Final answer:
Clear geometry formulas for calculating volume, area, and perimeter include V = lwh for rectangular prisms, A = bh for parallelograms, and C = πd for the circumference of a circle, among others.
Explanation:
Understanding Geometry, Area, and Volume
To help with remembering formulas from geometry, it's essential to understand the relationships between shapes and their dimensions. Here are the correct formulas for each of the items listed:
Volume of a rectangular prism is given by the formula V = lwh (length × width × height).Area of a parallelogram is found using A = bh (base × height).Circumference of a circle requires the formula C = πd or C = 2πr where d is diameter and r is radius.Area of a circle is calculated by A = πr² (pi times radius squared).Area of a triangle can be computed using A = 1/2 bh (half the base times the height).Area of a trapezoid is found with A = 1/2(b1 + b2)h where b1 and b2 are the bases and h is the height.Perimeter of a quadrilateral is the sum of the lengths of all four sides, often expressed as P = 2L + 2W for rectangles, with L being length and W being width.To solve problems in geometry effectively, it's helpful to visualize the shapes and understand how to derive their area and volume using standard formulas. This also applies when dealing with more complex objects, such as spheres and cylinders. In trigonometry, understanding the relationships within a right triangle can be crucial for solving spatial problems.
can some one plz help me...Banks cannot provide amortization schedules to borrowers.
A) true
B) false,
The correct answer is:
False.
Explanation:
When you take out a loan, banks provide all of the relevant information for the loan. This includes the interest rate, payment amount, and an amortization schedule, which shows the amount paid and the amount of principal this takes off of the loan every month for the life of the loan.
Find the equation of the axis of symmetry for the parabola y = x2 + 4x – 5 .
ALGEBRA 1 PLEASE HELP
5x+y=6
5x+3y=-5
The y-coordinate of the solution to the system shown as______
A) -5
B) -1
C) 1/2
D) 1
Which expression gives the area of the triangle shown below?
The expression gives the area of the triangle shown below 1/2cx is the answer.
The reason this is the answer is because to find the area of a triangle you will find half of the base times the height.
What is the formula of the triangle?
The formula of a triangle
A=1/2bh.
In this picture, the base is the length of the bottom part of the triangle (c).
It is the distance of the solid line only.
The height is represented as the straight line that is perpendicular to the base (forms a right/90-degree angle).
X is the height of the triangle.
Therefore, 1/2cx is the answer.
So option D is correct.
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how much would 500 invested at 4 interest compounded continuously be worth after 7 years round your answer to the nearest cent?
800% of what number is 4,240?
Name the property of real numbers illustrated by the equation 16(3t + 4v) = 48t + 64v.
A segment with the endpoint X(-6,2) and Y(-1,-3) is rotated 90 degrees about the origin. What are the coordinates of X' and Y'?
1- X' (-1,-3) Y'(-6,2)
2- X' (2,6) Y' (-3,1)
3- X' (-2,-6) Y' (3,-1)
4- X' (6,-1) Y' (1,3)
Thank you for helping, and looking. Thanks,
A valve in a full 6000 gallon water tank is slowly opening. Water flows out of the tank through the valve. The flow rate in gallons per hour is given by the function f(t)=300 t^2 where t is in minutes.
How much water flows out the tank in the first 7 minutes?
How many minutes does it take for the tank to be completely empty?,
Water flows: 34300 gallons in 7 minutes. Tank empties in about 3.914 minutes. (Rounded to three decimal places.)
To find out how much water flows out of the tank in the first 7 minutes, we need to integrate the flow rate function, [tex]\(f(t)\)[/tex], from [tex]\(t = 0\)[/tex] to [tex]\(t = 7\)[/tex]. The flow rate function is given as [tex]\(f(t) = 300t^2\)[/tex].
