Answer: -2
Step-by-step explanation: Find the slope of between the two points. P is the bottom point and Q is the top point. Both x and y numbers increase, meaning that the slope is positive. The x numbers increase by 6, and the y numbers increase by 12. This means that the rise is 12, and the run is 6. The slope is 12/6 but can be simplified to 2/1. The perpendicular slope is -1/2 because the perpendicular slope of a line is opposite reciprocal. This means to make the number negative and to flip it.
Answer:
-1/2
Step-by-step explanation:
So we are asked to find the slope of a line perpendicular to the line going through Q(-6,10) and P(-12,-2).
To do this we first need to find the slope of the line going through Q(-6,10) and P(-12,-2).
We can use the slope formula for a line given two points on that line which is (y2-y1)/(x2-x1).
I like to do something I consider easier to remember and is the same thing
It is:
A) line up the points
B) subtract vertically
C) put 2nd difference over first difference
D) done unless it needs reducing
So that is exactly what I'm going to do here:
(-6, 10)
-(-12,-2)
------------
6 12
So the slope is 12/6 or 2.
Now you might prefer to write 2 as a fraction now, because I'm about to tell you to find the slope of a line that is perpendicular, you just need to take the opposite reciprocal.
Opposite means to change the sign. I'm referring to negative or positive sign.
Reciprocal means to flip the number.
Let's put 2 through that process.
Opposite of 2: -2
Reciprocal of the opposite: -1/2
I got that reciprocal there by realizing -2 is just -2/1.
Anyways the slope of a line that is perpendicular to the one that goes through P and Q is -1/2 or -0.5.
Ayanna bought three dozen donuts from Dunkin Donuts. She wants to share these between herself and three friends. How many donuts will each person get? Show work and explain how you got the answer.
Answer:
9
Step-by-step explanation:
Ok... So there are 12 donuts in a dozen. And if she bought 3 dozen, she will have 36 donuts. If she plans to share them with her 3 friends, there will be 4 people total sharing the donuts. Then all you have to do is divide the 36 donuts among the 4 friends. 36/4=9. So they will all get 9 donuts.
3(12)/4=x
36/4=x
9=x
x=9
5. Regal Reflective signs make speed limit signs for the state department of transportation. By low these signs must be displayed every 5/8 of a mile. How many signs will be required on a new highway that is 34 3/8 miles long?
Write an equation of the line with the given slope and y-ntercept -5,b-4
Answer:
y = - 5x - 4
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + b ( m is the slope and b the y- intercept )
here m = - 5 and b = - 4, hence
y = - 5x - 4 ← equation of line
Simplify the quadratic term by squaring the (x+1) term.
Answer:
y = -2x^2 -4x +1
Step-by-step explanation:
y-3 = -2 (x+1)^2
Foil (x+1)^2
(x+1)(x+1) = x^2 +x+x+1 = x^2 +2x+1
Substitute this back in
y-3 = -2(x^2 +2x+1)
Distribute
y-3 = -2x^2 -4x -2
Add 3 to each side
y-3+3 = -2x^2 -4x -2+3
y = -2x^2 -4x +1
Which relation describes a function?
A) {(0, 0), (0, 2), (2, 0), (2, 2)}
B) {(−2, −3), (−3, −2), (2, 3), (3, 2)}
C) {(2, −1), (2, 1), (3, −1), (3, 1)}
D) {(2, 2), (2, 3), (3, 2), (3, 3)}
Explaine Why you chose your answer.
Answer:
B) {(−2, −3), (−3, −2), (2, 3), (3, 2)}
Step-by-step explanation:
For a relation to be a function, every x value must have only one y value. For a, c, and d, some of the x values have multiple different y values
Answer:
B) {(−2, −3), (−3, −2), (2, 3), (3, 2)}
Step-by-step explanation:
For a function to be valid, each value within the domain of the function must give exactly one value in the range of the function.
That is to say, for a function to be valid, every value of x must give only 1 unique value for y.
So basically if you have one value of x which gives a value for y, and if the same value for x gives you another value of y which is different than the first time, then you do NOT have a function.
With this in mind, we can see that for option B, every unique value for x, gives an equally unique value for y. Hence this is a function.
Lets compare this with option A (for example)
For A, we can see that for (0,0), an input of x=0, gave y=0. But then notice that the next set of coordinates (0,2), an input of x=0 gave y=2!!!! (this contradicts the first set (0,0), hence this is not a function.
you'll see similar contradictions for
option C (2,-1) vs (2,1)
option D (2,2) vs (2,3)
erika raked 5% more leaves than adam raked. erika raked 357liters of leaves. how many liters of leaves did adam rake?
Erica raked 5% more, so she racked 1.05 times as much.
Divide the amount she racked by the 1.05:
357 / 1.05 = 340
Adam racked 340 liters.
A large college wishes to determine the average SAT scores for students who apply from New York. They surveyed 105 students from New York and discovered a mean SAT score of 1519. Which of the statements below represent the parameter and the statistic, respectively, of the survey?
I. The mean SAT score of all students from New York
II. The mean SAT score of 105 students from New York
III. The 105 students who apply to the college from New York
IV. All students who apply to the college from New York
Statements I and IV
Statements II and III
Statements I and II
Statements II and IV
Answer:
Statements I and II
Step-by-step explanation:
In Statistics, parameter is any numerical value that characterizes a population while statistics are numerical values that characterizes a sample from a given population.
Statistics are most often used to estimate the population parameters
For example the sample mean is a statistic and the population mean is a paranmeter
The mean SAT score of all students from New York is the parameter.
The mean SAT score of 105 students from New York is called the statistic.
The correct choice is the third option.
Determine whether the vectors u and v are parallel, orthogonal, or neither.
u = <3, 0>, v = <0, -6>
Answer:
They are orthogonal.
Step-by-step explanation:
u = <3, 0> v = <0, -6>
u.v =|u| |v|cosθ
if u.v is 0 this means that cos θ is 0 so θ = 90°
[tex]\theta=cos^{-1}\frac{u.v}{|u|\ |v|}[/tex]
If u.v = 0 then they are orthogonal.
If u.v ≠ 0 then they are neither parallel nor orthogonal
If u.v ≠ 0 and u = kv where k is constant then they are parallel
u.v = 3×0+0×-6
⇒u.v = 0
They are orthogonal.
Which of the following is equivalent to Square root -63
Answer:
[tex]3i \sqrt{7}[/tex]
Step-by-step explanation:
The imaginary unit is [tex]i=\sqrt{-1}[/tex].
Now 63 itself is not a perfect square but 63 does contain a factor that is.
63=9×7 and 9 is a perfect square.
So [tex]\sqrt{-63}=i \sqrt{63}[/tex].
[tex]i \sqrt{63}=i \sqrt{9 \cdot 7}=i \sqrt{9} \sqrt{7}=i(3) \sqrt{7}=3i \sqrt{7}[/tex]
To find the square root of -63, you'll need to consider the concept of imaginary numbers because the square root of a negative number is not a real number. Here's how you can find the equivalent expression:
The square root of -63 can be expressed as √(-63). Since you cannot take the square root of a negative number in the real number system, you would use an imaginary unit, which we designate as "i". The imaginary unit "i" is defined as √(-1).
Now, you can factor -63 into -1 and 63, so the expression becomes:
√(-63) = √(-1 * 63)
This simplifies to:
√(-1) * √(63)
We already established that √(-1) is represented by the imaginary unit "i". So now the expression is:
i * √(63)
The √(63) doesn't simplify neatly into a whole number since 63 is not a perfect square. However, 63 can be factored into 9 and 7, where 9 is a perfect square. Let's do that:
√(63) = √(9 * 7)
√(63) = √(9) * √(7)
√(63) = 3 * √(7)
Therefore, the expression now looks like this:
i * 3 * √(7)
Since multiplication is commutative, you can reorder this:
3 * i * √(7)
Thus, the expression 3 * i * √(7) is equivalent to √(-63). This is because 3 * √(7) is the real number part and "i" indicates that it is an imaginary number due to the original square root of a negative number.
Write an equation:
The product of a number and 12 is 78
Answer: 12 x X=78
Step-by-step explanation: An equation of this would be 12 x X =78.
1. Identify the vertex and the y-intercept of the graph of the function y=-2(x+ 2)+2.
Answer:
Please let me know if your quadratic is [tex]y=-2(x+2)^2+2[/tex].
And if so your vertex is (-2,2) and your y-intercept is (0,-6)
Step-by-step explanation:
It says vertex so I'm thinking you meant [tex]y=-2(x+2)^2+2[/tex]. Please correct me if I'm wrong.
The vertex form of a quadratic is [tex]y=a(x-h)^2+k[/tex]. It is called that because it tells you the vertex (h,k).
So if you compare the two forms you should see -h=2 while k=2.
-h=2 implies h=-2.
So the vertex is (h,k)=(-2,2).
To find the y-intercept, set x=0 and find y.
[tex]y=-2(0+2)^2+2[/tex]
[tex]y=-2(2)^2+2[/tex]
[tex]y=-2(4)+2[/tex]
[tex]y=-8+2[/tex]
[tex]y=-6[/tex]
So the y-intercept is (0,-6).
How do you express 140 degrees in radians? Round to nearest tenth
Answer:
2.4 rad
Step-by-step explanation:
To convert degree measure to radian measure
radian measure = degree measure × [tex]\frac{\pi }{180}[/tex]
Thus for 140°
radian = 140 × [tex]\frac{\pi }{180}[/tex] = [tex]\frac{7\pi }{9}[/tex] ≈ 2.4
Answer:
7π/9
Step-by-step explanation:
Degrees To Radians : × · π/180
Radians To Degrees : × · 180/π
Plug into Equation And Solve: 140π/180
Simplify: 7π/9
A bag contains red and blue marbles, such that the probability of drawing a blue marble is 3/8. An experiment consists of drawing a marble, replacing it, and drawing another marble. The two draws are independent. What is the probability that both of the marbles drawn are blue?
Answer:
9/64
Step-by-step explanation:
The probability that the marble on the first draw is blue is 3/8.
The probability that the marble on the second draw is blue is also 3/8.
So the probability that both are blue is:
3/8 × 3/8 = 9/64 ≈ 14%
The probability that both of the marbles drawn from the bag are blue is 9/64.
What is the probability?
Probability is the chance that an event would occur. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that both of the marbles drawn are blue = fraction of blue marbles²
= 3/8 x 3/8 = 9/64
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Write an expression that is equivalent to 2.5x + ( 5y) -2.5
Answer:
2.5(x + 2y - 1).
Step-by-step explanation:
2.5x + ( 5y) -2.5
2.5x + 5y - 2.5 (we can just remove the parentheses without changing the value of the expression)
Each coefficient is divisible by 2.5 so by the distributive law:
2.5x + 5y - 2.5
= 2.5(x + 2y - 1).
By factorization of 2.5x + ( 5y) -2.5, the result is as follows-
2.5(x + 2y -1) is the expression equivalent to 2.5x + ( 5y) -2.5
What is factorization?
At first it is important to know about algebraic expression.
Algebraic expression consists of numbers and variables connected with addition, subtraction, multiplication and division.
Factorization is the process of breaking down of an algebraic expression into a product of algebraic expressions of smaller degree. Each smaller degree algebraic expressions are called factors.
Here,
2.5x + 5y - 2.5
2.5(x + 2y -1)
An expression that is equivalent to 2.5x + ( 5y) -2.5 is
2.5(x + 2y -1)
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HELP me please I need it !!
Answer:
A
Step-by-step explanation:
Using the substitution u = [tex]x^{\frac{1}{2} }[/tex]
noting that ([tex]\frac{1}{2}[/tex] )² = [tex]\frac{1}{4}[/tex], then
[tex]x^{\frac{1}{2} }[/tex] + 9[tex]x^{\frac{1}{4} }[/tex] + 20 = 0
Can be rewritten as
u + 9u² + 20 = 0, that is
9u² + u + 20 = 0 ← in standard form
a^3b^-2c^-1d if a=2 b=4 c=10 d=15 express as a reduced fraction
Answer:
Don't know if this is correct but, I think the answer is 3/4.
Answer:
[tex]\dfrac{3}{4}[/tex]
Step-by-step explanation:
The given expression is
[tex]a^3b^{-2}c^{-1}d[/tex]
We need to find the value of this expression in reduced fraction if a=2 b=4 c=10 d=15.
Substitute a=2 b=4 c=10 d=15 in given expression.
[tex](2)^3(4)^{-2}(10)^{-1}(15)[/tex]
Using the property of exponent, we get
[tex](2)^3\times \left(\dfrac{1}{4^2}\right)\times \left(\dfrac{1}{10}\right)\times (15)[/tex] [tex][\because a^{-n}=\dfrac{1}{a^n}][/tex]
[tex]8\times \left(\dfrac{1}{16}\right)\times \left(\dfrac{1}{10}\right)\times (15)[/tex]
Cancel out common factors.
[tex]1\times \left(\dfrac{1}{2}\right)\times \left(\dfrac{1}{2}\right)\times (3)[/tex]
[tex]\dfrac{3}{4}[/tex]
Hence, the required fraction is 3/4.
Please Help 25 points and brainliest ASAP (((((((:
Suppose △ABC≅△XYZ, m∠A=50°, and m∠Y=70°.
What is m∠C?
50º
60º
70º
110º
Answer:
60
Step-by-step explanation:
We are given the triangles are congruent, that means the angles are the same measurement
<A = <X
<B = <Y
<C = <Z
We know A = 50 so X = 50
We know <Y = 70 so < B = 70
The three angles of a triangle add to 180
<A + <B + <C = 180
Substituting into the equation
50 + 70 + <C = 180
Combining like terms
120 + <C =180
Subtracting 120 from each side
120-120 +<C =180-120
<C = 60
Answer:
∠C = 60°
Step-by-step explanation:
Corresponding angles are congruent, thus
∠B = ∠Y = 70°
The sum of the 3 angles in ΔABC = 180°
∠C = 180° - (70 + 50)° = 180° - 120° = 60°
Find the solution to the following system of equations using the ADDITION method. 3x + 2y = 7 -3x + 3y = 8
Answer:
x = 1/3 and y = 3
Step-by-step explanation:
It is given the system of equations
3x + 2y = 7 ----(1)
-3x + 3y = 8 ----(2)
To find the solution
Add eq(1) and eq (2) we get,
3x + 2y = 7 ----(1)
-3x + 3y = 8 ----(2)
0 + 5y = 15
y = 15/5 = 3
Substitute the value of y in eq(1)
3x + 2y = 7 ----(1)
3x + 2*3 = 7
3x + 6 = 7
3x = 7 - 6 = 1
x = 1/3
Therefore
x = 1/3 and y = 3
What is the domain for the following function?
Y= (x+1)/(x^2+x-6)
A) {x does not equal -1}
B) {x does not equal -3; x does not equal 2}
C) {x does not equal -3}
D) {x does not equal 0}
Answer:
it's B
Step-by-step explanation:
the set of numbers for which a function is defined is called a domain of a function
if a number is not in the domain of a function, then the function is undefined for that number
denominator must not be zero
if we plug -3 then the y
=(-3+1)/(9+-3-6)
=(-2)/9-9
=-2/0
which is undefined for x=-3
now
if we plug 2 we have
(2+1)/(4+2-6)
=3/0
the function is undefined for x=2
so
x≠3, x≠2
The domain of the given function is {x does not equal -3; x does not equal 2}.
Explanation:The domain of a function is the set of all allowable input values. In this case, we need to find the values of x that make the denominator of the function equal to zero, because division by zero is undefined.
To find the domain, we set the denominator equal to zero and solve for x. The denominator is x^2 + x - 6, so we set it equal to zero and factor it: (x+3)(x-2) = 0. Now, we set each factor equal to zero and solve for x: x+3=0, x=-3; x-2=0, x=2.
The domain is the set of all values of x that make the function defined, so the answer is: (B) {x does not equal -3; x does not equal 2}.
