Answer:
14
√
2
=
7
√
2
Step-by-step explanation:
An isosceles right triangle is a right triangle with two legs equal in length and has angles of
45
∘
−
45
∘
−
90
∘
.
By Pythagorean Theorem, we know that,
hypotenuse
c
2
=
a
2
+
a
2
,
⇒
c
=
a
√
2
where
c
is the hypotenuse and
a
is the leg.
So for an isosceles right triangle with side length
a
, the hypotenuse has a length of
a
√
2
.
Similarly, if the hypotenuse of an isosceles right triangle has length of
a
, the legs have a length of
a
√
2
or
a
√
2
2
each.
Given that the hypotenuse of the isosceles right triangle
=
14
,
⇒
the length of each leg
=
14
√
2
=
7
√
2
Check :
(
7
√
2
)
2
+
(
7
√
2
)
2
=
196
=
14
2
(OK)
The height (one of the legs) and the hypotenuse of an isosceles right triangle are 40 feet and 40√2 feet, respectively.
What is Pythagoras theorem?In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.
Given:
The triangle is an isosceles right triangle.
That means, the triangle has two equal sides.
Let, base b = height h.
The area of the triangle = 1/2 x base x height.
800 = (1/2)b²
b² = 1600
b = 40 feet.
Now, using the Pythagoras theorem,
Hypotenuse = √(1600 + 1600)
Hypotenuse = √(3200)
Hypotenuse = 40√2 feet.
Therefore, height = 40 feet and hypotenuse = 40√2 feet.
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simplify the fraction 37/8
What are the other two representations of this ratio 15 to 3
Answer:
you can answer it like 15 to 3 or
15:3
If triangle MAS Striangle TAR, which of the statements could be false?
[tex]\color{plum}\tt(B) \: segment \: \: MA \: ≅ \: segment \: SA[/tex]
Steps to derive the correct option :Given :△MAS ≅ △TARWhich means, the following are the corresponding(equal/similar) parts :
segment MA ≅ segment TAsegment AS ≅ segment SRsegment MS ≅ segment TR∠AMS ≅∠ARS∠ASM ≅∠ART∠MAS ≅∠TARThus, the statement (B) is false because there is no evidence to prove that segment MA ≅ segment SA.
Therefore, the correct option is - (B) segment MA ≅ segment SA
Please help ASAP
Paula used 134 cups of flour for a recipe. How many cups y of flour did Paula have if she had x cups before making the recipe? Write an equation to represent the situation.
Answer:
y = x - 1 3/4*
Step-by-step explanation:
If 1 3/4 is used, then subtracting that from the previous amount will give you the amount that Paula has currently
* My answer is only correct if you meant 1 3/4, not 134. If you meant 134, then the answer would be y = x - 134
Explain which hill is steeper: a hill woth rise of 5 and a run of 3 of a hill with rise of 3 and a run of 5.
A sequence is formed by adding 1 to each square number.
Here are the first five terms of the sequence.
2 5 10 17 26
Find the 10th term of the sequence.
Answer:
101
Step-by-step explanation:
the tenth term of the sequence would be 10x10 (10 squared), which equals 100. add 1 to that you get 101.
Answer:
101
Step-by-step explanation:
10 X 10 + 1 = 101
nth term = n^2 + 1
What is the exponent form? 6 x 6 x 6
A. 6 cubed
B. 6 to the power of 2
C. 6 squared
D. 6 x 3
Answer:
C.6 squared
Step-by-step explanation:
What is the factored form of z^2– 9?
Answer:
OR just 3
Step-by-step explanation:
z^2-9 becomes sqrt(z^2)=sqrt(9) becomes z=+-3
I need help please I would be happy
7384(x)748 (8967-888)
Answer: [tex](x,y) \to (4x,4y)[/tex] which is choice (3)
======================================================
Explanation:
The general transformation of [tex](x,y) \to (kx,ky)[/tex] describes a dilation with scale factor k. If k is not equal to 1, then the resulting image will not be the same size as the preimage.
In this case, k = 4. This means that the resulting image has its side lengths 4 times greater compared to the preimage side lengths. For example, if a side length is 5 units long in the preimage, then its corresponding length in the image is 5*4 = 20 units long.
If this is enlargement applied to all sides, then the perimeter also goes up by the same scale factor (since the perimeter is the sum of all exterior sides). The image perimeter will be four times that of the preimage perimeter.
In summary, if you apply a dilation (where k is not equal to 1), then the perimeter will change. If k > 1, then the perimeter gets larger. If 0 < k < 1, then the perimeter will shrink.
----------------------
Extra info:
Choice (1) describes a reflection over the line y = xChoice (2) is a reflection over the x axis.Choice (4) describes a translation of 2 units to the right and 5 units down.The transformations of reflections, translations, and rotations all are considered rigid transformations. This means that they keep the same size and shape. You can imagine the camera is moving around in some way and the shapes stay still (but give the illusion of movement). In other words, rigid transformations will keep the perimeter the same. Because of this, we can rule out choices (1), (2) and (4).How many squares would have to be shaded so that 2/9 of the shape is shaded?
