Answers
Answer:
[tex]x=16.4\ y=13.7[/tex]
Step-by-step explanation:
[tex][Kindly\ refer\ the\ attachment.]\\We\ are\ given\ that,\\\triangle ABC\ is\ a\ right-triangle\ and\ has\ it's\ legs\ x\ and\ z.\\It's\ altitude\ CD\ separates\ it\ into\ two\ triangles:\\\triangle BCD\ and\ \triangle ADC,\ both\ of\ which\ are\ right-triangles.\\Now,\\The\ Pythagoras\ Theorem\ tells\ us\ that:\\'The\ sum\ of\ squares\ of\ both\ the\ legs\ is\ equal\ to\ the\ square\ of\ the\\ hypotenuse'.\\Here,\\Lets\ consider\ three\ triangles\ separately.\\[/tex]
[tex]In\ \triangle ADC\ right\ angle\ is\ at\ \angle ADC.\\Hence,\\AC\ is\ the\ hypotenuse, and\ AD\ and\ DC\ are\ it's\ legs.\\Hence,\\AD^2+DC^2=AC^2\\Or,\\9^2+y^2=x^2\\\\Lets\ take\ the\ above\ equation\ as\ E_1.[/tex]
[tex]In\ \triangle BDC\ right\ angle\ is\ at\ \angle BDC.\\Hence,\\BC\ is\ the\ hypotenuse, and\ DC\ and\ DB\ are\ it's\ legs.\\Hence,\\DC^2+DB^2=BC^2\\Or,\\21^2+y^2=z^2\\Lets\ take\ the\ above\ equation\ as\ E_2.[/tex]
[tex]Now,\\In\ whole\ \triangle ACB\ right\ angle\ is\ at\ \angle ACB.\\Hence,\\AB\ is\ the\ hypotenuse, and\ AC\ and\ BC\ are\ it's\ legs.\\Hence,\\AC^2+BC^2=AB^2\\Or,\\x^2+z^2=(21+9)^2=30^2\\Lets\ take\ the\ above\ equation\ as\ E_3.[/tex]
[tex]Lets\ now\ gather\ the\ three\ equations:\\9^2+y^2=x^2\\21^2+y^2=z^2\\x^2+z^2=30^2\\Now,\\Lets\ pair\ and\ add\ E_1\ and\ E_2.\\Hence,\\(9^2+y^2)+(21^2+y^2)=(x^2)+(z^2)\\Hence,\\81+y^2+441+y^2=x^2+z^2\\Hence,\\2y^2+522=x^2+z^2\\Considering\ E_3,\\We\ already\ know\ that,\\x^2+z^2=30^2\\Hence,\\2y^2+522=30^2\\Hence,\\2y^2+522=900\\2y^2=900-522=378\\Hence,\\y^2=\frac{378}{2}=189\\Hence,\\y=\sqrt{189}=13.7\\[/tex]
[tex]Plugging\ in\ y=13.7\ in\ E_1,\\9^2+(13.7)^2=x^2\\81+189=x^2\\x^2=270\\x=\sqrt{270}=16.4[/tex]
Related Questions
Kaylin buys a greeting card for $3.79. She then buys 4 postcards that all cost the same amount. The total cost is $5.11. How much is each postcard?
Answers
Answer:
$0.33
Step-by-step explanation:
5.11-3.79=1.32 1.32/4
Hope this helps :)
Answer:
each postcard cost .33 or 33 cent
Step-by-step explanation:
5.11(total cost)-3.79(greeting card)= 1.32
1.32(cost of all postcards)/4= .33
Ryobi has a budget of $7200 for 80 chairs. They can buy leather chairs for $125 each, mesh chair for $100 each, and fabric chairs for $175 each. They want to have three times as many fabric chairs as leather chairs. How many of each chair should they buy?
Answers
Answer:
Step-by-step explanation:
Ryobi has a budget of $7200 for 80 chairs. They can buy leather chairs for $125 each, mesh chair for $100 each, and fabric chairs for $175 each. They want to have three times as many fabric chairs as leather chairs. How many of each chair should they buy?
