Answer:
Let's call the speed of Bug F v_F and the speed of Bug S v_S. Since both bugs started at 0, we can express their positions at any time t as:
Position of Bug F = 12 + v_F * t
Position of Bug S = 8 + v_S * t
To find out when F and S will be 100 units apart, we need to find the time t at which their positions differ by 100 units. In other words, we need to solve the following equation:
|12 + v_F * t - (8 + v_S * t)| = 100
We can simplify this equation by expanding the absolute value and rearranging the terms:
|4 + (v_F - v_S) * t| = 100
Now we can split this equation into two cases:
Case 1: 4 + (v_F - v_S) * t = 100
In this case, we have:
v_F - v_S > 0 (since Bug F is faster)
t = (100 - 4) / (v_F - v_S)
Case 2: 4 + (v_F - v_S) * t = -100
In this case, we have:
v_F - v_S < 0 (since Bug S is faster)
t = (-100 - 4) / (v_F - v_S)
Since we're only interested in positive values of t, we can discard the second case. Therefore, the time at which F and S will be 100 units apart is:
t = (100 - 4) / (v_F - v_S)
t = 96 / (v_F - v_S)
We don't know the values of v_F and v_S, but we can use the fact that Bug F is at 12 and Bug S is at 8, four seconds after they started. This gives us two equations:
12 = 4v_F + 0v_S
8 = 4v_S + 0v_F
Solving these equations for v_F and v_S, we get:
v_F = 3
v_S = 2
Substituting these values into the equation for t, we get:
t = 96 / (3 - 2)
t = 96
Therefore, F and S will be 100 units apart 96 seconds after they start.
Jason studied how quickly ants consume things. He counted the number of ants on a banana peel at the end of each minute for five minutes. His results formed the pattern below.
12, 19, 26, 33, 40
Let n represent the number of minutes since Jason began his study. Which expression could be used to predict the number of ants on the banana peel after n minutes?
5+7n
7+5n
12n
7n
The expression that could be used to predict the number of ants on the banana peel after n minutes is given as follows:
5 + 7n.
What is an arithmetic sequence?An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant, being called common difference d.
The nth term of an arithmetic sequence is given by the explicit formula presented as follows:
[tex]a_n = a_1 + (n - 1)d[/tex]
In this problem, the difference between consecutive terms is of 7, meaning that it represents an arithmetic sequence with a common difference of 7.
The first term is of 12, hence we obtained the explicit formula as follows:
12 + 7(n - 1) = 12 + 7n - 7 = 5 + 7n.
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Write an equivalent expression.
(x+7)+2
Answer:
The answer is x+9, I really hope this helps (:
The latus rectum of the parabola with the equation 2y^2 - 15x - 4y - 28 = 0 is
15
15/2
15/4
Answer: 15/2
Step-by-step explanation: Im doing this lesson right now and I looked up the answer on a math calculator online its called emathhelp.net and it gave me 15/2
What is an equation for the linear relationship in slope-intercept form?
A. y=2x+3
B. y=12x+3
C. y=12x−3
D. y=−12x−3
A: y=2x+3. This is an equation for the linear relationship in slope-intercept form. The equation states that the value of y is equal to the slope of the line, 2, multiplied by the value of x, plus 3.
What is slope?Slope is a measure of the steepness of a line. It is the ratio between the vertical change in a line (change in y-values) over the horizontal change in the same line (change in x-values). It is also referred to as the rate of change, as it is a measure of how quickly the value of y changes with respect to the x-value.
This equation is used to describe a straight line that has a constant rate of change between two variables. This equation can be used to determine the slope, y-intercept, and x-intercept of a line.
The slope, which is the coefficient of x in the equation (2 in this case), is the rate at which y changes with respect to x. It is the rise over run, or the change in y over the change in x. The y-intercept is the value of y when x is equal to 0 (in this case, it is 3). The x-intercept is the value of x when y is equal to 0 (in this case, it is -3/2).
This equation is often used to represent a linear relationship between two variables, such as the amount of money a person earns in relation to the number of hours they work.
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Factor.
f(x) = 6x^2 - 7x+2
Answer: f(x)=(2x−1)(3x−2)
Step-by-step explanation:
Answer:
Step-by-step explanation:
(2x−1)(3x−2)
Mr. Jonas's aquarium holds 8 gallons
of water. If he buys another that
holds 1½ times as many gallons,
how many gallons of water does
Mr. Jonas's new tank hold?
Find the length indicated.
7) Find FG
E
2x+1
F
16
2x+3
G
Please help i need it!!!
Which has more kinetic energy, a 5 kg rock hitting a car at 25 m/s or a 10 kg rock hitting a car at 15 m/s? Use the formula kinetic energy = (½)mv². Show your work using the graphical equation tool (Σ button in the toolbar above the text box).
Answer:
Σ Kinetic energy of 5 kg rock hitting car > Σ Kinetic energy of 10 kg rock hitting car
Step-by-step explanation:
We can use the formula for kinetic energy, which is:
Kinetic energy = (1/2) x mass x velocity^2
Let's start by calculating the kinetic energy of the 5 kg rock hitting the car at 25 m/s:
Kinetic energy = (1/2) x 5 kg x (25 m/s)^2
Kinetic energy = 1562.5 J
Now let's calculate the kinetic energy of the 10 kg rock hitting the car at 15 m/s:
Kinetic energy = (1/2) x 10 kg x (15 m/s)^2
Kinetic energy = 1125 J
Therefore, the 5 kg rock hitting the car at 25 m/s has more kinetic energy than the 10 kg rock hitting the car at 15 m/s.
We can represent this visually using the following equations:
Kinetic energy of 5 kg rock hitting car = (1/2) x 5 kg x (25 m/s)^2 = 1562.5 J
Kinetic energy of 10 kg rock hitting car = (1/2) x 10 kg x (15 m/s)^2 = 1125 J
Σ Kinetic energy of 5 kg rock hitting car > Σ Kinetic energy of 10 kg rock hitting car
CAN SOMEONE HELP WITH THIS QUESTION?
The rate of change of the area outside the circle but inside the square is 1 m² per minute.
What is area?Area is the measure of the size of a two-dimensional (2D) shape or planar region. It is expressed in terms of square units, such as square metres (m2) and square feet (ft2). The area of a shape is the total space contained within its boundaries.
To answer this question, we need to find out the area outside the circle but inside the square. This can be done by subtracting the area of the circle from the area of the square.
The area of the circle is equal to πr², where r is the radius of the circle. In this case, the radius is 3 meters, so the area of the circle is π×32 = 28.27 m².
The rate of change of the area outside the circle but inside the square is 1 m²per minute.
The area of the square is equal to side², where side is the length of one side of the square. In this case, the side is 16 meters, so the area of the square is 162 = 256 m².
Subtracting the area of the circle from the area of the square gives us the area outside the circle but inside the square. This is 256 - 28.27 = 227.73 m².
Now, we know the area outside the circle but inside the square, and we know that the radius of the circle is increasing at a rate of 1 meter per minute and the sides of the square are increasing at a rate of 2 meters per minute. This means that the area outside the circle but inside the square is increasing at a rate of (2 - 1) = 1 m²per minute.
Therefore, the rate of change of the area outside the circle but inside the square is 1 m² per minute.
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Who knows this? I need help
#16
Answer:
Step-by-step explanation:
adjacent: [tex]\angle BOC, \angle EOD[/tex] (both are adjacent)
complementary: [tex]\angle BOC[/tex]
supplementary: [tex]\angle EOD[/tex]
vertical angles: [tex]\angle AOE[/tex]
I have five people that can move 12 crates in an hour, how many people do I need to move 60to create in an hour, assuming that the rate of work is the same?
Answer:
Below
Step-by-step explanation:
You need to move 5 times as many crates in the same amount of time....so you will need 5 times as many people = 25 people
(-8)-(-2) porfa lo necesito
Answer:
-6
Step-by-step explanation:
Can anyone solve the following two maths?
In conclusion the team took 50 strokes to complete the final 500 meters of the race and at the end of the season, the team's mean split time should be 99 seconds.
How to find?
To find the answer to question 37, we know that the team rowed the final 500 meters in 108 seconds. We also know that they rowed at a rate of 28 strokes per minute during this split. To find out how many strokes they took to complete the final 500 meters, we need to convert the split time to minutes and then multiply by the stroke rate.
First, we convert the split time to minutes:
108 seconds ÷ 60 seconds per minute = 1.8 minutes
Then, we multiply by the stroke rate to find the total number of strokes:
1.8 minutes x 28 strokes per minute ≈ 50 strokes
Therefore, to the nearest whole number, the team took 50 strokes to complete the final 500 meters of the race.
To find the answer to question 38, we need to find the team's mean split time and then reduce it by 10%. The mean split time is found by taking the total race time and dividing by 4, since there are 4 splits in the race.
Total race time = 440 seconds
Mean split time = Total race time ÷ 4 = 110 seconds
To reduce the mean split time by 10%, we multiply it by 0.9:
New mean split time = 110 seconds x 0.9 = 99 seconds
Therefore, at the end of the season, the team's mean split time should be 99 seconds.
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The table shows the data of a random sample of fish that were collected from and later released into a lake.
Type of Fish Bass Eel Gar
Number of Fish 92 56 52
How many eels are estimated to be present if a sample of 1,000 fish is collected from the lake? (1 point)
a
112
b
280
c
320
d
380
Answer: d
Step-by-step explanation: its d
Kevin drove 18 1/2 miles in 2/3 hours. If he drove at a constant rate, how far did he travel in one hour
Answer:
27.75 miles
Step-by-step explanation:
(18 1/2 miles) / (2/3 hours) = (37/2 miles) × (3/(2 hours)) = 111/4 miles/hour
111/4 miles/hour = 27.75 miles/hour
Answer: 27.75 miles
PLEASE HELP ASAP ITS DUE IN AN HOUR
Answer:
[tex]3^2-5[/tex]
Step-by-step explanation:
Given equation:
( 3 - 2^2) + 5
3 - 4 + 5 (Simplify exponent)
-1 + 5 (Solve 3 - 4)
4 (Simplified)
Evaluation
2^2 + 5
4 + 5
9 (not the answer)
3^2 - 5
9-5
4 (answer)
3. Assume that there are only 2 commodities and that the utility function is multiplication of the form U = 1÷4qxqy.Find the demand function of the commodity x and y and explain the relationship between price and income in relation to the demand.
Answer:
Step-by-step explanation:
Pls answer today and fast!!!! Use the tools below to make a triangle with angle measures or 60 degrees, 40 degrees, and 80 degrees.
An angle is a geometric figure formed by two rays or line segments that share a common endpoint, called the vertex. Angles are measured in degrees or radians and are typically denoted by symbol ∠ followed by the name of the vertex, like ∠ABC.
What is the Angle?The size of angle is determined by amount of rotation needed to bring one of rays or line segments into coincidence with others.
Angles can be acute (less than 90 degrees), right (exactly 90 degrees), obtuse (greater than 90 degrees but less than 180 degrees), straight (exactly 180 degrees), or reflex (greater than 180 degrees).
Angles are fundamental to geometry and have many applications in physics, engineering, and other fields.
This is because the sum of the angles in a triangle must always be 180°, and 40° + 60° + 80° = 180°.
However, the angles do not satisfy the conditions of the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Therefore, It is not possible to construct a triangle with angle measures of 40°, 60°, and 80°.
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Find the value of each variable.
The values of the variables in the semicircle shown are:
x = 63 degrees; y = 90 degrees.
What is the Angle Inscribed in a Semicircle Theorem?A semi-circle is exactly half of a full circle and has a measurement of 180 degrees; the two endpoints of the diameter form the endpoints of the semi-circle. If an angle is enclosed inside a semi-circle, the angle formed measures 90 degrees.
Therefore, it means the value of the variable, y = 90 degrees.
Thus, using the triangle sum theorem, we have:
x = 180 - 90 - 27
x = 63 degrees.
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Find the volume of a cone with a radius of 4 ½ m. and a height of 10 m.
The volume of the cone is approximately 211.06 cubic meters.
Why is that?
Well, the formula for the volume of a cone is:
V = (1/3)πr^2h
where:
Substituting the given values, we get:V = (1/3)π(4.5m)^2(10m)
V = (1/3)π(20.25m^2)(10m)
V = (1/3)π(202.5m^3)
V = 67.5π
Using a calculator, we get:
V ≈ 211.06 cubic meters
Therefore, the volume of the cone is approximately 211.06 cubic meters.
6 7 2 4 6 6 9 5 3 3
Work out the median.
Answer:
5.5
Step-by-step explanation:
The median is the middle number in an ordered ascending/descending list.
The first step is to order the list. In this case I chose to do so in ascending order.
This gets you:
2 3 3 4 5 6 6 6 7 9
In this case there is an even amount of numbers, which means there will be 2 central numbers, 5 and 6.
Averaging these two numbers will get you the median.
(5+6) / 2 = 5.5
pls help i dont get this one
Answer:
f(-2) = 0
Step-by-step explanation:
f(x) = (2x+4)/6 is a "rule" or like, directions. It says take your number, times by 2, add 4 and then divide by 6.
f(-2) just means to put -2 in place of x. Do the "rule" or follow the directions on the number -2.
f(x) = (2x+4)/6
f(-2) = (2•-2 + 4)/6
= (-4+4)/6
= 0/6
= 0
So f(-2) = 0
Samir and Kylie are making fruit salads for a picnic. Samir mixes 1 cup of melon and 3 cups of apple and Kylie mixes 2 cups of melon and 9 cups of apple. Use Samir and Kylie’s percent of melon to determine whose fruit salad will taste more melony.
Samir's fruit salad has a higher percentage of melon and will taste more melony than Kylie's fruit salad.
What is percentage?Percentage is a way of expressing a proportion or a fraction as a number out of 100. It is represented by the symbol % (percent).
In the given question,
To determine whose fruit salad will taste more melony, we need to calculate the percentage of melon in each fruit salad.
For Samir's fruit salad:
The total amount of fruit is 1 + 3 = 4 cups
The amount of melon is 1 cup
The percentage of melon is (1/4) x 100% = 25%
For Kylie's fruit salad:
The total amount of fruit is 2 + 9 = 11 cups
The amount of melon is 2 cups
The percentage of melon is (2/11) x 100% = 18.18% (rounded to two decimal places)
Therefore, Samir's fruit salad has a higher percentage of melon and will taste more melony than Kylie's fruit salad.
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I need help finding the regression equation pls!
Answer:
i did this in 8th grade. (I'm homeschooled)
Step-by-step explanation:
Heres the best i got
A triangular bookshelf has a base of 10 inches and 18 inches will the bookshelf fit in the corner of a square living room
No, if fit indicates that the bookcase's sides must be flush with the wall, which means that they must touch the wall and that the bookshelf is correctly positioned in that location.
What are triangles?A triangle is a polygon with three edges and three vertices.
It belongs to the basic geometric shapes.
A triangle having vertices A, B, and C is known as triangle ABC.
Any three locations in Euclidean geometry that are not collinear result in a distinct triangle and a distinct plane.
I've discovered that using the 3:4:5 triangle is the simplest way to determine for sure if an angle is 90 degrees.
This rule states that a triangle is a right triangle even if one of its sides is 3 and the other is 4 if the diagonal connecting its two points measures 5.
So, we must check to see if any of the bookcase's vertices measure 90 degrees because a square room will naturally have corners that do.
We may utilize Pythagorean Theorem to find the solution because every right triangle contains a 90° angle.
Pythagorean The a, b, and c are the legs, and the theorem states that a² + b² = c².
For our bookshelf, 10 and 12 are the legs, and 18 would be the hypotenuse if it were a right triangle as the hypotenuse is always the longest side.
To determine whether the equation is true or false, enter the values.
10² + 12² = 18²
100 + 144 = 324
244 ≠ 324
Thus, the bookshelf does not form a straight angle and cannot be placed in the room's corner.
Therefore, no, if fit indicates that the bookcase's sides must be flush with the wall, which means that they must touch the wall and that the bookshelf is correctly positioned in that location.
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Correct question:
A triangular bookshelf has a base of 10 inches,12 inches, and 18 inches. Will the bookshelf fit in the corner of a square living room?
which expression is equivalent to the following 3( 8x - 2y + 7 )
Answer:
24x - 6y + 21
Step-by-step explanation:
3( 8x - 2y + 7 )
Multiply each term in the bracket by 3
= (3 x 8x) - ( 3 x 2y) + (3 x 7)
= 24x - 6y + 21
Solve the triangle MNO (find m<O and the lengths of sides m and n).
The measure of angle O is 56 and the value of m and n are 8.1 in and 14.5 in respectively.
What is trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The longest side is hypotenuse and it is the side facing the right angle. The other two sides are opposite and adjascent.
sin(tetha) = opp/hyp
cos(tetha) = adj/hyp
tan,(tetha) = opp/adj
angle O = 180-(90+34)
= 180- 124
= 56°
To find m,
Tan 34 = m/12
m = Tan34 × 12
m = 8.1 in
using Pythagoras theorem to find n,
n= √8.1²+12²
n = √65.61+144
n = √209.61
= 14.5 in
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Describe the possible values of x if the area of the rectangle is at least 40 square inches
The value of x is 32.
Describe Rectangle?A rectangle is a quadrilateral (a four-sided polygon) with four right angles (90-degree angles) and opposite sides that are parallel and congruent (the same length). The opposite sides of a rectangle are also perpendicular to each other, meaning they intersect at a 90-degree angle.
The rectangle is a special case of a parallelogram, where all the angles are right angles. A square is also a special type of rectangle, where all the sides are congruent.
We can use the formula for the area of a rectangle, which is:
Area = Length x Width
Substituting the given values, we get:
40 = (5/8)x + 5 x 4
Simplifying, we get:
40 = (5/8)x + 20
Subtracting 20 from both sides, we get:
20 = (5/8)x
Multiplying both sides by 8/5, we get:
x = 32
Therefore, the value of x is 32.
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Select the correct answer.
What is the simplified form of this expression?
(2x + 9) + (11x − 4)
A.
13x + 5
B.
13x + 13
C.
18x
D.
-9x + 5
Answer:
13x+5
Step-by-step explanation:
Here's why
2x+9+11x-4
subtract 4 from 9
2x+5+11x
combine like terms
13x+5
Darlena has started taking photos at amateur dog racing events, later offering the photos for sale to the dog owners by email. The prices she has charged per photo at each of her first three events, and the corresponding number of photos sold and total revenue raised, appear in the table below.
Treating revenue as a function of the number of photos sold, a graph of the three data points is also shown. If she uses quadratic regression to fit a curve to the data, what number of photos sold and what price per photo will maximize her revenue?
The maximum revenue is achieved when she sells 33 photos at a price of 25 per photo.
Using quadratic regression, [tex]y = ax^2 + bx + c[/tex]
where a, b and c are constants and x is the independent variable we can determine the equation of the curve that best fits the data. The equation will be in the form of[tex]y = ax^2 + bx + c[/tex], where y is the revenue, x is the number of photos sold, and a, b, and c are constants. The constants can be determined by solving the system of equations formed by the three data points.
After solving for the constants, we can determine the maximum revenue by finding the vertex of the curve. The vertex is located at x = -b/2a, and the corresponding revenue is[tex]y = ax^2 + bx + c[/tex]. Plugging in the values for a, b, and c, we can calculate that the maximum revenue is achieved when she sells 33 photos at a price of 25 per photo.
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Complete question
Darlena has started taking photos at amateur dog racing events, later offering the photos for sale to the dog owners by email. The prices she has charged per photo at each of her first three events, and the corresponding number of photos sold and total revenue raised, appear in the table below. Treating revenue as a function of the number of photos sold, a graph of the three data points is also shown. If she uses quadratic regression to fit a curve to the data, what number of photos sold and what price per photo will maximize her revenue?