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Using the equation y=2/3x-5, describe how to create a system of linear equations with an infinite number of solutions.
a system of linear equations with infinite solutions, is simply one that has the same equation twice, but but but, one of the equations is in disguise.
so, say we can just hmmm multiply the coefficient of the "x" variable, which is the slope, by something that gives us 1, recall same/same = 1, hmmm say let's multiply it by hmmmm 7/7.
[tex]\bf y=\cfrac{2}{3}x-5\implies \stackrel{\textit{multiplying the slope by }\frac{7}{7}}{\cfrac{2}{3}\cdot \cfrac{7}{7}\implies \cfrac{14}{21}}\implies \stackrel{\textit{so we get this equation}}{y=\cfrac{14}{21}x-5}[/tex]
now, let's notice that 14/21 simplifies to 2/3, so is really the same slope and the same y-intercept.
so if we use those two equations in a system of equations and graph them, what happens is, the first one will graph a line, the second one will graph another line BUT right on top of the first one drawn, so the two lines will just be pancaked on top of each other, making every point in each line, "a solution", since they're meeting at every point, and since lines go to infinite, "infinitely many solutions".
Answer:
Sample Response/Explanation: To have an infinite number of solutions, the equations must graph the same line. That means the equations must be equivalent. To form an equivalent equation, use the properties of equality to rewrite the given equation in a different form. Add, subtract, multiply, or divide both sides of the equation by the same amount.
Step-by-step explanation:
The width of a rectangle is 6 inches less than it’s length, and the area is 7 square inches. What are the length and width of the rectangle
Answer:
So length is 7 in while width is 1 in.
Step-by-step explanation:
We are given W is 6 inches less than L which mean as an equation we have W=L-6.
We are given the area of this rectangle, LW=7.
So we have the system:
W=L-6
LW=7.
Replace the second W with what the first W equals:
LW=7
L(L-6)=7
Distribute:
[tex]L^2-6L=7[/tex]
Subtract 7 on both sides:
[tex]L^2-6L-7=0[/tex]
We are luck since the coefficient of L^2 is 1. This means all we have to do is find two numbers that multiply to be -7 add at the same time add up to -6.
Those numbers are -7 and 1 since (-7)(1)=-7 and (-7)+(1)=-6.
So the factored form of our equation is:
(L-7)(L+1)=0
This gives us two equations to solve:
L-7=0 or L+1=0
L=7 or L=-1
L=-1 doesn't make sense for a length so L=7.
L=7 means the length is 7 inches.
If W=L-6 and L=7, then W=7-6=1.
The width is 1 inch since W=1.
So length is 7 in while width is 1 in.
Omar and Jacobs ages total 24 years. Omar is 3 times as old as JasonHow old is Jacob
If x and p are both greater than zero and 4x^2p^2+xp-33=0, then what is the value of p in terms of x?
A) -3/x
B) -11/4x
C) 3/4x
D) 11/4x
Answer:
11/ (4x)Explanation:
1) Make a change of variable:
u = xp2) The new equation with u is:
4x²p² + xp - 33 = 04(xp)² + xp - 33 = 04u² + u - 33 = 03) Factor the left side of the new equation:
Split u as 12u - 11u ⇒ 4u² + u - 33 = 4u² + 12u -11u - 33Group terms: (4u² + 12u) - (11u + 33)Extract common factor of each group: 4u (u + 3 - 11 (u + 3)Common factor u + 3: (u + 3)(4u - 11).4) Come back to the equation replacing the left side with its factored form and solve:
(u + 3) (4u - 11) = 0Use zero product propery: u + 3 = 0 or 4u - 11 = 0solve each factor: u = - 3 or u = 11/45) Come back to the original substitution:
u = xpIf u = - 3 ⇒ xp = - 3 ⇒ x or p is negative and that is against the condition that x and p are both greater than zero, so this solution is discarded.
Then use the second solution:
u = xp = 11/4Solve for p:
Divide both sides by x: p = 11/(4x), which is the option D) if you write it correctly.Given y = log3(x + 4), what is the range?
Answer:
The range is all real numbers.
The domain is all reals numbers that are greater than -4.
Step-by-step explanation:
[tex]y=\log_3(x+4)[/tex] only exists when [tex]x+4[/tex] is positive.
You can take the log of a negative or 0 number.
So [tex]x+4>0[/tex] implies [tex]x>-4[/tex]. (I just subtract 4 on both sides.)
So the domain is x>-4. You should see this also when you graph the curve that the curve only exist to the right of -4.
Now the range. The range is where the curve exist for the y-values.
The equivalent exponent form of [tex]y=\log_3(x+4)[/tex] is [tex]3^{y}=x+4[/tex]
We can solve this for x be subtract 4 on both sides:
[tex]x=3^y-4[/tex]
Now here y can be anything; there are no restrictions on the exponent.
Also if you look at the graph of [tex]y=\log_3(x+4)[/tex] you should see every y getting hit by the curve (look down to up; use the y-axis as a guide).
Let's think about the inverse I found above a little more (I'm going to swap x and y).
[tex]y=3^x-4[/tex].
If we look at the domain and range of this we can just swap it to get the domain and range of [tex]y=\log_3(x+4)[/tex].
[tex]y=3^x-4[/tex] is an exponential function of 3^x that has been moved down 4 units.
The range since it has been moved down 4 units is [tex](-4,\infty)[/tex].
The domain of an exponential function is all real numbers. There are no restrictions on what you can plug in for x.
So swapping these to find the domain and range of [tex]y=\log_3(x+4)[/tex]:
Domain: [tex](-4,\infty)[/tex]
Range : [tex](-\infty,\infty)[/tex]
Answer: For Edg is x> -4
And for the second on it is all real numbers
How many meters are in .02 kilometers?
Answer:
the answer is 20 meters
Answer:
20
Step-by-step explanation:
A soda bottle holds 1.5 liters of soda. How many milliliters does the bottle hold?
Answer:
1.5 = 1,500
Step-by-step explanation:
I actually converted 1.5 to milliliters.
That is how I got 1,500.
The bottle holds 1500 milliliters soda.
How to convert liter to milliliter ?We know that, 1 liter = 1000 milliliters
So, to convert something from liter to milliliter, we have to multiply the given value by 1000.
What is the required value ?Given, the bottle of soda holds 1.5 liters of soda.
So, we have to multiply 1000 with that to get the required value.
∴ 1.5 liters = (1.5 × 1000) milliliters
= 1500 milliliters
The required quantity of soda is 1500 milliliters.
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How do I find the value of the unknown variable
6x + 2 + 40 = 90
Let x = the unknown
6x + 42 = 90
6x = 90 - 42
6x = 48
x = 48/6
x = 8
Answer:
x=8
Step-by-step explanation:
We know that 40 + (6x+2) +90 = 180 since the three angles form a straight line
40 + (6x+2) +90 = 180
Combine like terms
132 + 6x = 180
Subtract 132 from each side
132-132 +6x= 180-132
6x = 48
Divide each side by 6
6x/6 = 48/6
x = 8
Doug can download new songs for $1.19 each. Write an equation to show how many songs he can download for $12.00
12x = 1.19
12+x=1.19
1.19+x=12
1.19x=12
Answer:
1.19x=12
Step-by-step explanation:
The 12 represents his budget and 1.19 is the cost of each song, x is the amount of songs.
Answer: [tex]1.19x=12[/tex]
Step-by-step explanation:
Given : Doug can download new songs for $1.19 each.
Let the number of songs downloaded be x .
Then the total cost of x songs will be :-
[tex]1.19x[/tex]
To find the number of songs he can download for $12.00 , we need to put [tex]1.19x[/tex] equals to 12.
We get, the equation to show how many songs he can download for $12.00 will be
[tex]1.19x=12[/tex]
Choose the correct sum of the polynomials (2x^3 - 5x - 1) + (4x^3 + 8x + 3)
Answer:
answer is b. 6x3 + 3x + 2
Step-by-step explanation:
which point is the image P
Answer:
(-5,2)
Step-by-step explanation:
It alogns with negative 5 on the X axis, and positive 2 on the Y axis, meaning its written as (-5,2)