The shorter leg of a 30°- 60°- 90° right triangle is 12.5 inches. How long are the longer leg and the hypotenuse?
Answers
The shorter leg would be the side BD (or CD) since D is the midpoint of side BC
We are to find the length of side AD (which is the height of the triangle ABC) and the hypotenuse AB (or AC ⇒ depends on which right angle triangle that you'd want to work with)
Since we know the three angles in the right angle triangle ABD, we can use the trigonometry ratio
Side AD is the opposite of the angle 60° and we know the length of side that is adjacent to 60° so we'll use the tangent ratio
tan (x°) = opposite ÷ adjacent
tan (60°) = AD ÷ 12.5
√3 = AD ÷ 12.5
AD = 12.5 × √3
AD = 21.65
We can then use the Pythagoras theorem to work out AB
AB² = AD² + BD²
AB² = 12.5² + 21.65²
AB² = 624.9725
AB = √624.9725
AB = 25 (rounded to 2 significant figures)
Related Questions
If you are making a scale drawing of a giraffe that is 6m tall, and the height of the giraffe in your drawing is 3 cm, what is the scale of the drawing?
Answers
The equation would look like 1/x = 600/3 then simplify so you would get 200
meaning the ratio would be 1:200 PLEASE MARK BRANLIEST!
HOPE IT HELPS!!!!!
Answer:
The scale of the drawing of girrafe is [tex]1:200[/tex].
Step-by-step explanation:
Given: scale drawing of a giraffe that is [tex]6\rm\;{m}[/tex] tall, and the height of the giraffe in your drawing is [tex]3\rm\;{cm}[/tex].
As per question,
Dimension of giraffe is [tex]6\rm\;{m}[/tex] tall and height is [tex]3\rm\;{cm}[/tex].
For scaling the drawing, the given unit must be same.
As we know that,
[tex]1\rm\;{m}= 100\rm\;{cm}\\6\rm\;{m}=600\rm\;{cm}[/tex]
Therefore, scale of the drawing is [tex]3\rm\;{cm}:600\rm\;{cm}=1:200[/tex].
Hence, the scale of the drawing is [tex]1:200[/tex].
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We can solve for x using a technique called successive approximations. step 1: if we assume that x is very small compared to 0.100 (such that 0.100 x ≈ 0.100) then our first approximation of x (let\'s call it x1) can be calculated as
Answers
Supposed that we are given the equation:
7.20 x 10^-5 = x(0.100+x)^2
So assuming that x is very small so that:
0.100 + x ~ 0.100
and calling it x1, so:
7.20 x 10^-5 = x1 (0.100)^2
Then we simply solve for x1:
x1 = 7.20 x 10^-5 / (0.100)^2
x1 = 7.20 x 10^-3
Final answer:
Successive approximations involve iterative guesses to find a solution, Newton's Method refines initial guesses using derivatives, and the Intermediate Value Theorem guarantees a solution in a given interval.
Explanation:
Successive Approximations: When solving for x using successive approximations, we make iterative guesses, refining our estimation with each step. The method involves making an initial guess, then refining it until a sufficiently accurate solution is obtained.
Newton's Method: Newton's method is a numerical technique used to find roots of a function. It involves making an initial guess and then iteratively improving upon it by using the function's derivative.
Intermediate Value Theorem: The intermediate value theorem states that a continuous function that takes on values of opposite signs at two points must have at least one root within that interval.
A bag contains 5 red marbles, two orange marbles, one yellow marbles, and two green marbles. Two marbles are drawn from the bag. What is the approximate probability of choosing an orange marble and a green marble?
Answers
orange-1 out of 10
Answer: 0.04444
Step-by-step explanation:
60 bricklayers began a 16-day project to build a castle. After five days, five of the bricklayers quit the job. If they work the same amount each day, how many extra day(s) (beyond the original estimate of 16) will the remaining bricklayers need?
Answers
(60)(16) = (5)(60) + (11 + x)(60 - 5)
where x is the number of extra days that the bricklayers will still have to work to complete the job. The value of x from the equation is 1
Answer: 1
a tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an inital speed of 120 feet per second. What is the maximum height, in feet, the ball will attain?
Answers
[tex]\bf ~~~~~~\textit{initial velocity}\\\\ \begin{array}{llll} ~~~~~~\textit{in feet}\\\\ h(t) = -16t^2+v_ot+h_o \\\\ \end{array} \quad \begin{cases} v_o=\stackrel{\textit{initial velocity of the object}}{120}\\\\ h_o=\stackrel{\textit{initial height of the object}}{2}\\\\ h=\stackrel{}{\textit{height of the object at "t" seconds}} \end{cases} \\\\\\ h(t)=-16t^2+120t+2[/tex]
[tex]\bf \textit{ vertex of a vertical parabola, using coefficients}\\\\ \begin{array}{llll} h(t)= &{{ -16}}t^2&{{ +120}}t&{{ +2}}\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right) \\\\\\ \left(-\cfrac{120}{2(-16)}~~,~~2-\cfrac{120^2}{4(-16)} \right)\implies \left( \cfrac{15}{4}~~,~~2+\cfrac{14400}{32} \right)[/tex]
[tex]\bf \left( \cfrac{15}{4}~~,~~2+450 \right)\implies \left( \stackrel{seconds}{3\frac{3}{4}}~~,~~\stackrel{feet}{452} \right)[/tex]
which of the fallowing is a factor? EXPLAIN:
Answers
Those two values are -7 and 4
-7 plus 4 = -3
-7 times 4 = -28
Since the numbers are -7 and 4, this means the given expression factors to (x-7)(x+4)
The two factors are x-7 and x+4
The factor x+4 isn't listed in the list of answer choices, so we can ignore it. The factor x-7 is listed as choice B, so that is the only answer.
A major stadium has 45,000 seats. If baseball fans have bought 5/8 of the seats for the next game, how many seats are available?
Answers
if 5/8 were bought then 3/8 are still available ( 5/8 +3/8 = 1)
45000 * 3/8 = 135000/8 = 16,875 seats are still available
Find the nth term of the follwing sequences 7,13,19,25
Answers
Hope this helps!
n=55
Estimated 65% of 152
Answers
Note that 65% is close to 66.666...%, or 2/3, and that 152 is close to 150.
2/3 of 150 is 100 (answer)
Jan has a 12 ounce milkshake four ounces in the milkshake are vanilla and the rest is chocolate what are two equivalent fraction of the milkshake is vanilla
Answers
Answer:
In this item, we are given that out of 12 ounces of ingredients comprising the milkshake, there are 4 ounces vanilla. Expressing this into fraction will give us an answer of 4/12. This fraction can be one of the answers. Since we are asked for two fractions, we can simplify 4/12 such that we get an equivalent fraction that is equal to 2/6. Hence, the answers to this question are 4/12 and 2/6...
hope it helps
mrs. ellis wants to tile a rectangular room that is 16 feet long and 12 feet wide with square tiles. each square floor is 2 feet. the tiles cost $0.84 per tile. what is the cost to tile the room not including labor?
Answers
192:2=96 tiles need Mrs Ellis
96*0,84 $=80,64 $ is the cost
Mrs. Ellis would need 48 tiles to cover the area of her room. The cost of a single tile is $0.84, so the total cost to tile the room not including labor would be $40.32.
Explanation:To determine the cost to tile the room, we first need to figure out how many tiles Mrs.Ellis needs. We know that each tile covers an area of 2ft * 2ft, which is 4 square feet. Now, we must find out the area of the room by multiplying the length by the width (16ft * 12ft), resulting in 192 square feet. To find out how many tiles are needed, we can divide the total area of the room by the area of one tile (192ft² / 4ft² = 48). Therefore, Mrs. Ellis needs 48 tiles to cover the entire room. Since each tile costs $0.84, the total cost would be 48 * $0.84 = $40.32. Thus, the cost to tile the room excluding labor charges is $40.32.
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Use the normal approximation to find the indicated probability. the sample size is n, the population proportion of successes is p, and x is the number of successes in the sample. n = 86, p = 0.68: p(54 x 61) 9)
Answers
P(54 ≤ X≤ 61)
0.6330 is the answer in this question which is the probability.
A box contains marbles of five different colors: red, green, blue, yellow, and purple. there is an equal number of each color. assign probabilities to each color in the sample space. (give your answers as fractions.)
Answers
P(green) = 1/5
P(blue) = 1/5
P(yellow) = 1/5
P(purple) = 1/5
The reason the fractions are all the same is that there are equal numbers of each color. For example, if there were 7 marbles of each color, there would be a total of 35 marbles.
P(red) = 7/35 = 1/5
Similar for the other colors.
To assign probabilities to each color in the sample space of marbles in a box, you need to determine the total number of marbles and the number of marbles of each color. Assuming there is an equal number of each color, the probability of drawing each color is 1/5.
Explanation:To assign probabilities to each color in the sample space, we need to determine the total number of marbles and the number of marbles of each color. Since there is an equal number of each color, let's assume there are n marbles of each color.
The total number of marbles is 5n. The probability of drawing a red marble is n/5n = 1/5. Similarly, the probability of drawing a green marble is n/5n = 1/5, the probability of drawing a blue marble is n/5n = 1/5, the probability of drawing a yellow marble is n/5n = 1/5, and the probability of drawing a purple marble is n/5n = 1/5.
A car travels down a highway at 45 m/s. An observer stands 200 m from the highway.
How fast is the distance from the observer to the car increasing when the car passes in front of the observer?
How fast is the distance increasing 40 s later?
Answers
so, the left-side is when the car is right in front of the observer, at that point, notice the y-distance, is pancaked, so is 0, but increasing, we know dy/dt is 45 m/s, and notice the "r" distance, is the same as the "x" distance, keeping in mind that whilst "r" is increasing or moving about, "x" is static, is a constant.
[tex]\bf \stackrel{\textit{pythagorean theorem}}{r^2=x^2+y^2}\implies 2r\cfrac{dr}{dt}=\stackrel{constant}{0}+2y\cfrac{dy}{dt} \\\\\\ 2r\cfrac{dr}{dt}=0+2(0)(45)\implies \cfrac{dr}{dt}=0[/tex]
now, 40 seconds later, since the car is going at 45 m/s, in 40 seconds it has covered 40 * 45 meters, or 1800, so y = 1800, x = 200, what is "r"?
[tex]\bf r^2=x^2+y^2\implies r=\sqrt{200^2+1800^2}\implies r=\sqrt{3280000} \\\\\\ r=\sqrt{200^2\cdot 82}\implies r=200\sqrt{82}\\\\ -------------------------------\\\\ 2r\cfrac{dr}{dt}=0+2y\cfrac{dy}{dt}\implies \cfrac{dr}{dt}=\cfrac{y\frac{dy}{dt}}{r}\quad \begin{cases} r=200\sqrt{82}\\ y=1800\\ \frac{dy}{dt}=45 \end{cases} \\\\\\ \cfrac{dr}{dt}=\cfrac{1800\cdot 45}{200\sqrt{82}}\implies \cfrac{dr}{dt}=\cfrac{405}{\sqrt{82}}\implies \cfrac{dr}{dt}=\cfrac{405\sqrt{82}}{82}[/tex]
The hypotenuse of right triangle ABC, line segment AC, measures 13 cm. The length of line segment BC is 5 cm. What is the approximate difference between m∠C and m∠A?
Answers
make sure your calculator is in Degree mode, if you need the angles in degrees, or Radian mode if you need them in radians.
and their difference is clearly just C - A.
Answer
Difference between m∠C and m∠A= 44.76
Step-by-step explanation:
The hypotenuse of right triangle ABC, line segment AC, measures 13 cm. The length of line segment BC is 5 cm.
Hypotenuse AC = 13 cm
So angle B is right angle = 90 degrees
AC is the hypotenuse
BC is the adjacent side for C
cos (c)= adjacent side / hypotenuse
C= cos^-1(BC/AC)
[tex]C= cos^{-1}(\frac{5}{13})= 67.38[/tex]
angle B is a right angle= 90 degree
Angle C= 67.38 degrees
Sum of angles in a triangle is 180°
A + B +C = 180
A + 90 + 67.38 = 180
A= 180 - 90 - 67.38=22.62
Difference between m∠C and m∠A= 67.38 - 22.62=44.76
Baruka has gallon of milk left in the 1/2 fridge. How many 5/64 gallon (10-ounce) servings of milk does she have left? Show your work
Answers
Baruka has [tex]\( \frac{32}{64} \)[/tex] gallons left. [tex]\( \frac{32}{5} \) servings of \( \frac{5}{64} \)[/tex] gallons; she has 6 servings.
To find out how many [tex]\( \frac{5}{64} \)[/tex] gallon servings of milk Baruka has left, we need to first convert the amount of milk she has in gallons to the same unit as [tex]\( \frac{5}{64} \)[/tex] gallons.
Since [tex]\( 1 \)[/tex] gallon is equivalent to [tex]\( \frac{64}{64} \)[/tex] gallons, and she has [tex]\( \frac{1}{2} \)[/tex] gallon left, she has [tex]\( \frac{1}{2} \times \frac{64}{64} = \frac{32}{64} \)[/tex] gallons left.
Now, we can find out how many [tex]\( \frac{5}{64} \)[/tex] gallon servings are in [tex]\( \frac{32}{64} \)[/tex] gallons:
[tex]\[ \frac{\frac{32}{64}}{\frac{5}{64}} = \frac{32}{5} \][/tex]
Now, we divide [tex]\( 32 \) by \( 5 \)[/tex] to find the number of servings:
[tex]\[ \frac{32}{5} = 6.4 \][/tex]
So, Baruka has [tex]\( 6.4 \)[/tex] servings of [tex]\( \frac{5}{64} \)[/tex] gallon servings of milk left. However, since she can't have a fraction of a serving, she has [tex]\( 6 \)[/tex] servings left.
Write an equation of the line that passes through (18, 2) and is parallel to the line 3y - x = -12
Answers
To find the equation of a line parallel to 3y - x = -12 that goes through the point (18, 2), first find the slope of the given line, which is 1/3. Then, use the point-slope form with the given point and the slope to write the equation of the desired line, which is y = (1/3)x - 4.
Explanation:To write an equation of the line that passes through the point (18, 2) and is parallel to the line 3y - x = -12, we first need to find the slope of the given line. For a line to be parallel, it must have the same slope as the line to which it is parallel. We start by putting the equation of the given line in slope-intercept form (y = mx + b).
First, isolate y:
3y = x - 12
y = (1/3)x - 4
The slope (m) of the given line is 1/3. Our parallel line should have the same slope, so we'll use this slope and the point (18, 2) in the point-slope form of a line equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line.
Now, plug in the values:
y - 2 = (1/3)(x - 18)
This is the point-slope form of the equation for our parallel line. To put it into slope-intercept form, we distribute and simplify:
y - 2 = (1/3)x - 6
y = (1/3)x - 4
Drag a statement or reason to each box to complete this proof. If 4x+5=17 , then x=3 .
Answers
The answer fam is........
Statement Reason
1) 4x + 5 = 17 Given
2) 4x + 5 - 5 = 17 - 5 Subtraction property of equality
3) 4x = 12 Simplifying
4) 4x/4 = 12/4 Division property of equality
5) x = 3 Simplifying
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Answer:
Here it is!
Step-by-step explanation:
Find the total amount due on a simple-interest loan if the principal is $3000 with a rate of 5% for 10 years.
Answers
Final answer:
The total amount due on the simple-interest loan is $4500.
Explanation:
To find the total amount due on a simple-interest loan, we can use the formula:
Total Amount = Principal + (Principal x Rate x Time)
Given that the Principal is $3000, the Rate is 5%, and the Time is 10 years, we can substitute these values into the formula to calculate the total amount:
Total Amount = $3000 + ($3000 x 0.05 x 10)Total Amount = $3000 + $1500Total Amount = $4500Therefore, the total amount due on the loan is $4500.
Does the function satisfy the hypotheses of the mean value theorem on the given interval? f(x) = x3 + x − 9, [0, 2]
Answers
which supports the mean value theorem, you want even better news
if the function is a polynomial it will always follow the mean value theorem
whats the answer for 5x+14=k
Answers
please give me brainliest.
Reorder the terms: 14 + 5x = k
Solving 14 + 5x = k
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-14' to each side of the equation.
14 + -14 + 5x = -14 + k
Combine like terms: 14 + -14 = 0
0 + 5x = -14 + k
5x = -14 + k
Divide each side by '5'. x = -2.8 + 0.2k
Simplifying x = -2.8 + 0.2k
Hope this helps :)
Brainliest would be great! but its ok if u don't
The three incoming currents at a node in an electrical circuit measure 0.7 amps, 0.68 amps, and 0.47 amps two of the three outgoing current measure 0.8 amps and 0.55 amps find the measure of the third outgoing current
Answers
The measure of the third outgoing current will be 0.5 amperes.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
The three incoming currents at a node in an electrical circuit measure 0.7 amps, 0.68 amps, and 0.47 amps two of the three outgoing currents measure 0.8 amps and 0.55 amps.
Then the measure of the third outgoing current will be
We know that the sum of the incoming current will be equal to the sum of the outgoing current at a junction.
Let the incoming current be I₁, I₂, and I₃. And the outgoing current is I₄, I₅, and I₆. Then we have
I₁ + I₂ + I₃ = I₄ + I₅ + I₆
0.7 + 0.68 + 0.47 = 0.8 + 0.55 + I₆
1.85 = 1.35 + I₆
I₆ = 0.5
Thus, the measure of the third outgoing current will be 0.5 amperes.
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What is an a priori proposition? an a posteriori proposition?
Answers
a posteriori means as things are after any event.
Final answer:
An a priori proposition is knowledge known through reason alone, such as mathematical truths, while an a posteriori proposition requires empirical experience, like knowledge of a physical location.
Explanation:
An a priori proposition is a type of knowledge or statement that is known to be true independently of experience. It relies on reason or logical deduction rather than empirical evidence. For example, mathematical truths, such as the statement "The square root of 9 is 3," are considered a priori because they can be known through reason alone. In contrast, an a posteriori proposition is one that requires experience or sensory input to be known. Empirical knowledge, like knowing the best route to a location, is typically a posteriori because it is based on observations from the world around us.
The foundational philosophical debate revolves around the nature of these propositions, with some philosophers questioning whether any knowledge is genuinely a priori or if all understanding comes from some form of experience. However, in many cases, a priori knowledge is associated with necessity, certainty, and independence from experience, while a posteriori knowledge is empirical and grounded in sense perception.
John is 3 years older than jim. jim is 4 years less than twice david's age. how old are the three boys if their ages add up to 35?
Answers
Only the Fahrenheit one plz
Answers
F = 1.8C + 32
The temperature C is given as -20
So, all you have to do is plug the given C temperature in the formula to get the corresponding F temperature as follows:
F = 1.8(-20) + 32 = -36 + 32 = -4 degrees Fahrenheit
please help im really dumb lol
Answers
Which expression is equivalent to 14a + 8?
14(a + 4)
7(7a + 1)
2(7a + 4)
14(a + 1)
Answers
The solution is Option C.
The value of the equation A = 14a + 8 can be simplified to A = 2 ( 7a + 4 )
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
A = 14a + 8 be equation (1)
Now , the equation (1) can be simplified as
Taking the common term as 2 in the equation , we get
A = 2 ( 7a + 4 )
The 2 is taken as common term , and the multiples are the values 7a and 4
So ,
The value of A = 2 ( 7a + 4 )
A = 2 ( 7a ) + 2 ( 4 )
The value of A = 14a + 8
Therefore , the value of A is 2 ( 7a + 4 )
Hence ,
The value of the equation A = 14a + 8 can be simplified to A = 2 ( 7a + 4 )
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Which of the following numbers is not part of the solution to x ≤ -2?
-2
-2.45
-8
-1.76
Answers
-2: -2 fulfills the statement, as it is equal to -2.
-2.45: Also fulfills the statement, since it is less than -2.
-8: Once again fulfills the statement, as it is less than -2.
-1.76: DOES NOT fulfill the statement, it is greater than -2.
The answer would be -1.76
Answer:
i think it is -1.76
Amy has 1/2 hour to do 3 chores. She plans to spend the same fraction of an hour on each chore. She wants to use the number line to help her determine what fraction of an hour she can spend on each chore. What is the correct number label for point A?
Answers
I would begin with 1/2 and divide that by 3:
1
--
2
====
3
--
1
Inverting the fraction in the denom. and multiplying, we get
1 1 1
-- * ---- = -----
2 3 6
So Amy will spend 1/6 th of an hour, or 10 minutes, on each chore.
Note that 3 times 1/6 comes out to 1/2 (hour), which is were we started.
Francis gets 6 paychecks in 12 weeks how many paychecks does she get in 52 weeks
Answers
Divide the time (12 weeks) by the number of checks (6 paycheck)
12/6 = 2
Francis gets one paycheck every two weeks.
Now to get the answer, simply divide the total (52 weeks) by 2.
52/2 = 26
The final answer is Francis gets 26 paychecks in 52 weeks.
Hope this helps!