If f(x) = 3x - 2 and g(x) = 2x + 1, find (f + g)(x).
​

Answer:

He is incorrect because the scale factor is 1/3.

Step-by-step explanation:

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

In this problem

Triangles CA'B' and CAB are similar

The pre-image is the triangle CAB

The image is the triangle CA'B'

therefore

The scale factor is equal to

CB'/CB

we have

CB'=2 units

CB=2+4=6 units

substitute

CB'/CB=2/6=1/3

therefore

He is incorrect because the scale factor is 1/3.

Answer:

Inverse of a relation

Reasoning:

the inverse of a function is a full function, this is just a set of pairs.  A set of pairs, or relation, where x and y values interchange are inverse of the relation.  A one to one function is when a function's inverse is also a function (doesn't have more than one y for each x) which can be tested for on the normal function's graph with a HORIZONTAL line test.  A normal parabola isn't one to one.  An onto function has to do with every value being used (I don't remember much about them, but once again this isn't a function, but rather a specific set of pairs/data)

Example of inverse of a relation:

Relation: {(0,5), (3,2)}

Inverse: {(5,0), (2,3)}

Example of inverse of a function:

f(x)=5x

f-1(x)=x/5

Example of a one to one function:

f(x)=x+1

Answer:

For Plato the inverse of a function

Step-by-step explanation:

Answer:

Step-by-step explanation:

The point-slope form of an equation of a line:

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

m - slope

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

=====================================

We have the points C(3, -5) and D(6, 0).

Substitute:

[tex]m=\dfrac{0-(-5)}{6-3}=\dfrac{5}{3}[/tex]

use (6, 0):

[tex]y-0=\dfrac{5}{3}(x-6)[/tex]

Convert to the standard form [tex]Ax+By=C[/tex]:

[tex]y=\dfrac{5}{3}(x-6)[/tex]       multiply both sides by 3

[tex]3y=5(x-6)[/tex]            use the distributive property

[tex]3y=5x-30[/tex]       subtract 5x from both sides

[tex]-5x+3y=-30[/tex]          change the signs

[tex]5x-3y=30[/tex]

Answer:

5x-3y=30

Step-by-step explanation:

took the unit test yall and got it right.

Answer:

Step-by-step explanation:

To move the graph 6 units to the right, subtract 6 in the absolute value.

y=|x+5-6|

To move it up, add 2 outside the absolute value.

y=|x+5-6|+2

Now remove the absolute values since x>1.

y=x+5-6+2

y=x+1

[tex]\bf \begin{array}{ccll} \stackrel{x}{\textit{sprayed times}}&\stackrel{f(x)}{\textit{left termites}}\\ \cline{1-2} 1&12000\left( \frac{1}{4} \right)^1\\\\ 2&12000\left( \frac{1}{4} \right)^2\\\\ 3&12000\left( \frac{1}{4} \right)^3\\\\ x&12000\left( \frac{1}{4} \right)^x\\ \end{array}[/tex]

Answer:

the answer is C

Step-by-step explanation:

Answer:

20/3 or 6 2/3

Step-by-step explanation:

Please mark brainliest and have a great day!

Answer: 28/3

7/3 x 4

=28/4

= 9&1/3

[tex]S_n=\dfrac{a_1+a_n}{2}\cdot n\\a_1=3\\d=3\\a_n=99\\n=?\\\\a_n=a_1+(n-1)\cdot d\\99=3+(n-1)\cdot 3\\3n-3=96\\3n=99\\n=33\\\\S_{33}=\dfrac{3+99}{2}\cdot33=51\cdot33=1683[/tex]

i think the answer to this question would be 1

Answer:

Step-by-step explanation:

[tex]\bold{METHOD\ 1}[/tex]

[tex]\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\text{x-intercept:}\ (x,\ 0).\\\\\text{Susbtitute the coordinates of the points to the formula of a slope}\\\\(-3,\ -4),\ (6,\ 2),\ (x,\ 0):\\\\m=\dfrac{2-(-4)}{6-(-3)}=\dfrac{2+4}{6+3}=\dfrac{6}{9}=\dfrac{6:3}{9:3}=\dfrac{2}{3}\\\\m=\dfrac{0-2}{x-6}=\dfrac{-2}{x-6}\\\\\text{Therefore we have the equation:}\\\\\dfrac{-2}{x-6}=\dfrac{2}{3}\qquad\text{cross multiply}\\\\2(x-6)=(-2)(3)\\\\2(x-6)=-6\qquad\text{divide both sides by 2}\\\\x-6=-3\qquad\text{add 6 to both sides}\\\\x=3[/tex]

[tex]\bold{METHOD\ 2}\\\\\text{Look at the picture.}[/tex]

Mark points in the coordinate system.

Lead a line through these points.

Read x-intercept.

Answer: the answer is D

Step-by-step explanation:

Answer: b would be the correct answer

Step-by-step explanation:

Answer:

y = - 5 x + 6

Step-by-step explanation:

to be parallel it will have the same slope and you solve for b by making a new equation

y = - 5 x  + b

and plugging in the x and y values from your coordinate point in for x and y

you then solve for b which will be 6 and you form the equation

Answer:

Y = -5x +12

Step-by-step explanation:

Answer:

x=-3

Step-by-step explanation:

f(x)=-2(x+3)^2-5

The equation is in the form

f(x) = a(x-h)^2 -k

where (h,k) is the vertex

The h value is also the axis of symmetry

f(x)=-2(x--3)^2-5

The vertex is (-3,-5)

so the axis of symmetry is x=-3

Let m = slope of the line

m = delta y divided by delta x

m = (4 - 2)/(0 - (-9))

m = 2/(0 + 9)

m = 2/9

The slope is 2/9.

Do you know what the answer really means?

Answer:

[tex]{\huge\boxed {\frac{2}{9}}}[/tex]

Step-by-step explanation:

Slope formula:

      ↓

[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]y_2=4\\y_1=2\\x_2=0\\x_1=(-9)\\[/tex]

[tex]\frac{4-2}{0-(-9)}=\frac{2}{9}[/tex]

The slope of the line is 2/9.

2/9 is the correct answer.

I hope this helps you, and have a wonderful day!

Answer:

[tex]\large\boxed{V=\dfrac{2}{9}s^3}[/tex]

Step-by-step explanation:

[tex]\text{The formula of a volume of a pyramid:}\\\\V=\dfrac{1}{3}BH\\\\B-base\ area\\H-height\\\\\text{The base of the pyramid os athe square with side length}\ s.\\\text{Therefore the base area}\ B=s^2.\\\\\text{The height of the pyramid is}\ \dfrac{2}{3}\ \text{that of it's side:}\ H=\dfrac{2}{3}s.\\\\\text{Substitute:}\\\\V=\dfrac{1}{3}(s^2)\left(\dfrac{2}{3}s\right)=\dfrac{2}{9}s^3[/tex]

Answer:

For plato users is OPTION D

Step-by-step explanation:

D. [tex]v=\frac{2}{9} s^{3}[/tex]

Answer:

Center (h,k) is (1,-2) and radius r = 2

Step-by-step explanation:

We need to find the center and radius of the circle of the given equation:

[tex]x^2-2x+y^2+4y+1=0[/tex]

We need to transform the above equation into standard form of circle

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

where(h,k) is the center of circle and r is radius of circle.

Solving the given equation:

[tex]x^2-2x+y^2+4y+1=0[/tex]

Moving 1 to right side

[tex]x^2-2x+y^2+4y=-1[/tex]

Now making perfect square of x^2-2x and y^2+4y

Adding +1 and +4 on both sides of the equation

[tex]x^2-2x+1+y^2+4y+4=-1+1+4[/tex]

Now, x^2-2x+1 is equal to (x-1)^2 and y^2+4y+2 =(y+2)^2

[tex](x-1)^2+(y+2)^2=4[/tex]

Comparing with standard equation of circle:

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

h = 1 , k =-2 and r =2 because r^2 =4 then r=2

So, center (h,k) is (1,-2) and radius r = 2

Answer:

39

Step-by-step explanation:

5x - 1 when x = 8

plug the variable in

5(8) - 1

40 -1

39

Answer:

39

Step-by-step explanation:

5(8) is 40, minus one is 39.

Answer:

15 x - 35 x y

Step-by-step explanation:

5 x (3-7 y)

5 * 3 x - 7 * 5 x y

= 15 x - 35 x y

Answer:

pentagon

Step-by-step explanation:

So at this point, we have a full rotation of 360 degrees round that point. The graph accounts for 36 degrees of that 360 degrees leaving 360-36=324 degrees left to be split between the three polygons at (Around) that point. So 324/3=108.  Now we got to figure out a polygon that has all of it's angles being 108 degrees.

We can usually find that if we know the number of sides of the polygon but we don't but here is the formula 180(n-2)/n=108

Cross multiply gives

108n=180(n-2)

Distribute

108n=180n-360

subtract 180n on both sides

-72n=-360

Divide both sides by -72

giving n=5

So a 5 side polygon is a pentagon

   Three identical regular polygons fitted together at one point are regular Pentagons.

   Measure of the interior angle of a polygon is given by,

Interior angle of a polygon = [tex]\frac{(n-2)\times 180^\circ}{n}[/tex]

Where 'n' = number of sides of the polygon

Let the number of regular polygons fitted together at one point = x

Therefore, sum of one interior angle of all polygons at a point = [tex]\frac{x(n-2)\times 180^\circ}{n}[/tex]

It has been given in the question "36° is the gap left when 3 identical regular polygons have fitted together at a point."

Therefore, sum of interior angles of all polygons joining at a point with the gap = [tex]\frac{3(n-2)\times 180^\circ}{n}+36^\circ[/tex]

Since, sum of angles at a point is always 360°.

[tex]\frac{3(n-2)\times 180^\circ}{n}+36^\circ=360^\circ[/tex]

[tex]\frac{3(n-2)\times 180^\circ}{n}=324^\circ[/tex]

[tex]540n-1080=324n[/tex]

[tex]540n-324n=1080[/tex]

[tex]216n=1080[/tex]

[tex]n=5[/tex]

  Therefore, polygons fitted at one point are Pentagons.

Learn more,

https://brainly.com/question/15307676

Answer:

No solution

Step-by-step explanation:

No values of x exist that make the equation true

Answer:

There are no solutions

Step-by-step explanation:

-7x-10-15x=-22x+83

Combine like terms

-22x -10 = -22x +83

Add 22x to each side

-22x +22x-10 = -22x+22x +83

-10 = 83

This is never true so there are no solutions

Answer:

[tex]500\ cm[/tex]

Step-by-step explanation:

step 1

Find the volume of hollow cylinder

[tex]V=\pi (r2^{2}-r1^{2})h[/tex]

we have

[tex]r2=8\ cm[/tex]

[tex]r1=6\ cm[/tex]

[tex]h=35\ cm[/tex]

substitute

[tex]V=\pi (8^{2}-6^{2})(35)[/tex]

[tex]V=\pi (28)(35)[/tex]

[tex]V=980\pi\ cm^{3}[/tex]

step 2

we know that

The wire is a solid cylinder with the same volume of the hollow cylinder

so

[tex]V=\pi r^{2}h[/tex]

we have

[tex]V=980\pi\ cm^{3}[/tex]

[tex]r=2.8/2=1.4\ cm[/tex] ----> the radius is half the diameter (thickness)

substitute and solve for h

[tex]980\pi=\pi (1.4)^{2}h[/tex]

[tex]980=(1.96)h[/tex]

[tex]h=980/(1.96)=500\ cm[/tex]

Answer:

Part A) [tex]sin(2\theta)=\frac{24}{25}[/tex]

Part B) [tex]cos(2\theta)=0[/tex]

Part C) [tex]tan(2\theta)=-\frac{240}{161}[/tex]

Step-by-step explanation:

Part A) we have [tex]cos(\theta)=-\frac{4}{5}[/tex]

θ is in quadrant 3 ----> the sine is negative

Find [tex]sin(2\theta)[/tex]

we know that

[tex]sin(2\theta)=2sin(\theta)cos(\theta)[/tex]

Remember that

[tex]cos^{2} (\theta)+sin^{2} (\theta)=1[/tex]

substitute

[tex](-\frac{4}{5})^{2}+sin^{2} (\theta)=1[/tex]

[tex](\frac{16}{25})+sin^{2} (\theta)=1[/tex]

[tex]sin^{2} (\theta)=1-\frac{16}{25}[/tex]

[tex]sin^{2} (\theta)=\frac{9}{25}[/tex]

[tex]sin(\theta)=-\frac{3}{5}[/tex] ---> remember that the sine is negative (3 quadrant)

Find [tex]sin(2\theta)[/tex]

we have

[tex]cos(\theta)=-\frac{4}{5}[/tex]

[tex]sin(\theta)=-\frac{3}{5}[/tex]

[tex]sin(2\theta)=2sin(\theta)cos(\theta)[/tex]

substitute

[tex]sin(2\theta)=2(-\frac{3}{5})(-\frac{4}{5})[/tex]

[tex]sin(2\theta)=\frac{24}{25}[/tex]

Part B) we have [tex]cos(\theta)=\frac{\sqrt{2}}{2}[/tex]

θ is in quadrant 1

Find [tex]cos(2\theta)[/tex]      

we know that

[tex]cos(2\theta)=2cos^{2} (\theta)-1[/tex]

substitute

[tex]cos(2\theta)=2(\frac{\sqrt{2}}{2} )^{2}-1[/tex]

[tex]cos(2\theta)=0[/tex]

Part C) we have [tex]sin(\theta)=\frac{8}{17}[/tex]

θ is in quadrant 2 ----> the cosine is negative

Find [tex]tan(2\theta)[/tex]  

we know that

[tex]tan(2\theta)=\frac{2tan(\theta)}{1-tan^{2} (\theta)}[/tex]

Remember that

[tex]cos^{2} (\theta)+sin^{2} (\theta)=1[/tex]

substitute

[tex]cos^{2} (\theta)+(\frac{8}{17})^{2}=1[/tex]

[tex]cos^{2} (\theta)=1-\frac{64}{289}[/tex]

[tex]cos^{2} (\theta)=\frac{225}{289}[/tex]

[tex]cos(\theta)=-\frac{15}{17}[/tex]

Find [tex]tan(\theta)[/tex]  

[tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]

substitute

[tex]tan(\theta)=\frac{(8/17)}{(-15/17)}[/tex]

[tex]tan(\theta)=-\frac{8}{15}[/tex]

Find [tex]tan(2\theta)[/tex]  

[tex]tan(2\theta)=\frac{2tan(\theta)}{1-tan^{2} (\theta)}[/tex]

substitute

[tex]tan(2\theta)=\frac{2(-\frac{8}{15})}{1-(-\frac{8}{15})^{2}}[/tex]

[tex]tan(2\theta)=\frac{(-\frac{16}{15})}{1-(\frac{64}{225})}[/tex]

[tex]tan(2\theta)=\frac{(-\frac{16}{15})}{1-\frac{64}{225}}[/tex]

[tex]tan(2\theta)=\frac{(-\frac{16}{15})}{\frac{161}{225}}[/tex]

[tex]tan(2\theta)=-\frac{240}{161}[/tex]

Answer:

75 degrees

Step-by-step explanation:

This is because all the angles in a triangle are supplementary which means they add up to 180 degrees.   This means that you subtract 180 from the other two angles

Please give Brainliest!!! Thanks! :D

Answer:

C. 75 degrees

Step-by-step explanation:

The angles in a triangle add up to 180 degrees.

You already know the degree of two angles: 70 & 35.

Now, subtract those numbers from 180 to find the degree of the missing angle.

180 - 70 - 35 = 75

So, the answer is C. 75 degrees.

I hope this helps!

Answer:

[tex] ^ 9 C _ 3 ( 0 . 5 ) ^ 3 ( 0 . 5 ) ^ 6 [/tex]

Step-by-step explanation:

We know that Aron flips a penny 9 times and gets exactly 3 heads .

Probability of getting a head or a tail is [tex] \frac { 1 } { 2 } [/tex].

Here, we need to find the probability of getting exactly 3 heads:

[tex]P(x=3)=^9C_3(\frac{1}{2})^3\times \frac{1}{2}^6\\\\P(x=3)=^9C_3(0.5)^3\times (0.5)^6\\\\P(x=3)=\frac{9!}{3!\tiems 6!}\times (0.5)^9\\\\P(x=3)=0.16[/tex]

So the expression representing this situation will be:

[tex] ^ 9 C _ 3 ( 0 . 5 ) ^ 3 ( 0 . 5 ) ^ 6 [/tex]

Final answer:

The probability of getting exactly 3 heads in 9 coin flips is calculated using the binomial probability formula, resulting in approximately 16.40625%.

Explanation:

The probability of getting exactly 3 heads when flipping a penny 9 times involves combinations and binomial probability. The probability of getting a head on any single flip is 50% (or 0.5), and the same is true for getting a tail.

To calculate the probability of getting exactly 3 heads (and therefore 6 tails), we use the binomial probability formula:

P(exactly k heads) = C(n, k) × ([tex]p^k[/tex]) × ([tex](1-p)^(n-k)[/tex])

Where:

Therefore, the probability is:

P(3 heads) = C(9, 3) × (0.5³) × (0.5⁽⁹⁻³)

Calculating C(9, 3) gives us 84 combinations. So the probability is:

P(3 heads) = 84 × (0.5³) × (0.5⁶) = 84 × (0.125) × (0.015625) = 0.1640625 or 16.40625%

Answer:

A. 25°

Step-by-step explanation:

From the diagram, in triangle JKL, JK=KL=7 units. This means triangle JKL is isosceles triangle with base JL.

In isoscels triangle angles adjacent to the base are congruent, so

∠KJL=∠KLJ=25°

Note that ∠KLJ is ∠L, so ∠L=25°

Answer: 25

Step-by-step explanation:

Answer:

can you help me with my answer when your done on my page? vvvvv

Step-by-step explanation:

1. **Separating 90 into Two Parts:**

  - The smaller part is [tex]\( 18 \)[/tex] and the larger part is [tex]\( 72 \)[/tex].

2. **Sum of Three Consecutive Integers:**

  - The three integers (in order) are [tex]\( 17, 18, \)[/tex] and [tex]\( 19 \)[/tex].

1. **Separating 90 into Two Parts:**

  - Let's denote the smaller part as [tex]\( x \)[/tex] and the larger part as [tex]\( 4x \)[/tex].

  - According to the problem, the sum of these two parts equals 90: [tex]\( x + 4x = 90 \)[/tex].

  - Combine like terms: [tex]\( 5x = 90 \)[/tex].

  - Divide both sides by 5 to solve for [tex]\( x \): \( x = 18 \)[/tex].

  - So, the smaller part is [tex]\( 18 \)[/tex] and the larger part is [tex]\( 4 \times 18 = 72 \)[/tex].

2. **Sum of Three Consecutive Integers:**

  - Let's denote the smallest integer as [tex]\( x \)[/tex].

  - The next two consecutive integers would be [tex]\( x + 1 \)[/tex] and [tex]\( x + 2 \)[/tex].

  - According to the problem, the sum of these three integers equals 54: [tex]\( x + (x + 1) + (x + 2) = 54 \)[/tex].

  - Combine like terms: [tex]\( 3x + 3 = 54 \)[/tex].

  - Subtract 3 from both sides: [tex]\( 3x = 51 \)[/tex].

  - Divide both sides by 3 to solve for [tex]\( x \): \( x = 17 \)[/tex].

  - So, the three consecutive integers are [tex]\( 17, 18, \)[/tex] and [tex]\( 19 \)[/tex].

The complete question is here:

Separate 90 into two parts so that one part is four times the other part. What are the sizes of the two parts? The smaller part is _____ and the larger part is ____.

The sum of three consecutive integers is 54. Find the three integers. The three integers (in order) are ____, ____, and ____.

Answer:

53.13

Step-by-step explanation:

Answer:

i got a whole bunch of numbers so you can try them all and see if its right

3279

2764800

30720

Step-by-step explanation:

Answer:

1 5/7 bags of flour to make three batches of cookies

Step-by-step explanatio

12/7 bag of the flour is required to make 3 batches of cookies

Mathematics written statement indicating the equality of 2 expressions. this consists of the sequence of the symbols that is split in to left or right sides joined by the equal sign. For example, 2 + 4 + 5 = 11 is an equation.

When equality holds, the total weight on the each side is the same. Equations often contain terms other than a unknowns. These other terms, which is assumed to be known, is usually known as constants, coefficients and parameters

From the question;

2/7 bag of flour makes 1/2 of a batch of cookies

x bag of flour will make 3 batches of cookies

Mathematically, we cross multiply

2/7 * 3 = 1/2 * x

6/7 = x/2

2 * 6 = 7 * x

12 = 7x

x = 12/7 bag of flour

Learn more about equations here https://brainly.com/question/2263981

#SPJ2

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill&\$6000\\ P=\textit{original amount deposited}\dotfill &\$5000\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years \end{cases}[/tex]

[tex]\bf 6000=5000\left(1+\frac{0.07}{12}\right)^{12\cdot t}\implies \cfrac{6000}{5000}\approx (1.0058)^{12t}\implies \cfrac{6}{5}\approx(1.0058)^{12t} \\\\\\ \log\left( \cfrac{6}{5} \right)\approx \log[(1.0058)^{12t}]\implies \log\left( \cfrac{6}{5} \right)\approx 12t\log(1.0058) \\\\\\ \cfrac{\log\left( \frac{6}{5} \right)}{12\log(1.0058)}\approx t\implies 2.63\approx t\impliedby \textit{about 2 years, 7 months and 16 days}[/tex]

It takes 2 years to have $6000 without depositing additional funds.

Given that,
Amount = $6000
Principal amount = $5000
rate = 7 % compounded monthly
Time = ?

In mathematics it deals with numbers of operations according to the statements.

It is defined as the fee you pay to borrow money or the fee you levy to lend money. Interest is considerable and frequently recalled as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.

[tex]6000/5000 = (1 + 0.07/12)^{12t}\\6/5 = (1.005)^{12t}\\[/tex]
[tex]1.20 = (1.005)^t\\1.20/ = (1.005)^{12t}[/tex]
taking ln both side
ln 1.13 = 12t ln(1.005)
t = ln 13/12 ln 1.005
t = 2.04 year

Thus, it takes 2 years to have $6000 without depositing additional funds.

Learn more about your interest here:

brainly.com/question/1040694

#SPJ2

Answer: 15/4 simplified to 3 3/4 or 3.75

Answer:

2 5/8 ÷ 7/10​  is actually

(21 / 8) * (10 / 7)

(21 / 8) * (10 / 7) = 210 / 56

= 105 / 28

= 3 (21 / 28)

= 3 (3 / 4)

Step-by-step explanation:

Rewrite 100  as  10 ^2 .  x^ 2  −  10 ^2

Since both terms are perfect squares, factor using the difference of squares formula,  a^2 -b^2= (a + b) (a - b) where a = x and b = 10.

(x + 10) (x - 10)