What is the value of y in the product of powers below?

[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).

To learn more about Function, click:

brainly.com/question/12431044

#SPJ3

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: (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

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:

[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:

The answer is D. 4r^6.

<3

-Callie

Step-by-step explanation:

Answer:

D. 4r^6.

Step-by-step explanation:

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:

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:

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,

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:

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:

5

Step-by-step explanation:

he can mow one lawn in 24 min

2 hours=120 min

120÷24=5

Bonsoir,

Combien fait 87$ augmenté de 200% ?

87 $ x 200/100 = 174 $ d'augmentation,  

174 + 87 = 261 $

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

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:

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..

Answer:

jk(x) = -16x^2 -12x+10

Step-by-step explanation:

j(x) = -4x+2

k(x) = 5+4x

jk(x) = (-4x+2) (5+4x)

FOIL

-4x*5 +-4x*4x +2*5 +2*4x

Combine like terms

-20x-16x^2 +10+8x

-16x^2 -12x+10

jk(x) = -16x^2 -12x+10

Put the answer into a calculator;

-√17 = -4.123105626

√17 = 4.123105626

Round to the nearest tenth by looking at the 2nd digit after the decimal point. If it is 5 or greater, round up, otherwise round down.

-√17 = 4.123105626

2 is less than 5, so we leave it as it is.

-√17  ≈ -4.12

√17 = 4.123105626

2 is less than 5, so we leave it as it is.

√17 = 4.12

v ≈ -4.12, 4.12

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:

[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:

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:

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:

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.

➷ Add 24 to both sides:

x^2 + 10x + 24

Find two values that multiply to make 24 but add to make 10

As you will notice, this is 6 and 4

Now factorize it:

(x + 4)(x + 6)

The values of x would be the opposite of what is in the parenthesis

Therefore x = -4 or x = -6

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

x= -6                    x=-4

Step-by-step explanation:

x2 + 10x = −24

Add 24 to each side

x2 + 10x+24 = −24+24

x2 + 10x +24=0

Factor

(x+6) (x+4) = 0

Using the zero product property

x+6 = 0             x+4 = 0

x+6-6 = 0-6      x+4-4 =0-4

x= -6                    x=-4

-- #34 is choice-C .

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

4 · x^4 · x^4 · y

4 x^8 y

In words: four times x to the eighth times y

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:

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:

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