In the figure, PQ is parallel to RS. The length of RP is 2 cm; the length of PT is 18 cm; the length of QT is 27 cm. What is the length of SQ?

Final answer:

The two consecutive positive odd integers that satisfy the given condition, where the square of the smaller plus three times the median equals 24, are 3 and 5.

Explanation:

The question asks to find two consecutive positive odd integers such that the square of the smallest integer, added to 3 times the median integer, is 24. Let's denote the smallest of these integers as n. Since they are consecutive odd integers, the next integer would be n+2. The equation based on the given condition would be n² + 3(n + 2) = 24.

Expanding and solving the equation gives:

n² + 3n + 6 = 24

n² + 3n - 18 = 0

(n+6)(n-3) = 0

Solving for n, we find n = 3 (since we are looking for positive integers and n+6=0 leads to a negative value).

Thus, the two consecutive positive odd integers are 3 and 5, meeting the given conditions.

For a better understanding of the solution provided here please go through the diagram in the attached file.

In the diagram, F is the foot of the tree.

T is the top of the tree. Then TF will be the height of the tree.

P is the point on the ground 47 feet from the foot of a tree. Therefore, PF=47.

Now, we know that the tree grows vertical from the ground and thus [tex] \angle F=90^{\circ} [/tex]

Thus, the triangle [tex] \Delta PFT [/tex] is a right triangle.

Now, we can apply the trigonometric ratio, tan in this triangle as:

[tex] tan(\angle P)=\frac{Perpendicular}{Base} =\frac{TP}{PF} [/tex]

[tex] \therefore tan(35^{\circ})=\frac{TF}{47} [/tex]

[tex] TF=47\times tan(35^{\circ})\approx32.91\approx33 [/tex]

Thus, the the height of the tree to the nearest foot is 33 feet.

The height of the tree is 32.90 feet.

P is the point on the ground, T is the top of the tree, and h is the height of the tree. We are given that PT = 47 feet and the angle of elevation from P to T is 35 degrees.

We want to find the height of the tree, which is represented by h in the diagram. We can use the tangent function to solve for h.

The tangent of an angle is defined as the ratio of the opposite side to the adjacent side in a right triangle.

In this case, the opposite side is h and the adjacent side is PT = 47 feet. Therefore, we have

tan(35°) = h/47

Solving for h, we get:

h = 47 * tan(35°) ≈ 32.90 feet

Rounding to the nearest foot, we find that the height of the tree is 33 feet.

The square root of 62 lies between the two consecutive whole numbers 7 and 8, since 7^2=49 is less than 62 and 8^2=64 is more than 62.

The square root of 62 falls into the range of two whole numbers. To ascertain the exact numbers, you need to find the square roots of the whole numbers around 62. These numbers would be 7 and 8, since the square of 7 is 49 and the square of 8 is 64. Therefore, the two consecutive whole numbers that square root of 62 lies between are 7 and 8.

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b for number 1 do u need all of them

Answer:

good luck

Step-by-step explanation:

1- a

2- c

3- b

To find the number of male and female cousins Jennifer Lopez met at a family reunion, we can set up a system of equations based on the given information. By solving the system, we can determine the values of the variables and find the answer.

The subject of this question is Mathematics and the grade level is Middle School. The question asks about the number of male and female cousins Jennifer Lopez met at a family reunion. Let's define the number of male cousins as x and the number of female cousins as y. From the given information, we know that x is 2 less than y.

So the equation can be written as: x = y - 2

Since Jennifer met a total of 9 cousins, we can write another equation: x + y = 9

Now we can solve this system of equations to find the values of x and y. Subtracting the first equation from the second equation, we get: (x + y) - (y - 2) = 9 - (y - 2)

Simplifying further, we have: x + 2 = 11 - y

Bringing the variables to one side, we get: x + y = 11 - 2

Combining like terms, we have: x + y = 9

Therefore, the value of x is 4 and the value of y is 5. So Jennifer Lopez met 4 male cousins and 5 female cousins at the family reunion.

The quarter circle's perimeter is 3.57 when the area of a quarter circle is 0.785 square kilometers.

Area of quarter circle is 0.785

This is a given value in the question.

Hence radius is 1 using the formula (pi*r*r)/4. This is derived after working out this formula.

Since radius is 1, perimeter is 3.57 using the formula (2*pi*r)/(4 + 2*r). This is also derived after working out this formula.

Hence this is the answer for the perimeter of the quarter circle since the given area of the quarter circle tends to be 0.785 square kilometers.

To learn more about area of the circle,

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Final answer:

The perimeter of a quarter circle with an area of 0.785 km² is 1.57 kilometers.

Explanation:

Let's call the radius of the circle "r".

Since the area of a quarter circle is a quarter of the whole circle's area, we can set up the following equation:

0.785=(1/4)πr^2

To solve for the radius (r), we can:

Multiply both sides by 4: 3.14=πr ^2

Divide both sides by π: r^2=1

Take the square root of both sides to find the radius: r=1 kilometer

Now that we know the radius, we can find the perimeter of the quarter circle.

The perimeter of a whole circle is 2πr, so the perimeter of a quarter circle is:

Perimeter=(1/4)×2πr=(πr)/2

Plugging in the value of r (1 kilometer):

Perimeter=(π×1)/2=  0.5π kilometers = 1.57 kilometers

We can use unitary method here.

First let us use the basic conversion from tons to ounces.

1 ton =32000 ounces

Now we have to find how many ounces are there in 1.5 tons.

Weight of hippopotamus in tons =1.5 tons

Weight of hippopotamus in ounces = 1.5 *32000 = 48000 ounces.

So the weight of hippopotamus in ounces is 48000 ounces.

Answer:

A,D,C APEX

Step-by-step explanation:

Answer:

We know that the rainwater outflow pipe must drop 1 inch per 25 horizontal inches, this ratio would be:

[tex]\frac{y}{x}=\frac{1}{25}=0.04[/tex]

So, if the drainage pipe has this ratio, then it will function properly. Let's find out:

[tex]\frac{y}{x}=\frac{25}{540}[/tex]

Because, 45 feet is equivalent to 540 inches.

So, the ratio would be:

[tex]\frac{25}{540} \approx 0.046[/tex]

Answer:

(0,-24)  

hope this helps you!

(p.s please mark me as brainlyest)

Step-by-step explanation:

I just took the test and got 100%

We are given the equation,

[tex] j= 4rb [/tex]

Here we have to solve for r.

r is in multiplication with 4b on the right side of equation.

So we apply opposite operation of multiplication on the left side.

opposite operation of multiplication is division.

So dividing left side by 4b,

[tex] \frac{j}{4b} =r [/tex]

So answer is r=j/4b.

Solution:

we are given that

In the library at Lenape Elementary School, there are 3/8 as many fiction books as there are nonfiction books.

There are 44 books in the school library.

we have been asked to find How many books are fiction books?

Let there are x non fiction books in the library. Then there will be [tex] \frac{3}{8}x [/tex] fiction books.

Hence we can write

[tex] x+\frac{3}{8}x=44\\\\\text{Now solve for x}\\\\\frac{8x+3x}{8}=44\\\\\frac{11x}{8}=44\\\\11x=44*8\\\\x=\frac{44*8}{11}\\\\x=4*8=32\\ [/tex]

Hence there are 32 non-fiction books in the library.

and 44-32=12 fiction books in the library.

Final answer:

To find out how many fiction books are at Lenape Elementary School's library, the total number of books is divided in the ratio of fiction to nonfiction books, which is 3:8. Solving the equation 11/8x = 44, where x is the number of nonfiction books, we find there are 32 nonfiction books and 12 fiction books.

Explanation:

The question asks us to determine how many fiction books there are in Lenape Elementary School's library, given the total number of books and the ratio of fiction to nonfiction books. We know that there is a total of 44 books and that the fiction books are 3/8 the number of nonfiction books.

Let's denote the number of nonfiction books as x. So, the number of fiction books would be 3/8 of x, or 3/8x.

The sum of fiction and nonfiction books is given by x + 3/8x, which equals the total number of books:

1x + 3/8x = 44

Combining like terms, we get:

11/8x = 44

Now, we can solve for x by multiplying both sides by the reciprocal of 11/8:

x = 44 * 8/11

Simplify:

x = 32

Thus, there are 32 nonfiction books and the number of fiction books is:

3/8 * 32 = 12

There are 12 fiction books in the library.

The answer would be D, because 4 8/6 is equal to 5 2/6.

Hope this helps ;}

Final answer:

The mixed number 5 2/6 simplified is 5 1/3 and when represented as an improper fraction it is 16/3. Upon reviewing the given options, only D) 4 8/6 is equivalent to 5 2/6 or 5 1/3.

Explanation:

To represent the mixed number 5 2/6 in another form, first simplify it by reducing the fraction to its lowest terms. The fraction 2/6 can be simplified to 1/3 because the numerator and denominator share a common factor of 2. So the number becomes 5 1/3. Now, to find an equivalent representation from the given options, you can convert it to an improper fraction: (5 × 3) + 1 = 15 + 1 = 16, so the equivalent improper fraction is 16/3. Looking at the choices provided, none match 5 1/3 exactly, but we can look at them to determine if any are equivalent:

Therefore, the correct answer is D) 4 8/6 as it is another way to represent 5 2/6.