Answers
Answer:
[tex]m = \frac{1}{2}[/tex]
Step-by-step explanation:
[tex]\frac{y2 - y1}{x2 - x1}[/tex]
[tex]\frac{2-1}{3-1}[/tex]
[tex]2-1 = 1\\ 3-1=2[/tex]
[tex]m = \frac{1}{2}[/tex]
For this case we have that by definition, the slope of a line is given by:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]
We have two points through which the line passes:
[tex](x_ {1}, y_ {1}) :( 1,1)\\(x_ {2}, y_ {2}) :( 3,2)[/tex]
Substituting:
[tex]m = \frac {2-1} {3-1} = \frac {1} {2}[/tex]
Thus, the slope of the line is [tex]\frac {1} {2}[/tex]
Answer:
Option C
Related Questions
Dan has the same number of nickels and dimes in his piggy bank. If the total amount of those coins is $0.90, how many of each coin does he have?
Answers
Hello There!
n - d = 0
5n+10d = 90
----------------------
n-d = 0
n+2d = 18
-------------------
Subtract and solve for "d":
3d = 18
d = 6 (# of dimes)
n = d = 6 (# of nickels)
which value of the 9 ten times in the number 920
Answers
Answer:
9000. the value of 9 in 920 is 900. and ten times anything is basically just adding a 0. so ten times 900 is 9000.
Step-by-step explanation:
Please mark brainliest and have a great day!
Can someone please help me out here ?
Answers
Answer:
D
Step-by-step explanation:
Since its less then the circle is open and the arrow goes to the left. The circle must be on -1. The answer is D.
If 2p+q=11 and p+2q=13, then p+q =
Answers
Answer:
the desired result is (p + q) = (3 + 5) = 8
Step-by-step explanation:
Let's solve this system of linear equations in the usual way: find the values of p and q. Then find (p + q) as a numerical result.
Solve:
2p+q=11
p+2q=13
Multiply the second equation by -2:
2p + q = 11
-2p - 4q = -26
Combining these two equations results in -3q = -15, and so q must be 5.
Subbing 5 for q in the first equation, we get:
2p + 5 = 11, or 2p = 6. Then p = 3.
Then the desired result is (p + q) = (3 + 5) = 8
The required answer is p + q is equal to 8 by solving systems of equations 2p+q=11 and p+2q=13. The required sum is 8.
To find the value of p + q, we can use the given system of equations:
Equation 1: 2p + q = 11
Equation 2: p + 2q = 13
We can solve this system of equations by either the substitution method or the elimination method. Let's use the elimination method:
Multiply Equation 1 by 2:
2(2p + q) = 2(11)
4p + 2q = 22 ...(Equation 3)
Subtract Equation 2 from Equation 3:
(4p + 2q) - (p + 2q) = 22 - 13
4p + 2q - p - 2q = 9
3p = 9
Divide both sides by 3 to solve for p:
p = 9 / 3
p = 3
Now substitute the value of p back into Equation 1:
2(3) + q = 11
6 + q = 11
Subtract 6 from both sides to solve for q:
q = 11 - 6
q = 5
Finally, we can find p + q:
p + q = 3 + 5
p + q = 8
Therefore, p + q is equal to 8 solving systems of equations 2p+q=11 and p+2q=13. The required sum is 8.
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Which of the following vectors are orthogonal to (2,1)? Check all that apply.
A. (1,-2)
B. (-3,6)
C. (1,2)
D. (-2,-3)
Answers
Answer:
A. (1,-2)
B. (-3,6)
Step-by-step explanation:
we know that
If two vectors are orthogonal, then the dot product ( or scalar product) of the vectors is equal to zero
so
Let
a (x1,y1) and b(x2,y2)
The dot product is equal to
a.b=(x1*x2+y1*y2)
Verify each case
case A) (2,1) with (1,-2)
(2,1).(1,-2)=(2)*(1)+(1)(-2)=2-2=0
therefore
(1,-2) is orthogonal to the given vector
case B) (2,1) with (-3,6)
(2,1).(-3,6)=(2)*(-3)+(1)(6)=-6+6=0
therefore
(-3,6) is orthogonal to the given vector
case C) (2,1) with (1,2)
(2,1).(1,2)=(2)*(1)+(1)(2)=2+2=4
therefore
(1,2) is not orthogonal to the given vector
case D) (2,1) with (-2,3)
(2,1).(-2,3)=(2)*(-2)+(1)(3)=-4+3=-1
therefore
(-2,3) is not orthogonal to the given vector
Answer: B, D, E
On EDGE
Step-by-step explanation:
The slope of the line below is 2. Which of the following is the point-slope form
of the line?
(1,-1)
A. Y+1 = -2(x - 1)
B. y-1 = 2(x+1)
c. y-1 =-2(x+1)
D. y+ 1 = 2(x-1)
Answers
Answer:
D
Step-by-step explanation:
point-slope form is y-y1=m(x-x1) . since the slope is 2 and not -2, you can automatically eliminate choices A and C. since the y-value in the point, (1,-1), is -1, you will add it to y because you are subtracting a negative. (- - = +) therefore, the final equation, in point-slope form, is y+1=2(x-1), or answer choice D.
Y+1 = 2x-2
Y= 2x-3
Hope this helps!
A circle with a center at (5,-2) also has the point (8,2) that lies on the circle. What is the equation of the circle?
Answers
Answer:
Step-by-step explanation:
You get the center just by reading the given point.
(x - 5)^2 + (x + 2)^2 = r^2 Notice that the center switches signs.
(8,2) is given so that you can figure out the radius.
The radius uses the distance formula to get from (5,-2) to (8,2)
x1 = 5
x2 = 8
y1 = -2
y2 = 2
==================
formula
d^2 = (x1 - x2)^2 + (y1 - y2)^2
solution
d^2 = (5 - 8)^2 + (-2 - 2)^2
d^2 = (-3)^2 + (-4)^2
d^2 = 9 + 16
d^2 = 25
==================
Answer
(x - 5)^2 + (y + 2)^2 = 25
the speed of a new microprocessor is 800mhz but a new test of its speed gives a measurement of 820mhz. what is the abolute error? what is the relative error?
Answers
The answers are:
[tex]AbsoluteError=20mhz[/tex]
[tex]RelativeError=2.5(Percent)[/tex]
Why?To solve the problem we need to remember that the absolute error is the difference between the expected value and the measured value, also, to calculate the relative error we first need to calculate the absolute error, and then, divide it by the expected measure.
So, calculating we have:
[tex]AbsoluteError=Expected-MeasuredValue\\\\AbsoluteError=800mhz-820mhz=-20mhz[/tex]
We can see that we obtained a negative value, however, when we are working with "absolute" values, the negative symbol is discarded, so, we have that:
[tex]AbsoluteError=20mhz[/tex]
Now, to calculate the relative error, we need to use the following formula:
[tex]RelativeError=\frac{AbsoluteError}{ExpectedValue}*100\\\\RelativeError=\frac{20}{800}*100=0.025*100=2.5(Percent)[/tex]
So, we have that the relative error is equal to 2.5%.
Hence, we have that:
[tex]AbsoluteError=20mhz[/tex]
[tex]RelativeError=2.5(Percent)[/tex]
Have a nice day!
Absolute error is 20 MHz and relative error is 2.5%.
Absolute error: Absolute error is the difference between the measured value and the actual value. In this case, the absolute error is 820 MHz - 800 MHz = 20 MHz.
