Answer: [tex]x=\frac{37}{9}[/tex]
Step-by-step explanation:
By the negative exponent rule, you have that:
[tex](\frac{1}{a})^n=a^{-n}[/tex]
By the exponents properties, you know that:
[tex](m^n)^l=m^{(nl)}[/tex]
[tex](m^n)(m^l)=m^{(n+l)}[/tex]
Rewrite 4, 8 and 32 as following:
4=2²
8=2³
32=2⁵
Rewrite the expression:
[tex](2^2)^{(x-7)}*(2^3)^{(2x-3)}=\frac{32}{2^{(x-9)}}[/tex]
Keeping on mind the exponents properties, you have:
[tex](2)^{2(x-7)}*(2)^{3(2x-3)}=32(2^{-(x-9)}[/tex]
[tex](2)^{2(x-7)}*(2)^{3(2x-3)}=(2^5)(2^{-(x-9)})\\\\(2)^{(2x-14)}*(2)^{(6x-9)}=(2^5)(2^{(-x+9)})\\\\2^{((2x-14)+(6x-9))}=2^{(5+(-x+9))}[/tex]
As the bases are equal, then:
[tex](2x-14)+(6x-9)=5+(-x+9)\\\\2x-14+6x-9=5-x+9\\\\8x-23=14-x\\9x=37[/tex]
[tex]x=\frac{37}{9}[/tex]
Answer:
[tex]x=4\frac{1}{9}[/tex]
Step-by-step explanation:
We are given the following linear equation and we are to solve it:
[tex] 4 ^ { x - 7 } \times 8 ^ { 2x - 3 } = \frac { 32 } { x ^ { x - 8 } } [/tex]
Changing the constants to the same base to make it easier to solve:
[tex] 2 ^ { 2 ( x - 7 ) } \times 2^ { 3 ( 2x - 3 ) } = \frac { 2 ^ 5 } { 2 ^ { x - 9 } } [/tex]
[tex]2^{2x-14} \times 2^{6x-9} = 2^{5}(2^{-x+9})[/tex]
[tex] 2 ^ { 2x - 14 + 6x - 9 } = 2 ^ { 5 - x + 9 } [/tex]
[tex] 2 x + 6x - 14 - 9 = 5 - x + 9 [/tex]
[tex]8x+x=14+9+5+9[/tex]
[tex]9x=37[/tex]
[tex]x=4\frac{1}{9}[/tex]
a taxpayer had a taxable income of 61900 and her spouse had a taxable income of 59400 if they wish to file their tax return jointly which tax bracket will they fall in to
Answer:
25%
Step-by-step explanation:
Just did test
If angle one and angle five a vertical angles and angle one equals 55° then angle five will equal _____?
55º
vertical angles are congruent
Nate mother drives 225 miles to work each month how many miles do she drives in one year show work
Answer:
2700
Step-by-step explanation:
I will mark brainlest
Answer:
Step-by-step explanation:
________
Good evening ,
________________
“”There are 9 pages in the album ,Farah puts the same number of photos on each page ,for a total of 63 photos “”
We can explain the last sentence this way : “ 9p = 63” then p=7
__
:)
A 180 second song is divided into 2 sections. The ratio of the two sections is 3:4. What is the length, to the nearest second, of the longer
Answer:
[tex]103\ seconds[/tex]
Step-by-step explanation:
Let
x-----> the length of the smaller section in seconds
y----> the length of the longer section in seconds
we know that
[tex]x+y=180[/tex] ----> equation A
[tex]\frac{x}{y}=\frac{3}{4}[/tex]
[tex]x=\frac{3}{4}y[/tex] -----> equation B
substitute equation B in equation A and solve for y
[tex]\frac{3}{4}y+y=180[/tex]
[tex]\frac{7}{4}y=180[/tex]
[tex]y=180*4/7[/tex]
[tex]y=103\ seconds[/tex]
A right triangle has legs measuring 4.5 meters and 1.5 meters. The length of a second triangle are proportional to the lengths of the legs of the first triangle. Which could be the length of the legs of the second triangle? A) 6m and 2m B) 8m and 5m C) 7m and 3.5m D) 10m and 2.5m E) 11.25 and 3.75m
