Answers
Answer: [tex]8\sqrt{2}[/tex]
================================================
Work Shown:
x = length of each leg
Use the pythagorean theorem to get...
[tex]a^2+b^2 = c^2\\\\x^2+x^2 = 16^2\\\\2x^2 = 256\\\\x^2 = 256/2\\\\x^2 = 128\\\\x = \sqrt{128}\\\\x = \sqrt{64*2}\\\\x = \sqrt{64}*\sqrt{2}\\\\x = 8\sqrt{2}\\\\[/tex]
Or as an alternative path, you can divide the hypotenuse by [tex]\sqrt{2}[/tex] and then rationalize the denominator.
Both of these methods apply to 45-45-90 triangles only.
Answer:
[tex]8\sqrt{2}[/tex]
Step-by-step explanation:
We can sum the angles in a triangle to 180°:
m<D + m<E + m<F = 180°
m<D + 90° + 45° = 180°
m<D = 45°
Therefore, the triangle is an isosceles right triangle, since the base angles, <F and <D are the same measure. Because the triangle is isosceles, the legs are congruent, meaning that
DE = EF
We can use the Pythagorean Theorem([tex]a^{2} + b^{2} = c^{2}[/tex]) and plug in 16 as c, and DE and EF as a and b:
[tex]DE^{2} + EF^{2} = 16^{2}[/tex]
Since DE is the same as EF, we can substitute it in:
[tex]DE^{2} + DE^{2} = 256\\2DE^{2} = 256\\DE^{2} = 128\\DE = \sqrt{128}[/tex]
The square root of 128 is the same as [tex]8\sqrt{2}[/tex] since 128 can be factored into 64 x 2. So [tex]8\sqrt{2}[/tex] is the answer.
If you are looking for an easier way to do this, once you are able to recognize DEF is an isosceles triangle, you can say [tex]DE \times \sqrt{2} = 16[/tex] as this applies to all isosceles right triangles. This simplifies to:
[tex]DE = \frac{16}{\sqrt{2}} \\DE = \frac{16}{\sqrt{2} } \times \frac{\sqrt{2}}{\sqrt{2} } \\DE = \frac{16\sqrt{2} }{2} \\DE = 8\sqrt{2}[/tex]
Related Questions
Two points A and B whose heights differ by 10 metres are shown 1.2 cm apart horizontally on a map whose scale is 1: 10 000. a) Work out the actual horizontal distance between A and B.
Answers
Answer:
120 meters
Step-by-step explanation:
1.2 x 10 000 = 12000 cm = 120 meters
the perimeter of a rectangle is 30cm while it breadth is 5cm find the length of the rectangle
Answers
Answer:
10 cm
Step-by-step explanation:
See attached image
Answer:
length = 10 cm
Step-by-step explanation:
Fyi, breadth is a synonym to width.
Since P=30, we must find the length.
l = length
w = width
P=w+w+l+l
30 = 5+5+l+l
30 = 10+2l
-2l = -20
l = 10
Hence, the length is 10 cm.
Which measure of central tendency can be used in finding the average of your grades in a quarter?
Answers
Explanation: Average can simply be defined as the sum of all the numbers divided by the total number of values. A mean is defined as the mathematical average of the set of two or more data values. Average is usually defined as mean or arithmetic mean.
I need two question please
Answers
In ΔABC, m∠A = 2m∠B and m∠B = 3m∠C.
What is m∠C?
Answers
A triangle is a three-edged polygon with three vertices. The measure of ∠C is 18°.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.
Let the measure of ∠C be represented by x. Given the measure of ∠A= 2(∠B), while the measure of ∠B=3(∠C). Therefore, the measure of angles can be written as,
∠A = 2(∠B) = 2[3(∠C)] = 6x
∠B = 3x
∠C = x
Now, since the sum of all the angles of a triangle is 180°. Therefore,
∠A + ∠B + ∠C = 180°
6x + 3x + x = 180°
10x = 180°
x = 18°
Hence, the measure of ∠C is 18°.
Learn more about Triangle:
https://brainly.com/question/2773823
#SPJ1
What is the area of the figure below
Answers
Answer:
Total Area = 68
Step-by-step explanation:
Comment
There is 1 square at each end.
There are 2 congruent trapezoids in the middle
Draw a 7 inch line across the widest part of the middle
Area of the squares
Area = s^2
s = 3
Area = 3^2
Area = 9
But there are 2 of them 18
Area of the 2 trapezoids
Area = (b1 + b2)*h / 2
b1 = 3
b2 = 7 Notice that 7 was the line you drew
h = 5
Area = (3 + 7)*5/2
Area = 50 / 2
Area = 25
But there are 2 of them 50
Total Area 68
On a coordinate plane, a curved line crosses the x-axis at (negative 1.5, 0), the y-axis at (0, negative 2), and the x-axis at (1.5, 0).
Determine the domain and range of the given function.
The domain is
all real numbers
.
The range is
.
Answers
Domain F(x) = All real numbers and the Range F(x) [ -2 , + ∞ ]
What is the domain and range of a function?A domain is the set of values for which the given function is defined.
Range is the set of all values which the given function can output.
The curve points are
P₁ ( -1,5 , 0 ) Q ( 0. -2 ) and P₂ ( 1,5 , 0 )
We can see that P₁ and P₂ are symmetric around the y-axis, and point Q looks like a vertex so we can conclude the curve as
ax² + bx + c = y
The curve is a parabola
when x = 0
y = -2
then c = - 2
The equations we get,
a (-1.5)² + b (-1.5) + c = 0
2.25a - 1.5b - 2 = 0
a (1.5)² + b ( 1.5) + c = 0
2.25a + 1.5b -2 = 0
Adding these two equations
4.5a - 4 = 0
a = 4/4.5
The vertex is Q ( 0 , -2 )
x = - b/2a
0 = - b/ 9
b = 0
Therefore the equation of the function :
ax² + c = 0
(4/4.5) x² - 2 = 0
Therefore, Domain F(x) = All real numbers and the Range F(x) [ -2 , + ∞ ]
Learn more about appropriate domain here:
https://brainly.com/question/20073127
#SPJ1
Answer:
In a shorter explanation of what the guy above me is saying
The domain is all real numbers or A
The range is "all real numbers greater than or equal to –2" or B
Step-by-step explanation:
2 over 5 of a bag of chips is in the cupboard. you eat 3 over 4 of what is left. how ,uch of the whole bag did you eat?
Answers
Answer:
3/10
Step-by-step explanation:
So you have 2/5 left in your cupboard. Say the amount of chips originally in your cupboard would be 30. 2/5 of 30 would be 12.
Then multiply 12 by 3/4 so it would be 3/4 of 12.
The result would be 9
9/30 = 3/10
this is complicated explanation
there are much easier explanations tho
ƒ(1) = −6
f(2)=-4
f(n) = f(n-2) + f(n-1)
f(3) =
Answers
Answer:
-10
Step-by-step explanation:
if we put f(n)=3 , Then
f(3)=f(3-2) + f(3-1)
= f(1) + f(2)
= -6+(-4). [since f(1)= -6 and f(2) = -4)
= -6-4
= -10
19) Florence has a strip of clothing that is 8 feet long. About how many 2 feet strips can she cut from the 8-foot strip?
I really need help with this
Answers
Answer:
4
Step-by-step explanation:
8/2 is 4
make w the subject of the formula p = 2w+7 divided by 12
Answers
Answer:
w = (12p - 7) / 2
Step-by-step explanation:
p = (2w + 7) / 12
12p = 2w + 7
2w = 12p - 7
w = (12p - 7) / 2
i needs help with it please
Answers
Answer:
d. ΔMNO
Step-by-step explanation:
In geometry, two figures are congruent if they are the same shape and size (they can also be a mirror image of each other). If they are the same shape but a different size (e,g, one is an enlargement or reduction of the other), then they are similar.
All the given triangles have the same interior angles, so we need to find a triangle with the same side lengths as ΔABC.
The only triangle that has the same side length as ΔABC is ΔMNO:
they both have bases of 8cm.
Therefore, ΔMNO is congruent to ΔABC.
A rectangle measures 12 m by 14 m. If the width is decreased by 3 m and the length is increased by 4 m, how much would the area change?
Answers
Answer:
6 m²
Step-by-step explanation:
Original area :
12 × 14 = 168 m²
New area :
(12-3) × (14+4) =
9 × 18 = 162 m²
168 - 162 = 6
Area would change by 6 m²
The area of a circle with a diameter of 240
Answers
Answer:
in terms of pi: A = 14,400pi
A = 14,400(3.14) is 45,216
Step-by-step explanation:
Area of a circle is pir^2
Radius = diameter / 2
Radius = 240 / 2 which is 120
A = pi(120)^2
A = 14,400pi
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to find the area of a circle with a diameter of 240.
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
First of all, we need to find the radius.We can find the radius by dividing the diameter by 2:
[tex]\star~\large\pmb{240\div2=120}[/tex]
The radius is 120. Now it's time to compute the area!
///\\\///\\\///\\\\////\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\////\\\///\\\///\\\///\\\
Computing The Area
The formula for the area is:
[tex]\star~\large\pmb{Area_{(circle)}=\pi r^2}}[/tex]
See, there's the radius, r; we found a minute ago, and it equals 120 cm.
Now, substitute the value of r into the formula:
[tex]\begin{gathered} \sf{\longmapsto{A=\pi (120)^2} \\ \sf{\longmapsto{A=\pi\times14,400} \\ \sf{\longmapsto{A=45,238.9\;cm^2 \end[/tex]
Hope it helps you out! :D
Ask in comments if any queries arise.
#StudyWithBrainly
~Just a smiley person helping fellow students :)
There are a rack of 14 billiard balls. Balls numbered 1 through 8 are solid-colored. Balls numbered 9 through 14 contain stripes. If one ball is selected at random, determine the odds against it being striped.
Answers
Answer:
3/7 / 42.8% chance
Step-by-step explanation:
There are 6 striped balls (9, 10, 11, 12, 13, 14) and 8 (1, 2, 3, 4, 5, 6, 7, 8) solid colored balls. So, 6 / 14 balls are striped.
(6 / 14 = 3 / 7)
this means that the probability of a ball being striped has the odds of 3/7
(3/7 = about 42.8% chance)
N(t) = 100,000e−(t − 10)2/8
The secant line can be used to approximate the derivative at a particular point on the graph by placing either the right or the left side of the secant line on that point. (Round your answer to the nearest integer.)
(a) Consider the point on the graph at t = 10 days and set one end of the secant line at this point. Set the other end of the secant line at the point that is 1 day earlier. What is the approximation of the slope of the graph at t = 10 days using this secant line?
(b) Consider again the point on the graph at t = 10 days. Set one end of the secant line at t = 10 days and the other end at the point that is 1 day later. What is the approximation of the slope of the graph at t = 10 days using this secant line?
Answers
The approximation of the slope of the graph at t = 10 days using this secant lines are 11750 and -11750, respectively.
How to determine the slope of the secant lines?(a) t = 10 days and a day earlier
This means that:
t = 10 and t = 9
The function is given as:
[tex]N(t) = 100000e^{\frac{-(t - 10)^2}{8}}[/tex]
Calculate N(10)
[tex]N(10) = 100000e^{\frac{-(10 - 10)^2}{8}}[/tex]
Evaluate
N(10) = 100000
Next, calculate N(9)
[tex]N(9) = 100000e^{\frac{-(9 - 10)^2}{8}}[/tex]
Evaluate
N(9) = 88249.6902585
The slope is then calculated using"
[tex]m = \frac{N(10) - N(9)}{10 - 9}[/tex]
This gives
[tex]m = \frac{100000 - 88249.6902585}{10 - 9}[/tex]
Evaluate
m = 11750.3097415
Approximate
m = 11750
(b) t = 10 days and a day later
This means that:
t = 10 and t = 100
The function is given as:
[tex]N(t) = 100000e^{\frac{-(t - 10)^2}{8}}[/tex]
In (a), we have:
N(10) = 100000
Next, calculate N(11)
[tex]N(9) = 100000e^{\frac{-(11 - 10)^2}{8}}[/tex]
Evaluate
N(11) = 88249.6902585
The slope is then calculated using:
[tex]m = \frac{N(11) - N(10)}{11 - 10}[/tex]
This gives
[tex]m = \frac{88249.6902585 - 100000}{11 - 10}[/tex]
Evaluate
m = -11750.3097415
Approximate
m = -11750
Hence, the approximation of the slope of the graph at t = 10 days using this secant lines are 11750 and -11750, respectively.
Read more about secant lines at:
https://brainly.com/question/14438198
#SPJ1
Which expression represents the perimeter of the triangle?
8x + 2
18x
8x
Answers
Answer:
8x
Step-by-step explanation:
We can add all of the side lengths of the triangle to figure out the perimeter. 3x-1+3x+1=6x+2x=8x
Halp me
Me too dum to know pls halp
Answers
Answer:
Coordinate pair for Friday (3, 55). This means the length of the eruption was 3 minutes, and the wait time between the eruptions was 55 minutes.
Paulo and Jason wear smaller shoe sizes than Carmen.
Jason and Carmen scored more runs than Paulo.
Step-by-step explanation:
Paulo wears size 5 and Jason wears size 4. Carmen wears size 10, therefore the players wear smaller shoe sizes than he does
Jason scored 10 runs, and Carmen scored 11. Since Paulo only scored 5 runs, the other players scored more than him
Which of the following could be the value of x in the equation x^2 - 21 = 100 Choose all the correct answers
Answers
How to solve your problem
x^{2}-21=100
Quadratic formula
Factor
1
Move terms to the left side
x^{2}-21=100
x^{2}-21-100=0
2
Subtract the numbers
x^{2}\textcolor{#C58AF9}{-21}\textcolor{#C58AF9}{-100}=0
x^{2}\textcolor{#C58AF9}{-121}=0
3
Use the quadratic formula
x=\frac{-\textcolor{#F28B82}{b}\pm \sqrt{\textcolor{#F28B82}{b}^{2}-4\textcolor{#C58AF9}{a}\textcolor{#8AB4F8}{c}}}{2\textcolor{#C58AF9}{a}}
Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.
x^{2}-121=0
a=\textcolor{#C58AF9}{1}
b=\textcolor{#F28B82}{0}
c=\textcolor{#8AB4F8}{-121}
x=\frac{-\textcolor{#F28B82}{0}\pm \sqrt{\textcolor{#F28B82}{0}^{2}-4\cdot \textcolor{#C58AF9}{1}(\textcolor{#8AB4F8}{-121})}}{2\cdot \textcolor{#C58AF9}{1}}
4
Simplify
Evaluate the exponent
Multiply the numbers
Add the numbers
Evaluate the square root
Add zero
Multiply the numbers
x=\frac{\pm 22}{2}
5
Separate the equations
To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.
x=\frac{22}{2}
x=\frac{-22}{2}
6
Solve
Rearrange and isolate the variable to find each solution
x=11
x=-11
what function is increasing at the highest rate
Answers
Brenda earns $18,200 per year. What’s her semi monthly salary.
Answers
Photo is attached!!!!!! Pleaseeee help!!!
Answers
Answer:
1.) ∞
2.) -∞
3.) 0
4.) 0
Step-by-step explanation:
As you approach x = -2 from the left, the "y" values are going to infinity. You never actually get a "y" value that equals x = -2 because of the vertical asymptote.
As you approach x = -2 from the right, the "y" values are going to -infinity. You never actually get a "y" value because there is a vertical asymptote.
As you approach x = 2, both sides converge to y = 0. At this point, there is a smooth, uninterrupted line.
The actual "y" value at x = 2 is 0 because the function goes straight through this point. So, you can just read this point as usual.
help I will gave u brilliant answer please help
Answers
Answer:
a) 15/8 b) 25/18
Step-by-step explanation:
a) First bring all the fractions to a common denominator (I'm going to use 8th's). 5/8 is already simplified, 1/2=4/8, and 3/4=6/8. Then, simply add the numerators and leave the denominator: [tex]\frac{5+4+6}{8} =\frac{15}{8}[/tex]
Since this can not be simplified any further, your final answer is 15/8.
b) Start by bringing all the fractions to a common denominator (for this problem, we'll use 18th's). 2/3=12/18, 1/6=3/18, and 5/9=10/18. Then just add all the numerators and leave the denominator the same: [tex]\frac{12+3+10}{18} = \frac{25}{18}[/tex]
Since this cannot be simplified further either, your final answer is 25/18.
Hope this helps! :)
Answer:
so to add we need to find lcm
Step-by-step explanation:
a) 5/8 + 1/2+3/4 lcm of 2,4 and 8 = 8
5/8 = 5/8
1x4
2x4 = = 4/8
3x2
4x2 = 6/8
5/8 + 4/8 + 6/8 = 15/8
b) 2/3 + 1/6 + 5/9 lcm of 3 , 6 and 9 = 18
2x6
3x6 = 12/18
1x3
6x3 = 3/18
5x2
9x2 = 10/18
12/18 + 3/18 + 10/18 = 25/18
Find the value of x. Round to the nearest tenth. X A B 68° 13 x = [?] X Law of Sines; sin A 83° C
Answers
Step-by-step explanation:
hope you have a great day
The value of x will be;
⇒ x = 13.9
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The triangle is shown in figure.
Now,
Since, We know that;
The sine rule is;
⇒ sin A / a = sin B / b = sin C / c
By given figure, we get;
⇒ sin 83° / x = sin 68° / 13
⇒ sin 83° × 13 / sin 68° = x
⇒ x = 0.99 × 13 / 0.92
⇒ x = 13.9
Learn more about the triangle visit:
https://brainly.com/question/17335144
#SPJ2
Solve for x. Round to the nearest tenth, if necessary.
Answers
Answer:
x = 3.4
Step-by-step explanation:
Use the sin formula, due to the fact of the hypotenuse being known, and the variable being across 70.
Sin(70) = x / 3.6
Sin(70) * 3.6 = x
3.3828934 = x
Round to nearest tenth, as question asked
3.4 = x
-- Gage Millar, Algebra 1/2 Tutor (Pending Pre-Calc Tutor)
What is the range of this data set?
{5, 12, 15, 11, 15, 7, 15, 10, 13}
options:
8
10
12
15
Answers
Answer: 10 is the range, option B/ option G
Step-by-step explanation: range is the most subtracted by the least, so organize the data set which makes it (5, 7, 10, 11, 12, 13, 15, 15, 15)
15 - 5 is 10.
Is this right if not please tell me explanation
Answers
Answer:
No, right answer is = 1017.36
Answer:
1017.36
Step-by-step explanation:
All your work is correct, but the final answer is not. In the problem it says to use 3.14 as pi, but when you multiplied you did:
[tex]\pi * 6^{2}*9 = 1017.88[/tex]
instead of
[tex]3.14*6^{2}*9 = 1017.36[/tex]
like you had written above. So the final is actually supposed to be 1017.36
5. In how many ways can four boys and three girls be seated in a row con taining seven seats ( a ) if they may sit anywhere , ( b ) if the boys and girls must alternate ?
Answers
Bobby is having a summer barbecue. He is inviting 7 of his friends. He wants to have enough food for everyone to have two hot dogs. How many hot dogs will bobby need to cook for himself and his friends?
Answers
Answer:
16
Step-by-step explanation:
7 friends = 14 hotdogs + bobby (2 hotdogs) = 16 hotdogs
Answer:
16 hot dogs
Step-by-step explanation:
since he has 7 friends + himself, we're going to have a total of 8 persons
and since it's expected for each person to have two hot dogs,
total hotdogs Bobby need to cook= 8×2= 16 hot dogs
Which shows a perfect square trinomial?
Answers
Answer:
-ax² + bx + c and satisfies the condition b² = 4ac
Step-by-step explanation:
that's my answer
{Correct me if I'm not correct}
Keep safe|