Allison drew a map of where she and her friends live. Allison's house is at point A, and her friends live at points B, C, and D. She only wrote some of the distances, in blocks, on the map. Also, AD¯¯¯¯¯¯¯¯ is a perpendicular bisector of BC¯¯¯¯¯¯¯¯. Allison wants to know the distance between her house and point C.What is the measure of AC?
Answers
Solution:
Given that;
Allison drew a map of where she and her friends live.
Allison's house is at point A, and her friends live at points B, C, and D
Where, line segment AD is a perpendicular bisector of BC,
And a perpendicular bisector is a line segment which bisects another line segment at 90 degrees, and divides it into two equal parts..
Since, AD is a perpendicular bisector of BC, then
[tex]\begin{gathered} BD=CD=3 \\ \angle ADB=\angle ADC \\ And,\text{ }AD=CD \\ Thus, \\ \Delta ADB\cong\Delta ADC\text{ \lparen SAS\rparen} \end{gathered}[/tex]Hence,
[tex]AB=AC=4.24[/tex]The measure of AC is 4.24
Related Questions
Graph ABCD with vertices B(2, 1), C(4,4) and D(4,0) and its image after the reflection in the line n: x=0.
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We have a triangle BCD with vertices
[tex]\lbrace(2,1),(4,4),(4,0)\rbrace[/tex]The transformation is a reflection in the line x = 0(also know as the y-axis). A reflection on the y-axis is given by the following transformation:
[tex](x,y)\rightarrow(-x,y)[/tex]Doing this transformation on each one of our vertices, we can find the transformed figure.
[tex]\begin{gathered} (2,1)\rightarrow(-2,1) \\ (4,4)\rightarrow(-4,4) \\ (4,0)\rightarrow(-4,0) \end{gathered}[/tex]Then, the image is
[tex]\lbrace(-2,1),(-4,4),(-4,0)\rbrace[/tex]The option that fits this transformation is option b.
x - 51Solve for x:42
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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]write the following degrees in radian measure (a) 80 degrees(b) 120 degrees (c) 90 degrees (d) 270 degrees(e) 135 degrees
Answers
Answer
(a) 80 degrees = (4π/9) radians = 0.444π radians = 1.397 radians.
(b) 120 degrees = (2π/3) radians = 0.667π radians = 2.095 radians.
(c) 90 degrees = (π/2) radians = 0.50π radians = 1.571 radians.
(d) 270 degrees = (3π/2) radians = 1.50π radians = 4.714 radians.
(e) 135 degrees = (3π/4) radians = 0.75π radians = 2.357 radians.
Explanation
To do degree to radians conversion, we need to first note that
360° = 2π radians
So, for each of these cases, if we let the value of the angle given in degree be x in radians, then we can easily solve for x for each ot them
(a) 80 degrees
80° = x radians
360° = 2π radians
We can write a mathematical relationship by cross multiplying
(360) (x) = (80) (2π)
360x = 160π
Divide both sides by 360
(360x/360) = (160π/360)
x = (4π/9) = 0.444π
80° = (4π/9) radians = 0.444π radians = 1.397 radians
(b) 120 degrees
120° = x radians
360° = 2π radians
We can write a mathematical relationship by cross multiplying
(360) (x) = (120) (2π)
360x = 240π
Divide both sides by 360
(360x/360) = (240π/360)
x = (2π/3) = 0.667π
120° = (2π/3) radians = 0.667π radians = 2.095 radians
(c) 90 degrees
90° = x radians
360° = 2π radians
We can write a mathematical relationship by cross multiplying
(360) (x) = (90) (2π)
360x = 180π
Divide both sides by 360
(360x/360) = (180π/360)
x = (π/2) = 0.50π
90° = (π/2) radians = 0.50π radians = 1.571 radians
(d) 270 degrees
270° = x radians
360° = 2π radians
We can write a mathematical relationship by cross multiplying
(360) (x) = (270) (2π)
360x = 540π
Divide both sides by 360
(360x/360) = (540π/360)
x = (3π/2) = 1.50π
270° = (3π/2) radians = 1.50π radians = 4.714 radians
(e) 135 degrees
135° = x radians
360° = 2π radians
We can write a mathematical relationship by cross multiplying
(360) (x) = (135) (2π)
360x = 540π
Divide both sides by 360
(360x/360) = (270π/360)
x = (3π/4) = 0.75π
135° = (3π/4) radians = 0.75π radians = 2.357 radians
Hope this Helps!!!
Please help me if you can! in the image it shows a problem I need guidance on.
Answers
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.
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.
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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.
An 8-sided die with numbers from 1 to 8 is rolled. What is the probability that a 4 is rolled? Write your answer as an exact fraction which is reduced as much as possible.
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Since it is an 8 sided dice
We have a sample space of 8 possible results 1,2,3,4,5,6,7,8
Just 4 is our favorable event, i.e. 1 possibility
Then we can write
P (4) = 1/8
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°
Answers
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"
I need help on question 6 and simple explanation please (8th grade algebra)
Answers
ANSWER
Linear function
EXPLANATION
6) To solve this, we have to observe the given data.
Notice that as each term comes, the circles are dropped by a specific factor:
Term 1: 16
Term 2: 8
Term 3: 4
Term 4: 2
Therefore, we see that the number of circles reduces by a certain factor which is ¹/ ₂.
Hence, there is a proportional relationship between the term and the number of circles.
Therefore, a proportional function will be used to model the pattern:
[tex]y=\frac{1}{2}x[/tex]This is also the form of a linear function without the constant. Hence, the answer is a linear function.
The male and female guests attending Patricia's party were surveyed to see if they drove to the party or did not drive. The data is displayed in the table below: MaleFemale 26 24 drove to the party 34 116 did not drive to the partyIf a guest is chosen at random from this group, what are the chances of choosing a guest who is male and did not drive to the party? 12%13%17%58%
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The given table is
Male Female Total
Drive 26 24 50
Did not drive 34 116 150
Total 60 140 200
From the table, total number of males and females = 200
number of guests that are males and did not drive = 34
Recall, Probability is expressed as
number of favorable outcomes/number of total outcomes
Therefore, the chances of choosing a guest who is male and did not drive to the party is
34/200 = 0.17
By converting to percentage, it is
0.17 x 100 = 17%
identify the y-intercept from the table:answer as an ordered pair (x,y)
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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.]
Factoring the expression 24a63 – 20a%b2 + 4a3b2 gives a new expression of the formUa" by (Wa? + Vb+ 2), where U > 0.What is the value of U?1What is the value of W?What is the value of V?What is the value of Z?What is the value of c?What is the value of y?
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Given the expression:
[tex]24a^3b^{3\text{ }}-20a^5b^2+4a^3b^2[/tex]Let's first re-arrange the expression:
[tex]-20a^5b^2+24a^3b^{3\text{ }}+4a^3b^2[/tex]Now factorize:
[tex]-4a^3b^2(5a^2\text{ + (-6b) + (-1))}[/tex]Now let's compare with this equation:
[tex]Ua^xb^y(Wa^2+Vb\text{ + Z)}[/tex]We can see that:
The value of U = -4
The value of V = -6
The value of W = 5
The value of Z = -1
The value of x = 3
The graph shows which quadratic equation?A)y = (x + 4)2 - 3B)y = (x - 4)2 + 3C)y = (x - 4)2 - 3D)y = -(x - 3)2 + 4
Answers
The answer is
[tex]y=-(x-3)^2+4[/tex]Emma wants to advertise how many chocolate chips are in each Big Chip cookie at her bakery. She randomly selects a sample of 64 cookies and finds that the number of chocolate chips per cookie in the sample has a mean of 8.3 and a standard deviation of 2.3. What is the 99% confidence interval for the number of chocolate chips per cookie for Big Chip cookies? Assume the data is from a normally distributed population. Round answers to 3 decimal places where possible. < μ <
Answers
Answer:
The 99% confidence interval is
7.558 - 9.042
Explanation:
The formula for the confidence interval is:
[tex]Confidence\text{ }interval=\bar{X}\pm\frac{\sigma}{\sqrt{n}}[/tex]Where:
X is the mean
σ is the standard deviation
z is the z-score for the confidence interval
n is the sample size.
Also, the interval has:
[tex]Upper\text{ }limit=\bar{X}+\frac{\sigma}{\sqrt{n}}[/tex][tex]Lower\text{ }limit=\bar{X}-\frac{\sigma}{\sqrt{n}}[/tex]Then, in this case,
The sample size is n = 64
The mean is X = 8.3
The z-score for a 99% confidence interval is z = 2.58
The standard deviation is σ = 2.3
Then:
[tex]Lower\text{ }limit=8.3-2.58\cdot\frac{2.3}{\sqrt{64}}=9.04175[/tex][tex]Upper\text{ }limit=8.3+2.58\cdot\frac{2.3}{\sqrt{64}}=7.55825[/tex]Thus, the confidence interval, rounded to 3 decimals is
7.558 - 9.042
SOMEONE PLS HELP
Solve.
−4 3/4=x−1 1/5
What is the solution to the equation?
Enter your answer as a simplified mixed number in the box.
X= ??
Answers
The solution to the equation is x = -71/20 i.e.
x = -3(11/20).
Given, an equation
-4(3/4) = x - 1(1/5)
On solving the mixed fraction, we get
-19/4 = x - 6/5
On adding 6/5 both the sides, we get
-19/4 + 6/5 = x
x = (-95 + 24)/20
x = -71/20
On converting the fraction into mixed fraction, we get
x = -3(11/20)
Hence, the solution to the equation is x = -71/20 i.e. x = -3(11/20).
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A passcode to enter a building is a sequence of 4 single digit numbers (0-9), and repeated digits aren'tallowed.Suppose someone doesn't know the passcode and randomly guesses a sequence of 4 digits.What is the probability that they guess the correct sequence?
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ANSWER
0.0001984
EXPLANATION
There are 10 possible values for each digit of the passcode to enter the building.
These include: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
So, there are:10 x 10 x 10 x 10 = 10^4 = 10,000 total possible passcodes.
For no repeat passcode
We have: 10 x 9x 8 x7 = 5040 total possible passcodes without repetition.
Probability of guessing correct sequence
Since there is only 1 correct sequence of 4 digits passcode (without repetition) to enter the building
[tex]\begin{gathered} Prob\text{ = }\frac{1}{5040} \\ Prob\text{ = 0.0001984} \end{gathered}[/tex]Hence, the probability that they guess the correct sequence is 0.0001984
Identify the constant term in this expression. 0.25 + 2× + 4z +0.75y
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the constant term is the term without any variable so the answer is 0.25
3x+2y=10 table of ordered pair
Answers
Answer:
Step-by-step explanation:
for sure
Part A Mrs. Finney is making slime with her kids. They find a recipe that calls for 1 part borax solution to 3 parts glue. What is the value of the ratio of borax solution to glue? 1/3 What is the value of the ratio of glue to borax solution? < 1/3 Part B Complete the ratio table for the slime recipe. 1 Glue 3 Borax Solution (B) (G) 1 3 2 3 9 12
Answers
Answer
Ratio of borax solution to glue = (1/3)
Ratio of glue to borax solution = (3/1)
Part B
The ratio table
B - Borax solution
G - Glue
B | G
1 | 3
2 | 6
3 | 9
4 | 12
5 | 15
Explanation
The recipe calls for
1 part borax solution to 3 parts glue
Ratio of borax solution to glue = (1/3)
Ratio of glue to borax solution = (3/1)
Part B
Since we know that 1 part of borax solution = 3 parts of glue, we just need to multiply the amounts of borax solution by 3 to obtain the amount of glue.
The ratio table
B - Borax solution
G - Glue
B | G
1 | 3
2 | 6
3 | 9
4 | 12
5 | 15
Hope this Helps!!!
Given the circle below with radius 5y centimeters, find its area. Do not approximate [tex]\pi[/tex]. ( A = [tex]\pi r^{2}[/tex] )
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The area of the given circle as represented in the image attached in the task content is; 550y² / 7.
What is the area of the given circle as in the task content?It follows from the task content that the area of the given circle is to be determined without approximating π.
Since the area of a circle is given by the formula;
A = π r²
where the radius, r = 5y.
The area of the circle is therefore;
A = π ( 5 y )²
The area of the circle is therefore;
A = 25 π y².
Hence, by substitution of 22 / 7 for π;
Area, A = 550y² / 7.
Ultimately, it can be inferred from the solution above that the area of the circle which is as described is; 550y² / 7.
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Question 20>Solve the given linear system of equations:- 1212ySy8Enter your answer in the form of an ordered pair(x, y).One solution:O No solutionO Infinite number of solutions
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the equation given was
[tex]\begin{gathered} 9x-12y=-12 \\ -6x+8y=8 \end{gathered}[/tex]now to solve this equation, we should solve the simultaneous equation and get the values of x and y
now, let's take equation 1 and solve for x
[tex]\begin{gathered} 9x-12y=-12 \\ \text{make y the subject of formula} \\ 9x=-12+12y \\ \text{divide both sides by 9} \\ \frac{9x}{9}=\frac{-12+12y}{9} \\ x=\frac{-12+12y}{9} \end{gathered}[/tex]put x into equation 2
[tex]\begin{gathered} -6x+8y=8 \\ x=\frac{-12+12y}{9} \\ \text{put x into the equation} \\ -6(\frac{-12+12y}{9})+8y=8 \\ \frac{72-72y}{9}+8y=8 \\ 8-8y+8y=8 \\ 0=0 \end{gathered}[/tex]from the solution, y = 0
put y = 0 into either equation 1 or 2
from equation 1
[tex]\begin{gathered} 9x-12y=-12 \\ \text{put y = 0} \\ 9x-12(0)=-12 \\ 9x-0=-12 \\ 9x=-12 \\ \text{divide both sides by 9} \\ \frac{9x}{9}=-\frac{12}{9} \\ x=-\frac{4}{3} \end{gathered}[/tex]from the above calculation, the above equation has only one solution.
the ordered pair is
[tex](x,y)=(-\frac{4}{3},0)[/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
Answers
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
Will someone explain to me how I get this done?
Answers
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
a juice box has a volume approximately 60in3 with a height of 5 in. The box is cut in half to a height of 2.5 in. How does the new volume compare to the original?
Answers
Height of the box = 5 in
write an equation of the line in the point- slope form that passes through the given points in the table. Then write the equation in slope-intercept form. (10,80) (15,95)
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We know that the line passes through the points (10,130) and (20,200).
First, we have to find the slope with the following formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where,
[tex]\begin{gathered} x_1=10 \\ ^{}x_2=15^{} \\ y_1=80 \\ y_2=95 \end{gathered}[/tex]Replacing these coordinates, we have
[tex]m=\frac{95-80}{15-10}=\frac{15}{5}=3[/tex]The slope is 7.
Now, we use one point, the slope, and the point-slope formula to find the equation
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-80=3(x-10) \end{gathered}[/tex]Therefore, the point-slope form of the line is[tex]y-80=3(x-10)[/tex]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
Answers
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]Mead II) 5x + 5 = 45 5x 45-5 12) 31-8x + 8 = 80 31-8x1+5290 278-30 wwxt8-80-8 24x272 15x1=40 5x -40 X> 512 5* = -40 X = -8 x=8 and 2-8 X-3 513+4x) = -115
Answers
Please provide an image of the question. If you still want an explanation for problem 13, please don't close the session before I am done with the session.
In our previous session we were analysing the following absolute value equation when the session was abruptly closed:
3 | - 8 x | + 8 = 80
we subtracted 8 to both sides to isolate the term in "x" on the left
3 | - 8 x | = 80 - 8
3 | - 8 x| = 72
divide both sides by 3:
|- 8 x| = 72 / 3
|- 8 x| = 24
Now remove the absolute value bars considering:
1) That the expression inside it is POSITIVE so we DON'T change anything when removing the bars:
- 8 x = 24
now we divide boths sides by "- 8"
x = 24 / (- 8)
x = - 3
Then, when x = -3 notice that the expression - 8 x becomes -8 * (-3) = 24
corroborating that the expression inside the bars was a posotive number.
2) Considering the case that "- 8 x" is NEGATIVE , then when removing the absolute value bars we CHANGE the sign of the expression into:
8 x
Then we have:
8 x = 24
divide by 8 both sides
x = 24 / 8
x = 3
Then we have TWO answers to this equation:
x = -3 and x = 3
both satisfy the equation.
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.
Answers
ANSWER :
EXPLANATION :
Find the coordinates of the vertices of the figure after the given transformation: T<2,4> translation 3A. J′(1,−1),E′(1,1),V′(4,3)B. J′(0,−2),E′(0,0),V′(3,2)C. J′(−2,−1),E′(−2,1),V′(1,3)D. J′(−3,−2),E′(−3,0),V′(0,2)
Answers
According to the given rule of transformation, any point (x,y) is transformed as follows:
[tex](x,y)\rightarrow(x+2,y+4).[/tex]Now, the coordinates of the vertices of the triangle are:
[tex]V(-1,-1),J(-4,-5),E(-4,-3).[/tex]Therefore:
[tex]\begin{gathered} V^{\prime}(-1+2,-1+4), \\ J^{\prime}(-4+2,-5+4), \\ E^{\prime}(-4+2,-3+4). \end{gathered}[/tex]Simplifying the above result, you get:
[tex]J^{\prime}(-2,-1),E^{\prime}\left(−2,1\right),V^{\prime}\left(1,3\right).[/tex]Answer: [tex]J^{\prime}(-2,-1),E^{\prime}(-2,1),V^{\prime}(1,3).[/tex]I'm checking my son's homework Tina Nguyen help me with this
Answers
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.
please help me with 168÷45
Answers
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