Answer:
The solution of the given two simultaneous equation
A( 3 ,6) and [tex]B(\frac{1}{2} ,\frac{17}{2} )[/tex]
The intersecting points of given two simultaneous equations are
A( 3 ,6) and [tex]B(\frac{1}{2} ,\frac{17}{2} )[/tex]
Step-by-step explanation:
Explanation:-
Step(i):-
Given simultaneous equation
y = 9-x ...(i)
y = 2 x² +4 x+6 ..(ii)
Equating (i) and (ii) equations , we get
9 -x = 2 x² +4 x+6
⇒ 2 x² +4 x + 6- 9 +x =0
⇒ 2 x² + 5 x - 3 =0
⇒ 2 x² +6 x -x -3 =0
⇒ 2 x ( x +3) -1 ( x+3) =0
⇒ (2 x -1 ) ( x+3) =0
⇒ (2 x -1 ) = 0 and ( x +3 ) =0
[tex]2 x =1[/tex] and x = -3
x = 1/2 and x =3
Step(ii):-
x = 3 ⇒ y = 9 - 3 =6
A( 3 ,6)
[tex]x = \frac{1}{2} , y = 9 - \frac{1}{2} = \frac{17}{2}[/tex]
[tex]B(\frac{1}{2} ,\frac{17}{2} )[/tex]
Final answer:-
The intersecting points of two simultaneous equations are
A( 3 ,6) and [tex]B(\frac{1}{2} ,\frac{17}{2} )[/tex]
The solution of the given two simultaneous equation
A( 3 ,6) and [tex]B(\frac{1}{2} ,\frac{17}{2} )[/tex]
The solution to the given simultaneous equation is (1/2, 8 1/2) and (-3, 12)
From the question,
We are to solve the given simultaneous equations
The given equations are
y = 9-x ---------- (1)
y = 2x²+4x+6 ---------- (2)
Substitute equation (1) into equation (2)
y = 2x²+4x+6
That is
9-x = 2x²+4x+6
Simplifying, we get
0 = 2x² +4x +x +6 -9
0 = 2x² +5x -3
∴ 2x² +5x -3 = 0
Now, solving the quadratic equation
2x²+6x -x -3 = 0
Factorizing
2x(x+3) -1(x+3) = 0
Then, we get
(2x -1)(x+3) = 0
∴ 2x - 1 = 0 OR x + 3 = 0
2x = 1 OR x = -3
∴ x = 1/2 OR x = -3
Now, substitute the values of x into equation (1) to determine the values of y
y = 9-x
When x = 1/2
y = 9 - 1/2
y = 8 1/2
and when x = -3
y = 9 --3
y = 9+3
y = 12
Hence, the solution to the given simultaneous equation is (1/2, 8 1/2) and (-3, 12)
Learn more here: https://brainly.com/question/24448700
[tex](\frac{15x^{2}y }{8x} )(\frac{4y}{9xy} )[/tex]
El impuesto general a las ventas ( IGV ) en el Perú es 18%.Este porcentaje incrementa el precio de cualquier artículo en venta . Si en una factura figura el precio de una cocina en 590 soles , ¿ Cual era el precio de la cocina antes de que fuera afectado por el IGV
Answer:
o preço da cozinha era 106,20 reais.
Step-by-step explanation:
porque 590-16% e iqual a 106,20 reais
foi o retirar o IGV
Which of the following are not polynomials?
Answer:
A B and D but don’t quote me on it
Step-by-step explanation:
which relation is a function ?
Pls help with this for brainliest answer
Answer:
the answer is 12pie
Step-by-step explanation:
6mm is radius
circumference is ×2
so its 12
How many litres of water (round to the nearest hundredth) can be poured into a tin can that has a diameter of 18 cm and a height of 0.3 m?
Answer:
Step-by-step explanation:
Diameter = 18cm
18 / 2 = Radius
Radius = 9cm
Formula: A=2πrh+2πr^2
2 x pi x 9 x 0.3 + 2 x pi x 9^2 = 525.90261
Nearest hundredth = 525.90
What is the difference of the fractions? Use the number line to help find the answer. 4/7-10/7
Answer:
4/7 - 10/7 = -6/7
Step-by-step explanation:
Answer:
4/7-10/7 =-6/7
Step-by-step explanation:
(−5 + 3i) ⋅ (1 − 2i)
Answer:
[tex] - 1[/tex]
Step-by-step explanation:
[tex](-5 + 3i) \times (1 - 2i) \\ ( - 5 + 6) \times (1 - 2) \\ ( 1) \times ( - 1) \\ = - 1[/tex]
Use the diagram to find the value of x to the nearest tenth of a foot.
a. 74.6 ft.
b. 5.3 ft.
c. 15.5 ft.
d. 73.3 ft.
Answer:
a
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan15° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{20}{x}[/tex] ( multiply both sides by x )
x × tan15° = 20 ( divide both sides by tan15° )
x = [tex]\frac{20}{tan15}[/tex] ≈ 74.6 ft ( to the nearest tenth of a foot )
what solution is 7x+7=6x+4+x+3
Answer:
infinite solutions (all real numbers)
Step-by-step explanation:
7x+7=6x+4+x+3
7x+7=7x+7
infinite solutions (all real numbers)
Answer:
Equation is alway true
All real numbers are solutions.
Step-by-step explanation:
Rearrange: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 7*x+7-(6*x+4+x+3)=0 Step by step solution :
Step 1 : Equations which are always true : 1.1 Solve 0 = 0This equation is a tautology
Hope this helps.
PLEASE HELP ITS FOR A TEST I WILL GIVE U BRAINLIEST
Danica and Darrelle have developed a lucrative business selling handmade silver bracelets. Darrelle makes the more complex bracelets and Danica makes the simpler ones. It takes Darrelle 4 hours to make 3 bracelets and Danica can make 5 bracelets every 2 hours.
a. Convert this scenario into linear equation(s); show both the standard form and the slope-intercept form of your equation(s).
b. Could any part of this scenario be graphed using any of the special functions discussed in the course text? Explain your answer.
c. Each bracelet Darrelle sells makes $10.50 in profit. Each bracelet Danica sells makes $3.50 in profit. If Darrelle and Danica work the same amount of time, explain each of the steps you will use and then calculate how many hours will it take for the whole business to make at least $500 profit?
Answer:
At the average rate of making profit, it will take slightly more than 30 hours for the business to reach a profit goal of $500. (30.075)
Step-by-step explanation:
a) It is not clear what linear equation is desired. We are given enough information to write an equation relating the number of bracelets produced by each worker to the time it takes.
Let n represent the number of bracelets Danica produces. Let r represent the number of bracelets Darrelle produces. Let h represent time in hours.
.. r/3 = h/4 ... Darrelle produces 3 bracelets in 4 hours
.. 4r - 3h = 0 ... equation in standard form
.. r = (3/4)h ... equation in slope-intercept form (the intercept is 0)
.. n/5 = h/2 ... Danica produces 5 bracelets in 2 hours
.. 2n - 5h = 0 ... equation in standard form
.. n = (5/2)h ... equation in slope-intercept form
b) We have no idea what special functions were discussed in the course. Of course these equations can be graphed. (2-dimensional equations are easily graphed.)
c) A profit function can be written in terms of the number of bracelets produced. Then it can be solved to find when (h=?) profit is equal to $500.
.. Let p represent the total profit from production of bracelets.
.. p = 10.50*r + 3.50*n ... profit in terms of bracelets produced
.. p = 10.50*((3/4)h) + 3.50*((5/2)h) ... profit in terms of hours, where both work the same hours
.. p = 16.625 h
.. 500 = 16.625 h ... we want to find hours until $500 profit
.. 500/16.625 = h ≈ 30.0752
At the average rate of making profit, it will take slightly more than 30 hours for the business to reach a profit goal of $500.
_____
If you work out the timing of when bracelets are finished, assuming they are made at a constant rate, you find that there will be 23 of Darrelle's bracelets and 76 of Danica's bracelets finished in 30 hours and 40 minutes. These will yield a profit of $507.50. After another 8 minutes, Danica will have finished bracelet 77 to add another $3.50 to the profit total.
pls hep for the brainliest
Answer:189.25 cm 189.3 cm if rounded to one decimal point
Step-by-step explanation:
You need to find the area of the rectangle, then the area of 1/2 the circle.
Rectangle Area =
L x w =
10 x 15 = 150cm
Circle Area =
A=πr^2 =
Diameter = 10, so radius = 5
π(5)^2 = 25π = (25)(3.14) = 78.5
Area of 1/2 Circle = 78.5/2 = 39.25
150 + 39.25 = 189.25 cm
The sum of a rational number and an irrational number produces an irrational number.
Answer:
True
Step-by-step explanation:
Example: sqrt(5) (which decimals continue forever) will mean that if you did 5+sqrt(5) it would still have those decimals.
Answer:
True. By definition, an irrational number in decimal form goes on forever without repeating (a non-repeating, non-terminating decimal). By definition, a rational number in decimal form either terminates or repeats. If you add a non-repeating, non-terminating decimal to a terminating decimal, you still have a non-repeating, non-terminating decimal. If you add a non-repeating, non-terminating decimal to a repeating decimal, you will no longer have a repeating decimal, so the result is irrational.
4y+18/5y= 2 what is the value of y?
Answer: 5/19
Step-by-step explanation:
4y + 18/5y = 2
20y + 18y = 10
38y = 10
y = 10/38
A certain solution contains 4.3 grams of salt per liter.
How much salt is there in 11 liters of the solution?
Round your answer, if necessary, to the nearest tenth.
Answer:
47.3 grams
Step-by-step explanation:
Given: A solution contains 4.3 grams of salt per liter.
To find: Amount of salt in 11 liters of the solution
Solution:
Amount of salt in 1 liter of the solution = 4.3 grams
So, amount of salt in 11 liters of the solution = 11 × Amount of salt in 1 liter of the solution = 11 × 4.3 = 47.3 grams
Hence, 11 liters of the solution contains 47.3 grams of salt.
Answer: 47.3
Step-by-step explanation: Khan Academy
What is the factored form of the polynomial?
x2 + 9x +20
1
(x - 4)(x - 5)
(x-2)(x - 10)
(x + 4)(x + 5)
(x + 2)(x + 10)
Please answer correctly !!!! Will mark brainliest !!!!!!!!!!!!
Answer:
[tex](x-7)(x-7)[/tex]
Step-by-step explanation:
We begin with the given quadratic expression:
[tex]49-14x+x^2[/tex]
Just for my own ease, I will rewrite this in descending order of powers
[tex]x^2-14x+49[/tex]
In order to factor this expression, we need to look for two numbers that meet the following criteria.
When they are added together, you get [tex]-14[/tex]
When they are multiplied together, you get [tex]49[/tex]
A simple way to find our answer is to begin with the product of multiplication and list each of the numbers that can be multiplied together to get us our given result
To get 49, we could multiply
1 and 49
-1 and -49
7 and 7
-7 and -7
Now, we can just add both of these terms together to see while one gives us our desired result
[tex]1+49=50\\-1-49=-50\\7+7=14\\-7-7=-14[/tex]
As you can see, -7 and -7 were the two values that gave us -14.
This means that they are the terms within our factor.
Therefore, our factored form would be [tex](x-7)(x-7)[/tex]
Answer:
(7 - x) (7 - x)
Step-by-step explanation:
First, I'm multiplying 49 by the co-efficient of x(1) to get 49. Then I'm going to see what factors of 49 add up to -14. Those are -7 and -7.
Next, I'm going to rewrite this polynomial:
49 - 7x - 7x + x^2
Then, I group them into two groups:
49 - 7x
&
-7x + x^2
Then, I factor them out:
49 - 7x = 7 (7 - x)
-7x + x^2 = -x (7 - x)
After that, I take the outer coefficients and put them in parenthesis:
7 (7 - x)
&
-x (7 - x)
= (7 - x)
Finally, I put both of our grouped parenthesis together:
(7 - x) (7 - x)
On a scale drawing, the height of a tree is 2.25 inches. If the scale drawing is 1 in. : 75ft, how tall is the tree?
Answer:
168.75ft
Step-by-step explanation:
We can just multiply by the scale
2.25*75=168.75
The actual height of the tree is 168.75 ft.
What is Height?The height is defined as the measurement of the distance of an object from the base to the top.
Here, Given
Height of tree (in drawing) = 2.25 inches
Scale is given ; 1 inch = 75 ft.
so, 2.25 inches = 2.25 X 75 ft.
≈ 168.75 ft.
Thus, the actual height of the tree is 168.75 ft.
Learn more about height from:
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Pls help, I will mark brainlessly and give 5 stars
Answer:
1.C 2.D
Step-by-step explanation:
Answer:
1 is C and 2 is D
Step-by-step explanation:
Veronica’s velocity was measured as 4.3 m/s. She displaced 20 meters in 4.7 seconds. Which piece of information is missing for the correct calculation of velocity?
Answer:
Direction
Step-by-step explanation:
poop
A golfer hits a golf ball with a club. The mass of the ball is 0.05 kg.
The ball accelerates at 2,000 m/s2
What is the net force, to the nearest newton, that accelerates the
ball?
Answer:
100 N
Step-by-step explanation:
f= 0.05*2000=100 N
Answer:100
Step-by-step explanation:
Please someone answer quick answer 5,6,7,8 QUICK
Answer:
64: 1, 2, 4, 8, 16, 32, 64
90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
88: 1, 2, 4, 8, 11, 22, 44, 88
100: 1, 2, 4, 5, 10, 20, 25, 50, 100
84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Lucy makes green paint by mixing yellow and blue paint in the ratio 5:2. Blue paint costs
£30 for 5 litres and yellow paint costs £28 for 7 litres.
Lucy sells her green paint for £4.50 per litre. Will she make a profit? Show your working
to justify your decision.
Answer:
No, she won’t make a profit
Step-by-step explanation:
Here, we are interested in determining if Lucy made a profit or a loss.
The cost of blue paint is 30 pounds for 5 liters. This means that a liter of blue paint is 30/5 = 6 pounds per liter
The cost of yellow paint is 28 pounds per 7 liters, the cost per liter is 28/7 = 4 pounds per liter
Now, in her mixing, she mixes 5 parts of yellow paint and 2 parts of blue paint.
This means that she mixed them the ratio as follows per liter;
For yellow, we have; 5/(5+2) = 5/7
For blue we have 2/(5+2) = 2/7
Now since a liter of yellow paint cost 4 pounds
5/7 of a liter will cost 5/7 * 4 = 20/7 pounds
For the blue paint, a liter cost 6 pounds, 2/7 of a liter will cost 2/7 * 6 = 12/7
The total cost in pounds in this;
20/7 + 12/7 = 32/7 = £4.57 pounds to 2 decimal place
Now she sells her green paint product at £4.5 per liter. Since this is less than the cost price of production which is £4.57, she is running at a loss
Calcylate the volume of this regular solid
What is the volume of the rectangular prism
6 cm
5 cm
9 cm
Answer:
V = 270 cm³
Step-by-step explanation:
Remember your volume formula: V=lwh
So, plug in all your variables and multiply:
(6)(5)(9) = 270
And we have our final answer!
PC=PD then (PA)PC)=(PB)(___)
Answer:
PD is the answer
Step-by-step explanation:
(PA) (PC) = (PB) (PD)
The formula for the volume of a cone is V=1/3bh
Solve V=1/3bh
for b, the base of the cone.
Answer:
b = 3Vh
Step-by-step explanation:
When they ask to solve for b, you are essentially rearranging the equation so that b is alone on one side.
V = 1/3bh
(V)(3) = (1/3bh)(3)
3V = bh
(3V)/h = (bh)/h
3Vh = b
b = 3Vh
Mr.Tola has a piece of wood that is 8 1/4 feet in length. He wants to cut it into pieces that are each 3/4 foot in length. How many 3/4 foot pieces of wood can Mr.Tola make?
Answer:
11
Step-by-step explanation:
1/4 is equal to 0.25. 3/4 is equal to 0.75.
8.25 divided by 0.75.
11
if a=(-1, -3) and b=(11, -8) what is the length of ab?
Answer: D. The length is 13 units.
Step-by-step explanation:
(-1, -3 ) Find the difference between the x values and y values.
(11, -8)
-3-(-8) = 5
-1-11 = -12 now find the absolute values.
The absolute value of 5 is 5 . The absolute value of -12 is 12.
Now use the Pythagorean Theorem formula a^2 + b^2 =c^2 where c square is the length between AB.
5^2 + 13^2 = C^2
25 + 144 = c^2
169=c^2
c= 13
Answer:
D. 13 Units
Step-by-step explanation:
I just took the test
Solve the equation 2x-1=4x+5
Answer:
-3
Step-by-step explanation:
2x-1=4x+5
-1=2x+5
-6=2x
x=-3
Answer:
x = -3
Step-by-step explanation:
Solve for x:
2 x - 1 = 4 x + 5
Subtract 4 x from both sides:
(2 x - 4 x) - 1 = (4 x - 4 x) + 5
2 x - 4 x = -2 x:
-2 x - 1 = (4 x - 4 x) + 5
4 x - 4 x = 0:
-2 x - 1 = 5
Add 1 to both sides:
(1 - 1) - 2 x = 1 + 5
1 - 1 = 0:
-2 x = 5 + 1
5 + 1 = 6:
-2 x = 6
Divide both sides of -2 x = 6 by -2:
(-2 x)/(-2) = 6/(-2)
(-2)/(-2) = 1:
x = 6/(-2)
The gcd of 6 and -2 is 2, so 6/(-2) = (2×3)/(2 (-1)) = 2/2×3/(-1) = 3/(-1):
x = 3/(-1)
Multiply numerator and denominator of 3/(-1) by -1:
Answer: x = -3
Latrell wants to paint his bedroom ceiling to look like the sky. He wants it to be 85% blue and 15% white. If he needs 4.25 gallons of blue, how many gallons of white does he need?
Answer:
0.75 gallons
Step-by-step explanation:
As the statement indicates that Latrell wants the bedroom ceiling to be 85% blue and 15% white and you know that he needs 4.25 gallons of blue which represents the 85%, you can use a rule of three to find the amount that represents the 15% to know the gallons of white that he needs:
4.25 gallons → 85%
x ← 15%
x= (4.25*15)/85
x=0.75
According to this, the answer is that if Latrell needs 4.25 gallons of blue, he needs 0.75 gallons of white.
