Answers
1/2x = -1/2x
Add 1/2x to both sides.
1x=0
Divide 1 to both sides.
x= 0
I hope this helps love! :)
Related Questions
What is the area of trapezoid ABCD ? (Enter your answer as a decimal or whole number)
Answers
bear in mind that, the "bases" are the two parallel sides, and the height is the distance between them.
[tex]\bf \textit{area of this trapezoid}\\\\ A=\cfrac{AB(BC+AD)}{2}\\\\ -------------------------------\\\\ \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) A&({{ -1}}\quad ,&{{ 5}})\quad % (c,d B&({{ 3}}\quad ,&{{ 2}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ AB=\sqrt{[3-(-1)]^2+[2-5]^2}\implies AB=\sqrt{(3+1)^2+(2-5)^2} \\\\\\ AB=\sqrt{16+9}\implies AB=\sqrt{25}\implies \boxed{AB=5}[/tex]
[tex]\bf -------------------------------\\\\ \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) B&({{ 3}}\quad ,&{{ 2}})\quad % (c,d C&({{ 0}}\quad ,&{{ -2}}) \end{array} \\\\\\ BC=\sqrt{(0-3)^2+(-2-2)^2}\implies BC=\sqrt{9+16} \\\\\\ BC=\sqrt{25}\implies \boxed{BC=5}[/tex]
[tex]\bf -------------------------------\\\\ \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) A&({{ -1}}\quad ,&{{ 5}})\quad % (c,d D&({{ -13}}\quad ,&{{ -11}}) \end{array} \\\\\\ AD=\sqrt{[-13-(-1)]^2+[-11-5]^2} \\\\\\ AD=\sqrt{(-13+1)^2+(-16)^2}\implies AD=\sqrt{144+256} \\\\\\ AD=\sqrt{400}\implies \boxed{AD=\sqrt{20}}[/tex]
so, the area for this trapezoid is then
[tex]\bf A=\cfrac{5(5+20)}{2}\implies A=\cfrac{125}{2}\implies A=62\frac{1}{2}[/tex]
Area of the trapezoid ABCD is
[tex]62\frac{1}{2}[/tex]
Given :
The diagram of a trapezoid ABCD
Area of trapezoid is [tex]\frac{base1+base2}{2} \cdot height[/tex]
Lets find the length of base 1 and base 2 using distance formula
Base 1 is AD. find the distance AD
[tex]AD=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}\\AD=\sqrt{\left(-13-\left(-1\right)\right)^2+\left(-11-5\right)^2}\\AD=20[/tex]
Now we find out BD that is base 2
[tex]BD=\sqrt{\left(0-3\right)^2+\left(-2-2\right)^2}\\BD=5[/tex]
Now find out height AB
A is (-1,5) and B(3,2)
[tex]AB=\sqrt{\left(-1-3\right)^2+\left(5-2\right)^2}\\AB=5\\[/tex]
[tex]Area =\frac{AD+BC}{2} \cdot AB\\Area=\frac{20+5}{2} \cdot 5\\Area=\frac{125}{2}\\Area=62\frac{1}{2}[/tex]
Area of the trapezoid ABCD is
[tex]62\frac{1}{2}[/tex]
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What is the scale factor of triangle ABC to triangle DEF
Answers
Answer:
The correct option is: 1
Step-by-step explanation:
Scale factor is the ratio of corresponding side lengths of two triangles.
Here....
[tex]\frac{DE}{AB}=\frac{5}{5}=1\\ \\ \frac{DF}{AC}=\frac{5}{5}=1\\ \\ \frac{EF}{BC}=\frac{5}{5}=1[/tex]
So, the scale factor of [tex]\triangle ABC[/tex] to [tex]\triangle DEF[/tex] is 1.
The slope of a line is -1/3, and the y-intercept is 10/3. What is the equation of the line written in general form?
10x + 3y - 1 = 0
x + 3y + 10 = 0
x + 3y - 10 = 0
Answers
______________________________________________________
Explanation:
______________________________________________________
Note the equation for a line; in 'slope-intercept form': "y = mx + b" ;
in which "y" is isolated alone, as a single variable, on the left-hand side of the equation;
"m" = the slope of the line; and is the co-efficient of "x" ;
b = the "y-intercept"; (or the "y-coordinate of the point of the "y-intercept").
______________________________________________________
So, given the information in this very question/problem:
______________________________________________________
slope = m = (-1/3) ;
b = y-intercept = (10/3) ;
______________________________________________________
And we can write the equation of the line; in "slope-intercept form"; that is:
______________________________________________________
" y = mx + b " ; as:
______________________________________________________
" y = (-1/3)x + (10/3) " ;
______________________________________________________
Now, the problem asks for the equation of this line; in "general form"; or "standard format"; which is:
________________________________________
"Ax + By + C = 0 " ;
________________________________________
So; given:
____________________________________
" y = (-1/3)x + (10/3) " ;
____________________________________
We can multiply the ENTIRE EQUATION (both sides) by "3" ; to get rid of the "fractions" ;
→ 3* { y = (-1/3)x + (10/3) } ;
→ 3y = -1x + 10 ;
↔ -1x + 10 = 3y ;
Subtract "(3y)" from each side of the equation:
____________________________________
-1x + 10 − 3y = 3y − 3y ;
to get:
-1x + 10 − 3y = 0 ;
↔ -1x − 3y − 10 = 0 ;
→ This is not one of the "3 (THREE) answer choices given" ;
→ So, multiply the ENTIRE EQUATION (both sides); by "-1" ; as follows:
-1 * {-1x − 3y − 10 = 0} ;
to get:
______________________________________________________
→ " x + 3y + 10 = 0 " ; which is: "Answer choice: [B] ."
______________________________________________________
Note that is equation is in the "standard format" ;
→ " Ax + By + C = 0 " .
______________________________________________________
The slope of a line is -1/3, and the y-intercept is 10/3. What is the equation of the line written in general form?
Answer:
x + 3y - 10 = 0
ABC preschool spun $1,475 on diapers this year.if the diapers cost $25 per box how many boxes did they used?
Answers
$1,475 = x boxes * $25
x = 1,475/25 = 59 boxes of diapers
If a line of one billion people standing shoulder to shoulder stretches 346,439 miles long, what is the average shoulder width, in feet, of the people in the line?
Answers
Answer: [tex]1.83\text{ feet}[/tex]
Step-by-step explanation:
Given : If a line of one billion people standing shoulder to shoulder stretches 346,439 miles long.
We know that 1 mile =5280 feet
Then, the length of line=[tex]346439\times5280=1829197920[/tex] feet
We know that 1 billion can be written as :
[tex]1,000,000,000=10^9[/tex]
Now, the average shoulder width of the people in the line :-
[tex]\dfrac{1829197920}{1000000000}=1.8291979\approx1.83\text{ feet}[/tex]
Hence, the average shoulder width of the people in the line is about [tex]1.83\text{ feet}[/tex]
A nail is 0.1875 inch thick. What is it’s thickness as a fraction? Is 0.1875 inch closer to 1/8 inch or 1/4 inch on a number line?
Answers
1/4 is .25-.1875 is .0625
For tax reasons, i need to create a rectangular vegetable patch with an area of exactly 50 square feet. the fencing for the east and west sides costs $4 per foot, and the fencing for the north and south sides costs only $2 per foot. what are the dimensions of the vegetable patch with the least expensive fence?
Answers
Final answer:
The dimensions of the vegetable patch with the least expensive fence are 10 feet by 5 feet.
Explanation:
To find the dimensions of the vegetable patch with the least expensive fence, we can use the formula for the area of a rectangle: length x width = area.
Let's assume the length of the vegetable patch is 'x' and the width is 'y.'
So, xy = 50.
The cost for the east and west sides is $4 per foot, and the cost for the north and south sides is $2 per foot.
Therefore, the cost of fencing the east and west sides would be 4x, and the cost of fencing the north and south sides would be 2y.
For the least expensive fence, we want to minimize the cost, which means minimizing the sum of 4x and 2y.
We can rewrite the equation as:
y = 50/x.
Now substitute the value of y in the cost equation:
cost = 4x + 2(50/x).
To find the minimum cost, we need to find the derivative of the cost equation and set it equal to zero.
Calculating the derivative and solving for x, we find x = √100 = 10.
Therefore, the dimensions of the vegetable patch with the least expensive fence are 10 feet by 5 feet.
If a 30 -meter pine tree casts a shadow of 30 meters, how far is the tip of the shadow from the top of the tree?
Answers
The distance from the tip of the shadow to the top of the tree is 42.426 meters.
What is Pythagoras' theorem?Pythagoras theorem is a relation between sides of a right-angle triangle.
It states that for a right-angle triangle the square root of Hypotenuse is equal to the sum of the individual base and perpendicular square.
So,
Hyp² = Base² + Perp²
Given the situation is making a right angle triangle with base and perpendicular as 30 meters.
By Pythagoras theorem,
Hyp² = Base² + Perp²
Hyp² = 30² + 30²
Hyp² = 1800
Hyp = 42.426 meter.
Hence "The distance from the tip of the shadow to the top of the tree is 42.426 meters".
To learn more about Pythagoras' theorem,
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How do you write 960,060 in expanded form
Answers
hope this helps
Answer:
[tex]900000 + 60000+60[/tex]
Step-by-step explanation:
write 960,060 in expanded form
In 960,060, from left to right
0 is in ones place is 0
6 is in tens place is 6 times 10 = 60
6 is in ten thousands place is 6 times 10000= 60000
9 is in hundred thousands place 9 times 100000= 900000
So the expanded form of the given number is
[tex]900000 + 60000+60[/tex]
Lacoste middle school surveyed its student population about their favorite mobile app. The 786 students who listed Facebook as their favorite app represened 32 fewer students than two times the number on Instagram as their favorite app. How many students listed Instagram as their favorite app?
Answers
-32
x2
786 - 32 = 754
754 divided by 2 = 377
Hence, the number of students who listed Instagram as their favorite app is 409
Step-by-step explanation:Let x denote the number of students who listed Instagram their favorite app.
Now the number of people who listed Fb as their favorite app is 32 less than two times number of students who have Instagram as their favorite app.
Hence, the equation so obtained is given by:
786 = 2x - 32
i.e. 2x = 818
i.e. x = 409
Hence, the answer is: 409
Which is greater 2.16 or 2.061
Answers
Adams Clothing Store buys coats for $50 and sells them
for $80. What percent of increase is this?
Answers
-join the gvcci gang
Answer is provided in the image attached.
Find two values of b that will make 9 x 2 + b x + 9 a perfect square trinomial.
Answers
What about a? Are we supposed to find a also?
One way in which to do this problem is to factor 9 out of the trinomial:
9 (x^2 + (b/9)x + a )
Concentrate now on making x^2 + (b/9)x + a into a perfect square trinomial.
x^2 + (b/9)x + a
Take half of the coefficient (b/9) and square the result: [(b/9)/2]^2 = b^2/81.
Then, x^2 + (b/9)x + b^2/81 - b^2/81 + a.
The above quadratic expression can be re-written as
(x + b/9)^2 - b^2/81 + a. This is a perfect square trinomial if
-b^2/81 + a = 0. Solve for b: b^2/81 = a,
b/9 = sqrt(a)
b = 9 sqrt a
What is a coplanar. You will earn good point.
Answers
cooperation
cosign
co-president
It's typically used to describe things that are shared or mutual. We say that two points are coplanar when they share the same plane.
Marcus recorded the high temperature each day for a week. the daily high temperatures in degrees Fahrenheit were: 68,74,66,78,72,80, and 74 which best describes what 74 represents in this data set?
A. median only
B. mean and mode
C. median and mode
D. mode only
Answers
Answer:
The answer is C. median and mode.
Step-by-step explanation:
First, we have to ensure that the list of the set of data is from least to greatest: 66, 68, 72, 74, 74, 78, 80 .
The mean = (66 + 68 + 72 + 74 + 74 + 78 + 80) ÷ 7 = 512 ÷ 7 = 73.14 . (Note that the mean is not equal to 74.)
The median = middle number when the set of data is listed in order from least to greatest = the fourth number = 74.
The mode = the temperature that occurred the most = 74 .
These results prove that the median and mode best describe what 74 represents in the data set, because they are the same value.
Answer: C
I think its right. Was it for the I ready diagnostic?
The sum of four consecutive odd integers is -72. Write an equation to model this situation, and ind the values of the four integers.
Answers
Answer:
equation: (x-3) +(x-1) +(x+1) +(x+3) = -72values: -21, -19, -17, -15Step-by-step explanation:
When dealing with consecutive integers, it often simplifies the problem to work with their average value. We know the average value of the integers in this problem is the even integer between the middle two. We can call it x, and write the equation ...
(x-3) +(x-1) +(x+1) +(x+3) = -72
This simplifies to ...
4x = -72 . . . . . . . we knew this before we wrote the above equation, since the sum of 4 numbers is 4 times their average.
x = -18 . . . . . . . . the middle number of the sequence
So, the numbers are:
-18-3 = -21-18-1 = -19-18+1 = -17-18+3 = -15_____
A more conventional approach is to define the variable as the integer at one end or the other of the sequence. If we make it be the lowest number, then the equation is ...
(x) +(x +2) +(x +4) +(x +6) = -72
and that simplifies to ...
4x +12 = -72 . . . . . collect terms
4x = -84 . . . . . . . . subtract 12
x = -21 . . . . . . . . . . divide by 4
Now, the other three numbers are found by adding 2, 4, and 6 to this one.
Classify the following triangle. Check all that apply
Answers
What is the reason for each step in the solution of the equation?
3+4xâ’3x=4
Drag and drop the reasons into the boxes to correctly complete the table.
3+x=43+x=4
x=1
Distributive property
Subtraction property of equality
Combine like terms
Division property of equality
Given
Answers
The number of customers for a new online business can be modeled by y = 6x2 + 75x + 200, where x represents the number of months since the business started. Which is the best prediction for the number of customers in month 25?
A. 5825
B. 3791
C. 2936
D. 4754
Answers
Answer:
A. 5825
Step-by-step explanation:
Given: The number of customers for a new online business can be modeled by y = 6x^2 + 75x + 200, where "x" represents the number of months.
We are asked to find number of customers in month 25.
To find the number of customers in 25th month, we need to plug x = 25 in the given function.
y = 6([tex]25)^2[/tex] + 75(25) + 200
y = 6(625) + 1875 + 200
y = 3750 + 1875 + 200
y = 5825
Therefore, the answer is A. 5825
there are 28 tables in the cafeteria.each table has 12 students sitting at it.fourth graders sit at 13 of the yables.fifth graders sit at the rest of the tables.how many fifth graders are there?
Answers
28 - 13 = 15
15 x 12 = 180 Fifth graders
Jorge says there are 198 inches in 5.5 yards. Is he correct?
Answers
5 times 36=180
1/2 of 36( to get the.5) = 18
180+18= 198
so he is right
The LCD for the fractions 1/3, 3/4, 5/32, and 8/9 is
Answers
Answer: LCD is 288.
Factor them by their prime factors:
3 = 3
4 = 2 x 2 or 2²
32 = 2 x 2 x 2 x 2 x 2 or [tex] 2^{5} [/tex]
9 = 3 x 3 or 3²
Since you can divide 32 by 4 and 9 by 3, you only need to use 32 and 9.
LCD = 2 x 2 x 2 x 2 x 2 x 3 x 3
LCD = [tex] 2^{5} [/tex] x [tex] 3^{2} [/tex]
LCD = 288
Hope This Helps You!
Good Luck :)
- Hannah ❤
Jasmine exchanges $100 for Yen before going to Japan if each US dollar is worth 87.747 Yen how many yen should Jasmine receive
Answers
f the polygon is translated 4 units down and 5 units right, what will the coordinates of the new image be
Answers
Which would take up more space, a pound of granite or a pound of basalt?
Answers
Answer:
1 pound of granite
Step-by-step explanation:
The density of granite is 168.6 lb/ft³. The volume occupied by 1 pound of granite is:
1 lb × (1 ft³/168.6 lb) = 0.00593 ft³
The density of basalt is 188 lb/ft³. The volume occupied by 1 pound of basalt is:
1 lb × (1 ft³/188 lb) = 0.00532 ft³
As we can see, 1 pound of granite takes up more space than 1 pound of basalt.
How much water should be added to 1 gallon of pure antifreeze to obtain a solution that is 35% antifreeze?
To obtain a 35% antifreeze solution, □ gallon(s) of water should be added
(Simplify your answer.)
Answers
To obtain a 35% antifreeze solution, you need to add approximately 1.857 gallons of water to 1 gallon of pure antifreeze.
Explanation:To obtain a 35% antifreeze solution, you need to add a certain amount of water to 1 gallon of pure antifreeze. Let's assume that x gallons of water should be added. In a 35% antifreeze solution, the amount of antifreeze is 35% of the total solution. So, we can set up the following equation:
1 gallon of antifreeze = (35/100) * (1 + x) gallons of solution
Simplifying this equation, we get:
1 = 0.35 * (1 + x)
Now, let's solve for x:
Divide both sides of the equation by 0.35:
1/0.35 = 1 + x
2.857 = 1 + x
Subtract 1 from both sides of the equation:
2.857 - 1 = x
x = 1.857 gallons of water
Therefore, you need to add approximately 1.857 gallons of water to 1 gallon of pure antifreeze to obtain a 35% antifreeze solution.
Final answer:
To obtain a 35% antifreeze solution from 1 gallon of pure antifreeze, approximately 1.857 gallons of water needs to be added. This calculation is based on a simple concentration equation, resulting in the given ratio.
Explanation:
To calculate the amount of water to be added to 1 gallon of pure antifreeze to obtain a solution that is 35% antifreeze, we need to perform a simple concentration calculation.
We are starting with pure antifreeze, so it's 100% antifreeze. We want to end with a solution that is 35% antifreeze. Let's denote the amount of water added as x gallons. Because we are diluting the antifreeze, the total volume of the solution after adding water will be 1 gallon (the initial volume of the antifreeze) plus x gallons (the volume of water added).
The concentration of antifreeze after adding water is the volume of antifreeze divided by the total volume of the solution:
Concentration of antifreeze = Volume of antifreeze / Total volume of solution
Thus, 0.35 = 1 / (1 + x)
Multiplying both sides by (1 + x) and then by 0.35 we get:
1 = 0.35 * (1 + x)
Dividing by 0.35 and then subtracting 1:
x = 1 / 0.35 - 1
After calculating:
x ≈ 1.857 gallons
To obtain a 35% antifreeze solution, approximately 1.857 gallons of water should be added.
If sale price of a shirt after giving 8% is RS.161,then find the written price? (By the written price means cost price)
Answers
you can do it, man
I believe in you
To find the original cost price of a shirt on which an 8% discount was given, resulting in a sale price of Rs.161, the formula CP = Sale Price / (1 - (Discount Percent / 100)) is used, calculating the cost price as Rs.175.
If the sale price of a shirt after giving an 8% discount is Rs.161, to find the written price, or the cost price before the discount, we can use the formula for discount calculation. Let CP represent the cost price. The formula for calculating the sale price after discount is:
Sale Price = CP - (Discount Percent * CP) / 100
Here, the sale price is given as Rs.161, and the discount percent is 8%. Therefore, we can rearrange the formula to solve for CP:
CP = Sale Price / (1 - (Discount Percent / 100))
Plugging in the values gives us:
CP = 161 / (1 - (8 / 100)) = 161 / 0.92 = Rs.175
Therefore, the written price or the cost price of the shirt before the discount was applied is Rs.175.
problem solving choose the correct answer that follows each sequence
3 4 6 9 13 18 24
.29
.31
.32
.33
Answers
it goes by 1 hen 2 then 3 then 4 then 5 then 6 then 7
you add each of the numbers to the last number
What is the estimate 323 +151
Answers
You could also find the estimate 320 + 150 = 470.
An international company has 26,900 employees in one country. If this represents 16.9% of the company's employees, how many employees does it have in total?
Answers
Answer:
89,349
Step-by-step explanation:
i just did this problem on aleks and this is the answer they gave me how it helps other in the future