Solve the formula for the perimeter of a rectangle with width w and length l,for the length P=2w+2l solve for l

Answer: 5 inches

Step-by-step explanation:

Given: Volume of clay = 48 cubic inches

If we make a solid square right pyramid with a base edge a= 6 inches.

Then its base area = [tex]a^2=6^2=36\ inches^2[/tex]

we know that volume of square right pyramid=[tex]\frac{1}{3}\times\ a^2h[/tex]

Therefore, volume of square right pyramid made by all of clay=[tex]\frac{1}{3}\times\ a^2h[/tex]=48 cubic inches

[tex]\Rightarrow\frac{1}{3}\times\ (36)\times\ h=48\\\Rightarrow12h=48\\\Rightarrow\ h=4\ inches.....\text{[Divide 12 on both sides]}[/tex]

Now, slant height [tex]l=\sqrt{(\frac{a}{2})^2+h^2}[/tex]

[tex]\\\Rightarrow\ l=\sqrt{3^2+4^2}\\\Rightarrow\ l=\sqrt{9+16}\\\rightarrow\ l=\sqrt{25}\\\Rightarrow\ l=5[/tex]

The slant height of the pyramid if Helen uses all the clay=5 inches

Answer:

The correct answer would be 5 inches.

Step-by-step explanation:

Answer:  The required value of the first term is 8.

Step-by-step explanation:  We are given to find the first term of the arithmetic  sequence for which the third term is 126 and sixty fourth term is 3725.

We know that

the nth term of an arithmetic sequence with first term a and common difference d is given by

[tex]a_n=a+(n-1)d.[/tex]

According to the given information, we have

[tex]a_{3}=126\\\\\Rightarrow a+(3-1)d=126\\\\\Rightarrow a+2d=126~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

and

[tex]a_{64}=3725\\\\\Rightarrow a+(64-1)d=3725\\\\\Rightarrow a+63d=3725~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

Subtracting equation (i) from equation (ii), we get

[tex](a+63d)-(a+2d)=3725-126\\\\\Rightarrow 61d=3599\\\\\Rightarrow d=59.[/tex]

From equation (i), we get

[tex]a+2\times59=126\\\\\Rightarrow a=126-118\\\\\Rightarrow a=8[/tex]

Thus, the required value of the first term is 8.

The probability that a student plays basketball given that the student plays football is 56%.

Given that,

Based on the above information, the calculation is as follows:

[tex]= 18\% \div 32\%[/tex]

= 56%

Therefore we can conclude that The probability that a student plays basketball given that the student plays football is 56%.

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Answer:

solve the equation.  

4n−18=52

n= 17.5

Final answer:

Sam drove 186 miles with the truck he rented. To calculate this, the total paid was subtracted by the base fee, and the result was then divided by the per-mile charge.

Explanation:

The student is asked to calculate the number of miles driven by Sam based on the total cost of truck rental and the additional charge per mile. We use a linear equation to represent the total cost (C) as the sum of the base fee (F) and the product of the number of miles (m) and the charge per mile (P).

The equation for this problem is:

C = F + (P × m)

We are given:

The total cost of rental (C) = $159.49

The base fee (F) = $19.99

The charge per mile (P) = $0.75/mile

Substituting the values we have into the equation gives us:

$159.49 = $19.99 + ($0.75 × m)

To find the number of miles (m), we need to isolate the variable m. We do this by subtracting the base fee from the total cost:

$159.49 - $19.99 = $0.75 × m

$139.50 = $0.75 × m

Now, divide both sides by the charge per mile to get:

m = $139.50 / $0.75

m = 186 miles

Therefore, Sam drove 186 miles.

The function for the length of a row of bookshelves is [tex]\( f(x) = \frac{4}{5} \sqrt{x} \)[/tex]. graph below.

To find the length of a row of bookshelves, you can use the given relationship that the total length of each row of bookshelves will be [tex]\( \frac{4}{5} \)[/tex] of the length of the storage space. Let's denote the area of the space Isabel rents as [tex]\( x \).[/tex] Then, the length of the side of the square storage space is [tex]\( \sqrt{x} \).[/tex]

So, the length of a row of bookshelves,[tex]\( f(x) \)[/tex], would be:

[tex]\[ f(x) = \frac{4}{5} \times \sqrt{x} \][/tex]

For the function expressing [tex]\( f(x) \)[/tex], it would be:

[tex]\[ f(x) = \frac{4}{5} \sqrt{x} \][/tex]

Now, let's graph this function.

Attached below:

Complete Question:

User

When Isabel began her book-selling business, she stored her inventory in her garage. Now that her business has grown, she wants to rent warehouse space. Lisa owns a large warehouse nearby and can rent space to Isabel. The area of the warehouse is 8,100 square feet. Lisa is willing to rent Isabel as little as 100 square feet of the space or up to as much as the entire warehouse. Her only requirement is that all spaces must be square. The total length of each row of bookshelves will be 4/5 of the length of the storage space.1)

Let x be the area of the space that Isabel rents and f(x) represent the total length of a row of bookshelves. How would you find the length of a row of bookshelves?

F(x)= 4/5 √ x 100 ≤ x ≤ 8100 8 ≤ y ≤ 722)

Write a function that expresses f(x). (I wrote) F(x)= 4/5 √ x3)

Graph the function.

The shortest side of the triangle with vertices at (-2, 5), (-2, -7), and (-6, -4) is 5 units. The lengths were calculated using the distance formula derived from the Pythagorean theorem.

The subject matter of the given question pertains to the discipline of Geometry, specifically, the calculation of the length of the sides of a triangle. To find the length of the shortest side of a triangle having vertices at (-2, 5), (-2, -7), and (-6, -4), we can use the distance formula, which is derived from Pythagoras' theorem.

The formula for calculating the distance between two points (x₁, y₁) and (x₂, y₂) in a coordinate plane is:

√((x₂ - x₁)² + (y₂ - y₁)²)

Thus, the shortest side of the triangle is the one with length 5 units.

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The length of the shortest side of the triangle is 5.

To find the shortest side of the triangle with vertices at (-2, 5), (-2, -7), and (-6, -4), use the distance formula [tex]\( \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)[/tex]:

1. Between (-2, 5) and (-2, -7):

[tex]\[ \sqrt{( -2 - (-2) )^2 + ( -7 - 5 )^2} = \sqrt{0 + 144} = 12 \][/tex]

2. Between (-2, 5) and (-6, -4):

[tex]\[ \sqrt{( -6 - (-2) )^2 + ( -4 - 5 )^2} = \sqrt{16 + 81} = \sqrt{97} \approx 9.85 \][/tex]

3. Between (-2, -7) and (-6, -4):

[tex]\[ \sqrt{( -6 - (-2) )^2 + ( -4 - (-7) )^2} = \sqrt{16 + 9} = 5 \][/tex]

Thus, the shortest side is 5 units.

Which graph represents the function r(x) = |x – 2| – 1

we have

[tex] r(x) = |x- 2|- 1 [/tex]

using a graph tool

see the attached figure

So

1) the domain of the function is all real numbers-----> interval (-∞,∞)

2) the range of the function is the interval [-1, ∞)

3) the function decrease on the interval (-∞,2)

4) the function increase on the interval (2,∞)

5) the function has two x-intercepts-----> (1,0) and (3,0)

6) the function has one y-intercept-----> (0,1)

therefore

the graph in the attached figure

The mean and mode of the data set shown would be 4.75 and 2, 5 and 6 are modes.

Mean is the ratio of sum of the observations to the total number of observations.

The given set of data is follows as;

{2, 4, 5, 6, 8, 2, 5, 6}

The mean can be calculated by adding all numbers and dividing by the count:

(2+4+5+6+8+2+5+6)/8

= 38/8

= 4.75

The mode is the number that occurs most often.

this is the case for 2, 5, and 6.

A data set can have multiple modes. 2, 5 and 6 are modes.

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Answer:

2. I don't know for sure, but I'm pretty sure it's 1.05x10^28
3. 5,600,000,000,000
4. 0.00000000021
5. 87,300,000,000,000,000

Step-by-step explanation:

2) Again, I'm not 100% sure, but I would say 1.05x10^28 because it's the only one with three digits while the other numbers have two digits
3 & 5) The way scientific notation works is that when you have a positive exponent (like 12 and 16) you move the decimal point to the right that amount of times. So for example, take 5.6E12 (E12 is the same thing as saying 5.6x10^12 btw) the exponent would be 12, so you move the decimal point over 12 times. If you want to double check that you have enough zeros, move the decimal point again, and if it ends up at the end of the number when you hit 12, then you're fine. If you hit 12 in the middle of the number, erase all zeros to the right of the decimal point, and if you hit the end too early, add more zeros until you get it right.
4) Now when you have a negative exponent (-10) you do the opposite of 3 & 5 and move the decimal point to the left that amount of times. In this case, you would move the decimal point 10 times to the left, and you can use the same trick as before to make sure you have enough zeros. I also don't know how nitpicky your teacher is, but I would make sure to add one more zero to the left of the decimal just to make sure (by this I mean getting a number like 0.0005 instead of .0005) because some teachers do want you to do that. I hope this explanation helped :)

Answer:

4.

Step-by-step explanation:

We are given that an equation

[tex]\frac{-3}{4}m-\frac{1}{2}=2+\frac{1}{4}m[/tex]

We have to find a number by which each term multiply and eliminate the fractions before solving

We can see that in the given expression

Denominator of first term is 4 and denominator of second term is 2 on left side.

Denominator of second term is 4 on right side

Therefore ,the  lcm of 2,4,4

2=[tex]2\times1[/tex]

4=[tex]2\times2\times1[/tex]

LCM of 2 and 4 =[tex]2\times2\times1= 4 [/tex]

Therefore, the number is 4 by which each term is multiplied to eliminate the fractions before solving.

Hence, the answer is 4.

The values of the coefficients and constant are 1, -8 and -5

The standard quadratic expression is given as:

y = ax^2 + bx + c

where a, b and c are the constant

Given the quadratic function f(p) = p2 – 8p – 5, on comparing:

a = 1

b = -8

c = -5

Hence the values of the coefficients and constant are 1, -8 and -5

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area of the bottom square = 11*9 =99 squre inches

 for the triangular top the area = 1/2 x b x h

you have hypotenuse and height so need to calculate the base dimension

4^2 +x^2 = 7^2

16 +x^2 = 49

x^2 = 33 x = sqrt(33) = 5.7

area = 1/2 4*5.7 = 11.489

 there are two similar triangles so 11.489*2 = 22.97

99+22.97 = 121.97

looks like they rounded the numbers slightly different

 so 121 in2 is their answer

Answer:

121 in^2

Step-by-step explanation:

The main difference between tangent and chord is that the tangent touches the curve at only one point whereas the chord touches the curve at two points.

Chord:

Tangent:

From above definitions of Chord and Tangent , we say that chord touches the curve at two points where as Tangent touches the curve at only one point .

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A tangent is a line that touches a circle at only one point and is perpendicular to the radius at the point of contact, while a chord is a line segment with both endpoints on the circle.

A tangent and a chord are lines that relate to the curve of a circle, but they have distinct differences. A tangent is a line that touches a circle at exactly one point, and at this point of contact, it is perpendicular to the radius of the circle, which is called the axis in this context. In sharp contrast, a chord is a line segment whose endpoints both lie on the circle. When constructing the perpendicular from the midpoint of a chord, you are drawing an axis. For tangents, the perpendicular erected from the point of contact with the circle is also an axis.

This shows that the tangent is unique in that it has a "no-cut" property; it is the only line that will touch the circle at that single point without cutting through it. When looking at the slope of curves, the slope of the tangent line at the point of contact represents the exact slope of the curve at that point. The differentiation process in mathematics is used to find this slope of the tangent, which is important for understanding the rate of change at a specific point on a curve.

The linear equation that is asked from the problem takes the form of:

y = m x + b

where,

y = the median salary

x = the number of years

m = the slope of equation

b = y-intercept

The slope of the equation (m) can be calculated using the formula:

m = (y2 – y1) / (x2 – x1)

m = (1326720 – 441300) / (2008 – 2000)

m = 110,677.5

The y-intercept is then obtained by using any of the data pair:

441300 = 110677.5 (2000) + b

b = -220913700

Therefore the complete equation is:

y = 110677.5 x – 220913700

The median salary in 2016 is therefore:

y = 110677.5 (2016) – 220913700

y = $2,212,140

Answer: 

$2,212,140