Answer:
4.
Step-by-step explanation:
There are 18 squares, if you want to shade 2/9 you have to make the denominator, which is 9 into 18, so you multiply by 2, you will do the same thing to the numerator, 2x2=4 9x2=18.
Brainiest would be appreciated.
There are 4 squares that would have to be shaded so that 2/9 of the shape is shaded.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.
We have to determine the number of squares that would have to be shaded so that 2/9 of the shape is shaded
According to the given figure,
There are 3 rows and 6 columns of squares
So the number of squares would be 3 × 6 = 18
There are 18 squares, therefore if you want to shade 2/9, you must first divide the denominator, which is 9 into 18, by 2, and then multiply by 2.
If 2/9 of the shape is shaded: 18 × 2/9 ⇒ 36/9 = 4
Hence, there are 4 squares that would have to be shaded so that 2/9 of the shape is shaded.
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how do i solve this??
Answer:
J (3; 9)
Step-by-step explanation:
Imagine each distance like a triangle and use Pythagorean theorem.
To illustrate I drew triangle ΔLON in the picture
Finding the distance between LN.
LO = [tex]y_{L} - y_{O}[/tex] = 5 - 1 = 4
NO = [tex]x_{N} - x_{O}[/tex] = 5 - 4 = 1
According to Pythagorean theorem
[tex]LN^{2} = LO^{2} + NO^{2}[/tex]
[tex]LN^{2}[/tex] = [tex]4^{2} + 1^{2}[/tex] = 17
LN = [tex]\sqrt{17}[/tex] (LN > 0)
Since ΔMLN ≅ ΔKLJ, JL = LN (they are clearly equal triangles)
Mark J coordinates as (x; y)
Draw another triangle JOL, ∠JOL = 90°)
OJ is parallel with x axis and OL is parallel with y axis. O coordinates then are (4; y)
OL = y - 5
OJ = 4 - x
Note that ΔLON = ΔJOL, so OL is the same as LO and therefore
OL = LO = y - 5 = 4;
y = 9
OJ = NO = 4 - x = 1
x = 3
So the coordinates of J are (3; 9)
Similarly find the coordinates of K
Find BC please help!
Answer:
BC=23
Step-by-step explanation:
Use sine rule:
x/sinX=y/sinY
BC/sinA=AB/sinC
BC/sin61=9/sin20
BC=26.3142396015*sin61
BC=23.0149525338
Factor as the product of two binomials.
x^2 – 100
Answer:
(x+10)(x-10)
Step-by-step explanation:
i will give brainliest
Answer:
230°
Step-by-step explanation:
Answer: 40
Step-by-step explanation:
Corresponding Angles Theorem
Please help me with this for brainliest.....
Answer:
a=542
Step-by-step explanation:
you welcome have a good day
Answer:
the answer will be a=524
Step-by-step explanation:
Evaluate
(-8) 2
31
Write your answer as a fraction in simplest form.
Answer:
in simplest form=81/64
decimal=1.265625
Ryan and Chaise are brothers. Ryan's age, y, us twice Chaise's age, x. Ryan is also 11 years older than Chaise. What is Ryan's age?
Ryan is 22 years old.
What is the system of equations?
A system of equations is a collection of one or more equations that are considered together. The system can consist of linear or nonlinear equations and may have one or more variables. The solution to a system of equations is the set of values that satisfy all of the equations in the system simultaneously.
Let's use the given information to set up a system of equations to solve for Ryan's age.
We know that Ryan's age, y, is twice Chaise's age, x, so we can write:
y = 2x (Equation 1)
We also know that Ryan is 11 years older than Chaise, so we can write:
y = x + 11 (Equation 2)
Now we can substitute Equation 1 into Equation 2:
2x = x + 11
Simplifying, we get:
x = 11
So Chaise is 11 years old.
To find Ryan's age, we can use either Equation 1 or Equation 2. Let's use Equation 2:
y = x + 11
y = 11 + 11
y = 22
Therefore, Ryan is 22 years old.
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The number of customers visiting a local business is 61,874 and has been continuously declining at a rate of 3.5% each year. What is the approximate number of
customers in 15 years?
A. 36,602
B. 29,309
C. 104,595
D. 36,259
A cell phone retailer used a mark-up rate of 60% on a cellphone case that originally cost $5. To find the new price of the case in ONE STEP, my equation Part = %*whole will be...
Answer:
$8
Step-by-step explanation:
5 increase 60% =
5 × (1 + 60%) = 5 × (1 + 0.6) = 8
What is the value of the expression of 1/2 divided by 6
Answer:
0.083
Step-by-step explanation:
Answer:
3 is it
Step-by-step explanation:
can anyone plz help me
HELP ASAP 40 POINTS
What is the equation for the nth term of the sequence
And what is the 52nd term of the sequence. -8,-12,-16
Given:
The sequence is -8, -12, -16.
