F and H are sets of real numbers defined as follows.
F = { v l v < 4}
H = { v l v ≥ 7}
Write F ∩ H and F ∩ H using interval notation. If the set is empty, write ∅.

Answer:

i.  P = -800t + 29900

ii.  as an inequality: 0≤t≤37.375;  interval notation: [0,37.375]

iii.  as an inequality: 0≥P≥29900;  interval notation: [0,29900]

iv.  the population decreases at a rate of 1600 people every 3 years

v.  2010

Step-by-step explanation:

i. a) use the points *(4,26700) and **(12,20300) to find the slope (m)

      *: the year 1995(4 years after 1991) and the population that year

      **: the year 2003(12 years after 1991) and the population that year

      m = (20300-26700)/(12-4) = -6400/8 = -800

  b) use one of the points and m in (a) to find b

      26700 = -800(4) + b

      26700 = -3200 + b

      29900 = b

ii. starting value for domain will be 0 since 1991 is year 0. Find the ending domain value by using P=0 and solving the equation for t:

   0 = -800t + 29900

   800t = 29900

   t = 37.375

iii. population starts at a high of 29900 people and can't go lower than 0 people.

iv. the slope is given in (population change) / (number of years)

v. make P=14700 and solve the equation for t

   14700 = -800t + 29900

   800t = 15200

   t = 19 (19 years after 1991)

The number of cows is 12 and number of chickens are 36.

A "system" of equations is a set or collection of equations that you deal with all together at once.

Given that, Farmer John has cows and chickens on his farm. His farm animals have 120 legs and 48 heads total.

Let the number of chickens be x and that of cows be y,

A cow has 4 legs and that of chickens have 2,

Setting the equations, we get,

2x+4y = 120

x+2y = 60

x+y = 48

Solving the equation by elimination, we get,

2y - y = 60 - 48

y = 12

Therefore, x = 36

Hence, The number of cows is 12 and number of chickens are 36.

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Answer:

48 miles

Step-by-step explanation:

i think thats it.

Answer: 4.

Step-by-step explanation: 8+8=16. count how many more until you get to 24, that is 8. Split 8 in half. We get 4.

                                Hope this helps!

Answer:

x= -9

Answer:

[tex]\boxed{\boxed{\tt x=-9}}[/tex]

Step-by-step explanation:

[tex]\tt 3x+\left(-1\right)=-10+2x[/tex]

[tex]\tt 3x-1=-10+2x[/tex]

Subtract 2x from both sides:-

[tex]\tt 3x-1-2x=-10[/tex]

Combine 3x and -2x to get x:-

[tex]\tt x-1=-10[/tex]

Add 1 to both sides:-

[tex]\tt x=-10+1[/tex]

Add -10 and 1 to get -9:-

[tex]\tt x=-9[/tex]

____________________

Hope this helps you!

Have a great day!

Step-by-step explanation:

Reasons for each step

1. Distribute: 15(2x + 3) = 30x + 45

2. Combine Like Terms: 45+100 = 145

3. Addition Property of Equality: 30x+5x+145 = 110-5x+5x => 35x+145 = 110

4. Subtraction Property of Equality: 35x+145-145 = 110-145 => 35x = -35

5. Division Property of Equality: 35x/35 = -35/35 => x = -1

Each correct pair using Principle of Zero Products are-

Part a: (x-9)(3x + 4) = 0: x = 9 or x = -4/3

Part b: (x-4) (9x + 1) = 0: x = 4 or x= -1/9

Part c: (x+9)(3x-4)= 0:  x = -9 or x = 4/3

Part d: (x+4)(9x-1)=0; x = -4 or x = 1/9

For the stated equation-

Part a: (x-9)(3x + 4) = 0

Equating each term to zero;

(x-9) = 0

x = -9

And, (3x + 4) = 0

x = -4/3

Option: x = 9 or x = -4/3

Part b: (x-4) (9x + 1) = 0

Equating each term to zero;

(x-4) = 0

x = 4

And, (9x + 1) = 0

x = -1/9

Option;  x = 4 or x= -1/9

Part c: (x+9)(3x-4)= 0

Equating each term to zero;

(x+9) = 0

x = -9

And, (3x-4) = 0

x = 4/3

Option: x = -9 or x = 4/3

Part d: (x+4)(9x-1)=0

Equating each term to zero;

(x+4) = 0

x = -4

(9x-1)

x = 1/9

Option: x = -4 or x = 1/9

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The complete question is-

Solve each of the following equations using the Principle of Zero Products and match it to its correct pair of solutions on the

right.

Each pair on the right will be used once.

(x-9)(3x + 4) = 0

(x-4) (9x + 1) = 0

(x+9)(3x-4)= 0

(x+4)(9x-1)=0

x = -4 or x = 1/9

x = -9 or x = 4/3

x = 9 or x = -4/3

x = 4 or x= -1/9

Answer:

- 14x - 12

Step-by-step explanation:

- 3(2x + 4) - 8x ← distribute terms in parenthesis by - 3

= - 6x - 12 - 8x ← collect like terms

= - 14x - 12

Answer:

-14x-12

Step-by-step explanation:

1) Expand by distributing terms.

-(6x+12)-8x

2) Remove parentheses.

-6x-12-8x

3) Collect like terms.

(-6x-8x)-12

4 Simplify.

−14x−12

Answer:

x = 11

Step-by-step explanation:

Since it's given n || m, we can write the following equation to find the value of x:

9x - 3 = 7x + 19 because these two are alternate exterior angles and have equal angle measurement.

9x - 7x = 19 + 3

2x = 22

x = 11

False

The sum is the total of an addition problem.

Addition of Positive Numbers

Most commonly, people add together positive numbers. Positive numbers are numbers greater than 0. The sum of 2 positive numbers is always greater than the addends. For example:

The sum of these positive numbers, 5, is greater than the larger number, 3. However, the addition of positive numbers is not the only way to add.

Addition of Negative Numbers

Negative numbers are numbers less than 0. If you add negative numbers, then the sum will be less than the addends. So, the statement above is not true. For example:

In this case, the sum, 1, is less than the larger number, 3. This disproves the statement given.

Answer:

each measure 120

Step-by-step explanation:

Answer:

Step-by-step explanation:

:On hand she has a 20% acid solution and a 50% acid solution. How many ml of each solution should sheStep-by-step explanation:this is the answer

A chemist needs 40mL of 20% acidic solution and 60mL of 50% acidic solution.

The percentage is the ratio of number expressed as a fraction of 100.

Assume chemist needs x mL of 20% of acidic solution and y mL of 50% acidic solution.

A total of 100mL solution is to be created.

x+y=100

x=100-y

The concentration of 20% acidic solution will be 0.2x, concentration of 50% acidic solution will be 0.5x and the sum of their concentrations should be 0.38(100).

0.2x+0.5y=0.38(100)

0.2x+0.5y=38

Substitute x=100-y into the obtained equation.

0.2(100-y)+0.5y=38

20-0.2y+0.5y=38

20+0.3y=38

0.3y=18

y=18/0.3

y=60

Substitute y=60 into x=100-y.

x=100-60

=40

So, the chemist needs 40mL of 20% acidic solution and 60mL of 50% acidic solution.

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Answer:

(0,-5)

Step-by-step explanation:

markdown = 20% x $300

markdown = $60

$300 - $60

sale price = $240

The solution of the expression is,

⇒ x = - 1 and x = 5

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Solve the expression,

x² – 3x − 2 = x + 3

Now, We can simplify as;

x² – 3x − 2 = x + 3

x² – 3x − 2 - x - 3 = 0

x² - 4x - 5 = 0

x² - 5x + x - 5 = 0

x (x - 5) + 1(x - 5) = 0

(x + 1) (x - 5) = 0

x = - 1

x = 5

Thus, The solution of the expression is,

⇒ x = - 1 and x = 5

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Solution:

2b would be the greatest common factor (GCF) between both 10b^3 and 4b.

Hope this helps!

Answer:

Step-by-step explanation:

There are 60 Seconds in a Minute.

60/10 = 6

25 x 6 = 150 beats in one minute

Answer: 150

Answer:

c = -(7/5)a + 15

Step-by-step explanation:

c= (8-15)/(4-0)×a+15

c= -(7/5)a + 15

The 7x side is half the length of the 28 side.

           7x = 14

             x = 2

Answer:

both are correct

Step-by-step explanation:

theyre the same answer I think the questions wrong

Answer:

sum of angles in a triangle is 180

it is an equilateral triangle so each angle gets 60 degrees.

6x +6 is 60

6x is 60 - 6

6x is 54

divide both sides by 2

6x/6 is 54/2

x is 9

The quantity of the cups of flour that would be added would be = 12 cups.

Flour is the product of wheat grains that is commonly used for baking of dough and it measured with measuring cups or weighting scales.

According to the recipe from the given question above;

2 cups of flour = 1/4 of raisin

X cups of flour = 1½ of raisin

Make X cups of flour the subject of formula:

X cups = 2×1½ /¼

X cups = 3/¼

X cups = 3×4 = 12 cups.

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Assuming [tex]\overline{BC}[/tex] is a diameter, minor arc [tex]AB[/tex] has a measure of [tex]180^{\circ}-108^{\circ}=72^{\circ}[/tex].

Using the inscribed angle theorem, [tex]36=x+3 \implies x=\boxed{33}[/tex].

Mathematically, it will take you 315 minutes (5 hours, 15 minutes) at most to visit with all 7 clients.

We can employ mathematical operations, including addition, subtraction, division, and multiplication to determine the total time required to visit the seven clients.

Since we know that a client requires 3/4 hours or 45 minutes of your visiting time, we can multiply 45 minutes by 7.

The product of the multiplication operation gives 315 minutes, which we can convert into hours and minutes by a division operation.

The number of clients visiting today = 7

The time it a client requires of your visit time = 3/4 hours

3/4 hours = 45 minutes (0.75 x 60)

For the 7 clients, it will take you 315 minutes (45 x 7)

315 minutes equal 5 hours and 15 minutes.

Thus, using basic mathematical operations, we can conclude that, at most, you require 5 hours and 15 minutes to attend to all seven clients today.

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Answer:

The rate of change is the same for both A and B (2)

Step-by-step explanation:

In the equation, the rate of change is shown as the coefficient of the variable x.  That is the number before the x which is 2.

In the table you find the rate of change as the change in y over the change in x.  In the table the y's are increasing by 4 (3- -1), 2 (5-3) and 4 (9-5).  The x's are increasing by 2 (3-1), 1 (4-3) and 2 (6-4).

If I take the change in y over the change in x, I will get 4/2 = 2, 2/1 = 2 or 4/2 = 2

From the table the rate of change is also 2.

The value of r in the given expression is 5.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

We are given that the expression as;

75 = 15r

Now we need to find the value of r.

Therefore, we wil divide the 15 both side;

r = 75/ 15

r = 5

Hence, the value of r in the given expression is 5.

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Answer:

ax + y = (21, -16, 29)

Step-by-step explanation:

ax + y = [(-6a + 3), (3a - 7), (-8a + 5)]

now,

-8a + 5 = 29

a = (29 - 5)/-8

a = -3

ax + y = [(-6)(-3)+3, 3(-3)-7, 29]

ax + y = (21, -16, 29)

Answer:172 cm²

when we put this in the pentagon formula, and it will get 172.03, and we round it and will be 172

formula of pentagon is 1/2 × p × a