The cost of admission for a group of 2 people is 50 dollars.
The given function C(P) represents the cost C (in dollars) of admission for a group of P people at the amusement park. The function is a simple linear equation with a slope of 25, indicating that the cost of admission increases by 25 dollars for each additional person in the group.
To find the cost of admission for a group of 2 people, we will substitute P = 2 into the function:
C(2) = 25 * 2
C(2) = 50
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How much fluid would a 19 kg dog receive in 10 hours if fluid was given at a rate of 40 mL/kg/day?
A. 316.7 mL
B. 760 mL
C. 31.6 mL
D. 76 mL
Answer:
76 mL
Step-by-step explanation:
40*19/10
40*19= 760 / 10 = 76mL
the correct answer is A. 316.7 mL.
The question involves calculating the fluid volume that a 19 kg dog would receive if fluids were administered at a rate of 40 mL/kg/day. Here is the step-by-step calculation:
First, we calculate the daily fluid requirement for the dog by multiplying the dog's weight by the rate of fluid administration: 19 kg × 40 mL/kg/day = 760 mL/day.Next, since we need to find out how much fluid the dog would receive in 10 hours, we need to determine what fraction of the day 10 hours is. There are 24 hours in a day, so 10 hours is 10/24th of a day.Finally, we calculate the volume of fluid for 10 hours by multiplying the daily fluid requirement by the fraction of the day: 760 mL/day × (10 hours / 24 hours) = 316.7 mL (rounded to one decimal place).Therefore, the correct answer is A. 316.7 mL.
The circumference of a circle is 8pi cm. what is the diameter?
Answer:
8 cm
Step-by-step explanation:
The circumference (C) of a circle is
C = π d ← d is the diameter
Here C = 8π, hence
πd = 8π ( divide both sides by π )
d = [tex]\frac{8\pi }{\pi }[/tex] = 8 cm
A circle is a curve sketched out by a point moving in a plane. The diameter of the circle whose circumference is 8π cm is 8cm.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.
The circumference of a circle is given by πD, where D is the diameter. Now, the circumference can be written as,
Circumference of the circle = πD
8π cm = πD cm
D = 8 cm
Hence, the diameter of the circle whose circumference is 8π cm is 8cm.
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Bismuth-212 has a half-life of 60.5 minutes. Find the amount of bismuth-212 left from a 100-gram sample after 242 minutes
Notice that 242 = 4*60.5. This means after 242 minutes, the sample decays to [tex]\dfrac1{2^4}=\dfrac1{16}[/tex] of its original amount. So you end up with
[tex]\dfrac{100\,\mathrm g}{16}=\boxed{6.25\,\mathrm g}[/tex]
After 242 minutes, 6.25 grams of Bismuth-212 remain from an original 100-gram sample, calculated based on its half-life of 60.5 minutes through the concept of radioactive decay.
The question involves calculating the amount of Bismuth-212 left from a 100-gram sample after 242 minutes, given its half-life of 60.5 minutes. To find the amount of Bismuth-212 remaining, we use the formula for radioactive decay which involves dividing the total time by the half-life to determine the number of half-lives that have passed.
First, calculate the number of half-lives passed:
Number of half-lives = Total time / Half-life = 242 minutes / 60.5 minutes = 4
Next, calculate the remaining amount after each half-life. After 1 half-life, 50 grams remain; after 2 half-lives, 25 grams; after 3 half-lives, 12.5 grams; and after 4 half-lives, 6.25 grams remain.
Therefore, 6.25 grams of Bismuth-212 remains after 242 minutes.
With which information can you construct a unique rhombus?
A.
measurements of all angles
B.
measurements of any two angles
C.
measurement of one angle and length of one side
D.
lengths of any two sides
I believe it would be C
Answer:
C. measurement of one angle and length of one side.
Step-by-step explanation:
A rhombus is a parallelogram with four sides of equal length and two different pairs of angles. Hence, the measurement of one angle and length of one side is need to construct a rhombus. The right answer is C.
What is the answer to this?
Answer:
8[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Rationalise the denominator by multiplying both the numerator and denominator by the radical on the denominator, that is
[tex]\frac{32}{\sqrt{8} }[/tex]
= [tex]\frac{32\sqrt{8} }{8 }[/tex] → ([tex]\sqrt{8}[/tex])² = 8
= [tex]\frac{32\sqrt{4(2)} }{8}[/tex]
= 4× 2[tex]\sqrt{2}[/tex]
= 8[tex]\sqrt{2}[/tex]
A hiker is making his way up a mountain. After resting for a night, he travels with a group toward the top of the mountain
Answer:
For the graph, 111 is the: y-intercept
In the situation, it represents the hiker's: starting distance
11 is the: slope
It represents the hiker's: speed
Hope this helped C:
The question pertains to the physics of a hiker ascending and descending a mountain, considering potential energy changes and work done by the hiker. The scenario's analysis includes calculations of potential energy at various altitudes relative to sea level, given the hiker's mass.
Explanation:Understanding the Physics of Hiking Up a MountainThe scenario involves a hiker ascending and descending a mountain, which can be analyzed from a physics perspective, particularly focusing on potential energy, work, and energy conservation. The hiker's journey begins at 200 m above sea level, progresses to an overnight hut at 800 m, descends to another hut at 500 m, and finally returns to the starting point. The mass of the hiker is given as 70 kg.
When the hiker ascends to a height of 800 m, she gains potential energy, which can be calculated using the formula Potential Energy (PE) = mass (m) × gravity (g) × height (h). Therefore, the increase in potential energy when reaching the first hut is:
PE = 70 kg × 9.8 m/s2 × (800 m - 200 m)
Similarly, when descending to the second hut, the hiker loses some potential energy. Finally, upon returning to the starting point, the hiker's potential energy returns to its initial value, assuming the starting point is the reference level of potential energy.
The exercise involved in hiking up and down the mountain also involves work done against the force of gravity and could be discussed in terms of energy expended by the hiker.
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Using Cramer's rule to solve linear systems.
Answer: Last Option
[tex]x=2,\ y=-5[/tex]
Step-by-step explanation:
Cramer's rule says that given a system of equations of two variables x and y then:
[tex]x =\frac{Det(A_X)}{Det(A)}[/tex]
[tex]y =\frac{Det(A_Y)}{Det(A)}[/tex]
For this problem we know that:
[tex]Det(A) = |A|=\left|\begin{array}{ccc}4&-6\\8&-2\\\end{array}\right|[/tex]
Solving we have:
[tex]|A|= 4*(-2) -(-6)*8\\\\|A|=40[/tex]
[tex]Det(A_X) = |A_X|=\left|\begin{array}{ccc}38&-6\\26&-2\\\end{array}\right|[/tex]
Solving we have:
[tex]|A_X|=38*(-2) - (-6)*26\\\\|A_X|=80[/tex]
[tex]Det(A_Y) = |A_Y|=\left|\begin{array}{ccc}4&38\\8&26\\\end{array}\right|[/tex]
Solving we have:
[tex]|A_Y|=4*(26) - (38)*8\\\\|A_Y|=-200[/tex]
Finally
[tex]x =\frac{|A_X|}{|A|} = \frac{80}{40}\\\\x=2[/tex]
[tex]y =\frac{|A_Y|}{|A|} = \frac{-200}{40}\\\\y=-5[/tex]
The side length of a square is represented by the expression n - 1.5. Which are equivalent expressions for the perimeter of the square?
A
n + n + n + n - 1.5 - 1.5 - 1.5 - 1.5
B
2(n - 1.5) + 2(n - 1.5)
C
2n - 1.5
D
4n - 1.5
E
2(n - 1.5)
F
4(n - 1.5)
Answer:
A
Step-by-step explanation:
That the answer Plss follow me thanks
The equivalent expressions for the perimeter of a square whose side length is represented by the expression n -1.5 are A and F, specifically: n + n + n + n - 1.5 - 1.5 - 1.5 - 1.5 and 4(n - 1.5)
Explanation:The length of a side of a square is given by the expression n - 1.5. The perimeter of a square is calculated by adding up all its four sides. Hence, in this case, the perimeter would be (n - 1.5) + (n - 1.5) + (n - 1.5) + (n - 1.5). Perform the addition to get 4n - 6, simplifying to 4(n - 1.5). From the provided options, the equivalent expressions for the perimeter of the square are A and F, that is, n + n + n + n - 1.5 - 1.5 - 1.5 - 1.5 and 4(n - 1.5).
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In geometry, what’s the difference between a postulate and a theorem? Give an example of each
Answer:
Step-by-step explanation:
This is a course specific question. What I think is a postulate may not be listed in your lesson. A postulate is a statement that is assumed to be true. There has not been an exception found in over 2000 years. A postulate does not require proof: its truth is accepted.
Example: Two points on the same plane have exactly 1 line that can go through them.
Theorem: using the postulates to begin with, a theorem is a statement that can (and should) be proved.
Example: Two lines that are on the same plane, if they intersect at all, intersect only once.
a^2 + b^2 = c^2
This well known theorem can be proved well over 100 ways.
In geometry, a postulate is an accepted statement without proof that serves as a fundamental assumption, while a theorem is a proven statement based on previously established postulates, theorems, and definitions.
An example of a postulate is the "Parallel Postulate," and an example of a theorem is the "Pythagorean Theorem."
To find the difference between a postulate and a theorem
Now,
A postulate is a statement that is accepted without proof and serves as a fundamental assumption. It provides the basis for building geometric reasoning.
An example of a postulate is the "Parallel Postulate," which states that if a line intersects two other lines forming congruent alternate interior angles, then the two lines are parallel.
On the other hand, a theorem is a statement that has been proven based on previously established postulates, theorems, and definitions.
An example of a theorem is the "Pythagorean Theorem," which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
So, while postulates are accepted as true without proof, theorems are derived from logical deductions and require proof.
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The blueprints for a police station show that one of the lamp posts has a motion detector on it, and that the equation (x+14)2+(y−6)2=9 describes the boundary within which motion can be sensed. What is the greatest distance, in feet, a person could be from the lamp and be detected?
3 ft
6 ft
9 ft
81 ft
Answer: The greatest distance, in feet is the first one 3ft.
Answer: 3 feet
Step-by-step explanation:
Given: The blueprints for a police station show that one of the lamp posts has a motion detector on it, and that the equation describes the boundary within which motion can be sensed. :
[tex](x+14)^2+(y-6)^2=9[/tex] → which is a equation of a CIRCLE.
When we compare it to the standard form of equation of circle i.e. [tex](x-(-14))^2+(y-6)^2=3^2[/tex] , we get the radius of the circle = 3
Consider the lamp post as the center of the area covered by the detector.
Then the greatest distance a person could be from the lamp and be detected = Radius of the circular area
=3 feet.
Help me find the lateral and the surface area I have to round to the nearest tenths if necessary
Answer:
L.A. = 384 cm²S.A. = 640 cm²Step-by-step explanation:
We have four congruent triangles with base b = 16cm and height h = 12cm.
The formula of an area of a triangle:
[tex]A=\dfrac{bh}{2}[/tex]
Substitute:
[tex]A=\dfrac{(16)(12)}{2}=(8)(12)=96\ cm^2[/tex]
The latearal area:
[tex]L.A.=4A\to L.A.=4(96)=384\ cm^2[/tex]
For the surface area we need the area of a base.
The base is a square with side a = 16cm.
The area of the base:
[tex]B=16^2=256\ cm^2[/tex]
The surface area:
[tex]S.A.=L.A.+B\to S.A.=384+256=640\ cm^2[/tex]
what is 25 1/2 × 5 –3 = 5 x
Answer:
249/10 = x, or x = 24.9
Step-by-step explanation:
25 1/2 × 5 –3 = 5 x should be written as 25 1/2 × 5 –3 = 5x
The goal here is to solve for x (you should state this specifically).
Start by multiplying 25 1/2 by 5, since we must multiply before addition or subtraction:
One way of doing this multiplication is to multiply 25 by 5 and then 1/2 by 5 and then summing up the results:
25×5 = 125, and 1/2 × 5 = 5/2, so the end result is:
125 + 5/2, or 125 + 2 1/2, or 127 1/2.
Next, subtract 3 from this result:
127 1/2 - 3 = 124 1/2
Then 124 1/2 = 5x. Solve for x. Converting 124 1/2 into an improper fraction:
249/2 = 5x. Dividing both sides by 5, we get:
249/10 = x, or x = 24.9
I gave my brother 1/5 of my candy, 1/4 to my friend and had 11 pieces left over. How many pieces did I give my brother?
x = total number of candies
[tex]\bf \stackrel{\textit{my brother}}{\cfrac{1}{5}x}+\stackrel{\textit{my friend}}{\cfrac{1}{4}x}+11~~=~~\stackrel{\textit{total}}{x} \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{20}}{20\left( \cfrac{x}{5}+\cfrac{x}{4}+11 \right)=20(x)}\implies 4x+5x+220=20x\implies 9x+220=20x \\\\\\ 220=11x\implies \cfrac{220}{11}=x\implies 20=x~\hspace{10em}\stackrel{\textit{to my brother}}{\cfrac{20}{5}\implies 4}[/tex]
Write an expression to describe the sequence 35, 36, 37.....
Answer:
Step-by-step explanation:
start with 35 and add 1 repeatedly.
y=x+1 for ex, y= 35+ 1 and so on
Sketch of the net of each solid. Label the measurements given.
Answer:
14 in
Step-by-step explanation:
Does it want me to explain what the in.cm,mm,m are or what id it in its
The net of cube has 6 identical squares with side 14 units.
What is a net diagram?Net diagram is a 2-dimensional plane figure which can be folded to form a 3-dimensional figure. Or we can say net diagrams are the figures which obtained by unfolding some 3D figures.
Given that, the cube with edges 14 units.
A solid shape with six square faces is called a cube. Because every square face has the same side length, each face is the same size. A cube has 8 vertices and 12 edges. An intersection of three cube edges is referred to as a vertex.
The net of cube has 6 squares
Therefore, the net of cube has 6 identical squares with side 14 units.
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the gas tax in our town is 23 cents per gallon . if you buy 20 gallons of gas , how much tax do you pay?
Answer:
$4.60
Step-by-step explanation:
To find the amount of tax, multiply the number of gallons by the tax per gallon.
20*.23 = $4.60
A right rectangular pyramid is sliced through its vertex and perpendicular to its base as shown in the figure. What is the shape of the resulting two-dimensional cross section? Select from the drop-down menu to correctly complete the statement. The shape of the resulting two-dimensional cross section is a . A right rectangular pyramid. A plane perpendicular to the base passes through the prism.
The shape of the resulting two-dimensional cross section is a . A right rectangular pyramid.
What is trapezoid?The trapezoid is a quadrilateral with one pair of opposite sides that are parallel. These are sometimes classified as having at most one pair of opposite sides parallel, and sometimes as containing one pair of different sides parallel.
This trapezoid limits the goaltender's ability to play the puck by giving them a small amount of space behind the goal line.
It was trapezoidal when we slice the pyramid, we obtain two shapes: a triangle and a trapezoid.
Trapezoidal is the appropriate two-dimensional shape.
Which shape is a cross section of a rectangular pyramid?a triangle
A rectangular pyramid can have several different types of cross sections. The cross section of a pyramid that is perpendicular to the base will be a triangle. The cross section of a pyramid that is parallel to the base will be a smaller version of the baseTo learn more about trapezoid, refer
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The resulting two-dimensional cross section of a right rectangular pyramid sliced through its vertex and perpendicular to its base is a triangle.
Explanation:The shape of the resulting two-dimensional cross section is a triangle.
When a right rectangular pyramid is sliced through its vertex and perpendicular to its base, the resulting cross section will be a triangle. This is because the cut passes through the top vertex of the pyramid and intersects all the edges of the base, forming a triangle shape.
For example, if the base of the pyramid is a rectangle, the resulting cross section will be an isosceles triangle with its top vertex at the center of the rectangle's longer side.
PLEASE HELP ASAPPPPPPPPPPPPPi
Answer:
I think it is a but it is hard to see
Step-by-step explanation:
Answer:
the first option
Step-by-step explanation:
Given the triangle is right, then use Pythagoras' theorem
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.
The hypotenuse is 5, hence
5² = 4² + b² OR 4² + b² = 5²
the average score for a biology test is 77 and the standard deviation is 8. which percent best represents the probability that any student scored between 61 and 93 on the test?
Using the Empirical Rule, it is found that the percent best represents the probability that any student scored between 61 and 93 on the test is of:
B. 95%.
What is the Empirical Rule?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.In this problem, the mean is of 77 while the standard deviation is of 8, hence scores between 61 and 93 are exactly 2 standard deviations from the mean, hence 95% of the students scored in this range, and option B is correct.
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what is the y value when x equals 21? y=310-25(x)
Answer:
Step-by-step explanation:
You subtract 310 from 25 and get 285 then you multiply 285 x 21 and I believe that should solve this equation.
To find the value of 'y' when 'x' equals 21 in this equation, we substitute 21 for 'x', perform the multiplication 25*21 first, and then subtract this result from 310, yielding a 'y' value of -215.
Explanation:This question pertains to the mathematical equation y=310-25x. To find the value of 'y' when 'x' equals 21, we simply substitute 21 for 'x' in the equation. So, y = 310 - 25*(21). Multiplication happens first (due to the order of operations), yielding 525. When you subtract this from 310 (310-525), you get -215. Therefore, the value of 'y' when 'x' is 21 in this equation is -215.
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Franco is adjusting a satellite because he finds it is not focusing the incoming radio waves perfectly. The shape of his satellite can be modeled by y^2+6y-3x+3=0, where x and y are modeled in inches. He realizes that the static is a result of the feed antenna shifting slightly off the focus point. What is the focus point of the satellite?
Answer:
focus point of satellite is (-125,-3)
Step-by-step explanation:
The question is on finding the focus point of a parabola
Given y²+6y-3x+3=0
Rewrite the equation
y²+6y=3x-3
Complete square on both sides
y²+6y+9=3x-3+9
Factorize
(y+3)²= 3x+6---------------------------------------(a)
(y+3)²= 3(x+2)
Compare equation (a) to standard equations for parabola
(y+3)²= 3(x+2)
(y-b) ²= 2p(x-a),,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,(b)
2p=3------------divide both sides by 2
p=3/2
Vertex (a,b)=( -2,-3)........from equation (b)
Focus point is given by (a+p/2 , b)...........................(c)
Substitute values in equation c above;
(-2+3/4 , -3) = (-5/4 ,-3) =(-1.25, -3)
P(1, 10)and Q(7,4) are the endpoints of a line segment. What is the midpoint M of that line segment
Answer:
(4, 7)
Step-by-step explanation:
The midpoint formula is (((x1 + x2)/2), ((y1+y2)/2)))
x1 +x2 = 1 +7 = 8
8/2 = 4
y1 + y2 = 10 + 4 = 14
14/2 = 7
(4, 7) is the midpoint
Answer:
M = (4, 7)
Step-by-step explanation:
Using the midpoint formula
M = [[tex]\frac{1}{2}[/tex](x₁ + x₂ ), [tex]\frac{1}{2}[/tex](y₁ + y₂ ) ]
with (x₁, y₁ ) = P(1, 10) and (x₂, y₂ ) = Q(7, 4)
M = [ [tex]\frac{1}{2}[/tex](1 + 7), [tex]\frac{1}{2}[/tex](10 + 4) ] = (4, 7)
Solve the equation
-3 2/3+b = 8 1/5
B= 5 3/5
B= 4 4/5
B= 11 3/5
B= 11 1/5
Answer:
11 13/15
Step-by-step explanation:
-3 2/3+b = 8 1/5
Add 3 2/3 to each side
-3 2/3 + 3 2/3+b = 8 1/5+ 3 2/3
b = 8 1/5 + 3 2/3
We need to get a common denominator of 15
8 1/5 = 8 3/15
3 2/3 = 3 10/15
----------------
11 13/15
Needd help please and thank you!! It’s 1/E just in case you couldn’t see that! Thx!
Answer:
option A
The base is e^-1
Step-by-step explanation:
Given in the question a function, f(x) = (1/e)[tex]^{x}[/tex]
This function can also be write as.
f(x) =[tex](e^{-1})^{x}[/tex]
by using Negative Exponent Rule
[tex]x^{-n}=\frac{1}{x^{n}}[/tex]
This says that negative exponents in the numerator get moved to the denominator and become positive exponents.
359, 357, 348, 347, 337, 347, 340, 335, 338, 348, 339, 356, 336, 358 a. median: 359 mode: 358 c. median: 347 mode: 347 AND 348 b. median: 340 mode: 350 d. median: 358 mode: 348
Answer:
Option C (Median: 347 and Mode: 347 and 348)
Step-by-step explanation:
Median is the middle point of the data and mode is the most repeated observation is the data. The first step involved in calculating the median it to list the observations in the ascending order. This gives:
335, 336, 337, 338, 339, 340, 347, 347, 348, 348, 356, 357, 358, 359
The second step is to identify the middle number (in case the observations are in odd numbers) or numbers (in case the observations are in even numbers) after the ascending order step has been done. It can be observed that the middle numbers in this data set are 347 and 347. Since there are two numbers, so their average will be the median of this data set. Therefore, the median is 347. It can be seen that maximum repetitions are 2 times for 347 and 348. So the mode is 347 and 348.
Therefore, Option C is the correct answer!!!
The correct option is c: Median: 347, Mode: 347 AND 348. This is determined by sorting the numbers and finding that 347 is the median and both 347 and 348 are the modes.
This question involves identifying measures of central tendency, specifically the median and the mode, from a list of numbers.
Option a: Median: 359, Mode: 358Option b: Median: 340, Mode: 350Option c: Median: 347, Mode: 347 AND 348Option d: Median: 358, Mode: 348To determine the correct answer, we proceed step-by-step to calculate the median and mode from the provided sequence: 359, 357, 348, 347, 337, 347, 340, 335, 338, 348, 339, 356, 336, 358.
Step 1: Sorting the List
The sorted list is: 335, 336, 337, 338, 339, 340, 347, 347, 348, 348, 356, 357, 358, 359
Step 2: Finding the Median
The median is the middle value of a sorted list. For a list of 14 numbers, it is the average of the 7th and 8th values:
Median = (347 + 347) / 2 = 347
Step 3: Finding the Mode
The mode is the number that appears most frequently. Here, 347 and 348 each appear twice.
Mode = 347 and 348
Based on these calculations, the correct option is Option c: Median: 347, Mode: 347 AND 348.
solve the inequality
Answer:
[tex]\large\boxed{x>-25}[/tex]
Step-by-step explanation:
[tex]-\dfrac{3}{10}x-7<\dfrac{1}{2}\qquad\text{multiply both sides by 10}\\\\10\!\!\!\!\!\diagup^1\cdot\left(-\dfrac{3}{10\!\!\!\!\!\diagup_1}x\right)-(10)(7)<10\!\!\!\!\!\diagup^5\cdot\dfrac{1}{2\!\!\!\!\diagup_1}\\\\-3x-70<5\qquad\text{add 70 to both sides}\\\\-3x<75\qquad\text{change the signs}\\\\3x>-75\qquad\text{divide both sides by 3}\\\\x>-25[/tex]
Find the measure of arc BDC
The whole circle is 360 degrees. So cut the circle in half and BDC=180
To find the measure of arc BDC, use the triangulation measurements and the angular displacements ZBOC and ZDOC. Apply geometric principles and the law of sines, then relate the arc's angle to the circle's circumference to approximate the arc measure.
Explanation:To find the measure of arc BDC, we must consider the geometrical properties of circles and triangles mentioned in the provided information. Since the arc length for a small part of the circle can be approximated as equal to the straight-line segment, we can use this approximation along with the given relationships to solve for the arc BDC measurement.
First, establish a second control point (B) in a triangulation network and measure the interior angles at points A, B, and C. The 'law of sines' can be used to determine lengths of the sides of the triangles formed. Once you have the lengths AC and BC, you can measure CD and BD to fix point D in a coordinate system.
This geometric consideration allows us to construct right triangles and use the Pythagorean theorem to find missing lengths. To calculate the measure of arc BDC, we can add the displacement angles (ZBOC and ZDOC) which can be found by using the angular displacement values between 2 and 2.5 seconds, and between 2.5 and 3 seconds. Using these angles and the lengths of segments BC, CD, and BD, we can apply the principle that in a circle, the ratio of the arc's length to the circumference is equal to the ratio of the angle to 360 degrees.
what is the value of [-4.6]
The value is:
-4
Step-by-step explanation:We are asked to find the value of the ceiling function: [tex]\left \lceil -4.6 \right \rceil[/tex]
As we know that the ceiling function always occupy the higher value in integers.
i.e. the ceiling function act as follows:
it takes value 0 when -1< x≤0
1 when 0 < x ≤ 1
2 when 1 < x ≤2
and so on.
As we know that:
-4.6 lie between -5 and -4.
Hence, we have:
[tex]\left \lceil -4.6 \right \rceil=-4[/tex]
Answer: -4
Step-by-step explanation:
The ceiling function (also known as the least integer function) is written as
[tex]f(x) = [x][/tex]
It gives the smallest integer greater than or equal to x .
For example : [5.6]=6
or [-1.9]= -1 [∵- 1 > -1.9 ]
To find : The value of [-4.6]
Clearly , [-4.6] is written in ceiling function notation.
Then, [-4.6] = smallest integer greater than or equal to -4.6
= -4 [∵ -4>-4.6]
Hence, the value of [-4.6] = -4
Factor each trinomial n^2+9n+20
Answer:
(n+4)(n+5)
Step-by-step explanation:
Answer:
(n + 4)(n + 5)
Step-by-step explanation:
to factor n² + 9n + 20, we need to find 2 numbers that when multiplied together equal 20 and when added together equal 9
these two numbers are 4 and 5 so the factorization looks like this:
(n + 4)(n + 5) < you can FOIL this out to check if the solution is correct, and you would get: n² + 9n + 20
what two- dimensional shape is formed by a cross section of the cube shown if the cross section passes through the midpoints of three edges that intersect at the same vertics of the cube A= scalene triangle B= square C= equilateral triangle D = rectangle
C= equilateral triangle
Step-by-step explanation:To find this answer we need to know what a cube is. A cube is a prism whose sides all have the same length. It's something like the three dimensional version of a square. In the figure below, we have labeled each length of the cube as [tex]x[/tex]. Also, the vertex we taken is in blue color, so we need to find each side length of the triangle. Since the cross section passes through the midpoints of three edges that intersect at the same vertices of the cube, then:
[tex]L_{1}=\sqrt{(\frac{x}{2})^2+(\frac{x}{2})^2} \\ \\ L_{1}=\sqrt{\frac{x^2}{4}+\frac{x^2}{4}} \\ \\ L_{1}=\sqrt{\frac{2x^2}{4}} \\ \\ L_{1}=\sqrt{\frac{x^2}{2}} \\ \\ L_{1}=\frac{x}{\sqrt{2}} \\ \\ L_{1}=\frac{x}{\sqrt{2}}\frac{\sqrt{2}}{\sqrt{2}} \\ \\ L_{1}=\frac{\sqrt{2}x}{2}[/tex]
Since this is a cube, then it is true that:
[tex]L_{1}=L_{2}=L_{3}=\frac{\sqrt{2}x}{2}[/tex]
Since the side lengths have the same value, this is an equilateral triangle.