At a hockey game a vender sold a combined total of 105 sodas and hot dogs. The number of sodas sold was 39 more than the number of hot dogs sold find the number of soda sold and the number is hot dog sold

The tangent is the ratio of the perpendicular and the base of the right triangle. Then tan A will be x/y.

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

The right-angle triangle ΔABC is given.

The angle ∠C is 90°.

And the perpendicular is x, the base is y, and the hypotenuse is z.

Then the value of the tangent of angle ∠A will be

The tangent is the ratio of the perpendicular and the base of the right triangle.

tan A = x/y

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Answer:

so the next 2 sequences would be 60 and 62

Step-by-step explanation:

The next two terms in the given arithmetic sequence are 60 and 62.

The arithmetic sequence is given as follows:

20, 32, 42, 50, 56, ?

To find the next two terms in the sequence, let's analyze the pattern:

The sequence increases by the following increments:

12, 10, 8, 6

We can observe that the increments are decreasing by 2 each time.

To find the next two terms, we can continue this pattern:

Increment: 4 (6 - 2)

Increment: 2 (4 - 2)

Adding the increments to the previous terms:

56 + 4 = 60

60 + 2 = 62

Therefore, the next two terms in the arithmetic sequence are 60 and 62.

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a) Triangle A is rotated 90 degrees anticlockwise about (-1,0) to give triangle A'.

Triangle A' is then reflected in the line y=0 to give triangle A''.

b) Rotation

a) Triangle A is rotated 90 degrees anticlockwise about (-1,0) to give triangle A'. Triangle A' is then reflected in the line y=0 to give triangle A''.

b) Rotation

Given,

Triangles A , A' , A'' .

Here,

The triangles are rotated and reflected to get different triangles .

Firstly ,

Triangle A is made to be rotated by 90° in anticlockwise direction at point (-1 , 0) .

To get A'' triangle A' is reflected from horizontal axis.

Triangle A maps into triangle A'' by rotation .

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Answer:

Step-by-step explanation:

The solution to a one-variable inequality can be graphed on a number line. The number line is shaded where the values satisfy the inequality. Boundaries of shaded regions are marked by points that are either a solid dot, or an open circle, depending on whether the point is included in the solution or not.

__

Here, the inequality tells us any value of x that is less than or equal to -1 will satisfy the inequality. Since -1 is part of the solution set, that boundary point will be marked with a solid dot. Values less than -1 are shown on a number line to the left of the point marked -1.

The graph will be a solid dot at x=-1, and shading to its left.

__

Possible solutions are any values less than or equal to -1. Some are ...

  -1

  -1.073

  -429

Answer:

£225

Step-by-step explanation:

[For percentage increase, add the percentage with 100, for percentage decreases substract the percentage from 100.]

100 + 25 = 125%

[tex]\frac{125}{100}[/tex] × 180 = £225

Answer:

Step-by-step explanation:

National car rental equation is

C = 14d + 0.20m  

- where C= total cost, d = the number of days and m = the total number of miles driven.

Answer: 20,-13

Step-by-step explanation:

We can rewrite the problem as an equation. This equation is x(x-7)=260 (x being the mystery number). We can simply this into x^2 -7x=260. We can then rewrite this as x^2 -7x -260=0. We need to find the roots of this quadratic, which are -13 and 20. You can find this by factoring the quadratic.

[tex]\large{\boxed{ \ g(x) = -\dfrac{7}{4} | x -5| +0 \ }}[/tex]

Absolute value of a graph formula:

Identify the vertex : (h, k) = (5, 0)

Take two points : (5, 0), (9, -7)

[tex]\sf Find \ slope \ (a) : \sf \ \dfrac{y_2 - y_1}{x_2- x_1} \ = \ \dfrac{-7-0}{9-5} \ = \ -\dfrac{7}{4}[/tex]

Join the variables together:   [tex]\bf g(x) = - \dfrac{7}{4} | x -5| +0[/tex]

Answer:

[tex]f(x) = -\dfrac{7}{4}|x-5|+0 [/tex]

Step-by-step explanation:

The function in the coordinate Plane is an absolute value function . Consider the parent function

[tex]f(x) = |x| [/tex]

Recall the properties of transformation

From the inspection of the graph,It has moved to right by 5 units, Thus

[tex]f(x - 5) = |x - 5| [/tex]

Apparently, It has neither shifted up or down, hence

[tex]f(x - 5) +0= |x - 5|+0 [/tex]

Looking at the graph, we can see that it has been reflected vertically. It tells us we have to multiply it by a negative constant

[tex] -a f(x - 5) +0= -a |x - 5| +0[/tex]

take (9,7) to figure out a.

[tex] -a | 9- 5| =7[/tex]

Solving the equation yields:

[tex] \boxed{a = - \frac{7}{4} }[/tex]

hence, our function is [tex]\boxed{f(x) = -\dfrac{7}{4}|x-5|+0} [/tex]

Answer:

It would most likely be 65

Step-by-step explanation:

180 - 115 = 65

Answer:

115°

Step-by-step explanation:

The measure of an arc is the measure of its central angle.

Since the central angle is 115°, its intercepted arc (which is marked with the questionmark) is also going to be 115°.

Answer:

10.672hrs ( maybe)

Step-by-step explanation:

A can complete the work in 20 hrs then 1/3 part can be completed in 20*1/3=6.67hrs

B can complete the 1/4 part of the work in same time then B can complete hole work in 6.67*4=26.68 hrs

B can complete the 1/5 part of work in 26.67/5=5.336hrs

according to question C can complete 1/2part of work in same time then the whole work can complete in

2*5.336=10.672hrs

Answer:

The rule a+b=b+a, for all real numbers a,b, is the commutative law for addition. The fact that we can have g∘h≠h∘g, for some functions g,h, says that composition of functions is not commutative. Composition of functions is not the same as multiplication of functions: f=h∘gmeansf(x)=h(g(x))j=h⋅gmeansj(x)=h(x)g(x).

A mean is an arithmetic average of a set of observations. The score of the student is equal to 63.4.

A mean is an arithmetic average of a set of observations. it is given by the formula,

Mean = (Sum of observations)/Number of observations

Given the mean score was 75, while the standard deviation was 8. Therefore, the score of the student is,

Scre of the student = μ - 1.45σ = 75 - 1.45(8) = 63.4

Hence, the score of the student is equal to 63.4.

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Answer:

$659 weekly

Step-by-step explanation:

John Dalton earns $34,268 annually (yearly)

We want to find his weekly rate if he is paid weekly.

To do so we divide his annual salary by the number of weeks in a year (52)

So weekly rate = 34,268 / 52 = 659

The slope of the given linear equation is 1/3 and the y-intercept will be 5/6. Then the correct option is D.

The slope is the ratio of rising or falling and running. The difference between the ordinate is called rise or fall and the difference between the abscissa is called run.

Identify the slope and y-intercept of the line whose equation is given. Write the y-intercept as an ordered pair.

The linear equation is given below.

[tex]\rm y =\dfrac{5}{6} + \dfrac{x}{3}[/tex]

Then the slope of the equation will be 1/3.

And the y-intercept will be 5/6.

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Answer:

d

Step-by-step explanation:

Answer:

Acount is a great place to work for a loved ones like you a few months

Answer:

165 divided by 11 = 15

154 divided by 14 = 11

306 divided by 17 = 18

322 divided by 14 = 23

Step-by-step explanation:

-10+7=-3 because 10 i greater and (-)(+)=-

-8-3=-11 because the greatest number is in negative form that's why its not in positive form

Hey there!

Guide:

Negative & negative = positive

Positive & positive = positive

Negative & positive = negative

Positive & negative = negative

For -10 + 7 = -3 it doesn’t give you a POSITIVE because you’re working with a negative (-10) and a positive (7), which it results out to be a negative number (-3)

Whereas, -8 - 3 = -11, it doesn’t also give you a positive because you’re working with a negative (-8) and a somewhat positive (3 or -3 it depends how you look at the equation), it gave you a negative result (-11).

KEEP THAT GUIDE IN MIND WHEN YOURE WORKING WITH INTEGERS, IT MAY HELP ON THE LONG WRONG! :)

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

C.

Step-by-step explanation:

7 7/8 rounds up to 8

2 1/10 rounds down to 2

8-3(2)=2

8 - 6 = 2

he would have about 2 pounds left

so the three pounds left is not reasonable

Answer:

4.03 < 16.5

Step-by-step explanation:

Four and three hundreths = 4.03

sixteen and five-tenths = 16.5

4.03 < 16.5

Answer:

1.45

Step-by-step explanation:

weight of all books= 14×1.1= 15.4

weight of all duster=7×0.2= 1.4

weight of books and duster= 15.4+1.4=16.8

weight of the empty box = 18.25-16.8=1.45

Answer:

80 feet

Step-by-step explanation:

Area = length x width

We need to find length

[tex]2280 = 28.5l[/tex]

divide both sides by 28.5

[tex]l = 80[/tex]

Answer:

Step-by-step explanation:

We can see that

The angle formed by intersecting chords measures the half the sum of intercepted arcs.

Answer: [tex]b^{2}(1-21a^{3})[/tex]

Step-by-step explanation:

[tex]b^{2} - 21a^{3} b^{2} \\b^{2}(1-21a^{3})[/tex]

Answer:

answer = 12

Step-by-step explanation:

Let the smallest number be x

So

X+(x+2)+(x+4)+(x+6)=60

4x+12=60

4x=48

X=12

Answer:

x = 10

Step-by-step explanation:

I assume you mean

sqrt(x + 6) = x - 6

let's square the whole equation :

x + 6 = (x - 6)² = x² - 12x + 36

x² - 13x + 30 = 0

the general solution to a quadratic equation is

x = (-b ±sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = -13

c = 30

x = (13 ±sqrt(13² - 4×1×30))/(2×1) =

= (13 ±sqrt(169 - 120))/2 = (13 ±sqrt(49))/2 =

= (13 ± 7)/2

x1 = (13 + 7)/2 = 20/2 = 10

x2 = (13 - 7)/2 = 6/2 = 3

for x = 10 we get for the original equation

sqrt(10+6) = 10-6 = 4

sqrt(16) = 4

4 = 4

so, x = 10 is a valid solution.

for x = 3 we get

sqrt(3 + 6) = 3 - 6 = -3

sqrt(9) = -3

3 = -3

so, this (x = 3) counts as an invalid solution, because most teachers nowadays expect the square root symbol operation to deliver only the positive solution.

although a square root is actually representing both : the positive AND the negative solution, because the negative number multiplied by itself is the same result as the positive number multiplied by itself.

so, actually

sqrt(9) = -3

± 3 = -3

is still correct and valid. but not what your teacher expects most likely.

in my younger days only the square root of a negative number counted as invalid operation (in the space of Real numbers, of course), and therefore only a solution leading to a square root of a negative number was an invalid solution.

Answer:

D. 496

Step-by-step explanation:

Start by finding original number of pens:

15 boxes x 40 pens per box = 600 pens in all

find number of pens taken:

26 workers x 4 pens each = 104 pens taken

Find number of pens left:

600 original - 104 taken = 496 left

Answer: D. 496

Answer:

D

Step-by-step explanation:

15x40=600

26x4=104

600-104=496

The result of expanding the trigonometry expression [tex]\sin^2(\theta) * (1 + \cos(\theta))[/tex] is [tex]cos^0(\theta) + \cos(\theta) - \cos^2(\theta) - \cos^3(\theta)[/tex]

The expression is given as:

[tex]\sin^2(\theta) * (1 + \cos(\theta))[/tex]

Express [tex]\sin^2(\theta)[/tex] as [tex]1 - \cos^2(\theta)[/tex].

So, we have:

[tex]\sin^2(\theta) * (1 + \cos(\theta)) = (1- \cos^2(\theta)) * (1 + \cos(\theta))[/tex]

Open the bracket

[tex]\sin^2(\theta) * (1 + \cos(\theta)) = 1 + \cos(\theta) - \cos^2(\theta) - \cos^3(\theta)[/tex]

Express 1 as cos°(Ф)

[tex]\sin^2(\theta) * (1 + \cos(\theta)) = cos^0(\theta) + \cos(\theta) - \cos^2(\theta) - \cos^3(\theta)[/tex]

Hence, the result of expanding the trigonometry expression [tex]\sin^2(\theta) * (1 + \cos(\theta))[/tex] is [tex]cos^0(\theta) + \cos(\theta) - \cos^2(\theta) - \cos^3(\theta)[/tex]

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A population about which we want to get some information is called the sample.

This is a portion of a population that is known to contain several parts of the population. The information that is gotten from the sample would be used to draw conclusion about the entire information.

Therefore from the definition above the answer to the question is the population sample.

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