Answer:
The two legs of the right triangle are approximately 3.1 cm and 5.1 cm and the hypotenuse is 6 cm.
Step-by-step explanation:
Let x be one leg of the right triangle.
Since the other leg is two centimeters longer, it can be represented by the expression:
[tex]x + 2 \text{ cm}[/tex]
According to the Pythagorean Theorem, for a right triangle:
[tex]a^2 + b^2 = c^2[/tex]
Where c is the hypotenuse and a and b are the two legs.
The hypotenuse is given to be 6 cm and the two legs are x and (x + 2). Hence:
[tex](x)^2 + (x+2)^2 = 6^2[/tex]
Solve for x. Simplify:
[tex]x^2 + (x^2 + 4x + 4) = 36[/tex]
Simplify:
[tex]2x^2 + 4x + 4 = 36[/tex]
Subtract:
[tex]2x^2 + 4x - 32 =0[/tex]
Divide:
[tex]x^2 + 2x - 16 = 0[/tex]
The equation is not factorable, so we can consider using the quadratic formula:
[tex]\displaystyle x = \frac{-b\pm\sqrt{b^2 -4ac}}{2a}[/tex]
In this case, a = 1, b = 2, and c = -16. Substitute:
[tex]\displaystyle x= \frac{-(2)\pm\sqrt{(2)^2-4(1)(-16)}}{2(1)}[/tex]
And evaluate:
[tex]\displaystyle \begin{aligned}x &= \frac{-2\pm\sqrt{68}}{2} \\ \\ &= \frac{-2\pm\sqrt{4\cdot 17}}{2} \\ \\ &= \frac{-2\pm2\sqrt{17}}{2} \\ \\ &= -1 \pm \sqrt{17} \end{aligned}[/tex]
Hence, our two solutions are:
[tex]\displaystyle x = -1 + \sqrt{17} \approx 3.1\text{ or } x = -1 - \sqrt{17} \approx -5.1[/tex]
Lengths cannot be negative, so we can ignore the second solution.
Hence, the value of x or the first side length is about 3.1 centimeters.
Since the other side length is two centimeters longer, the other side is about 5.1 centimeters.
In conclusion, the two legs of the right triangle are approximately 3.1 cm and 5.1 cm and the hypotenuse is 6 cm.
PLEASE HELP FAST!! I CANNOT GET THIS WRONG!!!!
Makayla and David work at a furniture store. Makayla is paid $230 per week plus 7.5% of her total sales in dollars, x, which can be represented by g(x)=230+0.075x. David is paid $321 per week plus 4% of his total sales in dollars, x, which can be represented by f(x)=321+0.04x. Determine the value of x, in dollars, that will make their weekly pay the same.
Answer:
6
Step-by-step explanation:
you kna mean?
24 - 8X = -16
Help pls
Answer:
5
Step-by-step explanation:
24-8X=-16
24+16=8X
40=8X
X=5
Answer:
x=5
Step-by-step explanation:
24 - 8x = -16
=> 24 + 16 = 8x
=> 8x = 24 + 16
=> 8x = 40
=> x = 40/8
=> x = 5
If you vertically stretch the exponential function f(x)= 2^x by the factor of 4, what is the equation of the new function
Answer:
to vertically strech a function by a factor of c, multiply the whole function by c
so
f(x) vertically streched by a factor of 4 is 4f(x)
so we get
the new function is f(x)=4(2)ˣ
Step-by-step explanation:
Which of the following angles is coterminal with -59˚? *
A. 2700˚
B. B. 301˚
C. C. 550˚
===============================================================
Explanation:
To find a coterminal angle, we add on 360 degrees
-59+360 = 301
The angles -59 degrees and 301 degrees point in the same exact direction. This is why they are coterminal.
Is KV=21, what does OZ=
Please help
Answer:
OZ = 23
Step-by-step explanation:
What is 1,025 divided by 68 full explanation
Answer:
15.1 (rounded to the nearest tenth decimal point)
Step-by-step explanation:
The explanation is, this is simple maths, nothing else. Let me know if it helps. Thank you
PLEASE HELP!!! HIGHSCHOOL GEOMETRY
(05.03 MC)
In the figure below, ΔABC ≅ ΔDEF. Point C is the point of intersection between segment AG and segment BF, while point E is the point of intersection between segment DG and segment BF.
Prove ΔABC ∼ ΔGEC. (10 points)
Step-by-step explanation:
ABC is congruent to DEF because angle C = angle C because of vertical angles angle E = angle E because of vertical angles angle G = angles A and D because of 3rd angle theorem triangle ABC ~ triangle GEC because of congruent angles.
