Hays builds model sailboats as a hobby. The dimensions of the sailboats are given. What is the height, x, of the smaller sailboat's sail? Enter your answer, as a decimal, in the box. x = in. Two sailboats with sails that are right triangles. The top angle on the sails are marked congruent to each other. The smaller sail has a height of x and a base of 7 inches. The larger sail has a height of 12 inches and a base of 8 inches.

Answers

Answer 1
The answer should be 10.5 
Answer 2

The smaller sail has a height of 10.5 inches.

Given to usTwo sailboats with sails that are right triangles.The top angle on the sails is marked congruent to each other.The smaller sail has a height of x and a base of 7 inches.The larger sail has a height of 12 inches and a base of 8 inches.

Similarity of triangles

We know that for the two sails of the sailboat,

the right angle will be equal,

the angles at the top of the sail are congruent, {given}

therefore, the third angle will be equal for both the triangles.

thus, both the triangles will be similar to each other.

For similar triangles,

The sides will be in ratio.

[tex]\dfrac{12}{8}=\dfrac{x}{7}[/tex]

[tex]\dfrac{12\times 7}{8}=x\\x = 10.5[/tex]

Hence, the smaller sail has a height of 10.5 inches.

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Related Questions

Jana wants to navigate page 35 of her report. what is the quickest way to navigate?

Answers

To navigate to page 35 of a report, you can use the 'find' function in a web browser with CONTROL or COMMAND + F, utilize the table of contents with hyperlinks, or enter the page number in a navigator window's spin box, depending on the device and format.

To quickly navigate to page 35 of a report, you have several options depending on the format and the device you are using. If you are viewing the report on a web browser, you can usually press CONTROL or COMMAND and the letter F to open the 'find' function and type '35' to jump to page 35. Alternatively, if the document has a table of contents with hyperlinks, you can click on the relevant section to navigate quickly. For documents with a navigator window, enter '35' in the spin box to jump straight to that page. In a mobile reading environment, you may find a Contents button at the top of the screen; clicking this can allow you to select and jump to the desired page or section.

Indicate a general rule for the [tex] n^{th}[/tex] term of this sequence.
-6a, -3a, 0a, 3a, 6a. . .
A.] [tex] a_{n}=3an+9a[/tex]
B.] [tex] a_{n}=-3an-9a[/tex]
C.] [tex] a_{n}=-3an+9a[/tex]
D.] [tex] a_{n}=3an-9a[/tex]

Answers

Answer: option D) An = 3an - 9a

Justification:

1) That is an arithmetic sequence which you prove by determining the difference between two consecutive terms (which shall be constant if it indeed is an arithmetic sequence):

2)

Second term - first term = -3a - (-6a) = -3a + 6a = 3a
Third term - second term = 0a - (-3a) = 3a
Fourth term - third term = 3a - 0a = 3a
Fith term - fourth term = 6a - 3a = 3a

Therefore, it is an arithmetic sequence with difference d = 3a.

3) the general rule for the nth term of an arithmetic sequence is given by the formula:

An = Ao + d (n - 1)

Where Ao = -6a and d, as determined above, is 3a

=> An = -6a + 3a (n - 1)

Expand the parenthesis (distributive property) =>

An = -6a + 3an - 3a = -9a + 3an = 3an - 9a = option D. <------- answer.

Northbound buses with tourists leave Waco for Dallas at 10 minute intervals. The trip takes exactly one hour. Southbound tourist buses leave Dallas for Waco at the same moment as their northbound counterparts and arrive an hour later. How many southbound buses does a northbound bus encounter between Waco and Dallas, including the one that is arriving in Waco just as the northbound bus leaves for Dallas and the one that is departing from Dallas just as the northbound bus arrives there?

Answers

Answer: 13 buses.

Explanation:

When a Northbound bus leaves Waco there are 7 buses on the way from Dallas, including the one that is arriving at Waco and one departing from Dallas.

If you do not visualize it, think that the Northbound bus departs at 6:00 am, then the bus arriving at Waco departed at 5:00 am, other departed at 5:10am, other at 5:20, other at 5:30, other at 5:40, other at 5:50 and other at 6:00 am. Those are 6 buses that the Northbound bus will encounter on its way.

After that, there will departure other 6 buses that the Nortbound bus will encounter. The times for those departures are: 6:10am, 6:20am, 6:30am; 6:40am, 6:50am and, the last one, 7:00am just when it is arriving.

Therefore, the Northbound bus will encounter 7 buses + 6 buses = 13 buses, which is the answer.

I need help on #9. The help would be grateful appreciated.

Answers

Original Figure:
Length = 15
Width = 5
Height = 10
Volume = Length*Width*Height
Volume = 15*5*10
Volume = 750

New Figure
Length = 3
Width = 1
Height = 2
Each dimension has been divided by 5 (eg: 15/5 = 3)
Volume = Length*Width*Height
Volume = 3*1*2
Volume = 6

The old volume was 750 and it changes to 6
Notice how 750/6 = 125
Which can be rearranged to 750/125 = 6

Answer: if you divide the old volume by 125, then you get the new volume

Note: the new volume is 125 times smaller than the old volume
Put another way, the old volume is 125 times larger compared to the new volume

The fact that 125 = 5^3 is not a coincidence. If you divide each dimension by some number k, then you divide the volume by k^3

18 points were scored by one figure skating pair that was 40% of your final score. What was the final score for that pair of figure skaters?

Answers

We can solve this problem using cross-multiplying method.

We have following information
18 points = 40%
We need to find out the final score. Let's use x for final number of points.
x points = 100%

We can write this:
18 points = 40%
x points = 100%

We cross multiply numbers
18*100=x*40
1800=40x /:40
1800/40=x
x=45

The final score was 45 points.

Choose the pair of numbers that is not a solution to the given equation.
y = 5 - 2x
My options are;
1,3
2,1
0,3

Answers

y = 5 - 2x 
3 = 5 - 2(1) True 
 1=5-2(2) True
 3=5-2(0) False 
 0,3 is not a solution

At the start of a race, a runner’s velocity changes from 0 to 4.0 m/s. It takes him 2 seconds to speed up. His acceleration is ______ m/s2.

Answers

To find the acceleration we divide the change of velocity by the change of time.
Change of velocity: 4 m/s
Change of time: 2 s

Acceleration = [tex] \frac{4}{2} = 2[/tex]

So the answer: his acceleration is 2 m/s^2

His acceleration is, 2 m/s^2!

Hope this helps! :)

Solve for x where a is an integer less than 0

Answers

Basically the question is asking to solve for x if a is negative.

So to do this, simply change the sign for a to -a in the original equation and solve for x.

-ax > -12

X < 12/a.

This is the solution.










The graph shows the number of copies a copier can make. What is the unit rate?
A)
1
25
B) 5
C) 15
Eliminate
D) 25

Answers

i think it D) 25 because if u look at the graph it show 75 copies number in 3 minutes.

Answer:

25

Step-by-step explanation:

A bakery sold 115 cupcakes in one day. The head baker predicted he would sell 95 cupcakes that day. What was the percent error of the baker's prediction?

Answers

It was about 17.4% 
======================================================================

% error=
actual value-estimated value 
Then divide that by actual value

The baker's prediction had a 17.39% error.

To calculate the percent error of the baker's prediction, we use the formula:

Percent Error = (|Actual Value - Predicted Value| / Actual Value) * 100%

In this case, the Actual Value is the number of cupcakes actually sold, 115. The Predicted Value is the number the baker predicted to sell, 95.

So, the computation will be:

Percent Error = (|115 - 95| / 115) * 100%

Percent Error = (20 / 115) * 100

Percent Error = 0.1739 * 100%

Percent Error = 17.39%

Find the ordered triple of these equations. 2x - 3y - 4z = -21 -4x + 2y - 3z = -14 -3x - 4y + 2z = -10

Answers

I did my best hope this helps

If you were given the equation f ( x ) = 3x⁵+6x, what behavior would the ends of the graph have?

a. Both ends will point up
b. Both ends will point down
c. the left end will start down at a large negative and the right end will go upwards
d. the left end will start up at a large positive and the right end will go downwards EXPLAIN ANSWER

Answers

The function given in the problem is a Polynomial Function of degree 5. These functions have the following form: f(x)=ax^5+bx^4+c^3+d^2+ex+f. They have an R domain and their graphs are continuous curves.
 
 You can know the behavior of the function f(x)=3x⁵+6x by given values to the variable x and plot each point obtained. For example:
 
 If x=-1⇒ f(-1)=3(-1)⁵+6(-1)=9
 
 If x=0⇒ f(0)==3(0)⁵+6(0)=0
 
 If x=1⇒ f(1)=3(1)⁵+6(1)=9
 
 Therefore, as you can see in the graph attached, the correct answer is:
 
  c. The left end will start down at a large negative and the right end will go upwards.


Final answer:

The ends of the graph of the function f(x) = 3x^5 + 6x will display the behavior described in option c. This is due to the highest power of x in the equation being an odd number and the coefficient being positive. As such, the left end of the graph will start down at a large negative and the right end will go upwards.

Explanation:

The behavior of the ends of the graph of the function f(x) = 3x^5 + 6x is determined by the highest power of x in the equation, which is 5 in this case. The coefficient of x^5 is positive, so as x approaches positive infinity, f(x) also approaches positive infinity. Conversely, as x approaches negative infinity, the value of f(x) would approach negative infinity. We can describe this behavior as the left end of the graph starting at a large negative and the right end going upwards. Thus, answer c. 'the left end will start down at a large negative and the right end will go upwards' is correct.

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What is the solution set for the quadratic equation x2 - 16 = 0?

A)
{4}


B)
{-4, 4}


C)
{256}


D)
{-256, 256}

Answers

B) {-4, 4} 

Proof:

Solve for x over the real numbers:
x^2 - 16 = 0

The left hand side factors into a product with two terms:
(x - 4) (x + 4) = 0

Split into two equations:
x - 4 = 0 or x + 4 = 0

Add 4 to both sides:
x = 4 or x + 4 = 0

Subtract 4 from both sides:

Answer:  x = 4 or x = -4

Find the area of circle B in terms of π.

Answers

Answer:

(2.25π) yd²

Step-by-step explanation:

The area of a circle is given by the formula:

[tex]\boxed{\text{Area of circle}=\pi r^{2} }[/tex] , where r is the radius.

In this question, the radius is 1.5 yd.

Substitute r= 1.5 into the formula:

Area of circle B

[tex]=\pi (1.5)^2[/tex]

= (2.25π) yd²

Additional:

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Does the interest rate increase at a constant rate?
6 months = 2.4%
9 months = 2.9%
12 months = 3.0%
18 months = 3.1%

Answers

No.

From 6 mo to 12 mo, it increases 0.6%.
From 12 mo to 18 mo, it increases 0.1%. The change over a 6 mo period gets smaller as the period gets longer or the rate gets higher.
neverminding for a second that the rate is in percents.

it seems what's being asked is, "is the change from a month to the next, constant", as in an arithmetic sequence, well, check the picture below, those coordinates do not give us a straight line, and therefore, we don't have an arithmetic sequence, and therefore, we don't have a "common difference".

and since we don't have a common difference, the rate is not constant.

the ordered pairs below represent a relation between x and y.
(-3,0), (-2,4), (-1,8), (0,12), (1,16), (2,20)

could this set of ordered pairs have been generated by a linear function?

A. No, because the distance between consecutive x-value is different than the distance between consecutive x-values.
B. Yes, because the relative difference between y-values and x-values is the same no matter which pairs of (x, y) values you use to calculate it.
C. No, because the y-values decrease and then increase
D. Yes, because the distance between consecutive x-values is constant.

Answers

Answer:

Yes because the relative difference between y-values and x-values is the same no matter what which pairs of (x,y) values you use to calculate it

Step-by-step explanation:


Yes, this set of ordered pairs have been generated by a linear function because the relative difference between y-values and x-values is the same no matter which pairs of (x, y) values you use to calculate it.

The correct option is (B)

What is graph?

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given are ordered pairs are: (-3,0) (-2,4)(-1,8)(0,12)(1,16)(2,20).

It can be seen that the there only unit increase in x coordinates and units increase in consecutive y- coordinates.

Now, if we set up the equation of line as:

Here, m =4 and b = 12

So the relationship is linear and represented by the equation

y=4x+12

Hence, the relative difference between y-values and x-values is the same no matter which pairs of (x, y) values you use to calculate it.

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The graph of a quadratic function touches, but does not cross, the x-axis at x = 4. Which function represents this situation? y = x2 – 16 y = x2 – 4x y = x2 – 8x + 16 y = x2 + 8x + 16

Answers

y = x2 - 8x + 16 doesn't cross the x axis

The quadratic equation is y = x^2 - 8x + 16

How to determine the equation?

From the question, we have:

x = 4

Since the graph only touches x = 4 and it does not cross it, then it means that the graph has a multiplicity of 2 at x = 4

The equation is then represented as:

y = (x - 4)^2

Expand

y = x^2 - 8x + 16

Hence, the quadratic equation is y = x^2 - 8x + 16

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Yu-Xi draws a triangle with two angles measuring 79 degrees and 23 degrees.What is the measure, in degrees, of the third angle?

Answers

79+23=102
180-102=78
the third angle is 78 degrees

Answer:

The Triangle Drawn by ,Yu-Xi,has measure of two angles ,79° and 23°.

All the Basic Learners who knows Math ,that,sum of Measures of three Interior angles of Triangle is 180°.

→79°+23°+Third Angle =180°

→102°+Third Angle =180°

→Third Angle =180° -102°

Third Angle =78°

What term can you add to 5/6x-4 to make it equivalent to 1/2x-4

Answers

You can add - 1/3. Hope it helps! If you could vote my answer as the brainiest, that would be awesome! :)

Answer:

-1/3

Step-by-step explanation:

We need a c number that:

5/6x + cx = 1/2x

We clear the equation:

cx = 1/2x -5/6x

c = 1/2 -5/6

c= -2/6 = -1/3

The perimeter of a square must be greater than 188 inches but less than 198 inches. find the range of possible side lengths that satisfy these conditions. (hint: the perimeter of a square is given by p=4s, where s represents the length of a side).

Answers

Final answer:

The range of possible side lengths for the square is from slightly more than 47 inches to slightly less than 49.5 inches. This is found by dividing the given perimeters by 4, using the formula p=4s.

Explanation:

In this problem, we need to find the range of possible side lengths of a square where the perimeter is more than 188 inches but less than 198 inches. Remember that the perimeter of a square is found by multiplying the length of one side by 4 (p=4s).

First, let's find the side length for a square with a perimeter of 188 inches. We do this by dividing the perimeter by 4: 188 / 4 = 47 inches. So, any square with side lengths greater than 47 inches would have a perimeter more than 188 inches.

Next, we find the side length for a square with a perimeter of 198 inches. Similarly, we divide the perimeter by 4: 198 / 4 = 49.5 inches. So any square with side lengths less than 49.5 inches would have a perimeter less than 198 inches.

Therefore, the range of possible side lengths that satisfy these conditions is from slightly more than 47 inches to slightly less than 49.5 inches.

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What scale factor was applied to the first rectangle to get the resulting image


Help me plsssssssssssssssssssssssssssssssssssssssssss!

Answers

2.5 / 5 = .5
.5 x 5 = 2.5 

scale factor should be 5.

WILL GIVE A BRAINLEST !!!!

The graph of a logarithmic function is shown below.

What is the domain of the function?
x < 0
x > 0
x < 1
all real numbers

Answers

The domain of the function is all numbers greater than 0, or x>0. 

Hope this helps!

Answer: The correct option is second, i.e., x>0.

Explanation:

As we know that the domain is the set of all possible inputs. If function is defined as, f(x) then all possible value of x for which the function f(x) is defined is called domain.

In a graph the domain is defined on the x axis and the range of the function is defined on y-axis.

In the given graph the function is defined from x=0 to [tex]x=\infty[/tex] because for [tex]x\leq 0[/tex] the graph is not defined. It means for [tex]x\leq 0[/tex] the function is not defined.

Sicen the graph is defined for all positive values of x, therefore the domain of the function is al real number greater than 0. It can be written as x>0 and the second option is correct.

If you were going to represent the top view of the figure, stated which boxed should be shaded.

Answers

The one on the far left...hope I helped

What is the derivative of e^(2x)

I am confused because the derivative e^x is e^x.
But they say you need to use the chain rule.

Which is f'(g(x))*g'(x).
I have used that on exponents but in this I just get, 2x * e^(2x-1) *e
Which is not the answer =/

Answers

Using the chain rule: The derivative of e^u is (e^u)(u').  Notice that e^u is rewritten exactly as is and then multiplied by the derivative of the exponent.  
Let u=2x. So u'=2  
So the derivative of e^u is e^(2x)*2 This can also be written as 2e^(2x).

If side a has a length of 3 and side b has a length of 4, use the Pythagorean Theorem to find the length of side c. Round the answer to the nearest tenth.

Answers

This the equation you will need to use (the Pythagorean Theorem)
[tex]a {}^{2} + b {}^{2} = c[/tex]
when you put the numbers in for the variables given it will look like this

[tex]( {3})^{2} + ( {4})^{2} = c[/tex]
3 squared equals 9 and 4 squared equals 16:
[tex]9 + 16 = 25[/tex]
so side c is 25 units

How would you get the answer??

Answers

The ratio for this situation would be 20:6, as this represents 6 red cars for every 20 cars sold. To get the fraction, just add the ratio on each side together, then place the number you want as a fraction on top, then simply if possible. This looks like this:
20+6=26
6/26
Divide the numerator and denominator by 2
3/13
So, the fraction is 3/13

Solve. 2m^2-7m-13=-10

Answers

[tex]2m^2-7m-13=-10\ \ \ |+10\\\\2m^2-7m-3=0[/tex]


[tex]a=2;\ b=-7;\ c=-3\\\\b^2-4ac=(-7)^2-4\cdot2\cdot(-3)=49+24=73\\\\m_1=\dfrac{-b-\sqrt{b^2-4ac}}{2a};\ m_2=\dfrac{-b+\sqrt{b^2-4ac}}{2a}\\\\m_1=\dfrac{-(-7)-\sqrt{73}}{2\cdot2}=\dfrac{7-\sqrt{73}}{4}\\\\m_2=\dfrac{-(-7)+\sqrt{73}}{2\cdot2}=\dfrac{7+\sqrt{73}}{4}[/tex]

Marcus has a total of 10 nickels and dimes in his pocket. he has a total of 70 cents. how many dimes does he have in his pocket?

Answers

10 coins in nickels & dimes = $0.70

1 nickel = $0.05
1 dime = $0.10

4 dimes = $0.40
6 nickels = $0.30

4 dimes + 6 nickels = 10 coins
$0.40 + $0.30 = $0.70



The answer is: He has a total of 4 dimes in his pocket.

Jen has 12 ounces milkshake. 4 ounces in the milkshake are vanilla, and the rest is chocolate. What are two equivalent fractions that represent the fractions of the milkshake that is vanilla?

Answers

Hello!

There are two parts two a fraction. The top part is called the numerator, which shows how many of the parts indicated by the denominator are taken.

The bottom part is called the denominator, which is the total amount of that particular thing.

In this case, 12 would be the denominator and the and 4 would be the numerator. Your fraction would look like:

4/12

Now, this question asks for equivalent fractions. An equivalent fraction is a fraction that is equivalent to the first fraction.

To equivalent fractions could be:

2/6 and 1/3

How I got these fractions? I simply divided the numerator and denominator by 2, and then again by 2 to get 1/3.

Good Day!

A person at the top of a cliff 100 ft. tall sees Gilligan's boat. He sees the boat at an angle of depression of 10. How far is the boat from the base of the cliff.

Answers

567.128181962 ft to be exact
or 567.128ft  rounded

hope this helps<3






















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