The support beams of truss bridges are triangles. James made a model of a truss bridge with a scale of 1 inch = 4 feet. If the height of the tallest triangle on the model is 9 inches, what is the height of the tallest triangle on the actual bridge?
Answers
The height of the tallest triangle on the actual bridge is 12 feet.
If James made a model of a truss bridge with a scale of 1 inch = 4 feet, we can use this information to find the height of the tallest triangle on the actual bridge.
Let x be the height of the tallest triangle on the actual bridge. Since the scale of the model is 1 inch = 4 feet, the height of the tallest triangle on the model can be converted to feet by multiplying by 4. Therefore, the height of the tallest triangle on the model is:
9 inches * (1 foot / 12 inches) * 4 = 3 feet
We can use the similarity of triangles to set up a proportion to find x. The corresponding sides of similar triangles are proportional. In this case, the height of the triangle on the model corresponds to the height of the triangle on the actual bridge, and the scale factor from the model to the actual bridge is 1/4 (since 1 inch on the model represents 4 feet on the actual bridge). Therefore, we have:
height of triangle on model / height of triangle on actual bridge = scale factor
3 feet / x = 1/4
Multiplying both sides by x, we have:
3 feet = (1/4) x
Multiplying both sides by 4, we have:
12 feet = x
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Related Questions
If 2 pints = 1 quart and 1 quart = 1 pint then how many pints are 2 quarts?
Answers
Step-by-step explanation:
1 qt = 2 pts multiply both sides by two
2 qt = 4 pints
which quadratic equation has the roots 3 + i and 3 - i
Answers
The quadratic equation that has the roots 3 + i and 3 - i is x² - 6x + 10 = 0.
The general form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants.
The roots of the quadratic equation are the values of x that make the equation equal to zero.
Therefore, if a quadratic equation has the roots 3 + i and 3 - i, it can be written in the factored form as (x - (3 + i))(x - (3 - i)) = 0. Expanding this product yields x² - (3 + i + 3 - i)x + (3 + i)(3 - i) = 0.
Simplifying this expression further results in the quadratic equation x² - 6x + 10 = 0.
The quadratic equation that has the roots 3 + i and 3 - i is x² - 6x + 10 = 0.
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Picture included!!! Please help! Suppose a = 10 and b = 24. Give the value of each of the following. Give answers as integers or rounded to 2 decimal places as appropriate.
Answers
Answer:
A = 22.62°
B = 67.38°
c = 26
Step-by-step explanation:
[tex]a^2+b^2=c^2\\10^2+24^2=c^2\\100+576=c^2\\676=c^2\\26=c[/tex]
[tex]\sin A=\frac{\text{Opposite}}{\text{Hypotenuse}}=\frac{10}{26}\\\\A=\sin^{-1}(\frac{10}{26})\\\\A\approx22.62^\circ[/tex]<-- You can also use other trig ratios
[tex]B=180^\circ-(90^\circ+22.62^\circ)=180^\circ-112.62^\circ=67.38^\circ[/tex]
There's no specific order in how to solve for A and B, so there may be more than one way to approach these solutions.
long division method of 616265
Answers
2.63 is the value or quotient of 616/265 using long division.
We have to find the value of 616/265
In the given division the numerator is a dividend and the number in the denominator is a divisor.
616 is the dividend and 265 is the divisor.
When we perform long division the quotient will be 2.63 which is the require value.
2.63
____________
265 | 616
-530
______
860
-795
______
650
-530
______
120
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2x + y ≤ 2
a. change the inequality into slope-intercept form, and then change it into an equation.
b. create a table. Use the x-values indicated
c. Graph the points and draw a line.
d. Shade the solution area.
e. Check your solution. Use (0,0) as your test point and see if it satisfies the conditions of the original inequality.
Answers
2x + y ≤ 2
y ≤ -2x + 2
To change it into an equation, we remove the inequality symbol and obtain:
y = -2x + 2
b. Using the x-values indicated, we can create a table of corresponding y-values:
|x | y |
|---|---|
|0 | 2 |
|1 | 0 |
|2 |-2 |
c. To graph the points and draw a line, we plot the points (0, 2), (1, 0), and (2, -2) on the coordinate plane and connect them with a straight line.
d. To shade the solution area, we need to determine which side of the line satisfies the inequality. Since the inequality is less than or equal to, we shade the area below the line.
e. To check the solution, we plug in the test point (0, 0) into the original inequality:
2x + y ≤ 2
2(0) + 0 ≤ 2
0 ≤ 2
The inequality holds, so the point (0, 0) is in the shaded area and satisfies the conditions of the original inequality. Therefore, the solution is valid.
Complete the proof that HJ LGI.
4
I
5
Statement
K
1
ZHKI ZGKH
2
m2GKH + mZHKI = 180°
3 m2GKH+mZGKH= 180°
mZGKH = 90°
HJ L GI
G
H
Reason
Given
Angles forming a linear pair sum to 180°
Definition of congruence
(
Answers
The complete sentence is shown below:
Reason: Given
Reason: Angles forming a linear pair sum to 180° (Given)
Reason: Substitution from Statement 1.
To complete the proof that HJ GI, we can use the given statements and reasons:
Statement 1: <HKI = <GKH
Reason: Given
Statement 2: m<GKH + m<HKI = 180°
Reason: Angles forming a linear pair sum to 180° (Given)
Statement 3: m,GKH + m<GKH = 180°
Reason: Substitution from Statement 1
Statement 4: m<GKH = 90°
Reason: From Statement 2 and Statement 3, we can subtract m<GKH from both sides, which results in m<GKH = 180° - m<GKH.
Since the angles forming a linear pair sum to 180°, m<GKH + m<GKH = 180° implies that m<GKH = 90°.
Therefore, based on the given statements and reasons, we can conclude that HJ and GI are congruent (m<GKH = 90°)
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answers
The area of the kite is 38 mm squared.
How to find the area of a kite?A kite is a quadrilateral with two pairs of adjacent sides equal. The diagonals of a kite are perpendicular. The vertex angle are bisected by the diagonals.
It has two pairs of consecutive equal sides and perpendicular diagonals.
Therefore,
area of a kite = ab / 2
where
a and b are the diagonalsTherefore,
a = 9.5 mm
b = 4 mm
Therefore,
area of a kite = 9.5 × 4 / 2
area of a kite = 38 / 2
area of a kite = 19 mm²
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Answer:
The area of the kite would be 19 mm².
Step-by-step explanation:
A kite is a quadrilateral with two pairs of equal-length adjacent sides. The diagonals of a kite are perpendicular to each other and intersect at a right angle, dividing the kite into four right triangles. The area of a kite can be calculated by finding the product of the lengths of its diagonals and dividing it by 2.
If we assume that the height and width you provided are the lengths of the diagonals, we can calculate the area using the following formula:
Area = (height * width) / 2
Substituting the given values:
Area = (9.5 mm * 4 mm) / 2
= 38 mm² / 2
= 19 mm²
Therefore, if the height and width represent the lengths of the diagonals, the area of the kite would be 19 square millimeters.
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What is the 10th term of the geometric sequence where a1 = 384 and a7 = 6?
0.75
3
6
1.5
Answers
Answer:
(a) 0.75
Step-by-step explanation:
You want the 10th term of the geometric sequence with a1 = 384 and a7 = 6.
N-th termThe equation for the n-th term can be written ...
an = a1·b^(n-1)
Using a1 = 384, we can find b from ...
a7 = 6 = 384·b^(7-1)
(6/384)^(1/6) = b
10th termThen the 10th term is ...
a10 = 384·(6/384)^((10-1)/6) = 0.75
The 10th term of the sequence is 0.75.
<95141404393>
For what value of x is the rational expression below undefined?
x-3
3+x
A. 3
OB. -1
O C. 0
OD. -3
Answers
The value of x that makes the rational expression undefined is x = -3.
The rational expression is undefined when the denominator is equal to zero, because division by zero is undefined.
In the given rational expression (x - 3) / (3 + x), we need to find the value of x that makes the denominator (3 + x) equal to zero.
To find this value, we set the denominator equal to zero and solve for x:
3 + x = 0
Subtracting 3 from both sides:
x = -3
Therefore, the value of x that makes the rational expression undefined is x = -3.
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Help me a123 sq ft
B61 sq ft
C49sq ft
D110 sq ft
Answers
The area of the required shaded portion is 123 ft²
Given is figure having some shaded portion we need to find the area of the same,
So, the shaded portion is two right isosceles triangles with equal side measuring 14 ft and 7 ft,
So, to find the same, we will calculate the area of the triangles and add them,
Area of a triangle = 1/2 x base x height
Area of the shaded portion = 1/2 x 7 x 7 + 1/2 x 14 x 14
= 122.5 ft²
≈ 123 ft²
Hence the area of the required shaded portion is 123 ft²
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answers
Next, we add the two bases to get 21: 6+15=21 (h=2 x 136.5)
Then, divide the total of the two bases (21) from the area to get 6.5: 136.5/21-6.5
Finally we multiply 2 by 6.5: 2 x 6.5= 13
The height if this trapezoid is 13.
Answer:
13cm
Step-by-step explanation:
The area of a trapezoid is given by the formula:
Area = ½*(b1+b2)*h
where:
b1 and b2 are the lengths of the bases of the trapezoid h is the height of the trapezoidIn this problem, we are given that b1 = 6 cm, b2 = 15 cm, and Area = 136.5 square centimeters.
Plugging these values into the formula, we get:
136.5 = ½*(6 + 15)*h
Solving for h, we get:
136.5=10.5h
h = 136.5/10.5=13centimeters
Therefore, the height of the trapezoid is 13 centimeters.
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answers
The angle ABC in the circle is 70 degrees.
How to find the angle in a circle?The intercepted arc is the arc that is inside the inscribed angle and whose
endpoints are on the angle. The arc angle is half the the inscribed angle.
The intercepted arc that is formed is equal to the inscribed angle,
multiplied by two (intercepted arc measure = inscribed angle × 2).
Therefore, let's find the arc angle ABC as follows:
∠ ABC = 1 /2 (360 - 120 - 100)
∠ ABC = 1 /2 (360 - 220)
∠ ABC = 1 /2 (140)
Therefore,
∠ ABC = 70 degrees
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Find x to the nearest hundredth.
16
X
40°
OA. x = 24.89
OB. x = 13.43
O C. x 10.28
OD. x = 12.26
Answers
Sin 40° = x/16
0.6428 = x/16
x = 0.643 × 16
x = 10.2848
x = 10.28
So, the value of x is 10.28 (C)
That's it :)
Find the missing dimension of the cylinder. Round your answer to the nearest whole number.
Volume = $\ 10,000\pi\ $ in.3
A cylindrical piece of a log is shown. The diameter of its base is 32 inches and height is h.
$h\ \approx$
in.
Answers
The nearest Whole number, the missing dimension (height) of the cylinder is approximately 39 inches.
The missing dimension of the cylinder, we can use the formula for the volume of a cylinder:
Volume = π * r^2 * h
Given that the volume is 10,000π in³ and the diameter of the base is 32 inches, we can determine the radius (r) of the cylinder.
The diameter is twice the radius, so the radius is half of the diameter:
r = 32 inches / 2 = 16 inches
Substituting the known values into the volume formula, we have:
10,000π in³ = π * (16 in)^2 * h
Cancelling out the common factor of π, we get:
10,000 = 16^2 * h
Simplifying further:
10,000 = 256 * h
To isolate h, we divide both sides of the equation by 256:
h = 10,000 / 256
Calculating the value of h:
h ≈ 39.06
Rounded to the nearest whole number, the missing dimension (height) of the cylinder is approximately 39 inches.
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Please help ASAP 7p-13p+4-5p
Answers
Hello!
[tex]7p-13p+4-5p\\\\= 7p-13p-5p+4\\\\= -6p-5p+4\\\\\Large\boxed{= -11p + 4}[/tex]
solve each equation 1/3a= -15
Answers
The solution to the equation 1/3a = -15 is a = -45
How to determine the solution to the equationfrom the question, we have the following parameters that can be used in our computation:
1/3a = -15
Multiply 3 to both sides of the equation
so, we have the following representation
3 * 1/3a = -15 * 3
When the products are evalated, we have
a = -45
Hence, the solution to the equation is a = -45
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Problem whenejewwssss
Answers
[tex] \begin{aligned}3 ^{3k} &= \frac{1}{81} \\3^{3k} &= \frac{1}{3^{4} } \\ 3^{ \blue{3k}} &= 3^{ - \blue{4}} \\ 3k&= - 4 \\ k&= \frac{ - 4}{3} \\ k&= \bold{ - \frac{4}{3} } \end{aligned}[/tex]
[tex]\rm{The\:value\:of\:\mathit{k}\:is\:\bold{ - \frac{4}{3}}} \\ \\ \small{ \blue{ \mathfrak{That's\:it\: :)}}}[/tex]
The aquarium has 10 more red fish than blue fish. 60 percent of the fish are red. How many blue fish are in the aquarium? Show your work. (10 points)
Answers
Answer:
There are 20 blue fish in the aquarium.
Step-by-step explanation:
If 60% of the fish are red than 40% are blue. That means that 20% fish is 10 fish. 20% = 10 fish. 40% = 20 fish.
Beth and Kelly spent the same total amount of money for dog sitting while on vacation. Beth took her dog, Pockets, to Rover Sleepover and was charged $24.50 per day and a fee of $90.50 for food and cleaning. Kelly took her dog, Monty, to Pet Palace and was charged $32 per day and a $45.50 cleaning fee. How many days were Beth and Kelly on vacation?
Answers
Beth and Kelly were on vacation for 6 days.
Let's assume that Beth and Kelly were on vacation for "x" days.
For Beth:
The cost per day for dog sitting at Rover Sleepover is $24.50.
Beth also paid a fee of $90.50 for food and cleaning.
So the total cost for Beth's dog sitting can be expressed as:
Total cost for Beth = (Cost per day × Number of days) + Cleaning fee
Total cost for Beth = ($24.50 × x) + $90.50
For Kelly:
The cost per day for dog sitting at Pet Palace is $32.
Kelly also paid a fee of $45.50 for cleaning.
So the total cost for Kelly's dog sitting can be expressed as:
Total cost for Kelly = (Cost per day × Number of days) + Cleaning fee
Total cost for Kelly = ($32 × x) + $45.50
Since both Beth and Kelly spent the same total amount of money, we can set up an equation:
($24.50 × x) + $90.50 = ($32 × x) + $45.50
Simplifying the equation, we get:
$24.50x + $90.50 = $32x + $45.50
Moving the variables to one side and constants to the other side:
$32x - $24.50x = $45.50 - $90.50
Combining like terms, we have:
$7.50x = $45
Dividing both sides of the equation by $7.50:
x = $45 / $7.50
x = 6
Therefore, Beth and Kelly were on vacation for 6 days.
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In the year 2000, population
Answers
In the year 2000, it was estimate that the population of the world was 6, 082, 966, 429 people.
What was the world population in 2000 ?Based on data provided by the table give, the global population in the year 2000 was estimated to be around 6, 082, 966, 429 individuals. This remarkable figure, serving as a testament to the expansive tapestry of humanity, reflects the vastness and intricacy of our interconnected world during that period.
Within the context of demographic analysis, the United Nations diligently compiled and analyzed extensive data to derive this population estimate for statistical reasons.
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The full question is:
In the year 2000 the world population was
find the center of the circle that you can circumscribe about triangle ABC. A(2,8) B(0,8) C(2,2)
Answers
The center of the circumscribed circle is (1, 5).
How do we calculate?We calculate the midpoint and slope of the line segment AB:
Midpoint of AB = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
Midpoint of AB = ((2 + 0) / 2, (8 + 8) / 2)
Midpoint of AB = (1, 8)
Slope of AB = (y₂ - y₁) / (x₂ - x₁)
= (8 - 8) / (0 - 2)
Slope= 0
We can notice that the equation of the perpendicular bisector of AB is x = 1.
We also find midpoint and slope of the line segment BC
Midpoint of BC = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
= ((0 + 2) / 2, (8 + 2) / 2)
= (1, 5)
Slope of BC = (y₂ - y₁) / (x₂ - x₁)
= (2 - 8) / (2 - 0)
= -3
y - 5 = -3(x - 1)
y - 5 = -3x + 3
3x + y = 8
we have the equations of two perpendicular bisectors which are
x = 1 and 3x + y = 8.
We Substitute x = 1 into 3x + y = 8:
3(1) + y = 8
3 + y = 8
y = 5
In conclusion, center of the circumscribed circle is (1, 5).
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The consistency of the diameters of wheel bearings is vital to the operation of the wheel. The specifications require that the variance of these diameters be no more than 0.0015 centimeter squared. The diameter is continually monitored by the quality-control team. Twenty subsamples of size 10 are obtained every day. One of these subsamples produced bearings that had a variance of 0.00317 centimeter squared. Conduct a hypothesis test to determine if the quality control team should advise management to stop production and search for causes of the inconsistency of the bearing diameters. Use a significance level of 0.05.
Answers
Find the surface area
of the figure below:
19 cm
30 cm.
Answers
The surface area of the figure is approximately 997.5π cm².
We have,
The figure has two shapes:
Cone and a semicircle
Now,
The surface area of a cone:
= πr (r + l)
where r is the radius of the base and l is the slant height.
Given that
r = 15 cm and l = 19 cm, we can substitute these values into the formula:
= π(15)(15 + 19) = 885π cm² (rounded to the nearest whole number)
The surface area of a semicircle:
= (πr²) / 2
Given that r = 15 cm, we can substitute this value into the formula:
= (π(15)²) / 2
= 112.5π cm² (rounded to one decimal place)
The surface area of the figure:
To find the total surface area of the figure, we add the surface area of the cone and the surface area of the semicircle:
Now,
Total surface area
= 885π + 112.5π
= 997.5π cm² (rounded to one decimal place)
Therefore,
The surface area of the figure is approximately 997.5π cm².
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30 POINTS!! PLEASE
A surveyor wants to determine the width of a river. She surveys the area and finds the following measures below.
She uses a pair of similar triangles, to help her find the answer.
Answers
Answer:
D = 90 FT
Step-by-step explanation:
40 / d = 20 / 45
cross multiply
45 × 40 = 20d
1800 = 20d
divide both sides by 20
1800 / 20 = 20d / 20
d = 90 ft
Factor the following and then fill in the blanks. 2x²7x-15 = (2x + )(x- Blank 1: Blank 2:
Answers
Answer:
(2x + 3)(x - 5)
Step-by-step explanation:
2x² - 7x - 15
consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 2 × - 15 = - 30 and sum = - 7
the factors are - 10 and + 3
use these factors to split the x- term
2x² - 10x + 3x - 15 ( factor the first/second and third/fourth terms )
= 2x(x - 5) + 3(x - 5) ← factor out (x - 5) from each term
= (2x + 3)(x - 5) ← in factored form
Blank 1 is 3
Blank 2 is 5
If (2x-7), (x-1), 3x, x, (x+2), 30 and 10
1. Find the value of x
2. Find the value of the largest angle
PLEASE HELP ME ASAP
Answers
The value of x in arithmetic progression is 5/3 and the largest angle is 30.
The given sequence is: (2x-7), (x-1), 3x, x, (x+2), 30, 10.
In an arithmetic progression, the common difference (d) between consecutive terms remains constant.
The common difference between the terms = (x - 1) - (2x - 7) = x - 1 - 2x + 7 = 6 - x
6 - x = 3x - (x - 1)
6 - x = 3x - x + 1
6 - x = 2x + 1
-x - 2x = 1 - 6
-3x = -5
x = -5 / -3
x = 5/3
Therefore, the value of x is 5/3.
2x-7 = 2 ×5/3 -7 = -3.66
x-1 = 5/3-7 = -5.33
3x = 3 × 5/3 = 5
x + 2 = 5/3+2 =3.66
Thus, the largest angle is 30.
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Your question is incomplete, most probably the full answer is:
If (2x-7), (x-1), 3x, x, (x+2), 30 and 10 are in AP, then
1. Find the value of x
2. Find the value of the largest angle
#8: Expand the logarithm shown below. *
log981xy
Answers
In order to expand the properties of logarithms log981x:
log981x = log98 + log1x
One must know that loga + logb = log(ab), and loga + logb = log(ab) may also be represented as loga(b) or logab.
Using this property, we can simplify the expression further:
log981x = log98 + log1x = log9 + log8 + log1 + logx
We know that log9 = 2 and log1 = 0, so we can simplify even further:
log981x = log9 + log8 + log1 + logx = 2 + log8 + 0 + logx = 2 + log8x.
Therefore, the expanded value would be log981x to 2 + log8x.
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answers
area of equilateral triangle =
[tex]( \sqrt{3 } \div 4) \times a {}^{2} [/tex]
(C) area = 84.9 in²
In the given circle the m∠J
is 88°, mArc DF is 62° and mArc BD is 136° what is the m∠
C ?
Answers
The measure of angle C is 13°.
To find the measure of angle C in the given circle, we need to use the properties of angles subtended by arcs in a circle.
Given information:
m∠J = 88° (angle J)
mArc DF = 62° (arc DF)
mArc BD = 136° (arc BD)
We can start by using the fact that the measure of an angle formed by a chord and an arc is equal to half the measure of the intercepted arc.
Since mArc DF = 62°, the measure of angle DJF (angle formed by chord DF and arc DF) is 62°/2 = 31°.
Next, we can use the fact that angles subtended by the same arc are equal.
Since mArc BD = 136°, angle BJD (angle formed by chord BD and arc BD) is also 136°.
Now, let's find angle BCD (angle formed by chord BD and chord CD). The sum of angles in a triangle is 180°, so angle BCD = 180° - angle DJF - angle BJD.
Angle BCD = 180° - 31° - 136°
Angle BCD = 180° - 167°
Angle BCD = 13°
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Tariq has $640 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
He buys a new bicycle for $291.24.
He buys 4 bicycle reflectors for $19.56 each and a pair of bike gloves for $16.52.
He plans to spend some or all of the money he has left to buy new biking outfits for $50.80 each.
Write and solve an inequality which can be used to determine
x, the number of outfits Tariq can purchase while staying within his budget.
Answers
Let's solve the inequality to determine the number of outfits Tariq can purchase while staying within his budget.
Given:
Amount Tariq has to spend: $640
Cost of a new bicycle: $291.24
Cost of 4 bicycle reflectors: $19.56 each
Cost of bike gloves: $16.52
Cost of each biking outfit: $50.80
Let's assume the number of outfits Tariq can purchase is represented by x.
The total cost of the items he has already purchased is:
Cost of bicycle = $291.24
Cost of 4 bicycle reflectors = $19.56 * 4 = $78.24
Cost of bike gloves = $16.52
The remaining amount Tariq has to spend can be calculated as:
Remaining amount = Total amount - (Cost of bicycle + Cost of reflectors + Cost of gloves)
Remaining amount = $640 - ($291.24 + $78.24 + $16.52)
Now, we need to determine the maximum number of outfits Tariq can purchase with the remaining amount. Each outfit costs $50.80.
Inequality: x * $50.80 ≤ Remaining amount
Substituting the values:
x * $50.80 ≤ $640 - ($291.24 + $78.24 + $16.52)
Simplifying further:
x * $50.80 ≤ $640 - $385
x * $50.80 ≤ $255
To solve for x, we divide both sides of the inequality by $50.80:
x ≤ $255 / $50.80
x ≤ 5
Therefore, the maximum number of outfits Tariq can purchase while staying within his budget is 5.