There are rabbits and chickens in Sally's backyard: 22 heads and 76 legs. How many rabbits and how many chickens are there?

Area = base * height

Area = 15 * 8 = 120 square centimeters

The given quadratic equation 2x² + 8x - 1 = 0 can be rearranged as (x + 2)² = 4.5 through the method of completing the square. Taking the square root of both sides gives two solutions for x: x = -2 + √4.5 and x = -2 - √4.5, when rounded to two decimal places.

To solve the equation 2x² + 8x - 1 = 0 by "completing the square", we first divide everything by the coefficient of x², in this case 2, to make the equation look like x² + 4x - 0.5 = 0. The coefficient of x now becomes 4.

We then take half of this coefficient, square it and add it to both sides of the equation. Half of 4 is 2, and squaring it gives us 4. So the equation now reads as x² + 4x + 4 = 4 + 0.5 which simplifies to x² + 4x + 4 = 4.5.

This equation can be further simplified by realizing that (x + 2)² = x² + 4x + 4, thus we have (x + 2)² = 4.5. Taking the square root of both sides finally gives us x = -2 ± √4.5, giving us two solutions for x to two decimal places, that are x = -2 + √4.5, and x = -2 - √4.5.

https://brainly.com/question/4822356

#SPJ3

To solve the equation by completing the square, divide by the leading coefficient, move the constant term to the other side, complete the square, take the square root of both sides, and then solve for x, yielding two solutions: approximately -0.12 and -3.88.

To solve the equation 2x²+8x-1=0 by completing the square, follow these steps:

https://brainly.com/question/4822356

#SPJ2

Answer:

31

Step-by-step explanation:

For rectangle ABCD, AC and BD are the lengths of the diagonals. The diagonals of a rectangle are congruent.

AC = BD

3x + 7 = 131 - x

Add x to both sides.

4x + 7 = 131

Subtract 7 from both sides.

4x = 124

Divide both sides by 4.

x = 31

Answer:

Your answer would be 288

Step-by-step explanation:

You start off with the equation ( V= Bh )

Where "B" represents the area of the base ( which case you multiply 8 and 12 and thus getting 96 as your answer for finding "B")

and Lastly you multiply your "B" with the "h" ( which represents the height) and therefore you multiply 96 and 3

which equals to 288

( hope this helps )

Answer: 144

Step-by-step explanation:

Answer:

Total number of plants = 3t - 15 = 3(t-5) tomato plants

Explanation:

We are given that:

Erin planted t tomato plants

Leo planted 5 fewer tomato plants than Erin, this means that:

Leo planted = t - 5 tomato plants

Fillip planted 10 fewer tomato plants than Erin, this means that:

Fillip planted = t - 10 tomato plants

Now, we want to find the total number of tomato plants

This means that we will add the number of plants planted by Erin, Leo and Fillip

Therefore:

Total number of plants = t + t - 5 + t - 10

Total number of plants = 3t - 15 = 3(t-5) tomato plants

Hope this helps :)

Final answer:

The expression that represents the total number of tomato plants Erin, Leo, and Filipe planted is 3t - 15, where t is the number of plants Erin planted.

Explanation:

If Erin planted t tomato plants, then we can express the number of tomato plants Leo and Filipe planted using algebraic expressions that are based on this initial quantity. Leo planted 5 fewer tomato plants than Erin, so we can describe the number of plants Leo planted as t - 5. Similarly, Filipe planted 10 fewer tomato plants than Erin, and his number can be represented by t - 10.

To find the total number of tomato plants all three of them planted together, you would add these expressions:

Total number of plants = Erin's plants + Leo's plants + Filipe's plants

Total = t + (t - 5) + (t - 10)

Simplify the expression by combining like terms:

Total = t + t - 5 + t - 10

Total = 3t - 15

So the expression that represents the total number of tomato plants Erin, Leo, and Filipe planted in all is 3t - 15.

given,

[tex] \frac{ {y}^{3} - {y}^{2} + y + 3}{y + 1} \\ = \frac{ {y}^{3} + {y}^{2} - 2 {y}^{2} - 2y + 3y + 3}{x + 1} \\ = \frac{{y}^{2} (y + 1) - 2y(y + 1) + 3(y + 1)}{(y + 1)} \\ = \frac{(y + 1)( {y}^{2} - 2y + 3) }{(y + 1)} \\ = {y}^{2} - 2y + 3[/tex]

Final answer:

The polynomial y^3 - y^2 + y + 3 divided by y + 1 results in a quotient of y^2 - y + 2, with a remainder of 1. The complete division statement is (y^3 - y^2 + y + 3) / (y + 1) = y^2 - y + 2 + 1/(y + 1).

Explanation:

To divide the polynomial y^3 - y^2 + y + 3 by y + 1, we use polynomial long division. First, divide y^3 by y to get y^2, subtract the result from the polynomial, and bring down the next term. Repeating this process gives us the following steps:

Divide y^3 by y to get y^2. Multiply y + 1 by y^2 and subtract from the original polynomial.

Bring down the next term, which is y, and divide -1 by y to get -1. Multiply y + 1 by -1 and subtract from the result of the first step.

Bring down the last term, which is 3, and divide 2 by y to get 2. Multiply y + 1 by 2 and subtract to get the remainder.

The final quotient of this division is y^2 - y + 2, and the remainder is 1.

The result of the division is y^2 - y + 2 with a remainder of 1. To express this as a complete division statement, we write:

(y^3 - y^2 + y + 3) ÷ (y + 1) = y^2 - y + 2 + 1/(y + 1)

Answer:

D

Step-by-step explanation:

because you need to times the indice 2 by the 3

Answer:

option D

Step-by-step explanation:

Given in the question, a right angle triangle FGH.

Base of triangle = 12

Height of triangle = 5

Hypotenuse of triangle = 13

To solve the question we will use trigonometry identity.

cos(F) = height / hypo

cos(F) = 5 / 13

So the cosine ration for angle F is 5 / 13

Find the Greatest Common Factor (GCF)

GCF = 6y^6

Factor out the GCF. (Write the GCF first. Then, in parenthesis divide each term by the GCF.)

6y^6(24y^8/6y^6 + 6y^6/6y^6)

Simplify each term in parenthesis

6y^6(4y^2 + 1)

Answer:

The area of the base B is equal to [tex]770\ cm^{2}[/tex]

The volume  is equal to [tex]10,087\ cm^{3}[/tex]

Step-by-step explanation:

I will proceed to resolve the problem indicated in the attached figure.

The figure shown a inverted rectangular pyramid

The base is a rectangle

The area of the base B is equal to

[tex]B=(35)(22)=770\ cm^{2}[/tex]

To find how many cubic centimeters of titanium are needed to manufacture one tip, calculate the volume of the figure

Find the volume of the inverted rectangular pyramid

The volume of the pyramid is equal to

[tex]V=\frac{1}{3}BH[/tex]

we have

[tex]B=770\ cm^{2}[/tex]

[tex]H=39.3\ cm[/tex]

substitute

[tex]V=\frac{1}{3}(770)(39.3)=10,087\ cm^{3}[/tex]

Answer:

  they are complementary

Step-by-step explanation:

The sum of angles in a triangle is 180°. When one of those angles is a right angle (90°), the sum of the other two must be 90°. When the sum of two angles is 90°, they are said to be complementary angles.

Step-by-step explanation:

for the each year, the interest is increased by 2%,

so after 1 year, earned interest is 2% of $400

=2/100 × 400=$8

so the earned balance is $(400+8)=$408

so after 2 year, earned interest is 2% of $408

=2/100 × 408=$8.16

so the earned balance is $(408+8.16)=$416.16

after 3 year, earned interest is 2% of $416.16

=2/100 × 416.16=$8.32

so the earned balance is $(416.16+8.32)=$424.48

after 4 year, earned interest is 2% of $424.48

=2/100 × 424.48=$8.48

so the earned balance is $(424.48+8.48)=$480.48

after 5 year, earned interest is 2% of $480.48

=2/100 × 480.48=$9.6

so the earned balance is $(480.48+9.6)=$490.08

after 6 year, earned interest is 2% of $490.08

=2/100 × 490.08=$9.8

so the earned balance is $(490.08+9.8)=$499.88

therefore the interest earned after 6 years is

$(8+8.16+8.32+8.48+9.6+9.8)=$52.36

and the balance after 6 years is $499.88

Answer:

slope = - 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0, - 3) ← 2 points on the line

m = [tex]\frac{-3-0}{0+1}[/tex] = [tex]\frac{-3}{1}[/tex] = - 3

Here it is described. Its really easy.

Answer:

D. 24+-0.114

Step-by-step explanation:

The question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle given the following statistics;

Sample mean = 24

standard deviation, σ = 0.4

Sample size , n = 49

The confidence interval for a population mean is calculated using the formula;

Sample mean ± z-score*(σ/sqrt(n))

The z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

Substituting these values into the formula;

24 ± 1.96*[tex]\frac{0.4}{\sqrt{49} }[/tex]

= 24 ± 0.112

From the choices given, choice D is closest to the above expression;

Answer:

1.69 ft (approx.)

Step-by-step explanation:

Formula for Volume of cylinder: pi x radius squared x height

Plug in 108 for volume, 3.14 for pi and 12 for height:

108 = 3.14 x r squared x 12

Multiply 3.14 and 12

108 = 37.68 x r squared

Divide both sides by 37.68

2.87 = r squared

"Unsquare" both sides (square root)

1.69 ft. = radius (approximate answer, rounded to nearest hundredth)

Answer:

1.69 ft

Step-by-step explanation:

V = πr²h formula  of a cylinder.

Volume = 108 ft

Height = 12 ft

Radius = r

V = πr²h

108 ft = 22/7 × r² × 12 ft

π = 22/7 or 3.14

108 ft = 264/7r²

108 ft  = 37.71r²

divide both sides by 37.71

108 ft/37.71 =r²

2.86 ft = r²

square root both side

√2.86 ft = √r²

the square cancels the square root

1.69 ft.

                                 To check

V = πr²h

108 = 22/7 × (1.69)² 12

108 = 22/7 × 2.8561 × 12

108 = 107.61≈108

108 ft = 108 ft.

Answer:

Option c) The scale on the y-axis misrepresents the difference in the heights of the bars.

Step-by-step explanation:

Given is a histogram that shows the number of properties in a town that are sold within certain periods.

On x axis is given number of days to sell and on y axis the number of properties

X axis is given in interval form with interval width 30 and on y axis scales are marked as 0,1,2....12,13 etc

The mistake is on y axis after 0, 10 is marked with unit distance from 0 but from 10 to 11 also distance is shown as 1 unit.

Hence correct option is

Option c) The scale on the y-axis misrepresents the difference in the heights of the bars.

Answer:

C

Step-by-step explanation:

E2020

The answer is:

There will be 15 graders attending the virtual field trip.

We know that there are 60 sixth graders taking an online math classes but only 25% are planning to attend the virtual field trip, so,  if we want to calculate how many sixth graders will be attending the virtual field trip, we need to calculate the 25% of the total sixth graders

Before solving, we need to convert the given percent number (25%) to a real number by dividing it by 100, so, solving we have:

[tex]\frac{25(percent)}{100}=0.25[/tex]

Now, calculating how many graders are 25% of the total graders, we have:

[tex]GradersAttending=TotalGraders*PercentOfGradersAttendingTheVirtualTrip[/tex]

[tex]GradersAttending=60graders*0.25=15graders[/tex]

So, we have that there will be 15 graders attending the virtual field trip.

Have a nice day!

Answer:

15

Step-by-step explanation:

To get 25% of 60, you need to divide 25 by 10, your answer should be 0.25, next, you multiply 0.25 by 60, the answer if 15, another way, is by multiplying 15 by 4, that would make 60. (Have a great day, hope this helps, please mark me brainliest if it does help, sorry for answering really late)

Shown below

What if you rotate a plane figure around a straight line called the axis? Well, in doing so, you will get what in mathematics is called a solid of revolution, which is a solid figure. In this case, we have a triangle with a side matching the axis and this side. The solid that result when rotating that triangle is a cone. The side that matches the axis is the height of the cone while the side perpendicular to the axis is the radius of the base of the cone. The rotation is performed by the hypotenuse of the triangle (a straight line) through the origin and by an angle of 360 degrees.

Answer:1/3

Step-by-step explanation:

3 (amount of reds)

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

3+2+4 (sum of all marbles red+Blue+Yellow)          

simplfy

3 /3    

----   =1/3

9 /3            

To find out the theoretical probability of drawing a red marble, divide the total number of red marbles (3) by the total number of marbles (9). Therefore, the theoretical probability is 1/3.

The subject of your question falls under the branch of Mathematics and it's about a concept known as theoretical probability. In this case, the total number of marbles in the bag is 3 red + 2 blue + 4 yellow = 9 marbles. The probability of drawing a red marble from the bag is calculated by dividing the number of red marbles by the total number of marbles. Therefore, the theoretical probability of pulling a red marble is 3/9 which simplifies to 1/3, meaning there is a one in three chance of drawing a red marble.

https://brainly.com/question/28040792

#SPJ3

Answer:

Step-by-step explanation:

88

The distance between the lions and the monkeys is 88 feet

To determine the distance between the lions and the monkeys, we make use of the following equivalent ratio

x : 132 = 80 : 120

Express as fraction

[tex]\frac{x}{132} = \frac{80}{120}[/tex]

Solve for x

[tex]x = \frac{80}{120} * 132[/tex]

Multiply

[tex]x = 88[/tex]

Hence, the distance between the lions and the monkeys is 88 feet

Read more about equivalent ratios at:

https://brainly.com/question/2328454

Answer:

Step-by-step explanation:

Height is 5 feet

Answer:

C

Step-by-step explanation:

To find the inverse, let y = f(x) then rearrange making x the subject, that is

y = 5(x + 3)³ - 2 ( add 2 to both sides )

y + 2 = 5(x + 3)³ ( divide both sides by 5 )

(x + 3)³ = [tex]\frac{y+2}{5}[/tex]

Take the cube root of both sides

x + 3 = [tex]\sqrt[3]{\frac{y+2}{5} }[/tex]

Subtract 3 from both sides

x = [tex]\sqrt[3]{\frac{y+2}{5} }[/tex] - 3

Change y back into terms of x, so

[tex]f^{-1}[/tex] (x ) = [tex]\sqrt[3]{\frac{x+2}{5} }[/tex] - 3 → C

Answer: Equation to describe this situation.

[tex]3s=6300[/tex]

Number of steps in one mile for Gustave =2100

Step-by-step explanation:

Given : Gustave measured his pace and determined that for him, s steps make up one mile.

1 mile = s steps  (1)

One day Gustave walked 6300 steps, which was 3 miles.

i.e. 3 miles = 6300 steps (2)

Using (2), the number f steps in 3 steps will be :_

3 miles = 3s steps                (3)

From (2) and (3), we have

[tex]3s=6300[/tex]

Dividing both sides by 3 , we get

[tex]s=\dfrac{6300}{3}=2100[/tex]

Hence, the number of steps in one mile for Gustave =2100

Gustave takes 189 steps to walk one mile. We derived this by dividing the total steps, 63,000, by the distance in miles, 333. The equation used was 63000 = s * 333.

To determine how many steps are in one mile for Gustave, we start with the information provided:

Step 1: Write the Equation

We can write the equation as:

63000 = s * 333

Step 2: Solve for s

To find out how many steps make up one mile, we solve for s by dividing both sides of the equation by 333:

s = 63000 / 333

Step 3: Calculate the Value

When we divide 63,000 by 333, we get:

s = 189

This means that Gustave takes 189 steps to walk one mile.

Example Calculation

Since 63,000 steps equal 333 miles, and dividing both 63,000 steps by 333 miles gives us the number of steps per mile:

189 steps per mile.

In conclusion, Gustave takes 189 steps to walk one mile. This equation and process help us determine the number of steps per mile based on the given total steps and distance covered.

Answer:

270 downloads

Step-by-step explanation:

Call x the number of times the standard quality version was downloaded and call y the number of times the high quality version was downloaded.

So, we know that

[tex]2.5x + 4.4y = 5427[/tex] MB     (1)

We also know that the high-quality version was downloaded four times as often as the standard version.

So

[tex]y = 4x[/tex]        (2)

We substitute equation (2) in equation (1) and solve for x.

[tex]2.5x + 4.4 (4x) = 5427\\\\2.5x +17.6x = 5427\\\\20.1x=5427\\[/tex]

[tex]x = 270\ downloads[/tex]

Answer:

2 (4/5) = 2.80

2 (11/20) = 2.55

2 (1/2) = 2.50

2 (9/20) = 2.45

2 (3/20) = 2.15

Step-by-step explanation:

I believe the time would be about 4 seconds

Answer:

9.29 seconds

Step-by-step explanation:

Attached is my work because it's difficult to type

Attached is an image of where I got my equations from

the answer may be wrong

Answer:

1/2

Step-by-step explanation:

Final answer:

The exact value of sin 30 degrees is 0.5, and this is derived from the special 30-60-90 triangle.

Explanation:

The value of sin 30 degrees is 0.5.

This can be determined using the unit circle or by using the trigonometric function of 30 degrees.

When we evaluate sin 30 degrees, we can look at the special right triangle with angles 30-60-90 where the ratio of the opposite to the hypotenuse in a 30-degree angle is 1/2. In this triangle, the side opposite to the 30-degree angle is half the length of the hypotenuse. Therefore, sin 30 degrees is equal to 1/2 or 0.5.

Answer:

D. Events E and B are independent.

Step-by-step explanation:

It can be determined that Events E and B are independent. The correct answer is: D.

To determine independence between events, we can use the formula:

[tex]\[ P(A \cap B) = P(A) \times P(B) \][/tex]

Let's check for events D and A:

[tex]\[ P(D \cap A) = 0.2 \][/tex]

[tex]\[ P(D) \times P(A) = 0.5 \times 0.2 = 0.1 \][/tex]

Since [tex]\(0.2 \neq 0.1\),[/tex] events D and A are not independent.

Checking for events D and B:

[tex]\[ P(D \cap B) = 0.3 \][/tex]

[tex]\[ P(D) \times P(B) = 0.5 \times 0.3 = 0.15 \][/tex]

Since [tex]\(0.3 = 0.15\)[/tex], events D and B are independent.

Similarly, events A and B:

[tex]\[ P(A \cap B) = 0.15 \][/tex]

[tex]\[ P(A) \times P(B) = 0.2 \times 0.5 = 0.1 \][/tex]

Since [tex]\(0.15 \neq 0.1\)[/tex],events A and B are not independent.

For events E and B:

[tex]\[ P(E \cap B) = 0.15 \][/tex]

[tex]\[ P(E) \times P(B) = 0.3 \times 0.5 = 0.15 \][/tex]

Since [tex]\(0.15 = 0.15\)[/tex], events E and B are independent.

Therefore, the correct answer is: D. Events E and B are independent.

Answer:

Your answer will be 30

Step-by-step explanation: