Translate the phrase into an algebraic expression.
3 times b

The Horizontal stretch of the function f(x)=3x-9 by a factor of 6 is g(x)=x/2-9 .

The graph of the function y=f(x/a) represents a Horizontal Stretch by a factor of a of the graph y=f(x)    , where a>0 and a≠1 .

To find the horizontal stretch we divide the input by a ,

In the given question

f(x)=3x-9 , is horizontally stretch by a factor of 6.

So we divide the inputs by 6 .

On dividing the inputs by 6 , we get

f(x/6)=3(x*1/6)-9        (...as 3/6=1/2)

Let g(x) represents the horizontal stretch of f(x) by factor 6 , So

g(x)=x/2-9

Therefore , the Horizontal stretch of the function f(x)=3x-9 by a factor of 6 is g(x)=x/2-9 .

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Answer:

y=2x+5y

x=−2

y=.5

Answer: 9

Step-by-step explanation:

Khan Academy

Answer:

- 66

Step-by-step explanation:

Evaluate g(- 4) then substitute the value obtained into f(x) , that is

g(- 4) = - 2(- 4)² = - 2 × 16 = - 32, then

f(- 32) = 2(- 32 - 1) = 2 × - 33 = - 66

1. There is a distance of 14

2. There is a distance of 17

Answer: B. ZX is parallel to CA

Step-by-step explanation:

B is the correct answer because ZX and CA form parallel lines which shows they are parallel to each other.

Answer:

one spool of thread costs $1.89

Step-by-step explanation:

$8.99x3=$26.97

$32.64-$26.97=$5.76

$5.76 divided by 3=$1.89

Answer:

1: yes

2:no

3:yes

Step-by-step explanation:

that's what i know

Answer:

C

Step-by-step explanation:

I inserted 5 for a and c is the correct answer

The number of times the bacterial cell is smaller than the amoeba cell is 7 * 10^-1

The given parameters are:

Bacteria cell = 3 x 10^-6 m

Amoeba cell = 4.5 x 10^-4 m

The number of times (n) is calculated as

n = Amoeba cell/Bacteria cell

This gives

n = (3 x 10^-6 m)/(4.5 x 10^-4 m)

This gives

n = 0.7 * 10^-2

Rewrite as

n = 7 * 10^-1

Hence, the number of times the bacterial cell is smaller than the amoeba cell is 7 * 10^-1

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Answer:

The line should look like: y=5x+4

Step-by-step explanation:

The equation for slope-intercept form is y=mx+b, where m is your slope and b is your y-intercept.

Therefore, if we plug in the given values, our equation should look like the following:

y=5x+4

Answer:

y=5x+4

y=mx+b

Answer: either 14

Step-by-step explanation:

Answer:

The 3rd term is 11

Step-by-step explanation:

The given parameters for the Arithmetic Progression, AP, are;

The ratio of the 7th term to the 10th term = (a + 6·d)/(a + 9·d) = -1

The 16th term = -15 = a + 15·d

The 3rd term= a + 2·d

From the 7th to the 10th term ratio, we have;

a + 6·d = -a - 9·d

2·a = -15·d

-2·a = 15·d...(1)

From the 16th term of the AP, we have;

-15 = a + 15·d =  a + -2·a = -a

a = 15

From equation (1), -2·a = 15·d, we have;

-2·a = -2 × 15 = 15·d

15·d = -2 × 15

d = -2 × 15/15 = -2

d = -2

The 3rd term = a + 2·d = 15 + 2 × -2 = 11

∴ The 3rd term = 11

Answer:

h'(t)= -12

Step-by-step explanation:

h'(t)=d/dt (-6t x 2 + 24 + 6)

h'(t)=d/dt (-12t + 24 + 6)

h'(t)=d/dt (-12t + 30)

h'(t)=d/dt (-12t) + d/dt (30)

h'(t)= -12+0

a) After 2 seconds the rock will be 30 feet above the surface.

b) After 3.83, 0.17 seconds the rock will be 10 feet above the surface.

a) Given that the height = h(t) =30

Plug it in the equation and find t.

[tex]30=-6t^2+24t+6\\6t^2-24t+24=0\\6(t^2-4t+4)=0\\6(t-2)^2=0\\t=2[/tex]

b) Given that the height = h(t) =10

Plug it in the equation and find t.

[tex]10=-6t^2+24t+6\\6t^2-24t+4=0\\2(3t^2-12t+2)=0\\3t^2-12t+2=0[/tex]

Then use the quadratic formula.

[tex]t=\frac{12 \pm \sqrt{(-12)^2-4(3)(2)} }{2(3)}\\ t=\frac{12 \pm \sqrt{120} }{6}\\\\t=3.83, 0.17[/tex]

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Step-by-step explanation:

1.05277777778

hope it helps!

Answer:

1 19/360

Step-by-step explanation:

What we know:

The addends in this equation are 7/8 and 8/45.

First, find the LCM of 8 and 45. Since 8 and 45 don't have any common factors other than 1, just multiply the two numbers.

8 * 45 = 360

After that, find the equivalent fraction for both addends

7/8 * 45/45 = 315/360

8/45 * 8/8 = 64/360

Then, add the two new fractions together, and simplify if needed.

315/360 + 64/360 = 379/360 = 1 19/360

Answer:

85+25x=y

Step-by-step explanation:

if you plug in the number of months for x, and multiply that number by 25, you will get the total amount.

Two standards $6$-sided dice are rolled. The probability that the sum rolled is a perfect square 7/36.

Likelihood is the part of math concerning mathematical portrayals of how likely an occasion is to happen, or how likely it is that a suggestion is valid. Likelihood is the part of science concerning mathematical depictions of how likely an occasion is to happen, or how likely it is that a recommendation is valid. Likelihood and measurements, the parts of science worried about the regulations administering arbitrary occasions, including the assortment, investigation, understanding, and show of mathematical information. While calculation and variable based math were concentrated on by old Greek mathematicians over long time back, the ideas of likelihood just arose in the seventeenth and eighteenth 100 years.

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The altitude of the airplane after it descends is 13,409 feet.

The meaning of ALTITUDE is the vertical elevation of an object above a surface (such as sea level or land) of a planet or natural satellite.

Now it is given that,

Initial Altitude of airplane = 14,382 feet

Then plane ascends = 9,372 feet

So, Altitude of airplane = 14,382 feet + 9,372 feet = 23,754 feet

Again airplane descends = 10,345 feet

So, Altitude of airplane = 23,754 feet - 10,345 feet

⇒ Altitude of airplane = 13,409 feet

Thus, the altitude of the airplane after it descends is 13,409 feet.

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Answer:

It will come out to about $134 even.

Mark brainlyest if this helps

Step-by-step explanation:

9514 1404 393

Answer:

  ∠4 = 45°

Step-by-step explanation:

Angles 1, 2, and 4 are all congruent.

  ∠4 = ∠2

  x +30 = 2x +15

  15 = x . . . . . . . . . . . . . subtract x+15

  x + 30 = 45 = ∠4

Answer:

26

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

6 +6=12

12+3=15

15+2=17

17+4=21

Step-by-step explanation:

a) For a 95% confidence interval we use the formula

First we need to establish the sample proportion

The sample size is

n = 200

and the critical value of z for a 95% confidence interval is

z* = 1.960

This gives us

This gives us an upper confidence limit of

.525 + .069 = .594 or 59.4%

and a lower confidence limit of

.525 - .069 = .456 or 45.6%

b) At this point her supporters wonder what her chances of winning are. 45.6% is below 50%, so she might lose. To find her chances of losing, consider the bell shaped curve

top

Her probability of winning is the area to the right of 50%. We need to turn the 50% into a z score

= -.708

We look up a z-score of -.71 in Table A and get an area of .2389. This is the probability that she will lose. the probability that she will win is

.7611

c) The candidate's supporters would like to be more sure that she will win. They decide to increase the sample size until the 95% confidence interval is only plus or minus 3%. They want to know how large of a sample they will need to get that kind of accuracy. We use the formula for the margin of error.

top

To solve for n, first square both sides to get rid of the radical.

Multiply both sides by n and divide both sides by m2.

For a 95% confidence interval z* = 1.96. We put in our other numbers

= 1064.4433

so they would have to survey 1065 people in order to get a 95% confidence interval that would only stretch up and down 3%.

top

Answer:

14

Step-by-step explanation:

these are similar triangles.

4*y = 7 (one side times cooficient is the side in the other triangle), cooficient (y) = 7/4

8 * 7/4 = solution

= 14

Answer:

The equation in point-slope is [tex]\mathbf{y+5=3(x-6)}[/tex]

Step-by-step explanation:

We need to write the point-slope form of the equation of the line passing through the point (6,-5) and perpendicular to the line [tex]y=-\frac{1}{3}x+4[/tex]

The general form of point-slope is; [tex]y-y_1=m(x-x_1)[/tex]

where m is slope and [tex](x_1,y_1)[/tex] is the point

We need to calculate slope.

We are given equation of line [tex]y=-\frac{1}{3}x+4[/tex] that is perpendicular to the required line.

The equation is given in slope-intercept form [tex]y=mx+b[/tex] where m is slope.

Comparing both equations we get m= -1/3

But we know that when lines are perpendicular their slopes are opposite reciprocal of each other i.e [tex]m=-\frac{1}{m}[/tex]

So, slope of required line is m = 3 (opposite reciprocal of -1/3)

Now, the equation in point-slope form having slope m=3 and point (6,-5) is

[tex]y-y_1=m(x-x_1)\\y-(-5)=3(x-6)\\y+5=3(x-6)[/tex]

So, The equation in point-slope is [tex]\mathbf{y+5=3(x-6)}[/tex]

Answer:

4-12x

Step-by-step explanation:

Answer:

4-12x so c

Step-by-step explanation:

Answer:

0- -3 1/4+1 3/4

Step-by-step explanation:

i belive this is the answer, but im not 100% sure sry if im wrong

Answer:

ya we have to tell its initial value after 11 years it too simple

Answer:

The value after 11 years would be: 2880 us dollars

Step-by-step explanation:

Given the function

[tex]v\left(t\right)=32,000\left(0.80\right)^t[/tex]

The initial value is basically the first output value when the input value = 0.

Here,

The initial value can be obtained by putting t=0 in the function

[tex]v\left(0\right)=32,\:000\left(0.80\right)^0[/tex]

[tex]\mathrm{Apply\:rule}\:a^0=1,\:a\ne \:0[/tex]

[tex]0.8^0=1[/tex]

Thus,

[tex]v\left(0\right)=32000\cdot \:\:1[/tex]

        [tex]=32000[/tex]

Thus, initial value  = v(0) = 32000

Value after 11 years can be obtained by putting t=11 in the function

[tex]v\left(11\right)=32,\:000\left(0.80\right)^{11}[/tex]

as

[tex]0.8^{11}=0.09[/tex]

so the expression becomes

[tex]v(11)=32000\cdot \:\:0.09[/tex]

         [tex]=2880[/tex] us dollars

Thus, the value after 11 years would be: 2880 us dollars

Answer:

17/30

Step-by-step explanation: