Don is 6 feet tall. at a given time of day, he measures his shadow to be 13 feet long. at the same time, he measures the shadow length of a nearby tree to be 51 feet. how tall is the tree
The height of the tree maintaining the given ratio is 23.54 feet.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
Given that,
Don height = 6 feet
His shadow = 13 feet
The ratio of height to shadow = 6/13
Tree height = x (let's say)
Tree shadow = 51 feet
Ratio = x/51
Both ratios must be the same, therefore,
x/51=6/13
x=23.54 feet
Hence "The height of the tree maintaining the given ratio is 23.54 feet".
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Please help! Given b = 4 and h = 1, what is the equation of the graph if the parent function is y = sqrt x?
A. y = sqrt (4x - 4)
B. y = sqrt (4x + 4)
C. y = - sqrt (4x - 4)
D. y = - sqrt (4x + 4)
To solve this problem, we make use of the formula:
y = a sqrt (b (x – h)) + k ---> 1
Since we are given the parent function:
y = sqrt (x) ---> 2
Then this automatically means that:
a = 1 and k = 0
So going back to equation 1 at a = 1 and k = 0:
y = 1 sqrt (b (x – h))
Since it is given that, b = 4 and h = 1, therefore:
y = sqrt (4 (x – 1))
y = sqrt (4 x – 4)
Answer:
A. y = sqrt (4 x – 4)
A basketball is thrown with an initial upward velocity of 25 feet per second from a height of 8 feet above the ground. The equation h=−16 t 2 +25t+8 h=−16t2+25t+8 models the height in feet t seconds after it is thrown. After the ball passes its maximum height, it comes down and then goes into the hoop at a height of 10 feet above the ground. About how long after it was thrown does it go into the hoop?
How you know when there is only one solution triangle possible from a side-side-angle?
Answer:
There will be only on solution if either of these conditions is met:
the given angle is opposite the longest sidethe triangle is a right triangle (the ratio of the side opposite the angle to the other given side is equal to the sine of the angle)Step-by-step explanation:
Consider the SSA geometry with the angle placed in standard position at the origin and its adjacent given side (the second side of SSA) extending along the +x axis. Draw a circle having a radius equal to the length of the first side of SSA, centered on the vertex between the two segments on the +x axis.
There are three possibilities for the way this circle intersects the other ray of the angle (the ray that is not the x-axis):
the first side is as long or longer than the second side, so there is one point of intersection (one solution to the triangle, purple in the attachment)the first side is just long enough to be tangent to the other ray, so there is one point of intersection (one solution to the triangle, green in the attachment)the first side is between these lengths, so intersects the other ray in two places, giving two solutions to the triangle, red in the attachment.Find 93 • 87 using mental math.
To estimate 93 × 87 using mental math, round 87 to 90, multiply by 93 to get 8370, and subtract 3 × 93 (279) for an estimate of 8091.
To find 93 × 87 using mental math, we can employ a strategy that simplifies the multiplication process. One way is to round one of the numbers to the nearest multiple of ten, perform the multiplication, and then adjust the result accordingly. Here, we can round 87 up to 90 and multiply 93 by 90. This is easier because 90 is a multiple of 10.
93 × 90 = (93 × 9) × 10 = 837 × 10 = 8370
Since we rounded 87 to 90, we overestimated by 3 per unit of 93. Hence, we need to subtract 3 times 93 from 8370.
3 × 93 = 279
Thus, 8370 - 279 = 8091.
The growth of a new strain of bacteria is represented by 7=79.31(1.48)^x,where x represents the number of days and y represents the number of bacteria. which is the best prediction for the number of bacteria on day 6
A.833
B.117
C.704
D.647
Answer:
A. 833
Step-by-step explanation:
Given:
The growth of a new strain of bacteria is represented by [tex]y = 79.31(1.48)^x[/tex], where "x" represents the number of days and "y" represents the number of bacteria.
We need to find the number of bacteria on day 6.
So, here x = 6, we need to plug in x = 6 in the given function and find the answer.
[tex]y = 79.31(1.48)^6[tex]
Simplify the above expression, we get
y = 833.49
The bacteria cannot be in decimal form, let's round off the answer to nearest whole number.
y = 833
Therefore, answer is A. 833
Which of the following sets is not finite?
Which of the following types of functions cannot have "all real numbers" as either its domain or its range? Exponential function Quadratic function Linear function Inverse Variation function
The point (-2, 6) is on the line given by which of the equations below?
A.
y = 4x
B.
y = 2x
C.
y = 3x
D.
y = -3x
What polynomial identity should be used to prove that 20 = 36 − 16
Diffrence of squares is the correct answer just score pract q
Find the value of x for which abcd must be a parallelogram 5x-1 2x+5
if a metal tool chest has the shape of a prism with a pentagonal base of 6194in squared in area, calculate the volume of the metal chest and pick where length c = 6 inches and length m = 19 inches
The volume of the metal tool chest is 37,164 cubic inches. To calculate the volume of the metal tool chest, we use the formula for the volume of a prism: Volume = Base area × Height
Given that the pentagonal base has an area of 6194 square inches, and the length c (which represents the height) is 6 inches, we can calculate the volume as follows:
Volume = 6194 in² × 6 in
Volume = 37,164 cubic inches
So, the volume of the metal tool chest is 37,164 cubic inches.
As for the lengths provided:
c = 6 inches (height)
m = 19 inches (unknown side length of the pentagon)
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(06.06) Which of the following demonstrates the Commutative Property of Multiplication? 3(4a − 2) = 12a − 6 3(4a − 2) = (4a − 2) ⋅ 3 12a − 6 = (4a − 2) ⋅ 3 (3 ⋅ 4a) − 2 = 3(4a − 2)
Whats the perimeter of a rectangle with length 12 m and width 5m
What is 5.928301 to 2 decimal places?
Final answer:
To round 5.928301 to 2 decimal places, we observe the third decimal place. It's 8, so we round up, making the answer 5.93.
Explanation:
When rounding the number 5.928301 to 2 decimal places, we need to look at the third decimal digit to decide whether to round up or down. Since the third decimal digit (8) is greater than 5, we round up. Therefore, the number 5.928301 rounded to 2 decimal places is 5.93.
Rounding a number to two decimal places involves examining the third decimal digit to determine whether to round up or down. In the case of 5.928301, the third digit is 8, which is greater than 5. Consequently, rounding up is necessary. Thus, the rounded value of 5.928301 to two decimal places is 5.93, emphasizing the role of the third digit in the rounding decision.
The length of a rectangle is eight times it's width. If the length was decreased by 10 meters and the width decreased by 2 meters the area would be decreased by 162 m. Find the original dimensions.
Geometry Question Please Help!!!!
PQRS is an isosceles trapezoid and m angle Q=127. Find M angle P.
Answer:
[tex]m<P=127\°[/tex]
Step-by-step explanation:
we know that
If the trapezoid PQRS is an isosceles trapezoid
then
[tex]PS=QR[/tex] ----> congruent sides
[tex]m<P=m<Q[/tex] -----> congruent angles
In this problem we have
[tex]m<Q=127\°[/tex]
therefore
[tex]m<P=127\°[/tex]
Sue took a taxi from her home to her friends house. It cost $3.58 per mile and she gave the driver a $5 tip. If she paid $87.34, how many miles does she live from her friend?
87.34-5 = 82.34
82.34/3.58 = 23
she lives 23 miles away
The parabola has a vertex of (1,-16) and y intercept of (0,-15) that crosses the x axis in two places. one x intercept is (5,0) what is the other x intercept
the leg of a right triangle is 5 units and the hypotenuse is 8 units.what is the length in units of the other leg of the triangle
The square of the hypotenuse is equal to the sum of the square of other two sides. The length in units of the other leg of the triangle is 6.2 units
What is Pythagoras theorem?The square of the hypotenuse is equal to the sum of the square of the other two sides.
Mathematically;
l^2 = a^2 + b^2
Given
l = 8 units
a = 5 units
Substitute
8^2 = 5^2 + b^2
64 - 25 = b^2
b^2 = 6.2units
Hence the length in units of the other leg of the triangle is 6.2 units
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The area of a rectangular wall of a barn is 75 75 square feet. its length is 10 10 feet longer than the width. find the length and width of the wall of the barn.
First, represent the unknown width as 'x'. Then, because the length is 10 feet more than the width, represent the length as 'x + 10'. Since the area is 75 square feet, set up and solve the equation x*(x + 10) = 75 for 'x'. This will give the width and the length will be this width plus 10 feet.
Explanation:This problem can be solved using algebra. First, let's denote the width of the wall as x in feet. If the length of the wall is 10 feet longer than the width, then we can express the length as x + 10. We're told that the area of the rectangle formed by the wall is 75 square feet. The area of a rectangle is calculated by multiplying its length by its width. Therefore:
x*(x + 10) = 75
You can solve this quadratic equation for x. The positive solution will be the width of the wall and the length will be that value plus 10 feet.
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What is
5.63×
10
−6
in decimal form?
a. 0.00000563
b. 0.000000563
c.5,630,000
d. 56,300,000
find the value of x if f(x) equals 7 f(x) equals 4x minus 1
Select the additive inverse of 51
if M and N are midpoints in a diagram below, determine values for x and y
a bag contains 5 red marbles, 3 yellow marbles, and 2 blue marbles. Once a marble is drawn, it is not replaced.what is the probability of drawing a blue on the first draw and a second blue marble on the next draw ?
The distance from earth to the moon is about 22^4 miles. the distance from earth to neptune is22^7 miles. which distance is the greatest and by how much
Determine whether the sequence shown are arithmetic or geometric 1,8,15,22,29
Neptune has 8 known moons. This is 2 more than 1/3 of the number of known moons on Saturn. How many moons is Saturn known to have?
Through setting up and solving the equation 1/3 * x + 2 = 8, where x represents the number of Saturn's moons, it was determined that Saturn is known to have 18 moons.
Explanation:The student's question pertains to a comparison of the moons of Neptune and Saturn, using mathematical operations to deduce the number of known moons of Saturn. First, we're told that Neptune has 8 known moons, which is said to be 2 more than 1/3 of the number of known moons on Saturn. We are seeking to solve for the number of moons that Saturn has.
To find out, we set up an equation where 1/3 of the number of moons of Saturn plus 2 equals the number of Neptune's moons: 1/3 * x + 2 = 8, where x represents the number of Saturn's moons. Solving for x, we subtract 2 from both sides to get 1/3 * x = 6. We then multiply both sides by 3 to isolate x and find that x = 18.
Therefore, Saturn is known to have 18 moons according to the given information.