[tex]10x+4y=16\\\\\implies 4y = 16-10x\\\\\implies y =\dfrac14(16-10x)\\\\\implies y = 4 - \dfrac 52 x\\\\\implies y=-\dfrac 52 x +4\\\\\text{This is the slope - intercept form (y=mx+b).}[/tex]
Answer:
y = - 2.5x + 4
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
10x + 4y = 16 ( subtract 10x from both sides )
4y = - 10x + 16 ( divide through by 4 )
y = [tex]\frac{-10}{4}[/tex] x + 4 , that is
y = - 2.5x + 4 ← in slope- intercept form
how to find inflection points from first derivative
Answer:
For finding the inflection points you'll have to put the first derivative equal to zero and solve for x. After you've done that, you can plug in the x you've just found into the original function and find also the y, so you'll find the ordered pair (x,y) of the inflection point(s).
what is the following product 3 sqrt 4 times sqrt 3
Answer:
c on edge YW
Step-by-step explanation:
The value of ∛4 × √3 is 2.75 or [tex]\sqrt[6]{432}[/tex].
What is multiplication?Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.
Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.
Given;
Expression,
product 3 sqrt 4 times sqrt 3.
In numerator form:
As per the given expression,
∛4 × √3
Simplifying,
∛4 × √3
= [tex]4^{1/3}[/tex] x [tex]3^{1/2}[/tex]
= [tex]4^{2/6}[/tex] x [tex]3^{3/6}[/tex]
= [tex]\sqrt[6]{16 + 27}[/tex]
= [tex]\sqrt[6]{432}[/tex]
= 2.749
= 2.75
Therefore, the product is 2.75 or [tex]\sqrt[6]{432}[/tex].
To learn more about the multiplication;
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Easy question, Worth 80 points, PLEASE HELP!! What are the angles and the side measurements for this triangle?
Answer:
the angles are 89.2°, 34.5°, 56.3° and the sides are √26units, √8units, √18units respectively
Step-by-step explanation:
Distance between points (2,5) and (-1,2)
Using the formula, √(X2 - X1)² + (Y2 - Y1)²
= √(-1-2)²+(2-5)²
=√(-3)²+(-3)²
=√9+9
=√18 or 3√2
Distance between points (-1,2) and (4,3)
=√[4-(-1)]²+(3-2)²
= √5²+1²
=√25+1
=√26
Distance between points (2,5) and (4,3)
=√(4-2)²+(3-5)²
=√2²+(-2)²
=√4+4
=√8
Using Cosine rule/formula, C²= A²+B²-2abcosc
Let C be √18, A be √26 and B be √8
√18²=√26²+√8² - 2√26.√8cosc
18= 26+8 - 2√208cosc
18= 34 -2√208cosc
2√208cosc= 34-18
Cosc = 16/2√208
Cosc= 0.5546
c= Cos`¹(0.5547)
c= 56.3°
Using sine rule/formula
Sinc/C= Sina/A=Sinb/B
Sin56.3/√18= Sina/√26
Sina= (0.8320 × √26)/ √18
Sina= 0.9999
a= Sin`¹(0.9999)
a= 89.2
56.3+89.2+b= 180°( sum of angles in a triangle)
145.5 + b =180
b=180-145.5
b= 34.5
Which equation could be solved using this application of the quadratic formula? A. -2x2 â’ 8 = 10x â’ 3 B. 3x2 â’ 8x â’ 10 = 4 C. 3x2 8x â’ 10 = -8 D. -2x2 8x â’ 3 = 4.
The given question can be solve using quadratic formula.
The correct option is (c) [tex]3x^2 +8x -10=-8[/tex].
Given:
The given equation is,
[tex]x=\dfrac{-8\pm\sqrt{8^2-4(3)(-1)}} {2(3)}[/tex]---------------------------(1)
Write the general quadratic equation.
[tex]ax^2 + bx +c=0[/tex]
Write the quadratic formula.
[tex]x =\dfrac {-b \pm \sqrt{(b^2 - 4ac)} } {2a}[/tex]------------------------------- (2)
Compare equation (1) and (2).
[tex]a=3\\b=8\\c=-2[/tex]
Substitute the value of [tex]a[/tex], [tex]b[/tex] and [tex]c[/tex] in general quadratic.
[tex]3x^2 +8x -2=0[/tex]
Subtract [tex]8[/tex] from each side of above equation.
[tex]3x^2 +8x -2 -8=0-8\\3x^2 +8x -10=-8[/tex]
Thus, the correct option is (c) [tex]3x^2 +8x -10=-8[/tex].
Learn more about quadratic equation here:
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A swimming pool already contains
a small amount of water when you start filling it at a
constant rate. The pool contains 45 gallons of water after
5 minutes and 120 gallons after 30 minutes. Find the
average rate of change and use it to write a linear model
that relates the amount of water in the pool to the time.
Answer:
Rate of change = 3 gallons/minute
Starting volume = 30 gallons
Step-by-step explanation:
A graph of the pool's water level would be useful. The slope of the line would represent the rate of change for filling the pool. It will also help us determine the amount of water that was in the pool to start. Although it is tempting to say the rate of fill is 45gallons/5 minutes, or 9 gallons/minute, it is not correct. The pool already started with an unknown volume of water. The rate of change after 5 minutes, however, can be used. The problem states it is being added at a constant rate. Let's find an equation for a line, in the format of y=mx+b, where m is the slope (rate of change) and b is the y-intercept.
We'll let y represent the volume of water in the pool, and x will be the time in minutes. The y-intercept will give us the amount of water in the pool at the start (x = 0).
The slope can be determined between the two given points:
(5,45) and (30,120):
Slope = Rise/Run [The change in y divided by the change in x].
Rise = (120 - 45) = 75
Run = (30-5) = 25
Slope = 75/25 or 3
The line, so far, becomes y=3x + b
The slope of 3 has units of gallons/minute. It is the rate at which the pool is being filled.
We can find b, the starting volume of water, by using one of the two points in the equation and solving for b:
y=3x + b [I'll use (5,45)]
45 = 3*(5) + b
b = 30 gallons
The pool had 30 gallons to start (at x = 0(minutes))
See the graph of the line, attached.
Solve the inequality T > l+d/B for D
Answer:
Second option = TB - L > D
Step-by-step explanation:
[Given] T > [tex]\frac{L +D}{B}[/tex]
[Multiply both sides by B] TB > L + D
[Subtract L from both sides] TB - L > D
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
What is the reason for each step in the solution of the equation?
18x – 2x = 4x
Match the reasons with each step in the equation.
Given
Answer:
18 - 2x = 4x (Given)18 = 6x (Addtion property of equality)3 = x (Division property of equality)Step-by-step explanation:
Given - This is the start of the proof. Use this for the information given from the start.
Addition property of equality - Use this when adding terms on both sides of an equation.
Division property of equality - Use this when dividing terms on both sides of an equation.
A large university accepts 60% of the students who apply. Of the students the university accepts, 45% actually enroll. If 30,000 students apply, how many actually enroll?
________ students would actually enroll. (Type a whole number)
Answer:
4,500 hope this help
Step-by-step explanation:
Which of the following tables represents a function?
X 6 6 7 7
y 2 -2 3-3
x 2-2 3-3
y 5 5 7 7
x 3 -3 3-3
y 6 7 8 9
X 4 4 5 5
y 1 2 3 4
Answer:
The second one:
x 2-2 3-3
y 5 5 7 7
Step-by-step explanation:
Each domain value or x can only have one range, y, so, with that said, the second one is the answer.
Jenny wants to build a concrete patio that will be 8 meters by 11 meters
Therefore, the total cost of the patio is $352.
Hoped this helped!
[tex]BrainiacUser1357[/tex]
The perimeter of the figure below is 41.6 in.
Find the length of the missing side.
Answer:
the answer is 5.9 since both sides are the same and on the other side its 5.9
Hope This Helps!!!
read what on the image then answer
Fraction 10/12 would be greater than 3/4
Which diagram is not a function please a need explanation
Answer:3
Step-by-step explanation:
It is because the letters in diagram A cannot go to 2 seperate numbers in diagram B
What is the value of -2
Answer:
11
Step-by-step explanation:
-2 lies in the second range that begins with -2 and ends with 8
whats 1 + 1
ahsdugiywayhdyhawdwahdwahidwadad
Answer:
11
Step-by-step explanation:
It's clearly 11
1 + 1 = 11
just put the 2 numbers together
Can someone please help !!
a store is having clearance sale where merchandise on the sales racks is reduced by 80% from the original price. if a jacket was originally priced at $76, what is the sale price?
Answer:
Sale price is [tex]15.2\$[/tex]
Step-by-step explanation:
Price is reduced by 80% from the original price.
Here original price is $76
Sale price is
[tex]=76-76\times\frac{80}{100}\\\\=0.2\times76\\\\=15.2\$[/tex]
1
Arrange the following steps in the right order so as to find the roots of the following quadratic equation.
22 +22 - 8=0
=
-2 +6
=
2
-2 +4+32
2.
=
= = =
I = -4; = 2
x = -13
TI
-2 = 36
2
-2 +(2) – 4(1)(-8)
2 (1)
2
= r = -1 -3: x = -1 +3
Answer:
22 +22 - 8=0
=
-2 +6
=
2
-2 +4+32
2.
=
= = =
I = -4; = 2
x = -13
TI
-2 = 36
2
-2 +(2) – 4(1)(-8)
2 (1)
2
= r = -1 -3: x = -1 +3 = sin \theta
Step-by-step explanation:
I need reassurance that my answer is right. Is this a rotation? :')
Answer:
Yes, it is a rotation!
Step-by-step explanation:
You know this because the shape rotated. It did not flip, change size, or remain the same.
I hope this helps!
____________ system is a system where each transaction is entered twice, once on the debit side and once on the credit side. *
Options -
Single entry
Double entry
Answer:
Double-entry bookkeeping,in accounting, is a system of bookkeeping where every entry to an account requires a corresponding and opposite entry to a different account. The double-entry system has two equal and corresponding sides known as debit and credit.
Step-by-step explanation:P I E C K_______Find the area of the shape shown below.
Answer:
14 sq units
Step-by-step explanation:
square - 4
triangle - 4
secong triangle - 6
4+4+6 = 14 sq units
Answer:
A = 10 sq. units
Step-by-step explanation:
Area of a trapezium is the average of the bases times the height.
Base 1 is 8 units
Base 2 is two units
Average is (8 + 2)/2 = 5 units
A = 5(2) = 10 sq. units
How i can answer this question?
Answer:
11n
Step-by-step explanation:
7+4 =11
so then 7n+4n=11n
Multiply. Enter your answer as a simplified mixed number. -4(3/14)
Answer:
-53 /14
Step-by-step explanation:
f(a)=2a+5
g(a)=a2-4
what is f(g(a))
You are running a concession stand at a basketball game. You are selling hot dogs and sodas. Each hot dog costs $2.25 and each soda costs $1.50. At the end of the night you made a total of $225.75. You sold a total of 126 hot dogs and sodas combined. You must report the number of hot dogs sold and the number of sodas sold. What equations did you use to solve this? How many hot dogs were sold and how many sodas were sold?
Answer:
49 hot dogs, 77 sodas
Step-by-step explanation:
2.25h + 1.5s = 225.75
h + s = 126, so s = 126 - h. Substitute that into the first equation.
2.25h + 1.5(126 - h) = 225.75
Solve for h
2.25h + 189 - 1.5h = 225.75
0.75h = 36.75
h = 49 So they sold 49 hot dogs
h + s = 126, so 49 + s = 126, s = 77
please help with this
Figure A is a scale image of figure B.
Pls help!!!
x = 5.25
since there is a scale factor of 1.75, you multiply 3 * 1.75 and get 5.25
hope this is helpful!
The graph shows a proportional relationship between the number of books sold at a yard sale and the amount of money collected from book sales.
Book Sales Revenue
What is the constant of proportionality?
0.67
1
1.5
2
Answer:
1.5
Step-by-step explanation:
6/4
Answer:
it's C. 1.5
Step-by-step explanation:
I did the test
Find the zeros of this polynomial:
p(x)= (x²+4x+3)(x²-4)
====================================================
Explanation:
Set each factor equal to zero and solve for x. I'm using the zero product property which says A*B = 0 leads to either A = 0 or B = 0.
Let's apply that idea to the first factor.
x^2+4x+3 = 0
(x+1)(x+3) = 0
x+1 = 0 or x+3 = 0
x = -1 or x = -3 are two roots
-------------
Do the same for the other factor as well.
x^2 - 4 = 0
(x-2)(x+2) = 0 .... difference of squares rule
x-2 = 0 or x+2 = 0
x = 2 or x = -2 are another two roots
--------------
In total, the four roots are:
x = -3x = -2x = -1x = 2Side note: The term "root" is the same as the zeros of a polynomial. Visually, this corresponds to the x intercepts. Plugging any of those four items into p(x) will lead to p(x) = 0.
The area of the triangle below is 5.52 square feet.
What is the length of the base?
Answer:
4.6 ft
Step-by-step explanation:
The formula for the area of a triangle is ...
A = 1/2bh
Fill in the given values and solve for the base.
5.52 = 1/2b(2.4)
5.52/1.2 = b = 4.6 . . . . divide by the coefficient of b
The base is 4.6 feet.