The expression used to represent the distance between the two birds on the number line is 2.5 - (-2.5) and the distance is 5 units.
Let us represent the bird A is sitting at one point on the number line.
Bird B is sitting at another point.
Both of them are at a an equal distance from a worm which is at the position O which is the origin.
Now it is given that A and B are at the positions of the number line marked 2.5 and -2.5
Now the distance between A and B can be calculated by finding the distance between A and O and adding the additive inverse to it to get the distance between O and B using subtraction.
AO = 2.5 - 0 = 2.5 units
The additive inverse of this is -2.5 units.
Therefore the distance AB :
= AO - BO
= 2.5 -(-2.5)
=2.5 +2.5
=5 units.
Hence they are at a distance of 5 units from each other.
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if 2/3n = -12 what is tbe vLue of n=
If 2/3n = -12
This can be re-written as
2n/3 = -12
Multiply both sides of the equation by 3 to eliminate the fraction on the left hand side
2n = -36
Divide both sides of the equation by 2 (to eliminate the 2 and isolate the n)
n = -18
7. The distance y (miles) that an athlete training for a marathon is from home after x(hours) is shown in the figure to the right.Distance from Homea. What is the y-intercept as an ordered pair?30b. Find the slope of this line. (Be aware of the scale)200Distance (miles)(1, 10)10C. What is the equation of this linear segment?0 0.5 1.0 1.5 2.0 2.5 3.0Time (hours)
The last one! Synthetic division please explain how to do this!!
The given expression is:
[tex](x^3+5x^2-18)\div(x-3)[/tex]This can be solved using the synthetic division as shown below
Therefore, the quotient = x² + 8x + 24
The remainder = 54
To confirm the remainder, substitute if f(54) = 0
f(x) = x³ + 5x^2
3x+2y=10 table of ordered pair
Answer:
Step-by-step explanation:
for sure
Given Point A, what is the coordinate for A' after the following transformation has occurred?(x, y) + (x – 5, -y + 2)A (5, 7)
So we have the point A=(5,7) and the following transformation:
[tex](x,y)\rightarrow(x-5,-y+2)[/tex]Transformations take a point as input and return another point that usually is different than the one used as input. Since our input is (5,7) then we just need to replace 5 and 7 in place of x and y on the transformation:
[tex]\begin{gathered} A^{\prime}=(x-5,-y+2)=(5-5,-7+2)=(0,-5) \\ A^{\prime}=(0,-5) \end{gathered}[/tex]Then, the point we are looking for is A'=(0,-5).
I'm checking my son's homework Tina Nguyen help me with this
The amount of money Lilianna has is: 68
The least amount of money she needs is: y
The amont of money for the phone is: 194.
The above situation can be expressed as,
[tex]68+y\ge194[/tex]From the above expression the minimum value of y is,
[tex]\begin{gathered} y\ge194-68 \\ y\ge126 \end{gathered}[/tex]Thus, Lilianna needs at least 126 dollars more to buy the phone, and the correct option is option A.
Graph the functions f ( x ) = x 2 , g ( x ) = x 2 + 7 , and h ( x ) = x 2 − 7 on the same rectangular coordinate system. Then describe what effect adding a constant, k , to the function has on the vertex of the basic parabola.
ANSWER :
EXPLANATION :
Financial statements use the formula working C=current Assets - current Liabilities. The formula can be written in symbols as C=A-L. Solve the formula for A.
Given that C = A - L
To solve for A, add L to both sides of the equation
C + L = A - L + L
C + L = A
=>A = C + L
2) A scuba diver descends to a location that is -12 1/3 m relative to sea level. He then descends another 8 1/4 M. What is the scuba divers final location relative to sea level.
NUMBERS ONLY
Answer: -20 7/12
Step-by-step explanation: Hope this helps!
In circle U m ∠TUs=107. Solve for x if m TS = (3x+39). If necessary round your answer to the nearest tenth
Answer:
x=22.7
Explanation:
In the circle:
• m∠TUS=107°
,• The measure of arc TS = (3x+39)°
In a circle:
Therefore:
[tex]\begin{gathered} m\widehat{TS}=m\angle TUS \\ \implies3x+39=107\degree \end{gathered}[/tex]We solve the equation for x:
[tex]\begin{gathered} \text{ Subtract 39 from both sides} \\ 3x+39-39=107-39 \\ 3x=68 \\ \text{ Divide both sides by 3} \\ \frac{3x}{3}=\frac{68}{3} \\ x\approx22.7\degree \end{gathered}[/tex]The value of x is 22.7 (correct to the nearest tenth).
Question 12Which equation contains a perfect square trinomial?O x2 - 6x + 72 = 0O x2 + 2x - 4 = 0O2? + 14x + 49 = 0O x2 – 5x + 64 = 0
A perfect square trinomial has a general structure which is
[tex]a^2\pm2ab+b^2[/tex]The one that meets this structure is
[tex]x^2+14x+49[/tex]We know it because it can be re written as
[tex]x^2+2\cdot7\cdot x+7^2[/tex]Which shows in a more explicit way the estructure of a perfect square trinomial. The right answer is c
in a table that shows no exact solutions, how do you know if there are any solutions? How can you find an approximate solution?
If we have a quadratic equation described in a table and it does not show the exact solution (roots) of the equation, we can look if, with the values of x or the independent variable sorted, we have a change of sign.
This indicates that there is a root between those two values of x.
For example:
x = 2 --> f(x) = -3
x = 3 --> f(x) = 4
We can see that from x=2 to x=3, we have a sign change. Then we know that, because of the continuity of the quadratic function, we must have a value between x=2 and x=3 for which f(x)=0. This is an application of the Intermediate Value Theorem.
We can then approximate the value of the root x=r as the average between x=2 and x=3. This is the bisection method to find roots of functions. In this case, it would give a result r=2.5.
There are other methods (Newton-Raphson or False position, for example), but this bisection method is the simplest approximation.
Translate each graph as specified below.(a) The graph of =yfx is shown. Translate it to get the graph of =y+fx2.(b) The graph of =ygx is shown. Translate it to get the graph of =yg−x5.
See graphs below
Explanation:[tex]\begin{gathered} a)\text{ y = f(x)} \\ f(x)\text{ + 2 is a translation of 2 units upward} \\ To\text{ get }y\text{ = f(x )+ 2, we will assign values to x and add 2 to its y coordinates in order to get } \\ \text{the coordinates of the new one} \end{gathered}[/tex]let x = -2, -1, 0, 1, 2
on the original
when x = -2, y = -3
new y coordinate = -3 + 2 = -1
when x = -1, y = 0.5
new y -coordinate = 0.5 + 2 = 2.5
when x = 0, y = 1
new y coordinate = 1 + 2 = 3
when x = 1, y = 1.5
new y oordinate = 1.5 +2 = 3.5
when x = 2, y = 5
new y-coordinate = 5 + 2 = 7
plotting the new points against x:
b) y = g(x)
y = g(x - 5)
subtract 5 from the x coordinate of the previous line
We will assign values for x, in order to get values of y
let x = 0, 1, 3
when x = 0, y = 0
new x coordinate = 0 - 5 = -5
when x = 1, y = 4
new x coordinate = 1 - 5 = -4
when x = 3, y = 7
new x coordinate = 3 - 5 = -2
plotting the points on the graph:
1 foot= 12 inches 2 feet= inches
Solution
We are given that
[tex]1\text{ foot = 12 inches}[/tex]To find
[tex]\begin{gathered} \text{2 f}eet\text{ = 2}\times12\text{ inches} \\ \text{2 f}eet\text{ =}24\text{ inches} \end{gathered}[/tex]1. Reasons quantitatively. AB lies on the number line. The coordinate of point A is -6. Given thay AB = 20, what are two possible coordinates for point B?2. Given: Point K is between points H and J, HK = x - 5, KJ = 5x - 12, and HJ = 25. Find the value of x.
The distance in a coordinate line is given by:
[tex]d(A,B)=\lvert B-A\rvert[/tex]in this case we know that A=-6 and we would like to know the value of B so that the distance is 20. Plugging this values in the equation we have:
[tex]\begin{gathered} \lvert B-(-6)\rvert=20 \\ \lvert B+6\rvert=20 \end{gathered}[/tex]Now we need to remember the property:
[tex]\begin{gathered} \lvert x\rvert=a \\ \text{implies} \\ x=\pm a \end{gathered}[/tex]Using this we have:
[tex]\begin{gathered} \lvert B+6\rvert=20 \\ B+6=\pm20 \\ B=-6\pm20 \end{gathered}[/tex]Then:
[tex]\begin{gathered} B=-6+20=14 \\ B=-6-20=-26 \end{gathered}[/tex]Therefore the two possible coordinates for B are 14 and -26.
1. Do you the following side lengths form a right triangle?2. Which measurement is closest to the value of X in centimeters?
Answer:
Part 1:
Yes, the side lengths form a right triangle.
Part 2:
Option d 37.1 cm
Explanation:
We need to use the pythagorean theorem.
In part 1, if the 3 side lengths are a right triangle, then, they must verify:
[tex]7.5^2=4.5^2+6^2[/tex]By the theorem. Then:
[tex]\begin{gathered} 7.5^2=56.25 \\ 4.5^2+6^2=20.25+36=56.25 \end{gathered}[/tex]They're equal, then the lengths correspond to a right triangle.
For part 2, we need to use again the theorem. In this case:
[tex]\begin{gathered} 12^2+x^2=39^2 \\ x=\sqrt{1521-144} \\ x=\sqrt{1377} \\ x\approx37.1cm \end{gathered}[/tex]When solving the system below algebraically using the substitution method, which of the following could be an equation you could create to solve for y?A. -4(2y - 20) + 3y = 30B. -4(-2y + 20) + 3y = 30C. -2y + 20 = -3y + 30D. 4(x + 2y = 20
The goal of the substitution method is to eliminate one of the variables using one of the equations of the systems. We are told that we want to solve for y, that is, we should use one equation to eliminate the variable x.
Since the coefficient of x in the first equation is 1, we will use the first equation to eliminate x in the second equation. So, we have the first equation
[tex]x+2y=20[/tex]So, by subtracting 2y on both sides, we get
[tex]x=20-2y[/tex]which is equivalent to
[tex]x=-2y+20[/tex]So, if we replace this value of x in the second equation,w e get
[tex]-4\cdot(-2y+20)+3y=30[/tex]which corresponds to option B
What is the slope-intercept form of a line? What two specific pieces of information do you need to write an equation of a line in slope-intercept form? Explain/discuss how you would find those two pieces of information if you were only given two points on the line. Use the points (-3,1) and (3,-5) to illustrate this process.
The slope-intercept form of a line is:
y = ax + b
In which a is the slope and b is the y-intercept, which is the value of y when x = 0.
To write an equation in this form, we need the slope and the y-intercept.
Using two points, we find the slope a dividing the change in y by the change in x. Then, having a, we can replace one of these points into the equation, to find the intercept b.
In this question:
We have points (-3,1) and (3,-5)
Finding the slope:
Change in y: -5 - 1 = -6
Change in x: 3 - (-3) = 3 + 3 = 6
Slope: a = -6/6 = -1
So
y = -x + b
Using the point (-3,1), we have that when x = -3, y = 1. So
1 = -(-3) + b
1 = 3 + b
3 + b = 1
b = 1 - 3
b = -2
The equation is:
y = -x - 2
Please help me if you can! in the image it shows a problem I need guidance on.
We can use trigonometric functions to determine how far it is across the lake.
Here, use tangent of angle A:
[tex]\begin{gathered} \tan 40^o=\frac{a}{630} \\ 0.839=\frac{a}{630} \\ 0.839\times630=a \\ 528.632=a \end{gathered}[/tex]Thus, the lake is 529 yards across.
which set of angle measures will not be the three interior angles of a triangle?A. 78°, 2°, 100°B. 52°, 52°, 52°C. 60°, 30°, 90°D. 13°, 37°, 130°
The sum of an interior angle of a triangle is 180 degrees.
[tex]\begin{gathered} A.78^{\circ}+2^{\circ}+100^{\circ}=180^{\circ} \\ B.52^{\circ}+52^{\circ}+52^{\circ}=156^{\circ} \\ C.60^{\circ}+30^{\circ}+90^{\circ}=180^{\circ} \\ D.13^{\circ}+37^{\circ}+130^{\circ}=180^{\circ} \\ \text{Hence, (B) is the right option.} \end{gathered}[/tex]Answer:
Step-by-step explanation:
"B" could not be angles of a triangle. It forms a straight line. So the answer is "B"
identify the y-intercept from the table:answer as an ordered pair (x,y)
We can see that the y-intercept is located at (0, 6).
[Remember that the y-intercept is where the line cuts the y-axis when x = 0.]
it was recently estimated that females outnumber males by about seven to three. if there are 2230 people in a county how many of them are females
Given:
7 out of 10 will be females.
[tex]No\text{ of females in country =}\frac{7}{10}\times2230[/tex][tex]No\text{ of females in country =}1561[/tex]x - 51Solve for x:42
Answer : x = 7
[tex]\begin{gathered} \text{Solve for x: }\frac{x\text{ - 5}}{4}\text{ = }\frac{1}{2} \\ \text{Firstly, introduce cross multiplication} \\ 2(x\text{ - 5) = 4 x 1} \\ \text{Open the parenthesis} \\ 2\cdot x\text{ - 2}\cdot5\text{ = 4} \\ 2x\text{ - 10 = 4} \\ \text{Make 2x the subject of the formula} \\ 2x\text{ = 4 + 10} \\ 2x\text{ = 14} \\ \text{Divide both sides by 2} \\ \frac{2x}{2}\text{ = }\frac{14}{2} \\ x\text{ = 7} \end{gathered}[/tex]10.{(0,8), (1, 2), (3, 7), (5,9), (3, 6)}
the image is downloading, please don't close the session
Circle B is a transformation of Circle A. Describe the transformations that show why Circle A is similar to Circle B. YA 12 Circle B is the result of dilating Circle A with A as the center of dilation and using a scale factor of . then translating the image 12 units down. 10 8 6 A А Circle B is the result of dilating Circle A with A as the center of dilation and using a scale factor of then reflecting the image in the y-axis. 4 N -2 0 -2 2 4 6 8 10 12 x -4 Circle B is the result of dilating Circle A with A as the center of dilation and using a scale factor of, then translating the image 12 units down. -6 B -8 -10 -12 Circle B is the result of dilating Circle A with A as the center of dilation and using a scale factor of then rotating the image 180°.
The two circles, A and B have different diameters. The diiameter of circle A is 5 units while the diameter of circle B is 4 units. This means that circle B is smaller than circle A. This means that there is a dilation and it is a reduction. Thus, we can say that B is 4/5 * A
4/5 * 5 = 4
The image was then translated 12 units down. The correct option is the third one
(4a²b) ?Simplify:(2a3b4)32a5710AB.4ab63с225510D4ab53
We would apply the following laws of exponents
(x^y)^z = x^(yz)
a^c * a^d = a^(c + d)
a^c / a^d = a^(c - d)
The given expression is
(4a^2b)^2/(2a^3b^4)^3
By applying the first law above, it becomes
[4^2a^(2*2)b^2]/[2^3a^(3*3)b^(4*3)]
= [16a^4b^2]/[8a^9b^12]
by applying the second and third laws, we have
16/8 * a^(4 - 9) * b^(2 - 12)
= 2a^-5b^-10
Also, x^-1 = 1/x
Thus, the final expression would be
2/a^5b^10
Option C is correct
plss help Solve for y.
−2y+5=−11
Responses
y = 8
y, = 8
y = 3
y, = 3
y=−3
y equals negative 3
y=−8
y equals negative 8
Responses
y = 8
y, = 8
y = 3
y, = 3
y=−3
y equals negative 3
y=−8
y equals negative
Will someone explain to me how I get this done?
The Solution:
The given system of equations are:
[tex]\begin{gathered} x-2y=4\ldots eqn(1) \\ 2x+y=-2\ldots eqn(2) \end{gathered}[/tex]We are asked to solve using the Substitution Method.
Step 1:
From eqn(1), we shall find x in terms of y.
[tex]\begin{gathered} x-2y=4 \\ \text{Adding 2y to both sides, we get} \\ x-2y+2y=4+2y \\ x=4+2y\ldots eqn(3) \end{gathered}[/tex]Putting eqn(3) into eqn(2), we get
[tex]\begin{gathered} 2x+y=-2 \\ \text{Putting 4+2y for x, we get} \\ 2(4+2y)+y=-2 \end{gathered}[/tex]Clearing the brackets, we get
[tex]\begin{gathered} 8+4y+y=-2 \\ \text{Subtracting 8 from both sides, we get} \\ 8-8+4y+y=-2-8 \\ 4y+y=-10 \\ 5y=-10 \end{gathered}[/tex]Dividing both sides by 5, we get
[tex]\begin{gathered} \frac{5y}{5}=\frac{-10}{5} \\ \\ y=-2 \end{gathered}[/tex]Substituting -2 for y in eqn(3), we have
[tex]\begin{gathered} x=4+2y \\ x=4+2(-2) \\ x=4-4=0 \\ \text{ So, the solution is (0,-2)} \end{gathered}[/tex]Therefore, the correct answer is x=0, y= -2
please help me with 168÷45
please help me with 168÷45
we know that
168=(2^3)(3)(7)
45=(3^2)(5)
so
[tex]\frac{168}{45}=\frac{2^3\cdot3\cdot7}{3^2\cdot5}=\frac{2^3\cdot7}{3\cdot5}=\frac{56}{15}[/tex]therefore
Convert to mixed number
56/15=45/15+11/15=3+11/15=3 11/15
therefore
the answer is
3 11/15 or 56/15
Part 2
Estimate te quotient using compatible numbers
so
168:45------------> 180:45=4do
Remember that
Compatible numbers are numbers that are easy to compute mentally
Which statement regarding the association shown could explain the relationship?A. class size appears to have little effect on test scores.B. schools is more affluent areas have larger class sizes, which is associated with higher test scores.C. schools in more affluent areas have smaller class sizes, which is associated with higher test scores. D. schools in less affluent areas have smaller class sizes, which is associated with lower test scores.