A 12 foot ladder leans against a wall so that the base of the ladder is 7 feet from the wall. How high up on the wall will the ladder reach? Round to the nearest hundredth of a foot.

Step-by-step explanation:

A function is continuous at x is

Limit as x approaches c= f(c).

Step 1: Find f(4).

4 is defined for 2x-1 so plug in. 4 for x.

[tex]2(4) - 1 = 7[/tex]

Note that what we just calculated was not only f(4) but also the left sided limit of f(x).

Step 2: Make sure the left sided and right sided limit are equal to 7.

[tex]a + 5x = 7[/tex]

Plug in 4 for x

[tex]a + 5(4) = 7[/tex]

[tex]a = - 13[/tex]

Answer: No solution

Step-by-step explanation:

Ths lines are parallel (as they have the same slope but different y-intercepts), and parallel lines never intersect. Thus, the system has no solutions because the lines never intersect.

Answer:

7 and 8

Step-by-step explanation:

49 - 1 = 48. (1)

48 - 3 = 45. (2)

45 - 5 = 40. (3)

40 - 7 = 33. (4)

33 - 9 = 24. (5)

24 - 11 = 13. (6)

13 - 13 = 0. (7) The answer is 7

64 - 1 = 63. (1)

63 - 3 = 60. (2)

60 - 5 = 55. (3)

55 - 7 = 48. (4)

48 - 9 = 39. (5)

39 - 11 = 28. (6)

28 - 13 = 15. (7)

15 - 15 = 0. (8) the answer is 8

Answer:

Step-by-step explanation:

      In this, the given number is subtracted by consecutive odd numbers (1,3,5,7,9.....)  till we fer zero at the end. Count the number of steps performed and this number will be square root of the given number.

a) 49

√49 = 7

b)  64

√64 = 8

The height of the triangle FGH is equal to 51 units.

Triangle FGH is an equilateral triangle, thus we understand that each of its sides is identical.

Every side's length is specified as 34√3 units.

In order to split HF into two equivalent halves, use a perpendicular bisector. This implies,

34√3/2=17√3

By using the Pythagorean theorem, which states that the total of a triangle's two sides matches the square of its hypotenuse, we may determine the height.

a²+b²=c²

Here, a=17√3

b=height &

c=34√3

Therefore, from the above equation, we can say,

b²=c²-a²

⇒b²=(34√3)²-(17√3)²

⇒b²=([tex]34^{2}*3[/tex])-([tex]17^{2} *3[/tex])

⇒b²=3468-867

⇒b²=2601

⇒b=[tex]\sqrt{2601}[/tex]

⇒b=51 units

Hence, it is concluded that the height of the triangle is (c)51 units.

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Answer:

C. 51 units

Step-by-step explanation:

Answer:

Function

Step-by-step explanation:

Yes, the graph is a function. For each x value, there is a unique y value that corresponds with it.

A graph can also be tested as a function by using the popular "vertical-line test".

The Sine or Sinθ in a right-angle triangle is the ratio of its perpendicular to its Hypotenuse. The principal value of sin⁻¹(1) is 90°.

The Sine or Sinθ in a right-angle triangle is the ratio of its perpendicular to its Hypotenuse. it is given as,

Sin(θ) = Perpendicular/Hypotenuse

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

The hypotenuse is the longest side of the triangle.

The principal value of sin⁻¹(1) is,

θ = Sin⁻¹(1)

θ = 90°

Hence, the principal value of sin⁻¹(1) is 90°.

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Answer:

so y represents her age right now so if we go back we are subtracting so he age would be y-5

a

Hope This Helps!!!

The number of cookies packs needed if the treasurer buys 1 package of brownies bites is 5 packs

15b + 12c = 75

If 1 package of brownies is bought

15b + 12c = 75

15(1) + 12c = 75

15 + 12c = 75

12c = 75 - 15

12c = 60

c = 60/12

c = 5 packs

If 9 packages of brownies are bought

15b + 12c = 75

15(9) + 12c = 75

135 + 12c = 75

12c = 75 - 135

12c = -60

c = -60/12

c = -5 packs

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The drag phase you have given the interference would be a positive x-axis.

As Sally determines the angle of rotation, since it is π, she lies on the negative x-axis.

The first block then should be the negative x-axis if r is positive and on the positive x-axis if r is negative.

It is a phenomenon in which two or more waves superimpose to form a resultant wave of greater or lower amplitude.

My other reason for changing the dragged phase would be as they used the word, therefore, in the last sentence.

Which would mean interference from the above statements, from the drag phase you have given the interference would be a positive x-axis.

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Answer:

28 portraits

Step-by-step explanation:

Let's first figure out how many portraits Lamy can paint in 1 week, which is his unit rate. To calculate this, we just have to divide the number of portraits he paints by the amount of time it takes him to paint them.

In this case, the former quantity is 84 portraits, and the latter quantity is 6 weeks, so his unit rate is [tex]\frac{84 \text \: portraits}{6 \text \: weeks}[/tex] = 14 paintings per week.

Now, we know that in 1 week, Lamy can paint 14 portraits. Therefore, since this is a directly proportional relationship, all we have to do to find how many portraits he can paint is 2 weeks is double the unit rate. This is because in a directly proportional relationship, if you multiply one variable by a number, you have to multiply the other by the same number to maintain equality, and here we are multiplying weeks by 2 so we need to multiply paintings by 2 as well.

Thus, Lamy can paint 14 · 2 = 28 paintings in 2 weeks.

Hope this helps!

Answer:

70 is the right answer....

Answer:

70 ways

Step-by-step explanation:

8 C 4 =   8 ! / ( 4! * 4!) = 70 ways

Answer: This looks like it is a reflection of the y-axis and then an enlarging dilation.

Answer:

20

Step-by-step explanation:

-10 + 20 = +10

Answer:

[tex]\fbox {20}[/tex]

Step-by-step explanation:

Let the required term be x

Then :

Answer:

111

Step-by-step explanation:

555÷5=111
and just to check, 5×111=555

Answer:

555 divided by 5 = 111

Step-by-step explanation:

This is common knowledge. The 5 in the hundreds place is divisible by 5 to get a quotient of 1. The 5 in the tens place is also divisible by 5 to get a quotient of 1 and the same is equally true for the 5 in the ones place.

Hence, the quotient of 555/5 = 111

Hope this helps! :D

Answer:

5.25

Step-by-step explanation:

Answer:

Step-by-step explanation:

type 63 : 12 in your calculator

see the example in the attachment.

Answer

The answer is A. y = x²

Answer:

C. 6

Step-by-step explanation:

6*1=6

6*3=18

6*4=24

6*7=42

Hope this helps!

If not, I am sorry.

Answer:

positive 1!

Step-by-step explanation:

i got it right on the test trust me!

Rational numbers are numbers that can be written in the form of a/b where a and b are integers.

Rational numbers are numbers that can be written in the form of a/b where a and b are integers.

Example: 1/2, 3.5 (which is writable as 7/5), 2(which is writable as 4/2), etc.

Irrational numbers are those real numbers that are not rational numbers.

For example √2, π, √13, etc.

It is an important thing to Know that all natural numbers are integers, and all integers are rational numbers. That means natural numbers are not irrational.

The given statement that any fraction is made up of two natural numbers is a rational number is true.

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The graph of the parent function is given below;

The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Here, the given function is;

         1, if -1<x≤0

f(x) = 2, if 0<x≤1

          3, if 1<x≤2

Now, the graph of given function is given below.

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Answer:

The correct graph is in the image below

Step-by-step explanation:

By evaluating the polynomial, we will see that the sign on the interval [-4, 2] is negative.

Here we have the polynomial:

f(x) = (x - 2)*(x + 4)*(x + 5).

You can see that the roots of the polynomial are at:

x = 2

x = -4

x = -5.

Then, on the interval [-4, 2], the sign of the polynomial don't change. So to get the sign of f(x) on that interval we can just evaluate it in any value of x that belongs to the interval, for example, x = 0.

f(0) = (0 - 2)*(0 + 4)*(0 + 5) = -2*4*5 = -40

With this, we can conclude that the sign of f(x) on the given interval is negative.

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Answer:

always negative

Step-by-step explanation:

The constructed bisector of line segment given below in the image.

Process to construct the bisector of a line segment :

Step 1 : Make the compass length ( the distance between the pointed leg and the pencil leg) slightly greater than half the length of the line segment OP. Place the point of the compass on O. Make arcs above and below the line segment OP.

Step 2 : Using the same compass length as same as the previous one, place the point of the compass on P. Make arcs above and below line segment OP. These arcs must intersect the arcs made in previous step.

Step 3 : Connect the points where the arcs intersect. Label the line segment MN and the point where the line intersects OP, Q.

Step 4 : Line segment MN bisects line segment OP at midpoint Q.

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Answer:

Math and Writing

Step-by-step explanation:

Well if we add up all the people we get (9 + 3 + 5 + 3 + 1) = 21. Half of that is 10.5 so the sum of the two subjects must be at least 11. The amount of people that like Math and Writing is 11 people so the two subjects that more than half the class like are Math and Writing.

Answer:

Math and Writing

Step-by-step explanation:

Number of students who like each subject:

Total number of students = 9 + 3 + 5 + 3 + 1 = 21

Half of 21 = 21 ÷ 2 = 10.5

Therefore, more than half the class would be > 10.5 students

Total number of students who like:

Therefore, the only combination of subjects that more than 10.5 students like is Math and Writing as 12 > 10.5

Answer:

E.  5

Step-by-step explanation:

Let's rewrite the equation in the form of y=mx+b, where m is the slope and b is the y-intercept (the value of y when x = 0).

2x + y = 5

y = -2x+5

M, the slope, is -2

5, b, is the y-intercept

See attached graph.

Answer:

-1/2

Step-by-step explanation:

sin(30 degrees) = sin (pi/6) = 1/2

cos(30 degrees) = cos (pi/6) = [sqrt(3)]/2]

sin (60 degrees) = sin(pi/3) = [sqrt(3)]/2]

1/2 - [sqrt(3)/2] / [sqrt(3)/2] = -1/2

[tex]i^{30}=(i^2)^{15}=(-1)^{15}=-1[/tex]