A lighthouse cast a shadow that is 36 meters long at the same time , a person who is 1.5 meter tall casts a shadow that is 4.5 meters long . Write and solve a proportion to find the height of the lighthouse
To find the height of the lighthouse, set up a proportion using the lengths of the shadows and solve for h. The height of the lighthouse is 12 meters.
Explanation:To find the height of the lighthouse, we can set up a proportion based on the lengths of the shadows. Let h be the height of the lighthouse. The proportion is:
(h / 36) = (1.5 / 4.5)
Now, we can cross multiply and solve for h:
h = (1.5 / 4.5) * 36
h = 12 meters
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Take 2y 2 - 3y - 5 from y ^3 - 6y ^2 + 5y. Select the correct answer.
y^3 - 2y^2 + 3y + 5
y^3 - 4y^2 + 2y - 5
y^3 - 4y^2 + 2y + 5
y^3 - 8y^2 + 8y + 5
Answer:
y^3-2y^2+3y+5
Step-by-step planation:
What are the odds of picking a "g" in the word Georgia?
Suppose the population of a certain city is 4252. it is expected to decrease to 3393 thousand in 50 years. find the percent decrease.
plz help cant get no help will mark brainliest . 1. Write an expression that represents the length of the south side of the field. (2 pts) 2. Simplify the polynomial expression that represents the south side of the field. (2 pts) 3. Write a polynomial expression that represents the perimeter of the pumpkin field. (2 pts)4. Simplify the polynomial expression that represents the perimeter of the pumpkin field.
What is the value of a, if a2 – 64 = 0 and a > 0? A) 0 B) 4 C) 8 D) 16
Answer:
C) 8
Step-by-step explanation:
Let's solve for:
[tex]a^2 -64=0\\\\a>0[/tex]
Add 64 to both sides:
[tex]a^2-64+64=0+64\\\\a^2=64[/tex]
Take the square root of both sides
[tex]\sqrt{a^2} = \sqrt{64} \\\\a=\pm 8[/tex]
Therefore, we got two solutions:
[tex]a=8\\\\or\\\\a=-8[/tex]
However, since:
[tex]a>0[/tex]
The only solution is:
[tex]a=8[/tex]
Which one is true? Thanks
Can some please help me?!
Every employee works 7 hours per day, Every employee works 5 days per week. Every employee works 49 weeks per year. Every employee works _ days per year, Every employee works _ hours per year. Fill in the blanks.
Solve for x: −3|x − 3| = −6
A marathon is 26 miles 385 yards long . That is about what 1.4 x10 feet how many feet long is half a marathon
I believe that the correct measurement in feet is 1.4 x 10^5 feet. You forgot to include the ^5.
So since that is the measurement of 1 marathon, therefore half a marathon would simply be also half of that, that is:
0.7 x 10^5 feet
or
7 x 10^4 feet
Final answer:
Half a marathon is 69,168 feet in length. To calculate the runner's time for a full marathon at an average speed of 9.5 mi/h, divide the distance (26.2 miles) by the speed, resulting in approximately 2.76 hours or about 2 hours and 45 minutes.
Explanation:
To find the length of half a marathon in feet, we first need to know the length of a full marathon in feet then divide that by 2. Since one marathon is approximately 26.2 miles, we first need to convert miles to feet. There are 5,280 feet in one mile. So, for a full marathon:
26.2 miles × 5,280 feet/mile = 138,336 feet for a full marathon.
Therefore, half a marathon would be:
138,336 feet ÷ 2 = 69,168 feet for half a marathon.
Next, let's look at the question about the marathon runner's time. If a runner averages 9.5 mi/h over a full marathon of 26.2 miles, we can calculate the time taken to run this distance. Time is distance divided by speed, so:
26.2 miles ÷ 9.5 mi/h = approximately 2.76 hours,
which can be converted to minutes: 2.76 hours × 60 minutes/hour = approximately 165.6 minutes or about 2 hours and 45 minutes.
Read the prompt and use complete sentences to answer parts A and B. Barry wants to surprise his family with a vacation to the Bahamas. Part A. Describe a scenario in which Barry uses responsible financial decisions to afford the vacation for his family. Part B. Describe a scenario in which Barry uses irresponsible financial decisions to afford the vacation for his family.
Barry wants to surprise his family with a vacation to the Bahamas. So he buys plane tickets with cash in hand and they all go.
Barry wants to surprise his family with a vacation to the Bahamas. So he uses all his cash, then uses his credit card to purchase the plane tickets.
suppose f(x)=x-2. describe the transformation from the graph of f(x) to the graph of g(x)=x+3. Use a graphing calculator to check your answer.
a^3+b=c^2 Solve for a and show me how you got that answer
Simplify. 1/4+4(1/2−3/4)^2 Enter your answer in the box.
The Simplest form of the expression 1/4+4(1/2−3/4)^2 is 1/2
What are equivalent expressions?Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.
To derive equivalent expressions of some expression, we can either make it look more complex or simple. Usually, we simplify it.
Using PEMDAS
1/4+4(1/2−3/4)^2
Subtract inside parenthesis
(1/2−3/4) = -1/4
Now, Square
1/4+4(-1/4)^2
1/4+4(1/16)
Then Multiply 4 and (1/16)
1/4+(1/4)
Now Adding;
2/4 = 1/2
Hence, The Simplest form of the expression 1/4+4(1/2−3/4)^2 is 1/2
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In January, you deposit $16 in your checking account. Each month, you deposit $15 more than you did the month before. How much money do you deposit in October?
Answer:
$151Step-by-step explanation:
This problem is about a arithmetic sequence, which is obtained by summing a term which is called "difference". In this case, we need to find the tenth term of the arithmetic sequence, because that's the term assigned for October. The formula of an arithmetic sequence is
[tex]a_{n}=a_{1}+(n-1)d[/tex]
Where:
[tex]n=10\\a_{1}=16\\d=15[/tex]
Replacing values, we have
[tex]a_{10}=16+(10-1)15=151[/tex]
Therefore, on October you will have $151 if you deposit $15 more each month, beginning with $16.
Write the sentence as an equation.
307 less than the product of h and 257 is 89
find the coordinates of the circumcenter of triangle ABC with vertices A(1,4) B(1,2) and C(6,2)
A. 5,2
B. 3,4
C. 2.5,1
D. 3.5,3
Answer:
D. (3.5, 3)
Step-by-step explanation:
Just something simple
Help Physics Class!!!
F = kx
k = ?
F/x
x/F
F + x
F - x
F= kx
so to get k divide both sides by x
so k = F/x
Algebra Help
Let f(x)=6x. The graph of f(x) is transformed into the graph of g(x) by a vertical compression of 1/3 and a translation of 2 units up.
What is the equation for g(x)?
Enter your answer in the box.
g(x)
The correct answers are actually : 2x+2 these are correct bc i just took the test.
Hope this helps.
The graph of f(x) after transforming into the graph of g(x) by a vertical compression of 1/3 and a translation of 2 units up is g(x) = 2x + 2.
What is translation?It is the movement of the shape in the left, right, up, and down directions.
The translated shape will have the same shape and shape.
There is a positive value when translated to the right and up.
There is a negative value when translated to the left and down.
We have,
The graph of f(x) = 6x
Vertical compression = 1/3.
Translation = 2 units up.
If there is a vertical compression of 1/3 on the graph f(x).
The graph of f(x) = 6x transformed as g(x) = 1/3 x 6x = 2x
Now,
If the graph g(x) 2x has a translation of 2 units up we get,
g(x) = 2x + 2
g(x) = 2(x + 1)
Thus,
The graph of f(x) after transforming into the graph of g(x) by a vertical compression of 1/3 and a translation of 2 units up is g(x) = 2x + 2.
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The coordinates of the vertices of quadrilateral DEFG are D(−2, 5) , E(2, 4) , F(0, 0) , and G(−4, 1) .
Which statement correctly describes whether quadrilateral DEFG is a rhombus?
Quadrilateral DEFG is a rhombus because opposite sides are parallel and all four sides have the same length.
Quadrilateral DEFG is not a rhombus because there is only one pair of opposite sides that are parallel.
Quadrilateral DEFG is not a rhombus because opposite sides are parallel but the four sides do not all have the same length.
Quadrilateral DEFG is not a rhombus because there are no pairs of parallel sides.
Quadrilateral DEFG is not a rhombus because the four sides do not all have the same length.
Explanation:The coordinates of the vertices of quadrilateral DEFG are D(-2, 5), E(2, 4), F(0, 0), and G(-4, 1). To determine if DEFG is a rhombus, we need to observe the properties of a rhombus. A rhombus has opposite sides that are parallel and all four sides have the same length. Using the distance formula, we calculate the lengths of the four sides of DEFG:
Side DE: √((-2 - 2)^2 + (5 - 4)^2) = 4.12Side EF: √((2 - 0)^2 + (4 - 0)^2) = 4.47Side FG: √((0 - (-4))^2 + (0 - 1)^2) = 4.12Side GD: √((-4 - (-2))^2 + (1 - 5)^2) = 4.47As we can see, the lengths of DEFG's sides are not all the same. Therefore, DEFG is not a rhombus.
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A baby weighed 7.25 lb at birth at the end of 8 months , the baby weighed 2 1/2 times its birth weight. how many pounds did the baby weigh at the end of 8 month ?
Answer:
The weight of baby at the end of 8 month is 18.125 lb.
Step-by-step explanation:
Given information:
The weight of baby at birth = 7.25 lb
At the end of 8 months, the baby weighed [tex]2\frac{1}{2}[/tex] times its birth weight.
We need to find the weight of baby at the end of 8 month.
[tex]2\frac{1}{2}=\frac{4+1}{2}=\frac{5}{2}[/tex]
The weight of baby at the end of 8 month is 5/2 times of its initial weight.
[tex]\text{Total weight}=7.25\times \frac{5}{2}[/tex]
[tex]\text{Total weight}=18.125[/tex]
Therefore the weight of baby at the end of 8 month is 18.125 lb.
The height of a building in a scale drawing is 9cm.The scale is 1:600.Explain how you would use the scale to find the actual height of the building.
The actual height of the building is 54 meters.
The actual height of the building is calculated by multiplying the scale drawing height by the scale factor.
Given that the scale is 1:600, this means that 1 centimeter on the drawing represents 600 centimeters in reality.
Therefore, to find the actual height of the building, one would multiply the height of the building on the scale drawing (9 cm) by the scale factor (600).
Using the scale, the actual height H of the building can be determined as follows:
[tex]\[ H = \text{scale drawing height} \times \text{scale factor} \] \[ H = 9 \, \text{cm} \times 600 \] \[ H = 5400 \, \text{cm} \][/tex]
To convert centimeters to meters, since there are 100 centimeters in a meter, we divide by 100:
[tex]\[ H = \frac{5400 \, \text{cm}}{100} \] \[ H = 54 \, \text{m} \][/tex]
Thus, the actual height of the building is 54 meters.
The length of a rectangle is 6 m longer than its width. if the perimeter of the rectangle is 48 m , find its area.
Answer:
135m²
Step-by-step explanation:
Perimeter = 2(l + w)
l = w + 6
Substituting for l, gives;
2(w+6+w)
48 = 2w + 12 +2w
48 = 4w + 12
48 - 12 = 4w
36 = 4w
w = 9
Since w = 9, then l = w +6
l = 9 + 6
l = 15
Area = l * w
Area = 15 * 9
Area = 135m²
The length of a rectangle is 3 more than twice its width. the perimeter is 48 feet. find the width.
Solve for r: d = rt *
A. d = rt
B. t = d/r
C. r = d/t
D. r = t/d
d =rt
to solve for r divide both sides by t
so r = d/t
Answer is C
What is the equation of a line that is parallel to −2x+3y=−6 and passes through the point (−2, 0) ?
Help Please!! Flip the inequality sign whenever you _____________ or _____________ the inequality by a _______________!
What is the volume of a cube that measures 5 cm on each side?
The measures of complementary angles have a sum of 90 degrees. Angle A and angle B are complementary, and their measures have a difference of 20°. What are the measures of the angles?
thanks.
To find the measures of complementary angles A and B with a known difference of 20 degrees, we set up a system of equations and solved them to find that angle A measures 55 degrees and angle B measures 35 degrees.
The problem involves finding the measures of two complementary angles, angle A and angle B, with a known difference in their measures. By definition, complementary angles are two angles whose sum is 90 degrees. Given the difference of 20 degrees between the angles, we can set up a system of equations to solve for their measures.
Let's denote the measure of angle A as a and angle B as b. Therefore, we have the two equations based on the problem statement:
a + b = 90 (because they are complementary)
a - b = 20 (the difference in their measures)
To find the values of a and b, we can add the two equations:
a + b = 90
a - b = 20
By adding them together, we get:
2a = 110
Dividing both sides by 2, we find a:
a = 55
To find b, we substitute a back into one of the original equations:
55 + b = 90
Subtracting 55 from both sides gives us b:
b = 35
Therefore, angle A measures 55 degrees and angle B measures 35 degrees.