Answers
all 3 angles in a triangle need to equal 180 degrees
62 +73 = 135 degrees are known
180-135 = 45
so angle B = 45 degrees
Related Questions
What is the length of the hypotenuse, x, if (12, 35, x) is a Pythagorean triple?
Answers
12^2 + 35^2 = c^2
144 + 1225 = c^2
1369 = c^2
sqrt 1369 = c
37 = c <=== ur hypotenuse is 37
so ur pythagorean triple is (12,35,37)
Answer:37
Step-by-step explanation:
12•12=144
35•35=1225
1225+144=1369
Square root 1369=37
are all semi circles simular
Answers
solve the following equation -2x + 4 = 2 (4x - 3) -3 (-8 + 4x)
a.7
b.2
c.-7
d.3
Answers
Answer:
[tex]A) 7[/tex]
Step-by-step explanation:
[tex]-2x+4=2\left(4x-3\right)-3\left(-8+4x\right)[/tex]
[tex]2\left(4x-3\right)-3\left(-8+4x\right)[/tex]
[tex]2 (4x - 3)[/tex]
[tex]\longrightarrow8x-6[/tex]
[tex]\longrightarrow 8x-6-3\left(-8+4x\right)[/tex]
[tex]-3 (-8 + 4x)[/tex]
[tex]\longrightarrow 24-12x[/tex]
[tex]8x-6+24-12x[/tex]
Combine like terms:
[tex]8x-12x-6+24[/tex]
Add: [tex]8x-12x=-4x[/tex]
Add: [tex]-6+24=18[/tex]
[tex]\longrightarrow-2x+4=-4x+18[/tex]
Subtract 4 from both sides:
[tex]\longrightarrow-2x+4-4=-4x+18-4[/tex]
[tex]\longrightarrow-2x=-4x+14[/tex]
Add 4x to both sides:
[tex]\longrightarrow-2x+4x=-4x+14+4x[/tex]
[tex]\longrightarrow2x=14[/tex]
Divide both sides by 2:
[tex]\longrightarrow\frac{2x}{2}=\frac{14}{2}[/tex]
[tex]\longrightarrow x=7[/tex]
____________________________
OAmalOHopeO
factors of 3x^2y^2+6x^2+12y^2+24
Answers
GCF = 3
so we have
3 (x^2y^2 + 2x^2 + 4y^2 + 8) Factor by grouping:-
= 3[ x^2(y^2 + 2) + 4(y^2 + 2)]
= 3(x^2 + 4)(y^2 + 2)
In the figure, if AB ≅ CD, then
A. AB ⊥ CD
B. CE ≅ BE
C. ∠CEA ≅ ∠CEB.
D. arc AB ≅ arc CD.
Answers
Answer:
D. arc AB ≅ arc CD.Step-by-step explanation:
To solve this problem, we need to use the Intersecting Chords Theorem which states "when two chords intersect each other inside a circle, the products of their segments are equal".
Applying this theorem, we have
[tex]AE \times EB = CE \times ED[/tex]
Where [tex]AB=AE+EB[/tex] and [tex]CD=CE+ED[/tex], also [tex]AB \cong CD[/tex], which means
[tex]AE+EB=CE+ED[/tex]
However, if both chords are equal, then their arcs are also equal, that's the easiest way to deduct it, that is
[tex]arc(AB) \cong arc(CD)[/tex]
Because an arc is defined by its chord basically, and in this case they are congruent.
Part A: Solve -vp + 30 < 45 for v .. show your work.
Part B: Solve 3w - 6r = 30 for r .. show your work.
Answers
-vp < 45 - 30
-vp < 15
-v < 15/p
v > -15/p <==
============
3w - 6r = 30 ...for r
-6r = 30 - 3w
r = (30 - 3w) / -6
r = -5 + 1/2w...or r = 1/2w - 5 <==
Part B: r = 1/2w - 5
Which of the following are vertical asymptotes of the function y = 2cot(3x) + 4? Check all that apply. A.x = pi/3 B.x = +/- pi/2 C.x = 2pi D.x = 0
Answers
The vertical asymptotes of the function y = 2cot(3x) + 4 are A.x = π/3 C. x = 2π D.x = 0
How to determine the vertical asymptote?The function is given as:
y = 2cot(3x) + 4
The above function is a cotangent function, represented as:
y = Acot(Bx +C) + D
By comparison, we have:
B = 3
The vertical asymptotes are then calculated using:
[tex]x = \frac{\pi}{B}n[/tex], where n are integers
Substitute 3 for B
[tex]x = \frac{\pi}{3}n[/tex]
Using the above format, the vertical asymptotes in the options are A.x = π/3 C. x = 2π D.x = 0
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Does arkansas lie south of 40 degrees latitude
Answers
2x − y = 3 4x = 6 + 2y
Answers
2x - y = 3
4x = 6 + 2y
The second equation, after diving through by 2, is
2x = 3 + y
or
2x - y = 3
The system of equations is
2x - y = 3 (1)
2x - y = 3 (2)
These two equations are identical, so we actually have only one equation for determining x and y.
That is,
y = 2x - 3
For any real value of x, there will be a corresponding value of y.
Therefore there an infinite number of solutions, and no unique solution exists.
Answer: There is no unique solution.
When constructing a circle circumscribed about a triangle, what is the purpose of constructing perpendicular bisectors?
Answers
-2(4g-3)= 30 how do i solve this
Answers
-8g+6= 30
-8g=30-6
-8g= 24
G= 24/-8
G= -3
Hope this helps!
-2(4g-3)=30
-8g+6=30
-8g=24
g= -3
Hope this helped!
the old price for school lunches is $5. The new price is $5.25. What is the percent increase in the cost if school lunches? Write answer as percent. The formula is p=b-a/a. b =new price for lunch. a=old price for lunch. P=percent increase
Answers
p=(5.25-5.00)/5.00
p=0.25/5.00
p=0.05
p = 5% increase
how many cups of grape punch containing 10% fruit juice and berry punch containing 20% fruit juice must be added together to create 12 cups of punch with 18% fruit juice?
Answers
let's say we need "b" of berry punch, now, is 20% juice, how much juice in "b"? well, (20/100) * b, or 0.2b.
whatever "g" and "b" are, they must add up to 12 cups, of 18%, how much juice in 12cups? well (18/100) * 12, or 2.16
[tex]\bf \begin{array}{lccclll} &amount&concentration& \begin{array}{llll} concentrated\\ amount \end{array}\\ &-----&-----&-----\\ \textit{grape punch}&g&0.10&0.10g\\ \textit{berry punch}&b&0.20&0.20b\\ -----&-----&-----&-----\\ mixture&12&0.18&2.16 \end{array}[/tex]
[tex]\bf \begin{cases} g+b=12\implies \boxed{b}=12-g\\ 0.1g+0.2b=2.16\\ ----------\\ 0.1g+0.2\left( \boxed{12-g} \right)=2.16 \end{cases} \\\\\\ 0.1g+2.4-0.2g=2.16\implies 2.4-2.16=0.2g-0.1g \\\\\\ 0.24=0.1g\implies \cfrac{0.24}{0.1}=g\implies \boxed{2.4=g}[/tex]
and of berry will then be 12 - g
A rectangle is placed around a semicircle as shown below. the width of the rectangle is 6ft . find the area of the shaded region. use the value 3.14 for π , and do not round your answer. be sure to include the correct unit in your answer.
Answers
Assumptions:
1) radius of the semicircle = width of the rectangle = 6ft
2) length of the rectangle = 2*radius of the semicircle = 12 ft
3) Area of the shaded region = area of the rectangle - area of the semicircle
Solution
area of the rectangle = width * length = 6 ft * 12 ft = 72 ft^2
area of the semicircle = [1/2]*π*(r^2) = [1/2]*3.14*(6ft)^2 = 56.52 ft^2
area of the shaded region = 72 ft^2 - 56.52 ft^2 = 15.48ft^2
Answer: 15.48 ft^2
The shaded region is by assumption the region which is not covered by the semicircle in in given rectangles.
The area of the shaded region is given by 15.48 sq. ft.
What is a semicircle?
A semicircle is a circle cut in half. Thus, one circle produces two semicircle.
Firstly we will find the area of the rectangle and then subtract the area of the semicircle to find the are of the shaded region.
Since the radius of the semicircle is equal to width of the rectangle(6 ft), thus the length of the diameter of the circle( twice the radius which is 12 ft) serves as length of the considered rectangle.
Thus, we have:
[tex]\text{Area of the given rectangle\:} = 6 \times 12 = 72 \: \rm ft^2[/tex]
Since the semicircle is having radius of 6 ft, thus:
[tex]\text{Area of semicircle} = \dfrac{\pi r^2}{2} = \dfrac{3.14 \times 6^2}{2} = 56.52 \: \rm ft^2[/tex]
Thus, area of the shaded region will be equal to area of rectangle - area of semicircle = 72 - 56.52 = 15.48 sq. ft.
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the base of an exponential function cannot be a negative number true or false
Answers
Answer:
True
Step-by-step explanation:
Given statement : The base of an exponential function cannot be a negative number.
We need to check whether the given statement is true or not.
The general form of an exponential function is
[tex]f(x)=ab^x[/tex]
where, a is the initial value and b is the base of exponential function.
The value of base b is always greater than 0 because
1. The terms like [tex](-3)^\frac{1}{2}[/tex] is an imaginary number and it make no sense. So, the base of an exponential function cannot be a negative number.
2. It b=0, then [tex](0)^x=0[/tex], which is a constant function. So, the base of an exponential function cannot be 0.
It means b>0.
Therefore, the given the given statement is true.
Final answer:
The base of an exponential function must be positive, as a negative base can lead to undefined values when raised to non-integer exponents. The rate of growth of an exponential function with a positive base near one can be approximated by 1+x for small x. Bases for exponential functions can often be connected to Euler's number e (approximately 2.71818).
Explanation:
The statement that the base of an exponential function cannot be a negative number is true. The base of an exponential function needs to be positive because a negative base can lead to undefined or complex values when raised to a fractional or irrational exponent. For example, the exponential function with base e (where e is the Euler's number, approximately equal to 2.71818) demonstrates natural growth, and its rate of growth for small x values approximates to 1+x. This approximation indicates how for a small change in x, the change in the value of the function is nearly proportional when the base is a positive number close to one.
Considering other bases, they can be related to base e using the identity ax = eln(a)x, where a is a positive real number, and ln(a) is the natural logarithm of a. Thus, whether for common or natural bases, the exponential function is well-defined only for positive bases.
please i need help....the question is.........
Answers
area = H/2*(b1+b2)
8.1 = 1.5/2*(6.7 +b2)
8.1=0.75*(6.7+b2)
10.8=6.7+b2
b2=10.8-6.7
b2=4.1m
Simplify 6 to the fifth power over 7 cubed all raised to the second power. 6 to the seventh power over 7 to the tenth power 6 to the tenth power over 7 to the sixth power 6 cubed over 7 12 to the fifth power over 14 cubed
Answers
Answer:
6 to the tenth power over 7 to the sixth power
Step-by-step explanation:
Given phrase,
6 to the fifth power over 7 cubed all raised to the second power,
[tex]\implies (\frac{6^5}{7^3})^2[/tex]
By using [tex](a^m)^n=a^{mn}[/tex]
[tex]=\frac{6^{5\times 2}}{7^{3\times 2}}[/tex]
[tex]=\frac{6^{10}}{7^6}[/tex]
= 6 to the tenth power over 7 to the sixth power
Simplify the expressions
(6⁵/7³)² = 2143588816/117649
(6⁷/7¹⁰) = 279936/282475249
(6¹⁰/7⁶) = 60466176/117649
(6³/7) = 216/7
(12⁵/14³) = 90855/1001
To simplify the given expressions, we can calculate the numerical values and perform the necessary operations. Let's evaluate each expression:
(6⁵/7³)²:
First, calculate the numerator and denominator:
Numerator: 6⁵ = 6 × 6 × 6 × 6 × 6 = 7776
Denominator: 7³ = 7 × 7 × 7 = 343
Now, substitute the values into the expression and square the result:
(7776/343)² = (7776/343) × (7776/343) = 2143588816/117649
The simplified form is 2143588816/117649.