Answer:
A. 6m and 2m
E. 11.25m and 3.75m
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional
so
Verify each case
case A) 6m and 2m
[tex]\frac{6}{4.5}=\frac{2}{1.5} \\ \\6(1.5)=2(4.5)\\ \\9=9[/tex]
therefore
The legs are proportional
case B) 8m and 5m
[tex]\frac{8}{4.5}=\frac{5}{1.5} \\ \\8(1.5)=5(4.5)\\ \\12\neq22.5[/tex]
therefore
The legs are not proportional
case C) 7m and 3.5m
[tex]\frac{7}{4.5}=\frac{3.5}{1.5} \\ \\7(1.5)=3.5(4.5)\\ \\10.5\neq15.75[/tex]
therefore
The legs are not proportional
case D) 10m and 2.5m
[tex]\frac{10}{4.5}=\frac{2.5}{1.5} \\ \\10(1.5)=2.5(4.5)\\ \\15\neq11.25[/tex]
therefore
The legs are not proportional
case E) 11.25m and 3.75m
[tex]\frac{11.25}{4.5}=\frac{3.75}{1.5} \\ \\11.25(1.5)=3.75(4.5)\\ \\16.875=16.875[/tex]
therefore
The legs are proportional
Which is the correct formula to find the distance between two points (p,q) and (m,n)?
Answer:
The answer is d = √[(p - m)² + (q - n)²] ⇒ first answer
Step-by-step explanation:
* The distance between any to points (x1 , y1) , (x2 , y2) is
- d = √[square the difference of x- coordinates plus
square the difference of y-coordinates]
∴ d = √[(x2 - x1)² + (y2 - y1)²] or
∴ d² = (x2 - x1)² + (y2 - y1)²
* x2 - x1 is the horizontal distance (h) and y2 - y1
is the vertical distance (v)
- By using Pythagoras theorem
∴ d = √[h² + v²]
∵ The two points are (p , q) and (m , n)
- Put x1 = m and y1 = n
- Put x2 = p and y2 = q
∴ d² = (p - m)² + (q - n)²
∴ d = √[(p - m)² + (q - n)²]
∴ The answer is d = √[(p - m)² + (q - n)²] ⇒ first answer
Answer:
The answer is d = √[(p - m)² + (q - n)²] ⇒ first answer
Step-by-step explanation:
Solve the linear equation:
[tex]4^{2x+7} = 8^{2x-3}[/tex]
Answer:
x = 11.5
Step-by-step explanation:
Taking the logarithm base 2 will transform this to a linear equation.
2(2x+7) = 3(2x -3)
0 = 3(2x -3) -2(2x +7) . . . . subtract the left side
0 = 2x -23 . . . . . . . . . . . . . simplify
0 = x - 23/2 . . . . . . . . . . . . divide by 2
11.5 = x . . . . . . . . . . . . . . . . add 11.5
The solution is x = 23/2 = 11.5.
_____
Check
This value of x makes the equation become ...
4^(2·23/2 +7) = 8^(2·23/2 -3)
4^30 = 8^20 . . . . . true
A polynomial function has roots – 6 and 2. Which of the following could represent this function?
f(x) = (x + 6)(x + 2)
f(x) = (x – 6)(x – 2)
f(x) = (x – 6)(x + 2)
f(x) = (x + 6)(x – 2)
Answer:
f(x) = (x + 6)(x – 2)
Step-by-step explanation:
The roots of a polynomial are the solutions to its factors. This means you can set the factors equal to 0 and the roots are the solution. Working backwards, if the roots are x = -6 and x = 2 then they must have resulted from factors x + 6 and x - 2. This is true since x + 6 = 0 has solution x = -6. And x-2 = 0 has solution x = 2.
So the polynomial has factors (x+6)(x-2). The solution is f(x) = (x + 6)(x – 2).
