3. Antoinette is building a rectangular pen with 78 feet of fencing. If the length of the pen is 5
feet longer than its width, what are the dimensions of the pen?
Width
Length


NUMBER 3

Answer:

y - 10 = -1/2(x + 4)

General Formulas and Concepts:

Algebra I

Coordinates (x, y)

Point-Slope Form: y - y₁ = m(x - x₁)

Step-by-step explanation:

Step 1: Define

Identify variables

m = -1/2

Point (-4, 10) → x₁ = -4, y₁ = 10

Step 2: Find

Answer: [tex]y=-\frac{1}{2} x+8[/tex]

Step-by-step explanation:

An equation of a line can be in slope intercept form which is y=mx+b

m is the slope, b is the y intercept, x it the x coordinate, and y is the y coordinate. Since we know the slope is -1/2 and we know a x coordinate is -4 and a y coordinate is 10 we can sub them in and solve for the value of b.

[tex]y=mx+b\\10=(-\frac{1}{2})(-4)+b\\10=2+b\\10-2=2+b-2\\8=b[/tex]

The value of b is 8. We can now sub it in for our equation of the line. This time with x and y as variables.

y=-1/2x+8

Answer:

27.3

Step-by-step explanation:

27.3

Answer:

Plays a musical instrument

Top left

Plays a sport: 0.46

Plays a musical instrument

Top right

Does not Play a sport: 0.54

Does not play a musical instrument

Bottom Left

Plays a sport: 0.73

Does not play a musical instrument

Bottom right

Does not Play a sport: 0.27

Step-by-step explanation:

I hope this helps you! :D

Answer:

what is the question?

Step-by-step explanation:

answer the question

Answer:

Hi, there the answer is

These are the equations with exactly one solution

-5x + 12 = –12x – 12

-5x + 12 = 5x + 12

-5x + 12 = 5x – 5

Hope This Helps :)

Step-by-step explanation:

First degree equations

A first degree equation has the form

ax + b = 0

There are some special cases where the equation can have one, infinitely many or no solution

If , the equation has exactly one solution

If a=0 and b=0 the equation has infinitely many solutions, because it doesn't matter the value of x, it will always be true that 0=0

If a=0 and  the equation has no solution, because it will be equivalent to b=0 and we are saying it's not true. No matter what x is, it's a false statement.

We have been given some equations, we only need to put them in standard form

-5x + 12 = –12x – 12

Rearranging

7x + 24 = 0

It has exactly one solution because a is not zero

.......................

-5x + 12 = 5x + 12

Rearranging

-10x + 0 = 0

It has exactly one solution because a is not zero

.......................

-5x + 12 = 5x – 5

Rearranging

-10x + 17 = 0

It has exactly one solution because a is not zero

.......................

-5x + 12 = -5x – 12

Rearranging

0x + 24 = 0

It has no solution, no matter what the value of x is, it's impossible that 24=0

Answer: These are the equations with exactly one solution

-5x + 12 = –12x – 12

-5x + 12 = 5x + 12

-5x + 12 = 5x – 5

Answer:

The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set.

Answer:

101 =x

Step-by-step explanation:

The measure of the exterior angle is equal to the sum of the opposite interior angles

143 = 42+x

Subtract 42 from each side

143-42 = 42+x-42

101 =x

Answer:

x = 101 degrees

Step-by-step explanation:

The sum of the external angle and its adjacent is 180 degrees

143 + y = 180

y = 37 degrees

The sum of the inner angles of a triangle is 180 degrees

37 + 42 + x = 180

79 + x = 180

x = 101 degrees

Answer:

Step-by-step explanation:

Given that:

[tex]y^2 (y^2-4) = x^2(x^2 -5)[/tex]

at point (0, -2)

[tex]\implies y^4 -4y^2 = x^4 -5x^2[/tex]

Taking the differential from the equation above with respect to x;

[tex]4y^3 \dfrac{dy}{dx}-8y \dfrac{dy}{dx}= 4x^3 -10x[/tex]

Collect like terms

[tex](4y^3 -8y)\dfrac{dy}{dx}= 4x^3 -10x[/tex]

[tex]\dfrac{dy}{dx}= \dfrac{4x^3 -10x}{4y^3-8y}[/tex]

Hence, the slope of the tangent line m can be said to be:

[tex]\dfrac{dy}{dx}= \dfrac{4x^3 -10x}{4y^3-8y}[/tex]

At point (0,-2)

[tex]\dfrac{dy}{dx}= \dfrac{4(0)^3 -10(0)}{4(-2)^3-8-(2)}[/tex]

[tex]\dfrac{dy}{dx}= \dfrac{0 -0}{4(-8)+16}[/tex]

[tex]\dfrac{dy}{dx}= 0[/tex]

m = 0

So, we now have the equation of the tangent line with slope m = 0 moving through the point (x, y) = (0, -2) to be:

(y - y₁ = m(x - x₁))

y + 2 = 0(x - 0)

y + 2 = 0

y = -2

Answer:

Point estimate of the corresponding population mean = $8,213

Step-by-step explanation:

Given:

Average cost of a wedding reception (x) = $8,213

Total number of sample (n) = 450

Standard deviation = $2185

Find:

Point estimate of the corresponding population mean

Computation:

Average cost of a wedding reception (x) = Point estimate of the corresponding population mean

Point estimate of the corresponding population mean = $8,213

Step-by-step explanation:

Given: [∀x(L(x) → A(x))] →

[∀x(L(x) ∧ ∃y(L(y) ∧ H(x, y)) → ∃y(A(y) ∧ H(x, y)))]

To prove, we shall follow a proof by contradiction. We shall include the negation of the conclusion for

arguments. Since with just premise, deriving the conclusion is not possible, we have chosen this proof

technique.

Consider ∀x(L(x) → A(x)) ∧ ¬[∀x(L(x) ∧ ∃y(L(y) ∧ H(x, y)) → ∃y(A(y) ∧ H(x, y)))]

We need to show that the above expression is unsatisfiable (False).

¬[∀x(L(x) ∧ ∃y(L(y) ∧ H(x, y)) → ∃y(A(y) ∧ H(x, y)))]

∃x¬((L(x) ∧ ∃y(L(y) ∧ H(x, y))) → ∃y(A(y) ∧ H(x, y)))

∃x((L(x) ∧ ∃y(L(y) ∧ H(x, y))) ∧ ¬(∃y(A(y) ∧ H(x, y))))

E.I with respect to x,

(L(a) ∧ ∃y(L(y) ∧ H(a, y))) ∧ ¬(∃y(A(y) ∧ H(a, y))), for some a

(L(a) ∧ ∃y(L(y) ∧ H(a, y))) ∧ (∀y(¬A(y) ∧ ¬H(a, y)))

E.I with respect to y,

(L(a) ∧ (L(b) ∧ H(a, b))) ∧ (∀y(¬A(y) ∧ ¬H(a, y))), for some b

U.I with respect to y,

(L(a) ∧ (L(b) ∧ H(a, b)) ∧ (¬A(b) ∧ ¬H(a, b))), for any b

Since P ∧ Q is P, drop L(a) from the above expression.

(L(b) ∧ H(a, b)) ∧ (¬A(b) ∧ ¬H(a, b))), for any b

Apply distribution

(L(b) ∧ H(a, b) ∧ ¬A(b)) ∨ (L(b) ∧ H(a, b) ∧ ¬H(a, b))

Note: P ∧ ¬P is false. P ∧ f alse is P. Therefore, the above expression is simplified to

(L(b) ∧ H(a, b) ∧ ¬A(b))

U.I of ∀x(L(x) → A(x)) gives L(b) → A(b). The contrapositive of this is ¬A(b) → ¬L(b). Replace

¬A(b) in the above expression with ¬L(b). Thus, we get,

(L(b) ∧ H(a, b) ∧ ¬L(b)), this is again false.

This shows that our assumption that the conclusion is false is wrong. Therefore, the conclusion follows

from the premise.

15

Answer:

how old are you gghhjjzetstu9u

Answer:

4 ft

Step-by-step explanation:

let's find radius first

radius=diameter/2

=6/2

=3 ft

radii=3 ft

Now by using pythagoras theorem

a^2 + b^2 = c^2

3^2 + 3^2 =AB^2

9+9=AB^2

18=AB^2

[tex]\sqrt{18}[/tex] AB

4.24 =AB

4 ft =AB (after converting to nearest foot)

Answer:

First find the SA of the triangular figure

4 x 3 = 12 cm^2 (the triangles on the sides)

2 x 3 = 6 cm^2 (the back square)

2 x 5 = 10 cm^2 (the slanted square)

*I'm not sure if this question includes the bottom of the triangle but here it is anyways

4 x 2 = 8 cm^2

Including the bottom the SA of the triangular figure is:

12 + 6 + 10 + 8 = 36 cm^2

Find the SA of the rectangular shape

4 x 2 = 8 cm^2 (the bottom square)

2 x 6 = 12 x 2 = 24 cm^2 (the sides)

4 x 6 = 24 x 2 = 48 cm^2 (the front and back)

Add them up

8 + 24 + 48 = 80 cm^2

If you wanted to find the SA of the whole figure it would be:

12 + 6 + 10 + 8 + 24 + 48 = 108 cm^2

Hope this helps!

Answer:

3/14

Step-by-step explanation:

Probability = # of favorable outcomes / # of possible outcomes

Favorable outcomes = we want to find the probability of pulling a blue marble. There are 3 blue marbles so 3 is the number of favorable outcomes

Possible outcomes: to find the number of possible outcomes we simply find the total number of marbles

3 + 7 + 4 which equals 14

So possible outcomes = 14

We now plug in the values into the probability formula

The probability of pulling a blue marble is 3/14

Answer:

3/14

Step-by-step explanation:

you add the red marbles, blue marbles, and green marbles together, which equal 14. Out of the 14, there are only 3 blue marbles so it would be 3/14.  

Answer:  -2

This is because (-2)^5 = -32. Applying the fifth root to both sides lets us say [tex]-2 = \sqrt[5]{-32}[/tex]

There are four other roots but they are complex. Effectively, we are solving the equation [tex]x^5 + 32 = 0[/tex]

Answer:

87

Step-by-step explanation:

Answer: C) Next year, 7 out of every 60 students will be taking music.

Step-by-step explanation:

A is wrong because it is an opinion which a table cannot prove.

B is wrong because it says "A representative sample of 60 students) while the answer incorrectly says 30.

C is correct because on the table it says 7 people are taking music and correctly identifies that it's out of 60 students.

D is incorrect for the same reason B is incorrect except this time it says 120.

Answer:

maybe if u translate it in English

Step-by-step explanation:

it wouldv been helpful if u mind?

Answer:

after 10 months

Step-by-step explanation:

Let x be the number of months and y be the amount they still owe.

Sin Ian borrows $1000 from his parents, then the y-intercept b= 1000 since he owes $1000 when x = 0. He pays them back $60 each month The slope is then m = -60 . Substituting in b = 1000 and m = -60 into the slope-intercept form of a line then gives y= mx + b=-60x +1000.

Sin Ken borrows $600 from his parents, then the y-intercept b = 600 since he owes $600 When x= 0. He pays them back $20 per month so the amount he owes decreases $20 each month. The slope is then m = -20 . Substituting in

b= 600 and m = -20 into the slope-intercept form then gives y = mx +b = -20x + 600.

They will owe the same amount when they have the same y-coordinate. Therefore -60x+ 1000= y= -20x+600. Solve this equation for x:

-60x+ 1000 = -20x+ 600

1000 = 40x+ 600

400 = 40x

10=x

They will then owe the same amount after 10 months.

Step-by-step explanation:

de hecho, la respuesta está en la imagen de arriba

Hope this help!!!

Have a nice day!!!

Answer:

A. 1/2 cups

Step-by-step explanation:

13/15 is close to 1

1/5 is a small amount

9/20 is just over 1/2

5/11 is just under 1/2

7/15 is just under 1/2

Estimate: 1 + 1/2 + 1/2 + 1/2 + a little = 2 1/2

He needs 3 cups, so he needs another 1/2 cup.

Answer: A. 1/2 cups

Answer:

it a 1/2

Step-by-step explanation:

Answer:

24 + y = 41

y = 17

Step-by-step explanation:

24 + y = 41

y + 24 = 41

y + 24 - 24 = 41 - 24

y = 17

Answer:

the equation of the regression line will be 1

Answer:

The triangle will triple in size.

Answer:

11 is the answer.....

Step-by-step explanation:

6x-15+39+90 = 180

Answer:

the answer is b because -(-6) becomes 6 and 6 is greater than 3

Answer: B.

Step-by-step explanation: A. 45 is not less than or equal to 18. I got 45 because 2 negatives make a positive and I got 18 because it was in absolute value bars making it positive. B. 6 is greater than -3. I got 6 because it is in an absolute value bar. C. 32 is not less 28. I used the same steps I used on the others. D. 9 is not greater than or equal to 10.

Answer:

f(d)=0.1d^2+d+2

Step-by-step explanation:

t(d)=−0.2d2+4d+12

a(d)=−0.3d2+3d+10

how many more teenagers than adults attend the festival on any day?

==>

f(d) = t(d) - a(d)

=0.1d^2+d+2

C = 25 deg

a ≈ 10.72 ft

b ≈ 11.83 ft

Answer:

C = 25

a = 10.72

b = 11.83

Step-by-step explanation:

C:

Solve; 180 - (90 + 65)

a:

Tan(65) = a/5

Tan(65) * 5 = a

10.72 = a

b:

Cos(65) = 5/b

Cos(65) * b = 5

b = 5 / Cos(65)

b = 11.83

Hope this helps!

Answer:

Pi is an irrational number, same is pi/4.

Step-by-step explanation:

9514 1404 393

Answer:

  x = 8/7

Step-by-step explanation:

The only real zero of this linear function is the value of x that makes y=0:

  0 = -7x +8

  7x = 8 . . . . . . add 7x

  x = 8/7 . . . . . .divide by 7