How do i solve this equation 3x2(9x)0=

-- #34 is choice-C .

-- See the picture attached to this answer, for both solutions.

[tex]\bf ~\hspace{10em}\textit{function transformations} \\\\\\ \begin{array}{llll} f(x)= A( Bx+ C)^2+ D \\\\ f(x)= A\sqrt{ Bx+ C}+ D \\\\ f(x)= A(\mathbb{R})^{ Bx+ C}+ D \end{array}\qquad \qquad \begin{array}{llll} f(x)=\cfrac{1}{A(Bx+C)}+D \\\\\\ f(x)= A sin\left( B x+ C \right)+ D \end{array} \\\\[-0.35em] ~\dotfill\\\\ \bullet \textit{ stretches or shrinks horizontally by } A\cdot B\\\\ \bullet \textit{ flips it upside-down if } A\textit{ is negative}[/tex]

[tex]\bf ~~~~~~\textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if } B\textit{ is negative}\\ ~~~~~~\textit{reflection over the y-axis} \\\\ \bullet \textit{ horizontal shift by }\frac{ C}{ B}\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is negative, to the right}\\\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is positive, to the left}\\[/tex]

[tex]\bf \bullet \textit{ vertical shift by } D\\ ~~~~~~if\ D\textit{ is negative, downwards}\\\\ ~~~~~~if\ D\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{ B}[/tex]

now, with that template in mind, let's take a look

[tex]\bf \begin{cases} f(x)=&2^x\\ g(x)=&f(x+k)\\ & f(x-5)\\ &2^{x-5} \end{cases}~\hspace{10em}g(x)=2^{\stackrel{A}{1}(\stackrel{B}{1}x\stackrel{C}{-5})}+\stackrel{D}{0} \\\\\\ \textit{horizontal shift by }\cfrac{C}{B}\implies \cfrac{-5}{1}\implies -5\qquad \qquad \textit{ of 5 units to the right}[/tex]

The graph of g(x) is shifted horizontally 5 units to the right of the graph of f(x).

The correct option is (b).

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).

As per the given data:

We are given 2 functions, and we have to find out the shift in the graph.

f(x) = 2^x

g(x) = f(x+k)

When the value of k = -5 we have to find out the shift in the graph of g(x).

For finding out the shift in the graph of g(x):

g(x) = f(x+k)

By substituting the given value of f(x) = 2^x and k = -5:

g(x) = 2^(x-5)

When y = f(x) is changed to y = f(x - 5) the graph of f(x) shifts 5 units to the right horizontally.

Similarly, for g(x) = 2^(x-5) the graph will shift by 5 units to the right.

Hence, The graph of g(x) is shifted horizontally 5 units to the right of the graph of f(x).

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Answer:

The answer is actually C. 3.5. I just answered this question on a quiz and I got it correct. I'm sorry for the late response but I hope this helps!

Answer:

5

Step-by-step explanation:

he can mow one lawn in 24 min

2 hours=120 min

120÷24=5

QUESTION 1

The given expression is

2+8

The greatest common factor of 2 and 8 is 2.

We can rewrite as: [tex]2+8=2\times1+2\times4[/tex]

Factor to get: [tex]2+8=2(1+4)[/tex]

QUESTION 2

Given: 9-3

Greatest common factor of 9 and 3 is 3.

Rewrite as: [tex]9-3=3\times3-3\times1[/tex]

Factor: [tex]9-3=3(3-1)[/tex]

QUESTION 3

Given: 30+25

Greatest common factor of 30 and 25 is 5.

Rewrite as: [tex]30+25=5\times6+5\times4[/tex]

Factor: [tex]30+25=5(6+4))[/tex]

QUESTION 4.

Given: 35-14

The greatest common factor of 35 and 14 is 7.

Rewrite as:  [tex]35-14=5\times7-2\times7[/tex]

Factor:  [tex]35-14=7(5-2)[/tex]

QUESTION 5

The given expression is 81-18.

The greatest common factor of 81 and 18 is 9.

Rewrite as: [tex]81-18=9\times9-9\times2[/tex]

Factor: [tex]81-18=9(9-2)[/tex]

QUESTION 6

Given: 60+100

The greatest common factor of 60 and 100 is 20.

Rewrite as : [tex]60+100=20\times3+20\times5[/tex]

Factor: [tex]60+100=20(3+5)[/tex]

QUESTION 7

Given: 28-20

The greatest common factor of 28 and 20 is 4.

Rewrite as: [tex]28-20=4\times7-4\times5[/tex]

Factor: [tex]28-20=4(7-5)[/tex]

QUESTION 8

Given: 72+48

The greatest common factor of 72 and 48 is 24.

Rewrite as: [tex]72+48=24\times3+24\times2[/tex]

Factor: [tex]72+48=24(3+2)[/tex]

QUESTION 9

The given expression is [tex]12x+18[/tex].

The greatest common factor of [tex]12x[/tex] and 18 is 6.

Rewrite as; [tex]12x+18=6\times2x+6\times3[/tex]

Factor; [tex]12x+18=6(2x+3)[/tex]

QUESTION 10

Given: [tex]4y+10[/tex]

The greatest common factor of [tex]4y[/tex] and 10 is 2.

Rewrite the expression as; [tex]4y+10=2\times2y+2\times5[/tex]

Factor:  [tex]4y+10=2(2y+5)[/tex]

Answer:

(6, - 4)

Step-by-step explanation:

A translation of 4 units right is equivalent to adding 4 to the x- coordinate

A translation of 3 units up is equivalent to adding 3 to the y- coordinate

(x, y) → (x + 4, y + 3) ← translation rule

Hence

(2, - 7) → (2 + 4, - 7 + 3) → (6, - 4)

Anwser: (−2,−7)→(−2+4,−7−2)=(2,−9)

Explanation: {right 4 units: add 4 to x-coordinate}

down 2 units: subtract 2 from y-coordinate

Answer:

First Column:

T

F

F

F

Second Column:

F

T

T

T

Step-by-step explanation:

I'm assuming ~ means NOT and ^ means AND.

Evaluate the first column using AND logic; both inputs must be true for the output to be true.

Only the first case has both inputs true, so it will be the only one with a true output, the rest are all false.

Next, take the outputs from column one and apply NOT logic; the output will be the inverse of whatever the input was

Since the first case is true, its output will be false. Since the remaining cases are false, their outputs will be all true.

Answer: (Width x = 7) (Length 10)

Step-by-step explanation:

(x+3) + = 34/2

2x + 3 = 17

2x = 14

x = 7 -----------Width

10 ---------------Length

Answer: Width= 7 in.

               Length= 10 in.

Step-by-step explanation:

[tex]l=w+3[/tex]

The perimeter of the rectangle is 34 inches.

[tex]2(w+l)=34[/tex]

substitute

[tex]2(w+w+3)=34[/tex]

[tex]2(2w+3)=34[/tex]

distributive property [tex]a(b+c)=ab+ac[/tex]

[tex]2\cdot 2w+2\cdot 3=34[/tex]

[tex]4w+6=34[/tex]

[tex]4w+6-6=34-6[/tex]

[tex]4w=28[/tex]

divide 4 on both sides

[tex]w=7[/tex]

Width is 7 inches

substitute w=7 in equation [tex]l=w+3[/tex]

[tex]l=7+3[/tex]

[tex]l=10[/tex]

Length is 10 inches

Answer:

20 kg

Step-by-step explanation:

If we want any value in grams to be in kilograms, we divide it by 1000

in this example: 20000/1000

=20 kg

When two events, A and B, are mutually exclusive, the probability that A or B will occur is the sum of the probability of each event. P(A or B) = P(A) + P(B) so you add them

hope this helps :)

Answer:

C

Step-by-step explanation:

A proportional graph is a line. Every line has a slope. The slope is found by subtracting two points as a ratio. The line has points (0,0) and (2,6).

6-0 = 6

2 -0 = 2

The ratio is vertical over horizontal so 6/2 = 3.

The equation is y = 3x.

Answer:

C) [tex]y=3x[/tex]

Step-by-step explanation:

1) Checking the coordinate points (2,6), (4,12),  (6,18), (8,24). And since the Proportionality Constant is given by

[tex]k=\frac{y}{x}[/tex]

[tex]k=\frac{y}{x}=\frac{6}{2}=\frac{12}{4}=\frac{18}{6}=\frac{24}{8}=3[/tex]

Then k=3

2) A Proportional Function is given by:

[tex]y=kx[/tex]

Thus we can state that proportional function rule as:

[tex]y=3x[/tex]

Answer:

[tex]A=\frac{5x^{2}}{6}[/tex]

Step-by-step explanation:

Let's solve this by using the Area formula for a triangle:

[tex]A=\frac{1}{2}bh[/tex]

Base: [tex]\frac{5}{3}x[/tex]

Height: [tex]x[/tex]

Solve for A (Area)

[tex]A=\frac{1}{2}(\frac{5}{3}x)(x)[/tex]

[tex]A=\frac{5x^{2}}{6}[/tex]

Since we do not have a given value for [tex]x[/tex], this is as far as we can condense the equation.

The area would be 5x^2/ 6x

See the image

Answer:

2 sections.

Step-by-step explanation:

Given that number of students that had homework last night = 8

Given that number of students that had not homework last night = 4

Then total number of students = 8+4= 12

Then fraction of students that had not homework last night = 4/12

Alaina used that data to design a spinner with 6 congruent sections.

Then number of sections of Alaina's spinner the represents students who did not have homework = ( 6 section) ( 4/12 fraction)

= 6(4/12)

=24/12

=2

Hence final answer is 2 sections.

Answer:

[tex]\large\boxed{f(-7b)=-35b+10}[/tex]

Step-by-step explanation:

[tex]\text{Put}\ v=-7b\ \text{to the function}\ f(v)=5v+10:\\\\f(-7b)=5(-7b)+10=-35b+10[/tex]

Answer:

9

Step-by-step explanation:

The 4 part of the ratio represents 12 girls

Divide 12 by 4 to find the value of one part of the ratio

[tex]\frac{12}{4}[/tex] = 3 ← value of 1 part of the ratio, hence

Multiply the 3 part of the ratio by 3 to obtain number of boys

3 × 3 = 9 ← number of boys

Answer:9

Step-by-step explanation: it is 3 to 4 so you multiply 4 by 3 you get 12 you multiply 3 by 3 you get 9

Answer:

20cm

Step-by-step explanation:

Answer:

The correct answer is option 2

45 cm

Step-by-step explanation:

It is given a circle with circumference C = 180 cm

To find the length of arc ABC

From the figure we can see that the central angle of arc ABC = 90°

Therefore the arc length = (90/360) * Circumference

Arc ABC  = (90/360) * 180 = (1/4) * 180 = 45

Therefore arc length = 45 cm

The correct answer is option 2

Answer: 113.1

Step-by-step explanation:

first you have to multiply 4/3*pie or 3.14 times 3

4/3 x 3.14 x 3 = 113.1

Answer:

D.

Your doing it for a week..5 days, his cases are 12, but how many cases(c) does he need to sell minus his rent vs what his goal is.

Answer:

see explanation

Step-by-step explanation:

Expand the right side and compare the coefficients of like terms

(5x + 2)(ax² + bx + c)

= 5x(ax² + bx + c) + 2(ax² + bx + c) ← distribute parenthesis

= 5ax³ + 5bx² + 5cx + 2ax² + 2bx + 2c ← collect like terms

= 5ax³ + x²(5b + 2a) + x(5c + 2b) + 2c

For the 2 sides to be equal then like terms must equate, that is

5ax³ = 5x³ ⇒ 5a = 5 ⇒ a = 1

2c = - 6 ⇒ c = - 3

5b + 2a = k

5c + 2b = - 7 ← substitute c = - 3

- 15 + 2b = - 7 ⇒ 2b = 8 ⇒ b = 4

Substitute a = 1, b = 4 into 5b + 2a = k

20 + 2 = k ⇒ k = 22

The required values are

a = 1, b = 4, c = - 3 and k = 22

Answer:

The principal amount was $23,393.45

Step-by-step explanation:

The total amount paid on a 35 year loan was $98,000 at the rate of interest 4.1%

We will calculate Principal amount by this formula

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Where A = amount (98,000)

           P = Principal amount (P)

           r = rate of interest 4.1% (0.041)

           n = number of compounding interest monthly (12)

           t = time (35 years)

[tex]98,000=P(1+\frac{0.041}{12})^{(12)(35)}[/tex]

[tex]98,000=P(1+0.003416)^{(420)}[/tex]

[tex]98,000=P(1.003416)^{(420)}[/tex]

98,000 = P(4.189386)

= 4.189386P = 98,000

P = [tex]\frac{98000}{4.189386}[/tex]

P = 23,392.4494 ≈ $23,392.45

The principal amount was $23,393.45

Answer:

$23,392

Step-by-step explanation:

Use the compound interest formula and substitute the values given: $98,000=P(1+.041/12)[tex]^{12(35)}[/tex]

Simplify using order of operations:

$98,000=P(1.003416667)[tex]^{420}[/tex]

P=$98,000(1.003416667)[tex]^{420}[/tex]

P≈$23,392

Answer:

It's B.

Step-by-step explanation:

A gives a triangle.

B gives a rectangle.

C gives a trapezoid.

D gives a square.

Step-by-step explanation:

the y-axis is the point (-x,y). Reflect over the y = x: When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places. If you reflect over the line y = -x, the x-coordinate and y-coordinate change places and are negated (the signs are changed).

Answer:

The rule for reflection on the x-axis is (x,y) -> (x,-y)

The rule for reflection on the y-axis is (x,y) -> (-y,y)

Step-by-step explanation:

A reflection is a transformation that represents a turn of a figure. The figures can be reflected in a point, a line, or a plane.

A reflection copies each point of a figure to an image through a fixed line. The fixed line is called the reflection line.

Answer:

Step-by-step explanation:

(- 4 - 2)² + (- 4 - 1)² = AC²

(- 6)² + (- 5)² = AC²

36 + 25 = AC²

AC² = 61

AC = √61

AC ~ 7.81 unitário

I hope I helped you.

The distance between points A and C is calculated using the displacement vector ĐAC, resulting in a distance of 4.5 km.

The student's question, 'What is the distance between points A and C', pertains to the calculation of displacement in a vector context within the field of Mathematics. To determine the displacement vector ĐAC, we apply the given information that point C is located three-quarters of the distance from point A to point B. If the full displacement from A to B, denoted as ĐAB, has a magnitude of 6 km, the displacement vector from A to C, which is ĐAC, has a magnitude of 0.75 times 6 km, which equals 4.5 km.

The displacement vector ĐAC is parallel to ĐAB and in the same northeasterly direction, indicating that the distance from A to C is simply 4.5 km. The student can understand that the magnitude of displacement is different from the distance traveled if the path taken is not a straight line; however, in this instance, the path is straight, and therefore, the displacement coincides with the actual distance covered.

To summarize, the distance between points A and C is the magnitude of the displacement vector ĐAC, which is 4.5 km.

Answer:

[tex]y\geq -1[/tex]

Step-by-step explanation:

The inequality has the attached picture as its graph.. The inequality passes through (0,-1) and is a horizontal line. This means the inequality has the form y < b or y > b where b is the y-coordinate. Since the \shading is above the line then the values must be greater than -1. It is also a solid line so the inequality is equal to. The inequality is [tex]y\geq -1[/tex]

Answer:

0 or undefined

Step-by-step explanation:

Answer:

The slope doesn't matter.

Step-by-step explanation:

Since the variable equals a constant, any y value would be perpendicular to x = 3.

So lines perpendicular to x = 3 would be,

4 · x^4 · x^4 · y

4 x^8 y

In words: four times x to the eighth times y

Answer:

C)  12/5

Step-by-step explanation:

Tan = Opposite / Adjacent

So

Tan(Z) = YX /YZ

Given: YZ = 5 and XZ = 13

so

(YZ)^2 = (XZ)^2   - (YZ)^2

= 13^2 - 5^2

= 169 - 25

= 144

YZ = 12

Tan(Z) = YX /YZ

Tan(Z) = 12/5

Answer:

Step-by-step explanation:

There are a couple of ways to do this. You could figure all four terms out and add them, which is likely the simplest way.

One:     6^(1 - 1) = 6^0 =      1

Two:     6^(2 - 1) = 6^1 =      6

Three:   6^(3 - 1) = 6^2 =   36

Four:     6^(4 - 1) = 6^3 =   216

Sum = 259

Answer:

Each side is 25cm long.

Step-by-step explanation:

75/3=25 (This is because each side of an equilateral triangle is equal to each other.) (The perimeter is all sides added together.)

Answer:

equilateral traingle mean all sides are equal..so 75÷3

=25cm

Step-by-step explanation:

its equal....so we just simply just divide..