Find the equation of a line perpendicular to y= 3x + 7 that passes through the
point (9,-7).

F - 1.47

The largest box represents 100 small cubes or 1. The four pillars represent 10 and there is four of them so it is 40. Then, the individual cubes are 7. So, 1.47.

Step-by-step explanation:

Pythagoras, Pythagoras, Pythagoras.

c² = a² + b²

for c being the Hypotenuse (the side opposite of the 90 degree angle).

that is something you should really burn into your brain for life. you will need that many times.

1.

89² = 80² + side²

side² = 89² - 80² = 1521

side = sqrt(1521) = 39 ft

2.

D

because here the x value of 2 has to different assigned result (y) values. but for a function it had to be exactly 1 value.

3.

the longer of the 2 given sides must be the Hypotenuse, because otherwise we would get a negative length.

97² - 72² = side² = 4225

sqrt(4225) = side = 65 cm

4.

the distance between 2 point is the Hypotenuse of a right-angled triangle, with its legs being the differences in x and y coordinates.

F = (-1, 6)

G = (3, 4)

FG² = (-1 - 3)² + (6 - 4)² = 16 + 4 = 20

FG = sqrt(20) = 4.472135955... ≈ 4.5

so, A is the right answer.

5.

that creates a right-angled triangle, with the flag pole and the distance on the floor to the flag pole as the legs, and the rope as Hypotenuse.

rope² = 53² + 28² = 3593

rope = sqrt(3593) ≈ 60 ft

6.

A

85² = 36² + 77²

7225 = 1296 + 5929 = 7225

correct. this is a right-angled triangle.

B

101² = 99² + 20²

10201 = 9801 + 400 = 10201

correct. this is a right-angled triangle.

C

123² = 120² + 27²

15129 = 14400 + 729 = 15129

correct. this is a right-angled triangle.

D

42² = 33² + 24²

1764 = 1089 + 576 = 1665

incorrect.

1764 - 567 = 1089 ?

1197 = 1089

also incorrect.

as is 1764 - 1089 = 567 and 1089 - 567 = 1764

so, this is not a right-angled triangle.

7.

the sum of all angles in a triangle (also in general triangles) is always 180 degrees.

since the right angle is already 90 degrees, it leave only 90 degrees for the other 2 angles.

A is the only correct option. 25 + 65 = 90.

8.

BC = 13

AC = 3

AB² = AC² + BC² = 3² + 13² = 9 + 169 = 178

AB = sqrt(178) = 13.34166406... meter

the tree was then originally

3 + 13.34166406... = 16.34166406... meter high

12.1.1

35² = 21² + side²

side² = 35² - 21² = 1225 - 441 = 784

side = sqrt(784) = 28 m

12.1.2

side² = 16² + 30² = 256 + 900 = 1156

side = sqrt(1156) = 34 ft

12.2.3

61² = 60² + 11²

3721 = 3600 + 121 = 3721

correct. this is a right-angled triangle.

12.2.4

40² = 37² + 9²

1600 = 1369 + 81 = 1450

incorrect. this is not a right-angled triangle.

neither is 1600 - 1369 = 81 nor 1600 - 81 = 1369 nor 1368 - 89 = 1600

12.2.5

38² = 35² + 15²

1444 = 1225 + 225 = 1450

incorrect. this is not a right-angled triangle.

neither is 1444-1225=225 nor 1444-225=1225 nor 1225-225 = 1444

12.2.6

53² = 45² + 28²

2809 = 2025 + 784 = 2809

correct. this is a right-angled triangle.

12.3.8

the x and y coordinate differences between A and B are 6 and 3.

AB² = 6² + 3² = 36 + 9 = 45

AB = sqrt(45) = 6.7

12.3.9

the x and y coordinate differences between B and C are 1 and 7.

BC² = 1² + 7² = 1 + 49 = 50

BC = sqrt(50) = 7.1

12.3.10

the x and y coordinate differences between A and C are 5 and 4.

AC² = 5² + 4² = 25 + 16 = 41

AC = sqrt(41) = 6.4

final question : you need that in many distance calculations, side lengths, diagonals, heights,... for rooms, yards, acres, buildings, mountains, ...

Answer:

4096

Step-by-step explanation:

Explanation:

The rule we use is (a^b)^c = a^(b*c). It says to multiply the exponents when we raise one exponential expression to another exponent. The base stays the same.

So, (2^4)^3 = 2^(4*3) = 2^12

You could take the slightly longer path to say the following

(2^4)^3 = (2^4)*(2^4)*(2^4) = 2^(4+4+4) = 2^12

Percent Change = (new quantity - old quantity) / old quantity

#2:

(64 - 52) / 52

12 / 52

0.2308

23%

#4:

(12 - 18) / 18

-6 / 18

-0.33

33% decrease

#5:

(10 - 16) / 16

-6 / 16

-0.375

38% decrease

Hope this helps! :)

Answer:

5 pens

Step-by-step explanation:

1.85 divided by 5 is .37

3.12 divided by 8 is .39

so 1.85 is a better deal

Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

A standard die has 6 numbers, so the probability it will be greater than 4 is 6-4, or 2. Therefore the answer is [tex]\frac{2}{6}[/tex], but this can be simplified to [tex]\frac{1}{3}[/tex].

Answer:

  x + y = 3 (infinite solutions)

Step-by-step explanation:

You observe that all of the numbers in the second equation are multiples of 3. When you divide the second equation by 3, it becomes identical to the first equation. The equations are said to be "dependent."

That means both equations graph as the same line, so will intersect at every point on the line. The system of equations has an infinite number of solutions.

_____

Additional comments

There are a number of ways to solve a system of equations. Two methods commonly taught are "substitution" and "elimination". Either one works here.

We can solve the first equation for y by subtracting x from both sides:

  x +y -x = 3 -x

  y = -x +3 . . . . . . simplify

In this form, the slope is the coefficient of x. Here, it is -1.

This expression for y can be substituted into the other equation:

  3x +3(-x +3) = 9

  3x -3x +9 = 9 . . . . . eliminate parentheses

  9 = 9 . . . . . . . . . . . simplify

This is true for all values of x or y. There are an infinite number of solutions.

Answer:

There are infinite numbers of solution.

Step-by-step explanation:

[tex]\begin{gathered}\begin{gathered}\begin{gathered}\small\begin{cases}\sf{x + y= \bf{3}} \\ \\ \sf{3x + 3y= \bf{9}}\end{cases} \end{gathered}\end{gathered}\end{gathered}[/tex]

Solving the question and finding the final answer.

Here,

Now, from equation (i),

[tex]\twoheadrightarrow{\sf{x + y = 3}} [/tex]

[tex]\twoheadrightarrow{\sf{x = 3 - y}} [/tex]

Now, putting the value of x in equation (ii)

[tex]\begin{gathered} \qquad{\longrightarrow{\sf{3x + 3y = 9}}} \\ \\ \qquad{\longrightarrow{\sf{3(3 - y) + 3y = 9}}} \\ \\ \qquad{\longrightarrow{\sf{9 - 3y + 3y = 9}}} \\ \\ \qquad{\longrightarrow{\sf{9 - 0 = 9}}} \\ \\ \qquad{\longrightarrow{\sf{9 - 0 = 9}}} \\ \\ \qquad{\longrightarrow{\sf{\underline{\underline{\red{9 = 9}}}}}}\end{gathered}[/tex]

This statement is true for all values of x and y.

So, there are infinite numbers of solution.

[tex]\underline{\rule{220pt}{3pt}}[/tex]

65% more than 140 is  231

Answer:

$30,2400

Step-by-step explanation:

First, we need to find how much interest he earns in a month

8.4% of $12,000 = $1,008

Next, we multiply the amount of interest per month by the number of months in 25 years

25 years = 300 months

Now we can multiply the two values to get our final answer

1,008 x 300 = $30,2400

Answer: What does I stand for? If you meant 1, 1 to the power of 5 is 1.

Answer:

i

Step-by-step explanation:

i^5=(i)(i)(i)(i)(i)

Since i^2=(i)(j)=-1,

it follows that i^4=(i^2)(i^2)=(-1)(-1)=1.

Thus i^4*i=i^5=1*i=i.

Therefore, i^5=i.

Answer: y = -2x + 8

Step-by-step explanation:

gradient = change in y/ change in x = 8/-4 = -2

y = -2x + c

substitute values in

8 = 0 + c

c = 8

y = -2x + 8

The graph of a line passes through the points (0, 8) and (4, 0), the equation of the line is y = -2x + 8

The line is the distance between two points. The equation of a line in slope-intercept form is y = mx + b

Slope = -8/4
Slope = -2

Determine the y-intercept

Since the y-intercept is the point where the line cross the y-axis, hence b = 8.

FInd the required equation

y = -2x + 8

Hence if the graph of a line passes through the points (0, 8) and (4, 0), the equation of the line is y = -2x + 8

Learn more on equation of a line here: https://brainly.com/question/18831322

Answer:

x < 6

Step-by-step explanation:

1) -5x > -30

2) divide both sides by -5

3) flip the sign as we divided inequality by a negative

4) x < 6

Answer:

Part A:

The equation describing the relationship between speed and time is:

s = 32t

Ordered pairs of the form (speed, time) are:

(32, 1)

(64, 2)

(96, 3)

(128, 4)

Part B:

s = 32t

s = 32 * 5 = 160 feet per second

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Height of the cliff = 500 feet

Speed after one second = 32 feet per second

Speed after four seconds = 128 feet per second

2. Assume the relationship between time, t, and speed, s, is linear and write an equation describing the relationship. Use ordered pairs of the form (speed, time)

The equation describing the relationship between speed and time is:

s = 32t

Ordered pairs of the form (speed, time) are:

(32, 1)

(64, 2)

(96, 3)

(128, 4)

3.  Use the equation to determine the speed of the rock 5 seconds after is dropped.

s = 32t

s = 32 * 5 = 160 feet per second

Answer:

y = 5

Step-by-step explanation:

-4(2y) +11y = 15

-8y + 11y = 15

3y = 15

y = 5

Step-by-step explanation:

4⁵ × 4^-7 / 4^-2

it is important to understand that a negative exponent means 1/...

a^-n = 1/(a^n)

in that sense we have therefore

4⁵ × 1/4⁷ × 4² (as (1/ 1/a^n) = a^n)

4⁵ × 4² × 1/4⁷ = 4⁷ × 1/4⁷ = 1

so, "1" is the fully simplified expression equal to the original expression.

Answer:

4

Step-by-step explanation:

Well 3 x 4 equals 12, 12 x 4 equals 48, and so on.

hope this helps!

Step-by-step explanation:

60 cookies with 4 cups

that means 60 per 4 = 60/4 = 15

and that means that he can make 15 cookies with 1 cup.

that is clear : from 60/4 we immediately know 15/1.

and now, as we know how many cookies can be made with 1 cup, it is easy to say how many cookies can be made with 3 cups. right, 3 times a much.

so, yes, we multiply 15 by 3 and get 45 cookies as answer.

=====================================================

Explanation:

Let's find the LCM of 4 and 5, which are the first two items of the list.

The smallest item in each list is 20, so the LCM of 4 and 5 is 20.

We can replace the "4,5" in the list "4,5,12,15" with "20". So our new list would be "20,12,15".

We then repeat the process of finding the LCM of the first two items

LCM of 20 and 12 is 60.

The list "20,12,15" condenses to "60,15".

Repeat this process of finding the LCM once more and you'll find the overall LCM is 60.

Therefore, the LCM of the entire set {4,5,12,15} is 60. This is the smallest multiple shared by all four values. Interestingly enough, the outer values pair up to multiply to 60, and so do the inner values.

4*15 = 60

5*12 = 60

The bells ring together every 60 minutes

In other words, all of the bells ring together at the same time every hour (perhaps at the top of every hour; eg at 7:00 pm and at 8:00 pm, etc).

Answer:

Youngest child: $2

oldest child: $6

Second oldest: $2.50

Step-by-step explanation:

Youngest child= x

oldest child= 3x

Second oldest: .50+x

x+3x+.50+x=10.5

5x+.50=10.5

    - .50= - .50

5x=10

divided both numbers by 5 and x is equal to 2. So, the youngest child is $2 and you add .50, which is $2.50, and thats for the second child. Last, you do 2 times 3 equals $6 which is the oldest child.

The youngest contributed $1.90, the oldest contributed $5.27, and the second oldest contributed $2.85.

Three children each contributing to their mother's birthday present. The eldest gave three times more than the youngest, while the second oldest contributed 50 cents more. If the gift costs $10.50 which is given in the question.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

Let the youngest sibling contribute the amount of x dollars

As per the given information,

3x + 0.50 x + x + x = 10.50

Apply the addition operation,

4.50x = 10.50

x = 10.50 / 6.50

Apply the division operation to get

x = 1.90

So the youngest sibling contributed = $1.90

The oldest contributed 1.90 × 3 = $5.27

And the second oldest contributed (1.50)1.90= $2.85

Therefore, the youngest contributed $1.90, the oldest contributed $5.27, and the second oldest contributed $2.85.

Learn more about Arithmetic operations here:

brainly.com/question/25834626

#SPJ5

Answer:

3 (x - 4)

Step-by-step explanation:

Answer:

y-intercept: (0,5)

x-intercept: (5/2,0)

Step-by-step explanation:

[tex]-4x+7=2y-3[/tex]

[tex]-4(0)+7=2y-3[/tex]

[tex]0+7=2y-3[/tex]

[tex]7=2y-3[/tex]

[tex]10=2y[/tex]

[tex]5=y[/tex] <-- y-intercept: (0,5)

[tex]-4x+7=2y-3[/tex]

[tex]-4x+7=2(0)-3[/tex]

[tex]-4x+7=-3[/tex]

[tex]-4x=-10[/tex]

[tex]x=\frac{5}{2}[/tex] <-- x-intercept: (5/2,0)

Answer:

(6 + n) - 8

Hope this helps.

Pls mark brainliest. :D

Answer:x < 2

Step-by-step explanation: 6+x < 8

x < (8-6)

x < 2

Answer:

I think that if u times it i will be 80 s and 320 f

Step-by-step explanation:

Answer:

390.377

Step-by-step explanation:

pi*r^2

Answer:add 126 and 21 and 1.19

Step-by-step explanation:

126+21+1.19=

hope this helped

Answer:

7.14

Step-by-step explanation:

126 miles divided by 21 miles is 6 miles

So 6 gallons for 126 miles

1.19 times 6 is 7.14

Answer:

110 squares

Step-by-step explanation:

= 10 x 11

= 110 small squares.

From the question,

Step one : • • = 1(2) small squares

Step two : • • • = 3 squares in two layers = 2(3) = 6 small squares

• • •

Step three : • • • • = 4 squares in 3 layers = 3(4) = 12 small squares

• • • •

• • • •

Answer:

k = 10

Step-by-step explanation:

the sum of any two interior angles is equal to the exterior angle of the unknown interior angle

4k+5 + 6k+10 = 115

10k + 15 = 115

10k = 100

k = 10