a. How far is the spot on the beach from the parking lot?
b. How far will he have to walk from the parking lot to get to the refreshment stand?
Show work please.
Answers
The altitude of the right triangle is the geometric mean of the 2 parts of the side it separates.
a. The answer would be sqrt(18*32)=24
The question to the second question can be answered by using the Pythagorean theorem.
32^2+24^2=1600=40^2
b. The answer would be sqrt40^2=40
The beach, the parking lot and the refreshment stand are illustrations of similar triangles.
The distance between the spot and the parking lot is 24 mThe distance between the refreshment stand and the parking lot is 40 m(a) The distance between the spot and the parking lot
Represent this distance with d.
So, the equivalent ratio is:
[tex]\mathbf{32:d = d : 18}[/tex]
Express as fractions
[tex]\mathbf{\frac {32}d = \frac{d}{ 18}}[/tex]
Cross multiply
[tex]\mathbf{d \times d = 32 \times 18}[/tex]
[tex]\mathbf{d^2 = 576}[/tex]
Take square roots
[tex]\mathbf{d = 24}[/tex]
Hence, the distance between the spot and the parking lot is 24 m
(b) The distance between the refreshment stand and the parking lot
Represent this distance with d.
Using Pythagoras theorem we have:
[tex]\mathbf{d^2 = 32^2 + 24^2}[/tex]
[tex]\mathbf{d^2 = 1600}[/tex]
Take square roots
[tex]\mathbf{d = 40}[/tex]
Hence, the distance between the refreshment stand and the parking lot is 40 m
Read more about similar triangles at:
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Related Questions
Find a quadratic polynomial with integer coefficients which has x = 2/9, ± SQRT23/9 as its real zeros.
Answers
Answer:
The quadratic polynomial with integer coefficients is [tex]y = 81\cdot x^{2}-36\cdot x -19[/tex].
Step-by-step explanation:
Statement is incorrectly written. Correct form is described below:
Find a quadratic polynomial with integer coefficients which has the following real zeros: [tex]x = \frac{2}{9}\pm \frac{\sqrt{23}}{9}[/tex].
Let be [tex]r_{1} = \frac{2}{9}+\frac{\sqrt{23}}{9}[/tex] and [tex]r_{2} = \frac{2}{9}-\frac{\sqrt{23}}{9}[/tex] roots of the quadratic function. By Algebra we know that:
[tex]y = (x-r_{1})\cdot (x-r_{2}) = x^{2}-(r_{1}+r_{2})\cdot x +r_{1}\cdot r_{2}[/tex] (1)
Then, the quadratic polynomial is:
[tex]y = x^{2}-\frac{4}{9}\cdot x -\frac{19}{81}[/tex]
[tex]y = 81\cdot x^{2}-36\cdot x -19[/tex]
The quadratic polynomial with integer coefficients is [tex]y = 81\cdot x^{2}-36\cdot x -19[/tex].
Write an equation for the nth term of the geometric sequence 5,30,180,1080
Answers
Answer: [tex]a_{n}[/tex]=5*[tex]6^{n-1}[/tex]
Step-by-step explanation:
math work pls help :)
Answers
Answer:
the theorum used here is sas one
How Many?pls help me.
Answers
Answer:
8
Step-by-step explanation:
Convert the following angle from degrees to radians. Express your answer in simplest
form.
285
Answers
?° × π/180 = ?rad
So put 285 in and...
285° × π/180 = 4.974rad
The answer is 4.97419rad
Answer:
Step-by-step explanation:
divide 220 in the ratio 3:8
Answers
Answer:
500/(7+3)=50; 3*50=150, 7*50=350. 150:350=3:7
Step-by-step explanation:
o Ayan sinolve kayan geh pa follow po
220 is divided in the ratio 3:8 as 60 and 160 respectively.
What is the ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
The given ratio is 3:8 and the number is 220.
Here, 3+8=11
Now, 3/11 ×220
= 3×20
= 60
8/11 ×220
= 8×20
= 160
Therefore, 220 is divided in the ratio 3:8 as 60 and 160 respectively.
