Answer:
[tex]\sqrt{x^2+y^2+1}=18[/tex]
Step-by-step explanation:
We are given:
[tex]x^2=18x+y\qquad\qquad[1][/tex]
[tex]y^2=18y+x\qquad\qquad[2][/tex]
Subtracting [1] and [2]:
[tex]x^2-y^2=18x+y-(18y+x)[/tex]
Operating:
[tex]x^2-y^2=18x+y-18y-x[/tex]
Recall:
[tex]x^2-y^2=(x-y)(x+y)[/tex]
Substituting:
[tex](x-y)(x+y)=18x+y-18y-x[/tex]
Rearranging:
[tex](x-y)(x+y)=18x-18y-(x-y)[/tex]
[tex](x-y)(x+y)=18(x-y)-(x-y)[/tex]
Dividing by x-y (recall x≠y):
[tex]x+y=18-1=17[/tex]
[tex]x+y=17\qquad[3][/tex]
Now we add [1] and [2]:
[tex]x^2+y^2=18x+y+18y+x[/tex]
Rearranging:
[tex]x^2+y^2=18x+18y+x+y[/tex]
[tex]x^2+y^2=18(x+y)+(x+y)[/tex]
[tex]x^2+y^2=19(x+y)[/tex]
Substituting from [3]
[tex]x^2+y^2=19*17=323[/tex]
Adding 1:
[tex]x^2+y^2+1=324[/tex]
Taking the square root:
[tex]\sqrt{x^2+y^2+1}=\sqrt{324}=18[/tex]
Thus:
[tex]\mathbf{\sqrt{x^2+y^2+1}=18}[/tex]
simplify the product. write (x + 2)(x − 5) in standard form. Show your work
Answer:
x^2-3x-10
Step-by-step explanation:
Answer:
The answer is x²-3x-10
Step-by-step explanation:
(x + 2)(x − 5)
x²-5x+2x-10
x²-3x-10
Write an equation of the line that passes through (5,9) and is perpendicular to the line y=-1/3x+1
48 people attended the Sunday matinee to watch a film. .Three over 8 of the people went to see a romantic comedy. .One over six of the people went to see an action movie. .The remaining people saw a horror movie. How many people saw a horror movie?
Answer:
22 people saw an horror movie
Step-by-step explanation:
Total people who attended the Sunday matinee = 48
People who saw romantic comedy = 3/8 of 48
= 3/8 × 48
= (3*48) / 8
= 144 / 8
= 18 people
People who saw action movie = 1/6 of 48
= 1/6 × 48
= 48/6
= 8 people
People who saw horror movie = x
Total people who attended the Sunday matinee = People who saw romantic comedy + People who saw action movie + People who saw horror movie
48 = 18 + 8 + x
48 = 26 + x
Subtract 26 from both sides
48 - 26 = 26 - 26 + x
22 = x
x = 22 people
22 people saw an horror movie
My teacher can grade 25 homework assignments in 20 minutes. Is she working at a faster rate or slower rate than Ms. Jones, who is grading 36 homework assignments in 30 minutes?
Answer:
Ms.Jones is faster
Step-by-step explanation:
59.5 is what percent of 17 ?
Answer:
350%
Step-by-step explanation:
59.5÷17=3.5
3.5•10=350
350%
Two sides of a triangle are two consecutive number, whose area is 17.5cm². Find the numbers
Answer:
The numbers associated with the triangle are 5.437 and 6.437 centimeters, respectively.
Step-by-step explanation:
Two numbers are consecutives, when their difference is equal to 1. The area of the triangle is determined by the following formula:
[tex]A = \frac{1}{2}\cdot n \cdot (n+1)[/tex]
[tex]A = \frac{1}{2}\cdot (n^{2}+n)[/tex]
[tex]A = \frac{n^{2}}{2}+\frac{n}{2}[/tex]
[tex]n^{2}+n = 2\cdot A[/tex]
Where [tex]n[/tex] is the shortest length of the triangle, measured in centimeters.
And we get the following second-order polynomial:
[tex]n^{2}+n -2\cdot A = 0[/tex] (1)
If we know that [tex]A = 17.5\,cm^{2}[/tex], then the shortest length of the triangle is:
[tex]n_{1} = 5.437\,cm[/tex] and [tex]n_{2} \approx -6.437\,cm[/tex]
Since length is a positive variable, the only possible solution is:
[tex]n\approx 5.437\,cm[/tex]
Then, the numbers associated with the triangle are 5.437 and 6.437 centimeters, respectively.
The next model of a sports car will cost 4.7% less than the current model the current model cost 31000. How much will the price decrease in dollars? What will be the price next model?
decrease in price $_
price of next model $_
please help me !
Step-by-step explanation:
decrease value is 1353
value 31,647
Round 639,121 to the nearest ten thousand.
Answer:
640,121
Step-by-step explanation:
Explain the difference between equilateral and equiangular :)
An equilateral polygon has congruent sides, like a rhombus.
An equiangular polygon has congruent interior angles, like a rectangle.
In other words: Equilateral doesn't necessarily have congruent INTERIOR angles while equiangular does have/need congruent interior angles.
what number makes the equation true? 6 equals 30 divided
Answer: 5
Step-by-step explanation:
This question is basically asking:
6 = 30 ÷ ?
We can use a fact family to find the value.
30 ÷ 6 = 5
The answer is 5.
y-28=95
y-28+ ? =95+28
y=?
Answer:
Step-by-step explanation:
y -28 = 95
y-28 + 28 = 95 +28
y=123
dummy ;)
99-45f+36b in factored form
The scale drawing of a building has a width of 6 inches and a height of 8 inches. If the height of the actual building is 48 feet, what is the width?
Answer:
36 feet
Step-by-step explanation:
48/8=6 so you need to multiply the 6 by 6 as well which gives you 36
A building in a shape of a cube has a width of 100 ft., a length of 100 ft., and a height of 100 ft. An architect wants to build a scale model of the building that is 10% smaller in volume. What is the height of the new building? Round to the nearest hundredth.
A) 90.75 ft.
B) 95.25 ft.
C) 96.55 ft.
D) 99.25 ft.
Answer: A) 90.75 ft.
Step-by-step explanation: because if we cut 10 from 100 we will get 90
Write an equation of the line that passes through (–2, 8) and (–4, –4).
PLEASE HEEEELP MEEE! PLEASE ACTUALLY PROVIDE AN EXPLANATION! BEST EXPLANATION AND ANSWER GETS BRAINLIEST! THANKS
Answer:
sorry bro
Step-by-step explanation:
Answer:
Y=6x+20
Step-by-step explanation:
A company has a monthly profit, or gain, of $6,400. The next month they have a loss of $4,700.
What expression would you use to find the difference in profit between the two months?
-4,700 - 6,400
6,400 - 4,700
6,400 - (-4,700)
4,700 - 6,400
Answer:
6,400-4,700
Step-by-step explanation:
5x + 2x + 2 = 9x + 4
Step-by-step explanation:
Given
5x + 2x + 2 = 9x + 4
9x - 5x - 2x = 2 - 4
9x - 7x = - 2
2x = - 2
x = - 2 / 2
Therefore x = -1.
therefore lhs is equal to rhs
the first blanks options are -2 , -1/2 , 2 , 1/2
The seconds are -5 , -3 , 5, 3
the thirds are -2, -1, 2, 1
and the fourths are -2, -1, 2, 1
Answer:
equation 1
y = -2x
equation 2
y = x-3
Solution to both
(1,-2)
Step-by-step explanation:
We need to get the equations of both lines
General form is;
y = mx + c
where m is slope and c is the y-intercept
Table 1
since we have a point 0,0; the y-intercept here is zero
Let us get the slope. We can do this by selecting any two points
m = (y2-y1)/(x2-x1)
m = (2-10)/(-1+5) = -8/4 = -2
So the equation of the first line is;
y = -2x
Table 2
we get the slope
m = (4+2)/(7-1) = 6/6 = 1
The partial equation is;
y = x + c
To get c, we select any two point and substitute
4 = 7 + c
c = 4-7
c = -3
So the equation is;
y = x-3
To get the solution to both systems, we equate the y
-2x = x - 3
-2x-x = -3
-3x = -3
x = -3/-3
x = 1
To get y, we substitute;
recall; y = -2x
y = -2(1)
y = -2
Solution to the system is;
(1,-2)
BRAINLIEST TO RIGHT WITHOUT WORK
If you increase the length of a rectangle by 50% and the width by 100% by what percent will the area of this rectangle increase
Answer:
200%
Step-by-step explanation:
if you substitute in numbers you'll find this as the answer.
as an example:
suppose the sides of the rectangle was 1 unit long.
area before change: 1 * 1 = 1
then, the length gets increase by 50% making it 1.5 ( 50% of 1 is 0.5, then you add it onto 1, 1 + 0.5 = 1.5 )
the width gets increased by 100% making it 2 ( 1 + 1 = 2 )
new area: 1.5 * 2 = 3
1 increased by 200% is 3, therefore the answer is 200%
Daisy is reading a 47 pg book. She read the first 20 pgs in 6 minutes. How long will it take her to read the entire book?
Answer:
About 15 minutes
Step-by-step explanation:
It takes her 6 minutes to read 20 pgs. If she reads 20 more pages (which will be 40 now) she will have been reading for 12 minutes. This leaves you with 7 pages left, about 3 or 4 minutes.
by the definition of supplementary angles, the base angles of the top isosceles triangle have the measure of
Answer:
128
Step-by-step explanation:
Top Triangle
Let the base angles of the top triangle = y
y + 102 = 180
y = 78
The vertex
Is found by adding the two base angles together and subtract that from 180
y + y + vertex = 180
78 + 78 + vertex = 180
156 + vertex = 180
vertex = 180 - 156
vertex = 24 degrees
Bottom Triangle
Because the base angles are connected by a vertically opposite angle on the bottom triangle, both base angles are 26
Therefore 26 + 26 + x = 180
52 + x = 180
x = 180 - 52
x = 128
HELP ME WITH MATH HOMEWORK
Step-by-step explanation:
Only option B shows a proportional relationship (y = 3x).
Answer:
D
Step-by-step explanation:
Y=3x-1 is written as the slope-intercept form y=mx+b don't let the -1 confuse you.
Jamal drew angle bisector AD with D on the line segment BC. If BD=3, DC=9 and AB+AC=28 find AB and AC.
Answer:
AB = 7
AC = 21
Step-by-step explanation:
Because AD is an angle bisector it divides the triangle into proportional parts. That is ...
AC/DC = AB/BD
(28 -AB)/9 = AB/3 . . . . use AC = 28 -AB
28 -AB = 3AB . . . . . . . . multiply by 9
28 = 4AB . . . . . . . . add AB
AB = 28/4 = 7 . . . . divide by 4
AC = 28 -7 = 21
The lengths AB and AC are 7 and 21, respectively.
_____
Additional comment
The triangle ABC cannot exist. The reason is that its side measures are 7, 12, and 21. The sum of 7 and 12 is not greater than 21, so the side measures do not satisfy the triangle inequality.
For the triangle to exist, the sum of AB and AC cannot exceed 24 for the given values of BD and DC.
Imani is taking apart a beaded necklace to make 4 identical bracelets. The necklace has 48 beads. How many beads will Imani use for each bracelet?
Answer:12 beads
Step-by-step explanation: If she has 48 beads and wants to make 4 bracelets, you will have to divide 48 by 4 which gives you 12
Please help ASAP 15 points
Answer:
B
Step-by-step explanation:
The answer is B because it tells you the letter atound triangle.
Answer:
b
Step-by-step explanation:
Solve the equation below for the value of x.
−314x + 25 = 214x − 1312
Answer:
x=1337/528
Step-by-step explanation:
-314x-214x=-1312-25
-528x=-1337
x=1337/528
Answer:
Step-by-step explanation:
add 314x to both sides
-314+25=214x-1312
+314x +314x
add 1312 to both sides
25=528x-1312
+1312 +1312
1337=528x
x=1337/528
i dont thing you can simplify to a whole number...hopefully this helps a little :)
Please answer!!
During what times is Ann driving a consistent speed? Give a reason to support your answer
Answer:
There are 3 intervals where Ann is driving a consistent speed
Between 1 and 4 minutes, Between 6 and 8 minutesBetween 9 and 11.5 minutes==========================================================
Explanation:
When she drives a consistent speed, this means her speed is the same.
This happens exactly when there are flat portions of the graph. This is because the speed y is not going up or down during these intervals.
The intervals where the graph is flat are mentioned at the top in the answer portion.
Any time the graph goes uphill, from left to right, Ann is increasing her speed. So she is accelerating.
In contrast, any time the graph goes downhill, she is decreasing her speed (or decelerating).
Side note: I'm not including the portion from roughly 4 to 5 minutes because during that time, she is stopped and the car isn't moving.
Use the information provided to write the equation of each parabola in vertex form and intercept form.
Please help I have searched this question and have not found it yet so please help me answer this, I am bad at math
You want to go to Africa for a photo safari. You need $2,800. You can get $1,000 from your savings and family and you can save $30 per week. How many weeks will it take you to save up the money for the trip?
A. 127 weeks
B. 60 weeks
C. 93 weeks
D. 84 weeks
Please select the best answer from the choices provide
Answer:
B 60
Step-by-step explanation:
because 30x60=1800 and since you already have 1k you add the 1800 to get 2800.
In 2008, the number of tourists visiting France was 7.94 x 10^7. The number of tourists visiting Italy was 4.27 x 10^7. Find the difference in the number of visitors.
Answer:
[tex]36700000[/tex]
Step-by-step explanation:
Difference between tourists visiting France and Italy = [tex](7.94 - 4.27)[/tex] ×[tex]10^{7}[/tex]
[tex]= 3.67[/tex] × [tex]10^{7}[/tex]
[tex]= 36700000[/tex]
[tex]\therefore[/tex] Difference between population of tourists in France and Italy are [tex]36700000[/tex] people.