Relative error: Relative error is the ratio of the absolute error to the actual value. The relative error can be calculated as (820 MHz - 800 MHz) / 800 MHz = 0.025 or 2.5%.
there are only blue cubes, yellow cubes and green cubes in a bag there are
three times as many blue cubes as yellow cubes
and five times as many green cubes as blue cubes
sarah takes a random cube from the bag
what is the probability sarah takes out a yellow cube?
give your answer in its simplest form
Answers
Answer: [tex]\bold{\dfrac{1}{19}}[/tex]
Step-by-step explanation:
Let x represent the quantity of yellow cubes
Yellow: x
Blue: three times yellow --> 3x
Green: five times blue --> 5(3x) = 15x
Yellow + Blue + Green = Total cubes
x + 3x + 15x = 19x
[tex]Probability=\dfrac{yellow}{total}=\dfrac{x}{19x}=\large\boxed{\dfrac{1}{19}}[/tex]
The probability of Sarah taking out a yellow cube from the bag is 0.7 or 5/7.
What is probability?The fraction of favorable outcomes of an event to the total number of outcomes of the event is said to be the probability. The fraction can also be written in the simplest form.
P(E)= n(E)/n(S) where E -event, n(E) - favorable outcomes and n(S) is the total outcomes.
Calculation:It is given that a bag contains blue cubes, yellow cubes, and green cubes.
Consider the number of blue cubes = n
So, the number of yellow cubes = 3 times as many as blue cubes
= 3n
Then, 5 times as many as green cubes = blue cubes
⇒ number of green cubes = n/5
Then the total number of cubes in the bag
= n + 3n + n/5
⇒ [5n + 15n + n]/5
⇒ 21n/5
Then the probability of taking out a yellow cube = (possible outcomes of a yellow cube)/(total number of cubes)
⇒ [tex]\frac{(3n)}{(21n/5)}[/tex]
⇒ 15n/21n
⇒ 5/7
∴ The probability of taking out a yellow cube = 5/7 = 0.7.
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Arjun is building a frame for his father's painting. Which measurement will tell him the minimum amount of wood that he
will need to build the frame?
A.the perimeter of the painting
B.the volume of the painting
C.the width of the painting
D.the area of the painting
Answers
Answer:
A
Step-by-step explanation:
measurement will tell him the minimum amount of wood that he will need to build the frame by the perimeter of the painting
The correct option is (A).
What is Perimeter?
The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape.
As Arjun need to build the frame for the painting.
For framing or fencing we generally use the concept of Perimeter.
For example,
Let us consider an example.
David wants to put a fence around his farm so that his sheep will not wander away.
He wants to know how much wire he would need to fence around his farm.
The shape of the field is rectangular.
Now, if we add the distance of all 4 sides of his farm, it will give us the perimeter.
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Find the greatest common factor: 24y8 + 6y6
Answers
For this case we must find the GCF of the following expression:
[tex]24y ^ 8 + 6y ^ 6[/tex]
By definition, the largest common factor (GCF) of two numbers is the largest number that is a factor of both numbers. We find the factors of each number:
24: 1,2,3,4,6,8,12,24
6: 1,2,3,6
Thus, the GCF of both numbers is 6
The GCF of the expression is: [tex]6y ^ 6[/tex]
Answer:
[tex]6y ^ 6[/tex]
What is the value of a in the equation a = 2 + 3a + 10?
Answers
Answer:
a= -6
Step-by-step explanation:
Given
a=2+3a+10
In order to find the value of a, we have to isolate a on a single side of the equation
So,
subtracting 3a from both sides
a-3a = 2+10+3a-3a
=>a-3a=12
=> -2a = 12
Dividing both sides by -2
=> -2a/-2 = 12/-2
=> a = -6
The value of a in the given equation is -6 ..
Vhat is the equation, in slope-intercept form, of the line
That is perpendicular to the given line and passes through
che point (2, -1)?
y=-23-
y=-2x-
y = 3x - 3
10 y = 3x - 7
Answers
Answer:
Step-by-step explanation:
There is no given equation, so it is impossible to figure this out. I apologize.
