Rule: If x is the leg of a 45-45-90 triangle, then x*sqrt(2) is the hypotenuse.
We can prove this by showing that x^2+x^2 = (x*sqrt(2))^2 is an identity. It's from the pythagorean theorem a^2+b^2 = c^2.
Put another way, if we know that a = x and b = x are the two congruent legs, then x^2+x^2 = c^2 leads to c = x*sqrt(2). This triangle is known as an isosceles right triangle.
So if 4*sqrt(2) is the hypotenuse, we match that up with the template x*sqrt(2) and see that x = 4 must be the case.
13x=6 what is x in number form please and thank you
Answer:
0.461538
Step-by-step explanation:
brainlest pls im try to rank up to ace
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{13x = 6}[/tex]
[tex]\huge\textsf{DIVIDE 13 to BOTH SIDES}[/tex]
[tex]\mathsf{\dfrac{13x}{13}=\dfrac{6}{13}}[/tex]
[tex]\rm{CANCEL \ out: \dfrac{13}{13} \ because \ that \ gives \ you \ 1}[/tex]
[tex]\rm{KEEP: \dfrac{6}{13} \ because \ that \ gives \ you \ the \ value \ of \ x}[/tex]
[tex]\boxed{\boxed{\mathsf {Answer: x = \bf \dfrac{6}{13}}}}\huge\checkmark[/tex]
[tex]\boxed{\textsf{or you could say \boxed{\mathsf{x = \underline{\bf 0.461538}}} they both equal to the same thing}}\huge\checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Which of the following is closest to the circumference of a circle whose radius is 21 m
Here Is your answer!!!!
The model represents an inequality. What is the solution set for the inequality?
Given:
The figure of an algebraic tiles model of an inequality.
To find:
The inequality for the given model.
Solution:
On the left hand side of the inequality sign in the model we have 8 tiles of x and 12 tiles of 1. So,
[tex]LHS=8(x)+12(1)[/tex]
[tex]LHS=8x+12[/tex]
On the right hand side of the inequality sign in the model we have 12 tiles of -1. So,
[tex]RHS=12(-1)[/tex]
[tex]RHS=-12[/tex]
Now, the inequality for the given model is:
[tex]8x+12\geq -12[/tex]
Therefore, the required inequality for the given model is [tex]8x+12\geq -12[/tex].
Kaden works 5 days. The median number of hours he works is 3. The mean number of hours he works is 4.
Answer:
(a) 1, 2, 3, 6, 8
Step-by-step explanation:
Given
[tex]Median = 3[/tex]
[tex]Mean = 4[/tex]
Required
The sequence of hours worked each day
See attachment for options
From the question, we understand that:
[tex]Median = 3[/tex]
This means that, the middle number is 3 (when sorted)
So, we can conclude that (b) and (c) cannot be true because their middle numbers are 6 and 5 respectively
Next, is to determine the mean of (a) and (d)
The mean of a data is calculated as:
[tex]\bar x = \frac{\sum x}{n}[/tex]
So, we have:
(a)
[tex]\bar x = \frac{1+ 2+ 3+ 6+ 8}{5}[/tex]
[tex]\bar x = \frac{20}{5}[/tex]
[tex]\bar x = 4[/tex]
(d)
[tex]\bar x = \frac{1+ 2+ 3+ 4+ 5}{5}[/tex]
[tex]\bar x = \frac{15}{5}[/tex]
[tex]\bar x = 3[/tex]
Option (a) is true, because it has:
[tex]Median = 3[/tex]
[tex]Mean = 4[/tex]
You are mowing your neighbor's lawn. He is going to pay you $20.00 for the first two hours and $5.00 for anything after that. Which algebraic expression represents how much you will be paid for working h hours?
Answer: H = 35
Step-by-step explanation:
You do 20.00+5*h
The formula s = StartRoot StartFraction S A Over 6 EndFraction EndRoot gives the length of the side, s, of a cube with a surface area, SA. How much longer is the side of a cube with a surface area of 480 square meters than a cube with the surface area of 270 square meters
Answer:
It's B
Step-by-step explanation:
I took the test
Answer:
B= (√30 - 2√5)
Step-by-step explanation:
Find the exact value of cot 330° in simplest form with a rational denominator.
Answer:
[tex]\cot 330^{\circ} = -\sqrt{3}[/tex]
Step-by-step explanation:
The cotangent function can be rewritten by trigonometric relations, that is:
[tex]\cot 330^{\circ} = \frac{1}{\tan 330^{\circ}} = \frac{\cos 330^{\circ}}{\sin 330^{\circ}}[/tex] (1)
By taking approach the periodicity properties of the cosine and sine function (both functions have a period of 360°), we use the following equivalencies:
[tex]\sin 330^{\circ} = \sin (-30^{\circ}) = -\sin 30^{\circ}[/tex] (2)
[tex]\cos 330^{\circ} = \cos (-30^{\circ}) = \cos 30^{\circ}[/tex] (3)
By (2) and (3) in (1), we have following expression:
[tex]\cot 330^{\circ} = -\frac{\cos 30^{\circ}}{\sin 30^{\circ}}[/tex]
If we know that [tex]\sin 30^{\circ} = \frac{1}{2}[/tex] and [tex]\cos 30^{\circ} = \frac{\sqrt{3}}{2}[/tex], then the result of the trigonometric expression is:
[tex]\cot 330^{\circ} = -\frac{\frac{\sqrt{3}}{2} }{\frac{1}{2} }[/tex]
[tex]\cot 330^{\circ} = -\sqrt{3}[/tex]
The exact value of cot 330° with a rational denominator is √3.
To find the exact value of cot 330°, we can first determine the reference angle. The reference angle for 330° is 30°, as it is the angle between the terminal side of 330° and the x-axis.
Cotangent (cot) is the reciprocal of the tangent function, so we need to find the tangent of the reference angle, which is tan 30°. The tangent of 30° is √3/3.
Since cot is the reciprocal of tan, the cotangent of 330° is the reciprocal of √3/3, which is 3/√3.
To rationalize the denominator, we multiply the numerator and denominator by the conjugate of the denominator, which is √3.
(3/√3) x (√3/√3) = 3√3/3
Simplifying further, we can cancel out the common factor of 3:
(3√3/3) = √3
Therefore, the exact value of cot 330° with a rational denominator is √3.
To learn more about trigonometric identities;
https://brainly.com/question/24377281
#SPJ6
product of -3/7a and -21/15b
Answer:
182857142857/100000000000
5 1/2 ÷ 3 2/3 + 1 4/5 , giving answer as a fraction in lowest terms
Answer:
6761/320
Step-by-step explanation:
[(51/2)÷32/3]+14/5
=6761/320
Answer two questions about Equations AAA and BBB: A. 2x-1+3x=0 B.5x-1=0. How can we get Equation BBB from Equation AAA? and is equation A and B equivalent?
Answer:
you would simplify equation a by combining 2x plus 3x. yes they are equivalent. you can use any x to make the equation true.
Step-by-step explanation:
Answer:
Multiply/divide both sides by the same variable expression
No
HELP PLEASE What is the area of the regular trapezoid below?
A trapezoid has a base of 10 centimeters, height of 8 centimeters, and top side length of 6 centimeters.
64 Centimeters squared
80 Centimeters squared
240 Centimeters squared
480 Centimeters squared
Answer:
64 Centimeters squared
Step-by-step explanation:
Formula for the Area of a trapezoid:
A = a+b
----- h
2
a (base) = 6
b (base) = 10
h (height) = 8
6+10 = 16
16/2 = 8
8 times 8 = 64
A piano instructor charges students a one-time fee for sheet music and an hourly rate for lessons. The graph below shows the total cost for a student who has taken x lessons.
hi guys i need help
cosx = 3/5
sinx+tanx = ?
cosx = 3/5
sin²x + cos²x = 1
sin²x = 1- 9/25
sin²x= 16/25
sinx = 4/5
tanx = sinx/cosx
tanx = 4/3
can someone pls help
Expand (p - q)(p+q).
Answer:
p^2 - q^2
Step-by-step explanation:
This is an example of "the product and difference of two squares."
The relevant formula is (a - b)(a + b) = a^2 - b^2 (no middle term).
Here,the desired product is (p - q)(p + q) = p^2 - q^2.
Answer:
(p - q)(p+q). :p²-q²....
The equation of the line of best fit is y=3x+2. x=the number of ice cream sales and y= the number of days. Answer the following questions. Show your work as proof.
a. How many days did it take, if the number of ice cream sales is $40?
b. How much ice cream was sold on day 8?
Step-by-step explanation:
y = 3(40) + 2y = 120 + 2y =122.
Help me it says use the figure for 1 and 2
On January 1, Mario had a savings account balance of $2742 and by April 1, his balance had increased to $3597. Find Mario's average savings rate in dollars per month for that period.