To find:
The nth and 52th term of the given sequence.
Solution:
We have,
-8, -12, -16
It is an AP because the difference between consecutive terms are equal. Here, first term is -8 and the common difference is
[tex]r=a_2-a_1[/tex]
[tex]r=-12-(-8)[/tex]
[tex]r=-12+8[/tex]
[tex]r=-4[/tex]
The nth term of an AP is
[tex]a_n=a+(n-1)d[/tex]
Where, a is first term and d is common difference.
Putting a=-8 and d=-4, we get
[tex]a_n=-8+(n-1)(-4)[/tex]
[tex]a_n=-8-4n+4[/tex]
[tex]a_n=-4-4n[/tex]
Putting n=52, we get
[tex]a_{52}=-4-4(52)[/tex]
[tex]a_{52}=-4-208[/tex]
[tex]a_{52}=-212[/tex]
Therefore, the equation for the nth term of the given sequence is [tex]a_n=-4-4n[/tex] and the 52nd term of the sequence is -212.
a) Which of the four curves, A, B, C or D,
is a sketch of the curve with equation y = 2* ?
A
b) Give the coordinates of any points of
intersection of the curve of y = 2with
the axes.
If there are no points of intersection
write, 'no points'.
(1)
Answer:
Step-by-step explanation:
This is for today can someone help me!!
Answer:
It's the third one!!
Step-by-step explanation:
grs
how do you work out what 8 cubed is ?
Step-by-step explanation:
so do you have building blocks cuz you use it and then after you do that you get the cue that has an eight on it and then you would keep on adding on and then that would be the answer
Answer:
512.
Step-by-step explanation:
8 cubed is the same as 8 to the third power.
We usually use other ways to represent certain number to the power to help make equations easier and write less so,
instead of saying: 2 to the second power; we say 2 squared.
Instead of saying 2 to the third power; we say 2 cubed.
The number 2 was used just as example, it could be any number.
so 8 cubed = 8 to the third power so,
8 cubed = [tex]8^{3}[/tex] = 8x8x8 = 512
X/5+ 7 = y Solve for x
pls hurry
Answer:
x=5y-35
Step-by-step explanation:
Rate A puppy not mine cant find a pic of mine but mine is a micro mini golden doodle
Answer:
10/10
Step-by-step explanation:
pretty good looking pup good snout good fur nice colors overall good pup
Find the value of x.
3x + 1
12.5
15
The value of x is 3.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
As, we know that The median (also called a midline or midsegment) is a line segment half-way between the two bases.
median = (a+ b ) / 2
So, 12.5 = (3x+1 + 15) / 2
12.5 = 3x + 16 / 2
25 = 3x + 16
3x = 9
x= 3
Hence, the value of x is 3.
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Given the function f(x)=-x^2-5x+12f(x)=−x 2 −5x+12, determine the average rate of change of the function over the interval -5\le x \le 4−5≤x≤4.
Given:
The function is
[tex]f(x)=-x^2-5x+12[/tex]
To find:
The average rate of change of the function over the interval −5 ≤ x ≤ 4.
Solution:
The average rate of change of a function f(x) over the interval [a,b] is
[tex]m=\dfrac{f(b)-f(a)}{b-a}[/tex]
Putting x=-5 in the given function, we get
[tex]f(-5)=-(-5)^2-5(-5)+12[/tex]
[tex]f(-5)=-25+25+12[/tex]
[tex]f(-5)=12[/tex]
Putting x=4 in the given function, we get
[tex]f(4)=-(4)^2-5(4)+12[/tex]
[tex]f(4)=-16-20+12[/tex]
[tex]f(4)=-24[/tex]
Now, the average rate of change of the function over the interval −5 ≤ x ≤ 4 is
[tex]m=\dfrac{f(4)-f(-5)}{4-(-5)}[/tex]
[tex]m=\dfrac{-24-12}{4+5}[/tex]
[tex]m=\dfrac{-36}{9}[/tex]
[tex]m=-4[/tex]
Therefore, the average rate of change of the function over the interval −5 ≤ x ≤ 4 is -4.
I will give brainliest!!
Find the surface area for the given prism.
Height: 8 Inches
Length: 10 Inches
Width: 14 Inches
564 in ^2
664 in ^2
1,120 in ^2
1,080 in ^2
Find the lateral area for the given prism.
Height: 26 CM
Width: 6 CM
Length: 14 CM
1,092 cm ^2
998 cm ^2
1,272 cm ^2
870 cm ^2
Answer:
SA: 664 in²
LA: it’s supposed to be 1040cm???
Step-by-step explanation:
SA: find the area of all sides of the prism first (I suppose it’s rectangular?)
80+80+112+112+140+140 = 664
LA: the lateral area formula is (perimeter of base)*height...
perimeter of base = (6+6+14+14) = 40
40 * 26 = 1040
I may be wrong on the second one since I don’t know what the prism’s shape is... Hope it helps though ;)
Answer:
1,092
Step-by-step explanation:
