Answer:
8 inches
Step-by-step explanation:
The computation of the length, in inches of Segment line G prime A prime is shown below:-
Data provided
In two quadrilateral GAME and G'A'M'E',
ME = 35 inches
AM = GE = 56 inches
M'E' = 14 inches
Also, the perimeter of quadrilateral GAME = 167 inches
GA + AM + ME + GE = 167
Now we will put the values into the above equation
GA + 56 + 35 + 56 = 167
GA + 147 = 167
So,
GA = 20 inch
Therefore
GAME is closely related to G'A'M'E'
Now,
By the property of similar figures,
[tex]\frac{M E}{M' E'} = \frac{GA}{G'A'}[/tex]
[tex]G'A' = \frac{M'E'\times GA}{ME} \\\\ = \frac{14\times 20}{35}[/tex]
= 8 inches
what is the greatest common factor of 6d² and 18d
gcd = 6 ⋅ d
Step-by-step explanation:
We have that
6 d ^2 = 6 ⋅ d ⋅ d and 18 d = 3 ⋅ 6 ⋅ d hence the gcd = 6 ⋅ d
(Hope this helps <3)
Find the following products: a) (−12) × (−11) × (10) b) (−25) × (−8) × (−2) WITH EXPLANATION
Step-by-step explanation:
Hey, there!!
a. (-12)×(-11)×10
Here, (-)×(-)=(+)
(-12)×(-11)=132
so,
=132×10
=1320.
For b.
(-25)×(-8)×(-2)
(-)×(-)=(+)
(-25)×(-8)=200
so,
=200×(-2) { (+)×(-)=(-)}.
= -400.
Therefore, the answer of a. no. is 1320, and no. b is (-400).
Hope it helps....
what is 1/16 times 1/4 as a fraction?
Answer:
[tex]\frac{1}{16}[/tex] x [tex]\frac{1}{4}[/tex] = [tex]\frac{1}{64}[/tex]
multiply 16 by 4 to get the denominator
The fraction 1/16 times 1/4 is equal to 1/64.
To find the product of 1/16 and 1/4, we can multiply the numerators (top numbers) together and the denominators (bottom numbers) together.
1/16 x 1/4
= (1 x 1) / (16 x 4)
The product of the numerators is 1 x 1 = 1, and the product of the denominators is 16 x 4 = 64.
So, the result is:
1/16 x 1/4 = 1/64
Therefore, 1/16 times 1/4 is equal to 1/64.
Learn more about fraction here:
https://brainly.com/question/29019463
#SPJ6
simplify the answer z-4/4+8
Answer:
= z/12 - 1/3
Step-by-step explanation:
z-4/(4+8)
= z-4/12
= z/12 - 4/12
= z/12 - 1/3
1. What is the name of a number that can be written in the form a+bi where a and b are nonzero real numbers?
A. a complex number
B. a real number
C. an imaginary unit
D. a pure imaginary number
2. Which of the following statements is not true?
A. In order for a+bi to be a complex number, b must be nonzero.
B. A complex number is a number that can be written in the form a+bi where a and b are real numbers.
C. For a complex number written in the form a+bi, the value of a is called the real part of the complex number.
D. Every real number is also a complex number.
3. What is the real part of 4−5i?
4. What is the imaginary part of 7−6i?
5. Determine if the statement below is true or false. If it is false, rewrite it so it is true. Rewriting −10−−−−√ in terms of i results in −10i.
A. This statement is true.
B. This statement is false. Rewriting −10−−−−√ in terms of i results in 10i.
C. This statement is false. Rewriting −10−−−−√ in terms of i results in −10−−−−√i.
D. This statement is false. Rewriting −10−−−−√ in terms of i results in 10−−√i.
Re-writing question 5:
5. Determine if the statement below is true or false. If it is false, rewrite it so it is true. Rewriting √-10 in terms of i results in −10i.
A. This statement is true.
B. This statement is false. Rewriting √-10 in terms of i results in (√10)i.
C. This statement is false. Rewriting √-10 in terms of i results in −10√i.
D. This statement is false. Rewriting √-10 in terms of i results in 10√i.
Answer:
1) C. an imaginary number
2) A. In order for a + bi to be a complex number, b must be nonzero
3) 4
4) -6
5) B. The statement is false. Rewriting √-10 in terms of i results in (√10)i
Step-by-step explanation:
1. When a number can be expressed in the form a+bi where a and b are real numbers, then the number is said to be a complex number.
For example, the following are complex numbers where i = √-1 ;
i. 3 + 5i
ii. 4 - 7i
iii. -3 - 9i
Well, even real numbers are a subset of complex numbers. For example,
=> 5 can be written as 5 + 0i
=> -12 can be written as -12 + 0i
-- But when a and b are non-zero real numbers or at least b is a non-zero real number, then the number is said to be an imaginary number.
-- If a is zero, then the number is a purely imaginary number
-- If b is zero, then the number is a purely real number
2. For a number to be called a complex number;
i. it can be written in the form a + bi where a and b are real numbers,
ii. either a or b, or both, may be zero,
iii. a is the real part of the complex number,
iv. b is the imaginary part of the complex number.
v. it could also be a real number since every real number is also a complex number.
3. Given 4 - 5i
The real part is 4
and the imaginary part is -5
4. Given 7 - 6i
The real part is 7
and the imaginary part is -6
5. Rewrite √-10 in terms of i
Remember that i = √-1
Therefore,
√-10 = √(-1 x 10) = √-1 x √10
=> √-10 = √-1 x √10
=> √-10 = i x √10
=> √-10 = (√10)i
On a quiz there are four multiple choice questions worth 3 points each
Answer:
12 pts total
Step-by-step explanation:
Answer:
The four multiple choice are worth 12 points total
Solve the following quadratic equation 3x²-8x+5=0
To solve this equation, let's factor the left side.
Although you can factor it in different ways, I will show you a trick.
First, forget about the 3 and we have x² - 8x + 5.
Now, multiply the 3 by the constant to get 15.
So we have x² - 8x + 15.
Now factor to get (x - 5)(x - 3).
Now divide each of the constants in the
binomials by the leading coefficient, 3.
So we have (x - 5/3)(x - 3/3).
Simplify to get (x - 5/3)(x - 1).
Now move any denominators in front of the x in the binomial.
Moving the 3 in front of the x, we have 3x.
So our answer is (3x - 5)(x - 1) = 0.
So either 3x - 5 = 0 or x - 1 = 0.
Solving from here, we get x = 5/3 or x = 1.
Solv for x for all of these 1. 3x+6=21 2. 33=7x-9 3. 28=7+x need to know now please help !!!!!!
Answer:
[tex] \boxed{ \sf{ \bold{1. \: \: \: x = 5}}}[/tex][tex] \boxed{ \sf{ \bold{2. \: \: x = 6}}}[/tex]
[tex] \boxed{ \bold{ \sf{3. \: \: x = 21}}}[/tex]
Step-by-step explanation:
1. [tex] \sf{3x + 6 = 21}[/tex]
Move constant to right hand side and change its sign
⇒[tex] \sf{3x = 21 - 6}[/tex]
Subtract 6 from 21
⇒[tex] \sf{3x = 15}[/tex]
Divide both sides of the equation by 3
⇒[tex] \sf{ \frac{3x}{3} = \frac{15}{3} }[/tex]
Calculate
⇒[tex] \sf{x = 5}[/tex]
--------------------------------------------------------
2. [tex] \sf{33 = 7x - 9 }[/tex]
Swap the sides of the equation
⇒[tex] \sf{7x - 9 = 33}[/tex]
Move constant to right hand side and change it's sign
⇒[tex] \sf{7x = 33 + 9}[/tex]
Add the numbers
⇒[tex] \sf{7x = 42}[/tex]
Divide both sides of the equation by 7
⇒[tex] \sf{ \frac{7x}{7} = \frac{42}{7} }[/tex]
Calculate
⇒[tex] \sf{x = 6}[/tex]
---------------------------------------------------------
3. [tex] \sf{28 = 7 + x}[/tex]
Swap the sides of the equation
⇒[tex] \sf{7 + x = 28}[/tex]
Move constant to right hand side and change it's sign
⇒[tex] \sf{x = 28 - 7}[/tex]
Subtract 7 from 28
⇒[tex] \sf{x = 21}[/tex]
Hope I helped!
