Answer:
Yes, it shows direct variation
Step-by-step explanation:
Given
The above table
Required
Is it a direct variation?
The constant of variation (k) is:
[tex]k = y/x[/tex]
For each pair x and y, we have:
[tex]k = 5/15 = 1/3[/tex]
[tex]k = 6/18 = 1/3[/tex]
[tex]k =9/27 = 1/3[/tex]
Since the calculate constant have the same value for all pair or x and y, then the table shows direct variation
Answer:1
Step-by-step explanation:3/3=1
Which of the following is equivalent to 2/x + 3/x−1 for x>1 ?
pls explain
Answer:
Step-by-step explanation:
3. Find the volume of the figure. Simplify.
Cube
x + 4
Answer:
[see below]
Step-by-step explanation:
V = s^3
V = (x+4)^3
V = x^3 + 3x^2 * 4 + 3x * 4^2 + 4^3
V = x^3 + 12x^2 + 48x + 64
Hope this helps.
Rab has trouble remembering the difference between addition of a positive and
negative number and multiplication of a positive and negative number. Explain how
you could clarify the concepts for him. Use an example to back up your explanation.
Addition of a positive and negative number always means that you are going to subtract the number e. g. 4+-1 = 3. However, multiplication of a positive and negative number means the answer is always negative e. g. 5 x - 3 = - 15.
The addition of positive and negative number will always subtract with sign of maximum value.
The multiplication of positive and negative number will have a negative sign always.
AdditionConcept for the addition of positive and negative numberWhen two numbers which have different sign are added, they will always be subtracted from each other. The sign will vary accordingly.
with negative sign: when two numbers are added such that the number with negative sign has the larger value, then both numbers will get subtracted but with negative sign.Example: Consider two number -5 and 4
= -5 + 4
= -1
Here, 5 is the larger value. So, the sign comes is negative.
with positive sign: when two numbers are added such that the number with positive sign has the larger value, then both numbers will get subtracted but with positive sign.Example: consider two number 5 and -4.
= 5 + (-4)
= 1
Here, 5 is the large number. So, the sign comes is positive.
MultiplicationConcept for the multiplication of positive and negative number:When two numbers with opposite signs are multiplied, the answer is always a negative number.
Example; Consider two numbers 4 and -5.
On multiplication,
4×(-5) = -20
Thus, the multiplication of two numbers with different signs will always give a negative number.
To know more about rational and irrational numbers, here
https://brainly.com/question/5796983
#SPJ2
The x- intercepts of a parabola are (0,-6) and (0,4). The parabola crosses the y- axis at -120. Lucas said that an equation for the parabola is y=5x^2+10x-120 and that the coordinates of the vertex are (-1, -125). Do you agree or disagree? List why?
Given:
The x- intercepts of a parabola are (0,-6) and (0,4).
The parabola crosses the y- axis at -120.
Lucas said that an equation for the parabola is [tex]y=5x^2+10x-120[/tex] and that the coordinates of the vertex are (-1, -125).
To find:
Whether Lucas is correct or not.
Solution:
The x- intercepts of a parabola are (0,-6) and (0,4). It means (x+6) and (x-4) are the factors of the equation of the parabola.
[tex]y=a(x+6)(x-4)[/tex] ...(i)
The parabola crosses the y- axis at -120. It means the equation of the parabola must be true for (0,-120).
[tex]-120=a(0+6)(0-4)[/tex]
[tex]-120=a(6)(-4)[/tex]
[tex]-120=-24a[/tex]
Divide both sides by -24.
[tex]\dfrac{-120}{-24}=a[/tex]
[tex]5=a[/tex]
Substituting [tex]a=5[/tex] in (i), we get
[tex]y=5(x+6)(x-4)[/tex]
[tex]y=5(x^2+6x-4x-24)[/tex]
[tex]y=5(x^2+2x-24)[/tex]
[tex]y=5x^2+10x-120[/tex]
So, the equation of the parabola is [tex]y=5x^2+10x-120[/tex].
The vertex of a parabola [tex]f(x)=ax^2+bx+c[/tex] is:
[tex]Vertex=\left(-\dfrac{b}{2a},f(-\dfrac{b}{2a})\right)[/tex]
In the equation of the parabola, [tex]a=5,b=10,c=-120[/tex].
[tex]-\dfrac{b}{2a}=-\dfrac{10}{2(5)}[/tex]
[tex]-\dfrac{b}{2a}=-\dfrac{10}{10}[/tex]
[tex]-\dfrac{b}{2a}=-1[/tex]
Putting [tex]x=-1[/tex] in the equation of the parabola, we get
[tex]y=5(-1)^2+10(-1)-120[/tex]
[tex]y=5-10-120[/tex]
[tex]y=-125[/tex]
So, the vertex of the parabola is at point (-1,-125).
Therefore, Lucas is correct.
Help me please guys if you don’t mind
Answer:
[tex]5 {x}^{2} - 11x + 6 \\ 5 {x}^{2} - (5 + 6)x + 6 \\ 5 {x}^{2} - 5x + 6x + 6 \\ 5x(x - 1) - 6(x - 1) \\ (5x - 6)(x - 1)[/tex]
P and Q are points on the line 3y - 4x = 12
a Complete the coordinates of P and Q.
P(0, 1) Q(,0)
Answer:
Step-by-step explanation:
Since the coordinates of P are (0, 1), this makes P the y-intercept of that line. The y-intercept exists where x = 0. And in the coordinate (0, 1), x does in fact equal 0.
Since the one coordinate given in Q is (?, 0), this means that Q is the x-intercept of the line. The x-intercept exists where y = 0. And in the coordinate (?, 0), y does in fact equal 0. So in order to solve for the x coordinate of Q, we plug in a 0 for y and solve for x:
3(0) - 4x = 12 and
-4x = 12 so
x = -3
A rectangle has an area of 32 square millimeters. The length of the rectangle is 888 millimeters. What is the width of the rectangle?
Answer:
0.036
Step-by-step explanation:
See image below:)
the area is 32 and the length is 888
you use the formula w= a/l
so a= 32 and l= 888
The width is 0.036mm.
What is area of a rectangle?Area of a rectangle (A) is the product of its length (l) and width (w).
A= l. w
Here, given that,
the area is 32 and the length is 888
We use the formula w= A/l
so, A= 32 and l= 888
Then, width= w= 32/888
=0.036 mm.
Hence, width is 0.036mm
To learn more on Area click:
https://brainly.com/question/20693059
#SPJ2
Complete the steps to solve the inequality:
0.2(x + 20) – 3 > –7 – 6.2x
Use the distributive property:
Combine like terms:
Use the addition property of inequality:
Use the subtraction property of inequality:
Use the division property of inequality:
0.2x + 4 – 3 > –7 – 6.2x
0.2x + 1 > –7 – 6.2x
6.4x + 1 > –7
6.4x > –8
Answer:
x>-1.25
Step-by-step explanation:
0.2x+4-3>-7-6.2x
0.2x+1>-7-6.2x
0.2x+6.2x>-7-1
6.4x>-8
x>-1.25
or x>-5/4,x>-1 1/4, xE(-1.25, infinite)
The solution to the inequality is x > -1.25.
The complete steps are:
the distributive property: 0.2x+4-3>-7-6.2x
Combine like terms: 0.2x+1>-7-6.2x
the addition property of inequality: 0.2x+6.2x +1 >-7 => 6.4x + 1 > –7
the subtraction property of inequality: 6.4x > -7 - 1 => 6.4x>-8
the division property of inequality: (6.4x)/6.4 > (-8)/6.4 => x>-1.25
Here, we have,
To solve the inequality 0.2(x + 20) - 3 > -7 - 6.2x,
let's go through the steps:
Step 1: Use the distributive property:
0.2x + 4 - 3 > -7 - 6.2x
Step 2: Combine like terms:
0.2x + 1 > -7 - 6.2x
Step 3: Use the addition property of inequality:
0.2x + 1 + 6.2x > -7
6.4x + 1 > -7
Step 4: Use the subtraction property of inequality:
6.4x > -7 - 1
6.4x > -8
Step 5: Use the division property of inequality:
Divide both sides of the inequality by 6.4 to isolate x:
(6.4x)/6.4 > (-8)/6.4
x > -8/6.4
Simplifying further, we have:
x > -1.25
Therefore, the solution to the inequality is x > -1.25.
To learn more on inequality click:
https://brainly.com/question/28841069
#SPJ5
How long is JK?
Choose 1 answer:
A: 3
B: 2 square root 3
C: 3 square root 3
D: 6
E: 9
Answer:
C) 3 times the sq root of 3
Step-by-step explanation:
In a right angle triangle, the COS is definned as the ajacent side over the hypotenuse. So
COS 60 = JK/JL
COS 60 = JK/(6*sq root 3)
.5 = JK/(6*3**1/2)
JK = .5 *(6*3**1/2)
JK = 3*3**1/2
2.
B. Melody had $25 and withdrew $300 from his bank account. She bought a pair of trousers for $30.00, 2 shirts for
$19.00 each, and 2 pairs of shoes for $40.00 each. Give the final expression, and determine how much money Mel had
at the end of the shopping day.
Answer:
25 + 300 = 325
trousers: spent 30 (a pair of trousers = one unity of trousers)
shirts: spent 19 x 2 = 38
shoes: spent 40 x 2 = 80
80 + 38 + 30 = 148
325 - 148 = 177
She had $177,00 left.
hope it helps.
Also, I think that Brainly is an awesome app, but there's an app which is doing great work for me in maths, named Gauthmath. I will suggest it. Video concepts and answers from real tutors.
Additional Mathematics
Answer:
a = 1000, p = 10
Step-by-step explanation:
Given
y = - 3lg x + lg a
in the form y = mx + c ( m is the slope and c the y- intercept )
From the graph
(a)
c = 3 , then
lg a = 3 , that is
a = 10³ = 1000
(b)
Replace x by p and y = 0 in the equation
0 = - 3lg p + 3 ( subtract 3 from both sides )
- 3 = - 3lg p ( divide both sides by - 3 )
1 = lg p
p = 10 [ [tex]log_{10}[/tex] 10 = 1 ]
91.55
Which equation has the solutions -
5:27
3
1?
I
3x2 - 5x + 7 = 0
03x2 - 5x – 1 = 0
3x2 - 10x + 6 = 0
O 3x2 _ 10x + 1 = 0
Answer:
the answer is 3x2-10x+6=0
Help pls it’s the last day of summer school
Find the TWO integers whos product is -12 and whose sum is 1
Answer:
[tex] \rm Numbers = 4 \ and \ -3.[/tex]
Step-by-step explanation:
Given :-
The sum of two numbers is 1 .
The product of the nos . is 12 .
And we need to find out the numbers. So let us take ,
First number be x
Second number be 1-x .
According to first condition :-
[tex]\rm\implies 1st \ number * 2nd \ number= -12\\\\\rm\implies x(1-x)=-12\\\\\rm\implies x - x^2=-12\\\\\rm\implies x^2-x-12=0\\\\\rm\implies x^2-4x+3x-12=0\\\\\rm\implies x(x-4)+3(x-4)=0\\\\\rm\implies (x-4)(x+3)=0\\\\\rm\implies\boxed{\red{\rm x = 4 , -3 }}[/tex]
Hence the numbers are 4 and -3
Let integers be x and x-1
ATQ
x+x-1=1[tex]\\ \sf\longmapsto 2x-1=1[/tex]
[tex]\\ \sf\longmapsto 2x=1+1[/tex]
[tex]\\ \sf\longmapsto 2x+2[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{2}{2}[/tex]
[tex]\\ \sf\longmapsto x=1[/tex]
Now
[tex]\\ \sf\longmapsto x-1=1-1=0[/tex]
The integers are 1 and 0But
Integers can be x and 1-x as their sum is 1
[tex]\\ \sf\longmapsto x(1-x)=-12[/tex]
[tex]\\ \sf\longmapsto x- x^2=-12[/tex]
[tex]\\ \sf\longmapsto x^2-x-12=0[/tex]
[tex]\\ \sf\longmapsto x^2-4x+3x-12=0[/tex]
[tex]\\ \sf\longmapsto x(x-4)+3(x-4)=0[/tex]
[tex]\\ \sf\longmapsto (x-4)(x+3)=0[/tex]
[tex]\\ \sf\longmapsto x=4,-3[/tex]
What is the volume of the sphere in terms of pi?
V=
6 in.
Answer:
= 288π in2
Step-by-step explanation:
Volume of a sphere is given by;
V =(4/3)πr3
V = volume
r is radius
Therefore V = {(4/3) × π × (6^3)} in3
= 288π in2
find the missing side of each triangle. i need help!!!
Answer:
√161 yd
Step-by-step explanation:
Hi there!
We're given a right triangle (notice the right angle), the measure of one of the legs (one of the sides that make up the right angle) as 8 yd, and the hypotenuse (the side opposite to the right angle) as 15 yd.
We need to find x, which is the other leg in the triangle
If we are given 2 sides and need to find a third, we can use Pythagorean Theorem, which states that a²+b²=c² if a and b are legs and c is the hypotenuse
In this case, a=8, b=x, and c=15
So let's substitute those values into the formula
(8)²+x²=(15)²
raise everything to the second power
64+x²=225
subtract 64 from both sides
x²=161
take the square root of both x and 161
x=√161, x=-√161
-√161 cannot work in this case, as distance cannot be negative.
The question asks for the answer to be in simplified radical form, but √161 cannot be simplified down further
so the answer is √161 yd
Hope this helps! :)
-x/8-11=12
/ means fraction
Answer:
Step-by-step explanation:
-x/8=12+11=23
-x=23*8=184
x=-184
x=-184Answer:
Step-by-step explanation:
What is the domain of the function on the graph?
•all real numbers
•all real numbers greater than or equal to -2
•all real numbers greater than or equal to -5
•all real numbers greater than or equal to 0
Answer:
all real numbers
Step-by-step explanation:
got it right
Answer:
A
Step-by-step explanation:
it is all real numbers
brainiest please
Micheal is selling lemonade.He sold 6 large lemonades at $3 each and 5 small lemonades at $2 each. How much money did he earn ?
Answer:
$28
Step-by-step explanation:
Answer:
6=$3
5=$2
6x3=18
5x2=10
18+10= 28
=$28
Step-by-step explanation:
Someone help me please if you don’t mind
Answer:
Multiply to -63
and add to -2
Step-by-step explanation:
I'm a genius.
Answer:
(x - 9)(x + 7)
Step-by-step explanation:
Given
x² - 2x - 63
Consider the factors of the constant term (- 63) which sum to give the coefficient of the x- term, that is
numbers that multiply to give - 63 and add to give - 2
The factors are - 9 and + 7 , since
- 9 × 7 = - 63 and - 9 + 7 = - 2 , then
x² - 2x - 63 = (x - 9)(x + 7) ← in factored form
plz help ASAP with explanation
Answer:
19.5 cm
Step-by-step explanation:
the remaining height = 1200 /(12×8)
= 1200/96 = 12.5 cm
so, the height of the tank = 7+ 12.5 = 19.5 cm
[tex]\displaystyle\bf \boxed{V=abh \ ; \ 1dm^3=1litre=1000cm^3} \\\\a=12cm \ ; \ b=8 cm ;\: h_1=7 \; ; \ h_0=h_1+h_2=?\\\\abh_2=1,2litre=1,2dm^3\ = 1200cm^3\\\\ 8\cdot 12 h_2=1200\\\\h_2=12.5 cm\: then \\\\h_0= 7+12,5=19,5 \\\\Answer : the \ height \ of \ the \ tank \ is \ 19,5 cm[/tex]
Please help me with this question.
Answer:
Step-by-step explanation:
-1 ≤ x < 3 Solution set = {-1, 0 ,1 , 2}
-2 < x < 2 Solution set = {-1 , 0 , 1}
Integer values that satisfies both inequalities are -1 , 0 , 1
I \\\\\\\\\ I
[-1] -3 I \\\\\\\\\\\ I -2 2 [tex]\displaystyle\bf x\in[-1;2)\\-1;0;\underline1\\\\Answer: 1[/tex]
AD = 6, DC = 8, find DB
Answer:
10
Step-by-step explanation:
use a^2+b^2=c^2
6^2+8^2=c^2
100=c^2
sqrt it and you get 10 for AC and AC=DB
Answer:
according to Pythagoras theorem, c²=a²+b²
|AC|²=|AD|²+|DC|²
|AC|²=6²+8²
|AC|²=36+64
|AC|²=100
√|AC|²=√100
|AC|=10
helppp plzzz right nowwwwwwww
Answer:
They are parallel so also -4/3
In AJKL, mZJ = (8x + 6)", mZK = (2x + 2)°, and młL = (4x + 4)º. Find m_L.
Answer:
Step-by-step explanation:
∠J + ∠K + ∠L = 180 {Angle sum property of triangle}
8x + 6 + 2x + 2 + 4x + 4 = 180
8x + 2x + 8x + 6 + 2 + 4 = 180
Combine like terms.
14x + 12 = 180
Subtract 12 form both sides
14x = 180 - 12
14x = 168
Divide both sides by 14
x = 168/14
x = 12
∠L = 4x + 4
= 4*12 + 4
= 48 + 4
∠L = 52
If an object looks the same
Answer:
I don't understand your question.............!
Step-by-step explanation:
Consider the original parallelogram and the enlargement. A parallelogram has side lengths 5 millimeters and 10 millimeters. A larger parallelogram has side lengths 15 millimeters and B. What is the length of side B in the enlarged parallelogram? 15 mm 30 mm 40 mm 50 mm
Answer:
B=30mm
Step-by-step explanation:
According to the Question,
we have, A parallelogram that has one side(A) 5 millimeters and the other side(C) 10 millimeters. A larger parallelogram has side one side(D) 15 millimeters.
The Enlargement Parallelogram And Original Parallelogram Sides Ratio Remain the same.
Therefore, A/C = D/B
5/10 = 15/B
B=150/5
B=30mm
Cindy is hosting a potluck dinner for her book club. The more book club members who attend, the more chairs she will need. m = the number of members who attend the potluck c = the number of chairs Cindy will need Which of the variables is independent and which is dependent? A. c is the independent variable and m is the dependent variable B. m is the independent variable and c is the dependent variable
Answer:
B.
Step-by-step explanation:
m is the driving number in this system of numbers. whatever its value, all the others need to adjust to it.
c depends fully on m. if and when m increases, then also c has to increase.
El ministerio de educación publicó los resultados obtenidos por los colegios en la última prueba icfes saber 11. En el colegio San estaban el promedio de los estudiantes en la prueba de razonamiento cualitativo fue de 75,8 ¿ que significa este resultado?
Answer:
El indicador mencionado en el enunciado indica que la suma de los resultados de las pruebas de razonamiento cualitativo de los estudiantes dividido por la población de los estudiantes arroja ese promedio.
El promedio indica el valor "central" del indicador, no estudia la dispersión de los resultados de las pruebas, es decir, como se distribuye la colección de indicadores.
Step-by-step explanation:
El indicador mencionado en el enunciado indica que la suma de los resultados de las pruebas de razonamiento cualitativo de los estudiantes dividido por la población de los estudiantes arroja ese promedio.
El promedio indica el valor "central" del indicador, no estudia la dispersión de los resultados de las pruebas, es decir, como se distribuye la colección de indicadores.
Why did U.S. leaders decide to create the Federal Reserve?
A. Economic panics showed that the banking system was not stable.
B. The United States needed to have a single type of currency.
C. Small banks requested additional government oversight.
D. State banks needed the power to create their own currencies.
Answer:
A
Step-by-step explanation:
A central bank was needed to oversee monetary policy
Answer:A
Step-by-step explanation:
I did the test
