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
Answer:
[tex] \displaystyle( {x}_{1} , y_{1}) =( - 3,4)\\ (x _{2}, y_{2}) = (4, - 3)[/tex]
Step-by-step explanation:
we are given two conditions
two integers whos product is -12two integers whos sum is 1let the two integers be x and y respectively according to the first condition
[tex] \displaystyle xy = - 12[/tex]
according to the second condition:
[tex] \displaystyle x + y = 1[/tex]
now notice that we have two variables therefore ended up with a simultaneous equation so to solve the simultaneous equation cancel x from both sides of the second equation which yields:
[tex] \displaystyle y = 1 - x[/tex]
now substitute the got value of y to the first equation which yields:
[tex] \displaystyle x(1 - x) = - 12[/tex]
distribute:
[tex] \displaystyle x- {x}^{2} = - 12[/tex]
add 12 in both sides:
[tex] \displaystyle x- {x}^{2} + 12 = 0[/tex]
rearrange it to standard form:
[tex] \displaystyle - {x}^{2} + x + 12 = 0[/tex]
divide both sides by -1:
[tex] \displaystyle {x}^{2} - x - 12 = 0[/tex]
factor:
[tex] \displaystyle ({x} + 3)(x - 4) = 0[/tex]
by Zero product property we acquire:
[tex] \displaystyle {x} + 3 = 0\\ x - 4= 0[/tex]
solve the equations for x therefore,
[tex] \displaystyle {x}_{1} = - 3\\ x _{2} = 4[/tex]
when x is -3 then y is
[tex] \displaystyle y _{1}= 1 - ( - 3)[/tex]
simplify
[tex] \displaystyle y _{1}= 4[/tex]
when x is 4 y is
[tex] \displaystyle y _{2}= 1 - ( 4)[/tex]
simplify:
[tex] \displaystyle y _{2}= - 3[/tex]
hence,
[tex] \displaystyle( {x}_{1} , y_{1}) =( - 3,4)\\ (x _{2}, y_{2}) = (4, - 3)[/tex]
[tex]frac{12(x+y)^{3} }{9(x+y)}[/tex]
Hey guys, can yall help me out? I will give brain to whomever answers correctly
Answer:
A is the correct answer.
For a right triangle ABC, you are told that cos A = x and sin A = y. Which option below gives an expression that is equivalent to tan A? a. x/y b. y/x c. x/√x^2+y^2 d. y/√x^2+y^2
Answer:
B
Step-by-step explanation:
We know that
cos A = adjacent / hypotenuse
sin A = opposite / hypotenuse
Therefore, sin A / cos A =
(opposite / hypotenuse) / (adjacent / hypotenuse)
= (opposite/hypotenuse) * (hypotenuse / adjacent)
= opposite / adjacent
= tan A
Therefore, tan A = sin A / cos A = y/x
Find the equation of the circle in standard form for the given center (h, k) and radius
Someone help
Answer:
3rd choice
Step-by-step explanation:
You can find the attached files
(PLS HELP NOW WILL GIVE BRINIEST!!!!!) A figure is formed by two pairs of parallel sides that are the same length. Which type of figure is it?
A.
hexagon
B.
square
C.
pentagon
D.
triangle
Answer: B. Square
Step-by-step explanation:
All sides of a square have the same lengthAll four angles of a square = 90°A square has two parallel sidesThe answer is B.), because if you have two pairs of parallel sides that means it looks like a square 1. || 2. _
_
- Chilio
Set up a proportion to solve for x in the following similar triangles.
Answer:
C
Step-by-step explanation:
I took the quiz and it was C! Hope this helps :)
Help me solve this problem please
Answer:
c
Step-by-step explanation:
Which of the following statements must be true about a rhombus?
The consecutive sides of a rhombus are parallel.
The diagonals of a rhombus are perpendicular.
The diagonals of a rhombus are congruent.
The opposite angles of a rhombus are supplementary.
Answer:
Step-by-step explanation:
The diagonals of a rhombus are perpendicular
Answer: Choice B) The diagonals of a rhombus are perpendicular
=============================================================
Explanation:
Let's go through the answer choices to see which are true statements, and which are false.
A) This is false because consecutive sides must meet up at a vertex point, or else they won't be next to each other. Consecutive sides can never be parallel (regardless what type of quadrilateral we're dealing with, or any polygon for that matter). In other words, consecutive sides share a common point on both segments, which is why they're not parallel. Instead, it should be phrased as "opposite sides of a rhombus are parallel" which is a true statement. B) This is true. If the diagonals are perpendicular, then we could have either a kite or a rhombus. C) This is false. If the diagonals are congruent, then we have a rectangle. We could have a square (which is both a rhombus and a rectangle at the same time), but that's only for specific cases. In a more general sense, we could have a non-square rectangle that isn't a rhombus. D) This is false. A rhombus is a type of parallelogram. For any parallelogram, the opposite angles are always the same measure. The only time the angles are supplementary is when we have a rectangle; otherwise, the angles won't add to 180.What term is used for a bell-shaped curve that is symmetrical regarding the average value of the population (the data being analyzed)?
Answer:
Normal distribution
Step-by-step explanation:
The answer is "normal distribution". This is because in a normal distribution, the mean, median and mode are equal. What this means is that the distribution will be symmetrical with a bell curve unlike in positive or negative skew where it is skewed to either the left or right.
what are the lengths of SV and QT? no links.
ok so we see that TR is 17 units, so RV is the same amount
3x+2 so 3x=15 so divide both sides by 3 we get x=5
now we know x=5 4x+1=21 and 9x-4=41
*drops microphone*
Answer:
TR = 12
=> 3x + 2 =17
=> x = 5
We have QT = QV (because QTV is an isosceles triangle)
=> QT = 4x+1=4x5+1=21 units
We have TS = SV (because TSV is an isosceles triangle)
=>SV = 9x-4= 9x5-4=41 units
4 times the square of a non-zero number is equal to 12 times the number.
what is the number?
Answer: 3
Step-by-step explanation:
Let the number be x.
4*(x squared) = 12x
Divide both sides by 4,
X squared = 3x,
divide both sides by x,
X=3
How can I solve this problem
Answer:
x = 27
Step-by-step explanation:
I'm going to use letters to label the parts of the triangle while explaining how to solve for x:
Angle A = x (bottom left angle of the triangle)
Angle B = 4x (top angle of the triangle)
Angle C = empty angle (bottom right angle of the triangle)
Angle D = 3x + 54 (angle outside of the triangle)
A line has a angle measurement of 180 degrees.
Angle C & D make up the line, meaning Angle C + Angle D = 180 degrees.
To find Angle C, we would subtract Angle D's equation from 180 like this:
180 - (3x + 54)
Now Angle C equals 180 - (3x + 54)
Now we have all the angles inside the triangle. To find x, we are going to sum up Angle A, B, & C and set it equal to 180.
We set the equation to 180 because a the sum of the interior angles for a triangle is 180.
The equation looks like this:
(180 - (3x + 54)) + 4x + x = 180
Now we use basic algebra to solve it:
(180 - (3x + 54)) + 4x + x = 180
(distribute the - to (3x + 54))
180 - 3x - 54 + 4x + x = 180
(add like terms on the left side of the equation)
126 + 2x = 180
(subtract 126 from both sides)
2x = 54
(divide both sides by 2)
x = 27
To prove this answer is correct, plug it back in the original equation and you'll see that it ends up equaling 180, which is the sum of interior angles for triangle.
Hope it helps (●'◡'●)
T is directly proportional to
[tex] \sqrt{x} [/tex]
T=400 when x = 625
(a) Find a formula for T in terms of x.
pls help i need it urgently Pls pls pls
Answer:
(a) T = 16√x
Step-by-step explanation:
T is directly proportional to √x, so we can say,
T=k√x (where k is a constant)
now, according to the question,
400=k×√625
400=k×25
k=16
so, putting the value of k in the equation, T=16√x
Answered by GAUTHMATH
Step-by-step explanation:
Given that ,
T is directly proportional to √x .Mathematically we can write it as ,
[tex]\implies T \propto \sqrt{x}[/tex]
Let k be the constant , therefore ,
[tex]\implies T = kx [/tex]
Now when T = 400 and x = 625 , lets find the value of k , as ,
[tex]\implies 400 = k\times 625 \\\\\implies k =\dfrac{400}{625}\\\\\implies k= 0.64 [/tex]
Therefore the required formula will be ,
[tex]\implies \underline{\underline{ T = 0.64x}} [/tex]
Write the sentence as an equation.
129 equals g subtracted from 21
Answer:
g-21=129
Step-by-step explanation:
what is the measure of 4?
Answer:
11x + 8 = 12x - 4
x=12
∠ 4 = 180-140 = 40°
Step-by-step explanation:
Can someone help me with this math homework please!
This frequency table represents the number of cars owned by each family on a street.
What is the mean number of the cars owned by each family?
A. 2.5
B. 3
C. 4
D. 5.5
Step-by-step explanation:
1+2+3+4+5=14 divided by 5=2.8 so, A.would be your answer.
What form do we place a quadratic in to find the Vertex, or "extrema” of a quadratic function?
Answer:
The vertex form of the quadratic function, f(x) = a·(x - h)² + k
Step-by-step explanation:
The general form of a quadratic function is given as follows;
f(x) = a·x² + b·x + c
The vertex form of the quadratic function is f(x) = a·(x - h)² + k
Where;
(h, k) = The coordinates of the vertex of the parabola
h = -b/2·a, k = f(h)
Can someone help me with this math homework please!
Answer:
3. The number of students that rode on each bus
Step-by-step explanation:
The equation they give us is:
2b + 6 = 70
The question already tells us that in this equation:
2 is the 2 buses that the school hired
6 is the 6 leftover kids who couldn't fit on the 2 buses
The question also tells us that the 2 buses only have a total of 64 seats, so 32 seats on 1 bus (64/2 = 32).
So that means b would equal the 32 seats on 1 bus, or the number of students that rode on each bus.
Hope it helps (●'◡'●)
3√75
simplest rationalizing factor
PLEASE DO ANSWER ONLY IF YOU KNOW IT
Answer:
the square root of 75 is 8.6
and 8.6 times 3 is
the answer is 25.8
Hope This Helps!!!
(X^2+3)^2 - (x^2-1)^2
Answer:
8(X^2+1)
Step-by-step explanation:
(X²+3)²-(X²-1)
(X²+3)(X²+3)-(X²-1)(X²-1)
X⁴+3X²+3X²+9-(X⁴-X²-X²+1)
X⁴+6X²+9-(X⁴-2X²+1)
X⁴+6X²+9-X⁴+2X²-1
8X²+8
Hi I really need help with this question.So if you can help me thank you so much and if you can help me can you explain it step by step please and thank you so much your a life saver <3
Answer:
Step-by-step explanation:
I'll answer the question, but before I do, let me crab about the reliance on a diagram. You should never have to answer a question where you make assumptions about the diagram. It should state the the longest leg in one triangle = 2x - 4, and the hypotenuse in the larger triangle is 42, while in the smaller one it is x + 8\
Added to which you have to state that there is a ratio between the large triangle and the small one.
24/(2x - 4) = (x + 8)/42 Cross Multiply
24*42 = (x + 8)*(2x - 4) Remove the brackets. Combine the left
1008 = 2x^2 - 4x + 16x - 32 Combine the right and switch
2x^2 + 12x - 32 = 1008 Subtract 1008
2x^2 + 12x - 1040 = 0 Divide by 2
x^2 + 6x - 520 = 0
(x + 26)(x - 20) = 0
x = - 26 which has no meaning
x = 20 which is the answer.
2x - 4 = 2*20 - 4 = 36
x + 8 = 28
I'm not sure what you want -- the side lengths or just x.
Step-by-step explanation:
the ratio
24:2x-4=x+8:42
24/2x-4=x+8/42
24×42=(x+8)(2x-4)
1008=2x(x+8)-4(x+8)
1008=2x²+16x-4x-32
1008=2x²+12x-32
1008+32=2x²+12x
1040=2x²+12x
0=2x²+12x-1040
OR
24/2x-4=x+8/42
LCM=42(2x-4)
42(2x-4)×24/2x-4=42(2x-4)×x+8/42
42×24=(2x-4)(x+8)
1008=2x(x+8)-4(x+8)
1008=2x²+16x-4x-32
1008=2x²+12x-32
1008+32=2x²+12x
1040=2x²+12x
0=2x²+12x-1040
Three less than the product of a number and six is twenty seven
Write an equation to represent the sentence:
Answer:
let the number be a
product of a number and six = 6 times a=6a
three less than the product of a number= 6a-3
then the full equation will be 6a-3=27
PLEASE HELP FAST WILL MARK BRAINLIEST!!!!!!
Which table of ordered pairs represents a proportional relationship? (Look at the picture and tap to see the full picture)
Answer: the second one
Step-by-step explanation:
Answer:
The asnwer is D
Step-by-step explanation:
D is a proportional relationship because
-3*-4 is 12
-6*-4 is 24
-9*-4 is 36
Hope this helps! :)
Somebody please help me! Very confused, the help is very much appreciated!
Answer:
18
Step-by-step explanation:
Because the diagonals in a parallelogram bisect each other, RS = SP = 18
BRAINLIEST PLEASEEEEE
Can someone help me with this math homework please!
Answer:
x = 48.125
Step-by-step explanation:
Explanation in progress! (●'◡'●)
Answer:
48.25
Step-by-step explanation:
first wirte the same qa and write long qa and write the ans in procesa
Find the value of y...........
Answer:
y=0
Step-by-step explanation:
9514 1404 393
Answer:
y = 0
Step-by-step explanation:
Factor out 3^y:
3^(2y-1) +2(3^(y-1)) = 1 . . . . . . given
(3^y)^2(3^-1) +2(3^y)(3^-1) = 1 . . . . factor out 3^y
(3^y)^2 +2(3^y) -3 = 0 . . . . . . . . . . subtract 1, multiply by 3
Let x = 3^y. Substituting, we have ...
x^2 +2x -3 = 0
(x -1)(x +3) = 0
x = 1 or x = -3 . . . . . values of x that satisfy this equation
Then the corresponding values of y are ...
x = 3^y . . . . . . . . . . . . relation of x and y
log(x) = y·log(3) . . . . . take logs to solve for y
y = log(x)/log(3) . . . . . divide by the coefficient of y
For x = 1, this is y = log(1)/log(3) = 0
For x = -3, this is y = log(-3)/log(3) . . . . no real solutions
The only real solution is y = 0.
_____
The attachment shows the solution of f(x) = 0, where ...
[tex]f(x)=3^{2x-1}+2\times3^{x-1}-1[/tex]
That solution is x=0. This means the (real) solution to the given equation is y=0.
Si el largo de un rectángulo mide el doble del ancho que es "a", ¿cuál es su área?
Answer:
El área es 2 veces el cuadrado del ancho del rectángulo.
Step-by-step explanation:
El área de un rectángulo viene dado por:
[tex] A = a*l [/tex]
En donde:
a: es el ancho
l: es el largo
Si el largo es el doble del ancho:
[tex] l = 2a [/tex]
Entonces el área es:
[tex] A = a*l = a*(2a) = 2a^{2} [/tex]
Por lo tanto, el área es 2 veces el cuadrado del ancho del rectángulo.
Espero que te sea de utilidad!
if <ABC measures 100 and is inscribed in a circle O. find <BAO and <BCO
Answer:
<BCO = <BAO = 20degrees
Step-by-step explanation:
If <ABC measures 100 and is inscribed in a circle O. find <BAO and <BCO
To get <BAO and <BCO, we need to get <AOC first.
From the figure, it can be seen that triangle ABC is an isosceles trinagle. Hence;
<BAC + <BCA + 100 = 180
Since <BAC = <BCA
<BAC + <BAC = 180 - 100
2<BAC = 80
<BAC = 80/2
<BAC = 40
Also;
<BAO = <BCO and <BAO = <BAC/2
<BAO = 40/2 = <BCO
Hence <BCO = <BAO = 20degrees
When a constant force acts upon an object, the acceleration of the object varies inversely with its mass. When a certain constant force acts upon an object with
mass 7 kg, the acceleration of the object is 4 m/s?. If the same force acts upon another object whose mass is 2 kg, what is this object's acceleration?
Answer:
14 m/s²
Step-by-step explanation:
From the question
a ∝ F/m.............. Equation 1
Where a = aceleration, m = mass, F = force
make F the subject of the equation
F = ma............ equation 2
Given: m = 7 kg, a = 4 m/s²
Therefore,
F = 7(4)
F = 28 N
For another object whose mass is 2 kg,
Make a the subject of equation 2
a = F/m
a = 28/2
a = 14 m/s²