Answer:
641.96
Step-by-step explanation:
1. What is the standard form of the equation of a circle and what do each of the variables represent?
2. What are the standard forms of the equation of a parabola and what do each of the variables represent?
3. Explain the relationship between the vertex, focus and directrix.
4. What are the standard forms of the equation of an ellipse and what do each of the variables represent?
5. Explain the relationship between the foci, vertices, and endpoints of the minor axis of an ellipse.
6. What are the standard forms of the equation of a hyperbola and what do each of the variables represent?
7. Explain the relationship between the foci, vertices, and conjugate axis of a hyperbola.
Answer:
1) The standard form of a circle's equation is (x - h)² + (y - k)² = r². (h,k) is the center and r is the radius.
2) The vertex is the midpoint of the directrix and the focus. It involves the parabola changing directions, and at any point the directrix and the focus will be equidistant from the parabola. The focus is a single point inside the curve of the parabola, and the directrix is a line outside the parabola.
3) The standard form of an equation of an ellipse is:
(x − h)2a 2 +( y − k) 2 b 2 = 1 ( x − h ) 2 a 2 + ( y − k ) 2 b 2 = 1. (h,k) is the center, a is the distance from the center to the horizontal vertices and b is the distance from the center to the vertical vertices.
4) The foci are (−c,0) and (c,0). The ellipse is the set of all points (x,y) which are the sum of the distances from (x,y) to the foci is constant. (a,0) is a vertex of the ellipse. Finally, the endpoints of the minor axis is a co-vertex of the ellipse.
5) A hyperbola has two standard equations. These equations of a hyperbola are based on its transverse axis and conjugate axis. The standard equation of the hyperbola is [(x² / a²) – (y² / b²)] = 1, where the X-axis is the transverse axis and the Y-axis is the conjugate axis.
6) The foci are located on the line that where the transverse axis is. The conjugate axis is perpendicular to the transverse axis and has the co-vertices as its endpoints. The center of a hyperbola is the midpoint of both the transverse and conjugate axes, where they intersect.
Let me know if I didn't answer all of your questions, I hope this helps! :)
Step-by-step explanation:
HELP ASAP 52 POINTS
How many solutions for x does the following equation have?
(6x + 6) = 4x + 4
Ο Α. 0
OB. 4
O c. infinite
O D. 1
On solving the provided question, we can say that equation 6+6=4+1 has 1 solution that is x= -1.
What is an equation?In mathematics, an equation is a formula that uses the equals sign to connect two expressions and express their equivalence. We can solve equations to find the value of unknown variable given in the equation and the number of values that variable takes is called the solution of equation.
We have to find the no. of solution of 6+6=4+4.
To solve this, we bring all the variables to one side of equality and al the numbers on the other side. So we get,
6-4=4-6
2= -2
Dividing both sides by 2,
x= -1.
Hence, the equation 6+6=4+4 has only 1 solution. Correct option is D.
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What is the relationship between <4 and <15? *
The Least Common Factor of 4 and 15 is 1. The factors of 4 are 1, 2 and 4, and the factors of 15 are 1, 3, 5 and 15. Hence, 1 is the Least Common Factor of 4 and 15.
What's meant by Factor?A factor is a number that fully divides another number.
To put it another way, if adding two whole figures results in a product, also the figures we're adding are factors of the product because the product is separable by them.
Factor simply translates to" doer" in Latin. therefore, a" factor" in English is a" actor,"" element," or" element" in a situation or number.
Success can depend on charm, and having a terrible constitution can affect from inadequate exercise.
Variable factors are those whose employment varies in proportion to affair; further are employed when product rises and smaller when product falls.
Labor, energy, and raw accoutrements employed directly in product are exemplifications of typical variable rudiments.
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What is an R value that tells you how well a line of best fit fits the data?
Correlation Coefficient (r) o A model is deemed to be "excellent fit" if r is near to 1 (or -1). o The model is "not a good match" if r is close to 0. o The model has a "perfect fit" if r = 1, with all data points falling on the line. o The two variables do not have a linear connection if r = 0.
What is Correlation Coefficient?The strength of the linear link between two separate variables, x and y, is shown by correlation coefficients.
A positive relationship is shown by a linear correlation coefficient greater than zero.
Indicating a negative association is a value less than zero. The two variables x and y do not have any relationship when their values are 0, to sum up.
The correlation coefficient (r2) is a statistic that expresses how closely two variables' movements are related to one another.
To determine the linear relationship between two variables, the Pearson product-moment correlation, the most popular correlation coefficient, is used.
However, this correlation value might not necessarily be a reliable indicator of reliance in a non-linear connection.
Hence, Correlation Coefficient (r) o A model is deemed to be "excellent fit" if r is near to 1 (or -1).
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epare for
D
Question 3
If 2*x+2*10%-55, x=? (please keep 1 decimal)
The value of x in the given equation is 17.5
What are the equations?A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. In this article, let's learn more about math equations.
What are the 3 types of equations?There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form.
In the given equation:-
2x+20-55=0
x=35/2
x=17.5
Hence the value of x is 17.5
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Drag a reason to each box to complete this proof. If 12=13x+5, then x = 21. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. Statement reason 12=13x+5 given 7=13x response area 21 = x response area x = 21 response area.
The equation which has been given is a linear equation, therefore in order to solve the equation, simply the basic mathematical operation is to be performed. The acquired value of x is not the same as the value. So, when 12=13.x+5, the value of x=21 is not true.
Given information:
The equation given in the question is: 12 = 3x + 5
The value of x=21
Perform the basic mathematical operations and find the value of a variable.
13x + 5 =12
⇒13x = 12 -5
⇒ 13x = 7
⇒ x = 7/13
⇒ x = 0.538
The acquired value of x is not the alike as the given value.
Hence, when 12=13.x+5 the value of x=21 is not true.
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Please help! Running out of time!
We can use some rules for exponents to simplify the expression, we will get:
7⁵/7¹ = 7⁴
How to simplify the expression?Here we need to use two properties about exponents, these are:
The exponent of 1 bassically does nothing:
x¹ =x
The rule for divisions is:
xᵃ/xᵇ = x⁽ᵃ ⁻ ᵇ ⁾
Now we have the expression:
7⁵/7
We can rewrite that as:
7⁵/7¹
Now we can use the second property to get:
7⁵/7¹ = 7⁵ ⁻ ¹ = 7⁴
That is the simplified expression.
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Luella owns two tire stores. The first store sells between 100 and 200 tires on
Friday. The other store sells between 200 and 250 tires on Friday.
If a represents the number of tires sold, what inequality would represent the
possible range of the total number of tires sold at both stores on Friday?
A/ tires < x <
A tires
Answer: 300 tires < x < 450 tires
Step-by-step explanation:
The first store sells between 100-200 tires. This means that the number it sells is greater than 100, but less than 200. This can be represented in this inequality:
100 < x < 200
The second store sells between 200-250 tires. This means that the number it sells is greater than 200, but less than 250. This can be represented in this inequality:
200 < x < 250
The total number of tires sold can be found by adding these two inequalities:
100 < x < 200
200 < x < 250
The following inequality represents the total amount of tires sold:
300 < x < 450
Carly is in an air balloon. When Carly is at a height of 21.6 meters (m)
she looks down to notice that the top of a tree is in the center of a large reflection pond in a garden. Upon returning to the ground Carly made a sketch, as shown.
Carly determined that horizontal distance, BD, the air balloon was from the base of the tree
was 30.24m and that the base of the tree was 12.96m from the center of the reflection pond.
What is the height, in meters, of the tree, KD? If necessary, round to the nearest hundredth.
Using the Pythagoras theorem, the height of the tree from the reflection pond is obtained as 27.3 m.
What is the height of the tree?We know that the height of the tree can be obtained from the formula for the Pythagoras's theorem and looking at the theorem, we are going to have that;
C^2 = A^2 + B^2
Where A is the height, in meters, of the tree.
Then we have that;
30.24^ = A^2 + 12.96^2
A^2 = 30.24^2 - 12.96^2
A =27.3 m
This is the length of the tree that have been measured from the ground to the given height as we have bene shown in the question above.
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1. Which angles are adjacent angles?
Three lines intersect at point B.
One line goes through point C in the upper left and point M in the lower right.
A second line goes through point Y in the lower left and point X in the upper right.
The third line is horizontal through point F on the left and G on the right. (1 point)
angleGMB and angleFBC
angleCBX and angleFBC
angleXBG and angleFBC
angleMBY and angleFBC
2. Find the sum of the interior angles of a nonagon. (1 point)
140°
1,620°
1,260°
1,450°
3. The measure of angle3 is101º. Find the measure of angle4.
Two lines intersect. The top angle at the intersection is labeled 1. The right angle is labeled 2. The bottom angle is labeled 3. The left angle is labeled 4. (1 point)
79°
106°
74°
101°
4. Find the measure of each interior angle of a regular polygon with 12 sides. (1 point)
1,800°
150°
180°
145°
5. Four of the angles of a pentagon measure 85°, 110°, 135°, and 95°. Find the measure of the missing angle. (1 point)
115°
95°
135°
85°
The measure of the missing angle in a given pentagon is 115°. Therefore, option A is the correct answer.
What is the formula for interior angle of a regular polygon?The formula for calculating the sum of interior angles is (n-2)×180° where is the number of sides. All the interior angles in a regular polygon are equal. The formula for calculating the size of an interior angle is: interior angle of a polygon = sum of interior angles ÷ number of sides.
2) The sum of the interior angles of a nonagon
Here, n=9
(9-2)×180°
= 1,260°
3) Here, ∠3+∠4=180°
∠3=101°
101°+∠4=180°
∠4=79°
So, option A is the correct answer.
4) Given that, a regular polygon with 12 sides.
Now, sum of the interior angles = (12-2)×180°
= 1800°
Measure of each angle = 1800/12
= 150°
5) Four of the angles of a pentagon measure 85°, 110°, 135°, and 95°.
Let the measure of fifth angle be x°
85°+110°+135°+95°+x°=540°
425°+x°=540°
x°=115°
So, option A is the correct answer.
The measure of the missing angle in a given pentagon is 115°. Therefore, option A is the correct answer.
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A local car dealership is offering a sale. All new cars are on sale for 23% off the sticker price. All used cars are 10% off the sticker price. You have narrowed your decision down to two cars:
Car 1 (new) sticker price = $20,000.00
Car 2 (used) sticker price = $17,000.00
Answer the following questions.
How much money would you save on car 1?
How much money would you save on car 2?
Which car would you choose to buy and why? Justify your answer using your calculations.
Answer:
Step-by-step explanation:
The proposed rule would prohibit motor vehicle dealers from ... Used vehicles sold by new-vehicle dealerships cost $24,542 on average. Sorry I don't know the rest.
Simplify the expression 4(2x−8y) + 3y.
Answer:
The answer is:
8x-29y
Step-by-step explanation:
4(2x-8y)+3y
8x-32y+3y
8x-29y
What angles have a cosine that is equal to sin(L)?
angels K and R are congruent
So on solving the provided question, we can say that the triangle are similar, angles have a cosine that is equal to sin(L) are angle K and angle R
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
the triangle are similar and angle K and angle R are congruent and is a right angled triangle
so, angles have a cosine that is equal to sin(L) are angle K and angle R
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Evaluate.
33 + (23)2 I will probally give u brainlest
A.27 4/9
B.9 2/3
C.9 4/9
D.27 2/3
Answer:
69
Step-by-step explanation:
33 + (23)2 =
= 33 + 46
= 69
This is the correct answer to the problem you posted. If you meant something else, you should have written it differently.
Use / for fractions and ^ for exponents.
Andrea is standing in the ground and can see the too of a cliff that is 215 feet tall. If the angle of elevation feom Andrea’s eyw level to the top of the cliff is 42 degrees and her eye level is 5.25 feet above groud, hiw far is Andrea from the base of the cliff? Round your answer to the nearest tenth.
Andrea's distance from the base of the cliff is given as follows:
233 feet.
What are the trigonometric ratios?The three trigonometric ratios are defined as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the opposite side.For this problem, we have a right triangle in which:
The base angle is of 42º.The adjacent side is the ground distance.The opposite side is the height of 215 - 5.25 = 209.75.Hence the distance is obtained as follows:
tan(42º) = 209.75/d
d = 209.75/tan(42º)
d = 233 feet.
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Identify or mark the missing side or angle that would make triangle ABC congruent to triangle PDF by SAS.
Answer: Angle C for AAS, Side AC for SAS
Step-by-step explanation:
Your instructions were confusing since in the text it asks for SAS and in the image it asks for AAS so I just gave both.
A 14-foot ladder is set up 4 feet from the base of a building. How far up the building does the ladder reach? Round your answer to the nearest tenth of a foot.
The distance up the building that the ladder would reach, given the ladder height and the base of the building, is 13.4 ft.
How to find the height ?To find out how far up the building the ladder reaches, we can use the Pythagorean theorem. The theorem states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side (the hypotenuse).
Assuming the height that the ladder reaches is x, the formula would be:
x ² + 4 ² = 14 ²
x ² = 14 ² - 4 ²
x ² = 196 - 16
x = √ 180
x = 13. 4 ft
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Kevin ran at a rate of 13 km/h. Convert his speed to meters per minute
Answer:
Step-by-step explanation:
m/s =kph divided by 3.600000
m/s =13 divided by3.600000
m/s =3.611111
Answer: 216.67 meters/ min
Step-by-step explanation: Converting 13 km/h to meters per minute
First, we will convert 13 km to meters
So, we know 1 km = 1000 meters
Then 13 km/ h = x
x = 1000 multiplied 13
x = 13,000 meters/ h
Now, we will convert to hours to minutes
We know 1 h = 60 min
Then 13,000 meters/ 60 min
That = 216.667 meters/ min
After approximating
Answer = 216.7 meters / min
Can all linear and exponential functions be defined with both recursive and explicit equations? Explain your answer.
Step-by-step explanation:
I never thought about this before, but yes, they can.
linear functions :
explicit :
y = ax + b
recursive :
xn+1 = xn + a
because
a(x + 1) + b = ax + b + a
ax + a + b = ax + a + b
exponential functions :
explicit :
y = a^x
recursive :
xn+1 = xn × a
because
a^(x + 1) = a^x × a = a^(x + 1)
remember,
a^x = a×a×a×a×a×...×a×a×a
x times a multiplied by itself.
Conider the problem, in 3/4 cup of oatmeal, there i no 1/10 of the recommended daily value of iron. What fraction of the daily recommended value of iron i in 1 cup of oatmeal. (1 multiplication and diviion equation)
The fraction which is recommended as value of iron in 1 cup of oatmeal as per the given relation is equal to 2/15.
As given in the question,
Daily recommended value of iron in the given cup of oatmeal
3 / 4 cup of oatmeal gives 1/10 daily value of iron.
Fraction recommended as daily value of iron is given by :
⇒ 3 /4 cup of oatmeal = 1 /10 value of iron
⇒ 1 cup of oatmeal = ( 1 × 4 ) / ( 3 × 10 ) value of iron
⇒ 1 cup of oatmeal = ( 4 ) / ( 30 ) value of iron
⇒ 1 cup of oatmeal = ( 2 ) / ( 15 ) value of iron
Therefore, the fraction recommended as daily value of iron is equal to
( 2/15 ).
The above question is incomplete, the complete question is :
In 3/4 cup of oatmeal, there is 1/10 of the recommended daily value of iron. What fraction of the daily recommended value of iron is in 1 cup of oatmeal? ( multiplication and division equation)
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10(b+2)+3=73 distributive property
Answer:
b = 5
Step-by-step explanation:
10(b+2) + 3 = 73
10b + 20 + 3 = 73
10b = 50
∴ b = 5
The line with equation y = mx is a tangent to the circle C₁ with equation
(x+4)² + (y-7)² = 13.
(a) Show that m satisfies the equation
3m² + 56m +36=0.
The tangents from the origin O to C₁ touch C₁ at the points A and B.
(b) Find the coordinates of the points A and B.
Another circle C₂ has equation x² + y² = 13. The tangents from the point (4, -7) to C₂ touch it at
the points P and Q.
(c) Find the coordinates of either the point P or the point Q.
On solving the provided question we can say that value equation is y = mx => -7 = m * 4 => m = -7/4 and x² + y² = 13 => x² + (-7)² = 13 => x
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence.
Squaring both sides and simplifying we get:
3m² + 56m + 36 = 0
The coordinates of the points A and B are (-12,103) and (-3,-89) respectively.
y = mx => -7 = m * 4 => m = -7/4
x² + y² = 13 => x² + (-7)² = 13 => x
So the equation of the tangent line is y = m(x - 0) + 0, where m = -(x+4)/(y-7)
Now we can substitute the coordinates of the center of the circle into the equation of the tangent line to get y = -(x+4)/(y-7) * x
Squaring both sides and simplifying we get:
3m² + 56m + 36 = 0
b) To find the coordinates of the points A and B, we can use the equation of the tangent line and the equation of the circle.
We know that the equation of the tangent line is y = -(x+4)/(y-7) * x and the equation of the circle is (x+4)² + (y-7)² = 13.
We can substitute y = -(x+4)/(y-7) * x into the equation of the circle and solve for x.
This equation simplifies to 3x² + 56x + 36 = 0, which factors to (x+12)(x+3) = 0
y = -(-12+4)/(y-7) * -12 = 8/(y-7) * 12 = 96/(y-7)
y = 96 + 7 = 103 and y = -96 + 7 = -89
The coordinates of the points A and B are (-12,103) and (-3,-89) respectively.
We know that the equation of the tangent line is y = mx and the equation of the circle is x² + y² = 13.
We can substitute the point (4, -7) for x and y in the equation of the tangent line and the equation of the circle and solve for m and x,y respectively.
y = mx => -7 = m * 4 => m = -7/4
x² + y² = 13 => x² + (-7)² = 13 => x
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Calculator What is the volume of this square pyramid? 48 cm³ 96 cm³ 144 cm³ 288 cm² 4 cm 8cm 5 cm 3 cm
This square pyramid has a volume of 48 cm³.
Explain about the square pyramid?The term "square pyramid" refers to a three-dimensional geometric form with a square base and four faces or sides that are triangular and meet at a single point (called the vertex). Its five faces give it the name "pentahedron."
The five faces of a square pyramid, four of which are triangles, are square in shape. An upright pyramid's base is also square-shaped.
Although the square pyramid and square prism both have a square base, the four lateral faces of the former are triangular and the latter are rectangular.
V=13s2h, where s is the length of the square base's sides, is a formula that may be used to calculate the volume of a pyramid whose base is square.
v = 1/3 * b² *h
v = 1/3 * 6² *4
v = 1/3 *36 *4
V = 48cm³
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a designer made two tunnels. Tunnel A is represented by x^2+y^2+28x+5=0 and tunnel b is resented by x^2-36x+16y+68=0, where al measurements are in feet. The designer wants to verify whether a 8 feet wide and 13.5 feet high can pass through the tunnel.
Determine the maximum height of each tunnel, is the truck able to pass through either tunnel without damage, if so which tunnel(s) and why
a) Tunnel A is a circle with center (-14, 0) and radius 12, meaning that both the width and the height are of 12.
b) Tunnel B is a parabola that has a width of 32 feet and a height of 16 feet.
c) The maximum height of Tunnel A is of 12 feet and of Tunnel B is of 16 feet, hence, since the height of the truck is of 13.5 feet, it can pass through Tunnel B without damage, as it's height is greater than 13.5 feet.
What is the equation of a circle?The equation of a circle of center and radius r is given by:
(x-x₀) +(y-y₀) = r²
For Tunnel A, the equation is given by:
x² + y² + 28x + 52 = 0
Completing the squares:
(x + 14)² + y² = -52 + 14²
(x + 14)² + y² = 144.
Tunnel A is a circle with center (-14, 0) and radius 12, meaning that both the width and the height are of 12.
A quadratic equation is modeled by:
y = ax^2 + bx + c
For Tunnel B, the equation is given as follows:
x² - 36x + 16y + 68 = 0.
16y = -x² + 36x - 68.
Simplifying by 16:
y = -0.0625x² + 2.25x - 4.25.
Hence the coefficients are a = -0.0625, b = 2.25, c = -4.25, and the maximum height is:
y₀=(2.25)²-49-0.0625)(-1.25)/4(-0.0625) = 16
The width is the difference between the roots, which, using a calculator, are: 2 and 34, hence the width is of 32 feet.
This implies that the tunnel B is a parabola that has a width of 32 feet and a height of 16 feet.
For item c, we have that:
The maximum height of Tunnel A is of 12 feet and of Tunnel B is of 16 feet, hence, since the height of the truck is of 13.5 feet, it can pass through Tunnel B without damage, as it's height is greater than 13.5 feet.
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Correct question:
An architect has designed two tunnels. Tunnel A is modeled by x2 + y2 + 28x + 52 = 0, and tunnel B is modeled by x2 – 36x + 16y + 68 = 0, where all measurements are in feet. The architect wants to verify whether a truck that is 8 feet wide and 13.5 feet high can pass through the tunnels.
Part A: Write the equation for Tunnel A in standard form and determine the conic section. Show your work. (4 points)
Part B: Write the equation for Tunnel B in standard form and determine the conic section. Show your work. (4 points)
Part C: Determine the maximum height of each tunnel. Is the truck able to pass through either tunnel without damage? If so, which tunnel(s) and why? Show your work. (7 points)
Ariana is older than Nora their ages are consecutive even integers find Ariana’s age if the sun of Ariana’s age and 2 times Nora’s age is 56
Ariana is 20 years old, and Nora is 18 years old.
what are consecutive even integers?
The word integers meaning a whole number but not fraction or decimal.
The positive whole number, zero and negative whole numbers are classified as integers.
Consecutive means following a specific sequence. Consecutive even integers mean the integers that follow a sequence and difference between each number is 2.
What is Ariana's age?Ariana is older than Nora and their ages are consecutive even integers.
let Ariana is (x+2) years old and Nora is X years old.
The statement says the sum of Ariana's age and 2 times Nora's age is 56
the equation that expresses it can be written as
x+2+2x = 56
3x = 56 -2
3x = 54
x = 18
Nora is 18 years old.
Ariana is x+2 = 18+2 =20 years old.
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Can anyone please solve these problems?
Answer: 1 is 15 and 2 is 10.
Step-by-step explanation:
15/3=5
5+2 equals 7
10/2=5
5+6=11
m=15
x=10
A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 447 gram setting. Based on a 24 bag sample where the mean is 444 grams and the standard deviation is 10, is there sufficient evidence at the 0.1 level that the bags are underfilled or overfilled? Assume the population distribution is approximately normal.
Step 3 of 5: Specify if the test is one-tailed or two-tailed.
The test that we have here is the one tailed test.
How do we know that the test is one tailed?From the direction of change of the parameter, we would be able to tell if the test is a one tailed test or not. That is, if the parameter is increasing or decreasing.
This test is looking to determine if the bags are underfilled (decreased) or if they are overfilled (increased).
The test's alternative hypothesis is written in a way that it predicts the direction of the difference between two groups. The test is one-tailed if the alternative hypothesis predicts a direction of change
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At the craft show, Mai purchases rings and bracelets. Rings cost `\$1` each and bracelets cost `\$2` each. Mai spends a total of `\$20` on these items. Let `r` represent the number of rings Mai buys. Let `b` represent the number of bracelets Mai buys.
(a) Write an equation relating the two variables.
(b) Rewrite your equation from part a so that it gives `b` as the dependent
(c) Rewrite your equation from part a so that it gives `r` as the dependent variable in terms of `b` as the independent variable. variable in terms of `r` as the independent variable.
Pleaseee hurry. In a really important test.
The equation relating the two variables is r + 2b = 20.
The equation with r as the dependent variable is r = 20 - 2b.
The equation with b as the dependent variable is b = (20 - r)/2.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2xx + 3 = 9 is an equation.
We have,
Number of rings = r
Number of bracelets = b
Cost of one ring = $1
Cost of one bracelets = $2
Total cost = $20
Now,
r + 2b = 20
The equation with r as the dependent variable.
r = 20 - 2b
The equation with b as the dependent variable.
2b = 20 - r
b = (20 - r)/2
Thus,
The equation with r as the dependent variable is r = 20 - 2b.
The equation with b as the dependent variable is b = (20 - r)/2.
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Can 0 have an exponent of 2?
Yes , 0 can have exponent of 2 , it is represented as 0² , and the value of 0 to exponent of 2 is 0 .
What is Exponent ?
The Exponent form form of numbers represents , how many times a number multiplied by itself .
For Example : if the number 3 is multiplied by 5 times by itself , then in the exponent form it can be written as : 3⁵ .
we have to check whether can 0 have an exponent of 2 ;
So, the representation of 0 to exponent of 2 is ⇒ 0² ,
that means 0 is multiplied by itself 2 times , and we know that if a number is multiplied by 0 , then the value of that number is 0 .
Therefore , 0 can have an exponent of 2 and it's value is 0 .
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Use the quadratic formula to find the solutions to the quadratic equation
below.
x-5x-4 = 0
O A. x =
O
-5+√41
2
B. x = 5±√41
O c. x =
C.
-5+√/29
D. x = 5√2
On solving the provided question we cans say that quadratic equation - x^2-5x-4 = 0 and x = 1 , 3
What is quadratic equation?A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.
here, we have
quadratic equation -
x^2-5x-4 = 0
x(x-1) -3(x-3) =
(x-1)(x-3) = 0
x = 1 , 3
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