Answer: a. y=5
b. RS = 37 , ST =16 and RT = 53 .
Step-by-step explanation:
Given: On number line we have,
RS = 7y + 2, ST = 2y +6, and RT = 13y - 12.
a. Since its on number line so we have
RT = RS+ ST
i.e. 13y - 12 = (7y + 2) + ( 2y +6)
⇒ 13y - 12 = 7y + 2 + 2y +6
⇒ 13y-12 = 9y+8
⇒ 13y-9y = 8+ 12 [Subtract 9y from both sides and add 12 in both sides]
⇒ 4y = 20
⇒ y= 5 [Divide both sides by 4 ]
b. Now , RS = 7(5) + 2 = 35+2= 37,
ST = 2y +6 = 2 (5)+6 = 10+6 =16,
and RT = 13y - 12 = 13 (5)-12 = 65-12 = 53.
Hence, RS = 37 , ST =16 and RT = 53 .
Mr. Drew wants to build a square sandbox with an area of 324 square feet. What is the total length
of wood Mr. Drew needs to make the sides of the sandbox?
He needs to buy __ feet of wood.
(Simplify your answer.)
Answer:
72ft.
Step-by-step explanation:
18(18)=324
18(4)=72
find the sum of
137 and -354
Answer:
-217
Step-by-step explanation:
Add them both together because it is asking for the "sum".
-354+137= -217
Which point is the best estimate of 11?
А А.
B
D
E
toh
to
.
3
4
Pls help me it’s due today! >_
Answer:
B
Step-by-step explanation:
Step 1: Find √11
√11 is between perfect squares √9 and √16
√9 < √11 < √16
3 < √11 < 4
So it is between 3 and 4
Step 2: Evaluate
√11 = 3.31662
Closest dot is B.
You and your family attend a Broadway show in New York City. The show begins at
6:58pm and ends at 9:46pm. How many seconds long is the show?
From 7:00 to 9:46 we see it passes 2 hours and 46 minutes.
But it started 6:58 . So we add +2 minutes. 46+2 = 48
2 hours and 48 minutes.
But we must find the second form.
1 hours = 60 minutes = 3600 seconds
So, 2 hours = 120 minutes = 7200 seconds.
and 1 minutes = 60 seconds
48 minutes = 60 x 48 = 2880 seconds.
7200 + 2880 = 10080 seconds.
(2x+ 2) +(3 - 5x) 4.) (3x - 4x4) +(2x + 5x4)
Step-by-step explanation:
Here,
[tex]1. \: (2x + 2) + (3 - 5x)[/tex]
open brackets,
[tex]2x + 2 + 3 - 5x[/tex]
[tex] = - 3x + 5[/tex]
now,
[tex]2. \: (3x - {4x}^{4} ) + (2x + {5x}^{4} [/tex]
open brackets,
[tex] = 3x - {4x}^{4} + 2x + {5x}^{4} [/tex]
simplifying like terms,
[tex] = {x}^{4} + x[/tex]
Hope it helps...
6. Audrey's monthly car payment is $350 and
she needs to save at least $35 each month for
gas. If Audrey is paid $17.50 an hour, write
and solve an inequality to represent the
number of hours she must work in a month to
pay for her car payment and gas.
Answer:
22 hours
Step-by-step explanation:
For one month, Audrey has to pay $350 for her payment and $35 for gas, meaning that she will need to pay $385 per month.
$350 + $35 = $385
Audrey makes $17.50 an hour. Set up an equality to find the amount of hours she must work to pay for her car payment and gas.
17.50x > 385
(17.50x)/17.50 > 385/17.50
x > 22
Audrey must work at least 22 hours to pay for her car payment and gas.
Darrin is hanging 200 feet of Christmas garland on the fencing that encloses his rectangular front yard. The length is 5 feet less than 5 times the width. Find the length and width of the fencing. Give the measurements in decimal form.
