These equatiοns represent the fact that the slοpes and y-intercepts οf the lines fοrming the sides οf the triangle are related, and that the lines intersect at the vertices οf the triangle.
What is equatiοn?
An equatiοn is a mathematical statement that asserts that twο expressiοns are equal. It cοnsists οf twο sides, a left-hand side and a right-hand side, cοnnected by an equal sign "=". The expressiοns οn either side οf the equal sign can be numbers, variables, οr cοmbinatiοns οf bοth.
Here,
Part a: If the three sides οf the triangle are denοted by a, b, and c, then we can write the fοllοwing system οf equatiοns:
a + b = c
b - a = 3
These equatiοns represent the fact that the sum οf twο sides οf a triangle is equal tο the third side (a + b = c), and that the difference between twο sides is equal tο a given value (b - a = 3).
Part b: If the cοοrdinates οf the vertices οf the triangle are given by (x₁, y₁), (x₂, y₂), and (x₃, y₃), then we can write three equatiοns representing the three sides οf the triangle. Fοr example, the equatiοn οf the line passing thrοugh (x₁, y₁) and (x₂, y₂) is given by:
(y₂ - y₁)/(x₂ - x1) = (y - y₁)/(x - x₁)
where (x, y) are the cοοrdinates οf any pοint οn the line. Similarly, we can write equatiοns fοr the οther twο sides οf the triangle, and οbtain a system οf three linear equatiοns.
Part c: If the equatiοns οf the three sides οf the triangle are given by Ax + By + C = 0, Dx + Ey + F = 0, and Gx + Hy + I = 0, then we can write the fοllοwing system οf equatiοns:
A/Bx + C/B = -(A/By + C/B) (frοm the first equatiοn)
D/Ex + F/E = -(D/Ey + F/E) (frοm the secοnd equatiοn)
G/Hx + I/H = -(G/Hy + I/H) (frοm the third equatiοn)
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Complete question:
The lines that form the three sides of the triangle can be grouped into three different systems of two linear equations. Create 3 equations using different methods.
In a class of 40 students each student take at least One of Physics and Chemistry. If the number of student that take Physics is three times the number that take both Subsect and the number that take chemistry is twice the number that take Physic, find the number of Student that take Physics only
the number of students who take only Physics is 15.
Define equationAn equation is a mathematical statement that shows that two expressions are equal. It is typically written using an equal sign (=) between the two expressions. The expressions on either side of the equal sign are called the left-hand side (LHS) and the right-hand side (RHS) of the equation.
Let's denote the number of students who take only Physics by x.
The total number of students who take Physics or Chemistry=40The number of Physics students is three times the number who take both: number of Physics students = 3The number of Chemistry students is twice the number who take Physics: number of Chemistry students = 2We can use these equations to solve for x, the number of students who take only Physics:
40 = 3(number who take both) + 2(number of Physics students) - number who take both40 = 2(number who take both) + 2(number of Physics students)20 = number who take both + number of Physics studentsSubstituting the expression for the number of Physics students in terms of the number who take both, we get:
20 = number who take both + 3(number who take both)
20 = 4(number who take both)
number who take both = 5
this value in the expression for the number of Physics students, we get:
number of Physics students = 3(number who take both) = 15
Finally, we can use the first equation to solve for the number of students who take only Physics:
40 = 15 + 2(number of students who take only Physics) - 5
40 = 10 + 2(number of students who take only Physics)
number of students who take only Physics = 15
Therefore, the number of students who take only Physics is 15.
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Please, someone help me. This is geometry, 10th grade level.
Find the areas listed below, round to the nearest
hundredth if necessary. Make sure you use 3.14
for pie
The area of the circle is 200.96 square kilometers, the area of the polygon is 181.02 square kilometers and the shaded region is 19.94 square kilometers.
The area A of a circle with radius r can be found using the formula:
A = πr^2
Plugging in the given value of radius, we get:
A = π(8 km)^2
Simplifying the expression, we get:
A = 64π km^2
So, we have
A ≈ 64 x 3.14 km^2
A ≈ 200.96 km^2
To find the area of an octagon with a radius of 8 km, we can break it up into eight congruent isosceles triangles.
