The vending machine holds 10 bags of pretzels and 8 packs of cheese crackers. Both the pretzels and crackers dispenseat 2 bags per hour. How many hours will elapse when there is the same number of snacks remaining in the vending machine? How many of each item will there be at this point?퐸푞1______________________________퐸푞2_______________________________Hours: ___________________________ Items: ____________________________What does each equation have n common? ______________________How does this affect the solution? _________________________________________________________________________________________________________Show work here.

Answer:

t(n+1) = t(n) +9

Step-by-step explanation:

Let the Term position be represented by n.

and term value is represented by t.

so term value at any position can be represented by t(n).

Here look closely

t(1)=3, t(2)=12, t(3)=21, t(4)=30

By examining, we notice that the next term is 9 more than the previous one.

e.g

t(2)= t(1)+9

       3+9

t(2)=12

t(3) = t(2)+9

t(3) = 21

we can represent them in mathematical form as:

t(n+1) = t(n) +9

Answer:

Δ QRS is an obtuse triangle ⇒ according to its angle

Δ QRS is an isosceles triangle ⇒ according to its sides

Step-by-step explanation:

In Δ QRS

∵ m∠Q = 8x - 17

∵ m∠R = 19x + 4

∵ m∠S = 5x + 1

→ The sum of the interior angles of a Δ is 180°

∴ m∠Q + m∠R + m∠S = 180°

→ Substitute their values in the equation above

∵ 8x - 17 + 19x + 4 + 5x + 1 = 180

→ Add the like terms

∴ (8x + 19x + 5x) + (-17 + 4 + 1) = 180

∴ 32x + (-12) = 180

∴ 32x - 12 = 180

→ Add 12 to both sides

∵ 32x - 12 + 12 = 180 + 12

∴ 32x = 192

→ Divide both sides by 32

∵ [tex]\frac{32x}{32}[/tex] = [tex]\frac{192}{32}[/tex]

∴ x = 6

→ Substitute the value of x in each measure of angles to find them

∵ m∠Q = 8(6) - 17 = 48 - 17

∴  m∠Q = 31°

∵ m∠R = 19(6) + 4 = 114 + 4

∴  m∠R = 118°

∵ m∠S = 5(6) + 1 = 30 + 1

∴  m∠S = 31°

∵ m∠R > 90°

∴ ∠R is an obtuse angle

∴ Δ QRS is an obtuse triangle

∵ m∠Q = m∠S

→ In any Δ if two angles are equal in measures, then the two sides

  opposite to these angles are equal in length and the Δ is isosceles

∴ RQ = RS

∴ Δ QRS is an isosceles triangle

Answer:

The equation of the line with slope = 4 and point (-5, -13)

will be:

Step-by-step explanation:

Given

As the point-slope form of the equation of line is

[tex]y-y_1=m\left(x-x_1\right)[/tex]

where m is the slope.

substituting the values m = 4 and the point (-5, -13)

[tex]y-y_1=m\left(x-x_1\right)[/tex]

[tex]y-\left(-13\right)=4\left(x-\left(-5\right)\right)[/tex]

[tex]y+13=4\left(x+5\right)[/tex]

subtract 13 from both sides

[tex]y+13-13=4\left(x+5\right)-13[/tex]

[tex]y=4x+7[/tex]

Therefore, the equation of the line with slope = 4 and point (-5, -13)

will be:

[tex]y=4x+7[/tex]

Answer:

[tex]\displaystyle n^3-\frac{1}{n^{2}}[/tex]

Step-by-step explanation:

Exponents Properties

We need to recall the following properties of exponents:

[tex](a^x)^y=(a^y)^x=a^{xy}[/tex]

[tex]\displaystyle a^{-x}=\frac{1}{a^x}[/tex]

We are given the expression:

[tex]2^m=n[/tex]

We need to express the following expression in terms of n.

[tex]8^m-4^{-m}[/tex]

It's necessary to modify the expression to use the given equivalence.

Recall [tex]8=2^3 \text{ and }4 = 2^2[/tex]. Thus:

[tex](2^3)^m-(2^2)^{-m}[/tex]

Applying the property:

[tex](2^m)^3-(2^m)^{-2}[/tex]

Substituting the given expression:

[tex]n^3-n^{-2}[/tex]

Or, equivalently:

[tex]\mathbf{\displaystyle 8^m-4^{-m}= n^3-\frac{1}{n^{2}}}[/tex]

Step-by-step explanation:

what is the numbers to choose from

Answer:

13n + 20  

Step-by-step explanation:

the shipping rate never changes but the cost of books does depend on how many books you buy.

I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!

Answer:

5 x n

Step-by-step explanation:

This is the answer because:

1) 5 times a number n is just 5 times n

Hope this helps!

Answer:

0

Step-by-step explanation:

The expression we are given is (2 * x - 4).

We need to find the value of expression when x = 2.

Let's substitute 2 in as x.

Now our expression is (2 * 2 - 4).

First, let's multiply our 2 with our substituted 2.

1.  2 * 2 = 4

We're left with (4 - 4).

Finally, let's evaluate this expression.

2.  (4 - 4) = 0.

Our answer is 0.

So (2 * x - 4) when x = 2 is 0.

Feel free to give brainliest.

Have a great day!

Answer:

4

Step-by-step explanation:

By Using the Transformations of the parabola

[tex]y = -(x+5)^2+7\\y=4x^{2} +7\\y = -(x-2)^2+3[/tex]

[tex]y = x^2+ k[/tex]

[tex]y = (x - h)^2[/tex]

Reflection in x-axis  

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

Reflection in y-axis

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

stretches away from the x-axis or compresses toward the x-axis

[tex]y = a .x^2[/tex]

| a | > 1 is a stretch;

0 < | a | <1 is a compression

stretches away from the y-axis or compresses toward the y-axis

[tex]y=\frac{1}{a} x^{2}[/tex]

| a | > 1 is a compression by factor of 1/a;

0 < | a | <1 is a stretch by factor of 1/a

Now, we have [tex]y=x^2[/tex]

4). Reflect over x-axis, shift to the left 5 units, shift up 7 units

[tex]y = -(x+5)^2+7[/tex]

5) Vertical stretch by a factor of 4, shift down 11 units

[tex]y=4 x^{2} +7[/tex]

6) Vertical compression by a factor of, reflect over x-axis, shift to the right 2 units, shift up 3 units.

[tex]y=-(x-2)^{2} +3[/tex]

Learn more:https://brainly.com/question/20369546

Answer: (0, -2)

Step-by-step explanation:

Answer:

I don't get it

Step-by-step explanation:

but okay!!!!?!!?!?!?

Answer:

5

Step-by-step explanation:

8/1.6 = 5 divide the two and get the answer!

Brainliest please!

Answer:

5 miles

Step-by-step explanation:

divide 8 by 1.6

Answer:

The answer is 50.

Step-by-step explanation:

Answer: Angle MNO

Step-by-step explanation: Supplementary angles equal 180, or a straight line.

Answer: 14

MNJ is angle 13 so angle 14 is the other angle that makes a straight line or 180°.

Answer:

23 yellow, 30 pink and 12 blue balls

Step-by-step explanation:

Let the number of yellow, pink, blue, and black balls be y, p, b, and x respectively.

From 1st sentence:

y +p +b +x= 90

"60 of them are not pink"

➜ y +b +x= 60

Given that 25 are black, x= 25.

"67 of them are not yellow"

➜ p +b +x= 67

Subst. x= 25 into the above equations:

y +p +b +25= 90

y+ p +b= 65 -----(1)

y +b +25= 60

y +b= 35 -----(2)

p +b +25= 67

p +b= 42 -----(3)

I will rewrite the 3 equations for better clarity:

y +p +b= 65 -----(1)

y +b= 35 -----(2)

p +b= 42 -----(3)

(1) -(2):

p= 65 -35

p= 30

(1) -(3):

y= 65 -42

y= 23

Substitute p= 30 and y= 23 into (1):

23 +30 +b= 65

b= 65 -53

b= 12

Thus, there 23, 30 and 12 yellow, pink and blue balls respectively.

Answer: So the trick I was taught to use was PEMDAS which stands for Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction. You solve the parenthesis first, followed by exponents if there are any. Multiplication and division are equal. So if there's multiplication and division in the problem, you solve the one closest to the left or start of the equation first. The same rules apply for addition and subtraction. They are both equal so you solve the first one first, even if the subtraction is before the addition.

Step-by-step explanation:

Answer:

65 oop

Step-by-step explanation: o0iiutdgc vhy

Answer: 1/2

Step-by-step explanation:

1) Put the equation into y=kx form

- add 4x to both sides

- divide by 8 on both sides to get y=1/2x

2) k is the constant of proportionality

Answer:

64000

Step-by-step explanation:

sorry if wrong

Answer:

64000

Step-by-step explanation:

Answer:

THE CORRECT ANSER OF THIS QUESTION IS 5.

Step-by-step explanation:

Here,

a23=6

a12=5

a32=6

Now,

a23+a12-a32

=6+5-6

=5

Given:

Cost to rent a raft = $7 per person

Number of people a raft can hold = 6

Lunch cost = $3 per raft

To find:

The total cost for a group of 6.

Solution:

A raft can hold 6 people. So, one raft is required for group of 6.

Lunch cost = $3

Cost to rent a raft for one person = $7

Cost to rent a raft for 6 person = 6 × $7 = $42

Now,

Total cost = Lunch cost + Cost to rent a raft for 6 person

                = $3 + $42

                = $45

Therefore, the total cost for a group of 6 is $45.

Answer:

a yard stick, maybe I'm right

Answer:

a fence

Step-by-step explanation:

HAHAHA LOL

In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions[1][2]) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others. They are among the simplest periodic functions, and as such are also widely used for studying periodic phenomena, through Fourier analysis.

Basis of trigonometry: if two right triangles have equal acute angles, they are similar, so their side lengths are proportional. Proportionality constants are written within the image: sin θ, cos θ, tan θ, where θ is the common measure of five acute angles.

The trigonometric functions most widely used in modern mathematics are the sine, the cosine, and the tangent. Their reciprocals are respectively the cosecant, the secant, and the cotangent, which are less used. Each of these six trigonometric functions has a corresponding inverse function (called inverse trigonometric function), and an equivalent in the hyperbolic functions as well.[3]

The oldest definitions of trigonometric functions, related to right-angle triangles, define them only for acute angles. To extending these definitions to functions whose domain is the whole projectively extended real line, geometrical definitions using the standard unit circle (i.e., a circle with radius 1 unit) is often used. Modern definitions express trigonometric functions as infinite series or as solutions of differential equations. This allows extending the domain of sine and cosine functions to the whole complex plane, and the domain of the other trigonometric functions to the complex plane (from which some isolated points are removed).

Contents

Right-angled triangle definitions Edit

A right triangle always includes a 90° (π/2 radians) angle, here labeled C. Angles A and B may vary. Trigonometric functions specify the relationships among side lengths and interior angles of a right triangle.

Plot of the six trigonometric functions, the unit circle, and a line for the angle θ = 0.7 radians. The points labelled 1, Sec(θ), Csc(θ) represent the length of the line segment from the origin to that point. Sin(θ), Tan(θ), and 1 are the heights to the line starting from the x-axis, while Cos(θ), 1, and Cot(θ) are lengths along the x-axis starting from the origin.

In this section, the same upper-case letter denotes a vertex of a triangle and the measure of the corresponding angle; the same lower case letter denotes an edge of the triangle and its length.

Given an acute angle A = θ of a right-angled triangle, the hypotenuse h is the side that connects the two acute angles. The side b adjacent to θ is the side of the triangle that connects θ to the right angle. The third side a is said to be opposite to θ.

If the angle θ is given, then all sides of the right-angled triangle are well-defined up to a scaling factor. This means that the ratio of any two side lengths depends only on θ. Thus these six ratios define six functions of θ, which are the trigonometric functions. More precisely, the six trigonometric functions are:[4][5]

sine

{\

Answer:

8

Step-by-step explanation:

The sum of two interior angles in a triangle is equal to an exterior angle

7x - 4 + 9x + 4 = 128° add like terms

16x = 128 divide both sides by 16

x = 8

Answer:

They are axis so it would be 6 for x and 15 for y

Step-by-step explanation: