the area of the top face of a cube is 9 meters. what is the volume? {I need to know how to actually do this}
A rectangular lot with a 50-ft frontage and a 230-ft depth sold for $8625. Find the cost of the lot per square foot
94.99 in expanded form
the sum of three consecutive integers is 63 find the three integers
663/3 = 21
21 is the middle number,
21+1 = 22
21-1 = 20
20 + 21 + 22 = 63
Our three consecutive integers can be represented as
X → first integer
X + 1 → second integer
X + 2 → third integer
If the sum of our three consecutive integers is 63, our equation will read...
X + X + 1 + X + 2 = 63
Now, we can simplify on the left. Once we simplify, our equation will now read
3x + 3 = 63
-3 -3 ← subtract 3 on both sides
3x = 60 ← divide both sides by 3
X = 20
Our three consecutive integers can be represented as
X → first integer = 20
X + 1 → second integer = 21
X + 2 → third integer = 22
Therefore, the three consecutive integers are 20, 21, and 22.
If g(t)=4t-t^2, find g(t+h)-g(t)/h.
Which is greater, the greatest whole number with 4 digits or the least whole number with 5 digits?
What is the greatest whole number that rounds to 54,300
When determining slope, data points do not usually fall within a straight line, so you need to draw a _____ line, with as many points above and below the line as possible.
accurate
precise
best fit
correct
Answer:
The correct option is 3.
Step-by-step explanation:
If a straight line passes through some of the points, none of the points, or all of the points of a scatter plot and best represents the data, then it is called a best fit line.
Best fit line minimizes the squared distance of each point. Some points of the scatter plot lie above and below the best fit line.
When determining slope, data points do not usually fall within a straight line, so you need to draw a best fit line, with as many points above and below the line as possible.
Therefore the correct option is 3.
A soccer ball is kicked from the ground. After traveling a horizontal distance of 35m, it just passes over a 1.5m tall fence before hitting the ground 37m from where it was kicked. How far has the ball travelled horizontally to reach the maximum height?
Answer:
18.5 meters
Step-by-step explanation:
As the maximum height ona projectile motion that starts from the ground and finishes at the ground is simmetric, the maximum height of the projectile will be found exactly at half of the distance tranveled horizontally, so the exact half of the total distance traveled horizontally is 18.5 meters, since distance is 37 meters and divided by 2 is 18.5.
The ball will travel 18.5 meters to reach its maximum height.
Sorry if I'm bothering you! But can you guys figure out this problem for me? "A car travels at 65 miles per hour. Going through Construction, it travels 3/5 this speed. Write this fraction as a decimal and find the speed.
Thanks,
-Laura B.
solve the equation 0.4+0.5=-4.7-0.6z
find two consecutive odd integers such that 54 more than the lesser is five times the greater
Find a + b, 2a + 3b, |a|, and |a − b|. a = 5i + j, b = i − 3j
What is the solution of the system? Use substitution. x = –2y + 10 –6y = 6x – 6 z = –3x + 10y
To solve the given system of equations using substitution, we'll start by solving the first equation for x in terms of y. We'll substitute this expression for x in the other two equations to find the values of y and z.
Explanation:To solve the given system of equations using substitution, we'll start by solving the first equation for x in terms of y: x = -2y + 10. We'll substitute this expression for x in the other two equations to find the values of y and z. Substituting -2y + 10 for x in the second equation, we have -6y = 6(-2y + 10) - 6.
Simplifying this equation, we get y = -2. Substituting y = -2 in the first equation, we find x = -2*(-2) + 10 = 14. Finally, substituting x = 14 and y = -2 in the third equation, we find z = -3*14 + 10*(-2) = -52.
what is 165% written as a decimal and fraction
Find the area of the region bounded by the parabola y = x2, the tangent line to this parabola at the point (2, 4), and the x-axis.
The area of the region is [tex]\(\frac{64}{3}\)[/tex] square units.
To find the area of the region bounded by the parabola \(y = x^2\), the tangent line at the point (2, 4), and the x-axis, we'll first determine the points of intersection.
The tangent line at (2, 4) has the same slope as the derivative of the parabola at x = 2. The derivative of [tex]\(y = x^2\)[/tex] is [tex]\(2x\)[/tex], so at x = 2, the slope is [tex]\(2 \times 2 = 4\)[/tex]. Thus, the equation of the tangent line is [tex]\(y - 4 = 4(x - 2)\)[/tex].
Now, let's find the points of intersection between the parabola and the tangent line:
[tex]\[x^2 = 4(x - 2) + 4\][/tex]
Solving for x, we get [tex]\(x^2 - 4x = 0\)[/tex], which factors to [tex]\(x(x - 4) = 0\)[/tex]. So, [tex]\(x = 0\)[/tex] and [tex]\(x = 4\)[/tex].
Now, integrate the absolute difference of the functions from 0 to 4 to find the area:
[tex]\[A = \int_0^4 |x^2 - (4x - 4)| \,dx.\][/tex]
Evaluate the integral:
[tex]\[A = \int_0^4 (x^2 - 4x + 4) \,dx = \frac{1}{3}x^3 - 2x^2 + 4x \Big|_0^4 = \frac{64}{3}.\][/tex]
Therefore, the area of the region is [tex]\(\frac{64}{3}\)[/tex] square units.
The answer is: [tex]\frac{8}{3}[/tex].
The area of the region bounded by the parabola [tex]\( y = x^2 \)[/tex], the tangent line to this parabola at the point (2, 4), and the x-axis is given by the integral of the difference between the parabola and the tangent line from [tex]\( x = 0 \) to \( x = 2 \)[/tex].
First, we need to find the equation of the tangent line to the parabola at the point (2, 4). The slope of the tangent line is the derivative of the parabola's equation at \( x = 2 \). The derivative of [tex]\( y = x^2 \)[/tex] is [tex]\( y' = 2x \).[/tex] At[tex]\( x = 2 \)[/tex], the slope is [tex]\( 2 \cdot 2 = 4 \)[/tex].
Using the point-slope form of a line,[tex]\( y - y_1 = m(x - x_1) \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( (x_1, y_1) \)[/tex] is a point on the line, we get the equation of the tangent line as follows:
[tex]\[ y - 4 = 4(x - 2) \][/tex]
[tex]\[ y = 4x - 8 + 4 \][/tex]
[tex]\[ y = 4x - 4 \][/tex]
Now, we will find the area under the parabola and above the tangent line from [tex]\( x = 0 \) to \( x = 2 \)[/tex]. The integral of [tex]\( x^2 \)[/tex] from 0 to 2 is:
[tex]\[ \int_{0}^{2} x^2 \, dx = \left[ \frac{x^3}{3} \right]_{0}^{2} = \frac{2^3}{3} - \frac{0^3}{3} = \frac{8}{3} \][/tex]
The integral of the tangent line \( y = 4x - 4 \) from 0 to 2 is:
[tex]\[ \int_{0}^{2} (4x - 4) \, dx = \left[ 2x^2 - 4x \right]_{0}^{2} = (2 \cdot 2^2 - 4 \cdot 2) - (2 \cdot 0^2 - 4 \cdot 0) = (8 - 8) - (0 - 0) = 0 \][/tex]
The area between the parabola and the tangent line is the difference between these two integrals:
[tex]\[ \text{Area} = \int_{0}^{2} x^2 \, dx - \int_{0}^{2} (4x - 4) \, dx \][/tex]
[tex]\[ \text{Area} = \frac{8}{3} - 0 \][/tex]
[tex]\[ \text{Area} = \frac{8}{3} \][/tex]
Therefore, the area of the region bounded by the parabola [tex]\( y = x^2 \)[/tex], the tangent line at the point (2, 4), and the x-axis is [tex]\( \boxed{\frac{8}{3}} \)[/tex] square units.
a tour bus cost $75 plus $6 for each passenger. write and evaluate an expression to find the total cost for 25 passengers. then. make a table showing the cost for 26, 30, 35, 40 passengers
Assume f(x)=4x+8 and g(x)=5. What is the value of (g o f)(-1)?
Using place value to alter the amount of 194753 by two thousand
Jesse was ranked 11th in his graduating class of 180 students. At what percentile is Jesse's ranking? (Round your answer to the nearest whole number.)
give an example of an addition problem in which you would and would not group the addends differently to add
Find two integers whose sum is -7 and whose product is 12. Explain how you found the numbers.
Yolanda walks 1.5km every day. How far does she walk in 9 days? Write your answer in meters.
The pie below is cut into 6 equal slices. Show shade2/3 of this pie
The distribution of the amount of money spent by students for textbooks in a semester is approximately normal in shape with a mean of 235andastandarddeviationof235andastandarddeviationof 20. according to the standard deviation rule, how much did almost all (99.7%) of the students spend on textbooks in a semester?
a circus performer walks on a tightrope 25 feet above the ground. the tightrope is supported by two beams and two support cables. if the distance between each beam and the base of its support cable is 15 feet, what is the length of the support cable?
Answer:29.15475947 (not rounded)
Step-by-step explanation:
5. Suppose that a and b are both real numbers such that a < b. What can you conclude about the inequality 1/a < 1/b?
a. 1/a < 1/b is always true.
b. 1/a < 1/b is sometimes true.
c. 1/a < 1/b is never true.
d. A valid conclusion cannot be determined from the given information.
Simplify the expression and eliminate any negative exponent(s). Assume that all letters denote positive numbers.
√s√s^9
.002 is 1/10 of what
.002 is 1/10 of 0.02. To find this, we multiply .002 by 10. This is seen as moving the decimal point to the right once because we are multiplying by a power of ten.
Explanation:The student asked: ".002 is 1/10 of what". To find the answer to this question, we can set up a simple equation where we multiply .002 by 10 because we know that if .002 is 1/10 of a number, then multiplying it by 10 will give us that whole number.
So the equation is:
.002 x 10 = 0.02Therefore, .002 is 1/10 of 0.02.
This can also be understood by recognizing that when dividing by powers of 10, you move the decimal to the left by the number of zeros in the power of ten. So, in the reverse process, when we want to find a number that is ten times larger (i.e., 1/10 of the original), we move the decimal one place to the right.
The dress store is having a sale where all merchandise is 1/4 off. A woman buys $48 of merchandise at the sale price
The woman should have paid \$64 for the regular price of the merchandise.
To find out what the woman should have paid for the regular price, we need to reverse engineer the discount. Here's the step-by-step calculation:
Calculate the Discount Amount: Since the sale is 1/4 off, the discount is 1/4 of the regular price. So, the discount is:
[tex]\[ \frac{1}{4} \times \text{Regular Price} \][/tex]
[tex]\[ \text{Discount} = \frac{1}{4} \times \text{Regular Price} \][/tex]
Subtract the Discount from the Regular Price to Get the Sale Price: The sale price is the regular price minus the discount:
[tex]\[ \text{Sale Price} = \text{Regular Price} - \text{Discount} \][/tex]
Calculate the Sale Price: We know the woman bought $48 worth of merchandise at the sale price, so:
[tex]\[ \text{Sale Price} = \$48 \][/tex]
Find the Regular Price: Now we can set up an equation using the information we have:
[tex]\[ \$48 = \text{Regular Price} - \text{Discount} \][/tex]
Substituting the discount calculated earlier:
[tex]\[ \$48 = \text{Regular Price} - \left(\frac{1}{4} \times \text{Regular Price}\right) \][/tex]
Solve for the Regular Price:
[tex]\[ \$48 = \left(\frac{4}{4}\right) \times \text{Regular Price} - \left(\frac{1}{4}\right) \times \text{Regular Price} \][/tex]
[tex]\[ \$48 = \left(\frac{3}{4}\right) \times \text{Regular Price} \][/tex]
To isolate the regular price, multiply both sides by [tex]\( \frac{4}{3} \)[/tex]:
[tex]\[ \text{Regular Price} = \$48 \times \frac{4}{3} \][/tex]
[tex]\[ \text{Regular Price} = \$64 \][/tex]
So, the woman should have paid $64 for the regular price of the merchandise.
Complete Question:
The dress store is having a sale where all merchandise is 1/4 off a woman buys $48 of merchandise at the sale price what should she have paid for the regular price