Answer:
the answer is a parabola
the perimeter of a rectangle is twice the sum of its length and width. The perimeter is 34 meters and its length is 2 meters more than twice its width. What is its length? ...?
Write an equation in point-slope form for the line with the given slope
that contains the given point.
slope 3; (4, 2)
Answer:
[tex]y-2=3(x-4)[/tex]
Step-by-step explanation:
Pre-SolvingWe are given that a line has a slope (m) of 3 and passes through (4, 2). We want to write this equation in point-slope form.
Point-slope form is given as [tex]y-y_1=m(x-x_1)[/tex] where m is the slope and [tex](x_1,y_1)[/tex] is a point.
SolvingWe can substitute what we know into the equation.
First, substitute 3 as m.
[tex]y-y_1=3(x-x_1)[/tex]
Now, substitute 4 as [tex]x_1[/tex] and 2 as [tex]y_1[/tex].
[tex]y-2=3(x-4)[/tex]
Find an equation in standard form for the hyperbola with vertices at (0, ±2) and foci at (0, ±7).
To find the standard form equation of a hyperbola with given vertices and foci, calculate the values of a and b using distances from the origin, and then insert into the standard form equation (y²/a²) - (x²/b²) = 1. The final equation for the hyperbola with vertices at (0, ±2) and foci at (0, ±7) is 45y² - 4x² = 180.
To find the equation of a hyperbola in standard form, we need the vertices and the foci. Given that the vertices are at (0, ±2), we know that the hyperbola is vertical, and the distance between the vertex and the center, which is the origin, is 2 units, so a=2. Since the foci are at (0, ±7), the distance from the center to a focus is 7 units, which means c=7.
With these values, we can calculate b by using the relationship c² = a² + b². Plugging in the known values gives us 7² = 2² + b², so b² = 49 - 4 = 45. Therefore, b = √45.
The standard form equation of a vertical hyperbola with a center at the origin is (y²/a²) - (x²/b²) = 1. Replacing a and b with the found values, the equation becomes (y²/4) - (x²/45) = 1. Multiplying through by 180, which is the least common multiple of 4 and 45, we get the equation in standard form: 45y² - 4x² = 180.
The perimeter of a square is equal to the perimeter of an equilateral triangle. The length of a side of the square is given by x, and the length of a side of the equilateral triangle is given by x=1. Which equation can be used to find the value of x?
To solve for x, given that the perimeter of a square is equal to the perimeter of an equilateral triangle, the equation 4x = 3(x + 1) can be used.
Explanation:To find the value of x when the perimeter of a square is equal to the perimeter of an equilateral triangle, we set up an equation. Since the side of the square is given by x, and the perimeter of a square is 4 times the length of a side, the perimeter of the square is 4x. The length of a side of the equilateral triangle is given by x + 1, and since the perimeter of the equilateral triangle is 3 times the length of a side, its perimeter is 3(x + 1). Setting these two perimeters equal to each other gives us the equation 4x = 3(x + 1).
Which transformations map the strip pattern onto itself?
dP dP dP d
a horizontal translation and a 180° rotation
a horizontal translation and a reflection across a vertical line
a horizontal translation and a glide reflection
a horizontal translation only
Answer:
a horizontal translation and a glide reflection
Step-by-step explanation:
the exterior angles of a triangle have measures of (x+10) degrees, (2x+20) and 3x degrees. what is the measure of the smallest interior angle of the triangle ...?
Answer: X= 55
Step-by-step explanation:
The sum of exterior angles of any polygon will always equal to 360 degrees. which means, we can write:
360 = (x+10) + (2x+20) + 3x
x = 55
The exterior angles have values of 65, 130 and 165. The exterior that will have the largest value will correspond to the smallest interior angle and therefore have a value of 15 degree!. ;)
Final answer:
By calculating the value of x and using the relationship that each exterior angle and its corresponding interior angle are supplementary, we find that the measure of the smallest interior angle of the triangle is 115 degrees.
Explanation:
To find the measure of the smallest interior angle of the triangle, we first need to use the fact that the sum of the exterior angles of a triangle is always 360 degrees. So, we set up the equation (x+10) + (2x+20) + 3x = 360 and solve for x. This gives us:
x + 10
2x + 20
3x
Combining like terms, we get 6x + 30 = 360. Subtracting 30 from both sides, we get 6x = 330. Dividing both sides by 6, we find that x = 55 degrees. Therefore, the exterior angles are 65 degrees, 130 degrees, and 165 degrees. To find the smallest interior angle, we take the smallest exterior angle, 65 degrees and subtract it from 180 degrees (since the exterior angle and interior angle at the same vertex are supplementary). Thus, the smallest interior angle is 180 degrees - 65 degrees = 115 degrees.
The main tank has a radius of 70 feet. What is the volume of the quarter-sphered sized tank? Round your answer to the nearest whole number.
How to write 7 95/125 as a decimal?
A fisherman rows up stream at 4mph and downstream at 6mph. He started rowing upstream until he got tired and then rowed downstream to his starting point. How far did the fisherman row in the whole trip in 7 hours?
By setting the upstream and downstream distances equal and solving for the time rowed upstream, we find that the fisherman rowed 4.2 hours upstream and 2.8 hours downstream. Since he rowed back to his starting point, the total distance rowed upstream and downstream is the same, amounting to 33.6 miles for the entire trip.
To solve this problem, we need to determine how much time the fisherman spent rowing upstream and downstream. Let's call the upstream speed U, which is 4 mph, and the downstream speed D, which is 6 mph. He rows for a total of 7 hours. Let's call the time spent rowing upstream T and the time spent rowing downstream (7 - T) since the entire trip takes 7 hours.
Since distance equals rate times time, the upstream distance will be U × T and the downstream distance will be D × (7 - T). Because the fisherman returns to his starting point, the upstream and downstream distances are equal.
Setting them equal gives us the equation:
4T = 6 (7 - T)
Solving for T gives us:
T = 42 / 10 = 4.2 hours
Hence, the time spent rowing downstream is 7 - 4.2 = 2.8 hours.
To find the total distance rowed, we use the downstream distance (since it's equal to the upstream distance) which is calculated as:
Distance = D × (7 - T) = 6 × 2.8 = 16.8 miles
Therefore, the fisherman rowed a total of 16.8 miles upstream and 16.8 miles downstream, summing up to 33.6 miles for the entire trip.
find the x-intercepts of the parabola with vertex(6,27) and y-intercept (0,-81). write answer in form (x1,y1)(x2,y2). if necessary ,round to the nearest hundredth .
Answer:
(8.33) , (236.67)
Step-by-step explanation:
This is correct
What is the point in the middle of a circle called?
A. Radius
B. Center
C. Circumference
D. Epicenter
Answer:
center
Step-by-step explanation:
The point in the middle of a circle called, B. Center
What are the circumference and diameter of a circle?The circumference of a circle is the distance around the circle which is 2πr.
The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.
We know, The largest chord that passes through the center of a circle is called a diameter.
All the other line segments that can be drawn with endpoints touching the circumference of a circle are called chords.
The radius is half the length of the largest chord(diameter).
A circle is defined as if we fix a point and mark points in a plane such that each point is equidistant from that fixed point a circle will be formed.
That fixed point is called the center of a circle.
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1.There are 10 kids running a race. How many ways are there for them to come in first, second, and third place?
2.In a drawing, a jar holds the numbers 1 to 8. If you draw three numbers to form a three-digit number (without replacement), what is the probability you will draw 135?
