AB lies on a number line. The coordinate of point A is -6. Given that AB=20, what are two possible coordinates for point B?
Answers
Answer:
-26 or 14
Step-by-step explanation:
Given that
Coordinate of point A is -6.
Length of AB = 20
To find:
Coordinates for the point B = ?
Solution:
We are given that:
AB = 20
In other words, we can use modulus function to define the distance between A and B:
|Coordinates of B - Coordinates of A| = 20
Let the coordinates of B = [tex]x[/tex]
Kindly refer to the attached image for the given situation.
Point B might be either on the left or on the right side of A.
That means:
[tex]|x-(-6)| = 20\\\Rightarrow |x+6|=20[/tex]
Now, let us have a look at the modulus function:
[tex]|y|=\left \{ {-{y}\ if\ y<0 \atop {y}\ if\ y>0} \right.[/tex]
So,
[tex]|x+6|=\left \{ {-{(x+6)}\ if\ (x+6)<0 \atop {(x+6)}\ if\ (x+6)>0} \right.[/tex]
[tex](x+6 ) =20\\\Rightarrow x =14[/tex]
[tex]-(x+6 ) =20\\\Rightarrow x =-26[/tex]
Therefore, the answer is:
-26 or 14
Related Questions
9. This piecewise function represents the Social Security taxes for 2009. How much did Rachel pay in Social
Security tax if she earned $102,000 in 2009?
(0.062x
when 0< x < 106,800
($6,621.60
when x > 106,800
Nax)
a. $6,824.60
b. $6,355.10
c. $6,324.00
d. $6,220.00
Answers
Answer:
Option c.
Step-by-step explanation:
It is given that the piecewise function represents the Social Security taxes for 2009.
[tex]Tax=\begin{cases}0.062x & \text{ when } 0< x < 106,800 \\ \$6,621.60 & \text{ when } x > 106,800 \end{cases}[/tex]
We need to find Rachel's security tax if she earned $102,000 in 2009.
Since 102,000 lies in [tex]0<x<106,800[/tex], therefore
[tex]Tax=0.062x[/tex]
Put x=102000.
[tex]Tax=0.062(102000)[/tex]
[tex]Tax=6324[/tex]
So, the Social Security tax is $6324.
Therefore, the correct option is c.
what is the horonzontial distance between the two points(3,4) and (8,4)
Answers
Answer:
Distance = 5.099
Step-by-step explanation:
8(4√7 - √18) I breed the answer fast please
Answers
Answer:
32[tex]\sqrt{7}[/tex] - 24[tex]\sqrt{2}[/tex]
Alternative form:
≈50.72292
Step-by-step explanation:
Step one,
Simplify the radical expression:
8(4√7 - √18)
Still Stuck? *( √18 Simplified is 3√2)*
Your answer should look like this: 8(4√7 - 3√2)
Step two,
Distribute 8 through the parentheses:
8(4√7 - 3√2)
Still Stuck? *( Use distribuitave property to distribute 8 to (4) and (-3). You should get (32) and (-24)*
Your answer should look like this: 32√7 - 24√2
Solution,
32[tex]\sqrt{7}[/tex] - 24[tex]\sqrt{2}[/tex]
Alternative form:
≈50.72292
*For alternative form, plug the final answer into your calculator. Round it if necessary*
Daniel growing corn in a square field. The length of one side is 100 yards he needs to purchase fertilizer for the corn field. Each bag covers 50 square yards .How many bags do he need?
Answers
Answer:
200 bags are needed
Step-by-step explanation:
First let us determine the area of the corn field:
Shape of cornfield = square
Area of a square = Length × Length
where: Length = 100 yards
∴ Area = 100 × 100 = 10,000 square yards
1 bag of fertilizer is needed to cover 50 square yards:
50 square yards = 1 bag of fertilizer
[tex]\therefore 1 \ square\ yard\ = \frac{1}{50}\ bag\\10,000\ square\ yards\ =\ \frac{1}{50} \times 10,000 = \frac{10l000}{50} \\ = 200 bags[/tex]
Hence, 200 bags are needed.
Answer:
200 bags are needed
Step-by-step explanation:
I did the test and got it correct good luck everyone !!
AG bisects ∢RAZ , and ∢RAG =. 8x+5 , and ∢ZAG = 4 x + 29 find the x .
