He claims that the measures of the three sides of triangle ABX are all equal to AX, making AABX equilateral. Since this makes central angle AXB
measure 60°,mAB = 60°. Dylan also claims that by repeatedly applying the same argument, he can prove that the inscribed hexagon is regular.
Which statement is true?
Answers
Statement A " Dylan's reasoning about arc AB is correct, and the hexagon is regular. option (A) is correct.
What is a regular polygon?A polygon is a geometric figure with a finite number of sides in two dimensions. On the sides or edges of a polygon, straight-line segments are joined end to end to form a closed shape. The vertices, also known as corners, are the points where two line segments meet and form an angle.
[tex]\rm Area = |\dfrac{(x_1y_2-y_1x_2)+(x_2y_3-y_2x_3)....+(x_ny_1-y_nx_1)}{2}|[/tex]
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have:
Three sides of the triangle ABX are all equal to AX, making ΔABX equilateral. Since this makes central angle AXB measure 60°,
m(arc)AB = 60°
AX = BX = AB
The measure of AXB = 60 degrees
m(arc)AB = 60 degrees
On applying the same argument, the inscribed hexagon is regular.
Statement A is correct.
Thus, statement A " Dylan's reasoning about arc AB is correct, and the hexagon is regular. option (A) is correct.
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Related Questions
Total score: ____ of 20 points A marching band performs on the football field at half-time. As they perform, the members of the band stand in the shape of a sinusoidal function. While playing, they move, but still maintain the sinusoidal function, transforming it in different ways. Darla is a member of the marching band. As the band begins to play she is positioned in the exact center of the field. The person closest to her on the same horizontal line, stands 10 yards away. The sinusoidal function extends to the ends of the playing field. The playing area of football field measure 300 feet by 160 feet. Place the playing area of a football field on the coordinate plane such that the origin is the lower left corner of the football field. (Score for Question 1: ___ of 2 points) 1. What is the period and the amplitude of the sine function representing the position of the band members as they begin to play? Answer: (Score for Question 2: ___ of 6 points) 2. Edna is sitting in the stands and is facing Darla. Edna observes that sine curve begins by increasing at the far left of the field. What is the equation of the sine function representing the position of band members as they begin to play? Answer: (Score for Question 3: ___ of 4 points) 3. As the band begins to play, band members move away from the edges, and the curve reverses so that the function begins at the far left by decreasing. Darla does not move. The sine curve is now half as tall as it was originally. What is the equation of the sine curve representing the position of the band members after these changes? Answer: (Score for Question 4: ___ of 3 points) 4. Next, the entire band moves closer to the edge of the football field so that the sine curve is in the lower half of the football field from Edna’s vantage point. What is the equation of the sine curve representing the position of the band members after these changes? Answer: (Score for Question 5: ___ of 5 points) 5. At the end of the performance, the band marches off the field to the right, moving the entire sine curve. Asa grabs his camera to takes a picture of the entire football field. At the instant he takes the picture, the first person forming the curve now stands at the 5 yard line. What is the equation of the sine curve representing the position of the band members in Asa’s picture? Answer: Please help me explain step-by-step thank you
Answers
Answer:
1) Amplitude; A = 80 ft
Period = 60 ft
2)y = 80 sin ((π/30)x - 5π) + 80
3)y = 40 sin ((π/30)x - 5π) + 80
4)y = 40 sin ((π/30)x - 5π) + 40
5)y = -65sin ((π/30)x - 5π) + 80
Step-by-step explanation:
The general formula for sinusoidal wave equation is given by;
y = A sin (Bx - C) + D
Where;
A is amplitude = D_max or D_min
Period = 2π/B
So; B = 2π/Period
Phase Shift = C/B
So; C = B · Phase Shift
D: center
We are Given:
Height of the field is 160 ft and so the center is at y = 80. Thus; D = 80 ft
Thus; A = 80 ft
The person closest to Darla on the same horizontal line, stands 10 yards(30 ft) Thus, period = 2 × 30 = 60 ft
Thus; B = 2π/60 = π/30
Field is 300 ft wide and so the center is 300/2 = 150 ft
Thus; Phase Shift = 150.
