Write the domain of the function given in the graph in set builder notation.


a. {x|x<=10}
b. {x|x<=0}
c. {x|x>10}
d. {x|x>0}


I can't get a picture of the graph so I'll try to explain. Y axis 0-5, going up by 1's, x axis 0-50, going up by 5's. Line starts at 10 on the x axis, goes up at an angle and stops at 40.

To compute for distance from a to b:

Distance A = 4 miles, base of triangle formed between a and b

Distance B = 3 miles, height of triangle formed between a and b

Distance AB = (A^2 + B^2)^0.5    hypotenuse of triangle formed between a and b, or square root of (A^2 + B^2)

Distance AB = ((4)^2 + (3)^2)^0.5

Distance AB = (16 + 9)^0.5

Distance AB = (25)^0.5

Distance AB = 5 miles

To compute for distance from b to where bank employee got stuck

BC = distance from b to c

BC  = 4 miles

Total distance driven by bank employee

= AB + 0.5(BC)

= 5 + 0.5(4)

= 5 + 2

= 7 miles, total distance driven by the bank employee

Answer:

The minimum total distance the employee may have driven before getting stuck in traffic is 9.0 miles.

Step-by-step explanation:

Given information: a(−3, 1), b(2, 4), and c(4, −2).

On a town map, each unit of the coordinate plane represents 1 mile.

Distance formula:

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Distance between bank a and bank b is

[tex]ab=\sqrt{(2-(-3))^2+(4-1)^2}[/tex]

[tex]ab=\sqrt{(5))^2+(3)^2}[/tex]

[tex]ab=\sqrt{25+9}[/tex]

[tex]ab=\sqrt{34}[/tex]

Distance between bank b and bank c is

[tex]bc=\sqrt{(4-2)^2+(-2-4)^2}[/tex]

[tex]bc=\sqrt{(2)^2+(-6)^2}[/tex]

[tex]bc=\sqrt{4+36}[/tex]

[tex]bc=\sqrt{40}[/tex]

[tex]bc=2\sqrt{10}[/tex]

A bank employee drives from branch a to branch b and then drives halfway to branch c before getting stuck in traffic. It means total distance employee may have driven before getting stuck in traffic is

[tex]Distance=ab+\frac{1}{2}bc[/tex]

[tex]Distance=\sqrt{34}+\frac{1}{2}(2\sqrt{10})[/tex]

[tex]Distance=\sqrt{34}+\sqrt{10}[/tex]

[tex]Distance=8.99323[/tex]

[tex]Distance\approx 9.0[/tex]

Therefore the minimum total distance the employee may have driven before getting stuck in traffic is 9.0 miles.

132 + 56 + 79 = 267

360 - 267 = 93

answer is 93 degrees

The value of x is the quantity x−9 negative would be negative for all values of x less than 9.

Algebra is the analysis of mathematical representations, while logic is the manipulation of those symbols.

What is inequality?

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

To determine the values of x is the quantity x−9 negative

As per the given condition, translate the phrase into an algebraic expression:

⇒ x - 9 < 0

Add 9 to both sides of the inequality,

⇒ x - 9 + 9   < 9

⇒ x < 9

So x - 9 is negative for all values of x less than 9.

Hence, the value of x is the quantity x−9 negative would be negative for all values of x less than 9.

Learn more about inequalities here:

brainly.com/question/20383699

#SPJ2

The perimeter of the rectangle ABCD is 14 units after using the distance formula.

It is defined as the two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

The missing figure is in the picture, please attached to the picture.

We have:

Rectangle ABCD is graphed in the coordinate plane.

As we know,

The distance formula: it can be defined as the formula for finding the distance between two points. It has given the shortest path distance between two points.

The distance formula can be given as:

[tex]\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

After using the distance formula:

The perimeter of the rectangle = AB + BC + CD + DA

The perimeter of the rectangle = 2 + 5 + 2 + 5

The perimeter of the rectangle = 14 units

Thus, the perimeter of the rectangle ABCD is 14 units after using the distance formula.

Learn more about the rectangle here:

https://brainly.com/question/15019502

#SPJ2

Answer:  12

Step-by-step explanation:

Given : You are making identical gift bags using 24 candles and 36 bottles of lotion .

Then, the greatest number of gift bags you can make with no items left over= greatest common factor of 24 and 36

Prime factorization of 24 and 36 :_

[tex]24=2\times2\times2\times3\\\\ 36=2\times2\times3\times3[/tex]

GCF(24 , 36)= [tex]2\times2\times3=12[/tex]

Hence, the greatest number of gift bags you can make with no items left over =12

1) There are no prime numbers whose sum is divisible by 7 and is a perfect square.

2) 1 pipe will take 2 hours to fill 1 pool, as it fills at the same rate as all 5 pipes combined.

3) Ron's score is 20%.

4) There are 20 students in the class.

5) Katie is 14 years old.

Let's evaluate each of the statements you provided:

1) The sum of 2 prime numbers is ALWAYS even, so if x and y are prime numbers, then (x+y)/7 = z².

In this case either x = 2 or y = 5 (or vice versa). This is the only possibility to be divisible by 7.

Then (5+2)/7 = 1² = 1.

The first part is correct; the sum of two prime numbers is always even. However, the statement about (x+y)/7 = z² doesn't hold true for all prime numbers. It might work for the specific values of x and y you mentioned, but it's not a general rule.

5 pipes → 2 hours → 2 pools, then 1 pipe takes (5x2) 10 hours to fill 2 pools, or 1 pipe takes (10/2) 5 hours to fill 1 pool.

This is a correct interpretation of the information provided. If 5 pipes can fill 2 pools in 2 hours, then each pipe alone takes 10 hours to fill 2 pools, or 5 hours to fill 1 pool.

It's 6/30 = 0.2 or 20%.

Correct, 6/30 simplifies to 0.2, which is equivalent to 20%.

35% represents 7 students, and 100% of the class represents x students. Therefore, 35%/7 = 100%/x. Cross-multiplying, we get 0.35x = 7, and x = 7/0.35, which simplifies to x = 20 students.

Let K be the age of Katie, and B her brother's age. K + 2 = B (Today). In 12 years, B+12 will be twice K (remember K = B-2):

B+12 = 2(K) OR B+12 = 2(B-2)

B+12 = 2(B-2)

B+12 = 2B - 4

12 + 4 = B, and B = 16. If the brother is 16, then Kate is 14.

The calculations and logic are correct. If Katie's brother is 16, then Katie is indeed 14 years old.

for such more question on prime numbers

https://brainly.com/question/145452

#SPJ12

Answer: The slope intercept form of a linear equation has the following form where the equation is solved for y in terms of x: y = a + bx. b is the slope. a is a constant term. It is the y intercept, the place where the line crosses the y axis.

Hope this helps:)

For this case we have that by definition:

Answer:

False. The average value of a given set of dates is the mean.

Answer:

cbd is 23 degrees

Step-by-step explanation:

Midpoint, as the word suggests, means the point which lies in the middle of something. If m is the midpoint of PQ then PM will be half of PQ.

Midpoint, as the word suggests, means the point which lies in the middle of something. The midpoint of a line segment means a point that lies in the mid of the given line segment.

Given that m is the midpoint of PQ. Therefore, it will divide PQ into two equal parts. Therefore,  we can write,

PQ = PM + MQ

But since PM = MQ,

PQ = PM + PM

PQ = 2 PM

PM = PQ/2

Hence, if m is the midpoint of PQ then the relationship between PM and PQ will be half of PQ.

Learn more about Midpoint here:

https://brainly.com/question/5127660

#SPJ2

In this case, we are simply asked to find for the value of:

xbya or abxy

Since we know that given values of ab and xy, therefore abxy is:

abxy = 37 * (1 / 37)

abxy = 37 / 37

abxy = 1

Answer:

y= -2x-2

Step-by-step explanation:

point slope- y=mx+b

y-y1=m(x-x1)

you have the point   (-1,0) and you have to use (x1, y1)

your slope is -2      

Substitute

y-0= -2(x +1)        

Distribute

y-0=-2x-2

+0         +0

y= -2x-2

1.30 or 130

Step-by-step explanation:

Answer:

1. x-5=2 7

2. 6+x=9 3

3. 10=4+x 6

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

5. 3x=5+x 2 1/2

6. 2x+4=6 1

7. 8=2x-5 6 1/2

8. x+3/2=7 5 1/2

9. x+4=10 6

10. 9=5x-3x 4 1/2

11. 12=3x-4 5 1/3

12. 2(x+1)=12 5

13. 2x-3/2x=2 1

I hope this helps!

The mathematical equation 'Twice the number n is no less than 10 units from -1' can be solved as two inequalities, yielding a solution of n ≤ -5.5 or n >= 4.5.

This is a math problem asking about the absolute value inequality of an equation. The question states 'Twice the number n is no less than 10 units from -1'. This can be written as |2n + 1| >= 10. To solve it, we'll divide it into two inequalities: 2n + 1 >= 10 and -2n - 1 >= 10. Solving the first inequality yields n >= 4.5, and solving the second inequality yields n <= -5.5. Thus, the solution to the equation is n ≤ -5.5 or n >= 4.5.

https://brainly.com/question/33786594

#SPJ3

its actually y=>3x-1 because it's shaded below the line.

below the line: < or <=

above the line: > or>=