the sixth grade class from Franklin Middle School is going to the zoo on a field trip. there are 270 students who want to go on the field trip. if the school requires one adult for every 15 students, how many adults will be needed for the field trip?

Answer:

(1) x= 5, y = 3

(2) x = -27, y = -29

Step-by-step explanation:

If the frist equation is 16x - 2y = 74

[tex]\\\\\left\{\begin{array}{ccc}8x-y=37\\x-y=2&\text{add y to both sides}\end{array}\right\\\\\left\{\begin{array}{ccc}8x-y=37&(1)\\x=2+y&(2)\end{array}\right\\\\\\\text{substitute (2) to (1):}\\\\8(2+y)-y=37\qquad\text{use the distributive property:}\ a(b+c)=ab+ac\\16+8y-y=37\qquad\text{subtract 16 from both sides}\\7y=21\qquad\text{divide both sides by 7}\\\boxed{y=3}[/tex]

[tex]\text{put the value of y to (2):}\\\\x=3+2\\\boxed{x=5}[/tex]

If the first equation is 16 - 2y = 74

[tex]\left\{\begin{array}{ccc}16-2y=74&\text{divide both sides by 2}\\2-2y=4&\text{divide both sides by 2}\end{array}\right\\\left\{\begin{array}{ccc}8-y=37&\text{subtract 8 from both sides}\\x-y=2\end{array}\right\\\left\{\begin{array}{ccc}-y=29&\text{change the signs}\\x-y=2\end{array}\right\\\left\{\begin{array}{ccc}y=-29&\text{put it to the second equation}\\x-y=2\end{array}\right\\\left\{\begin{array}{ccc}y=-29\\x-(-29)=2\end{array}\right\\\left\{\begin{array}{ccc}y=-29\\x+29=2&\text{subtract 29 from both sides}\end{array}\right[/tex]

[tex]\left\{\begin{array}{ccc}y=-29\\x=-27\end{array}\right[/tex]

Answer:

x=42

Step-by-step explanation:

Add by 26 from both sides of equation.

6x-26+26=58+4x+26

Simplify.

6x=4x+84

Subtract by 4x from both sides of equation.

6x-4x=4x+84-4x

Simplify.

2x=84

Divide by 2 from both sides of equation.

2x/2=84/2

Simplify, to find the answer.

84/2=42

x=42 is the correct answer.

I hope this helps you, and have a wonderful day!

Answer:

A'(-4,4)

B'(-2,11)

Step-by-step explanation:

6 unit up and 3 unit left

A (-1,-2) : 6 unit up → (-1,4) → 3 unit left → (-4,4)

A'(-4,4)

B (1,5) : 6 unit up → (1,11) → 3 unit left → (-2,11)

B'(-2,11)

For this case we have the following functions:

[tex]f (x) = 7x + 1\\g (x) = x ^ 2[/tex]

We must find[tex](g_ {0} f) (x).[/tex]

By definition of composition of functions we have to:

[tex](g_ {0} f) (x) = g (f (x))[/tex]

So:

[tex](g_ {0} f) (x) = g (f (x)) = (7x + 1) ^ 2 = 49x ^ 2 + 2 (7x) (1) + 1 = 49x ^ 2 + 14x + 1[/tex]

ANswer:

[tex](7x + 1) ^ 2 = 49x ^ 2 + 14x + 1[/tex]

[tex]\bf 3x^3+27x^2-15x\div 3x\implies \cfrac{3x^3+27x^2-15x}{3x}\implies \stackrel{\textit{distributing the denominator}}{\cfrac{3x^3}{3x}+\cfrac{27x^2}{3x}-\cfrac{15x}{3x}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill x^2+9x-5~\hfill[/tex]

63-5x

So you do PEMDAS

There aren’t any parenthesis

There aren’t any exponents

So you multiply 3*3 and get 9

Multiply 27 by 2 and get 54

And divide 15x by 3x

Now moving on to addition/subtraction

The equation is now 9+54-5x

9+54 is 63

So the answer is 63+5x

Answer:

x = 53, y = 33

Step-by-step explanation:

Let one of the numbers = x, & the other = y. Set the equations:

x + y = 86

x - y = 20

This is a system of equation, in which the variables must be true for both of them.

First, choose a equation to use. In this case, I will choose x + y = 86. Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Subtract y from both sides.

x + y = 86

x + y (-y) = 86 (-y)

x = 86 - y

Now, note the other equation: x - y = 20. You now know that x = 86 - y. Plug in 86 - y for x in the "other" equation:

x - y = 20

(86 - y) - y = 20

Simplify. Combine like terms:

86 - y - y = 20

86 - 2y = 20

Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS (Parenthesis, Exponents (& Roots), Multiplication, Division, Addition, Subtraction):

First, subtract 86 from both sides:

86 (-86) - 2y = 20 (-86)

-2y = 20 - 86

-2y = -66

Isolate the variable, y. Divide -2 from both sides:

(-2y)/-2 = (-66)/-2

Note: Before we go any further, I want to remind you of division & multiplication rules. There are 3 kinds, when you are multiplying two positive numbers (+/+), when you are multiplying a positive number with a negative number (+/-), and when you are multiplying a two negative numbers (-/-). Note the "table" in the bottom:

________________________________________________________

(+/+) : Two positive numbers multiplied/divided with each other will always result in a positive answer:

Examples:

10/5 = 2

20/10 = 2

(+/-) : One positive number and one negative number multiplied/divided with each other will always result in a negative answer:

Examples:

20 x -5 = -100

50 x -3 = -150

(-/-) : Two negative numbers multiplied/divided with each other will always result in a positive answer:

Examples:

-30 x -5 = 150

-200/-10 = 20

________________________________________________________

Now, solve the equation:

(-2y)/-2 = (-66)/-2

y = -66/-2

Divide.

y = 33

One of your numbers (y) is 33. Plug in 33 for y in one of the equations:

x + y = 86

x + (33) = 86

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Subtract 33 from both sides.

x + 33 (-33) = 86 (-33)

x = 86 - 33

x = 53

Your answers: x = 53, y = 33.

Check: Plug in 53 for x, 33 for y in the equations:

x + y = 86:

(53) + (33) = 86

86 = 86 (True)

x - y = 20:

(53) - (33) = 20

20 = 20 (True)

Your answers: x = 53, y = 33

~

Answer: 53 and 33

Step-by-step explanation:

Let be "x" the first number and "y" the second number.

Based on the information provided we can set up a system of equations:

[tex]\left \{ {{x+y=86} \atop {x-y=20}} \right.[/tex]

Applying the Elimination method, we can add both equations and solve for the variable "x":

[tex]\left \{ {{x+y=86} \atop {x-y=20}} \right.\\................\\2x=106\\\\x=\frac{106}{2}\\\\x=53[/tex]

Now we can substitute [tex]x=53[/tex] into one of the original equations and solve for the variable "y":

[tex]53+y=86\\\\y=86-53\\\\y=33[/tex]

Answer:

[tex] f ( x ) = 2 . 2 5 ( 1 + 0 . 4 ) ^ x [/tex]

Step-by-step explanation:

We are given that the price of gas started at $2.25 and increased at a rate of 4% per year.

We are to write a function which models this situation using numerical values of A and r into the expression.

A = $2.25

r = 4%

Assuming x to be the time in years, the function would be:

[tex] f ( x ) = 2 . 2 5 ( 1 + 0 . 4 ) ^ x [/tex]

Answer:

Isosceles and obtuse

Step-by-step explanation:

It is not a scalene triangle because it has two same lengths 41 degrees and 41 degrees.

It is a Isosceles triangle because two of the sides have the same lengths 41 degrees and 41 degrees

It is an obtuse triangle because it has on obtuse angle which is 98 and two acute angles that are 41 degrees

It is not an equilateral because not all of the sides are the same lengths

It is not a right triangle because there are 90 degree angles

It is not an acute triangle because not all the angles are acute angles

A triangle can be classified based on its angles and sides. A Trigonal Bipyramidal triangle has angles of 90 degrees or 120 degrees, and atoms can be positioned equatorially (in the plane of the triangle) or axially (above or below the plane). Always remember that the sum of all interior angles of a triangle is 180°.

The classification of a triangle depends on its angles and sides. If you have a triangle like a Trigonal Bipyramidal, the angles of such a triangle can be 90 degrees or 120 degrees. This relates to a three-dimensional trigonal bipyramidal molecular geometry where three atoms or groups of atoms are positioned in a flat triangle around a central atom, symmetrically positioned with 120° angles between each pair.

Another element you mentioned is the position of an attached atom in a triangle. This can be either equatorial (in the plane of the triangle) or axial (above or below that plane).

For detailed classification, always keep in mind that the sum of all interior angles of a triangle is always 180°. A triangle with one angle measuring 90° is a right triangle. An equilateral triangle has all angles measuring 60°. In the trigonal planar case, all atoms are in one plane, and bond angles are 120°.

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For this case we have the following expression:

[tex]-1.5x-3.1 <5.5[/tex]

Adding 3.1 to both sides of the inequality:

[tex]-1.5x <5.5 + 3.1\\-1.5x <8.6[/tex]

Dividing between -1.5 on both sides of the inequality, keeping in mind that the sign changes direction:

[tex]x> \frac {8.6} {- 1.5}\\x> -5.73333[/tex]

Answer:

[tex]x> -5.73333[/tex]

Answer:

1) 33.33%

2) 16.66%

Step-by-step explanation:

1) Since multiples of 3 in 1,2,3,4,5,6 include and limited to 3 and 6.  This means that 2 / 6 or 1 / 3.  This fraction is equal to 33.33%.

2) Since multiples of 4 in 1,2,3,4,5,6 include and limited to only 4.  This means that 1/6 and this fraction is equal to 16.66%.

Answer:

1/2.

Step-by-step explanation:

A multiple of 3 is 3 or 6 and a multiple of 4 is 4.

Probability(3 or 6) = 2/6 = 1/3.

Probability(4 ) = 1/6.

So Probability ( multiple of 3 or a multiple of 4) = 1/6 + 1/3

= 1/2.

Answer:

Yes, [tex]y=-x[/tex]  describes "y" as a funcion of "x", because  each input value (value of "x") has only one ouput value (value of "y").

 Step-by-step explanation:

By definition, a relation is a function if  each input value (value of "x")has only one ouput value (value of "y").

We need to remember that "y as a function of x" means that  "x" is the independent variable and "y" is the dependent variable or, in other words,  the value of the variable "y" depends upon the value of the variable "x".

Then, [tex]y=-x[/tex] is a function, because each input value has one and only one output value. For example:

If [tex]x=-2[/tex], then:

[tex]y=-(-2)=2[/tex]

If [tex]x=1[/tex], then:

[tex]y=-(1)=-1[/tex]

If [tex]x=5[/tex], then:

[tex]y=-(5)=-5[/tex]

Therefore,  [tex]y=-x[/tex]  describes "y" as a funcion of "x".

Answer:

P = 4 / 6 = 2/3 = 0.66 = 66%

Step-by-step explanation:

Assuming the die is numbered 1 to 6.

To answer the question, we first need to know many prime numbers can be represented on the die.  What are the prime numbers equal to 6 or lower?

We have 2, 3 and 5.  (since 4 and 6 are not prime numbers).  So we have 3 prime numbers, plus the number 1... so there are 4 possibilities valid for rolling a 1 or a prime number: 1,2,3 and 5.

4 possibilities out of 6 total possible outcomes, so...

P = 4 / 6 = 2/3 = 0.66 = 66%

Answer:

The probability of rolling a 6 sided die and getting a 1 or a prime number = 2/3

Step-by-step explanation:

The numbers on the die are 1, 2, 3, 4, 5 and 6

To find the probability

Total outcomes of rolling a die = 6

Prime numbers less than 6 are 2, 3 and 5

Possible outcomes(getting 1 or a prime number) =  1, 2, 3 and 5

Probability of getting 1 or prime number when rolling a die = 4/6 = 2/3

Answer:

the answer is x=0,-(3/7)

Step-by-step explanation:

Answer:

x = { - [tex]\frac{3}{7}[/tex], 0 }

Step-by-step explanation:

Given

7x² + 3x = 0 ← factor out x from each term

x(7x + 3) = 0

Equate each factor to zero and solve for x

x = 0

7x + 3 = 0 ⇒ 7x = - 3 ⇒ x = - [tex]\frac{3}{7}[/tex]

Answer: B and F

Hope it helps!!!

Answer: OPTION B AND OPTION D.

Step-by-step explanation:

Analyze  the triangle provided.

You can observe that the lenghts of its sides are: 10.9, 15, 14

Then the lenghts of its sides are not equal.

 By definition, when all sides of a triangle are different this is called: "Scalene".

You can notice that the measures of its angles are: 63°, 44° and 73°

Then, all its angles are less than 90 degrees.

By definition if all three angles of a triangle are less than 90 degrees, then is called: "Acute".

Answer:

A

Step-by-step explanation:

Answer:

[tex]\frac{3}{2}[/tex]

Step-by-step explanation:

Using the addition formulae for cosine

cos(x ± y) = cosxcosy ∓ sinxsiny

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

cos(120 + x) = cos120cosx - sin120sinx

                   = - cos60cosx - sin60sinx

                   = - [tex]\frac{1}{2}[/tex] cosx - [tex]\frac{\sqrt{3} }{2}[/tex] sinx

squaring to obtain cos² (120 + x)

= [tex]\frac{1}{4}[/tex]cos²x + [tex]\frac{\sqrt{3} }{2}[/tex]sinxcosx + [tex]\frac{3}{4}[/tex]sin²x

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

cos(120 - x) = cos120cosx + sin120sinx

                   = -cos60cosx + sin60sinx

                   = - [tex]\frac{1}{2}[/tex]cosx + [tex]\frac{\sqrt{3} }{2}[/tex]sinx

squaring to obtain cos²(120 - x)

= [tex]\frac{1}{4}[/tex]cos²x - [tex]\frac{\sqrt{3} }{2}[/tex]sinxcosx + [tex]\frac{3}{4}[/tex]sin²x

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

Putting it all together

cos²x + [tex]\frac{1}{4}[/tex]cos²x + [tex]\frac{\sqrt{3} }{2}[/tex]sinxcosx + [tex]\frac{3}{4}[/tex]sin²x + [tex]\frac{1}{4}[/tex]cos²x - [tex]\frac{\sqrt{3} }{2}[/tex]sinxcosx + [tex]\frac{3}{4}[/tex]sin²x

= cos²x + [tex]\frac{1}{2}[/tex]cos²x + [tex]\frac{3}{2}[/tex]sin²x

= [tex]\frac{3}{2}[/tex]cos²x + [tex]\frac{3}{2}[/tex]sin²x

= [tex]\frac{3}{2}[/tex](cos²x + sin²x) = [tex]\frac{3}{2}[/tex]

Answer:

b=128

Step-by-step explanation:

Answer:

Option D b = 128°

Step-by-step explanation:

There are two parallel lines p and q

These lines are crossed by a transversal m

then ∠b and ∠128° are the alternate angles.

which should be equal in measure.

Therefore, ∠b = 128°

Option D b = 128° is the answer.

Answer:

W, I believe

Step-by-step explanation:

Answer:

W

Step-by-step explanation:

The y intercept is where the graph crosses the y axis (where x=0)

This is the point W

Answer:

box contains - 3

Step-by-step explanation:

a(x - 3) + 2x = -(x - 5) +4              Remove the brackets on both sides

ax - 3a + 2x = -x + 5   + 4             Subtract 2x from both sides.

ax - 3a + 2x - 2x = -x - 2x + 9

ax - 3a = - 3x + 9

ax - 3(-3) = - 3x + 9

ax + 9 = - 3x + 9

Now if you make a = -3 then both sides with have - 3 for the x coefficient.

Any number could be put in for x and it will make the answer on both sides equal. Notice you could subtract 9 from both sides and it will not change the condition of the problem.

Answer:

c = -3

Step-by-step explanation:

Call the unknown c

c(x-3) +2x = -(x-5) +4

Distribute the negative sign

c(x-3) +2x = -x+5+4

Combine like terms

c(x-3) +2x = -x +9

Subtract 2x from each side

c(x-3) +2x-2x = -x-2x +9

c(x-3) = -3x+9

Factor a -3 from the right side

c(x-3) = -3(x-3)

Divide by (x-3)

c = -3

The right and left hand side need to be equal for there to be infinite solutions, so c = -3

Answer:

Option C is correct.

Step-by-step explanation:

The x-intercepts of the function (x − 1)(x − 4)(x + 7) can be found by putting this function equal to zero

(x − 1)(x − 4)(x + 7) = 0

Now,

x-1 = 0

x-4 = 0

and x+7 = 0

Now finding the values of x

x-1 = 0 + 1

x - 1 + 1 = 1

=> x = 1

or (1,0)

x - 4 = 0

x -4 + 4 = 0 + 4

x = 4

or (4,0)

x + 7 = 0

x +7 -7 = 0 -7

x = -7

or (-7,0)

SO, the x-intercepts of the function (x − 1)(x − 4)(x + 7) are (1,0),(4,0) and (-7,0)

Option C is correct.

Answer:

+ 1  + 4   -7

Step-by-step explanation:

when they ask for x intercepts you simply have to set the function to 0 and then solve for x or in other words just reverse the number for example. here we have -1 -4 and +7 so just reverse the negative and positive signs

Answer:

Option d) all real numbers

Step-by-step explanation:

we have

[tex]y=\log8^x[/tex]

using a graphing tool

The graph of the equation is a line that represent a direct variation ( the line passes through the origin)

therefore

The domain is all real numbers ---->interval (-∞,∞)

The range is all real numbers ---->interval (-∞,∞)

see the attached figure to better understand the problem

Domain means all the x - values included in a set of data:

{(3, 5), (8, 6), (2, 1), (8, 6)}

It is unnecessary to put two of the same numbers. You only need to put one.

{2, 3, 8}

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer: Last option.

Step-by-step explanation:

By definition, the Domain is the set of all the x-coordinates of the ordered pairs (input values) and the Range is the set of all the y-coordinates of the ordered pairs (output values)

In this case you have the following relation:

[tex]R:[/tex]{[tex](3, 5), (8, 6), (2, 1), (8, 6)[/tex]}

You can identify that the set of all the x-coordinates is:

{[tex]3,8,2,8[/tex]}

You can observe that the input value 8 appears twice, but you only need to write it once.

Therefore, the Domain of that relation is:

[tex]Domain:[/tex]{[tex]2,3,8[/tex]}

Answer:

C, D,F

Step-by-step explanation:

Answer:

Its C

Step-by-step explanation:

Answer:

(x-2) (x-7)

Step-by-step explanation:

x^2 -9x+14

What two numbers multiply to 14 and add to -9

-2*-7 = 14

-2+-7 = -9

(x-2) (x-7)

Answer:

7

Step-by-step explanation:

Givens

x = 4

y = 2

z =-3

equation

xy - z^y

Solution

(4)(2) - (-3)^2     be sure and add the brackets. Otherwise it won't come out correctly.

16 - (9) = 7

Answer:

a. I=5350E +37100

Step-by-step explanation:

The trend line does not start at the origin so we can immediately rule out option C

The equation should be in slope intercept form so we can rule out option D, since E is the x axis and we are looking for y = mx + b not x = mx + b.

Option B is ruled out because if we plug in the value of E = 2 then we get:

I = 5350(2) - 37100

I = 10700 - 37100

I = -16400

Which is wrong since we are not in the negative so your answer is A

Answer:

wdawdwd

Step-by-step explanation:

Answer:

Step-by-step explanation:

Simply by comparing the given

f(x)=(x-2)^2-3   to

f(x) = (x-h)^2 + k, we see that h = 2 and k = -3, which tells us that the vertex of the graph is (2, -3).  This parabola opens up because the coefficient of (x-2)^2 is +1.

Evaluating f(x)=(x-2)^2-3 at x = 4 (an arbitrary value), we see that

                 f(4) = (4-2)^2 - 3 = 4 - 3 = 1.

The point (4, 1) is also on the graph of this parabola.

Graph the vertex (2, -3) and the arbitrarily chosen point (4, 1).  Remember that (2, -3) is the minimum of this function, so for x other than 2, the y-value is greater than -3.

Answer:

C(w) = 6w + 9

Step-by-step explanation:

Anytime 0 is given somewhere, it should be given close scrutiny. In an equation whose general form is

y = mx + b

0 will determine the y intercept immediately.

So when x = 0, y will equal

y = 0*m + 9

So b = 9

y = mx + 9 Now we need to find m

I should start using your variables.

C(w) = m*w + 9

when w = 3 then C(3) = 27

27= 3m +9

27-9 =3m + 9 -9

18 = 3m

18/3 = 3m/3

x = 6

So the complete equation is

C(w) = 6w + 9

Answer:

[tex]P(w)=6w+9[/tex]

Step-by-step explanation:

To find the linear equation, first we need to calculate the slope of that line, we is defined as

[tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]

Where we need to use two points from the table: (0,9) and (4,33).

Replacing these points, we have

[tex]m=\frac{33-9}{4-0}=\frac{24}{4} =6[/tex]

Now, we use the point-slope formula to find the equation

[tex]y-y_{1} =m(x-x_{1} )\\y-9=6(x-0)\\y=6x+9[/tex]

Let's call [tex]y=P(w)[/tex] and [tex]x=w[/tex].

The equation that models the given table is

[tex]P(w)=6w+9[/tex]

Answer:

see below

Step-by-step explanation:

2/3 ÷ 4

We use copy dot flip

The flip means make a reciprocal of the second number

2/3 * 1/4

Multiply the numerators

2*1 = 2

Multiply the denominators

3*4 =12

Put the numerator over the denominator

2/12

Simplify

1/6

To use equivalent fractions to find the quotient of \( \frac{2}{3} \) ÷ 4, follow these steps:

### Step 1: Understand the Operation
Division of fractions can be thought of as multiplying by the reciprocal. The reciprocal of a number a is simply \( \frac{1}{a} \).

### Step 2: Find the Reciprocal of the Divisor
The divisor here is the whole number 4. Its reciprocal is \( \frac{1}{4} \).

### Step 3: Multiply the Dividend by the Reciprocal of the Divisor
Instead of dividing \( \frac{2}{3} \) by 4, you can multiply \( \frac{2}{3} \) by \( \frac{1}{4} \).

### Step 4: Perform the Multiplication
Now, multiply the two fractions:

\[ \frac{2}{3} \times \frac{1}{4} = \frac{2 \cdot 1}{3 \cdot 4} \]

This results in a new fraction:

\[ \frac{2}{12} \]

### Step 5: Simplify the Resulting Fraction
Finally, you need to simplify the fraction to its simplest form. To do that, find the greatest common factor (GCF) of the numerator and the denominator and divide both by this number.

For \( \frac{2}{12} \), the greatest common factor is 2. So we divide both the numerator and the denominator by 2:

\[ \frac{2 \div 2}{12 \div 2} = \frac{1}{6} \]

### Conclusion
Therefore, the quotient of \( \frac{2}{3} \) ÷ 4 is \( \frac{1}{6} \). This is the simplest form of the fraction you obtain when \( \frac{2}{3} \) is divided by 4.