Answer:
3√5 unitssolution,
A(0,0)---->(X1,y1)
B(6,3)---->(x2,y2)
Now,
[tex]ab = \sqrt{ {(x2 - x1)}^{2} + (y2 - y1) ^{2} } \\ \: \: \: = \sqrt{ {(6 - 0)}^{2} + {(3 - 0)}^{2} } \\ \: \: \: = \sqrt{ {(6)}^{2} + {(3)}^{2} } \\ \: \: \: \: = \sqrt{36 + 9} \\ \: \: \: \: = \sqrt{45} \\ \: \: \: = 3 \sqrt{5 } \: units[/tex]
Hope this helps...
Good luck on your assignment..
21%
For all values of x
(2)
f(x) = (x + 2)2 and g(x) = 3(x - 1)
a) Find gf(x), giving your answer in the form a(x2 + bx + c)
where a, b and care integers.
(x² +
x +
b) Find g '(12)
(2)
Answer:
f(x) = (x + 2)2 = 2x + 4
g(x) = 3(x - 1) = 3x - 3
gf(x) = (2x + 4)(3x - 3)
= 6x² - 6x + 12x - 12
= 6x² + 6x - 12
To write the final answer in the form
a(x² + bx + c) we factorize the expression
Thus
6x² + 6x - 12
= 6( x² + x - 2)
where a = 6, b = 1 and c = - 2
b.) to find g '(12) we first find g ′
To find g′ equate g(x) to y
Thus
g(x) = y
y = 3x - 3
x = 3y - 3
3y = x + 3
Divide both sides by 3
We get
y = x+3/3
That's g′ = x + 3 / 3
g′(12) = 12 + 3 / 3
= 15/3
= 5
Hope this helps
Subtract simplify your answer completely
Answer:
Answer is A
Step-by-step explanation:
Answer:
[tex] \frac{3x + 13}{ {x}^{2} + 4x + 5} [/tex]Option A is the correct option
solution,
[tex] \frac{8x + 7}{ {x}^{2} + 4x + 5 } - \frac{5x - 6}{ {x}^{2} + 4x + 5} \\ = \frac{8x + 7 - (5x - 6)}{ {x}^{2} + 4x + 5} \\ = \frac{8x+ 7 - 5x + 6}{ {x}^{2} + 4x + 5 } \\ = \frac{8x - 5x + 7 + 6}{ {x}^{2} + 4x + 5 } \\ = \frac{3x + 13}{ {x}^{2} + 4x + 5 } [/tex]
Hope this helps...
Good luck on your assignment...
Help asap please It says. the graph of the relation:y=x^2-2. Use the graph to find the domain and range using interval notation. What did I do wrong for the one with the x.
Answer:
The mistake you made is that it should be [-2, infinity) not (-2, infinity).
Amy works for 36 hours per week for 10 weeks during the summer, making $\$3000$. If she works for 30 weeks during the school year at the same rate of pay and needs to make another $\$3000$, how many hours per week must she work?
Answer:
12 hours
Step-by-step explanation:
$3000 / 36hours / 10weeks = $8.33333333333
$3000 / 30weeks / $8.33333333333 = 12hours
Answer:
12
Step-by-step explanation:
Since she only needs to make the same amount of money, if she works for 3 times as many weeks, she can work 3 times fewer hours per week, meaning she can work 1/6x36= 12 hours per week
Identifying the values a, b, and c is the first step in using the Quadratic Formula to find solution(s) to a quadratic equation. What are the values a, b, and c in the following quadratic equation? −3x2 − 5x + 9 = 0 a = 5, b = 9, c = 0 a = 3, b = 5, c = 9 a = −3, b = −5, c = 9 a = −5, b = 9, c = 0
Answer:
a = -3 b = -5 and c = 9
Step-by-step explanation:
−3x^2 − 5x + 9 = 0
The quadratic function is written as
ax^2 + bx+c =0
So a = -3 b = -5 and c = 9
Answer:
a = -3, b = -5 and c = 9
Step-by-step explanation:
Given Quadratic Equation is:
=> [tex]-3x^2-5x+9[/tex]
Comparing it with standard form of quadratic equation [tex]ax^2+bx+c[/tex], we get
=> a = -3, b = -5 and c = 9
what is 2 Square of 100? what is 3 Square of 250
Answer:
10,000
15,625,000
Step-by-step explanation:
Squaring a number means multiplying a number by itself.
