Consider sets a = { x | x is a prime number less than 7} and b = { y | y is perfect square of an integer and y is less than 29}. what is the cardinality of the cartesian product of a and b ?

Answer:

B

Step-by-step explanation:

The slope of a line is written as a fraction of the vertical distance to the horizontal distance. The line drops down from (0,1) to (4,-2). This is a vertical distance of -3 and a horizontal distance of 4. The slope if the fraction -3/4.

Answer:

[tex] \sf \: b) \: \frac{ - 3 \: }{ 4} [/tex]

Step-by-step explanation:

The coordinates are,

→ x1 = 4, y1 = -2

→ x2 = -4, y2 = 4

Formula we use,

→ Slope(m) = (y2 - y1)/(x2 - x1)

Now the required slope will be,

→ m = (y2 - y1)/(x2 - x1)

→ m = (4 -(-2))/(-4 - 4)

→ m = (4 + 2)/-8

→ m = 6/-8

→ [ m = -3/4 ]

Hence, the option (b) is correct.

Answer:

For High School A, let  denote the number of students after  years. Define  analogously.

Then  and .

After 6 years the number of students in both high schools would be the same.

Step-by-step explanation:

For High School A, let  denote the number of students after  years. Define  analogously.

Since we start out at 850 students at High School A and it is growing by 35 students every year, we must have that .

Since we start out at 700 students at High School B and it is growing by 60 students every year, we must have that .

Setting the two equations equal to each other, we see that

So after 6 years the number of students in both high schools would be the same.

Answer:

I think it would be 71ft

Step-by-step explanation:

Since the cliff was 85ft and she dove 6 ft underwater, the total distance she traveled was 71ft

Answer:

91 feet

Step-by-step explanation:

Theyre asking for how far he leaped.

The cliff jump above ocean level is 85 ft.

But he went an additional 6 ft underwater.

85+6=91 feet

Answer:

For f (x):

f (x) = (x + 3) ^ 2 - 2

For x = -1

f (-1) = (-1 + 3) ^ 2 - 2

f (-1) = (2) ^ 2 - 2

f (-1) = 4 - 2

f (-1) = 2

For x = 3

f (3) = (3 + 3) ^ 2 - 2

f (3) = (6) ^ 2 - 2

f (3) = 36 - 2

f (3) = 34

AVR = ((34) - (2)) / ((3) - (- 1))

AVR = 8

For g (x):

linear graph with and intercept of negative 3 over 2 and x intercept of 3

y = mx + b

b = -3/2

For me we have:

0 = m (3) - 3/2

3m = 3/2

m = 1/2

The function g (x) is:

g (x) = (1/2) x - 3/2

For x = -1

g (-1) = (1/2) (- 1) - 3/2

g (-1) = -1/2 - 3/2

g (-1) = -4/2

g (-1) = -2

For x = 3

g (3) = (1/2) (3) - 3/2

g (3) = 3/2 - 3/2

g (3) = 0

AVR = ((0) - (- 2)) / ((3) - (- 1))

AVR = 1/2

For h (x):

Using the table we have:

AVR = ((62) - (14)) / ((3) - (- 1))

AVR = 12

Step-by-step explanation:

Answer:

from least to greatest:

1) g (x)

2) f (x)

3) h (x)

Step-by-step explanation:

answer is -1 < x < 5

-|x - 2|+ 9 > 6

Rearrange the terms

-|x - 2| > 6 - 9

-|x - 2| > - 3

then divide both sides of the inequality by the co- efficient of variable

|x - 2| < 3

convert the absolute inequality to standard inequality

-3 <x - 2 < 3

separate compound inequalities into system of inequality

{x - 2}> -3

{x - 2 < 3}

Rearrange variable to the left side of the equation

x > -3 + 2                    

calculate the sum or difference

x > -1

x -2 < 3

Rearrange variable to the left side of the equation

x < 3 + 2

calculate the sum or difference

x < 5

x > -1 and x < 5

Find intersection

-1 < x < 5

Equations and inequalities are both mathematical sentences formed by relating two expressions to each other. In an equation, the two expressions are deemed equal which is shown by the symbol =. Where as in an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

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Answer:

The numbers that make up today's date—12, 16, and 20—form a Pythagorean triple. That is, 12² + 16² = 20².

Step-by-step explanation:

Answer:Yes, these are pythagorean triplets because they are multiples of 4. 4 times 3 is twelve.4 times 4 is 4.And 4 times 5 is 20.

∠24°

What is an inscribed angle in a circle?

Inscribed angles are angles whose vertices are on a circle and that intersect an arc on the circle. The measure of an inscribed angle is half of the measure of the intercepted arc and half the measure of the central angle intersecting the same arc.

given that intercepted arc = ∠48°

The intercepted arc is the arc that is inside the inscribed angle and whose endpoints are on the angle.

If the intercepted arc is twice the size of the inscribed angle, then the inscribed angle is half the size of the intercepted arc. So if the intercepted arc is 48 degrees, the inscribed angle is 48 / 2 = 24 degrees.

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Answer:

1/3

Step-by-step explanation:

Gradient or slope can be found using the point-slope formula:

[tex]y-y_{1} =m(x-x_{1} )[/tex]

We can rearrange the equation to find slope (m) like so:

[tex]m=\frac{y-y_{1} }{x-x_{1} }[/tex]

To use this formula we need to find two well-defined points and use their coordinates.

Let's use (0,2) and (3,3) because they are clear points on the graph.

(0,2) will represent [tex]x[/tex] and [tex]y[/tex] in the equation respectively, and (3,3) our other point will represent [tex]x_{1}[/tex] and [tex]y_{1}[/tex].

Now we just need to plug the numbers into the equation:

[tex]m=\frac{2-3}{0-3} \\\\m=\frac{-1}{-3} \\m=\frac{1}{3}[/tex]

The gradient of the graph is 1/3.

Hope this helped!

Answer: 19

Step-by-step explanation:

2+1+1+12+3=19

The expression for g(x) is 9x + 26

A function can be defined as an expression, law or rule explaining the relationship between an independent and dependent variable.

Given the function;

g(x) = f(x + 4) - 10  

Where f = 9

Substitute into the function;

g(x) = 9( x + 4) -10

expand the bracket

g(x) = 9x + 36 - 10

collect like terms

g(x) = 9x + 26

Thus, the expression for g(x) is 9x + 26

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Answer:

[tex]e=\frac{-5e-90}{216}[/tex]

Step-by-step explanation:

[tex]\frac{2}{5}d+\frac{4}{9}e=-2d+\frac{7}{18}e-1[/tex]
[tex]\frac{2}{5}d+\frac{4e}{9}=-2d+\frac{7}{18}e-1 < - Muiltiply[/tex]
[tex]\frac{2}{5}d+\frac{4e}{9}=-2d+\frac{7e}{18}- < - Muiltiply Again\\[/tex]
[tex]\frac{2}{5}d+\frac{4e}{9}-\frac{4e}{9}=-2d+\frac{7e}{18}-1-\frac{4e}{9} < - Subtract BothSides[/tex]
[tex]\frac{2}{5}d=-2d-\frac{e}{18}-1 < - Simplify[/tex]
[tex]\frac{2}{5}d+2d=-2d-\frac{e}{18}-1+2d < - AddToBothSides[/tex]
[tex]\frac{12}{5}d=-\frac{e}{18}-1 < - Simplify[/tex][tex]\frac{12d}{12}=-\frac{\frac{5e}{18}}{12}-\frac{5}{12} < - DivideBothSides[/tex]
[tex]e=\frac{-5e-90}{216}[/tex]

Answer: -1/2

Step-by-step explanation:

The inequality that depicts when Gilberta has much more wallpaper left throughout her room than Mara does in hers using linear functions is:

t< 5.

A linear function has a straight line as its graph. The following is the form of a linear function. a + bx = y = f(x). One independent variable but one dependent variable make up a linear function. X and Y are the independent and dependent variables, respectively.

Following t hours, the quantities Gilberta and Maria have remaining are determined by:

G(t) = 35 - 4.3t.

M(t) = 30.5 - 3.4t.

Gilberta has more papers when:

G(t) > M(t).

So,

35 - 4.3t > 30.5 - 3.4t

-0.9t < -4.5

Multiplying by -1:

0.9t < 4.5

t < 4.5/0.9

t < 5.

The inequality is:

t < 5.

The inequality that depicts when Gilberta has much more wallpaper left throughout her room than Mara does in hers using linear functions is:

t< 5.

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Probability are important information when applying descriptive statistics. Probability is the branch of mathematics concerning numerical descriptions. the correct option is (B).

Descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur.

here, we have,

A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%).

The probability formula defines the likelihood of the happening of an event. It is the ratio of favorable outcomes to the total favorable outcomes. The probability formula can be expressed as,

Probability formula:

P(A) = Probability(Event) = Favorable Outcomes/Total Outcomes

P(A) =   x/n

where,

P(B) is the probability of an event 'B'.

n(B) is the number of favorable outcomes of an event 'B'.

n(S) is the total number of events occurring in a sample space

Descriptive statistics are brief informational coefficients that summarize a given data set, which can be either a representation of the entire population or a sample of a population. Descriptive statistics are broken down into measures of central tendency and measures of variability (spread). Measures of central tendency include the mean, median, and mode, while measures of variability include standard deviation, variance, minimum and maximum variables, kurtosis, and skewness.

The main purpose of descriptive statistics is to provide information about a data set. In the example above, there are hundreds of baseballs players that engage in thousands of games. Descriptive statistics summarizes the large amount of data into several useful bits of information.

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Answer:

56

Step-by-step explanation:

The mode of a data set is the number that appears the most, which in this situation would be 56

:D

Answer:

16^6

Step-by-step explanation:

Answer: The value of (1 + sin 8)(1-sin 8) (1 + cos 0) (1 - cos8) =0.2086

and [tex]cot^{1}[/tex]θ=7/8

Step-by-step explanation:

Let base and height of a triangle be 7k and 8k

By applying Pythagoras theorem in Δ ABC, we get

[tex]AC^{2} = AB^{2} +BC^{2}[/tex]

= (7k)2 + (8k)2

= 49k2 + 64k2

= 113k2

AC = √113k2

= √113k

so hypotenuse =[tex]\sqrt{133}k[/tex];

now ;

=(1 + sin θ) (1 - sin θ)(1 + cos θ) (1 - cos θ)[since : (a + b)(a - b) = (a2 - b2)]

=(1 - [tex]sin^{2}[/tex]θ)(1 - [tex]cos^{2}[/tex]θ)

=[1 - (8/√113)2] [1 - (7/√113)2]

= (1 - 64/113) (1 - 49/113)

= (49/113) (64/113)

= 0.2086

hence;

The value of (1 + sin 8)(1-sin 8) (1 + cos 0) (1 - cos8) =0.2086

and [tex]cot^{1}[/tex]θ=7/8

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Answer:

Step-by-step explanation:We will use the basic concepts of trigonometric ratios to solve the problem.

Consider ΔABC as shown below where angle B is a right angle.

If cot θ = 7/8, evaluate: (i) (1 + sin θ)(1 - sin θ) / (1 + cos θ)(1- cos θ), (ii) cot²θ

cot θ = side adjacent to θ / side opposite to θ = AB/BC = 7/8

Let AB = 7k and BC = 8k, where k is a positive integer.

By applying Pythagoras theorem in Δ ABC, we get

AC2 = AB2 + BC2

= (7k)2 + (8k)2

= 49k2 + 64k2

= 113k2

AC = √113k2

= √113k

Therefore, sin θ = side opposite to θ / hypotenuse = BC/AC = 8k/√113k = 8/√113

cos θ = side adjacent to θ / hypotenuse = AB/AC = 7k/√113k = 7/√113

(i) (1 + sin θ) (1 - sin θ) / (1 + cos θ) (1 - cos θ) = 1 - sin2θ / 1 - cos2θ  [Since, (a + b)(a - b) = (a2 - b2)]

= [1 - (8/√113)2] / [1 - (7/√113)2]

= (1 - 64/113) / (1 - 49/113)

= (49/113) / (64/113)

(ii) cotФ≈

= 49/64

The constant of proportionality for y = 5.5x will be 5.5.

A directly proportional relationship relation is shown below.

y ∝ x

where

∝  = the proportionality symbol

The variables that are related are y and x. Therefore,

y = kx

where

k is the proportionality constant.

For each chore Faith does, her mom gives her $5.50, which is shown by;

Using y = kx, the equations y = 5.5x can be designed as a directly proportional relationship.

As a result, k = 5.5 has been the proportionality constant.

The proportionality constant for y = 5.5x is 5.5.

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Answer:

(-5,3)

Step-by-step explanation:

That's the coordinates of it being reflected over X axis for point P.

The measure of angles are

i) Angle ABD = 67°

ii) Angle CBD = 67°

iii) Angle ABC = 134°

We have been given that ray BD bisects angle ABC and also

Angle ABC = (25x+34)°

Angle CBD = (11x + 23)°

Note that angle ABC = angle ABD + angle CBD          (1)

And angle ABD = angle CBD = (11x + 23)° as it is bisected into two equal half.

Therefore putting the required values of angle in equation (1) we get

          (25x+34)° = 2(11x+23)°

           25x+34 = 22x+46

           25x – 22x = 46 – 34

                3x = 12

                  x = 4

Hence,   angle ABD = (11*4 + 23) ° = 44+23 = 67°

               Angle CBD = (11*4 + 23) ° = 44+23 = 67°

               angle ABC = (25*4 + 34)° = 100+34 = 134°

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to apply a vertical translation we changed the value of k, which is the y-value of the vertex of the quadratic equation.

Then the correct option is the second one.

First, remember that for a general function f(x) we define a vertical translation of N units as:

g(x) = f(x) + N

In this case, we have the function:

f(x) = (x - h)^2 + k

If we apply a vertical translation of N units, then we get the new function:

f'(x) = (x - h)^2 + k + N

Now we have two constants, we can define:

k ' = k + N

Then the new quadratic function is:

f'(x) = (x - h)^2 + k'

So, as you can see, to apply a vertical translation we changed the value of k, which is the y-value of the vertex of the quadratic equation.

Then the correct option is the second one.

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Amount of one tin of paint is $14 and the total amount Mr. Chong  have is $172.

Let amount of one tin of paint = x

Let the total amount Mr. Chong  having = y

On buying 18 tins of paint, he will need another $80. This can we mathematically represented as,

18x = y + 80            

On rearranging this equation can be written as,

18x - y = 80                                         equation 1

On buying 10 tins of paint, he will will have $32 left. This can we mathematically represented as,

10x = y - 32

On rearranging this equation can be written as,

-10x + y = 32                                      equation 2

On adding equation 1 and equation 2, we get

18x - y -10x + y = 80 + 32

8x = 112

x = (112/8) = 14

On substituting x = 14 in equation 2 , we get

-140 + y = 32

y = 172

So, amount of one tin of paint is $14 and the total amount Mr. Chong  have is $172.

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Answer:

breakeven point,

Step-by-step explanation:

There will be only 6  cubes with only one side painted red.

Cube : A cube is a 3D shape having 6 equal square sides. it has 6 faces , 8 vertices and 12 edges.

According to the question

A 3 cm cube is divided into one centimeter cube.

Every face will have 9 cube each and from that 9 cube there will be only one 1 cube that will have one side painted red.

Since there are 6 faces,

cubes painted one side red = 6x1=6.

Therefore , There will be only 6  cubes with only one side painted red.

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The price of a clematis vine, rose bush, and peony plant is given by a set of three linear equations with three variables: 29, 14, 13.

A linear equation is one that has a degree of 1 as its maximum value .In a linear equation, no variable has an exponent bigger than 1, thus.. A linear equation's graph will always be a straight line.

An algebraic equation known as a linear equation has an exponent of 1 for each term, and when it is graphed, it always yields a straight line.

According to given data;

let c is price of clematis vine

let r is price of rose

P is price of peony plants.

bush

c=2p+3

r=c+5+

=3c + 4r+ 2p = 233

b) putting(1) in 2

a 2p+ 3 + 5 2 p +8 -9 putting(1) and (4)in 3

3(2p+3)+4(2p+8) + 2 p² 233

2

6p+9+8p+16+2p = 233

16p=25=233

16 p= 233-25

16p = 208

p=208÷13

p= 13

putting value of p in (1)and(4)

c= 2 p +3

=2X13+3

C = 29

r= 2p+8

 =2×13+8

 =34

price of clematis vines =29

rose bush = 34.

peony plants = 13.

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Answer: -r(8r^3-2r-3)

Step-by-step explanation:

Answer:

Yep,

Step-by-step explanation:

First the expression is in this way:

x+4=10

Now shift the 4 ro RHS, then it will become as follows:

x=10-4

Now 10-4 is 6

Therefore, x=6

Answer:

The and is –6

Step-by-step explanation:

–2A= –2[0 , –6]

2B= 2[–8 , –1]

–2A= –2 [0 , +12]

2B= 2[–16 , –2]

–2A + 2B=[0 ,12] + [–16 ,–2]

=[0+(–16) + 12+(–2)]

=[0–16+12–2]

= –16+10

= –6.

Hope it was helpful

Answer:

91/7=13

so x=11×13

x=143