Write the following phrase as an expression.
half of n
Answers
Translating the half to symbols would be 1/2. Therefore, your answer is 1/2(n)
Hope this helps!
Answer:
1/2n
Step-by-step explanation:
half of n
of means multiply
1/2 * n
n/2
Celia simplified the expression - 4x{1-3)-(2x+2). She checked her work by letting X-5 in both expressions. Her work for the
original expression is shown below.
Answers
Answer: I think it is the last one
Step-by-step explanation: if you work it out, it equally 6x-2
Answer:
6x-2
Step-by-step explanation:
[tex]- 4x(1-3)-(2x+2)[/tex]
When x=5 the value of the expression is 28
Now we check with each expression given in the options
Plug in 5 for x in each option
[tex]-6x-1=-6(5)-1=-30-1= -31[/tex]
[tex]-6x+2=-6(5)+2=-30+2= -28[/tex]
[tex]6x+1=6(5)+1=30+1= 31[/tex]
[tex]6x-2=6(5)-2=30-2=28[/tex]
So 6x-2 gives us 28 when x=5
When a nursery owner orders plants from the distributor, 92% of the plants arrive alive. If the nursery owner wants their inventory of a particular plant to be 540 living plants, how many plants should the owner order?
Answers
You must make a [tex]\frac{part}{whole}[/tex] proportion.
92% is part of 100%
540 would need to be the 92% of the plant bought. That means 540 is the part and the whole would be the unknown (let's make this x)
Set up your proportion like so...
[tex]\frac{540}{x} =\frac{92}{100}[/tex]
Cross multiply...
92x = 540 * 100
92x = 54000
Isolate x by dividing 92 to both sides...
92x/92 = 54000/92
x = 586.9565
Since you can't buy a decimal of a plant you will have to round this number up to the next whole number...
587
To have 540 of the plants arrive alive the nursery owner must order 587 plants
Hope this helped!
~Just a girl in love with Shawn Mendes
9(x-2) + 3(5-2x) = 2
Answers
3x -3= 2
3x= 5
X= 5/3
Hope this helps!
First you must distribute the numbers outside the parentheses to the numbers inside the parentheses
Let's start with the first one:
9(x-2) + 3(5-2x) = 2
9(x - 2)
9*x + 9*-2
9x + (-18)
9x - 18
so...
9x - 18 + 3(5-2x) = 2
Now on to the second set of parentheses:
9x - 18 + 3(5-2x) = 2
3(5 - 2x)
3*5 + 3*-2x
15 + (-6x)
15 - 6x
so...
9x - 18 + 15 - 6x = 2
Now you must combine like terms. This means the numbers with the same variables must be combined...
First set of like terms:
9x - 18 + 15 - 6x = 2
9x + (-6x)
3x
so...
3x - 18 + 15 = 2
Second set of like terms:
3x - 18 + 15 = 2
-18 + 15
-3
so...
3x - 3 = 2
Now bring -3 to the right side by adding 3 to both sides (what you do on one side you must do to the other). Since -3 is being negative on the left side, addition (the opposite of negative/subtraction) will cancel it out (make it zero) from the left side and bring it over to the right side.
3x + (- 3 + 3) = 2 + 3
3x + 0 =5
3x = 5
Next divide 3 to both sides to finish isolating x. Since 3 is being multiplied by x, division (the opposite of multiplication) will cancel 3 out (in this case it will make 3 one) from the left side and bring it over to the right side.
3x/3 = 5/3
x = [tex]\frac{5}{3}[/tex]
Hope this helped!
~Just a girl in love with Shawn Mendes
How do you know if something is divisible by four
Answers
Answer:
To test whether or not a number is divisible by 4 is to check to see if the number that’s made from the final two digits of the original number is itself divisible by 4. If it is, then the entire number is divisible by 4 too.
. The temperature at noon was -2°F.
At 3:00 P.M. the temperature had
dropped by 9°F. What was the
temperature at 3:00 P.M.?
Answers
Answer:
-11 F
Step-by-step explanation:
The temperature dropping means to subtract
-2 -9
-11
The temperature at 3 pm is -11 F
Answer:-11°F
Step-by-step explanation:
HELP Geometry can someone help
Answers
ANSWER
B'(5,-2).
EXPLANATION
The coordinates of B are (-2,5).
We want to find the image of this point after a reflection in the line y=x.
The mapping is
[tex](x,y)\to (y,x)[/tex]
We just have to swap the ordered pairs.
[tex]( - 2,5)\to (5, - 2)[/tex]
Hence the image of B(-2,5) is B'(5,-2).
The correct answer is (5,-2).
In your lab, a substance's temperature has been observed to follow the function T(x) = (x − 2)3 + 8. The turning point of the graph is where the substance changes from a solid to a liquid. Using complete sentences in your written answer, explain to your fellow scientists how to find the turning point of this function. Hint: The turning point of the graph is similar to the vertex of a quadratic function. (10 points). Please help
Answers
Answer:
The turning point is (2,8)
Step-by-step explanation:
we know that
The general equation of the substance's temperature is equal to
[tex]T(x)=(x-h)^{3}+k[/tex]
where
(h,k) is the vertex (turning point)
In this problem we have
[tex]T(x)=(x-2)^{3}+8[/tex]
so
(h,k)=(2,8)
therefore
The turning point is (2,8)
Which of the following is the equation of a circle whose center is at the origin and whose radius is 4?
Answers
Answer:
x²+y²=16
Step-by-step explanation:
the general equation for a circle is given as :
(x−h)²+(y−k)²=r²
where (h, k) is the coordinate of the center of the circle and r is the radius
in this case h=0, k=0 and r = 4
equation becomes
x²+y²=4²
or
x²+y²=16
Answer: Last option.
Step-by-step explanation:
The equation of a circle in Center-radius form is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Where the center is at the point (h,k) and "r" is the radius.
If the center of this circle is at the origin, means that:
[tex]h=0\\k=0[/tex]
Since the radius is 4, then:
[tex]r=4[/tex]
Now we need to substitute these values into the equation of the circle.
[tex](x-0)^2+(y-0)^2=(4)^2[/tex]
Simplifying the equation, we get:
[tex]x^2+y^2=16[/tex]
This matches with the last option.
What expression is equivalent to (3x^2-7)
Answers
Answer:
C.(10x^2-4) - (7x^2+3)
In option C,
(10x^2-4) - (7x^2+3) = 10x^2 - 4 - 7x^2 - 3 = 3x^2 - 7
⇒ Option C is correct
Which geometric object is defined as the set of all points in a plane that are equidistant from the two sides of a given angle ?
A.Parabola
B. Bisector of an angle
C. Circle
D. Hyperbola
Answers
Answer:
B) Bisector of an angle ~apex
Step-by-step explanation:
Option B is correct, bisector of an angle is defined as the set of all points in a plane that are equidistant from the two sides of a given angle.
What is Coordinate Geometry?A system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.
The bisector of an angle is a straight line or a line segment that divides an angle into two equal angles.
In other words, the bisector of an angle is the set of all points in a plane that are equidistant from the two sides of a given angle.
The geometric object defined as the set of all points in a plane that are equidistant from the two sides of a given angle is the Bisector of an angle.
Hence, bisector of an angle is defined as the set of all points in a plane that are equidistant from the two sides of a given angle.
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screw it im wiling to give 50 points whoever can answer this question
Jernel has to figure out the area of her square garage. She knows that one side of the garage is equal to the length of her rabbit pen. The dimensions of the rectangular rabbit pen are 18 by 10.What is the area of the garage?
Answers
Answer:
Rabbit pen: 180
Garage: 720
180x4=720
Hope this helps :)
One leg of an isosceles right triangle measures 5 inches. Rounded to the nearest tenth, what is the approximate length of the hypotenuse?
