Use technology to create an appropriate model of the data.
(-2,-9), (0,-3), (1,0), (3,6), (5,12)
f(x) = – 3x - 3
f(x) = 3x - 3
f(x) = - 3x + 3
f(x) = 3x + 3

Answer:

The required inequality is [tex]y<\frac{2}{3}(x)-1[/tex].

Step-by-step explanation:

From the given graph it is clear that the related line passes through the points (-3,-3) and (3,1).

If a line passes through two points, then the equation of line is

[tex]y-y_1=\frac{y-y_1}{x-x_1}(x-x_1)[/tex]

The equation of related line is

[tex]y-(-3)=\frac{1-(-3)}{3-(-3)}(x-(-3))[/tex]

[tex]y+3=\frac{4}{6}(x+3)[/tex]

[tex]y+3=\frac{2}{3}(x+3)[/tex]

[tex]y+3=\frac{2}{3}(x)+2[/tex]

Subtract 3 from both the sides.

[tex]y=\frac{2}{3}(x)+2-3[/tex]

[tex]y=\frac{2}{3}(x)-1[/tex]

The equation of related line is [tex]y=\frac{2}{3}(x)-1[/tex]. The related line is a dotted and the shaded region is below the line. So, the sign of inequality is <.

The required inequality is

[tex]y<\frac{2}{3}(x)-1[/tex]

Therefore the required inequality is [tex]y<\frac{2}{3}(x)-1[/tex].

Answer:

  the associative property

Step-by-step explanation:

The associative property of addition lets you move the parentheses without changing the order of the operands.

Answer:

B

Step-by-step explanation:

Euler's formula for polyhedra states that

F + V - E = 2

where F is faces, V is vertices and E is edges

Substitute the values given and solve for F, that is

F + 13 - 26 = 2

F - 13 = 2 ( add 13 to both sides )

F = 15 → B

The correct option is (B) 15

Euler's formula states the relationship between the number of Faces, Edges and Vertices of any polyhedron. It is given as

[tex]F+V=E+2[/tex]

where

[tex]F=\text{number of faces}\\V=\text{number of vertices}\\E=\text{number of edges}[/tex]

From the question

[tex]V=13,E=26[/tex]

so

[tex]F+V=E+2\\F+13=26+2\\F=26+2-13=15[/tex]

Learn more about Euler's formula here: https://brainly.com/question/12716048

For this case we have that by definition of trigonometric relations of a rectangular triangle, that the sine of an angle is given by the opposite leg to the angle on the hypotenuse of the triangle. While the tangent of the same angle is given by the leg opposite the angle on the leg adjacent to the angle.

Then, according to the figure we have:

[tex]sin (B) = \frac {7} {25} = 0.28\\tg (B) = \frac {7} {24} = 0.2917[/tex]

Answer:

[tex]sin (B) = \frac {7} {25}\\tg (B) = \frac {7} {24}[/tex]

Answer:

[tex]\text{sin}(B)=\frac{7}{25}[/tex]

[tex]\text{tan}(B)=\frac{7}{24}[/tex]

Step-by-step explanation:

We have been given a right triangle. We are asked to find the [tex]\text{sin}(B)[/tex] and [tex]\text{tan}(B)[/tex] for our given triangle.

We know that sine relates opposite side of right triangle to its hypotenuse.

[tex]\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]

We can see that AC is opposite side to angle B and  AB is hypotenuse of the given triangle.

[tex]\text{sin}(B)=\frac{AC}{AB}[/tex]

[tex]\text{sin}(B)=\frac{7}{25}[/tex]

We know that tangent relates opposite side of right triangle to its adjacent.

[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]

We can see that AC is opposite side to angle B and  BC is adjacent side of the angle B.

[tex]\text{tan}(B)=\frac{AC}{BC}[/tex]

[tex]\text{tan}(B)=\frac{7}{24}[/tex]

Answer:

  32. -30°

  33. 45° or 135°

  34. 90°

Step-by-step explanation:

The table below shows a short list of trig function values.

32. -tan(x) = tan(-x)

33. -cos(x) = cos(180°-x)

34. sec(x) = 1/cos(x). 1/0 is "undefined".

The values shown above are the ones that are in the range of the inverse trig functions: arctan (-90°, 90°), arccos [0°, 180°], arcsec [0°, 90°)∪(90°, 180°].

[tex]32.\quad tan\theta=-\dfrac{\sqrt3}{3}\\\\.\qquad \dfrac{sin\theta}{cos\theta}=-\dfrac{\sqrt3}{3}\\\\\text{Since there is no "3" on the Unit Circle, un-rationalize the denominator:}\\.\qquad \dfrac{sin\theta}{cos\theta}=-\dfrac{\sqrt3}{3}\bigg(\dfrac{\sqrt3}{\sqrt3}\bigg)\implies \dfrac{sin\theta}{cos\theta}=-\dfrac{3}{3\sqrt3}=-\dfrac{1}{\sqrt3}\\\\\implies sin\theta =\pm\dfrac{1}{2}\quad and \quad cos\theta = \pm\dfrac{\sqrt3}{2}\quad and \text{ coordinate is in Quadrant 2 or 4}[/tex]

[tex]\text{Look on the Unit Circle (below) for coordinates }\bigg(\dfrac{-\sqrt3}{2},\dfrac{1}{2}\bigg)\ and\ \bigg(\dfrac{\sqrt3}{2},\dfrac{-1}{2}\bigg)\\\\\bold{Answer:}\large\boxed{150^o\ and\ 330^o\implies \dfrac{5\pi}{6}\ and\ \dfrac{11\pi}{6}}[/tex]

[tex]33.\quad cos^2\theta=\dfrac{1}{2}\\\\\\.\qquad \sqrt{cos^2\theta}=\sqrt{\dfrac{1}{2}}\\\\\\.\qquad cos\theta=\pm\dfrac{1}{\sqrt2}\\\\\\\text{Rationalize the denominator:}\\.\qquad cos\theta=\pm\dfrac{1}{\sqrt2}\bigg(\dfrac{\sqrt2}{\sqrt2}\bigg)\implies cos\theta=\pm\dfrac{\sqrt2}{2}\\\\\\\text{Look on the Unit Circle to find when }cos\theta=\dfrac{\sqrt2}{2}\ and\ \dfrac{-\sqrt2}{2}[/tex]

[tex]\bold{Answer:}\large\boxed{45^o, 135^o, 225^o, 315^o\implies \dfrac{\pi}{4}, \dfrac{3\pi}{4}, \dfrac{5\pi}{4}, \dfrac{7\pi}{4}}[/tex]

[tex]34.\quad sec\theta=\text{unde fined}\implies sec\theta=\dfrac{1}{0}\\\\\\.\qquad \dfrac{1}{cos\theta}=\dfrac{1}{0}\implies cos\theta=0\\\\\\\text{Look on the Unit Circle to find when }cos\theta=0\\\\\bold{Answer:}\large\boxed{90^o\ and\ 270^o\implies\dfrac{\pi}{2}\ and\ \dfrac{3\pi}{2}}[/tex]

Answer:

an = 15 (1/5)^(n-1)

Step-by-step explanation:

In a geometric series, each term is multiplied by a common ratio to get the next term.  Such that:

an = a₁ (r)^(n-1)

Here, the first term, a₁, is 15.  The common ratio, r, is 1/5, because each term is divided by 5 to get the next term.  So:

an = 15 (1/5)^(n-1)

Your answer is correct, well done!

I think this is an example of it

Answer:

y = 3.4

Step-by-step explanation:

Given 2 secants and a tangent drawn to the circle from an external point then

The square of the measure of the tangent is equal to the product of the external part of the secant to the entire secant.

Using the secant with measure y + 11, then

y(y + 11) = 7²

y² + 11y = 49 ( subtract 49 from both sides )

y² + 11y - 49 = 0 ← in standard form

with a = 1, b = 11 and c = - 49

Using the quadratic formula to solve for y

y = ( - 11 ± [tex]\sqrt{11^2-4(1)(-49)}[/tex] ) / 2

  = ( - 11 ± [tex]\sqrt{121+196}[/tex] ) / 2

  = ( - 11 ± [tex]\sqrt{317}[/tex] ) / 2

y = [tex]\frac{-11-\sqrt{317} }{2}[/tex] or y = [tex]\frac{-11+\sqrt{317} }{2}[/tex]

y = - 14.4 or y = 3.4

However y > 0 ⇒ y = 3.4 ( nearest tenth )

Answer:

9% + 5%

Step-by-step explanation:

Answer:

$1644.

Step-by-step explanation:

We have been a typical household in the United States has an average after-tax income of $41,100. We are asked to find how much more is spent on insurance/pensions than on health care.

We have been given that 5% is spent on health care and 9% is spent on insurance/pensions. This means that 4% (9%-5%) is more on insurance/pensions than on health care.

Now, we need to find 4% of $41,100.

[tex]\text{Amount more spent on insurance/pensions than on health care}=\frac{4}{100}\times \$41,100[/tex]

[tex]\text{Amount more spent on insurance/pensions than on health care}=4\times \$411[/tex]

[tex]\text{Amount more spent on insurance/pensions than on health care}=\$1644[/tex]

Therefore, $1644 is more spent on insurance/pensions than on health care.

Answer: Second Option

[tex]P =0.00476[/tex]

Step-by-step explanation:

The probability sought is calculated by calculating the quotient between the number of possible ways to select 4 seniors from a group of 4 seniors among the number of ways to select 4 seniors from a group of 10 people.

So:

[tex]P =\frac{4C4}{10C4}[/tex]

Where

[tex]nCr = \frac{n!}{r!(n-r)!}[/tex]

is the number of ways in which a number r of people can be selected from a group of n people

Then

[tex]P =\frac{\frac{4!}{4!(4-4)!}}{\frac{10!}{4!(10-4)!}}\\\\\\P =\frac{1}{\frac{10!}{4!(10-4)!}}\\\\P =\frac{1}{210}\\\\P=0.00476[/tex]

Answer:

It is unlikely

Step-by-step explanation:

The probability of a sticky dart landing in the green section of the board, assuming that it lands on the board is possible but very unlikely.

The green section of the board has the least area compare to an other section of the board. Therefore, the dark is unlikely to land in this section.

Answer:

it is unlikey

Step-by-step explanation:

the possibility of the sticky dart landing on the green part is unlikley

Answer:

c(m)<=45+0.4m

Step-by-step explanation:

A linear inequality involves a linear function. It contains one of the symbols of inequality. It exactly looks like a linear equation,with the inequality sign replacing the equality sign.

According to the statement Nancy has negotiated a special rate and the maximum charge is $45.00 per day with the addition of $ 0.40 per mile.

So,

a linear inequality that models the total cost of the daily rental as a function of the total miles driven,m is:

c(m)<=45+0.4m

Answer:

see explanation

Step-by-step explanation:

Using the coefficients of the polynomial and evaluating for h = - 3

- 3 | 1   - 4   - 9   36

      ↓   - 3   21   - 36

      -------------------------

       1   - 7   12   0 ← remainder

Since remainder is 0 then (x + 3) is a factor, so

y = (x + 3)(x² - 7x + 12)

To factor the quadratic

Consider the factors of the constant term (+ 12) which sum to give the coefficient of the x- term (- 7)

The factors are - 4 and - 3, since

- 4 × - 3 = + 12 and - 4 - 3 = - 7, then

x² - 7x + 12 = (x - 4)(x - 3), and

y = (x + 3)(x - 4)(x - 3)

Answer:

45 feet

Step-by-step explanation:

This is a classic right triangle trig problem.  We have a reference angle, which is the angle made between the ground and the belt, of 32 degrees.  The height up the side of the barn, which is the side across from the reference angle, is 24 feet.  Which of our trig ratios relates side opposite to the hypotenuse?  It's the sin ratio, so let's set it up and solve for the length of the belt, which is the hypotenuse of the right triangle.

[tex]sin(32)=\frac{24}{x}[/tex]

Doing some algebraic acrobatics that with we get

[tex]x=\frac{24}{sin(32)}[/tex]

Plug that into your calculator in degree mode and you'll get 45.28991.  Rounded to the nearest foot is 45 feet.

The length of the conveyor is approximately 45 feet.

The subject of the question is Mathematics, and it deals with determining the length of a conveyor belt that makes an angle with the horizontal. This type of problem involves trigonometry, specifically the use of sine, cosine, or tangent functions to find the length of the hypotenuse of a right-angled triangle.

To find the length of the conveyor belt, we consider the belt as the hypotenuse of a right-angled triangle, with the vertical height of the barn door as the opposite side, and the angle given as the angle between the belt (hypotenuse) and the ground (adjacent side).

The height of the barn door is 24 feet, and the angle between the belt and the ground is 32 degrees. We can use the sine function (sin) since we have the opposite side and need to find the hypotenuse (length of the conveyor belt).

The formula to find the length (L) of the conveyor belt is:

L = height / sin(angle)

L = 24 feet / sin(32 degrees)

L = 24/0.5299

L = 45.29 feet

Solve the inequality for x:

5x - 3 ≤ 7x +7

Subtract 7x from each side:

-2x -3 ≤ 7

Add 3 to each side:

-2x ≤ 10

Divide both sides by -2, also when dividing  both sides of an inequality you flip the direction of the inequality sign:

x ≥ -5

The dot will be on -5, because the inequality includes equal to, the dot is solid and is greater than, the arrow will point to the right.

The correct answer is D.

Answer:

The graph  attached below is for r=2+ 2sin θ where θ=pi

Step-by-step explanation

The coordinates in a polar equation are written as (r,θ)

r= radius and θ is the angle

⇒⇒⇒ so this mean we rotate θ radians and of the size r units

In our case assume θ=[tex]\pi[/tex] where 0≤θ≤2[tex]\pi[/tex]

Answer:

8% difference I think.

Step-by-step explanation:

72 - 64 = 8.

The temperature increase from 64 degrees to 72 degrees represents a 12.5% increase. You calculate this by dividing the difference in temperature by the original temperature and then multiplying by 100.

To calculate the percent increase in temperature from 64 degrees to 72 degrees, you subtract the original temperature from the new temperature and divide by the original temperature. Then, multiply the result by 100 to get the percentage.

Here is the calculation:

Percent Increase = ((New Temperature - Original Temperature) / Original Temperature) × 100

Percent Increase = ((72 - 64) / 64) × 100

Percent Increase = (8 / 64) × 100

Percent Increase = 0.125 × 100

Percent Increase = 12.5%

Therefore, the temperature has increased by 12.5%.

The answer is:

The correct option is:

C) [tex]4^{3}*4^{4}=4^{7}[/tex]

To solve the problem, we need to remember the product of powers with the same base property, the property is defined by the following relation:

[tex]a^{m}*a^{n}=a^{m+n}[/tex]

If we are multiplying two or more powers with the same base, we must keep the base and add/subtract the exponents.

So, we are given the expression:

[tex]4^{3}*4^{4}[/tex]

We can see that both powers have the same base (4), so solving we have:

[tex]4^{3}*4^{4}=4^{4+3}=4^{7}[/tex]

Hence, we have that the correct option is:

C) [tex]4^{3}*4^{4}=4^{7}[/tex]

Have a nice day!

Answer:

The correct answer is option C

4^7

Step-by-step explanation:

Points to remember

Identities

xᵃ/xᵇ = x⁽ᵃ ⁻ ᵇ⁾

xᵃ * xᵇ = x⁽ᵃ ⁺ ᵇ⁾

x⁻ᵃ = 1/xᵃ

To find the correct option

It is given that,

4^3 * 4^4

⇒ 4³ * 4⁴

By using identities we can write,

4³ * 4⁴  = 4⁽³ ⁺ ⁴)

 = 4⁷

Therefore the correct option is option C.  4^7

[tex]a = \frac{b \times h}{2} [/tex]

33.6 × 2 = b×h

67.2 = b×h

h=4

67.2÷4 =b

16.8=b

answer: b=16.8inches

No. Asher figured that just subtracting 4 from 4x, which is 64, would get him the value of x. However, since 64=4x, one needs to divide 64 by the number of x's to get x's value. 64/4= 16, which is the value of x.

The method of solving the equation by asher is; Incorrect because she is supposed to divide directly and not subtract.

We are told that she wants to solve the equation;

4x = 64

Now, she decided to subtract 4 from both sides to get the value of x. That will not be correct because she is meant to divide both sides by the coefficient of x to get the value of x.

4x = 64

x = 64/4

x = 16

Read more about Equations at; https://brainly.com/question/1214333

A half life means that half the sample decays.

If the sample size is 1 , then after one half life there would be x  * 1/2 =  1/2 of the sample left.

For the 2nd half life, multiply 1/2 by 1/2 to get 1/4.

So after 2 half lives, there is 1/4 of the sample left, which means 3/4 of the sample decayed.

The answer is 3/4

It takes 90 days for a single drop of water to travel the Mississippi River's entire length.

Hence  margin of error for population proportion is option c which is 0.6

MoE refers to estimated point value that tells us how much difference is there from actual value.

critical value * SD of population

Given max sample proportion =0.28 and min sample proportion=0.16

Hence we can directly calculate MOE by subtracting both = 0.28=0.16=0.6

which is option no. c

Hence option c is 0.6 which is correct.

learn more about margin of error https://brainly.com/question/24289590

#SPJ2

Answer:

0.6 is the answer

Final answer:

Ken will require 150 cm² of decorative paper to cover his triangular prism souvenir. This is calculated by determining the area of the two triangular bases and the three rectangular sides and adding them together.

Explanation:

To calculate the total area of decorative paper Ken requires to cover his triangular prism souvenir, we need to consider the area of all the sides of the prism. The prism has two triangular bases and three rectangular sides.

For the triangular bases, we use the formula for the area of a triangle: A = (base × height) / 2. Since we have two bases with base=5 cm (a) and height=6 cm (h), the total area for the two triangular bases would be

2 × (5 cm × 6 cm) / 2 = 30 cm²

For the three rectangular sides, the dimensions are height (h=6 cm) and width (w=10 cm), plus two sides with a side length equal to the height of the triangular base. The area of each rectangle is given by length × width. Therefore, the total area for the rectangular sides is:

2 × (5 cm × 6 cm) + (10 cm × 6 cm) = 60 cm² + 60 cm² = 120 cm²

Adding the areas of the bases and the sides, we obtain the total area of decorative paper needed:

Total area = Area of bases + Area of sides = 30 cm² + 120 cm² = 150 cm²

Therefore, Ken will require 150 cm² of decorative paper to cover his triangular prism souvenir.

Answer:

Step-by-step explanation:

Let's calculate the probability of selecting a blue shirt from a total of 10 shirts:

It's 5/10, or 0.5, which stems from there being 5 blue shirts among the 10 Jeremy owns.  50/50 is not a standard way of expressing probability; 0.5 is proper.

Answer:

No, because each group of n items does not have an equal chance of being selected.

Step-by-step explanation:

Answer:

2 : 3

Step-by-step explanation:

Calculate the ratio of corresponding sides

AB : LM = 4 : 6 = 2 : 3

AD : LO = 2 : 3

DC : ON = 4 : 6 = 2 : 3

CB : NM = 2 : 3

The ratio of corresponding sides is 2 : 3

Answer:

Option B.

Step-by-step explanation:

we have

[tex](x-3)^{2}=5[/tex]

take square root both sides

[tex](x-3)=(+/-)\sqrt{5}[/tex]

[tex]x=3(+/-)\sqrt{5}[/tex]

Answer:0.1

Step-by-step explanation:

Answer:

314 m³

Step-by-step explanation:

The volume (V) of a cone is calculated using the formula

V = [tex]\frac{1}{3}[/tex]πr²h

where r is the radius and h the perpendicular height

To find h use the right triangle from the vertex to the midpoint of the base and the radius.

Using Pythagoras' identity on the right triangle

where the slant height is the hypotenuse, then

h² + 5² = 13²

h² + 25 = 169 ( subtract 25 from both sides )

h² = 144 ( take the square root of both sides )

h = [tex]\sqrt{144}[/tex] = 12, hence

V = [tex]\frac{1}{3}[/tex]π × 5² × 12

   = π × 25 × 4 = 100π ≈ 314 m³

11125 ft2. I hope i got it right