Answer:
Step-by-step explanation:
hello : 2,2×10² where : A =2,2 ( A < 10) qnd n =2 (is integer)
How many solutions does the system formed by x - y = 2 and ay - ax + 2a = 0 have for a nonzero
number a? Give your answer and complete the explanation.
The system has (select)
solution(s). Rearranging the left side of the 2nd equation and
subtracting 2a from both sides gives-ax + ay =
a. Dividing both sides by-a gives
x-y=
So, the equations describe the same line.
Answer:
1
y = 0
x = 2
Step-by-step explanation:
The first thing we want to do to solve a system of equations is to solve one of them in terms of a single variable.
Lets start with x - y = 2
If we add y to both sides we get: x = 2 + y
Now to solve the system of equations we can substitute that value for x into the other equation. In any system of equations a solution for one must be a solution for the other as well.
ay - ax + 2a = 0
When we substitute our value of x into this equation and get the folowing:
ay - a(2 + y) +2a = 0
ay -2a - ay + 2a = 0
All of the terms cancel out on the left side leaving us with:
0 = 0
This means that the only way this system can be solved is if y is equal to 0.
Going back to the first equation x - y = 2
x - 0 = 2 so x = 2
This is the only solution to that system of equations, which means it forms a point instead of a line.
How do I do these problems?
Answer:
12) x= 21
13) x = 1
14) x = 9
15) x = 1
Step-by-step explanation:
Here, we are being asked to solve the given equations and check our work.
To check the work, we need to substitute the found value of x into the equation to check if it makes a true and correct statement.
12) Solve for x:
[tex]\sf 12)\ \dfrac{2}{3}x + 2 = 16\ \textsf{[subtract 2 from both sides]}\\\\\implies \dfrac{2}{3}x + 2 - 2 = 16 - 2\\\\\implies \dfrac{2}{3}x = 14\ \textsf{[multiply both sides by 3]}\\\\\implies 3\left(\dfrac{2}{3}\right)x = 14(3)\\\\\implies 2x = 42\ \textsf{[divide both sides by 2]}\\\\\implies \dfrac{2x}{2}=\dfrac{42}{2}\\\\\implies \boxed{\sf x = 21}[/tex]
Check your work:
[tex]\sf \dfrac{2}{3}x + 2 = 16\ \textsf{[substitute 21 for the value of x]}\\\\\implies \dfrac{2}{3}(21) + 2 = 16\ \textsf{[multiply]}\\\\\implies \dfrac{42}{3} + 2 = 16\ \textsf{[divide]}\\\\\implies 14 + 2 = 16\ \textsf{[add]}\\\\\implies 16 = 16\ \checkmark \textsf{[true statement]}[/tex]
13) Solve for x:
[tex]\sf 13)\ \dfrac{x}{2} + \dfrac{x}{3} = \dfrac{5}{6}\ \textsf{[multiply both sides by 6 - LCM of 2, 3, and 6]}\\\\\implies 6\left(\dfrac{x}{2} + \dfrac{x}{3}\right) = 6\left(\dfrac{5}{6}\right)\ \textsf{[multiply]}\\\\\implies \left(\dfrac{6x}{2} + \dfrac{6x}{3}\right) = \dfrac{30}{6}\ \textsf{[divide]}\\\\\implies 3x+2x=5\ \textsf{[combine like terms]}\\\\\implies 5x = 5\ \textsf{[divide both sides by 5]}\\\\\implies \dfrac{5x}{5}=\dfrac{5}{5}\\\\\implies \boxed{\sf x = 1}[/tex]
Check your work:
[tex]\sf \dfrac{x}{2} + \dfrac{x}{3} = \dfrac{5}{6}\ \textsf{[substitute 1 for the value of x]}\\\\\implies \dfrac{1}{2} + \dfrac{1}{3} = \dfrac{5}{6}\ \textsf{[rewrite the fractions with a common denominator of 6]}\\\\\implies \dfrac{1\times3}{2\times3} + \dfrac{1\times2}{3\times2} = \dfrac{5}{6}\ \textsf{[multiply]}\\\\\implies \dfrac{3}{6} + \dfrac{2}{6} = \dfrac{5}{6}\ \textsf{[add]}\\\\\implies \dfrac{5}{6} = \dfrac{5}{6}\ \checkmark \ \textsf{[true statement]}[/tex]
14) Solve for x:
[tex]\sf 14)\ \dfrac{x-1}{6} - \dfrac{x+1}{8} = \dfrac{1}{12}\ \textsf{[multiply both sides by 24 - LCM of 6, 8, and 24]}\\\\\implies 24\left(\dfrac{x-1}{6} - \dfrac{x+1}{8}\right) = 24\left(\dfrac{1}{12}\right)\ \textsf{[multiply]}\\\\\implies \left(\dfrac{24x-24}{6}\right) - \left(\dfrac{24x+24}{8}\right) = \dfrac{24}{12}\ \textsf{[divide]}\\\\[/tex]
[tex]\sf\\\implies (4x-4)-(3x+3)=2\ \textsf{[distribute the negative sign]}\\\\\implies (4x-4)+(-3x-3)=2\ \textsf{[combine like terms]}\\\\\implies x - 7 = 2\ \textsf{[add 7 to both sides]}\\\\\implies x - 7 + 7 = 2 + 7\\\\\implies \boxed{\sf x = 9}[/tex]
Check your work:
[tex]\sf 14)\ \dfrac{x-1}{6} - \dfrac{x+1}{8} = \dfrac{1}{12}\ \textsf{[substitute 9 for the value of x]}\\\\\implies \dfrac{9-1}{6} - \dfrac{9+1}{8} = \dfrac{1}{12}\ \textsf{[simplify]}\\\\\implies \dfrac{8}{6} - \dfrac{10}{8} = \dfrac{1}{12}\ \textsf{[rewrite the fractions with a common denominator of 24]}\\\\\implies \dfrac{8\times4}{6\times4} - \dfrac{10\times3}{8\times3} = \dfrac{1\times2}{12\times2}\ \textsf{[simplify]}\\\\[/tex]
[tex]\sf\\\implies \dfrac{32}{24}-\dfrac{30}{24}=\dfrac{2}{24}\ \textsf{[subtract]}\\\\\implies \dfrac{2}{24}=\dfrac{2}{24}\ \textsf{[reduce]}\\\\\implies \dfrac{1}{12}=\dfrac{1}{12}\ \checkmark\ \textsf{[true statement]}[/tex]
15) Solve for x:
[tex]\sf \dfrac{1}{4}+\dfrac{x+1}{8}=\dfrac{1}{2}\ \textsf{[multiply both sides by 8 - LCM of 2, 4, and 8]}\\\\\implies 8\left(\dfrac{1}{4}+\dfrac{x+1}{8}\right)=8\left(\dfrac{1}{2}\right)\textsf{[multiply]}\\\\\implies \left(\dfrac{8}{4}+\dfrac{8x+8}{8}\right)=\dfrac{8}{2}\ \textsf{[divide]}\\\\\implies 2 + x + 1 = 4\ \textsf{[add]}\\\\\implies x + 3 = 4\ \textsf{[subtract 3 from both sides]}\\\\\implies x + 3 - 3 = 4 - 3\\\\\implies \boxed{\sf x = 1}[/tex]
Check your work:
[tex]\sf \dfrac{1}{4}+\dfrac{x+1}{8}=\dfrac{1}{2}\ \textsf{[substitute 1 for the value of x]}\\\\\implies \left(\dfrac{1}{4}+\dfrac{1+1}{8}\right)=\dfrac{1}{2}\ \textsf{[simplify]}\\\\\implies \left(\dfrac{1}{4}+\dfrac{2}{8}\right)=\dfrac{1}{2}\ \textsf{[reduce]}\\\\\implies \left(\dfrac{1}{4}+\dfrac{1}{4}\right)=\dfrac{1}{2}\ \textsf{[add]}\\\\\implies \dfrac{2}{4}=\dfrac{1}{2}\ \textsf{[reduce]}\\\\\implies \dfrac{1}{2}=\dfrac{1}{2}\ \checkmark\ \textsf{[true statement]}[/tex]
4/3 of a number is more than 3/4 of its number by 1 . find the number
4/3 of a number is more than 3/4 of its number by 1 . find the number .
Given : -4/3 of a no. is more than 3/4 of its no. by 1To Find : -We have to find the number .To Assume : -Let the no. be xSo Solution goes from here :According to question 4/3 of a number is equal to :
[tex] \longmapsto \: \frac{4}{3} \times x[/tex]
Which means ,
[tex]\longmapsto \: \frac{4x}{3} [/tex]
According to question 3/4 of a number is equal to :
[tex]\longmapsto \: \frac{3}{4} \times x[/tex]
Which means ,
[tex]\longmapsto \: \frac{3x}{4} [/tex]
Now , forming equation :
As the question says that 4/3 of a number is more than 3/4 of its number by 1 . So :
[tex]\longmapsto \: \frac{4x}{3} = \frac{3x}{4} + 1[/tex]
Now , transposing 3x/4 to left hand side :
[tex]\longmapsto \frac{4x}{3} - \frac{3x}{4} = 1[/tex]
Now , taking L.C.M :
[tex]\longmapsto \: \frac{4(4x) - 3(3x)}{12} = 1[/tex]
Now by calculating :
[tex]\longmapsto \: \frac{16x - 9x}{12} = 1[/tex]
Now Subtracting 16x with 9x and transposing 12 to right hand side :
[tex]\longmapsto \: 7x = 12[/tex]
So ,
[tex]\longmapsto \: \boxed{ \bold{ x = \frac{12}{7} }}[/tex]
Therefore , the number is 12/7 .#[tex] \sf{Keep \: Learning }[/tex]18.
Is the data point, P, an outlier, an influential point, both, or neither?
A. Neither
B. Influential point
C. Outlier
D. Both
Find the slope and the y-intercept of the linear equation: 2x+y=7
slope: 7; y-intercept: 2
slope: 2; y-intercept: 7
slope: -2; y-intercept: 7
slope: 1/2; y-intercept: 7
Answer:
The slope-intercept form is y=mx+b y = m x + b , where m m is the slope and b b is the y-intercept. Subtract 2x 2 x from both sides of the equation. Reorder 7 7 and −2x - 2 x . Using the slope-intercept form, the slope is −2 .
A giant tortoise can walk about
1/10 meter per second on land. A cooter turtle can walk about
1/2 meter per second on land.
How long would it take a giant tortoise to travel 2 meters?
2 ÷ 1/10 = 2 ? 10 =
Answer:
its already on brainy hope this helps
Step-by-step explanation:
The rate of giant tortoise is 1/10 meters per each second.
The rate of cooter turtle is 1/2 meters per each second.
How long would it take a giant tortoise to travel 5 meters?
1 second : 1/10 m = X : 5 m
1/10x = 5
x = 50 seconds
How much longer would it take a giant tortoise than a cooter turtle to travel 10 meters on land?
1 second : 1/2 m = X : 10 m
1/2x = 10
x = 20 seconds
So the giant turtle can travel 5 meters in 50 seconds.
So the cooter turtle can travel 10 meters in 20 seconds.
A hot-air balloon is flying at an altitude of 2958 feet. If the angle of depression from the pilot in the balloon to a house on the ground below is 28, how far is the house from the pilot?
Answer:
6300.70 feetStep-by-step explanation:
Let the distance between pilot and house be d.
The three points form a right triangle, with height of 2958 ft and opposite angle 28 degrees.
Find d using trigonometry
sine = opposite / hypotenusesin 28° = 2958/dd = 2958/sin 28°d = 6300.70 feetLets see
sinØ=P/Hsin28=2958/HH=2958/sin28H=6300.7ft100 POINTS! PLEASE ANSWER!!! WILL MARK BRAILIEST!! THANKS! (show work if you can)
Answer:
5.7594087
Step-by-step explanation:
0.03x8888^14
Find (f+g)(x) if f(x)=2√m and g(x)= 3√4m
Answer Options:
1. (f+g)(x)= 11√m
2. (f+g)(x)= -4√m
3. (f+g)(x)= 8√m
4. (f+g)(x)= -7√m
Answer: 3
Step-by-step explanation:
A number is chosen at random from 1 to 12. Find the probability of selecting a prime number.
Answer:
1/2
Step-by-step explanation:
Prim number are 1, 2, 3, 4, 7, and 11. That is six numbers out of twelves, 6/12, is 50%.
Jalece and Kaylyn are making brownies and muffins for a bake sale. They make 40 more muffins than brownies. They made a total of 126 sweet items for the sale. How many of each type of baked good did they make?
I really don't know I hope you can figure it out
Answer: 43 brownies and 83 muffins.
Step-by-step explanation: There are 126 sweet items in total. Jalece and Kaylyn make 40 more muffins than brownies, which means that there are more muffins than brownies. Let's try 83 muffins and 43 brownies to see if it suits what we need. With 83 muffins and 43 brownies, there are 40 more muffins than brownies, so that's correct. 83 and 43 also add up to 126, which is the total that we need.
Therefore, there are 43 brownies and 83 muffins.
Let me know if this is right! :)
can somebody explain how to do this
Answer:
The area of figure = 260 cm²
Step-by-step explanation:
Area of figure = area of rectangle+ area of triangle
=> l×b + 1/2 ×b×h
=> 10×20 + 1/2 × 20 × 6
=> 200 + 60
=> 260 cm²
Answer:
260 cm²
Step-by-step explanation:
Area of the rectangle
= l × w
= 20 × 10
= 200 cm²
Area of the triangle
= ½bh
= ½ × 20 × 6
= ½ × 120
= 60 cm²
Area of the total figure
= Area of the rectangle + Area of the triangle
= 200 cm² + 60 cm²
= 260 cm²
________
Hope it helps ⚜
Drag the tiles to the correct boxes to complete the pairs.
Match each object with the characteristic it represents.
a broom handle
the letter T
a sun ray
a cookie crumb
the horizon
rows of seats on
an airplane
ray
line segment
point
line
perpendicular lines
parallel lines
Answer:
a broom handle - line segment
the letter T - perpendicular lines
a sun ray - ray
a cookie crumb - point
the horizon - line
row of seats of airplane - parallel lines
Step-by-step explanation:
a broom handle is straight and has a beginning and end, same goes for a line segment
the letter T has two lines that intersect with one another, these lines are perpendicular
a sun ray is well, a ray
a cookie crumb is small and round, similar to a point
lines do not have a beginning or end, like the horizon line
and the row of seats on an airplane all line up together like lines that are parallel.
Hope this helps :)
Please help me on this
Answer:
The answer is $3. 75
Step-by-step explanation:
The question is somehow I just did what they said but I hope it helps
The Art Club is displaying the students' works in the main hallway. In a row of 12 randomly ordered
paintings, what is the probability that Tim's and Abby's paintings are in the 6th and 7th positions?
The probability is the ratio of the favorable event to the total number of events. Then the probability is 0.76%.
What is probability?
Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen.
The Art Club is displaying the students' works in the main hallway. In a row of 12 randomly ordered paintings.
Then the probability that Tim's and Abby's paintings are in the 6th and 7th positions will be
[tex]P = \dfrac{1}{^{12}P_2} \\\\\\P = \dfrac{1}{\dfrac{12!}{(12-2)!}}\\\\\\P = \dfrac{1}{132}\\\\\\P= 0.007575 \approx 0.0076 \ or \ 0.76 \%[/tex]
More about the probability link is given below.
https://brainly.com/question/795909
#SPJ1
give me full working and explanation and I give you stars. deal..?
Length: 44 metre
perimeter of rectangle = 2(length+breadth)Here given,
length = L
breadth = 12 metre
perimeter = 112 metre
P = 2(L+B)112 = 2(L+12)12 + L = 112/2L = 56 - 12L = 44 mMr. Althouse has 3/4 of a quart of orange juice in a pitcher he is using to pour drinks. He needs to fill cups that hold 1/8 of a quart. How many cups will he be able to fill if he uses half of the juice in his pitcher?
Answer:
the answer should be 6.
Step-by-step explanation:
You have to make the fractions have the same denominator, this can be done by converting the 3/4. In this case you multiply both the denominator and the numerator by 2 to get 6/8. Complete the equation 6/8 ÷ 1/8 to get 6 as the full amount. half of this number would be 3 so the final result is 3.
Drag the tiles to the correct boxes to complete the pairs. Match the pairs of coordinates with the distances between them.
Answer:
See belowStep-by-step explanation:
Use distance formula and find the result for each pair of points.
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]1)
[tex]d=\sqrt{(1-4)^2+(-2-2)^2} =\sqrt{9+16} =\sqrt{25} =5[/tex]2)
[tex]d=\sqrt{(2-(-8))^2+(-3-7)^2} =\sqrt{100+100} =\sqrt{200}[/tex]3)
[tex]d=\sqrt{(1-9)^2+(9-1)^2} =\sqrt{64+64} =\sqrt{128}[/tex]4)
[tex]d=\sqrt{(-8-(-2))^2+(2-(-6))^2} =\sqrt{36+64} =\sqrt{100} =10[/tex]#1
√(4-1)²+(2+2)²√3²+4²√5²5units#2
√(-8-2)²+(7+3)²√10²+10²√200units#3
√(9-1)²+(1-9)²√8²+8²√128units#4
√(-2+8)²+(-6-2)²√6²+8²√10²10units3. Explain the relationship between area and square units
Answer:
In geometry, the area of a two dimensional object is the amount of space an area takes up. A square unit is a square with sides of length one unit.
61, 98, 60, 60, 57, 81, 93
Mean
Median
Mode
Range
find the sum of all the values and divide the sum by the number of values.
[tex] \frac{(61 + 98 + 60 + 60 + 57 + 81 + 93)}{7} = \frac{510}{7} [/tex]
[tex] = 72.86[/tex]
median:arrange the values in either ascending or descending, and find the number in the middle.
[tex]57 \: 60 \: 60 \: 61 \: 81 \: 93 \: 98[/tex]
[tex] = 61[/tex]
mode:the most frequently occurred number.
[tex] = 60[/tex]
range:arrange the values in ascending order and subtract the lowest value from the highest one.
[tex]98 - 57[/tex]
[tex] = 41[/tex]
Selim walked 1/12 of a mile to the coffee shop in 712 of a mile to the dry cleaners how far apart is the coffee shop from the dry cleaners grid your answer NOTE: grid your answer as a fraction not a mixed number
Answer:
6/12 of a mile
Step-by-step explanation:
7/12-1/12=16/12
Need help with math please
Answer:
45°
Step-by-step explanation:
if angle 3 is 135 the angle 2 is 45 and angle 2 is equal to angle 4 which is 45°
Y=x+8
find the slope and the y-intercept of the line.
Slope: 1
y-intercept: 8
Solution:The given equation is written in slope-intercept form, which looks like so:y=mx+bIn the above formula, m stands for the slope, and b stands for the y-intercept.Notice that the slope is the coefficient of x (the number next to x) and b is the y-intercept.Therefore, the slope is equivalent to 1, and the y-intercept is equivalent to 8.Hope it helps.
Do comment if you have any query.
lines l and m are parallel. Measure def is three times abc. Measure bcd=25%, measure cde=55%. Find measure abc.
Answer:
<ABC= 45 degrees
Angles on a straight line add up to 180
3x+ x= 180
4x=180
x=180÷4
x=45
Answer:
Measure of ABC = 15 degrees.
Step-by-step explanation:
We draw 2 lines parallel to l and m , one passing through pont C ( n) and the other passing through point D (p).
If < abc = x degrees then the angle below line n = 25 - x. As the one above = x degrees ( alternate to < ABC).
The angle below line p = < DEF 3x degrees (alternate angles)
So as < CDE = 55:
25 - x + 3x = 55
2x = 30
x = 15.
So < ABC = 15 degrees.
Find the measure of each labeled angle.first,find x=……..,m(angle)A=……,m(angle)B=…..,m(angle)C=……..
Answer:
24
Step-by-step explanation:
you slove the sides and find x
Answer:
x=40 m∠A=100° m∠B=80° m∠C=65°
Step-by-step explanation:
Step 1: Find relationships between the angles (corresponding, alternate exterior, alternate interior, consecutive interior, or consecutive exterior)
Step 2: m∠A + m∠B = 180°
So, (3x-20)° + (2x)° = 180°
Step 3: Solve for x (x=40)
Step 4: Plug in x to the angles
m∠A= 3(40) - 20
m∠B= 2(40)
m∠C= 2(40)-15
7) There are 260 athletes at a meeting.
How many handshakes were there?
Answer:
130
Step-by-step explanation:
Assuming everyone handshakes at the meeting. There will be 130 handshakes in total.
It takes 2 people to handshake, and thus to find the number of handshakes we need to do 260/2=130
130 total handshakes
Hope this helps ^^
32,000 is what fraction of 106,000
Step-by-step explanation:
I hope this helps, you can ask any questions for clarification
Josh is cutting a 25-inch beard inte tinch sections How many whole sections will the end up with
A necklace has 16 charms, and each charm weighs 1 ounce. How many pounds does the necklace weigh?
A) 1/2 pound
B) 1 pound
C) 1 1/2 pounds
D) 2 pounds
Answer:
B. 1 pound
Step-by-step explanation:
16 * 1 = 16
1 ounce = 0.0625 pounds
1 pound
show how
4
×
3
4
4
×
3
4
can be solved using multiplication and division.
Answer:
46784
Step-by-step explanation:
You would multiply all.the numbers and then your w
answer will be 46784
