Evaluate the following, expressing your result as a simplified fraction:
3
-0.4+
4

Answer:

[tex]\sin(\theta_1)=-\dfrac{4}{5}[/tex]

Step-by-step explanation:

Given the angle [tex]\theta_1[/tex] located in [tex]\text {Quadrant IV}[/tex].

[tex]\cos(\theta_1)=\dfrac{3}{5}[/tex]

We want to determine the value of [tex]\sin(\theta_1)[/tex]

Now,

[tex]\cos(\theta)=\dfrac{Adjacent}{Hypotenuse}\\$Therefore:\\Adjacent=3\\Hypotenuse=5\\Using Pythagoras theorem\\Hypotenuse^2=Opposite^2+Adjacent^2\\5^2=Opposite^2+3^2\\Opposite^2=5^2-3^2=16\\Opposite^2=4^2\\$Opposite=4[/tex]

In Quadrant IV,  x is positive, and y is negative.

Therefore, Opposite=-4

[tex]\sin(\theta_1)=-\dfrac{4}{5}[/tex]

Answer:

cos(\theta_1)=\dfrac{84}{85}cos(θ  

1

​  

)=  

85

84

Step-by-step explanation:

Answer:

hope this help

Step-by-step explanation:

10x + 4 = 10x + 16 -12 = 10x + 4

infinite solution of x ( for x is real number)

Answer:

15.8 I think.........

Answer:

Mark me brain list pls pls pls pls pls pls

Step-by-step explanation:

16.9

Answer:

Step-by-step explanation:

Set the Format menu to ExprOn and CoordOn. Press [2nd][TRACE] to access the Calculate menu. Press [2] to select the zero option. If necessary, repeatedly press Set the Left Bound for the zero you desire to find.

Answer:

Areas = (10x+4)(3x+2)

Area = 30x^2 + 20x +12x +8

Area = 30X^2 +32x +8 sq. ft.

Step-by-step explanation:

Answer:

1 an -5/2

Step-by-step explanation:

Answer:

20cm

Step-by-step explanation:

pythagorean theorem

15^2 + b^2 = 25^2

225 + b^2 = 625

b^2 = 400

b = 20

Answer:

20 cm

Step-by-step explanation:

This is a right triangle so we can use the Pythagorean theorem

a^2 +b^2 = c^2

where a and b are the legs and c is the hypotenuse

15^2 +b^2 = 25^2

225+b^2 = 625

Subtract 225 from each side

225+b^2 -225 = 625-225

b^2 = 400

Take the square root of each side

sqrt(b^2) = sqrt(400)

b = 20

Answer:

x=3

Step-by-step explanation:

13-1=12

12÷4=3

Answer:

You just add the 2 equations together and fill in the 3 into the x where the f(x) equation is located and 7 into the x where the g(x) equation is located. I hope this helps. Have a great rest if your day!

Answer:

1. 6 6/10

2. 7 6/10

Step-by-step explanation:

Answer:

1. 8 6/10

2. 9 6/10

Step-by-step explanation:

Answer:

x =144.3

Step-by-step explanation:

Let x  be the unknown angle

The two angles add to 180

x+35.7 = 180

Subtract 25.7 from each side

x+35.7 -35.7 = 180-35.7

x =144.3

Answer:

60 pairs of shoes

Step-by-step explanation:

To find the answer, multiply 4x15. The words four times as many mean to do the operation of multiplication. 4x15= 60 So finally, each have 60 pairs of shoes.

i hope this helped:)

Answer:

7.5

Step-by-step:

Julie: ?

Her brother: ?

Total number: 15

So: 15 divided to julie and her brother-

There for 15 divide by 2 is 7.5

7.5+7.5=15

Answer: A) Option B

B) 22.3 minutes.

Step-by-step explanation:

The temperature decreases in an exponential decrease, this means that we can write the equation as:

T(x) = A*r^x + B

Where A is the difference between the initial temperature and the room temperature, B is the room temperature, and r is a positive number smaller than 1, that says "how fast" the temperature decreases (and x is the variable, in units of time)

We know that the initial temperature

A = 200° - 72° = 128°

B = 72°

T(x) = 128°r^x + 72°

The only option with those two values is option B.

T(x) =  128(0.989)^x + 72

We should check that when x = 2m, the temperature must be 197°

T(2m) = 128*(0.989)^2 + 72 = 197.2° (that we can round down to 197°)

So this equation is correct

Now we want to find the time such the temperature is 172°F

then:

172° = 128°(0.989)^x + 72°

100° = 128°(0.989)^x

100/128 = (0.989)^x

x = ln(100/128)/ln(0.989) = 22.3 minutes.

Let's check in our equation:

T(22.3) =  128°(0.989)^22.3 + 72 = 172°

Answer:

The area of this circle is [tex]176.74cm^2[/tex]

Step-by-step explanation:

The formula for the area of a circle is : [tex]\pi *radius^2[/tex]

The radius is the length from one side of the circle to the centre.

To work this out you would simply multiply pi by the radius of 7.5. squared. This gives you 176.74.

1) Multiply pi by 7.5 squared.

[tex]\pi *7.5^2=176.74cm^2[/tex]

In this question pi is to be 3.142

Answer:

100 not so good seats

50 good seats

Step-by-step explanation:

Let x represent good seats and y represent not so good seats

[i] 3x + 2y = 350

[ii] x+y = 150

[iii] y = 150 - x

substitute this to equation [i]

3x + 2y = .350

3x + 2 (150-x ) = 350

3x + 300 - 2x = 350

3x-2x = 350 - 300

x = 50 good seats

now substitute what you got to equation [iii]

y = 150 - 50 = 100 not so good seats

when we check the answer by using equation [i] we find that it is correct:

3x + 2y = 350

3(50) + 2(100) = 350

150 + 200 = 350

350 = 350

Answer: x = 33

Step-by-step explanation:

Subtract 2/11x from both sides

Subtract 4 from both sides

Multiply both sides by 11/4

Answer:

The result is [tex]x = 33[/tex] .

Step-by-step explanation:

Solve the equation:

[tex]\frac{6}{11} x +4 = \frac{2}{11} x + 16[/tex]

-Subtract [tex]\frac{2}{11} x[/tex] from [tex]\frac{6}{11}x[/tex] :

[tex]\frac{6}{11} x +4 -\frac{2}{11}x = \frac{2}{11} x - \frac{2}{11}x + 16[/tex]

[tex]\frac{4}{11} x +4 = 16[/tex]

-Subtract from both sides by 4:

[tex]\frac{6}{11} x + 4 - 4 = 16 -4[/tex]

[tex]\frac{6}{11} x = 12[/tex]

-Multiply both sides by [tex]\frac{11}{4}[/tex] :

[tex]x = 12[/tex] × [tex](\frac{11}{4})[/tex]

[tex]x = 33[/tex]

So, the answer for the equation is [tex]x =33[/tex] .

The fire is a distance of 9.33 miles from Station A and 4.67 miles from Station B.

Let's denote the distance of the fire from station A as "x" and the distance of the fire from station B as "y".

From station A, the bearing of the fire is N 35° E. This means that if we draw a line connecting station A and the fire, the angle between this line and the north direction is 35°.

Similarly, from station B, the bearing of the fire is N 30° W. This means that the angle between the line connecting station B and the fire and the north direction is 30°.

Now, let's construct a triangle with vertices at Station A, station B, and the fire. The line connecting station A and station B represents the base of the triangle, and the lines connecting station A and the fire and station B and the fire represent the two sides of the triangle.

Since the triangle is isosceles (both sides are equal), the angles opposite the two sides will also be equal.

Let's denote the angle opposite side x as α and the angle opposite side y as β.

From the given bearings, we can determine the values of α and β:

α = 180° - 35° = 145°

β = 180° - 30° = 150°

Now, using the Law of Sines, we can set up the following ratios:

sin(α) / x = sin(β) / y

Solving for y, we get:

y = (sin(β) / sin(α)) * x

Substituting the known values, we have:

y = (sin(150°) / sin(145°)) * x

Using a calculator, we can evaluate the sin(150°) and sin(145°) to get:

y = (0.5 / 0.996) * x

y = 0.501 * x

Since the two stations are 14 miles apart, we know that x + y = 14.

Substituting the value of y from the previous equation, we have:

x + 0.501 * x = 14

1.501 * x = 14

x = 14 / 1.501

x ≈ 9.33

Now, to find the value of y, we can substitute the value of x into the equation:

y = 0.501 * x

y = 0.501 * 9.33

y ≈ 4.67

Therefore, the fire is 9.33 miles from Station A and 4.67 miles from Station B.

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The fire is approximately 38.7 miles away from station A and 38.4 miles away from station B.

To solve this problem, we can use trigonometry and create a diagram to visualize the situation.

Now, let's label the diagram. We'll use the following labels:

A: Fire-lookout station A

B: Fire-lookout station B

F: Fire's location

Next, we need to determine the angles and distances involved. From the problem statement, we know the bearing of the fire from station A is N 35° E, and the bearing of the fire from station B is N 30° W. Let's mark these angles on the diagram.

To find the distance of the fire from each station, we can consider the angles formed between the stations and the fire. The sum of these angles should be 180° since we have a straight line. Let's find the missing angles by subtracting the given angles from 180°.

For station A:

Angle A = 180° - 35° = 145°

For station B:

Angle B = 180° - 30° = 150°

Now, let's draw lines from each station to the fire, and label the distances as dA and dB.

We can use trigonometry (specifically, the tangent function) to find the distances dA and dB. Tangent of an angle is equal to the opposite side divided by the adjacent side.

For station A:

tan(145°) = opposite side (dA) / adjacent side (14 miles)

dA = 14 * tan(145°)

For station B:

tan(150°) = opposite side (dB) / adjacent side (14 miles)

dB = 14 * tan(150°)

Now, let's calculate these distances using a calculator.

dA = 14 * tan(145°) ≈ 38.7 miles

dB = 14 * tan(150°) ≈ 38.4 miles

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Answer:

20 cents per unit

Step-by-step explanation:

Since it is 1$ 5 pencils and 100/5=20, the unit cost is 20 cents

Answer:

the unit price is $0.20 for 1 pencil

Step-by-step explanation:

if u see 5 pencils cost 1 dollars and unit price means the value of one item, so like the cost of 1 pencil

write it as a ration of cost to pencil

the ratio is 1/5

now divided 5 on the top and the bottom to get the unit price

1 divided by 5= 0.2

so now the ratio is 0.2/1

Answer:

Step-by-step explanation:

x three point shots: 8*3=24

x two point shots: 2*2=4

The point would Anthony score is : 24+4=28

I hope it'll help you much

Thank you for asking

Answer:

98.4

Step-by-step explanation:

Since one cake equals 8.2 g of sugar, we can multiply this by 12 to get 12 cakes equals 98.4 g of sugar

Answer:

98.4 Grams because 8.2 times 12 is 98.4

Step-by-step explanation:

Plz give brainliest

Answer:

B

Step-by-step explanation:

Answer:

The owner of the supermarket had 9207  at first

Step-by-step explanation:

The key to unlocking this question is to first of all determine how much the supermarket owner paid to employees:

amount paid as weekly wages=number of employees*pay per employee

there are 28 employees

the pay per week is 320 each

amount paid as weekly wages=28*320=8960

The amount the owner of the supermarket had at first is the amount paid as weekly wages plus the balance left after the wages have been settled.

balance after payment of wages is 247

Amount he had at first=8960+247=9207

Answer:

None of input and output table work for the rule.

Step-by-step explanation:

Start with the numbers given at A, B,C.

According to the rule you need to multiply by 666 to get the output.

A 000 * 666 = 0 (=NOT the output)

B 111 * 666 = 73926 (=NOT the output)

C 222 * 666 = 147852 (=NOT the output)

None of input and output table work for the rule.

Answer:

c

Step-by-step explanation:

khan academy

Answer:

Volume, [tex]V=169.56\ \text{units}^3[/tex]

Step-by-step explanation:

We have,

Radius of cylinder is 3 units

Height of the cylinder is 6 units

It is assumed to find the volume of the cylinder. The formula of the volume of cylinder is given by :

[tex]V=\pi r^2 h \\\\V=3.14\times 3^2 \times 6\\\\V=169.56\ \text{units}^3[/tex]

So, the volume of the cylinder is [tex]169.56\ \text{units}^3[/tex].

Answer:

perimeter = 107.4 m

area =  640.82 m²

Step-by-step explanation:

The line connecting the the centers of the adjacent sides of the garden is 20 m long. The line is a diagonal that forms an hypotenuse sides of a triangle.

The length of side of the rectangle has a ratio of 1 : 2. This means one side has a length a meters and the other 2a meters.

Pythagoras theorem can be use to get a since a right angle is formed due to the diagonal.

(a/2)² + (2a/2)² = 20²

(a/2)² + (a)² = 20²

a²/4 + a² = 400

(a² + 4a²)/4 = 400

5a²/4 = 400

cross multiply

5a² = 1600

a² = 1600/5

a² = 320

square root both sides

a = √320

a = 17.88854382

a ≈ 17.90  

The required length is a = 17.90 m and the other side will be 17.90 × 2 = 35.80 m.

Area = length × breadth

area = 17.90 × 35.80 = 640.82 m²

perimeter = 2(l + b)

perimeter = 2(35.80 + 17.90)

perimeter = 2(53.7)

perimeter = 107.4 m

Answer:

The explicit formula is Tn = 34 + 3n

Step-by-step explanation:

The nth term of an arithmetic sequence can be represented using the formula

Tn = a + (n-1)d

where a is the first term , n is the number of terms and d is the common difference

For the 12 term(a12), n = 12

70 = a + (12-1)d

70 = a + 11d •••••••(i)

For the 30th term, n = 30

124 = a + (30-1)d

124 = a + 29d •••••••(ii)

Now, directly subtract equation i from ii, we have;

124-70 = (a-a) + (29d-11d)

54 = 18d

d = 54/18

d = 3

To get a , we substitute the value of d in any of the equations

let’s use the first

70 = a + 11d

substituting d = 3

70 = a + 11(3)

70 = a + 33

a = 70-33

a = 37

Thus the explicit formula for the nth term will be

Tn = a + (n-1)d

where a = 37 and d = 3

Tn = 37 + (n-1)3

Tn = 37 + 3n -3

Tn = 34 + 3n

Answer:

Its B. y-5x+5

Step-by-step explanation:

Use the slope formula

The equation of the linear model is y = 5x + 5. The correct answer is option B.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

We can find the equation of the linear model passing through two points using the slope-intercept form of a line:

y = mx + b

where m is the slope of the line and b is the y-intercept.

First, we need to find the slope of the line:

m = (y₂ - y₁) / (x₂ - x₁)

Let (0, 5) be the first point, and (3, 20) be the second point:

m = (20 - 5) / (3 - 0) = 15 / 3 = 5

Now that we know the slope, we can plug in one of the points and solve for the y-intercept:

y = mx + b

5 = 5(0) + b

b = 5

Hence, the equation of the linear model is:

y = 5x + 5

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Answer:

Possible monomials: 3x² and 3xy

Step-by-step explanation:

We are asked to find a monomial of the 2nd degree with a leading coefficient of 3.

A monomial is a polynomial with only one term. This monomial has to be of 2nd degree, that is, if only one variable is present, the exponent of it is 2, like in x² or y²; but if two variables are present, the exponent of each one is one, so that, the degree is still two, like in xy (degree = 1 + 1 = 2)

In a monomial there is only one coefficient, the leading coefficient, which is the multiplicative factor of the variables. Then, with one variable, the monomial is 3x², and with two, it is 3xy

Answer:

3n^2 is the answer

Step-by-step explanation:

Khan academy lol

Answer:

54 combinations.

Explanation:

3x3x2x3= 54