the equation y=-7x-5 and another equation have a solution of (-2,9). what is the second equation?
Answers
I'm guessing there's a menu of choices to go with this one, and we just need to try (-2,9) with each choice. But it's a much more interesting problem without the menu.
First we verify (-2,9) is on the line y=-7x-5,
-7(-2)-5 = 14-5 = 9, good.
There's a whole family of possibilities for the second equation, basically all the other lines through (-2,9). Believe it or not, that's called a pencil of lines. We need two parameters a and b, whose values only matter in ratio, to represent all these. If we tried to do it with just the slope we'd miss one line, the vertical line x=-2.
We'll do the line through (-2,9) and (a,b). A little thought tells us it's
(a + 2)(y - 9) = (b - 9)(x + 2)
When we plug in (-2,9) we get 0=0, good. When we plug in (a,b) we get
(a + 2)(b - 9) = (b - 9)(a + 2)
which is also true.
(a + 2)(y - 9) = (b - 9)(x + 2)
(b - 9)x - (a+2)y = -9(a + 2) - 2(b-9)
(b - 9)x - (a+2)y = -9a - 2b
We can choose any a and b and we'll get the line through (-2,9) and (a,b), so it will have a solution (-2,9) where it meets y = -7x - 5.
We need to make sure (a,b) isn't already on y = -7x - 5 which is the same line twice.
For arbitrary a,b, b ≠ -7a - 5, the lines y = -7x - 5 and
(b - 9)x - (a+2)y = -9a - 2b
meet at exactly one point, namely (-2,9)
Let's generate a few and plot. We'll do a vertical and horizontal an a couple of others.
a=-2, b=0, (b - 9)x - (a+2)y = -9a - 2b
-9x = 18
x = -2
a=0, b=9, (b - 9)x - (a+2)y = -9a - 2b
-2y = -18
y = 9
a=1, b=1, (b - 9)x - (a+2)y = -9a - 2b
-8x - 3y = -11
a=1, b=3, (b - 9)x - (a+2)y = -9a - 2b
-6x - 3y = -15
2x + y = 5
plot y=-7x+5, x = -2, y = 9, -8x - 3y = -11, 2x - y = 5
Related Questions
How do you write twenty five increased by six in a numerical expression
Answers
Answer:
25+6
Step-by-step explanation:
How much water should be added to 50 ml of 45 percent acid solution to dilute it to a 35 percent acid solution?
(Will Mark as Brainliest)
Answers
Answer:
dont drink water .
Step-by-step explanation:
Answer:
12.5
Step-by-step explanation:
A right triangle is inscribed in a circle as shown. What is the area of the shaded region. Diameter of 12 and 9 cm in triangle
Answers
Answer:
[tex]36\pi -18\sqrt{7}[/tex]
Step-by-step explanation:
Every inscribed right triangle has its hypotenuse as the same size of the Diameter. Assuming that, this is the case check the picture below.
So the hypotenuse= D=2R=12
Shaded Area = Area of the Circle- Area of the TriangleArea of Circle:[tex]A_{circle}=\pi (6)^{2}=36\pi[/tex]
Area of the Triangle:Finding the Triangle base via the Pythagorean Theorem
[tex]a^2=b^2+c^2\\12^2=9^2+c^2\\144-81=c^2\\c=\sqrt{63}\\c=3\sqrt{7}\approx 7.94[/tex]
Now plugging in the base of the triangle on that formula:
[tex]A=\frac{bh}{2}\\A=\frac{3\sqrt{7}*12}{2}\\A=18\sqrt{7}[/tex]
Finally,
Shaded Area = [tex]36\pi -18\sqrt{7} cm^{2} \approx 65.48 cm^{2}[/tex]
x2 - 14x + 40
O A.
(x + 3)(x + 5)
OB. (x - 10)(x-4)
O C. (x-8)(x - 5)
O D. (x+ 10)(x+4)
Answers
Answer:
B
Step-by-step explanation:
(x-4) x (x-10)
Answer:
B
Step-by-step explanation:
Given
x² - 14x + 40
Consider the factors of the constant term (+ 40) which sum to give the coefficient of the x- term (- 14)
The factors are - 10 and - 4, since
- 10 × - 4 = + 40 and - 10 - 4 = - 14, thus
x² - 14x + 40 = (x - 10)(x - 4) → B
Which expression is equivalent to 5 divided by 2
A. 5•1\2
B. 2/5
C. 10
D. 2•1/5
Answers
Answer:
a
Step-by-step explanation:
Answer:
= 5 × 1/2
Step-by-step explanation:
Five divided by 2
= 5 ÷ 2
= 5/2
Which is same as
= 5 × 1/2
I hope this was helpful, please rate as brainliest
Uta invests an amount into a compound interest investment account that pays 6% a year. After six years, she withdraws her total balance of $500. Using the formula A = P (1 + r) Superscript t, how much money did Uta initially invest?
