Answer:
hypotenuse = 13
shortest side = 5
third side = 12
Step-by-step explanation:
Given sides a, b, and c, with c representing the hypotenuse of a right triangle, we can say that
a²+b² = c² using the Pythagorean Theorem.
We are given that the hypotenuse (c) = 8 cm more than the shortest side. Representing the shortest side as a, we can say that c= 8 + a. Then, the third side, which we can represent as b, is 1cm shorter than the hypotenuse, so c-1 = b
c= 8+a
c-1 = b
a²+b² = c²
One thing we can do is to solve for everything in terms of c and solve the third equation from there
c= 8+a
subtract 8 from both sides
c-8 = a
a²+b² = c²
(c-8)²+b² =c²
b = c-1
(c-8)² + (c-1)² = c²
expand
c²-16c + 64 + c² - 2c + 1 = c²
2c² - 18c + 65 = c²
subtract c² from both sides to make this an equation that we can more easily solve
c² - 18c + 65 = 0
To factor, we can find two numbers that add to (-18) and multiply to 65. Two numbers that work at 13 and 5, so we have
c²-13c-5c + 65 = 0
c(c-13) -5(c-13) = 0
(c-5)(c-13) = 0
Therefore, the hypotenuse, or c, is 5 or 13. Because a=c-8, if c=5, a would be negative 3. This is not possible, so c cannot be 5. Therefore, c=13, a=c-8=5, and b=c-1= 12
A company ships coffee mugs using boxes in the shape of cubes. The function g(x) = gives the side length, in inches, for a cube with a volume of x cubic inches. Suppose the company decides to double the volume of the box. Which graph represents the new function?
Answer:
The graph is attached below.
Step-by-step explanation:
The volume of the box containing the coffee mugs is,
[tex]V=x^{3}[/tex]
Then the function representing the side length, in inches, for the box is:
[tex]g(x)=x[/tex]
Now, it is provided that the company decides to double the volume of the box.
That is, the new volume will be:
[tex]V_{n}=2x^{3}[/tex]
Then the side length, in inches, for the box will be:
[tex]g_{n}(x)=\sqrt[3]{2x^{3}} =\sqrt[3]{2}x[/tex]
Then the graph representing the function, formed using the following points is:
[tex]x\ \ \ \ \ \ \ \ \ g_{n}(x)\\\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\\0\ \ \ \ \ \ \ \ \ \ \ 0\\1\ \ \ \ \ \ \ \ \ \ \ 2^{1/3}[/tex]
Answer:
c
Step-by-step explanation:
-1/4 (x+2)+5=-x I really need help
Answer:
x = -6
Step-by-step explanation:
Answer:
-6
Step-by-step explanation:
-1/4 (x+2)+5=-x
-1/4x-1/2+5=-x
-1/4x+4.5=-x
+1/4x +1/4x
(4/3) 4.5=-3/4x (4/3)
6=x
x=6
find the supplement of 3/4 of a right angle
Answer:
Step-by-step explanation:
¾*90=67.5
180-67.5=112.5°
Answer:
60°
Step-by-step explanation:
You can see the explanation in the picture
If EH = 23, calculate AB.
Youngblood say you want me back in your life...
Answer:
2/4 = 23/AB
1/2 = 23/AB
AB= 46
Hope it helps ^_^
Can someone help me with 1-5 and create problems for 6-10
Final answer is x=4
Help me out with question 4
Answer: x = 4/5
Step-by-step explanation:
[tex]\tan\ y=\dfrac{\text{side OPPOSITE y}}{\text{side ADJACENT to y}}=\dfrac{1}{6}\\\\\\.\qquad \qquad \qquad \qquad \qquad \qquad \dfrac{x}{x+4}=\dfrac{1}{6}\\\\\\\text{Cross multiply, distribute, and solve for x:}\\6(x)=1(x+4)\\6x=x+4\\5x=4\\\\\large\boxed{x=\dfrac{4}{5}}[/tex]
One thousandth of the base unit in length :
One millionth of the base unit in mass :
One thousandth of the base unite in time :
Step-by-step explanation:
[tex]1 \div 100th[/tex]
find the center of a circle with the equation: x^2+y^2-32x-60y+1122=0
A. (24, 30)
B. (13, 20)
C. (14, 28)
D. (16, 30)
Answer:
-32x-60y+1122=0
-(32x+60y-1122)=0
32x+60y-1122=0
by factorize
Answer:
24,30
Step-by-step explanation:
Mrs.magar sold 40 kg of fruits at rate of RS 60 per kg and gained Rs 600 . calculate purchasing rate and profit percent.
Answer:
Purchasing rate = ₹45 per kg
Profit percent = 33.33%
Step-by-step explanation:
Selling price of 1 kg fruit = ₹60
Therefore, S. P. of 40 kg fruits = 40*60 = ₹2400
Gain = ₹ 600 (given)
Cost price (C. P.) = S. P. - Gain
= ₹2400 - ₹600
= ₹ 1800
Rate of purchasing
= C. P. /quantity of fruits
= 1800/40
= ₹45 per kg
Profit percent
= (Gain* 100)/C.P.
= (600*100)/1800
= 60000/1800
=33.33%
Which list shows the numbers 13.5, 1.35, 1.352, 0.135 in ascending order?
13.5, 1.352, 1.35, 0.135
0.135, 1.352, 1.35, 13.5
0.135, 13.5, 1.35, 1.352
0.135, 1.35, 1.352, 13.5
Answer: Choice D
0.135, 1.35, 1.352, 13.5
=====================================================
Explanation:
Ascending order means "smallest to largest"
The smallest item is 0.135, then we move to 1.35, then to 1.352, and finally 13.5
The reason why 1.35 is smaller than 1.352 is to think of the first value is 1.350; then note how 350 is smaller than 352.
Below are a list of costs and discounts for groceries. Round to the nearest dollar to estimate the total cost
+ $12.34
+ $5.07
- $0.73
+ $2.84
- $1.50
Answer:
$18
Step-by-step explanation:
$18.02 rounds to $18
Answer:
$17
Step-by-step explanation:
Rounded, the listed numbers are ...
12 + 5 -1 +3 -2 = 17
The estimate of total cost is $17.
Raj correctly determined that ray LH is the bisector of AngleGLI. A line contains points K, L, M. 4 lines extend from point L. One line extends to point F, another to G, another to H, and another to I. Which information could he have used to determine this? AngleGLH Is-congruent-to AngleILM mAngleKLM = 5mAngleILM mAngleGLI = 2mAngleGLH mAngleGLI = mAngleGLH + mAngleHLI
Answer: C.) mAngleGLI = 2mAngleGLH
Step-by-step explanation:
Hope it helps!!!
For ray LH as the bisector of angle GLI, we can determine that the relation ∠GLI = 2∠GLH holds
What is an angle?An angle is formed from the intersection of two lines. Types of angles are acute, obtuse and scalene.
∠GLI is bisected by LH, hence:
∠GLH = ∠HLI (definition of bisection)
∠GLI = ∠GLH + ∠HLI (angle addition)
∠GLI = 2∠GLH
The information that can be used to determine this is ∠GLI = 2∠GLH
Find out more on angle at: https://brainly.com/question/25770607
a) Simplify the expression and explain each step. (2 points)
4(3x+2) -2
= ?
Answer:
6 (2 x + 1)
Step-by-step explanation:
Simplify the following:
4 (3 x + 2) - 2
Hint: | Distribute 4 over 3 x + 2.
4 (3 x + 2) = 12 x + 8:
12 x + 8 - 2
Hint: | Group like terms in 8 + 12 x - 2.
Grouping like terms, 8 + 12 x - 2 = 12 x + (8 - 2):
12 x + (8 - 2)
Hint: | Subtract 2 from 8.
8 - 2 = 6:
12 x + 6
Hint: | Factor out the greatest common divisor of the coefficients of 12 x + 6.
Factor 6 out of 12 x + 6:
Answer: 6 (2 x + 1)
Please help with this question
9514 1404 393
Answer:
27.932 in
Step-by-step explanation:
The initial angle (or height) is not shown, so we have assumed it is 30°. The equation for the height of the valve cap can be written as a function of angle:
y = 15.375 +14.5·sin(x +30) . . . . . . where x is in degrees
The angle measured from the +x axis is already 30° when the rotation angle is zero. Evaluating the above equation with x = 390° gives an angle of 420°, or 60° beyond one full rotation.
y = 15.375 +14.5·sin(60°) ≈ 27.932 . . . . inches above the ground.
