If A = {even natural numbers) and
B = {odd natural numbers}, which of
the following is true?
Enter a, b, c, d, or e.
a. 39 € A
c. 48 € B
b. An B=0
d. A UB=A

The value of x for which (-1, 4) and (x, -2) make a slope of m = 5/4 is - [tex]\frac{29}{5}[/tex]

The slope of a line is the ratio of the amount that y increases as x increases some amount. Slope tells you how steep a line is, or how much y increases as x increases. The slope is constant (the same) anywhere on the line.

equation of straight line is y = mx + c

when x = -1, y = 4, m = 5/4

so that

4 = -1(5/4) + c

c = 4 + 5/4

4 can be written as fraction as 16/4

c = 16/4 + 5/4

Adding the numerator

c = 12/4

at x = x, y = -2

substituting

-2 = x( 5/4) + 21/4

-2 = 5x/4 + 21/4

-2 = [tex]\frac{5x + 21}{4}[/tex]

cross multiplying

5x + 21 = -8

collect like terms

5x = -8 - 21

5x = -29

x = -29/5

In conclusion, the value of x is -29/5

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The length of the perpendicular line from side AC to point B is approximately 43cm to the nearest whole number using the trigonometric ratio of sine rule.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratio of sine to be used states that for any triangle say ABC, then (a/sinA) = (b/sinB) = (c/sinC) where a,b, and c are the sides.

Considering right-angled triangle ABC, by Pythagoras rule

AC = √(54² + 72²)

AC = √1800

AC = 90°

so using sine rule;

AC/sinB = AB/sinC

90/sin90 = 72°/sinC

C = sin^-1[(72°×sin90°)/90°] {cross multiplication}

C = 53.13°

The new triangle formed has hypotenuse 54cm with the opposite side as the length of the perpendicular line from side AC to point B(which we can call x)

hence;

sinC = x/54

sin53.13° = x/54

x = 54 × sin53.13° {cross multiplication}

x = 43.2cm

Therefore, the length of the perpendicular line from side AC to point B is approximately 43cm to the nearest whole number, by application the trigonometric ratio of sine and it's rule for triangle.

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Answer: 36

Step-by-step explanation:

4 sections are 2,000 lbs or 1 ton

To find the pounds Girard has to build, we know we have 9 tons, therefore if each ton is 2,000 lbs, multiply 2,000 by 9 to get 18,000 lbs to use

2,000 lbs per ton x 9 tons= 18,000 lbs to use

now take the 18,000lbs and divide by 500 to find the number of sections we can build

18,000lbs / 500 pounds per section = 36

36 sections is the answer

The amount of mango juice you need is 8 litres

From the question, we have the following parameters that can be used in our computation:

Orange juice = 3 parts

Mango juice = 6 parts

When these parameters are represented as ratio, we have the following expression

Ratio = Orange : Mango

This is then represented as

Orange : Mango = 3 : 6

When the litres of orange juice is 4, we have

4: Mango = 3 : 6

Express as fraction

Mango/4 = 6/3

Multiply through by 4

Mango = 4 * 6/3

Evaluate

Mango = 8

Hence, the mango juice is 8 litres

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Answer: B. The Total profit made when a person buys a car for $10,000 and sells it for $10,000.

Step-by-step explanation:

Answer A would be wrong since when there is a temperature change from 15 degrees to -15 degrees would lead to an overall change of 30 degrees.

Answer C would be wrong as well since it is decreasing 500 feet in altitude, meaning that there is a negative change in altitude.

Answer D would also be wrong since the train is traveling 35 miles north, then south. That means that even though the train is in the same place that is was before, it traveled a total of 70 miles to return to where it was previously at.

Hope this helps!

The point slope form of the equation of the line that passes through the points (6, -9) and (7, 1) is y - 1 = 10(x - 7)

Linear equation can be represented in different form such as point slope form, slope intercept from, standard form and general form.

The line passes through the points (6, -9) and (7, 1). The point slope form can be represented as follows:

y - y₁ = m(x - x₁)

where

Therefore, let's find the equation of the line that passes through the points (6, -9) and (7, 1).

Let's find the slope.

slope = m = 1 + 9 / 7 - 6

slope = 10 / 1

slope = 10

Therefore,

y - 1 = 10(x - 7)

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The solutions of the absolute value equations are:

1) |3x - 1| - |2x + 5 - 5 + x| = 0

x = 1/6

2) |2*(x + 1) - 4| = |2 - 2*(2 - x)|

x can be any real number.

3) | (x - 2)/4 | - 1/3 = x

This absolute value equation has two solutions, these are:

x = 2/15

x = -10/9

Here we need to solve some absolute value equations, the first one is:

|3x - 1| - |2x + 5 - (5 - x)| = 0

First, we need to simplify the arguments of both absolute values, then we get:

|3x - 1| - |2x + 5 - 5 + x| = 0

|3x - 1| - |3x| = 0

|3x - 1| = |3x|

Now we can remove the absolute value parts, obviusly this is ony true if the right part is negative:

3x - 1 = -3x

-1 = -3x - 3x

-1 = -6x

-1/-6 = x

1/6 = x

That is the solution of the first equation.

2) The second part is:

|2*(x + 1) - 4| = |2 - 2*(2 - x)|

Simplify this:

|2x + 2 - 4| = |2 - 4 + 2x|

|2x - 2| = |2x - 2|

this is true for all values of x, we have the same thing in both sides.

3)

| (x - 2)/4 | - 1/3 = x

|(x - 2)/4| = x + 1/3

We can separate the absolute value part in two equations:

(x - 2)/4 = x + 1/3

(x - 2)/4 = -(x + 1/3)

The first equation gives:

(x - 2) = 4*x + 4/3

x - 4x = 4/3 + 2

-3x = 4/3 + 6/3

x = (10/3)*(-1/3) = -10/9

The second equation gives:

(x - 2)/4 = -(x + 1/3)

(x - 2) = -4*(x + 1/3)

x - 2 = -4x - 4/3

x + 4x = 2 - 4/3

5x = 2/3

x = 2/3/5 = 2/15

This equation has two solutions, x = 2/15 and x =  -10/9

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The rate that Joe’s distance from the start of the path is changing with respect to time, in yards per minute is; 1.91 yards per minute

We are given the equation that represents Joe’s distance from the start of the path as;

D = 4s²/(5s + 10)

where;

D is distance measured in yards.

s is the total number of steps Joe has taken.

When s = 200, we have;

D = 4(200²)/(5(200) + 10)

D = 158.4158 yards

We are old that the constant rate is;

s/t = 100 steps per minute

From conversion rates, we know that , we know that;

1 step = 0.83 yards

Thus; 100 steps per minute = 83 yards per minute

Thus;

83 yards = 1 minute

Time for D = 158.4158 yards is;

158.4158 yards/83 yards per minute = 1.91 minutes

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The surface area of the triangular prism is 1090 metres squared.

A triangular prism  is a polyhedron made up of two triangular bases and three rectangular sides.

Therefore, let's find the surface area of the triangular prism.

Surface area of the triangular prism = bh + l(a + b + c)

where

Therefore,

Surface area of the triangular prism = 16 × 15 + 17(17 + 17 + 16)

Surface area of the triangular prism = 240 + 17(50)

Surface area of the triangular prism =240 + 850

Surface area of the triangular prism = 1090 metres squared

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Answer:

its right

Step-by-step explanation:

Answer: Its right i just got the same question

Step-by-step explanation:

The present age of Melody is 9 and her sister is 24 .

the two digit number is 39

How to find the ages of a person ?

Consider the difference between the individual's birthdate and the present day: days = current day - birth date. Age = (years 365) + (months 31) + days should be replaced with these variations. The individual's age is expressed in days. To get the age in years, divide the outcome by 365.

Let present age of melody be y and her sister age be x

Four years ago  age of Melody be (y - 4) and her sister age be (x - 4)

After six years age of Melody be (y + 6) and her sister age be (x + 6)

∴ [tex]\frac{(x-4)}{4} = (y - 4)[/tex]

[tex]\frac{(x+6)}{2} = (y + 6)[/tex]

The equation becomes

x + 6 = 2y + 12

x = 2y +6  ⇒ (1)

x - 4 = 4y -16

x = 4y - 12 ⇒(2)

Solving (1) and (2)

x - 2y = 6

x - 4y = -12

  2y = 18

    y = 9

Substituting the value of y in eq(1)

x = 2*9 + 6

x = 18 +6

x = 24

Let xy be the two digit number.  

10x + y

The value of this number is 6 less (-6) than five times the unit digit (5y).  So:

10x + y = 5y - 6

The sum of the digits of the 2-digit number is 12:

x + y = 12

So y = 12 - x

Substitute 12-x for y:

10x + y = 5y - 6

10x + 12 - x = 5(12-x) - 6      [Substituted 12-x in place of y]

9x + 12 = 60 - 5x - 6

14x = 42

x = 3

y = 12 - x

  = 12 - 3

  = 9

The two digit number is 39

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Answer:

1 [tex]\frac{19}{20}[/tex] cups

Step-by-step explanation:

[tex]\frac{cookies}{sugar}[/tex] = [tex]\frac{cookies}{sugar}[/tex]

[tex]\frac{5}{\frac{3}{4} }[/tex] = [tex]\frac{13}{x}[/tex]  Cross multiply and solve for x

5x = (13)([tex]\frac{3}{4}[/tex])

5x = [tex]\frac{39}{4}[/tex]  Divide both sides by 5

x = [tex]\frac{39}{4}[/tex]÷5

x = [tex]\frac{39}{4}[/tex] x [tex]\frac{1}{5}[/tex]

x = [tex]\frac{39}{20}[/tex]= 1 [tex]\frac{19}{20}[/tex]

Answer:

[tex]Area = 153.938040026m^2[/tex]

[tex]Circumference= 43.9822971503m[/tex]

Step-by-step explanation:

Area

[tex]Area = \pi r^2\\Area = \pi *7^2\\Area = 49\pi\\Area = 153.938040026[/tex]

Circumference

[tex]C = 2\pi r\\C = 2\pi*7\\C= 14\pi\\C=43.9822971503[/tex]

The absolute functions |3x - 1| - |2x + 5 - (5 - x)| = 0,  |2(x + 1) - 4| - 4| = |2 - 2(2 - x)|, |(x - 2) / 4| - 1/3 = x and 1/2|x - 3| - 1 = |x - 3| + 2 have solutions of 1/6, 1, 2/15 and no solutions respectively

An absolute value function is a function in algebra where the variable is inside the absolute value bars. This function is also known as the modulus function and the most commonly used form of the absolute value function is f(x) = |x|, where x is a real number. Generally, we can represent the absolute value function as, f(x) = a |x - h| + k, where a represents how far the graph stretches vertically, h represents the horizontal shift and k represents the vertical shift from the graph of f(x) = |x|. If the value of 'a' is negative, the graph opens downwards and if it is positive, the graph opens upwards.

In the questions given;

1) |3x - 1| - |2x + 5 - (5 - x)| = 0

x = 1/6

2) |2(x + 1) - 4| - 4| = |2 - 2(2 - x)|

x = 1

3) |(x - 2) / 4| - 1/3 = x

x = 2 / 15

4) 1/2|x - 3| - 1 = |x - 3| + 2

The equation has no solution

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Answer:

Step-by-step explanation:

If f(x)=x²+4 then (fof⁻¹)(x)=(f⁻¹of)(x)=x is proved

A relation is a function if it has only One y-value for each x-value.

Composite functions are when the output of one function is used as the input of another.

If f(x)=x²+4

Then we have to prove f⁻¹of(x)=f⁻¹(f(x)

Let us consider fof⁻¹(x)

f(f⁻¹(x))

x

So (fof⁻¹(x))=x

Now f⁻¹of(x)=f⁻¹(f(x)

=x

Hence, If f(x)=x²+4 then (fof⁻¹)(x)=(f⁻¹of)(x)=x is proved

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The solution of the given expression will be 9/16.

Expressions in maths are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given an expression, [-3*(10+(-7))]²÷[(3-(-9)]²

= [-3*(10+(-7))]²÷[(3-(-9)]² = (-9)²/12²

= 9/16

Hence, The solution of the given expression will be 9/16.

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Answer:

78(0.08n)+78

The answer options might not look exactly like this, it may be in different orders but if all these numbers are there like this it should be right

Step-by-step explanation:

When you are increasing by a percent you always turn the percent to a decimal is a formula

8%=0.08

This can be multiplied by n to show how many years

0.08n

And we multiply this by 78 since it’s 8 percent of this

78(0.08n)

And now we add 78 since the tree starts off as 78

78(0.08n)+78

Also to check when n=0 the height will be 78

78(0.08(0)+78

78(0)+78

78

Hopes this helps please mark brainliest

Answer: 3.2

Step-by-step explanation:

i did this

AP Statistics students generally scored very well on questions about Units 1, 2, and 3, with 18% of students answering all such questions correctly.” “The most challenging units were 4 (Probability, Random Variables, and Probability Distributions) and 5 (Sampling Distributions).

Hope it helps you.

The hardest part of AP stats is Physics 1, AP U.S. History and AP Chemistry.

The course and exam for AP Statistics frequently prove to be difficult, especially for students who have not previously taken algebra II or calculus.

Newtonian mechanics, electrical charge and force, and other subjects are covered in AP Physics 1, which is regarded as one of the hardest AP courses. Students also complete college-level lab experiments and write reports for around 25% of the class period.

In general, AP Statistics students  do find it hard or difficult in "Probability, Random Variables, and Probability Distributions Unit 4 and Unit 5.

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The amount of points of each question in each part are given as follows:

It is stated in the problem that:

Hence the amount of points of each part is the least common multiple of 6 and 8, obtained by factoring by prime factors as follows:

6 - 8|2

3 - 4|2

3 - 2|2

3 - 1|3

1

Hence:

lcm(6,8) = 2³ x 3 = 24.

Meaning that each part was worth 24 points, and the number of questions is given as follows:

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The equation y = 8 does not describe a​ function

A function is an equation that has only one output or answer (y) for every input (x) e.g y = 2x

If we plot y =8 on a coordinate plane, you would see that at the point of (0, 8) is a horizontal line.

Also, no matter the value of the input (x), the value of when of the output (y) will always remain 8. This does not fit the description of a function  

Therefore, the equation y =8 does not  describe a​ function

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Answer: 1. 50 stops.

Step-by-step explanation:

There is 1,000 meters in a Kilometer. So 20,000/400=50

Answer:

1) 50 stops

2) a: 60 meters

   b: 6,000 centimeters

Step-by-step explanation:

A) we have to convert 20k into meters to solve it

To do that we multiply by 1000

20x1000

20,000 meters now we divide by 400 to see how many stops

20,000/400

50 stops

2)

to find perimeter is meters we add all of the sides together

20+10+5+5+15+5

30+10+20

30+30

60 m is the perimeter

Now in centimeters we multiply by 100

60x100

6,000 centimeters

Hopes this helps please mark brainliest

Answer:

See attached file

Step-by-step explanation:

See attached file for the answer!

If you need help with more like these, I would suggest checking out Khan Academy.

They provide great free videos on every topic you could imagine!

Hope this helped!

The equation of the linear relationship in slope-intercept form is: y = 2/3x + 50/3.

The equation in slope-intercept form for a linear relationship can be expressed as y = mx + b, where the slope is m and the y-intercept is b.

Using two points on the graph, (20, 30) and (50, 50), find the slope:

Slope (m) = change in y / change in x = (50 - 30) / (50 - 20)

Slope (m) = 20/30

Slope (m) = 2/3.

Find the y-intercept (b) by substituting m = 2/3 and (x, y) = (20, 30) into y = mx + b:

30 = 2/3(20) + b

30 = 40/3 + b

30 - 40/3 = b

50/3 = b

b = 50/3

Write the equation of the linear equation in slope-intercept form by substituting b = 50/3 and m = 2/3 into y = mx + b:

y = 2/3x + 50/3

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Answer:

1200 dollars

Step-by-step explanation:

1.) Create an equation. If we use x as a variable for the total money, we get [tex]\frac{504}{x}=\frac{42}{100}[/tex] .

2.) By solving this equation, we get 42x = 50400, and x = 1200.

Therefore, their total budget was 1200 dollars.

Yes, the equation:

y = 8

describes a function.

A function is a relation that maps elements x into elements y, such that each element x is mapped into a single value of y.

In this case, we have the equation:

y = 8

So all our points are of the form (x, 8).

Notice that all the inputs x are mapped into a single output y = 8, then this relation is a function.

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Answer:

Chips are $0.80 a bag

A bottle of water is $1.60

A gallon of milk costs $3.80

Step-by-step explanation:

Answer:

$3.80 = cost of one gallon of milk.

$1.60 = cost of one bottle of water.

$0.80 = cost of one snack-size bag of chips.

Step-by-step explanation:

Define the variables:

Total items purchased:

Given information:

Create a system of equations with the given information:

[tex]\begin{cases}3x+4y+7z=23.40\\y=2z\\x=y+2.20\end{cases}[/tex]

Rearrange the second equation to make z the subject:

[tex]\implies z=0.5y[/tex]

Substitute the found expression for z and the third equation into the first equation and solve for y:

[tex]\implies 3(y+2.20)+4y+7\left(0.5y\right)=23.40[/tex]

[tex]\implies 3y+6.6+4y+3.5y=23.4[/tex]

[tex]\implies 10.5y+6.6=23.4[/tex]

[tex]\implies 10.5y=16.8[/tex]

[tex]\implies y=1.60[/tex]

Substitute the found value of y into the third equation and solve for x:

[tex]\implies x=1.60+2.20[/tex]

[tex]\implies x=3.80[/tex]

Substitute the found value of y into the second equation and solve for z:

[tex]\implies 1.60=2(z)[/tex]

[tex]\implies z=0.80[/tex]

Conclusion:

Answer:

[tex] p(x)= -2x^3-4x^2+6x[/tex]

Step-by-step explanation:

We need to write a polynomial with zeroes -3 , 0 and 1 , with a leading coefficient of 2 . We know that if a polynomial has 3 zeroes say [tex]\alpha[/tex] , [tex]\beta[/tex] and [tex]\gamma[/tex] , then the polynomial can we written as ,

[tex]\longrightarrow p(x) = k[ ( x -\alpha)(x-\beta)(x-\gamma)] [/tex]

So , similarly we can write it as;

[tex]\longrightarrow p(x) = -2[ (x -(-3)) (x-0) (x-1)\\[/tex]

Simplify,

[tex]\longrightarrow p(x) = - 2[ (x+3)(x)(x-1) ]\\[/tex]

[tex]\longrightarrow p(x) = -2[ (x^2+3x)(x-1)]\\[/tex]

[tex]\longrightarrow p(x) = -2[ x(x^2+3x)-1(x^2+3x)\\ [/tex]

[tex]\longrightarrow p(x) = -2[ x^3 +3x^2 -x^2-3x ]\\[/tex]

[tex]\longrightarrow p(x)= -2[ x^3 +2x^2 -3x]\\[/tex]

[tex]\longrightarrow\underline{\underline{ p(x)= -2x^3-4x^2+6x }} [/tex]

And we are done!

The proper order from greatest to least is option (C) I, III, IV and II

Convert each term to the decimal form

The first terms is 58/ 67

58 / 67 = 0.87

The second term is 0.58%

Convert the percentage to simple fraction

0.58% = 0.58 / 100

= 0.0058

The third term is 58%

Convert the percentage to simple fraction

58% = 58/100

= 0.58

The fourth term is 5.8%

Convert the percentage to simple fraction

5.8% = 5.8/100

= 0.058

The order from greatest to least is

0.87 > 0.58 > 0.058 > 0.0058

Hence, the proper order from greatest to least is option (C) I, III, IV and II

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The values of l, ll, lll, lV respectively,

→ 58/67, 0.58%, 58%, 5.8%

→ 0.87, 0.0058, 0.58, 0.058

Arranging them in descending order,

→ 0.87 > 0.58 > 0.058 > 0.0058

→ 0.87, 0.58, 0.058, 0.0058

→ l, lll, lV, ll

Therefore, the option (c) is correct.

Answer:

Step-by-step explanation:

[tex]l=w+4[/tex]

[tex]A=l*w\\l=w+4\\A=(w+4)w\\A=w^2+4w[/tex]

[tex]P=2l+2w\\A=4p-4\\A=4(2l+2w)-4\\A=8l+8w-4\\l=w+4\\A=8(w+4)+8w-4\\A=8w+32+8w-4\\A=16w+28[/tex]

[tex]16w+28=A=w^2+4w\\16w+28=w^2+4w\\w^2-12w-28=0\\w^2-14w+2w-28=0\\(w^2-14w)+(2w-28)=0\\w(w-14)+2(w-14)=0\\w+2=0=w-14\\w=-2and14[/tex]

Since w represents a measurement of a physical object in inches, it cannot be negative.  So, [tex]w\neq-2[/tex].  The width of the rectangle is 14 inches.

The length is given as 4 inches more than the width, so the length is 18 inches.

This satisfies all the requirements of the question:

[tex]4P-4=A\\P=2(18)+2(14)=64in\\4P=64in(4)=256in\\A=18in*14in=252in^2\\256-4=252\\252=252[/tex]