Answer: $285
Step-by-step explanation:
First and foremost, we should note that from January 1 to April 1 is 3 months. Since Mario had a savings account balance of $2742 on January 1 and by April 1, his balance had increased to $3597. The increase in balance will be:
= $3597 - $2742
= $855
Then the average savings rate will be:
= Total amount saved / Number of months
= $855/3
= $285
He had an average savings of $285 per month.
plz help i beg!! 50 points
Answer:
63.25 sq. ft
Step-by-step explanation:
the area of fig. =
(½×8×6)+(½×3.14×5²)
= 24 + 39.25
= 63.25 sq. ft
Answer:
The area of the figure is 63.25 square feet
Step-by-step explanation:
yes
https://brainly.com/question/14200006
im confused on how to do this
Answer:
150
Step-by-step explanation:
Surface area is the area of all the surfaces (or sides). To find the surface area, find the area of one side of the cube. Since a side of a cube is a square, all the lengths are the same. So, 5*5= 25. There are 6 sides to a cube, so multiply 6 by one of the faces 's area (aka sides), so 6*25=150.
Question 13.
Calculate X + Y
A. 9 12
0 1
B. 9 -12
0 -5
C. 9 -2
-18 -1
D. 9 2
-8 -1
Answer:
D is your correct answer.
What is the arithmetic mean for 8,10,8,5,4,7,5,10,8
Answer:
57.8
Step-by-step explanation:
I am sure that this is the answer.
Answer:
57.8
Step-by-step explanation:
8+10+8+5+4+7+5+10+8 ÷9 = 57.8
Hope this helps!
What is the missing length?
Answer:
16
Step-by-step explanation:
The area of a triangle is
A =1/2 bh where b is the base length and h is the height
Substitute the values in
69.6 = 1/2 ( 8.7) * p
69.6 = 4.35p
Divide each side by 4.35
69.6/4.35 = p
16 = p
The formula for the area of a triangle is: A = 1/2 * base * height.
Using this formula, let's plug in what we know.
69.6 = 1/2 * 8.7 * height
Next, we'll go ahead and get rid of that 1/2 by multiplying everything by its reciprocal, 2.
139.2 = 8.7 * height
Then, all that's left is to divide both sides by 8.7.
Height = 16 yards
Hope this helps!! :)
The equation for the line of best fit is y=–0.7x+39. In this equation, what does the y-intercept of 39 tell you?
Help me please
Point K(–5, 2) is the midpoint of line segment Y Z , with endpoint Y(1, –3). What are the coordinates of Z?
Bryson hopes to win a three-day vacation in a drawing that is being held at his office. He purchased 40 raffle tickets. There were 500 raffle tickets sold. What is the theoretical probability of Bryson winning the trip?
StartFraction 2 over 25 EndFraction
One-fifth
Four-fifths
StartFraction 500 over 40 EndFraction
Answer:
A is correct 2/25.
Step-by-step explanation:
Thats what answer I got from doing the math
How can you tell from the equation of a rational function if the function has a hole in the graph ( a removable discontinuity) at x, rather than a vertical asymptote? Give an example
Consider that,
x^2+4x+4 = (x+2)(x+2)
x^2+7x+10 = (x+2)(x+5)
Dividing those expressions leads to
(x^2+4x+4)/(x^2+7x+10) = (x+2)/(x+5)
The intermediate step that happened is that we have (x+2)(x+2) all over (x+2)(x+5), then we have a pair of (x+2) terms cancel as the diagram indicates (see below). This is where the removable discontinuity happens. Specifically when x = -2. Plugging x = -2 into (x+2)/(x+5) produces an output, but it doesn't do the same for the original ratio of quadratics. So we must remove x = -2 from the domain.
Which best describes a triangle
Answer:
i think the answer may be acute and isosceles
Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 15 hours. Together they charged a total of $2475 . What was the rate charged per hour by each mechanic if the sum of the two rates was $200 per hour?
plssssssss help !!!!!!!!!
Answer:
Rates :
$95 per hour and $105 per hour
Step-by-step explanation:
Let their rate = x and y respectively :
10x + 15y = 2475 - - - - (1)
x + y = 200 - - - - (2)
x = 200 - y - - (3)
Put (3) into (1)
10(200 - y) + 15y = 2475
2000 - 10y + 15y = 2475
5y = 2475 - 2000
5y = 475
y = 95
x = 200 - y
x = 200 - 95
x = 105
4. A car is travelling 75 kilometers per hour. How many meters does the car travel in one
minute?
Answer:
1250 Meters
Step-by-step explanation:
75 kilometers divided by 60 minutes is 1.25 kilometers per minute.
1 kilometer = 1000 meters
Answer:
75km/hr =75000
60 sec =1min,60 min=1hr
75000÷60=1250m