Answer:
1: 720
2: [tex]\frac{1}{336}[/tex]
Step-by-step explanation:
1: There are 10 kids in a race so the number of ways such that they come first , second and third=10×9×8
=720
(since the first place is occupied by any one of the ten students i.e. we have ten choices after occupying first position there are only 9 students left for second position and after occupying second for the third position only 8 choices are left)
2: We have to find the probability such that there is no replacement such that we draw 135.
for the first position we have to find the probability([tex]P_{1}[/tex]) that '1' comes out of 8 numbers=[tex]\frac{1}{8}[/tex]
similarly for second choice we could not take 1 as there is no replacement
so probability that 3 comes([tex]P_{2}[/tex]) =[tex]\frac{1}{7}[/tex]
similarly probability that 5 comes at third position([tex]P_{3}[/tex]) = [tex]\frac{1}{6}[/tex]
hence, probability that 135 is drawn= [tex]\frac{1}{8}\times\frac{1}{7}\times\frac{1}{6}=\frac{1}{336}[/tex]
If the integral of f(x)dx = 2.3 from 1 to 3 and F'(x) = f(x), what is the value of F(3) - F(0). The graph will be inserted as a picture. ...?
A lake was stocked with 80 trout, 20 bass, 70 walleye and 30 catfish. What is the probability that a fisherman catches a trout first then a second trout.
The probability of a fisherman catching a trout first and then a second trout from this lake is 0.158.
Explanation:The subject of this question pertains to the field of probability in mathematics and requires an understanding of fundamental concepts related to this topic.
The total number of fish in this lake is 200 (80 trout + 20 bass + 70 walleye + 30 catfish). The probability of catching a trout first can be calculated by dividing the number of trout by the total number of fish, which is 80/200 = 0.4. After catching the first trout, there are now 79 trout left, and the total number of fish is 199. Therefore, the probability of catching a second trout is 79/199. To find the overall probability of both events happening, we multiply the probabilities of each individual event:0.4 x (79/199) = 0.158.
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Why would you want to solve a literal equation for a variable when you could simply plug in known values and then solve the resulting linear equation?
Solving literal equations for a variable is beneficial for finding general solutions that apply to multiple situations, saves time by avoiding repetitive calculations, and reduces potential errors when working with complex numbers.
Why Solve Literal Equations for a Variable
Solving a literal equation for a variable is fundamental in mathematics because it allows one to find a general solution that can apply to various situations. Instead of replacing a variable with a given number each time, which can be time-consuming and error-prone especially when dealing with long decimals and complex fractions, working with no numbers—just variables—simplifies the process. Having found the values that make the equation true, one can easily convert words to an algebraic expression or equation that best models a given problem. This results in the ability to find a solution more swiftly and with less room for error.
For example, in computer programs, solutions to equations are frequently required for multiple sets of input values. Algebraically solving an equation provides a general form that can easily be reused with different inputs, saving substantial time and resources. Additionally, in complex problems involving multiple unknowns, solving for one variable in terms of others can lead to a simplified equation, making it easier to solve the problem.
The price p of a pizza is $6.95 plus $.95 for each topping t on the pizza
Angie and kenny play online video games. angie buys 1 software package and 1 month of game play. kenny buys 1 software packages and 5 months of game play. each software package costs $20. if their total cost is $154 what is the cost of one month of game play? the cost of one month of game play is ______
What is 598% divided by 26%
Is the relation a function? {(14, 9), (15, 8), (8, 7), (1, 9), (15, 2)}
In order to apply the law of sines to find the length of the side of a triangle, it is enough to know which of the following?
A. Two angles and a side
B. All three angles
C. Two sides and one angle
D. The area of the triangle ...?
Answer:
We must have two angles and a side.
A is the correct option.
Step-by-step explanation:
For any triangle ABC, the law of sine is given by
[tex]\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]
From this formula it is clear that in order to find the length of the side of the triangle, we must have two angles and a side.
Let us understand this by assuming that we need to find a (length of the side). From the formula, we have
[tex]\frac{a}{\sin A}=\frac{b}{\sin B}\\\\a=\frac{b\sin A}{\sin B}[/tex]
Thus, to find the length a, we must have b, sin A and sin B.
Hence, o find the length of the side of the triangle, we must have two angles and a side.
What is the solution to the following of equations {5x-3y=34 x-2y=4?
Which is greater 0.12 or 1.2?
Jeans costs $15 each and shirts costs $9 each. You have at most $90 to spend clothing. You must purchase at least 3 pairs of jeans. Let x be the amount of jeans purchased and y be the amount of shirts purchased. What is a possible solution?
