The possible values of x are 5 and -1/12
Complete questionGiven that 2x − 1∶ x − 4 = 16x + 1 ∶ 2x − 1 find the possible values of x
How to determine the possible values of x?The ratio is given as:
2x − 1∶ x − 4 = 16x + 1 ∶ 2x − 1
Express as fraction
[tex]\frac{2x - 1}{x-4} = \frac{16x + 1}{2x -1}[/tex]
Cross multiply
4x^2 -4x + 1 = 16x^2 + x -64x - 4
Collect like terms
-16x^2 + 4x^2 + 64x - x - 4x + 1 + 4 = 0
Evaluate the like terms
-12x^2 + 59x + 5 = 0
Divide through by -1
12x^2 - 59x - 5 = 0
Expand
12x^2 + x - 60x - 5 = 0
Factorize
x(12x + 1) - 5(12x + 1) = 0
Factor out 12x + 1
(x - 5)(12x + 1) = 0
Expand
x - 5 = 0 or 12x + 1 = 0
Solve for x
x = 5 or x = -1/12
Hence, the possible values of x are 5 and -1/12
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Peter's dog weighs 12 pounds more than Joe's dog. The dogs weigh 36
pounds all together. Write an equation to find the weight of Joe's dog.
What are the domain and range of the function below?
A. Domain: (-4,0)
Range: [-2,∞)
B. Domain: (-3,0)
Range: [-2,∞)
C. Domain: (-∞,∞)
Range: [-2,∞)
D. Domain:
Range: (-∞,∞)
PS don't mind that dot on the graph, didn't mean to put it there.
The domain is (-∞,∞) and the range is [-2,∞)
How to determine the domain and the range?From the graph, we can see that the x values extend at both sides of the graph.
This means that the domain is the set of real values i.e. (-∞,∞)
However, the minimum y value is -2 and it increases from their
This means that the range is [-2,∞)
Hence, the domain is (-∞,∞) and the range is [-2,∞)
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Can I have the solution with steps
Answer:
1/6
Step-by-step explanation:
As usual in trigonometry, there are so many relationships between the trigonometric functions, there is bound to be more than one method to arrive at the answer.
Knowing values for the sine and cosine function for certain angles on the unit circle proves to be quite helpful. In general, I recommend 0°, 30°, 45°, 60°, and 90° at a minimum.
Recall the following 6 things:
[tex]\cos(30^o)=\frac{\sqrt{3}}{2}[/tex][tex]\cos(60^o)=\frac{1}{2}[/tex][tex]\sin(30^o)=\frac{1}{2}[/tex][tex]\sin(60^o)=\frac{\sqrt{3}}{2}[/tex][tex]\tan(\theta)=\dfrac{\sin(\theta)}{\cos(\theta)}[/tex][tex]\tan^2(\theta)=\tan(\theta)\tan(\theta)[/tex]Knowing these 6 things (4 things from the unit circle, a way to write the tangent function in terms of sine and cosine, and the definition of a squared trig function), we can simplify the given expression down to a single number:
The definition of the tangent squared function is that the output of the tangent function is squared...
[tex]\dfrac{1-\tan^2(30^o)}{1+\tan^2(60^o)}=\dfrac{1-(\tan(30^o))^2}{1+(\tan(60^o))^2}[/tex]
Using fact 5, and turning the tangent function into sines and cosines...
[tex]=\dfrac{1-\left(\frac{\sin(30^o)}{\cos(30^o)}\right)^2}{1+\left(\frac{\sin(60^o)}{\cos(60^o)}\right)^2}[/tex]
Using facts 1-4, and substituting known values for sines and cosines...
[tex]=\dfrac{1-\left(\frac{(\frac{1}{2})}{(\frac{\sqrt{3}}{2})}\right)^2}{1+\left(\frac{(\frac{\sqrt{3}}{2})}{(\frac{1}{2})}\right)^2}[/tex]
Division is multiplication by the reciprocal...
[tex]=\dfrac{1-\left(\frac{1}{2}*\frac{2}{\sqrt{3}}\right)^2}{1+\left(\frac{\sqrt{3}}{2}*\frac{2}{1}\right)^2}[/tex]
Reducing/simplifying common factors of 2...
[tex]=\dfrac{1-\left(\frac{1}{\sqrt{3}}\right)^2}{1+(\sqrt{3})^2}[/tex]
Squaring a square root...
[tex]=\dfrac{1-\left(\frac{1}{3}\right)}{1+(3)}[/tex]
Finding a common denominator...
[tex]=\dfrac{\frac{3}{3}-\frac{1}{3}}{4}[/tex]
Definition of subtracting fractions...
[tex]=\dfrac{\frac{3-1}{3}}{4}[/tex]
Arithmetic...
[tex]=\dfrac{\frac{2}{3}}{4}[/tex]
Division is multiplication by a reciprocal...
[tex]=\dfrac{2}{3}*\dfrac{1}{4}[/tex]
Simplification and reducing the fraction...
[tex]=\dfrac{1}{6}[/tex]
So, [tex]\dfrac{1-\tan^2(30^o)}{1+\tan^2(60^o)}=\dfrac{1}{6}[/tex]
For her job, natasha spent a total of n minutes processing id card applications and driver's license applications. it takes natasha 15 minutes to process and id card aplication and 20 minutes to process a driver's license application. what is the value of n
Step-by-step explanation:
if I understand the question, write an equation for n in terms of i for number of Id cards an d for number driver license.
n = 15i + 20d
The value of n for a total minutes processing id card applications and driver's license applications would be 35 minutes.
Used the concept of addition that states,
The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
Given that,
For her job, Natasha spent a total of n minutes processing id card applications and driver's license applications.
And, it takes Natasha 15 minutes to process an id card application and 20 minutes to process a driver's license application.
Now by the given condition, we get;
n = 15 minutes + 20 minutes
n = 35 minutes
Therefore, the value n is 35 minutes.
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How much is the bill for a person who used 700 kWh in a month?
Answer:
700 kWh which is more than 200 so
0.10(x - 200) + 30
0.10( 700 -200)+ 30
0.10( 500) + 30
50 + 30
80
$80
Could someone help me with this question real quick?
Answer:
Width is 46 meter
Length is 86 meter
Given:
width = wlength = (w + 40)Formula:
Area of rectangle = Length × WidthTrial and improvement:
1st try with w = 50
w(w + 40) = 4000
50(50 + 40) = 4000
4500 ≠ 4000
Value too high.
2nd try with w = 45
w(w + 40) = 4000
45(45 + 40) = 4000
3825 ≠ 4000
Value too small
3rd try with w = 46
w(w + 40) = 4000
46(46 + 40) = 4000
3956 ≠ 4000
This value is somewhat near to the area value.
It is found that width = 46 m then length = (w + 40) = (46 + 40) = 86 m
In a certain region of space, the potential is given by v=2x−5x2y 3yz2. How much is the magnitude of the electric field at point (-2, 2, 0)?
The magnitude of the electric field at the point (-2, 2, 0) is 46.52 V/m
How to calculate the electric field?Since in a certain region of space, the potential is given by v = 2x − 5x²y 3yz²,
The electric field, E = -grad(V) where grad(V) = (dV/dx)i + (dV/dy)j + (dV/dz)k
Since V = 2x − 5x²y + 3yz²
dV/dx = d(2x − 5x²y + 3yz²)/dx
= d2x/dx - d5x²y/dx + d3yz²/dx
= 2 - 10xy + 0
= 2 - 10xy
dV/dy = d(2x − 5x²y + 3yz²)/dy
= d2x/dy - d5x²y/dy + d3yz²/dy
= 0 - 5x² + 3z²
= - 5x² + 3z²
dV/dz = d(2x − 5x²y + 3yz²)/dz
= d2x/dz - d5x²y/dz + d3yz²/dz
= 0 - 0 + 6z
= 6z
The electric field
So, E = -grad(V)
= -[(dV/dx)i + (dV/dy)j + (dV/dz)k]
= -[(2 - 10xy)i + (- 5x² + 3z²)j + (6z)k]
So, the electric field at (-2, 2, 0) is
E = -[(2 - 10xy)i + (- 5x² + 3z²)j + (6z)k]
E = -[(2 - 10(-2)(2))i + (- 5(2)² + 3(0)²)j + (6(0))k]
E = -[(2 + 40)i + (- 5(4) + 0)j + (0)k]
E = -[42i + (-20 + 0)j + (0)k]
E = -[42i - 20j + 0k]
E = -42i + 20j - 0k
The magnitude of the electric field
So, the magnitude of E at (-2, 2, 0) is
|E| = √[(-42)² + 20² + 0²]
= √[1764 + 400 + 0]
= √2164
= 46.52 V/m
So, the magnitude of the electric field at the point (-2, 2, 0) is 46.52 V/m
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which of the following is a rational number
a.√5
b.π
c.1/2
d.√(77)
Which equation represents the graph below?
Answer:
D
Step-by-step explanation:
The slope-intercept form is the equation of a straight line (y=mx+b)
m= gradient and b= y-intercept
m=2/3 (rise over run) b= 4 (it goes through the point (0,4)
y=(2/3)x+4
Get rid of the fraction by multiplying everything by 3
3y=2x+12
which is also -2x+3y=12
What is the domain of f(x) = 5x – 7?
{x | x > –7}
{x | x < –7}
{x | x > 0}
{x | x is a real number}
Answer: Choice D) x is a real number
Reason:
We can replace x with any number we want without any restriction. There's no issues dealing with division by zero errors for instance, and we also don't have negatives under square roots to worry about. The domain of any linear function is always "the set of all real numbers".
Extra info: The domain in interval notation is [tex](-\infty, \infty)[/tex] which could be thought of as [tex]-\infty < x < \infty[/tex], i.e. x is between negative infinity and positive infinity.
Answer:
d
Step-by-step explanation:
What is the area of rectangle ABCD?
coordinate plane with rectangle ABCD at A 0 comma negative 1, B 0 comma 4, C 4 comma 4, and D 4 comma negative 1
Answer:
Area = 20 units
Step-by-step explanation:
A (-1,0)
B (0,4)
C (4,4)
D (4,-1)
i hope this is right
Answer:
Area = 20
Step-by-step explanation:
A (0,-1)
B (0, 4)
C (4, 4)
D (4, -1)
Drag each expression to the correct location on the table.
Simplify each exponential expression using the properties of exponents and match it to the correct answer.
The solution to the exponential expression is as follows:
[tex]\mathbf{\dfrac{(2\times 3^{-2})^3(5\times 3^2)^2}{(3^{-2})(5\times 2)^2} = 2}[/tex][tex]\mathbf{=(3^3)(4^0)^2(3\times 2)^{-3}(2^2)=\dfrac{1}{2}}[/tex][tex]\mathbf{\dfrac{(3^7\times 4^7)(2 \times 5)^{-3}(5^2)}{12^7\times 5^{-1}\times 2^{-4}} = 2}[/tex][tex]\mathbf{\dfrac{(2\times 3)^{-1}\times 2^0}{(2\times 3)^{-1}}= 1}[/tex]What are exponential expressions?Exponential expressions are convenient ways to express the mathematical power of a number in short forms.
Simplifying the following expressions given:
1.
[tex]\mathbf{\dfrac{(2\times 3^{-2})^3(5\times 3^2)^2}{(3^{-2})(5\times 2)^2} }[/tex]
Applying the exponent rule: [tex]\mathbf{(a\times b)^n = a^n b^n}[/tex]
[tex]\mathbf{\implies \dfrac{(2\times 3^{-2})^3\times 5^2\times 81}{3^{-2}\times 5^2\times2^2} }[/tex]
cancel out the common factor, we have:
[tex]\mathbf{\implies \dfrac{(2\times 3^{-2})^3\times 81}{3^{-2}\times2^2} }[/tex]
[tex]\mathbf{\implies \dfrac{(2\times 3^{-2})^3\times 3^4}{3^{-2}\times2^2} }[/tex]
[tex]\mathbf{\implies \dfrac{(2\times 3^{-2})^3\times 3^6}{2^2} }[/tex]
[tex]\mathbf{\implies \dfrac{2^3 \times \dfrac{1}{729} \times 3^6}{2^2} }[/tex]
[tex]\mathbf{\implies \dfrac{2^3 \times \dfrac{1}{729} \times729}{2^2} }[/tex]
[tex]\mathbf{\implies \dfrac{2^3 }{2^2} = 2}[/tex]
2.
[tex]\mathbf{=(3^3)(4^0)^2(3\times 2)^{-3}(2^2)}[/tex]
= [tex]\mathbf{\dfrac{1}{2}}[/tex]
3.
[tex]\mathbf{\dfrac{(3^7\times 4^7)(2 \times 5)^{-3}(5^2)}{12^7\times 5^{-1}\times 2^{-4}} = 2}[/tex]
4.
[tex]\mathbf{\dfrac{(2\times 3)^{-1}\times 2^0}{(2\times 3)^{-1}}= 1}[/tex]
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Please help me on this question!
Answer:
u = 10 ft
Step-by-step explanation:
cuboid volume = w × h × l
width * hight * length
560 = 7 × 8 × u
u = 10 ft
Answer:
u = 10 ft
Step-by-step explanation:
Volume of a rectangular prism = lwh
where:
l = lengthw = widthh = heightGiven:
Volume = 560 ft³width = 7 ftlength = 8 ftheight = uSubstitute the given values into the formula and solve for h:
⇒ 560 = 8 × 7 × u
⇒ 560 = 56u
⇒ 56u ÷ 56 = 560 ÷ 56
⇒ u = 10 ft
Therefore, the height of the prism is 10 ft.
True or false for 1 and 3
Step-by-step explanation:
I think 1 is true.
3 is false. it's $10 per hour
Use the Pythagorean theorem to find the distance on the coordinate plane.
Anne is visiting a friend who lives 18.5 km away. She travels 10 km by
train, 1.5 km by bus, and walks the rest of the way. If she walks at a rate
of 3.5 km per hour, for how long will Anne walk?
Answer:
Anne will walk for 2 hours.
Step-by-step explanation:
Distance formula = velocity × time
Total distance is 18.5 km
Anne travels by train = 10 km
and by bus = 1.5 km
let the distance covered by anne by walking be x
10 + 1.5 + x = 18.5
x = 18.5 - 10 - 1.5
x = 7km
Rate of walking is 3.5 km per hour
the time she will take while walking = 7 ÷ 3.5 = 2 hours.
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Adam wins $30 in a "spot the ball" competition. He decides to save the money and opens a saving account with the $30. After his win, he continues to put $8 into his savings account each week. Identify a rule for the linear function that describes Adam's savings. Use the rule to find the amount Adam saved during the first 5 weeks.
Answer:
$110
Step-by-step explanation:
$30-$8=$22 each week
$22×5weeks=$110
Linear equations in two variables
Graph y = -4 then explain why it is not a function, can somone ELI5
Answer:
y=-4 is a function
Step-by-step explanation:
It passes the vertical line test, and each x has only one y, so it is a function.
x = -4 is NOT a function because one x has multiple y values. It does not pass the vertical line test.
If f(x) = 4x² + 1 and g(x)=x2-5, find (f- g)(x).
Answer:
3x² +6
Step-by-step explanation:
(f-g)(x) = f(x) -g(x) = (4x²+1) -(x²-5) . . . . . substitute the function definitions
... = 4x² +1 -x² +5 . . . . . . . . . . . eliminate parentheses
... = (4-1)x² +(1+5) . . . . . . . . . . . collect like terms
... = 3x² +6
La siguiente operación 147.3 = 441 es una:
División b- Sustracción c- Multiplicación
plis necesito la respuesta ahora dare estrellas lo juro
La operación que representa 147.3 = 441 es dada por una multiplicación, por eso opción c es correcta.
¿Qué operación está representada por 147 . 3 = 441?El resultado del producto entre 147 y 3 es de 441, por lo que se hace una operación de multiplicación.
Así, hay que la opción c es correcta.
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In the square pyramid shown below, the slant height is 12 centimeters and the height of the pyramid is 7 centimeters.
To the nearest whole number, find the diagonal length of the base of the pyramid. In your final answer, include your calculations with reasoning for each step.
The diagonal of the square pyramid will be equal to 33.10 centimetres.
What is diagonal?The lines which connect the two opposite corners of any quadrilateral are called diagonal. here we have a square pyramid whose slant height and the vertex height are given and we have to find the diagonal length of the base.
Let the side of the square base of the pyramid is "a". Now the side will be calculated by the following relation.
[tex](\dfrac{a}{2})^2[/tex] = s² - H
[tex](\dfrac{a}{2})^2[/tex] = 12² - 7 = 137
a² = 137 x 4 = 548
a = √548 = 23.40 cm
Now the diagonal will be calculated by using the Pythagorean theorem
D² = 23.04² + 23.40²
D² = 548 + 548
D = √1096
D = 33.10 centimeter
Therefore the diagonal of the square pyramid will be equal to 33.10 centimetres.
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Matching a Table to a Graph On a coordinate plane, a line goes through points (negative 1, 0), (0, 1), and (1, 2). Which table goes with the graph? A 2-column table with 4 rows. Column 1 is labeled x with entries negative 1, 0, 1, 2. Column 2 is labeled y with entries 0, 4, 6, 8. A 2-column table with 4 rows. Column 1 is labeled x with entries negative 1, 0, 1, 2. Column 2 is labeled y with entries 0, 2, 4, 6. A 2-column table with 4 rows. Column 1 is labeled x with entries negative 1, 0, 1, 2. Column 2 is labeled y with entries 0, 1, 2, 3.
At x = -1 , 0 ,1 ,2 , the y value = 0, 1, 2, 3, Option C is the correct answer.
What is a Function ?A function is a law that relates a dependent variable to an independent variable.
The points of line are
(- 1, 0), (0, 1),(1, 2).
The equation of the line formed will be
y = mx +c
[tex]\rm m = \dfrac{y_2-y_1}{x_2-x_1}[/tex]
m = 1
y = x +c
at x = 0 , y =1
c = 1
The equation is
y = x+1
The option 1 is
x = - 1, 0, 1, 2.
y1 = 0, 4, 6, 8.
y2= 0, 2, 4, 6
y3 =0, 1, 2, 3.
From the equation
at x = -1 , 0 ,1 ,2
the y value = 0, 1, 2, 3
Therefore Option C is the correct answer.
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The function f(x) = -√x is shown on the graph.
-6
43
4-
N
-7-6-5-4-3-2-₁ 1 2 3 4 5 6 7 x
-2+
-3-
-4
Which statement is correct?
The domain of the function is all real numbers less
than or equal to -1.
The range of the function is all real numbers greater
than or equal to 0.
O The range of the function is all real numbers less
than or equal to 0.
The domain of the function is all real numbers less
than or equal to 0.
Answer: The range of the function is all real numbers less
than or equal to 0.
The correct statement for the given function f(x) = -√x is "The range of the function is all real numbers less than or equal to 0." So, the correct option is C.
The domain of the function is all real numbers that are greater than or equal to 0 but we know that the square root of a negative number is in the real number system.
The graph of the function shows that for each positive input i.e. the range values we get the output values that are negative or zero.
Therefore, the range of the function is all real numbers less than or equal to 0, which is option C.
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Which equation represents a side that is perpendicular to side d? O y = 2x+5 Oy=-2x+5 NG 0 Y=2x-5/2 OY--12-12 = Which equation represents a side that is perpendicular to side d ? O y = 2x + 5 Oy = -2x + 5 NG 0 Y = 2x - 5 / 2 OY -- 12-12 =
The equation represents a side that is perpendicular to side d is y = -2x+5. Option B is correct.
What is the slope?A numerical assessment of a line's angle relative to the ground is known as the slope.
The inclination of any line, ray, or line segment is the fraction of the perpendicular to the horizontal distance between any two positions on it.
The given linear equation in the problem is;
y = 2x+5
Compare the equation with the standard equation;
[tex]\rm y = mx+ c[/tex]
where,
m is the slope and c is the intercept. After comparing, we will get; Hence, the slope and y-intercept will be;
m = 2
The product of the slope of the two-line perpendicular to each will be -1.
m₁×m₂ = -1
The equation represents a side that is perpendicular to side d is;
y = -2x+c.
m₁=2
m₂=-2
m₁×m₂ = -1
The equation represents a side that is perpendicular to side d is y = -2x+5.
Hence, option B is correct.
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Lines l1 and l2 are parallel and l3 is a transversal.
Which statement is true?
A
m∠2+m∠4=180°
B
m∠2+m∠3=180°
C
m∠1=m∠4
D
m∠1=90°
Answer:
C. m∠1 = m∠4
Step-by-step explanation:
A. m∠2 + m∠4 = 180°
∠2 and ∠4 are vertically opp. angles which means m∠2 = m∠4.
Hence, it's a false statement.
B. m∠2 + m∠3 = 180°
∠2 and ∠3 are corresponding angles which means m∠2 = m∠3.
It's a false statement.
C. m∠1 = m∠4
∠1 and ∠4 are another pair of corresponding angles which clearly states that m∠1 = m∠4.
Therefore, it's a true statement.
D. m∠1 = 90°
As clearly visible in the diagram;
It's a false statement.
Please answer both questions math
Answer:
[tex]3[/tex] and perpendicular
Step-by-step explanation:
It's important to remember that equations of lines are always set up in the format of [tex]y=mx+c[/tex].
[tex]y[/tex] is the [tex]y[/tex] value, [tex]m[/tex] is the gradient/slope, [tex]x[/tex] is the [tex]x[/tex] value and [tex]c[/tex] is the y-intercept.
Therefore, we must always rearrange our line equations so that [tex]y[/tex] is the subject.
In the first question, we are given the equation [tex]2x+6y=12[/tex].
We rearrange to make [tex]y[/tex] the subject:
[tex]6y = 12-2x[/tex]
Then, we divide both sides by 6 to have the [tex]y[/tex] isolated:
[tex]\frac{6}{6} y = \frac{12}{6} - \frac{2}{6}x\\\\ y = 2 - \frac{1}{3}x[/tex]
To find a perpendicular slope, we use the negative reciprocal of the original slope. The negative part of that means we negate the value (it becomes inverse) and the reciprocal part means that we flip the fraction.
So here, the slope is [tex]-\frac{1}{3}[/tex].
So, the negative reciprocal of that would be [tex]3[/tex] because we inverse the sign (the negative becomes positive) and the fraction is flipped to create [tex]\frac{3}{1}=3[/tex].
So, the perpendicular slope is [tex]3[/tex].
In the second question, we have two equations. They both need to be rearranged to isolate the [tex]y[/tex].
[tex]4x-y=5\\4x = 5 + y\\y = 4x - 5\\\\4y = -x-12\\y = -\frac{1}{4}x - 3[/tex]
Look at the slopes of the two equations. If you look carefully, you will see that they are inverse of each other (one is positive and one is negative) and if you imagine [tex]4 = \frac{4}{1}[/tex], the fraction is flipped.
This means that the values are negative reciprocals of each other, meaning the lines are perpendicular.
(08.01)
A new video game is expected to sell 120 copies the first hour at a local game store. After that, the sales will follow the function s(x) = 15(=
1) where x is the number of hours. What is the function that shows total sales, including the first hour?
Answer:
f(x)=15x+120
Step-by-step explanation:
trust
find the area of the rectangle below
(3x+4) feet x
(x+3) feet
select the correct answer
Answer:
3x^2+ 13x + 12
Step-by-step explanation:
Multiply the length and width:
(3x+4) * (x+3)
FOIL method:
3x^2 + 9x + 4x + 12
Combine like terms
3x^2+ 13x + 12
HURRRRYYY
Hurry pleaseee use elimination show your work
15y - 9x =-9 -8y+9x=12
Two planes that do not intersect are _____ parallel.
sometimes always never
Two planes that do not intersect are always parallel.
