Answer:
[tex]\displaystyle y' = \frac{\big( -2 \cos x \sin x - \frac{3}{2\sqrt{x}} \big) \big( \tan^2 x + 5x \big) + \big( \cos^2 x - 3\sqrt{x} + 6 \big) \big( 2 \sec^2 x \tan x + 5 \big)}{ \big( \csc^2 x + 3 \big) \big( \sin^2 x + 6 \big)} + \frac{2 \cot x \csc^2 x \big( \cos^2 x - 3\sqrt{x} + 6 \big) \big( \tan^2 x + 5x \big)}{\big( \csc^2 x + 3 \big)^2 \big( \sin^2x + 6 \big)} - \frac{2 \cos x \sin x \big( \cos^2 x - 3\sqrt{x} + 6 \big) \big( \tan^2 x + 5x \big)}{\big( \csc^2 x + 3 \big) \big( \sin^2 x + 6 \big)^2}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]:
[tex]\displaystyle (cu)' = cu'[/tex]
Derivative Property [Addition/Subtraction]:
[tex]\displaystyle (u + v)' = u' + v'[/tex]
Derivative Rule [Basic Power Rule]:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Product Rule]:
[tex]\displaystyle (uv)' = u'v + uv'[/tex]
Derivative Rule [Quotient Rule]:
[tex]\displaystyle \bigg( \frac{u}{v} \bigg)' = \frac{vu' - uv'}{v^2}[/tex]
Derivative Rule [Chain Rule]:
[tex]\displaystyle [u(v)]' = u'(v)v'[/tex]
Step-by-step explanation:
*Note:
Since the answering box is way too small for this problem, there will be limited explanation.
Step 1: Define
Identify.
[tex]\displaystyle y = \frac{\cos^2 x - 3\sqrt{x} +6}{\sin^2 x + 6} \times \frac{\tan^2 x + 5x}{\csc^2 x + 3}[/tex]
Step 2: Differentiate
We can differentiate this function with the use of the given derivative rules and properties.
Applying Product Rule:
[tex]\displaystyle y' = \bigg( \frac{\cos^2 x - 3\sqrt{x} + 6}{\sin^2 x + 6} \bigg)' \frac{\tan^2 x + 5x}{\csc^2 x + 3} + \frac{\cos^2 x - 3\sqrt{x} +6}{\sin^2 x + 6} \bigg( \frac{\tan^2 x + 5x}{\csc^2 x + 3} \bigg) '[/tex]
Differentiating the first portion using Quotient Rule:
[tex]\displaystyle \bigg( \frac{\cos^2 x - 3\sqrt{x} + 6}{\sin^2 x + 6} \bigg)' = \frac{\big( \cos^2 x - 3\sqrt{x} + 6 \big)' \big( \sin^2 x + 6 \big) - \big( \sin^2 x + 6 \big)' \big( \cos^2 x - 3\sqrt{x} + 6 \big)}{\big( \sin^2 x + 6 \big)^2}[/tex]
Apply Derivative Rules and Properties, namely the Chain Rule:
[tex]\displaystyle \bigg( \frac{\cos^2 x - 3\sqrt{x} + 6}{\sin^2 x + 6} \bigg)' = \frac{\big( -2 \cos x \sin x - \frac{3}{2\sqrt{x}} \big) \big( \sin^2 x + 6 \big) - \big( 2 \sin x \cos x \big) \big( \cos^2 x - 3\sqrt{x} + 6 \big)}{\big( \sin^2 x + 6 \big)^2}[/tex]
Differentiating the second portion using Quotient Rule again:
[tex]\displaystyle \bigg( \frac{\tan^2 x + 5x}{\csc^2 x + 3} \bigg) ' = \frac{\big( \tan^2 x + 5x \big)' \big( \csc^2 x + 3 \big) - \big( \csc^2 x + 3 \big)' \big( \tan^2 x + 5x \big)}{\big( \csc^2 x + 3 \big)^2}[/tex]
Apply Derivative Rules and Properties, namely the Chain Rule again:
[tex]\displaystyle \bigg( \frac{\tan^2 x + 5x}{\csc^2 x + 3} \bigg) ' = \frac{\big( 2 \tan x \sec^2 x + 5 \big) \big( \csc^2 x + 3 \big) - \big( -2 \csc^2 x \cot x \big) \big( \tan^2 x + 5x \big)}{\big( \csc^2 x + 3 \big)^2}[/tex]
Substitute in derivatives:
[tex]\displaystyle y' = \frac{\big( -2 \cos x \sin x - \frac{3}{2\sqrt{x}} \big) \big( \sin^2 x + 6 \big) - \big( 2 \sin x \cos x \big) \big( \cos^2 x - 3\sqrt{x} + 6 \big)}{\big( \sin^2 x + 6 \big)^2} \frac{\tan^2 x + 5x}{\csc^2 x + 3} + \frac{\cos^2 x - 3\sqrt{x} +6}{\sin^2 x + 6} \frac{\big( 2 \tan x \sec^2 x + 5 \big) \big( \csc^2 x + 3 \big) - \big( -2 \csc^2 x \cot x \big) \big( \tan^2 x + 5x \big)}{\big( \csc^2 x + 3 \big)^2}[/tex]
Simplify:
[tex]\displaystyle y' = \frac{\big( \tan^2 x + 5x \big) \bigg[ \big( -2 \cos x \sin x - \frac{3}{2\sqrt{x}} \big) \big( \sin^2 x + 6 \big) - 2 \sin x \cos x \big( \cos^2 x - 3\sqrt{x} + 6 \big) \bigg]}{\big( \sin^2 x + 6 \big)^2 \big( \csc^2 x + 3 \big)} + \frac{\big( \cos^2 x - 3\sqrt{x} +6 \big) \bigg[ \big( 2 \tan x \sec^2 x + 5 \big) \big( \csc^2 x + 3 \big) + 2 \csc^2 x \cot x \big( \tan^2 x + 5x \big) \bigg] }{\big( \csc^2 x + 3 \big)^2 \big( \sin^2 x + 6 \big)}[/tex]
We can rewrite the differential by factoring and common mathematical properties to obtain our final answer:
[tex]\displaystyle y' = \frac{\big( -2 \cos x \sin x - \frac{3}{2\sqrt{x}} \big) \big( \tan^2 x + 5x \big) + \big( \cos^2 x - 3\sqrt{x} + 6 \big) \big( 2 \sec^2 x \tan x + 5 \big)}{ \big( \csc^2 x + 3 \big) \big( \sin^2 x + 6 \big)} + \frac{2 \cot x \csc^2 x \big( \cos^2 x - 3\sqrt{x} + 6 \big) \big( \tan^2 x + 5x \big)}{\big( \csc^2 x + 3 \big)^2 \big( \sin^2x + 6 \big)} - \frac{2 \cos x \sin x \big( \cos^2 x - 3\sqrt{x} + 6 \big) \big( \tan^2 x + 5x \big)}{\big( \csc^2 x + 3 \big) \big( \sin^2 x + 6 \big)^2}[/tex]
∴ we have found our derivative.
---
Learn more about derivatives: https://brainly.com/question/26836290
Learn more about calculus: https://brainly.com/question/23558817
---
Topic: Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
2/5n+ 3/6+ 1/8n
what does it equal
Answer:
[tex]\frac{21}{40}n[/tex] + [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
The important part to understand about this problem is that you need to find a common denominator. You can ONLY add two fractions if they have the same denominator. A way to change the denominator of a fraction is to multiply the numerator and denominator of the fraction by the same number.
So, You want to make the 2/5n and 1/8n to have the same denominator so you can add them. An easy rule of thumb is multiply the one of the fraction by the other fraction's denominator, so in this problem:
[tex]\frac{2 * 8}{5*8} n[/tex] and [tex]\frac{1*5}{8*5}n[/tex]
this comes out as
16/40n and 5/40n
NOW, they have the same denominator and you can add the numerators together to make it one happy fraction
[tex]\frac{16}{40} + \frac{5}{40} = \frac{16+5}{40} = \frac{21}{40}[/tex]
Then, for the 3/6, you can simplify this fraction into:
1/2
This is because if you divide the top and bottom of the fraction by 3 like so:
[tex]\frac{3/3}{6/3}[/tex] (Always make sure you do the same for the top as you do to the bottom)
This comes out as
[tex]\frac{1}{2}[/tex]
Then for the full equation:
[tex]\frac{21}{40} n + \frac{1}{2}[/tex]
Math tangent of a circle Also sorry my sister got a hold of it
ASAP!!!
Imagine we drew a line from the centre (2,0) to the point (0,4).
Essentially the line we drew from the centre to that point on the circle is perpendicular to the tangent line slope-wise.
The slope of that line from the centre to the point is -2 based on the slope's equation or formula.
slope = [tex]\frac{y2-y1}{x2-x1}=\frac{4-0}{0-2} =-2[/tex]
Therefore the tangent equation's slope is 1/2 since any perpendicular line's slope is the negative reciprocal of the original line's slope.
By using the point-slope form, we must have the point on the tangent plane (0,4) and the slope we found which is 1/2.
[tex]y - 4 = \frac{1}{2}(x-0)\\ y= \frac{1}{2}x + 4[/tex]
Hope that helps!
What is the area Of the desk
Answer:
28 ft²
Step-by-step explanation:
area of the desk = (5×4) + (4×2) = 20 + 8 = 28 ft²
Answer:
28
Step-by-step explanation:
5 times 4 = 20
4 times 2= 8
20 plus 8=28
You are designing a large rectangular fish tank for your tropical fish. The length will be 1 yard 3 inches, the width will be 1. 5 feet, and the height will be 20 inches. Part A Find the volume of the fish tank in cubic inches. The volume is cubic inches. Part B Your math teacher tells you that your fish tank will have a capacity of about 976 cups. You have a total of 30 tropical fish. For them to flourish in a fish tank, there needs to be an average of 2 gallons of water for each fish. Convert 976 cups to gallons. 976 cups equals gallons.
Unit conversion is a way of converting some common units into another without changing their real value. 30 fishes can flourish in a fish tank with a capacity of 976 cups.
What is Units conversion?Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimetre is equal to 10 mm, though the real measurement is still the same the units and numerical values have been changed.
As it is given that the length will be 1 yard 3 inches, the width will be 1. 5 feet, and the height will be 20 inches. Therefore, Converting all the dimensions to inches.
Length = 1 yard 3 inches = 36 inches + 3 inches = 39 inches
Width = 1.5 feet = 1.5×12 = 18 inches
Height = 20 inches
A.) The volume of the fish tank can be written as,
[tex]\rm \text{Volume of the Fish Tank} = Length \times Width \times Height[/tex]
[tex]= 39 \times 18 \times 20\\\\= 14,040\rm\ in^3[/tex]
Thus, the volume of the fish tank is 14,040 in³.
B.) As we know that a cup is equal to 0.0625 gallons. Therefore, the capacity of the fish tank in gallons can be written as,
[tex]\rm 1\ cup= 0.0625\ gallons\\\\976\ cup= 976 \times 0.0625\ gallons\\\\976\ cup= 61\ gallons[/tex]
Now, for a total of 30 fish, the water that will be needed is one fish needs 2 gallons of water is,
[tex]\rm Water\ Needed = 30 \times 2 = 60\ gallons[/tex]
As the water needed for the 30 fishes to flourish is 60 gallons while the tank has a capacity of 61 gallons.
Hence, 30 fishes can flourish in a fish tank with a capacity of 976 cups.
Learn more about Units conversion:
https://brainly.com/question/4736731
Find X using the diagram.
Answer:
58°
Step-by-step explanation:
Refer to the letters in my diagram.
Angle AOB measures 64°. Angle ACB, since itis a circle angle o nthe same chord AB, measure half of it, or 32°.
Furthermore, angle ABC is a right angle since triangle ABC has side AC on a diameter and B on the circle.
Now, since the sum of all internal angles in a triangle is 180°, we have , [tex]x+32\°+90\°=180\°\rightarrow x = 58°[/tex]
Write an equation (a) in slope-intercept form and (b) in standard form for the line passing through (1,8) and perpendicular to 3x + 5y = 1
Step-by-step explanation:
a) 2y = 3x + 4
b) given the perpendicular
3x + 5y = 1
5y = 1 - 3x
y = 1/5 - 3x/5
m¹ = -3/5
perpendicular
m¹m² = -1
-3m²/5 = -1
m² = 5/3
so (1,8)
x¹ = 1 y¹ = 8
m² = (y - y¹)/(x - x¹)
5/3 = (y - 8)/(x - 1)
5x - 5 = 3y - 24
3y - 5x + 5 - 24 = 0
3y = 19 + 5x
In ΔVWX, x = 110 inches, v = 700 inches and ∠W=9°. Find ∠X, to the nearest degree.
