Final answer:
Upon reviewing the proof and the assumed relationship between the angles, the given information leads to an incorrect conclusion of angle BAC being 90°. The mistake indicates a reassessment of angle relationships is required to determine the true measure of angle BAC in this question.
Explanation:
To prove that angle BAC is 72° in a triangle ABC where angle B is twice angle C and where AD bisects angle BAC with AB equal to CD, we proceed as follows:
Let angle BAC be represented as 2x. Therefore, since AD bisects angle BAC, each angle BAD and DAC is x.
Since angle B is twice angle C, let angle C be x and angle B then is 2x. It is given that AB is equal to CD, meaning triangle ABD is isosceles with angles BAD = DAC.
In isosceles triangle ABD, the angles at base AD are equal, which means each of these angles is x. Thus, the sum of angles in triangle ABD is x (at A) + 2x (at B) + x (at D) = 180°.
Combining these angles, we get 4x = 180°. Dividing both sides by 4, we obtain x = 45°.
Since angle BAC is 2x and x is 45°, angle BAC is therefore 90°.
This leads to a contradiction to the original assumption and upon review reveals the mistake in the assumption about the relationship of the angles given as twice. The correct relationship should be considered to find the accurate measure of angle BAC.
How do I find dy/dx of the equation 4x^3-3xy^2+y^3=28 at the point (3,4)?
To find dy/dx of the equation 4x^3 - 3xy^2 + y^3 = 28 at the point (3,4), you can use implicit differentiation and solve for dy/dx.
Explanation:To find dy/dx of the equation 4x^3 - 3xy^2 + y^3 = 28 at the point (3,4), we need to use implicit differentiation. We differentiate both sides of the equation with respect to x, treating y as a function of x. Thus, we get:
12x^2 - 3y^2 - 3x(2y(dy/dx)) + 3y^2(dy/dx) = 0
Now we substitute x = 3 and y = 4 into the equation and solve for dy/dx:
12(3)^2 - 3(4)^2 - 3(3)(2(4)(dy/dx)) + 3(4)^2(dy/dx) = 0
Paco buys a carton of eggs. the carton has 2 rows of eggs. there are 6 eggs in each carton. how many eggs are in the carton
The total number of eggs in the carton is 12, as there are 2 rows with 6 eggs each, and you calculate the total by multiplying these two numbers.
Paco buys a carton with 2 rows of eggs and there are 6 eggs in each row.
To find the total number of eggs in the carton, you multiply the number of rows by the number of eggs in each row: 2 rows× 6 eggs per row equals a total of 12 eggs in the carton.
So, in this case, the number is 12, and the unit is eggs.
Find the equation of the straight line parallel to 2y=3x-7 and passing though the point (0.5,-1)
22 is 33 1/3% of what number
Denise has $78.22. she wants to buy a computer that cost $29.99. about how much money will denise has left
Simplify the given expression:
4/3-2i
which set of data could be used for the box-and-whisker plot shown below
Answer:
therers no box
Step-by-step explanation:
what is the domain of the composite function G ( F ( x ) )
Which of the following ratios is not equivalent to 6:10?
3/5
9/15
48/80
24/45
The ratio that is not equivalent to 6:10 is 24/45, as it simplifies to 8/15 instead of 3/5 like the other options.
To determine which of the given ratios is not equivalent to 6:10, we can simplify the ratio 6:10 or convert it to a fraction and then reduce it to its simplest form. In fraction form, 6:10 can be written as 6/10, which simplifies to 3/5 when both the numerator and the denominator are divided by their greatest common divisor, which is 2.
3/5 is clearly equivalent to 3/5, so this option is not the one we're looking for.9/15 also simplifies to 3/5 (divide both by 3).48/80 simplifies to 3/5 as well (divide both by 16).24/45, however, simplifies to 8/15 when both the numerator and the denominator are divided by 3. This is not equivalent to 3/5.Therefore, the ratio that is not equivalent to 6:10 is 24/45.
Find the volume of the solid formed by rotating the region inside the first quadrant enclosed by y=x^3 and y=9x about the x-axis.
...?
The volume of the solid formed by rotating the region enclosed by y = x^3 and y = 9x about the x-axis in the first quadrant can be found by integrating from 0 to 3, the square of the outer and inner radius, multiplied by π. Solve the integral to get the volume.
Explanation:To find the volume of the solid formed by rotating the region enclosed by y = x^3 and y = 9x about the x-axis, we need to use the method of discs/washers. The volume V is given by the following integral:
∫[a,b] π(r(x)^2 - R(x)^2) dx
For our given curves, r(x) = 9x and R(x) = x^3 since 9x ≥ x^3 for 0 ≤ x ≤ 3. Therefore, we get:
V = ∫[0,3] π[(9x)^2 - (x^3)^2] dx
Solving this integral will yield the volume of the solid:
V = π ∫[0,3] (81x^2 - x^6) dx
Calculating this integral will give the volume of the solid.
Learn more about Volume of solid here:https://brainly.com/question/23705404
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What is the absolute value or −|9| = −9?
A bag contains only red and blue marbles. Yasmine takes one marble at random from the bag. The probability that she takes a red marble is 1 in 5. Yasmine returns the marble to the bag and adds five more red marbles to the bag. The probability that she takes one red marble at random is now 1 in 3. How many red marbles were originally in the bag?
find the limit 3/x^2-6x+9 as x approaches 3 ...?
The number of days between Aug. 9 and Jan. 3 is
What is the solution to the system of linear equations
A. (-3,0)
B. (-3,3)
C. (0,2)
D. (3,1)
On monday, deborah ran 3 2/5 miles and on tuesday she ran 4 1/5 miles how many miles did she run on these 2 days togehter
Final answer:
Deborah ran a total of 7 3/5 miles combined on Monday and Tuesday. This was determined by adding 3 2/5 miles and 4 1/5 miles together after converting them to improper fractions.
Explanation:
On Monday, Deborah ran 3 2/5 miles and on Tuesday she ran 4 1/5 miles. To find the total distance Deborah ran over these two days, we need to add the two distances together. When working with mixed numbers, it's often easiest to convert them to improper fractions before adding.
3 2/5 miles is the same as (3 × 5 + 2)/5 = 17/5 miles.
4 1/5 miles is the same as (4 × 5 + 1)/5 = 21/5 miles.
Adding these two fractions:
17/5 miles + 21/5 miles = (17 + 21)/5 miles
= 38/5 miles
= 7 3/5 miles
So, Deborah ran a total of 7 3/5 miles on Monday and Tuesday combined.
Write the following number in scientific notation:
0.000721
Note from userneedshelp12: I do not understand scientific notation at all. So, if you help, will you please explain how you got your answer?
A highway map of Ohio has a coordinate grid superimposed on top of the state. Springfield is at point (1, –4) and Columbus is at point (7, 1). The Springfield youth soccer team is going to Columbus to see a professional soccer match. The map shows a highway rest area halfway between the cities. What are the coordinates of the rest area? What is the distance between Springfield and Columbus? (One unit = 5.38 miles)
jika f(x)= 1/2 x - 1 dan g(x)= 2x 4. Maka nilai (gof)^-1 (10) adalah ...
a. -9
b. -8
c. 8
d. 9
e. 10
Write an equation that models the sequence 400, 200, 100, 50, ...
Find the area of a triangle with sides of length 6 and 26 and included angle 74 degrees.
Combine as indicated by the signs. Write answer in descending powers of x.
(x+6/x^2+8x+15) + (3x/x+5) - (x-3/x+3) ...?
The student is required to combine three algebraic fractions with different denominators using factoring to find a common denominator and then simplify the expression.
Explanation:The question entails a topic in algebra, specifically with respect to combining expressions with different denominators, which requires finding a common denominator, and working with signs and exponents. The problem presents three fractions that should be combined: (x+6)/(x^2+8x+15), (3x)/(x+5), and (x-3)/(x+3).
Firstly, note that the denominator x^2+8x+15 can be factored into (x+3)(x+5). This will allow us to identify a common denominator for all three fractions, which is (x+3)(x+5). We rewrite the fractions so that each has the common denominator:
(x+6)/((x+3)(x+5))(3x)/(x+5) will be rewritten as (3x)(x+3)/((x+3)(x+5))(x-3)/(x+3) will remain as (x-3)/(x+3) because it already has part of the common denominatorNow we simply combine these three fractions over the common denominator:
((x+6) + (3x)(x+3) - (x-3)) / ((x+3)(x+5))After the combination, the terms must be simplified and ordered in descending powers of x, which is the final answer.
Descending powers of x is [tex]\[ \frac{2x^2 + 8x + 15}{(x + 3)(x + 5)} \][/tex].
To combine the given expressions, we need to find a common denominator and then combine the numerators. Here are the expressions given:
[tex]\[ \frac{x}{x^2 + 8x + 15} + \frac{3x}{x + 5} - \frac{x - 3}{x + 3} \][/tex]
First, let's factor the quadratic denominator in the first term if possible and identify the common denominator:
The quadratic [tex]\( x^2 + 8x + 15 \)[/tex] can be factored into [tex]\( (x + 3)(x + 5) \)[/tex], since 3 and 5 are factors of 15 that add up to 8.
Now we have:
[tex]\[ \frac{x}{(x + 3)(x + 5)} + \frac{3x}{x + 5} - \frac{x - 3}{x + 3} \][/tex]
The common denominator will be [tex]\( (x + 3)(x + 5) \)[/tex].
Now, let's rewrite each fraction with the common denominator:
The second term already has [tex]\( x + 5 \)[/tex] in the denominator, so we multiply the numerator and denominator by [tex]\( x + 3 \)[/tex]to have the common denominator.
[tex]\[ \frac{3x}{x + 5} \rightarrow \frac{3x(x + 3)}{(x + 5)(x + 3)} \][/tex]
The third term has [tex]\( x + 3 \)[/tex] in the denominator, so we multiply the numerator and denominator by \( x + 5 \) to have the common denominator.
[tex]\[ \frac{x - 3}{x + 3} \rightarrow \frac{(x - 3)(x + 5)}{(x + 3)(x + 5)} \][/tex]
Now all terms have a common denominator, and we can combine them as follows:
[tex]\[ \frac{x}{(x + 3)(x + 5)} + \frac{3x(x + 3)}{(x + 3)(x + 5)} - \frac{(x - 3)(x + 5)}{(x + 3)(x + 5)} \][/tex]
Combine the numerators while keeping the denominator the same:
[tex]\[ \frac{x + 3x(x + 3) - (x - 3)(x + 5)}{(x + 3)(x + 5)} \][/tex]
Now, let's expand and simplify the numerator:
[tex]\[ x + 3x^2 + 9x - (x^2 + 2x - 15) \][/tex]
[tex]\[ x + 3x^2 + 9x - x^2 - 2x + 15 \][/tex]
Combine like terms:
[tex]\[ 3x^2 - x^2 + x + 9x - 2x + 15 \][/tex]
[tex]\[ 2x^2 + 8x + 15 \][/tex]
Now, let's put it all over the common denominator:
[tex]\[ \frac{2x^2 + 8x + 15}{(x + 3)(x + 5)} \][/tex]
This is the simplified expression in descending powers of \( x \). Since the numerator is already in descending powers of \( x \), this is the final answer. There is no further simplification possible because the numerator and the denominator do not have common factors other than 1.
15-28i=3m+4ni find the values of m and n that make this equation true
Final answer:
The values of m and n that satisfy the equation 15 - 28i = 3m + 4ni are m = 5 and n = -7 after equating and solving the real and imaginary parts separately.
Explanation:
To find the values of m and n that make the equation 15 - 28i = 3m + 4ni true, we must equate the real parts and the imaginary parts of both sides of the equation separately. The real part of the left side of the equation is 15, and the imaginary part is -28i. Similarly, for the right side, the real part is 3m, and the imaginary part is 4ni.
Equate the real parts: 15 = 3m
Dividing both sides by 3, we get m = 5.
Equate the imaginary parts: -28i = 4ni
Dividing both sides by 4i, we get n = -7.
Hence, the values that satisfy the equation are m = 5 and n = -7.
A radio commercial for a loan company states: “You only pay $0.29 a day for
each $500 borrowed.” If you borrow $1,500 for 120 days, what amount will you
repay, and what annual interest rate is the company actually charging?
Which of the following represents the general term for the sequence 2, 4, 6, 8, 10, . . .?
n + 1
2n
2n - 1
Answer:
Option (b) is correct.
The general term of the sequence is 2n
Step-by-step explanation:
Given : The sequence 2, 4, 6, 8, 10, . . .
We have to find the representation of the general term of the given sequence 2, 4, 6, 8, 10, . . .
Consider the given sequence 2, 4, 6, .....
The general term of an arithmetic sequence is given by [tex]a_n=a+(n-1)d[/tex]
where, a = first term
d is common difference
For the given sequence a = 2
and d = 2
Then [tex]a_n=2+(n-1)2=2+2n-2=2n[/tex]
Thus, The general term of the sequence is 2n
What does 28 tens divided by 4 equal?
You calculate this by first understanding that '28 tens' means 280, and then dividing 280 by 4. So, 28 tens divided by 4 equals 70.
The phrase '28 tens' refers to 28 multiplied by 10, 28 x 10 = 280.
To find the result of dividing this by 4, we calculate 280 ÷ 4 = 70.
Therefore, 28 tens divided by 4 equals 70.
In ∆ABC shown below, ∡BAC is congruent to ∡BCA. Given: Base ∡BAC and ∡ACB are congruent.
Prove: ∆ABC is an isosceles triangle.
Construct a perpendicular bisector from point B to line segment AC.
Label the point of intersection between this perpendicular bisector and line segment AC as point D.
m∡BDA and m∡BDC is 90° by the definition of a perpendicular bisector.
∡BDA is congruent to ∡BDC by the definition of congruent angles. Line segment AD is congruent to line segment DC by _______1________.
∆BAD is congruent to ∆BCD by the _______2________. Line segment AB is congruent to line segment BC because corresponding parts of congruent triangles are congruent (CPCTC).
Consequently, ∆ABC is isosceles by definition of an isosceles triangle.
options are:
a)1. Angle-Side-Angle (ASA) Postulate
2. corresponding parts of congruent triangles are congruent (CPCTC)
b) 1. corresponding parts of congruent triangles are congruent (CPCTC)
2. Angle-Side-Angle (ASA) Postulate
c) 1. the definition of a perpendicular bisector
2. Angle-Side-Angle (ASA) Postulate
d) 1. corresponding parts of congruent triangles are congruent (CPCTC)
2. the definition of a perpendicular bisector
Refer to the image attached.
Given: [tex]\angle BAC[/tex] and [tex]\angle BCA[/tex] are congruent.
To Prove: [tex]\Delta ABC[/tex] is an isosceles triangle.
Construction: Construct a perpendicular bisector from point B to line segment AC. Label the point of intersection between this perpendicular bisector and line segment AC as point D.
Proof:
Consider [tex]\Delta BDA, \Delta BDC[/tex]
[tex]\angle BDA = \angle BDC= 90^\circ[/tex]
(By the definition of perpendicular bisector)
[tex]AD=DC[/tex] (By the definition of perpendicular bisector)
So, Line segment AD is congruent to DC by the definition of perpendicular bisector.
[tex]\angle BAC[/tex] = [tex]\angle BCA[/tex] (given)
So, [tex]\Delta BDA \cong \Delta BDC[/tex] by ASA congruence postulate.
∆BAD is congruent to ∆BCD by the ASA congruence Postulate.
Line segment AB is congruent to line segment BC because corresponding parts of congruent triangles are congruent (CPCTC).
So, Option C is the correct answer.
sophia is saving money for a new bicycle. The bicycle will cost at least $623. Sophia makes $8.22 per hour.
Which inequality could be used find the number of hours Sophia needs to work to make enough money to buy a new bicycle?
$8.22h > $623
$8.22h ≤ $623
$8.22h ≥ $623
$8.22h < $623
Answer:
C.[tex]8.22 h\geq[/tex]$ 623
Step-by-step explanation:
We are given that Sophia is saving money for a new bicycle.
The bicycle will cost atleast $623.
Sophia makes $8.22 per hour.
We have to find the inequality that could be used to find the number of hours Sophia needs to work to make enough money to buy a new bicycle.
Let Sophia works h hours to make enough money to buy a new bicycle.
Sophia makes money per hour =$8.22
Total money made by Sophia in h hours =[tex]8.22 h[/tex]
According to question
[tex]8.22 h\geq [/tex]$623
Hence, option C is true.
SOLVE. integration of (1-v) /(1+v^2)
Answer:
[tex]tan^-1( v) - \frac{1}{2} ln(1+{v}^2) +c[/tex] is the answer.
Step-by-step explanation:
∫[tex]\frac{1-v}{1+{v}^2} \\\frac{1}{1+{v}^2}- \frac{v}{1+{v}^2}}[/tex]
∫[tex]\frac{dv}{1+{v}^2}[/tex]-∫[tex]\frac{2v}{1+{v}^2}[/tex]dv
[tex]{tan}^{-1} (v)-\frac{1}{2} ln(1+{v}^2) +c[/tex]
What is the equation of a line with a slope of –2 that passes through the point (6, 8)?
Answer with explanation:
Slope of Line= -2
The line passes through the point , (6,8).
⇒Equation of line passing through point , (a,b) having slope ,m is
y -b = m (x -a)
⇒≡Equation of line passing through point , (6,8) having slope ,-2 is
→y -8 = -2× (x -6)
→y -8 = -2 x + 12⇒⇒ Using Distributive property of multiplication with respect to Subtraction
→2 x + y= 12 + 8
→2 x + y=20
Required Equation of line.