8. Solve the system. (1 point)

x+y=5
-2x+4y=8

The amount of money spent on a pass and lunch for each student is given by A = $ 16.02

Given data ,

The school spends $ 837.14 on passes for 36 students and 2 teachers

And , school also spends $ 307.44 on lunch for just the students

Now , 837.14 - 2x = amount spent on passes for 36 students

where x is the cost of a pass for a teacher

And , (837.14 - 2x) + 307.44 = 36y

where y is the cost of a pass and lunch for each student

On simplifying the equation , we get

1144.58 - 2x = 36y

Now we can solve for y:

y = (1144.58 - 2x)/36

We know that the school spent 307.44 dollars on lunch for just the students, so the amount spent on passes for 36 students is:

837.14 - 2x = 36y - 307.44

Substituting the expression we found for y into this equation, we get:

837.14 - 2x = (1144.58 - 2x)/36 * 36 - 307.44

Simplifying this equation, we get:

2x = 897.58

x = 448.79

Now , the value of y is

y = (1144.58 - 2(448.79))/36

y = 16.02

Hence , the school spent $ 16.02 on a pass and lunch for each student

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Label XY with 3.

Label angle X with 53 degrees.

Label angle Y with 90 degrees.

Label angle C with 37 degrees.

Label angle A with 53 degrees.

Label BC with 4.

Label AC with 5.

Answer: i don't know if you want degrees or the lengths so i did both

∠ACB = 37°

∠BAC = 53°

∠ZXY = 53°

∠XYZ = 90°

∠XZY = 37°

∠ABC = 90°

BC = 4

AC = 5

AB = 3

YZ = 4

XY = 3

XZ = 5

Step-by-step explanation:

37 + 90 = 127

180 - 127 = 53

37 + 90 + 53 = 180

Answer:

a. Possible outcomes for this chance experiment are:

(Here, D means a defective battery, and N means a nondefective battery.)

b. The number of outcomes in the sample space is infinite, as the experiment could potentially continue indefinitely. However, in practice, we can define a maximum number of batteries that could be examined before the experiment is stopped.

c. The event E, that the number of batteries examined is a number, would include outcomes where the experiment stopped at a particular number of batteries. For example, if the experiment stopped after examining three batteries (i.e., the fourth battery was nondefective), then the outcome would be DDDN, and it would be included in event E. However, outcomes where the experiment continued indefinitely (e.g., DDDDD...) would not be included in event E.

Answer:

21 & 11

Step-by-step explanation:

Let x = first number and y = second number. We need to find the values of x and y, so we need to set up a system of linear equations. The first equation would be x + y = 32 because x and y add up to 32. Then the second equation would be x - y = 10 to represent that the two numbers have a difference of 10. Solving by elimination, we add and get 2x = 42, so x = 21. Then substitute 21 for x in either one of the equations to get y = 11.

Answer:

The coefficient is 3.

Step-by-step explanation:

The coefficient is the number that is grouped with an unknown number represented by a letter.

Answer:

Step-by-step explanation:

60 minutes per hour
2.82gal *60mins = 169.2gal per hour.
303 gallons / 169.2 gph = about 1.7907 hours

Answer:

i dont know sorry

Step-by-step explanation:

sorry hdhrhfjbdhehrhdve

1. The sentences translated to equations looks like:

a) 4x = 32.

b) x + 6y = 43.

c) 3x + 7 = 9x - 4.

d) 76 - 2x = 8x.

2. The equations translated to sentences looks like:

a) The sum of 16 and 9 times x is 50.

b) The sum of the square of x and 6 times y is 4 times w.

c) Three times x is 52.

d) Five-sixth is equal to the product of -10 and x.

Practice Part 1: Translate sentence to equation

a)Four times a number is thirty-two.

Assuming the number to be x, we get the equation, 4x = 32.

b)The sum of and six times  is equal to forty-three.

The sentence, when translated to an equation looks like, x + 6y = 43.

c)The sum of 7 and three times  equals the difference of 9 times  and 4.

The sentence, when translated to an equation looks like, 3x + 7 = 9x - 4.

d)Two times  less than 76 is equal to the product of 8 and

The sentence, when translated to an equation looks like, 76 - 2x = 8x.

Practice Part 2: Translate equation into sentence

a) 9x + 16 = 50.

- The sentence for the given equation is, the sum of 16 and 9 times x is 50.

b) x² + 6y = 4w.

- The sentence for the given equation is, the sum of the square of x and 6 times y is 4 times w.

c) 3x = 52.

- The sentence for the given equation is, three times x is 52.

d) 5/6 = -10x.

- The sentence for the given equation is, five-sixth is equal to the product of -10 and x.

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Answer:

where do you live

Step-by-step explanation:

Answer:

  x = -5

Step-by-step explanation:

You want the solution to 8-(x+12)=1.

Eliminate parentheses using the distributive property:

  8 -x -12 = 1

Combine like terms.

  -4 -x = 1

We like to have the x-coefficient be positive, so we're going to add x to both sides:

  -4 = 1 +x

Subtract 1 to get x by itself.

  -5 = x

The value of x is -5.

__

Additional comment

We could have solved this by adding 4 to both sides in the third step:

  -x = 5

Now, we need to multiply (or divide) by -1:

  x = -5

Any operation (add, subtract, multiply, divide, root, log, or any other function) is done to both sides of the equation, according to the properties of equality.

In order for the relationship zyx ~ wvu to be correct, the following conditions must be true:

Corresponding angles are congruent: The angles formed by matching vertices should have the same measures in both triangles. This ensures that the corresponding angles are equivalent.

Corresponding sides are proportional: The lengths of the sides that connect the corresponding vertices of the triangles should have a consistent ratio. This implies that the corresponding sides are proportional to each other.

These conditions are based on the definition of similarity between two triangles. If both the corresponding angles are congruent and the corresponding sides are proportional, then the triangles zyx and wvu are considered similar (denoted by ~).

Therefore, in order for zyx ~ wvu to be correct, the congruence of corresponding angles and the proportionality of corresponding sides must hold true.

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For function f(t) = 1.25^t, it is an exponential growth.

The percent rate of change per unit t is found by taking the derivative of the function:

f'(t) = ln(1.25) * 1.25^t ≈ 9.2%

Since f'(t) is positive, the function represents exponential growth.

For function g(t)=5^-t:

The percent rate of change per unit t is found by taking the derivative of the function:

g'(t) = -ln(5) * 5^-t ≈ -13.9%

Since g'(t) is negative, the function represents exponential decay.

For function h(t) = 1.20(t/11):

The percent rate of change per unit t is found by taking the derivative of the function:

h'(t) = 1.20/11 ≈ 10.9%

Since h'(t) is positive, the function represents exponential growth.

For function k(t) = 0.63t:

The percent rate of change per unit t is found by taking the derivative of the function:

k'(t) = 0.63 ≈ 63.0%

Since k'(t) is positive, the function represents exponential growth.

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Each dish contains 1/9 pound of butter.

Dividing 2/3 pound by 6 can be done by multiplying the numerator by the reciprocal of the denominator:

⇒ (2/3) / 6

⇒ (2/3) * (1/6)

When we multiply the numerators (2 * 1), we get 2. And when we multiply the denominators (3 * 6), we get 18.

⇒ (2/3) / 6  

⇒ 2/18

To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 2:

⇒ 2/18

⇒ (2/2) / (18/2)

⇒ 1/9.

Therefore, each dish contains 1/9 pound of butter.

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Answer:

The choice that is equivalent to the quotient values of X in √7x² ÷ √3x is Option C : (√7x/3).

What is the quotient about?

Since the expression is √7x² ÷ √3x

So, one need to  rationalize the denominator and thus:

√7x² ÷ √3x  x √3x  ÷ √3x  

or write as √7x² x√3x ÷ √3x

or write as√(21x³)/3x

or write as √3*7*x³/3x

or write as √3*7*x/3

= √7x/√3

Therefore, The choice that is equivalent to the quotient values of X in √7x² ÷ √3x is Option C : (√7x/3).

Step-by-step explanation:

Answer:

6x+6x2+3

Step-by-step explanation:

6x2+5x+1+x+2

Combine 5x and x to get 6x.

6x2+6x+1+2

Add 1 and 2 to get 3.

6x2+6x+3

Multiplication of the given matrix is not possible by definition of matrix multiplication.

Since, To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

Expression for multiply,

⇒ [4, 0, -1, 2, -3, -1] x [0, 1, -3, 1]

Since, We can see that;

First matrix have order 1 x 6

And, Second matrix have order 1 x 4

We know that;

Matrix multiplication is possible when number of column in first matrix is same as number of rows in second matrix.

Hence, By given matrices we get;

Number of column in first matrix (6) ≠ number of rows in second matrix (1)

So, Multiplication of the given matrix is not possible by definition of matrix multiplication.

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The remainder must be 7 when z(x) is divided by x + 4

The equation is given as

z(-4) = 7

The function is represented as

z(x)

This means that

x = -4

So, we add 4 to both sides of the equation

This gives

x + 4 = 0

So, when the equation in interpreted, it means

The remainder when z(x) is divided by x + 4 is  7

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\(1\frac{3}{4}\) feet as a multiplication expression using the unit, 1 foot, as a factor is \(1\frac{3}{4}\)×1.

The given fraction is \(1\frac{3}{4}\).

\(1\frac{3}{4}\) feet can be written as a multiplication expression as follows: 1 foot × 1 3/4. This is because \(1\frac{3}{4}\) is the same as 1 + 3/4.

Furthermore, 3/4 can be written as 0.75, which is the same as 0.75 × 1 foot.

Therefore, the multiplication expression is 1 foot × \(1\frac{3}{4}\) = 1 foot × (1 + 0.75) = 1 foot × 1 + 1 foot × 0.75 = 1 foot + 1.75 feet.

Therefore, \(1\frac{3}{4}\) feet as a multiplication expression using the unit, 1 foot, as a factor is \(1\frac{3}{4}\)×1.

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Step-by-step explanation:

1ft=12in

1¾ft=x

x=12×7/4=21in

1¾ft=1¾×1 ft

Answer: D. Simple Random Sampling

Step-by-step explanation: When selection is made or based on chance which is equal or the same for all members within a population. In the scenario described above, there is no prior shuffling, arrangement or segregation of members within the population into groups or subgroups, rather the interviewed voters were chosen at random directly from within the larger population based on equal chance. Therefore voters already have their numbers, then using a random number generator, voters whose number corresponds were interviewed is a clear scenario of simple Random Sampling.

Using sampling concepts, it is found that the correct option is:

d. simple random sampling

Samples are classified as:

In this problem, a random number is generated to select each voter, hence it is a simple random sampling, and option d is correct.

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Answer:

40; 0.1 and 0.16

Step-by-step explanation:

a. We know that p(w)=230(1.1)^W represents the number of specialty items produced at the old factory.

This equation is in the form of an exponential growth function:

f(x)=a(1+r)^x

where a is the initial value, r is the growth rate, and x is the number of time intervals.

That means that for p(w)=230(1.1)^W:

230 is the initial value, and 0.1 is the growth rate. (1.1-1)

Therefore, for week 0, there were 230 specialty items produced at the old factory.

We can also plug in 0 for w (0 time intervals) to get the same answer

That would look like:

p(0)=230(1.1)^0

p(0)=230(1)

p(0)=230

On the other hand, for the new factory, if you go find 0 on the x-axis, you'll notice that 190 specialty items were produced in week 0.

230-190=40

This means that our answer for a is that 40 more specialty items were produced at the old factory than the new factory.

_____

b. Our first step for this question would be to find the equation for the graph.

We can immediately recognize that this is an exponential growth function, similar to the other equation.

As a reminder, exponential growth functions are in the form: f(x)=a(1+r)^x

We can put it in terms of production and weeks:

p(w)=a(1+r)^w

We know that the initial value is 190 by the graph.

p(w)=190(1+r)^w

Now we just need to find the growth rate:

We can do this by choosing a value (other than the first point) and plugging it in.  Let's use (1, 220) which is in the form (w, p)

Plug it in to the equation:

220=190(1+r)^1

220=190(1+r)

Distribute

220=190+190r

Subtract 190 from both sides

30=190r

Divide 190 from both sides

r=0.1578947368 (round how your teacher asks)

Next, all we have to do is find the growth rate for the old factory:

p(w)=230(1.1)^W

1.1=1+r

Therefore, r=0.1

The growth rate at the old factory is 0.1.

When comparing them, we'll realize that the growth rate at the new factory is about 0.06 higher.

#1

For old factory

So

\(\\ \rm\dashrightarrow p(0)=230(1.1)^0=230(1)=230\)

For nEW factory

Difference:-

40 items were more produced

#2

For old factory

\(\\ \rm\dashrightarrow 230(1+0.1)^t\)

For new factory

Find slope:-

\(\\ \rm\dashrightarrow m=\dfrac{220-190}{1}=30\)

Find growth rate

New factory has greater growth rate

In order to have a parallelogram, the opposite sides need to be parallel.

And in order to be a trapezoid, just one pair of sides needs to be parallel.

Looking at the image, the sides FG and JH are parallel, since they have the same slope (we can also see that both these sides have no variation in the y-coordinate, so they are parallel).

Then, looking at the sides FJ and GH, they are not parallel, because they have different slopes (the side FJ has a run of 1 and a rise of -3, and the side GH has a run of 2 and a rise of -3).

Since the quadrilateral FGHJ has just one pair of parallel sides, it is a trapezoid but not a parallelogram.

9514 1404 393

Answer:

  1.53 minutes faster

Step-by-step explanation:

A question of this nature can be answered a number of ways. Often, when athletes compare speeds over a course of a specific length, they do it by comparing times.

Here, Jill"s time is ...

  21.00 -19.47 = 1.53

minutes less than Grace"s time.

Jill swam a mile 1.53 minutes faster than Grace did.

Answer:

\(x \leq -4\)

There will be a filled-in hole at -4.

Step-by-step explanation:

We can solve an inequality the same way we do for equations. The only thing to keep in mind, is that multiplying by a negative number will result in flipping the inequality sign (< to > and vice versa)

\(-7x + 13 \geq 41 \text{ //}-13\\-7x \geq 28 \text{ //}:-7 \text{ (Notice we multiply by a negative number.)}\\x \leq -4\)

The difference between a filled-in and an empty hole in terms of inequality graphs, is whether or not the number limiting the inequality is included in it.

For example, in x > 3, 3 is limiting the inequality, however, it is not included in it, therefore, x would always be greater than 3.

In another example, \(x \leq -4\), -4 is limiting inequality and is included in it. Therefore, x would always be less than or equal to -4.

A filled-in hole means the number is included in the inequality, while an empty one means it isn't.

In our cases, -4 is included in the inequality (notice the line under the inequality sign that resembles "less than or equal to"), therefore there will be a filled-in hole at -4.

The transformations that map the strip pattern onto itself is a horizontal translation, a reflection across a vertical line, a reflection across a horizontal line, a glide reflection, and a 180°. Option A is the correct option.

Here, we have,

the conditions for mapping the strip transformation pattern onto itself:

The strip pattern can be mapped onto itself in two different ways.

The first way is to translate the strip pattern horizontally and then rotate it by 180° degrees.

The second way is to reflect the strip pattern across a vertical line.

Hence, the transformations that map the strip pattern onto itself can be achieved through a horizontal translation, a reflection across a vertical line, a reflection across a horizontal line, a glide reflection, and a 180°.

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complete question:

Which transformations map the strip pattern onto itself?

a horizontal translation, a reflection across a vertical line, a reflection across a horizontal line, a glide reflection, and a 180°

a horizontal translation only

a horizontal translation, a reflection across a horizontal line, and a glide reflection only

a horizontal translation and a 180° rotation only

Answer: In point C.

Step-by-step explanation:

Plane ADB is the plane that contains the points A, D and B.

If you look in the image, you can see that point C also does belong to this plane.

Line EC is the line that connects the points E and C.

Now, remember that Point C does belong to the plane ADB, then the point where the plane ADB and line EC intersect is in point C, because it is a common point to both elements.

The best representation of the number of tiles that will be needed to cover the Floor is 80 tiles.

The number of tiles needed to cover the floor, we can calculate the total area of the floor and divide it by the area of each tile.

The area of the floor is given by the product of its length and width: 15 feet * 12 feet = 180 square feet.

The area of each tile is given by the product of its length and width: 1.5 feet * 1.5 feet = 2.25 square feet.

To find the number of tiles needed, we divide the total area of the floor by the area of each tile:

Number of tiles = (Total area of the floor) / (Area of each tile) = 180 square feet / 2.25 square feet = 80 tiles.

therefore, the best representation of the number of tiles that will be needed to cover the floor is 80 tiles.

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Answer: for the factor one: The expression isn't factorable with rational numbers

Step-by-step explanation: Since the polynomial can be factored it isn't prime (i don't know if that is what you meant or not but I hope this helps and I got all of them correct )

a) The percentage is 73%.

b) The ratio is 73:27

d) The decimal form is 0.73

e) The fraction is 73/100

The percentage of the model that is shaded is given by:

P = 100%*(shaded squares)/(total number of squares)

There are 100 squares in total, of these 73 are shaded, then the percentage is:

P = 100%*(73)/100 = 73%

b) The ratio is "shaded squares to non shaded squares"

There are 73 shaded squares and 27 non-shaded ones, then the ratio is 73:27

c) To get the equivalent decimal to a percentage, just divide it by 100%.

p = 73%/100%  =0.73

d) The equivalent fraction is the fraction we wrote on the first step, it is:

fraction = 73/100

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Answer:

D, g(x) = 1/4 x^2

Step-by-step explanation:

You can try plugging in the x and y values into each equation. The answer to this would be D, where if you plug in 2 as the x value, you get 1/4 * 4 which equals 1. This also makes sense because 2x would have a narrower curve while 1/2x would have a wider curve.