Given:
In △ABC is a right angle triangle.
AC is 6 units longer than side BC.
[tex]Hypotenuse=2\sqrt{17}[/tex]
To find:
The length of AC.
Solution:
Let the length of BC be x.
So, Length of AC = x+6
According to the Pythagoras theorem, in a right angle triangle
[tex]Hypotenuse^2=Base^2+Perpendicualar^2[/tex]
△ABC is a right angle triangle and AC is hypotenuse, so
[tex](2\sqrt{17})^2=(x)^2+(x+6)^2[/tex]
[tex]68=x^2+x^2+12x+36[/tex] [tex][\because (a+b)^2=a^2+2ab+b^2][/tex]
Subtract 68 from both sides.
[tex]0=2x^2+12x+36-68[/tex]
[tex]0=2x^2+12x-32[/tex]
[tex]0=2(x^2+6x-16)[/tex]
Divide both sides by 2.
[tex]x^2+6x-16=0[/tex]
Splitting the middle term, we get
[tex]x^2+8x-2x-16=0[/tex]
[tex]x(x+8)-2(x+8)=0[/tex]
[tex](x+8)(x-2)=0[/tex]
[tex]x=-8,2[/tex]
Side cannot be negative, so x=2 only.
Now,
[tex]AC=x+6[/tex]
[tex]AC=2+6[/tex]
[tex]AC=8[/tex]
Therefore, the length of AC is 8 units.
Use the digits 5, 3 and 2 two only once in each number how many different three digit numbers can you make
what is 576 - 354 + 7 = ?
S= √3+2√3+3√3+...10√3
write S as a√3
Answer:
S = 55√3Step-by-step explanation:
S=
√3+2√3+3√3+...10√3 =√3( 1 + 2 + 3+...+ 10) =√3(1/2)(10)(10 + 1) =√3(55) =55√3S = 55√3
Answer:
s=✓3(1+2+3+...10)
s=✓3[10/2×(10+1)]
here, applying sum of 1st n natural number is n/2×(n+1)
so, s=✓3×5×11
hence, s=55✓3.
what is 205÷5 please help!
Answer:
41
Step-by-step explanation:
Just used the calculator :D
Help plz answer this quickly!!!!!!!!!!!!
Answer:
4.7x
Step-by-step explanation:
235x20=4,700
4.7
SUPER URGENT ANSWER BOTHHHHH QUESTIONS
I WILL DEF MARK BRAINLYEST
READ CARFULLY!
Answer:
Step-by-step explanation:
563 people / 15 classes= 37 8/15. They should offer 38 classes.
2146 questions in 45 weeks.
2146/45= 47 31/45. round to 48 questions a week.
I would choose the first one. Even though the 2000 is an underestimate, the 50 weeks is overestimate , when divided it comes out to 50 questions a week which is closer to the 48 it actually is. I'd rather write too many questions then not enough.
PROBABILITY! PLEASE HELP!
Samuel wants to create a password containing one, two, or three lowercase vowels followed by two digits. How many different passwords are possible? (Note: assume the letters "a", "e", "i", "o", and "u" are the ONLY vowels of the English alphabet.)
Using the fundamental counting principle, it is found that 15500 different passwords are possible.
----------------------------
The fundamental counting principle states that if there are p ways to do one things, and q ways to do other thing, and they are independent, there are p*q ways to do both things.
----------------------------
For each digit, there are 10 ways.For each vowel, there are 5 ways.The digits and the vowels are independent, thus, the fundamental counting principle is applied.----------------------------
With one vowel followed by two digits, there are [tex]5 \times 10^2 = 5 \times 100 = 500[/tex] passwords.With two vowels followed by two digits, there are [tex]5^2 \times 10^2 = 25 \times 100 = 2500[/tex] passwords.With three vowels followed by three digits, there are [tex]5^3 \times 10^2 = 125 \times 100 = 12500[/tex] passwords.In total, there are [tex]500 + 2500 + 12500 = 15500[/tex] passwords.A similar problem is given at https://brainly.com/question/23855405
Joanna bought a gallon container of milk at the store what is the volume of the container in cups
Answer:
16 cups.
Step-by-step explanation:
A cup is 8 ounces, and a gallon is 128 ounces.
Answer:
16
Step-by-step explanation:
it's just how it is. it's right though I promise
a quarter has a diameter of 2.4. if it makes 8 rotations how far did it roll
Answer:
7.536
Step-by-step explanation:
I think it means to find the perimeter and multiply it by 8.
The perimeter of a circle is called the circumference.
C = pi(d)
C = pi(2.4)
C = 7.536
My teacher has us use 3.14 for pi so if your teacher has you use something else just multiply it by 2.4.
Which algebraic expression is equivalent to the expression below?
(16x + 1) - 5x
A.
21x + 1
B.
16x + 4
C.
11x - 1
D.
11x + 1
Answer:
D
Step-by-step explanation:
(16x +1) -5x
you basically subtract the -5x from 16x
11x +1
Help pleaseeeeeeeeeeeeeeeeeeeeee
Answer:
A) 2 1/12
Step-by-step explanation:
I just added all the fractions and subtracted from 10 1/12 :)
Determine whether the ordered pair (10, 4) is a solution to the equation 3x – 5y = 10
Yes, (10,4) is a solution.
No, (10,4) is not a solution.
Answer:
Yes, (10,4) is a solution.
Step-by-step explanation:
3x - 5y = 10
Substitute x and y to see if you get 10;
x = 10
y = 4
3(10) - 5(4) = 10
30 - 20 = 10
10 = 10
True!!!
What is the measure of angles DEC and GAH?
Answer:
DEC is 30°
because 180° - 50° would be 40°
x + p = q
make x the subject of the formula
Could someone please explain this to me so i can do it myself?
a car travels 304 miles on 16 gallons of gas how far can a car travel on 5 gallons
Answer: 95
304/16=19
19X5=95
Seven more than a number, x, is at most 20
Answer:
x+7 ≤ 20
Just take it step by step:
seven more than a number is a number plus 7 (x+7)- keep in mind we dont know what the number is so we use x to represent the number.
it then says it's equal to at most 20.
This means that it cant equal anything above 20 since 20 is the max. Therefore, it must be 20 and below that x+7 equals
x+7≤ 20
≤ -this symbol means less than or equal to
Step-by-step explanation:
wait what about not in decimal form?
Answer:
don't know which question?
Step-by-step explanation:
¿???????
The points A (0,4), B (6, 4) and C (6, -2) are 3 corners of a square ABCD.
What are the coordinates of D, the 4th corner?
Answer: It would be (0,-2)
Step-by-step explanation:
CLOTHING A online retailer is running a special on jeans. All pairs of jeans are $39. The function f(x) = 39x models the total cost of buying x pairs of jeans. The retailer also charges $6 flat rate shipping fee. a. Write a function g(x) that represents the cost of purchasing jeans and having them shipped. b. Find the cost of purchasing 3 pairs of jeans before and after shipping
Answer:
a. g(x) = 39x + 6
b. The price before shipping is $117 and the price after shipping is $123
Step-by-step explanation:
To represent the cost of purchasing jeans and shipping them, add 6 to the function, since it is a flat rate.
So, the function will be g(x) = 39x + 6.
Then, use this function to find the cost of 3 pairs of jeans after shipping:
g(x) = 39x + 6
g(3) = 39(3) + 6
g(3) = 117 + 6
= $123
Then, use the original function, f(x) = 39x, to find the price before shipping:
f(x) = 39x
f(3) = 39(3)
= $117
So, the price before shipping is $117 and the price after shipping is $123
While playing pool, you try to shoot the eight ball into the corner pocket.
Imagine that the coordinate plane is placed over the pool table. The eight ball is at ( 4, 3⁄4) and the pocket you are aiming for is at (10,4). You are going to make a bank shot at (6, 0).
a.) Write an equation for the path of the ball. b.) Do you make your shot? Why or why not?
Answer:
Step-by-step explanation:
to go from (4, 3/4 ) to (6, 0) you need
a line with slope m= (y2-y1)/(x2-x1) = [tex]\frac{3}{4}[/tex] -0 / 4-6 = [tex]\frac{3}{4} /\frac{-2}{1} =\frac{3}{4} *\frac{-1}{2} =\frac{-3}{8}[/tex]
use the quation of a line point-slope
(y-y1)=m(x-x1)
substitute m= -3/8 and (x1,y1) with (6,0)
[tex]y=\frac{-3}{8} (x-6)[/tex]
Now does point (10,4) where is the aim is verified by this equation?
substitute x=10, y=4 in the equation to check
4= -3(10-6)/8
4= -3*4/8
4=-3/2 this is never true so you do NOT make the shot
a.) The equation for the path of the ball is:[tex]\(y = -\frac{3}{8}x + \frac{9}{4}\).[/tex]
b.) The equation is not true because 4 is not equal to -3/2. Therefore, the ball does not make it into the pocket. The bank shot is not successful.The reason the shot fails is that the path of the ball (as represented by the linear equation) does not intersect the pocket point (10, 4), so the ball does not reach the desired target.
a.) To find the equation for the path of the ball, we can use the concept of a linear equation, which represents a straight line on the coordinate plane. The general form of a linear equation is:
[tex]\(y = mx + b\)[/tex]
where:
- y is the y-coordinate of a point on the line.
- x is the x-coordinate of the same point.
- m is the slope of the line (change in y divided by change in x).
- b is the y-intercept, which is the point where the line intersects the y-axis (x = 0).
a.) Equation for the path of the ball:
We can find the slope m of the line passing through (4, 3/4) and (6, 0) as follows:
[tex]\(m = \frac{{y_2 - y_1}}{{x_2 - x_1}} \\= \frac{{0 - \frac{3}{4}}}{{6 - 4}} \\= \frac{{-\frac{3}{4}}}{{2}} \\= -\frac{3}{8}\)[/tex]
Now, let's find the y-intercept b by substituting the values of (x, y) from one of the given points (let's use (4, 3/4)) and the calculated slope m :
[tex]\(y = mx + b\)\\\(\frac{3}{4} = -\frac{3}{8} \times 4 + b\)\\\(\frac{3}{4} = -\frac{3}{2} + b\)[/tex]
Now, solve for
[tex]\(b\): \(b = \frac{3}{4} + \frac{3}{2}\\ = \frac{3}{4} + \frac{6}{4} \\= \frac{9}{4}\).[/tex]
b.) To determine if the ball makes it into the pocket at (10, 4), we need to check if the y-coordinate (4) of the pocket point lies on the path of the ball. Substitute [tex]\(x = 10\) and \(y = 4\)[/tex] into the equation for the path of the ball:
[tex]\(4 = -\frac{3}{8} \times 10 + \frac{9}{4}\)\\\(4 = -\frac{30}{8} + \frac{9}{4}\)[/tex]
Now, let's find a common denominator and simplify:
[tex]\(4 = -\frac{30}{8} + \frac{18}{8}\)\\\(4 = -\frac{12}{8}\).[/tex]
To know more about linear equation:
https://brainly.com/question/34495857
#SPJ2
{ colours in the rainbow}
Answer:
The colours of the rainbow are Red, Orange, Yellow, Green, Blue, Indigo and Violet.
Can you use the properties of exponents you discovered to simplify 5^2 · 2^5 ?
5² × 2⁵ = 25 × 32 =. 800
Hope this helps
What reason could you use in a proof to prove two triangles are congruent by SSS?
Answer:
D
Step-by-step explanation:
BECAUSE SSS IS SAYING THIS TRIANGLES ARE CONGRUENT BY SIDE SIDE SIDE
-4-5(2x -4) = 76
-6
9
-4
7
9514 1404 393
Answer:
x = -6
Step-by-step explanation:
-4 -10x +20 = 76 . . . . . eliminate parentheses
-10x = 60 . . . . . . . . . . . subtract 16
x = -6 . . . . . . . . . . . . . . divide by -10
Two particles are projected simultaneously towards each other from opposite ends of a straight
horizontal tube. One particle travels 97 cm in the 1st 2 seconds, 93 cm in next 2 seconds , 89 cm in
another next 2 seconds, etc. The other particle travels 49 cm in the 1st 2 seconds, 47 cm in the next 2
seconds , 45 cm in another next 4 seconds, etc. Find how long it takes for the particles to meet and
hence, determine the distances travelled by each particle.
Answer:
Confusion is real
Step-by-step explanation:
Please help. -----------------------------------------
Answer:
D
Step-by-step explanation:
the equation tells you that 1 yard is 3 feet
so when you move one unit to the right on the x-axis, you should move three units up on the y-axis
What molecules does a plant need to make glucose in the process of photosynthesis? Choose all correct answers. oxygen water carbon dioxide light
Answer: water, carbon dioxide , light
Step-by-step explanation:
Answer:
water and carbon dioxide
Step-by-step explanation:
i gut finched the quiz for k12 and this is the right answer
light is wrong
Factor this expression completely.
6x^2- 13x - 28
Answer:
this is the solution
(2−7)(3+4)
Step-by-step explanation:
Answer:
(X+1)(6x-21)
Step-by-step explanation:
6x^2- 13x - 28
6x^2-(21-6)x-28
6x^2-21x+6x-28
X(6x-21)+1(6x-21)
(X+1)(6x-21)
Find x. Round to the nearest tenth if needed.
Answer:
x = 16
Step-by-step explanation:
Use that the addition of all internal angles of a triangle must add up to 180, and the fact that the two given triangles are similar:
51 + 65 + 4 x = 180
combine and solve for "x"
116 + 4 x = 180
4 x = 180 - 116
4 x = 64
x = 64 / 4
x = 16
Answer:
x = 16
Step-by-step explanation:
A triangle is 180 degrees. Since two of the angles are congruent to each other, the third angle must be congruent as well. This means that the third measure for both triangles is 4x. Knowing all of this, we can solve for x:
65 + 51 + 4x = 180
116 + 4x = 180
4x = 64
x = 16
The number line shows four points. Which point represents the approximate location of V12?
A) point A
B). point B
C) point C
D) point D
Answer:
point A
Step-by-step explanation:
Answer:c
Step-by-step explanation:
