Answer:
See below.
Step-by-step explanation:
Approximation:
The wall is 8 ft wide.
The frame is 22 1/4 inches wide. 22 1/4 inches is close to 2 ft since 2 ft = 24 inches.
8 ft - 2 ft = 6 ft
There will be approximately 6 ft of space tot he sides of the frame.
6 ft/2 = 3 ft
3 ft * 12 in./ft = 36 in.
There will be approximately 36 in. on each side of the frame.
Exact:
8 ft - 22 1/4 in. = 8 * 12 in. - 22 1/4 in. =
= 96 in. - 22 1/4 in.
= 95 4/4 in. - 22 1/4 in.
= 73 3/4 in.
The total amount of width of the wall not occupied by the frame is 73 3/4 in.
Half of that amount is on each side of the frame.
(73 3/4 in.)/2 = (73 3/4 in.) * 1/2 = (73 * 1/2 + 3/4 * 1/2) in. =
= 36 1/2 in. + 3/8 in.
= 36 4/8 in. + 3/8 in.
= 36 + 7/8 in.
= 36 7/8 in.
Which of the following lengths and widths represents a rectangle whose diagonal is rational? Question 3 options: length = 2, width = 1 length = 4, width = 4 length = 3, width = 2 length = 4, width = 3
Answer:
Correct option is length = 4, width = 3.
Step-by-step explanation:
Given:
Diagonal of a rectangle is rational.
To find:
Which of the following length and width options represent a rectangle ?
options:
length = 2, width = 1
length = 4, width = 4
length = 3, width = 2
length = 4, width = 3
Solution:
First of all, let us consider a rectangle as shown in the attached answer image.
Rectangle ABCD.
Width of rectangle is AB.
Width of rectangle is BC.
And the diagonal AC or BD can be found by using Pythagorean Theorem:
[tex]\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow AC^{2} = AB^{2} + BC^{2}\\\Rightarrow Diagonal^{2} = Length^{2} + Width^{2}[/tex]
Now, let us find diagonal for each option and check whether it is rational or not.
Option 1:
length = 2, width = 1
[tex]Diagonal^{2} = 2^{2} + 1^{2}\\\Rightarrow Diagonal^{2} = 5\\\Rightarrow Diagonal = \sqrt5[/tex]
Not rational
Option 2:
length = 4, width = 4
[tex]Diagonal^{2} = 4^{2} + 4^{2}\\\Rightarrow Diagonal^{2} = 32\\\Rightarrow Diagonal = 4\sqrt2[/tex]
Not rational.
Option 3:
length = 3, width = 2
[tex]Diagonal^{2} = 3^{2} + 2^{2}\\\Rightarrow Diagonal^{2} = 13\\\Rightarrow Diagonal = \sqrt{13}[/tex]
Not rational.
Option 4:
length = 4, width = 3
[tex]Diagonal^{2} = 4^{2} + 3^{2}\\\Rightarrow Diagonal^{2} = 25\\\Rightarrow Diagonal = \sqrt{25} = 5[/tex]
Diagonal is rational.
Correct option is length = 4, width = 3.
A plumber’s apprentice needs to cut a 54-inch length of pipe so that one piece is twice the length of the other piece. How far from the endpoint should the apprentice cut the pipe?
Answer:
18 inches
Step-by-step explanation:
To to this you would just divide 54 by 3 and you would get how far away from the endpoint which is 18 inches
What the correct answer now
Answer:
527.52 m²
Step-by-step explanation:
The surface area (A) of the cone is calculated as
A = area of base + curved area
= πr² + πrl ( r is the radius and l the slant height )
= 3.14 × 7² + 3.14 × 7 × 17
= 3.14 × 49 + 3.14 × 119
= 3.14(49 + 119)
= 3.14 × 168
= 527.52 m²
50 points and brainliest, please show your work :D (trying to learn so an explanation would be appreciated)
( a ) Well we know that the limit for the range is 400 dollars, as ( 1 ) her greatest balance was 400 dollars, and ( 2 ) the balance is dependent on the days, and hence represents the range. Respectively the limit for the domain would be 3 weeks.
( b ) Remember that B(0) models the balance over the course of 0 days. As you can see that starting mark is about half of the greatest balance on the graph, 400 dollars. Therefore you can estimate B(0) to be $200.
( c ) B(12) models the balance over the course of 12 days. It mentions that at B(12) the balance reaches $0, so in function notation that would be :
B(12) = 0
( d ) Segment 4 would represent that information. As you can see on the graph, the only time period with which the balance became 0 is represented by the fourth segment.
4n-6 (n - 2) = -24 + 7n
O No Solutions
O All Real Numbers
O n = 4
O n = 2.9
The sum of the digits of a two digit number is 10 when the dishes are reversed the number increases by 18 find the original number
Answer:
Step-by-step explanation:
Hello, we can write this number ab where a and b are integer betwen 0 and 9.
For instance, 54, a = 5, b = 4
And then, we can say ab = 10 * a + b.
For instance, 54 = 50 + 4 = 5*10 + 4.
The sum of the digits of a two digit number is 10.
a + b = 10
When the dishes are reversed the number increases by 18.
10b + a = 18 + 10a + b
9b = 18 + 9a
b = 2 + a
We replace in the first equation to get.
a + 2 + a = 10
2a = 10 -2 = 8
a = 4
and then, b = 6
So, the number is 46.
Thank you
Multiply. √6x⋅√15xy⋅√20 Please answer as quickly as possible
Answer:
[tex]30x\sqrt{2y}[/tex]
Step-by-step explanation:
First, multiply sqrt.(6x) by sqrt.(15xy)
That equals sqrt.[tex]\sqrt{90x^{2}y } *\sqrt{20}[/tex]
then, rewrite [tex]90x^{2} y[/tex] as (3x)^2 * (10y)
you have [tex]\sqrt{(3x)^{2} *(10y)} *\sqrt{20}[/tex]
Next, pull the terms from out under the radical, to get:
[tex]3x\sqrt{10y} *\sqrt{20}[/tex]
Now rewrite 20 as 2^2 * 5
You get [tex]3x\sqrt{10y} *(2\sqrt{5} )[/tex]
Multiply everything together to get: [tex]6x\sqrt{50y}[/tex]
Now rewrite 50 y as 5^2 * 2y
You end up with [tex]6x\sqrt{5^{2}*(2y)}[/tex]
Then, pull out the terms from under the radical. You get:
[tex]6x(5\sqrt{2y})[/tex]
Finally, multiply the 5 and 6 together to get: [tex]30x\sqrt{2y}[/tex]
Answer:
[tex]\boxed{30\sqrt{2} x^2 y}[/tex]
Step-by-step explanation:
[tex]\sqrt{6} *x*\sqrt{15} * x*y*\sqrt{20}[/tex]
[tex]\sf Multiply[/tex]
[tex]\sqrt{6}\sqrt{15}\sqrt{20}*x*x*y[/tex]
[tex]\sqrt{6*15*20}*x^2 *y[/tex]
[tex]\sqrt{1800}x^2y[/tex]
[tex]\sf Simplify[/tex]
[tex]\sqrt{900} \sqrt{2} x^2y[/tex]
[tex]30\sqrt{2} x^2 y[/tex]
Two angles form a
linear pair. The
measure of one
angle is three times
the measure of the
other. Find the
measure of each
Answer:
45° and 135°
Step-by-step explanation:
A linear pair of angles sum to 180°
let one angle be x , then the other is 3x ( 3 times the other ), thus
x + 3x = 180
4x = 180 ( divide both sides by 4 )
x = 45
Thus the 2 angles are
x = 45° and 3x = 3 × 45° = 135°
The measure of two angles are 135 and 45 degrees if the two angles form a linear pair. The measure of one angle is three times the measure of the other.
What is an angle?When two lines or rays converge at the same point, the measurement between them is called a "Angle."
It is given that:
Two angles form a linear pair. The measure of one angle is three times the measure of the other.
As we know,
If two angles form a linear pair it means the angle made by the pair is 180 degrees
Let the two angles are x and y
x + y = 180
x = 3y (one angle is three times the measure of the other)
Solving the two linear equations in two variable:
3y + y = 180
4y = 180
y = 180/4
y = 45 degrees
x = 3(45) = 135 degrees
Thus, the measure of two angles are 135 and 45 degrees if the two angles form a linear pair. The measure of one angle is three times the measure of the other.
Learn more about the angle here:
brainly.com/question/7116550
#SPJ2
Please help me answer this question. -15 - g/3 = -5.
What is g?
Answer:
g = -30
Step-by-step explanation:
-15 - g/3 = -5
Add 15 to each side
-15+15 - g/3 = -5+15
-g/3=10
Multiply by -3 to each side
-g/3 * -3 = 10*-3
g = -30
Answer:
g= -30
Step-by-step explanation:
after writing down the problem, multiply both sides of the equation by 3 to get -45-g= =15. then subtract 15 from both sides to get g=-30, which is your answer. hope this helps!
Write the equation 5x − 2y = 10 in the form y = mx + b. y equals start fraction five over two end fraction x minus 10 y equals start fraction five over two end fraction x minus five y equals start fraction five over two end fraction x plus five y equals negative start fraction five over two end fraction x minus five
Answer:
y = 5/2x - 5
Step-by-step explanation:
You have to rearrange the equation so that it is equal to y.
5x - 2y = 10
(5x - 2y) - 5x = -5x + 10
-2y = -5x + 10
(-2y)/-2 = (-5x)/-2 + (10)/-2
y = 5/2x - 5
The parent council is in charge of making lemonade for field day.They purchased 19 bags of lemon.each bag has 24 lemons.The recipe says that a gallon of lemonade will require 8 lemons.they will be able to pour 12 cups of lemonade from each gallon that they make.How many cups of lemonade will the parent council be able to serve?
Answer:
684
Step-by-step explanation:
19 x 24 = 456
456 divided by 8 = 57
57 x 12 = 684
Complete the square to solve 4x2 + 24x = 4.
Answer:
x = - 3 ± [tex]\sqrt{10}[/tex]
Step-by-step explanation:
Given
4x² + 24x = 4 ( divide through by 4 )
x² + 6x = 1
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(3)x + 9 = 1 + 9
(x + 3)² = 10 ( take the square root of both sides )
x + 3 = ± [tex]\sqrt{10}[/tex] ( subtract 3 from both sides )
x = - 3 ± [tex]\sqrt{10}[/tex]
Answer:
X=1/8
Step-by-step explanation:
Calculate the product 4x×2 + 24x = 4
Collect like terms 8x + 24x = 4
Divide both sides of the equation by "32" 32x = 4
Solution x = 1/8
What is difference between internal and external trade
Answer:
Trade which takes place inside a country is known as internal trade. If trade takes place with other countries of the world, it is known as external trade.
Step-by-step explanation:
Answer:Internal refers to trade within the country itself while
External refers to trade with other countries whether foreign or bordering countries
Step-by-step explanation:
''Internal'' trade-Trade within the locals of the country itself
''External'' trade-refers to ;outside of the country...trade with other countries
help..? why are there so many parentheses..?can you plz give a step by step on how to slove the equation?
Answer:
= -11
Step-by-step explanation:
-(-(11-22))
= -(-11+22)
= 11 - 22
= -11
I need help with #7 I got no clue what to do
Triangle L J K is shown. Angle J L K is a right angle. The length of the hypotenuse is 15 inches and the length of the side adjacent to the right angle is 10 inches. The angle between the 2 sides is x. Which equation can be used to find the measure of angle LJK? sin(x) = Ten-fifteenths sin(x) = Fifteen-tenths cos(x) = Ten-fifteenths cos(x) = Fifteen-tenths
Answer:
cos(x) = Ten-fifteenths
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that the relation between the adjacent side and the hypotenuse is ...
Cos = Adjacent/Hypotenuse
cos(x) = 10/15
Answer:
c
Step-by-step explanation:
The estimated product of 20.7 and 9.18, after rounding both factors to the nearest whole number, is . The exact product of 20.7 and 9.18 has decimal places.
Answer:
Estimated=189
Exact=190.026
Step-by-step explanation:
Estimated values
20.7 to nearest whole number= 21
9.18 to nearest whole number= 9
Product means multiplication
Estimated product of 20.7 and 9.18
=21×9
=189
Exact product of 20.7 and 9.18
=20.7 × 9.18
=190.026
It has 3 decimal places
Answer:
The estimated product of 20.7 and 9.18, after rounding both factors to the nearest whole number,
is
✔ 189
.
The exact product of 20.7 and 9.18 has
✔ 3
decimal places.
Step-by-step explanation: Hope this helps(:
what is 2/3 divided by -1 1/3
Need help with mark brainlist.
Nam worked on a job for 10 days. On each of the last 2 days, he worked 2 hours more than the mean number of hours he worked per day during the first 8 days. If he worked 69 hours in all, how many hours did he work during the last 2 days together?
Answer: 17 hours
Step-by-step explanation:
Given that On each of the last 2 days, he worked 2 hours more than the mean number of hours he worked per day during the first 8 days. That is he worked additional 4 hours for the two days.
Let the total hours for the 8 days = E
The mean = E/8 = 0.125E
For the two last days, he worked
( 0.125E + 2 ) × 2 = 0.25E + 4
If he worked 69 hours in all, then
E + 0.25E + 4 = 69
Collect the like terms
1.25E = 69 - 4
1.25E = 65
E = 65/1.25
E = 52.
Now find the mean of the first 8 days
Mean = 52 / 8 = 6.5 hours
Nam works during the last 2 days together for:
(6.5 + 2)×2
8.5 × 2 = 17 hours
A triangle has sides of lengths 16, 63, and 65. Is it a right triangle? Explain.
Answer:
Yes
Step-by-step explanation:
If a triangle is a right triangle, the 3 side lengths will check out in the Pythagorean Theorem.
[tex]a^2+b^2=c^2[/tex]
where a and b are the legs and c is the hypotenuse.
The legs are the 2 shorter lengths and the hypotenuse is the longest length. The 3 side lengths are: 16,63 and 65. Therefore, 16 and 63 are the legs and 65 is the hypotenuse.
a=16
b=63
c=65
[tex]16^2+63^2=65^2[/tex]
Evaluate each exponent.
16^2=16*16=256
[tex]256+63^3=65^2[/tex]
63^2=63*63=3969
[tex]256+3969=65^2[/tex]
65^2=65*65=4225
[tex]256+3969= 4225[/tex]
Add 256 and 3969
[tex]4225=4225[/tex]
The statement above is true; 4225 is equal to 4225. Therefore, this is a right triangle because the side lengths check out when plugged into the Pythagorean Theorem.
find y of a paralagram
Answer:
y = 15
Step-by-step explanation:
In a parallelogram, opposite sides are congruent.
5y - 20 = 2y + 25
3y = 45
y = 15
Answer:
y = 15
Step-by-step explanation:
The top and bottom sides have to be equal in length
5y-20 = 2y+25
Subtract 2y from each side
5y-2y-20 = 2y-2y+25
3y -20 = 25
Add 20 to each side
3y = 20+25
3y = 45
Divide each side by 3
3y/3 = 45/3
y = 15
f(x) = x2. What is g(x)?
pls help it’s due soon!!