Answers
Answer:
7.1 inches
Step-by-step explanation:
An Isosceles right triangle is one with two sides equal and the angles equal too.The angles in this case are 45°
For this question, to get the hypotenuse, you apply the Pythagorean relationship where the legs will be represented by a and b where as the hypotenuse will be represented by c.
[tex]a^2+b^2=c^2\\[/tex]
Given;
One leg = 5 inches, but you know that in this triangle, the two sides are equal, hence the other side/leg is 5 inches.
Lets take one side of the triangle as a=5 inches
The other side as b=5 inches
The hypotenuse as c=?
Apply the expression;
[tex]a^2+b^2=c^2\\\\5^2+5^2=c^2\\\\25+25=c^2\\\\50=c^2\\\\c=\sqrt{50} =7.071[/tex]
To the nearest tenth 7.071 = 7.1 inches
Which system of equations below has no solution?
y = 4x + 5 and y = 4x-5
y = 4x + 5 and 2y = 8x + 10
y = 4x + 5 and y =
x+5
y = 4x + 5 and y = 8x + 10
Answers
Answer:
y = 4x + 5 and y = 4x - 5Step-by-step explanation:
(1) y = 4x + 5 and (2) y = 4x - 5
substitute (1) to (2):
4x + 5 = 4x - 5 subtract 4x from both sides
5 = -5 FALSE (no solution)
(1) y = 4x + 5 and (2) 2y = 8x + 10
substitute (1) to (2):
2(4x + 5) = 8x + 10 divide both sides by 2
4x + 5 = 4x + 5 subtract 4x from both sides
5 = 5 TRUE (infinitely many solutions)
(1) y = 4x + 5 and (2) y = x + 5
substitute (1) to (2):
4x + 5 = x + 5 subtract 5 from both sides
4x = x subtract x from both sides
3x = 0 divide both sides by 3
x = 0
Put it to (2):
y = 0 + 5 = 5
One solution (0, 5)
(1) y = 4x + 5 and (2) y = 8x + 10
substitute (1) to (2):
4x + 5 = 8x + 10 subtract 5 from both sides
4x = 8x + 5 subtract 8x from both sides
-4x = 5 divide both sides by (-4)
x = -1.25
Put it to (1):
y = 4(-1.25) + 5 = -5 + 5 = 0
One solution (-1.25, 0)
Why is causation so much more difficult to prove than correlation?
Answers
Is g(x)= 5x-1 an odd function
Answers
Answer:
No
Step-by-step explanation:
g(x)= 5x-1 is the same as g(x)= 5x^1 - 1x^0, which contains one odd power (x^1) and one even power (x^0). Therefore, g(x)= 5x-1 is neither even nor odd.
Answer:
This is not an odd function.Step-by-step explanation:
[tex]\text{If}\ f(-x)=f(x)\ \text{then}\ f(x)\ \text{is an even function.}\\\\\text{If}\ f(-x)=-f(x)\ \text{then}\ f(x)\ \text{is an odd function.}[/tex]
======================================================
[tex]g(x)=5x-1\\\\g(-x)=5(-x)-1=-5x-1=-(5x+1)\\\\g(-x)\neq-g(x)\ \wedge\ g(-x)\neq g(x)[/tex]
please help! i was wondering how you would solve this question!
Answers
Answer: C. 150 km²
Step-by-step explanation:
Use similar triangle proportion to find x:
[tex]\dfrac{x}{4.5}=\dfrac{15.3+7.4}{7.4}\\\\\\x=\dfrac{4.5(22.7)}{7.4}\\\\\\x=13.8\\\\\text{Notice that x is the diameter of the circle}\implies r=\dfrac{13.8}{2}=6.9\\\\\\\text{Find the area of the circle using }A=\pi r^2\\A=\pi (6.9)^2\\\\.\ =\pi (47.6)\\\\.\ =149.6\\\\.\ \approx150[/tex]