What is the equation of the axis of symmetry of the graph of y + 3x – 6 = –3(x – 2)2 + 4?

Answer:

8.91 units.

Step-by-step explanation:

If the height = h then the radius = h/3.

The volume = 247 = π r^2 h

247 = π (h/3)^2 h

(h/3)^2 h = 247/π

h^3 / 9 = 247 /π

h^3 = 9*247/ π

h= 8.91 units.

The value of height of the cylinder is,

⇒ 13.14 units.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We know that;

The volume of the cylinder is,

⇒ V = πr²h,

Where V is the volume, r is the radius, and h is the height.

Given that;

The volume of the cylinder is 247 cubic units,

Also, we are told that the height of the cylinder is 3 times the radius of the base.

Hence, We get;

⇒ 247 = πr²h

And, Mathematically expressed, h = 3r.

Hence, Substituting value of h in the above equation,

247 = πr²(3r)

Simplifying further, we get:

247 = 3πr³

Dividing both sides by 3π,

r³ = 82.33

Taking the cube root of both sides,

r ≈ 4.38

Now, use the value of r and find the height of the cylinder, using the equation h = 3r.

Therefore, the height of the cylinder is:

h = 3 × r

h = 3 × 4.38

h ≈ 13.14

So, The value of height of the cylinder is 13.14 units.

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the answer to your equation is x=2

To show your work I’ll do

37x-14=60

37x=60+14

37x=74

X=2

Answer:

11

Step-by-step explanation:

The solution to the equation [tex]\rm log_4 (5x + 9) = 3\\\\[/tex] is x = 11.

In mathematics, the logarithmic function is an inverse function to exponentiation.

The given equation is;

[tex]\rm log_4 (5x + 9) = 3\\\\[/tex]

The solution to the equation is determined in the following steps given below.

[tex]\rm log_4 (5x + 9) = 3\\\\ Taking \ exponetital \ on \ both \ sides\\\\5x+9 =4^3\\\\5x+9=64\\\\5x=64-9\\\\5x=55\\\\x=\dfrac{55}{5}\\\\x=11[/tex]

Hence, the solution to the equation [tex]\rm log_4 (5x + 9) = 3\\\\[/tex] is x = 11.

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It was reflected. this is bc it is the same shape, just flipped.

Answer:Reflection about the y-axis followed by a translation to the left by 2 units

Step-by-step explanation:I took the test

considering the total figure,

lenght = 7+x

height =10

Area= L×B

106=10(7+x)

106=70+10x

106-70=10x

36=10x

x=3.6cn

To calculate the size of x when the area of a compound shape is 106 cm², specific information about the shape's dimensions or the relationship of x to the area is needed. Once we have a formula, we can solve for x and express it to the correct number of significant figures.

The student is tasked with calculating the size of x given that the area of a compound shape is 106 cm². To solve for x, we must have a description of the shape with its dimensions, or a formula relating x to the area. Without additional information about the shape or how x is defined within the context of this shape, we cannot provide a numerical answer.

If x represents a length or width of a rectangular part of the compound shape, we might use the formula for the area of a rectangle, A = l×w, to solve for x by dividing the area by the known dimension. However, if the compound shape includes circles, triangles, or other geometric figures, different area formulas would be required. Once we have the correct formula, we would isolate x and calculate its value ensuring the answer is given to the correct number of significant figures as specified by the area given by the question.

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Answer

2/5

Hoped this helped

Answer:

2/5

Step-by-step explanation:

3

____

7 1/2

3

____

15/2

= 2/5

Answer:

x = 20; the labeled angles are 80° and 100° ⇒ the last answer

Step-by-step explanation:

* Lets revise some facts about a parallelism

- If two lines are parallel, and intersected by a line, there are 3

 pair of angles are formed

1) Alternate angles equal in measures (corners of Z letter)

2) Corresponding angles equal in measure (corners in F letter)

3) Interior supplementary angles their sum is 180° (corners of U letter)

* Now lets solve the problem

∵ There are two parallel lines intersect by another line

- The formed U letter

∴ The labeled angles are interior supplementary angles

∴ Their sum = 180°

∴ 5x + 4x = 180° ⇒ add the like terms

∴ 9x = 180° ⇒ divide both sides by 9

∴ x = 20°

* Lets find the measure of the labeled angles

∵ The measure of one of them is 4x°

∴ Its measure = 4(20) = 80°

∵ The measure of the other is 5x°

∴ Its measure = 5(20) = 100°

Answer:

0.4437

Step-by-step explanation:

First we will define independent events.

Two events are said to be independent when the occurrence of one event doesn't affect the probability of occurrence of second event.

Given

P(Q)=0.87

and  

P(R)=0.51

The probability of independent events is given as:

P(Q∩R)=P(Q)*P(R)

=0.87*0.51

=0.4437

So the probability of Q and R is 0.4437 ..  

Answer:

The rate of decline is [tex]r=0.1455[/tex]  or [tex]r=14.55\%[/tex]

Step-by-step explanation:

we know that

The  formula to calculate the depreciated value  is equal to  

[tex]D=P(1-r)^{t}[/tex]  

where  

D is the depreciated value  

P is the original value  

r is the rate of depreciation  in decimal  

t  is Number of Time Periods  

in this problem we have  

[tex]P=\$19,400\\D=\$12,105\\t=3\ years[/tex]

substitute in the formula above and solve for r

[tex]\$12,105=\$19,400(1-r)^{3}[/tex]  

Simplify

[tex](12,105/19,400)=(1-r)^{3}[/tex]  

[tex](1-r)=\sqrt[3]{(12,105/19,400)}[/tex]

[tex]r=1-\sqrt[3]{(12,105/19,400)}[/tex]

[tex]r=0.1455[/tex]

Convert to percentage

[tex]r=14.55\%[/tex]

bearing in mind that perpendicular lines have negative reciprocal slopes hmmmmm wait a second, what's the slope of that line above anyway?

[tex]\bf y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{1}{3}} x+5\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

therefore any perpendicular line to that

[tex]\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-\cfrac{1}{3}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{3}{1}}\qquad \stackrel{negative~reciprocal}{+\cfrac{3}{1}\implies 3}}[/tex]

so, we're really looking for the equation of a line whose slope is 3 and runs through (1, -10)

[tex]\bf (\stackrel{x_1}{1}~,~\stackrel{y_1}{-10})~\hspace{10em} slope = m\implies 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-10)=3(x-1) \\\\\\ y+10=3x-3\implies y=3x-13[/tex]

Answer:

use M=(Y-Y)/(X-X)format and see what you get

Step-by-step explanation:

so it should be

-10-3/1-1

Im not sure how to explain this without having the proper set up

(2,2) = (x,y)

(1,1) = (x,y)

so if we set this up right

-13/0....

Yhats how to get the answer, but it said I have to put words so ignore this.

Option: A is the correct answer.

              A.  -0.903

The formula to calculate correlation coefficient r is given by:

[tex]r=\dfrac{n\sum xy-(\sum x)(\sum y)}{\sqrt{n(\sum x^2)-(\sum x)^2}\sqrt{n(\sum y^2)-(\sum y)^2}}[/tex]

        x          y         xy          x²            y²        

        4         23        92        16           529

        5          12        60        25          144

        8          10        80        64          100

        9          9          81         81            81

        13         2          26       169           4

-------------------------------------------------------------------------

∑     39       56        339      355         858

Also n=5 ( as there are 5 data points )

Hence, we get:

[tex]r=\dfrac{5\times 339-39\times 56}{\sqrt{5\times 355-(39)^2}\times \sqrt{5\times 858-(56)^2}}\\\\\\r=\dfrac{-489}{\sqrt{254}\times \sqrt{1154}}\\[/tex]

[tex]r=-\dfrac{489}{541.40188}=-0.9032[/tex]

     Hence,  the r-value of the following data, to three decimal places is:

                               A.  -0.932

Answer: A. -0.903

Step-by-step explanation: I just did this on A P E X and got it right

Answer:

Correct choice is A. [tex]y=x-8[/tex].

Step-by-step explanation:

pick any two points from the table say (0,-8) and (2,-6)

Now we we can use both points to find the equation of line.

slope [tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{-6--8}{2-0}=\frac{2}{2}=1[/tex]

now plug slope m=1 and any point say (0,-8) into point slope formula

[tex]y-y_1=m\left(x-x_1\right)[/tex]

[tex]y--8=1\left(x-0\right)[/tex]

[tex]y+8=1\left(x\right)[/tex]

[tex]y+8=x[/tex]

[tex]y=x-8[/tex]

Hence correct choice is A. [tex]y=x-8[/tex].

The answer is:

The total height of the 17-story building is 74.29 meters.

This a unit convertion problem. We know that there is a 17-story building and the height of each story, we need to convert the units and then, calculate the total height.

We need to use the following convertion factors:

[tex]1meter=100cm[/tex]

[tex]1decimeter(dm)=10cm[/tex]

Now, converting the given units we have:

Meters to centimeters:

[tex]1meter=100cm[/tex]

[tex]4*1meter=4*100cm[/tex]

[tex]4m=400cm[/tex]

Decimeters to centimeters:

[tex]1decimeter(dm)=10cm[/tex]

[tex]2*1decimeter(dm)=2*10cm[/tex]

[tex]2dm=20cm[/tex]

So, we know that one story measures 4 meters, 2 decimeters (dm) and 17 centimeters (cm), and if we want to calculate the total height of the 17-story building, we need to use the following equation:

[tex]TotalHeight=17*(HeightDimension)[/tex]

[tex]TotalHeight=17*(400cm+20cm+17cm)=17*(437cm)=7429cm[/tex]

Now,

Converting from centimeters to meters, we have:

[tex]7429cm=7429cm*\frac{1m}{100cm}=74.29m[/tex]

Hence, we have that the total height of the 17-story building is 74.29 meters.

Have a nice day!

Answer:

h = 74.29 meters

Step-by-step explanation:

We know that a decimeter is equal to 10 cm.

and 100 cm equals 1 meter,

Then, each floor measures 4 meters + 2 decimetres + and 17 centimeters

This is:

4m + 20cm + 17cm

= 4m + 37cm

= 4m + 0.37 m

= 4.37 m.

If the building has 17 floors then its height is:

[tex]h = 17 * 4.37\\[/tex]

h = 74.29 meters

Answer: [tex](y-7)=-4(x+2)[/tex]

Step-by-step explanation:

The equation of a line in point slope form with slope m and passing through point (a,b) is given by :-

[tex](y-b)=m(x-a)[/tex]

Given : The slope of the line : m= -4

The point from which line is passing : (a,b) =(-2,7)

Then , the point  slope equation of a line with slope -4 that contains the point (-2,7) will be :-

[tex](y-7)=-4(x-(-2))\\\\\Rightarrow\(y-7)=-4(x+2)[/tex]

Answer:the red box

Step-by-step explanation:

the red box since  1.26 is greater than 1.026, because the tenths place has the most power after a decimal. and the tenths place in the green box of sugar is 2, while the tenths place in the red box of sugar is 0 and 2 is greater than 0

hope this helps!

Answer:

Green box contains more sugar.

Step-by-step explanation:

Consider the provided information.

Ashley found 2 boxes of sugar in the kitchen.

The green box says 1.26 kg and the red box says 1.026 kg.

we need to find which box contains more sugar.

To find this we will first check the digit at ones place.

Both the digit has 1 at the ones place. So now check the digit at tenths place.

1.26 has 2 at tenths place while 1.026 has 0 at tenths place.

As we know 2 is greater than 0, thus the number 1.26 is greater than 1.026.

Hence, green box contains more sugar.

Karina needs to pay $35 for 8 weeks to pay the amount of her earrings.

A unit rate is defined as a ratio that compares the first quantity to one unit of the second quantity.

Given that, Karina put a $300 pair of earrings on lay away by making a 10% down payment and agreeing to pay $35 a week.

10% of 300 = 300x10/100 = 30

Therefore, she has already paid $30 for her earrings

Amount she needs to pay = 300-30 = $270

Let x be the total weeks in which she pays her remaining amount,

Establishing the equation,

35x = 270

x = 270/35

x = 7.71 ≈ 8

Hence, Karina needs to pay $35 for 8 weeks to pay the amount of her earrings.

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Answer:

It would be the same as the similar polygons length. so 6:11.

Step-by-step explanation:

Hope i have helped you!

For this case we have the following expression:

[tex]3 + 2 \sqrt {2} + \frac {1} {3 + 2 \sqrt {2}} =[/tex]

We rationalize the second term multiplying by:

[tex]\frac {3-2 \sqrt {2}} {3-2 \sqrt {2}}:[/tex][tex]\frac {1} {3 + 2 \sqrt {2}} * \frac {3-2 \sqrt {2}} {3-2 \sqrt {2}} = \frac {3-2 \sqrt {2} } {9-6 \sqrt {2} +6 \sqrt {2} -4 (\sqrt {2}) ^ 2} = \frac {3-2 \sqrt {2}} {9-4 * 2} = \frac {3-2 \sqrt {2}} {1} = 3-2 \sqrt {2}[/tex]

So, we have:

[tex]3 + 2 \sqrt {2} + 3-2 \sqrt {2} = 3 + 3 = 6[/tex]

Answer:

6

Hey there! :)

y = 3/4x - 2

To find the slope and y-intercept, simply use slope-intercept form to understand this.

Slope-intercept form is : y = mx + b ; where m = slope, b = y-intercept.

Therefore, you must ask yourself : which value is in the "m" spot and which value is in the "b" spot in our given equation?

Using this logic, we can come to the conclusion that :

Slope = 3/4 & Y-intercept = -2

~Hope I helped! :)

Answer:

The vertex form is y = -3(x + 2)² + 10

Step-by-step explanation:

* Lets revise how to put the quadratic in the vertex form

- The general form of the quadratic is y = ax² + bx + c, where

 a , b , c are constants

# a is the coefficient of x²

# b is the coefficient of x

# c is the numerical term or the y-intercept

- The vertex form of the quadratic is a(x - h)² + k, where a, h , k

 are constants

# a is the coefficient of x²

# h is the x-coordinate of the vertex point of the quadratic

# k is the y-coordinate of the vertex point of the quadratic

- We can find h from a and b ⇒ h = -b/a

- We find k by substitute the value of h instead of x in the general form

 of the quadratic

 k = ah² + bh + c

* Now lets solve the problem

∵ y = -3x² - 12x - 2

∵ y = ax² + bx + c

∴ a = -3 , b = -12

∵ h = -b/2a

∴ h = -(-12)/2(-3) = 12/-6 = -2

- Lets find k

∴ k = -3(-2)² - 12(-2) - 2 = -3(4) + 24 - 2 = -12 + 24 - 2 = 10

* Lets writ the vertex form

∵ y = a(x - h)² + k

∵ a = -3 , h = -2 , k = 10

∴ y = -3(x - -2)² + 10

∴ y = -3(x + 2)² + 10

* The vertex form is y = -3(x + 2)² + 10

ANSWER

The vertex form is:

[tex]y = - 3{(x + 2)}^{2} +10[/tex]

EXPLANATION

The given equation is:

[tex]y = - 3 {x}^{2} - 12x - 2[/tex]

[tex]y = - 3( {x}^{2} + 4x) - 2[/tex]

We add and subtract the square of half the coefficient of x.

[tex]y = - 3( {x}^{2} + 4x + {2}^{2} ) - - 3( {2})^{2} - 2[/tex]

We simplify to get,

[tex]y = - 3{(x + 2)}^{2} + 3(4)- 2[/tex]

[tex]y = - 3{(x + 2)}^{2} +10[/tex]

This is in the vertex form.

[tex]\bf ~\hspace{5em} \textit{ratio relations of two similar shapes} \\\\ \begin{array}{ccccllll} &\stackrel{\stackrel{ratio}{of~the}}{Sides}&\stackrel{\stackrel{ratio}{of~the}}{Areas}&\stackrel{\stackrel{ratio}{of~the}}{Volumes}\\ \cline{2-4}&\\ \cfrac{\stackrel{similar}{shape}}{\stackrel{similar}{shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array}~\hspace{6em} \cfrac{s}{s}=\cfrac{\sqrt{Area}}{\sqrt{Area}}=\cfrac{\sqrt[3]{Volume}}{\sqrt[3]{Volume}} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf \cfrac{\textit{sphere A}}{\textit{sphere B}}\qquad \stackrel{\stackrel{sides'}{ratio}}{\cfrac{1}{4}}\qquad \qquad \stackrel{\stackrel{sides'}{ratio}}{\cfrac{1}{4}}=\stackrel{\stackrel{volumes'}{ratio}}{\cfrac{\sqrt[3]{288}}{\sqrt[3]{v}}}\implies \cfrac{1}{4}=\sqrt[3]{\cfrac{288}{v}}\implies \left( \cfrac{1}{4} \right)^3=\cfrac{288}{v} \\\\\\ \cfrac{1^3}{4^3}=\cfrac{288}{v}\implies \cfrac{1}{64}=\cfrac{288}{v}\implies v=18432[/tex]

[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b \qquad \begin{cases} c=\stackrel{hypotenuse}{13}\\ a=\stackrel{adjacent}{12}\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{13^2-12^2}=b\implies \sqrt{25}=b\implies 5=b[/tex]

Answer:

5

Step-by-step explanation:

a^2 + b^2 = c^2

13 is the hypotenuse because it is the longest side.

12^2 + b^2 = 13^2

144 + b^2 = 169

subtract the 144 from both sides to isolate the variable you are solving for

b^2 = 25

Square root both sides to solve

b = 5

[tex]\sigma_A=\sum_{1}^{3}=180\Longrightarrow\sum{\frac{180}{3}}=\boxed{60}[/tex]

Answer: all together a triangle = 180 degrease that means if there are three angles then each one would = 60 degrease each

Final answer:

The recursive rule for the geometric sequence 1/2, -2, 8, -32 is defined by the first term a1 = 1/2, and for n > 1, the nth term is given by aₙ = aₙ₋₁ × (-4), illustrating the sequence's common ratio of -4.

Explanation:

The question asks for the recursive rule for a geometric sequence: 1/2, -2, 8, -32. To find the recursive rule, we need to determine the common ratio by dividing each term by its preceding term. For instance, dividing -2 by 1/2 gives -4, and similarly dividing 8 by -2 also gives -4. This shows that the common ratio (r) is -4. A geometric sequence can be defined recursively by specifying the first term and the rule for obtaining each term from the previous one.

The first term, represented as a1, is 1/2. Given that the common ratio is -4, the recursive rule for finding the nth term (an) can be expressed as aₙ = aₙ₋₁ ×  r, where n > 1. Substituting the common ratio, we get aₙ = aₙ₋₁ ×  (-4) for n > 1.

Answer: -2 is the correct answer

Step-by-step explanation: All the other values in the options represent an input (x) instead of an output f(x). Al the values in the chart that are on your left are x inputs and all the values on the right are f(x) outputs Leaving you with -2 as the only correct answer.

Hope this helps have a good one!

The value is an output of the function is -2.

What is function?

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Here -6,4 and 7 are in column of x which they are the inputting value for function f(x).

The number -2 is on column of f(x) which means it is output corresponding to the input value 3.

Hence, -2 is the output value for f(x).

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X equals negative B and plus and minus the square root of b squared minus 4ac all over 2a

Answer:

Step-by-step explanation:

The quadratic formula is as follows:

[tex]\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]

It is used for factoring second degree polynomials ONLY!!!  That's why it's called the quadratic formula...quadratics are second degree polynomials.  The a, b and c are found in the standard form of a quadratic equation:

[tex]y=ax^2+bx+c[/tex]

Just plug them into the formula, but be careful with the "-4ac".  Sometimes that mistakenly leads to an unwanted negative sign under you radical.  Unless you are dealing with imaginary numbers, your solutions should be real.

[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{1}{~~y^{-\frac{1}{4}}~~}\implies y^{\frac{1}{4}}[/tex]

Answer:

Option b. 12

Step-by-step explanation:

This exercise asks us to find the derivative of a function using the definition of a derivative.

Our function is [tex]f(x) = x^{3}[/tex]. Therefore:

[tex]f(2+h) = (2+h)^{3}[/tex]

[tex]f(2) = (2)^{3} = 8[/tex]

Then:

[tex]\lim_{h \to \0} \frac{f(2+h)-f(2)}{h}=\lim_{h \to \0} \frac{(2+h)^{3}-8}{h}[/tex]

Expanding:

[tex]\lim_{h \to \0} \frac{(2+h)^{3}-8}{h} =\lim_{h \to \0} \frac{8+ h^{3} +6h(2+h) -8}{h} =\lim_{h \to \0} \frac{h^{3} +6h(2+h)}{h}[/tex]

[tex]\lim_{h \to \0} \frac{h^{3}+ 6h(2+h)}{h} =\lim_{h \to \0} h^{2} + 6(2+h) [/tex]

Now, if x=0:

[tex]\lim_{h \to \0} \frac{f(2+h)-f(2)}{h} = (0)^{2} +6(2+0) = 12[/tex]

Multiply the first bracket by 2

Multiply the second bracket by 5

6-8a+5a-35

6-35-8a+5a ( just rearranging)

-29-3a or -3a-29 same answer just rearranging.

Answer is -29-3a or -3a-29

Answer:

2(3-4a)+5(a-7)

=6-8a+5a-35

=-3a-29

Step-by-step explanation: