The function is f(x) = 25100(1 + 0.06)ˣ and the estimate fox population in the year 2008 is 40,0005.
What is an exponential function?It is defined as a function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent y = a^x
where a is a constant and a>1
It is given that:
The fox population in a certain region has a continuous growth rate of 6 percent per year
f(x) = a(1 + r)ˣ
f(x) = 25100(1 + 0.06)ˣ
Plug x = 8 years
f(8) = 25100(1 + 0.06)⁸
f(8) = 40,0005
Thus, the function is f(x) = 25100(1 + 0.06)ˣ and the estimate the fox population in the year 2008 is 40,0005.
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In the diagram, the length of segment VS is 39 units. Line n is a perpendicular bisector of line segment T V. It intersects line segment T V at point R. Line n also contains points Q and S. Line segment Q V is 3 x + 4. Line segment R V is 2 x + 5. Line segment T S is 6 x minus 3. What is the length of segment TV? 14 units 19 units 38 units 50 units
On solving the provided question, by help of the Linear Equation we got that TV = 38 units.
what is linear equation?Any equation with a degree of 1 or above is considered linear. This shows that the exponent of the linear equation's variable is bigger than 1. A linear equation will always have a straight line as its graph.
RST and RSV, two equal right triangles, are shown in the illustration.
Notice that:
TS = VS
We know that,
TS = 6x - 3
VS = 39
6x - 3 = 39
6x = 42
[tex]x = \frac{42}{6}[/tex]
x = 7
Now, you can identify in the figure that:
RV = 2x + 5
The length of segment RV may be determined by substituting the above-calculated value of "x" into the equation and evaluating:
RV = 2(7)+ 5
RV = 19 units
Now,
TV = 19 + 19
TV = 38 units
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40 POINTS Use photo
Find BA.
The function c(r) = 0.47x + 20 represents the cost (in dollars) of a one-day truck rental when the truck is
driven x miles.
a. What is the truck rental cost when you drive 80 miles?
b. How many miles did you drive when your cost is $35.51?
Answer: the cost is $35.51, That must mean it would be driven 33.0 miles.
Step-by-step explanation: The given function c(r) represents the cost of a one-day truck rental when the truck is driven x miles. This means that the cost in dollars is a linear function of the number of miles driven.
To answer the first part of the question, we can plug in x = 80 into the function to find the truck rental cost when we drive 80 miles:
$$c(r) = 0.47x + 20 = 0.47(80) + 20 = \boxed{35.6}$$
To answer the second part of the question, we can solve the equation $c(r) = 0.47x + 20 = 35.51$ for x to find the number of miles driven when the cost is $35.51:
$$35.51 = 0.47x + 20 \Rightarrow 15.51 = 0.47x \Rightarrow x = \boxed{33.0}$$
Therefore, when the cost is $35.51, we must have driven 33.0 miles.
what are two diffrent if-then statements implied by Theorem 2-13?
The two different if-then statements implied by Theorem 2-13 are:
If lines and are both not vertical then p || q if and only if the slope of the line p is equal to the slope of the line q.If lines p and q are both vertical then p || q.What is the Parallel Lines & Perpendicular Lines?
Parallel Lines :Two or more lines that lie in the same plane and never intersect or meet each other are known as parallel lines,
Perpendicular Lines are formed when two lines meet each other at the right angle or 90 degrees.
Given: The theorem 2-13 is given.
We have to find what are two different if-then statements implied by Theorem 2-13.
The two different if-then statements implied by Theorem 2-13 are:
If lines and are both not vertical then p || q if and only if the slope of the line p is equal to the slope of the line q.If lines p and q are both vertical then p || q.Hence, The two different if-then statements implied by Theorem 2-13 are:
If lines and are both not vertical then p || q if and only if the slope of the line p is equal to the slope of the line q.If lines p and q are both vertical then p || q.To learn more about the Parallel Lines & Perpendicular Lines visit,
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If R = {(x, y): y=x²-4 and y ≤5], then Find a) Domain and Range of R b) Inverse relation (R') c) Domain and Ranpe of R d) To Sketch the graphs of R. and Ro
a) The Domain is [-∞, 5]
And the range is [-∞, 3]
b) The area covered by a relation's inverse is the same as its domain. In other words, the relationship's x-values are its inverse's y-values.
c) The Domain is [-∞, 5]
And the range is [-∞, 3]
d) The graph of R is shown below:
What is meant by Domain?The set of inputs that a function will accept is referred to as the domain of the function in mathematics. It is important to note that in contemporary mathematical terminology, a function's domain is a component of its definition rather than a quality.
The function f can be plotted in the Cartesian coordinate system in the special case where X and Y are both subsets of R. In this example, the graph's x-axis shows the domain as the projection.
Given,
R = {(x, y): y=x²-4 and y ≤5]
For x=0, y=-4
For x=1, y=-3
For x=2, y=0
For x=3, y=5
Therefore, the Domain is [-∞, 5]
And the range is [-∞, 3]
The area covered by a relation's inverse is the same as its domain. In other words, the relationship's x-values are its inverse's y-values.
The graph of R is shown below:
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For triangle ABC, tell what information is given (i.e. SAS, SSS, ASA, etc.) in Column A. Solve for the indicated angle or side in Column B. If there are two solutions, give both. Express answers to the nearest tenth.
1. A=52°, b=120, c = 160, find a
2. a=13.7, A=2543°, B=78°, find b
3. A=38°, B=63°, c=15, find b
4. a=1.5, b=2.3, c=1.9, find B
5. b=795.1, c=775.6, B=51.85°, find C
6. b=40, c=45, A=51°, find a
7. b=50, a=33, A=132°, find B
8. a=20, b=12, c=28, find C
9. a=125, A=25°, b=150, find B
10. b=15.2, A=12.5°, C=57.5°, find c
Using the laws of sines and cosines, answers to the questions are as follows,
1. A=52°, b=120, c = 160,
SAS property, a=128
2. a=13.7, A=25.43°, B=78°,
AAS property, b=31.21
3. A=38°, B=63°, c=15,
ASA property, b=14
4. a=1.5, b=2.3, c=1.9,
SSS property, B=84
5. b=795.1, c=775.6, B=51.85°,
SAS property, C=50
6. b=40, c=45, A=51°,
SAS property, a=37
8. a=20, b=12, c=28
SAS property, C=120
9. a=125, A=25°, b=150
SAS property, 2 solutions are there, B1=149, B2=30.4
10. b=15.2, A=12.5°, C=57.5°
SAS property, c=14
What are the laws of sine and cosine?
We can determine a triangle's one side's length or one of its angles' measurements using the laws of sine and cosine.
In most cases, the unknown sides or angles of an oblique triangle are calculated using the law of sines formula.
The equation that connects the lengths of the triangle's sides and the cosines of its angles is known as the law of cosine or cosine rule.
1. Given A=52°, b=120, c = 160.
If we construct the triangle, we see that it is satisfying the SAS property
By using the law of cosine we get,
[tex]a^{2}=b^{2} +c^{2}-2.b.c.\cos A\\a=\sqrt{b^{2}+c^{2}-2.b.c.\cos A}\\a=\sqrt{120^{2}+160^{2}-2.120.160.\cos 52}\\a=127.9[/tex]
2. Given, a=13.7, A=25.43°, B=78°
From angle A, angle B, and side a, we calculate side b, by using the Law of Sines,
[tex]\frac{b}{a}=\frac{\sin B}{\sin A}\\b=a.\frac{\sin B}{\sin A}\\b=13.7. \frac{\sin 78}{\sin 25.43}\\b=31.21[/tex]
3. A=38°, B=63°, c=15
From angle A and angle B, we calculate angle C,
[tex]A+B+C=180\\C=180-A-B\\C=180-38-63\\C=79[/tex]
Next, From angle A, angle C, and side c, we calculate side a, by using the Law of Sines
[tex]\frac{a}{c}=\frac{\sin A}{\sin C}\\a=c.\frac{\sin A}{\sin C}\\a=15. \frac{\sin 38}{\sin 79}\\a=9.41[/tex]
Calculation of the third side b of the triangle using a Law of Cosines,
[tex]b^{2}=a^{2} +c^{2}-2.a.c.\cos B\\b=\sqrt{a^{2}+c^{2}-2.a.c.\cos B}\\b=\sqrt{9.1^{2}+15^{2}-2.9.41.15.\cos 63}\\b=13.68[/tex]
4. a=1.5, b=2.3, c=1.9
Calculation of the inner angles of the triangle using a Law of Cosines
[tex]b^{2}=a^{2}+c^{2}-2.a.c.{\cos B}\\B=arc {\cos} \frac{a^{2}+c^{2}-b^{2} }{2.a.c} \\ B=arc {\cos} \frac{1.5^{2}+1.9^{2}-2.3^{2} }{2 . 1.5.1.9}\\B=84.15[/tex]
5. b=795.1, c=775.6, B=51.85°
From angle B, side c, and side b, we calculate side a. by using the Law of Cosines and quadratic equation:
[tex]b^2 = c^2 + a^2 - 2.c. a. {\cos B} \\ 795.1^2 = 775.6^2+a^2-2. 775.6. a . \cos 51\ \\ a > 0 \\ a = 989.175[/tex]
Calculation of angle C of the triangle using a Law of Cosines
[tex]c^{2}=a^{2}+b^{2}-2.a.b.{\cos C}\\C=arc {\cos} \frac{a^{2}+b^{2}-c^{2} }{2.a.b} \\ C=arc {\cos} \frac{989.175^{2}+795.1^{2}-775.6^{2} }{2 . 989.795}\\C=50.5[/tex]
6. b=40, c=45, A=51°
Calculation of the third side a of the triangle using a Law of Cosines
[tex]a^{2}=b^{2} +c^{2}-2.b.c.\cos A\\a=\sqrt{b^{2}+c^{2}-2.b.c.\cos A}\\a=\sqrt{40^{2}+45^{2}-2.0.45.\cos 51}\\a=36.87[/tex]
8. a=20, b=12, c=28
Calculation of angle C of the triangle using a Law of Cosines
[tex]c^{2}=a^{2}+b^{2}-2.a.b.{\cos C}\\C=arc {\cos} \frac{a^{2}+b^{2}-c^{2} }{2.a.b} \\ C=arc {\cos} \frac{20^{2}+12^{2}-28^{2} }{2 . 20.12}\\C=120[/tex]
9. a=125, A=25°, b=150
2 solutions are possible for this,
solution for B1:
From the angle A, side b, and side a, we calculate side c. by using the Law of Cosines and quadratic equation:
[tex]a^2 = b^2 + c^2 - 2b c \cos A \ \\ 125^2 = 150^2 + c^2 - 2 \cdot \ 150 \cdot \ c \cdot \ \cos 25\degree \ \ \\ c > 0 \ \\ c = 28.21[/tex]
Calculation of angle B of the triangle using a Law of Cosines
[tex]b^{2}=a^{2}+c^{2}-2.a.c.{\cos B}\\B=arc {\cos} \frac{a^{2}+c^{2}-b^{2} }{2.a.c} \\ B=arc {\cos} \frac{125^{2}+28.21^{2}-150^{2} }{2 . 125.28}\\B=149[/tex]
solution for B2:
From the angle A, side b, and side a, we calculate side c. by using the Law of Cosines and quadratic equation:
[tex]a^2 = b^2 + c^2 - 2b c \cos A \ \\ 125^2 = 150^2 + c^2 - 2 \cdot \ 150 \cdot \ c \cdot \ \cos 25\degree \ \ \\ c > 0 \ \\ c = 243.679[/tex]
Calculation of angle B of the triangle using a Law of Cosines
[tex]b^{2}=a^{2}+c^{2}-2.a.c.{\cos B}\\B=arc {\cos} \frac{a^{2}+c^{2}-b^{2} }{2.a.c} \\ B=arc {\cos} \frac{125^{2}+243^{2}-150^{2} }{2 . 125.243}\\B=30.28[/tex]
10. b=15.2, A=12.5°, C=57.5°
From angle A and angle C, we calculate angle B:
[tex]A+B+C=180\\B=180-A-C\\B=180-12.5-57.5\\B=110[/tex]
From the angle A, angle B, and side b, we calculate side a, by using the Law of Sines.
[tex]\ \\ \dfrac{ a }{ b } = \dfrac{ \sin A }{ \sin B } \\ a = b \cdot \ \dfrac{ \sin A }{ \sin B } \\ a = 15.2 \cdot \ \dfrac{ \sin 12.30 }{ \sin 110\degree } = 3.5[/tex]
Calculation of the third side c of the triangle using a Law of Cosines
[tex]c^{2}=a^{2} +b^{2}-2.a.b.\cos C\\c=\sqrt{a^{2}+b^{2}-2.a.b.\cos C}\\c=\sqrt{15.2^{2}+3.5^{2}-2.15.4.\cos 57.30}\\c=13.64[/tex]
Therefore, we have found the solutions of all of the above bits using the law of sine and cosine.
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Which answer choice correctly complete the sentence?
The Problem Solving Plan is a method to
OA) show all your work in math.
O B) give an example of a real-life problem.
OC) make solving a word problem easier.
OD) check to see if your answer is reasonable.
Answer: C
Step-by-step explanation:
The problem solving plan is a method to make solving a word problem easier.
Use the figure to find the missing angles
Answer:
Angel 5 is 73
Angel 1 is 37
Angel 2 is 42
Angel 3 is 132
Angel 4 is 73
Angel 6 is 30
Step-by-step explanation:
A man walks for 2 hours at a certain speed. He then cycles at three times that seed for
4 hours. He goes 77km altogether. Find the speed at which he walks.
5.5km/hr is the speed at which he walks.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given
w = walking speed
t = time walking = 2
Given, A man walks for 2 hours at a certain speed which is 2w
He then cycles at three times that seed for 4 hours.
We can form a equation by given data
2w + 3×w×4 = 77
2w+12w=77
14w = 77
Divide both sides by 14
w = 5.5 km/hr
Hence, 5.5km/hr is the speed at which he walks.
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The circumference of a tree at different heights above the ground is given in the table below. Assume that all horizontal cross-sections of the tree are circles. Estimate the volume of the tree.
Estimated volume of the tree as per given height and circumference using trapezoidal rule is equal to 30907.5 cubic inches.
As given in the question,
Given height 'x' and circumference 'y=f(x)',
Height (inches) 'x' : 0 15 30 45 60 75 90
Circumference (inches) 'y=f(x)': 31 28 21 17 12 8 2
Trapezoidal rule :
Δx = (b - a ) n
Here b = 90
a = 0
n =6
Δx = ( 90 - 0)/6
= 15
Substitute the value to get the volume using trapezoidal rule:
T₆=(Δx/2)[f(x₀)²+ 2{f(x₁)²+ f(x₂)²+f(x₃)² + f(x₄)²+f(x₅)²}+ f(x₅)²]
= (15/2)[ 31² + 2 (28² + 21² + 17² + 8²) + 2² ]
= ( 15/2) [961 + 2{ 784+ 441 + 289 + 64} + 4]
= 15 × 2060.5
= 30907.5 cubic inches
Therefore, the volume of the tree as per given given table using trapezoidal rule is equal to 30907.5 cubic inches.
The above question is incomplete , the complete question is:
The circumference of a tree at different heights above the ground is given in the table below. Assume that all horizontal cross-sections of the tree are circles. Estimate the volume of the tree using the trapezoid rule. There needs to be six subdivisions in the trapezoid rule.
Height (inches) : 0 15 30 45 60 75 90
Circumference (inches): 31 28 21 17 12 8 2
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The plane is perpendicular to the axis but does not go through the vertex.
The plane intersects the double cone at only the vertex.
The plane is not intersecting the vertex, not parallel to the axis, not perpendicular to the axis, not parallel to the side of the cone, and it intersects only one cone.
The plane is tangent to both of the cones.
answers:
line
point
circle
elipse
match these
The plane is perpendicular to the axis but does not go through the vertex. The plane intersects the double cone at only the vertex is ellipse.
What is an ellipse ?A planar curve with two focal points is called an ellipse if at every point on the curve the sum of the two distances from the focal points is constant. It generalises the shape of a circle, a unique variety of ellipse in which the two focus points coincide.The plane is not intersecting the vertex, not parallel to the axis, not perpendicular to the axis, not parallel to the side of the cone, and it intersects only one cone is circle.A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre.To learn more about ellipse refer :
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I need help with this.
Answer:
Step-by-step explanation:
ax² + bx + c = 0
D = b² - 4ac
If D > 0 , then quadratic equation has 2 roots.
If D = 0 , then quadratic equation has 1 roots.
If D > 0 , then quadratic equation has No roots in the set of real numbers.
~~~~~~~~~~~~~~~~~~~~
2y² + 4y = 3
2y² + 4y - 3 = 0
a = 2 , b = 4 , c = - 3
D = 4² - 4(2)( - 3) = 40 > 0 ( 2 solutions )
[tex]y_{12}[/tex] = ( - 4 ± 2√10 ) ÷ 4
[tex]y_{1}[/tex] = [tex]\frac{-2+\sqrt{10} }{2}[/tex]
[tex]y_{2}[/tex] = [tex]\frac{-2-\sqrt{10} }{2}[/tex]
find the area of 10x^2+9x+2 when the the width is 2x+1
B={x|x is an integer and -4
The resultant answer in roster form is B = {-3, -2, -1, 0, 1, 2, 3, 4, 5}.
What is roster form?In the set-builder form, a short, statement, or formula is written inside a pair of curly braces, as opposed to the roster form, where the listed items are enclosed in a pair of curly braces and separated by commas.
Roster or tabular form: In roster form, all of the components of a set are listed, with commas used to divide them and braces used to enclose them.
For instance, Z = the set of all integers = {…,−3,−2,−1,0,1,2,3,…}.
So, we have:
B = {x:x is an integer and -4 < x < 6}
B has numbers from -4 and 6.
Now, write B in roster form as:
B = {-3, -2, -1, 0, 1, 2, 3, 4, 5}
Therefore, the resultant answer in roster form is B = {-3, -2, -1, 0, 1, 2, 3, 4, 5}.
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Complete question:
Write the following sets in roster form:
B = {x:x is an integer and -4 < x < 6}
Find the missing length in the triangle below. Round to the nearest
tenth if necessary. Show all your work for credit.
0:05
9 ft
X
4 ft
The missing length in the triangle
is approximately
feet.
A phone company offers two monthly plans. plan A cost $19 plus an additional $0.11 for each minute of calls. plan B has no initial fee but costs $0.15 for each minute of calls.
Answer: 475 minutes.
Step-by-step explanation: To compare the cost of these two plans, you need to find how many minutes of calls are needed for the cost of each plan to be the same. Let's call this number of minutes x.
For plan A, the total cost will be $19 plus $0.11 for each minute of calls, or a total of 19 + 0.11x dollars.
For plan B, the total cost will be $0.15 for each minute of calls, or a total of 0.15x dollars.
Since the cost of the two plans is equal, we can set these expressions equal to each other and solve for x:
19 + 0.11x = 0.15x
Subtracting 0.11x from both sides, we get:
19 = 0.04x
Dividing both sides by 0.04, we get:
475 = x
Therefore, the number of minutes of calls needed for the cost of the two plans to be the same is 475 minutes.
Use the quadrilateral below to help answer the next two questions.
If L is (-2,-5) and M is (4,-1), what should the slope of NO be in order for LMNO to be a parallelogram?
Note: Enter negatives when necessary with no space between the negative sign and the number.
If the answer is a fraction, leave as an improper fraction in simplest form. Ex. 4/3 for 8/6
The required slope of the side NO is given as 2/3 and the Slope of the LO is given as -3/2.
Given that,
A figure shown of a quadrilateral in order to prove the quadrilateral as a rectangle, the slope of the sides LO and NO is to be determined.
The rectangle is 4 sided geometric shape whose opposites are equal in length and all angles are about 90°.
here,
Because of the parallel sides,
The slope of the side NO is = Slope of the side LM
= [-1 + 5] / [4 + 2] = 2/3
Because of the perpendicular sides,
The slope of the side LO = - 1 / slope of the side LM
= -1 / 2/3 = -3/2
Thus, the required slope of the side NO is given as 2/3 and the Slope of the LO is given as -3/2.
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There were 169 tickets for a major league baseball game. The lower box tickets cost $12.50 and the upper box tickets cost $10.00. The total amount of money spent was $1795.00. How many of each kind of ticket were purchased?
Answer:
42 lower box127 upper boxStep-by-step explanation:
You want the number of tickets of each kind sold if 169 tickets were sold for $1795, and lower box tickets were $12.50 while upper box tickets were $10.
SetupLet x represent the number of lower box tickets sold. Then 169 -x is the number of upper box tickets sold. The total revenue is ...
12.50(x) + 10.00(169 -x) = 1795.00
SolutionSimplifying, we get
2.50x +1690 = 1795
2.5x = 105 . . . . . . . . . . . subtract 1690
x = 42 . . . . . . . . . . . . divide by 2.5; the number of lower box ticket sold
169 -42 = 127 . . . . . . the number of upper box tickets sold
42 lower box and 127 upper box tickets were purchased.
If a box of chocolate costs $8.00 and weighs 1 lb.
what is the cost per ounce?
Answer:
$0.50 per ounce
Step-by-step explanation:
To find the cost per ounce of the chocolate, you will need to divide the price of the box by the weight of the box in ounces. Since there are 16 ounces in a pound, the weight of the box in ounces is 1 * 16 = <<1*16=16>>16 ounces.
To find the cost per ounce, divide the price of the box by the weight of the box in ounces: $8.00 / 16 ounces = $0.50 per ounce.
Therefore, the cost per ounce of the chocolate is $0.50.
Find dy, dx if f(x) = (x + 1)2x.
Options:
A. 2xln(x + 1)
B. 2 times the natural log of the quantity x plus 1 plus 2 times x divided by the quantity x plus 1
C. 2x(x + 1)(2x - 1)
D. the product of the quantity 2 times the natural log of the quantity x plus 1 plus 2 times x divided by the quantity x plus 1, and the quantity x plus 1 raised to the 2x power
Answer:
D, I've taken the test already!
Step-by-step explanation:
there
PLEASSEEEE HEELPPP ASAPPPPP!!! (FOR 10 POINTS!)
For each system of equations below, choose the best method for solving
and solve. Show your work.
a. 3x+y=24
-x-y=-10
The solution to the system of equations 3x+y=24 and -x-y=-10 is x = 7, y = 3
How to determine the solution to the system?The system of equations is given as
3x+y=24
-x-y=-10
Make x the subject in the second equation
So, we have the following representation
x = 10 - y
Substitute x = 10 - y in the equation 3x+y=24
3(10 - y) +y=24
Expand the bracket
30 - 3y + y = 24
Evaluate the like terms
-2y = -6
Divide by -2
y = 3
Recall that
x = 10 - y
So, we have
x = 10 - 3
x = 7
Hence, the solution is x = 7, y = 3
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(2k^3)^2
answer should contain only positive exponents
bro i need help so bad
its congruent angles and whatever
GEOMETRY 50 POINTSS
Answer:
x = 20°y = 70°Step-by-step explanation:
I need help with this
Step-by-step explanation:
If M is the midpoint of AB then,
AM = BB so we can write the following equation:
4x + 13 = 3x + 17
transfer like terms to the same side of the equation4x - 3x = 17 - 13
add/subtractx = 4
Now on to the length of BM, we can replace x with 4 to find it.
3*4 + 17 = 29
determine each feature of the graph of the given function
f(x)= -5/2x-1
horizontal asymptote: y =
vertical asymptote: x =
y intercept: ( _, 0)
x intercept: (0, _ )
hole: ( _ , _ )
Answer:
Step-by-step explanation:
HORIZONTAL ASYMPTOTE
lim x-> oo -5/(2x-1)
-5/(oo-1)
-5/oo
0
y = 0
VERTICAL ASYMPTOTE
2x - 1 = 0
2x = 1
2/2 x = 1/2
x = 1/2
y INTERCEPT
-5/(0-1)
-5/-1
5
(5,0)
X INTERCEPT
-5 = 0
Impossible
no x intercept
What is the remainder when 3x^3-5x^2-23x+24 is divided by x-3?
The remainder you got when 3x³ - 5x² - 23x + 24 is divided by x - 3 is -9.
What is Polynomials?Polynomials are expressions in algebra which consist of both variables and coefficients. Sometimes, variables are also known as indeterminates. Polynomials are classified as monomials, binomials, and trinomials based on the degree of the variables in the expression.
Variables in the monomials, binomials and trinomials have the highest degree equals 1, 2 and 3 respectively.
By doing the long division method, we will bet the quotient as 3x² + 4x - 11 and the remainder equals -9.
Let's check this using division algorithm.
Dividend = 3x³ - 5x² - 23x + 24
Divisor = x - 3
Quotient = 3x² + 4x - 11
Remainder = -9
By division algorithm,
Dividend = (Divisor × Quotient) + Remainder
3x³ - 5x² - 23x + 24 = [(x - 3) (3x² + 4x - 11)] + -9
= [3x³ + 4x² - 11x - 9x² - 12x + 33] + -9
= 3x³ + 4x² - 9x² - 11x - 12x + 33 - 9
= 3x³ - 5x² - 23x + 24
Hence -9 is the remainder of this division process.
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Write the equation of the line in slope-intercept form (y = mx + b) based on the given information. 11. Passes through (12,-6) and perpendicular to y = 3x + 1
The equation of the line that is perpendicular to y = 3x + 1, in slope-intercept, is: y = -1/3*x - 2.
How to Write the Equation of a Perpendicular Line in Slope-intercept Form?If we are given a line that passes a point (12, -6) and is perpendicular to y = 3x + 1, we can find the equation of the line in slope-intercept form following the steps below.
First, find the slope of y = 3x + 1. The slope is 3. Since both lines are perpendicular to each other, therefore, the slope of the line that passes through (12, -6) would be the negative reciprocal of 3, which is m = -1/3.
Substitute m = -1/3 and (a, b) = (12, -6) into y - b = m(x - a):
y - (-6)) = -1/3(x - 12)
y + 6 = -1/3(x - 12)
Rewrite in slope-intercept form:
y + 6 = -1/3*x + 4
y + 6 - 6 = -1/3*x + 4 - 6
y = -1/3*x - 2
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Kara has five exam scores of 89, 82, 69, 79, and 70 in her biology class. What score does she need on the final exam to have a mean grade of 80? Round your answer to two decimal places, if necessary. (All exams have a maximum of 100 points.
Answer:
91
Step-by-step explanation:
[tex]\frac{89+82+69+79+70+x}{6}[/tex] = 80 Combine like terms
[tex]\frac{389+ x}{6}[/tex] = 80 Multiple by sides by 6
380 + x = 480 Subtract 389 from both sides.
x = 91
Hannah invested $2,500 in an account earning 3.4% annual interest that is compounded semi-annually. How long will it take the investment to triple?
(Round your answer to the nearest hundredth.)
Based on the fact that Hannah's investment will triple in 10 years and 10 months when compounding occurs every six months.
What is compounding?The process through which interest is added to the existing principal sum and the interest that has previously been paid is known as compounding.
As a result, compounding, sometimes known as the "magic of compounding," can be thought of as interest on interest, which has the effect of making returns on interest larger over time.
The amount of time required to triple the investment is as follows:
$2500 was invested.
3.4% interest rate.
Compounding: Every 6 months (Semiannually)
Now think about a time frame of two years:
3.4 * 6/12 = 1.7%
The effective interest rate will be 1.7%.
The current value of the 1.7% compounded rate over 65 factors is equivalent to 2.9913.
The value will therefore be $2,500 2.9913 = 7,478.25.
Six years divided by 65 months yields a total of 10.833 years.
10 months make up a year, or 0.833 * 12.
Therefore, based on the fact that Hannah's investment will triple in 10 years and 10 months when compounding occurs every six months.
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a) The base of the pyramid is a Hexagon
b) The height of the pyramid is
c) The vertex of the pyramid is
Blank 1: Hexagon
Blank 2:
For the given hexagonal pyramid, the base of the pyramid is a Hexagon, The height of the pyramid is 13 units, and the vertex of the pyramid is 7.
What is a hexagonal pyramid?
A hexagonal pyramid features isosceles triangles as the faces that join the pyramid together at the top and a hexagonal-shaped base.
Given, for a hexagonal pyramid
a) The base of the pyramid is a Hexagon.
b) The height of the pyramid is 13 units.
c) The vertex of the pyramid is 7.
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