So, we have
Area = 8 * Area of triangle
This gives
Area = 8 * 1/2 * r² sin(central angle)
So, we have
Area = 8 * 1/2 * 8² sin(45)
Evaluate
Area = 181.02
The shaded area is
Shaded = 200.96 - 181.02
Shaded = 19.94
Hence, the shaded area is 19.94 square kilometers.
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if lines m and n are parallel, and ∠ 8 measures 110°, which is the measure of ∠7
Answer:
∡7 = 70°
Step-by-step explanation:
∡7 and ∡8 are supplementary angles
∡7 + ∡8 = 180°
If:
∡8 = 110°
Then:
∡7 = 180 - 110
∡7 = 70°
Use this tax table to find how much tax you need to pay on a taxable income of $25,000.
If taxable income is over-- But not over-- The tax is:
$0 $7,825 10 percent of the amount over $0
$7,825 $31,850 $782. 50 plus 15 percent of the amount over 7,825
$31,850 $77,100 $4,386. 25 plus 25 percent of the amount over 31,850
$77,100 $160,850 $15,698. 75 plus 28 percent of the amount over 77,100
$160,850 $349,700 $39,148. 75 plus 33 percent of the amount over 160,850
$349,700 no limit $101,469. 25 plus 35 percent of the amount over 349,700
Based on the information provided, the total tax this person will need to pay is $2,622,2.
What is the total tax in this case?The amount of money you pay for taxes depends on your income as there are specific percentages to be paid. In the case the income is $25000, this income matches the range $7,825 - $31,850, and therefore you should pay 50 plus 15 percent of the amount over 7,825. Based on this, let's calculate the money to be paid:
$25,000 - $7852 = $17, 148 x 0.15 (15%) = $2,572.2 + $50 = $2622.2
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Given mn, find the value of x.
+
(8x+6)°
(9x-30)°
B
PLS HURRY!!
value of variable x on the parallel line is 12.
Define co exterior angleIn geometry, a co exterior angle is an angle that is formed outside of a geometric figure by extending one of its sides. More specifically, a co exterior angle is formed when a transversal intersects two parallel lines, and it is an angle that is located outside of the parallel lines and on the same side of the transversal as one of the angles formed by the intersection.
Given
m ║n
8x+6 and 9x-30 are co exterior angle
8x+6+9x-30=180°
17x-24=180°
x=12
hence, value of variable x on the parallel line is 12.
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Find the general term of 6,12,24,48,...
Answer:
an = 6 * 2^(n-1)
Step-by-step explanation:
To find the general term of the sequence 6, 12, 24, 48, ... , we need to observe that each term is obtained by multiplying the previous term by 2. Therefore, the sequence is a geometric sequence with first term a = 6 and common ratio r = 2.
The formula for the nth term of a geometric sequence is:
an = a * r^(n-1)
Substituting a = 6 and r = 2, we get:
an = 6 * 2^(n-1)
Therefore, the general term of the sequence 6, 12, 24, 48, ... is given by the formula an = 6 * 2^(n-1).
1. 2. 4 journal:Algebraic Properties and expressions
The distributive property states that we can distribute a factor across a sum or difference, add or subtract like terms by adding or subtracting their coefficients and The power rule states that when raising a power to another power, we multiply the exponents. and Algebraic Properties explained as
Journal Entry 1:
Today, I learned about the algebraic properties of addition and multiplication. These properties are commutative, associative, and distributive. The commutative property states that the order in which we add or multiply numbers does not affect the result. For example, 2+3 is the same as 3+2, and 2x3 is the same as 3x2. The associative property states that we can group numbers in different ways without changing the result. For example, (2+3)+4 is the same as 2+(3+4), and (2x3)x4 is the same as 2x(3x4). The distributive property states that we can distribute a factor across a sum or difference. For example, 2x(3+4) is the same as 2x3 + 2x4.
Journal Entry 2:
Today, I learned about algebraic expressions and how to simplify them using the properties of addition and multiplication. An algebraic expression is a combination of numbers, variables, and operations. For example, 2x + 3y - 4z is an algebraic expression. To simplify an expression, we use the properties of addition and multiplication to combine like terms and simplify the expression as much as possible. Like terms are terms that have the same variables raised to the same powers. For example, 2x and 5x are like terms, but 2x and 5y are not. We can add or subtract like terms by adding or subtracting their coefficients. For example, 2x + 5x is 7x. We can also multiply terms by using the distributive property. For example, 2(3x + 4y) is 6x + 8y.
Journal Entry 3:
Today, I learned about algebraic expressions with exponents. An exponent is a small number written to the right of a base number that indicates how many times to multiply the base by itself. For example, in 2³, the base is 2 and the exponent is 3. To simplify an expression with exponents, we use the properties of exponents, such as the product rule and the power rule. The product rule states that when multiplying two powers with the same base, we add their exponents. For example, 2³ x 2² is 2^(3+2) or 2^5. The power rule states that when raising a power to another power, we multiply the exponents. For example, (2²)³ is 2^(2x3) or 2^6. We can also simplify expressions with exponents by combining like terms, just like we did with expressions without exponents.
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1.2.4Journal: Algebraic Properties and ExpressionsJournalAlgebra I Sem 1Name:Date:Scenario:The ArcadeInstructions:
•View the video found on page 1 of this journal activity
.•Using the information provided in the video, answer the questions below
.•Show your work for all calculation
Find the surface area of the pyramid.
A triangular pyramid. The base triangle has a base of 20 yards and a height of 17.3 yards. The height of a triangular face is labeled 12 yards.
The surface area is
square yards.
Skip to navigation
Find the surface area of the pyramid.
A triangular pyramid. The base triangle has a base of 20 yards and a height of 17.3 yards. The height of a triangular face is labeled 12 yards.
The surface area is
square yards.
Skip to navigation
Find the SA of a triangular pyramid, the base triangle is 20, the height of 17.3 yard, and 12
Step-By-Step:
The height triangle has a height of 17.3 yards and a width of 12 yards. 3. Finally, connect the two triangles to create the pyramid's surface area. The surface area of the pyramid is 116.7 yards².
Answer:
116.7 yards².
Answer:
The first step is to find the area of the base triangle:
Area = (1/2) x base x height
Area = (1/2) x 20 yards x 17.3 yards
Area = 173 square yards
To find the surface area of the pyramid, we need to find the areas of the four triangular faces and add them to the base area.
Area of a triangular face = (1/2) x base x height
Area of each face = (1/2) x 20 yards x 12 yards
Area of each face = 120 square yards
Now we can add up all the areas:
Surface area = base area + area of four faces
Surface area = 173 square yards + 4 x 120 square yards
Surface area = 653 square yards
Therefore, the surface area of the pyramid is 653 square yards.
a man sets out to travel from A to C via B. from A he travel a distance of 8km on a bearing of north 30°east to B. from B he travel a further 6km due east. calculate how far c is from north of A, east of A.
Plssss help I need now!!!
"A medicine is effective for 80% of patients. The table shows 30 randomly generated numbers from 0 to 999. Use the table to estimate the probability of the event."
6. The medicine is effective on each of three patients.
7. The medicine is effective on fewer than two of the next three patients.
first part.
The probability that the medicine is effective on each of three patients is 0.512 or 51.2%.
second part.
The probability that the medicine is effective on fewer than two of the next three patients is 0.104 or 10.4%.
How to calculate?
Let p be the probability that the medicine is effective for a given patient. p = 0.8.
6. calculating the probability that the medicine is effective for all three patients. , we will multiply their individual probabilities of being effectively treated, because the patients are independent
P(event 6) = p * p * p = 0.8 * 0.8 * 0.8 = 0.512 or 51.2%.
7.
event 7, we will calculate the probability that the medicine is effective on fewer than two of the next three patients.
We apply the binomial distribution with n = 3 (the number of patients) and p = 0.8 (the probability of success).