(4,-5)
(4, 5)
(4,2)
(2,4)
Answer: 4,2 is the correct answer
Step-by-step explanation:
Why are their bad people in the world?
write the area A of a square as a function of its perimeter P. ...?
Final answer:
The area of a square as a function of its perimeter is A = (P/4)².
Explanation:
The area of a square can be represented as a function of its perimeter. Let's say the side length of the square is a. The perimeter of the square is given by P = 4a. So, to write the area A as a function of the perimeter P, we can use the formula:
A = (P/4)²
A kite is flying on the end of a 300-ft string. The kite string makes a 65 degree angle with the ground. How far above the ground the kite?
The profit P (in thousands of dollars) for a company spending an amount s (in thousands of dollars on advertising is
P= -(1/10)s^3 + 6s^2 + 400
Find the amount of money the company should spend on advertising in order to yield a maximum profit
To find the maximum profit, take the derivative of the profit function and set it equal to zero, then solve for s. This gives the advertising spend that yields the maximum profit.
Explanation:To find the amount of money the company should spend on advertising in order to yield a maximum profit, we first need to find the derivative of the profit function P(s) = -(1/10)s^3 + 6s^2 + 400. The derivative, P'(s), gives the rate of change of profit with respect to advertising spending.
The derivative of the function is P'(s) = -(3/10)s^2 + 12s. We find the maximum of the function by setting the derivative equal to zero and solving for s.
Setting P'(s)=0 we get: -(3/10)s^2 + 12s = 0
Solving this equation will provide the advertising spend for maximum profit.
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Find the value of the coefficient of
1/x
in the expansion of (2x −
1/x )^5
. ...?
Final answer:
To find the coefficient of 1/x in the expansion of (2x - 1/x)^5, we use the binomial theorem, specifically the term where the exponent of x is -1. We find that the coefficient of 1/x is -80.
Explanation:
To find the coefficient of 1/x in the expansion of (2x - 1/x)^5, we can use the binomial theorem. The binomial theorem states that:
(a + b)^n = Σ (n choose k) a^(n-k) b^k
where 'n choose k' is the binomial coefficient, computed as:
n! / [(n-k)!k!]
In our case, a = 2x and b = -1/x, and we want the term where the power of x is -1, which occurs when k = 4:
(5 choose 4) (2x)^(5-4) (-1/x)^4 = 5 * 2 * 1 * 1/x^4 = 10/x^4
However, to get the term with 1/x, we need a positive power of 1 for x. We achieve this when k = 1:
(5 choose 1) (2x)^(5-1) (-1/x)^1 = 5 * 16x^4 * (-1/x) = -80
Therefore, the coefficient of 1/x in the expansion is -80.
Determine whether the graphs of the given equations are parallel, perpendicular, or neither
y=x+11
y=-x+2
A.Parallel
B.Perpendicular
C.Neither
Keywords
parallel, perpendicular, graphing, linear equation, slope, lines
we know that
If two lines are perpendicular, then the product of their slope is equal to minus one
so
[tex]m1*m2=-1[/tex]
If two lines are parallel, then their slope are equal
[tex]m1=m2[/tex]
In this problem we have
[tex]y=x+11[/tex] --------> linear equation A
the slope is [tex]m1=1[/tex]
[tex]y=-x+2[/tex] --------> linear equation B
the slope is [tex]m2=-1[/tex]
Find the product
[tex]m1*m2=-1[/tex] ---------> the lines are perpendicular
therefore
the answer is the option B
Perpendicular
using a graphing tool
see the attached figure
Answer:
Perpendicular
Step-by-step explanation:
Given are two equations as
[tex]y=x+11\\y=-x+2[/tex]
We have to find whether these two are parallel or perpendicular or neither
For this first we have to find the slope of these two lines
I line slope = 1
II line slope =-1
Since slopes are not equal, the lines are not parallel.
Let us check product of these slopes. IF product =-1 the lines are perpendicular
We find that product = [tex]1*-1=-1[/tex]
Hence two lines are perpendicular
how to factor x3-x2-4x-4