Give the standard form for 900.000 + 50.000 + 9.000 + 600 + 20 + 7
Answers
Answer:
1.586 x 10³
Step-by-step explanation
900.000 + 50.000 + 9.000 + 600 + 20 + 7=1586
standard form:
1.586 x 10³
Help help HELPP plsss
Answers
Answer:
130
Step-by-step explanation
that corner is same as the one across it sorry I don’t know how to explain it very well but it’s Angel is linear to the one across it mean it’s the same
Answer:
C. 130 degrees
Step-by-step explanation:
The total degrees of the interior angels of a six sided ploygon is 720, so all you need to do is add the shown angles together and subtract that number from 720:
130 + 130 + 130+ 100 + 100 = 590
720 - 590 = 130
HELP NEEDED ASAP! I NEED HELP ASAP !! IF YOU ANSWER WITHOUT ACTUALLY ANSWERING AND ONLY FOR POINTS YOU WILL BE REPORTED!!
Answers
Answer:
They are congruent because they have all the same angles
Step-by-step explanation:
What is the smaller angle formed by the minute and hour hands at 3:30pm?
[asy]
unitsize(50);
draw(Circle((0,0),1),black+1);
dot((0,0));
for(real i=0;i<360;i+=6){
draw(0.96*(cos(i*pi/180),sin(i*pi/180))--(cos(i*pi/180),sin(i*pi/180)),black+0.5);
};
for(real i=30;i<390;i+=30){
draw(0.93*(cos(i*pi/180),sin(i*pi/180))--(cos(i*pi/180),sin(i*pi/180)),black+0.5);
label(string(i/30),0.83*(sin(i*pi/180),cos(i*pi/180)));
};
real h=3.5; real m=30;
draw(0.65*(sin(pi/6*(h)),cos(pi/6*(h)))--(0,0)--0.9*(sin(pi/30*m),cos(pi/30*m)),black+1,Arrows(TeXHead));
draw(anglemark(dir(-90),origin,dir(-15),5));
[/asy]
Answers
Answer:
75 degrees
Step-by-step explanation:
At 3:30, the hour hand is halfway between the 3 and the 4. The minute hand is exactly on the 6.
There are 360/12 = 30 degrees between each of the marked hours. The angle between the hands covers 2.5 of these gaps, so the angle between the hands is 2.5(30) = 75 degrees.
Hope this helps!
The angle between the hands at 3:30 pm is 90°.
What is the angle between the hands of a clock at 3:30 pm?
At that time, one hand points at the 3, and the other hand points at the 6.
Now, there is a rule to transform time into angles.
We know that a clock has 12 hours in a full revolution, and a circle has 360° in a complete revolution.
Then we know that:
12 hours = 360°
Then:
1 hour = (360°/12) = 30°
So each between each number in the clock we have an angle of 30°.
Then, between 3 and 6 (3 hours) we have:
3*30° = 90°
The angle between the hands at 3:30 pm is 90°.
If you want to learn more about angles, you can read:
https://brainly.com/question/17972372
HELPPPPP GIVING BRAINLIEST
Which event typically causes upwelling?
Wind blows warm water away from the shore.
Warm water rises to the surface of the ocean.
Neap tides move cold water away from the shore.
Cold water falls to the bottom of the ocean and pushes warm water up.
Answers
it's wind blows warm water away from the shore.
Step-by-step explanation:
it is one hundred percent correct
Answer:
A
Step-by-step explanation:
Wind blows warm water away from the shore.
Pls help How many sides does this regular polygon have?
Answers
Answer:
9
Step-by-step explanation:
interior angle + exterior angle = 180°, that is
7y + 2y = 180
9y = 180 ( divide both sides by 9 )
y = 20
Then
2y = 2 × 20 = 40°
The sum of the exterior angles of a polygon = 360°
Divide the sum by 40 for number of sides (n)
n = [tex]\frac{360}{40}[/tex] = 9
Find the slope of the line through each pair of points.
Type your answer as a fraction.
(-1, -11), (16, -8)
Answers
Answer:
m = 3/17
Step-by-step explanation:
M = -1y/-11c + 16y/-8x = 3/17
what is the nth term of 5,11,17,23
Answers
Answer:
6n - 1.
Step-by-step explanation:
Arithmetic sequence.
a1 = 5, d = 6.
nth term = a1 + d(n - 1)
= 5 + 6(n - 1)
= 5 + 6n - 6
= 6n - 1.
HELPPPPP
Question 15(Multiple Choice Worth 4 points)
(05.06 LC)
Given the scatter plot, choose the function that best fits the data.
scatter plot with data points that form an upward curve staring at the origin and continuing to the right
f(x) = 4x
f(x) = −4x
f(x) = 4x2
f(x) = 4x
Answers
Answer:
f(x) = 4x²
Step-by-step explanation:
This function curves while the others don't.
Hope it's correct and helps!
The function that best fits the data is [tex]y=4^x[/tex]
What is function?"It defines a relation between input and output values.""In function, for each input there is exactly one output."What is exponential function?"The function of the form [tex]y=ab^x[/tex] where a, b are real numbers and a ≠ 0 "
For given question,
The scatter plot with data points that form an upward curve staring at the origin and continuing to the right.
The graph represents an exponential function.
At (0, 1),
[tex]\Rightarrow 1=ab^0\\\Rightarrow a=1[/tex]
At (1, 4) we have,
[tex]\Rightarrow 4 = ab^1\\\Rightarrow 4=(1)b\\\Rightarrow b=4[/tex]
So, we have exponential function of the form [tex]y=4^x[/tex]
Hence, the function that best fits the data is [tex]y=4^x[/tex]
Learn more about exponential function here:
https://brainly.com/question/11464095
#SPJ3
what is the simplified form of this equation f(x)=
x2 + 4x + 10
Answers
Answer:
6x + 10
Step-by-step explanation:
2+4=6
and 10 doesn't have an x next to it so it doesn't count
(sat prep) find the value of x
Answers
Answer:
140 degrees
Step-by-step explanation:
Im only a freshman, but i think i got it, i just assumed that the other small part at the bottom was also 20 degrees, which would mean that you are missing the 140 degrees from the 180 degree line
Answer:
120 degrees
Step-by-step explanation:
The bottom part is 40 degrees,
the two lines are parallel, so theoretically, you can just put them together. Then using vertical angles, you can tell it's 40 degrees.
40 + 20 = 60
180-60 degrees is 120 degrees.
The length of a car measures 30 feet what is the length of a model car if the scale factor is 1:64
Answers
Answer:
5 5/8 inches
Step-by-step explanation:
Set up and solve an equation of ratios:
x 1
------- = -------
30 ft 64
Then 64x = 30 ft, and x (the length of the model car) is 30/64 ft, or
x = 0.469 ft, or 5 5/8 inches
Help please help me
Answers
Answer:
Step-by-step explanation:
Range = maximum value - minimum value
= 25 - 6 = 19
Option D is the correct answer
X-2y=10 x+3y=5 please hellppppppp
Answers
Answer:
x=8,y=-1
Step-by-step explanation:
x-2y=10
x=10+2y
10+2y+3y=5
5y=-5
y=-1
x-2(-1)=10
x=8
The solution to the system of equations x - 2y = 10 and x + 3y = 5 is x = 8 and y =-1
How to solve the equation?The system of equations is given as:
x - 2y = 10
x + 3y = 5
Subtract both equations
-2y - 3y = 10 - 5
Evaluate
-5y = 5
Divide both sides by -5
y = -1
Substitute y = -1 in x - 2y = 10
x - 2(-1) = 10
This gives
x + 2 = 10
Subtract 2 from both sides
x = 8
Hence, the solution to the equations is x = 8 and y =-1
Read more about system of equations at:
https://brainly.com/question/14323743
#SPJ2
Linda can attend either community college or university the annual cost for each are shown below. in the table what total cost to attend the university for four years
Answers
Answer:
I believe it's 19279 if u need the answer to community college too tell me
What is the slope between the two points (8, -2) and (-7, 10)?
Answers
Answer:
slope ={10--2}/(-7-8)=12/-15=-4/5
The Suarez family paid $12.00 for 3 movie tickets. How much would they have paid for 9 tickets?
Answers
Answer:
$36 (see below)
Step-by-step explanation:
First, you have to find how much they paid for one ticket.
If they paid $12 for 3, then they paid $4 for 1.
You could've also use a ratio:
$12 $x
-------- = --------
3 1
Cross multiply:
$12 (1) = $3x
$12 = $3x
$4 = x
So $4 for 1 ticket.
To find the cost of 9 tickets, just multiply the price by the number of tickets, which is:
$4 (9) = $36
LA Galaxy have won 60% of their soccer matches. If they have played 40 matches, how many have they won?
Answers
Answer: LA Galaxy has won 24 of their soccer matches.
Step-by-step explanation:
To find 60% of 40, you can multiply 60/100 by 40.
60/100 x 40 = 24.
In conclusion, LA Galaxy has won 24 of their soccer matches.
Savannah is deciding between two parking garages. Garage A chargers an initial fee of $9 to park plus $1.50 per hour
Answers
Answer: 4 hours
Step-by-step explanation:
Assume x is the number of hours taken.
Garage A would therefore charge a total of:
= $9 + $1.50 * x
= 9 + 1.50x
Garage B would charge:
= $5 + $2.50 * x
= 5 + 2.50x
To find the number of hours it would take for them to be the same, equate both equations:
9 + 1.50x = 5 + 2.50x
9 - 5 = 2.50x - 1.50x
4 = 1x
x = 4 hours
That cost would be:
= 9 + 1.50 * 4
= 9 + 6
= $15
What is the base of the expression 11 and 12 square? 3 11 12 21
Answers
Answer:
your answer is 11
Step-by-step explanation:
An exponential has the base at the bottom
In GeoGebra, you should see a sketch of William’s kite. You’ll use the sketch to find the lengths of the dowels needed to make the kite. William has indicated that he would like the kite to be AD = 120 cm wide across the bottom, which is labeled on the sketch. Using the width of the kite and the fact that the kite is made from two congruent right triangles, what is AC?
Answers
Answer:
60
Step-by-step explanation:
i added a comment instead of a answer so yeah
Answer:
60 cm
Step-by-step explanation:
AD = 120cm
AC = 1/2 AD = 1/2(120) = 60 cm
Rosie has £m in her pocket she is given £4 pocket money write an expression for how much money she has now
Answers
Answer:
m+4
Step-by-step explanation:
She currently has a variable "m" in her pocket which we don't know, BUT we know how much she is getting, which is 4.
WILL MARK BRAINLIEST!! PLZ HELP!! ASAP!
SELECT ALL THAT APPLY!!!! Sales tax is 7%. If c represents the retail cost of an item, which of the following expressions represent(s) the total cost of the item?
0.93 c
c - 0.07 c
1.07 c
0.07 c
c + 0.07 c
Answers
Answer:
c + 0.07c and 1.07c
Step-by-step explanation:
the sales cost will be added to the retail cost
Which percent is equivalent to 0.3?
Answers
Answer:
30%
Step-by-step explanation:
smart highschooler brain
Grades
AllianceRMMS.com
2 points
3) Tati wants to save money to be ready to shop for presents during
Christmas 2021. Tati has $25 in her piggy bank and continues to save $40
per month. What is the rate of change and constant; write Tati's savings
plan in slope-intercept form.*
O y = 65 next month
O y = 25x + 40
y = 40x + 25
O y = 15x + 25
Answers
Answer:
AllianceRMMS.com
2 points
3) Tati wants to save money to be ready to shop for presents during
Christmas 2021. Tati has $25 in her piggy bank and continues to save $40
per month. What is the rate of change and constant; write Tati's savings
plan in slope-intercept form.*
O y = 65 next month
O y = 25x + 40
y = 40x + 25
O y = 15x + 25
do thatand u find out
Step-by-step explanation:
Matthew is training to participate in a half marathon. Each week, Matthew increases the number of miles he runs in the previous week by the same percent. The table below shows the number of miles he runs in weeks 1 and 2.
Week Number of Miles Run
1 12.5
2 15.5Complete the sentence. Do not round your answer.
Matthew runs
miles in week 3.
Answers
Answer:
Step-by-step explanation:
3/12.5 = x/15.5 so x is 3.72
Then 3.72 + 15.5 = 19.22
Answer:
answering so they can get brainliest ^^
Step-by-step explanation:
Solve this problem, please!
Answers
Answer:
B
Step-by-step explanation:
Alvin is 15 years younger than Elga. The sum of their ages is 49. What is Elga's age?
Answers
Answer:
32
Step-by-step explanation:
Suppose Alvin is x years old. Then Elga is x+15 years old.
x+x+15=49
2x=34
x=17
17+15=32