=O LINEAR EQUATIONS AND INEQUALITIESFinding a side length given the perimeter and side lengths with...The perimeter of the rectangle below is 176 units. Find the length of side QR.Write your answer without variables.S3y + 1R4y + 3QR = 0P

The area of each rhombus is 8.75 \(cm^2\). The correct option is 8.75 \(cm^2.\)

To find the area of each rhombus, we can use the formula for the area of a rhombus:

Area = (diagonal1 × diagonal2) / 2

Given that the diagonals of the rhombus-shaped pieces are 3.5 centimeters and 5 centimeters, we can substitute these values into the formula:

Area = (3.5 cm × 5 cm) / 2

Area = 17.5 \(cm^2\) / 2

Area = 8.75 \(cm^2\)

Therefore, the area of each rhombus is 8.75 \(cm^2\). The correct option is 8.75 \(cm^2.\)

for such more question on area

https://brainly.com/question/15822332

#SPJ8

Answer:

23/100 equals 23%.

Answer: 23%

Step-by-step explanation: When doing these problems, remember, 100 and a 100% are the same thing, so when you have a problem like this, divide 25 by 100, then multiply by a 100.

Answer:

58

Step-by-step explanation:

i think the answer is 58 please give brainliest

Answer:

(a) 18.5ft

(b) 388.5 ft²

Step-by-step explanation:

(a)

She has 79ft of fence = the perimeter will be 79.

Perimeter of a rectangle = 2(length) +2(width)

79 = 2(21)+2(width)

2(width) = 79 - 42

width = 37/2

width = 18.5ft

(b)

Area of a rectangle = (length)(width) = (21)(18.5) = 388.5 ft²

It would take Fran and Denise (working together) approximately \(\frac{24}{7}\) hours to paint the living room.

To solve this problem, we can use the concept of "work rates."

Let's find out how much work Fran and Denise can do individually in one hour.

If Fran takes 6 hours to paint the living room alone, her work rate is \(\frac{1}{6}\) of the room per hour \((\frac{1 room}{6 hours } = \frac{1}{6}room/hour )\).

Similarly, if Denise takes 8 hours to paint the living room alone, her work rate is \(\frac{1}{8}\) of the room per hour \((\frac{1 room}{8 hours } =\frac{1}{8}room/hour )\).

When they work together, their work rates are additive.

So, their combined work rate would be:

\(\frac{1}{6} room/hour+\frac{1}{8} room/hour\)

\(=(\frac{4}{24} )room/hour + (\frac{3}{24} )room/hour\)

\(=\frac{7}{24} room/hour\)

This means that working together, Fran and Denise can paint \(\frac{7}{24}\) of the living room in one hour.

To determine the total time required for them to paint the entire room, we can invert their combined work rate:

\(\frac{(1 room) }{(\frac{7}{24}room/hour) } =\frac{24}{7}hour\)

Therefore, it would take Fran and Denise (working together) approximately \(\frac{24}{7}\) hours to paint the living room.

For such more questions on living room

https://brainly.com/question/31126272

#SPJ8

Answer:

100 hours

Step-by-step explanation:

20eggs × 2 hours=40hours

20 eggs × 3hours= 60 hours

altogether:

40 + 60 =100

Answer:

Step-by-step explanation:

Assuming both birds have just laid an egg when the clock starts.

at 1 hour, no egg             egg count

at 2 hrs  goose egg               1

at 3 hrs hen egg                    2            

at 4 hrs goose egg                3

at 5 hrs no egg                      3

at 6 hrs goose and hen egg  5

we are now back to where we started where each bird has laid an egg

We get 5 eggs every 6 hours

We need 20/5 = 4 six hour periods to complete the task

6(4) = 24 hrs to complete the task

ANSWER

75 feet

EXPLANATION

The scale factor means that the ratio of the model to the actual size of the dinosaur is 1 : 20.

The model is 3.75 feet long.

Let the actual length of the dinosaur be x.

So, it means that:

The actual length of the dinosaur is 75 feet.

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

Perhaps you want a graph of ...

  x^2/49 +(y +1)^2/4 = 1

This is an ellipse centered at (x, y) = (0, -1) with a major axis in the x-direction of 14, and a minor axis in the y-direction of 4.

Answer:

its either 98 cm or 28 cm

Step-by-step explanation:

7 x 7 = 49 x 2 = 98 cm

14 x 2 = 28

Given (x-7)^2=36, select the values of x.

x=13

x=1

x=-29

x=42

Given (x-1)^2=50, select the values of x.

x=-49

x=51

x=1+5√2

x=1-5√2

Answer: x=1+5√2  and x=1-5√2

Answer:r=2 cos^4(theta)

Step-by-step explanation:To find the values of theta where the maximum r-values occur on the graph of the polar equation r = 2 cos^4(theta), we need to find where the derivative of r with respect to theta is equal to zero, since the maximum r-values occur at these points.

