The length of a rectangle is 4 yards longer than its width. If the perimeter of the rectangle is 52 yards, find its length and width.

The measurements of the given sides are x = 24, y = 40, and z = 40.

The triangle in which at least one right angle exists is known as a Right angle triangle.

By the Pythagorean theorem in a right angle triangle, the sum of the squares of sides will equal the square of the hypotenuse.

The altitude drawn on a hypotenuse will divide the triangle into two similar triangles

Here we have

Two right-angle triangle  

As we know in right angle triangle,

=> Hypotenuse² = Side² + Side²  

From the smaller right-angle triangle,

=> y² = (32)² + (24)²  

=> y² = 1024 + 576  

=> y² = 1600

=> y = 40    

Here the altitude drawn on the hypotenuse of the triangle divides the triangle into two similar triangles

Hence, the ratio of the corresponding angles in two triangles will be equal  

=> 32/x =  32/24  

=> 24(32) = 32(x)

=> x = 24

In 2nd largest triangle,  

=> z² = (32)² + (24)²  

=> z² = 1024 + 576

=> z² = 1600  

=> z = 40  

Therefore,

The measurements of the given sides are x = 24, y = 40, and z = 40.

Learn more about Right angle triangle at

https://brainly.com/question/6322314

#SPJ1

Both BODMAS and PEMDAS are valid and in use in various parts of the globe. In the UK, BODMAS is frequently utilized, whereas in the US, PEMDAS is. Brackets, Order, Division, Multiplication, Addition, and Subtraction are all referred to as BODMAS.

The acronym PEMDAS, which stands for parenthesis, exponents, multiplication and division from left to right, as well as addition and subtraction from left to right, can be used to recall the order of operations. Start by using parenthesis first.

For the list of operations, we wish to create an expression.

9 to the second power raised then, determine the ratio between the outcome and z

First, raise 9 to the second power.

9 divided by two equals

Find the product of the result and z in step two.

Today, quotient refers to "division."

The outcome of step 1 is =[tex]9^2[/tex]

Therefore:

Indicator of and z

As a result, the statement that describes the specified order of operations is [tex]\frac{9^2}{z}[/tex]

To know more about exponents visit:-

brainly.com/question/11709654

#SPJ1

Answer:

51 3/4 %

Step-by-step explanation:

There are 5040 ways to arrange these seven leaders in a row. There are 1440 ways to arrange these seven leaders in a row, so that the leader of japan and the leader of canada stand next to each other.

Using the multiplication principle, we multiply all the possible arrangements to determine the total number of configurations if we have seven individuals and want to know how many ways there are to place them in a row of seven seats. For instance, the first seat has seven alternatives, the second has six (as one has been taken), the third has five, the fourth has four, and so on.

So, these seven leaders in a row, so that the leader of japan and the leader of canada stand next to each other.

6! * 2! = 720 * 2 = 1440 .

To arrange these seven leaders in a row we just have to find,

7! = 7x6x5x4x3x2x1

= 5040

These two configurations are both permutations. Therefore, in the case, there are only two potential permutations.

It becomes more difficult if there are seven of us. The multiplication concept must be applied.

Learn more about Probability:

https://brainly.com/question/30253073

#SPJ4

Keeping a healthy weight will lower your risk of stroke, according to the 95% confidence interval of (0.54, 0.62), which suggests that if the survey were conducted repeatedly, 95% of the intervals produced would represent the real population percentage of individual, who are aware of this.

In other words, there is a 95% confidence interval between 0.54 and 0.62 for the genuine population fraction of those who are aware of this knowledge.

It should not be assumed from this range that 95% of respondents indicated that they were aware of this knowledge.

Instead, it offers a range of numbers that, with a given level of certainty, are likely to include thee genuine population percentage.

To know more about Percentage

https://brainly.com/question/24877689

#SPJ4

The number of visits to the Craft Depot in which you'll receive a free craft kit and the discount of $6 is 15 visits.

On every 3rd visit= a Free craft

On every fifth visits = a discount of $6

Based on the given task content; it can be solved using the concept of lowest common multiple of both third visit and fifth visit.

3 = 3, 6, 9, 12, 15, 18

5 = 5, 10, 15, 20

The lowest common multiple of third and fifth visits is 15 visits.

Therefore, you'll receive a free craft kit and the discount on the 15th visits

Read more on lowest common multiple:

https://brainly.com/question/10749076

#SPJ1

The truth table for the statement is

r     s     ¬r    s ∧ ¬r

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

T     T     F     F  

T     F     F     F  

F     T     T     T

F     F     T     F

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

s ∧ ¬r

To construct the truth table, we make use of the following notations

s, r and ¬r

The truth table for the statement s ∧ ¬r is then represented as follows:

r     s     ¬r    s ∧ ¬r

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

T     T     F     F  

T     F     F     F  

F     T     T     T

F     F     T     F

The condition for ∧ is that it is true if both statements are true

Read more about truth table at

brainly.com/question/14458200

#SPJ1

The precise quadratic equation, according to the provided assertion, is y = (1/9)x² + (2/9)x - 1/3.

Three elements decide a quadratic function of the formula f(x) = ax² + bx + c. A quadratic function can be determined by getting a, b, and c algebraically given three locations on the graph. In order to do this, a system of eqs with three unknowns must be solved.

To find the quadratic function that passes through the point (-8, 5) and has zeros at x = -3 and x = 1, we can start by using the factored form of a quadratic function:

y = a(x - r)(x - s)

where r and s are the zeros of the function. Substituting in the given zeros, we get:

y = a(x + 3)(x - 1)

To find the value of a, we can use the fact that the function passes through the point (-8, 5). Substituting these values into the equation, we get:

5 = a(-8 + 3)(-8 - 1)

Simplifying this expression, we get:

5 = a(-5)(-9)

5 = 45a

a = 1/9

Substituting this value of a into the equation we get:

y = (1/9)(x + 3)(x - 1)

Expanding the equation, we get:

y = (1/9)(x² + 2x - 3)

Multiplying both sides by 9 to eliminate the fraction, we get:

9y = x² + 2x - 3

So the quadratic function that passes through the point (-8, 5) and has zeros at x = -3 and x = 1 is:

9y = x² + 2x - 3

or

y = (1/9)x² + (2/9)x - 1/3.

To know more about Quadratic function visit:

https://brainly.com/question/1214333

#SPJ1

Mantago should borrow the money for 72.7 months or approximately 6 years,

We can use the following formula to determine the loan length:

Loan length = Loan amount / (Monthly payment - Monthly interest payment)

We must first determine the monthly interest payment, which may be done by applying the following formula:

Monthly interest payment = (APR / 12) * Loan amount

Plugging in the values:

Monthly interest payment = (7.5 / 12) * $10,000 = $62.5

The values can now be entered into the calculation to determine the length of the loan:

Loan length = $10,000 / ($200 - $62.5) = $10,000 / $137.5 = 72.7 months

Therefore, Mantago should borrow the money for 72.7 months, or approximately 6 years, in order to afford the monthly payment of $200.

To learn more about borrow,  visit the link below:

https://brainly.com/question/29968576

#SPJ4

Answer:

Step-by-step explanation:

The function is increasing over the interval from x=3 to x=5.

First we draw the graph of function g(x) = 8x

The graph of the function g(x) = 8x is shown below.

We can observe that the graph of g(x) is a staright line passing through origin (0, 0)

Now we find the value of the function at the endpoints of the interval [3, 5]

For x = 3, the value of function would be,

g(3) = 8 × 3

g(3) = 24

And for x = 5, the value of g(x) would be,

g(5) = 8 × 5

g(5) = 40

Also, at x = 4,

g(4) = 8 × 4

g(4) = 32

This means that the value of function g(x) increases from x = 3 to x = 5

Also, from the graph the function g(x) we can observe that the function g(x) is increasing over the interval [3, 5]

Learn more about the function here:

https://brainly.com/question/28193994

#SPJ4

Answer:

Step-by-step explanation:

The slope of the line passing through the points (0,2) and (6,6) can be found using the slope formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) = (0, 2) and (x2, y2) = (6, 6)

slope = (6 - 2) / (6 - 0)

slope = 4 / 6

slope = 2/3

Therefore, the slope of the line is 2/3.

Answer: 50%

Step-by-step explanation: There is an equal chance of both events occurring so there is a half chance for it to occur or no.

True, a simple random sample is a sample of n observations that has the same probability of being selected from the population as any other sample of n observations.

What does standard deviation mean ?

The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean.

                                Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high.

What does a simple random sample mean?

A subset of participants is randomly chosen from a population by the researcher using simple random sampling, a sort of probability sampling.

                          The probability of being chosen is the same for every person in the population. Then, data are gathered from as much of this randomly selected subgroup as possible.

Learn more about standard deviation

brainly.com/question/23907081

#SPJ4

The number 5 will be placed in the middle.

In order to make the sums across and down equal, we have to arrange the numbers in such a way that they balance each other out. We know that the middle number will be the average of the four numbers surrounding it.

So, if we place 2 and 8 on either side of the middle number, the sum of these two numbers is 10. To make the sum equal, we need two more numbers that add up to 10. The only two numbers that fit the criteria are 4 and 6.

Hence, the middle number will be the average of 4 and 6, which is 5. So, the answer is 5.

To know more about average, here

https://brainly.com/question/24057012

#SPJ4

--The given question is incomplete; the complete question is

"Place the numbers 2, 4, 5, 6, and 8 in the circles so that the sums across (horizontally) and down (vertically) are equal. Which number will you place in the middle?"--

Answer:

90°/• is the probability

By applying total cost concept, it can be concluded that the expression represents the total cost is 1.45d (option A).

Algebra is a branch of mathematics that uses symbols and mathematical operations, such as addition, subtraction, multiplication, and division to solve problems.

It is usually used to solve a problem in various fields of study, such as chemistry, biology, economics, and so on.

One of the most familiar uses of algebra is how to calculate the total cost:

Total cost = n x p , where:

n = number of products

p = product price per piece

We know that Jim is going to buy donuts for his family:

p = $1.45

n = d

So the total cost can be calculated by multiplying 1.45 by d, which equals 1.45d.

Thus the expression represents the total cost is 1.45d (option A).

To learn more about total cost, click here: https://brainly.com/question/25109150

#SPJ4

The distance across the lake is 190m. Rounding to the nearest hundredth of a meter, the answer is 190.00m.

We can use similar triangles to find the distance across the lake (DE). Since triangle CGF is similar to triangle CED, we can use ratios of the sides to find DE.

Let's call DE = x. Then, we have:

CE/FG = x/142.1

Solving for x, we have:

x = (CE * 142.1) / FG

CE = CF + FD = 130 + 60 = 190m

x = (190 * 142.1) / 142.1 = 190m

The distance across the lake is 190m. Rounding to the nearest hundredth of a meter, the answer is 190.00m.

Learn more about triangles :

https://brainly.com/question/14366937

#SPJ4

The complete question is :

To indirectly measure the distance across a lake, Dominic makes use of a couple landmarks at points D and E. She measures CF, FD, and FG as marked. Find the distance across the lake (DE), rounding your answer to the nearest hundredth of a meter.

Answer:

x = 2.33

Step-by-step explanation:

3x - 4 = 3

3x = 7

x = 7/3

x = 2.33

The percent decrease in price of video game was equals to the 34% .

When Iris purchased, the price of video game is $85. That is original price of video game = $85

The selling price of video game = $56

As we see Selling price < Original price

=> loss or decrease

Let the decrease in price be "x".

Decrease in value is equals to original price minus selling price.

=> x = $85 - $56 = $29

Now, percent decrease is obtained by dividing the decrease in price by original price, then multiply the resultant by 100.

Decrease percent = decreased price/original price)100

=> x% = (29/85)100

=> x% = 2900/85

=> x% = 34.117

Hence, the required percent decrease is 34%.

To learn more about percent decrease, refer:

https://brainly.com/question/13631568

#SPJ4

The value of the expression x²+1/x²  is 18

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms.

Given here: x²-4x=1

simplifying we get

x²-4x=1

Dividing both sides by x we get

x²/x-4x/x=1/x

x-4=1/x

x-1/x=4

Now squaring both sides we get

(x-1/x)²=4²

x²-2×x×1/x+1/x² =16

x²+1/x²=16+2

x²+1/x²=18

Learn more about algebraic expressions here:

brainly.com/question/29159730

#SPJ1

The slope is negative two thirds, and the y-intercept is 8. The candle starts at a height of 8 inches and decreases two thirds of an inch every hour. The solution has been obtained by using the concept of slope.

What is a slope?

In mathematics, a line's slope is the ratio of the change in the y coordinate to the change in the x coordinate.

We are given that the graph of the line passes through (0,8) and (3,6) .

So,

Slope of the line = (6 - 8) ÷ (3 - 0) = -2/3

From this, we get the equation of line as

y - 6 = -2/3 (x - 3)

Now, for y-intercept, we need to put x = 0

So, we get

⇒y - 6 = -2/3 (-3)

⇒y - 6 = 2

⇒y = 8

Hence, the slope is negative two thirds, and the y-intercept is 8.

Learn more about slope from the given link

https://brainly.com/question/12763756

#SPJ1

Answer:

Step-by-step explanation: So, you have to find a number that can be multiplied both by 4 and 3 to get x and 21. So x is 28, 4:3 = 28:21, you can multiply both by 7.

Using percentages we can conclude that out of 800 people, 20% of the people who attended the football match were teenagers, 160.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics.

If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.

The proportion, therefore, refers to a component per hundred. Per 100 is what the word percent means.

A % is a number that indicates how many out of 100 it is, and it can also be expressed as a decimal or a fraction.

Put the percentage value in the numerator and 100 in the denominator to convert a percentage to a fraction.

So, we know that:

800 people attended the football game.

20% were teenagers.

Then, the number of teenagers was:

= 800/100*20

= 8*20

= 160

Therefore, using percentages we can conclude that out of 800 people 20% of the people who attended the football, match were teenagers, and 160 were.

Know more about percentages here:

https://brainly.com/question/24877689

#SPJ4

The probability of a student being chosen at random and taking exactly one language class is 65%.

Probability is the likelihood or chance of an event happening. In this case, the event is a student taking exactly one language class.

First, we need to find the total number of students taking at least one language class. We have 28 students in the Spanish class, 26 students in the French class, and 16 in the German class. However, some students are taking multiple classes, so we need to subtract these students from the total. The 12 students taking both Spanish and French, 4 taking both Spanish and German, and 6 taking both French and German should only be counted once. In addition, the 2 students taking all three classes should also only be counted once.

So, the total number of students taking at least one language class is

=> 28 + 26 + 16 - 12 - 4 - 6 + 2 = 40 students.

To find the number of students taking Spanish only, we need to subtract the number of students taking both Spanish and French (12) and the number of students taking both Spanish and German (4) from the number of students taking Spanish (28).

So, the number of students taking Spanish only is

=> 28 - 12 - 4 = 12 students.

Similarly, the number of students taking French only is

=> 26 - 12 - 6 = 8 students

and the number of students taking German only is

=> 16 - 4 - 6 = 6 students.

Finally, to find the probability of a student being chosen at random and taking exactly one language class, we divide the number of students taking exactly one language class by the total number of students taking at least one language class.

So, the probability of a student taking exactly one language class is

=> (12 + 8 + 6) / 40 = 26 / 40 = 0.65 or 65%.

To know more about probability here.

https://brainly.com/question/11234923

#SPJ4

Complete Question:

An elementary school is offering 3 language classes: one in Spanish, one in French, and one in German. The classes are open to any of the 100 students in the school. There are 28 students in the Spanish class, 26 students in the French class,, and 16 in the German class. There are 12 students that are in both Spanish and French, 4 that are in both Spanish and German, and 6 that are in both French and German. In addition, there are 2 students taking all 3 classes.

If a student is chosen randomly, what is the probability that he or she is taking exactly one language class?

Answer:

450

Step-by-step explanation:

the speed of mass is 450

The dimensions of furniture in a rectangular bedroom in my scale drawing is equals to the 18 in. by 21 in.

To draw dimensions on scale drawing :

I want to a scale drawing of my bedroom which help me to arrange my furniture.

Dimensions of rectangular bedroom= 12 ft by 15 ft

that is length of room, l = 15 ft

width of rectangle room, w = 12 ft

Area of rectangular bedroom = l×w = 12 × 15

= 180 ft²

scale of furniture = 3 in. = 2 ft

=> 2 ft = 3 in

=> 1 ft = 3/2 in

Now 12 ft by 15 ft in inches :

=> 12 × 3/2 in by 15 × 3/2 in

=> 18 in by 22.5 in

Hence, required dimensions are 18 inches by 22.5 inches.

To learn more about scale drawing, refer:

https://brainly.com/question/12626179

#SPJ4

Point slope form is y - y1 = m ( x - x1 ), where m represents the slope, y1 represents the y value of the point, and x1 represents the x value of the point.

filling in the variables with the given information gives you

y - (-5) = -1 ( x - 1 ) which is also y + 5 = -1 ( x - 1)