how do i solve problem a. and problem b? (using the pythagorean theorem). a. the median to the hypotenuse. b. the altitude to the hypotenuse.
Answers
from mathopenref: median: "A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side."
if we draw a median to the hypotenuse, then we have to draw from the right angle to the hypotenuse.
we use a theorem: "In a right triangle, the median drawn to the hypotenuse has the measure half the hypotenuse. "
the length of the median to the hypotenuse is half the hypotenuse: 5
for altitude:
we draw line on hypotenuse that is perpendicular to hypotenuse to a vertex of the angle opposite to it.
look at my diagram: h is the altitude length
x and y are segments of the original hypotenuse
we have ΔABD with legs of x and h and hypotenuse of 6
ΔABD: x² + h² = 6²
we have ΔBCD with legs of 10-x and h and hypotenuse of 8
ΔBCD: (10-x)² + h² = 8²
this is a system of equations
x² + h² = 6²
(10-x)² + h² = 8²
isolate h² in x² + h² = 6² so that we can substitute:
h² = 6² - x²
h² = 36 - x²
substituting into (10-x)² + h² = 8² we have
(10-x)² + h² = 8²
(10-x)² + (36 - x²) = 8² ...............substitution done
(10-x)² expands to 100 - 20x + x²
100 - 20x + x² + (36 - x²) = 64
+x² and -x² cancel
100 - 20x + 36 = 64
136 - 20x = 64
-20x = -72
x = 3.6
Since h² = 36 - x², then h = √(36 - x²) and
h = √(36 - 3.6²) =4.8
the altitude is 4.8
Related Questions
Translate shapes , pls help me with this
Answers
B. (-3,-4)
C. (0,2)
D. (-2,-1)
Try this
Answer:
A: (-4,-2)
B: (-3,-4)
C: (0,2)
D: (-2,-1)
Hope this helps! I'm not the best at math though, so it could be incorrect.
What is the relative minimum of the function?
Answers
(1,-5)
relative min = -5
Answer:
The required relative minimum is -5
Step-by-step explanation:
Relative minimum is the point where the graph shows its minimum point or the lowest point of the graph.
Like here, we have been given a parabolic shape so, the minimum of this parabola is the coordinate of y in its vertex point.
So, its relative minimum is -5.
Find the area of the circle if the square has an area of 900 in2. Give your answer in terms of pi
Answers
If so, the first thing is finding the side measure:
[tex]A_{square}=l^2 \\ l= \sqrt{A} = \sqrt{900} \;\;\Rightarrow l=30\;in[/tex]
Now, radius is half this measure: 15 in.
And circle area is:
[tex]A_{circle}=\pi r^2=\pi\cdot(15)^2\:\;\Rightarrow A_{circle}=225\pi\;in^2[/tex]
Final answer:
The area of the inscribed circle within a square with an area of 900 in² is 225π in².
Explanation:
The subject here is circle geometry, which is a part of Mathematics. Given that the area of the square is 900 in², we want to find the area of the inscribed circle. The side length a of the square can be found by taking the square root of the area, so a = √{900} = 30 inches. The diameter of the circle is the same as the side of the square, which means the radius r is half of that, so r = 30 / 2 = 15 inches. The formula for the area of a circle is A = πr², and substituting in our value of r, we get:
A = π * (15 in)² = 225π in²
A segment has endpoints at (3,−4) and (3,−17). How many units long is the segment?
Answers
[tex]\text{The formula of a distance between two points:}\\\\d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\\text{We have the points}\ (3,\ -4)\ \text{and}\ (3,\ -17).\ \text{Substitute:}\\\\d=\sqrt{(3-3)^2+(-17-(-4))^2}=\sqrt{0^2+(-13)^2}=\sqrt{(-13)^2}=13\\\\Answer:\ \boxed{13\ units}[/tex]
What is the value of X?
Sin64 degree= cos x
Enter your answer in the box.
Answers
cos x = sin 64°
x = cos⁻¹ (sin 64°)
x = 26°
Answer:
x = 26° is the answer.
Step-by-step explanation:
We have to find the value of x from the given equation.
sin 64° = cos x
since sin 64° = 0.8987
Therefore cos x = 0.8987
[tex]x = cos^{-1}(0.8987) = 26[/tex]
x = 26°
Javier is 175% heavier than his brother. If Javier’s brother weighs 80 pounds, how much does Javier weigh?
Answers
Let us say weight of Javier is x pounds.
Weight of his bother = 80 pounds
Javier is 175 % or 1.75 times heavier than his brother.
So Javier's weight = x pounds= 1.75 *80 = 140 pounds.
Answer: Javier's weight is 140 pounds.
Name the Property of Equality that justifies the statement: If m<A + M<B = M<C. Then, M<A = M<C - M<B
Transitive Property
Symmetric Property
Reflexive Property
Subtraction Property
Answers
Answer:
subtraction property
Step-by-step explanation:
What are the x and y intercepts of the line? 2x - 3y = 12
Answers
2x0-3y=12 Now that would be 3y=12
y=4
So the y intercept is 4
then do the same to find x
Like 2x-3x0=12 That would be 2x=12
x=6
That is how you find x and y intercepts. Hope this helped
The cake store is having a 25\%25%25, percent off sale on all of its cakes. If the cake you want regularly costs \$9$9dollar sign, 9, how much would you save with the discount?
Answers
9*0.25 = 2.25.
You save $2.25 with the discount.
Answer:
$2.25.
Step by step explanation:
We have been given that the cake store is having a 25% off sale on all of its cakes.
To find our savings with the discount we will find 25% of $9 (regular cost of cake).
[tex]\text{Savings with the discount}=9\times\frac{25}{100}[/tex]
[tex]\text{Savings with the discount}=9\times\frac{1}{4}[/tex]
[tex]\text{Savings with the discount}=\frac{9}{4}=2.25[/tex]
Therefore, we will save $2.25 with the given discount.
6. Angle ABC is congruent to which angle?
1. Angle CAB
2. Angle XYZ
3. Angle XZY
4. Angle YZX
~
7.
Side CA is congruent to which side?
1. ZX
2.YX
3.XY
4.YZ
Answers
7. ZX
Answer:
[tex]\angle ABC \cong \angle XYZ[/tex]
[tex]CA \cong ZX[/tex]
Step-by-step explanation:
According to the given figures:
[tex]\angle ABC \cong \angle XYZ[/tex]
Also,
[tex]CA \cong ZX[/tex]
Therefore, the answer to the first question is Angle XYZ, and the answer to the second question is ZX.
You can deduct these answers by observing the number of line that match each pair of congruent elements.
What is the value represented by the letter A on the box plot of data?
{5, 20, 40, 50, 50, 85}
Enter your answer in the box.
Answers
The lowest number is always the farthest to the left.
I hope this helps!
If two 6-sided number cubes are rolled, what is the probability that you will roll a 1 first and then roll a 5 with the second cube?
Answers
If you were to ask what the odds of getting a 1 and a 5, it would be higher, but the fact that they need to come in that order give you the above answer.
Final answer:
The probability of rolling a 1 first and then rolling a 5 with two 6-sided number cubes is 1/36.
Explanation:
To find the probability of rolling a 1 first and then rolling a 5 with the second cube, we need to consider the probabilities of each event separately. The probability of rolling a 1 on the first cube is 1/6, since there is only one face with a 1 out of six possible outcomes.
The probability of rolling a 5 on the second cube is also 1/6. Since these events are independent, we can multiply their probabilities to find the overall probability:
Probability of rolling a 1 first and then rolling a 5 = (1/6) * (1/6) = 1/36
Which answer describes the transformation of f (x) = x^2 −1 to g(x)=(x+2)^2−1 ?
a horizontal compression by a factor 2
a vertical stretch by a factor of 2
a horizontal translation 2 units to the left
a vertical translation 2 units down
Answers
In this case, we are changing the variable x before it is being squared. This will have the effect of changing the input of the function. Imagine input 2 into the equation. Your first step would be to add 2. Therefore, you would need to start with a negative 2 to get us back to 0, or the beginning.
Since -2 is to the left of 0, the graph is moving 2 units to the left.
Help please! Math Nation Section 6 Test Yourself Practice Tool.
Answers
Answer: D) [tex]y=-5(x-5)^2+1125[/tex]
Step-by-step explanation:
Let x be the number of $2 increases in price and y be the revenue.
By using the given table , lets check all the options
A) [tex]y=(x+5)^2-1125[/tex]
For x=1, y=1045
[tex]y=(1+5)^2-1125=36-1125=-1089\\\\But\ 1045\neq-1089[/tex]
B) [tex]y=(x-5)^2+1125[/tex]
For x=1, y=1045
[tex]y=(1-5)^2+1125=14+1125=1139\\\But\ 1045\neq1139[/tex]
C) [tex]y=-5(x+5)^2-1125[/tex]
[tex]y=-5(1+5)^2-1125=-5(36)-1125=-1305\\\\But\ 1045\neq-1305[/tex]
D) [tex]y=-5(x-5)^2+1125[/tex]
[tex]y=-5(1-5)^2+1125=-5(16)+1125=1045[/tex]
Hence, this is the quadratic equation that models the data.
Based on the table of values, an equation of the quadratic that models the data is: D. [tex]y = -5(x-5 ) ^2+ 1125[/tex]
In Mathematics and Euclidean Geometry, the vertex form of a quadratic function is represented by the following mathematical equation:
[tex]y = a(x - h)^2 + k[/tex]
Where:
h and k represents the vertex of the graph.a represents the leading coefficient.In order to determine an equation for the line of best fit or quadratic regression line that models the data points contained in the table of values, we would have to use a graphing calculator (Microsoft Excel).
Based on the scatter plot (see attachment) which models the relationship between the number of $2 increase in price (in dollars), x and revenue, y, the quadratic regression is given by:
[tex]y =-5x^2 + 50x + 1000\\\\y = -5(x^2 - 10x) + 1000\\\\y = -5(x^2 - 10x + (\frac{10}{2})^2 ) + 1000+ (\frac{10}{2})^2\\\\y = -5(x^2 - 10x + 25 ) + 1000+25\\\\y = -5(x-5 ) ^2+ 1125[/tex]
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answers
The coefficient of the x term is -32.
Two f-18s are catapulted off an aircraft carrier and fly on courses that diverge at a 60° angle. if each flies at a constant rate of 500 mph, after how many hrs will the fighters be 1200 mi apart?
Answers
First draw a picture of an angle of 60 degrees. The vertex is the starting point of the plane and they are flying away from it.
If you drew points for the new positions of the plane and connected them, you would have triangle. The planes are flying at the same speed, so they would be isosceles triangles. And since the vertex angle is 60 degrees, the other angles have to be 60 as well. This makes it an equilateral triangles, meaning all the sides are the same.
So the distance between the planes is equal to the distance that they have flow.
Simply divide 1200 by 500 to get 2.4 hours.
Derive the equation of the parabola with a focus at (0, –4) and a directrix of y = 4. (2 points)
A f(x) = –16x2
B f(x) = – x2
C f(x) = x2
D f(x) = 16x2
Answers
Equation of parabola with focus at (0,-4) and directrix is y=4 .
As we know parabola is the locus of all the points such that distance from fixed point on the parabola to fixed line directrix is same.
The parabola is opening downwards.
Let any point on parabola is (x,y).
Distance from focus(0,-4) to (x,y) = [tex]\sqrt{(x-0)^{2} +(y+4) ^{2}}=\sqrt{x^{2}+ (y+4)^{2}}[/tex]
Distance from (x,y) to directrix, y=4 is =[tex]\left | y-4 \right |[/tex]
As these distances are equal.
[tex]\sqrt{x^{2}+ (y+4)^{2}}=\left | y-4 \right |\\{x^{2}+ (y+4)^{2}=(y-4)^{2}[/tex]
→x²+y²+8 y +16 = y² - 8 y+16
→ x² = -8 y - 8 y= -16 y [ Cancelling y² and 16 from L.H.S and R.H.S ]
So , equation of parabola is , x²= - 16 y or f(x)= -x²/16
The Equation of parabola is [tex]f(x)=-\dfrac{x^2}{16}[/tex]
Equation of parabola with focus at [tex](0,-4)[/tex] and directrix is [tex]y=4[/tex] .
Parabola is the locus of all the points such that distance from fixed point on the parabola to fixed line directrix is same.
The parabola is opening downwards.
Let any point on parabola is [tex](x,y)[/tex].
Distance from focus [tex](0,-4)[/tex] to [tex](x,y)[/tex] = [tex]\sqrt{(x-0)^2+(y+4)^2[/tex]
[tex]d=\sqrt{x^2+(y+4)^2[/tex]
Distance from [tex](x,y)[/tex] to directrix, [tex]y=4[/tex] is =[tex]\left | y-4 \right |[/tex]
As these distances are equal.
[tex]\sqrt{x^2+(y+4)^2}=\left | y-4 \right |[/tex]
[tex]d={x^2+(y+4)^2=(y-4)^2[/tex]
[tex]x^2+y^2+8y+16=y^2-8y+16[/tex]
[tex]x^2=-8y-8y[/tex]
[tex]x^2=-16y[/tex]
[tex]y=\dfrac{-x^2}{16}[/tex]
So, the Equation of parabola is [tex]f(x)=-\dfrac{x^2}{16}[/tex]
Learn more about parabola here:
https://brainly.com/question/21685473?referrer=searchResults
Determine the 10th term 0.1,0.5,2.5
Answers
An=AR^n-1
A(10)=0.1(5)^(10-1)
A(10)=195312.5
Consider the two functions shown here. What is the rate of change of each function?
Function 2: y = ½ x + 7
Answers
Let's find the slope of function 1 using the Rise Over Run rule.
The rise is 2 and run is 1. So your rate of change is 2/1 or 2 for function 1
Function 2 is a y = mx + b equation, the slope is usually "m" or before the x
y = 1/2x + 7
1/2 is your rate of change for function 2
If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalent to x from the second equation is substituted into the first equation. 3x + 2y = −21 x − 3y = 4
Answers
[tex] \left \{ {{3x+2y=-21} \atop {x-3y=4}} \right. \\\\ \left \{ {{3x+2y=-21} \atop {x=4+3y}} \right. \\\\ \left \{ {{3(4+3y)+2y=-21} \atop {x=4+3y}} \right. \\\\ \left \{ {{12+9y+2y=-21} \atop {x=4+3y}} \right. \\\\ \left \{ {{12+11y=-21} \atop {x=4+3y}} \right. \\\\ \left \{ {{11y=-21-12} \atop {x=4+3y}} \right. \\\\ \left \{ {{11y=-33} \atop {x=4+3y}} \right. \\\\ \left \{ {{y=-3} \atop {x=4+3(-3)}} \right. \\\\ \left \{ {{y=-3} \atop {x=5}} \right. \\\\ Sol=\{(5,-3)\}\\\\ [/tex]
Line segment AC has endpoints A (-1,-3.5) and C (5,-1). Point B is on line segment AC and is located at (0.2,-3). What is the ratio of AB/BC
Answers
The distance between two points can be thought of as a line.
To find the length of this line, you can use the distance formula:
d = √ (x2 - x1) ^ 2 + (y2 - y1) ^ 2
We have then:
AC distance:
AC = root ((5 - (-1)) ^ 2 + (-1 - (-3.5)) ^ 2) = 6.5 units
AB distance:
AB = root ((0.2 - (-1)) ^ 2 + (-3 - (-3.5)) ^ 2) = 1.3 units
BC distance:
BC = 6.5-1.3 = 5.2 units
Answer:
The ratio is:
AB / BC = (1.3) / (5.2)
Answer:
AB/BC = (1.3) / (5.2). Hope this helps :)
Step-by-step explanation:
Solve the single variable equation for n.
4(-n + 4) + 2n = 2n
a. n = 4
b. no solution
c. infinitely many solutions
Answers
-4n + 16 + 2n = 2n
-4n + 16 = 0
-4n = -16
n = 4
answer
a. n = 4
will give brainlist
what is the approximate area of the figure
Answers
The rectangle is 8 cm by 14 cm, so that has an area of 112.
Now, add 25 and 112. This will give you about 137.
Answer:
the answer is 137.1
Step-by-step explanation:
Divide the figure into recognizable shapes. Find the area of each shape and add them together.
A cup of coffee contains 130 mg of caffeine. If caffeine is eliminated from the body at a rate of 11% per hour, how much caffeine will remain in the body after 3 hours?
Write the exponential function and solve.
a.
4072-06-01-04-00_files/i0260000.jpg; 184 mg
b.
4072-06-01-04-00_files/i0260001.jpg; about 346 mg
c.
4072-06-01-04-00_files/i0260002.jpg; less than 1 mg
d.
4072-06-01-04-00_files/i0260003.jpg; about 92 mg
Answers
y(t) = a*e^(kt)
---
now:
130 mg
---
one hour from intake:
130 * (1 - 0.11) = 115.7 mg
---
y(1) = 115.7 = 130*e^(k(1))
115.7 = 130*e^k
115.7/130 = e^k
ln( 115.7/130 ) = ln( e^k )
ln( 115.7/130 ) = k
k = -0.1165338
---
three hours from intake:
y(3) = 130*e^(3k)
y(3) = 91.64597
---
answer:
three hours after drinking a cup of coffee, 91.6 mg of caffeine will remain in the body
10 POINTS!!! FULL ANSWER WITH FULL STEP BY STEP SOLUTION PLEASE. DO BOTH PARTS OF 1 AND ALL OF 2.
Answers
y = e^x
dy/dx = e^x The f(x) = the differentiated function. Any value that e^x can have, the derivative has the same value. x is contained in all the reals.
One B
y = x*e^x
y' = e^x + xe^x Using the multiplication rule.
You want the slope and the value of the of y to be the same. The slope is y' of the tangent line
xe^x = e^x + xe^x
e^x = 0
This happens only when x is very "small" like x = - 4444444
y = e^x * ln(x) Using the multiplication rule again, we need the slope of the line with is y'
y1 = e^x
y1' = e^x
y2 = ln(x)
y2' = 1/x
y' = e^x*ln(x) + e^x/x So at x = 1 the slope of the line =
y' = e^1*ln(1) + e^1/1
y' = e*0+e = e
y = mx + b
y = ex + b
to find b we use y= e^x ln(x)
e^x ln(x) = e*x + b
e^1 ln(1) = e*1 + b
ln(1) = 0
0 = e + b
b = - e
line equation and answer.
y = e*x - e
Which is the best estimate for (6.3x10^-2)(9.9x10^-3) written in scientific notation?
Answers
Answer:
[tex]6 \times 10^{-4}.[/tex]Step-by-step explanation:
We are given expression [tex](6.3 \times 10^{-2})(9.9\times 10^{-3})[/tex].
In order to multiply above given expression, we need to multiply 6.3 by 9.9 first.
On multiplying 6.3 by 9.9 , we get 62.37.
Now we would multiply [tex]10^{-2} \ by \ 10^{-3}.[/tex]
Therefore,
[tex]10^{-2} \times 10^{-3}= 10^{-2-3}= 10^{-2-3} = 10^{-5}.[/tex]
Therefore,
[tex](6.3 \times 10^{-2})(9.9\times 10^{-3}) =62.37 \times 10^{-5}[/tex]
Again [tex]62.37 \times 10^{-5}[/tex] could be written as [tex]6.237 \times 10^{-4}[/tex].
Now, [tex]6.237 \times 10^{-4}[/tex] could be round to [tex]6 \times 10^{-4}.[/tex]
Therefore, correct answer is [tex]6 \times 10^{-4}.[/tex]
Val rented a bicycle while she was on vacation. A paid a flat rental fee of $55 plus $8.50 each day the total cost was 123 dollars write an equation you can use to find the number of days when she rented to bicycle
Answers
Flat fee= $55
Daily cost= $8.50
d= number of days rented
Total cost equals (the daily cost times the number of days rented) plus the flat fee.
T= (Daily cost)(# Days) + Flat fee
$123= $8.50d + $55
ANSWER: $123= $8.50d + $55
Hope this helps! :)
35 points!
What is the area of this triangle? Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
Answers
Here is the formula for area: ¹⁄₂ • c • b • sin(A)
¹⁄₂ • 11 • 9 • sin63
¹⁄₂ • 99 • sin63
49.5 • sin63
49.5 • .8910065242...
≈44.1
That should be the area of the triangle. The other way to do this is to just start by using the law of cosines, and then finding the height of the triangle, and then using the area formula. I believe the way I showed you is the easier way though. Message me if you have any questions.
Also make sure to include units : 44.1cm²
A parallelogram has vertices E(−8, 3), F(2, −2), G(−1, 3), and H(−5, −2). What are the coordinates of the midpoint of each diagonal?
(3, −0.5)
(−4.5, 3)
(−3, 0.5)
(0.5, −1.5)
Answers
Then, join the points to find the parallelogram sought.
We observe that the half point of both diagonals is the same.
Therefore, it is enough to calculate the half point of only one of the diagonals.
The half point is calculated according to the expression:
(((x1 + x2) / 2), ((y1 + y2) / 2))
Substituting values of one of the diagonals:
(((-1-5) / 2), ((3-2) / 2))
(-3, 0.5)
Answer:
(-3, 0.5)
Which are the solutions of this equation 4x2-7x=3x+24
Answers
Answer: x = -3/2 x =4
Answer:
3rd and last choice on ed
Step-by-step explanation: