Find an equation of the line L that passes through the point (2,-12) and satisfies the given condition.
L is perpendicular to the line 8x + 2y = -8.

Answer:

option C is correct.

Step-by-step explanation:

The area of triangle with sides a, b and c can be found by using formula

[tex]Area = \sqrt{s(s-a)(s-b)(s-c)} \\where \\s= \frac{1}{2}(a+b+c)[/tex]

We are given:

a= 20

b=30

c=40

Finding s:

Putting values in the formula and solving:

[tex]s= \frac{1}{2}(a+b+c)\\s=\frac{1}{2}(20+30+40)\\s=\frac{90}{2}\\s= 45[/tex]

Now, Finding the area:

Putting values in the formula and solving:

[tex]Area = \sqrt{s(s-a)(s-b)(s-c)}\\Area =\sqrt{45(45-20)(45-30)(45-40)}\\Area =\sqrt{45(25)(15)(5)}\\Area = \sqrt{84,375}  \\Area = 290.5 units^2[/tex]

So, option C 290.5 units^2 is correct.

Answer:

option C 290.5 units^2 is correct.

Step-by-step explanation:

Answer:

y = -5x + 46

Step-by-step explanation:

We are trying to find an equation in y=mx+b form

Okay so we know two points on the graph,  from which we can get the slope (value of m) by the formula [tex]\frac{y_{2} -y_{1}}{x_{2}-x_{1}}[/tex]

plugging in the values:  [tex]\frac{6 -1}{8-9}[/tex]

the resulting slope is -5

to find our b value we can plug in one of our coordinants into the equation and solve for b

1 = -5(9) + b

1 = -45 + b

46 = b

so our equation in y = -5x + 46

To solve the equation (j)/5 + 1 = -4, subtract 1 from both sides and then multiply by 5 to isolate j, which gives the solution j = -25.

To solve the equation (j)/5 + 1 = -4, you must first isolate the variable, j. Begin by subtracting 1 from both sides of the equation.

(j)/5 + 1 - 1 = -4 - 1

(j)/5 = -5

Next, multiply both sides by 5 to solve for j:

5 * (j)/5 = -5 * 5

j = -25

Therefore, the solution to the equation is j = -25.

Remember to always check your solution by substituting it back into the original equation to ensure it makes sense.

Check the picture below.

for "b", well, recall that the sum of all interior angles in a triangle is 180°.

for "a", "c" and "d", well, all those are just intercepted arcs.

Answer:

the front part of a person's head from the forehead to the chin, or the corresponding part in an animal.

Answer: 325 feet per minute

Step-by-step explanation: If 65 feet is one minute, all you have to do is multiply 65 by 5.

Answer:

325 feet

Step-by-step explanation:

65 x 5 = 325

for every minute, she travels 65ft

Answer:

(x-5) (x+1)

Step-by-step explanation:

x^2-4x-5

We need to find what 2 numbers multiply to -5 and add to -4

-5*1 = -5

-5+1 = -4

(x-5) (x+1)

5) We want to find the union and the intersection of the given intervals.

A1(0,3] ; A2 [2,6)

From the diagram we can see that the intersection is

[2,3]

The union is from the lower boundary of the first interval to the upper boundary of the second interval.

The union is (0,6)

6) The second interval is

A1= (-∞, 6) A2 =(6,∞)

From the diagram, this interval has no intersection.

The intersection is a null set

[tex] \emptyset[/tex]

The union of this set is

(-∞,∞)

Answer:

0.50

Step-by-step explanation:

0.30 + 0.20 = 0.50

(That answer feels almost too easy so I am not positive. I would wait for other answers to come in before submitting for your quiz/homework)

Answer:

B.0.44

Step-by-step explanation:

0.3+0.2=0.5 that is the probability that the player will either throw the ball into

the basket or kick the ball through the goal

0.5-0.06=0.44

0.06 is the probability of the player doing both, but the question said not both so just minus it and there comes your answer.

[tex]\bf \textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh~~ \begin{cases} b=base\\ h=height\\ \cline{1-1} A=56 \end{cases}\implies 56=\cfrac{1}{2}bh\implies 112=bh \\\\\\ \boxed{112=2\cdot 2\cdot 2\cdot 2\cdot 7}\to \begin{cases} 16\cdot 7\\ 8\cdot 14\\ 4\cdot 28\\ 2\cdot 56 \end{cases}\qquad or\qquad \begin{cases} 7 \cdot 16\\ 14 \cdot 8\\ 28 \cdot 4\\ 56 \cdot 2 \end{cases}[/tex]

so their product is 112, so tis just a matter of doing some quick prime factoring and combining the factors about.

The triangle with an area of 56 m² can have the base-height pairs: (1, 112), (2, 56), (4, 28), (7, 16), (8, 14), (14, 8), (16, 7), (28, 4), (56, 2), and (112, 1). These pairs satisfy the equation base × height = 112.

The formula for the area of a triangle is 1/2 × base × height. Given that the area of a triangle is 56 m², we can write this as:

Area = 1/2 × base × height

Rearranging for whole number dimensions, we get:

base × height = 2 × Area

Therefore, base × height = 112 m².

Next, we find all pairs of whole numbers (base, height) whose product is 112:

These are all the possible sets of whole number dimensions for the base and height of the triangle with an area of 56 m².

Answer:

x<168

Step-by-step explanation:

Answer:

(-1, 5.5)

Step-by-step explanation:

There are a number of techniques that can be used to solve a system of linear equations. Some of these techniques include;

Elimination method

Substitution method

Graphical method

In the graphical approach, we simply graph the linear equations on a cartesian plane. The solution to the system of equations is the co-ordinate of the point of intersection of the equations.

I use desmos graphing tool to graph the two equations;

y = -1/2x + 5

y = 1/2x + 6

From the attachment below, we can see that the lines intersect at (-1, 5.5)

Therefore, the solution to the given system of equations is (-1, 5.5)

Answer:

Associative property of addition

Step-by-step explanation:

We are given the statement [tex] ( a + b ) + c [/tex] and we are to determine whether which of the given answer options allows it to be written as [tex] c + ( a + b ) [/tex].

According to the associative property of addition, you can add the numbers regardless of how they are grouped.

Therefore, (a + b) + c = c + (a + b) is possible with associative property of addition.

The answer is commutative - addition!

The reason it is not associative is because while the direction changes, the parentheses does not move! In the associative, the parenthesis moves, but in (a + b) + c = c + (a + b), the parenthesis contains a + b in both of them. Also here is some picture proof. (Attached)

⭐ Answered by Hyperrspace (Ace) ⭐

⭐ Brainliest would be appreciated, I'm trying to reach genius! ⭐

⭐ If you have questions, leave a comment, I'm happy to help! ⭐

Answer:

x=3

Step-by-step explanation:

25x+57+x=45x

26x+57=45x

57=19x

x=57/19

x=3

ANSWER

x=96°

EXPLANATION

The sum of exterior angles of a polygon is 360°.

So we add all the exterior angles and equate to 360°

130°+134°+x=360°

264°+x=360°

x=360°-264°

x=96°

I think you are asking for 3 different ways of diving 100 pounds of potatoes into 5 and 2 pounds bags.

Alright:

I think you are asking for 3 different ways of diving 100 pounds of potatoes into 5 and 2 pounds bags.

Alright:

5 two pounds bags and 18 five pounds ones

10 two pounds bags and 16 five ones

15 two pounds bags and 14 five pounds ones

P(7) = 1/8 = 0.125 out of 1

The value of P(7) = 1/8 = 0.125

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty.

We can predict only the chance of an event to occur i.e. how likely they are to happen, using it.

There are 8 possibilities, all equally spaced

each one has a probability of 1/8

landing on a 7 is one options

so the P(7) is 1/8

P(7) = 1/8 = 0.125 out of 1

Toss a coin 100 times, how many Heads will come up, Probability says that heads have a ½ chance, so we can expect 50 Heads.

To learn more about Probability, refer

https://brainly.com/question/13604758

#SPJ2

Answer:

(6,-2)

Step-by-step explanation:

2x + 3y = 6

 x + y = 4

Multiply the second equation by -2 to eliminate x

-2(x+y) = -2*4

-2x-2y = -8

Add this to the first equation

2x + 3y = 6

-2x -2y = -8

---------------------

       y = -2

Now we need to find x

x+y = 4

x-2 = 4

Add 2 to each side

x-2+2 = 4+2

x = 6

(6,-2)

Answer:

(6,-2)

Step-by-step explanation:

Given equations are [tex]2x + 3y = 6[/tex] and [tex]x + y = 4[/tex].

Solve 2nd equation  [tex]x + y = 4[/tex] for y

[tex]x + y = 4[/tex]

[tex]y = 4-x[/tex] ...(i)

Plug value of y from equation (i) into first equation  [tex]2x + 3y = 6[/tex]

[tex]2x + 3(4-x) = 6[/tex]

[tex]2x + 12-3x = 6[/tex]

[tex]12-x = 6[/tex]

[tex]-x = 6-12[/tex]

[tex]-x = -6[/tex]

[tex]x = 6[/tex]

Plug x=6 into equation (i)

[tex]y = 4-x[/tex]

[tex]y = 4-6[/tex]

[tex]y = -2[/tex]

Hence final answer is x=6, y=-2 or we can write that in (x,y) form as (6,-2)

The value of the natural logarithm when x = 0.5 is rounded to the nearest hundredth is -0.69. So option B is correct.

When you raise a number with an exponent, there comes a result.

Let's say you get

a^b = c

Then, you can write 'b' in terms of 'a' and 'c' using a logarithm as follows

[tex]b = \log_a(c)[/tex]

'a' is called the base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'

Since x is lesser than 1, then the value of its natural logarithm must be negative.

The natural logarithm is a transcendental function and an irrational number, then it can be estimated by approximations.

ln ( 0.5) = -0.69

The value of the natural logarithm when x = 0.5 is rounded to the nearest hundredth is -0.69. So option B is correct.

Learn more about logarithm here:

https://brainly.com/question/20835449

#SPJ2

Answer:

a. 9.5x + 6.5(x+c) < 8   when c>0

b. Must be one child more than the no. of adults.

Step-by-step explanation:

For Cinema 1:

for adult = $9.50

for child = $6.50

For Cinema 2:

Per person regardless of age = $8.00

First of all, we will find out the condition when per person rates in both cinema are equal.

Assume x = no. of adults

y = no. of children

Rate per person in Cinema I = Rate per person in Cinema II

(9.5x + 6.5y)/(x+y)   =   8

9.5x + 6.5y = 8(x+y)

9.5x + 6.5y = 8x + 8y

9.5x-8x = 8y-6.5y

=> x = y

So rates are equal when no. of adults equals no. of children

For Cinema I to have better rates, no. of children should be atleast 1 more than the no. of adult. In this way the rate per person of Cinema I will be less than 8

Hence we form an inequality when y = x+c and c > 0

9.5x + 6.5(x+c) < 8   when c>0

Hence there must be 1 more children than the no. of adults attending Cinema I for it to be a better deal.

Answer:

9.50a+6.50c < 8.00(a+c), 6 children

Step-by-step explanation:

Let the number of adults be a

the number of children be c

Part 1 :

Cinema 1:

Cost for adults = $9.50 x a = 9.50a

Cost of children = $6.50 x c = 6.50c

Total cost = 9.50a+6.50c

Cinema 2 :

Total cost = 8.00(a+c)

The inequality which shows that the cinema I is cheaper

9.50a+6.50c < 8.00(a+c)

9.50a+6.5c<8a+8c

9.5a-8a<8c-6.5c

1.5a<1.5c

a<c

Case 2:

6 adults goes to cinema , let they are accompanied by c number of children

Cinema 1

Total cost = 9.5 x 6 + 6.5 x c

for cinema 2 the total cost will be

8 ( 6+c)

for cinema 1 to be a better deal

9.5 x 6 + 6.5 x c  < 8(6+c)

57+6.5c<48+8c

57-48<8c-6.5c

9<1.5c

c>6

Hence for Cinema 1 to be a better deal , there must be 6 children accompanying them

Answer:

Step-by-step explanation:

I can give you an answer, but I'm afraid it will only be true on paper.

Area = L * W

(x^2- 6x - 7) = L * (x - 7)

(x - 7)(x + 1) = L * (x - 7)

(x - 7)(x + 1)

=========     = L

(x - 7)

(x + 1) = L

The expression representing the length of a rectangle could vary depending on context, such as using graph measurements (Δx = 41 m), significant figures (1.25 cm), or scaling factors (4 inches × 2 = 8 inches).

To determine the expression that represents the length of a rectangle, we generally use the formula for the perimeter or area, depending on what information is available. In this case, information provided suggests different scenarios involving measurements and area calculations. From one scenario, the length of a rectangle is calculated using graph paper measurements, resulting in Δx = 41 m. In another scenario, we're given information about a rectangle's width being 1.25 cm with three significant figures.

In physics-related contexts, references to frame of reference and speed c suggest considering displacement in spacetime, though this might not relate directly to the geometrical dimensions of a rectangle. Lastly, one mention involves the scaling up by a factor, such as a square with side length doubled, resulting in a side length expression of 4 inches × 2 = 8 inches. Without further context, it is not possible to provide a definitive expression for the length of a rectangle.

Using the given inequality 16w≤ 40

Divide both sides by 16:

w ≤ 40/16

w ≤2.5

The answer would be: at most 2.5 ft wide.

The answer is A: at most 2.5 ft wide

Answer:

The solution to this system is (4, 1/6).

Step-by-step explanation:

Please separate these two equations for clarity.  I like to write them in column format:

2.5y + 3x = 27

5x – 2.5y = 5

---------------------

8x           = 32, and x = 4.

Subbing 4 for x in the second equation yields 5(4) - 2.5y = 5.

Then 20 - 2.5y = 5, or 15 = 2.5y.  Solving for y, we get y = 1/6.

The solution to this system is thus (4, 1/6).

Answer: The resultof adding the two equations is 3x= 32.  

The solution to the system is ( 4; 6).

Step-by-step explanation:

Hi, first we add the two equations.

2.5y + 3x =27

+

-2.5y +5x   = 5

----------------------

8x= 32

The resultof adding the two equations is 3x= 32

the next step is solving the equation:

8x= 32

x=32/8

x= 4

Substituting the value of x in any of the original equations:

2.5y +3x= 27

2.5y +3(4) =27

2.5y +12=27

2.5y  = 27-12

2.5y = 15

y= 15/2.5

y=6

So, the solution to the system is ( 4; 6)

Feel free to ask for more if it´s necessary or if you did not understand something.

Answer:

19/50

Step-by-step explanation:

.38 is equal to 38/100 so if you do half of that it is 19/50

Hope this helps!

Answer:

[tex]\frac{19}{50}[/tex]

Step-by-step explanation:

0.38 ← note 38 represents 38 hundredths, that is

0.38 = [tex]\frac{38}{100}[/tex] ← divide numerator/denominator by 2

       = [tex]\frac{19}{50}[/tex] ← in simplest form

Answer:

15 two-point questions and 5 four-point questions.

Step-by-step explanation:

Let x represent number of two-points questions and y represent number of four-points questions.

We have been given that Janice wants to create a test containing 20 questions. We can represent this information in an equation as:

[tex]x+y=20...(1)[/tex]

Since all questions are worth 50 points. We can represent this information in an equation as:

[tex]2x+4y=50...(2)[/tex]

From equation (1), we will get:

[tex]x=20-y[/tex]

Upon substituting this value in equation (2), we will get:

[tex]2(20-y)+4y=50[/tex]

[tex]40-2y+4y=50[/tex]

[tex]40+2y=50[/tex]

[tex]40-40+2y=50-40[/tex]

[tex]2y=10[/tex]

[tex]\frac{2y}{2}=\frac{10}{2}[/tex]

[tex]y=5[/tex]

Therefore, there are 5 questions that are worth 4 points each.

Now, we will substitute [tex]y=5[/tex] in equation (1) to solve for x.

[tex]x+5=20[/tex]

[tex]x+5-5=20-5[/tex]

[tex]x=15[/tex]

Therefore, there are 15 questions that are worth 2 points each.

Answer: C, the mean is most likely about 28 lbs.

Step-by-step explanation: The mean of a data set is the average value. When looking at this histogram, you can determine how many bags were checked in  total by adding up the frequencies for each weight.

Add the Weights

1+16(4)+20(5)+24(6)+28(5)+32(4)+36(3)+40+48+52+56+60

**16(4)=64. The number in parenthesis represents how many times each weight occurred in the data set. To make it easier, you can combine some of these instead of typing the extended equation into your calculator.

12+64+100+144+140+128+108+208= 904

Solve for the Mean

To do this, divide 904 by the number of bags checked (32).

Mean: 28.25

**The answer is MORE than 28, but it would round down because the decimal is less than half.

Hope this helps,

LaciaMelodii :)

The mean is most likely more than 28 pounds

The median is given as:

Median = 27.5 pounds

The mean is calculated as:

[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]

So, we have:

[tex]\bar x = \frac{12+16(4)+20(5)+24(6)+28(5)+32(4)+36(3)+40+48(0)+52+56+60}{32}[/tex]

[tex]\bar x = \frac{904}{32}[/tex]

[tex]\bar x = 28.25[/tex]

28.25 is approximately 28, and it is more than 28

Hence, the mean is most likely more than 28 pounds

Read more about mean and mode at:

https://brainly.com/question/14532771

Answer: 82.26 yd^2

Step-by-step explanation:

Solve this question in steps.

Find the area of the rectangle.

9x6=54

Now, find the area of the circle.

The diameter is 6 so the radius must be 3.

3^2xpi=9pi=28.26

Add the values together.

54+28.26=82.26

Hope this helps!

The equation for the annual driving cost, C, in terms of d, the number of miles driven is C = 0.125 d + 5000.

In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .

Now it is given that,

annual cost of driving = $5000 per year

operating costs of car =  12.5 cents per mile = $0.125

Let total distance drive annually be dmile

So, operating costs of car annually  = $0.125 of total distance drive

⇒operating costs of car annually  = $0.125  of d

⇒operating costs of car annually  = $0.125 d

So,  equation for the annual driving cost, C, in terms of d, the number of miles driven is given as,

annual driving cost, C = operating costs of car annually + annual cost of driving

⇒ C = 0.125 d + 5000

Hence,The equation for the annual driving cost, C, in terms of d, the number of miles driven is C = 0.125 d + 5000.

To learn more about annual driving cost :

https://brainly.com/question/24296898

#SPJ2

For this case we have that by definition, the Greatest Common Factor or GFC of two or more numbers, is the largest number that divides them without leaving residue.

So, we have to:

We look for the factors of 18 and 36:

18: 1,2,3,6,9,18

36: 1, 2,3,4, 6,9,18 ...

It is observed that the GFC of both numbers is 18.

Then, the GFC of [tex]18x ^ 2[/tex] and [tex]36x[/tex] is:

18x

Answer:

18x

Answer:

6 miles per hour

Step-by-step explanation:

speed = distance/time

speed = 1/2÷1/12 which is the same as

1/2 x 12/1 = 6

6 miles per hour.

or ou could change the 1/2 to become 0.5

and the 1/12 to become 0.083333333

and divide 0.5 ÷ 0.083333333 = 6.000000024

rounded to one decima place become 6.0

6 miles per hour

Answer:

8 hour is the answer hope this help

Step-by-step explanation:

Answer:

The answer is 41.

Answer:

41

Step-by-step explanation:

Gabrielle's age = G

Mikhail's age = M

G = M - 15

G + M = 67

Substituting:

M - 15 + M = 67

2M = 82

M = 41

Mikhail is 41.