100^2=100*100=10,000
Cubing a number means multiplying a number by itself 3 times.
250^3=250*250*250=15,625,000
Hope this helps ;) ❤❤❤
Answer:
10000
15,625,000
Step-by-step explanation:
100 x 100 = 10000
250 x 250 x 250 = 15,625,000
Sarah dreams of going to medical school and giving quality medical care to people who live in countries in crisis. Which of the following is an organization she might want to work for? Peace Corps. World Health Organization. United Nations. Alliance for small island states
I would say World Health Organization because that is for the world and Sally dreams of going to medical school and giving quality medical care to people who live in countries in crisis.
Answer:
B
Step-by-step explanation:
I took the test ;P
Write down the gradient and y-intercept of each line
y=4x - 1
y=
[tex] \frac{1}{3} x + 3[/tex]
help pls
Answer:
Equation of a line is y = mx + c
where m is the gradient
c is the y intercept
a.)y = 4x - 1
Comparing with y = mx + c
The gradient = 4
y intercept = - 1
b.)[tex]y = \frac{1}{3} x + 3[/tex]
Comparing with y = mx + c
The gradient is 1/3
The y intercept is 3
Hope this helps you
Answer:
4 and -1
1/3 and 3
Step-by-step explanation:
for y=4x-1
y intercepts where x=0 so f(0)=4*0-1=-1
y intecepts = - 1
the gradient is y2-y1/x2-x1 where y2=f(x2)=4x2-1 and y1=f(x1)=4x1-1
the gradient is 4x2-1-4x1+1/x2-x1=4 ( the coeficient of x)
for y=1/3x+3
the gradient is 1/3
y intercepts is f(0)=3
Write the following Arithmetic sequence using an Explicit Formula: a1 = 8, an = an-1 -2
Answer:
an = 8 - 2*(n - 1)
Step-by-step explanation:
a1 ; .... ; an-1 ; an
r = an - an-1
r = (an-1 - 2) - an-1
r = an-1 - 2 - an-1
r = -2
So:
an = a1 + r*(n - 1)
an = 8 + (-2)*(n - 1)
an = 8 - 2*(n - 1)
The nth term of the arithmetic sequence using the explicit formula will be [tex]a_{n}[/tex] = 8 - 2(n - 1) thus option (A) is correct.
What is Arithmetic progression?The difference between every two successive terms in a sequence is the same this is known as an arithmetic progression (AP).
The arithmetic progression has wider use in mathematics for example sum of natural numbers.
As per the given,
First term a₁ = 8
[tex]a_{n} =a_{n-1}-2[/tex]
The common difference between the AP will is,
d = [tex]a_{n} -a_{n-1}[/tex]
d = -2
The nth term of an AP is given as a + (n - 1)d
Thus,
[tex]a_{n}[/tex] = 8 + (n - 1)(-2)
[tex]a_{n}[/tex] = 8 - 2(n - 1)
Hence "The nth term of the arithmetic sequence using the explicit formula will be [tex]a_{n}[/tex] = 8 - 2(n - 1)".
For more about Arithmetic progression
https://brainly.com/question/20385181
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You are selling decorative eggs for your club.
Medium Eggs sold for $3 each. Large Eggs sold for
$6 each. A total of 190 Eggs were sold, and sales
totaled $870. How many Large Eggs did you sell?
(-2a-4b-6c) - (-a - 2b +3c)
━━━━━━━☆☆━━━━━━━
▹ Answer
-a - 2b - 9c
▹ Step-by-Step Explanation
(-2a - 4b - 6c) - (-a - 2b + 3c)
Remove parentheses
-2a - 4b - 6c - (-a - 2b + 3c)
Collect like terms
-a - 4b - 6c + 2b - 3c
Final Answer
-a - 2b - 9c
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Answer: -a - 2b -9c
Step-by-step explanation:
-2a - (-a) = -a
-4b - (-2b) = -2b
-6c - (3c) = -9c
-a - 2b - 9c
Draw the graph of y=4x. From the graph find the value y when x= -2
here is the answer hope this helps
Here is a list of ingredients to make biscuits.
200 g butter
180 g caster sugar
400 g plain flour
20g chocolate chips
Andrew only has 300 g of plain flour.
How much of the other ingredients should he use?
g butter
g caster sugar
Help due tomorrow and I'm a bit thick and tired
g chocolate chips
Answer:
[tex]\frac{200}{1} * \frac{3}{4} = 150g[/tex] < butter
[tex]\frac{180}{1}*\frac{3}{4} = 135g[/tex] < castor sugar
[tex]\frac{20}{1}*\frac{3}{4} = 15g[/tex] < chocolate chips
full working out :)
sin law or cos law?!!!!!!!!!!!!!
Answer:
Law of Sines
Step-by-step explanation:
Law of Sines: [tex]\frac{A}{sina} =\frac{B}{sinb} =\frac{C}{sinc}[/tex]
Step 1: Solve for m∠B
[tex]\frac{25}{sin36} =\frac{27}{sinx}[/tex]
25sinx = 27sin36°
sinx = 27sin36°/25
[tex]x = sin^{-1}(\frac{27sin36}{25} )[/tex]
m∠B ≈ 39.4°
Step 3: Find m∠C
180 - (36 + 39.4)
180 - 75.4
m∠C = 104.6°
Find the enthalpy change per mole of sodium when sodium reacts with water 8 grams of sodium reacts with 227 cm of water, producing a temperature change from 298
Kto 308.4 K The specific heat capacity of water is 4.18 J/K 9.
Answer:
The enthalpy change per mole of sodium when sodium reacts with water is 28.36 kJ
Step-by-step explanation:
The given parameters are;
Mass of sodium = 8 grams = 0.008 kg
Volume of water = 227 cm³ = 0.000227 m³
Initial water temperature, T₁ = 298 K
Final water temperature, T₂ = 308.4 K
Specific heat capacity of water = 4.18 J/(K·g)
Density of water = 1000 kg/m³
Mass of water = 1000×0.000227 = 0.227 kg = 227 g
Heat change, ΔH = m×c×ΔT = m×c×(T₂ - T₁)
ΔH = 227*4.18*(308.4 - 298) = 9868.144 J = 9.868 kJ
Molar mass of sodium = 22.989769 g/mol
Therefore, 8 grams contains;
8/22.989769 = 0.348 moles of Na
Which gives the enthalpy change per 0.348 moles of Na when sodium reacts with water = 9.868 kJ
Therefore, when one mole of Na reacts with water we have;
The enthalpy change per 0.348/0.348 = 1 mole of Na when sodium reacts with water = 9.868 kJ/0.348 = 28,358.3 J = 28.36 kJ.
please help Select the correct answer. Find the inverse of function f. F(x) = 9x-7
Answer:
f-1(x)=(x+7)/9
Step-by-step explanation:
Try going at the problem backwards. The function first multiplies x by 9 then subtracts 7, so the opposite route for the inverse. Add 7 to x and then divide everything by 9
Question:
Find the inverse of function f. F(x) = 9x-7
Answer:
D. F-1(x)= 1/9x-7/9
Which of the following is the complete factorization of the polynomial below
x3 + x2 - 17x+15
Answer:
[tex]\boxed{\sf \ \ \ (x-1)(x-3)(x+5) \ \ \ }[/tex]
Step-by-step explanation:
Hello,
1 is a trivial zero so we can write
[tex]x^3+x^2-17x+15=(x-1)(x^2+2x-15) = (x-1)(x^2+5x-3x-15)\\==(x-1)(x(x+5)-3(x+5))=(x-1)(x-3)(x+5)[/tex]
hope this helps
Work out the perimeter of a semi circle with radius 3cm give your answer in terms of pi
Answer:
6(π + 1) cm
Step-by-step explanation:
d = 2r
P(s.circle) = πd + d
= π·2·3cm + 2·3cm
= π·6cm + 6cm
= 6(π + 1) cm
Jerry's motorcycle tank holds 6gallons of gas. There are 3 gallons of gas currently in the tank. How much more gasoline will
it take to fill the tank? (Simplify your answer and write it as a mixed numner
Answer:
It takes 3 more gallons to fill the tank.
Step-by-step explanation:
6-3=3
Find the value of the trigonometric ratio, cos L.
Answer:
b/h
Step-by-step explanation:
remember SOH CAH TOA. Sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent. So in this case use CAH for cos L. Adjacent to L is b, and the hypotenuse is h. Therefore the answer is b/h.
In 6 years, John will be 3 times the age he was 2 years ago. What is his current age?
7
U8
5
Answer:
John is currently 6 years old.
Step-by-step explanation:
2 years ago: x years
Current time: x+2
In 6 years: x+8
EQUATION:
3(x)=x+8= 3x=x+8
(subract x from both sides)
2x=8
x=4
Therefore, John is 6 years old in current time
In △ABC, AB=BC=29, and AC=42. What is the area of △ABC?
Answer:
420 unit^2.
Step-by-step explanation:
Use the formula area = √(s(s-a)(s-b)(s-c) where s = the semi-perimeter and ab and c are the 3 sides. (it is called Heron's Formula).
s = (29+29+42)/ 2
= 100/2
= 50.
Area = √50(50-29)(50-29(50-42)
= √176400
= 420.
The area of △ABC is 420 square units.
The formula for calculating Heron's formula is expressed as √(s(s-a)(s-b)(s-c)
where:
s = the semi-perimeter and abc are the 3 sides.Get the value of "s"
s = (29+29+42)/ 2
s = 100/2
s = 50.
Get the required area:
Area = √50(50-29)(50-29(50-42)
Area = √176400
Area = 420.
Hence the area of △ABC is 420 square units.
Learn more on area of triangle here: https://brainly.com/question/17335144
Mr. Brown is creating examples of systems of equations. He completes the steps to find the solution of the equation below.
5x+2y=8
-4(1.25x+0.5y=2)/5x+2=8
-5x-2y=-8/0=0
Based on this work, what is the solution to the system?
(-4, -4)
(0, 0)
no solution
infinitely many solutions
Answer:
Option D.
Step-by-step explanation:
The given system of equations is
[tex]5x+2y=8[/tex] ...(1)
[tex]-4(1.25x+0.5y=2)[/tex] ...(2)
On simplifying the second equation, we get
[tex]-5x-2y=-8[/tex]
On dividing by -1, we get
[tex]5x+2y=8[/tex] ...(3)
It is clear that equation (1) and (3) are same equations. It means equation (1) and (2) represent the equivalent equation.
So, the given system of equations has infinitely many solutions.
Therefore, the correct option is D.
Answer:
infinitely many solutions
Step-by-step explanation:
Because if it is at zero zero the equations represent the same line on a graph.
It can't be A because -4 -4 is a point on a graph would intersect there and that means -4-4 is answer to the equation
It cant be B for the same reason as A
It cant be no solution because then the graph lines would be parellel
Finnaly i took the test on edge2020 and got a 100
Hope this helps yall pls hit that THANKS button below have a great day
This is the question that is after it and it goes along with the question above so I thought why not kill two birds with one stone
The system of equations shown is solved using the linear combination method
StartLayout 1st row 1st column 6 x minus 5 y = negative 8 right-arrow 2nd column 6 x minus 5 y = negative 8 right-arrow 6x minus 5 y = negative 8 2nd row 1st column negative 24 x + 20 y = 32 right-arrow one-fourth (negative 24 x + 20 y = 32) right-arrow negative 6 x + 5 y = 8 with Bar Underscript 3rd row 3rd column 0 = 0 EndLayout
What does 0 = 0 mean regarding the solution to the system?
There are no solutions to the system because the equations represent parallel lines.
There are no solutions to the system because the equations represent the same line.
There are infinitely many solutions to the system because the equations represent parallel lines.
There are infinitely many solutions to the system because the equations represent the same line.
The correct answer is C also because of my first answer and response to the other question
there are 4 blue counters and 3 red counters in a bag. Suzy put some more red counters into the bag. The ratio between blue and red counters is now 2:5. How many red counters did suzy put into the bag
Answer:
i think suzy will put 15 red counters into the bag
Step-by-step explanation:
What’s the evaluation to 5x(2) + x for x =3
Answer:
48
Step-by-step explanation:
5 x^2 +x
Let x = 3
5 * 3^2 +3
Exponents first
5 * 9+3
Multiply next
45+3
48
Answer:
33
Step-by-step explanation:
If x=3, we have to plug it into 5x(2)+x.
1: Plug it into the equation
(5(3))(2)+3
2: Mutiply it all out
15(2)+3
30+3
33
Hope this helped! :)
Considering the following statements, what is X → Z? X → Y: If the sum of the interior angles of a shape is 180°, then it's a triangle. Y → Z: If a shape is a triangle, then it has three sides.
A) X → Z: If a shape has three sides, then it's a triangle.
B) X → Z: If the sum of the interior angles of a shape isn't 180°, then it doesn't have three sides.
C) X → Z: If the sum of the interior angles of a shape is 180°, then it has three sides.
D) X → Z: If a shape has three sides, then the sum of the interior angles of the shape is 180°.
Answer: X → Z: If the sum of the interior angles of a shape is 180°, then it has three sides.
Step-by-step explanation:
Answer: The answer is C.
Step-by-step explanation: I did the test and it was right
Can someone please help me graph these 4?
Answer:
These are ordered 1, 2, 3, 4
A person has to walk 100 m to go from position X in the north of east direction to the position B and then to the west of Y to reach finally at position Z. The position Z is situated at the north of X and at a distance of 60 m from X. Find the distance between X and Y.
Answer:
The distance between X and Y is 68m
Step-by-step explanation:
Consider the diagram attached:
A person starts from X, goes to Y, and then finally goes to Z, covering a total of 100m, where Z is located 60m in north of X.
We have to find distance XY.
Let the distance XY be x
Total distance covered by the person = XY + YZ
We know that total distance covered is 100m, so
100m = x + YZ
YZ = (100 - x)m
See the diagram, XZY forms a right angled triangle such that:
Hypotenuse = XY = x
Base = XZ = 60m
Perpendicular = YZ = (100-x)m
Using Pythagoras theorem
Hypotenuse² = Base² + Perpendicular²
x² = (60)² + (100-x)²
Solve the equation for x, we get:
x = 68m
An arithmetic sequence has this recursive formula: What is the explicit formula for this sequence? A. an=-6+(n-2)8 B. an=8+(n-6)(-1) C. an=8+(n-1)(-6) D. an=8+(n-1)6
Answer:
an = 8 + (n-1) *(-6)
Step-by-step explanation:
The explicit formula is
an = a1+ d (n-1) where a1 is the initial value and d is the common difference
The initial value is 8 so a1 = 8
The common difference is what we are adding or subtracting each time
We are subtracting 6 each time as we see from the recursive forumla
so d = -6
an = 8 -6(n-1)
or
an = 8 + (n-1) *(-6)
Answer:
C
Step-by-step explanation:
[tex]a_{n}-a_{n-1}=-6\\d=-6\\a_{n}=a_{1}+(n-1)d\\a_{n}=8+(n-1)(-6)[/tex]
what is 6-3 plus the square root of 4
Answer:
5
Step-by-step explanation:
6 - 3 = 3
√4 = 2
3 + 2 = 5
Answer:
5
Step-by-step explanation:
6-3 + sqrt(4)
PEMDAS says do the sqrt first
6-3 +2
Then add and subtract
3 +2
5