First, we can simplify the equation by using the identity cos(2theta) = 2cos^2(theta) - 1 and substituting cos^2(theta) = (1 + cos(2theta))/2. This gives:

r = 2 cos^4(theta) = 2(1/2 + 1/2 cos(2theta))^2 = 1 + cos(2theta) + cos^2(2theta)/2.

Next, we can take the derivative of r with respect to theta, using the chain rule:

dr/dtheta = -sin(2theta) - 2cos(2theta)sin(2theta).

Setting this equal to zero and factoring out sin(2theta), we get:

sin(2theta)(-1 - 2cos(2theta)) = 0.

This equation is satisfied when sin(2theta) = 0 or cos(2theta) = -1/2.

When sin(2theta) = 0, we have 2theta = k*pi for some integer k. Therefore, theta = k*pi/2.

When cos(2theta) = -1/2, we have 2theta = 2*pi/3 + 2*k*pi or 2theta = 4*pi/3 + 2*k*pi for some integer k. Therefore, theta = pi/3 + k*pi or theta = 2*pi/3 + k*pi.

These are the values of theta where the maximum r-values occur on the graph of the polar equation r = 2 cos^4(theta).

The required reference angle of 13π/8 is 3π/8.

The reference angle of an angle in standard position is the positive acute angle formed between the terminal side of the angle and the x-axis.

Given an angle of 13π/8, we can determine its reference angle as follows:

Angle: 13π/8

Since the angle is in the fourth quadrant, we subtract it from 2π (one full revolution) to find the reference angle:

Reference angle: 2π - 13π/8 = 3π/8

Therefore, the reference angle of 13π/8 is 3π/8.

For more information on reference angles, you can visit brainly.com/question/30741629.

#SPJ1

Answer:

18

Step-by-step explanation:

Answer:

\(y=3x+17\)

Step-by-step explanation:

Use point-slope form

\(y-y_1=m(x-x_1)\\y-(-4)=3(x-(-7))\\y+4=3(x+7)\\y+4=3x+21\\y=3x+17\)

The function g(x) = x³ - x² - 4x + 4 has zeros at 1, 2 and -2. The y intercept is at 4.

An equation is an expression that shows the relationship between two or more numbers and variables.

The zeros of the function is at:

g(x) = 0, hence:

x³ - x² - 4x + 4 = 0

(x - 1)(x² - 4) = 0

(x - 1)(x + 2)(x - 2) = 0

x = 1, x = -2 and x = 2

The y intercept is at x = 0, hence:

g(0) = 0³ - 0² - 4(0) + 4 = 4

The function g(x) = x³ - x² - 4x + 4 has zeros at 1, 2 and -2. The y intercept is at 4.

Find out more on equation at: https://brainly.com/question/2972832

The statement "for every positive rational number x, there exist positive integers n1, ..., nk such that x = n1/n2 + ... + nk/nk" is known as the Egyptian fraction representation theorem and is proved.

Let x be a positive rational number with numerator p and denominator q, where p and q are coprime. Let's assume that x can't be represented as a sum of positive unit fractions (i.e., fractions with numerator 1).

Then, construct a sequence of positive rational numbers x1, x2, ..., xk such that x1 = x and for each i, xi is equal to the difference between xi-1 and the largest unit fraction that is less than or equal to xi-1.

Since x is a positive rational number, it follows that xi is also a positive rational number for all i. Since x can't be represented as a sum of positive unit fractions, it follows that xi can't be represented as a sum of positive unit fractions for all i. Since the sequence x1, x2, ..., xk is constructed as the difference of two positive rational numbers, it follows that xi is a positive rational number for all i.

Since x1 = x, it follows that there exists a positive integer n such that x1 is equal to n/n + 1. But this contradicts our assumption that x can't be represented as a sum of positive unit fractions. Thus, our assumption is false, and it follows that x can be represented as a sum of positive unit fractions.

Therefore, we have proved that for every positive rational number x, there exist positive integers n1, ..., nk such that x = n1/n2 + ... + nk/nk.

To know to more about Rational number theorem here:

https://brainly.com/question/15468166

#SPJ4

_____The given question is incomplete, the complete question is given below:

prove: let x be a positive rational number, then there exist positive integers n1, ..., nk such that x = n1/n2 + ..... + nk/nk.

Answer:

2600

Step-by-step explanation:

Answer:

2600

Step-by-step explanation:

60% of what number is 1560

Let x be the total daily calories recommended.

.6x =  1560  Divide both sides by .6

x = 2600

The slope is

\(\frac{-13-31}{1-(-10)}=-4 \)

So, the equation is

\(y+13=-4(x-1)

\)

The y-intercept is when x=0, so

\(y+13=-4(0-1) \\ \\ y+13=4 \\ \\ \boxed{y=-9}\)

6) The solution to the fraction problem ¹⁵/₁₆ - ³/₄ is; ³/₁₆

7) The solution to the fraction problem 10¹¹/₁₂ + 7¹/₄ is; 18¹/₆

There are different forms of fractions such as proper fraction, improper fraction and then mixed fraction.

6) We want to solve the fraction expression given as;

¹⁵/₁₆ - ³/₄

Since 16 is the lowest common multiple of the denominators, we factorize it out to get;

¹/₁₆(15 - 4(3))

Solving the bracket gives;

¹/₁₆(3)

= ³/₁₆

7) We want to solve the fraction expression given as;

10¹¹/₁₂ + 7¹/₄

Converting both to improper fraction gives us;

¹³¹/₁₂ + ²⁹/₄

Since 12 is the lowest common multiple of the denominators, we factorize it out to get;

¹/₁₂(131 + 3(29))

Solving the bracket gives;

¹/₁₂(218) This will reduce to; 109/6

= 18¹/₆

Read more about Fraction Problems at; https://brainly.com/question/78672

#SPJ1

When 'x' is 5, the Algebraic  expression 3x - 4 evaluates to 11.

To find the algebraic expression for "4 less than the product of 3 and some number," let's break it down step by step.

First, let's define the unknown number as 'x.' Since the problem states "the product of 3 and some number," we can express this as 3 * x or simply 3x.

Next, we want to subtract 4 from this product. The phrase "4 less than" indicates subtraction, so we subtract 4 from 3x. This can be represented as 3x - 4.

In summary, the algebraic expression for "4 less than the product of 3 and some number" is 3x - 4, where 'x' represents the unknown number.

To calculate the value of this expression for a specific value of 'x,' you substitute that value into the expression and simplify. For example, if 'x' is 5, you would substitute 5 into the expression:

3(5) - 4

This simplifies to:

15 - 4 = 11

So, when 'x' is 5, the expression 3x - 4 evaluates to 11.

In general, the algebraic expression allows us to represent a mathematical relationship between quantities using symbols and operations. By substituting specific values into the expression, we can calculate the corresponding results.

For more such question Algebraic  expression visit:

https://brainly.com/question/2164351

#SPJ8

Note the complete question:

Algebraic expression for 4 less than the product of 3 and some number

What is the algebraic expression for "4 less than the product of 3 and some number?

Please help me understand the meaning of how to calculate.

Answer:

∠ x = 58°

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠  BAD is an exterior angle of the triangle , then

x + 56° = 114° ( subtract 56° from both sides )

x = 58°

Answer:

( Use this formula below to help you find the volume of all equations using volume)

Volume formal = L × W × H

Volume formal = 24 × 15 × 5

Answer = 24 × 15 × 5 = 1,800

Answer:

FALSEEEEE Teellll me if its right

Step-by-step explanation:

As given by the question

There are given that the system of the equation

Now,

From equation (1), find the value of x

Then,

Put the value of x into the equation (2)

So,

Now,

Put the value of y into the equation (3)

So,

From the equation (3)

Hence, the value of x is 2, and the value of y is -2.

Answer:

B is the answer to the problem

Answer:

0.5

Step-by-step explanation:

Given that: An average concentration of 1 coliform bacteria per 20 cc of the river water.

This implies that in 20 cc of the water, it is certain that 1 coliform bacteria would be found. So that:

pr(1 bacteria in 20 cc of water) = 1

i.e the probability of getting 1 bacteria in 20 cc of water is 1.

The probability of the 10 cc sample of water containing 2 coliform bacteria can be determined as:

pr(2 bacteria in 10 cc of water) = \(\frac{1}{2}\)

                                                   = 0.5

As you can see below, both expressions result in the same value of 105. This demonstrates the application of the associative law in regrouping terms and maintaining the equivalence of the expression.

The associative law in mathematics states that the grouping of numbers in an addition or multiplication operation does not affect the result. In other words, you can regroup terms within parentheses without changing the value of the expression.

Using the associative law, we can regroup the terms in the expression s + (r + 75) by removing the parentheses and rearranging the terms:

s + (r + 75) = (s + r) + 75

The expression (s + r) + 75 is equivalent to s + (r + 75) because the addition operation is associative.

Let's take an example to illustrate this:

Suppose s = 10 and r = 20.

Using the original expression:

s + (r + 75) = 10 + (20 + 75) = 10 + 95 = 105

Using the expression with regrouped terms:

(s + r) + 75 = (10 + 20) + 75 = 30 + 75 = 105

As you can see, both expressions result in the same value of 105. This demonstrates the application of the associative law in regrouping terms and maintaining the equivalence of the expression.

For more questions on expressions

https://brainly.com/question/30715930

#SPJ8