Answer:
the answer is 4
Step-by-step explanation:
just did it on edge.
your welcome
13) Convert 300 seconds to minutes. There are 60 seconds in 1 minute. A) 5 minutes B) 15 minutes C) 30 minutes D) 150 minutes
Answer:
5 minutes
Step-by-step explanation:
300 seconds / x minutes = 60 seconds / 1 minute
300 = 60x; divide both sides by 60 to get x; 5 = x
A certain volume of water contains 100,000 hydrogen atoms and 50,000 oxygen atoms.
How many hydrogen atoms are in a volume of water containing 4,000,000 oxygen atoms?
Answer:
Based off of the given information I believe the answer is 8,000,000 hydrogen atoms because it appears that the ratio between hydrogen and oxygen atoms in 2:1.
Step-by-step explanation:
Using the 2:1 ratio of hydrogen to oxygen atoms in water (H2O), a volume of water with 4,000,000 oxygen atoms would contain 8,000,000 hydrogen atoms.
We know that water, with the chemical formula H2O, consists of two hydrogen atoms for every oxygen atom. Using this information, for every oxygen atom in water, we need to account for two hydrogen atoms.
Given that a certain volume of water contains 100,000 hydrogen atoms and 50,000 oxygen atoms, we have a 2:1 ratio of hydrogen to oxygen atoms. If we want to determine how many hydrogen atoms are in a volume of water containing 4,000,000 oxygen atoms, we must apply the same 2:1 ratio.
To do so, we multiply the number of oxygen atoms by 2 (since there are two hydrogen atoms for every one oxygen atom), obtaining: 4,000,000 oxygen atoms times 2 = 8,000,000 hydrogen atoms.
given the two sets, which statement is true?
A = {1, 2}
B = {1, 2, 3, 4}
a. B c A
b. 3 c A
c. 4 c A
d. A c B
e. none of the above
Answer:
[tex]\large\boxed{A\subset B}[/tex]
Step-by-step explanation:
[tex]A=\{1,\ 2\},\ B=\{1,\ 2,\ 3,\ 4\}\\\\A\subset B,\ \text{because all elements of the set A are the elements of the set B.}[/tex]
Which polynomial identity will prove that 64+27=91?
A. Difference of Squares
B. Difference of Cubes
C. Sum of Cubes
D. Square of a Binomial
Answer:
Sum of cubes. I just did this test.
Step-by-step explanation:
Honestly I have no real explanation other than a sum would be adding, whereas difference would be subtracting.
Hence, the polynomial identity shows the sum of cubes.
What is the polynomial?
Polynomials are sums of terms of the form [tex]kx^n[/tex], where [tex]k[/tex] is any number and [tex]n[/tex] is a positive integer.
Here given that,
[tex]64+27=91[/tex]
Addition of two values gives us the third number.It is representing the sum of cubes.
Hence, the polynomial identity shows the sum of cubes.
To know more about the polynomial
https://brainly.com/question/11154053
#SPJ5
It said four friends share 3 apples equally what fraction of an apple does each friend get?
Answer:
if i don't doubt then 1/4
Step-by-step explanation:
Brooke gave her dog two whole biscuits and a half of a biscuit.Write a mixed number the represents the amount of dog biscuits she gave her dog.
Your Answer: 2 1/2 (The integer two, and the proper fraction one all over two.)
Explanation: If Brooke gave her dog two whole biscuits and then a half, it would sum up to the improper fraction 5/2 (Five all over two.) When you divide 5 by 2, you get 2.5, which is equivalent to 2 1/2.
Hope this helps ya :D
Kevin and Levi go to the movie theater and purchase refreshments for their friends. Kevin spends a total of $44.50 on 3 bags of popcorn and 4 drinks. Levi spends a total of $84.00 on 4 bags of popcorn and 8 drinks. Write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink. Using these equations, determine and state the price of a bag of popcorn, to the nearest cent.
Answer:
Popcorn costs: $5.75, and drink costs: $2.25.
Step-by-step explanation:
Answer:
44.50 = 3 x + 4 y
84= 4x +8 y
each popcorn bag costs $2.5
Step-by-step explanation:
Hi, to answer this question we have to write a system of equations:
The total cost for Kevin (44.50) is equal to the product of the number of popcorn bags bought (x ) and the price of each bag, plus the product of the number of drinks purchased (y) and the price of each drink (y).
Mathematically speaking
Kevin : 44.50 = 3 x + 4 y
Using the same process for Levi:
Levi : 84= 4x +8 y
The system is
44.50 = 3 x + 4 y (k)
84= 4x +8 y (L)
If we multiply Kevin's equation by 2 and subtract it to Levi's equation:
89 = 6x +8y
-
( 84= 4x +8 y)
----------------------
5 = 2x
solving for x
5/2= x
2.5 =x
each popcorn costs $2.5
I need help on this please guys, thank you.
1. Add or subtract. Show your work for each problem by using boxes, circles, colored underlines, OR grouping
to identify the like terms before you simplify.
4 points each (1 point for correct answer, 3 points for showing ALL work.)
a. (−2x
^2 −4x+ 13)+ (12x
^2 + 2x −25) b. (7x
^2 + 4x − 26)− (−7x^
2 − 3x + 15)
2. Multiply. Show all your work including boxes, circles, colored underlines, distributing, OR grouping to identify
the like terms before you simplify.
6 points (1 point for correct answer, 5 points for showing ALL work)
(5x − 1)(6x
^2 + 3x + 7)
3. Find the roots. Show your work. List your steps correctly.
6 points (2 points for correct answer, 2 points for showing ALL work, 2 points for writing the steps of the
problem)
(n) = n
^2 − 6n − 16
Answer:
The solutions to your three problem question are:
1.
a. 10x^2 −2x -12
b. 14x^2 + 7x -41
2. 30x^3 + 9x^2 + 32x - 7
3.
n1 = 8
n2 = -2
Step-by-step explanation:
1. First problem
We need to Add or subtract the expressions to find the equivalent terms
a) (−2x^2 −4x + 13)+ (12x^2 + 2x −25)
We add together the terms with the same exponent
= (−2x^2 + 12x^2 ) + (−4x + 2x) + (13 - 25)
= (10x^2 ) + (−2x) + (-12)
= 10x^2 −2x -12
b) (7x^2 + 4x − 26)− (−7x^2 − 3x + 15)
= (7x^2 + 4x − 26) + (7x^2 + 3x - 15)
We add together the terms with the same exponent
= (7x^2 + 7x^2 ) + (4x + 3x) + (- 26 -15)
= (14x^2 ) + (7x) + (-41)
= 14x^2 + 7x -41
2. Second problem
(5x − 1)(6x^2 + 3x + 7)
We need to multiply to find the equivalent expression\
(5x − 1)(6x^2 + 3x + 7) = (5x)*(6x^2 + 3x + 7) + (-1)*(6x^2 + 3x + 7)
= [(5x)*(6x^2 + 3x + 7)] + [-6x^2 - 3x - 7]
= [(5x*6x^2) + (5x*3x) + (5x*7)] + [-6x^2 - 3x - 7]
= [(30x^3) + (15x^2) + (35x)] + [-6x^2 - 3x - 7]
We add together the remaining terms
= [(30x^3) + (15x^2 - 6x^2) + (35x - 3x) - 7]
= (30x^3) + (9x^2) + (32x) - 7
= 30x^3 + 9x^2 + 32x - 7
3. Third problem
f(n) = n^2 − 6n − 16
We need to find the roots for the polynomial f(n)
That is, the values of n for which f(n) = 0
We can find an analysis of the function in the images below.
Lets use the quadratic formula
Let y = ax2 + bx + c
a = 1
b = -6
c = -16
x = -b/(2*a) ± sqrt(b^2 -4ac)/(2*a)
x = 3 ± 10/2 = 3 ± 5
roots
n1 = 8
n2 = -2
(Q3) Decide if the function is an exponential growth function or exponential decay function, and describe its end behavior using limits. y=7^-x
Answer:
Choice D is correct
Step-by-step explanation:
We are given the exponential function;
[tex]y=7^{-x}[/tex]
Using the law of exponents the function can be re-written as;
[tex]y=(\frac{1}{7})^{x}[/tex]
The base 1/7 is less than 1 hence this represents an exponential decay function.
For any exponential decay function y;
as x approaches infinity, y will always tend to 0
as x approaches negative infinity, y will always tend to infinity
See the attachment;
Help with this question, please! I don't understand it!
Answer:
18 cm
Step-by-step explanation:
The area (A) of a kite is
A = [tex]\frac{1}{2}[/tex][tex]d_{1}[/tex][tex]d_{2}[/tex], that is
[tex]\frac{1}{2}[/tex] × 8 × [tex]d_{2}[/tex] = 72
4 × [tex]d_{2}[/tex] = 72 ( divide both sides by 4 )
[tex]d_{2}[/tex] = 18 cm
Please help me out................
Answer: 90 Degrees
Step-by-step explanation:
I believe the answer is 90° because the diagonals of a rhombus, just like a square form right triangles. in reality, a rhombus is just a square that was pulled to the side a bit.
A good source to play with rhombuses is on mathisfun. It can help you build a study guide and further your understanding of the subject.
how much tax is owned or how much refund is expected tax due 1324 and tax withheld 678
the proper term is tax LIABILITY ( i e what you would owe if you had not paid in anything ).
then because the liability is greater than the w/h ; 1374 - 678 = owed
Hope this helps!
The tax due is $1,324 and the tax withheld is $678. By subtracting the tax withheld from the tax due, we find that an additional $646 is owed and no refund is expected.
Tax is due or the expected refund, you need to compare the total tax owed to the amount of tax withheld. In this scenario, the tax due is $1,324, and the tax withheld is $678.
First, subtract the tax withheld from the tax due: $1,324 (tax due) - $678 (tax withheld) = $646.
If the result is positive, as it is in this case, it means that you owe $646 more in taxes. If the result were negative, it would indicate an expected refund of that amount.
Therefore, no refund is expected because the tax withheld does not cover the total amount of tax due. The individual will owe an additional $646.
Kelly has 236 feet of fence to use to enclose a rectangular space for her dog. She wants the width to be 23 feet. Draw a rectangle that could be the space for Kelley's dog. Label the length and the width
Answer:
The draw in the attached figure
Step-by-step explanation:
Let
L-----> the length of the rectangle
W----> the width of the rectangle
we know that
The perimeter of a rectangle is equal to
[tex]P=2(L+W)[/tex]
we have
[tex]W=23\ ft[/tex]
so
[tex]P=2L+46[/tex] -----> equation A
[tex]P\leq 236\ ft[/tex] ----> inequality B
substitute equation A in the inequality B and solve for L
[tex]2L+46\leq 236[/tex]
[tex]2L\leq 236-46[/tex]
[tex]2L\leq 190[/tex]
[tex]L\leq 95\ ft[/tex]
The maximum possible value of L is 95 ft
therefore
The rectangle could be
Length 95 ft
Width 23 ft
see the attached figure to see the draw
WILL THANK, GIVE FIVE STARS, AND BRAINLIEST!!!!!
(a) Let the function [tex]$f$[/tex] be defined on the complex numbers as [tex]$\[f(z) = (1+i)z.\]$[/tex] Prove that the distance between [tex]$f(z)$[/tex] and [tex]$0$[/tex] is a constant multiple of the distance between [tex]$f(z)$[/tex] and [tex]$z$[/tex], and find the value of this constant.
(b) Let the function [tex]$g$[/tex] be defined on the complex numbers as [tex]$\[g(z) = (a + 2 i)z\]$[/tex] for some real value of [tex]$a$[/tex]. Then if [tex]$g(z)$[/tex] is equidistant from [tex]$0$[/tex] and [tex]$z$[/tex] for all [tex]$z$[/tex], what is [tex]$a$[/tex] equal to?
Answer:
(a) √2
(b) 1/2
Step-by-step explanation:
(a) The ratio of distances will be the magnitude of the ratio f(z)/(f(z) -z), so will be ...
|(1+i)z/((1+i)z -z)| = |(1+i)/i| = |1-i| = √(1+1) = √2
___
(b) You want |g(z) -0| = |g(z) -z|, so you have ...
|(a +2i)z -0| = |(a +2i)z -z|
|(a +2i)|·|z| = |a-1 +2i|·|z|
Dividing by the magnitude of z and squaring both sides, we have ...
a^2 +4 = (a-1)^2 +4
0 = -2a +1 . . . . . . subtract a^2+4 and simplify
1/2 = a . . . . . . . . . divide by -2, add 1/2
In Cherokee County, the fine for speeding is $17 for each mile per hour the driver is traveling over the posted speed limit. In Cherokee County, Kirk was fined $221 for speeding on a road with the posted speed limit of 30mph. Kirk was fined for traveling at what speed, in miles per hour? Explain you answer in 3 sentences. (2 points)
Answer:
43 miles per hour
Step-by-step explanation:
We know that in Cherokee County, the speed tickets amounts are calculated on the basis of $17 for each mile above the speed limit.
Since Kirk was fined $221, we can easily calculate the excess speed he was caught at by dividing $221 by $17/mile, which gives us 13 miles.
Since he was caught in a zone where the posted speed limit was 30, and that he exceeded it by 13 miles per hour... we know he was going at 43 miles per hour.
The coffee Lily likes is composed of 97.3% water and 2.7% cocoa. The coffee John likes is composed of 96% water and 4% cocoa. How many ounces of water, x, should be added to 30 ounces of coffee that John likes to make the coffee that Lily likes?
30 ounces of the coffee John likes consists of
[tex]0.96\cdot30=28.8[/tex] ounces of water[tex]0.04\cdot30=1.2[/tex] ounces of cocoaTo this mixture we're adding [tex]x[/tex] ounces of water, so that the new mix has a total volume of [tex]30+x[/tex] ounces and matches the composition of the coffee Lily likes. This means it would consist of
[tex]0.973\cdot(30+x)=28.8+x[/tex] ounces of water[tex]0.027\cdot(30+x)=1.2[/tex] ounces of cocoa (same amount of cocoa as before because pure water is being added)Solve for [tex]x[/tex]:
[tex]0.973(30+x)=28.8+x\implies29.12+0.973x=28.8+x[/tex]
[tex]\implies0.39=0.027x[/tex]
[tex]\implies x\approx14.4[/tex]
###
Just to confirm: the new mixture consists of
[tex]28.8+14.4=43.2[/tex] ounces of water[tex]1.2+0=1.2[/tex] ounces of cocoagiving a total volume of [tex]43.2+1.2=44.4[/tex] ounces of coffee, and [tex]\dfrac{43.2}{44.4}\approx0.973[/tex], as required.
A kite is designed on a rectangular grid with squares that measure 1cm by 1 cm. A hexagonal piece within the kite will be reserved for the company logo. Use the grid to identify the perimeter and area of the space reserved for the logo.
Answer:
The answer is the first answer
P = 8 + 8√17 cm
A = 96 cm²
Step-by-step explanation:
* Lets study the figure
- Its a kite with two diagonals
- The shortest one is 12 cm
- The longest one is 26 ⇒ axis of symmetry of the kite
* To find the area reserved for the logo divide
the hexagonal piece into two congruent trapezium
- The length of the two parallel bases are 4 cm and 8 cm and
its height is 8 cm
- The length of non-parallel bases can calculated by Pythagoras rule
∵ The lengths of the two perpendicular sides are 2 cm and 8 cm
- 8 cm is the height of the trapezium
- 2 cm its the difference between the 2 parallel bases ÷ 2
(8 - 4)/2 = 4/2 = 2 cm
∴The length of the non-parallel base = √(2² + 8²) = 2√17
* Now we can find the area of the space reserved for the logo
- The area of the trapezium = (1/2)(b1 + b2) × h
∴ The area = (1/2)(4 + 8) × 8 = (1/2)(12)(8) = 48 cm²
∵ The space reserved for the logo are 2 trapezium
∴ The area reserved for the logo = 2 × 48 = 96 cm²
* The area of the reserved space for the logo = 96 cm²
* The perimeter of the reserved space for the logo is the
perimeter of the hexagon
∵ The lengths of the sides of the hexagon are:
4 cm , 4 cm , 2√17 cm , 2√17 cm , 2√17 cm , 2√17 cm
∴ The perimeter = 2(4) + 4(2√17) = 8 + 8√17 cm
* The perimeter of the reserved space for the logo = 8 + 8√17 cm
If Joe works eight hours per week at $10.75 an hour, how much will he make in one month?
$10.75 x 8 = $86 x 4(weeks) = $344
Multiply his hourly rate by the number of hours per week:
$10.75 x 8 hours = $86.00 per week.
An average month has 4 weeks, so in a 4 week month, multiply his weekly pay by the number of weeks in a month. ( Some months have 5 weeks, so you would need to multiply the weekly amount by 5 weeks).
$86 x 4 weeks = $344
In triangle ABC, c is the hypotenuse, 0=25°, and b =3, Find the length of c ?
Answer:
[tex]\large\boxed{c\approx3.31}[/tex]
Step-by-step explanation:
Use cosine:
[tex]cosine=\dfrac{adjacent}{hypotenuse}[/tex]
[tex]\cos\theta=\dfrac{b}{c}[/tex]
We have:
[tex]\theta=25^o\to\cos25^o\approx0.9063\\\\b=3[/tex]
Substitute:
[tex]\dfrac{3}{c}=0.9063[/tex]
[tex]\dfrac{3}{c}=\dfrac{9063}{10000}[/tex] cross multiply
[tex]9063c=30000[/tex] divide both sides by 9063
[tex]c\approx3.31[/tex]
Lines MA and MB tangent circle k(O) at A and B. Point C is symmetric to point O with respect to point B . Prove: m∠AMC=3m∠BMC.
Answer:
See explanation
Step-by-step explanation:
If MA is tangent to the circle k(O), then radius OA is perpendicular to segment MA.
If MB is tangent to the circle k(O), then radius OB is perpendicular to segment MB.
Consider two right triangles MOA and MOB. In these triangles:
MO is common hypotenuse;∠OAM=∠OBM=90°, because MA⊥OA, MB⊥OB;OA=OB as radii of the circle k(O).Thus, triangles MOA and MOB are congruent by HL theorem. So
∠AMO=∠BMO.
If point C is symmetric to point O with respect to point B, then OC⊥MB. Consider two right triangles MOB and MCB. In these triangles:
MB is common leg;∠OBM=∠CBM=90°, because OC⊥MB;OB=BC, because point C is symmetric to point O.Thus, triangles MOB and MCB are congruent by HL theorem. So
∠BMO=∠BMC.
Hence,
∠AMC=∠AMO+∠BMO+∠BMC=3∠BMC.
Henley could draw 12 sketches in 5 hours . How many sketches could she draw in 3 hours
Henley can draw 7.2 sketches in 3 hours based on the proportion of 12 sketches in 5 hours; however, when rounding to the nearest whole number, she can complete 7 sketches.
The problem at hand is a simple proportion problem where we want to find out how many sketches Henley can make in 3 hours given that she can make 12 sketches in 5 hours. To solve this, we set up a ratio that relates her drawing rate to the time spent drawing:
12 sketches x sketches
----------- = ------------
5 hours 3 hours
We can solve for x by cross-multiplying and then dividing by the coefficient of x:
12 sketches [tex]\times[/tex] 3 hours = 5 hours [tex]\times[/tex] sketches
x = ([tex]12 sketches \times 3 hours[/tex]) / 5 hours
x = 7.2 sketches
Therefore, Henley can draw 7.2 sketches in 3 hours. However, since one cannot draw a fraction of a sketch, we round down to the nearest whole number. Henley can thus draw 7 sketches in 3 hours assuming a consistent drawing speed.