Solve each proportion. 9/8 = x/7

Using translation concepts, it is found that the equation for function g(x) is given by:

g(x) = 4x².

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, the parent function is given by:

f(x) = x².

This function passes through point (1,1). Function g(x) passes through point (1,4), that is, it is horizontally compressed by a factor of 4, hence g(x)  is given by:

g(x) = 4x².

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See

x is decreased by 3 .

and y is increased by 5

So translation is

Hence

So

x will go 3 units right

y will go 5units up

Graph attached

Answer:

Translations

For [tex]a > 0[/tex]

[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]

Parent function:

[tex]f(x)=\left(\dfrac{1}{4}\right)^x[/tex]

Translated 3 units to the right:

[tex]f(x-3)=\left(\dfrac{1}{4}\right)^{x-3}[/tex]

Translated 5 units up:

[tex]f(x-3)+5=\left(\dfrac{1}{4}\right)^{x-3}+5[/tex]

[tex]\implies g(x)=f(x-3)+5[/tex]

Therefore:

[tex]\textsf{g(x) is a translation of f(x) by }\left(\begin{array}{c}3\\5\\\end{array}\right)[/tex]

The price of each comb is $0.5, if the linear equation y = x/2 models the income, in dollars, from selling x plastic combs

An equation is an expression that shows the relationship between two or more number and variables.

Profit = income - cost

Given that the linear equation y = x/2 models the income, in dollars, from selling x plastic combs. Hencee:

Price of each comb = (x/2) / x = 0.5

The price of each comb is $0.5, if the linear equation y = x/2 models the income, in dollars, from selling x plastic combs

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Answer:

$0.50

Step-by-step explanation:

The answer above is correct.

Applying the trigonometric ratios and the triangle sum theorem, the missing lengths and angles are:

AB = 27.2 units

BC = 33.5 units

AC = 50.4 units.

m∠A = 38°

m∠ABC = 112°

The trigonometric ratios, SOHCAHTOA, are used to find the sides or angles of a right triangle.

Find BD using TOA:

tan ∅ = opp/adj

tan 30 = BD/29

BD = tan 30 × 29

BD = 16.7 units

Find AD using TOA:

tan ∅ = opp/adj

tan 52 = AD/16.7

AD = (tan 52)(16.7)

AD = 21.4 units

Find AB using SOH:

sin 52 = 21.4/AB

AB = 21.4/sin 52

AB = 27.2 units

Find BC using CAH:

cos 30 = 29/BC

BC = 29/cos 30

BC = 33.5 units

Find AC:

AC = AD + DC

AC = 21.4 + 29

AC = 50.4 units.

m∠A = 180 - 52 - 90 = 38° (triangle sum theorem)

m∠ABC = 180 - m∠A - m∠C (triangle sum theorem)

m∠ABC = 180 - 38 - 30

m∠ABC = 112°

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Answer:

6

Step-by-step explanation:

Answer:

[tex]6 \frac{2}{13} [/tex]

1.a. Typical number chosen = the median value = 6

b. 27

2. a. 21

b. b. How the scores vary = Range of the scores = 5

c. Mode = 8

d. Median = 8

Range = Highest value - least value

Mode = most occurred data point

Median = center value of the data distribution (typical value of a dot plot).

1. a. Typical number chosen = the median value (center value) on the dot plot = 6

b. The number enrolled = number of student represented on the dot plot + 2 students absent = 25 + 2 = 27.

2. Data given: 5, 5, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 10, 10

a. There are 21 data points given, therefore, the number of students in the afternoon math class is: 21.

b. How the scores vary = Range of the scores = 10 - 5 = 5

c. Mode of the data = 8

d. Median score = 8

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Answer:

Below in bold

Step-by-step explanation:

The sequence is:

3, x, y, 18

If this is an A P then

x - 3 = y - x  

2x - y = 3      (A)  and

y - x = 18 - y

2y - x = 18      (B)

Multiply  (A) by 2:

4x - 2y = 6    (C)

Adding B and C:

3x = 24

x = 8.

and

2y - 8 = 18

2y = 26

y = 13.

So x = 8 and y = 13.

b)   ar + ar^2 = 6ar^3  where a = first term and r = common ratio

Divide by a:

r + r^2 = 6r^3

6r^3 - r^2 - r = 0

r(6r^2 - r - 1) = 0

r(3r  + 1)(2r  - 1) = 0

So the 2 possible values of r

= -1/3 and 1/2.

i) The common ratio is positive so it must be 1/2.

Second term ar = 8

1/2 a = 8

a = 16.

So the first 6 terms are:

16, 8, 4, 2, 1, 1/2.

Answer:

were is the circle to be to be equated

Answer:

see below

Step-by-step explanation:

You will need the hypotenuse   12 ^2 + 9^2 = h^2   h = 15

In a right triangle:

S O H   C A H  T O A

sin s  =   S A H  = Opposite / Hypotenuse =   12/15

cos r = C A H  = Adjacent / Hypotenuse    = 12/ 15

Tan s = T O A =  12 / 9

cos (theta) = cos s  = 9 / 15

Tan r = 9/12

arc cos(theta) = theta = arccos(9/15) = 53.13 degrees

Answer:

B

Step-by-step explanation:

Answer:

50-50

Step-by-step explanation:

If yoiu have 4 and divide it b

Answer:

See below

Step-by-step explanation:

Start with  sin x

  amplitude of 5

      5 sin x

      midline 4

          5 sin (x)  + 4

         period of 4

                   2 pi / 4 = pi/2

                5 sin ( x pi/2 ) + 4

Answer:

1/2

Step-by-step explanation:

The x-intercept is a point on the graph that is located on any point of x but must have a y-value of 0. To find the x-intercept, we must set y in the given equation equal to 0.

8x + 2y = 4

8x + 2(0) = 4

8x = 4

x = 4/8

x = 1/2

Step-by-step explanation:

[tex]2 {}^{2} \times 2 {}^{3} \times 2 {}^{1} \times 3 {}^{ - 1} {}^{ (- 2)} [/tex]

[tex]2 {}^{6} 3 {}^{2} [/tex]

Answer:

Step-by-step explanation:

Comment

A rational number is one that can be expressed as x/y. The first statement is false. All whole numbers are rational. They can always be expressed as x/1

Some rational numbers are not whole numbers. That's true. 4/7 is rational but not whole.

Some irrational numbers are not integers. I'm tempted to say this is true.

pi is irrational and it certainly is not an integer.

Answer

false

true

true.

Answer:

b.

Step-by-step explanation:

The inequality says that x is bigger than 5. The number line shows the arrow starting from 5 and going bigger. Therefore, that number line is correct.

Answer:

Step-by-step explanation:

Step 1: What are the couch's original coordinates?

Step 2: Rotate the couch 90° counterclockwise.

Rule: (x, y) → (-y, x)

Step 3: Now reflect the "new" couch over the y-axis.

Rule: (x, y) → (-x, y)

Step 4: Finally translate the new new" couch right 1 unit and up 5 units.

Rule: (x + 1, y + 5)

Step 5: Use the distance formula to show that the length of EG is the same as the length of E'''G'''.

Distance between E(-5, 4) and G(-1, 3)

[tex]\large \textsf {d = $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$}\\\\\large \textsf {d = $\sqrt{(-1-(-5))^2+(3-4)^2}$}\\\\\large \textsf {d = $\sqrt{(-1+5)^2+(3-4)^2}$}\\\\\large \textsf {d = $\sqrt{4^2+(-1)^2}$}\\\\\ \large \textsf {d = $\sqrt{16+1}$}\\\\\large \textsf {d = $\sqrt{17}$}\\\\\large \textsf {d = ${4.12}$}[/tex]

Distance between E'''(5, 0) and G'''(4, 4)

[tex]\large \textsf {d = $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$}\\\\\large \textsf {d = $\sqrt{(4-5)^2+(4-0)^2}$}\\\\\large \textsf {d = $\sqrt{(-1)^2+4^2}$}\\\\\large \textsf {d = $\sqrt{1+16}$}\\\\\ \large \textsf {d = $\sqrt{17}$}\\\\ \large \textsf {d = ${4.12}$}[/tex]

This means that the length of EG is the same as the length of E'''G'''.

Hope this helps!

Answer:

a. 10 - [tex]\frac{2}{5}[/tex] = [tex]9\frac{3}{5}[/tex] or 9.6

b. 25 - [tex]\frac{3}{25}[/tex]= [tex]24 \frac{22}{25}[/tex] or 24.88

c. 105-[tex]\frac{84}{84}[/tex] = 104.0

d. 170 - [tex]\frac{125}{125}[/tex] = 169.0

Answer:

Correct answer is B. 0.08

Step-by-step explanation:

A) the value of the population proportion of people who would watch the new series is 5 out of 8 viewers, and B) a 99% confidence interval for the population proportion of people who would watch the new series indicates that between 61.87% and 63.13% of viewers will watch the new series.

Given that Netflix is considering a new romcom (romantic comedy) series, and a random sample of 1,000 viewers was selected and 625 viewers indicated they would watch the new series, for A) estimate the value of the population proportion of people who would watch the new series, and B) develop a 99% confidence interval for the population proportion of people who would watch the new series, the following calculations must be made:

A)

625 = 1

1000 = X

1000 / 625 = X

1.6 = X

10 out of 16, or 5 out of 8.

B)

62.5 x 0.99 = 61.875

62.5 x 1.01 = 63.125

Therefore, A) the value of the population proportion of people who would watch the new series is 5 out of 8 viewers, and B) a 99% confidence interval for the population proportion of people who would watch the new series indicates that between 61.87% and 63.13% of viewers will watch the new series.

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Answer:

68 mph

Step-by-step explanation:

80 m/hr * 2 hr = 160 miles

60 m/hr * 3 hr = 180 miles

total miles / total time = average speed

340 miles / 5 hr = 68 m p h

Answer:

the answers is -4 for this exerxises

Answer:

   (i) 126 ways

  (ii)

  (a) 1/126

  (b) 5/14

Step-by-step explanation:

(i) Possible selections

(ii) (a) all girls

(ii) (b) more boys than girls

    2. 4 boys, no girls

⇒ 40 + 5 = 45 ways

⇒ P = 45/126 = 15/42 = 5/14

Since f(x) is a cubic polynomial, it has at most 3 distinct roots. If f(x) has 3 real roots, then f(x) = 0 for more than one instance of x.

But if f(x) is one-to-one, then there must be only one real root and the other two are non-real. Let a + bi and a - bi be these non-real roots and c the single real root; then we can factorize f(x) as

[tex]f(x) = x^3 - kx^2 + 12x + 7 = (x - (a + bi)) (x - (a - bi)) (x - c)[/tex]

Expand the right side to get

[tex]f(x) = x^3 - kx^2 + 12x + 7 = (x^2 - 2ax + a^2+b^2) (x - c)[/tex]

[tex]f(x) = x^3 - kx^2 + 12x + 7 = x^3 - (2a + c) x^2 + (a^2 + 2ac + b^2) x - (a^2c + b^2c)[/tex]

from which it follows that

[tex]\begin{cases}k = 2a + c \\ 12 = a^2+2ac+b^2 \\ 7 = -a^2c-b^2c\end{cases}[/tex]

Since f(x) has only one root, its graph will have no turning points/extrema. If f(x) has a critical point, it must be a saddle point. Differentiating f(x) yields

[tex]f'(x) = 3x^2 - 2kx + 12[/tex]

Solve for the critical point:

[tex]f'(x) = 3x^2 - 2kx + 12 = 0[/tex]

[tex]x^2 - \dfrac{2k}3 x = -4[/tex]

[tex]x^2 - \dfrac{2k}3 x + \dfrac{k^2}9 = \dfrac{k^2}9-4[/tex]

[tex]\left(x - \dfrac k3\right)^2 = \dfrac{k^2}9-4[/tex]

[tex]x = \dfrac k3 \pm \sqrt{\dfrac{k^2}9-4}[/tex]

There is at most one real critical point, so either the square root term vanishes or it produces a non-real number. This happens for

[tex]\dfrac{k^2}9 - 4 \le 0 \implies k^2 \le 36 \implies -6 \le k \le 6[/tex]

So, if f(x) is one-to-one, then

[tex]k \in \left\{\kappa \in \Bbb R \mid -6 \le \kappa \le 6\right\}[/tex]

Answer: f(x) = x + 2

Step-by-step explanation:

A = {1, 2, 3, 4, 5, 6]

B = {3, 4, 5, 6, 7, 8)

for each A, B is 2 more

f(1) = 1 + 2 = 3

f(2) = 2 + 2 = 4

f(3) = 3 + 2 = 5

and so on...

⇒ f(x) = x + 2