C = B × Phase Shift = π/30 · 150 = 5π
1) From the calculations above,
Amplitude; A = 80 ft
Period = 60 ft
2) As they begin to play, from the calculations above and y = A sin (Bx - C) + D, equation of the sine function is now;
y = 80 sin ((π/30)x - 5π) + 80
3) In this, since the sine wave is half as tall, then after the changes, we have;
y = 40 sin ((π/30)x - 5π) + 80
4) since they have moved closer, then equation is now;
y = 40 sin ((π/30)x - 5π) + 40
5) We are Given:
Height of the field is 160 ft and so the center is at y = 80. Thus; D = 80 ft
Since the first person forming the curve now stands at the 5 yard line, the minimum is at 5 yds (15 ft). Thus;
D_min = 80 - 15 = 65. Thus; A = 65 ft
The person closest to Darla on the same horizontal line, stands 10 yards(30 ft) Thus, period = 2 × 30 = 60 ft
Thus; B = 2π/60 = π/30
Field is 300 ft wide and so the center is 300/2 = 150 ft
Thus; Phase Shift = 150.
C = B × Phase Shift = π/30 · 150 = 5π
The band ends down (at 15 feet) and thus A is negative
The equation is;
y = -65sin ((π/30)x - 5π) + 80
Part(1): The required values are,
Amplitude=[tex]80 ft[/tex] and Period: [tex]60 sec[/tex]
Part(2):
The equation of the sine function is
[tex]y=80 cos(\frac{\pi x}{30}+\pi)+80[/tex]
Part(3):
The equation of the sine curve is,
[tex]y=40cos(\frac{\pi x}{30})+80[/tex]
Part(4):
The equation of the sine curve representing the position of the band members after these changes is [tex]y=40cos(\frac{\pi x}{30})+40[/tex]
Part(5):
The required graph is attached below,
Simple harmonic motion:Simple Harmonic Motion or SHM is defined as a motion in which the restoring force is directly proportional to the displacement of the body from its mean position
Part(1):
Amplitude=[tex]\frac{1}{2} width=80ft[/tex]
Period=[tex]2\times 30=60 sec[/tex]
Part(2):
Let the equation be,
[tex]y=80 cos(\frac{\pi x}{30}+\pi)+80\\ y'=-\frac{8\pi}{3} sin((\frac{\pi x}{30}+\pi))[/tex]
Darla is at the point [tex]D(150,80)[/tex] which is on the graph at [tex]x=0[/tex] then,
[tex]80=80 cos(5\pi+\pi)=0\\y=-80 cos (\frac{\pi x}{30} )+80[/tex]
Part(3):
Since the wave is now [tex]\frac{160}{2} =80 ft[/tex] then,
Amplitude=40 ft
[tex]y=-4 cos (\frac{\pi x}{30} -\pi)+80\\y=40cos(\frac{\pi x}{30})+80[/tex]
Part(4):
The graph shifts downward 40 ft then,
[tex]y=-4 cos (\frac{\pi x}{30} -\pi)+80-40\\y=40cos(\frac{\pi x}{30})+40[/tex]
Part(5):
Start at:[tex]Y(x)=80sin (\frac{2\pi x}{60} )+80\\[/tex]
End at: [tex]Z(x)=80sin[ (\frac{2\pi }{60}(x-15) )]+80\\[/tex]
The graph is attached below:
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Before hosting their annual Chess Tournament and Spelling Bee, a school received 7 boxes of honorary medals: one medal for every participant. After the Chess Tournament, two boxes were empty and the rest were still closed. After the Spelling Bee, which had twice as many participants, there were 72 medals left. How many people competed in the Chess Tournament?
Answers
Answer:
144 people competed in the Chess Tournament
Step-by-step explanation:
So as you can see, after the Chess Tournament took place, two boxes were empty, the rest closed. That would mean that there were 2 boxes of medals that were given out to honor the participants in the chess tournament. The spelling bee had twice as many participants, and hence used 2 [tex]*[/tex] 2 = 4 boxes. The remaining box had to have 72 medals in it, as it was the remaining amount of medals.
After the Chess Tournament, 2 boxes were given out, and we can assume they contained 72 medals in them. Therefore, the number of medals given after the chess tournament would be 2 [tex]*[/tex] 71 = 144 medals. Each medal corresponds to a participant, so the number of chess tournament participants would also be 144, 144 participants.
Translate to an equation and sole: The quotient of h and 26 is -52
Answers
find the maximal area of a right triangle with hypotenuse of length 8
Answers
Answer:
Max area is 16
Step-by-step explanation:
If A² + B² = C², then A² + B² = 64. The largest triangle area is when both A² and B² are equal to 32, so 32 + 32 = 64.
So equal side of the triangle is √32 or about 5.6568. The area of the triangle is then 1/2(5.6568 × 5.6568) or 16.
The maximal area of a right triangle is 90.496
What is differentiation?Derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus.
Given:
let the perpendicular be 'x'
and base be 'y'
Using Pythagoras theorem
x² + y² = 8²
x² + y² = 64
y²= 64- x²
y = √64-x²
Now, Area of triangle
= 1/2* base* height
=xy/2
=x *√64-x²*1/2
On differentiating both side
A' = 64-2x²/√64-x²*1/2
Setting derivative function equal to zero,
64= 2x²
32=x²
x=5.656
So, Area of triangle = x *√64-x²*1/2
= 90.496
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Find the equation for the plane through the point Upper P 0equals(2 comma 5 comma 9 )and normal to the vector nequals5 Bold i plus 8 Bold j plus 2 Bold k.
Answers
Answer:
5x+8y+2z = 68
Step-by-step explanation:
Given the point P0 = (2, 5, 9), to Find an equation for a plane through that point and normal to the vector n = 5i+8j+2k the following steps must be followed:
The equation for the plane passing through the point is expressed as;
a(x-x0)+b(y-y0)+c(z-z0) = 0 where;
(x0, y0, z0) is the point on the plane and (a,b,c) is the normal vector n.
Given the point (2, 5, 9) and normal vector n =(5, 8, 2)
x0 = 2, y0 = 5, z0 = 9, a = 5, b = 8 and c= 2.
Substituting this values into the equation of the plane above will give;
5(x-2)+8(y-5)+2(z-9) = 0
On expansion:
5x-10+8y-40+2z-18 = 0
5x+8y+2z-10-40-18 = 0
5x+8y+2z-68 = 0
The required equation of the plane is 5x+8y+2z = 68
Determine the value of X. 30 POINTS
Answers
you can use the value of sin\
sin(theta) = 12/16
Now solve for theta, and do inverse sine
so theta would be 48.59037789 , or around 50 degrees
Answer:
48.59°Step-by-step explanation:
Since, it is a right triangle.
Perpendicular (p) = 12
hypotenuse ( h) = 16
now,
[tex]sin \: (x \: degree) = \frac{perpendicular}{hypotenuse} [/tex]
[tex]sin \: x \: = \frac{12}{16} [/tex]
[tex] x = {sin}^{ - 1} ( \frac{12}{16} )[/tex]
[tex]x = 48.59 \: degree[/tex]
hope this helps...
good luck on your assignment..
In a simple regression analysis for a given data set, if the null hypothesis β = 0 is rejected, then the null hypothesis ρ = 0 is also rejected. This statement is ___________ true. always
Answers
Answer:
Null hypothesis: [tex]\rho =0[/tex]
Alternative hypothesis: [tex]\rho \neq 0[/tex]
The statistic to check the hypothesis is given by:
[tex]t=\frac{r \sqrt{n-2}}{\sqrt{1-r^2}}[/tex]
And is distributed with n-2 degrees of freedom
And the statistic to check the significance of a coeffcient in a regression is given by:
[tex] t_1 = \frac{\hat{\beta_1} -0}{S.E (\hat{\beta_1})}[/tex]
For this case is importantto remember that t1 and p value for test of slope coefficient is the same test statistic and p value for the correlation test so then the answer would be:
Always
Step-by-step explanation:
In order to test the hypothesis if the correlation coefficient it's significant we have the following hypothesis:
Null hypothesis: [tex]\rho =0[/tex]
Alternative hypothesis: [tex]\rho \neq 0[/tex]
The statistic to check the hypothesis is given by:
[tex]t=\frac{r \sqrt{n-2}}{\sqrt{1-r^2}}[/tex]
And is distributed with n-2 degrees of freedom
And the statistic to check the significance of a coeffcient in a regression is given by:
[tex] t_1 = \frac{\hat{\beta_1} -0}{S.E (\hat{\beta_1})}[/tex]
For this case is importantto remember that t1 and p value for test of slope coefficient is the same test statistic and p value for the correlation test so then the answer would be:
Always
Which choice is equivalent to 4 square root 8
Answers
Answer:
A
Step-by-step explanation:
............................ ....
Which equation shows y-5=x converted to slope intercept form.
Answers
Answer:
C) y = x + 5
Step-by-step explanation
Add 5 to both sides
I will give brainliest
Answers
Answer: 10.246950766
Step-by-step explanation:
based on Pythagorean’s theorem:
[tex]\sqrt{19^{2}-16^{2} } =\sqrt{105} = 10.246950766[/tex]
6th grade math help me, please. :)
Answers
Answer: 120 ice creams total
The answer is option D
A sector with a central angle measure of 200 degrees has a radius of 9 cm. What is the area of the sector?
Answers
Answer:
[tex]\boxed{Area\ of\ sector = 141.4\ cm^2}[/tex]
Step-by-step explanation:
Radius = r = 9 cm
Angle = θ = 200° = 3.5 radians
Now,
[tex]Area \ of \ sector = \frac{1}{2} r^2 \theta[/tex]
Area = 1/2 (9)²(3.5)
Area = 1/2 (81)(3.5)
Area = 282.7 / 2
Area of sector = 141.4 cm²
Answer:
45 pi cm^2 or 141.3 cm^2
Step-by-step explanation:
First find the area of the circle
A = pi r^2
A = pi (9)^2
A = 81 pi
A circle has 360 degrees
The shaded part has 200
The fraction that is shaded is
200/360 =5/9
Multiply by the total area
5/9 * 81 pi
45 pi
Using 3.14 for pi
141.3
45 pi cm^2 or 141.3 cm^2
James determined that these two expressions were equivalent expressions using the values of x - 4 and x-6.
Which statements are true? Check all that apply.
7x+4 and 3x+5+4x-1
When x-2, both expressions have a value of 18.
The expressions are only equivalent for x = 4 and x-6.
The expressions are only equivalent when evaluated with even values.
The expressions have equivalent values for any value of x.
The expressions should have been evaluated with one odd value and one even value.
When x-0, the first expression has a value of 4 and the second expression has a value of 5.
The expressions have equivalent values if x - 8.
Answers
Answer:
1 - Correct
2 - incorrect
3- incorrect
4 - incorrect
5 - Correct
Step-by-step explanation:
Notice that
3x + 5 + 4x -1 = 3x + 4x + 5 -1 = 7x + 4
therefore the two expressions are equivalent for ANY number, specially x = 4 and x = 6 therefore
1 - Correct
Since that is true for all numbers
2 - incorrect
3- incorrect
4 - incorrect
The expressions are equivalent for all numbers therefore
5 - Correct
Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
x2 + y2 = (4x2 + 2y2 − x)2
(0, 0.5)
(cardioid)
Answers
Answer:
y = x + 0.5
Step-by-step explanation:
This is a very trivial exercise, follow the steps below:
Step 1: Perform the implicit differentiation of the given equation
[tex]x^2 + y^2 = (4x^2 + 2y^2 - x)^2[/tex]
[tex]2x + 2y \frac{dy}{dx} = 2(4x^2 + 2y^2 - x) ( 8x + 4y\frac{dy}{dx} - 1)\\\\[/tex]
Step 2: Make dy/dx the subject of the formula, this will be the slope of the curve:
[tex]x + y \frac{dy}{dx} = (4x^2 + 2y^2 - x) ( 8x + 4y\frac{dy}{dx} - 1)\\\\x + y \frac{dy}{dx} = 32x^3 + 16x^2y \frac{dy}{dx} - 4x^2 + 16xy^2 + 8y^3\frac{dy}{dx} - 2y^2 - 8x^2 - 4xy\frac{dy}{dx} + x \\\\\frac{dy}{dx}(y + 4xy - 8y^3) = 32x^3 - 12x^2 + 16xy^2 - 2y^2\\\\\frac{dy}{dx} = \frac{32x^3 - 12x^2 + 16xy^2 - 2y^2}{y + 4xy - 8y^3}[/tex]
Step 3: Find dy/dx at the point (0, 0.5)
[tex]\frac{dy}{dx}|(0,0.5) = \frac{32(0)^3 - 12(0)^2 + 16(0)(0.5)^2 - 2(0.5)^2}{(0.5) + 4(0)(0.5) - 8(0.5)^3}\\\\\frac{dy}{dx}|(0,0.5) =\frac{-0.5}{-0.5} \\\\\frac{dy}{dx}|(0,0.5) =1\\\\m = \frac{dy}{dx}|(0,0.5) =1[/tex]
Step 4: The equation of the tangent line to a curve at a given point is given by the equation:
[tex]y - y_1 = m(x-x_1)\\\\y - 0.5 = 1(x - 0)\\\\y = x + 0.5[/tex]
An ice sculpture is melting at a constant rate. It's weight changes -1 4/5 pounds every hour. What is the total change in weight of the sculpture after 3 1/2 hours?
Answers
Answer:
It will decrease by 6 3/10 lbs in the 3 1/2 hours
Step-by-step explanation:
The rate is -1 4/5 lbs per hour
The time is 3 1/2 hours
Multiply to find the weight change
-1 4/5 * 3 1/2
Change to improper fractions
- ( 5*1 +4) /5 * ( 2* 3+1)/2
- 9/5 * 7/2
-63/10
Changing back to a mixed number
-6 3/10
It will decrease by 6 3/10 lbs in the 3 1/2 hours
Answer:
-6 3/10 pounds
Step-by-step explanation:
The weight of ice sculpture changes -1 4/5 pounds every 1 hour.
In 3 1/2 hours, multiply the time with the weight.
-1 4/5 × 3 1/2
Multiply.
-9/5 × 7/2
-63/10 = -6 3/10
Two passenger trains traveling in opposite directions meet and pass each other. Each train is 1 12 mi long and is traveling 50 mph. How many seconds after the front cars of the trains meet will their rear cars pass each other?
Answers
Answer:
Time taken = 6 sec (Approx)
Step-by-step explanation:
Given:
Total distance = 1/12 mi = 0.083333
Speed of train = 50 mph = 50 / 3600 = 0.01388889 mps
Find:
Time taken
Computation:
Time taken = Total distance / Speed
Time taken = Total distance / Speed of train
Time taken = 0.0833333 / 0.01388889
Time taken = 6 sec (Approx)
by what number 7whole 2/3be divided to get 4whole1/3
Answers
Answer: 1 30/39
Step-by-step explanation:
Because y/x=z and y/z=x are true with the same values, simply do 7 2/3 divided by 4 1/3 to get 69/39.
Hope it helps <3
Consider a binomial experiment with 15 trials and probability 0.35 of success on a single trial.
(a) Use the binomial distribution to find the probability of exactly 10 successes (Round your answer to three decimal places.)
(b) Use the normal distribution to approximate the probability of exactly 10 successes. (Round your answer to three decimal places.) (
(c) Compare the results of parts (a) and (b).
A. These results are fairly different.
B. These results are almost exactly the same.
Answers
Answer:
a
[tex]P(X = 10 ) = 0.0096[/tex]
b
[tex]P(X = 10 ) = 0.0085[/tex]
c
Option A is correct
Step-by-step explanation:
From the question we are told that
The sample size is n = 15
The probability of success is [tex]p = 0.35[/tex]
The number of success we are considering is r = 10
Now the probability of failure is mathematically evaluated as
[tex]q = 1- p[/tex]
substituting value
[tex]q = 1- 0.35[/tex]
[tex]q = 0.65[/tex]
Now using the binomial distribution to find the probability of exactly 10 successes we have that
[tex]P(X = r ) = [\left n } \atop {r}} \right. ] * p^r * q^{n- r}[/tex]
substituting values
[tex]P(X = 10 ) = [\left 15 } \atop {10}} \right. ] * p^{10}* q^{15- 10}[/tex]
Where [tex][\left 15 } \atop {10}} \right. ][/tex] mean 15 combination 10 which is evaluated with a calculator to obtain
[tex][\left 15 } \atop {10}} \right. ] = 3003[/tex]
So
[tex]P(X = 10 ) = 3003 * 0.35 ^{10}* 0.65^{15- 10}[/tex]
[tex]P(X = 10 ) = 0.0096[/tex]
Now using the normal distribution to approximate the probability of exactly 10 successes, we have that
[tex]P(X = r ) = P( r < X < r )[/tex]
Applying continuity correction
[tex]P(X = r ) = P( r -0.5 < X < r +0.5)[/tex]
substituting values
[tex]P(X = 10) = P( 10-0.5 < X < 10+0.5)[/tex]
[tex]P(X = 10 ) = P( 9.5 < X < 10.5)[/tex]
Standardizing
[tex]P(X = r ) = P( \frac{9.5 - \mu }{\sigma } < \frac{X - \mu }{\sigma } < \frac{10.5 - \mu}{\sigma } )[/tex]
The where [tex]\mu[/tex] is the mean which is mathematically represented as
[tex]\mu = n * p[/tex]
substituting values
[tex]\mu = 15 * 0.35[/tex]
[tex]\mu = 5.25[/tex]
The standard deviation is evaluated as
[tex]\sigma = \sqrt{n * p * q }[/tex]
substituting values
[tex]\sigma = \sqrt{15 * 0.35 * 0.65 }[/tex]
[tex]\sigma = 1.8473[/tex]
Thus
[tex]P(X = 10 ) = P( \frac{9.5 - 5.25 }{1.8473 } < \frac{X - 5.25 }{1.8473 } < \frac{10.5 - 5.25}{1.8473 } )[/tex]
[tex]P(X = 10 ) = P( 2.30 < Z < 2.842 )[/tex]
[tex]P(X = 10 ) = P(Z < 2.842 ) - P(Z < 2.30 )[/tex]
From the normal distribution table we obtain the [tex]P(Z < 2.841)[/tex] as
[tex]P(Z < 2.841) = 0.99775[/tex]
And the [tex]P(Z < 2.30)[/tex]
[tex]P(Z < 2.30) = 0.98928[/tex]
There value can also be obtained from a probability of z calculator at (Calculator dot net website)
So
[tex]P(X = 10) = 0.99775 - 0.98928[/tex]
[tex]P(X = 10 ) = 0.0085[/tex]
Looking at the calculated values for question a and b we see that the values are fairly different.
Find the value of x.
Answers
Explanation:
For any quadrilateral that is inscribed in a circle, ie has all four points on the circle like this, the opposite angles are always supplementary. They add to 180 degrees.
x+125 = 180
x+125-125 = 180-125 ... subtract 125 from both sides
x = 55
4.5/y = 12.5/4 PLEASE HELP!!! SOS
Answers
Answer:
y = 1.44
Step-by-step explanation:
What are you aiming to do here? Please share all instructions with each problem.
If you want to solve 4.5/y = 12.5/4 for y: Multiply both sides by 4y:
18 = 12.5y. Then y = 1.44
A chemical company makes two brands of antifreeze. The first brand is 45% pure antifreeze, and the second brand is 95% pure antifreeze. In order to obtain 70 gallons of a mixture that contains 65% pure antifreeze, how many gallons of each brand of antifreeze must be used?
Answers
Answer:
42 gallons 45% antifreeze
28 gallons 95% antifreeze
Step-by-step explanation:
If x is volume of 45% antifreeze, and y is volume of 95% antifreeze, then the total volume is:
x + y = 70
And the total amount of antifreeze is:
0.45 x + 0.95 y = 0.65 (70)
Solving by substitution:
0.45 x + 0.95 (70 − x) = 0.65 (70)
0.45 x + 66.5 − 0.95 x = 45.5
21 = 0.5 x
x = 42
y = 28
Which best describes the meaning of the statement if A then B
Answers
Answer:
[tex]a => b \equiv ( \neg a \ \lor \ b )[/tex]
Step-by-step explanation:
You can understand the statement from many perspectives, but in terms of proposition logic it is best to understand it as "negation of a" or " b" in mathematical terms is written like this
[tex]a => b \equiv ( \neg a \ \lor \ b )[/tex]
You can show that they are logically equivalent because they have the same truth table.
what is the slop of y= -5+4x
Answers
Hey there! :)
Answer:
m = 4.
Step-by-step explanation:
We are given the formula y = -5 + 4x. Rearrange the equation to be in proper slope-intercept form (y = mx + b)
Where 'm' is the slope and 'b' is the y-intercept. Therefore:
y = -5 + 4x becomes y = 4x - 5
The 'm' value is equivalent to 4, so the slope of the equation is 4.
Answer:
4
Step-by-step explanation:
because of y= mx + b where m is the slope
m= 4 in the equation
A 5.5-foot woman casts a shadow that is 3 feet longer than her son's shadow. The son casts a shadow 13.5 feet long.
Height of son =______
Woman
Height (ft)_______
Lenght of shadow (ft)_______
Son
Height (ft)_______
Lenght of shadow (ft)_______
Answers
Answer: 19!!
Step-by-step explanation:
What is the equation of the line perpendicular to y=5x-3 that passes through the point (3, 5)?
Answers
Answer:
[tex]y=-\frac{1}{5}x\ +\ 5.6[/tex]
Step-by-step explanation:
Hey there!
Well the slope of the perpendicular line is -1/5 because that's the reciprocal of 5.
Look at the image below ↓
By looking at the image we can conclude that the equation for the perpendicular line is,
[tex]y=-\frac{1}{5}x\ +\ 5.6[/tex].
Hope this helps :)
Answer:
[tex]\boxed{y=-\frac{1}{5}x+\frac{28}{5}}[/tex]
Step-by-step explanation:
Part 1: Finding the new slope of the line
Perpendicular lines have reciprocal slopes of a given line - this means that the slope you are given in the first equation will be flipped and negated.
Because the slope is 5 in the first line, it gets flipped to become [tex]-\frac{1}{5}[/tex].
Part 2: Using point-slope formula and solving in slope-intercept form
Input the new slope into the slope-intercept equation: [tex]y=mx+b[/tex]. This results in [tex]y=-\frac{1}{5} x+b[/tex].
Then, use the point-slope equation to get b, or the y-intercept of the equation.
[tex](y-y_{1})=m(x-x_{1})[/tex]
[tex](y-5)=-\frac{1}{5}(x-3)\\\\y-5=-\frac{1}{5}x+\frac{3}{5} \\\\y=-\frac{1}{5}x+\frac{28}{5}[/tex]
Question 3 (5 points)
POINT
-POINT A
POINT B
What are the coordinates of the point labeled B in the graph shown above?
A) (3, 2)
B) (-3,2)
OC) (-2,3)
D) (-2, -3)
Question 4 (5 points)
Answers
Answer:
(D) -2,-3
Step-by-step explanation:
From the origin, we can find the current position of point B by counting.
B is 2 to the left of the y-axis, meaning that it's x value is -2.
B is 3 down of the x-axis, making it's y value -3.
Therefore, the coordinates of point B are -2,-3.
Hope this helped!
Answer: (D) -2,-3
Step-by-step explanation:
A triangle has side lengths of 13, 9, and 5. Is the triangle a right triangle? Explain.
Use complete sentences in your explanation.
Hint: Pythagorean Theorem: a^2+ b^2 = c^2
Answers
Answer:
see below
Step-by-step explanation:
Using the Pythagorean Theorem:
a^2+ b^2 = c^2
5^2+ 9^2 = 13^2
25+81 = 169
106 = 169
This is not true so it is not a right triangle
Answer:
[tex]\boxed{\sf Not \ a \ right \ triangle}[/tex]
Step-by-step explanation:
Apply Pythagorean theorem to check if the triangle is a right triangle.
[tex]a^2+ b^2 = c^2[/tex]
[tex]5^2+ 9^2 = 13^2[/tex]
[tex]25+81=169[/tex]
[tex]106=109[/tex]
False statement.
The triangle is not a right triangle.
PLEASE HELP
Divide. Write your answer using the smallest numbers possible. 47 pounds 13 ounces divided by 15 = ___pounds ___ounces
Answers
Answer:
3 pounds
51 ounces
Step-by-step explanation:
The slope intercept form of a line is
y=mx+b
The slope is represented by____
The y-intercept is represented by____
Answers
Answer:y=Mx+b
Step-by-step explanation:
What the answer now fast
Answers
Answer:
[tex]m < C = 60[/tex]
Step-by-step explanation:
From the given right angled triangle, ∆ABC,
[tex] BC = Hypotenuse = 2\sqrt{11} [/tex]
[tex] AC = Adjacent = \sqrt{11} [/tex]
Thus, m<C can be found by applying the following trigonometric ratio formula as shown below:
[tex] cos(C) = \frac{adjacent}{hypotenuse} [/tex]
[tex] cos(C) = \frac{\sqrt{11}}{2\sqrt{11}} [/tex]
Evaluate: √11 cancels √11
[tex] cos(C) = \frac{1}{2} [/tex]
[tex] cos(C) = 0.5 [/tex]
[tex] C = cos^{-1}(0.5) [/tex]
[tex] C = 60 [/tex]
[tex]m < C = 60[/tex]