So, the amount of water that flows out of the tank in the first 7 minutes, denoted as [tex]\(W_{\text{out}}\)[/tex], is given by the integral of [tex]\(f(t)\)[/tex] over the interval [tex]\([0, 7]\)[/tex]:
[tex]\[W_{\text{out}} = \int_{0}^{7} f(t) \, dt\][/tex]
[tex]\[= \int_{0}^{7} 300t^2 \, dt\][/tex]
[tex]\[= 300 \int_{0}^{7} t^2 \, dt\][/tex]
To find the integral of [tex]\(t^2\)[/tex], we use the power rule for integration:
[tex]\[= 300 \left[\frac{t^3}{3}\right]_{0}^{7}\][/tex]
[tex]\[= 300 \left(\frac{7^3}{3} - \frac{0^3}{3}\right)\][/tex]
[tex]\[= 300 \left(\frac{343}{3}\right)\][/tex]
[tex]\[= 34300\][/tex]
So, [tex]\(W_{\text{out}} = 34300\)[/tex] gallons.
Now, to find out how many minutes it takes for the tank to be completely empty, we need to find the time, [tex]\(T\)[/tex], at which the tank is empty. The tank will be empty when the integral of the flow rate function from [tex]\(t = 0\)[/tex] to [tex]\(t = T\)[/tex] is equal to the total volume of the tank, which is 6000 gallons.
So, we have:
[tex]\[6000 = \int_{0}^{T} f(t) \, dt\][/tex]
[tex]\[= \int_{0}^{T} 300t^2 \, dt\][/tex]
[tex]\[= 300 \int_{0}^{T} t^2 \, dt\][/tex]
Using the power rule for integration again:
[tex]\[6000 = 300 \left[\frac{t^3}{3}\right]_{0}^{T}\][/tex]
[tex]\[= 300 \left(\frac{T^3}{3} - \frac{0^3}{3}\right)\][/tex]
[tex]\[= 100T^3\][/tex]
Now, solving for [tex]\(T\):[/tex]
[tex]\[T^3 = \frac{6000}{100}\][/tex]
[tex]\[T^3 = 60\][/tex]
[tex]\[T = \sqrt[3]{60}\][/tex]
[tex]\[T \approx 3.914\][/tex]
So, it takes approximately 3.914 minutes for the tank to be completely empty.
You roll a number cube twice. Find the probability of the events.
1.Rolling a 3 twice
2.Rolling an even number and a 5
3.Rolling an odd number and a 2 or 4
4.Rolling a number less than 6 and a 3 or a 1
Answer:
In a number cube, a dice, you have six sides with the numbers 1, 2, 3, 4, 5 and 6. And when you roll it, each number has the same probability of showing.
a) rolling a 3 twice.
In the first roll you get a 3, with a probability of 1/6, and with the second roll you also get a 3, also with a probability of 1/6. The probability of bot evets to happen is equal to the product of the individual probabilities.
P = 1/6*1/6 = 1/36
b) An even number and a 5.
In the first roll you can get 2, 4 or 6, so you have 3 out of 6 options, the probability is 3/6 = 1/2, in the second roll you need you get a 5, the probability is 1/6.
P = 1/2*1/6 = 1/12.
But we also have the probability where the first dice is a 5 and the second a pair number, so the real probability is 2*P = 1/6
c) an odd number and 2 or 4.
for an odd number the probability is 3/6 = 1/2, for getting 2 or 4 the probability is 2/6 = 1/3
then we have that P = 2*(1/3)*(1/2) = 1/3
d) a number less than 6, you have 5 options, then the probability is:
p = 5/6, and for 3 or 1 the probability is 2/6 = 1/3
then P = 2*(5/6)*(1/3) = 5/9
Which graph shows a line that is perpendicular to line QR?
A watch manufacturer has two factories (FA, FB) and 60% of their watches are made at FA. It is known that 10% of them are made at FA and 15% made at FB are defective. What is the probability that a selected defective watch was manufactured at FB?
What is the slope of the line passing through the points (-4, 3) and (5, -3)?
Answer:
2/3
Step-by-step explanation:
My cousin just took this on odyssey
Which number system BEST describes this set? {-10, 0, 28 7 , 102.9} A) integers B) natural numbers C) rational numbers D) irrational numbers
please help asap! 14 points
Construct two tangents to circle O, at A and at B, where AB is a diameter. What relationship exists between the two tangents
When two tangents are drawn to a circle at endpoints A and B of a diameter, the tangents are perpendicular to the radii at their points of tangency and are parallel to each other, forming two congruent right triangles.
Explanation:The question involves constructing two tangents to a circle from two points, A and B, where AB is the diameter of the circle. By the properties of circles and tangents, we know that a tangent to a circle is perpendicular to the radius at the point of tangency. Since AB is the diameter, points A and B are on opposite ends of the circle, and when we draw tangents at these points, each tangent will be perpendicular to the radii OA and OB respectively. Additionally, since AB is a diameter, it creates a linear pair with the two tangents, meaning that the two tangents are parallel to each other. This setup creates two congruent right triangles, namely triangle OAT and triangle OBT, where T represents the points of tangency on each tangent.
Two tangents to a circle from points A and B, where AB is a diameter, are congruent and parallel to each other, forming right angles with the diameter.
Explanation:When constructing two tangents to a circle at points A and B, where AB is a diameter, an interesting relationship exists between those tangents. By the properties of tangents to a circle from an external point, we know that two tangents drawn to a circle from the same external point are equal in length. Therefore, the two tangents you would draw from points A and B to any point on the circumference of the circle would be congruent to each other.
Additionally, since each tangent is perpendicular to the radius of the circle at the point of tangency, the tangents are parallel to each other because they are both perpendicular to the same diameter. In the context of circle O with AB as a diameter, we can also conclude that the angles formed between the tangents and the diameter AB are right angles due to the geometric properties of tangents.
HELP PLEASE!!! Which figure shows a reflection of pre-image DEFG over the x-axis ? ( there’s only an A B and C )
which expression is equivalent to 6a+12
Answer:
2(3a + 6) would be correct.
Hope this was helpful !
Step-by-step explanation:
Help!! Would the answer be c??
The steps below show the incomplete solution to find the value of x for the equation 7x − 3x − 4 = −1 + 21:
Step 1: 7x − 3x − 4 = −1 + 21
Step 2: 7x − 3x − 4 = 20
Step 3: 4x − 4 = 20
Which of these is most likely the next step? (4 points)
Select one:
a. 4x = 24
b. 4x = 16
c. 4x = 5
d. 4x = 80
Answer: is a
Step-by-step explanation:
Which statement justifies that angle XAB is congruent to angle ABC?
A. Corresponding angles of parallel lines cut by a transversal are congruent.
B. Vertical angles are congruent.
C. Same-side interior angles of parallel lines cut by a transversal are supplementary.
D. Alternate interior angles of parallel lines cut by a transversal are congruent.
Given: m || CB
Prove: m∠ABC + m∠BAC + m∠ACB = 180°
Answer: D. Alternate interior angles of parallel lines cut by a transversal are congruent.
Step-by-step explanation:
In the given picture m is parallel to CB .
Since m is a straight line and the angle of straight line is 180° .
Therefore, m∠XAB+m∠BAC+m∠YAC=180° ........................ (a)
Also, m is parallel to CB and AB is a transversal and because Alternate interior angles of parallel lines cut by a transversal are congruent.
⇒m∠XAB=m∠ABC and m∠YAC=m∠ACB
Put the values of m∠XAB and m∠YAC in equation (a), we get
m∠ABC + m∠BAC + m∠ACB = 180°.
Hence proved.
Statement D Alternate interior angles of parallel lines cut by a transversal are congruent is the most relevant to the congruence of XAB and ABC.
It is proved that m∠ABC + m∠BAC + m∠ACB = 180°.
For angle XAB being congruent to angle ABC, and then prove the equation m∠ABC + m∠BAC + m∠ACB = 180°.
Parallel lines m and CB.
Points X, A, and Y are on line m.
To prove that angle XAB is congruent to angle ABC.
Justification for Congruence:
In this context, use the Alternate Interior Angles Theorem,
which states that when a transversal intersects two parallel lines, the alternate interior angles formed are congruent.
Here's the reasoning:
Line m is parallel to line CB.
The line XY is a transversal line that intersects m and CB.
Therefore, the alternate interior angles formed by this setup are congruent.
This means that angle XAB and angle ABC are congruent.
Now, let's prove the equation m∠ABC + m∠BAC + m∠ACB = 180°.
Angle XAB is congruent to angle ABC (justified by the Alternate Interior Angles Theorem).
Now, let's consider the triangle ABC. By the angle sum property of triangles, the sum of the angles in a triangle is always 180°. Therefore:
m∠ABC + m∠BAC + m∠ACB = 180°
Since angle XAB is congruent to angle ABC, replace angle ABC with angle XAB:
m∠XAB + m∠BAC + m∠ACB = 180°
Now, the equation holds true, and you have successfully proven that m∠ABC + m∠BAC + m∠ACB = 180°.
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A triangle with vertices at A(20, –30), B(10, –15), and C(5, –20) has been dilated with a center of dilation at the origin. The image of B, point B', has the coordinates (2, –3). What is the scale factor of the dilation?
110110
1515
5
10
Answer:
5
Step-by-step explanation:
If x is 6, then 7x = _____. 13 42 42x 76
Answer: 42
Step-by-step explanation:
x = 6 now that you know what x represents switch it out the x by the 7 with a 6 like this 7(x)- 7(6) seven times six is 42 in other words x
=42
The town recreation department ordered a total of 100 baseballs and bats for the summer baseball camp. Baseballs cost $4.50 each and balls cost $20 each. The total purchase was $822. How many of each item was ordered
76 baseballs and 24 bats were ordered.
Explanation:Let's assume that 'x' represents the number of baseballs ordered and 'y' represents the number of bats ordered.
We can set up two equations to solve for 'x' and 'y':
x + y = 100 (since the total number of items ordered is 100)4.50x + 20y = 822 (since the total cost of the purchase is $822)We can solve the system of equations using the substitution or elimination method. Let's use the elimination method by multiplying the first equation by 4.50:
4.50x + 4.50y = 4504.50x + 20y = 822Subtracting the first equation from the second equation eliminates 'x' and we can solve for 'y':
15.50y = 372
y = 24
Substituting the value of 'y' back into the first equation, we can solve for 'x':
x + 24 = 100
x = 100 - 24
x = 76
Therefore, 76 baseballs and 24 bats were ordered.
76 baseballs and 24 bats were ordered for the summer camp, costing $822 in total.
Let's denote the number of baseballs as [tex]\( B \)[/tex] and the number of bats as [tex]\( T \)[/tex].
We're given two pieces of information:
1. The total number of items ordered is 100, so [tex]\( B + T = 100 \)[/tex].
2. The total cost of the items is $822, so [tex]\( 4.50B + 20T = 822 \)[/tex].
We can solve this system of equations by substitution or elimination. Let's use the elimination method.
1. Multiply the first equation by 20 to match the coefficient of [tex]\( T \)[/tex] in the second equation:
[tex]\[ 20(B + T) = 20(100) \][/tex]
[tex]\[ 20B + 20T = 2000 \][/tex]
2. Subtract this modified first equation from the second equation:
[tex]\[ (4.50B + 20T) - (20B + 20T) = 822 - 2000 \][/tex]
[tex]\[ 4.50B + 20T - 20B - 20T = -1178 \][/tex]
[tex]\[ -15.50B = -1178 \][/tex]
3. Divide both sides by -15.50 to solve for [tex]\( B \)[/tex]:
[tex]\[ B = \frac{-1178}{-15.50} \][/tex]
[tex]\[ B \approx 76 \][/tex]
4. Now, substitute the value of [tex]\( B \)[/tex] back into the first equation to find [tex]\( T \)[/tex]:
[tex]\[ 76 + T = 100 \][/tex]
[tex]\[ T = 100 - 76 \][/tex]
[tex]\[ T = 24 \][/tex]
So, there were 76 baseballs and 24 bats ordered.
Write the expression as either the sine, cosine, or tangent of a single angle. tan5x - tan2y / 1 + tan5x tan2y
Final answer:
The expression tan5x - tan2y / 1 + tan5x tan2y simplifies to tan(5x + 2y) using the tangent sum formula, illustrating how two tangent values can be combined into a single tangent of the sum of two angles.
Explanation:
The expression given is tan5x - tan2y / 1 + tan5x tan2y. This can be simplified using the tangent sum formula, which is a key concept in trigonometry. The tangent sum formula states that tan(a + b) = (tan a + tan b) / (1 - tan a tan b).
By comparing the given expression to this formula, we can see that the expression represents the tangent of the sum of two angles, specifically tan(5x + 2y). This simplification uses trigonometric identities to represent the combination of two different tangent values as a single tangent value of the sum of the angles.
What is the area of a sector with a central angle of 3π5 radians and a diameter of 21.2 cm?
Use 3.14 for π and round your final answer to the nearest hundredth.
Enter your answer as a decimal in the box.
cm²
The area of the sector has a diameter of 21.2 cm and a central angle of 3π/5 radians is 105.90 square cm.
What is a circle?It is a locus of a point drawn at an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.
The central angle of 3π/5 radians and a diameter of 21.2 cm.
Then the area of the sector will be
[tex]\rm Area = \dfrac{\theta}{2\pi} *\dfrac{\pi}{4} d^2[/tex]
Then put the values, we have
[tex]\rm Area = \dfrac{\frac{3\pi}{5}}{2\pi} *\dfrac{\pi}{4} (21.2)^2\\\\\\\rm Area = \dfrac{3\pi}{10\pi} *\dfrac{3.14}{4} *449.44\\\\\\Area = \dfrac{3}{10} *\dfrac{3.14}{4} *449.44\\\\\\Area = 105.8968 \approx 105.90 \ cm^2[/tex]
The area of the sector has a diameter of 21.2 cm and a central angle of 3π/5 radians is 105.90 square cm.
More about the circle link is given below.
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The rate of change of y with respect to t is proportional to 50 - y
Create an equation to model a population of cells which starts with 10 cells and doubles in size every day. How many days will it take to reach 1,000,000 cells?
The t represents days, and we can't have a fraction of a day for the population to reach [tex]1,000,000[/tex] cells, we need to round up to the nearest whole number. Therefore, it will take approximately [tex]17[/tex] days for the population to reach [tex]1,000,000[/tex] cells.
To model the population of cells, we can use an exponential growth equation. Since the population doubles every day, the equation would be:
[tex]P(t)=P_{0} *2^{t}[/tex]
Where:
[tex]P(t)[/tex] is the population size at time t.
[tex]P_{0}[/tex] is the initial population size ([tex]10[/tex] cells in this case).
[tex]t[/tex] is the time in days.
So, for this scenario, the equation becomes:
[tex]P(t)=10*2^{t}[/tex]
Now, we want to find out how many days it will take for the population to reach [tex]1,000,000[/tex] cells. We can set up the equation:
[tex]1,000,000=10*2^{t}[/tex]
To solve for t, we need to isolate it. First, divide both sides by [tex]10[/tex] :
[tex]100,000=2 t[/tex]
Now, take the logarithm base 2 of both sides to solve for t:
[tex]log_{2} (100,000)=t[/tex]
Using a calculator, we find:
[tex]t=16.61[/tex]
Since t represents days, and we can't have a fraction of a day for the population to reach [tex]1,000,000[/tex] cells, we need to round up to the nearest whole number. Therefore, it will take approximately [tex]17[/tex] days for the population to reach [tex]1,000,000[/tex] cells.
COMPLETE QUESTION:
Create an equation to model a population of cells which starts with [tex]10[/tex]cells and doubles in size every day. How many days will it take to reach [tex]1,000,000[/tex] cells?
The coordinates of the vertices of / are G(–2, 3), H(–1, 2), and I(–3, 1). If / is reflected across the x-axis to create /, find the coordinates of the vertex located at point W.
Answer:
A. (–2, –3)
that is the answer
Which is a zero od the quadratic function f(x)=16x²+32x-9?
To find the slope of a line using two points on the line, you can use the slope formula. Which formula will find the slope of a line
y = rise/run
y = run/rise
Final answer:
The slope of a line is calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line. The formula represents the rise over run between these points.
Explanation:
We can use a specific formula to calculate the slope of a line using two points on that line. The slope is found by taking the difference in the y-value (also known as the rise) and dividing it by the difference in x-value (also known as the run). In mathematical terms, if we have two points (x1,y1) and (x2,y2), the formula for slope (m) is as follows:
m = (y2 - y1) / (x2 - x1)
Therefore, between two given points, you subtract the y-value of the starting point from the y-value of the end point to find the rise, and then remove the x-value of the starting point from the x-value of the end point to determine the run. The slope is then the quotient of these two differences.