(6⁷/7¹⁰):
Calculate the numerator and denominator:
Numerator: 6⁷ = 6 × 6 × 6 × 6 × 6 × 6 × 6 = 279936
Denominator: 7¹⁰ = 7 × 7 × 7 × 7 × 7 × 7 × 7 × 7 × 7 × 7 = 282475249
Substitute the values into the expression:
279936/282475249
This expression cannot be simplified further.
(6¹⁰/7⁶):
Calculate the numerator and denominator:
Numerator: 6¹⁰ = 6 × 6 × 6 × 6 × 6 × 6 × 6 × 6 × 6 × 6 = 60466176
Denominator: 7⁶ = 7 × 7 × 7 × 7 × 7 × 7 = 117649
Substitute the values into the expression:
60466176/117649
This expression cannot be simplified further.
(6³/7):
Calculate the numerator and denominator:
Numerator: 6³ = 6 × 6 × 6 = 216
Denominator: 7
Substitute the values into the expression:
216/7
This expression cannot be simplified further.
(12⁵/14³):
Calculate the numerator and denominator:
Numerator: 12⁵ = 12 × 12 × 12 × 12 × 12 = 248832
Denominator: 14³ = 14 × 14 × 14 = 2744
Substitute the values into the expression:
248832/2744 = 90855/1001
The simplified form is 90855/1001.
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Simplify 6 to the fifth power over 7 cubed all raised to the second power. 6 to the seventh power over 7 to the tenth power 6 to the tenth power over 7 to the sixth power 6 cubed over 7 12 to the fifth power over 14 cubed
(6⁵/7³)²
(6⁷/7¹⁰)
(6¹⁰/7⁶)
(6³/7)
(12⁵/14³)
Give the degree and classify the polynomial by the number of terms- 3
A)degree 1, monomial
B)degree 1, binomial
C)degree 0, monomial
D)degree 0, binomial
Answers
Answer:
Step-by-step explanation:
the answer is a
What is the solution to the system of linear equations graphed below?
A. (3.5, -4)
B. (-4, 3.5)
C. (0,3)
D. (0,-4)
Answers
Look at the picture.
Answer: A. (3.5, -4)
Adult male heights are normally distributed with a mean of 70 inches and a standard deviation of 3 inches. The average basketball player is 79 inches tall. Approximately what percent of the adult male population is taller than the average basketball player? 0.135% 0.875% 49.875% 99.875%
Answers
P (Z > 3)? = 1 - F (z) = 1 - F (3) = 0.00135
Answer:
A. 0.135%
Step-by-step explanation:
We have been given that adult male heights are normally distributed with a mean of 70 inches and a standard deviation of 3 inches. The average basketball player is 79 inches tall.
We need to find the area of normal curve above the raw score 79.
First of all let us find the z-score corresponding to our given raw score.
[tex]z=\frac{x-\mu}{\sigma}[/tex], where,
[tex]z=\text{z-score}[/tex],
[tex]x=\text{Raw-score}[/tex],
[tex]\mu=\text{Mean}[/tex],
[tex]\sigma=\text{Standard deviation}[/tex].
Upon substituting our given values in z-score formula we will get,
[tex]z=\frac{79-70}{3}[/tex]
[tex]z=\frac{9}{3}[/tex]
[tex]z=3[/tex]
Now we will find the P(z>3) using formula:
[tex]P(z>a)=1-P(z<a)[/tex]
[tex]P(z>3)=1-P(z<3)[/tex]
Using normal distribution table we will get,
[tex]P(z>3)=1-0.99865 [/tex]
[tex]P(z>3)=0.00135[/tex]
Let us convert our answer into percentage by multiplying 0.00135 by 100.
[tex]0.00135\times 100=0.135%[/tex]
Therefore, approximately 0.135% of the adult male population is taller than the average basketball player and option A is the correct choice.
HELP! Will give Brainliest! Using dimensional analysis, convert 293 cm into m. (1 m= 100 cm)
(and this is also a Chemistry Question)
I get how to work out the other question, but I'm confused on this one
Answers
293 cm ( 1 m / 100 cm ) = 2.93 m
A regular octagon has a radius of 6 ft and a side length of 4.6 ft. what is the approximate area of the octagon? 71 ft2 101 ft2 110 ft2 202 ft2
Answers
Answer:
Option B is correct.
The approximate area of regular octagon is, 101 square ft.
Step-by-step explanation:
Given: A regular octagon has a radius of 6 ft and a side length of 4.6 ft.
To find the area of a regular octagon(A) of side length a is given by :
[tex]A=2\cdot(1+\sqrt{2})a^2[/tex]
Given the length of side, a= 4.6 ft
Substitute the value of a=4.6 ft in the given formula of area:
[tex]A=2\cdot(1+\sqrt{2})\cdot(4.6)^2[/tex] or
[tex]A=(2+2\sqrt{2})\cdot (21.16)[/tex] or
[tex]A=(2+2.828)\cdot(21.16)[/tex]
Simplify:
[tex]A=4.828\cdot 21.16 =102.16048[/tex] square ft.
therefore, the approximate area of regular octagon is, 101 square ft
If x2 + xy + y3 = 1, find the value of y''' at the point where x = 1.
Answers
The third derivative of the function is [tex]y^{'''}=\dfrac{\left(3y^2+12xy-x\right)y''+y'\left(6yy'+12xy'+12y-1\right)-\left(6y-1\right)y'-6yy'}{\left(3y^2+x\right)^2}-\dfrac{2\left(6yy'+1\right)\left(\left(3y^2+12xy-x\right)y'-y\cdot\left(6y-1\right)\right)}{\left(3y^2+x\right)^3}[/tex]and the value at the point x = 1 is 42
How to determine the third derivative at the point x = 1
From the question, we have the following parameters that can be used in our computation:
[tex]x^2 + xy + y^3 = 1[/tex]
Differentiate implicitly
So, we have
[tex]3y^2y' + xy'+y+2x=0[/tex]
Make y' the subject of formula
So, we get
[tex]y'=-\dfrac{y+2x}{3y^2+x}[/tex]
Differentiate the second time
Using a graphing tool, we have
[tex]y''=\dfrac{\left(3y^2+12xy-x\right)y'-6y^2+y}{\left(3y^2+x\right)^2}[/tex]
Differentiate the third time to get the third derivative
Using a graphing tool, we have
[tex]y^{'''}=\dfrac{\left(3y^2+12xy-x\right)y''+y'\left(6yy'+12xy'+12y-1\right)-\left(6y-1\right)y'-6yy'}{\left(3y^2+x\right)^2}-\dfrac{2\left(6yy'+1\right)\left(\left(3y^2+12xy-x\right)y'-y\cdot\left(6y-1\right)\right)}{\left(3y^2+x\right)^3}[/tex]
Recall that
x = 1
Calculating y, we have
[tex]1^2 + (1)y + y^3 = 1[/tex]
[tex]1 + y + y^3 = 1[/tex]
[tex]y^3 + y = 0[/tex]
Factorize
[tex]y(y^2 + 1) = 0[/tex]
So, we have
y = 0 or [tex]y^2 + 1 = 0[/tex]
The equation [tex]y^2 + 1 = 0[/tex] will give a complex solution
So, we have
x = 1 and y = 0
Calculating y', we have
[tex]y'=-\dfrac{0+2(1)}{3 * 0^2+1}[/tex]
[tex]y'=-\dfrac{2}{1}[/tex]
y' = -2
Calculating y", we have
[tex]y''=\dfrac{\left(3y^2+12y-1\right)y'-6y^2+y}{\left(3y^2+1\right)^2}[/tex]
[tex]y''=\dfrac{\left(3(0)^2+12(1)(0)-1\right)(-2)-6(0)^2+0}{\left(3(0)^2+1\right)^2}[/tex]
[tex]y''=\dfrac{\left2}{1}[/tex]
y" = 2
Calculating y", we have
[tex]y^{'''}=\dfrac{\left(3y^2+12xy-x\right)y''+y'\left(6yy'+12xy'+12y-1\right)-\left(6y-1\right)y'-6yy'}{\left(3y^2+x\right)^2}-\dfrac{2\left(6yy'+1\right)\left(\left(3y^2+12xy-x\right)y'-y\cdot\left(6y-1\right)\right)}{\left(3y^2+x\right)^3}[/tex]
Simplifying the denominators, we have
[tex](3y^2 + x)^2 = (3(0)^2 + 1)^2 = 1[/tex]
[tex](3y^2 + x)^3 = (3(0)^2 + 1)^3 = 1[/tex]
So, we have
[tex]y^{'''}=\dfrac{\left(3y^2+12xy-x\right)y''+y'\left(6yy'+12xy'+12y-1\right)-\left(6y-1\right)y'-6yy'}{1}-\dfrac{2\left(6yy'+1\right)\left(\left(3y^2+12xy-x\right)y'-y\cdot\left(6y-1\right)\right)}{1}[/tex]
Divide
[tex]y^{'''}=[\left(3y^2+12xy-x\right)y''+y'\left(6yy'+12xy'+12y-1\right)-\left(6y-1\right)y'-6yy']-[2\left(6yy'+1\right)\left(\left(3y^2+12xy-x\right)y'-y\cdot\left(6y-1\right)\right)][/tex]
Simplifying each term:
[tex](3y^2+12xy-x)y''+y'(6yy'+12xy'+12y-1)-(6y-1)y'-6yy' = (3(0)^2+12(1)(0)-(1))(2) + (-2)(6(0)(-2) +12(1)(-2) + 12(0) - 1) - (6(0) - 1)(-2) - 6(0)(-2)[/tex]
[tex](3y^2+12xy-x)y''+y'(6yy'+12xy'+12y-1)-(6y-1)y'-6yy' = 46[/tex]
Also, we have
[tex]2(6yy'+1)((3y^2+12xy-x)y'-y(6y-1)) = 2(6(0)(-2) + 1)((3(0)^2 + 12(1)(0) - 1)(-2) - 0(6(0)-1))[/tex]
[tex]2(6yy'+1)((3y^2+12xy-x)y'-y(6y-1)) = 4[/tex]
So, the expression becomes (by substitution)
[tex]y^{'''}= 46 -4[/tex]
This gives
[tex]y^{'''}= 42[/tex]
Hence, the third derivative at the point x = 1 is 42
A high-altitude spherical weather balloon expands as it rises, due to the drop in atmospheric pressure. Suppose that the radius r increases at the rate of 0.07 inches per second, and that r = 36 inches at time t = 0. Determine the equation that models the volume V of the balloon at time t, and find the volume when t = 400 seconds.
Answers
The equation for a linear growth/decay is given by the form [tex]y=mx+c[/tex] where [tex]m[/tex] is the rate of increase and [tex]c[/tex] is the value of [tex]y[/tex] when [tex]x=0[/tex]
We have
[tex]m = 0.07[/tex]
[tex]c=36[/tex] when [tex]t=0[/tex]
So the equation is [tex]r=0.07t+36[/tex]
The length of the radius when [tex]t=400 [/tex] seconds is
[tex]r=0.07(400)+36[/tex]
[tex]r=64[/tex] inches
Candis took out a payday loan with an effective interest rate of 15,400%. if she had 220 to invest for a year at this interest rate, how much would make in interest?