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Suhana's father is a farmer. He deposits Rs.1200 of the remaining amount in the bank at 9% p.a. for 3 yrs
Calculate the amount the farmer will receive at the end of 3 yrs
Answers
Answer:
Given :principle =Rs. 1200
rate of interest =9%
time =3yrs
we know that simple interest =PTR /100
=1200*9*3/100
=Rs. 324
Amount of the farmer will receive at the end of the 3 yrs =principle + interest
=1200+324=1524/-
how many seconds in an hour
Answers
Answer:
there are 3,600 seconds in one hour.
(60 x 60)
Conversion Factors -
1000 milliseconds = 1 second
60 seconds = 1 minute
60 minutes = 1 hour
Find the value of x in 4000(1.5^x) = 25,000. Show your work.
Answers
Answer:
4.17
Step-by-step explanation:
6000x = 25000
x = 25000 / 6000
x = 4.17
An angle measures 106.4° less than the measure of its supplementary angle. What is the measure of each angle
Answers
Answer:
The two supplementary angles are 10 and 170 degrees.
Step-by-step explanation:
Two angles are supplementary when that add up to 180 degrees. In this case, we are given that one of the two angles is 160 degrees more than the other. We can construct the following equation. x + ( x + 160 ) = 180 x
represents the degree measure of the smaller angle. Now, all we need to do is solve the equation for x. 2 x + 160 = 180 2 x = 20 x = 10
Now that we have the value of the smaller angle, we can easily solve for the larger angle. We are told that it is 160 degrees larger than the other one.
10 + 160 = 170. Therefore, the two supplementary angles are 10 and 170 degrees.
The temperature at 12 am was 44 degrees. The temperature dropped steadily for the next 8 hours to reach the daytime low of 20 degrees. Solve for the hourly temperature change.
Answers
Answer:
-3 degrees per hour
Step-by-step explanation:
Points: (12,44) and (20,20)
Slope = -3
A group of preschoolers was asked to name their favorite fruit. What percent of the kids chose grapes?
29%
79%
21%
31%
Answers
answer is 21%
.
.
.
.
21
TL;DR
The answer is 21%
3 less than four-sevenths of x is y
Answers
y = 4/7x - 3
hope this helps
Answer:4/7-3
Step-by-step explanation:
Yep
Bernard built 15 model cars one year. He did not build as many model cars as his sister, Abby. In the inequality, n represents the number of model cars Bernard needed to build to have more than Abby.
Which number of model cars did Bernard need to build to have more model cars than Abby?
A.1
B.2
C.3
D.4
Answers
Answer:
The answer is 1
Step-by-step explanation:
Write an equation of the linear relationship in slope-intercept form. I need help on this question, I don’t know if it’s 3/2x+80/3 or 2/3x+80/3
Answers
Answer:
2/3x
Step-by-step explanation:
ANYONE PLZ ANSWER THIS QUESTION!!!!!!
Answers
Answer:
E. 40°, 25°, -2°, -16°Step-by-step explanation:
Temperatures given:
25°, -2°, - 16°, 40°Descending order of the numbers is:
40°, 25°, -2°, -16°Correct choice is E
Rachel runs 4 miles in 23 minutes. How many miles does she run per minute?
Answers
Answer:
To calculate how many total miles Rachel runs per minute, setting up a unit rate, that is a rate with a denominator of 1, would be helpful.
Step-by-step explanation:
Use the current problem to determine a rate.
23 minutes/4 miles
Now, set up a unit rate.
1 minute/x miles = 23 minutes/4 miles
To solve for x, we can use simple division strategies. We divide 23 by 23 to receive 1 minute. Likewise, dividing the current milage by 23 would wield the correct unit rate. To do this, divide 4 by 23.
4/23 = 0.1739130434782609
Finally, simplify your answer to receive 0.17.
Therefore, Rachel runs ~0.17 miles per minute. (Note that this answer is only a rounded answer of her actual milage per minute)
what is 2 2/3 dived by 1 1/4 equal
Answers
22 1/2= 23/2
then we get:
(23/2)/(1/4)=?
we can flip the 1/4 to 4/1 and multiply instead of dividing so we get:
(23/2)X(4/1)=?
multiply numerators and denominators:
(23/2)X(4/1)=92/2
simify:
=46
The volume of a cylinder is 63 pi cm^3 . If the radius is 3cm, what is the height of the cylinder?
A. 3.5 cm
B. 21 cm
C. 10.5 cm
D. 7 cm
will give brainliest
Answers
Answer:
Step-by-step explanation:
volume = πr²h = π·3²h = 63π
h = 7 cm
The height of the given cylinder is 7 cm. Therefore, option D is the correct answer.
What is the volume?Volume is the measure of the capacity that an object holds.
Formula to find the volume of the object is Volume = Area of a base × Height.
Given that, the volume of a cylinder is 63π cm³ and the radius is 3 cm.
We know that, the formula to find the volume of a cylinder is πr²h.
Now, πr²h=63π
π×3²×h=63π
h= 7 cm
Therefore, option D is the correct answer.
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I need help with 1 over x minus 8 so like 1/x-8
Negative Exponent
Answers
Answer:
1-8x
Step-by-step explanation:
1/x - 8
x × 1/x - 8× x
1-8x
Only 3% of turtle hatchlings will live to become breeding adults. How many turtles must have been born if the current number of breeding adults is 1,200?
Answers
Answer:
116400 I believe not 100% sure tho
The total number of turtles born is 40,000.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Given that, only 3% of turtle hatchlings will live to become breeding adults.
The current number of breeding adults is 1,200
Let the total number of turtles born be t.
Now, 3% of t=1200
3/100 ×t=1200
3t=120000
t=40000
Therefore, the total number of turtles born is 40,000.
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70
А
In the diagram, point is the center of the circle. If
mZABC = 70°, what is m ZAOC?
OA. 100°
OB.
110°
Ос.
140°
OD
130°
i need help quick plssss
Answers
Answer:
140°
Step-by-step explanation:
∠ABC is an inscribed angle and its measure is half the measure of the intercepted arc, which is arc AC
Therefore the measure of arc AC is 2(70) = 140°
∠AOC is a central angle and its measure is equal to its intercepted arc, which is arc AC.
So, m∠AOC = 140°
The angle AOC from the given circle is 140°. Therefore, option C is the correct answer.
What is relation between angle at the center and the angle at the circumference?The angle subtended by an arc at the center is twice the angle subtended at the circumference. More simply, the angle at the center is double the angle at the circumference.
From the given circle, angle ABC is 70°.
Here, 2∠ABC=∠AOC
∠AOC=2×70°
∠AOC=140°
Therefore, option C is the correct answer.
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What is the first step when multiplying mixed numbers.
Answers
Answer:
To multiply mixed numbers, first change any mixed number to an improper fraction. Then multiply the numerators together and the denominators together, as shown in Example .
Step-by-step explanation:
please help :) will mark brainliest
Answers
Answer:
I cant see your problome I dont know why but what is it
Step-by-step explanation:
Help me plssssss!!!!!
Answers
Answer:
si yo lo sé tú también cierto
Jocelyn needs to write a 12-page paper for class. If she has already written 4 pages and can write 2 more pages per day, how many days will it take her to finish her paper?
Answers
Answer:
5 days
Step-by-step explanation:
skip counting
4, 6, 8, 10, 12 then count those and you have 5 days
Write an Equation given the point (1, -1) and a rate of 2.
Answers
Answer:
y+1=2(x-1)
Step-by-step explanation:
use point slope form
plug in the numbers to find b
-1 = 2(1) + b
simplify
-1 = 2 + b
-3 = b
write out the equation with the new info
the answer should be:
y = 2x - 3
What is -3(4q-7) Bc I’m confused
Answers
Answer:
-3(4q-7)=
4q+3-7
4q-4
Please help! I need the answers with an explanation to these questions ASAP. Thanks!
Question 1. What value could complete this given equation that would make it true for no values of x? Show or explain your thinking.
Question 2. What value could complete this equation that would make it true for every value of x? Show or explain.
Answers
Answer:
0
Step-by-step explanation:
Given equations is
x+2y=8,5x+10y=c
The equations a
1
x+b
1
y=c
1
and a
2
x+b
2
y=c
2
will have uique solutions if
a
2
a
1
=
b
2
b
1
=
c
2
c
1
but from equations,
a
2
a
1
=
5
1
,
b
2
b
1
=
10
2
,
c
2
c
1
=
c
8
∴
a
2
a
1
=
b
2
b
1
The given equations does not have unique solution, so the given statement is false, The correct answer is 0
Jamal has 30 ounces of a 20% saline solution. This means 20% of the solution is salt. He combines this solution with 25 ounces of a
30% saline solution
What is the total amount, in ounces, of salt in the combined moxture?
Answers
Answer:
13.5 ounces
Step-by-step explanation: