The hypotenuse is √2 times as long as either leg of a 45-45-90 triangle
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the triangle be represented as ΔABC
Now , the measure of ∠ACB = measure of ∠BAC = 45°
And , the measure of ∠ABC = 90°
So , the triangle is a 45-45-90 triangle
Now , the measure of the sides be AB = BC = 1 unit
And , From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
The measure of side AC ( hypotenuse ) = √ ( AB )² + ( BC )²
The measure of side AC ( hypotenuse ) = √ ( 1 + 1 )
The measure of side AC ( hypotenuse ) = √2 units
Hence , the measure of the hypotenuse of 45-45-90 triangle is √2 units
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If k, m, and n are all prime numbers, list all factors of k∙m∙n.
Answer:
Factors of kmn are 1, k, m, n, km, mn, kn and kmn
Step-by-step explanation:
Given: k, m, and n are prime numbers
To find: factors of k∙m∙n
Solution:
A number is said to be prime if it has exactly two factors: 1 and the number itself
x is said to be a factor of y if x can divide y exactly.
Here,
1 can divide kmn
k can divide kmn
m can divide kmn
n can divide kmn
km can divide kmn
kn can divide kmn
mn can divide kmn
kmn can divide kmn
So, factors of kmn are 1, k, m, n, km, mn, kn and kmn
The stem-and-leaf plot below shows the number of kilometers walked by participants in a benefit walk. Number of Kilometers Walked by Participants 12 0 3 6 7 9 9 13 0 1 4 5 5 14 0 0 2 3 3 8 8 9 15 0 2 2 2 2 3 5 5 7 16 0 5 5 9 9 17 0 4 5 (Key: 12 | 3 means 12.3 km) How many of the walkers traveled more than 16 km? What is the furthest that someone walked?
Answer:
Would you mind taking a screen shot of it?
Step-by-step explanation:
Graph the equation y = 1/3x - 5
Answer:
(0,-5) (3,-4) (6,-3) draw a straight line through them all
Step-by-step explanation:
the -5 means it goes down on the y-axis by 5
the 1/3 means it goes up 1 and right 3
Answer:
(0,-5) (3,-4) (6,-3) draw straight line across them :)
PLEASE HELP ME!!! 80 POINTS FOR 3 QUESTIONS!!!
Answer:
A are 20, 15. The first (x) coordinate tells how far along the horizontal (x) axis it is, here 20. The second (y) coordinate tells how far up the vertical (y) axis it is, here 15.
Step-by-step explanation:3D space we add a third coordinate called z. This tells how far the point is in the third dimension. You can think of this third (z) dimension
Answer:
Step-by-step explanation:
is there a third question because it is loading
WILL MARK BRAINILEST IF CORRECT
Express the answer as [tex]a^n[/tex].
[tex](3^2)^6 * (4^2)^4[/tex]
Answer:
81 x 12^8
Step-by-step explanation:
3^12 x 4^8
Use the properties of exponents
3^4 x 12^8
= 81 x 12^8
Answer:
2.156489996 * 10^21
Step-by-step explanation:
Standard Form:
Ax + By = C
Write a linear equation in slope-intercept form
with a slope of 1/2 and a y-intercept of -3
Answer:
y = (1/2)x - 3
Step-by-step explanation:
slope-intercept form: y =mx + b
m - slope,
b - y - intercept.
m = 1/2
b= - 3
y = (1/2)x - 3
2x^3y^2 (3x^2 – 5xy + y^2)
Answer:
6x⁵y² -10x⁴y³+2x³y⁴
Step-by-step explanation:
2x³y²(3x² -5xy+y²)
6x⁵y² -10x⁴y³+2x³y⁴
In the diagram, point O is the center of the circle and m∠ADB = 43°. If m∠AOB = m∠BOC, what is m∠BDC?
Answer:
B - 43
Step-by-step explanation:
The required measure of the angle m∠BDC is 43°.
Given that,
In the diagram, point O is the center of the circle, and m∠ADB = 43°. If m∠AOB = m∠BOC, what is m∠BDC is to be determined.
The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by
(x - h)² + (y - k)² = r²
where h, k is the coordinate of the center of the circle on the coordinate plane and r is the radius of the circle.
Property of circle -
"The angle subtended by an arc of the circle to the center point of the circle is double the angle subtended by the same arc on any point the circumference of the circle."
So,
From the above property,
Angle subtended by Arc AB at center or m∠AOB is 2 * 43 = 86°
From given m∠AOB = m∠BOC,
Implies
m∠BOC = 86°
Angel subtended by arc BC at D is m∠BDC = m∠BOC /2
= 86 /2
= 43°
Thus, the required measure of the angle m∠BDC is 43°.
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PLEASE HELP FAST WILL MARK BRAINLYEST!!!.which choices are in the solution set of the equation below 10x=15 A. 2.5 B. 2 C.5 D. 3 E. 1 F. 1. 5
Answer:
F) 1.5
Step-by-step explanation:
10x = 15
Divide both sides by 10
10x/10 = 15/10
x = 1.5
Answer:
Option F
Step-by-step explanation:
=> 10x = 15
Dividing both sides by 10
=> x = 1.5
Charles wants to analyze his last 9 math test scores with a
box plot to see how spread apart they are.
Arrange the scores in order, from lowest (on the left) to
highest
Answer:
We need numbers to graph it.
Step-by-step explanation:
You gotta give us the functions.
Answer:
80,84,86,87,90,91,92,94,100
Start is 80. End is 100. Lower Q is 85. Higher Q is 93
Range of scores is 20
Median of scores is 90
The LQR of scores is 8
Edge. 2021
Find the GCF (Greatest Common Factor) of 64 and 144
The calculated value of the gcf of 64 and 144 is 16
Calculating the gcf of 24 and 40From the question, we have the following parameters that can be used in our computation:
Expressions = 64 and 144
Expand both expressions
So, we have
64 = 2 * 2 * 2 * 2 * 2 * 2
144 = 2 * 2 * 2 * 2 * 3 * 3
Multiply the common factors
GCF = 2 * 2 * 2 * 2
Evaluate
GCF = 16
Hence, the gcf of 64 and 144 is 16
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what is the approximate area of the cirlle shown below
Answer:
43ft^2
Step-by-step explanation:
A=πr^2
A=π×3.7^2
A=π×13.69ft^2
A=43ft ^2
Plzz mark brianliest if it suit your question..
Which of the following types of statement can be used to explain the steps of a proof?
Check all that apply.
A. Guess
B. Theorem
C. Conjecture
D. Postulate
Answer:
its postulate, and theorem
Step-by-step explanation:
i did this assignment
The types of statement can be used to explain the steps of a proof is postulate and theorem.
What is Theorem?A statement that has been proven true or that can be proven is known as a theorem in mathematics. A logical argument is used to prove a theorem by using the deductive system's inference rules to show that the theorem follows logically from the axioms and other theorems that have already been proven.
Guessing and Conjecture is just striking some ideas without any definite conclusion.
A claim that is accepted as true without evidence, also referred to as an axiom. Lemmas and theorems are deduced from postulates, which serve as their fundamental building block.
Thus, the statement used in proof is Postulate or Theorem.
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Anna wants to rent movies from either Service A or Service B. Service A charges $37.92 as a subscription fee with a charge of $2.18 per movie.
Service B charges $33.25 as a subscription fee plus $3.55 per movie. Service B is running a special offer where the first movie is free.
Given that Anna always rents at least 1 movie in a given subscription period, how many movies would she have to rent for the average cost per
movie to be equal at Service A or Service B?
OA 6
OB.
0
O c.
1
OD. 7
Answer:
6 is your answer :)
4. You sketch a right triangle that has a
hypotenuse of 12 centimeters, and one leg
that is 7 centimeters. How many centimeters
Is the other leg?
Answer:
√95 cm
Step-by-step explanation:
To solve, you need to use the pythagorean theorem, or a^2 + b^2 = c^2
The hypotenuse is the c and let one leg be b. You can write:
a^2 + 7^2 = 12^2
a^2 + 49 = 144
Now, you need to solve for a:
a^2 = 144 - 49
a^2 = 95
a = √95 cm, or about 9.75cm
What is the equation, in slope-intercept form, of the line that is perpendicular to the line
y-4 = (x – 6) and passes through the point (-2, -2)?
Answer:
y=x
Step-by-step explanation:
slope intercept form:
y= mx +c, where m is the gradient and c is the y-intercept.
Let's rewrite the given equation in the form of y=mx+c, so that we can determine the gradient of the line.
y-4= x-6
y= x -6 +4
y= x -2
Thus, the gradient of the given line is 1.
the product of the gradients of perpendicular lines is -1.
(gradient of line)(1)= -1
gradient of line= 1
Thus, m=1.
y= 1x +c
y= x +c
To find c, substitute a coordinate.
When x= -2, y= -2,
-2= -2 +c
c= -2 +2
c=0.
Thus the equation of the line is y=x.
Please look at the image provided.
Answer:
[tex]x=3[/tex]
Step-by-step explanation:
[tex]\frac{6\left(x-2\right)}{2}=\frac{3\left(x+5\right)}{8}\\\mathrm{Apply\:fraction\:cross\:multiply:\:if\:}\frac{a}{b}=\frac{c}{d}\mathrm{\:then\:}a\cdot \:d=b\cdot \:c\\6\left(x-2\right)\cdot \:8=2\cdot \:3\left(x+5\right)\\Simplify\\48\left(x-2\right)=6\left(x+5\right)\\\mathrm{Expand\:}48\left(x-2\right):\quad 48x-96\\48\left(x-2\right)\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b-c\right)=ab-ac\\a=48,\:b=x,\:c=2\\=48x-48\cdot \:2\\\mathrm{Multiply\:the\:numbers:}\:48\cdot \:2=96[/tex]
[tex]=48x-96\\\mathrm{Expand\:}6\left(x+5\right):\quad 6x+30\\6\left(x+5\right)\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac\\a=6,\:b=x,\:c=5\\=6x+6\cdot \:5\\\mathrm{Multiply\:the\:numbers:}\:6\cdot \:5=30\\=6x+30\\48x-96=6x+30\\\mathrm{Add\:}96\mathrm{\:to\:both\:sides}\\48x-96+96=6x+30+96\\Simplify\\48x=6x+126\\\mathrm{Subtract\:}6x\mathrm{\:from\:both\:sides}\\48x-6x=6x+126-6x\\\mathrm{Simplify}\\42x=126\\\mathrm{Divide\:both\:sides\:by\:}42[/tex]
[tex]\frac{42x}{42}=\frac{126}{42}\\Simplify\\x=3[/tex]
I NEED TO QUICKLY PLS HELP ME PPLLSSSSS
AB, BE, and CF are all diameters of the circle. The measure of angle AOB is 40 degrees. The measure of angle DOF is 120 degrees.
Find the measure of angle COD.Find the measure of angle BOC.
Find the measure of angle COD
Angle COD is 60 degrees
angle BOC is 80 degrees
Because angle DOE is vertically opposite to angle boa, it is also 40 degrees. we know that angle DOF is 120, so angle FOE is 120-40 = 80 degree, and angle BOC is vertically opposite do it is 80 degrees.
since angle COD lies on a straight line it adds up to 180 degrees, so 180- 120 = 60 degrees
If the complex number x = 3 + bi and |x| 2 = 13, which is a possible value of b?
Answer:
A.2
Step-by-step explanation:
We know that |x|² = 13 and x = 3+bi:
(3+bi)² = 13
3² + b² = 13
9 + b² = 13
Subtract 9 from each side:
9 + b² - 9 = 13 - 9
b² = 4
Take the square root of each side:
√b² = √4
b = 2
Answer:
A 2
Step-by-step explanation:
Edge
What is the numerator of the simplified sum?
Answer:
Maybe 4x+6 i'm not sure
Step-by-step explanation:
Answer:
It's 4x+6
Step-by-step explanation:
A leaf hangs from a branch 12 feet in the air. It falls to the ground at a rate of 0.25 feet per second. Which graph could represent the leaf’s height in feet as a function of time, in seconds, after leaving the branch? A coordinate plane showing Falling Leaf, Time in seconds on the x-axis and Height in feet on the y-axis. A line is passing through (4, 20 ), (6, 14), and (12, 0). A coordinate plane showing Falling Leaf, Time in seconds on the x-axis and Height in feet on the y-axis. A line is passing through (0, 12), (8, 8), and (20, 2). A coordinate plane showing Falling Leaf, Time in seconds on the x-axis and Height in feet on the y-axis. A line is passing through (0, 16), (6, 8), and (12, 0). A coordinate plane showing Falling Leaf, Time in seconds on the x-axis and Height in feet on the y-axis. A line is passing through (0, 12), (8, 10), and (16, 8).
Answer:
A coordinate plane showing Falling Leaf, Time in seconds on the x-axis and Height in feet on the y-axis. A line is passing through (0, 12), (8, 10), and (16, 8).
Step-by-step explanation:
The y-intercept of the graph is the height of the leaf at the beginning, that is, 12 ft. This means that point (0, 12) is on the line.
The leaf falls to the ground at a rate of 0.25 feet per second, this means that after 8 seconds, the leaf travel 8*0.25 = 2 ft. Given that it started at 12 ft, its height is 12 - 2 = 10 ft. In other words, the point (8, 10) is on the line. Similarly, its height after 16 seconds is 12 - 16*0.25 = 8 ft, that is, the point (16, 8) is on the line.
Answer:
the answer is D
Step-by-step explanation:
A line is passing through (0, 12), (8, 10), and (16, 8).
Which of the following scenarios could be modeled by a step function? A. A moving company charges $65 per hour. They round minutes up to the next hour.
B. A sports shop tracks its total monthly sales of surfboards over 5 years. They note a peak in sales every year in the months of June and July followed by a steady decline and almost no sales during the winter months.
C. A restaurant allows patrons to choose one meat and two sides from their lunch menu for a set price. Additional sides are $2.50 each.
D. A savings account at Best Bank provides an interest rate of 8% per year on accounts with balances of at least $1,000
Answer:
A. A moving company charges $65 per hour. They round minutes up to the next hour.
Step-by-step explanation:
Let's define
x: hours worked
C(x): cost charged
The step function will be:
C(x) = 65 0 ≤ x ≤ 1
C(x) = 130 1 < x ≤ 2
C(x) = 195 2 < x ≤ 3
and so on.
Find the volume of the pyramid.
Answer:
7
Step-by-step explanation:
Formula=area of base x height / 3
A= ( 3 x 1 ) x 7 / 3
A= 3 x 7 / 3
A= 21 / 3
A= 7
What are the solutions of x²-2x+2=0?
Answer:
A
Step-by-step explanation:
[tex]x^2-2x+2=0[/tex]
Plugging this into the quadratic formula:
[tex]x=\dfrac{2\pm \sqrt{4-8}}{2}=\dfrac{2\pm 2i}{2}= 1\pm i[/tex]
Therefore, the correct answer is choice A. Hope this helps!
plss help due today !!!!
Answer:
$30
Step-by-step explanation:
She paid $24.72 for the 2 packages of chicken because $12.36×2=$24.72.
She paid $0.99 for the broccoli because $1.98×1/2=$0.99.
She paid $3.49 for the milk because one gallon of milk costs $3.49.
$24.72+$0.99+$3.49=$29.20.
$29.20+$0.80=$30.00.
She used $30.00 to pay for the items.
Answer:
$30
Step-by-step explanation:
Explain how to use a graph of the function f(x) to
find f(3).
Answer:
You would plug in the number 3 into both the F(x) and the x of the equation. By solving for x of your new equation, you would be able to find the value of f(3)!
Step-by-step explanation:
Please PLEASE PLEASE HELP for 20 POINTS
Answer:
x ≥ 4
Step-by-step explanation:
There is a closed circle at 4 so it means equals
The line goes to the right so that means greater
x ≥ 4
Answer:
D or x≥4
Step-by-step explanation:
The number has to be 4, since the dot lies on it, so that excludes A and B.
It is greater, because the arrow is pointing right instead of left.
Since the circle is closed, then it means that it includes 4.
So, C would not be the answer, because it is read as " x is greater than 4"
it should be D, which is " x is greater than or equal to 4" (since the circle is closed).
Thus, D is the answer
Answer these questions.
What is the value of x, if 105% of 90 is equal to 200% of x?
Luke is flying a kite and realizes that 400 feet of string are out. The angle of the stream with the ground is 50°. How high is Luke’s kite above the ground
Answer:
Luke's kite is 306.4 feet high above the ground
Step-by-step explanation:
To find the height of Luke's kite above the ground, we will follow the steps below:
We can solve the problem using trigonometric ratio;
that is;
SOH CAH TOA
sinФ = opposite/hypotenuse
cosФ= adjacent/hypotenuse
tanФ=opposite/adjacent
From the diagram below:
opposite = x where x represents the height of Luke's kite above the ground
hypotenuse = 400
Ф = 50
The best trig ratio to use is sin
sinФ = opposite / hypotenuse
sin 50° = [tex]\frac{X}{400}[/tex]
cross-multiply
x = 400 sin 50°
x≈306 .4 feet
Luke's kite is 306.4 feet high above the ground
For the function above is the discriminate, positive, negative, or zero?
Answer:
0
Step-by-step explanation:
When there is one x-intercept, the discriminant is zero.
__
The discriminant is used to compute the difference between the roots. When it is positive, the real roots are different, so there are two x-intercepts.
When the discriminant is zero, there is no difference between the roots, so there is one x-intercept (as here).
When the discriminant is negative, there are no x-intercepts and the two roots are complex.