On a number line, a number, b, is located the same distance from 0 as another number, a, but in the opposite direction
The number b varies directly with the number a. For example b= 2 when a = -2
-2. Which equation represents this
direct variation between a and b?
Obra
O b = a
Ob-a= 0
Ob(-a) = 0
Answers
Answer:
b = -a
Step-by-step explanation:
We know that:
On a number line, the distance between 0 and b is the same distance that between 0 and a (but b and a are in opposite sides of zero).
And we know that, for example, when:
b = 2, a = -2
Remember that the distance between two values is given by:
|n - m|
Then the distance between 0 and b is:
|0 - b|
and the distance between 0 and a is:
|0 - a|
we have:
|-b| = |-a|
|b| = |a|
But the numbers are in opposite sides of the zero, so one must be positive and the other negative, then we can conclude that:
b = -a
or
-b = a
(these are equivalent)
Then the correct option is the first option:
b = -a
Related Questions
I need help with this question
v2–2v–24
Answers
Answer:
(v - 6)(v + 4)
Step-by-step explanation:
v² - 2v - 24
v² + 4v - 6v - 24
v(v + 4) - 6(v + 4)
(v - 6)(v + 4)
Using f(x) = 8x + 5 and g(x) = 7x - 2, find:g(f(6))
Answers
Answer:
369
Step-by-step explanation:
g(f(x)) simply means to put the whole expression of function f(x) into the place of "x" in g(x).
and to find the functional value for a specific x we just need to calculate functional value for f(x) and use that result as input for g(x).
f(6) = 8×6 + 5 = 48 + 5 = 53
and now
g(53) = 7×53 - 2 = 371 - 2 = 369
to check we do the general functional substitution :
g(f(x)) = 7×(8x+5) - 2 = 56x + 35 - 2 = 56x + 33
g(f(6)) = 56×6 + 33 = 336 + 33 = 369
correct
Class width is 2
Find mode
Answers
Answer:
7.22
Step-by-step explanation:
solved in the diagram
What are the two possible measures of the angle below?
Answers
Answer:
90 or -270
Step-by-step explanation:
Of the teacups in Bonnie's Tea Shop, 1/12 are blue and another 1/12 are orange. What fraction of the teacups are either blue or orange?
Answers
Answer: 1/6
Step-by-step explanation:
This is a question that has to do with the addition of a fraction. Since we are given the information that of the teacups in Bonnie's Tea Shop, 1/12 are blue and another 1/12 are orange.
Then, the fraction of the teacups that are either blue or orange will be calculated as:
= 1/12 + 1/12
= 2/12
= 1/6
Therefore, the fraction of the teacups that are either blue or orange is 1/6.
Can someone help
Write an equivalent expression for
63.62.65.6.
Answers
When multiplying the same number raised to different powers add the powers together.
3 + 2 + 5 = 10
Because you are also multiplying a value without a power you need to add 1 to the sum of the powers:
10 + 1 = 11
Answer: 6^11
Use this system of linear equations to solve for x. 3x+5y=6 and 2x+y=4
Answers
Answer:
x=2
HPT 3x+5y=6 (1) và 2x+y=4 (2)
Nhân phương trình (2) với 5 để hệ số y của 2 phương trình bằng nhau. Ta có:
(2)⇔ 10x+5y=20(3)
Trừ (3) cho (1), có: 7x+0y=14⇒x=2
Answer:
3x+5y=6.....eqn 1
2x+y=4.......eqn 2
y=4-2x.....eqn 3
Step-by-step explanation:
substitute eqn 3 into eqn 1
3x+5(4-2x)=6
3x+20-10x=6
-7x = -14
x=2
pls tell by step by step
Answers
Answer:
x = 50 degree
Step-by-step explanation:
x + 10 + x + x + 20 = 180 degree (being linear pair)
3x + 30 = 180
3x = 180 - 30
x = 150/3
x = 50 degree
Please answer correctly to get brainliest
Answers
Answer:
Step-by-step explanation:
This is only my guess, as I haven’t done this topic in a few months
A. 398/427
0.93
B. 123/1192
0.10
C. 339/403
0.84
Can someone help me? It's urgent and thank you!
Answers
Answer:
480,700
Step-by-step explanation:
C(25,7)
25!/(7!*(25-7)!)
15511210043330985984000000/(6402373705728000*5040)
480700
find'x' 2log_5x = 1+log_5(x-6/5)
Answers
Answer:
x = 2 and x = 3
Step-by-step explanation:
Formulas used :
[tex]log_5 \ 5 = 1[/tex]
[tex]log_5 \ x + log_5 \ y = log_5 \ (xy)[/tex]
[tex]log_5 \ x = log_5 \ y => x = y[/tex]
Steps :
[tex]2 \ log_5 \ x = 1 + log_5 (x - \frac{6}{5} )\\\\2 \ log_5 \ x = log_5 \ 5+ log_5 (x - \frac{6}{5} )\\\\2 \ log_5 \ x = log_5 \ ( 5(x - \frac{6}{5} ))\\\\x^2 = 5(x - \frac{6}{5})\\\\x^2 = 5x - 6\\\\x^2 - 5x + 6 = 0\\\\x^2 - 2x - 3x + 6 = 0\\\\x(x - 2 ) - 3 (x - 2) = 0\\\\(x - 3)(x-2) = 0\\\\x = 3 , x = 2[/tex]
Find three consecutive odd integers such that the product of the second and the third integers is twenty-six more than three times the first integer.
Answers
Step-by-step explanation:
first number=x
second number=x+2
third number=x+4
(x+2)(x+4)=3x+26
x(x+4)+2(x+4)=3x+26
x²+4x+2x+8=3x+26
x²+6x+8=3x+26
x²+6x-3x=26-8
x²+3x=18
x²+3x-18=0
you can use that to find the numbers
Answer:
6, 8 and 10
Step-by-step explanation:
Let the 3 consecutive odd numbers be x, x+2, x+4
product of the second and the third integer
(x+2)(x+4)
twenty-six more than three times the first integer is expressed as;
3x + 26
Equate
(x+2)(x+4) = 3x + 26
x²+4x+2x+8 = 3x + 26
x²+6x +8= 3x+26
x²+3x +8-26 = 0
x²+3x-18 = 0
Factorize
x²-6x+3x-18 = 0
x(x-6)+3(x-6) = 0
x+3 = 0 and x-6 = 0
x = -3 and 6
The first 3 number is are 6, 8 and 10
I need some help; if you don't know the answer, don't answer
Answers
Answer:
B is the right answer and if you want learn this, than learn algebric expression
An arrow is shot vertically upward from a platform 19ft high at a rate of 163ft/sec. When will the arrow hit the ground? Use the formula: h=−16t2+v0t+h0. (Round your answer to the nearest tenth.)
Answers
Answer: 10.3 s
Step-by-step explanation:
Given
The height of the arrow is given by [tex]h=-16t^2+v_ot+h_o[/tex]
At [tex]t=0, h=19\ ft[/tex]and [tex]v_o=163\ ft/s[/tex]
When arrow hits ground, h becomes 0 i.e.
[tex]\Rightarrow 0=-16t^2+163t+19\\\Rightarrow 16t^2-163t-19=0\\\\\Rightarrow t=\dfrac{163\pm \sqrt{(-163)^2+4(16)(19)}}{2(16)}\\\\\Rightarrow t=-0.115,10.30\ s[/tex]
Neglecting the negative value of t
So, the arrow hits the ground after 10.30 s
If y varies inversely as x2 and y=6 when x=30, what is y when x=6
Answers
Answer:
y = 150
Step-by-step explanation:
y varies inversely as x²
yx² = k
----------------
y = 6 when x = 30
6(30²) = k
6(900) = 5400
--------------------------
what is y when x = 6
y(6²) = 5400
y(36) = 5400
y = 5400/36
y = 150
Answer:
y= 150
Step-by-step explanation:
[tex]y\ \alpha \ \frac{1}{x^2}\\\\y = k \times \frac{1}{x^2}\\\\[/tex]
Given y = 6, and x = 30. Find k.
[tex]6 = k \times \frac{1}{30^2}\\\\6 \times 900 = k\\\\5400 = k[/tex]
Given x = 6 and k = 180. Find y
[tex]y = 5400\times \frac{1}{6^2}\\\\[/tex]
[tex]=5400 \times \frac{1}{36}\\\\=150[/tex]
Select the graph that would represent the best presentation of the solution set.
|xl > 5
Answers
4. In slope-intercept form, what is the equation of a line perpendicular toy - 2x + 7 that passes
through the point (5,8)?
a y - 4x + 21
b. y - 2x ***
a.y=2x-31
Answers
Answer:
y = (-1/2)x + 21/2
Step-by-step explanation:
Given equation:
y - 2x + 7
Coordinates = (5,8)
Find:
Perpendicular equation
Computation:
y = mx + c
y - 2x + 7
y = 2x - 7
So,
m = 2
The negative reciprocal of 2 is -1/2
So,
For,
Coordinates = (5,8)
y = mx + c
8 = (-1/2)(5) + c
8 = -5/2 + c
c = 8 + 5/2
c = 21 /2
So,
y = mx + c
y = (-1/2)x + 21/2
a rectangular swimming pool is 15 meters long, 12 1/2 meters wide and 2 1/2 meters deep. what is the pools volume?
Answers
Answer:
468.75 Cubic meters
Step-by-step explanation:
15 x 12.5 x 2.5 = volume
187.5 x 2.5 = volume
468.75 = volume
Answer:
its 393.75 cubic meters
Step-by-step explanation:
I hope this helps
Kevin correctly answered 75% of 32 test questions.
Part A
How many questions did Kevin answer correctly?
Part B
How many more questions would Kevin have to answer correctly to get more than 80% correct?
Answers
Answer:
part a-24 questions
part b-2 or 3 more questions
Step-by-step explanation:
part a-to find the number, change the percent into a decimal (.75) and multiply (24)
part b-first find how many questions need to be right to get 80% (.80 times 32=25.6). then subtract by how many he would get with a 75% (25.6-24=about 2 to 3 more questions, rounded 2)
. A man travels 13km by bus , 8km by car and y km by train . If the man has to travel a total of 30 km , find y. *
Answers
Answer:
9km
Step-by-step explanation:
30-(13+8)=9km
I hope you understand
please answer this !!
x/2 + 50
Answers
Answer:
x = 260
Step-by-step explanation:
Add the two angles together. They will sum to 180
x/2+ 50 = 180
Subtract 50 from each side
x/2+50-50 = 180-50
x/2 = 130
Multiply by 2
x/2*2 = 130*2
x = 260
Answer:
260°
Step-by-step explanation:
To calculate the two angles together . They will added to 180°.x / 2 + 50° = 180°
Subtract 50° from each side
x/2 + 50° - 50° = 180° - 50°
x / 2 = 130°
Multiply each side by 2
2 × x/2 = 130° × 2
x = 260°
A typical serving of fish is 4 ounces. What is this serving size in grams?
Answers
Answer:
the answer is 113.398 grams
4 ounces is 113.398 in grams
Hey guy, can yall please help me?
Answers
Answer:
x is greater than or equal to 3
Step-by-step explanation:
x ≥ 3
x is greater than or equal to 3
so you got the plot right
Suppose the hypotenuse of a right triangle is 13 cm and one of the legs is 10 cm. Use the Pythagorean Theorem to find the measure of the triangle’s other leg.
Answers
Answer:
3
Step-by-step explanation:
Pythagorean rule
[tex]hyp = opp + adj \\ therefore. \\ opp = hyp - adj \\ and \\ adj = hyp - opp[/tex]
opp=13-10
opp=3
1)Rút gọn:
(√9+4√5)-(√9-4√5)-√5+(√23-8√7)
2)Chứng minh:
x²+x√3+1 luôn luôn dương với mọi x.
Answers
Answer:
si sumas 9+4×5 te da la respuesta
2. If the sales tax on a $825 television set is 7%, how
much will you pay in total?
Please help!!Either question is fine!
Answers
Answer:
$882.75
Step-by-step explanation:
In order to calculate tax, you need to multiply the percentage by the purchase costs. First, start by finding the decimal value of the percentage.
7 ÷ 100 = 0.07 — Percentage converted to a decimal.
[tex]825 \times 0.07 = 57.75[/tex]
— The tax. Now, in order to find the whole price, the tax and retail price must be added together.
[tex]825 + 57.75 = 882.75[/tex]
As per linear equation, the amount I have to pay in total is $645.
The simplified value of the given expression is (8 - 17x).
What is a linear equation?"A linear equation is an equation in which the highest power of the variable is always 1."
1. Given, the cost of television is $825.
The sales tax rate is 7%.
Therefore, total price of the television is
= $[tex][825 + (\frac{825(7)}{100})][/tex]
= $[tex](825+57.75)[/tex]
= $[tex]882.75[/tex]
2. The given expression is:
[tex]-4(3x - 2)- 5x\\= -12x + 8-5x\\= 8-17x[/tex]
Learn more about a linear equation here:
brainly.com/question/1751327
#SPJ2
Please help my teacher will kill me
Answers
2nd image: since those angels are parrelled they’re the same number, so you just need to solve the equation.
6x+2=56
6x=54
6x/6 = 54/6
x=9
hope that helps!
Determine whether the dilation from the figure on the left to the figure on the right is an enlargement or a reduction. Then find the scale factor of the dilation.
A : Reduction scale factor 1/14
B : Enlargement; scale factor 14
C : Enlargement scale factor 0.5
Answers
Answer:
A.
Step-by-step explanation:
we are going from a large shape to a smaller shape. the proof is that the side lengths go down from 7m to 0.5m. so, it is a reduction.
and the scaling factor s ? what do we need to multiply the original side lengths with to get the new ones ?
7 × s = 0.5 = 1/2
s = (1/2)/7 = (1/2)/(7/1) = (1×1)/(2×7) = 1/14
=> answer A is correct
The dilation from the figure on the left to the figure on the right is a reduction.
Reduction scale factor 1/14.
The correct option is A.
What is a scale factor?The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).
Given:
We have given that two figures.
The dilation from the figure on the left to the figure on the right is a reduction.
And the scale factor is,
= actual / scale
= 1/(7 / 0.5)
= 1/14
Therefore, the scale factor is 1/14.
To learn more about the scale factor;
https://brainly.com/question/29464385
#SPJ2
The rule g = b + 3 expresses the relationship between the
number of girls g and the number of boys b in a classroom.
Rewrite this rule another way.
Answers
Answer:
g = 3 + b
b + 3 = g
3 + b = g
Step-by-step explanation:
Answer:
[see below]
Step-by-step explanation:
Rewriting the rule so 'b' would be the subject:
[tex]g = b + 3\\\\g - 3 = b + 3-3\\\\g-3=b\\\\\boxed{b=g-3}[/tex]
Hope this helps.
Find the missing side lengths. Round all answers to the nearest tenth.
Answers
Answer:
81
Step-by-step explanation:
90+25= 115
115 - 34 = 81