$180.00
$320.00
$352.48
$471.70
Answers
Answer: $352.48
Step-by-step explanation:
Hi, to answer this question we have to apply the formula:
A = P (1 + r)^t
Where
A: total balance after invest
P: principal amount invested
r = interest rate (in decimal form)
t = time (years)
Replacing with the values given:
500= P (1+0.06)^6
Solving for P:
500 = P (1.06)^6
500 / ( (1.06)^6)=P
500 / 1.4185 =P
$352.48= P
Answer:
352.48
Step-by-step explanation:
What is the value of log8 512
Answers
Answer:3
Step-by-step explanation:
Logarithm base 8 of 512 is 3.
Answer:3
Step-by-step explanation:
Calculating Factorials
Quick
Check
Evaluate each expression.
6! =
Answers
Answer:
6! = 720
Step-by-step explanation:
In evaluating factorial functions, generally
n! = n(n-1)(n-2)(n-3)...× 1
We can see that as we are moving, the value keep decreasing by 1 until it reaches the least value which is 1.
6! = 6(6-1)(6-2)(6-3(6-4)(6-5)
6! = 6×5×4×3×2×1
6! = 720
Please help me please!!!!
Answers
Answer:
1 F
2 C
3 G
4 D
5 A
6 E
7 B
Step-by-step explanation:
p implies q (conditional)
Which is G
It's converse would be
q implies p
Which is G
F and G together become bi-conditional
Which is B
Contraposition is
not q implies not p
Inverse of p implies q is
not p implies not q
Which is D
Conjunction is p and q,
Which is F
Disjunction is p or q,
Which is C
2A - 5B + 4X = C - 8X
Answers
Answer:
(5B+C-2A)/8 = x
Step-by-step explanation:
2A - 5B + 4X = C - 8X
subtract 4x from both sides
2A - 5B + 4X-4x = C - 8X-4x
2A - 5B = C - 12X
subtract C from both sides
2A - 5B -C = C-C - 8X
2A - 5B -C = - 8X
divide both sides by -8
(2A - 5B -C)/-8 = - 8X/-8
(-2A+5B+C)/8 = x
(5B+C-2A)/8 = x
15 kilograms of rice are separated equally into 4 containers. How many kilograms of rice are in each
container? Express your answer as a decimal and as a fraction,
Answers
Final answer:
Each container will have approximately 3.75 kilograms of rice, which can be expressed as 3.75 kg or 15/4 kg.
Explanation:
To find out how many kilograms of rice are in each container, we need to divide the total weight of the rice by the number of containers. In this case, we have 15 kilograms of rice and 4 containers, so we divide 15 by 4. The result is 3.75 kilograms.
So, each container will have 3.75 kilograms of rice.
As a decimal, this can be expressed as 3.75 kg. As a fraction, it can be written as 15/4 kg.
sergio runs 6 miles in three days. At this rate, how many miles will he run in 20 dayshelp
Answers
Answer:
40 miles
Step-by-step explanation:
We have to find how many miles he runs per day. So if we divide 3 days by 3 to get 1 day, that means he would run 2 miles per day. So if we are trying to figure out how many miles he runs in 20 days, we do 20*2 which equals 40. Hope this helps.
(please mark me brianliest)
Answer:
40 miles
Step-by-step explanation:
He runs 2 miles per day
6 miles over 3 days is 2 miles per day
6 divided by 3 is 2
HELP PLEASE ASAP 30 PTS I’ll MARK YOU BRAINLIEST
Answers
Answer:
x=50 ∠BCX=65
Step-by-step explanation:
The angles is a triangle add up to 180 so
70+45+∠BCX=180 so
115+∠BCX=180 (subtract 115 from both sides)
∠BCX=65
A line adds up to 180
so 2x+15+65=180
so 2x+80=180 (subtract 80 from both sides)
2x=100 (divide by 2)
x=50
If the diameter of a circle is 15 inches, what is the radius?
Answers
Answer:
7.5
Step-by-step explanation:
R= d/2
Divide 15 by 2
Answer:
7.5
Step-by-step explanation:
So the formula is:
[tex]\frac{d}{2}[/tex]=r
So Divide 15 by 2. Which is 7.5
14 divided by 2 is 7, and the 1 left over would be a .5
Hope this helped!
IM giving 15 points please help!
a 42 meter lighthouse is observed by a ships officer at a 65 degree anlge to a path of the ship. At the next sighting, the lighthouse is observed at a 42 degree angle. To the nearest meter what is the distance between the 2 sightings?
Answers
Answer:
the hhh
Step-by-step explanation:
What is 3=7(4 - 2u)-6u
Answers
Answer:
u = 5/4
Step-by-step explanation:
to evaluate for the value of u we would simply open the bracket and then evaluate for the value of u by collecting the like terms together.
solution
3=7(4 - 2u)-6u
3 = 28- 14u - 6u
collect the like terms
3 + 14u + 6u = 28
20u = 28 - 3
20u = 25
divide both sides by the coefficient of u which is 20
20u/20 = 25/20
u = 5/4
Answer:
[tex]u = 5/4[/tex]
Step-by-step explanation:
Step 1: Distribute on the right side
[tex]3 = 7(4 - 2u) - 6u[/tex]
[tex]3 = (7 * 4) + (7 * -2u) - 6u[/tex]
[tex]3 = 28 - 14u - 6u[/tex]
Step 2: Combine like terms
[tex]3 = 28 + (-14u - 6u)[/tex]
[tex]3 = 28 + -20u[/tex]
Step 3: Subtract 28 from both sides
[tex]3 - 28 = 28 - 20u - 28[/tex]
[tex]-25 = -20u[/tex]
Step 4: Divide both sides by -20
[tex]-25 / -20 = -20u / -20[/tex]
[tex]5/4 = u[/tex]
Answer: [tex]u = 5/4[/tex]
If the ratio of red socks to blue socks is 1:6, how many red socks would I have if I had 24 blue socks?
Answers
Answer:4
Step-by-step explanation:
1:6
Divide 6 by 24
you will get 4
Times your answer by 1 and then u will get your final answer
8(3x+1) please give me your Brainly answer
Answers
Answer:
its 3
Step-by-step explanation:
Simplifying
8 = 3x + -1
Reorder the terms:
8 = -1 + 3x
Solving
8 = -1 + 3x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-3x' to each side of the equation.
8 + -3x = -1 + 3x + -3x
Combine like terms: 3x + -3x = 0
8 + -3x = -1 + 0
8 + -3x = -1
Add '-8' to each side of the equation.
8 + -8 + -3x = -1 + -8
Combine like terms: 8 + -8 = 0
0 + -3x = -1 + -8
-3x = -1 + -8
Combine like terms: -1 + -8 = -9
-3x = -9
Divide each side by '-3'.
x = 3
Simplifying
x = 3 this took forever to type hope it helped
60% of x is equal to 87. Write an equation that expresses the relationship between 60%, x, and 87.
Answers
Answer: 0.6x = 87
Step-by-step explanation:
Hi, to answer this question we have to write en equation:
We have to multiply the variable x by the percentage given (60%) in decimal form (divided by 100). That expression must be equal to 87.
Mathematically speaking:
x (60/100) = 87
0.6x = 87
Feel free to ask for more if needed or if you did not understand something.
This equation states that 60% (or 0.60) of x is equal to 87.
To express the relationship between 60% of x and 87, we can set up an equation. Since 60% can be written as 0.60, we can write:
0.60x = 87
To solve for x, we divide both sides of the equation by 0.60:
x = 87 ÷ 0.60
So, x will be:
x = 145
This shows that 60% of 145 is equal to 87.
Which expression represents the total surface area, in square centimeters, of the square pyramid?
(8.2) (8.2) + 4 (one-half (8.2) (10.3))
(8.2) (8.2) + 4 (one-half (8.2) (11.1))
(8.2) (10.3) + 2 (one-half (10.3) (10.3)) + 2 (one-half (8.2) (10.3))
(8.2) (10.3) + 2 (one-half (10.3) (11.1)) + 2 (one-half (8.2) (11.1))
Answers
Answer:
(8.2) (8.2) + 4 (one-half (8.2) (11.1))
Step-by-step explanation:
Formula for calculating the surface area of a square based pyramid is expressed as:
Surface area = A + 1/2ps
A is the base area
P is the perimeter of base
S is the slant side.
Since the base of the pyramid is a square, then
Base Area A = L²
A = 8.2²
A = 67.24cm²
Perimeter of square = 4L = 4(8.2)
= 32.8cm
Slant Height = 11.1cm
On substituting the gotten value:
Surface area = 8.2(8.2) + 1/2 [4(8.2 (11.1)]
Based on the solution above, the expression below is correct.
S =(8.2) (8.2) + 4 (one-half (8.2) (11.1))
There are 14 books on a shelf. 6 of these books are new.
(a) What is the ratio of used books to all books?
(b) What is the ratio of new books to used books?
?
Answers
a) 8:14
b) 6:8
yeah its telling me I'm short of words
b6:8
hdhdbe cbdvddbdb
List the possible rational zeros.
m(x) = - 4x + 11x² +6x+14
How do I solve this
Answers
[tex]m(x)=-4x+11x^2+6x+14\\m(x)=11x^2+2x+14[/tex]
Equating the equation to 0 and solving it
[tex]11x^2+2x+14=0\\D=2^2-4*11*14=-612<0[/tex]
This equation has no solution, so we can't find rational zeros
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
P.S. Hello from Russia
How many solutions does this equation have?
4x − 10
2
= 2x − 5
A) no solution
B) exactly one solution
C) exactly two solutions
D) infinitely many solutions
Answers
Answer:
The correct answer is infinitely many
Step-by-step explanation:
4x-10/2=2x-5
after that you will multiply the 2 times 2x and 2 times -5
so now it becomes
4x-10=4x-10 that's why it's infinitely many
Answer:
D) infinitely many solutions
Step-by-step explanation:
The equation yields a statement that is always true, −10 = −10.[
So, the equation has infinitely many solutions.
4x − 10 2 = 2x − 5 4x − 10 = 4x − 10 −10 = −10
The length of the hypotenuse of a right triangle is 15 in. and one leg has length of 6 in. Find the length of the other leg.
Answers
Answer:
C. square root 189 in.
Step-by-step explanation:
What is the value of a?
Answers
Answer:
a = 2
Step-by-step explanation:
The sum of the exterior angles of a polygon = 360°
Sum the exterior angles and equate to 360, that is
66a + 56a + 31a + 27a = 360, that is
180a = 360 ( divide both sides by 180 )
a = 2
ok i do not know how to do this please help asap ;-;
Answers
Answer:
Look and see >:/
Step-by-step explanation:
1) 13, 34 Rate of change: 3
2) 15, 1 Rate of change: -2
3) 17, 32 Rate of change: 0.75
4) 9, -1 Rate of change: -0.4
The width of a human hair is about 0.002 inches, which can be written as
2 x 10" inches. What is n?
Answers
Answer:
-3
Step-by-step explanation:
[tex]2*10^{-3}[/tex], n= -3.
What is fraction?A fraction is a number which represents the part of a whole or collection of objects. It is in the from of a/b where a represents the numerator part and the b represents the denominator parts.
The width of a human hair is about 0.002 inches,
It can be written in fraction form as,
[tex]\frac{2}{1000}[/tex]⇒ [tex]\frac{2}{10^{3} }[/tex]
By writing [tex]10^{3}[/tex] in reciprocal from we get,
[tex]2*10^{-3}[/tex], then n= -3.
Hence, [tex]2*10^{-3}[/tex], n= -3.
Learn more about fractions here:
https://brainly.com/question/8482939
#SPJ5
Volume of a rectangular prism is 275 cubic Inches. The base is a square with the
side length of 5 inches. Find the height of this prism. Write the formula, and solve
as an equation. V=s?h
Answers
Answer:
11 in
Step-by-step explanation:
Starting with the base, we know the side length is 5 inches. So with that in mind, we can do 5 x 5 to get the area of the base, 25. We also know the volume of the whole rectangular prism is 275, so we can do 275 ÷ 25. The quotient of that is 11.
We can check our answer by doing 11 x 25. This gives us 275, proving that it is correct.
Hope this helped! :)
It takes 41.7 BTUs to heat a 5 gallon jug of water. What is the density of a gallon of water. Round your answer to the nearest hundredth
Answers
Answer: The density is 0.002 lb/cm^3
Step-by-step explanation:
1 BTU is neded to increment the temperature of 1 Lb of water by 1° F
Then if we need 41.7 BTU to increment 1°F of 5 gallons of water, this means that in the 5 gallons we have a mass of 41.7 lbs of water.
And as you know, density = mass/volume
now, 1 gallon = 3.78 liters = 3780 cm^3
then 5 gallons = 5*3780 cm^3 = 18900 cm^3
The density is D = 41.7Lb/18900 cm^3 = 0.002 lb/cm^3
Rewrite 10^32 x 10^6 using a single exponent
Answers
10^38
Step-by-step explanation:
Given that,
10^32 x 10^6
Here the base is same (10) and the powers are 32 and 6.
These 2 bases are in multiplication form so the powers can be added up.
10^32 x 10^6 = 10^(32+6)
= 10^38