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Answer:

The equivalent expression is cos(40° – 10º) ⇒ D

Step-by-step explanation:

The rule of cosine the compound angles is

cos (A + B) = cos A cos B - sin A sin B

cos (A - B) = cos A cos B + sin A sin B

Let us use these rules to solve the question

∵ cos(40°)cos(10°) + sin(40°)sin(10º)

∵ The middle sign is plus

∴ We will use the 2nd rule above

→ Compare the rule by the given expression to find the value of A and B

∵ A = 40° and B = 10°

∴ cos (A - B) = cos (40° - 10°)

∴ cos (40° - 10°) = cos(40°)cos(10°) + sin(40°)sin(10º)

∴ The equivalent expression is cos(40° – 10º)

Answer:

The present age of the artifact is 1,600 years

Step-by-step explanation:

let the present age of the artifact = x

let the present age of the book, = y

x = 4y ---- equation (1)

x + 200 = 3(y + 200) ------equation (2)

x + 200 = 3y + 600

substitute in the value of x into the equation;

4y + 200 = 3y + 600

4y - 3y = 600 - 200

y = 400

Then, x = 4 x 400

x = 1,600 years

Therefore, the present age of the artifact is 1,600 years

Answer:

The present age of the artifact is 1,600 years  

Step-by-step explanation:  

let the present age of the artifact = x  

let the present age of the book, = y  

x = 4y ---- equation (1)  

x + 200 = 3(y + 200) ------equation (2)  

x + 200 = 3y + 600  

substitute in the value of x into the equation;  

4y + 200 = 3y + 600  

4y - 3y = 600 - 200  

y = 400  

Then, x = 4 x 400

x = 1,600 years

Answer:

D

Step-by-step explanation:

Just took the test

Answer:

3 berries

Explanation:

Opportunity costs for the Orange group:

Opportunity cost of pumping 1 gallon of water = 3/1 = 3 berries

Opportunity cost of picking 1 berry = 1/3 = 0.333 gallons of water

Opportunity costs for the Yellow group:

Opportunity cost of pumping 1 gallon of water = 8/2 = 4 berries

Opportunity cost of picking 1 berry = 2/8 = 0.25 gallons of water

Opportunity cost for both groups combined:

Opportunity cost of pumping 1 gallon of water = 3 berries (Orange group should pump water since opportunity cost is lower)

Opportunity cost of picking 1 berry = 0.25 gallons of water (Yellow group should pick berries since opportunity cost is lower)

Opportunity costs are the extra costs or benefits lost resulting from choosing one investment or activity over another alternative. In this case, people can either pump water or pick berries, but they cannot do both at the same time. When they are pumping water, the opportunity cost is the amount of berries that they will not be able to collect, and vice versa.

Answer:

im not 100% sure what your asking but i think its you make 9.65 per hour for 40 hours then 5 more hours how much are you making?

Step-by-step explanation:

its 434.25 here is why 9.65x40=386

+5hours 9.65x5=48.25

386+48.25=434.25

Answer:

9

Step-by-step explanation:

DB^2=AD^2+AC^2

15^2=12^2+AC^2

AC^2=225-144

AC^2=81

AC=√81

AC=9

Answer:

1/7 Brainliest plz

Step-by-step explanation:

Answer:

five times a number is greater than the sum of four times that number and seven

Answer:

$35 per plant

Step-by-step explanation:

You take the 140 and divide that by 4 to get your answer.

Answer:

ill Put the answer in the comments if you give a pic of the image for this problem

Step-by-step explanation:

Answer:

The perimeter of triangular sign is 12x+3

Step-by-step explanation:

Length of side1 of triangle = x inches

Length of side2 of triangle = 4x-5 inches

Length of side3 of triangle = 7x+8 inches

We need to find perimeter of triangular sign.

The formula used is: [tex]Perimeter \ of \ triangle = Sum \ of \ all \ three \ sides[/tex]

Now, finding perimeter of triangular sign:

[tex]Perimeter \ of \ triangle = Sum \ of \ all \ three \ sides\\Perimeter \ of \ triangle = x+4x-5+7x+8\\Perimeter \ of \ triangle = x+4x+7x-5+8\\Perimeter \ of \ triangle = 12x+3[/tex]

The perimeter of triangular sign is 12x+3

Answer:

John has 357 marbles left.

Step-by-step explanation:

120 marbles went to Bob

48 went to Pat

and 75 to Matt.

z =(2-√-116)/-20=1/-10+i/10√ 29 = -0.1000-0.5385i

z =(2+√-116)/-20=1/-10-i/10√ 29 = -0.1000+0.5385i

Step-by-step explanation:

Answer:

The amount invested at 15% = $257.14

The amount invested at 8% = $942.86

Step-by-step explanation:

Let the amount invested at:

15% = a

8% = b

Total invesment = $1200

Hence:

a + b= $1200....... Equation 1

a = 1200 - b

15% × a + 8% × b = 9.5% × 1200

0.15a + 0.08b = 0.095 × 1200

0.15a + 0.08b = 114..... Equation 2

We substitute 1200 - b for a in Equation 2

0.15(1200 - b) + 0.08b = 114

180 - 0.15b + 0.08b = 114

- 0.15b + 0.08b = 114 - 180

- 0.07b = - 66

b = -66/-0.07

b = $942.85714286

Approximately = $942.86

Note that:a = 1200 - b

a = $1200 - $942.86

a = $257.14

Answer:

14.72

Step-by-step explanation:

Answer:

7 recipes could be made with [tex]2\frac{1}{3}[/tex] cups of sugar.

Step-by-step explanation:

Quantity of sugar required for a recipe [tex]=\frac{1}{3}[/tex] cups

Quantity of sugar required in a pantry [tex]=2\frac{1}{3}[/tex] cups

Here,

[tex]2\frac{1}{3}=\frac{7}{3}[/tex]

So,

Quantity of sugar required in a pantry [tex]=\frac{7}{3}[/tex] cups

Number of recipes that could be made  [tex]=\frac{\frac{7}{3} }{\frac{1}{3} } =7[/tex]

Therefore, 7 recipes could be made with [tex]2\frac{1}{3}[/tex] cups of sugar.

Answer:

13.5

Step-by-step explanation:

Answer:

i would say answer A

Step-by-step explanation:

Answer:  27 kg of sugar can be bought for Rs. 877.50.

Step-by-step explanation:

Answer:

you could buy 28518.75 sugar for 877.500

Step-by-step explanation:

260 / 8 = 32.5

this gives you how much it cost per 1 (units)

32.5 * 877.50 = 28518.75

Answer:

1 & 2

Step-by-step explanation:

Answer:

Unidades a vender= 644 unidades

Step-by-step explanation:

Dada la siguiente información:

Costos fijos= $1.348

Costo unitario= $3,5

Precio de venta= $8

Ganancia deseada= 775*2= $1.550

Para calcular el número de unidades a vender, debemos usar la siguiente formula:

Unidades a vender= (costo fijo + ganancia deseada) / contribución marginal unitara

Unidades a vender= (1348 + 1550) / 4,5

Unidades a vender= 644 unidades

Answer:

-7 and 7

Step-by-step explanation:

Answer:

8 large glasses can be filled by a large bottle.

Step-by-step explanation:

First we calculate the volume of a small bottle:

Now we calculate the volume of a small glass:

" A small bottle fills 6 small glasses with no juice left over.", this means that

Then we calculate the volume of a large glass:

Finally we divide the volume of a large bottle by the volume of a large glass:

So 8 large glasses can be filled by a large bottle with juice left over.

Step-by-step explanation:

let no of years be x.

55000 + 2500x = 62000 + 2000x

500x = 7000

x = 14

therefore, 14 years.

Topic: algebraic eqns

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