Let p: A student plays basketball.
Let q: A student plays tennis.



How many students play both basketball and tennis?

Answer:

Output

Step-by-step explanation:

A function takes values of x (the horizontal axis on a plane)and returns the corresponding values of y (the vertical axis on a plane).

Thus, the values we get for y depends on the value of x.

The x's values that we give in a function are called the domain, and the values that the function returns to us are called the range of the function (the y's).

So a word that describes the range of a function well is that the range is the output of the function. Because the range is the set of values that the function returns to us when we plug an x value.

Answer:

[tex] a_1 = -2;~a_n = -2a_{n - 1}, ~n \ge 2 [/tex]

Step-by-step explanation:

The first number in the sequence, [tex] a_1 [/tex], is -2.

Each number after that is the previous number multiplied by -2.

[tex] a_1 = -2 [/tex]

[tex] a_2 = a_1 \times (-2) = -2 \times (-2) = 4 [/tex]

[tex] a_3 = a_2 \times (-2) = 4 \times (-2) = -8 [/tex]

etc.

[tex] a_n = -2a_{n - 1} [/tex]

We start by stating that [tex] a_1 = -2 [/tex].

Now we need to show that for all n greater than or equal to 2, each number in the sequence is the previous number multiplied by -2.

[tex] a_n = -2a_{n - 1} [/tex]

Answer:

[tex] a_1 = -2;~a_n = -2a_{n - 1}, ~n \ge 2 [/tex]

A recursive formula represents the relationship between each term and the ones before it. In the given geometric sequence (-2, 4, -8, 16,...), each term is -2 times the preceding term, hence the recursive formula is [tex]a_{n} = -2a_{n-1}[/tex] for n>1.

The given sequence is -2, 4, -8, 16, ..., which is an example of a geometric sequence. In a geometric sequence, each term after the first is found by multiplying the previous term by a fixed, non-zero number called the 'common ratio'.

Looking at the pattern, we notice that each term is -2 multiplied by the prior term. Therefore, the recursive formula for this sequence is [tex]a_{n} = -2a_{n-1}[/tex] where 'an' represents the nth term and 'an-1' represents the previous term, and n > 1.

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Answer:

A=280in^2

Step-by-step explanation:

3*3=9

A=2LW+2WH+2LH

A=2(8*4)+2(4*9)+2(8*9)

A=2(32)+2(36)+2(72)

A=64+72+144

A=280in^2

Answer:

1698

Step-by-step explanation:

Answer:

They would need 1698 dominoes to complete the chain.

Step-by-step explanation:

all you would do is subtract 2,505 by 807 and you would get the same answer.

Answer:

9

Step-by-step explanation:

(9*3) = 27 which is 20 more than 7

Answer: 9

Step-by-step explanation:

Answer:

[tex]x=7[/tex]

Step-by-step explanation:

we have

[tex]3x-\frac{1}{9}y=18[/tex]

Substitute the value of y=27 in the equation and find the value of x

so

[tex]3x-\frac{1}{9}(27)=18[/tex]

[tex]3x-3=18[/tex]

[tex]3x=18+3[/tex]

[tex]3x=21[/tex]

[tex]x=7[/tex]

Final answer:

Yes, 4/2 and 14/7 form a proportion because both ratios simplify to 2/1, which indicates they are equal and therefore proportional.

Explanation:

To determine if two ratios, 4/2 and 14/7, form a proportion, we need to compare the simplified forms of each ratio and see if they are equivalent. A proportion exists when two ratios are equal to each other. Simplifying both ratios, we get 4/2 = 2/1 and 14/7 = 2/1. Since both simplified ratios are equal to 2/1, we can conclude that 4/2 and 14/7 indeed form a proportion.

No the negative slope means the line moves down from left to right.

Hope this helps.

r3t40

Answer:

It slopes upwards from right to left.

Step-by-step explanation:

A negative slope means that a line rises from right to left. Like a back slash \.

Answer:

 [tex]f(-\frac{1}{2}) = 1[/tex]

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

Step-by-step explanation:

Given the function [tex]f(x) = 4x + 3[/tex] and the function [tex]g(x) = 3x[/tex], to evaluate for [tex]x=-\frac{1}{2}[/tex], you need to substitute it into each function.

Then, for the function f(x), when  [tex]x=-\frac{1}{2}[/tex], you get:

 [tex]f(-\frac{1}{2}) = 4(-\frac{1}{2}) + 3[/tex]

 [tex]f(-\frac{1}{2}) = 4(-\frac{1}{2}) + 3[/tex]

 [tex]f(-\frac{1}{2}) = -\frac{4}{2}+ 3[/tex]

 [tex]f(-\frac{1}{2}) = -2 + 3[/tex]

 [tex]f(-\frac{1}{2}) = 1[/tex]

For the function g(x), when  [tex]x=-\frac{1}{2}[/tex], you get:

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

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

Answer:

f(-1/2) = 1

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

Step-by-step explanation:

f(x) = 4x+3

Let x = -1/2

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

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

f(-1/2) =1

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

          = -3/2  

Answer: Yes A is correct

Step-by-step explanation:

Multiply the first equation by 3...

2x+3y=k+1 needs to be subtracted by 3x+3y=3k

which equals -x=-2k-1

Then you can multiply the equation by -1 to make them all positive. Resulting in x=2k+1

The correct option is c.

To solve the given simultaneous linear equations x + y = k and 2x + 3y = k + 1 using the elimination method, multiply the equations by suitable constants to eliminate one variable. The values of x and y in terms of k are x = 2k - 1 and y = 1 - k.

To solve the given simultaneous linear equations x + y = k and 2x + 3y = k + 1 using the elimination method, we can eliminate one variable by multiplying the equations by suitable constants. Let's multiply the first equation by 2 and the second equation by -1 to eliminate x.

2x + 2y = 2k

-2x - 3y = -k - 1

Adding these equations together, we get:

2y - 3y = 2k - (k + 1)

-y = k - 1

Multiplying both sides by -1:

y = 1 - k

Substituting this value of y back into the first equation:

x + (1 - k) = k

x = 2k - 1

So, the values of x and y in terms of k are x = 2k - 1 and y = 1 - k.

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Answer:

[tex]P =4.83\%[/tex]

Step-by-step explanation:

First we calculate the number of possible ways to select 2 cards an ace and a card of 10 points.

There are 4 ace in the deck

There are 16 cards of 10 points in the deck

To make this calculation we use the formula of combinations

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

Where n is the total number of letters and r are chosen from them

The number of ways to choose 1 As is:

[tex]4C1 = 4[/tex]

The number of ways to choose a 10-point letter is:

[tex]16C1 = 16[/tex]

Therefore, the number of ways to choose an Ace and a 10-point card is:

[tex]4C1 * 16C1 = 4 * 16 = 64[/tex]

Now the number of ways to choose any 2 cards from a deck of 52 cards is:

[tex]52C2 =\frac{52!}{2!(52-2)!}[/tex]

[tex]52C2 = 1326[/tex]

Therefore, the probability of obtaining an "blackjack" is:

[tex]P = \frac{4C1 * 16C1}{52C2}[/tex]

[tex]P = \frac{64}{1326}[/tex]

[tex]P = \frac{32}{663}[/tex]

[tex]P =0.0483[/tex]

[tex]P =4.83\%[/tex]

Answer:

Probability = 0.0483

Percentage = 4.83%

Step-by-step explanation:

We know that a blackjack hand played with one deck consists of:

1 of the 4 aces = [tex]\frac{4}{52}[/tex]

So 1 out of the 16 cards worth 10 points will be equal to = [tex]\frac{16}{52}[/tex]

Finding the probability of getting a blackjack hand assuming that the cards were not replaced:

P (blackjack hand) =  P(1st ace) × P(2nd 10 point card) +  P(1st 10 point card) × P(2nd ace)

P (blackjack hand) = [tex]\frac{4}{52} \times \frac{16}{51} + \frac{16}{52} \times \frac{4}{51}[/tex] = 0.04827

Percentage of getting blackjack hand = 4.83%

For this case we have the following equation:

[tex]2x-1 = 3[/tex]

If we add 1 to both sides of the equation we have:

[tex]2x = 3 + 1\\2x = 4[/tex]

Dividing between 2 on both sides of the equation we have:

[tex]x = \frac {4} {2}\\x = 2[/tex]

The graph of the solution is shown in the attached figure.

Answer:

See attached image

Answer:

8.1 ft

Step-by-step explanation:

hyp² = side² + side²

hyp² = 7² + 4²

hyp² = 49 + 16

hyp² = 65

hyp = sqrt of 65

hyp = 8.1 ft

PLEASE DO MARK ME AS BRAINLIEST UWU

Answer:

[tex]\large\boxed{\sqrt{65}\ ft}[/tex]

Step-by-step explanation:

Use the Pythagorean theorem:

[tex]leg^2+leg^2=hypotenuse^2[/tex]

We have

[tex]leg=4ft,\ leg=7ft,\ hypotenuse=AB[/tex]

Substitute:

[tex]AB^2=4^2+7^2\\\\AB^2=16+49\\\\AB^2=65\to AB=\sqrt{65}[/tex]

Answer:

-39/8y

Step-by-step explanation:

-4/y(2)+(-7/8y)

the least possible quotient of the two numbers would be C.) 111

Answer:

6w + 7

Step-by-step explanation:

There is nothing to simplify. Just remove the parentheses.

Answer:

[tex]\large\boxed{(f+g)(x)=-8x-6}[/tex]

Step-by-step explanation:

[tex](f+g)(x)=f(x)+g(x)\\\\f(x)=-5x-4,\ g(x)=-3x-2\\\\\text{Substitute:}\\\\(f+g)(x)=(-5x-4)+(-3x-2)\\\\=-5x-4-3x-2\qquad\text{combine like terms}\\\\=(-5x-3x)+(-4-2)\\\\=-8x-6[/tex]

Despite different rental costs, the rental costs for company A and company B will be the same, after 50 miles.

To solve this, we need to set up an equation based on their pricing structures and solve for the number of miles.

Let m represent the number of miles driven. The cost for company A would be $40 + $0.30m, and the cost for company B would be $20 + $0.70m.

We set these two expressions equal to each other to find the breakeven point:

$40 + $0.30m = $20 + $0.70m

Subtracting $0.30m from both sides gives us:

$40 = $20 + $0.40m

Next, we subtract $20 from both sides:

$20 = $0.40m

Dividing both sides by $0.40, we get:

m = 50

Answer:

x = 20

Step-by-step explanation:

see attached

From Pythagoras, [tex]\(z^2 - y^2 = 369\)[/tex]. Solving, z - y = 19, z + y = 19, yielding z = 19. Substituting, x = 17.

Given that Triangle A and Triangle B are right angle triangles with similar heights 'x' and different perpendicular (say 'y' and 'z' respectively).

From the Pythagoras theorem, we know that:

[tex](Hypotenuse)^2 = (Base)^2 + (Perpendicular)^2[/tex]

Substituting the given values, we get:

[tex]y^2 = 16^2 + x^2[/tex]

[tex]z^2 = 25^2 + x^2[/tex]

Subtracting the two equations, we get:

[tex]z^2 - y^2 = 25^2 - 16^2[/tex]

(z - y)(z + y) = 625 - 256 = 369

z - y = 19

z + y = 369 / 19 = 19

Adding the two equations, we get:

2z = 38

z = 19

Substituting the value of 'z' in the equation:

[tex]z^2 = 25^2 + x^2[/tex]

[tex]19^2 = 25^2 + x^2[/tex]

[tex]x^2 = 19^2 - 25^2 = 289[/tex]

[tex]x = sqrt(289)[/tex] = 17

Therefore, the value of 'x' is 17.

For more such questions on Pythagoras:

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Answer:

The scale factor is 2

Step-by-step explanation:

AB -->A'B' : enlargement , scale factor is greater than 1

From QA to QA' : 1.25 to 2.5 so the ratio is 1:2

The scale factor is 2

Answer:

Similarity cannot be determined ⇒ answer D

Step-by-step explanation:

* Lets revise the cases of similarity

1) AAA similarity : two triangles are similar if all three angles in the first

  triangle equal the corresponding angle in the second triangle

- Example : In ΔABC and ΔDEF, m∠A = m∠D, m∠B = m∠E and

 m∠C= m∠F then ΔABC ≈ ΔDEF by AAA

2) AA similarity : If two angles of one triangle are equal to the

   corresponding angles of the other triangle, then the two triangles

   are similar.

- Example : In ΔPQR and ΔDEF, m∠P = m∠D, m∠R = m∠F then

  ΔPQR ≈ ΔDEF by AA

3) SSS similarity : If the corresponding sides of two triangles are

   proportional, then the two triangles are similar.

- Example : In ΔXYZ and ΔLMN, if [tex]\frac{XY}{LM}=\frac{YZ}{MN}=\frac{XZ}{LN}[/tex]

  then the two triangles are similar by SSS

4) SAS similarity : In two triangles, if two sets of corresponding sides

   are proportional and the included angles are equal then the two

   triangles are similar.

- Example : In triangle ABC and DEF, if m∠A = m∠D and [tex]\frac{BA}{ED}=\frac{CA}{FD}[/tex]

  then the two triangles are similar by SAS

* Now lets solve the problem

- In the triangles ABC and DEF

∵ m∠B = m∠E = 105°

∵ AB/DE = 16/4 = 4

∵ AC/DF = 36/9 = 4

∴ AB/DE = AC/DF = 4

∴ The two pairs of sides are proportion

∵ ∠B and ∠E are not the including angles between the sides AB , AC

  and DE , DF

∵ We could not find the including angles from the information of the

  problem

∴ We cannot prove the similarity

* Similarity cannot be determined

Answer:

D- can't be determined

Step-by-step explanation:

a p e x work

Answer:

The quotient is 3x-8

Step-by-step explanation:

(6x^2-x-40)÷ (5 + 2x)

The above equation can be written as

(6x^2-x-40)÷ (2x + 5)

The division is shown in the figure below.

The quotient is 3x-8

Answer:

(6x^2-x-40)÷ (5 + 2x)

The above equation can be written as

(6x^2-x-40)÷ (2x + 5)

The division is shown in the figure below.

The quotient is 3x-8

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

It turns out from similar triangles, that 7/BD = BD / 18. Use triangles  ABD and BDC to show this relationship. Solving this equation will give you BD

BD^2 = 7*18

BD^2 = 126     Just leave it in this form. Do your rounding at the end.

Because triangle BDC is a right angle triangle, use the Pythagorean Theorem to solve for m

m^2 =  BD^2 + 7^2

m^2 = 126 + 49

m^2 = 175                         Take the square root of both sides.

sqrt(m^2) = sqrt(175)

m = 13.22

so the answer is D

To rationalize the denominator and simplify the given expression, multiply both the numerator and denominator by the conjugate of the denominator. Simplify the resulting expression by applying the FOIL method and simplifying square roots. The final simplified expression is 72+24 √6+20 √12/84.

To rationalize the denominator and simplify √6+5 √2/4 √6-3 √2, we need to eliminate the square root from the denominator. To do this, we can multiply both the numerator and denominator by the conjugate of the denominator, which in this case is 4 √6+3 √2. The conjugate of a binomial in the form a+b is a-b. So, we will multiply the numerator and denominator by 4 √6+3 √2:

(3 √6+5 √2)(4 √6+3 √2)/[(4 √6-3 √2)(4 √6+3 √2)]

Next, we can apply the FOIL method in the numerator and the difference of squares in the denominator to expand the expression:

(3*4*6+3*4*2 + 5*4 √6 √2 + 3* √2 √6)/ (16*6 - 9*2)

Simplifying further, we get:

(72+24 √6+20 √12)/102 - 18

The final simplified expression is:

72+24 √6+20 √12/84

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Answer:

The answer is the first one.

Step-by-step explanation:

What helped me figure this out was going to desmos.com which is a great site for graphing. If you put in the equations this should help you find the answer. I hope this helps love! :)

Answer: A. [tex]\dfrac{x^2}{100}+\dfrac{y^2}{64}=1[/tex]

Step-by-step explanation:

The equation of ellipse centered at origin is when the horizontal major axis (2a) and verticel minor axis (2b) is the major axis  :-

[tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1[/tex]

From the given picture , [tex]a=10[/tex]

[tex]b=8[/tex]

Now, the equation of the given ellipse :-

[tex]\dfrac{x^2}{(10)^2}+\dfrac{y^2}{(8)^2}=1\\\\\Rightarrow\ \dfrac{x^2}{100}+\dfrac{y^2}{64}=1[/tex]

Answer:

x=0.76 or -5.26

Step-by-step explanation:

You can apply the completing square method to solve this ;

[tex]2x^2+9x=8\\\\[/tex]

Rewrite the equation with a zero like below

[tex]2x^2+9x-8=0[/tex]

This is by taking 8 to the left side of the equation

Divide the terms by 2 in x²

[tex]\frac{2x^2}{2} +\frac{9x}{2} -\frac{8}{2} =\frac{0}{2}[/tex]

[tex]=x^2+4.5x-4=0[/tex]

Move the number term to the right side of the equation

[tex]x^2+4.5x=4[/tex]

complete square on the lefts side of the equation, how?

[tex]=(\frac{b^}{2})^2 =(\frac{4.5}{2} )^2=5.0625[/tex]

balance the equation by adding this value to the right side , in this form

[tex]x^2+4.5x+5.0625=4+5.0625\\\\[/tex]

Factorize the left side

[tex](x+2.25)(x+2.25)=9.0625\\\\\\(x+2.25)^2=9.0625\\[/tex]

Eliminate the square on the left side

[tex]x+2.25=\sqrt{9.0625}[/tex]

x+2.25= ± 3.010

Solve for x

x=+3.010-2.25=0.76

or

x=-3.010-2.25=-5.26

Answer:

x = 0.76 or x= -5.26

Step-by-step explanation:

Points to remember

Solution of a quadratic equation ax² + bx + c = 0

x = [-b ± √(b² - 4ac)]/2a

It is given a quadratic equation,

2x² + 9x = 8

⇒ 2x² + 9x - 8 = 0

To find the solution

Here a = 2, b = 9 and c = -8

x = [-b ± √(b² - 4ac)]/2a

 = [-9 ± √(9² - 4*2*(-8))]/2*2

 = [-9 ± √(81 +64)]/4

 =  [-9 ± √(145]/4

 =  [-9 ± 12.04]/4

x =  [-9 + 12.04]/4 or x =  [-9 - 12.04]/4

x = 0.76 or x= -5.26

Answer:

1 - x - 2 + 2x = 10x - 25 - x

Step-by-step explanation:

We have the expression: 1 - (x+2) + 2x = 5(2x - 5) - x

Applying the distributive property we get:

1 - x - 2 + 2x = 10x - 25 - x

So, the following equation is the result of that step: 1 - x - 2 + 2x = 10x - 25 - x

Answer:

The equation is:

[tex]1-x-2 + 2x = 10x-25-x[/tex]

Step-by-step explanation:

The distributive property says that

[tex]c(a+b) = ac + bc[/tex]

In this case we have the following equation

[tex]1-(x+2) + 2x = 5(2x-5)-x[/tex]

Then apply the distributive property as shown below

[tex]1-1*x-1*2 + 2x = 5*2x-5*5-x[/tex]

Now simplify the expression

[tex]1-x-2 + 2x = 10x-25-x[/tex]

So the equation that results after applying the distributive property is:

[tex]1-x-2 + 2x = 10x-25-x[/tex]

Answer:

B. y=-2+x and 2y-2x=-2

Step-by-step explanation:

Two lines are parallel if they have the same slope.

The equation 0of a line is tipically written as y=mx + b, where 'm' represents the slope and 'b' the y-intercept.

Let's evaluate each of the options:

A. y=4x+1 and y+4x=5

Writing the equations in the slope-intercept form, we get:

y=4x+1 → m=4

y=5-4x → m=-4

Given that they have different slopes, they are not parallel.

B. y=-2+x and 2y-2x=-2

Writing the equations in the slope-intercept form, we get:

y=-2+x → m=1

y=-1 + x → m=1

Given that the equations have the same slope, they are parallel.

C. y=1/4x + 2 and y-2=1/2x

Writing the equations in the slope-intercept form, we get:

y=1/4x + 2  → m=1/4

y=1/2x+2 → m=1/2

Given that they have different slopes, they are not parallel.

D. y=1/5x+1 and 5y+x= 10

Writing the equations in the slope-intercept form, we get:

y=1/5x+1 → m=1/5

5y+x= 10 → y=2 - 1/5x → m=-1/5

Given that they have different slopes, they are not parallel.

The temperature started at -12 degrees then increases by 8 degrees. This means that you can make an expression to solve this like so...

-12 + 8

When adding a positive number with a negative number you will act as if you are subtracting the two numbers, then take the sign of the largest number. In this case the largest number is 12 and its sign is negative. Your answer will  have a negative sign.

Act as if you are subtracting...

12 - 8 = 4

Take the sign of  the largest number (12)

-4 (third option)<<<This is the temperature now.

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

-4F

Step-by-step explanation:

We start at -12

We rise 8

-12 +8

-4

We will then be at -4