex]

[tex] = 180[/tex]

Now the selling price of the iPad including VAT

[tex]1200 + 180[/tex]

[tex] = 1380[/tex]

Therefore, the selling price of the ipad including VAT is R1380

To find the selling price of the iPad including 15% VAT, calculate 15% of R1200, which is R180, and add it to the base price, leading to a total of R1380.

The selling price of an iPad including VAT can be calculated by first determining what 15% of the base price is, and then adding it to the base price. The base price is R1200.

To calculate 15% VAT:

Convert 15% to a decimal by dividing by 100: 15% / 100 = 0.15.

Multiply the base price by this decimal to get the VAT amount: R1200  imes 0.15 = R180.

Add the VAT to the base price to find the total selling price: R1200 + R180 = R1380.

Therefore, including 15% VAT, the selling price of the iPad is R1380.

Answer:

8 inches

Step-by-step explanation:

The area of a triangle is given by

A = 1/2 b*h

The area is 52 and the height is 13

52 = 1/2 b*13

52 = 13/2 b

Multiply each side by 2/13 to isolate b

52*2/13 = 2/13*13/2 b

8 = b

The length of the base is 8 inches