Answer:
Length = 82.5 feet
Width = 17.5 feet
Step-by-step explanation:
The formula for the Perimeter of a rectangle = 2(Length + Width)
= 2L + 2W
We are told in the question that: Darrin is hanging 200 feet of Christmas garland on the fencing that encloses his rectangular front yard
Hence, The perimeter of the rectangular front yard = 200 feet
200 = 2( L + W).........Equation 1
Also, the length is 5 feet less than 5 times the width
L = 5W - 5
Hence,
200= 2(5W - 5 + W)
200 = 2(5W + W - 5)
200 = 2(6W - 5)
200 = 12W - 10
Collect the like terms
200 + 10 = 12W
210 = 12W
W = 210/12
W = 17.5 feet
Substitute 17.5 for W in Equation 1
200 = 2( L + W).........Equation 1
200 = 2( L + 17.5)
200 = 2L + 35
200 - 35 = 2L
2L = 165
L = 165/2
L = 82.5 feet
Therefore, the Length of the rectangular fence = 82.5 feet while the Width of the rectangular fence is 17.5 feet.
what is the answer to 1.2(x-3) +4 (x+7)
Answer:
5.2x + 24.4
Step-by-step explanation:
1.2(x-3) + 4 (x+7)
=1.2x - 3.6 + 4x + 28
=5.2x + 24.4
Hope this helps..
Which is f(5) for the function –2x2 + 2x – 3?
–107
–63
–43
–37
Answer: C
Step-by-step explanation:
Answer:
(C) -43
Step-by-step explanation:
♥☺
PLEASE HELP FAST!!!!!! How many triangles can be constructed using the following three side lengths: 4.8 cm, 2.1 cm, and 2.6 cm?
one triangle
no triangles
an infinite number of triangles
Answer:
no triangles
Step-by-step explanation:
why?
the triangle inequality theorem
this theorem states that the sum of any two sides must be bigger than or equal to the third side. however, the sum of 2.1 and 2.6 is less than 4.8
How do you think business owners determine how much of each of their products to make?
Answer:
They determine how much to make by how much demand there is for said product from the consumer.
Step-by-step explanation:
1. Write the interval shown on the number line
below
3 4 5 6 7 8
as an inequality
using set notation
Answer:
[tex]x\geq 5[/tex]
[tex]\{x\ |\ x \geq 5\}[/tex] OR {5, 6, 7, 8, .....}
Step-by-step explanation:
First of all, let us have a look at the interval shown on the number line and try to understand it properly.
The number line shows positive numbers starting from 3 that means numbers indicated will be positive numbers.
The number highlighted starts from 5 and there is filled circle at 5.
So, 5 is included in the interval.
The arrow is from 5 towards 8 and so on..
That means Numbers greater than or equal to 5 are represented by the interval.
So, writing as an inequality
Let [tex]x[/tex] represents one of the numbers.
Hence, inequality can be written as:
[tex]x\geq 5[/tex]
Using the set notation:
[tex]\{x\ |\ x \geq 5\}[/tex]
OR
{5, 6, 7, 8, .....}
3) Taylor's soccer team purchased uniforms and equipment for a total of $912. The equipment costs $612 and the uniforms cost $25 each. How many uniforms did the school purchase?
Answer: They purchased 12 uniforms
Step-by-step explanation:
If the equipment cost $612 in total and the uniforms cost $25 each and they spent a total for $912 then we could represent it by the equation 25x + 612 = 912 where x is the number of uniforms that the school purchase.
25x + 612 = 912 solve for x by subtracting 612 from both sides
612 612
25x = 300 divide both sides by 25
x = 12
Prove the identity
[tex]4 \sin(x) \cos(x) = \frac{ \sin(4x) }{ \cos(2x) } [/tex]
=> R.H.S
[tex] \frac{ \sin(4x) }{ \cos(2x) } = \frac{ \sin(2x + 2x) }{ \cos(2x) } [/tex]
[tex] = \frac{ 2 \sin(2x) \cos(2x) }{ \cos(2x) } [/tex]
[tex] = 2 \sin(2x) [/tex]
[tex] = 2(2 \sin(x) \cos(x) )[/tex]
[tex] = 4 \sin(x) \cos(x) [/tex]
R.H.S = L.H.S
PROVED!
Answer:
Below
Step-by-step explanation:
● 4 sin(x) cos(x) = sin(4x)/cos(2x)
Let's prove that:
● 4 sin(x) cos(x) cos(2x) = sin(4x)
It's easier to prove it than the first one
■■■■■■■■■■■■■■■■■■■■■■■■■■
● 4 sin(x) cos(x) cos (2x)
● [2 sin(x) cos(x)] 2 cos(2x)
We khow that [2 sin(x) cos(x)]= sin(2x)
So:
● sin(2x) 2 cos(2x)
Based on the same relation
● sin(4x)
It's proved
Which numbers are rational? Check all that apply.
-19
2
5
0
4
ī
1.091502...
2.89
Answer:
-19
-2/5
0
4/7
2.89
Step-by-step explanation:
a rational number is any number that can be converted to a fraction, I know this because I took a test a while back and it helped me understand it. I hope this helps!!! :)
the probability that a civil servant own a car is 1/6,if two civil servants are selected at random.find the probability that
a.each own a car
b.only one owns a car
Answer:
The data we have is:
the probability that a civil servant own a car is 1/6
Two civil servants are selected at random.
a) The probability that each own a car.
Ok, here we have two events:
Person 1 haves a car.
Person 2 haves a car.
The probability of each of those events is the same, 1/6.
P1 = 1/6
P2 = 1/6
Now, the probability of both events happening at the same time is equal to the product of the individual probabilities.
P = P1*P2 = (1/6)*(1/6) = 1/36.
b) Only one has a car.
Suppose that Person 1 has the car and Person 2 has not a car.
The probability for person 1 is 1/6.
And for person 2, is the negation of having a car:
So if we have prob of having a car = 1/6
Then the probability of not having a car is = 1 - 1/6 = 5/6.
Then we have:
P1 = 1/6
P2 = 5/6.
The joint probability is:
P = P1*P2 = (1/6)*(5/6) = 5/36.
But we also have the case where person 1 does not have a car, and person 2 does have one, then we have a permutation, and the actual probability is two times the obtained above.
P = 2*(5/36) = 10/36
Evaluate the expression:
x^2+2x−xy when x = 250 and y = −120
Answer:
33000
Step-by-step explanation:
Substituting 250 for x and -120 for y, we get:
(250)^2 + 2(250) - (250)(120) = 62500 + 500 - 30000, or
32500 + 500, or 33000
Q3) If B is directly proportional to A and B = 3 when A = 18, find the value of B when A = 24.
Answer:
B = 4
Step-by-step explanation:
Given that B is directly proportional to A then the equation relating them is
B = kA ← k is the constant of proportionality
To find k use the condition B = 3 when A = 18 , then
3 = 18k ( divide both sides by 18 )
k = [tex]\frac{3}{18}[/tex] = [tex]\frac{1}{6}[/tex]
B = [tex]\frac{1}{6}[/tex] A ← equation of proportion
When A = 24, then
B = [tex]\frac{1}{6}[/tex] × 24 = 4
31*r+1.1*(35−31)*r = 410.64.
Answer:
11.6
Step-by-step explanation:
Solving with steps as below:
31*r+1.1*(35−31)*r = 410.6431r + 1.1*4r = 410.6431r + 4.4r = 410.6435.4r = 410.64r = 410.64/35.4r = 11.6Answer is: r =11.6
-3(2x -1) plz help, asap will give brainliest
Answer:
Hey there!
-3(2x-1)
-6x+3
Let me know if this helps :)
Answer:
[tex]- 6x + 3[/tex]
Step-by-step explanation:
[tex] - 3(2x - 1) \\ = - 6x + 3[/tex]
In a math contest of 10 problems, 5 points were given for each correct answer and 2 points were deducted for each incorrect answer. If Nancy answered all 10 problems and scored 29 points, how many correct answers did she have?
Answer:
Nancy had 7 correct answers.
Step-by-step explanation:
To solve this problem, we can set up a system of equations. Let's assign the variable c to represent the number of correct answers Nancy had and the variable i represent the number of incorrect answers she had.
We know that the total number of answers is 10 because it is given that she answered all 10 problems. This lets us set up the first equation as follows:
c + i = 10
Then, we can set up a second equation using the number of points (29 total). We know that +5 points were added for each correct response (c) and -2 points were added for each incorrect response (i). Our next equation will look like this:
5c - 2i = 29
There are many different strategies one can use to solve systems of equations. In this case, I am going to use combination. This means I am going to add the two equations together. However, first I should multiply our first equation by 2 so that the "I" variable terms cancel out. This is modeled below:
2c + 2i = 20
Now we can add the two equations:
5c + 2c +2i - 2i = 20 +29
Now we can simplify the equation by combining the like terms to get:
7c = 49
Finally, we should divide both sides of the equation by 7 in order to get the variable c by itself on the left side of the equation.
c = 7
Therefore, the correct number of responses Nancy gave was 7.
Hope this helps!
URGENT! Will earn 100 points if you can answer all of these questions on PAPER OR DOCUMENT. Send link to email, messages, or through the answer page.
( MESSAGE JamSandwitch FOR EMAIL AND TO SEND DOCUMENT / ANSWERS ! )
Answer:
see below
Step-by-step explanation:
3) 8
4) 4
5) 14
6) 47
7) 18/5
8) 3/2
9) 255/4
10) 16
11) 21
12) 40
13) 73.5
14) 1
15) 25/2 or 12.5
16) 0
17) 48
18) 862
19) 9765625
20) 343
21) 8.1x10⁻³
22) 10.24
23) 1/156
24) n⁷
25) y⁶
26) t⁴
27) error is 0.4² should be 0.02²
28) 5⁴ = 5 x 5 x 5 x 5 = 625
29) 9
30) 100
31) 1
32) 1331
33) 125
34) 1024
35) 64
36) 1296
37) 1/16
38) 16/81
39) 27/125
40) 1/216
hope you enjoy the answers.
Answer:
thx
Step-by-step explanation:
The area of a rectangular garden is given by the trinomial x2 + x – 42. What are the possible dimensions of the rectangle? Use factoring.
Answer:
Step-by-step explanation:
Hello, please consider the following.
[tex]x^2+x-42\\\\\text{The sum of the zeroes is -1=-7+6 and the product is -42=-7*6.}\\\\\text{So, we can factorise.}\\\\x^2+x-42\\\\=x^2+7x-6x-42\\\\=x(x+7)-6(x+7)\\\\=(x+7)(x-6)[/tex]
So, the possible dimensions of the rectangle are (x+7) and (x-6).
Thank you.
Answer:
[tex] \boxed{ \boxed{ \bold{ \sf{(x + 7) \: and \: (x - 6)}}}}[/tex]Step-by-step explanation:
[tex] \sf{ {x}^{2} + x - 42}[/tex]
Here, we have to find two numbers which subtracts to 1 and multiplies to 42
⇒[tex] \sf{ {x}^{2} + (7 - 6)x - 42}[/tex]
⇒[tex] \sf{ {x}^{2} + 7x - 6x - 42}[/tex]
Factor out x from the expression
⇒[tex] \sf{x(x + 7) - 6x - 42}[/tex]
Factor out 6 from the expression
⇒[tex] \sf{x(x + 7) - 6(x + 7)}[/tex]
Factor out x + 7 from the expression
⇒[tex] \sf{(x + 7)(x - 6)}[/tex]
So, the possible dimensions of the rectangle are x + 7 and x - 6 .
Hope I helped!
Best regards!
Casey wants to buy some instruments for his niece and nephew. He has $40 to spend. Based on the prices listed below, what is the estimated total, rounded to the nearest dollar? Which explains why he can afford the tambourine and xylophone? Tambourine: $13.95
Xylophone $23.50
The estimated total to the nearest dollar is $38, so he can afford them. The estimated total to the nearest dollar is $37, so he can afford them. The estimated total to the nearest dollar is $36, so he can afford them. The estimated total to the nearest dollar is $37.45, so he can afford them.
Answer:
It’s the estimate tidal to the nearest dollar is $38 so he can offered them
Step-by-step explanation:
Help needed ASAP will give brainliest.
Answer:
10
Step-by-step explanation:
We can show this as:
√90 = √9*10Since
9*9 < 9*10 < 10*10Then
9 < √90 < 10The closest number in the list is 10 as all the rest are greater than 10
Second choice is the correct one
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
[tex]\sqrt{90}[/tex]
[tex]= \sqrt{10}[/tex] (Decimal: 9.486833)
( I don't know it might be wrong )
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Have a great day/night!
❀*May*❀
Can someone give me the answers for the number frame and how you did it, I’m confused :)
Answer:
16, 56, ...
Step-by-step explanation:
It looks like you have to put in each cell the multiplication of the row and the column, so the columns are 2, 7, 4 etc., and the row is always 8.
First cell: 2x8 = 16
Second cell: 7x8 = 56
and so on
It teaches you to apply the multiplication in a random sequence; you should be able to do this in your head.
Please help to write the following
Answer: option 2. x²-1
Step-by-step explanation:
concept to know: a²-b²=(a+b)(a-b)
------------
(a+b)(a-b)=a²+b²
(x+1)(x-1)=x²-1
Hope this helps!! :)
Please let me know if you have any question
a train travelled from city a to city b for the first 14 hours, it travelled at an average speed of 120 km/h. for the next 10 hours it traveled at an average speed of 90 km/h
what was the average speed of the whole journey?
Answer: 107.5
Step-by-step explanation:
120 x 14= 1680
90 x 10= 900
Now you add 1680+900= 2580
Then you divide the distance (2580) between the speed (14+10)
2580/24= 107.5
The vertices of ∆ABC are A(7,3),B(−8,6),C(0,−5). If ∆ABC is translated along the vector <−9,5>, what are the coordinates of the vertices of ∆A'B'C' ?
Answer:
The coordinates of the vertices of [tex]\bigtriangleup A'B'C'[/tex] are [tex]A'=(-2,8)[/tex], [tex]B'=(-17,-4)[/tex] and [tex]C'=(-9,0)[/tex].
Step-by-step explanation:
Let be [tex]A =(7,3)[/tex], [tex]B = (-8,6)[/tex] and [tex]C = (0,-5)[/tex] the vertices of the original triangle, as well as [tex]\vec t = \left<-9, 5\right>[/tex], the coordinates of the vertices of the new triangle are, respectively:
[tex]A' = A + \vec t[/tex]
[tex]A' = (7,3)+(-9,5)[/tex]
[tex]A' = (7-9,3+5)[/tex]
[tex]A'=(-2,8)[/tex]
[tex]B' = B + \vec t[/tex]
[tex]B' = (-8,6)+(-9,5)[/tex]
[tex]B' = (-8-9,-9+5)[/tex]
[tex]B'=(-17,-4)[/tex]
[tex]C' = C + \vec t[/tex]
[tex]C' = (0,-5)+(-9,5)[/tex]
[tex]C' = (0-9,-5+5)[/tex]
[tex]C'=(-9,0)[/tex]
The coordinates of the vertices of [tex]\bigtriangleup A'B'C'[/tex] are [tex]A'=(-2,8)[/tex], [tex]B'=(-17,-4)[/tex] and [tex]C'=(-9,0)[/tex].
help please it’s my last question it should be two answers
Answer:
Choices 1 and 5
Step-by-step explanation:
155 + 166 = 25 + 296
Correct choices:
155 - 296 = 25 - 166
This is obtained by subtracting 296 and 166 from both sides of initial equation166 - 25 = 296 - 155
This is obtained by subtracting 25 and 155 from both sides of initial equation