Best regards!!
Which option is an example of an experiment
Answer: Testing the effectiveness of a mouthwash by allowing one group to use it and comparing the results with those of a group that doesn't use it.
Step-by-step explanation: It's the most effective
I WILL GIVE YOU LOTS OF Points
Answer:
D
Step-by-step explanation:
7^2 + 4^2 = [tex]\sqrt{65\\[/tex]
assume it is a triangle and x is the hypotenuse and use Pythagorean theorem
Answer:
D
Step-by-step explanation:
7^2 + 4^2 =
assume it is a triangle and x is the hypotenuse and use Pythagorean theorem
3 packs of soda cost $10 less than 5 packs of soda. Write an equation and solve to find the cost of one pack of soda *
1 point
Answer:
3s = 5s - 10
Step-by-step explanation:
A scientist was in a submarine, 95.7 feet below sea level, studying ocean life. Over the next ten minutes, she went down 25.3 feet. How many feet was she now below sea level?
Answer: she is now 121 feet below sea level.
Step-by-step explanation:
Given, A scientist was in a submarine, 95.7 feet below sea level, studying ocean life.
Over the next ten minutes, she went down 25.3 feet.
Then, she was (95.7+25.3) feet below sea level now. [we will add both distances ]
Then, she was 121 feet below sea level now.
Hence, she is now 121 feet below sea level.
what is 7 over 2 as a decimal
Answer:
3.5
Step-by-step explanation:
I recommend using a calculator. Divide 7/2.
the length of tangent is 15 cm drawn from point whose distance from center of circle is 17 cm find the radius of circle
Answer:
Then what is the radius of the circle? Since, the tangent of any point of a line is perpendicular to the radius through the point of contact. Hence, radius of the circle = 8 cm.
Which equation represents this sentence? SIx times the difference of a number and eight is equal to twelve. A. 6n−8=12 B. 6n+8=12 C. 6(n−8)=12 D. 6(n+8)=12
Answer:
The answer is option CStep-by-step explanation:
Let the number be n
The statement
the difference of a number and eight is written as
n - 8
It's multiplied by 6
That's
6( n - 8)
The result is 12
So we have the final answer as
6( n - 8) = 12Hope this helps you
A manufacturing plant has 25 fuses. 12 failures occurred within 30 days. After each failure, the molding fuse is immediately replaced. What is the MTTF for the fuses
Answer:
MTTF for the fuses = 62.5
Step-by-step explanation:
Given:
Total fuses = 25
Number of failures = 12
Number of days = 30
Find:
MTTF for the fuses.
Computation:
MTTF for the fuses = Total operation time / Number of failures
MTTF for the fuses = (25 × 30) / 12
MTTF for the fuses = 62.5
100 is deposited into an investment account on January 1, 1998. You are given the following information on investment activity that takes place during the year:
April 19,1998 October 30, 1998
Value immediately prior to deposit 95 105
Deposit 2X X
The amount in the account on January 1, 1999 is 115. During 1998, The annual effective dollar weighted yield is 0%, and the annual effective time weighted yield is y. Calculate y.
Answer:
y = - 0.681 % ≈ -0.7 %
Step-by-step explanation:
Given:
April 19,1998 October 30, 1998
Value immediately prior to deposit 95 105
Deposit 2X X
amount in the account on January 1, 1999 = 115
effective dollar weighted yield = 0%
annual effective time weighted yield = y
To find:
Calculate y
Solution:
Given that the dollar weighted return is 0%
100 is deposited into investment account on January 1, 1998. So, add 100 to the deposits 2X X
100 + 2x + x = 115
3x = 115 - 100
3x = 15
x = 15/3
x = 5
Compute y
1 + y = (95/100)(105/105)(115/110)
1 + y = 0.95 * 1 * 1.045
1 + y = 0.99318
y = 0.99318 - 1
y = - 0.0068 * 100
y = - 0.681 % ≈ -0.7 %
y = -0.7 %
Determine if the following relation is a function.
Answer:
It is a function.
Step-by-step explanation:
It is proven via the vertical line test.
Khalid wants to buy a long sandwich for a party. Store A sells a 5 foot sandwich for $42.50. Store B sells a 6 foot sandwich for $49.50. Which store has the better buy? Show your work.
Store A: 1 foot= 42.50÷5 = $8.50
Store B= 1 foot= 49.50÷6 = $8.25
Answer:
Store B has a better buy because the price for 1 foot sandwich is cheaper than Store A.
Hello, I need some help resolving this problem of Trigonometric Identities. Use the reciprocal identities to resolve it SinA+cosA*cotA= cscA
Answer:
Please see steps below
Step-by-step explanation:
Start by writing all trig functions in the equation in terms of their simplest forms using the two basic trig functions: [tex]sin(\alpha) \,\,and\,\,cos(\alpha)[/tex]:
[tex]sin(\alpha)+ cos(\alpha)\,\frac{cos(\alpha)}{sin(\alpha)} = \frac{1}{sin(\alpha)}[/tex]
Now work on the left side (which is the most complicated one), trying to simplify it using the properties for adding fractions with different denominators:
[tex]sin(\alpha)+ cos(\alpha)\,\frac{cos(\alpha)}{sin(\alpha)}=sin(\alpha)+\frac{cos^2(\alpha)}{sin(\alpha)} =\frac{sin^2(\alpha)}{sin(\alpha)} +\frac{cos^2(\alpha)}{sin(\alpha)}=\frac{sin^2(\alpha)+cos^2(\alpha)}{sin(\alpha)}=\frac{1}{sin(\alpha)}[/tex]
where in the last step we have used that the Pythagorean identity for:
[tex]sin^2(\alpha)+cos^2{\alpha)=1[/tex]
Notice that we arrived at the expression: [tex]\frac{1}{sin(\alpha)}[/tex], which is exactly what appears on the other side of the initial equation/identity we needed to prove, so the prove has been completed.
Through a host of various investors, you have finally raised enough capital to begin producing the next summer blockbuster. You have a budget of 279 million dollars, which you must allocate between filming and editing. The general consensus among experts is that filming tends to cost twice as much as editing. How much money should you allocate to filming?
Answer:
$186 million
Step-by-step explanation:
The ratio of costs is ...
filming : editing = 2 : 1
So, the filming cost as a fraction of the total cost is ...
filming : total cost = 2 : (2+1) = 2/3
The allocation to filming is ...
(2/3)($279 million) = $186 million
How much is 2/3 cups plus 1 1/4 cups
[tex]1\frac{11}{12}[/tex]
Step-by-step explanation:[tex]\frac{2}{3}+1\frac{1}{4}=\frac{2}{3}+\frac{5}{4}=\frac{8}{12}+\frac{15}{12}=\\ \\=\frac{8+15}{12}=\frac{23}{12}=1\frac{11}{12}[/tex]
A ladder 10 m long,leans against a vertical wall at an angle of 70° to the ground.if the ladder slips down the wall 4m,find,correct to 2 significant figure
(a) the new angle which the ladder makes with the ground
(b) the distance the ladder slipped back on the ground from it's original position
Answer:
(a) the new angle the ladder makes with the ground is [tex]32.7^o[/tex]
(b) the ladder slipped back about 5 meters
Step-by-step explanation:
Notice that the ladder doesn't change its length in the process.
So let's start from the initial situation , finding the distance from the ground at which the ladder touches the wall when the angle with the ground is 70^o. Notice that this situation is represented by a right angle triangle with the right angle between the wall and the ground (see attached image), and that we can use the sine function to find the side opposite to the 70 degree angle:
[tex]sin(70^o)=\frac{opposite}{hypotenuse} \\sin(70^o)=\frac{h}{10}\\h=10\, sin(70^o) \approx 9.4 \,\,m[/tex]
therefore 9.4 meters is approximately the height at which the ladder touches the wall initially.
Now, if the tip of the ladder goes down the wall 4 meters, it is now at 9.4 m - 4 m = 5.4 m from the ground. We can therefore use again the sine function to solve for the new angle:
[tex]sin(x)=\frac{opposite}{hypotenuse} \\sin(x)=\frac{5.4}{10} \\sin(x)=0.54\\x=arcsin(0.54)\\x= 32.7^o[/tex]
To answer the second question we need to find the original distance from the wall that the bottom of the ladder was originally, and for that we can use the cosine function:
[tex]cos(70^o)=\frac{adjacent}{hypotenuse} \\cos(70^o)=\frac{x}{10}\\x=10\,cos(70^o)\\x\approx 3.4 \,\,m[/tex]
Now fro the new position of the bottom of the ladder relative to the wall:
[tex]cos(32.7^o)=\frac{adjacent}{10} \\adjacent=10\,cos(32.7^o)\\adjacent\approx 8.4\,\,m[/tex]
then the difference in between those two distances is what we need:
8.4 m - 3.4 m = 5 m
what is the simplest form of fraction
Answer:
A fraction is in simplest form when the top and bottom cannot be any smaller, while still being whole numbers. To simplify a fraction: divide the top and bottom by the greatest number that will divide both numbers exactly (they must stay whole numbers).
FOR EXAMPLE
5/10 = 1/2
HERE 1/2 IS THE SIMPLEST FRACTION
log(16x+2) - log(4x+2)= log(2x+4)
Same as my answer last time:
Answer:
NO solution
Step-by-step explanation:
log(16x+2) - log(4x+2) = log((16x+2)/(4x+2)).
remove log
(16x+2)/(4x+2) = 2x + 4
multiply both sides by 2x + 1
8x + 1 = (2x + 4)(2x + 1)
distribute
8x + 1 = 4x^2 + 10x + 4
move to one side
4x^2 + 2x + 3 = 0
factor
but you can't
so you try to use quadratic formula, but you find that the discriminate is less than zero.
So there is no solution when x is a real number.
someone Help if u know the answer pls put the step by step
6 = √v-2
Answer:
64
Step-by-step explanation:
I am assuming the -2 is outside the sqrt.
8 = sqrt(v)
v = 64
A rectangular piece of metal is 20 in longer than it is wide. Squares with sides 4 in long are cut from the four corners and the flaps are folded upward to form an open box. If the volume of the box is 1200 in3,
what were the original dimensions of the piece of metal?
Answer:
width = 12.5
Step-by-step explanation:
rectangular volume = height * width * length
1200 = 4 * w * (20 + 4)
1200 = 4 * w * 24
1200 = 96w
12.5=w
use each of the digits 5 4 3 2 1 exactly once to create two different five digit numbers. Write each number on the line and compare the two numbers by using the symbols < > =
Answer:
12345 < 54321
21435 > 12534
:
Step-by-step explanation:
Given the digits:
1, 2, 3, 4 and 5
We have to use every digit only once and have to make two different five digit numbers.
Using these 5 numbers only once without repetition, we have many numbers possible.
Let us have a look at a few sets and let us compare them.
Set 1: 12345 and 54321
We can see that 12345 is lesser than 54321.
Therefore, we can write (using lesser than sign):
12345 < 54321
Set 2: 21435 and 12534
We can see that 21435 is greater than 12534.
Therefore, we can write (using greater than sign):
21435 > 12534
Question 1 (1 point)
Danny wants to buy a truck in 4 years. He is going to put away $2,500.00 into his savings account that will pay him 6.75% interest compounded
monthly. How much will he have when he withdraws the funds to give a down payment?
Answer:
Amount after 4 years = $3274.125
Step-by-step explanation:
Time t= 4 years
Principal amount p= $2500
Interest rate R= 6.75%
Number of times compounded n= 4*12
Number of times compounded n= 48
Amount A = p(1+r/n)^(nt)
A= 2500(1+0.0675/48)^(48*4)
A= 2500(1+0.001406)^(192)
A= 2500(1.001406)^192
A= 2500(1.30965)
A= 3274.125
Amount after 4 years = $3274.125
Simplify 5x + 3x + 2 +4
Hi
add "x" with "x" and numbers with numbers
5x+3x+2+4 = 8x+6
Answer: [tex]8x+6[/tex]
Add
[tex]5x+3x=8x\\2+4=6\\8x+6[/tex]