Answers
Answer:
x = 6
Step-by-step explanation:
Given AG bisects ∠ RAZ , then
∠ RAG = ∠ ZAG , that is
8x + 5 = 4x + 29 ( subtract 4x from both sides )
4x + 5 = 29 ( subtract 5 from both sides )
4x = 24 ( divide both sides by 4 )
x = 6
Given h(x)= 4x^2, find h(3)
Answers
Explanation:
h(x) = 4x^2
Find h(3):
Simply plug x = 3 in the function:
h(3) = 4(3)^2
h(3) = 4(9)
h(3) = 36
Is 22 + 32 = 42 a true statement?
Answers
False because 22 + 32 =54
Answer:
No. 22+32=54
Step-by-step explanation:
889×27+50 is blank than 889×27
Answers
Answer:
50
Step-by-step explanation:
889*27=24003
889*27+50=24053
24053
-24003
00050
Do these two expressions represent equivalent expressions? Explain why or why not. 36 + 20 4(9 + 5)
Answers
Answer:
yes because 4 times 9 is equal to 36 and 4 times 5 is equal 20
Step-by-step explanation:
Yes, both the expressions ( 36 + 20 ) and 4 ( 9 + 5 ) are equivalent to each other.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The given expressions are solved as:-
First expression,
36 + 20 = 56
Second expression,
4( 9 + 5 ) = 36 + 20
= 56
From the above calculations,
( 36 + 20 ) = 4 ( 9 + 5 )
Therefore, both the expressions ( 36 + 20 ) and 4 ( 9 + 5 ) are equivalent to each other.
To know more about Expression follow
https://brainly.com/question/723406
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Please help me! I am so bad at math. 7(6+5x)=3x-22
Answers
42+35x–3x=–22
42+32x=–22
32x=–22–42
32x=–64
x=–64/32
The answer is x= –2
Answer:
-2
Step-by-step explanation:
42+35x=3x-22
35x-3x=-22-42
32x=-64
therefore, x= -64/32
and through further simplification you will get
-2
hope this helped you ( ꈍᴗꈍ)
1.5y-9.82=-9.37-10.1y-14.37 solve for y
Answers
Step-by-step explanation:
1.5y - 9.82 = -9.37 - 10.1y - 14.37
1.5y + 10.1y = 9.82 -9.37 - 14.37
11.6y = −13.92
y = (-13.92)/11.6
y = -1.2
Which statement is true? 2.289 < 2.297 2.297 < 2.289 3.01 < 2.297 2.289 > 3.01
Answers
Answer:
The first one, 2.2289<2.297
Step-by-step explanation:
Answer:
The answer is 2.2289<2.297 because if you look in the hundredths place there is a 9 in 2.297 but in 2.2289 there is an 2 and 9>2 so that is your answer.
QUESTION 11
(01.02)
Given the function f(x) = 3(x+2) - 4, solve for the inverse function when x = 2. (1 point)
O -4
Oo
O 4
08
Answers
Answer:
8
Step-by-step explanation:
3( 2 + 2 ) - 4
3( 4 ) - 4
12-4
8
solve for x: 4/x=5/10
Answers
1. 4/x = 1/2
multiply both sides by x
2. 4= 1/2 x
simply 1/2x to x/2
3. 4= x/2
multiply both sides by 2
4. 4x2= x
simplify 4 x 2 to 8
5. 8= x
switch sides
x= 8
ANSWER; x= 8
Answer:
x = 8
Step-by-step explanation:
4/x = 5/10
=> 4/x = 1/2
=> 4 x 2 = x
=> 8 = x
=> x = 8
write an expression that represents the total amount of fencing needed to enclose the two fields. -how would you do this?-
Answers
Answer:
8x + 60
Step-by-step explanation:
4(x + 5) + 2(x - 10) + 2(x + 30)
= 4x + 20 + 2x - 20 + 2x + 60 (combine like terms)
= 8x + 60
Point E is on line segment DF. Given DE = 2x, EF = 2x – 6, and
DF = 3x + 5, determine the numerical length of EF.
Answer: EF =
Answers
Answer:
EF is 16.
Step-by-step explanation:
So we know that Point E is somewhere on Line DF. In other words, DE plus EF must equal DF. In an equation, this is:
[tex]DF=DE+EF[/tex]
We are given that DE is 2x, EF is 2x-6, and DF is 3x+5. So, substitute:
[tex](3x+5)=(2x)+(2x-6)[/tex]
Now, solve for x.
On the right, combine like terms:
[tex]3x+5=4x-6[/tex]
Subtract 4x from both sides:
[tex]-x+5=-6[/tex]
Subtract 5 from both sides:
[tex]-x=-11[/tex]
Divide both sides by -1:
[tex]x=11[/tex]
Now that we know x is 11, substitute this back into the equation for EF to find EF.
[tex]EF=2x-6[/tex]
Substitute 11 for x:
[tex]EF=2(11)-6[/tex]
Multiply:
[tex]EF=22-6[/tex]
Subtract:
[tex]EF=16[/tex]
And we're done!
What is 350 divided by 55 as a decimal? A) 6.6 B) 6.36 C) 6.363 D) 6.363
Answers
350 divided by 55 = 6.36
The result of 350/55 is a non-terminating, repeating decimal. The repeating pattern above, 36, is called repetend, and denoted overlined with a vinculum. The answer is C
6.363 is the correct answer as it represents the repeating decimal correctly.
So, the correct answer is D) 6.363
To find the decimal equivalent of the division 350 divided by 55, you simply divide 350 by 55 using long division. Here's the step-by-step calculation:
6.363636...
_______________
55 | 350.000000
- 330
_______
200
- 165
______
350
- 330
______
200
- 165
______
350
- 330
______
200
- 165
______
...
The division continues indefinitely with the decimal repeating the sequence 36.
Therefore, the decimal equivalent of 350 divided by 55 is 6.363636...
Based on the options provided:
A) 6.6 is not correct as it rounds up the decimal prematurely.
B) 6.36 is not correct as it does not account for the repeating decimal.
C) 6.363 is not correct as it rounds down the decimal prematurely.
D) 6.363 is the correct answer as it represents the repeating decimal correctly.
So, the correct answer is D) 6.363.
Learn more about repeating decimal click;
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Point Q'Q ′ Q, prime is the image of Q(0,6)Q(0,6)Q, left parenthesis, 0, comma, 6, right parenthesis under the translation (x,y)\to(x+7,y-5)(x,y)→(x+7,y−5)left parenthesis, x, comma, y, right parenthesis, \to, left parenthesis, x, plus, 7, comma, y, minus, 5, right parenthesis. What are the coordinates of Q'Q
Answers
Q is located at (0,6)
The translation rule is [tex](x,y) \to (x+7,y-5)[/tex] which says to add 7 to the x coordinate and subtract 5 from the y coordinate. Doing that to (0,6) moves it to (7,1) which is where point Q' is located.
In other words, if you shift point Q(0,6) seven units to the right and five units down, then it arrives at Q ' (7,1)
Answer: (7, 1)The coordinates of Q' are [tex]Q'(x,y) = (7, 1)[/tex].
Note - There are typing mistakes in the question. Correct statement is presented below:
Point Q' is the image of [tex]Q(0,6)[/tex] under the translation [tex](x,y) \to (x+7, y-5)[/tex]. What are the coordinates of Q'.
In this question we should use the point and the operation described in statement. Vectorially speaking, a translation is defined by the following operation:
[tex]P'(x,y) = P(x,y) + T(x,y)[/tex] (1)
Where:
[tex]P(x,y)[/tex] - Original point.[tex]P'(x,y)[/tex] - Translated point. [tex]T(x,y)[/tex] - Translation vector.If we know that [tex]Q(x,y) = (0,6)[/tex], then the coordinates of [tex]Q'(x,y)[/tex] are:
[tex]Q'(x,y) = Q(x,y) + (7,-5)[/tex]
[tex]Q'(x,y) = (0,6) + (7,-5)[/tex]
[tex]Q'(x,y) = (7, 1)[/tex]
The coordinates of Q' are [tex]Q'(x,y) = (7, 1)[/tex].
We kindly invite to see this problem on rigid transformations: https://brainly.com/question/18613109
PLEASE HELP ASAP Write the following equation in general form.
-x - 5y = -19
–x - 5y + 19 = 0
x + 5y - 19 = 0
x + 5y + 19 = 0
Answers
Answer: -x - 5y + 19 = 0, choice A
All we're doing is adding 19 to both sides to get everything on the same side.
General form is Ax+By+C = 0. Some books use Ax+By = C which is just a variation of the same idea.
Solve the inequation (2x+3x)4 using distributive method.
Answers
Answer:
First, distribute the 4.
2x times 4 = 8x
3x times 4 = 12x
then add/ combine like terms.
8x + 12x = 20x
Step-by-step explanation:
Answer:
20x
Step-by-step explanation:
distribute the 4 to the 2x and 3x: 4 * 2x= 8x and 4 * 3x= 12x
then add the x's together: 8x+12x=20x
so the answer is 20x
O points
Mr. Freeman has a square cornfield. Which of the following could be the
area of the cornfield if the sides are measured in whole numbers?
150 square acres
189 square acres
200 square acres
225 square acres
Answers
Step-by-step explanation:
Notice that 15 squared = (3 * 5)^2 = 9 * 25 = 225.
So the area of the cornfield can be 225 square acres.
x2 + y2 = 13
x² - y2 = -16
Solve
Answers
x + 2y = 4 , x - y = -3
x - y = 9 , x - y = 6
There
What is the greatest four-digit integer that meets the following three restrictions? 1- All of the digits are different. 2- The greatest digit is the sum of the other three digits. 3- The product of the four digits is divisible by 10 and not equal to zero.
Answers
10
Write the numbers in order from least to greatest (**HINT: You need to
make them all decimals or all fractions***): 5/1000, 0.003, 9/1000
Answers
Answer:
0.003, 5/1000, 9/1000
Step-by-step explanation:
0.003 is thousandths.
5/1000 is thousandths.
9/1000 is thousandths.
I converted them to fractions.
5/1000 is already a fraction
Same for 9/1000
0.003=3/1000
So 3/1000, 5/1000, 9/1000
What is the ratio for 2 red paper clips to 6 blue paper clips? Write it as a fraction.
Answers
Answer:
2 over 6 as a fraction simplifies as 1 over three.
Step-by-step explanation:
If you are writing as a fraction, you put 2 over 6 and simplify. Your answer is 1 over 3
Answer:
2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6
Step-by-step explanation:
its just 2/6
- 3(4r - 8) = 36 - 2r
Answers
Answer:
r= -1.2
Step-by-step explanation:
first use distributive property
- 3(4r - 8) = 36 - 2r
-12r +24 = 36-2r
+2r. +2r
-10r +24= 36
-24. -24
-10r = 12
/-10. /-10
r= -1.2
Answer:
Step-by-step explanation:
Equation: -3(4r - 8) = 36 - 2r
Step 1:
-12r + 24 = 36 - 2r Multiply (4r - 8) by -3 using the Distributive Property.
Step 2:
-10r + 24 = 36 Add -12r and -2r by 2r.
Step 3:
-10r = 12 Subtract 24 and 36 by 24.
Step 4:
r = -12/10 Divide both sides by -10
Step 5:
r = -6/5 Simplify the fraction.
Convert the given amount to the given unit.
27 yd; ft
27 yd = ft
Answers
Answer:
81 ft
Step-by-step explanation:
1 yard=3ft
27 x 3=81
So the answer is 81 ft
Which angle refers to the same angle as ∠ D E F
Answers
Answer:
It is angle FED which is equal to angle DEF
What does x equal?
2(3x - 2) = 20
Answers
Answer:
4
Step-by-step explanation:
2(3x-2)=20
3x-2=10
3x=12
x=4
Answer:
x=4
Step-by-step explanation:
What is 90% of 81?
X
Answers
Answer:72.9
Step-by-step explanation:
Answer:
72.9
Step-by-step explanation:
Fractions method:
[tex]81*\frac{90}{100}[/tex] because 90/100 is the same thing as 90%
That gives us 7290/100, from 81*90/100
Simplify: =729/10 = 72.9
Decimals method:
81*9 = 729, add in decimal and that's 72.9
Cross-multiplication:
90 100
? 81
This is read as 90 to 100, (as a ratio) so how many to 81? To solve, cross-multiply - 81*90=7290, then divide by 100 to get 72.9.
This is my first answer , hope it helped!