Create a Fundamental Counting Principle problem and determine the number of ways it can be fulfilled. Write in complete sentences.

Answer:

[tex] →\cos(x - y) = \cos(x)\cos(y) + \sin(x) \sin(y) \\ =(\frac{ - 8}{17}\times \frac{3}{5}) +(\frac{ - 15}{17} \times \frac{4}{5}) \\ = \frac{ - 24}{85} + \frac{ - 60}{85} \\ = \frac{ (- 24) + ( - 60)}{85} \\ = \boxed{ \frac{ - 84}{85} }✓[/tex]

Answer: Both

Step-by-step explanation:

Answer and Step-by-step explanation:

Sin = [tex]\frac{Opposite}{Hypotenuse}[/tex]

Cos = [tex]\frac{Adjacent}{Hypotenuse}[/tex]

Tan = [tex]\frac{Opposite}{Adjacent}[/tex]

sin A = [tex]\frac{10}{26} = \frac{5}{13}[/tex]

cos A = [tex]\frac{24}{26} = \frac{12}{13}[/tex]

tan A = [tex]\frac{10}{24} = \frac{5}{12}[/tex]

Those are the answers.

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Answer:

The machine can make 24 soda bottles each minute

Step-by-step explanation:

We can find the number of bottles the machine can make using the slope formula

Mathematically, this can be given as;

m = (y2-y1)/(x2-x1)

m = (192-120)/(8-5) = 72/3

m = 24

Answer:

C on edge 2021

Step-by-step explanation:

The solution of x for the trigonometric inequality [tex]2sin(x)+3 > sin^2(x)[/tex] is x will lie between  0≤x< [tex]\frac{3\pi}{2}[/tex]  

An inequality of the standard form R(x) > 0 (or < 0) that consists of 1 or a few trigonometric functions of the variable arc x is a trigonometric inequality. Finding a solution to the inequality means determining the values of the variable arc x whose trigonometric functions make the inequality true.

According to the question

The trigonometric inequality :

[tex]2sin(x)+3 > sin^2(x)[/tex] and the interval 0<=x<=2pi radians

Let sin(x) = t  

Now, inequality is :

[tex]2t+3 > t^{2}[/tex]

0 > t² - 2t - 3

0>  t² - (3-1)t - 3

0>  t² - 3t + t - 3

0> t( t - 3) + 1(t - 3)

0> ( t - 3) (t+1)

t < -1 or t < 3

sin(x) < -1 or sin(x) < 3

as sin(x) can not be 3  because sin oscillates between 1 and -1. Sine will never result in 3 so we disregard this as a solution.

sin(x) < -1

sin(x) < sin ([tex]\frac{3\pi}{2}[/tex] )

x < [tex]\frac{3\pi}{2}[/tex]  

And the given interval for x

0<=x<=2pi radians

Therefore,  

x will lie between

0≤x< [tex]\frac{3\pi}{2}[/tex]  

Hence, The solution of x for the trigonometric inequality [tex]2sin(x)+3 > sin^2(x)[/tex] is x will lie between  0≤x< [tex]\frac{3\pi}{2}[/tex]  

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Complete Question

Ballio's family traveled 3/10 of the distance to his aunt's house on Saturday. They traveled 4/7 of the remaining distance on Sunday. What fraction of the total distance to his aunt's house was traveled on Sunday?

Answer:

4/10

Step-by-step explanation:

Let us represent, the total distance travelled as:

1

Ballio's family traveled 3/10 of the distance to his aunt's house on Saturday.

Distance left to travel = 1 - 3/10

= 7/10

They traveled 4 /7 of the remaining distance on Sunday.

The fraction of the total distance to his aunt's house was traveled on Sunday is calculated as:

4/7 × Distance left to travel

= 4/7 × 7/10

= 4/10

Answer:

1 tin of beans = £2.15

Step-by-step explanation:

£10.00-£0.70 = £9.30

£9.30-£2.20=£7.10

£7.10-£2.80=£4.30

£4.30 divided by 2 = £2.15

1 tin of beans = £2.15

Answer:

are we supposed to do something?

Step-by-step explanation:

Answer: ok a withdrawal of $200

The slope of the line that passes through the points (- 3, 13) and (5, - 7) will be 3/4.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (- 3, 13) and (5, - 7).

Now,

Since, Two points on the line are (- 3, 13) and (5, - 7).

Hence, The slope of the line that passes through the points (- 3, 13) and (5, - 7) is,

⇒ m = (y₂ - y₁) / (x₂ - x₁)

⇒ m = (- 7 - (-13)) / (5 - (-3))

⇒ m = 6/8

⇒ m = 3/4

Thus, The slope of the line that passes through the points (- 3, 13) and

(5, - 7) is,

⇒ m = 3/4

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Answer:

C

Step-by-step explanation:

the x,y matrix will have the form of some x coefficient value, some y coefficient value and then the answer. if one of these values are missing you use a 0 as placeholder. look at the coefficients here. you know one equation will have an x coefficient of 2 and a y coefficient of -3 with a solution of 8 and the other equation will have x coefficient of 5 and no y at all with a solution of 10. only option c meets these criteria

Step-by-step explanation:

120+b= 180

b=60

x+50+60=180

x=70

The value of angle [tex]x[/tex]  will be [tex]70^0[/tex] .

A triangle is a polygon with three edges and three vertices. Its angles sum property says that the sum of all angles of a triangle is equals to [tex]180^0[/tex]  . i.e.

[tex]\angle A + \angle B + \angle C = 180^0[/tex]

We have,

[tex]\triangle ABC[/tex], in which,

[tex]\angle A =50^0[/tex]

[tex]\angle C =x^0[/tex]

Let, [tex]\angle B =y^0[/tex]

Now,

Work out for [tex]\angle B[/tex],

A straight line always makes an angle of [tex]180^0[/tex] i.e. line [tex]CBD[/tex], which is divided into parts at [tex]B[/tex] by [tex]AB[/tex],

So,

[tex]120^0 + y =180^0[/tex]

[tex]y=180-120[/tex]

[tex]y=60^0[/tex]

Now,

Using angle sum property;

[tex]\angle A + \angle B + \angle C = 180^0[/tex]

[tex]50^0+60^0+x=180^0[/tex]

⇒ [tex]x=180-110[/tex]

[tex]x=70^0[/tex]

Hence, we can say that the measure of  [tex]x[/tex] in the triangle will be [tex]70^0[/tex]  .

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Answer:

The  answer  is  36 x⁴ y⁴

Step-by-step explanation:

Answer:

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

−5−5(6x−8)=−5x+19

−5+(−5)(6x)+(−5)(−8)=−5x+19(Distribute)

−5+−30x+40=−5x+19

(−30x)+(−5+40)=−5x+19(Combine Like Terms)

−30x+35=−5x+19

−30x+35=−5x+19

Step 2: Add 5x to both sides.

−30x+35+5x=−5x+19+5x

−25x+35=19

Step 3: Subtract 35 from both sides.

−25x+35−35=19−35

−25x=−16

Step 4: Divide both sides by -25.

−25x

−25

=

−16

−25

x=

16

25

The value of x is 16/25.

Algebra, a discipline of mathematics where abstract symbols rather than concrete numbers are subjected to arithmetic operations

As per the given data:

We are given an expression, and we have to find out the value of x by solving the given expression.

-5 - 5(6x-8) = -5x + 19

In LHS, multiplying by 5 in the whole bracket.

-5 - [5 × 6x - 5 × 8] = -5x + 19

-5 - [30x - 40] = -5x + 19

In LHS, multiplying by -ve in the bracket.

-5 - 30x + 40 = -5x + 19

Adding 5x both the sides.

-5 - 25x + 40 = 19

Taking all the constants to the RHS after switching signs.

-25x = 19 - 40 + 5

-25x = -16

Multiplying by -ve both the sides.

25x = 16

x = 16/25

The value of x is 16/25.

Hence, The value of x is 16/25.

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Answer:

The number of gallons are "18".

Step-by-step explanation:

According to the question,

⇒ [tex]\frac{5}{6} V-\frac{1}{3}V =9 \ gallons[/tex]

On taking L.C.M, we get

⇒ [tex](\frac{5-2}{6})V =9[/tex]

⇒ [tex]\frac{3}{6}V=9[/tex]

⇒ [tex]V=9\times 2[/tex]

⇒ [tex]V=18[/tex]

Answer:

Step-by-step explanation:

The total cost for a large pizza is given by the equation:

C=2t+8

where t is the number of toppings.

Now, when t=0 we have:

C=8

when t=1 we have:

C=10

when t=2 we have:

C=12

when t=3 we have:

C=14

when t=4 we have:

C=16

when t=5 we have:

C=18

i.e. the graph of this equation is the ordered pair:

(0,8) , (1,10) , (2,12) , (3,14) , (4,16) and (5,18)

Now, the slope of this function means the cost of each topping.

and the y-intercept represents the cost of the pizza when there are no toppings.

Answer:

The slope of line = m = 6

The y-intercept = b = 3

Please check the attached graph below.

Step-by-step explanation:

Given the line

[tex]y = 6x + 3[/tex]

We know that the slope-intercept form of the line is

y = mx+b

here

now compare the slope-intercept form with the given line

[tex]y = 6x + 3[/tex]

so

The slope of line = m = 6

The y-intercept = b = 3

Please check the attached graph below.

-7,5 maaf kalau salah,,,,,,

Answer:

Option (B)

Step-by-step explanation:

From the figure attached,

ΔBCD and ΔACE are the similar triangles.

Therefore, by the property of similar triangles, corresponding sides of these similar triangles will be proportional.

[tex]\frac{AC}{BC}= \frac{EC}{DC}[/tex]

[tex]\frac{AB+BC}{BC}= \frac{ED+DC}{DC}[/tex]

[tex]\frac{AB+6}{6}= \frac{24+8}{8}[/tex]

[tex]\frac{AB+6}{6}= \frac{32}{8}[/tex]

[tex]\frac{AB+6}{6}=4[/tex]

AB + 6 = 24

AB = 18

Option (B) will be the answer.

Answer:

D

Step-by-step explanation:

Answer:  x = 9.6

=========================================================

Explanation:

We have two smaller right triangles that are glued together so to speak.

The base of the smaller triangle on the left is 5 while the height is h.

Let's use the tangent rule to find the value of h

tan(angle) = opposite/adjacent

tan(55) = h/5

5*tan(55) = h

h = 5*tan(55)

h = 7.14074003371058

Make sure your calculator is in degree mode. That value of h above is approximate.

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

Now focus on the smaller triangle on the right

It has the same height value h. This side is the adjacent side while x is the hypotenuse.

We'll use the cosine ratio

cos(angle) = adjacent/hypotenuse

cos(42) = h/x

cos(42) = 7.14074003371058/x

x*cos(42) = 7.14074003371058

x = 7.14074003371058/cos(42)

x = 9.6088135029715

x = 9.6

Answer:

$83.69

Step-by-step explanation:

Given the following

Initial Cost of the brunch = $72.80

Percentage tip = 15%

Tip paid = 15% of $72.60

Tip paid = 0.15 * 72.60

Tip paid = $10.89

Total cost of brunch =  $72.80 + $10.89

Total cost of brunch = $83.69

Hence the total cost of her brunch is $83.69

Answer:

C

Step-by-step explanation:

The rational expression satisfies the conditions  x ≠ 5 or x = - 3 is,

B. x + 3/x - 5.

Polynomials can be found in the numerator, denominator, or both of rational expressions, which are fractions.

Given, An expression in variable 'x' which is x ≠ 5 or x = - 3.

Now, From the given options the rational expression satisfying the statement is,  x + 3/x - 5.

As, If x = 5 then the denominator will be zero and the expression will be undefined and on the numerator x + 3 = 0 ⇒ x = - 3.

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Answer:

1 : 4

Step-by-step explanation:

Circumference of the first one: 3 * 2 * π = 6π.

Circumference of the second one: 12 * 2 * π = 24π

Ratio: 6π:24π

divide both sides by 6π

1: 4

Answer:

move each point (vertex) 2 units to the left and 1 unit up

Answer:

106

Step-by-step explanation:

You divide to find the quotient, the actual answer is 105.7, but I rounded it up for simplicity's sake.

Answer:

105.7

Step-by-step explanation:

you have to find what 1.51×70

Unit price = total price / quantity

Unit price = 45.50 / 10

Unit price = $4.55

Answer:

$4.55 because I look it up

Answer:

it's easy just put it over 1 like 11,031/1 and there's your fraction

Step-by-step explanation:

Answer:

12 Minutes

Step-by-step explanation:

60 minutes in fifths

60 ÷ 5

Answer:

12 min

Step-by-step explanation:

60= 1hr

60/5=12

Answer:

I think is (1, 2) opcion B

The vertex for the parabola shown is, (1, 2).

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The parabola is shown in figure.

Now, We know that;

Vertex of parabola is passing through the line of symmetry.

So, By graph;

The vertex for the parabola shown is,

⇒ (1, 2)

Thus, The vertex for the parabola shown is, (1, 2).

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