The sides of a triangular lot are represented by x, 3x, and 3x + 2. Find each side if the perimeter is 632 feet.

rotate the triangles so r and c line up

 when you do that Q=B, a=p, C=R, b=q, A=P

 so answer would be B. p:a

we know that

If triangle ABC is similar to triangle PQR

then

the corresponding sides are proportional

so

[tex]\frac{RQ}{CB} =\frac{RP}{AC}= \frac{PQ}{AB}[/tex]

substitute the values

[tex]\frac{p}{a} =\frac{q}{b}= \frac{r}{c}[/tex]

therefore

[tex]\frac{r}{c}[/tex]

is equal to

[tex]\frac{q}{b}[/tex] and [tex]\frac{p}{a}[/tex]

the answer is the option B

[tex]\frac{p}{a}[/tex]

The percent of 67.5 is equal to 7.02 is for the number 10.4.

To find what percent of 67.5 is 7.02, we can use proportions.

Let's represent the unknown percentage as 'x'. The proportion can be set up as follows:

(7.02 / 67.5) = (x / 100)

Now, solve for 'x':

7.02 × 100 = 67.5 × x

702 = 67.5x

x = 702 / 67.5

x ≈ 10.4

Therefore, 7.02 is approximately 10.4 percent of 67.5.

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Final answer:

To find the width of a rectangle with a perimeter of 54 cm and a length of 6 cm, use the formula P = 2l + 2w. After plugging in the given values and simplifying, the width is calculated to be 21 cm.

Explanation:

Finding the Width of a Rectangle

To solve this problem, we remember that the perimeter of a rectangle is calculated by the formula P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. Given the perimeter is 54 centimeters and the length is 6 centimeters, we can set up the equation as follows: 54 = 2(6) + 2w. Simplifying this, we get 54 = 12 + 2w, and then subtracting 12 from both sides gives us 42 = 2w. Dividing both sides by 2, we find the width w to be 21 centimeters.

Step-by-Step Calculation

Therefore, the width of the rectangle is 21 centimeters.

Answer:

x [tex]\geq[/tex] 18

Step-by-step explanation:

You can travel a distance of 468 miles on 12 gallons of gasoline and a distance of 234 miles on 6 gallons of gasoline.

Proportion is the setting of two or more ratios to be equal.

That is, if there is a ratio between a and b and another ratio between c and d, then we can say that,

a : b = c : d ⇒ a/b = c/d ⇒ a d = b c

We have,

Distance travelled is 156 miles on 4 gallons of gasoline.

We have to find the distance travelled on 12 gallons and 6 gallons of gasoline.

Let x be the distance travelled on 12 gallons of gasoline and y be the distance travelled on 6 gallons of  gasoline.

We have a proportional relation here,

156 : 4 = x : 12 = y : 6

First taking the relation,

156 : 4 = x : 12

⇒ 156/4 = x/12

⇒ 39 = x/12

⇒ x = 39 × 12

⇒ x = 468

Taking the second relation,

156 : 4 = y : 6

⇒ 156/4 = y/6

⇒ 39 = y/6

⇒ y = 39 × 6

⇒ y = 234

Hence you can travel 468 miles on 12 gallons and 234 miles on 6 gallons.

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The result of dividing 36 by 8 is 4.5. This means that there is no whole number that when multiplied by 8 equals 36; the closest is 4, giving us 32, with a remainder that results in 4.5 as the exact quotient.

The question the student is asking relates to basic arithmetic multiplication. Specifically, they're looking for a number that, when multiplied by 8, results in 36. To solve for this, we would generally divide 36 by 8.

However, because 36 is not a multiple of 8, we cannot get a whole number as the result. Instead, the closest we can get without going over is 4, because 4 multiplied by 8 equals 32. If we divide 36 by 8, the result is 4 with a remainder, or 4.5 (which can be expressed as 41/2).

The correct approach to find the quotient is to perform the division 36 / 8, which equals 4.5. To understand this better, you can think of it as having 36 objects that you want to divide into groups of 8 and trying to see how many full groups you can make. You would be able to make 4 full groups with 4 objects left over, or you could see it as making 4 and a half groups.

Answer:  The required area of the room that is NOT covered by the carpet is 192 ft².

Step-by-step explanation:  Given that the Smith wants to buy a 9 ft. by 12 ft. carpet and center it in a 15 ft. by 20 ft. room.

We are to find the area of the room that is NOT covered by the carpet.

We know that the area of a rectangle is given by the product of its length and breadth.

So, the area of the carpet bought by Smith is

[tex]A_c=9\times12=108~\textup{ft}^2,[/tex]

and the are of the room is

[tex]A_r=15\times 20=300~\textup{ft}^2.[/tex]

Therefore, area of the room that is NOT covered by the carpet will be

[tex]A=A_r-A_c=300-108=192~\textup{ft}^2.[/tex]

Thus, the required area of the room that is NOT covered by the carpet is 192 ft².

By acknowledging the linear relationship between X and Y, we set up a proportion based on the given values and solve for Y when X = 32, finding Y approximately equals 40.

This problem relates to the concept of

linear relationships

in mathematics. By understanding the relationship between two variables x and y, you can find the value of one by knowing the value of the other. Here, if y = 15 when X = 12, we can say that the ratio of y to x is constant. Therefore to find the value of Y when X = 32, we will maintain the same ratio. Now, set up a proportion 15/12 = Y/32 and solve for Y. Cross-multiplication gives us: Y = 15 * 32 / 12. After calculating this, Y equals approximately 40. Therefore, the value of Y when X is 32 will be around 40, keeping the relationship linear.

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To cook a 12 3/4 pounds ham which requires 2/5 of an hour for each pound, it will take approximately 5.1 hours. If dinner is at 4:45 pm, you should start cooking around 11:39 am.

The subject of your question is Mathematics. To solve this problem, let's understand first that the cooking time for a ham is 2/5 of an hour for each pound. This means that for each pound of ham, it should be cooked for 2/5 hour.

A.) To find how long you should cook a ham that weighs 12 3/4 pounds, you need to multiply that weight by 2/5. (12 3/4) * (2/5) ≈ 5.1 hours. So, you would need to cook the ham for approximately 5.1 hours.

B.) If dinner time is at 4:45 pm, and you know that the ham takes about 5.1 hours to cook, simply subtract 5.1 hours from the dinner time to find out when you should start cooking. 4:45pm - 5.1 hours ≈ 11:39am. Hence, you should begin cooking at around 11:39am to have the ham ready by 4:45pm.

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Answer:

Answer is option A

Step-by-step explanation:

Given that  there is a fifth degree polynomial. The three zeroes are given as

1/3, 4-6i, -2+11i

Since the polynomial having real coefficients will have imaginary roots occurring in conjugates only we can say that the imaginary roots will have conjugates also as zeroes of the polynomial.

We have one real root 1/3.

The imaginary roots are 4-6i and -2+11i

Hence these conjugates will be zeroes

i.e. [tex]4-6i, -2-11i[/tex] are the other zeroes

Option A is right.

Answer:

Factors of the expression given in the question i.e 9y² - 12y + 4 is (3y -2)(3y -2) .

Step-by-step explanation:

As the expression is given in the question be .

= 9y² - 12y + 4

Simplify the above

= 9y² -6y -6y + 4

= 3y (3y -2) -2 (3y - 2)

= (3y-2)(3y-2)

Therefore factors of the expression given in the question i.e 9y² - 12y + 4 is (3y -2)(3y -2) .

The next number in the pattern -0.8, -3.2, -12.8, -51.2 is -204.8.

A proportional relationship is a relationship between two expressions and where changes in one expression means some constant change in the other expression as well. Generally, it is represented as x/y = k, where x and y are two expressions and k is constant.

Given:

The numbers are -0.8, -3.2, -12.8, -51.2.

To find the pattern:

Divide the number to find the proportionate rate,

-3.2/-0.8 = 4

-12.8/-3.2 = 4

-51.2 /-3.2 = 4

So, the proportionality relationship is,

number = 4 x previous number.

So, the next number,

-51.2 x 4

= -204.8

Therefore, the number is -204.8.

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Answer:

milliliters

Step-by-step explanation:

Factorizing the polynomial expression x² - 18x + 81 = (x - 9)²

Factorization is the simplification of an expression into a smaller expression using its factors.

To factor this polynomial expression. x² - 18x + 81, we proceed as follows

Since we have the polynomial expression x² - 18x + 81, we multiply x² by 81 to get x² × 81 = 81x².

Now, we look for the factors of 81x² such that the sum of those factors equal - 18x

So, we have that 81x² = -9x × (-9x)

So, -18x = -9x - 9x

So, replacing this with -18x, we have that

x² - 18x + 81 = x² - 9x - 9x + 81

Now, factorizing, we have that

x² - 9x - 9x + 81 =  x(x - 9) - 9(x - 9)

= (x - 9)(x - 9)

= (x - 9)²

So, factorizing x² - 18x + 81 = (x - 9)².

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Answer:

The required answer is $2839.25.

Step-by-step explanation:

[tex]112\times12=1344[/tex] dollars

Plus down payment = [tex]1344+275=1619[/tex] dollars

Now, compound interest is found as:

[tex]A=p(1+\frac{r}{n})^{nt}[/tex]

p = 3592

r = 21.80% or 0.2180

n = 12

t = 1

Substituting the values in formula:

[tex]A=3592(1+\frac{0.2180}{12})^{12}[/tex]

=> [tex]A=3592(1.018167)^{12}[/tex]

A = $4458.25

So, Balance = [tex]4458.25-1619=2839.25[/tex] dollars

Therefore, the required answer is $2839.25.

Answer:Since there is no cluster formed in the scatterplot, the two variables are not related. Therefore, based on the data shown in the scatterplot, the number of fish in a lake is not dependent on the size of the lake.

Step-by-step explanation:

Answer: The measure of angle PCD is 42 degree.

Explanation:

It is given that in ∆ABC,

AB = CB  

BD − altitude to AC

P ∈ BD, PB = PC

∠ABC = 48°

Since the AB and CB are equal therefore by property of isosceles triangle the angle BAC and angel BCA are equal.

According to the angle sum property the the sum of interior angles of a triangle is 180.

[tex]\angle ABC+\angle BAC+\angle BCA=180^{\circ}[/tex]

[tex]48^{\circ}+2\angle BAC=180^{\circ}[/tex]

[tex]\angle BAC=66^{\circ}[/tex]

The altitude BD on AC divides the angle b in two equal parts because triangle ABC is an isosceles triangle.

[tex]\angle PBC=\frac{48}{2}=24^{\circ}[/tex]

Since PB=PC , so triangle BPC is an isosceles triangle.

[tex]\angle PBC=\angle PCB=24^{\circ}[/tex]

From the figure it is noticed that,

[tex]\angle PCD+\angle PCB=\angle BCA[/tex]

[tex]\angle PCD+24^{\circ}=66^{\circ}[/tex]

[tex]\angle PCD=66^{\circ}-24^{\circ}[/tex]

[tex]\angle PCD=42^{\circ}[/tex]

Therefore, the measure of angle PCD is 42 degree.