The probability mass function for the binomial distribution is:
P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
P(event 7) = P(X=0) + P(X=1)
= (3 choose 0) * 0.8^0 * 0.2^3 + (3 choose 1) * 0.8^1 * 0.2^2
= 0.008 + 0.096
= 0.104 or 10.4%.
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what is the equation for a cosecant function with vertical asymptotes found at such that n is an integer?
The equation for a cosecant function with vertical asymptotes found at x = nπ such that n is an integer is `y = csc(x - nπ)`.
The cosecant function is the reciprocal of the sine function. The cosecant of a particular angle in a right triangle is the ratio of the hypotenuse to the side opposite the angle.
The cosecant function is written as follows: `csc(x) = 1/sin(x)`
Asymptotes are straight lines or curves that a graph approaches but never touches.
As a result, the graph of a curve gets closer and closer to the asymptote as it moves further away from the origin, but it never touches it.
For a function to have vertical asymptotes at `x = nπ`, the denominator of the function should equal zero. In the cosecant function, the denominator is equal to `sin(x - nπ)`.
Therefore, the vertical asymptotes are where `sin(x - nπ) = 0`.
The general form of the cosecant function is `y = A csc(B(x - C)) + D`.
The constants A, B, C, and D are used to alter the form of the graph of the cosecant function.
They can be used to alter the amplitude, period, phase shift, and vertical displacement of the graph, respectively.
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What single percentage change is equivalent to a 17% decrease followed by a 12% increase?
2.96% decrease
7.04% increase
7.04% decrease
92.96% increase
2.96% increase
92.96% decrease
let's call our number hmmm Z, now, let's reduce it by 17%, so 100% - 17% = 83%, so the new size for Z is 83% off the original, hmm how much is that?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{83\% of Z}}{\left( \cfrac{83}{100} \right)Z}\implies 0.83Z[/tex]
now, let's increase it by 12%, so the new size will be 100% + 12% = 112%, so 112% of 0.83Z, let's check how much is that
[tex]\stackrel{\textit{112\% of 0.83Z}}{\left( \cfrac{112}{100} \right)0.83Z}\implies 0.9296Z[/tex]
now, let's convert that to a percent format by simply multiplying it by 100, so that'd be 100 * 0.9296Z = 92.96% of Z. Well, hell 92.96% is less than 100%, so is really 100% - 92.96% = 7.04% less.
So, instead of all that rigamarole, we could have just reduced Z by 7.04% in one fell swoop and obtain the same thing.
Find the area of a segment of a circle if the central angle of the segment is 50° and the radius is 15
In conclusion the area of the segment is approximately 32.76 square units.
How to find?
To find the area of a segment of a circle, we can use the formula:
Area of segment = (θ/360)πr²2 - (1/2)rsin(θ)
where:
θ is the central angle of the segment in degrees
r is the radius of the circle
π is a constant approximately equal to 3.14
sin is the sine function
In this case, the central angle is 50° and the radius is 15. Substituting these values into the formula, we get:
Area of segment = (50/360)π(15)²2 - (1/2)(15)sin(50)
= (5/36)π(225) - (1/2)(15)(0.766)
= 32.76 square units (rounded to two decimal places)
Therefore, the area of the segment is approximately 32.76 square units.
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Which is the graph of y = −1/2 (x−3)^2−1?
Emergency help needed will mark brainliest
Answer: The first graph
Step-by-step explanation: because the vertex is (3,-1)
Then plug in number like is 1 is x solve for y which will be -3
if x is 2, y is -3/2
x is 3, y is -1
x is 4, y is -3/2
x is 5, y is -3
Answer:
Vertex at (3,-1) and flipped upside down (opening downward)
*looks like the first one of the first attachment*
Step-by-step explanation:
The normal untransformed parabola is a U-ish, V-ish curve that has its vertex at (0,0) and it opens upward. There are "nice" points at (1,1) and (2,4) also at (-1,1) and (-2,4) Your parabola has had four changes made to it:
□The negative sign in front on your equation will FLIP the whole thing upside down so it opens downward.
□The 1/2 in front will "smash" the parabola so it is flatter and wider.
□The - 3 that's in close next to the x will shift (slide, translate) the whole thing to the right 3 units **left and right shifts are kind of the opposite of what you might think: - shifts right and + shifts left**
□The -1 tacked on to the end will shift (slide, translate) the whole thing down one unit. **more intuitive, - shifts down and + shifts up**
Peter has hats. He can divide them into equal groups of 2,6 and 8. How many hats does Peter have?
Answer:
24
Step-by-step explanation:
Answer: 24 hats
Step-by-step explanation:
1. Find common multiples: 2: 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36 6: 6,12,18,24,30,36 8: 8,16,24,32
2. Find the least common multiple: 24
Please help! Solve for y. Round your answer to the nearest tenth and type it as a number
The value of y is 7.5 for the given similar triangle.
Define the Similar triangle?The sides of comparable triangles are relative to one another. For instance, if the proportion of the lengths of two comparing sides of one triangle to another is 2:1, then the other two relating sides will likewise be in the proportion of 2:1.
According to the figure; two triangles are similar because its identities,
So, (2y + 25) = 2 times of (2y + 5)
we can write as,
⇒ (2y + 25) = 2 × (2y + 5)
⇒ 2y + 25 = 4y + 10
⇒ 2y - 4y = 10 - 25
⇒ - 2y = - 15
⇒ y = 15/2 = 7.5
Therefore, the value of y is 7.5 of the given similar triangle.
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1. Determine the scale factor. The point of center is the origin.
M(-12,18) M(-2,3)
Scale factor = 36
(new/old)
2. Determine the scale factor. The point of center is the origin.
M(-2,3) M'(-12,18)
scale factor = 4/9
(new/old)
3. A dilation with a scale factor less than 1 is an enlargement
A. True
B. False
please help me!!
(1) The scale factor for this dilation is 1/6.
(2) The scale factor for this dilation is 6.
(3) False. A dilation with a scale factor less than 1 is a reduction, not an enlargement.
What is the scale factor?1. To find the scale factor for the dilation with center at the origin that maps point M(-12,18) to M(-2,3) we can use the formula:
new coordinate / old coordinate = scale factor
For the x-coordinate:
-2 / -12 = 1/6
For the y-coordinate:
3 / 18 = 1/6
Since both coordinates have the same scale factor, we can conclude that the scale factor for this dilation is 1/6.
2. To find the scale factor for the dilation with center at the origin that maps point M(-2,3) to M'(-12,18) we can again use the formula:
new coordinate / old coordinate = scale factor
For the x-coordinate:
-12 / -2 = 6
For the y-coordinate:
18 / 3 = 6
Since both coordinates have the same scale factor, we can conclude that the scale factor for this dilation is 6.
3. False. A dilation with a scale factor less than 1 is a reduction, not an enlargement. An enlargement is a dilation with a scale factor greater than 1.
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a reporter for an international newspaper is given an assignment that is randomly chosen from the following destinations worldwide: 8 continental united states assignments, 29 south american assignments, 15 european union assignments, and 22 asian assignments. find the probability that he gets an assignment in the united states or asia . express your answer as a fraction
The probability that the reporter gets an assignment in the United States or Asia is 15/37.
To find the probability that the reporter gets an assignment in the United States or Asia, we first need to determine the total number of assignments in the pool.
Total number of assignments = 8 + 29 + 15 + 22 = 74
Next, we need to determine the number of assignments that are in the United States or Asia.
Number of assignments in the United States or Asia = 8 + 22 = 30
Finally, we can calculate the probability of the reporter getting an assignment in the United States or Asia by dividing the number of assignments in the United States or Asia by the total number of assignments:
Probability of getting an assignment in the United States or Asia = (Number of assignments in the United States or Asia) / (Total number of assignments)
Probability of getting an assignment in the United States or Asia = 30/74
Therefore, the probability of the reporter getting an assignment in the United States or Asia is 30/74, which can be simplified by dividing both the numerator and denominator by their greatest common factor (GCF), which in this case is 2:
Probability of getting an assignment in the United States or Asia = 15/37
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Perform the indicated operation, and write the answer in lowest terms.
−16/5 ⋅ (−15/56)
Answer:
6/7
Step-by-step explanation:
First, cancel out 16 and 56 by a common factor of 8. The resulting expression is -2/5*-15/7. Then, simply 5 and 15 by a common factor of 5. Then, you will get: -2*(-3/7). The negatives cancel out, so the answer is 6/7.
PLEASE HELP FAST THIS IS DUE TODAY
Sophia throws a dart at this square-shaped target:
A square is shown with sides labeled 9. A shaded circle is shown in the center of the square. The diameter of the circle is 3.
Part A: Is the probability of hitting the black circle inside the target closer to 0 or 1? Explain your answer and show your work. (5 points)
Part B: Is the probability of hitting the white portion of the target closer to 0 or 1? Explain your answer and show your work. (5 points)
Part A: If assuming 0 means the white part, then nο.
Part B: If assuming 0 means the black part, then yes.
What is prοbability?The prοbability οf an οccurrence is a figure that represents hοw likely it is that the event will take place. In terms οf percentage nοtatiοn, it is expressed as a number between 0 and 1, οr between 0% and 100%. The higher the likelihοοd, the mοre likely it is that the event will take place.
Part A: If assuming 0 means the white part, then nο, there is a chance tο hit the black circle but the circle is οnly abοut 1/9th, then the whοle target, sο putting it in numbers, it wοuld be abοut 1/9 cοmpared tο 8/9.
8/ 9 has a higher chance.
Part B: If assuming 0 means the black part, then yes, as I said in Part A, it's basically cοmparing 1/9 tο 8/9.
1/9 being the black part and 8/9 being the white [tex]8/9 > 1/9[/tex] which means the white pοrtiοn has a higher prοbability.
Hence, Part A: If assuming 0 means the white part, then nο.
Part B: If assuming 0 means the black part, then yes.
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Find the value of < Z O X
< Z O X = °
The unknown angles on the straight line is as follows:
∠ZOX = 64 degrees
How to find the angles on a straight line?The sum of angles in a line segment is 180 degrees. Therefore, let's find the angle ∠ZOX as follows:
∠YOX = ∠YOZ + ∠ZOX
Therefore,
∠ZOX = ∠YOX - ∠YOZ
∠YOX = 180°
Therefore,
5x + 6 + 3x - 2 = 180
8x + 4 = 180
8x = 180 - 4
8x = 176
x = 176 / 8
x = 22
Hence,
∠ZOX = 3x - 2
∠ZOX = 3(22) - 2
∠ZOX = 66 - 2
∠ZOX = 64 degrees
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Pls pls pls helpp 10 points
Answer:
y^10
Step-by-step explanation:
The velocity (in meters per second) with which a roller coaster moves can be given by the function f(t) = (t - 3)3 t. find the acceleration function a(t).
The acceleration function is a(t) = 6(t - 3).
Acceleration is the rate at which an object changes its velocity. The acceleration function is a mathematical function that gives the acceleration of an object at any given time
To find the acceleration function, we need to take the second derivative of the given velocity function f(t).
f(t) = (t - 3)^3 + t
First, let's find the first derivative of f(t)
f'(t) = 3 × (t - 3)^2 + 1
Now, let's find the second derivative of f(t) ( the acceleration function )
a(t) = f''( t )
= d/dt [3 × (t - 3)^2 + 1]
Do the derivation
= 6(t - 3)
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The given question is incomplete, the complete question is:
The velocity (in meters per second) with which a roller coaster moves can be given by the function f(t) = (t - 3)^3 + t. find the acceleration function a(t).
Points D,B, and E are collinear. Find the value of x so that points A,B, and C are collinear
Answer:
11? I only think this because it says that EBD are collinear and it equals 99 so for (9x) to equal 99, it would have to be nine times 11.
What is the range of the function f(x) = |x| – 3?
{f(x) ∈ ℝ | f(x) ≥ –3}
{f(x) ∈ ℝ | f(x) < –3}
{f(x) ∈ ℝ | f(x) ≤ –3}
{f(x) ∈ ℝ | f(x) > –3}
Answer:
{f(x) ∈ ℝ | f(x) ≥ –3}
Step-by-step explanation:
f(x)=|x|-3
|x| have range x≥0 .
f(x)≥0-3
f(x)≥-3
First answer {f(x) ∈ ℝ | f(x) ≥ –3}
Find two sets of three positive single digit integers with mmr equal to 4/5'
We find sets of three positive single digit integers with a mean of 4 and a range of 5 is {1, 5, 6} and another possible set is {2, 4, 6}.
Here mmr is mean, median, and range of a set of numbers. The mean of a set of numbers is the sum of all the numbers divided by the total number of numbers in the set. The median of a set of numbers is the middle number when the numbers are arranged in order.
The range of a set of numbers is the difference between the largest and smallest numbers in the set.
To find two sets of three positive single digit integers with a mean of 4 and a range of 5, we can use the formula:
Mean = (sum of numbers) / (number of numbers)
Since we want the mean to be 4, the sum of the three numbers in each set must be 12. Since we want the range to be 5, the largest number in each set must be 5 more than the smallest number.
One possible set of three numbers that satisfies these conditions is {1, 5, 6}. The mean of this set is (1+5+6)/3 = 4, and the range is 6-1 = 5.
Another possible set of three numbers that satisfies these conditions is {2, 4, 6}. The mean of this set is (2+4+6)/3 = 4, and the range is 6-2 = 4.
Therefore, two sets of three positive single digit integers with a mean of 4 and a range of 5 are {1, 5, 6} and {2, 4, 6}.
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What are the x- and y-intercepts of the function f(x) = 2x² + x + 5?
O A. y-intercept: 5, x-intercept: 0
OB. y-intercept: 8; x-intercept: 0
O C. y-intercept: 5; x-intercept: none
OD. y-intercept: 8; x-intercept: none
The x- and y-intercepts of the function f(x) = 2x² + x + 5 is A.
we put x as equal to 0 first and we get y = 5 (y=f(x))
once we get y = 5 we can replace it in the equation and we get 2x^2+x=0 solving the quadratic equation, we get x=0, -1/2
The quadratic equation can be solved by taking x common then we are left with (2x+1).
the x we take common is equal to 0
(2x+1) = 0 gives x=-1/2
hence the x intercept = -1/2, 0 and y intercept =5
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consider parallelogram vwxy below use the information given in the figure to findx m
In the given parallelogram vwxy: x = 3; m∠Y = 65° and ∠YVX = 61° by (alternate interior angle).
Explain about the parallelogram?A quadrilateral with the opposing sides parallel is called a parallelogram (and thus opposite angles equal).
A parallelogram with all right angles is known as a rectangle, and a quadrilateral having equal sides is known as a rhombus. Rectangles and squares are both particular varieties of parallelograms since a square is just a degenerate instance of a rectangle.In the given parallelogram vwxy:
Parallel sides are equal.
So, 2x = 6
x = 6/2 = 3
Opposite pair of angles are also equal.
So,
∠W = ∠Y = 65°
Now,
∠YVX = 61° (alternate interior angle).
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In a marathon race of 21 km a runner has been running at a constant speed of 5 by 3 m per second for the last 3 hour. How much distance remain to be run to finish the marathon
the runner still needs to run a distance of 15 km to finish the marathon.
To find out how much distance remains to be run in the marathon, we can first calculate how far the runner has already run in the last 3 hours. We can use the formula:
distance = speed x time
where speed is in meters per second and time is in hours.
The runner has been running at a constant speed of 5/3 m/s for 3 hours, so the distance covered so far is:
distance = (5/3) m/s x 3 hours x 3600 seconds/hour
distance = 6000 meters or 6 km
Therefore, the runner has already completed 6 km of the marathon, which means that the remaining distance to be run is:
remaining distance = total distance - distance already covered
The total distance of the marathon is 21 km, so the remaining distance is:
remaining distance = 21 km - 6 km
remaining distance = 15 km
Therefore, the runner still needs to run 15 km to finish the marathon.
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PLS HELP WITH THIS QUESTION
Answer:
even
Step-by-step explanation:
It lands on 10, and 8, take that, divide by 2, and mutiply by 8.