Using the concept of similar triangles, the height of the second building is calculated to be 150 feet, since its 25-foot shadow corresponds proportionally to the 60-foot building's 10-foot shadow.
Explanation:To find the height of the second building given that a 60-foot-tall building casts a 10-foot shadow, and another building casts a 25-foot shadow, we can use the concept of similar triangles. The idea behind similar triangles is that corresponding sides of similar triangles are proportional. Therefore, if one building is 60 feet tall and casts a 10-foot shadow, the ratios of the height to shadow length will be the same for the second building.
To set up the proportion, we have:
We can write the proportion as:
h1/s1 = h2/s2
Substituting the known values into the proportion gives us:
60/10 = x/25
Now we solve for x:
x = (60/10) * 25
x = 6 * 25
x = 150
Therefore, the height of the second building is 150 feet.
What is the most precise name for quadrilateral ABCD with vertices A(-4, -4), B(-4, -2), C(-1, -2), and D(-1, -4)?
A) quadrilateral
B) parallelogram
C) rhombus
D) rectangle
Answer:
Option D.
Step-by-step explanation:
The given vertices of quadrilateral ABCD are A(-4, -4), B(-4, -2), C(-1, -2), and D(-1, -4).
Distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using distance formula, we get
[tex]AB=\sqrt{\left(-4-\left(-4\right)\right)^2+\left(-2-\left(-4\right)\right)^2}=\sqrt{0^2+(2)^2}=\sqrt{4}=2[/tex]
Similarly,
[tex]BC=\sqrt{\left(-1-\left(-4\right)\right)^2+\left(-2-\left(-2\right)\right)^2}=3[/tex]
[tex]CD=\sqrt{\left(-1-\left(-1\right)\right)^2+\left(-4-\left(-2\right)\right)^2}=2[/tex]
[tex]AD=\sqrt{\left(-1-\left(-4\right)\right)^2+\left(-4-\left(-4\right)\right)^2}=3[/tex]
[tex]AB = CD[/tex]
[tex]BC = AD[/tex]
Measure of diagonals:
[tex]AC=\sqrt{\left(-1-\left(-4\right)\right)^2+\left(-2-\left(-4\right)\right)^2}=\sqrt{13}[/tex]
[tex]BD=\sqrt{\left(-1-\left(-4\right)\right)^2+\left(-4-\left(-2\right)\right)^2}=\sqrt{13}[/tex]
[tex]AC = BD[/tex]
Since measure of opposite sides are equal and measure of diagonals are equal, therefore the given quadrilateral ABCD is a rectangle.
Hence, the correct option is D.
Ria is an Indian student who was admitted to a US university. Her annual tuition is $42,000. She has to pay her tuition fees in US dollars. She needs to calculate how many Indian rupees she will need to buy one dollar. The dollar to rupee exchange rate is 63.76 and rupee to dollar exchange rate is 0.015. How many Indian rupees will Ria need to buy one dollar?
50.00 rupees
56.00 rupees
63.76 rupees
76.63 rupees
Answer:
C:63.76
Hope this helps
Final answer:
Ria will need 63.76 Indian rupees to buy one US dollar according to the given exchange rate.
Explanation:
The student is asking how many Indian rupees are needed to buy one US dollar based on the given exchange rates. According to the given information, the exchange rate from dollars to rupees is 63.76. This means that one US dollar is equivalent to 63.76 Indian rupees. The other exchange rate provided, which is the value of a rupee in terms of dollars (0.015), is not directly relevant to the question being asked. Therefore, Ria will need 63.76 Indian rupees to buy one US dollar.
Which pair of angles must be congruent?
A. Supplementary angles
B. Complementary angles
C. Adjacent angles
D. Vertical angles
What is the volume of a cube where the length of each side is 6 centimeters?
Answer:
The answer is A
Step-by-step explanation:
Write the tangent ratios for P and Q. The figure is not drawn to scale.
Answer:
tan P = 24/7 and tan Q = 7/24
Step-by-step explanation:
tangent of any angle in a right angle triangle is always represented by
tan x = opposite side/ adjacent side = height / base
from the question we have to write tangent of P and Q.
tan P = QR/PR = 24/7
tan Q = PR / RQ = 7/24
So the answers are tangent ratios for P and Q are 24/7 and 7/24.
The formula for the area of a square is A = s2, where s is the length of one side. Rearrange the formula to solve for s and select the correct option below.
s = square root of A
s = A2
s = 2A
s = A over 2
The sum of 8 and 7, doubled
Randolph has 8 ties, 6 pairs of pants, and 4 dress shirts. how many days can randolph go without wearing the same combination of these three items?
what is the squar root of 21
Three identical coins, labeled A, B, and C in the figure, lie on three corners of a square 10.0 cm on a side. Determine the x coordinate of each coin, xA, xB, and xC.
A system of equations has no solution. If y = 8x + 7 is one of the equations, which could be the other equation?
y = 8x + 7
y = 8x – 7
y = –8x + 7
y = –8x – 7
Answer:
Option B. y = 8x - 7
Step-by-step explanation:
Parallel lines don't have the common points or the points of intersection.
In a system of equations has no solutions out of which one equation is y = 8x + 7
So a line parallel to this line will have no solutions.
For parallel lines slope will be same as 8, so the equation will be
y = 8x - 7
Option B. y = 8x - 7 will be the answer.
jamal is 167 cm tall which expression expression finds jamals height in dekametres
A.167 times 100
B.167 times 1000
C.167 divided by 100
D.167 divided by 1000
Jamal's height can be converted to dekametres by dividing his height in centimeters (167 cm) by 1000, because there are 1000 centimeters in a dekametre.
To convert Jamal's height from centimeters to dekametres, we should recall that 1 dekametre equals 10 meters or 1000 centimeters. Since Jamal is 167 cm tall, we need to divide his height in centimeters by the number of centimeters in a dekametre to get his height in dekametres.
Therefore, the correct expression to find Jamal's height in dekametres is:
167 divided by 1000
This is option D: 167 / 1000.
rewrite 6 3/4 as an decimal number
Solve for y.
7y - 6y - 10 = 13
y = -23
y = -3
y = 3
y = 23
y = 1/2 x + 2
x = 8
y = __
When Katie was born her mother invested $5000 in an account for her college savings. The interest rate is 3.5% compounded annually. To represent this, we can use the formula V = 5000(1 + r)t where r represents the interest rate and t represents the time in years. How much will Katie have in her account when she turns 18? A) $5,175 B) $7,127 C) $9,287 D) $12,472
After performing the calculations based on the provided formula and values, Katie will have approximately $9127 in her college savings account when she turns 18. The closest option given in the question would be C) $9287.
Explanation:To solve this problem, you would input the given values into the formula V = P(1 + r)t where P is the principal amount (in this case $5000), r is the annual interest rate (3.5% or 0.035 when expressed as a decimal), and t is the number of years (18).
When you substitute these values in, the equation becomes V = 5000(1 + 0.035)18.
Using a calculator, you'll find that V equates to approximately $9127. Therefore, Katie will have approximately $9127 in her account when she turns 18. The correct answer among the given options is thus closest to option C) $9287.
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Joshua used two wood beams, PC and QA, to support the roof of a model house. The beams intersect each other to form two similar triangles QRP and ARC as shown in the figure below. The length of segment PR is 4.8 inches and the length of segment CR is 7.2 inches. The distance between A and C is 9.6 inches.
What is the distance between the endpoints of the beams P and Q?
7.2 inches
3.6 inches
6.4 inches
12.0 inches
Answer:
The answer is C, 6.4 inches
Step-by-step explanation:
what happens to the graph of a line when the slope is negative? Check all that apply. may choose more then 1.
A. As the absolute value of the negative slope gets bigger, the graph of the line gets steeper.
B. As the absolute value of the negative slope gets smaller, the graph of the line gets steeper.
C. The line goes down from left to right.
D. The line shifts down.
E. The line goes up from left to right
An obtuse triangle with area 12 has two sides of lengths 4 and 10. Find the length of the third side. (There are two answers.) (Use law of cosines) ...?
Final answer:
Using the Law of Cosines, the length of the third side of the obtuse triangle is x = sqrt(52) or x = 2sqrt(13).
Explanation:
To find the length of the third side of an obtuse triangle with sides of lengths 4 and 10 and an area of 12, you can use the Law of Cosines. The Law of Cosines states that in a triangle with sides a, b, and c, and angle C opposite side c, the equation c^2 = a^2 + b^2 - 2ab * cos(C) can be used to find the length of side c.
In this case, let's assume that the third side of the triangle has length x. We can set up the equation as x^2 = 4^2 + 10^2 - 2*4*10 * cos(C), where C is the angle opposite side x.
Simplifying the equation, we get x^2 = 116 - 80*cos(C).
Since we know that the area of the triangle is 12, we can use the formula Area = 0.5 * a * b * sin(C) to find the value of sin(C). Plugging in the given values, we get 12 = 0.5 * 4 * 10 * sin(C). Solving for sin(C), we find sin(C) = 0.6.
Using this value of sin(C), we can then find the value of cos(C) by using the trigonometric identity sin^2(C) + cos^2(C) = 1. Substituting sin(C) = 0.6, we get 0.6^2 + cos^2(C) = 1. Solving for cos(C), we find cos(C) = 0.8.
Now, we can substitute the value of cos(C) into the equation x^2 = 116 - 80*cos(C), giving us x^2 = 116 - 80*0.8. Simplifying further, we get x^2 = 52, which means that the length of the third side is either x = sqrt(52) or x = -sqrt(52).
However, since we are dealing with the length of a side, it cannot be negative. Therefore, the length of the third side is x = sqrt(52), which simplifies to x = 2sqrt(13).
What is the number of real solutions?
–11x2 = x + 11
cannot be determined
one solution
two solutions
no real solutions
Answer:
no real solutions.
Step-by-step explanation:
-11[tex]x^{2}[/tex] = x+11. Put into standard form of a quadratic equation.
11[tex]x^{2}[/tex] + x + 11 = 0 Find a, b, and c.
a = 11, b =1, c = 11 Write and substitute into the quadratic equation[tex]\frac{-b+/-\sqrt{b^{2}-4ac}}{2a}[/tex] .
[tex]\frac{-1 +/- \sqrt{1^{2} - 4(11)(11)} }{2(11)}[/tex] Simplify.
[tex]\frac{-1 +/- \sqrt{1-484} }{2(11)}[/tex]=
[tex]\frac{-1 +/-\sqrt{-483} }{22}[/tex] BUT because the [tex]b^{2} -4ac[/tex] part under the √ is less than 0, THERE IS NO SOLUTION!
Which description represents the expression 3x+4 ? A.4 less than 3 times a number B.4 divided by the product of 3 and a number C. 4 added to 3 plus a number D.the sum of 3 times a number and 4
WHAT IS THE BENEFIT OF A "SPACE CUSHION" AROUND YOUR VEHICLE?
A 'space cushion' increases safety by providing more time to react and decreasing the force of impact in a collision, akin to how airbags and crumple zones function in a vehicle.
Explanation:The concept of a "space cushion" around your vehicle pertains to having a safe distance between your vehicle and others on the road. This increases the time you have to react to unexpected events and minimizes the force of impact during a collision, related to the physics principle of impulse. A larger space cushion effectively reduces the net force on your vehicle and its occupants by allowing more time for the vehicle to come to a stop or slow down. Features like airbags and crumple zones in cars serve a similar purpose by increasing the time over which a collision occurs, thereby reducing the impact force. This is crucial because the severity of injuries incurred during a vehicle accident is often directly related to the force exerted on the occupants.
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Use the polynomial identity to determine which values of x and y generate the values of the sides of the following right triangle.
x = 8, y = 3
x = 3, y = 8
x = 6, y = 4
x = 4, y = 6
if y=15 when x=3/4, find x when y=25
The value of the x is 5/4 when y=25 if y=15 when x=3/4 the answer would be 5/4
What is a proportional relationship?It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.
It is given that:
x and y are in a proportional relationship if y=15 when x=3/4,
y ∝ x
y = kx
15 = k(3/4)
k = 20
y = 20x
Plug y = 25
25 = 20x
x = 25/20
x = 5/4
Thus, the value of the x is 5/4 when y=25 if y=15 when x=3/4 the answer would be 5/4
The complete question is:
x and y are in a proportional relationship if y=15 when x=3/4, find x when y=25.
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n is a positive integer.
Explain why n(n-1) must be an even number.
In a linear equation, the independent variable increases at a constant rate while the dependent variable decreases at a constant rate. The slope of this line is
A. zero
B. negative
C. positive
D. undefined
...?
Answer: B. negative
Step-by-step explanation:
Given: In a linear equation, the independent variable increases at a constant rate while the dependent variable decreases at a constant rate.
We know that the slope of a line is given by :-
[tex]k=\dfrac{\text{change in y}}{\text{change in x}}[/tex]
According to the given information, if independent variable increases at a constant rate while the dependent variable decreases at a constant rate, then the slope of line will be :-
[tex]k=\dfrac{\text{Negative}}{\text{Positive}}=\text{Negative}[/tex]
Hence, the slope of line = Negative.
on a grid, what is the distance between two points located at (2,1) and (14,6)
A.) 5
B.) 13
C.) 12
D.) 17.46
Find the perpendicular slope of the line 3X-9Y=15
You buy a bicycle helmet for $22.26, which includes 6% sales tax. The helmet is discounted 30% off the selling price. What is the original price?
The exponential expression 4^-2 is equal to what fraction value