Need help with 10 and 11
Answer:
10: A 11: B i think
Step-by-step explanation:
[tex]\small\bold\color{gray}{\colorbox{white}{√CarryOnLearning}}[/tex]
(ノ^_^)ノ
Please help :)
Please explain your answer also because I need to learn this!
A paratrooper and counter stronger winds than anticipated while parachuting from 1350 feet, causing him to drift at an 8° angle. How far from the drop zone will the paratrooper land?
Answer:
189 feet
Step-by-step explanation:
the distance from the drop zone the paratrooper will land = h × tan 8°
= 1350 × 0.14 = 189 feet
A car is traveling at 55 mph. What is the
speed of the car in feet per second (ft/s)?
Answer:
80 feet per second
Step-by-step explanation: At 55 mph, your vehicle is traveling at about 80 feet per second. Feet-per-second is determined by multiplying speed in miles-per-hour by 1.47 (55 mph x 1.47 = 80 feet per second.)
wats 10 to the 2nd power divied by 5 to the 2nd power
Answer:
4
Step-by-step explanation:
10^2/5^2
Do the exponents first
10 to the 2nd power is 100
5 to the 2nd power is 25
100/25
100 divided by 25 is 4
So the answer is 4
Hope this helps!
How is constructing an angle bisector similar to constructing a perpendicular bisector?
A. Both constructions begin with a given angle
B. Both constructions allow you to find the midpoint of a segment.
C. Both constructions require that you draw a ray.
D. Both constructions require the point where two arcs intersect.
Answer:
D. Both constructions require the point where two arcs intersect.
Step-by-step explanation:
D is your answer
Both constructions require the point where two arcs intersect. Then the correct option is D.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
Building an angle bisector is similar to building a perpendicular bisector in that both constructs call for the intersection of two arcs.
Angle bisector means dividing an angle into two equal parts. And the perpendicular bisector means the line is divided into two equal line segments.
Both constructions require the point where two arcs intersect.
Then the correct option is D.
More about the angled link is given below.
https://brainly.com/question/15767203
#SPJ2
What percentage of Americans would you predict wear contact lenses?
Please can you solve this questions for me!!
It's important
15:-
[tex]\\ \qquad\quad\sf\longmapsto \dfrac{x^5y^6}{xy^2}[/tex]
[tex]\\ \qquad\quad\sf\longmapsto x^{5-1}y^{6-2}[/tex]
[tex]\\ \qquad\quad\sf\longmapsto x^4y^4[/tex]
16:-
[tex]\\ \qquad\quad\sf\longmapsto \dfrac{x^2y^5}{xy^4}[/tex]
[tex]\\ \qquad\quad\sf\longmapsto x^{2-1}y^{5-4}[/tex]
[tex]\\ \qquad\quad\sf\longmapsto xy[/tex]
17;-
[tex]\\ \qquad\quad\sf\longmapsto \left(\dfrac{4x^5y}{16xy^4}\right)^3[/tex]
[tex]\\ \qquad\quad\sf\longmapsto (4^{1-2}x^{5-1}y^{1-4})^3[/tex]
[tex]\\ \qquad\quad\sf\longmapsto (4^{-1}x^4y^{-3})^3[/tex]
[tex]\\ \qquad\quad\sf\longmapsto 4^{-3}x^{12}y^{-9}[/tex]
18:-
[tex]\\ \qquad\quad\sf\longmapsto \left(\dfrac{5x^3y}{20xy^5}\right)^4[/tex]
[tex]\\ \qquad\quad\sf\longmapsto (4^{-1}x^{2}y^{-4})^4[/tex]
[tex]\\ \qquad\quad\sf\longmapsto 4^{-4}x^8y^{-16}[/tex]
19:-
[tex]\\ \qquad\quad\sf\longmapsto y^{-7}[/tex]
[tex]\\ \qquad\quad\sf\longmapsto \dfrac{1}{y^7}[/tex]
20:-
[tex]\\ \qquad\quad\sf\longmapsto 7^{-2}[/tex]
[tex]\\ \qquad\quad\sf\longmapsto \dfrac{1}{7^2}[/tex]
[tex]\\ \qquad\quad\sf\longmapsto \dfrac{1}{49}[/tex]
21:-
[tex]\\ \qquad\quad\sf\longmapsto \dfrac{1}{x^{-5}}[/tex]
[tex]\\ \qquad\quad\sf\longmapsto x^5[/tex]
22:-
[tex]\\ \qquad\quad\sf\longmapsto \dfrac{1}{2^{-4}}[/tex]
[tex]\\ \qquad\quad\sf\longmapsto 2^4[/tex]
[tex]\\ \qquad\quad\sf\longmapsto 16[/tex]
23:-
[tex]\\ \qquad\quad\sf\longmapsto x^5\times x^{-1}[/tex]
[tex]\\ \qquad\quad\sf\longmapsto x^{5-1}[/tex]
[tex]\\ \qquad\quad\sf\longmapsto x^4[/tex]
24:-.
[tex]\\ \qquad\quad\sf\longmapsto x^{-6}[/tex]
[tex]\\ \qquad\quad\sf\longmapsto \dfrac{1}{x^6}[/tex]
25:-
[tex]\\ \qquad\quad\sf\longmapsto x^9(x^{-7})[/tex]
[tex]\\ \qquad\quad\sf\longmapsto x^{9-7}[/tex]
[tex]\\ \qquad\quad\sf\longmapsto x^2[/tex]
PLEASE HELP! 10 points!
Step-by-step explanation:
It easy isn't it my friend
Solve the equation for Y. Then find the value of y for each value of X.
y+2x=5;x=-2,0,4
help me on this pls
Answer:
y=5-2x
2 5-2(2)=5-4=1
0 5-2(0)=5
4 5-2(4)=5-8=-3
The sum of two consecutive even integers is 214. What are the integers?
Answer:
Let the numbers be a and a + 2
According to question,
a + a + 2 = 214
=> 2a + 2 = 214
=> 2a = 212
=> a = 106
First number = 106
Second number = 108
Step-by-step explanation:
plz mark me brainliest
Answer:
106, 108
Step-by-step explanation:
even numbers
say n, n+2
n+n+2=214
2n=212
n=212/2=106
even numbers are 106 and 108
If f(x) = x^2 + 8x – 2 and f(0), then the result is:
-2.
0.
8.
Answer:
-2.
Step-by-step explanation:
f(0) = 0^2 + 8(0) - 2
= -2.
bobby's mom gets a small pot of water on the stove and lights a burner. ten minutes later, bobby notices small bubbles and sees that the water is almost boiling. which of the following could possibly be the tempeture of the water in the pot.
a 120F
b 95 C
c 99 F
d 110 C
m²+16m=4 give the number that must be added to both side
this is correct solution thank you
Mr.ford drove 224 miles in 4 hours. At what rate of speed did he drive?
Answer:
56 miles per hour i think
Step-by-step explanation:
There are 2.54 centimeters in 1 inch. There are 100 centimeters in 1 meter.
To the nearest meter, how many meters are in 197 inches? Enter the answer in the box.
meters
Answer:
5 meters
Step-by-step explanation:
If in 1 inch have 2.54 centimeters, in 197 inches will have:
197×2.54 = 500.38 centimeters
If 100 centimeters are 1 meter, 500 centimeters will have 5 meters, so 197 inches have 5 meters
23° is equal to
1
23
01
23
Step-by-step explanation:
I am sure there is something missing or horribly mistyped.
if you really meant 23⁰, then that is 1.
whats number 26.
..............................
Answer:
y = 1/3mx + b
Step-by-step explanation:
x = 3(y - b)/m
~Multiply m to both sides
mx = -3b + 3y
~Add 3b to both sides
mx + 3b = 3y
~Divide everything by 3
1/3mx + b = y
y = 1/3mx + b
Best of Luck!
[tex]\\ \rm\longmapsto x=\dfrac{3(y-b)}{m}[/tex]
[tex]\\ \rm\longmapsto mx=3(y-b)[/tex]
[tex]\\ \rm\longmapsto mx=3y-3b[/tex]
[tex]\\ \rm\longmapsto 3y=mx+3b[/tex]
[tex]\\ \rm\longmapsto y=\dfrac{1}{3}mx+b[/tex]
Find the slope of the line with points (-3, -8) and (-3, 5)
Step-by-step explanation:
let ,(-3,-8)=(X2,y2)(-3,5) =(x1,y1)
then
slope (M) =
[tex](y2 - y1 ) \div x2 - x1)[/tex]
={(-8)-5 }÷{(-3)-(-3)}
= -13÷ 0
=0
Is √5x - 12 = 0 nonlinear or linear?
this one is for the math experts!
Please help and get it correct for a chance to get brainly!
Answer:
-52
Step-by-step explanation:
i think its -52 i don't know this. just a guess not being rude<3
Answer:
-52 has a greater value
|-52| = 52
............
32 divided by 752.4 help me pppplease
Answer:
0.0425
Step-by-step explanation:
just use a calculator
48 ounces of liquid detergent
for $6.19. Find the unit rate
Hi there!
»»————- ★ ————-««
I believe your answer is:
Around 13 cents.
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\rightarrow \frac{dollars}{ounces}= \frac{6.19}{48}=\frac{6.19/48}{48/48}=0.128958... \approx \$0.13[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
please help ill mark brainliest
Answer:
AED = 136
Step-by-step explanation:
plz mark me as a brainlist