Answers
Answer:
x = 6.5 units
Step-by-step explanation:
The 2 given squares are the on the legs of the right triangle with hypotenuse x
Using Pythagoras' identity in the right triangle
The square on the hypotenuse is equal to the sum of the squares on the other 2 legs , then
x² = 13 + 29.25 = 42.25 ( take square root of both sides )
x = [tex]\sqrt{42.25}[/tex] = 6.5 units
Related Questions
What function represents the next graph?
Answers
Answer:
Option 1: y = (x - 2)² + 2
Step-by-step explanation:
Given the vertex, (2, 2), of an upward-facing parabola, and using the y-intercept of the graph, (0, 6):
Definitions:The vertex form of the quadratic equations is:
y = a(x - h)² + k
where:
(h, k) is the vertex.
The value of h represents the horizontal translation of the graph. h > 0 represents the horizontal shift of the graph h units to the right. h < 0 shifts the graph |h | units to the left. The value of k represents the vertical translation of the graph. k > 0 shifts the graph k units upward. k < 0 shifts the graph |k | units down.The sign of a determines the direction of the graph's opening. The value of a also determines the vertical stretch or shrink of the graph.
If a is positive (or a > 1), then the graph opens upward. The value of a > 1 also represents the vertical stretch of the graph. If a is negative (or a < 0), then the graph opens down.The value of 0 < a < 1 represents the vertical shrink or compression of the graph. Solution:Substitute the values of the vertex (2, 2) and the y-intercept, (0, 6) into the vertex form to solve for the value of the coefficient, a:
y = a(x - h)² + k
6 = a(0 - 2)² + 2
6 = a(-2)² + 2
6 = 4a + 2
Subtract 2 from both sides
6 - 2 = 4a + 2 - 2
4 = 4a
Divide both sides by 4 to solve for a :
[tex]\displaytext\mathsf{\frac{4}{4} \:=\frac{4a}{4}}[/tex]
a = 1
Quadratic Equation in Vertex Form:Therefore, given the vertex, (2, 2) and a = 1, the quadratic equation in vertex form is: y = (x - 2)² + 2, thereby matching Option 1.
Given that rectangle ABCD has coordinates A(0,0), B(12,0), C(12,6), and D(0,6), F is the midpoint of AB¯¯¯¯¯, and G is the midpoint of CD¯¯¯¯¯, which of the following proves that FB=GC?
1. By the Distance Formula, the coordinates of F are (6, 0) and the coordinates of G are (6, 6).
Then FB = 12, and GC = 12.
Thus FB = GC.
2. By the Distance Formula, the coordinates of F are (6, 12) and the coordinates of G are (6, 0).
Then FG = 6, and GC = 6.
Thus FG = GC.
3. By the Midpoint Formula, the coordinates of F are (6, 0) and the coordinates of G are (6, 6).
Then FB = 6, and GC = 6.
Thus FB = GC.
4. By the Midpoint Formula, the coordinates of F are (6, 6) and the coordinates of G are (6, 0).
Then FB = 6, and GC = 6.
Thus FB = GC.
Answers
The midpoint of the sides [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are the points that half way between [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] respectively.
The option that proves [tex]\overline{FB}[/tex] = [tex]\overline{GC}[/tex] is option 3
3. By the Midpoint Formula, the coordinates of F are (6, 0) and the coordinates of G are (6, 6). Then [tex]\overline{FB}[/tex] = 6, and [tex]\overline{GC}[/tex] = 6. Thus [tex]\overline{FB}[/tex] = [tex]\overline{GC}[/tex]Reasons:
The given coordinates of the vertices of rectangle ABCD are;
A(0, 0), B(12, 0), C(12, 6), and D(0, 6)
The midpoint of side [tex]\overline{AB}[/tex] = Point F
The midpoint of side [tex]\overline{CD}[/tex] = Point F
The coordinates of point F is given by the midpoint formula, as follows;
[tex]\displaystyle \mathrm{The \ midpoint \ of \ a \ line \ with \ endpoints \ (x_1, \ y_1) \ and \ (x_2, \ y_2) = \mathbf{ \left(\frac{x_1 + x_2}{2}, \ \frac{y_1 + y_2}{2} \right) }}[/tex]
Which gives;
[tex]\displaystyle \mathrm{The \ coordinate \ of \ F \ the \ midpoint \ of \ \overline{AB} = \mathbf{ \left(\frac{0 + 12}{2}, \ \frac{0 + 0}{2} \right)} =(6,\ 0)}[/tex]
The coordinates of point F = [tex]\underline{(6, \ 0)}[/tex][tex]\displaystyle \mathrm{The \ coordinate \ of \ G \ the \ midpoint \ of \ \overline{CD} = \left(\frac{12 + 0}{2}, \ \frac{6 + 6}{2} \right) =(6,\ 6)}[/tex]
The coordinates of point G = [tex]\underline{(6, \ 6)}[/tex][tex]\overline{FB}[/tex] is parallel to the x-axis, therefore;
The length of [tex]\overline{FB}[/tex] = 12 - 6 = 6Similarly, [tex]\overline{GC}[/tex] is parallel to the x-axis, therefore;
The length of [tex]\overline{GC}[/tex] = 12 - 6 = 6Which gives;
[tex]\overline{FB}[/tex] = [tex]\overline{GC}[/tex] = 6The correct option is that proves [tex]\overline{FB}[/tex] = [tex]\overline{GC}[/tex] is option 3.
By the Midpoint Formula, the coordinates of F are (6, 0) and the coordinates of G are (6, 6). Then [tex]\overline{FB}[/tex] = 6, and [tex]\overline{GC}[/tex] = 6. Thus [tex]\overline{FB}[/tex] = [tex]\overline{GC}[/tex]
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Which expression is equivalent to the given expression?
Answers
Step-by-step explanation:
16x²y⁵16x²y⁵ is the answer
Mark me BRAINLIEST pls!When solving an equation, Tina gets to the last of line of her work and is left with "7=7." What does this mean?
A
The solution is 7
B
There is infinite solutions.
С
There is only one solution
D
There is no solution.
Answers
Answer:
B , there are infinite solutions.
Step-by-step explanation:
If you end an equation with a true statement, such as 0 = 0, then any value of the variable(s) you are solving for will satisfy the equation. This means that there are infinite solutions.
ashtons containor of water holds 80 milliliters. nelsons container holds 9/16 of that amont. how many milliniters of water do the two containors hokd together
Answers
Answer: Neither
Step-by-step explanation: Technically the containers hold no water at all as they hold only the bottles in which the water is actually contained. So the answer I suppose is 'Neither'.
Identifying values in the domain PLS HELP
Answers
equivalent to -36 - 8
Answers
Answer:
-44
Step-by-step explanation:
Answer: -44
Step-by-step explanation: same as 36 + 8 and make the answer negative.
Please answer quickly
Part 1. Using the two functions listed below, insert numbers in place of the letters a, b, c, and d so that f(x) and g(x) are inverses.
f(x)=x+a/b
g(x)=cx-d
Part 2. Show your work to prove that the inverse of f(x) is g(x).
Part 3. Show your work to evaluate g(f(x)). Part 4. Graph your two functions on a coordinate plane. Include a table of values for each function. Include five values for each function. Graph the line y=x on the same graph.
Part 4. Graph your two functions on a coordinate plane. Include a table of values for each function. Include five values for each function. Graph the line y=x on the same graph.
Task 2
Part 1. Create two radical equations: one that has an extraneous solution, and one that does not have an extraneous solution. Use the equation
a√x+b+c=d
Part 2. Use a constant in place of each variable a, b, c, and d. You can use positive and negative constants in your equation. Part 2. Show your work in solving the equation. Include the work to check your solution and show that your solution is extraneous.
Part 3. Explain why the first equation has an extraneous solution and the second does not.
Answers
f(x)=(x+a)/b
or bf(x)=x+a
let f(x)=y
by=x+a
flip x and y
bx=y+a
or y=bx-a
or f^{-1}(x)=bx-a
also g(x) is inverse of f(x)
bx-a=cx-d
so b=c,a=d
again let g(x)=y
y=cx-d
flip x and y
x=cy-d
cy=x+d
y=(x+d)/c
or g^{-1}(x)=(x+d)/c
also f(x) is inverse of g(x)
so (x+a)/b=(x+d)/c
so a=d,b=c
so in either case a=d,b=c
take b=c=1
a=d=2
f(x)=(x+2)/1=x+2
g(x)=1x-2=x-2
so f(x) and g(x) are two parallel lines f(x) with y- intercept=1 and slope 0
g(x) with y-intercept -2 and slope 0
if we take b=c=2,a=d=3
f(x)=(x+3)/2=x/2+3/2
g(x)=2x-3
here f(x) is of slope 1/2 and y-intercept 3/2
g(x) is of slope 2 and y intercept -3
part 3.
f(f(x))=g((x+a)/b)=c[(x+a)/b]-d=(c/b)(x+a)-d
An inverse function or an anti function exists described as a function, which can change into another function. In other words, if any function “f” carries x to y then, the inverse of “f” will carry y to x.
Part 1: f(x) = (x+2) / 3 and g(x) = 3y-2.
Part 2: g(x) = 3x - 2, the inverse.
Part 3: g(f(x)) = x showing that f(x) and g(x) are mutual inverses.
What is inverse function?
An inverse function in mathematics exists function which "reverses" the another function.
TASK 1
Part 1
Let y = f(x) = (x + a) / b
x = g(y) = by-a = cy-d,
so c = b and d = a.
Let d = a = 2 and c = b = 3
f(x) = (x+2) / 3 and g(x) = 3y-2.
Part 2
y = f(x) = (x+2) / 3
3y = x+2
x = 3y-2 = g(y)
so g(x) = 3x - 2, the inverse.
Part 3
g(f(x)) = 3
f(x)-2 = 3(x+2)/3-2 = x+2-2 = x,
so g(f(x)) = x showing that f(x) and g(x) exists mutual inverses.
x -2 -1 0 1 2
f(x) 0 1/3 2/3 1 4/3
g(x) -8 -5 -2 1 4
Part 4
The graph is given below.
TASK 2
Part 1
(a) Let a=1, b=2, c=3, d=6: [tex]$\sqrt{x}[/tex]+2+3=6 ; [tex]\sqrt{x}[/tex]-6=-5
(b) Let a=-1, b=2, c=3, d=4
(a) Multiply both sides by
[tex]$\sqrt{x}+6: x-36=-5(\sqrt{x}+6)=-5 \sqrt{x}-30[/tex]
[tex]$ x-36+30=-5 \sqrt{x }[/tex]
[tex]$ x-6=-5 \sqrt{x}$[/tex]
Square both sides:
[tex]$x^{2} -12 x+36=25 x ; x^{2} -37 x+36=0=(x-36)(x-1)$[/tex].
Part 2
(a) So x=36 or 1 (apparently).
Substitute x=36 in the original equation: 6+2+3=6, 11=6 is not true.
So x=36 is an extraneous solution.
substitute x=1: 1+2+3=6 is true, so x=1 exists the actual solution.
(b) [tex]$-\sqrt{x}+2+3=4 ;-\sqrt{x}=-1$[/tex]; multiply both sides by -1: [tex]$\sqrt{x}=1$[/tex]; square both sides: x=1.
Substitute x=1 in the original equation: -1+2+3=4 is true.
So x = 1 is the solution.
Part 3
(a) the act of squaring both sides resulted in creating an extraneous solution [tex]$\left((-5)^{2} =25=5^{2} \right)$[/tex].
(b) the solution was simpler and there was no ambiguity.
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Choose the correct definition of
(2)
from below.
A.
kI
n!(n – kỳ!
B.
n!
(n-k)!
C.
!
k!(n-k)!
D.
n!
K!(K-n)!
Answers
Answer:
Answer is C noumber
Step-by-step explanation:
We know that a combination is a collection of the items where the order doesn't matter. It is a way to calculate the total outcomes of an event where order of the outcomes does not matter. It is denoted by C(n,k) or (n,k) or (n/k).
The formula for the number of combinations of n things taken r at a time is given by :-
C(n,k)=(n/k)=\frac{n!}{k!(n-k)!}C(n,k)=(n/k)=
k!(n−k)!
n!
Hence, C is the right option.
please answer it i need help
Answers
This is karma for doing this to some one else :)
regdcd gvfd vcds xgrcd xre dse dxf crdx vcfx gvf c fcvr fvcrdgbv
What would the slope of a line perpendicular to y=-4x+5 equal?
Answers
Answer:
Using the slope-intercept form, the slope is 4 4 .
Answer: Using the slope-intercept form, the slope is 4 4 .
Explanation: so your answer is 4 4.
A builder is buying boxes of nails. She has $187 to spend and each box of nails costs $4.
Answers
Answer:
46 boxes of nails
Step-by-step explanation:
She has $187 to spend, the maximum.
187/4 = 46.75
Since she cannot buy 0.75 of a box of nails, she can only buy 46. So she is left with an extra $3 and buys 46 boxes of nails.
Hope this helps, and please mark me the brainliest! :D
can someone help me please
Answers
Answer:
Step-by-step explanation:
One
The exterior angles of a triangle add up to 360. You know two of them. Therefore you can find w.
125 + 90 + w = 360 Combine like terms on the left
215 + w = 360 Subtract 215 from both sides
w = 360 - 215 Combine
w = 145
Two.
The polygon has 4 exterior angles. They too should add up to 360.
88 + x + 108 + 115 = 360 Combine the left had side
x + 311 = 360 Subtract 311 from both sides
x = 360 - 311 Combine
x = 49
What have you learned? You should notice that all polygons have exterior angles that add up to 360
A pile of newspapers in Mr. Moore’s ELA class was 17 ¾ inches high. Each consecutive week, for the next 5 weeks, the height of the pile of newspapers increases by 8 712 inches each week. What was the height, in inches , of the pile after 3 weeks? Step by step plz
Answers
Answer:
43 1/2
Step-by-step explanation:
answer will be:
original height plus 3 times 8 7/12 inches
3 times 8 7/12 can be done by converting the mixed number to an improper fraction:
[tex]\frac{3}{1}[/tex] · [tex]\frac{103}{12}[/tex] = [tex]\frac{103}{4}[/tex] = 25 3/4
25 3/4 added to 17 3/4 equals 42 6/4 which is 42 + 1 1/2 = 43 1/2
Benny has a baseball card collection he has 13,789 cards he wants to put the card in a scrapbook that holds 15 cars on a page how many pages does Denny need in his scrapBook.
Answers
Answer:
920 pages
Step-by-step explanation:
Divide 13,789 by 15, you should get 919.27 so just round up so you can hold all the cards.
A trader has a mixture of 5c and 10c coins. He has 50 coins in all, with a total value of $4.20. How many of each coin does he have?
Answers
Answer:
16 5c coins
34 10c coins
Step-by-step explanation:
(I prefer to use whole numbers)
5x + 10y = 420
x+y=50
multiply the bottom problem by -5
5x +10y =420
-5x -5y = -250
combine the problems
5y = 170
divide by 5
y = 34
that means x = 16
34 10c coins
16 5c coins
-- Gage Millar, Algebra 1/2 tutor
The number of 5 cent coins are 16 and the number of 10 cent coins are 34.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Given that, a trader has a mixture of 5 c and 10 c coins.
Let the the number of 5 c coins be x and the number of 10 c coins be y.
He has 50 coins in all, with a total value of $4.20.
So, x+y=50 ---------(I)
5x+10y=420 ---------(II)
Multiply equation (I) by 5, we get
5x+5y=250 ---------(III)
Subtract equation (III) from (II), that is
5x+10y-(5x+5y)=420-250
⇒ 5y=170
⇒ y=34
Substitute y=34 in equation (I), we get
x=16
Therefore, the number of 5 cent coins are 16 and the number of 10 cent coins are 34.
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A car is sold for £7,800 If this represents a depreciation in value to 60% of its original
price, then calculate the original price of the car.
Answers
Answer:
6,543
Step-by-step explanation:
This is my guess ONLY.
For the problem 12(-3)(-2), will the answer be positive or negative?
Answers
Answer:
the answer is positive.
Step-by-step explanation:
12(-3)(-2)
the 2 negatives cancel out, so you get a positive 6
12(6)
72
positive 72
hope this helped!
mark me brainliest :D
Find the distance between the points (6,3) and (-5,3)
Answers
Answer:
11
Step-by-step explanation:
Here is the problem: (Picture)
Answers
Answer:
c
Step-by-step explanation:
6 of 10
Type the expression that results from the following series of
steps:
Start with k, subtract 2, multiply by 6, then add 8.
Answers
Step step :
k k - 2k - 2 × 6 k - 2 × 6 + 8-HayabusaBrainly
Could someone help me solve for this question? I have a hard time
Understanding. Thanks, the question is
Which statement describes the end behavior of the exponential equation y = 3^x?
A as x -> - ♾ , y -> - ♾
B as x -> - ♾ , y -> 0
C as x - > ♾ , y -> - ♾
Answers
Answer:
the answer is b ok understand
Geometry:
Classify the relationship between each pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
1. <6 and <3
2. <4 and <7
3. <5 and <4
Pls help me i have no idea what i'm doing:(
Answers
Answer:
Step-by-step explanation:
.<6 and <3
SOLUTION:
Interior angles that are non adjacent and lie on
opposite. In the figure, angles <5 and <4 are consecutive interior
angles. sides of the transversal are alternate interior
angles.
<4 and <7
SOLUTION:
In the figure, angles 1 and 3 are corresponding
angles. Use the Corresponding Angles Postulate:
If two parallel lines are cut by a transversal, then
each pair of corresponding angles is congruent
HELP ME PLEASE
whats 9+10?
Answers
Answer:
21
Step-by-step explanation:
Answer:
19
Step-by-step explanation:
CAN SOMEONE PLEASE HELP ME!! this is like my 4th time trying to re-answer this question so PLEASE help!
Using the information below draw a diagram, making sure to label the sides and angles, to help answer the following 2 questions. Don’t forget to label your answer.
∆ABC ≅∆DEF
AC = 15 in., AB = 24 in., m∠A = 34°, m∠C = 124°
What are the values of DE and m∠E?
DE = ______ m∠E = ________
Answers
Answer:
go to https://www.rcboe.org/cms/lib010/GA01903614/Centricity/Domain/1030/Ch.%203.3.pdf
Step-by-step explanation:
i think that will help
pls help plsss
help
plss
Answers
Answer:
number 2 is c, number 3 is c
What is its inverse? F= {5,-1),(4,8),(6,8),(4,9)
Answers
Answer:
Hence, f −1 (x) = x/3 + 2/3 is the correct answer.
Step-by-step explanation:
Verify (f ∘ f−1) (x) = x
(f ∘ f−1) (x) = f [f −1 (x)]
= f (x/3 + 2/3)
⟹ 3(x/3 + 2/3) – 2
⟹ x + 2 – 2
= x
Hence, f −1 (x) = x/3 + 2/3 is the correct answer.
Step-by-step explanation:
m(gradient) =y2-y1/x2-x1
=8-(-1) /4-5
=8+1/-1
=9/-1
=-9
y-y1=m(x-x1)
y-(-1)=-9(x-5)
y+1=-9x+45
y=9x+45-1
y=9x+44(rule)
Inverse>y+44=9x
y+44/9=9x/9
x=y+44/9
Therefore inverse is y=x+44/9
The ratio of boys to girls in Mr. Baker’s social studies class is 2 to 3. If there are 30 total students in the class, how many more girls are in the class than boys?
Answers
Answer:
There would be 10 more Girls.
Solve for x using
multiplication.
Cross
-
3x - 3
5
=
2x - 2
4.
x = [?]
Answers
Answer:
x = 1
Step-by-step explanation:
[tex]\frac{3x-3}{5}[/tex] = [tex]\frac{2x-2}{4}[/tex] ( cross- multiply )
4(3x - 3) = 5(2x - 2) ← distribute parenthesis on both sides
12x - 12 = 10x - 10 ( subtract 10x from both sides )
2x - 12 = - 10 ( add 12 to both sides )
2x = 2 ( divide both sides by 2 )
x = 1
Someone could help me with problem 3-76 (b) pls
Answers
Answer:
ok so you see the equation at the top... you are going to "plug in" the number in the "in" row to get the "out number
Step-by-step explanation:
example
in: 4
-2(-4)+1
8+1
9
so for the out row under -4 you would put 9
-2(-3)+1
6+1
7
so for the out row under 3 you would put 7
Answer:
...
Step-by-step explanation: