Find the value of sin c

Answer:

(6, 7) and (-2, -1)

Step-by-step explanation:

if y=x+1 intersects with y=x^2-3x-11

then we need to find x and y such that both of those equations are true.

If y = x + 1 is true and y=x^2-3x-11, then

y - y = x^2-3x-11 - x - 1 is also true

0 = x^2 - 4x - 12

use your preferred method to solve the quadratic equation

0 = (x - 6)(x + 2)

x = 6 or x = -2

now for each x we take y from either equation, but y = x + 1 is simpler.

for x = 6 the coordinates are (6, 7) and for x = -2 the coordinates are (-2, -1)

Answer:

The 5 is in the thousandths place.  

825/1000

Step-by-step explanation:

Simplified this would be 33/40

825/1000  Divide the top and bottom by 25

Answer:

923.08

Step-by-step explanation:

48000/52 weeks

Answer:

923.08

Step-by-step explanation:

There are 52.1429 weeks in a year, so divide.

The correct option is the first one, (1.176*10¹) is 14.7 times larger than (8*10⁻¹)

Here we want to see how many times larger is (1.176*10¹) larger than (8*10⁻¹), we can see that both numbers are in scientific notation.

To check that, we just need to take the quotient between the two numbers, we will get:

(1.176*10¹)/(8*10⁻¹) = (1.176/8)*(10¹/10⁻¹)

(1.176/8)*(10¹/10⁻¹) =  (1.176/8)*(10¹⁻⁽⁻¹⁾) =  (1.176/8)*10² = 0.147*10²

Now, returning to standard notation, we can rewrite:

0.147*10² = 14.7

The correct option is the first one, (1.176*10¹) is 14.7 times larger than (8*10⁻¹)

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Work Shown:

x = amount of sales

0.05x = five percent of sales to represent commission earned

21,000+0.05x = add on the base salary to get total salary

21,000+0.05x = 70,000

0.05x = 70,000-21,000

0.05x = 49,000

x = (49,000)/(0.05)

x = 980,000

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Check:

If the real estate agent sold $980,000 worth of property, then s/he earned 5% of 980,000 = 0.05*980,000 = 49,000 dollars in commission.

The total salary for the year is 21,000+49,000 = 70,000 dollars. The answer is confirmed.

The required two numbers are 6 and 8.

Let us denote the required numbers by c and d.

Given that the difference between two natural numbers is 2.

If we assume d > c, then d – c = 2

⇒ d = 2 + c → equation 1.

Also given that the sum of their squares is 100.

⇒ c² + d² = 100

⇒ c² + (2 + c)² = 100 (using the value of d from equation 1)

⇒ 2c² + 4c + 4 = 100

⇒ 2c² + 4c = 96

⇒ 2c(c+2) = 96

⇒ c(c+2) = 48

Using the factorization for 48, we get 6 × 8 = 48

⇒ c = 6

⇒ c+2 = 8

⇒ d = 8

Therefore, the required two numbers are 6 and 8.

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The original amount borrowed was $517.

Simple Interest is the method to calculate the interest charged for a given number of years and given rate , in simple interest the principle remains same for each year.

Simple interest =[tex]\frac{P*R*T}{100}[/tex]

where P= principle, R=rate in % , T= time

We know that Amount= Principle+ Simple Interest........(1)

According to the question

Amount=$610.06

Rate=18%

time = 1yr

Substituting the value in equation (1) we get

[tex]610.06=P+\frac{P*18*1}{100}[/tex]

[tex]610.06=\frac{100P+18P}{100}[/tex]

[tex]610.06=\frac{118P}{100}[/tex]

[tex]61006=118P[/tex]

[tex]P=\frac{61006}{118}[/tex]

[tex]P=517[/tex]

Therefore  , The original amount borrowed was $517.

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The 715 cm² area of the disc and the ±5 cm² error tolerance, gives;

a) x = √(715/π) cm

b) The range for the radius is; [√(710/π) cm, √(720/π) cm]

c)

f(x) = π•x²

L = 715 cm²

E = 5 cm

d = √(5/π) cm

Area of the circular metal disk = 715 cm²

a) Required; The disk radius

Let A represent the area of the disk and let x represent the radius, we have;

A = π•x²

Therefore;

x = √(A/π)

Which gives;

x = √(715/π) cm

b) Allowed area error tolerance = ± 5 cm²

The allowed range of values for the area is therefore;

Which gives;

√(710/π) ≤ x ≤ √(720/π)

c) From the [tex] \epsilon / \delta [/tex] definition of limits, we have;

[tex] \lim\limits_{x → √(715/π)} f(x) = 715 [/tex]

Which gives;

f(x) = A = π•x²

L = 715

|f(x) - L| < E = 5 cm

|x - √(715/π)| < d = √(5/π)

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Answer:

Step-by-step explanation:

Answer:

1; 1

2:3

3:9

4:27

5:81

6:243

7:729

8:2,187

9:6,561

10:19,683

11:59,049

12:177,147

The given expression is simplified as 6x+3y³. Therefore, option A is the correct answer.

The given expression is [tex]\frac{18x^{3}y^{2}+9x^{2} y^{5}}{3x^{2} y^{2} }[/tex].

We need to divide and simplify the given expression.

Division of polynomials by monomial means dividing the polynomials which are written as numerators by a monomial which is written as denominators to find their quotient.

Split the denominators to each numerator and cancel out the common terms and simplify.

Now, [tex]\frac{18x^{3}y^{2}+9x^{2} y^{5}}{3x^{2} y^{2} }=\frac{18x^{3}y^{2}}{3x^{2} y^{2}} +\frac{9x^{2} y^{5}}{3x^{2} y^{2}}[/tex]

=6x+3y³

The given expression is simplified as 6x+3y³. Therefore, option A is the correct answer.

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9. Enrique would earn $7. 50 per hour. Option B

10. The number of girls that were at the assembly is 1390 . Option J

11. 40% of 60 is 24 . Option C

12. The simple interest is $72. 00 . Option F

13. The factory produces 1080 shoes on Tuesday. Option D

9. From the information given, we have;

He would earn;

= 420/ 56

= $7. 50 per hour

10. We have that;

The number of girls at the assembly would be;

= 23/ 20 × 1200

= 1. 15 × 1200

= 1380

11. Let the number be x

40% of x = 24

40/ 100x = 24

0. 4 x = 24

Make 'x' the subject

x = 24/ 0. 4

x = 60

12. The formula for simple interest is expressed as;

Simple interest = PRT / 100

Simple interest = 300 × 4 × 6/ 100

Simple interest = 7200/ 100

Simple interest = $72. 00

13. We have that;

Monday's production = 900 shoes

Tuesday's production = 900 + 900 × 20% = 900 × 20/ 100 = 18000/ 100 = $900 + 180

= $1080

Thus, the total amount Enrique earns per hour is $7. 50 .Option B

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Answer:

y=-x+13

Step-by-step explanation:

m=-1

m is slope

point is (9, 4)

first use point slope equation

y-y1=m(x-x1)

y-9=-1(x-4)

distribute

y-9=-x+4

isolate the y variable

y=-x+13

The ratio of the donation to the bill in a table from a similar question is constant, which gives;

The possible values in the table as obtained from a similar question are as follows;

Dinner Bill ($) Donation ($)

25 4.50

30 5.40

35 6.30

40 7.20

Let B represent the dinner bill, and let D represent the donation.

The amount of donation is proportional to the dinner bill if each corresponding value of D/B is constant.

Checking gives;

4.5/25 = 5.4/30 = 6.3/35 = 7.2/40 = 9/50

Which gives;

D/B = 9/50

Therefore

If the dinner bill is $50, we have;

B = 50

Which gives;

D = 9/50 × 50 = 9

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Answer:

on what nothing there

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

10⁰=1

9⁰=1

7⁰=1

5⁰=1

3⁰=1

1¹⁰⁰=1

so,

10⁰+9⁰+7⁰+5⁰+3⁰+1¹⁰⁰=1+1+1+1+1+1=6

Answer:

6

Step-by-step explanation:

We are working with exponents

Any number to the power of 0 is 1

a^0 = 1

1 to a power is 1

10⁰+9⁰+7⁰+5⁰+3⁰+1¹⁰⁰​

1 + 1 + 1 + 1 + 1 + 1

6

Using the normal distribution, it is found that 21% of the riders go on more than 10 rides.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 8.4, \sigma = 2[/tex]

The proportion of riders that go on more than 10 rides is one subtracted by the p-value of Z when X = 10, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (10 - 8.4)/2

Z = 0.8

Z = 0.8 has a p-value of 0.7881.

1 - 0.7881 = 0.2119 = 21.19% = 21%(rounded to the nearest percent)

21% of the riders go on more than 10 rides.

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Answer:

$1.43

Step-by-step explanation:

To find how much one roll of paper towels cost, we have to divide the total purchase ($20.02) by the number of paper towel rolls (14).

20.02 ÷ 14

= $1.43

One paper towel roll costs $1.43

Have a lovely rest of your day! :)

Answer:

4,      -1,         5,          -2

Step-by-step explanation:

Based on the angles addition theorem, the measure of the original angle = 44°.

The angles addition theorem states that if an angle is bisected to form two smaller angles, then the sum of the measures of the two smaller angles equals the measure of the original angle that is bisected.

Given that the two smaller angles formed when bisected are: (3+30)° and (5+6)°. Based on the angles addition theorem:

The measure of the original angle = (3+30)° + (5+6)°

The measure of the original angle = 33° + 11°

The measure of the original angle = 44°

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Answer:

pqr²−p²r−q²r+pq

Step-by-step explanation:

Let's simplify step-by-step.

pq(r²+1)−r(p²+q²)

Distribute:

=(pq)(r²)+(pq)(1)+−p²r+−q²r

=pqr²+pq+−p²r+−q²r

=pqr²−p²r−q²r+pq

Answer:

2x – 12 + 12 = x + 9

2x = x + 9

x = 9

Answer:

Line 3

Step-by-step explanation:

Proportional relationship:

• They are straight lines that have a constant slope

• The line must pass through the origin at (0,0)

• The y intercept is zero

The only line passing through the origin at the point (0,0), is Line 3

The half life period is the time in which only half of the given population remains. It can be represented through this equation:

[tex]f(t)=a\times(1/2)^{\frac{t}{h}}[/tex]

We're given:

For most questions like this, we would have to plug these values into the equation mentioned above. However, this question asks for the time elapsed after 3 half-lives.

This can be calculated simply by multiplying the given half-life by 3:

28 million years x 3

= 84 million years

84 million years

Answer:

The length is 225 yd, and the width is 175 yd.

Step-by-step explanation:

Let w = width.

Then the length = w + 50.

perimeter = 2(length + width)

800 = 2(w + 50 + w)

400 = 2w + 50

2w = 350

w = 175

w + 50 = 225

The length is 225 yd, and the width is 175 yd.

Answer:

225 * 175 yards,

Step-by-step explanation:

If the width is x then the length is x+50.

Perimeter = 2(width + length)

800 = 2( x + x + 50)

2x + 50 = 400

2x = 350

x = 175

So, the width is 175 yd and length is 225yd.

Answer:

270

Step-by-step explanation:

From (1) and (2), we get,

> y + 90 = 2/3X

> 1/3 X + 90 = 2/3X

> 90 = 1/3 X

> X = 270

Therefore

Answer:

Could I see the available choices?

Step-by-step explanation:

Answer:

didnt have the choices but any that would have it as the same problem different order

Step-by-step explanation:

17+14+13=13+14+17=14+13+17=14+17+13=17+13+14=13+17+14

Answer:

-18

Step-by-step explanation:

From 3 to 10th term is 7 d's       ( d = common difference)

3 - 7d = third term

3 - 7(3)  =  -18