A farmer had a total of 995 horses and cows. After selling some of the horses and cows, he had 510 horses and 390 cows left. How many horses and cows did he sell altogether?

The radius of a circle with center at  [tex]C (0, 4)[/tex] and point [tex]P(-2, -1)[/tex] will be [tex]\sqrt{29}[/tex].  

Equation of a circle is written in the form of [tex](x-h)^2+(y-k)^2=r^2[/tex]  where [tex](h,k)[/tex]  represents the center and  [tex]r[/tex]  is the radius.

We have,

Center at  [tex]C (0, 4)[/tex]

i.e. [tex]h=0,\ k=4[/tex]

And,

Point  [tex]P(-2, -1)[/tex]

i.e. [tex]x=-2,\ y=-1[/tex]

Now,

To determine Radius of the circle;

[tex]r^2=(x-h)^2+(y-k)^2[/tex]

[tex]r^2=(-2-0)^2+(-1-4)^2[/tex]

[tex]r^2=(-2)^2+(-5)^2[/tex]

[tex]r=\sqrt{4+25}[/tex]

[tex]r=\sqrt{29}[/tex]

So, radius of the circle is [tex]\sqrt{29}[/tex] , which is find out using equation of a circle.

Hence, we can say that the radius of a circle with center at  [tex]C (0, 4)[/tex] and point [tex]P(-2, -1)[/tex] will be [tex]\sqrt{29}[/tex].

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The length of the radius of the circle is sqrt(29) or approximately 5.39 units.

To find the length of the radius of a circle, we can use the distance formula. The distance between the center of the circle (0, 4) and the point on the circle (-2, -1) is given by:

d = sqrt((x2-x1)^2 + (y2-y1)^2)

Plugging in the values, we get:

d = sqrt((-2-0)^2 + (-1-4)^2)

d = sqrt((-2)^2 + (-5)^2)

d = sqrt(4 + 25)

d = sqrt(29)

Therefore, the length of the radius of the circle is approximately sqrt(29) or 5.39 units.

Answer:

  31 5/8 pounds

Step-by-step explanation:

The total weight is ...

  9(2 7/8 lb) + 2(2 7/8 lb) = (2 7/8 lb)(9 +1) = (23/8 lb)(11) = 253/8 lb

  = 31 5/8 lb

The total of package weights is 31 5/8 pounds.

Final answer:

The total weight of all ten packages that Jeff wants to mail is 31 5/8 pounds.

Explanation:

Jeff has ten packages to mail, with nine identical packages weighing 2 7/8 pounds each and one package weighing double the weight of one of the nine.

To find the total weight of all the packages, we first calculate the weight of the nine identical packages by multiplying their weight by the number of packages, which is:

2 7/8 pounds/package × 9 packages = 25 7/8 pounds

Next, we determine the weight of the tenth package:

2 × 2 7/8 pounds = 5 6/8 pounds, which simplifies to 5 3/4 pounds.

Finally, we add the total weight of the nine packages to the weight of the tenth package:

25 7/8 pounds + 5 3/4 pounds = 31 5/8 pounds.

Therefore, the total weight of all ten packages is 31 5/8 pounds.

The solution of the inequality is 8.5 < x.

Solution:

Given inequality is 2x + 5 > 22.

2x + 5 > 22

Subtract 5 from both sides of the inequality.

2x + 5 – 5 > 22 – 5

2x > 17

Divide by 2 on both sides of the inequality.

[tex]$\frac{2x}{2}>\frac{17}{2}[/tex]

[tex]$x>\frac{17}{2}[/tex]

x > 8.5

8.5 < x

The graph of the solution is attached below.

Answer:

6d - 447

Step-by-step explanation:

(15+6d) - 2 + (-502 - 18 + 60)

(13+6d) + (-460)

6d + 13 - 460

6d - 447

The required answer is 6d - 531

Simplification generally means finding an answer for the complex calculation that may involve numbers on division, multiplication, square roots, cube  roots, plus and minus.

Now the given expression is,

(15 +6d - (2) + (-502 - 18 + 60)

Thus,

(15 +6d - (2) + (-502 - 18 + 60)

= 15 + 6d - 2 - 502 + 18 - 60

Rearranging we get,

= 15 + 18 + 6d - 2 - 502 - 60

= 33 + 6d - 564

= 6d - 564 + 33

= 6d - 531

this is the required answer.

Thus, the required answer is 6d - 531.

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Answer:

6 14/15

Step-by-step explanation:

I would say simplifie the paratensies.

First:

3 2/3+ 17 1/5 =

Common factor of 3 and 5 is 15

3 10/15 + 17 3/15 = 20 13/15

Second:

11 3/5 + 2 1/3 =

Common factor of 3 and 5 is 15

11 9/15 + 2 5/15 = 13 14/15

20 13/15 - 13 14/15 = 7 13/15 - 14/15 = 7 - 1/15 = 6 14/15

Quadratic equation is x² - x - 30

Step-by-step explanation:

⇒ Factors are (x - 6) and (x + 5)

⇒ (x - 6)(x + 5) = x² + 5x - 6x - 30 = x² - x - 30

Answer:

84

Step-by-step explanation:

72/x = 6/7

muliply by x on both sides

72 = 6/7x

mulitply by 7 on both sides

504 = 6x

divide by 6 on both sides

84

Answer:84

Step-by-step explanation:

6*12=72

7*12=84

Answer:

yes

Step-by-step explanation:

can i get brainliest please and thank you.

Answer:

Option C. X=A/4

Step-by-step explanation:

we know that

The area of the rectangular post it note is equal to

[tex]A=LW[/tex]

where

L is the length

W is the width

In this problem we have

[tex]W=4\ in[/tex]

[tex]L=X\ in[/tex]

substitute

[tex]A=4X[/tex]

solve for x

That means ----> isolate the variable x

Divide by 4 both sides

[tex]X=\frac{A}{4}[/tex]

Answer:

9/16 m.

Step-by-step explanation:

When you cut two pieces along its diagonal it causes it to be two congruent triangular pieces.

You need to multiply the length and the width to find an area:

1 1/2 × 3/4

Now you need to change it into an improper fraction:

1*2+1 = 2+1 = 3; this gives us 3/2:

3/2 × 3/4 = 9/8 = 1 1/8

Dividing it by 2:

9/8 ÷ 2

Step-by-step explanation:

Given triangle is 30°, 60° & 90° angled triangle.

We know that in 30°, 60° & 90° angled triangle. Side opposite to 30° is half of hypotenuse and side opposite to 60° is root 3 upon 2 times of hypotenuse.

[tex] \therefore \: 9 = \frac{1}{2} \times y \:\:\:(side \: opposite \: to \: 30 \degree)\\ \\ \therefore \: 9 \times 2 = y \\ \\ \therefore \:y = 18 \: units \\ \\ next \\ \\ x = \frac{ \sqrt 3}{2} \times y \:\:\: (side \: opposite \: to \: 60 \degree)\\ \\ \therefore \: x = \frac{ \sqrt 3}{2} \times 18 \\ \\\therefore \: x = \sqrt 3 \times 9 \\ \\ \therefore \: x = 9 \sqrt 3 \: units[/tex]

Answer: 191,000

Step-by-step explanation:

Answer:

the answer is 10,10and 20

Step-by-step explanation:

becoz 2 sides are equal n the other is not

Answer:

your answer is D.) 10,10 and 20

Step-by-step explanation:

Answer:

34

Step-by-step explanation:

We know that the sum of angles in a quadrilateral must be 360.

As such, we can sum up all given values for all 4 angles and set it equal to 360

[tex]360=108+88+2x+(3x-6)\\360=190+5x\\170=5x\\x=34\\\\[/tex]

Answer:

x=59

Step-by-step explanation:

the sum is 360 degrees.. Therefor

x + x + 2x + 3 + 2x + 3 = 360

combine alike terms

6x + 6 = 360

6x = 354

x = 59

Answer:

5x+2x-2y

7x-2y

Step-by-step explanation:

Answer:

7x-2y

Step-by-step explanation:

distribute the 2 to the numbers in the parenthesis then combine like terms

Answer:

the rope is 25 inches long

1. 20×5=100%

2. 5×5=25 inches

3. 100% of the rope is equal to 25 inches

Final answer:

The entire rope is 25 inches long, as the given 5-inch section is 20% of the whole rope, and multiplying by 5 gives us the full length.

Explanation:

If a section of rope 5 inches long represents 20% of the length of the entire rope, we can find the full length of the rope by setting up a proportion. Considering that 20% is equivalent to the fraction 1/5, we would multiply the length of the shortened rope by 5.

The calculation would be as follows:

5 inches (given length representing 20%) × 5 (since 20% is 1/5 of 100%) = 25 inches.

Thus, the entire length of the rope would be 25 inches.

Answer:

x=2i, -2i

Step-by-step explanation:

Answer:

2,-2 or maybe no real solutions but i went with 2,-2

Step-by-step explanation:

Answer:

The domain is [1,∞)

Step-by-step explanation:

The given functions are:

[tex]a(x)=3x+1[/tex]

and

[tex]b(x) = \sqrt{x - 4} [/tex]

We want to find the domain of

[tex](b\circ a)= \sqrt{3x + 1 - 4} [/tex]

Simplify to get:

[tex](b\circ a)= \sqrt{3x -3} [/tex]

This function is defined when the expression under the radical is greater or equal to zero.

[tex]3x -3 \geqslant 0 \\ x \geqslant 1[/tex]

Answer:

C on Edge 2021

Step-by-step explanation:

Took the test

Answer:

23.44%

Step-by-step explanation:

The probability of getting a 4 on the first 2 throws and different numbers on the last 5 throws = 1/6 * 1/6 * (5/6)^5

= 0.01116

There are 7C2 ways of the  2 4's  being in different positions

= 7*6 / 2 = 21 ways.

So the required probability =  0.01116 * 21

= 0.2344 or 23.44%.

Answer:

(4, 12)

Step-by-step explanation:

When the two lines intersect on a graph, it is when you can put the same value for "x" into both equations, and the same value for "y" into both equations.

Because they both equal "y", and y = y, you can equate the expressions together.

y = y

2x + 4 = 2.50x + 2

Now the goal is to move all the numbers with "x" to the left. Move the the numbers to the right side. (This is called isolating "x" because it will be alone).

2x + 4 - 4 = 2.50x + 2 - 4            Subtract 4 from both sides

2x = 2.50x - 2            

2x - 2.50x = 2.50x - 2.50x - 2            Subtract 2.50x from both sides

-0.50x = -2            

-0.50x/-0.50 = -2/-0.50            Divide both sides by -0.50

x = 4            Found "x" coordinate

Choose one of the original equations. Change "x" to 4 (called substitution).

y = 2x + 4

y = 2(4) + 4            Multiply first

y = 8 + 4            Add

y = 12            Found "y" coordinate

Now write the coordinates like an ordered pair (x, y).

The lines intersect at (4, 12).

Answer:

Expression = 25

Step-by-step explanation:

2xy+2x^2 = ?

2(-2.5)(-7.5)+2(-2.5)^2 = ?

37.5 + (-12.5) = ?

= 25

Final answer:

The value of the expression 2xy + 2x² for x=-2.5 and y=-7.5 is 50.

Explanation:

To find the value of the expression 2xy + 2x² for x=-2.5 and y=-7.5, we substitute these values into the expression:

2(-2.5)(-7.5) + 2(-2.5)²

Simplifying this expression, we get:

(7.5) + 2(6.25)

= 37.5 + 12.5

= 50

Therefore, the value of the expression 2xy + 2x² for x=-2.5 and y=-7.5 is 50.

Answer:

The new area of the triangle is (1 / 9) th of the original area.

That is to say the original area of the triangle is decreased to (1/9) th of its value.

Step-by-step explanation:

The area of a triangle is given by, Area = 1/2 [tex]\times[/tex] base  [tex]\times[/tex]  height

If each side of a triangle is cut to 1/3 of its original size then the base will also become one third and the height will also become one third.

Therefore the new area  will be given by  = 1/2  [tex]\times[/tex] (1/3 [tex]\times[/tex] base)  [tex]\times[/tex]  (1/3  [tex]\times[/tex] height)

   = 1/9  [tex]\times[/tex] 1/2  [tex]\times[/tex] base  [tex]\times[/tex] height

   = 1/9  [tex]\times[/tex] Area.

The new area of the triangle is 1 / 9 th of the original area.

When the sides of a triangle are reduced to 1/3 of their original size, the area of the triangle becomes 1/9 of its original area.

When the length of each side of a triangle is cut to 1/3 of its original size, the area of the triangle is affected by the square of the scale factor applied to the sides.

Let's use some mathematics to understand why this happens. The area of a triangle is given by the formula:

A = 1/2 * base * height, where 'base' represents the base of the triangle and 'height' represents the height of the triangle.

If each side of the triangle is reduced to 1/3 of its original size, both the base and the height will become 1/3 of their respective original sizes.

The new area (A') can be calculated as follows:

Simplifying this:

A' = 1/2 * (base * height) * (1/3 * 1/3)

A' = 1/2 * base * height * 1/9

A' = (1/2 * base * height) * 1/9

A' = A * 1/9

Therefore, the area of the triangle becomes 1/9 of its original area.

(a) Jason arrives at the factory first

(b) It takes 5 minutes until the other person arrives

Step-by-step explanation:

Jason and Jeremy work together at a juggling-ball factory

We need to know who arrives at the factory first and how long it is until the other person arrives

Time = Distance ÷ speed

∵ Jason lives 25 miles away from the factory

∴ The distance = 25 miles

∵ He drives at 60 miles per hour

∴ The speed = 60 miles per hour

- Use the rule above to find the time

∵ Time = 25 ÷ 60 = [tex]\frac{5}{12}[/tex] hour

∵ 1 hour = 60 minutes

∴  [tex]\frac{5}{12}[/tex] hour =  

∴ Jason arrives to the factory in 25 minutes

∵ Jeremy lives 35 miles away from the factory

∴ The distance = 35 miles

∵ He drives at 70 miles per hour

∴ The speed = 60 miles per hour

- Use the rule above to find the time

∵ Time = 35 ÷ 70 = [tex]\frac{1}{2}[/tex] hour

∵  [tex]\frac{1}{2}[/tex] hour =  

∴ Jeremy arrives to the factory in 30 minutes

∵ They leave their houses at the same time

∵ 25 minutes < 30 minutes

∴ Jason arrives first

(a) Jason arrives at the factory first

∵ Jason arrives to the factory in 25 minutes

∵ Jeremy arrives to the factory in 30 minutes

∵ 30 - 25 = 5 minutes

∴ Jeremy arrives after Jason by 5 minutes

(b) It takes 5 minutes until the other person arrives

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Final answer:

Jason arrives at the factory first, taking approximately 25 minutes, while Jeremy arrives 5 minutes later, taking around 30 minutes to reach.

Explanation:

The question involves calculating time taken for different scenarios involving motion and relative speed. In the given scenario, Jason lives 25 miles away from the factory and drives at 60 miles per hour, while Jeremy lives 35 miles away and drives at 70 miles per hour. To find out who arrives at the factory first, we calculate the time each person takes to reach the factory.

For Jason: Time = Distance / Speed = 25 miles / 60 mph = 0.4167 hours.
For Jeremy: Time = Distance / Speed = 35 miles / 70 mph = 0.5 hours.
Clearly, Jason will arrive first.

The difference in arrival time between Jeremy and Jason is:
Jeremy's time - Jason's time = 0.5 hours - 0.4167 hours = 0.0833 hours, which is 5 minutes.

Jason arrives at the factory first, and Jeremy arrives 5 minutes later.

[tex]\(33 \frac{1}{3}\)[/tex] % of 687 is 229.

To find [tex]\(33 \frac{1}{3}\)[/tex] the percent of 687, you can first convert [tex]\(33 \frac{1}{3}\)[/tex]% to a decimal, then multiply by 687.

[tex]\[33 \frac{1}{3}\% = \frac{33\frac{1}{3}}{100} = 0.3333\][/tex]

Now, multiply this decimal by 687:

[tex]\[0.3333 \times 687 = 229\][/tex]

So, [tex]\(33 \frac{1}{3}\)[/tex] % of 687 is 229.

Correct question:

what is [tex]\(33 \frac{1}{3}\)[/tex]  of 687?

Question:

A shopper bought a watermelon, a pack of napkins, and some paper plates. In his state, there is no tax on food. The tax rate on non-food items is 5%. The total for the three items he bought was $8.25 before tax, and he paid $0.19 in tax. How much did the watermelon cost?

Answer:

Cost of watermelon is $ 4.45

Solution:

From given,

Total amount for three items before tax = $ 8.25

Tax amount = $ 0.19

Tax on non food = 5 %

Here, non food means napkin and paper plates

Let "x" be the cost spent for napkin and paper plates

Then,

5 % = 0.19

100 % = x

This forms a proportion

[tex]5 \times x = 0.19 \times 100\\\\5x = 19\\\\x = 3.8[/tex]

Thus cost spent for napkin and paper plates is $ 3.8

Therefore,

Watermelon cost = total amount before tax - cost spent for napkin and paper plates

Watermelon cost = 8.25 - 3.8 = 4.45

Thus cost of watermelon is $ 4.45

The watermelon cost $4.45, calculated by subtracting the cost of the non-food items ($3.80) taxed at 5% from the total cost before tax ($8.25).

The information provided gives us the total cost before tax ($8.25) and the total tax amount ($0.19). Because only non-food items are taxed, and the tax rate is 5%, we can find the cost of the non-food items by dividing the total tax amount by the tax rate (expressed as a decimal).

Convert tax rate to decimal: 5% = 0.05

Divide the total tax by the tax rate: $0.19 / 0.05 = $3.80

Deduct the cost of the non-food items from the total cost before tax: $8.25 - $3.80 = $4.45

The cost of the watermelon, which is a food item and thus not taxed, is $4.45.

Answer:3x6x5

Step-by-step explanation:

39 ft of carpet

11x3+3x2=39

Answer:

-15

Step-by-step explanation:

3 x 5 = 15

when negative numbers are multiplied by positive numbers the product will be negative.

Final answer:

The product of -3 and 5 is -15, as per the multiplication rules where a negative number multiplied by a positive number results in a negative product.

Explanation:

The product of -3 and 5 is -15. In mathematics, when we talk about the product of two numbers, we are referring to the result of multiplying them. According to multiplication rules, when two numbers have opposite signs, the product has a negative sign. If we multiply a negative number by a positive number, the answer will also have a negative sign.

It's important to remember that multiplication is commutative, meaning that changing the order of the numbers does not change the product. The key concepts are similar to those used when figuring out subtraction and addition of signed numbers. For example, subtracting a negative is the same as adding a positive.

If we apply this to -3 multiplied by 5, we multiply the absolute values (3 and 5) to get 15. Since we have one positive number (5) and one negative number (-3), our final product is -15.

Answer:

0.785398163 rad

Step-by-step explanation:

The value of arctan(1) is equal to π/4 or 45 degrees.

The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle.

For the angle whose tangent is 1, we can visualize a right triangle where the length of the side opposite to the angle is 1 and the length of the adjacent side is also 1.

Using the Pythagorean theorem, we can calculate the length of the hypotenuse:

hypotenuse² = opposite² + adjacent²

hypotenuse² = 1² + 1²

hypotenuse² = 1 + 1

hypotenuse² = 2

hypotenuse = √2

Now, we can use the definition of the arctan function to find the angle whose tangent is 1:

arctan(1) = angle whose tangent is 1 = angle whose opposite side is 1 and adjacent side is 1

This angle is a well-known special angle in trigonometry.

It is a 45-degree angle (π/4 radians) or a quarter of a full circle.

Therefore, arctan(1) is equal to π/4 or 45 degrees.

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2(2x) + 1x = 40 or 4x + 1x = 40 is the result of combining by substitution

Solution:

Given that we have to combine 2y + 1x = 40 and y = 2x using substitution method

The substitution method for solving systems of equations involves expressing one variable in terms of another, thus removing one variable from an equation.

Given equations are:

2y + 1x = 40 -------- eqn 1

y = 2x ----------- eqn 2

We can substitute eqn 2 in eqn 1

Which means, substitute y = 2x in place of y in eqn 1

2(2x) + 1x = 40

4x + 1x = 40

5x = 40

x = 8

From eqn 2,

y = 2(8)

y = 16

Thus by combining using substitution method we found the solution