Trent will need approximately 2.86 bottles of waterproof spray to cover his tent.
To calculate the number of bottles of waterproof spray Trent will need to cover his tent, we first need to find the surface area of the tent.
The surface area of a square-based pyramid is given by the formula:
Surface Area = Base Area + (0.5 x Perimeter of Base x Slant Height)
The base of the pyramid is a square with a side length of 14 feet, so the base area is:
Base Area = (Side Length)^2 = 14^2 = 196 square feet
To find the slant height of the pyramid, we can use the Pythagorean theorem. The slant height is the hypotenuse of a right triangle formed by one side of the base, the height of the pyramid, and the slant height. The height of the pyramid is given as 8 feet, and half the length of the base is 7 feet.
Using the Pythagorean theorem:
[tex]Slant Height^2 = (Half Base Length)^2 + Height^2[/tex]
[tex]Slant Height^2 = 7^2 + 8^2Slant Height^2 = 49 + 64Slant Height^2 = 113Slant Height ≈ √113 ≈ 10.63 feet[/tex]
Now we can calculate the surface area of the tent:
Surface Area = 196 + (0.5 x 4 x 10.63)
Surface Area = 196 + (2 x 10.63)
Surface Area = 196 + 21.26
Surface Area ≈ 217.26 square feet
Since each bottle of waterproof spray covers 76 square feet, we can divide the total surface area of the tent by the coverage of each bottle to find the number of bottles needed:
Number of Bottles = Surface Area / Coverage per Bottle
Number of Bottles = 217.26 / 76
Number of Bottles ≈ 2.86
Therefore, Trent will need approximately 2.86 bottles of waterproof spray to cover his tent. Since we can't have a fraction of a bottle, he will need to round up to the nearest whole number. Therefore, Trent will need 3 bottles of waterproof spray to fully waterproof his tent.
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find the value x, round the lengths of segments to nearest tenth and the measure of angles to the nearest degree
Answer:
Step-by-step explanation:
39 !!!!!
A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window. What is the maximum area of a Norman window whose perimeter is 9 feet?
The maximum area of a Norman window with a perimeter of 9 feet is 81π/4 square feet.
To find the maximum area of a Norman window with a given perimeter, we can use calculus. Let's denote the radius of the semicircle as r and the height of the rectangular window as h.The perimeter of the Norman window consists of the circumference of the semicircle and the sum of all four sides of the rectangular window. Therefore, we have the equation:
πr + 2h = 9We also know that the area of the Norman window is the sum of the area of the semicircle and the area of the rectangle, given by:
A = (πr^2)/2 + rh
To find the maximum area, we need to express the area function A in terms of a single variable. We can do this by substituting r from the perimeter equation:
r = (9 - 2h)/(π)
Now we can rewrite the area function in terms of h only:
A = (π/2) * ((9 - 2h)/(π))^2 + h * (9 - 2h)/(π)
Simplifying this equation, we get:
A = (1/2)(9h - h^2/π)
To find the maximum area, we differentiate the area function with respect to h, set it equal to zero, and solve for h:
dA/dh = 9/2 - h/π = 0
Solving this equation, we find:h = 9π/2
Substituting this value of h back into the area function, we get:
A = (1/2)(9 * 9π/2 - (9π/2)^2/π) = (81π/2 - 81π/4) = 81π/4
Therefore, the maximum area of a Norman window with a perimeter of 9 feet is 81π/4 square feet.
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which graph represents this function
f(x)=1/2x-5
help would be appreciated
The graph of the equation f(x) = 1/2x - 5 is the graph (b)
How to determine the graph of the equationFrom the question, we have the following parameters that can be used in our computation:
f(x) = 1/2x - 5
The above expression is a linear equation that implies that
Slope = 1/2
y-intercept = -5
Next, we determine the graph
The graph that has a slope of 1/2 and y-intercept of -5 is (b)
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If is an acute angle and =35 then =?
Answer:
A acute angle is a angle that is less than 90*
the peterson family and the stewart family each used their sprinklers last summer. the water output rate for the peterson family’s sprinkler was 35 L per hour. the water output rate for the stewart family’s sprinkler was 40 L per hour. the families used their sprinklers for a combined total of 45 hours, resulting in a total water output of 1,650 L. how long was each sprinkler used?
The Peterson family used their sprinkler for 30 hours, while the Stewart family used theirs for 15 hours.
Let's assume that the Peterson family used their sprinkler for a certain number of hours, which we'll denote as x, and the Stewart family used their sprinkler for the remaining hours, which would be 45 - x.
The water output rate for the Peterson family's sprinkler is given as 35 L per hour. Therefore, the total water output for the Peterson family can be calculated by multiplying the water output rate (35 L/h) by the number of hours they used the sprinkler (x): 35x.
Similarly, for the Stewart family, with a water output rate of 40 L per hour, the total water output for their sprinkler is given by 40(45 - x).
According to the problem, the combined total water output for both families is 1,650 L. Therefore, we can write the equation:
35x + 40(45 - x) = 1,650.
Simplifying the equation, we get:
35x + 1,800 - 40x = 1,650,
-5x = 1,650 - 1,800,
-5x = -150.
Dividing both sides of the equation by -5, we find:
x = -150 / -5 = 30.
So, the Peterson family used their sprinkler for 30 hours, and the Stewart family used theirs for 45 - 30 = 15 hours.
Therefore, the Peterson family used their sprinkler for 30 hours, while the Stewart family used theirs for 15 hours.
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One of the graphs represents the statement, "y is greater than two less than the product of x and three." Which graph is it?
Based on the analysis, the graph that represents the statement "y is greater than two less than the product of x and three" is Option C.
To determine which graph represents the statement "y is greater than two less than the product of x and three," we need to analyze the given options and match them with the statement.
The statement "y is greater than two less than the product of x and three" can be represented mathematically as:
y > 2 - 3x
Now let's examine the given graphs and compare them to the equation:
Option A: This graph shows a horizontal line at y = 2. It does not involve any product of x and three, so it does not match the given statement.
Option B: This graph shows a line with a positive slope passing through the point (0, 2). While it includes the product of x and three, it does not satisfy the condition of "y is greater than two less than the product of x and three." Therefore, it does not represent the given statement.
Option C: This graph shows a line with a positive slope passing through the point (0, 2) and includes the region above the line y = 3x - 2. This region satisfies the condition of "y is greater than two less than the product of x and three." Therefore, Option C represents the given statement.
Option D: This graph shows a horizontal line at y = -2. It does not match the given statement.
Option C is correct.
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Note: This is the final question on search engine
Printing orders for Magma printers arrive at an average rate of 5 orders per hour. Assume these
orders follow a Poisson distribution.
(a) Calculate the probability that exactly 4 orders will arrive in 30 minutes? (4)
(b) Determine the probability that at least 2 orders will arrive in an hour?
Answer:
Step-by-step explanation:
To solve these problems, we can use the Poisson probability formula:
P(x; λ) = (e^(-λ) * λ^x) / x!
Where:
P(x; λ) is the probability of x events occurring
e is the base of the natural logarithm (approximately 2.71828)
λ is the average rate of events occurring in the given time period
x is the number of events
(a) Probability of exactly 4 orders arriving in 30 minutes:
The average rate of orders is given as 5 orders per hour. To find the average rate of orders in 30 minutes, we divide it by 2 (since 30 minutes is half an hour):
λ = 5 orders/hour / 2 = 2.5 orders/30 minutes
Using the Poisson probability formula:
P(x = 4; λ = 2.5) = (e^(-2.5) * 2.5^4) / 4!
Calculating this:
P(x = 4; λ = 2.5) ≈ (0.082 * 39.0625) / 24
P(x = 4; λ = 2.5) ≈ 3.22265625 / 24
P(x = 4; λ = 2.5) ≈ 0.134
Therefore, the probability that exactly 4 orders will arrive in 30 minutes is approximately 0.134, or 13.4%.
(b) Probability of at least 2 orders arriving in an hour:
To find the probability of at least 2 orders, we need to calculate the probabilities of having 0 and 1 order and subtract it from 1 (since it's the complement).
Using the Poisson probability formula:
P(x = 0; λ = 5) = (e^(-5) * 5^0) / 0! = e^(-5) ≈ 0.0067
P(x = 1; λ = 5) = (e^(-5) * 5^1) / 1! ≈ 0.0337
P(at least 2 orders) = 1 - P(x = 0) - P(x = 1) ≈ 1 - 0.0067 - 0.0337 ≈ 0.9596
Therefore, the probability of at least 2 orders arriving in an hour is approximately 0.9596, or 95.96%.
PLEASE HELP! EXPLAIN THOROUGHLY EACH QUESTION SHOULD BE ANSWERED IN A 2 SENTENCE EXPLINATION AND I WILL MARK IT BRAINLIEST!
7.
This figure shows a quadrilateral made of triangle ABF
and triangle DEC
.
a. What does it mean for triangles to be congruent?
b. Jane is told that angle A
is congruent to angle D
and angle B
is congruent to angle E
She concludes that the triangles are congruent because of AAA. Explain why she thinks this, and whether or not you think she is right.
c. George is told the same thing as Jane, but he concludes that the triangles are congruent because of ASA. Explain why he thinks this, and whether or not you think he is right.
d. Are there any other ways the two triangles could be congruent with the information Jane and George have been given? Explain why you think this.
The required answers of the given questions are answered below.
a), b), c), d)
What is quadrilateral?A quadrilateral is geometric structure enclosed in 4 sides.
A) Because,
1) the angle A = Angle D
2) its has a common side
3) the angle D = Angle B
∵ ΔEAB ≅ EDC
Thus, Both the triangle is congruent by ASA.
B.)
Jane conclusion is also write for AAA
because by angle E is congruent to angle B, implies angle F is congruent to angle C.
So that is why Jane conclude AAA.
C.) George conclusion is also perfect
George thinks the following conditions-
1) the angle A = Angle D
2) its has a common side
3) the angle D = Angle B
∵ ΔEAB ≅ EDC
Thus, Both the triangle is congruent.
Hence, Both the triangles are congruent by SSS.
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Sin(theta)=2/3 and theta is in quadrant II, find cos theta
Answer: Choice C. [tex]\displaystyle \boldsymbol{-\frac{\sqrt{5}}{3}}[/tex]
===================================================
Work Shown:
Part 1
[tex]\sin^2(\theta)+\cos^2(\theta) = 1\\\\\cos^2(\theta) = 1-\sin^2(\theta)\\\\\cos(\theta) = -\sqrt{1-\sin^2(\theta)} \ \ \text{ ..... cosine is negative in Q2}\\\\\cos(\theta) = -\sqrt{1-\left(\frac{2}{3}\right)^2}\\\\\\cos(\theta) = -\sqrt{1-\frac{4}{9}}\\\\[/tex]
Part 2
[tex]\cos(\theta) = -\sqrt{\frac{9}{9}-\frac{4}{9}}\\\\\cos(\theta) = -\sqrt{\frac{9-4}{9}}\\\\\cos(\theta) = -\sqrt{\frac{5}{9}}\\\\\cos(\theta) = -\frac{\sqrt{5}}{\sqrt{9}}\\\\\cos(\theta) = -\frac{\sqrt{5}}{3}\\\\[/tex]
If p1=(2,4,-3) and p=(3,-1,1) find parametric equation of
The parametric equation of the line passing through P1(2, 4, -3) and P(3, -1, 1) is:
x = 2 + t
y = 4 - 5t
z = -3 + 4t
To find the parametric equation of the line passing through points P1(2, 4, -3) and P(3, -1, 1), we can use the vector equation of a line.
Let's denote the direction vector of the line as d = (a, b, c). Since the line passes through P1 and P, the vector between these two points can be used as the direction vector.
d = P - P1 = (3, -1, 1) - (2, 4, -3) = (1, -5, 4)
Now, we can express the parametric equation of the line as follows:
x = x0 + at
y = y0 + bt
z = z0 + ct
where (x0, y0, z0) is a point on the line and (a, b, c) is the direction vector.
Let's choose P1(2, 4, -3) as the point on the line. Substituting the values, we get:
x = 2 + t
y = 4 - 5t
z = -3 + 4t
Therefore, the parametric equation of the line passing through P1(2, 4, -3) and P(3, -1, 1) is:
x = 2 + t
y = 4 - 5t
z = -3 + 4t
where t is a parameter that varies along the line.
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Which of the following functions is graphed below ?
Answer:
A) [tex]\displaystyle y=\left \{ {{x^3-4,\,x\leq 1} \atop {x^2-3,\,x > 1}} \right.[/tex]
Step-by-step explanation:
The first "piece" of the piecewise function, [tex]y=x^3-4[/tex], contains [tex]x=1[/tex] because of the closed dot there.
The second "piece" of the piecewise function, [tex]y=x^2-3[/tex], doesn't contain [tex]x=1[/tex] because of the open dot there.
What occurs between the two pieces is called a jump discontinuity.
Therefore, A is the correct answer.
GEOMETRY 80POINTS
ty!
Answer:
x ≈ 77.79 ft
Step-by-step explanation:
using the sine ratio in the right triangle
sin40° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{50}{x}[/tex] ( multiply both sides by x )
x × sin40° = 50 ( divide both sides by sin40° )
x = [tex]\frac{50}{sin40}[/tex] ≈ 77.79 ft ( to the nearest hundredth )
The physician’s order reads to administer Lasix 80 mg PO STAT. You have Lasix 20 mg tablets on hand. How many tablets will you administer to the patient ?
The nurse should administer 4 Lasix 20 mg tablets to the patient to achieve the prescribed dose of 80 mg.
To determine the number of Lasix 20 mg tablets that should be administered to the patient, we need to calculate how many tablets are equivalent to the prescribed dose of 80 mg.
Given that each Lasix tablet contains 20 mg of the medication, we can divide the prescribed dose (80 mg) by the dosage strength of each tablet (20 mg) to find the number of tablets needed.
Number of tablets = Prescribed dose / Dosage strength per tablet
Number of tablets = 80 mg / 20 mg
Number of tablets = 4 tablets
Therefore, the nurse should administer 4 Lasix 20 mg tablets to the patient to achieve the prescribed dose of 80 mg.
It is important to note that this calculation assumes that the Lasix tablets can be divided or split if necessary. However, it is crucial to follow the specific instructions provided by the prescribing physician or consult with a pharmacist if there are any concerns about the appropriate administration of the medication.
Additionally, it is important to consider any additional instructions, such as the frequency and timing of administration, as specified by the physician's order.
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Write the equation of the trigonometric graph.
Answer:
[tex]y=\boxed{2}\:\cos \left(\boxed{1}\;x\right)+\boxed{3}[/tex]
Step-by-step explanation:
The graph of the solid black line is the cosine parent function, y = cos(x).
The standard form of a cosine function is:
[tex]\boxed{y = A \cos(B(x + C)) + D}[/tex]
where:
A is the amplitude (height from the mid-line to the peak).2π/B is the period (horizontal distance between consecutive peaks).C is the phase shift (horizontal shift - positive is to the left).D is the vertical shift (the mid-line is y = D).From inspection of the graph, the x-values of the turning points (peaks and troughs) of the parent function and the new function are the same. Therefore, the period of both functions is the same, and there has been no horizontal shift. So, B = 1 and C = 0.
The mid-line of the new function is y = 3. Therefore, D = 3.
The y-value of the peaks is y = 5. The amplitude is the distance from the mid-line to the peak. Therefore, A = 2.
Substituting these values into the standard formula we get:
[tex]y = 2 \cos(1(x + 0)) + 3[/tex]
[tex]y=2 \cos (1(x))+3[/tex]
[tex]y= 2 \cos(x) + 3[/tex]
Therefore, the equation of the trigonometric graph is:
[tex]y=\boxed{2}\:\cos \left(\boxed{1}\;x\right)+\boxed{3}[/tex]
special right triangle
Find the zeros of the function shown below
Answer:
x = - 5 , x = 2
Step-by-step explanation:
f(x) = x² + 3x - 10
to find the zeros let f(x) = 0 , that is
x² + 3x - 10 = 0
consider the factors of the constant term (- 10) which sum to give the coefficient of the x- term (+ 3)
the factors are + 5 and - 2 , since
5 × - 2 = - 10 and 5 - 2 = + 3 , then
(x + 5)(x - 2) = 0 ← in factored form
equate each factor to zero and solve for x
x + 5 = 0 ( subtract 5 from both sides )
x = - 5
x - 2 = 0 ( add 2 to both sides )
x = 2
the zeros are x = - 5 , x = 2
Input an ordered pair that satisfies the system of inequalities:
-
y < − x − 3
y> 2x - 4
To find an ordered pair that satisfies the given system of inequalities, we need to find a point that lies below the line y = -x - 3 and above the line y = 2x - 4.
One such point that satisfies both inequalities is (-1, 0).
Let's check if this point satisfies both inequalities:
For the first inequality, y < -x - 3:
0 < -(-1) - 3
0 < 1 - 3
0 < -2 (True)
For the second inequality, y > 2x - 4:
0 > 2(-1) - 4
0 > -2 - 4
0 > -6 (True)
Therefore, the ordered pair (-1, 0) satisfies the system of inequalities y < -x - 3 and y > 2x - 4.
Given the calculator output below, determine the following: (round all answers to four decimal places)
LinReg
y=ax+b
a=.1186440678
b=3.677966102
r2=.0353407862
r. 1879914523
a.) What is the value of the correlation coefficient?
b.) What is the value of the slope of the regression line?
c.) What is the value of the coefficient of determination?
d.) What is the value of the y-intercept of the regression line?
Answer:
a) r = .1880
b) a = .1186
c) r² = .0353
d) b = 3.6780
What number completes the sequence below? Enter your answer in the input
box at the bottom.
8————-4
16————8
24———-12
32———-?
Answer here
Answer:
The number is 16
Step-by-step explanation:
This follows a multiplication rule,
4 times 1 = 4
4 times 2 = 8
4 times 3 = 12
4 times 4 = 16
So, the number is 16
what is the square root of the fraction, 3/25?
Answer: 0.3464 (correct upto 4 decimal places )
Step-by-step explanation:
[tex]\sqrt{3/25}[/tex]= [tex]\sqrt{3} /\sqrt{25\\}[/tex] (as the square root of 25 is 5)
=1.73205/5
=0.3464
Let S be a set that contains atleast two different elements. Let R be the relation on P(S),
thesetofallsubsetsofS,definedby(X,Y)∈RifandonlyifX∩Y =φ.
(i) Determine whether R is reflexive, symmetric, antisymmetric, or transitive.
(ii) Why is it important that S has atleast 2 different elements?
(iii) Would any of the answers change in (i) if S was empty or had only one element?
(i) R is not reflexive, symmetric, vacuously antisymmetric, and not transitive.
(ii) It is important that S has at least two different elements because if S had only one element, then the power set P(S) would contain only two sets: the empty set and the set S itself.
(iii) If S was empty, there would be no elements in S, and hence the power set P(S) would only contain the empty set. The answers regarding reflexivity, symmetry, antisymmetry, and transitivity would all change, and the relation R would not possess any of these properties. If S had only one element, the power set P(S) would contain two sets: the empty set and the singleton set containing the one element of S. The relation R would be reflexive, symmetric, antisymmetric, and transitive, as it satisfies all these properties by definition.
(i)Let's analyze the properties of relation R on P(S):
Reflexive: A relation R is reflexive if for every element x in the set S, (x, x) belongs to R. In this case, since the intersection of any set with itself is never empty, the relation R is not reflexive.
Symmetric: A relation R is symmetric if for every pair (x, y) in R, (y, x) also belongs to R. In this case, since the intersection of two sets is commutative, if (X, Y) belongs to R, then (Y, X) also belongs to R. Thus, the relation R is symmetric.
Antisymmetric: A relation R is antisymmetric if for every distinct pair (x, y) in R, (y, x) does not belong to R. Since the relation R is defined by the condition X∩Y = φ, there are no distinct pairs (X, Y) that satisfy the condition. Therefore, the relation R is vacuously antisymmetric.
Transitive: A relation R is transitive if for every three sets X, Y, and Z such that (X, Y) belongs to R and (Y, Z) belongs to R, then (X, Z) also belongs to R. In this case, if X∩Y = φ and Y∩Z = φ, it does not imply that X∩Z = φ. Hence, the relation R is not transitive.
(ii) In this scenario, the relation R would not have any pairs (X, Y) where X and Y are non-empty subsets of S, because the intersection of any two non-empty subsets would never be empty. Thus, the relation R would be trivial and uninteresting.
(iii) In this case, since there are no non-empty subsets in P(S), the relation R would not have any pairs (X, Y) where X and Y are non-empty subsets of S.
In this case, the relation R would have only one possible pair (X, Y) with X and Y being the empty set, and their intersection would indeed be empty.
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priya and han each wrote an equation of a line with slope 1/3 that passes through the point (1,2). priyas equation is y - 2 = 1/3 (x-1) and hans equation is 3y-x=5. do you agree with either of them? explain or show your reasoning
I agree with both Priya's and Han's equations.
To determine if either Priya or Han equation is correct, we can substitute the coordinates of the given point (1,2) into each equation and check if the equation holds true.
For Priya's equation, y - 2 = (1/3)(x - 1), substituting x = 1 and y = 2:
2 - 2 = (1/3)(1 - 1)
0 = 0
The equation holds true, so Priya's equation is correct.
For Han's equation, 3y - x = 5, substituting x = 1 and y = 2:
3(2) - 1 = 5
6 - 1 = 5
5 = 5
The equation also holds true, so Han's equation is correct.
Both Priya's and Han's equations are valid equations of the line with a slope of 1/3 passing through the point (1,2). The equations have different forms, but they are algebraically equivalent and represent the same line. Therefore, I agree with both Priya's and Han's equations.
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3. Determine whether the triangles are similar. If they are, write a similarity statement.
Look at picture for reference
Please show work
The triangles DEF and SRQ are not similar triangles
Identifying the similar triangles in the figure.From the question, we have the following parameters that can be used in our computation:
The triangles in this figure are
DEF and SRQ
These triangles are not similar
This is because:
The corresponding angles in the triangles are not equal
For DEF, the angles are
50, 90 and 40
For SRQ, the angles are
51, 90 and 39
This means that they are not similar by any similarity statement
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Determine the perimeter of a soccer field with a length of 97 metres and a width of 69 metres
Answer: Therefore, the perimeter of the soccer field is 332 meters.
Step-by-step explanation:
To determine the perimeter of a soccer field with a length of 97 meters and a width of 69 meters, we can use the formula for the perimeter of a rectangle, which is given by:
Perimeter = 2 * (length + width)
Plugging in the values, we have:
Perimeter = 2 * (97 + 69)
Perimeter = 2 * 166
Perimeter = 332 meters
What is the volume of this
figure?
A 774 cm³
B 3,546 cm³
C 843 cm3
D 2,250 cm³
Hello!
Volume
= (18cm * 15cm * 6cm) + ((13cm - 6cm) * 15cm * 6cm)
= 1,620cm³ + 630cm³
= 2,250cm³
If 2x2 - 4x + 6 = 1 then A = 2, B = -4, and C = 6 in general form.
In general form, the equation 2x^2 - 4x + 6 = 1 can be represented as A = 2, B = -4, and C = 5.
To determine the values of A, B, and C in the general form of the quadratic equation 2x^2 - 4x + 6 = 1, we can compare the given equation with the standard form of a quadratic equation, which is ax^2 + bx + c = 0.
In the given equation, we have:
2x^2 - 4x + 6 = 1
To put it in the general form, we need to move all the terms to the left side of the equation, so the right side is equal to 0:
2x^2 - 4x + 6 - 1 = 0
2x^2 - 4x + 5 = 0
Now we can identify the coefficients A, B, and C in the general form:
A = 2 (coefficient of x^2)
B = -4 (coefficient of x)
C = 5 (constant term)
The values of A, B, and C in the general form of the equation 2x^2 - 4x + 6 = 1 are A = 2, B = -4, and C = 5.
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Find the co-vertices of the hyperbola defined by the equation.. 100pts
Answer:
(-13, -9) and (-5, -9)
Step-by-step explanation:
The given equation of the hyperbola is:
[tex]\dfrac{(y+9)^2}{25}-\dfrac{(x+9)^2}{16}=1[/tex]
As the y²-term of the given equation is positive, the transverse axis is vertical, and so the hyperbola is vertical (opens up and down).
The standard equation for a vertical hyperbola is:
[tex]\boxed{\dfrac{(y-k)^2}{a^2}-\dfrac{(x-h)^2}{b^2}=1}[/tex]
where:
center = (h, k)vertices = (h, k±a)co-vertices = (h±b, k)foci = (h, k±c) where c² = a² + b²Compare the given equation with the standard equation to find the values of h, k, a and b:
h = -9k = -9a² = 25 ⇒ a = 5b² = 16 ⇒ b = 4The formula for the co-vertices of a vertical hyperbola is (h±b, k).
Substitute the values of b, h and k into the formula:
[tex]\begin{aligned}\textsf{Co-vertices}&=(h\pm b,k)\\&=(-9\pm 4, -9)\\&=(-13,-9)\;\;\textsf{and}\;\;(-5, -9)\end{aligned}[/tex]
Therefore, the co-vertices of the given hyperbola are:
(-13, -9) and (-5, -9)The co-vertices of the hyperbola are (-4, -9) and (-14, -9).
What are the co-vertices of the hyperbola?To find the co-vertices of the hyperbola defined by the equation:
[(y + 9)² / 25] - [(x + 9)² / 16] = 1
We can compare the equation to the standard form of a hyperbola:
[(y - h)² / a²] - [(x - k)² / b²] = 1
In this case, we have h = -9 and k = -9.
The co-vertices of a hyperbola lie on the transverse axis, which is the line passing through the center of the hyperbola. The center of the hyperbola is given by (h, k), which in this case is (-9, -9).
For a hyperbola with the equation in this form, the co-vertices are located a units to the right and left of the center. In this case, since the equation is [(y + 9)² / 25] - [(x + 9)² / 16] = 1, we have a = 5.
Therefore, the co-vertices are located at (-9 ± a, -9), which gives us:
(-9 + 5, -9) = (-4, -9)
(-9 - 5, -9) = (-14, -9)
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The base of a rectangular prism is a square whose sides each measure 9 inches. The height of the rectangular prism is 11 inches, find it’s volume?
Answer:
99
Step-by-step explanation:
since the height is 9 and the base is 11 we use the formula BH=V
substitute 9x11 and get 99
Which property best describes the conditional statement below If triangle ABC= triangle DEF then triangle DEF=triangleABC
Answer:
would this not be a converse statement?
Step-by-step explanation:
triangle ABC is the hypothesis and it's conclusion is triangle DEF
In circle P with m LN RQ = 60, find the
m/NPQ.
Answer:
∠ NPQ = 120°
Step-by-step explanation:
the central angle NPQ is twice the angle on the circle NRQ , subtended by the same arc NQ , then
∠ NPQ = 2 × 60° = 120°