Gilligan sees a ship coming close to the shore he's standing on. He wants to determine the distance (segment SD) from the ship to the shore. He walks 130 ft along the shore from point D to point C and marks that spot. Then he walks 23 ft further and marks point B. He turns 90°and walks until his location (point A), point C, and point S are collinear.
Answer the following questions making sure to show all your work.
(a) Can Gilligan conclude that triangle ABC and triangle SDC are similar? Why or why not?
(b) Suppose AB = 50 ft. What is the distance from the ship to the shore? Show all your work and round your final answer to the nearest tenth of a foot.
Answers
The two triangles are both right triangles and are both formed by the
intersection of the lines AS and BD and are therefore similar.
Response:
(a) Yes, ΔABC is similar to ΔSDC according AA similarity postulate
(b) The distance from the ship to the shore is approximately 282.6 feet
How can similarity between the triangles used to find the distance SD?(a) Yes, Gilligan can conclude that ΔABC and ΔSDC are similar by
Angle-Angle, AA, similarity postulate.
Reason:
Angle ∠SCD in ΔSDC and ∠ACB in ΔABC are vertically opposite angles,
and they are therefore congruent by vertical angles theorem.
∠SDC = 90° and ∠ABC = 90° therefore ∠SDC ≅ ∠ABC because all 90°
are congruent.
Therefore, two angles in ΔABC are congruent to two angles in ΔSDC,
therefore, ΔABC is similar to ΔSDC according to AA similarity postulate
(b) The ratio of corresponding sides in similar triangles are equal,
therefore;
[tex]\dfrac{BC}{DC} = \mathbf{\dfrac{AB}{SD}}[/tex]
Which gives;
[tex]\dfrac{23}{130} = \dfrac{50}{SD}[/tex]
[tex]SD = \dfrac{130}{23} \times 50 \approx 282.6[/tex]
The distance from the ship to the shore, SD ≈ 282.6 ft.Learn more about triangle similarity postulates here:
https://brainly.com/question/16854084
Related Questions
I already tried D but it wasnt correct
Answers
Answer:
A. E bisects AB and CD
Step-by-step explanation:
If E is a bisector, it creates two pairs of congruent sides. The included angles are congruent because they are vertical angles. The triangles will be congruent by SAS.
Olivia has a dozen apples of the same size
and a dozen pineapples of the same size.
Olivia uses her juicer to extract 12 ounces of
pineapple juice from 7 pineapples and 16
ounces of apple juice from 4 apples. She
makes a pineapple-apple juice blend from an
equal number of pineapples and apples.
What percent of the blend is pineapple juice?
Answers
Answer: 30% of the blend is pineapple juice
Step-by-step explanation:
Since 7 pineapples yield 12 oz of juice, 1 pineapple yields 1 5/7 oz of juice.
Since 4 apples yield 16 oz of juice, 1 apple yields 4 oz of juice.
She’s making a pineapple-apple juice where the ratio of apples and pineapples used is 1:1. To find what percent of the blend is pineapple juice:
1 apple to 1 pineapple. The combined amount of juice they produce is 5 5/7 oz. The formula to find what percent of teh blend is pineapple juice is oz of pineapple juice divided by the combined amount of juice in the blend.
1 5/7 divided by 5 5/7 equals 3/10, or 30%.
The fraction of the blend that is pineapple and apple gives the
percentage that is pineapple.
Response:
The percentage of the blend that is pineapple juice is 30%How can the percentage of pineapple juice in the blend be calculated?Amount of juice extracted from 7 pineapples = 12 ounces
Amount of juice extracted from 4 apples = 16 ounces
Therefore;
The amount of juice from 1 pineapple = [tex]\mathbf{\frac{12}{7}}[/tex] ounces = [tex]1\frac{5}{7}[/tex] ounceThe amount of juice from 1 apple = [tex]\frac{16}{4}[/tex] ounces
The amount of juice from 1 apple = 4 ouncesWhich gives;
The amount of juice from 1 pineapple and 1 apple = [tex]\frac{12}{7}[/tex] + 4 = [tex]\frac{40}{7}[/tex] = [tex]5\frac{5}{7}[/tex]
The amount of juice from 1 pineapple and 1 apple = [tex]5\frac{5}{7}[/tex] ouncesThe percentage of pineapple juice is therefore;
[tex]Percentage \ pineapple \ juice \ in \ blend= \dfrac{\dfrac{12}{7} }{\dfrac{40}{7} } \times 100 = \dfrac{12}{7} \times \dfrac{7}{40} \times 100 = \underline{30\% }[/tex]Learn more about percentages here:
https://brainly.com/question/26150306
In △ABC,c=9, m∠B=65°, and a=105. Find b.
Answers
Answer:
Step-by-step explanation:
b² = a² + c² - 2ac × cos (m∠B)
b² = 105² + 9² - 2(9)(105)cos65°
b ≈ 101.5
What is the slope of the line represented by the equation y = -1/2x + ¼?
Answers
Given :-
y = -1/2x + 1/4To Find :-
The slope of the equation .Solution :-
Here a equation is given to us and we need to find out the slope of the line . The given equation is ,
→ y = -1/2x + 1/4
We know that slope intercept form of the line is ,
→ y = mx + c
where m is the slope of the line .
On comparing ,
→ m = -1/2
Hence the slope of the line is -1/2.
I hope this helps .
Which number does not
belong to the pattern below? Explain.
5,470, 547, 54.7, 0.547
Answers
The sum of 3, 4, and a number amounts to 16
Answers
X= 16- (3+4)
X = 16-7
X= 9
Would be appreciated if someone could help on this transformation question
A. -105
B. -75
C. 75
D. 105
Answers
Answer:
B. -75
Step-by-step explanation:
Consider segments AC and A'C'. Point A' is clockwise from point A by an amount less than 90°. Positive angles are measured counterclockwise, so this suggests the angle of rotation is about -75°.
__
In the attached, we have used the invariant point on segments AC and A'C' as the vertex of the angle we want to measure. The angle between the lines appears to be about 75°, matching the answer choices.
Consider the equation 7x+2(x+5)=9x+10.
(a) Show that x=-5 and x = 2 are both solutions to this equation.
Answers
Answer:
7*-5+2(-5+5)=-35
9*-5+10=-35
7*2+2(2+5)=28
9*2+10=28
Step-by-step explanation:
when plugging the x values in, you get the same answer for both equation, make the equation equal.
Richard tosses a football with an initial velocity of 10ft/sec from an initial height of 6ft. What is the maximum height the ball will reach?
A. About 7.6ft
B. About 0.3ft
C. 1ft
D. 6ft
Answer: A
Answers
The maximum height the ball will reach is 7.6 ft.
Maximum height of the projectileThe maximum height attained by the projectile is calculated as follows;
v² = u² - 2gh
where;
v is the final velocity at maximum height = 0u is the initial velocityh is the heightg is acceleration due to gravity0 = u² - 2gh
2gh = u²
[tex]h = \frac{u^2}{2g} \\\\h = \frac{10^2}{2(32.2)} \\\\h = 1.6 \ ft[/tex]
Thus, the maximum height the ball will reach = 1.6 ft + 6ft = 7.6 ft.
Learn more about maximum height here: https://brainly.com/question/12446886
An equivalent fraction to 5/16 is 10/32 correct?
Answers
Answer:
correct
Step-by-step explanation:
Yes.
You multiply both 5 and 16 by the same number, 2, to get 10/32.
Problem 4: Solve the initial value problem
[tex]y' = (y + 1)(y - 2)[/tex]
[tex]y(0) = 1[/tex]
Answers
Separate the variables:
[tex]y' = \dfrac{dy}{dx} = (y+1)(y-2) \implies \dfrac1{(y+1)(y-2)} \, dy = dx[/tex]
Separate the left side into partial fractions. We want coefficients a and b such that
[tex]\dfrac1{(y+1)(y-2)} = \dfrac a{y+1} + \dfrac b{y-2}[/tex]
[tex]\implies \dfrac1{(y+1)(y-2)} = \dfrac{a(y-2)+b(y+1)}{(y+1)(y-2)}[/tex]
[tex]\implies 1 = a(y-2)+b(y+1)[/tex]
[tex]\implies 1 = (a+b)y - 2a+b[/tex]
[tex]\implies \begin{cases}a+b=0\\-2a+b=1\end{cases} \implies a = -\dfrac13 \text{ and } b = \dfrac13[/tex]
So we have
[tex]\dfrac13 \left(\dfrac1{y-2} - \dfrac1{y+1}\right) \, dy = dx[/tex]
Integrating both sides yields
[tex]\displaystyle \int \dfrac13 \left(\dfrac1{y-2} - \dfrac1{y+1}\right) \, dy = \int dx[/tex]
[tex]\dfrac13 \left(\ln|y-2| - \ln|y+1|\right) = x + C[/tex]
[tex]\dfrac13 \ln\left|\dfrac{y-2}{y+1}\right| = x + C[/tex]
[tex]\ln\left|\dfrac{y-2}{y+1}\right| = 3x + C[/tex]
[tex]\dfrac{y-2}{y+1} = e^{3x + C}[/tex]
[tex]\dfrac{y-2}{y+1} = Ce^{3x}[/tex]
With the initial condition y(0) = 1, we find
[tex]\dfrac{1-2}{1+1} = Ce^{0} \implies C = -\dfrac12[/tex]
so that the particular solution is
[tex]\boxed{\dfrac{y-2}{y+1} = -\dfrac12 e^{3x}}[/tex]
It's not too hard to solve explicitly for y; notice that
[tex]\dfrac{y-2}{y+1} = \dfrac{(y+1)-3}{y+1} = 1-\dfrac3{y+1}[/tex]
Then
[tex]1 - \dfrac3{y+1} = -\dfrac12 e^{3x}[/tex]
[tex]\dfrac3{y+1} = 1 + \dfrac12 e^{3x}[/tex]
[tex]\dfrac{y+1}3 = \dfrac1{1+\frac12 e^{3x}} = \dfrac2{2+e^{3x}}[/tex]
[tex]y+1 = \dfrac6{2+e^{3x}}[/tex]
[tex]y = \dfrac6{2+e^{3x}} - 1[/tex]
[tex]\boxed{y = \dfrac{4-e^{3x}}{2+e^{3x}}}[/tex]
A square has 12 cm length and it's area is equal to the area of a rectangle having length 16 cm.What is the breadth of the rectangle?
Answers
Step-by-step explanation:
Hope this helps you......
[tex] \displaystyle{ \blue{ \frak{DisneyPrincess29}}}[/tex]
Answer:
Breadth = 9 cm
Explanation:
Find the area of square using; area of square: length²area of the square:
→ 12²
→ 144 cm²
The rectangle has similar area. rectangle area: 144 cm²use the formula to find area of rectangle:
length * breadth = area of rectangleusing the formula:
→ length * breath = 144
→ 16 * breadth = 144
→ breadth = 144/ 6
→ breadth = 9 cm
can someone help me with this question?
Answers
Answer:
The answer is D.
Step-by-step explanation:
Translate the sentence into an equation.
Twice the difference of a number and 7 is equal to 9 .
Use the variable Y for the unknown number.
Answers
Answer:
equation: 2(Y-7) = 9
Here the number is twice the difference.the difference is 7, so Y - 7Equals to 9.1. Physicians There are about 900,000 active physicians in the United States, and they have annual incomes with a distribution that is skewed instead of being normal. Many different sam- ples of 40 physicians are randomly selected, and the mean annual income is computed for each sample.
a. What is the approximate shape of the distribution of the sample means (uniform, normal, skewed, other)?
b. What value do the sample means target? That is, what is the mean of all such sample means?
Answers
Using the Central Limit Theorem, it is found that:
a) The shape is approximately normal.
b) It targets the population mean.
Central Limit TheoremThe Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the sampling distribution is also approximately normal, as long as n is at least 30.
Item a:
The variable is skewed, however, the sample size is greater than 30, hence the approximate shape of the distribution is normal.
Item b:
According to the mean of the sampling distributions, given by the Central Limit Theorem, it targets the population mean.
More can be learned about the Central Limit Theorem at https://brainly.com/question/24663213
Which expression is a fourth root of -1 + i sqrt{3} please help
Answers
Answer:
r e^iT = r cos T + i r sin T
r cos T = -1
r sin T = sqrt 3
30, 60 90 triangle in second quadrant r = 2, T = 180-60 = 120
so
2e^120i
foruth root is 2^.25 e^(120/4)i
2^.25 e^30 i
2^.25 ( cos 30 + i sin 30)
Step-by-step explanation:
Evan has 381 bagels to put into packages. Each package must hold 6 bagels. How many packages of bagels can Evan make? How many bagels will be left over?Enter your answers in the boxes. Evan can make ___________ packages with __________ bagels left over. what goes on the blank spaces its for 30 pts please help
Answers
Based on the division computed, the number of packages is 63 and there will be a remainder of 3.
How to solve divisionFrom the question, we are informed that Evan has 381 bagels to put into packages and that each package must hold 6 bagels.
The number of packages will be:
= 381/6
= 63 packages
It should also be noted that there will be a remainder of 3 bagels left.
Learn more about division on:
https://brainly.com/question/25289437
Answer: The number of packages is 63 and there will be a remainder of 3
Step-by-step explanation:
if 9<15mx-8<27, where m is a positive constant, what is the possible range of values of 8/3 -5mx?
Answers
Answer:
Any value greater than -9 and less than -3
Step-by-step explanation:
Explained and uploaded
Whats point slope formula again
i forgot-
Answers
Answer:
● Whats point slope formula
[tex]➢ \: formula = y - {y}^{1} = m \: (x - {x}^{1} \\ y = coordinate \: of \: second \: point \\ {y}^{1} \: coordinate \: of \: point \: one \\ m = slope \\ x = coordinate \: of \: second \: point \\ {x}^{1} = coordinate \: of \: point \: one.[/tex]
[tex]TextFromYourMrEx[/tex]
#CarryOnLearning
Hi!
I can help you with joy! :)
Remember, point-slope form
[tex]\rm{y-y1=m(x-x1)[/tex]
Where
y1 is the y-coordinate of the point
m is the slope
x1 is the x-coordinate of the point
Hope it helps!
Enjoy your day!
[tex]\bf{erutaNtneliS[/tex]
Kenzie bakes 9 oatmeal cookies. Kenzie bakes 7 fewer
cookies than Lisa. How many oatmeal cookies does
Lisa bake?
Answers
Answer:
16 oatmeal cookies
Step-by-step explanation:
We can represent this situation as an equation.
L - 7 = 9 L represents Lisa's cookies, (-7) represents 7 fewer cookies, and 9 represents Kenzie's cookiesStep 1: Add 7 to both sides.
[tex]L-7+7=9+7[/tex] [tex]L=16[/tex]Therefore, Lisa baked 16 oatmeal cookies.
Write the recursive formula for the following sequence:
16, 8, 4, 2, ...
Answers
Answer:
Answer is in the image
HOPE IT HELPS, BE SAFE KIDDO :3
look at the simultaneous equations: x+y=a and 2x+y=b. write an expression for x in terms of a and b. write and expression for y in terms of a and b, giving your answer as simply as possible
Answers
An expression for x in terms of a and b is y = b - 2x and an expression for y in terms of a and b is y = 2a - b.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, A system of equations x + y = a and 2x + y = b.
Now,
x + y = a.
x = a - y and y = a - x.
2x + y = b.
2x = b - y.
x = (b - y)/2.
y = b - 2x.
An expression for x in terms of a and b is,
x + y = a
x + b - 2x = a.
- x = a - b.
x = b - a.
An expression for y in terms of a and b is,
2(a - y) + y = b.
2a - 2y + y = b.
2a - y = b.
- y = b - 2a.
y = 2a - b.
learn more about numerical expressions here :
https://brainly.com/question/29199574
#SPJ2
Rewrite the mixed number as an improper fraction.
Answers
Answer:
12/4. & 22/5
Step-by-step explanation:
3 2/4 you have to multiply 3x4 which equals to 12 then you add 2. your answers is 14 but you need to keep the denominator 4. your final answer is 12/4. this is the improper fraction. you do the same to 4 2/5.
Six times the sum of a number and 20 is at least 26. Use the variable b for the unknown number.
Answers
Answer:
6(b + 20) ≥ 26
Step-by-step explanation:
6(b + 20) ≥ 26
Answer:
6(b + 20) ≥ 26
b ≥ -15 2/3
Step-by-step explanation:
6(b + 20) ≥ 26
6b + 120 ≥ 26
6b ≥ -94
b ≥ -15 2/3
Can someone help me with this geometry question!? ASAP
Answers
Answer:
D.
I hope it's help:))))))))))))))
Help I Will Give Brainliest If Correct
Answers
Hi!
The formula for volume is length * width * height
We are given the area of the base of the figure and the height.
The volume for area is length * width
That means that the length * width part of the volume formula is already done, so we just have to multiply that by the height.
[tex]3 \frac{3}{8}[/tex] * [tex]2[/tex]
[tex]6 \frac{6}{8}[/tex] [tex]= 6\frac{3}{4}[/tex]
For other volume-related questions, see:
https://brainly.com/question/18571772
We know that:
Volume = L × B × HIf L and B are multiplied, they will find the area of the base.L × B = Area of base of rectangular prism.If L and B are multiplied, they will find the area of the base.
This means that:
Area of base of rectangular prism = L × B = 3 3/8 units²Volume = Area of base of rectangular prism × HSubstitute the area of base of rectangular prism in the volume formula.
Volume = Area of base of rectangular prism × H=> Volume = 3 3/8 × HSubstitute the height in the volume formula.
=> Volume = 3 3/8 × 2You can further solve this in two methods. You can use any of them.
Method #1:Convert the mixed fractions into improper fraction.
=> Volume = [(3 × 8 + 3)/8] × 2=> Volume = [(24 + 3)/8] × 2 [Multiplication first]=> Volume = [(27)/8] × 2=> Volume = 27/8 × 2Multiply the fractions
=> Volume = 54/8 units³ = 27/4 units³Convert the volume into mixed fraction:
27/4 = 24/4 + 3/4 = 6 + 3/4 = 6 3/4 units³Method #2:Break 3 3/8 into smaller parts:
(3 3/8) × 2=> (24/8 + 3/8) × 2Simplify the distributive property:
=> 2(3) + 2(3/8)=> 6 + 6/8 = 6 6/8 = 6 3/4 units³Likewise, you can use any method, it will give the same result.
~If you have questions about my answer, don't hesitate to post it in the comments~
Hoped this helped!
factorise 8x+12 please
Answers
Answer: 4(2x+3)
Step-by-step explanation:
The greatest common factor in the two terms is 4.
Therefore, by factoring out a 4 we get
4(2x+3)
Which statement is true?
A The value of x is 116, because the two angles shown add up to 180
B. The value of x is 64 because the two angles shown are congruent
C. The value of x is 26. because the two angles shown are complementary
D. The value of x is less than 90 because the two angles shown are acute angles
Answers
Answer:
A
Step-by-step explanation:
Sum of angles in a straight line is 180°
180° - 64° = 116°
PLEASE HELP FOR MY MATH PROJECT
A family with 3 adults and 3 children purchase 6 lines each for $35 at ATT. Another family with 2 adults and 4 children purchase 6 lines each for $25 at A-Mobile. Solve for X and Y
what does X and Y represent? I've solved this equation (i got 65 and 5) what do they represent?
Answers
Answer:
Step-by-step explanation:
X would be adults Y would be children
3x+3y=35
2x+4y=25
One of the variables have to be equal to each other. So multiply all the terms in the bottom equation by 1.5
You get 3x+6y=37.5
Subtract one equation from another
3x+3y=35
3x+6y=37.5
You get 3y=2.5
Divide both sides by 3
y = 5/6
Now do the same but for X
Multiply the equation by 4/3
4x+4y=46 2/3
Minus the other equation
2x=21 2/3
Divide by 2
x = 10 5/6
Plug numbers in to double check, and they check out
If a> 1 then prove that a^2>1
Answers
Step-by-step explanation:
a² = a × a
a > 1
a² = (1+d) × (1+d) = 1² + 2d + d²
with d > 0
since d > 0, then so is 2d and also d².
so, a² is the sum of 1² = 1 and something greater than 0.
so, a² > 1