Answers
You have to use similar figures to work this out.
15 ft / 8 ft has to equal d ft / 6 ft
So, you divide 15 by 8, which equals 1.875
You then times 1.875 by 6 = 11.25
The Distance, d, across the lake is 26.25 feet.
Similar TrianglesWhen two triangles have all the corresponding angles equal to each other, then their sides are in a ratio.
Given to us,AB = 8 feet,
BC = 15 feet,
BP = 6 feet,
PQ = d,
AP = AB + BP = 8 + 6 = 14 feet
In the figure, [tex]\triangle ABC \sim \triangle APQ[/tex]
[tex]\dfrac{BC}{AB}=\dfrac{PQ}{AP}[/tex]
[tex]\dfrac{15}{8}=\dfrac{d}{14}[/tex]
[tex]d = \dfrac{15\times 14}{8}[/tex]
[tex]d = 26.25[/tex]
Hence, the Distance, d, across the lake is 26.25 feet.
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Related Questions
sixty eight is one fourth of what number
Answers
68 times 4 equals 272.
or if you did 272 divided by 4 you would get 68.
l To finance a bridge costing $94,500, the state contributed twice as much as the county and the county contributed twice as much as the city. How much did each contribute?
Answers
Let x = the amount the city contributes.
The county contributes twice this amount, or 2x.
The state contributes twice as much as the county, or 2(2x)=4x.
Together, they all contribute 94500:
x+2x+4x=94500
Combining like terms,
7x = 94500
Divide both sides by 7:
7x/7 = 94500/7
x=13500
The city contributes 13500.
The county contributes 2(13500) = 27000.
The state contributes 2(27000) = 54000.
the perimeter of a triangle is 75 cm. The triangle is isosles now, but if its base were lenghthened by 2 cm and each leg were shortened by 7 cm, it would be equilateral. find the length of the base of the original triangle
Answers
(-14)+2=(-12)
75-12=63
63/3=21
21-2=19 BASE=19
21+7=28 EACH LEG=28
28+28+19=75
new triangle 21+21+21
19+2=21
28-7=21
To find the original base length of the isosceles triangle, we set up equations based on the given perimeter and the condition for the triangle turning into an equilateral triangle after changes to its sides. Solving these equations, we find that the original base length is 19 cm.
Explanation:The student is asking about solving a problem related to the perimeter of an isosceles triangle and finding the original base length given certain conditions that would turn it into an equilateral triangle.
In the original isosceles triangle, we'll denote the equal sides as 'a' and the base as 'b'. Since the perimeter is the sum of all sides, we have:
a + a + b = 75 cm
When altered, the base becomes 'b + 2 cm' and the equal sides become 'a - 7 cm'. To form an equilateral triangle, all sides must be equal:
b + 2 = a - 7
Simplifying gives us two equations:
2a + b = 75b + 2 = a - 7Rearranging the second equation we get a = b + 9. Substituting 'a' in the first equation we get:
2(b + 9) + b = 75
Which simplifies to:
3b + 18 = 75
b = 19 cm
Therefore, the length of the base of the original isosceles triangle is 19 cm.
a jewelry store buys 24 necklaces for $300. the store wants to make a profit of $540. assuming it sells all 24 necklaces, how much should the store charge for each necklace?
Answers
540+300=840
840/24= 33.60
They would charge $33.60 per necklace.
If you were meaning a profit of $540 total then:
540/24=22.5
They would charge $22.50 per necklace.
Answer:
i agree with the other person
Step-by-step explanation:
paula earned a 56% on her science test if she got 14 problems correct then how many questions were on the test
Answers
1% = 14 ÷ 56 = 0.25 questions
100% = 0.25 x 100 = 25 questions
Answer: 25 questions.
Let P = amount of problems on the test.
P = 14 / (1 - 0.56)
= 14/ 0.44
≈ 31.818 repeating.
You can have part of a question (in this math, that is. Partial credit IRL exists) so we round to the nearest whole question, 32.
The test had 32 questions.
u=1-3v/vt-w make t the subject
Answers
By isolating terms involving 't' and solving for 't', we manage to rearrange the provided equation to get t = (1-u+w)/(3v^2).
Explanation:To rearrange the provided equation u=1-3v/vt-w with t as the subject, we can follow these steps:
Start by isolating terms involving t to one side, i.e., bring all other terms to the opposite side. We get: vt = (1-u+w)/3v.The next step is to solve for t by dividing both sides of the equation by v. Hence, the final rearranged equation is: t = (1-u+w)/(3v2).Learn more about Equation Rearrangement here:https://brainly.com/question/10945620
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Will mark as Brainliest.
Michaela drops a ball vertically from a height of 80 feet. The peak height after each bounce is half the previous height. How far does the ball travel from the time she drops it until it reaches the peak height after the 5th bounce?
155 ft
230 ft
232.5 ft
312.5 ft
Answers
On a map, 0.25 inches represents 1 mile. What is the area of a rectangle on the map that is 3.75 inches long and 2.25 inches wide?
Answers
First we need to find 3.75/0.25, then multiply that with 1(same number),since 0.25 inch =1 mile
3.75/0.25=15
That means length=15 miles
Find width in the same way.
2.25/0.25=9
Width=9 miles
a=l*b
a=15*9
a=135 sq. miles
Hope this helps you.
Answer:
135 Square Miles
Step-by-step explanation:
On a map, 0.25 inches represents 1 mile. What is the area of a rectangle on the map that is 3.75 inches long and 2.25 inches wide?
270 square miles
135 square miles
48 square miles
24 square miles
Odyssey
simplify this expression 3x^2 y^2/24x
Answers
3x ^ 2 y ^ 2 / 24x
Rewriting we have:
(3/24) (x ^ 2 y ^ 2 / x)
Simplifying we have:
(1/8) (xy ^ 2)
Answer:
The simplified expression for this case is given by:
(1/8) (xy ^ 2)
Equation:
3x ^ 2 y ^ 2 / 24x
=(3/24) (x ^ 2 y ^ 2 / x)
SO simplify it is
= (1/8) (xy ^ 2)
The simplified expression for this case is given by:
(1/8) (xy ^ 2)
The length of a rectangle is 5/2 units greater than twice its width. If its width is w, which expression gives the perimeter of the rectangle in terms of w?
Answers
perimeter = 6w + 5 units
Explanation:
Perimeter of a rectangle can be calculated as follows:
Perimeter = 2(width + length)
We are given that:
width = w units
length is 5/2 units greater than twice the width. This means that:
length = 2w + 5/2
Now, substitute in the above equation to get the expression for the perimeter as follows:
Perimeter = 2(width + length)
Perimeter = 2(w + 2w + 5/2)
Perimeter = 2(3w + 5/2)
Perimeter = 2(3w) + 2(5/2)
Perimeter = 6w + 5
Hope this helps :)
Answer:
D: 6w + 5
Step-by-step explanation:
The perimeter of a rectangle can be calculated as follows:
Perimeter = 2(width + length)
We are given that:
width = w units
length is 5/2 units greater than twice the width. This means that:
length = 2w + 5/2
Now, substitute in the above equation to get the expression for the perimeter as follows:
Perimeter = 2(width + length)
Perimeter = 2(w + 2w + 5/2)
Perimeter = 2(3w + 5/2)
Perimeter = 2(3w) + 2(5/2)
Perimeter = 6w + 5
Sally is making sun tea. Every hour the concentration of the tea doubles. If it takes 6 hours for the tea to be ready how long would it take the tea to reach half of the final concentration?
Answers
It is given Sally is making sun tea. Every hour the concentration of the tea doubles.Let the concentration of tea at start is nil.Then after first hour concentration will be 2.After third hour concentration will be double of 2 that is 4.After fourth concentration will be 4(2)=8.After fifth hour concentration will be 8(2)=16.After sixth hour concentration will be 16(2)=32.
It is given:it takes 6 hours for the tea to be ready.WE need to find how long would it take the tea to reach half of the final concentration.Half of final concentration is 32÷2=16.
Concentration of 16 is after fifth hour.
Evaluate square root of 24 - x when x = 6 . Write the answer in simplified radical form.?
Answers
24 - 6 = 18
So we now need to find the square root of 18
If you're allowed to use a calculator, the square root is 4.242
But if you don't, let's get as close as we can:
√(9 * 2)
Because the square root of 9 is 3:
3 * √2
The perimeter of a rectangle is dependent on the length of each of its sides. Suppose the base of a rectangle is two more than its height. Complete an input/output table for at least three pairs of inputs and outputs. Make sure to use values that make sense within the context of this situation.
Answers
x---------> length of the base of a rectangle
y--------->height of the base of a rectangle
we know that
perimeter of a rectangle=2*[x+y]
and
x=y+2------> y=x-2
step 1
inputs
x=3
x=5
x=10
step 2
find the outputs
for x=3
y=x-2----> y=3-2-----> y=1
perimeter=2*[3+1]-----> 8
for x=5
y=x-2----> y=5-2-----> y=3
perimeter=2*[5+3]-----> 16
for x=10
y=x-2----> y=10-2-----> y=8
perimeter=2*[10+8]----->36
see the attached table
A stop sign has 8 equal sides. If each side is 11 inches in length, what is the perimeter of the stop sign?
Answers
Please help on the fraction question
Answers
please help ...... ............
Answers
in the diagram below bc is an altitude of abd.to the nearest whole unit.what is the length of cd
Answers
AB = √30^2 + 16^2 = 34
These are similar triangles.
∠BAC is congruent to ∠BAD
∠ACB is congruent with ∠ABD (both right angles)
Using ratios:
AC / AB = AB / (AC + CD)
AC + CD = AB² / AC
CD = AB² / AC - AC
CD = 34² / 16 - 16
CD = 56.25
The answer to this question is 56.
The trigonometric function gives the ratio of different sides of a right-angle triangle.The correct option is C.
What is Trigonometric functions?The trigonometric function gives the ratio of different sides of a right-angle triangle.
[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\[/tex]
where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.
Let the length of the line segement CD be represented by x.
In ΔABC, Using the pythgorus theorem, we can write,
AB² = BC² + AC²
AB² = 30² + 16²
AB = 34 units
In ΔABC, the measure of ∠A be written as,
tan(∠A) = BC/AC
tan(∠A) = 30/16
∠A = tan⁻¹ (30/16)
∠A = 61.9275°
Now, in ΔABD, the measure of ∠A can be written as,
Cos(∠A) = AB/AD
Cos(61.9275°) = 34/(AC+CD)
0.47 = 34/(16+CD)
16 + CD = 72.25
CD = 56.25 ≈ 56
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A factory machine produces 5/10 kilograms of chocolate every 1/6 minutes.
At what rate does the machine produce chocolate?
A. 1/3 kg/min
B. 2/5 kg/min
C. 3 kg/min
D. 6 kg/min
Answers
:) Have a nice day and maybe consider grading this answer brainliest? <3
1. Suppose the population of deer in a region was 3500 in the year of 2000 since when the population has grown by 3.5% annually what will the approximate population be in the year of 2020 y equals 8 x b x where a is the starting amount B is the growth rate increasing add to 1 and X is time.
2.
The population of New Haven was 148220 in 2004 since when the population has been decreasing at an annual rate of 2.9% if the rate of the decline continues what will the population be in the year 2015
Answers
To calculate future population growth, we use a formula incorporating the initial population, annual growth rate, and number of years. For growth, we add one to the growth rate and raise it to the power of elapsed years, then multiply by the initial population. For decline, we subtract the rate from one and then do similar exponentiation and multiplication.
Calculating Future Population Growth
To calculate the future population of deer given a starting population and a constant annual growth rate, we use the formula y = a(1+b)^x, where 'a' is the starting amount, 'b' is the growth rate, and 'x' is the number of years elapsed. For the deer population, from 2000 to 2020, there are 20 years of growth at 3.5% annually. Using a=3500, b=0.035, and x=20, the calculation is as follows:
Convert the percentage to a decimal: 3.5% becomes 0.035.
Add 1 to the growth rate: 1 + 0.035 = 1.035.
Raise this sum to the power of 20: (1.035)^20.
Multiply the result by the initial population: 3500 * (1.035)^20.
For the New Haven population, which is decreasing at 2.9% annually from 2004 to 2015 (11 years), the steps are similar. However, we subtract the percentage decline from 1 instead since the population is decreasing.
Convert the percentage to a decimal: 2.9% becomes 0.029.
Subtract this from 1: 1 - 0.029 = 0.971.
Raise this to the power of 11: (0.971)^11.
Multiply the result by the initial population of New Haven: 148220 * (0.971)^11.
After performing these calculations, we will get the estimated populations for both the deer and New Haven in the specified years.
QUESTION 1:
The probability that an event will occur is 15%. Which of these best describes the likelihood of the event occurring?
A: Likely
B: Certain
C: Unlikely
D: Impossible
QUESTION 2:
The probability that an event will occur is 1/8 . Which of these best describes the likelihood of the event occurring?
A: Likely
B: Certain
C: Unlikely
D: Impossible
Thanks :)
Answers
2. Unlikely
Can I have Brainliest, please?Thanks!!
What is (x-5)1/2+5=2
Answers
(x-5) 1/2 + 5 = 2
Rewriting correctly we have:
(x-5) ^ (1/2) + 5 = 2
Clearing x we have:
(x-5) ^ (1/2) = 2-5
(x-5) ^ (1/2) = -3
(x-5) = root (-3)
x = 5 + i * root (3)
Answer:
The value of x is given by:
x = 5 + i * root (3)
What’s the ratio decimal of
2:3
3:7
3:6
3:8
2:5
3:7
2:4
Answers
2:3= 2/3= 0.6666666= 0.67 rounded
3:7= 3/7= 0.42857= 0.43 rounded
3:6= 3/6= 1/2= 0.5
3:8= 3/8= 0.375
2:5= 2/5= 0.4
3:7= 3/7= 0.42857= 0.43 rounded
2:4= 2/4= 1/2= 0.5
Hope this helps! :)
Need help on #16 ASAP
Answers
c. ΔABC to ΔA"B"C" using translation (x, y) → (x - 2; y - 8)
the denominator of a certain number was 147 greater than its numerator. What was the denominator of this fraction, if after the fraction was reduced it became 5/12
Answers
[tex] \frac{x}{x+147} = \frac{5}{12} [/tex]
[tex]12x=5(x+147)[/tex]
[tex]12x=5x+735[/tex]
[tex]7x=735[/tex]
[tex]x= \frac{735}{7} [/tex]
[tex]x=105[/tex]
Now we can replace 105 in our original fraction to get our number:
[tex] \frac{x}{x+147} [/tex]
[tex] \frac{105}{105+147} = \frac{105}{252} [/tex]
We can conclude that the original number was [tex]\frac{105}{252} [/tex]
Look at the model below and write an expression to match.
Answers
The rectangular blocks are x and the squares are 1 unit. There are 2 x's, or 2x, and 6 units; 2x+6.
A class of 24 students was asked to identify a team sport in which they have participated. Their responses are shown in the line plot.
ty <3
Answers
b) The number of students polled is 24.
c) One or more students must have participated in more than 1 sport, that would explain why there was a higher number of sport participation than students.
a) The total responses recorded from the line plot is n = 28 responses
b) The number of students polled = 24 students
c) The fact that there were more responses than students polled suggests that one or more students engaged in more than one sport.
What is a line plot ?A line plot is a graph that shows data as points or check marks above a number line, indicating the frequency of each value.
If we need to compare two different groups , a line chart does have one advantage for visualizing frequency distributions
It displays information as a series of data points called 'markers' connected by straight line segments
Given data ,
Let the line plot be represented as A
Now , the total number of students in the class = 24 students
So , the total number of polls = 24 students
The total number of responses recorded from the points on the line plot is give by
The number of responses for football = 4
The number of responses for soccer = 8
The number of responses for baseball = 7
The number of responses for basketball = 5
The number of responses for football = 4
The total number of responses recorded from the points on the line plot is n = 28
Given that there were more replies than students asked, it is likely that some students participated in several sports.
Hence , the line plot is solved
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write a translation rule that maps D(7,-3) onto point (2,5)
Answers
If the location of point D is defined by coordinates (x, y) equal to (7, -3), and the location of point D' is defined by coordinates (x', y') equal to (2, 5), the point D translated becomes point D' means that each point (x, y) is shifted onto the point (x', y'), that is,
(x, y) → (x', y')
Dtranslation = < (x' - x), (y' - y) >
= < 2 - 7, 5 - (-3) >
= < -5, 8 >
Therefore, point D moved 5 units to the left and 8 units up:
D(x, y) → (x-5, y+8)
(Photo) Please help me
Which of the following is an example of empirical probability?
Answers
Answer:
The answer is D, and with the others you aren't experimenting with anything
Step-by-step explanation:
A sided cube labeled 1-6 is rolled 200 times. An even number is rolled 115 times. Compare the theoretical probability of rolling an even number with the relative frequency of rolling an even number and select one statement.
Probability the same, Probability is smaller. Probability is larger. There's not enough information
Answers
Answer:
Probability is smaller.
Step-by-step explanation:
Need help with 2 3 4 5 6
Answers
Answer:
all answers are shown and pictured