A. 3,388,000
B 338,800
C.. 3388
D 33,880
Answers
I=prt
I interest?
P 220
R 15400/100=154
T time 1 year
I=220×154×1
I=33,880
It's d
To find the interest Candis would make from a 15,400% interest rate on a $220 investment for one year, we calculate using the simple interest formula, resulting in $33,880.
Explanation:The question asks us to determine how much interest Candis would make from a payday loan with an effective interest rate of 15,400% if she invested $220 for a year. To calculate the interest earned, we can use the formula for simple interest which is I = Prt, where I is interest, P is principal amount (the initial amount of money), r is the annual interest rate (in decimal form), and t is the time in years.
Converting 15,400% to a decimal, we get 154. Then, apply the formula:
I = $220 × 154 × 1
This gives us:
I = $33,880
Therefore, Candis would make $33,880 in interest after one year, which corresponds to option D.
The first term of a geometric sequence is –2 and the common -1/4. What are the next three terms of the sequence?
Answers
-2(-1/4)(-1/4)(-1/4)
1/2, -1/8, 1/32
Find the length of an arc that subtends a central angle of 135° in a circle of radius 2 mi
Answers
arc length = (3.14 * 2 * 135)/180 = 4.71
A security fence encloses a rectangular area on one side of a park in a city. three sides of fencing are? used, since the fourth side of the area is formed by a building. the enclosed area measures 392392 square feet. exactly 5656 feet of fencing is used to fence in three sides of this rectangle. what are the possible dimensions that could have been used to construct this? area?
Answers
Let y = width of the park
Because the area is 392392 ft², therefore
xy = 392392 (1)
Because three sides of fencing measure 5656 ft, therefore
2x + y = 5656 (2)
That is
y = 5656 - 2x (3)
Substitute (3) into (1).
x(5656 - 2x) = 392392
5656x - 2x² = 392392
2x² -5656x + 392392 = 0
x² - 2828x + 196196 = 0
Solve with the quadratic formula.
x = (1/2)*[2828 +/- √(2828² - 4*196196)]
= 2756.83 or 71.17
Answer:
The possible dimensions are 2756.8 ft and 71.2 ft (nearest tenth)
What is the probability of getting exactly 2 heads, given that the first toss is a head?
Answers
there is a 1/2 probability of getting heads on any one flip
since the first one landed on heads you have a 1/2 probability f getting a 2nd one
Probability = 1/2
Write the standard form of the equation of the line passing through the point (2,5) and perpendicular to the line 4x - y = 2. The answer key says that the answer is x + 4y = 22, but I'm confused on how to get there
Answers
Multiply through by -4, you get -4y + 20 = x - 2, which can be rearranged as x + 4y = 22
To find the perpendicular line's equation, first find the negative reciprocal of the original line's slope. Next, use the point-slope form with the given point. Lastly, rearrange the equation into standard form, resulting in x + 4y = 22.
To find the equation of a line that is perpendicular to another line and passes through a given point, you need to perform a series of steps. The first line's equation is given as 4x - y = 2. Firstly, solve for y to put it in slope-intercept form, y = mx + b. Here, the equation becomes y = 4x - 2, so the slope (m) is 4. The slope of the perpendicular line will be the negative reciprocal of this, which is -1/4.
The next step is to use the point-slope form of the line, which is y - y1 = m(x - x1), where (x1, y1) is the point through which the line passes. For the point (2,5), the equation of the line is y - 5 = -1/4(x - 2). Multiplying both sides by 4 to clear the fraction gives 4y - 20 = -x + 2.
Finally, rearrange the equation to get it into standard form, Ax + By = C, giving us x + 4y = 22. This is the standard form of the equation we were seeking.