Answer:
A. g(x) = (2x)²
Step-by-step explanation:
From the diagram of the two functions graph f(x) is the parent function and g(x) is the transformed function. you can see that the graph of g(x) is stretched vertically compared to the graph of g(x). The Parent function has y =1 corresponding to x =1 while for the transformed function when x = 1, y = 4 the graph is vertically stretched by a factor of 4, and horizontally The Parent function has y =1 corresponding to x =1. while for the transformed function when x = 0.5, y = 1, it is stretched horizontally by 2 (√4), i.e
This means that g(x) = 4x² = (2x)²
Tuition for one year at the University of Atlantis costs $12,000 per year. Rachel would like to attend this university and will save money each month for the next 3 years. Her parents will contribute $3,000 for her first year's tuition. How much money will Rachel need to save each month to have enough money for the first year of college at the University of Atlantis?
Answer:
250 dollars per month.
Step-by-step explanation:
We first need to subtract the amount of money her parents are giving her.
12000-3000=9000.
Since she is saving money every month for 3 years we have to multiply 3×12=36 months.
We than need to divide how much money she needs by the amount of months she has to get it.
9000÷36=250
PLEASE HURRY!!!!! Simplify the expression. (x – 4x2 + 7) – (-5x2 + 5x – 3)
Answer:
[tex]x^{2}-4x+10[/tex]
Step-by-step explanation:
[tex](x-4x^{2}+7)-(-5x^{2}+5x-3)\\x-4x^{2}+7+5x^{2}-5x+3\\x^{2}-4x+10[/tex]
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
Let's simplify step-by-step.
[tex]( x - 4x^2 + 7 ) - ( -5x^2 + 5x - 3)[/tex]
Distribute the Negative Sign:
[tex]= x - 4^2 + 7 + -1 ( -5x^2 + 5x -3) \\= x + -4x^2 + 7 + -1 ( -5x^2) + -1 (5x) + ( -1) (-3)\\= x + -4x^2 + 7+ 5x^2 + -5x + 3[/tex]
Combine Like Terms:
[tex]= x + -4x^2 + 7 + 5x^2 + -5x + 3 \\= (-4x^2 + 5x^2) + ( x + -5x) + ( 7 + 3) \\= x^2 + -4x + 10[/tex]
Answer : [tex]\boxed {x^2 -4x + 10}[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Have a great day/night!
❀*May*❀
(10 PTS) How do I solve for this? Please show work
Answer:
4
Step-by-step explanation:
8 ^ 2/3
Rewriting 8 as 2^3
( 2^3) ^ 2/3
We know that a^ b^c = a^ (b*c)
2 ^ ( 3 * 2/3)
2 ^ 2
4
⚠️URGENT!!⚠️ PLEASE HELP ILL GIVE BRAINLIEST I PROMISE THE QUESTION IS ATTACHED BELOW I REALLY NEED HELP
Answer:
m∠M = 116° m∠N = 111° m∠O = 64° m∠P = 69°Step-by-step explanation:
A quadrilateral can be inscribed in a circle only if the sum of its opposite angles is equal to 180°, so:
7x - 15 + 3x + 15 = 180° and 2(17y - 10) + 13y + 12 = 180°
10x = 180° 34y - 20 + 13y + 12 = 180°
x = 18° 47y = 188°
y = 4°
m∠M: 2(17•4 - 10) = 2•58° = 116
m∠N: 7•18 - 15 =126 - 15 = 111
m∠O: 13•4 + 12 = 52 + 12 = 64
m∠P: 3•18 + 15 = 54 + 15 = 69
Please answer thanks!
Answer:
see explanation
Step-by-step explanation:
tan x = -1
[tex]x = tan^{-1}(-1)[/tex]
x = -45
tan x = 5
[tex]x = tan^{-1}(5)[/tex]
x = 78.69
Answer:
See below.
Step-by-step explanation:
So we want to find the solutions to the two equations:
[tex]\tan(x)=-1 \text{ and } \tan(x)=5[/tex]
I)
[tex]\tan(x)=-1\\x=\tan^{-1}(-1)[/tex]
Recall the unit circle. First, note that the number inside tangent is negative. Because of this, we can be certain that the x (in radians) must be in Quadrant II and/or IV (This is because of All Students Take Calculus, where All is positive in QI, only Sine is positive in Q2, only Tangent is positive in Q3, and only Cosine is positive in QIV. Tangent is negative so the only possible choice are QII and QIV).
From the unit circle, we can see that x=3π/4 is a possible candidate since tan(3π/4)=-1.
Since tangent repeats every π, 7π/4 must also be an answer (because 3π/4 + π = 7π/4). And, as expected, 7π/4 is indeed in QIV.
Therefore, for the first equation, the solutions are:
[tex]x=3\pi/4 \text{ and } 7\pi/4[/tex]
II)
For the second equation, there is no exact value for which tangent of an angle would be equal to 5. Thus, we need to approximate.
So:
[tex]\tan(x)=5\\x=\tan^{-1}(5)\\x=\tan^{-1}(5) \text{ and } \tan^{-1}(5)+\pi[/tex]
We got the second answer because, like previously, tangent repeats every π, so we only need to add π to get the second answer.
In approximations, this is:
[tex]x\approx1.3734 \text{ and } x\approx4.5150[/tex]
Note: All the answers are in radians.
03. O preço a ser pago por uma corrida de táxi inclui uma parcela fixa, denominada bandeirada, e uma parcela que depende da distância percorrida. Se a bandeirada custa R$ 3,20 e cada quilômetro rodado custa R$ 1,50, qual o valor de v a pagar em uma corrida de n quilômetro? * 1 ponto a) v = 1,50 + 3,20n b) v = 3,20.N c) v = 3,20.N - 1,50 d) v = 3,20 + 1,50n e) v = 1,50n
Answer: d) v = 3.20 + 1.50n.
Step-by-step explanation:
Let 'v' be the price to pay in a 'n' kilometer.
Given: The price to be paid for a taxi ride includes a fixed parcel, called a flag, and a parcel that depends on the distance traveled.
Flag costs = $ 3.20 and
Each kilometre run costs = $ 1.50
Then, the amount of 'v' to pay in a 'n' kilometer race = Flag costs + (n)× (Each kilometre run costs )
⇒ v= 3.20 + 1.50n
Hence, the correct option is d) v = 3.20 + 1.50n.
Plug in the values from the set {12, 15, 18, 19} to find the value of x. The value that holds true for the equation is . So, Jenny is years old and her mother is years old.
Answer:
Jenny´s age is 19 and her mother is 43.
Step-by-step explanation:
Given that
x + 2x + 5 = 62
where,
x = Jenny’s age
Now the following cases occured
a.
x = 12
Now put the x value to the above equation
12 + 2(12) + 5 = 62
12 + 24 + 5 = 62
41 = 62
It is not equaled so the Jenny age is not 12
b.
x = 15
Now put the x value to the above equation
12 + 2(15) + 5 = 62
15 + 30 + 5 = 62
50 = 62
It is not equaled so the Jenny age is not 15
c.
x = 18
Now put the x value to the above equation
18 + 2(18) + 5 = 62
18 + 36 + 5 = 62
59 = 62
It is not equaled so the Jenny age is not 12
d.
x = 19
Now put the x value to the above equation
19 + 2(19) + 5 = 62
19 + 38 + 5 = 62
62 = 62
It is equaled so the Jenny age is 19
Now the mother age is
as we know that
x + y = 62
19 + y = 62
y = 62 - 19
= 43
Also it proved that if we doubles the jenny age i.e 38 and then add 5 so the total is 43 i.e. equivalent to her mother age
help me please!! i am already failing the test
Answer:
2x²+2x
Step-by-step explanation:
you have f(x)= x+1 and g(x)= 2x
you must multiply the 2 polynomials
(1x·2x) +( 1·2x)
1·2=2 x^1·x^1=x²
2x²
1·2x=2x