The valve cap is 27.932 in. above the ground.
WILL GIVE BRAINLIEST AND 20 POINTS! SHOW WORK!
How many different 6-digit phone numbers do not contain the digit 6? Assume that any digit in the phone number can be any of the remaining numbers. Use the Multiplication Principle of Counting to solve the problem.
Answer:
Step-by-step explanation:
We don't know if the number can start with a 0 or 1. Since we don't know, I will assume the number can start with either. The restriction is on 6s.
The way this is worded, I'm not sure if the digits can be repeated or not. It sounds like they can.
9 * 9 * 9 * 9 * 9 * 9 = 531441
If you are not allowed to repeat and no digit is a 6 then you get
9 *8 * 7 * 6 * 5*4 = 60480
I need help and I will give five stars and a big thank you comrades
Answer:
A.
Step-by-step explanation:
A way to find the equation of the graph is to find the solutions.
On the graph, the solutions are where the function intersects the x-axis. That would be where x = -2, x = 1, and x = 3.
In the equations, you will need to find factors when the x is inputted, the factor equals 0. For example, one of the factors is (x + 2). This is because x + 2 = 0, so x = 0 - 2, so x = -2. So, the three factors are (x + 2), (x - 1), and (x - 3).
The correct equation is A.
Hope this helps!
Simplify 7.5 + n + 9.63.
Answer: Hi!
The only thing we're able to do to simplify this equation is combine our like terms. We have two like terms in the equation: 7.5 and 9.63.
7.5 + 9.63 = 17.13
Our equation now looks like this:
n + 17.13
We have nothing left to simplify, so we're done!
Hope this helps!
how to simplify 75-3y
[tex]\\ \sf\longmapsto 75-3y[/tex]
We can see 75 is a multiple of 3Take 3 common[tex]\\ \sf\longmapsto 3(25-1y)[/tex]
[tex]\\ \sf\longmapsto 3(25-y)[/tex]
Hence simplifiedAnswer:
Step-by-step explanation:
75-3y
3(25+y)
Can somebody please help me
You can pick one or the other to have as your answer
===========================
Explanation:
The formula you use is
A = pi*r^2
The radius is r = d/2 = 10/2 = 5
So,
A = pi*r^2 = pi*5^2 = pi*25 = 25pi
is the exact area
Replace pi with 3.14 to get 25*pi = 25*3.14 = 78.5
which is the approximate area
To get a better approximation, you would use more decimal digits of pi.
help help help
help
help help
Answer:
R= (-9, -10) S=(-1,-10) T=(-1, -8) U=(-9, -8)
Step-by-step explanation:
There isn't really an explanation it's just reading the points on the graph. Hope this helps!! :)
A plane set off to Paris at a speed of 300mph. On the return flight of 12 hours, the plane cruised at 242mph. How many hours long was the flight to Paris
Answer:well the answer is 2 hours 16 minutes.
Step-by-step explanation:
To find your plane's rate of speed, you calculate the distance ... amount of time in the air (2 hours and 16 minutes) to.
A group of students is arranging squares into layers to create a project. The first layer has 4 squares. The second layer has 8 squares. Which formula represents an arithmetic explicit formula to determine the number of squares in each layer?
Answer:
answer is d
Step-by-step explanation:
Help me you guys! it's important!
Answer:
hey mate
surface area of cuboid is 2(lh+bh+hl)
doing for first cuboid
h = 20
l = 6
b = 5
surface area for this cuboid on calculating u get 500 sq.cm
now
second cuboid
h = 12
l = 6
b = 4
calculaye it by formula and u get 288 sq.cm
so total surface area is 500 + 288 = 788 but in this one side is getting counted 2 times which is rectangle with length 6 and 12 so it's area is 12×6 = 72
final ans = 788-72 = 716 cm2
as per me that's ans
brinliest pls
If LM = x + 3, MN = 2x and LN = 24, what does x equal
Answer:
[tex]\displaystyle 7 = x[/tex]
Step-by-step explanation:
[tex]\displaystyle 24 = [3 + x] + 2x → 24 = 3 + 3x → \frac{21}{3} = \frac{3x}{3} \\ \\ 7 = x[/tex]
I am joyous to assist you at any time.
Will Mark Brainlest helppp plss
Answer:
you can ask from it will be easy for you actually I don't know answern
solve the equation:
|x+3| >2x-1
Answer:
x < 4
Step-by-step explanation:
|x+3| >2x-1 [|a| is the absolute value of a]
x+3 > 2x-1
4 > x
Therefore,
x < 4
The negative case doesn't have equal RHS and LHS so, it isn't valid.
The altitude (i.e., height) of a triangle is increasing at a rate of 2 cm/minute while the area of the triangle is increasing at a rate of 1.5 square cm/minute. At what rate is the base of the triangle changing when the altitude is 12 centimeters and the area is 99 square centimeters
Answer:
A = 1/2 B H area = 1/2 base X height
B = 2 A / H = 2 * 99 / 12 = 16.5 cm
dA / d t = 1/2 * (B dH / dt + H dB / dt)
dB / dt = (2 dA / dt - B dH / dt) / H
dB / dt = (2 * 1.5 cm^2 / min - 16.5 cm * 2 cm / min) / 12 cm
dB / dt = (3 - 33) / 12 cm/min = -2.5 cm/min
The weight of a box varies directly as the volume of the box. If a 138-pound box has a volume of 23 gallons, what is the weight of a box that has a volume of 25 gallons? A. 31 pounds B. 150 pounds C. 138 pounds D. 29 pounds
Answer:
150 pounds
the weight is directly proportional to the volume. hence:
138/23 = 6
now, 25*6 = 150
Answer:
B. 150 pounds
Step-by-step explanation:
Consider this polynomial, where a is an unknown real number.
p(t) = x^4 +5x^3 + ax^2 - 3x + 11
The remainder of the quotient of P(x), and (x+ 1) is 17.
Braulio uses synthetic division to find the value of a, and Zahra uses the remainder theorem to find the value of a.
Answer:
Brauilo is wrong because he divided by (x+1) instead of (x-1)
Step-by-step explanation:
The remainder Theorem states that
if polynomial f(x) is divided by binomial x-a, the remainder will equal f(a). The factor is positive so the binomial is the same as
which is why we divide by -1, or subsitue -1 into the equation p(x).
The remainder of a polynomial division can be gotten using remainder theorem or synthetic division.
The true statement is: Brauilo did not find the value of a, because he divided by (x+1) instead of (x-1)
From the question, we have the following parameters:
[tex]\mathbf{p(x) = x^4 +5x^3 + ax^2 - 3x + 11}[/tex]
[tex]\mathbf{Divisor =x+ 1}[/tex]
[tex]\mathbf{Remainder = 17}[/tex]
First, we set the divisor to 0.
[tex]\mathbf{Divisor =x+ 1 = 0}[/tex]
So, we have:
[tex]\mathbf{x+ 1 = 0}[/tex]
Solve for x
[tex]\mathbf{x= -1}[/tex]
The above equation means that, the value of x that will be used to test the polynomial is -1
From the question,
Zahra used [tex]\mathbf{x= -1}[/tex]; this is represented as: P(-1)Braulio used [tex]\mathbf{x= 1}[/tex]; this is represented in the synthetic divisionHence, Braulio is incorrect, because he used the wrong value of x
Read more about polynomial division at:
https://brainly.com/question/12011809
A laptop has a listed price of $703.98 before tax. If the sales tax rate is 9.25% , find the total cost of the laptop with sales tax included. Round your answer to the nearest cent, as necessary.
Answer:
The cost of the laptop is $769.10Step-by-step explanation:
In this problem we are required to find the cost of the laptop when 9.25% of the cost is added as tax
we are given that the tax rate is 9.25% of the initial cost
and the initial cost is $703.98
let us calculate 9.25% of $703.98
(9.25/100)* 703.98= 0.0925*703.98= $65.12
Hence the charges for tax is $65.12
The total cost of the laptop when tax is included is
the initial cost Plus the tax charges= $703.98+$65.12= $769.098
$769.10