Find the area of a circle with radius,
r
= 46cm.
Give your answer rounded to 3 SF.

Answer:

13 sheep, 19 chicken

Step-by-step explanation:

You can start to solve this problem by assigning variables. First, let's assign the number of sheep there are as \(x\) and the number of chickens there are as \(y\).

Because each sheep has 4 legs, the number of legs for each sheep would be \(4x\). Similarly, because each chicken has 2 legs, the number of legs for each chicken would be \(2y\). Each animal would have 1 head, so the number of heads would just be \(x\) and \(y\). Because the number of legs in total are 90, \(4x + 2y=90\). Because the number of heads in total are 32, \(x+y=32.\)

There is now a system of equations with two unknown variables and two equations. There are many ways to solve this, but for me, the easiest would be elimination. First, I would double the second equation, \(2x+2y=64\). Then, I would subtract that from the first equation, eliminating \(y\). \(2x=26\). Solving for x gives 13. We can then plug that value into the second equation, making y be \(32-13=19\). This means that \(x=13\) and \(y=19\), meaning that there are 13 sheep and 19 chicken.

Using sine rule and cosine rule, the value of angle d, e and f are 60.77, 59.39 and 59.78 degrees

To find the values of the angles, we need to use cosine rule and sine rule.

Since we have 3 sides and no angle, we have to use sine rule first.

d² = e² + f² - 2(e)(f)cos(d)

substituting the values into the equation;

6.1² = 6.02² + 6.04² - 2(6.02)(6.04)cos(d)

37.21 = 36.24 + 36.48 - 72.72cos(d)

72.72cos(d) = 72.72 - 37.21

72.72cos(d) = 35.51

cos (d) = 35.51 / 72.72

d = 60.77°

Using sine rule;

d / sin D = e / sin E

6.1 / sin(60.77) = 6.02 / sin E

sin E = 6.02 * sin (60.77) / 6.1

E = 59.45°

d + f + e = 180 degree

reason: sum of angle in a triangle is equal to 180

60.77 + 59.45 + f = 180

f =  59.78°

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Answer:

x (or AB)=35

Step-by-step explanation:

x/25=28/20

20x=28x25

20x=700

x=35

The length of AB is 35 units

If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable. Similar figures are described as items with the same shape but varying sizes, such as two or more figures.

These three theorems, known as Angle - Angle (AA), Side - Angle - Side (SAS), and Side - Side - Side (SSS),

Given:

ΔABC  ~  ΔDEF then the ratio of their corresponding sides are equal

AB/ DE = BC/ EF = AC / DF

So, AB/ DE= BC / EF

x/ 25 = 28 / 20

x/25 = 7/5

x= 5 x 7

x= 35

Hence, the length of AB is 35 units

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Answer:Can you find the sum [5.5 + (-2.3)] + (-5.5 + 2.3) without performing any additions? - Slader.

1 answer

Missing: 7.25-5.5 ‎7.25)

Step-by-step explanation:

Answer:

Step-by-step explanation:

so the whole question is as follows

Answer:

It intersects the y-axis at point (0, 2).

Step-by-step explanation:

x + 3y = 6

3y = -x + 6

y = -1/3x + 2

Answer:

4. (6,0)

Step-by-step explanation:

Plug the points into the equation.

6+3(0)=6

6+0=6

6=6

The function that is decreasing on the same interval as the given function f(x) is h(x) = 2x^2 + 8x + 3.

To determine if a function is increasing or decreasing, we look at the sign of its derivative. If the derivative is positive, the function is increasing, and if the derivative is negative, the function is decreasing.

Taking the derivative of h(x) with respect to x, we get h'(x) = 4x + 8. To find the interval on which h(x) is decreasing, we need to find the values of x for which h'(x) < 0.

Setting h'(x) < 0, we have 4x + 8 < 0. Solving this inequality, we find x < -2.

Therefore, h(x) is decreasing for x < -2. Since the interval where h(x) is decreasing matches the interval for the given function f(x), we can conclude that h(x) = 2x^2 + 8x + 3 is the function that is decreasing on the same interval as f(x).

Overall, the function h(x) = 2x^2 + 8x + 3 is decreasing on the interval x < -2, which aligns with the interval of the given function f(x).

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Answer:

1/27  at (x.y)= (1/3, 1,3)

Step-by-step explanation:

Hope this helps:)

Answer:

sub

gghhhhhhhhgtyyuuiiiiii

Answer:

3/4 bags of trail mix

Step-by-step explanation:

She ate 1/2 of a bag, she gave 1/3 of a bag, and she dropped 1/6 of a bag. In total she "lost" 1/2+1/3+1/6=1 bag of trail mix. So she has 1 3/4-1=3/4 bags left

The best way to solve an equation of the form Ax+by=c could be either substitution, completing the squares or graphical method depending on the type of equation given.

Quadratic equation

The equation in the form Ax+by=c is a quadratic problem which could be approached in different ways depending on the specific equation given and the information provided.

The methods of approach are substitution, completing the squares or graphical method which all have proven to be suitable ways to arrive at the solution.

Hence, either of the three methods are good ways to solve such equation.

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For expression  x+1= √19-x, the value of x is approximately 3.

What exactly are expressions?

In mathematics, an expression is a combination of symbols and operators that represents a quantity or a mathematical relationship. It can contain numbers, variables, operators, functions, and other mathematical symbols. Expressions are used to represent mathematical operations and relationships, and they can be evaluated or simplified using mathematical rules and properties. Examples of expressions include 3x + 2, (x + y) / (x - y), and sin(x) + cos(y).

Now,

Starting with the given equation:

x + 1 = √(19 - x)

We can begin by squaring both sides of the equation to eliminate the square root:

(x + 1)² = (√(19 - x))²

Simplifying the right-hand side:

(x + 1² = 19 - x

Expanding the left-hand side:

x² + 2x + 1 = 19 - x

Moving all the terms to one side:

x² + 3x - 18 = 0

Now we can solve this quadratic equation using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a = 1, b = 3, and c = -18:

x = (-3 ± √(3² - 4(1)(-18))) / 2(1)

x = (-3 ± √(81)) / 2

x = (-3 ± 9) / 2

This gives us two solutions:

x = 3 or x = -6

However, we must check both solutions to make sure they are valid in the original equation:

Checking x = 3:

x + 1 = √(19 - x)

3 + 1 = √(19 - 3)

4 = √16

4 = 4

This solution works.

Checking x = -6:

x + 1 = √(19 - x)

-6 + 1 = √(19 + 6)

-5 = √25

-5 ≠ 5

This solution does not work.

Therefore, the solution to the equation x + 1 = √(19 - x) is x = 3.

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Correct question:

What is the solution to the equation below ?

x+1= √19-x

Enseñanza Básica is the term used to describe the first level of education in the Chilean education system, which includes the first to eighth grades. A teacher of Enseñanza Básica asked his students to choose three-digit mixed numbers that can be formed.

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The difference between the greatest and the least mixed numbers is 9.87 - 6.0789 ≈ 3.7911.

The three digits different from {1, 2, 3, 4, 5} can be chosen from {0, 6, 7, 8, 9}.

The greatest mixed number is formed by placing the largest digit as the whole number and the remaining two digits as the fraction in descending order, i.e., 9 87/100 or 9.87.

The smallest mixed number is formed by placing the smallest non-zero digit as the whole number and the remaining two digits as the fraction in ascending order, i.e., 6 07/90 or 6.0789.

The difference between the greatest and the least mixed numbers is 9.87 - 6.0789 ≈ 3.7911.

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The Question in English

A Basic Education teacher tells his students to choose three digits

different from the set {1, 2, 3, 4, 5} and form mixed numbers by placing the digits

in the locker It also reminds them that the fractional part has to be

less than 1, for example

2

3

5

. What is the difference between the greatest and the least of the

mixed numbers that can be formed?

Answer:

Step-by-step explanation:

The difference of a number and fifteen is two. Write and Algebra Sentence then solve the number.

x - 15 = 2

x = 2 + 15

x = 17

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

check

17 - 15 = 2

2 = 2

the answer is good

Answer:

231,000

Step-by-step explanation:

In the ratio of 11:13, if you plug in 13, the corresponding value is 11.

Dividing 11 by 13 shows that if you also multiply 13 by 0.846 (Rounded) it also equals 11.

So multiplying 0.846 by the original price of 273,000, we get 231,000.

The new selling price of the car will be 231,000. Then the correct option is A.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

The original selling price of a used automobile is N273,000. The price is dropped by the dealer by a ratio of 11:13.

The new selling price of the car will be given as,

Selling price = 273,000 x 11/13

Selling price = 21,000 x 11

Selling price = 231,000

Thus, the correct option is A.

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The time interval between the first two instants when this element has a position of y = 0. 175 m is 21 ms.

The time interval between the first two instants when this element has a position of y = 0. 175 m is calculated as;

y (x, t) = ( 0.35 m sin[1.25 rad/m)x  + (99.6 rad/s)t]

x = 0

y(0,t) =  0.35 sin(1.25 rad/m)0 + 99.6t ) = 0.175

0.35 sin(99.6t) = 0.175

sin (99.6t) = 0.175/0.35

sin (99.6t) = 0.5

99.6t = sin⁻¹ (0.5)

99.6t = (π/6 ) or ( π - π/6) = 5π/6

time, t₁ = ( π/6 ) / ( 99.6 ) = 5.257 x 10⁻³ s

time, t₂ = ( 5π/6 ) / ( 99.6 ) = 26.28 x 10⁻³ s

time interval = t₂ - t₁

= 26.28 x 10⁻³ s - 5.257 x 10⁻³ s

= 21 x 10⁻³ s

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The complete question is below:

A transverse wave on a string is described by the equation

y (x, t) = ( 0.35 m) sin[1.25 rad/m)x  + (99.6 rad/s)t]

Consider the element of the string at x = 0.

What is the time interval between the first two instants when this element has a position of  y = 0. 175 m?

Answer:

Step-by-step explanation:

Assuming that the given dimensions of 13, 13, 13 refer to the base of the rectangular pyramid, we can calculate the surface area of the pyramid as follows:

First, we need to calculate the area of the rectangular base, which is simply length x width:

Area of rectangular base = 13 x 13 = 169 square units

Next, we need to calculate the area of each triangular face of the pyramid. Since the rectangular base has two sets of parallel sides, there are two types of triangular faces: the isosceles triangles on the sides and the right triangles on the front and back.

To calculate the area of the isosceles triangles, we need to first find the length of the slant height, which can be found using the Pythagorean theorem:

a² + b² = c²

where a and b are the base and height of the triangle (both equal to 13 in this case), and c is the slant height.

13² + 13² = c²

338 = c²

c ≈ 18.38

Now that we have the slant height, we can calculate the area of each isosceles triangle using the formula:

Area of isosceles triangle = (1/2) x base x height

Area of isosceles triangle = (1/2) x 13 x 18.38

Area of isosceles triangle ≈ 119.14 square units

To calculate the area of each right triangle, we need to use the same slant height of 18.38, along with the height of the pyramid, which is also 13. Then we can use the formula:

Area of right triangle = (1/2) x base x height

Area of right triangle = (1/2) x 13 x 18.38

Area of right triangle ≈ 119.14 square units

Since there are two of each type of triangular face, the total surface area of the pyramid is:

Surface area = area of rectangular base + 2 x area of isosceles triangle + 2 x area of right triangle

Surface area = 169 + 2 x 119.14 + 2 x 119.14

Surface area = 546.28 square units

Therefore, the surface area of the rectangular pyramid with base dimensions of 13 x 13 and height of 13 is approximately 546.28 square units.

Yes, Jalen is correct because the rectangle has a perimeter of 20 inches with the smaller side measuring 3 inches and the longer side of the rectangle had to be 7 inches.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;

P = 2(3 + 7)

20 = 2(10)

20 = 20 (True).

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Answer:

2x-5x+14=-72.6x-8=2( 3x-4 )

or, 2x-5x+72.6x=-8-14=6x - 8

or, -3x+72.6x-6x=-22+8

or, 69.6x-6x=-14

or, 63.6x=-14

or, 378x=-14

or, x=378÷(-14)

or, x=-27

Answer:

Step-by-step explanation:

(a) Mean = (39+50+50+55+55+55+65+85+100+125+175+175+200+

209+250+250+325+400+425+500+500+500+500+1500+2500) ÷ (25)

               = (9088) ÷ (25)

              = 363.52

The mean of the data is 363.52

(b) Given: 39, 50, 50, 55, 55, 55, 65, 85, 100, 125, 175, 175, 200, 209, 250, 250, 325, 400, 425, 500, 500, 500, 500, 1500, 2500.

the median value is 200.

(c) The mode is the value with highest frequency. The mode is 500.

(d)  Mid range = \(\frac{39+2500}{2} \\\)

                      = 1269.5

An outlier is a value that is significantly different from other values in the data, thus affects the mean considerably. Yes, 2500 is the outlier.

Answer:

\(the \: answer \: for \: the \: question \: is \: 50\)

Answer:

28. B

29. D

30. A

Step-by-step explanation:

28.

2 5/8 yd × 5/6 yd =

= 21/8 × 5/6 yd²

= 105/48 yd²

= 35/16 yd²

= 2 3/16 yd²

Answer: B

29.

2641 becomes 6241.

In 6241, the 6 is in the thousands place.

6 × 1000 = 6000

Answer: D

30.

90 + 7 × (7 - 1) =

Use the correct order of operations.

= 90 + 7 × 6

= 90 + 42

= 132

Answer: A

Answer:

Step-by-step explanation: m=s-c/c

There is a Weak positive association between the amount of goals scored and the number of wins a hockey team has. Most of the data points fall between 4 goals scored and 5  number of wins. Causation cannot be established because their relationship was not in a controlled setting.

When if a relationship between two variables is said to be  negative, it is one that does not just necessarily mean that the association is weak. Although though both variables tend to increase in reaction to one another, a weak positive correlation depicts that the relationship is not very strong.

Therefore, even though  the data tells us that there is a weak positive relationship that exist between the two variables, it is vital to know that that correlation does not equal causation.

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To simplify the expression \(\displaystyle\sf 5x-3(-5y+6x)+4y\), we can follow the order of operations, which involves simplifying the expressions within parentheses, applying the distributive property, and combining like terms.

Using \(\displaystyle\sf \) tags for formatting, the expression becomes:

\(\displaystyle\sf 5x-3(-5y+6x)+4y\)

First, we simplify the expression within the parentheses:

\(\displaystyle\sf 5x-3(-5y+6x)+4y\)

\(\displaystyle\sf 5x+15y-18x+4y\)

Next, we can combine the like terms:

\(\displaystyle\sf 5x-18x+15y+4y\)

\(\displaystyle\sf -13x+19y\)

Therefore, the simplified expression is \(\displaystyle\sf -13x+19y\).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

Solution:

Given,

Work = 27 N

Displacement = 3 m

According to question,

Force = ?

As we know,

Work = Force × Displacement

or, 27 = Force × 3

or, Force = 27/3

i.e, Force = 9 N

The three solutions are (0,3), (1, 3/2) and (2,0)

Given the equation below expressed as;

y = -3/2x + 3

If the value of x is zero, then;

y = -3/2(0) + 3

y = 3

Hence one of the solution is  (0, 3)

If the value of x is 1 then;

y = -3/2(1) + 3

y = -3/2 + 3

y = 3/2

Hence another solution is  (1, 3/2)

If the value of x is 2, then;

y = -3/2(2) + 3

y = -3 + 3

y = 0

Hence another of the solution is  (2, 0)

The three solutions are (0,3), (1, 3/2) and (2,0)

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One bag of popcorn costs $7.

The question asks for the cost of one bag of popcorn based on the given information. Let's solve this step by step:

1. We are given that the first family bought 5 bags of popcorn and 6 souvenir cups for a total of $65.
2. The second family bought 10 bags of popcorn and 4 souvenir cups for a total of $90.

To find the cost of one bag of popcorn, we can set up a system of equations:

Let's say the cost of one bag of popcorn is x dollars and the cost of one souvenir cup is y dollars.

From the first family's purchase:
5x + 6y = 65

From the second family's purchase:
10x + 4y = 90

To solve this system of equations, we can use the method of substitution or elimination.

Let's use the method of elimination:

Multiply the first equation by 2 and the second equation by 3 to make the coefficients of x equal:

10x + 12y = 130
30x + 12y = 270

Now, subtract the second equation from the first equation:

(10x + 12y) - (30x + 12y) = 130 - 270
-20x = -140
x = -140 / -20
x = 7

Please let me know if you need further assistance!

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The calculated volume of the prism is 702 cubic cm

From the question, we have the following parameters that can be used in our computation

The trapezoidal prism (see attachment)

The formula of the volume of a trapezoidal prism is

Volume = Base area * Height

Where we have

Base area = 1/2 * (8 + 10) * 6

Evaluate the sum of 8 and 10

Base area = 1/2 * 18 * 6

Evaluate the products of 1/2, 18 and 6

Base area = 54

Also, we have

Height = 13

So, the volume is calculated as

volume = 13 * 54

Evaluate

volume = 702

Hence, the volume of the prism is 702 cubic cm

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