The value of ∠X in triangle VWX ( ΔVWX) to the nearest degree is 2 degrees.
The angle X can be found using the cosine rule.
Cosine rulew² = x² + v² - 2xv cos W
w² = 110² + 700² - 2 × 110 × 700 cos 9°
w² = 12100 + 490000 - 154000 cos 9°
w² = 502100 - 154000 × 0.98768834059
w² = 502100 - 152104.004452
w = √349995.995548
w = 591.604593921
w = 591.60 inches
Using sine rule, let's find ∠X
Sine rule
110 / sin X = 591.60 / sin 9°
Therefore,
110 sin 9 = 591.60 sin X
sin X = 110 sin 9 / 591.60
sin X = 110 × 0.15643446504 / 591.60
sin X = 17.2077911544 / 591.60
X= sin⁻¹ 0.02908686807
∠X = 1.66678986656
∠X = 2 degrees
learn more on cosine law here : https://brainly.com/question/15268683
Determine whether or not the equation below is balanced. If it isn’t balanced, write the balanced form. Also, identify the reactant(s) and product(s) in this equation. Finally, label this as one of the five types of reactions: combination, decomposition, substitution, double replacement, or reversible.
Zn+ HCl → ZnCl2 + H2
Answer:
1. The equation isn't balanced because there aren't equal numbers of hydrogen or chlorine atoms on both sides of the equation. To correct this, a coefficient of 2 must be placed in front of HCl on the left-hand side of the equation.
Zn+2HCl→ZnCl2+H2
Zn and 2HCl are the reactants; ZnCl2 and H2 are the products. This is a substitution reaction because a free element (Zn) replaces another element (H) in a compound.
2. This is a balanced equation because the same types of atoms and the same numbers of each atom are present on both sides of the equation. 8 S atoms are found on both sides of the equation, and 48 F atoms are found on both sides of the equation. S8 and 24F2 are the reactants; 8SF6 is the product. This is a combination reaction because two substances (S8 and 24F2) undergo a chemical union to form a more complex substance (8SF6).
S8+24F2→8SF6
3. In ferric oxide (Fe3O4), there are 3 atoms of iron (Fe) and 4 atoms of oxygen (O). From the Periodic Table of Elements, we know that the atomic mass of iron is 55.8457 and the atomic mass of oxygen is 15.9994.
Fe3 = 55.8457 × 3 = 167.5371
O4 = 15.9994 × 4 = 63.9976
167.5371 + 63.9976 = 231.5347 (231.535 rounded)
Therefore, the molecular mass of ferric oxide is 231.535.
4. The percentage composition of chlorine in CaCl2 is derived as follows:
The molecular mass of the entire compound is:
Ca = 40.078 × 1 = 40.078
Cl2 = 35.4527 × 2 = 70.9054
40.078 + 70.9054 = 110.9834 (110.983 rounded)
The atomic mass of each element (or its multiple) is divided by the molecular mass of the compound:
Ca = 40.078 ÷ 110.983 = 0.361
Cl2 = 70.9054 ÷ 110.983 = 0.639
Multiplying each by 100 will turn these into percents. Therefore, the percentage composition of chlorine is 63.9%.
5. i. a, c, f, h
ii. e
iii. b, d, g, i
iv. i
Step-by-step explanation:
PENN FOSTER
The given chemical equation represents a type of reaction known as a single replacement (or displacement) reaction. In this reaction, zinc (Zn) displaces hydrogen (H) from hydrochloric acid (HCl) to form zinc chloride ([tex]ZnCl_2[/tex]) and hydrogen gas ([tex]H_2[/tex]).
The given chemical equation is:
[tex]Zn + HCl \rightarrow ZnCl_2 + H_2[/tex]
To determine if the equation is balanced, we need to check if the number of atoms of each element is the same on both sides of the equation.
On the left side (reactant side):
Zinc (Zn) atoms: 1
Hydrogen (H) atoms: 1
Chlorine (Cl) atoms: 1
On the right side (product side):
Zinc (Zn) atoms: 1
Hydrogen (H) atoms: 2 (from[tex]ZnCl_2 + H_2[/tex])
Chlorine (Cl) atoms: 2 (from [tex]ZnCl_2[/tex])
The number of hydrogen (H) and chlorine (Cl) atoms is not balanced between the reactants and products. To balance the equation, we need to have the same number of atoms on both sides.
Balanced equation:
[tex]Zn + 2HCl → ZnCl_2 + H_2[/tex]
Now, the equation is balanced with the following number of atoms on both sides:
On the left side (reactant side):
Zinc (Zn) atoms: 1
Hydrogen (H) atoms: 2
Chlorine (Cl) atoms: 2 (2 from HCl)
On the right side (product side):
Zinc (Zn) atoms: 1
Hydrogen (H) atoms: 2 (from H2)
Chlorine (Cl) atoms: 2 (from ZnCl2)
Identification of reactants and products:
Reactants: Zn (zinc) and HCl (hydrochloric acid)
Products: [tex]ZnCl_2[/tex] (zinc chloride) and [tex]H_2[/tex] (hydrogen gas)
To know more about equation:
https://brainly.com/question/17216476
#SPJ2
Jonah's lunch cost $27.50, he paid $1.65 sales tax. What is the percent of sales tax?
Answer:
6%
Step-by-step explanation:
To get sales tax, you multiply the percentage of sell tax to the total price. In this case, we were looking for the percent of sell tax so we needed to divide the total amount into the amount he payed in sells tax. You will get the decimal value so you will have to multiply it by 100 to get the percent.
Sam wants to create a linear function and an exponential function, both of which have a y-intercept
of (0,8) and pass through the point (9,512). Help Sam create his functions.
Step-by-step explanation:
Exponential function is
[tex]y = a \times {b}^{x} [/tex]
where a is the y intercept, or the initial value.
b is the constant rate.
Since a is the y intercept, this means a is 8. So we have
[tex]y = 8 \times {b}^{x} [/tex]
Now, plug in 9 for x. 512 for y to find b.
[tex]512 = 8 \times {b}^{9} [/tex]
[tex]64 = {b}^{9} [/tex]
[tex] \sqrt[9]{64} = b[/tex]
[tex]64 {}^{ \frac{1}{9} } = b[/tex]
[tex]4 {}^{ \frac{1}{3} } = b[/tex]
[tex] \sqrt[3]{4} = b[/tex]
So the equation is
[tex]y = 8( \sqrt[3]{4} ) {}^{x} [/tex]
Find x. Perimeter.
What is the value of x?
What is the perimeter of this triangle?
Step-by-step explanation:
the distance of a vertex on the 2 outgoing sides to the touching points with the inscribed circle is the same for both sides.
and that applies to all 3 vertexes.
so, we know for the top left vertex the distance to both touching points is 4.
that means the distance to the touching points from the bottom left vertex is 7-4 = 3.
and that means that the distance to the touching points from the bottom right vertex is 16-3 = 13.
so, x = 13
it is the distance to one of the touching points for the bottom right vertex.
and the perimeter of the triangle is therefore
7 + 16 + (13 + 4) = 40
Which value, when placed in the box, would result in a system of equations with infinitely many solutions? y = -2x 4 6x 3y =
The missing value is 12 in a system of equations with infinitely many solutions conditions.
It is given that in the system of equations there are two equations given:
[tex]\rm y =n -2x+4\\\rm and \\\rm 6x+3y= ?[/tex]
It is required to find the missing value in the second equation.
What is a linear equation?It is defined as the relation between two variables if we plot the graph of the linear equation we will get a straight line.
We have equations:
[tex]\rm y = -2x+4 ....(1)\\ \\\rm 6x+3y= ? ....(2)[/tex]
Let's suppose the missing value is 'Z'
We know that the two pairs of equations have infinitely many solutions if and if they have the same coefficients of variables and the same constant on both sides.
From equation (1)
[tex]\rm y = -2x+4 \\\\\rm 2x+y=4[/tex](multiply both the sides by 3)
[tex]\rm 6x+3y=12[/tex] ...(3)
By comparing the equation (2) and (3), we get
M = 12
Thus, the missing value is 12 in a system of equations with infinitely many solutions conditions.
Learn more about the linear equation.
brainly.com/question/11897796
The exponential function f is given by f(x) = 3x. by what factor does f increase when the exponent x increases by 2? explain how you know. a 3 b 6 c 9 d 12
The exponential function f(x) = 3^x, when x has a value of 2 increases by 9.
What is an exponential function?An exponential function is a function that is in the form: m = ab^x
Where:
a = initial value b = rate of increase x = number of yearsF(x) = 3^x
3^2 = 9
To learn more about exponential functions, please check: https://brainly.com/question/26331578
I’ll give Brainly but can somebody help me with this?
Answer:
give me 2 minutes and I will
is it adjacent or vertical
find the value of X
Answer:
Adjacent, x = 60°
Step-by-step explanation:
Adjacent angles are pairs of angles next to each other. Vertical angles make an x shape, are across from each other, and have the same measure. These are adjacent angles.
This is a 90° angles, which is signified by the little red box. To solve for x, make an equation by adding the two angles together and set them equal to 90.
x - 30 + x = 90
2x - 30 = 90
2x - 30 + 30 = 90 + 30
2x = 120
2x/2 = 120/2
x = 60°
Here, the angles x° and (x - 30)° both are complementary angles, so they will add upto 90°, thus we can obtain a equation as ;
[tex]{:\implies \quad \sf x^{\circ}+(x-30)^{\circ}=90^{\circ}}[/tex]
[tex]{:\implies \quad \sf 2x^{\circ}-30^{\circ}=90^{\circ}}[/tex]
[tex]{:\implies \quad \sf 2x^{\circ}=120^{\circ}}[/tex]
[tex]{:\implies \quad \sf x^{\circ}=\dfrac{120^{\circ}}{2}=\bf \boxed{60^{\circ}}}[/tex]
Hence, the required value of x is 60
Please Help this is due soon
The table below represents an exponential function.
table represents an exponential function.
What is the interval between neighboring
x-values shown in the table?
1
What is the ratio between neighboring y-values?
4
What is the equation for this pattern?
y = _^x
I only need the last one answered
Answer:
[tex]y = {4}^{x} [/tex]
is the answer
PLEASE HELP QUICK !!!!
For each of the following functions, list the excluded values from the
domain:
f (x) =
g(x) =
2-3
22 9
h(x) = V16 – 22
Answer:
fx is 4, gx is 3, hx is anything greater than, not equal to, 4.
Hope this helps!
What is the area of a circle with a radius of 10.2 feet? 10.2
Evaluate the expression for m = -3.
-4|5 + m|
Type the correct answer in the box. Use numerals instead of words.
Answer:
The answer is -8
-4 l5 +(-3)l
-4 (2) = -8
Answer: Correct answer is -8
Step-by-step explanation:
Substitute the given value of m into the expression:
-4|5 + (-3)|.
Then evaluate using the order of operations:
-4|5 + (-3)|
= -4|2|
= -4(2)
= -8
Edmentum Answer
Bananas cost $0.48 per pound. If you spent $1.84, how many pounds of bananas did you
purchase?
Answer:
3 pounds of bananas
Step-by-step explanation:
1.84 ÷ 0.48 = 3.8333etc
since you can't buy 4 pounds with the money you have its 3 pounds of bananas
Andrea thought that x = 15 would be a good guess to solve 6x + 19 = 150. Should her second guess be higher or lower? Why?
Answer:
higher
Step-by-step explanation:
should be higher since 6 x 15 is 90, which is far away from 150
Answer:
should be higher
Step-by-step explanation:
because 6×15=90 and 90+19 is lower than 150
surface area of prisms: find it and. fix it
Answer:
Step-by-step explanation:
i can't solve without seeing the prism
I need help, please? I am just really confused about this.
Answer:
blank space 1: 120
blank space 2: 85
Step-by-step explanation:
you subtract 35 from it
Help!!! 8. Determine whether each pair of functions f and g are inverses. Explain your reasoning.
Answer:
I would say that a is NOT an inverse, however b is.
Step-by-step explanation:
If you look at the two tables for a, you can tell that every pair has swapped places (as they should) except 0 and 9. In which in the second table, what should be the 9 in the x row, is just another 0 in its place.
While if you look at the two tables for b, every single pair has been swapped like it should, meaning the second table is the inverse of the first table.
Hope this helps you btw. I'm sorry if it doesn't though.
100 BRAINLY POINTS!!!
Each point on the scatter plot below represents the number of hours a student studied for a test and the
student's test scores.
Which equation is the closest approximation to the line of best fit?
A. y = -10x + 92
B. y = 6x + 59
C. y = 10x + 45
D. y = 15x + 30
PLEASE HURRY CUH
EXPLAIN YOUR ANSWER
SHOW YOUR WORK
Let's take 1 of x axis from plot (It has three values in y so much useful)
#A
y=-10x+92=-10+92=82#B
y=6x+59=6+59=65#C
y=10x+45=10+45=55#D
y=15x+30=15+30=45A and D are out of radar .Now we need to find most approx between B and C
Go to 2 now.(Same 3 values)
#B
y=12+59=71#C
y=20+45=6565 lies between 60 and 70 ,most approximately equal .
Option C is correct
Answer:
C [tex]y=10x+45[/tex]
Step-by-step explanation:
Line of best fit (trendline) : a line through a scatter plot of data points that best expresses the relationship between those points.
All the given options for the line of best fit are linear equations.
Therefore, we can add the line of best fit to the graph (see attached), remembering to have roughly the same number of points above and below the line.
Linear equation: [tex]y=mx+b[/tex]
(where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept)
From inspection of the line of best fit, we can see that the y-intercept (where x = 0) is approximately 45. So this suggests that option C is the solution.
We can also see that the line of best fit appears to be the same distance from points (3, 75) and (4, 85). So we can use the slope formula with these points to give a rough estimate of the slope of the line of best fit:
[tex]\sf{slope=\dfrac{y_2-y_1}{x_2-x_1}}=\dfrac{85-75}{4-3}=10[/tex]
Therefore, this concurs that C is the solution and that the closet approximation to the line of best fit is [tex]y=10x+45[/tex]
Mayrin has rectangular rug with an area of 36 square feet. The area is represented by the equation f(x)= x2 + 5x – 36 and this rug is 5 feet longer than it is wide. What are the dimensions of the rug?
Answer:
B) width = 4 ft
length = 9 ft
Step-by-step explanation:
Area = 36 ft²
Let width = x
⇒ length = x + 5
Area of a rectangle = width × length
⇒ 36 = x(x + 5)
⇒ x² + 5x - 36 = 0
⇒ x² + 9x - 4x - 36 = 0
⇒ (x² + 9x) + (-4x - 36) = 0
⇒ x(x + 9) - 4(x + 9) = 0
⇒ (x + 9)(x - 4) = 0
⇒ x = -9, x = 4
As distance is positive, x = 4 only
Therefore,
width = x = 4 ft
length = x + 5 = 4 + 5 = 9 ft
What is the domain of the function in this table?
х
2
3
4
5
у
5
8
11
14
Baba Clothing store is a having a 5% off sale on all of its clothing. Which expression represents the discounted price if p is the original price?
Answer:
The total of the prices of all of the baby shirts and sweaters that the store sold during the sale was $420.00. It's possible that 12 sweaters and 8 shirts are sold a bargen
Step-by-step explanation:
A kite is inscribed in a square with a side length of 9 units. What is the area of the kite? 27. 5 square units 36. 0 square units 40. 5 square units 45. 0 square units.
45. 0 square units.
The area of the kite is 40.5 unit square.
The side of the kite inscribed in square is 9
We have to find the area of the kite
What is the formula for the area of the kite?The area of a kite is,
[tex]A = (d_1d_2) / 2[/tex]
Where [tex]d_1[/tex] and [tex]d_2[/tex] are the diagonals of the kite.
The kite is inscribed in the square, and the sides of the square are 9 units, the diagonals of the kite are both 9 units.
Therefore we get,
[tex]d_1 = 9 units[/tex]
[tex]d_2 = 9 units[/tex]
[tex]A = (9units \times 9units) / 2[/tex]
[tex]A = 81units^2 / 2[/tex]
[tex]A = 40.5 units^2[/tex]
So the third option is correct .
Therefore ,The area of the kite is 40.5 unit square.
To learn more about the area of the kite visit:
https://brainly.com/question/16424656
Help me In this question it’s urgent
Answer:
CD = 13.75
Step-by-step explanation:
Focus on only half of the rectangle as a triangle
We'll use pythagorean theorem to find the unknown side
[tex]10^{2} +CD^{2}=17^{2}\\CD^{2} = (17^{2} - 10^{2})\\CD^{2}=\sqrt{189} \\CD = 13.75[/tex]