How high up on a wall will a 20-foot ladder touch if the foot of the ladder is placed
4 feet from the base of the wall?

Considering the angle relations when two parallel lines are cut by a transversal, the measures of the angles are given as follows:

18. <4 = 56º.

19. <3 = 132º.

20. <2 = 55º.

21. <8 = 120º.

22. <6 = 129.5º.

23. <2 = 61.3º.

When two parallel lines are cut by a transversal, there are multiple relations among the angles, which are going to be used to solve this question.

In item 18, the angles 1 and 4 are consecutive interior angles, hence they are supplementary angles, meaning that the measure of angle 4 is found as follows:

<4 + <1 = 180º

<4 + 124º = 180º

<4 = 56º.

In item 19, angles 2 and 3 are also consecutive interior angles, hence:

<2 + <3 = 180º

48º + <3 = 180º

<3 = 132º.

For item 20, angles 2 and 4 are alternate interior angles, hence they are congruent and their measures are given by:

<2 = <4 = <55º.

For item 21, angles 6 and 8 are alternate exterior angles, also being congruent, hence their measures are given as follows:

<6 = <8 = 120º.

For item 22, angles 7 and 6 are same side exterior angles, meaning that they are supplementary, hence:

<6 + <7 = 180º

<6 + 50.5º = 180º

<6 = 129.5º.

For item 23, the relation is the same as item 19, hence:

<3 + <2 = 180º

<2 = 180 - 118.7

<2 = 61.3º.

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Answer:

Maybe 30°

Cause 12:4 is 3

3x10 30

The central angle of a regular dodecagon is 30 degrees. Option A is the correct option.

The central angle - The angle created at the polygon's center by two adjacent radii—the lines that connect the polygon's center to its vertices—is known as the central angle.

We know it is a regular dodecagon, which means all the sides will be of equal size.

As it is a dodecagon there will be a total of 12 equal central angles added to give an angle of 360 degrees.

Let's assume the central angle is x.

12x = 360

x = 360/12

x = 30

Hence, the central angle in a regular dodecagon is 30 degrees.

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Answer:

The given expression is not a complete equation or function. It seems like a linear function, but it is missing an input variable and an equal sign.

A linear function in the form of y = mx + b, where y is the output, x is the input, m is the slope, and b is the y-intercept.

Without the input variable, we cannot evaluate the function. Can you please check if you have provided the complete equation or function?

Step-by-step explanation:

Answer: 10.7%

Step-by-step explanation:

The percentage error will be calculated as:

Estimated value - Actual value / Actual value × 100

= (40 - 48) / 48 × 100

= 8/48 × 100

= 1/6 × 100

= 10.7%

On solving the question, The expression that most effectively represents u's value would be:  u = 2s

A area that is formed by a secant or chord and the matching arc of the circle is referred to as a segment of a circle. The major section is the one that shows a greater region, while the minor segment is the one that shows a smaller area.

We have

In ΔABC,

E is the midpoint in the segment AC,

While D is the midpoint of BC,

As different letters are provided equivalent to different segments. For example; Segment ED = s ; Segment CE = p ; Segment EA = r

\(Segment CD = q ; \\Segment DB = t ; \\Segment ED = s ; \\Segment AB = u\)

As,

CE = 0.5 × AC(midpoint)

CD = 0.5 × CB (midpoint)

Thus,

\(\frac{CE}{AC} = \frac{CD}{CB} = \frac{ED}{AB} = \frac{1}{2}\)        (Through side angle side similarity)

Since ED = s and AB = u

Therefore,

u = 2s                                   (using midpoint theorem)

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To find the integrating factor for the given

ODE

, we need to first rearrange the

equation

into the standard form of y' + p(x)y = q(x), where p(x) = 0 and q(x) = Ndx + x - t^3 + e^(-Nt^2).

Dividing both sides of the equation by N, we get:

dx/dt + (1/N)x = (1/N)t^3 - e^(-Nt^2)

Now, we can find the

integrating factor

by taking the exponential of the

antiderivative

of p(x), which is:

e^∫(1/N)dx = e^(x/N)

Therefore, the integrating factor for the given ODE is e^(x/N). Multiplying both sides of the ODE by this integrating factor, we get:

e^(x/N)dx/dt + (1/N)e^(x/N)x = (1/N)e^(x/N)t^3 - e^((x/N)-Nt^2)

Recognizing the left-hand side as the product rule of (e^(x/N)x), we can simplify the equation to:

d/dt(e^(x/N)x) = (1/N)e^(x/N)t^3 - e^((x/N)-Nt^2)

Integrating

both sides with respect to t, we get:

e^(x/N)x = (1/N)e^(x/N)(1/4)t^4 + (1/2N)e^((x/N)-Nt^2) + C

where C is the constant of integration. Solving for x, we get:

x = (1/N)(1/4)t^4 + (1/2N)e^(-Nx^2) + Ce^(-x/N)

where we have used the fact that e^(x/N) is never zero since x > 0. Therefore, we have found the

general solution

for the given ODE.

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If d represents how many dozens of eggs were ordered, then the expression that represents the number of eggs that were ordered is 12d. Therefore, if we order d dozen of eggs, we will have 12 * d eggs.

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Ans

Step-by-step explanation:

a solution is always inside the shaded area!

Answer:

D=375g/cubic inch

Step-by-step explanation:

D=500 divided by 4/3

The test statistic value for the hypothesis test is -2.5, indicating that the efficiency measures have reduced the gasoline prices of the major oil company in Europe. So, the correct answer is option c).

To determine the test statistic for this hypothesis test, we need to calculate the z-score, which is the number of standard deviations that the sample mean is away from the population mean under the null hypothesis.

The null hypothesis is that the efficiency measures have not reduced prices, which means the population mean is still $1.25 per liter. The alternative hypothesis is that the efficiency measures have reduced prices, which means the population mean is less than $1.25 per liter.

The formula for the z-score is:

z = (sample mean - population mean) / (standard deviation / sqrt(sample size))

Plugging in the values from the paragraph:

z = (1.20 - 1.25) / (0.14 / sqrt(49)) = -2.5

So the value of the test statistic for this hypothesis test is -2.5.

Therefore, the answer is C) -2.5.

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Therefore, Bonnie mixes approximately 0.67 milliliters of vinegar with every 1 milliliter of soy sauce.

To determine how much soy sauce Bonnie mixes with every 1 milliliter of vinegar, we divide the total amount of soy sauce (150 milliliters) by the amount of vinegar (100 milliliters):

150 milliliters of soy sauce / 100 milliliters of vinegar = 1.5 milliliters of soy sauce per 1 milliliter of vinegar

Therefore, Bonnie mixes 1.5 milliliters of soy sauce with every 1 milliliter of vinegar.

To determine how much vinegar Bonnie mixes with every 1 milliliter of soy sauce, we divide the total amount of vinegar (100 milliliters) by the amount of soy sauce (150 milliliters):

100 milliliters of vinegar / 150 milliliters of soy sauce ≈ 0.67 milliliters of vinegar per 1 milliliter of soy sauce

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Answer:

It would be (3,0) its in the 1st grid and if you rotate it 90 degrees its now in the second grid which flips the sign on the x value.

Step-by-step explanation:

Jeremiah average velocity during the drive was 80 km/h while the instantaneous velocity at one point was 105 km/h

An equation is used to show the relationship between numbers and variables.

Average velocity is the ratio of total distance travelled to total time taken. Instantaneous velocity is the velocity at a particular point in time.

Jeremiah completed a straight, 120 km drive in 1.5 hours, hence:

Average velocity = total distance / total time

Average velocity = 120 km / 1.5 hours = 80 km/h

At one point during the drive, he saw that his speedometer read 105 km/h, hence:

Instantaneous velocity = 105 km/h

The average velocity is 80 km/h while the instantaneous velocity is 105 km/h

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Answer:

Option B = 108 cm

Step-by-step explanation:

Please refer the figure attached

As the given figure have four 90° angles,

AB = CH

BC = AH

So, AB = 30 cm , CH = 30 cm

BC = 15 cm, AH = 15 cm

Already given ED = FG = 5 cm, EF = 11 cm

Working note : As, AB = CH = 30 cm

CH = CD + 3cm + GH

30 = CD + 3cm + GH

CD + GH = 27 cm

Perimeter is the overall measure of the boundary of the given figure, ie

AB + BC + CD + DE + EF + FG + GH + AH

= 30 + 15 + CD + 5 + 11 + 5 + GH + 15

= CD + GH + 81

= 27 + 81

Perimeter = 108 cm

c.) 3(2x-6)

Reason:-

3(2x-6) = 6x-18

Answer:

C, D, and E are your answers

3 x 2x = 6x, 3 x 6 = 18

6x - 18

x + 5x = 6x

6x - 18

2 x 3x = 6x

2 x 9 = 18

6x - 18

well, let's pick any two random x-values on the quadratic, hmmm say let's use x = 4  and x = 7, so hmm f(4) = 5 and f(7) = 32, that'd give us the points of (4, 5) and (7 , 32).

To get the equation of any straight line, we simply need two points off of it, let's use those two above.

\((\stackrel{x_1}{4}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{32}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{32}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{7}-\underset{x_1}{4}}} \implies \cfrac{ 27 }{ 3 } \implies 9\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{ 9}(x-\stackrel{x_1}{4}) \\\\\\ y-5=9x-36\implies {\Large \begin{array}{llll} y=9x-31 \end{array}}\)

Check the picture below.

Refer to the attached images.

Answer:

1. 3.2 x 10^4

2. 6 x 10^4

3. 1.04 x 10^5

4. 1.82 x 10^7

5. 9.23 x 10^6

6. 4.05 x 10^5

7. 2.019 x 10^3

8. 3.02 x 10^4

Step-by-step explanation:

Next time don't randomly comment on other people's questions to get points without putting in the effort. Spread credibility, not liability. Do the rest by yourself; there are multiple resources online that you can learn from!

Answer:

1. 3.2 x 10^4

2. 6 x 10^4

3. 1.04 x 10^5

4. 1.82 x 10^7

5. 9.23 x 10^6

6. 4.05 x 10^5

7. 2.019 x 10^3

8. 3.02 x 10^4

Step-by-step explanation:

I really hoped this helped

Answer:

The Great Western Trail = 4,455 miles

Step-by-step explanation:

The Iditarod Trail = 1,025 miles long

The Great Western Trail is 355 miles longer than 4 times the length of the Iditarod Trail.

The Great Western Trail = (4 × 1,025) miles + 355 miles

= 4,100 miles + 355 miles

= 4,455 miles

The Great Western Trail = 4,455 miles

Answer:

1.c

Step-by-step explanation:

please click the heart and rate excellent and brainleist to☻❤☺️☺️❤☻

The polynomial can be factored as\($(3x + 6)(x^2 - 3x - 18)$\). This can be done by factoring out the greatest common factor of 3x and then factoring the remaining expression using the quadratic formula.

\($3x(x^2 + 6x - 18)$\)

\($x^2 + 6x - 18 = (x + 6)(x - 3)$\)

\($3x(x + 6)(x - 3) = (3x + 6)(x^2 - 3x - 18)$\)

The polynomial 3x3 + 18x2 - 9x - 54 can be factored by first factoring out the greatest common factor of 3x. This leaves us with the expression x2 + 6x - 18, which can be further factored using the quadratic formula. The quadratic formula states that any expression of the form ax2 + bx + c can be factored as (x + a)(x + c). In this case, a = 6 and c = -3. Thus, the expression can be factored as (x + 6)(x - 3). Combining the two factors, we get (3x + 6)(x2 - 3x - 18). This is the factored form of the polynomial. By factoring the polynomial, we are able to easily identify the zeroes of the polynomial, which are +6 and -3. In addition, factoring the polynomial allows us to easily identify the degree of the polynomial, which is 3.

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The complete question is

How do you factor this polynomial 3x^3 + 18x^2 - 9x - 54 ?

Answer:

3(x - 2)² - 17

Step-by-step explanation:

The equation of a quadratic in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Using the method of completing the square.

Given

3x² - 12x - 5 ← factor out 3 from the first 2 terms

= 3(x² - 4x) - 5

To complete the square

add/subtract ( half the coefficient of the x- term)² to x² - 4x

= 3(x² + 2(- 2)x + 4 - 4 ) - 5

= 3(x - 2)² - 12 - 5

= 3(x - 2)² - 17 ← in vertex form

Answer:

YZ=16

Step-by-step explanation:

Because they are parallel

9514 1404 393

Answer:

  m∠CAB = 62°

  m∠CBG = 114°

Step-by-step explanation:

Given:

  the above figure

Find:

  What are the measures of angles CAB and CBG

Solution:

The total angle at C is 32°+52° = 84°. We know that "remote interior" angles ECB and EBE have a sum that matches angle CEF.

So, angle CBE = 150° -84° = 66°

Angle CBG is the supplement of this, so is ...

  m∠CBG = 180° -66° = 114°

That angle is the total of "remote interior" angles BCA and CAB. So angle CAB is ...

  m∠CAB = 114° -52° = 62°

The equations of the two circles are (x-0)^2 + (y-0)^2 = 2^2 or x^2 + y^2 = 4 and (x-1)^2 + (y-1)^2 = 1^2 or (x-1)^2 + (y-1)^2 = 1.

The equation of a circle with centre (a,b) and radius r is given by (x-a)^2 + (y-b)^2 = r^2.

C1 has centre (0,0) and radius 2, so its equation is (x-0)^2 + (y-0)^2 = 2^2 or x^2 + y^2 = 4.

C2 touches the x and y axes each in one point, so it must have a centre on the line y=x and a radius equal to the distance from the centre to either of those points of tangency. Since the centre of C2 is on the line y=x and it is in the first quadrant, the coordinates of the centre are (1,1). The distance from the centre to the point of tangency on the x-axis is 1, so the radius is 1. The equation of C2 is (x-1)^2 + (y-1)^2 = 1^2 or (x-1)^2 + (y-1)^2 = 1.

Therefore, The equations of the two circles are (x-0)^2 + (y-0)^2 = 2^2 or x^2 + y^2 = 4 and (x-1)^2 + (y-1)^2 = 1^2 or (x-1)^2 + (y-1)^2 = 1.

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Answer:

Step-by-step explanation:

We know that:

We don't know:

Let's count up by tenths:

It suddenly stops at 0.8.

Let's count up by hundredths:

It stops at 0.85.

0.85 is your answer.

Answer:

C. 128ft

Step-by-step explanation:

it's C because whenever it says and you're supposed to multiply always remember that :) = (which means area ofc) you're finding the so you multiply 16x8 and the you get your answer (: ignore the 640 you just focus on the 16 and 8 ok? 16x8=128! :))

>:(

roots = {-2, -6}

Factors: (x + 6) and (x + 2)

Answer: a. in the step by step explanation.  b. 20x - 15

Step-by-step explanation:

I think that Denise thought that the 5 only appplied to 4x since they were closer and since she multiplied them both, she thought there would be no use of it.

Example - 2 (3x+2)

                 2 x 3x = 6x

                 6x + 2

Of course this is wrong since the real answer should be 6x + 12 but someoneone like Denise may see it that way, only multiplying the ones closest and not opening it fully.

The value of x in the parallelogram is 21.

To find the value of x in the parallelogram, we can equate the lengths of the opposite sides of the parallelogram. In this case, we have side AD equal to 36 and side BC equal to 2x - 6.

Setting these two expressions equal to each other, we have:

36 = 2x - 6

To solve for x, we can isolate it on one side of the equation. Adding 6 to both sides of the equation, we get:

36 + 6 = 2x

To simplify, we have:

42 = 2x

Finally, we can solve for x by dividing both sides of the equation by 2:

x = 42/2

Evaluating the expression on the right side, we find:

x = 21

Therefore, the value of x in the parallelogram is 21.

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Answer:

1

Step-by-Step Explanation:

30° and 60° are angles of one of the standard triangles

sin (30°) = 1/2

cos(30°) = √3/2

sin(60°) = √3/2

cos(60°) = 1/2

So,

sin(60°) · cos(30°) + sin(30°) · cos(60°)

= (√3/2)(√3/2) + (1/2)(1/2) = 3/4 + 1/4

= 1

One of the conventional triangles' angles is 30 degrees and 60 degrees.

sin (30)= 1/2

cos (30)= √3/2

sin (60)= √3/2

cos (60)= 1/2

So, Sin (60)・cos (30) + sin (30) ・cos (60)