A line has the equation y = 3x + 4.
(a) This line has slope 3/1
(b) Any line parallel to this line has slope
(c) Any line perpendicular to this line has

Answer:

[tex]y = \frac{1}{2}x +2[/tex]

Step-by-step explanation:

From the table of function given, you would observe that if you subtract 2 from half of the x-variable values, you'd get the y-variable values.

For example, half of -8 = -4. If you add 2 to -4, you'd get: -4 + 2 = -2. Same applies to other x-values on the table.

Thus, an expression for the function represented by the table values can be written as,

[tex]y = \frac{1}{2}x +2[/tex]

Answer:

[tex] d = \sqrt{113} = 10.63014 [/tex]

Step-by-step explanation:

Distance between the endpoints of the graph, (-3, 3) and (5, -4), can be calculated using distance formula, [tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex].

Where,

[tex] (-3, 3) = (x_1, y_1) [/tex]

[tex] (5, -4) = (x_2, y_2) [/tex]

Thus,

[tex] d = \sqrt{(5 - (-3))^2 + (-4 - 3)^2} [/tex]

[tex] d = \sqrt{(8)^2 + (-7)^2} [/tex]

[tex] d = \sqrt{64 + 49} = \sqrt{113} [/tex]

[tex] d = \sqrt{113} = 10.63014 [/tex]

Answer:

C

Step-by-step explanation:

We know that A is not true because the angle is formed by rays, not line segments. We know this because the ends of the lines are arrowheads, which indicates that they are rays. You might be saying that A is true because BA and BC form the angle but actually, even if you removed points A and C, you would still have the angle. B is not correct because according to the diagram, the vertex is point B, not point A. The vertex of an angle is the common endpoint of the two rays that form the angle, therefore it would be point B. D is not correct because angles can have multiple names, the letters do not have to be in alphabetical order. Therefore, C is correct.

Answer:

331.52 ounces

Step-by-step explanation:

For this problem, we need to know the conversion from gallon to ounces.  The conversion is for every one gallon, there are 128 ounces.  Using this, we simply will perform the conversion.

2.59 Gallons * ( 128 ounces / 1 Gallon) == 331.52 ounces

So in 2.59 gallons, there are 331.52 ounces.

Cheers.

Answer: Hi!

121 ÷ 3 = 40.3

987 ÷ 9 = 109.7

675 ÷ 5 = 135

432 ÷ 7 = 61.7

Hope this helps you!

Answer:

40 1/3

109 2/3

135

61.7

Step-by-step explanation:

Hey there!

Well lets divide all given expressions,

121 ÷ 3 = 40 1/3

987 ÷ 9 = 109 2/3

675 ÷ 5 = 135

432 ÷ 7 = 61.7 rounded to the nearest tenth

Hope this helps :)

Answer:

x = 18

Step-by-step explanation:

ΔABC ≅ ΔDEC

∠ B ≅ ∠E

40 = 2x + 4

-2x = 4 - 40

-2x = -36

2x = 36

x = 36/2

x = 18

Answer:

x = 9.0

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adj/ hyp

cos 39 = 7/x

x cos 39 = 7

x = 7/cos 39

x =9.007316961

x = 9.0

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{29 \: mm}}}}}[/tex]

Step-by-step explanation:

Let the width of a rectangle be 'w'

Length of a rectangle be 4w - 5

Perimeter of a rectangle = 75 mm

First, finding the width of the rectangle ( w )

[tex] \boxed{ \sf{perimeter \: of \: a \: rectangle = 2(length + width)}}[/tex]

[tex] \dashrightarrow{ \sf{75 = 2(4w - 5 + w)}}[/tex]

[tex] \dashrightarrow{ \sf{75 = 2(5w - 5)}}[/tex]

[tex] \dashrightarrow{ \sf{75 = 10w - 10}}[/tex]

[tex] \dashrightarrow{ \sf{10w - 10 = 75}}[/tex]

[tex] \dashrightarrow{ \sf{10w = 75 + 10}}[/tex]

[tex] \dashrightarrow{ \sf{10w = 85}}[/tex]

[tex] \dashrightarrow{ \sf{ \frac{10w}{10} = \frac{85}{10} }}[/tex]

[tex] \dashrightarrow{ \sf{w = 8 .5 \: mm}}[/tex]

Replacing / substituting the value of width of a rectangle in order to find the length of a rectangle

[tex] \sf{length \: of \: a \: rectangle = 4w - 5}[/tex]

[tex] \dashrightarrow{ \sf{4 \times 8.5 - 5}}[/tex]

[tex] \dashrightarrow{ \sf{34 - 5}}[/tex]

[tex] \dashrightarrow{ \sf{29 \: mm}}[/tex]

Length of a rectangle = 29 mm

Hope I helped!

Best regards! :D

Answer:

x = 16.08

Step-by-step explanation:

x - 8.9 = 7.18

Add 8.9 to each side

x - 8.9+8.9 = 7.18+8.9

x = 16.08

Answer:

The piecewise function would be as follows :

[tex]\mathrm{C(g) = \left \{ {{25\:if\: 0 < g < 2} \atop {10g\:if\:g>2}} \right. }[/tex]

Step-by-step explanation:

This piecewise function is composed of one segment, and a ray. Let's start by identifying the properties of this segment.

Segment : As you can see the segment extends from 0 to 2 on the x - axis. This is at y = 25. Therefore our first expression would be 'C(g) = 25 at {0 < g < 2}.'

Ray : As this is ray, we have C(g) = 10g, as the slope is apparently 10. As you can see the rise is 10, over a run of 1, given the points (2, 25) and (3, 35) lie on the plane. The ray starts at the coordinate (2, 25), leaving us with the inequality g > 2.

So now that we have the expressions 'C(g) = 25 at {0 < g < 2}' and 'C(g) = 10g at {g > 2}' we can combine them to create the following piecewise function,

[tex]\mathrm{C(g) = \left \{ {{25\:if\: 0 < g < 2} \atop {10g\:if\:g>2}} \right. }[/tex]

Answer:

Angle of elevation from Kim to the satellite launch = 6.654°

Step-by-step explanation:

The distance from Kim to the satellite launch

= 6 miles

Height of the satellite launch

= 0.7 miles

Angle of elevation from Kim to the satellite launch = b

Tan b = height of satellite/distance from Kim

Tan b= 0.7/6

Tan b= 0.1166667

b = tan^-1 (0.1166667)

b= 6.654°

Angle of elevation from Kim to the satellite launch = 6.654°

Answer:

We conclude that the population mean is greater than 10.

Step-by-step explanation:

The complete question is: A random sample of 10 observations is selected from a normal population. The sample mean was 12 and the sample standard deviation was 3. Using the 0.05 significance level: a. State the decision rule. b. Compute the value of the test statistic. c. What is your decision regarding the null hypothesis [tex]H_0= \mu \leq 10[/tex] and [tex]H_A=\mu >10[/tex].

We are given that a random sample of 10 observations is selected from a normal population. The sample mean was 12 and the sample standard deviation was 3.

Let [tex]\mu[/tex] = population mean

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq 10[/tex]    {means that the population mean is less than or equal to 10}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 10    {means that the population mean is greater than 10}

The test statistics that will be used here is One-sample t-test statistics because we don't know about the population standard deviation;

                             T.S.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~   [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean = 12

             s = sample standard deviation = 3  

            n = sample of observations = 10

So, the test statistics =  [tex]\frac{12-10}{\frac{3}{\sqrt{10} } }[/tex]  ~  [tex]t_9[/tex]

                                    =  2.108  

The value of t-test statistics is 2.108.

Now, at a 0.05 level of significance, the t table gives a critical value of 1.833 at 9 degrees of freedom for the right-tailed test.

Since the value of our test statistics is more than the critical value of t as 2.108 > 1.833, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the population mean is greater than 10.

Answer:

x^2+y

Step-by-step explanation:

simply because you have x squared and a variable y that needs to be added.

Answer:

23

Step-by-step explanation:

18+5=23

The value of AD for the given line segment such that AC = 18 and CD = 5 will be 23.

The line is here! It extends endlessly in both directions and has no beginning or conclusion.

In other words, a line segment is just part of a big line that is straight and going unlimited in both directions.

A line section that can connect two places is referred to as a segment.

As per the given line segment, AC and CD have been drawn below,

Since, AD = AC + CD

AD = 18 + 5 = 23

Hence "The value of AD for the given line segment such that AC = 18 and CD = 5 will be 23".

For more about line segments,

https://brainly.com/question/25727583

#SPJ2

Answer:

512

Step-by-step explanation:

In a geometric sequence, the ratio between the second term and the first term is equal to the ratio between the third term and the second term.

(m² + 4) / m = 16m / (m² + 4)

Solve:

(m² + 4)² = 16m²

m² + 4 = 4m

m² − 4m + 4 = 0

(m − 2)² = 0

m = 2

The first three terms of the geometric sequence are therefore 2, 8, 32.

The common ratio is 4, and the first term is 2.  So the 5th term is:

a = 2 (4)⁵⁻¹

a = 512

Answer:

Approximately 36.5885

Approximately 4.2426

Step-by-step explanation:

Please reference the drawing I've provided (sorry it's kind of awful. Drawing on a computer is hard :(

Problem 1)

So, the trapezoid can be split into a right triangle and a rectangle. To find the perimeter, we just need to find all the side lengths and add them.

We already know the dimensions of the rectangle. So, we need to find the dimensions of the right triangle.

We know that the height is 9 since it's opposite to the rectangle. Importantly, we know that the angle opposite to 9 is 60°.

This means that the other angle is 30°. So, the right triangle is a "special right triangle." In the 30-60-90 triangle, the hypotenuse is 2x, the side opposite to 60° is x√3, and the side opposite to 30° is x.

So, we know that 9 is the side opposite to 60°. Substitute and solve for x:

[tex]9=x\sqrt{3}\\ x=\frac{9}{\sqrt{3} } \\ x=\frac{9\sqrt3}{3}=3\sqrt3[/tex]

So, x is 3√3. This means that the side opposite of angle 30 or d is 3√3.

And since x is 3√3, this means that the hypotenuse is 2(3√3) or 6√3.

Therefore, the perimeter of the figure would be:

[tex]9+6+6+3\sqrt3+6\sqrt3\\=21+9\sqrt3\\\approx36.5885[/tex]

Problem 2:

For the bookcase, we simply need to find the value of c.

The braces that will be built is simply the hypotenuse of the right triangles. Therefore:

[tex]a^2+b^2=c^2\\[/tex]

Plug in 3 for a and b:

[tex]3^2+3^2=c^2\\c^2=9+9=18\\c=\sqrt{18}=\sqrt{9\cdot 2}=3\sqrt2\approx4.2426[/tex]

Therefore, each of the braces will be approximately 4.2426 feet long.

Edit: Grammar

Answer:

[tex]-4.2=q[/tex]

Step-by-step explanation:

To do this you would just add 4.8 to both sides to get rid of the -4.8 so then the equation would look like [tex]-4.2=q[/tex] and that would be our answer.

Answer:

q=-4.2

Step-by-step explanation:

-9 = q - 4.8

Add 4.8 to each side

-9+4.8 = q - 4.8+4.8

-4.2 = q

q=-4.2

Answer:

[tex]\huge \boxed{8t + 56}[/tex]

Step-by-step explanation:

[tex]8(7 + t)[/tex]

[tex]\sf Expand \ brackets.[/tex]

[tex]8(7) + 8(t)[/tex]

[tex]56 + 8t[/tex]

Answer:

Step-by-step explanation:

Since the figure above is a right angled triangle we can use trigonometric ratios to find x

To find x we use tan

tan∅ = opposite/ adjacent

From the question

x is the opposite

10 is the adjacent

Substitute the values into the above formula and solve for x

That's

[tex] \tan(20) = \frac{x}{10} [/tex]

x = 10 tan 20

x = 3.63970

We have the final answer as

Hope this helps you

Answer:

Answer: {4,5}. 13) ∪ . Put the sets together in one large set. {1,2,3,5} ... {2,3,1,5}. There are no duplicates to remove, but I can write this in a nicer order.

Step-by-step explanation:

Answer:

Lol hi emelio

Step-by-step explanation:

Complete question:

The growth of a city is described by the population function p(t) = P0e^kt where P0 is the initial population of the city, t is the time in years, and k is a constant. If the population of the city atis 19,000 and the population of the city atis 23,000, which is the nearest approximation to the population of the city at

Answer:

27,800

Step-by-step explanation:

We need to obtain the initial population(P0) and constant value (k)

Population function : p(t) = P0e^kt

At t = 0, population = 19,000

19,000 = P0e^(k*0)

19,000 = P0 * e^0

19000 = P0 * 1

19000 = P0

Hence, initial population = 19,000

At t = 3; population = 23,000

23,000 = 19000e^(k*3)

23000 = 19000 * e^3k

e^3k = 23000/ 19000

e^3k = 1.2105263

Take the ln

3k = ln(1.2105263)

k = 0.1910552 / 3

k = 0.0636850

At t = 6

p(t) = P0e^kt

p(6) = 19000 * e^(0.0636850 * 6)

P(6) = 19000 * e^0.3821104

P(6) = 19000 * 1.4653739

P(6) = 27842.104

27,800 ( nearest whole number)

Complete Question

Apabila a =2 b = 3 dan c =12 tentukan nilai dari bentuk :

a⁶× b⁴ × c²

(ab)² ×c³

Answer:

1) a⁶× b⁴ × c² = 746496

2) (ab)² ×c³ = 62208

Step-by-step explanation:

a =2, b = 3, c =12

a) a⁶× b⁴ × c²

2⁶× 3⁴ × 12²

= (2 × 2 × 2 × 2 × 2 × 2) × (3 × 3 × 3 × 3) × (12 × 12)

= 64 × 81 × 144

= 746496

b) (ab)² ×c³

(2 × 3)² × 12³

= 6² × 12³

= (6 × 6 )× (12 × 12 × 12)

= 36 × 1728

= 62208

Answer:

Step-by-step explanation:

[tex] \sf{ \frac{a}{9} = - 4}[/tex]

Apply cross product property

⇒[tex] \sf{a = - 4 \times 9}[/tex]

Multiply the numbers

⇒[tex] \sf{a = - 36}[/tex]

Hope I helped!

Best regards!!

Answer:

Step-by-step explanation:

The distance between two points can be found by using the formula

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(0,5) and (8,0)

So the distance between them is

d = 9.4339811

We have the final answer as

Hope this helps you

Answer: y = 4

Step-by-step explanation: If y = x + 2, then the value of y will correspond

to the values that are located in the x-column.

In other words, for the first column, we know that 2 = x.

So if y = x + 2, then y = 2 + 2 or y = 4.

Answer:

4×(-5)=-20

Step-by-step explanation:

Answer:

[tex]\huge \boxed{-20}[/tex]

Step-by-step explanation:

[tex]4*(-5)[/tex]

[tex]\Rightarrow 4* -5[/tex]

Multiplying.

[tex]\Rightarrow -20[/tex]

Complete Question

The complete question is shown on the first uploaded image

Answer:

a

  [tex]P(X > 66) = P(Z> 1 ) = 0.15866[/tex]

b

[tex]P(\= X > 66) = P(Z> 2 ) = 0.02275[/tex]

c

[tex]P(\= X > 66) = P(Z> 10 ) = 0[/tex]

Step-by-step explanation:

From the question we are told that

   The  population mean is  [tex]\mu = 64 \ inches[/tex]

    The standard deviation is  [tex]\sigma = 2 \ inches[/tex]

The probability that a randomly selected woman is taller than 66 inches   is mathematically represented as

    [tex]P(X > 66) = P(\frac{X - \mu }{\sigma } > \frac{ 66 - \mu }{\sigma} )[/tex]

Generally [tex]\frac{ X - \mu }{\sigma } = Z(The \ standardized \ value \ of \ X )[/tex]

So  

      [tex]P(X > 66) = P(Z> \frac{ 66 - 64 }{ 2} )[/tex]

     [tex]P(X > 66) = P(Z> 1 )[/tex]

From the z-table  the value of  [tex]P(Z > 1 ) = 0.15866[/tex]

 So  

       [tex]P(X > 66) = P(Z> 1 ) = 0.15866[/tex]

Considering b

 sample mean is  n  =  4  

Generally the standard error of mean is mathematically represented as

        [tex]\sigma _{\= x} = \frac{\sigma }{\sqrt{4} }[/tex]

=>    [tex]\sigma _{\= x} = \frac{2 }{\sqrt{4} }[/tex]

=>    [tex]\sigma _{\= x} = 1[/tex]

The probability that the sample mean height is greater than 66 inches    

     [tex]P(\= X > 66) = P(\frac{X - \mu }{\sigma_{\= x } } > \frac{ 66 - \mu }{\sigma_{\= x }} )[/tex]

=>   [tex]P(\= X > 66) = P(Z > \frac{ 66 - 64 }{1} )[/tex]

=>  [tex]P(\= X > 66) = P(Z> 2 )[/tex]

From the z-table  the value of  [tex]P(Z > 2 ) = 0.02275[/tex]

=> [tex]P(\= X > 66) = P(Z> 2 ) = 0.02275[/tex]

Considering b

 sample mean is  n  =  100

Generally the standard error of mean is mathematically represented as

        [tex]\sigma _{\= x} = \frac{2 }{\sqrt{100} }[/tex]

=>    [tex]\sigma _{\= x} = 0.2[/tex]

The probability that the sample mean height is greater than 66 inches

   [tex]P(\= X > 66) = P(Z > \frac{ 66 - 64 }{0.2} )[/tex]

=>  [tex]P(\= X > 66) = P(Z> 10 )[/tex]

From the z-table  the value of  [tex]P(Z > 10 ) = 0[/tex]

[tex]P(\= X > 66) = P(Z> 10 ) = 0[/tex]

Answer:

So how many days do we need to solve for?

Step-by-step explanation: