You make a scale drawing of a tree using the scale 5 inches. = 27 feet. If the tree is 67.5 feet tall, how tall is the scale drawing?

Th measure of arc AB will be 60 degrees

The figure shown shows a circle with lines AC and BD intersecting the circle at the point E

From the figure given the measure of the arc AB is congruent to the arc CD.Given that the measure of arc CD is 60 degrees, hence the measure of arc AB will also be 60 degrees

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Hello,

[tex]y = ax + b[/tex]

We know the slope is 2 so :

[tex]y = 2x + b[/tex]

The equation of the line that passes through the point (5,4) so :

[tex]4 = 2 \times 5 + b[/tex]

[tex]4 = 10 + b[/tex]

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

[tex]b = - 6[/tex]

The equation of the line that passes through the point (5,4) and has a slope of 2 is :

[tex]y = 2x - 6[/tex]

y = 2x - 6

Most lines are written in slope-intercept form, but we can use slope-point form in situations like this.

Slope-Point Form

The formula for slope-point form is [tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]. So, we can plug in the information we have, the point and slope.

This is an equation for the line given to us. However, this form can be simplified further.

Slope-Intercept Form

Slope-intercept form is written as y = mx + b, where m is the slope and b is the y-intercept. To find the most simplified form of the equation we need to use the properties of equality.

First, distribute the 2

Next, add 4 to both sides

Now, we have the equation for the line in slope-intercept form. Both of the equations technically meet the requirements for the question, but slope-intercept is more common to use.

The solution to [tex]\left(2+\sqrt{2}\right)^{\log_2\left(x\right)}+x\left(2+\sqrt{2}\right)^{\log_2\left(x\right)} = 1 + x^2[/tex] is x = 1

The equation is given as:

[tex]\left(2+\sqrt{2}\right)^{\log_2\left(x\right)}+x\left(2+\sqrt{2}\right)^{\log_2\left(x\right)} = 1 + x^2[/tex]

Split the equation as follows:

[tex]y\ =\ \left(2+\sqrt{2}\right)^{\log_2\left(x\right)}+x\left(2+\sqrt{2}\right)^{\log_2\left(x\right)}[/tex]

[tex]y = 1 + x^2[/tex]

Next, we plot the graph of both equations (see attachment)

From the attached graph, the intersection point is (1, 2)

Remove the y value

x = 1

Hence, the solution to [tex]\left(2+\sqrt{2}\right)^{\log_2\left(x\right)}+x\left(2+\sqrt{2}\right)^{\log_2\left(x\right)} = 1 + x^2[/tex] is x = 1

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It is possible to arrange the total of mangoes by using 20 piles of 9 mangoes, 18 piles of 10 mangoes, or 15 piles of 12 mangoes.

The conditions for mangoes to be arranged are that the piles should have either 9, 10 or 12 mangoes and reminders are not allowed. This means you need to fit all the mangoes and no mangoes can be left.

Based on the conditions and the total number of mangoes (180 mangoes), here are the possibilities that you can determine using division:

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The transformation that occurred after the dilation of the parallelogram is a translation of 9 units to the right.

A unique variety of quadrilateral made up of parallel lines is called a parallelogram. A parallelogram can have any angle between its neighboring sides, but it must have opposite sides that are parallel for it to be a parallelogram. If the opposite sides of a quadrilateral are parallel and congruent, it will be a parallelogram. Consequently, a quadrilateral in which both pairs of opposite sides are parallel and equal is referred to as a parallelogram.

The initial parallelogram was dilated by a scale factor of 2 about point P.

The points of the initial parallelogram are: (-4, 0), (-2, 0), (-3, -3), (-5, -3).

The parallelogram obtained on dilation will have the points: (-6, 0), (-2, 0), (-4, -6), (-8, -6).

The points of the final parallelogram are: (3, 0), (7, 0), (5, -6), (1, -6).  

(-6,0) →(3,0)  ⇒ (x,y)→(x+h , y+k)

x = -6 , x+h = 3 ⇒ h=3-x = 3-(-6) = 9

y = 0 , y+k = 0 ⇒ k = 0

The transformation rule is (x,y)→( x+9 , y )

That is, a translation of 9 units to the right.

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Answer:

A. a translation of 9 units to the right

Step-by-step explanation:

Edge 2023

Answer:

2.603 degrees

Step-by-step explanation:

This word problem is talking about a triangle. 500 meters high would be the height and 11 Kilometers would be the base. We should convert kilometers to meters in order to make this easier. 11 kilometers = 11,000 meters.

Height = 500

Base = 11,000

The hypotenuse ends up being 11,011.35777

in order to find the angle of depression (assuming it is a constant rate) we would measure the angle where the hypotenuse meets the base. (11,000 & 11,011.35777) the angle comes out at 2.603 degrees. Hope this helped!

Answer:

C. 16 days

Step-by-step explanation:

Let´s say each worker does 1 ¨work¨, for each day, in order to complete the job in 15 days. That´s a total of 150 work.

If only 6 workers worked for the first 5 days, then we only do 30 by Day 5.

2 more workers join, so they do 8 work each day, 24 work in 3 days, 54 work by Day 8.

4 more workers join to complete the job, so we now do 12 work each day.

150 - 54 = 96

96 work is left to do, which would be done in 8 days by 12 workers.

8 days + 8 days = 16 days

Answer:

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Answer:

108°

Step-by-step explanation:

We know for a theorem that A = B, so:

4x + 28 = 2x + 68

Isolating the x:

2x = 40

x = 20

Now let's plug in the equation for A:

4(20) + 28 = 108°

By applying trigonometric expression and direct comparison, we conclude that a = 2 such cos 255° - cos 195° = √a / 2

In this question we need to simplify a trigonometric expression in order to find the value of a. In this case, we need to use the following formula:

[tex]\cos \theta - \cos \xi = - 2\cdot \sin \left(\frac{\theta + \xi}{2} \right)\cdot \sin \left(\frac{\theta - \xi}{2} \right)[/tex]

Then,

cos 255° - cos 195° = - 2 · sin 225° · sin 30°

cos 255° - cos 195° = - 2 · sin (- 135°) · sin 30°

cos 255° - cos 195° = 2 · sin 135° · sin 30°

cos 255° - cos 195° = 2 · (√2 / 2) · (1/2)

cos 255° - cos 195° = √2 / 2

Then, by direct comparison we find that a = 2.

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Answer:

The answer is circle.

Step-by-step explanation:

For all the rest of the shapes, we use certain base x height formulas.  Square uses base x height along with parallelograms and trapezoids. For a triangle, we use [tex]\frac{base x height}{2}[/tex]. Though, for a circle, we use the formula  [tex]\pi r^{2}[/tex] where r= radius.

The answer is: 2(m+1)

First combine like terms.
we do 6m-4m which is 2m
2m+2=?

Second we factor. We notice that both terms have 2.
2(m+1)

by distributive law, the 2 is distributed to m and 1.

The sum of the first five terms is 11/2

The series is given as:

1/2, -1,2,-4…

Calculate the common ratio of the series using

r = -4/2

Evaluate

r = -2

The sum is then calculated as:

[tex]S_n = a\frac{1 - r^n}{1 - r}[/tex]

This gives

[tex]S_n = \frac{1}{2} * \frac{(1 - (-2)^5}{1 + 2}[/tex]

Evaluate

[tex]S_n = \frac{1}{2} * \frac{33)}{3}[/tex]

Evaluate

[tex]S_n =\frac{11}{2}[/tex]

Hence, the sum of the first five terms is 11/2

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Answer:

[tex]r=\sqrt{\frac{V}{\pi h}}[/tex]

Step-by-step explanation:

[tex]V = \pi r^{2} h \\ \\ r^{2} =\frac{V}{\pi h} \\ \\ r=\sqrt{\frac{V}{\pi h}}[/tex]

The return on the investment is 3%

The given parameters are:

Buying rate = 7%

Selling rate = 10%

The return on the investment is

ROI = Selling - Buying

So, we have:

ROI = 10% - 7%

Evaluate

ROI = 3%

Hence, the return on the investment is 3%

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The expected value of the outcome of the bid is $0.18

So let's start by counting how many bids are placed up to a total of 160.

100*160 = 16000.

What will be your arbitrary bid? As each bid has an equal chance of success, the average of all bids is used. (One cent plus 160 dollars) / 2 = 80 dollars (rounded)

Your odds of winning are 1/16000 (1 bid out of 16000).

If you win, your profit is 1920 ($2000 minus $80.00).

1920/16000 is $0.12

Your cost to enter the auction is $1, and your average winning offer is $0.12.

The result is $0.18 (0.12-1=-0.88).

Thus the expected value of the outcome of the bid is $0.18

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It's 4 buns & 5 cakes

Hope my explanation to the other one helps, if not, you can draw them; while following the steps & you may get it better.

E.g draw a box for the bun & a circle for the cake, then, adding them up to get the 95p. Also, you keep taking away from 435p

Answer:

BC = 18 cm

Step-by-step explanation:

As we can see from the diagram:

AB + BC + CD = AD

⇒ 10 cm + BC + 11 cm = 39 cm

⇒ BC + 21 cm = 39 cm

⇒ BC = 39 cm - 21 cm

⇒ BC = 18 cm

The measure of arc RT is 156 degree.

Given:

arc TRM=102°

Hence:

arc RST=2×1O2°

arc RST=204°

Measure of arc RT

arc RT= 2(180° - 102°)

arc RT = 2(78°)

arc RT = 156 degrees

Therefore the correct option is B.

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Using proportions, it is found that the total percentage increase in the investor's stock account was of 6.2%.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

The values of the stocks of Company A and Company B, after the increase are given, respectively, by:

The total values are given as follows:

The percent increase is given by the increase divided by the initial value and multiplied by 100%, hence:

P = (8668 - 8160)/8160 x 100% = 6.2%.

The total percentage increase in the investor's stock account was of 6.2%.

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The solution to the system of equation is (0, 1)

Given the following system of equation as shown below

2^(x)+3^(y)=5,

2^(x+2)+3^(y+1)=18

Rewrite

2^(x)+3^(y)=5,

2^x*2^2 + 3^y*3^1 = 18

___________

2^(x)+3^(y)=5,

4(2^x) + + 3(3^y) = 18

Let a = 2^x and b = 3^y

Substitute

a + b = 5

4a + 3b = 18

a = 5 - b

Substitute

4(5-b) + 3b = 18

20 - 4b + 3b = 18

-b = -2

b = 2

since a = 5 - b

a = 5 - 2

a = 3

Recall that a = 2^x and b = 3^y

2^x = 2

x = 0

Similarly

3^y = 3

y =1

Hence the solution to the system of equation is (0, 1)

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The information given about the landscape is illustrated below:

a. You'll need a measuring tape, two range poles, pegs, and three people.

The first person holds the zero mark between their thumbs and fingers, the second person holds the 3m mark on the tape between their thumbs and fingers, and the third person holds the 8m. When all sides of the rope are stretched, a triangle is created, and an angle near one is a right angle.

Wrap one loop of the rope around peg A with a peg through the other loop, draw a circle on the ground, place pegs B and C where the circle crosses the base line, and place peg D half way between pegs B and C, allowing pegs D and A to form lines perpendicular to the base line, forming a right angle.

B. Method 1; Take a measurement of the distance between both trees and divide by 2 to get the midpoint.

Method 2; By use of a compass to bisect the distance between both points.

Method 3; By using a protractor to mark the 90° vertical point when placed between the two endpoints.

C The three different ways he can do this.

1) by using a protractor

2) by finding a point

3) by extending the line of the angle until it reaches the other side of the field.

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Since Angle ABD and Angle DBC are complementary angles, the measure of Angle ABC is 90 degrees.

Hence, option D is the correct answer.

Two angles are called complementary when their measures add to 90 degrees.

From the diagram; Angle ABD and Angle DBC are complementary angles that add up to make 90 degrees.

Since Angle ABD and Angle DBC are complementary angles, the measure of Angle ABC is 90 degrees.

Hence, option D is the correct answer.

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well, we know the suits are all reduced by 20%, so the man saved 20% of 231.20

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{20\% of 231.20}}{\left( \cfrac{20}{100} \right)231.20}\implies 46.24[/tex]

the equation of the new function is:

[tex]g(x) = 2^{x - 5} - 7[/tex]

We have a function:

[tex]f(x) = 2^x[/tex]

And we want to shift it five units to the right, and seven units down, then the new function will be:

[tex]g(x) = f(x - 5) - 7[/tex]

If we now replace f(x), we get:

[tex]g(x) = 2^{x - 5} - 7[/tex]

That is the equation of the new function.

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Answer: Look at step by step

Step-by-step explanation:

(a) There are 119 stocks that increased in price out of 246 stocks so the probability of selecting a stock that is increased in price is 119/246 = 48.37%

(b) There are 112 stocks where it pays dividends so the probability so the probability of selecting a stock that pays dividends is 112/246 = 45.53%

(c) There are 49 stocks which satisfy the question so the probability is 49/246 = 19.92%

(e) There are 34 stocks which increase in price and pay dividends out of the 119 stocks that increase in price so the probability is 34/119 = 28.57%

(f) Using the same logic as (e), the probability is 85/134 = 63.43%

(g) From the requirements, we see that 49 stocks don't satisfy the requirements, so the probability is (246-49)/246 = 80.08%

Answer: m > -16

Step-by-step explanation:

[tex]\frac{3}{4}m > -12\\\\m > -\frac{4}{3}(12)=-16[/tex]

The general solution of the logistic equation is [tex]y(t) = \frac{14}{1 - C\cdot e^{-\frac{14\cdot t}{3} }}[/tex].

The particular solution of the logistic equation is [tex]y(t) = \frac{14}{1 + 0.4 \cdot e^{-\frac{14\cdot t}{3} }}[/tex].

In this question we are before a type of ordinary differential equation known as equation with separable variables, that is to say, that variables t and y can be separated at each side of the expression in order to find a solution:

dy / dt = 3 · y · (1 - y /14)

dy / [(- 3 / 14 ) · y · (y - 14)] = dt

Then, we simplify the expression by partial fractions and integrate the resulting expression:

- (1 / 14) ∫ dy / y + (1 / 14)∫ dy / (y - 14) = - (14 / 3)∫ dt

- (1 / 14) · ㏑ |y| + (1 / 14) · ㏑ |y - 14| = - (14 / 3) · t + C, where C is the integration constant.

㏑ |(y - 14) / y| = - (14 / 3) · t + C

[tex]1 - \frac{14}{y} = C\cdot e^{-\frac{14\cdot t}{3} }[/tex]

[tex]\frac{14}{y} = 1 - C \cdot e^{-\frac{14\cdot t}{3} }[/tex]

[tex]y(t) = \frac{14}{1 - C\cdot e^{-\frac{14\cdot t}{3} }}[/tex]

The general solution of the logistic equation is [tex]y(t) = \frac{14}{1 - C\cdot e^{-\frac{14\cdot t}{3} }}[/tex].

If y(0) = 10, then the particular solution of the differential equation is:

10 = 14 /(1 - C)

1 - C = 1.4

C = - 0.4

The particular solution of the logistic equation is [tex]y(t) = \frac{14}{1 + 0.4 \cdot e^{-\frac{14\cdot t}{3} }}[/tex].

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Step-by-step explanation:

1. if the number of pages in the 1st day is 'x', then the 2d day - 'x+10', the 3d day - 'x+20', the 4th day - 'x+30', the 5th day - 'x+40' and the last day - 'x+50' pages;

2. if the sum of all the pages is 300, then it is possible to make up the equation:

x+x+10+x+20+x+30+x+40+x+50=300;

3. x=25, it means:

1st day - 25;

2d day - 35;

3d day - 45;

4th day - 55;

5th day - 65;

6th day - 75 pages.