Answers
Answer:
Part 1) [tex]HD=\sqrt{105}\ units[/tex]
Part 2) [tex]JD=2\sqrt{34}\ units[/tex]
Part 3) [tex]KD=6\sqrt{2}\ units[/tex]
Step-by-step explanation:
step 1
Find the length HD
In the right triangle HDF
Applying the Pythagoras Theorem
[tex]FD^{2} =HF^{2} +HD^{2}[/tex]
substitute the values and solve for HD
[tex]19^{2} =16^{2} +HD^{2}[/tex]
[tex]HD^{2}=19^{2}-16^{2}[/tex]
[tex]HD^{2}=105[/tex]
[tex]HD=\sqrt{105}\ units[/tex]
step 2
Find the length JD
In the right triangle JDF
Applying the Pythagoras Theorem
[tex]FD^{2} =JD^{2} +FJ^{2}[/tex]
we have
[tex]FD=19\ units[/tex]
[tex]FJ=JG=15\ units[/tex] ----> because JD is a perpendicular bisector
substitute the values and solve for JD
[tex]19^{2} =JD^{2} +15^{2}[/tex]
[tex]JD^{2}=19^{2}-15^{2}[/tex]
[tex]JD^{2}=136[/tex]
[tex]JD=\sqrt{136}\ units[/tex]
[tex]JD=2\sqrt{34}\ units[/tex]
step 3
Find the length KD
In the right triangle KDG
Applying the Pythagoras Theorem
[tex]GD^{2} =KD^{2} +GK^{2}[/tex]
we have
[tex]GD=FD=19\ units[/tex]
[tex]GK=17\ units[/tex]
substitute the values and solve for KD
[tex]19^{2} =KD^{2} +17^{2}[/tex]
[tex]KD^{2}=19^{2}-17^{2}[/tex]
[tex]KD^{2}=72[/tex]
[tex]KD=\sqrt{72}\ units[/tex]
[tex]KD=6\sqrt{2}\ units[/tex]
Related Questions
The bottom of a circular swimming pool with a diameter of 30 feet is painted blue. How many square feet are blue?
Answers
if its diameter is 30, then its radius is half that, or 15.
[tex]\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=15 \end{cases}\implies A=\pi 15^2\implies A=225\pi \implies A\approx 706.86[/tex]
Area of the circle is the area which is occupied by the circle in the two- dimensional plane. The area of the circle is equal to the area of the bottom of the circular swimming pool. Thus the blue paint is total 707.143 square feet.
Given-The diameter of the circular swimming pool is 30 feet.
To find out the square feet of blue the area of the circle has to be calculated.
What is area of the circle?Area of the circle is the area which is occupied by the circle in the two- dimensional plane. The area of the circle with diameter [tex]d[/tex] can be calculated as,
[tex]A=\pi\times \dfrac{d^2}{4}[/tex]
Put the value of the diameter, we get,
[tex]A=\dfrac{22}{7} \times \dfrac{30^2}{4}[/tex]
[tex]A=707.143[/tex]
The area of the circle is 707.143 square feet.
As the area of the circle is equal to the area of the bottom of the circular swimming pool. Thus the blue paint is total 707.143 square feet.
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Which equation is satisfied by all three of the plotted points?
Answers
ANSWER
B. y=2x+1
EXPLANATION
The graph has a y-intercept of 1.
Let y=mx +b be the equation of the straight line graph.
where b=1 is the y-intercept.
We put this value into the equation to get,
y=mx +1.
Thie point (1,3) must also satisfy this line.
3=m(1)+1
m=3-1
m=2
The equation is
y=2x+1
What is the x-intercept of the graph of 3x + 12 = -6
Answers
Answer:
It's -6. She did a bunch of weird work under my answer.
Step-by-step explanation:
The x-intercept of the graph of the equation 3x + 12 = -6 can be found by solving for x. Performing the necessary operations we get x=-6, thus, the x-intercept is -6.
Explanation:To find the x-intercept of the graph of the equation 3x + 12 = -6, let's first solve the equation for x. The x-intercept is the value of x where the graph intersects with the x-axis, this is the point where y = 0. By rearranging the equation, we can first subtract 12 from both sides to get 3x = -18, then divide both sides by 3 to get x = -6. So, the x-intercept of the graph is -6.
Here, we haven't needed to use information about the slope or the y-intercept, which do not affect the x-intercept. The slope of the line determines its steepness and direction, while the y-intercept determines where it crosses the y-axis. These shape the line but will not change where it crosses the x-axis.
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ana preparo chicha morada con 30 porciento de maiz morado y 70 porciento de agua.Si bebio el 30 porciento de la chicha morada y reemplazo esa cantidad de agua.Que porcentaje de la nueva mezcla es concentrado de maiz morado?
Answers
Answer:nise xdxxxxdddd
Step-by-step explanation:
Conociendo los porcentajes de cada componente y usando algebra simple, veremos que el porcentaje de la nueva mezcla que es maiz morado es el 49%.
Asumamos que comenzamos con una cantidad A de chicha morada.
Sabemos que:
0.3*A es maiz morado.0.7*A es agua.Ahora mezclamos eso.
Ana se bebe el 30% de la chicha morada, es decir, la cantidad restante de chicha morada es:
0.7*A
Conociendo las proporciones con las que esto se preparo, podemos ver que la cantidad de agua restante es:
0.3*0.7*A
Y la cantidad de maiz restante es:
0.7*0.7*A
Ahora reemplaza el 0.3*A faltante con agua, es decir, la cantidad total de agua será:
0.3*0.7*A + 0.3*A
(0.3*0.7 + 0.3)*A
0.51*A
Es decir, en la nueva mezcla un 51% es agua.
Entonces el porcentaje de la nueva mezcla que es maiz morado es el 49% restante.
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Rewrite the following expression in logarithmic form and use that to solve for the variable. Show all work done in this process. 2ex = 6
Answers
Answer:
[tex]ln(e^x)=ln(3)[/tex]
[tex]x=1.099[/tex]
Step-by-step explanation:
You have the following exponential expression:
[tex]2e^x=6[/tex]
You need to divide both sides of the equation by 2:
[tex]\frac{2e^x}{2}=\frac{6}{2}\\\\e^x=3[/tex]
Now apply the function Natural logarithm to both sides of the function:
[tex]ln(e^x)=ln(3)[/tex]
Note that now the exponential function is transformed into a logarithmic function.
By definition:
[tex]ln(e^x)=x[/tex] Because the base of the Natural logarithm is the Euler's number "e".
Then you can solve for "x":
[tex]x=ln(3)\\x=1.099[/tex])
add [1 -4 3 5]+[-2 6 -2 4]
Answers
Answer:
11
Step-by-step explanation:
Answer:
The sum (answer) is [-1, 2, 1, 9].
Step-by-step explanation:
Here we're asked to sum up two matrices of the same dimensions (1 by 4).
The value in the first matrix, first column, is 1; that in the second matrix, first column, is -2. Combining 1 and -2, we get -1, which is the first column value in the answer matrix.
Continuing in the same manner: -4 + 6 = 2; 3 - 2 = 1; and 5 + 4 = 9.
The sum (answer) is [-1, 2, 1, 9].
Which points are 3.5 units apart?
Answers
.5 and 4 I think there should be a abcd questions
Answer:
(7.5, 1.2) and (7.5, –2.3)
Step-by-step explanation:
Hope this helps
PLEASE HELP ASAP!
A 6-foot-tall man is standing atop a 9-foot wall. The distance along the hypotenuse from the top of the man’s head to the ground, as shown, is 17 feet. Each kneeling child takes up 1 foot of space. How many children can kneel along the bottom of the triangle as shown? Assume the wall and the man are vertical, forming a right angle with the ground.
Answers
Answer:
8
Step-by-step explanation:
hypotenuse = c = 17 feet
Height = a = 9 feet + 6 feet = 15 feet
Children's space = b
a^2 + b^2 = c^2
15^2 + b^2 = 17^2
225 + b^2 = 289 Subtract 225 from both sides
225-225+b^2=289-225
b^2 = 64 Take the square root of both sides.
sqrt(b^2) = sqrt(64)
b = 8
Since each child takes up 1 foot, 8 children can sit on side b.
HELPP IN THE PICTURE
Answers
Answer:
Given in the question an expression,
y = 3x/(8+x)
Step1
interchange the variables
x = 3y/(8+y)
Step 2
x(8+y) = 3y
Step 3
8x + xy = 3y
Step 4
8x = 3y - xy
Step 5
8x = y(3 - x)
Step 6
8x = y(3 - x)
Step 7
y = 8x/(3-x)
Step 8
y = f(x^-1) = 8x/(3-x)
So the inverse of f(x)= 3x/(8+x) is f(x^-1) = 8x/(3-x)
Order the following from least to greatest: -0.3, 4/5, -5/12, 0.92
Answers
Answer:
-5/12, -0.3, 4/5, 0.92
Step-by-step explanation:
because: -5/12 = -0.41666666666
-0.3
4/5 = 0.8
0.92
and the negatives are always the least especially if it's a great number with a negative sign.
Each brick in the wall has the dimensions shown below. What is the volume of each brick
Answers
Answer:
Step-by-step explanation:
a
Answer:
A is the answer.
Step-by-step explanation:
59
72
118
144
The measure of two complementary angles are in the ratio 1 : 4. What are the degree measures of the two angles?
A 18° and 72°
B. 22.5° and 67.5°
C. 36° and 144°
D. 45° and 135°
Answers
Answer:
A 18° and 72°
Step-by-step explanation:
As you know, the sum of two complementary angles = 90
The ratio 1 : 4 = 1 + 4 = 5
So 90/5 = 18
1 x 18 = 18
4 x 18 = 72
The two complementary angles are 18° and 72°
Answer
A 18° and 72°
The inequality 6 - 2/3x < x - 9 is equivalent to...
A) x>9
B) x<9
C) x>-3/5
D) x<-3/5
Answers
Start with
[tex]6-\dfrac{2}{3}x<x-9[/tex]
Add 9 to both sides
[tex]15-\dfrac{2}{3}x<x[/tex]
Add [tex]\frac{2}{3}x[/tex] to both sides
[tex]15<\dfrac{5}{3}x[/tex]
Multiply both sides by 3/5
[tex]9<x[/tex]
Which is the same as
[tex]x>9[/tex]
How much are exams worth in k12 8th grade
Answers
It completely depends on the teacher, but typically exams seem to be worth at least 50% of your final grade.
I depends on what school you go to and how many subjects you have to study. It also depends on the type of teacher you have. But generally I would say exams are worth over 50% of your final grade.
Hope this helps!
For the given pair of events A and B, complete parts (a) and (b) below.
A. When a baby is born, it is a girl.
B. When a 16-sided die is rolled, the outcome is 1.
a. Determine whether events A and B are independent or dependent. (If two events are technically dependent but can be treated as if they are independent according to the 5% guideline, consider them to be independent.)
b. Find P(A and B), the probability that events A and B both occur.
Answers
Answer:
(a) Option A. independent
(b) [tex]P(A\ and\ B) = 0.0312[/tex]
Step-by-step explanation:
Two events A and B are considered dependent if the occurrence of one affects the probability of occurrence of another.
In this case, the events are independent because the birth of a girl or a boy does not affect the probability of obtaining a 1 by throwing a 16-sided die.
In the same way, throwing a die and obtaining the number 1 does not affect the probability that a baby is a girl or a boy.
When two events are independent then
[tex]P(A\ and\ B) = P(A)*P(B)[/tex]
The probability that a baby is a girl is
[tex]P(A) = 0.5[/tex]
The probability of obtaining a 1 when casting a 16-sided die is:
[tex]P(B) = \frac{1}{16}[/tex]
Then:
[tex]P(A\ and\ B) = 0.5 * \frac{1}{16}[/tex]
[tex]P(A\ and\ B) = 0.0312[/tex]
Raju wanted to plough his field. He asked the farmers "how many days will it take to plough the field? The farmers said “The field can be ploughed in 14 days. If 20 hectares of land is ploughed more daily, the work will be finished in 10 days”. Find the area of the land which can be ploughed daily. Also find the area of the field?
Answers
Answer:
1. Area of the land which can be ploughed daily is 50 hectares (and 70 hectares at higher rate)
2. Area of the field is 700 hectares
Step-by-step explanation:
Let x hectares be the number of hectares the farmers normally ploughed in a day. At this rate, they will complete the work in 14 days, so they have to plough
[tex]14\cdot x=14x\ hectares.[/tex]
Then x+20 hectares is the number of hectares the farmers ploughed in a day when they increased their productivity of work. At this rate, they will complete the work in 10 days, so they have to plough
[tex]10\cdot (x+20)=10(x+20)\ hectares.[/tex]
The work is the same, so
[tex]14x=10(x+20)\\ \\14x=10x+200\\ \\14x-10x=200\\ \\4x=200\\ \\x=50[/tex]
Ploughing 50 hectares each day 14 days in a row they will plough
[tex]14\cdot 50=700\ hectares[/tex]
find the area of the rhombus
Answers
Answer:
Step-by-step explanation:First of all you don't have anything to solve and the formal of a rhombus is base times height.
Okay so like maybe next time try to include a picture so we can see it, because we cant solve anything
The probability of winning a prize from a scratch
off card is 60%. A sample of 30 cards is taken.
What is the standard error of the proportion,
rounded to the nearest thousandth?
Answers
Answer:
The standard error of the proportion is
[tex]E=0.089[/tex]
Step-by-step explanation:
Assuming that the size of population N is large enough, and with a sample [tex]n = 30[/tex], so that:
[tex]\frac{n}{N}\leq0.05[/tex] then the standard error of the proportion is:
[tex]E = \sqrt{\frac{p(1-p)}{n}}[/tex]
Where
[tex]n = 30\\\\p= 0.6\\\\E = \sqrt{\frac{0.6(1-0.6)}{30}}\\\\E =\sqrt{\frac{0.6(0.4)}{30}}\\\\E=\frac{\sqrt{5}}{25}=0.089[/tex]
The height of a person in a scale drawing is 4 inches. The person's actual height is 64 inches.
Answers
Answer:11.4
Step-by-step explanation:
Every scale inch is 16 inches
what is the slope of a line that contains the points (1,9) and (4,3)
Answers
Answer:
The slope is -2
Step-by-step explanation:
To find the slope of a line when we have 2 points, we use the formula
m = (y2-y1)/(x2-x1)
= (3-9)/(4-1)
= -6/3
-2
The slope of the line is -2
To find the slope of a line using two points, there are many formulas, however the easiest one to use is (rise/run)
The rise is the difference in the Y value and the run is the difference in the X value
(9-3)/(1-4) = (6/-3) = -6/3, which can be simplified to -2
Megan has $50 in a savings account that earns 10% annually. The interest in not compounded. How much will she have in 1 year?
And
How much will she have in 3 years?
Answers
en un año gano 55 $ locual es un dato clave
Step-by-step explanation:
When 60% of a number is added to the number, the result is 208
Answers
Answer:
x=120
CK
0.60*120=72
120+72=192
192=192
Hope this helps
Step-by-step explanation:
THE ANSWER IS 192
Alyssa and Anna bought three toy cars for their three cousins from a store on line
The price for one car was $3.85. A shipping fee of $4.56 was added to the total
cost. The two girls shared the total cost equally How much did each girl pay?
Answers
Answer: 14.555
Step-by-step explanation: so you take $3.85 multiplied by 3 because they bought 3 toy cars plus a $4.56 and take the answer of that and divide by 2 because they split the cost. Hope this helps
Answer:
each girl had to pay around $8.06
Step-by-step explanation:
They bought 3 toy cars and each car was $3.85.
You have to multiply $3.85*3 which is $11.55.
Then add the $4.56 of shipping fee which is $16.11.
since the 2 girls shared the total cost, divide 16.11/2
16.11/2= $8.06
A machine makes 312 bolts in 30 minutes, at the same rate, how many minutes would it take to produce 260 bolts?
Answers
Answer:
25 minutes
Step-by-step explanation:
By using the rule of three we can solve this problem:
If a machine makes 312 bolts in 30 minutes, how much time it would take to produce 260 bolts?
312 bolts -----> 30 minutes
260 bolts ------> X
X = (260*30)/312 = 25 minutes
312/30=10.4.
260/10.4=25
look at the map below. which is the distance between kensington and greenwich?
Answers
Answer:
choice c is believe is the answer
Step-by-step explanation:
Applying the Pythagorean theorem, the distance between kensington and greenwich is: b. 20√5 mi.
What is the Pythagorean Theorem?To solve a right triangle, where a and b are the legs and c is the longest side (hypotenuse), the Pythagorean theorem states that, c = √(a² + b²).
Apply the Pythagorean theorem to find the distance:
Distance between kensington and greenwich = √(40² + 20²)
= √(1,600 + 400)
= √2,000
= 20√5 mi.
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Evaluate the square.
112 =
Answers
Ok ima be your math teacher. So basically 11 squared by two equals 121. Well you may be like Why!??!?! And it is because 11 squared by two is 11X11. Lets say the question was 11 squared by 4 then the answer would be 11X11X11X11 4 times! GET IT?!
What is the simplified expression for -3cd-d(2c-4)-4d
Answers
Answer:
-5cd
Step-by-step explanation:
-3cd-d(2c-4)-4d
Distribute the -d
-3cd-d2c-+d4-4d
-3cd -2cd +4d-4d
Combine like terms
-5cd
Zeros are never significant digits.
Please select the best answer from the choices provided
A:True
B:False
Answers
It is false because they could be at the end of a number
How do I answer this
Answers
Answer:
15, 94
Step-by-step explanation:
Pictures from an artists are numbered 1 through 60. What is the probability that the artist will chose a picture that is not a multiple of 13? Provide the final answer as a fraction
Answers
ANSWER
[tex]P( \bar E) =\frac{14}{15} [/tex]
EXPLANATION
The sample space is S={1,23,4,5,...60}
n(S)=60
The multiples of 13 are:
E={13,26,39,52}
n(E)=4
Probability of choosing a picture that is a multiple of 13 is
[tex]P(E)= \frac{n(E)}{n(S)} [/tex]
[tex]P(E)= \frac{4}{60} [/tex]
Probability of choosing a picture that is NOT a multiple of 13 is
[tex]P( \bar E)= 1 - \frac{4}{60} = \frac{56}{60} = \frac{14}{15} [/tex]