Abdul is making a map of his neighborhood. He knows the following information:
His home, the middle school, and high school are all on the same street.
His home, the elementary school, and his friend's house are on the same street.
The distance between his home and the middle school is 3 miles.
The distance between his high school and the middle school is 6 miles.
The street between the middle school and elementary school is parallel to the street between his friend's home and the high school.
What theorem can Abdul use to determine the remaining distances for his map?
Pythagorean Theorem
Midsegment Theorem
Triangle Proportionality Theorem
Side-Angle-Side Similarity Theorem
Answers
Answer:
Triangle Proportionality Theorem
Step-by-step explanation:
Just took the test xD
Abdul can use the Pythagorean Theorem to calculate the straight-line distances on his map, utilizing the formula a² + b² = c² for right triangles created by the intersections of his neighborhood's streets.
To determine the remaining distances for his map, Abdul can apply the Pythagorean Theorem. The streets in question form right angles at their intersections, as implied by the parallel streets mentioned. Thus, if Abdul needs to find the distance between two points that form a right angle with another point (essentially creating a right triangle), he can use the formula a² + b² = c², where a and b are the legs (sides forming the right angle) of the triangle and c is the hypotenuse (the side opposite the right angle).
For example, if Abdul wants to find the straight-line distance (hypotenuse) between his home and the high school, and he knows the distance to the middle school (3 miles) and the distance from the middle school to the high school (6 miles), he can use the Pythagorean Theorem to calculate this. Assuming his home, the middle school, and the high school form a right triangle, the formula becomes: 3² + 6² = c², which after calculations gives c =
√(3² + 6²).
Therefore, the correct answer is pythagoras theorm.
Related Questions
Find the perpendicular slope of the line 3X-9Y=15
Answers
So --9/3=3
(-b/a) is the equation of the slope
-9y = -3x + 15
y = (-3/-9)x + (-15/9)
y = 1/3x - 5/3....slope here is 1/3. A perpendicular line will have a negative reciprocal slope.All that means is " flip " the slope and change the sign.
So our perpendicular slope will be : -3 ( I flipped 1/3 and it became 3/1 or just 3...I then changed the sign and it became -3)
so the perpendicular slope is -3
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
Answers
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.
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?
Answers
6*22,26/100 =
1,3356
22,26 - 1,3356 = 20,9244
70% de 20,9244 =
70*20,9244/100 =
14,64708 ~ 14,64
[tex] \frac{22.26}{1.06} = 21.06[/tex]
The sales price is $21.06
Sales price/.70 (70% of the original price) = original price
[tex] \frac{21.06}{.70} = 30.09[/tex]
The original price of the helmet was $30.09
What is the number of real solutions?
–11x2 = x + 11
cannot be determined
one solution
two solutions
no real solutions
Answers
that would be -22=x+11
x=-33
so there's only one solution.
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!
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) ...?
Answers
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).
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.
Answers
The line is 1/2 the length of the square's diagonal :
(1/2)(10√2) = 5√2.
Let CG be a distance x from the vertex of the right angle in the triangle.
Remaining distance = 5√2 - x.
(1)(x) = (2)(5√2 - x)
x = 10√2 - 2x
3x = 10√2
x = (10/3)√2.
Using Pythagorean theorem,
x^2 + y^2 = c^2
c = (10/3)√2,
and x = y,
so 2x^2 = 200/9
x = √(100/9) = 10/3 = y.
x = y = 3.333
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
Answers
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.
rewrite 6 3/4 as an decimal number
Answers
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
...?
Answers
The slope of this line is NEGATIVE.
I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
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.
n is a positive integer.
Explain why n(n-1) must be an even number.
Answers
3 * (3-1). According to BIDMAS/BODMAS, we must first work out the brackets and then multiple it by the 3.
Do 3-1 = 2, 2*3 = 6 which is an even number. If we try with an even number we also get an even number:
4-1 = 3, 3*4 = 12. Even if we try this with a number like 7, 9 or 10 - we will always get an even integer, this is because, whenever we multiple an even number with an even or odd number - we always get an even number. So when we take away 1 by an even number, and multiple it with an odd number, we get even. Same applies to when we take away an odd number by 1 to get an even number and then times it by an odd number - we always get even.
The ordered pairs (1, 81), (2, 100), (3, 121), (4, 144), and (5, 169) represent a function. What is a rule that represents this function?
y = x^8
y = 8^x
y = (x + 8)^2
y = 8x ...?
Answers
Answer:
[tex]y=(x+8)^{2}[/tex]
Step-by-step explanation:
we have that
The ordered pairs [tex](1, 81), (2, 100), (3, 121), (4, 144)[/tex], and [tex](5, 169)[/tex] represent a function
The rule that that represent this function is equal to
[tex]y=(x+8)^{2}[/tex]
Verify
For [tex]x=1[/tex] -----> Find the value of y in the equation
[tex]y=(1+8)^{2}=81[/tex] -----> is correct
For [tex]x=2[/tex] -----> Find the value of y in the equation
[tex]y=(2+8)^{2}=100[/tex] -----> is correct
For [tex]x=3[/tex] -----> Find the value of y in the equation
[tex]y=(3+8)^{2}=121[/tex] -----> is correct
For [tex]x=4[/tex] -----> Find the value of y in the equation
[tex]y=(4+8)^{2}=144[/tex] -----> is correct
For [tex]x=5[/tex] -----> Find the value of y in the equation
[tex]y=(5+8)^{2}=169[/tex] -----> is correct
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
Answers
Since x² = y is x = √y, then:
A = s²
s² = √A
√A is square root of A.
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
Answers
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.
A fair coin is tossed n times. What is the probability that no two consecutive heads appear? A fair coin is tossed n times. What is the probability that no two consecutive heads appear?
Answers
There are 2^10 = 1024 total possible outcomes of 10 tosses.
Now we count the number of possible outcomes with no two consecutive heads. Let x_n be this number for n tosses - we wish to find x_10. For n > 2, the string of tosses must fall into one of two disjoint categories:
(i) tosses ending with a tail
(ii) tosses ending with a tail then a head
(i.e. tosses ending with a head then a head is impossible)
Given that the first n-1 or n-2 tosses must also have no two consecutive heads, we sum the number of possibilities of case (i) and (ii) and find
x_n = x_{n-1} + x_{n-2}.
We also easily see that x_1 = 2, x_2 = 3. From the above recurrence we can compute x_n as terms of the Fibonacci sequence until x_10 = 144.
Since the coin is unbiased all these possibilities are equally likely and the answer is 144/1024 = 9/64.
Solve for y.
7y - 6y - 10 = 13
y = -23
y = -3
y = 3
y = 23
Answers
-collect like terms
y-10=13
-move the constant to the right side and change its sign
y=13+10
add the numbers
answer is y=23
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
Answers
the sum of 3 times a number and 4
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
Answers
since triangle PRQ and ARC are similar
PR = QR = PQ
AR CR AC
so we can use
PR = PQ
AR AC
but AR = CR finally, PQ = AC x PR / CR
PQ = 9.6 x 4.8 / 7.2 = 6.4
the true answer is 6.4 inches
Answer:
The answer is C, 6.4 inches
Step-by-step explanation:
What is the volume of a cube where the length of each side is 6 centimeters?
Answers
Answer:
The answer is A
Step-by-step explanation:
if y=15 when x=3/4, find x when y=25
Answers
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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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
Answers
y=kx+n
k is coefficient which tells us about slope. The higher the k is, the faster y changes for same change of x value.
Therefore A is correct and B isnt
C is correct. because for positive changes of x you have negative change of y because of negative coeficient which when multiplied by positive value of x will give negative value.
D isnt correct. n is parameter that influences shifting.
E is oposite from C therfore it isnt correct.
Express the number in scientific notation.
0.042
Answers
Tomas wrote the equation y = 3x +3/4. When Sandra wrote her equation, they discovered that her equation had all the same solutions as Tomas’s equation. Which equation could be Sandra’s?
–6x + y = 3/2
6x + y = 3/2
–6x + 2y = 3/2
6x + 2y = 3/2
Answers
or, 2y= 6x + 3/2
or, y= (6x + 3/2)/2
or, y = 6x/2 + 3/4
or, y = 3x + 3/4
Therefore, –6x + 2y = 3/2 is Sandra's equation.
So now we need to transform options in tomas equation form and compare.
First option:
y = 6x + 3/2 not the same
Second option:
y = -6x + 3/2 not the same
Third option:
-6x + 2y = 3/2 when -6x goes on other side it changes its sign and will become:
2y = 6x + 3/2
when we divide by 2 we get
y = 3x + 3/4 which marks with Tomas's equation
Answer is third option.
The exponential expression 4^-2 is equal to what fraction value
Answers
X ^-m = 1/X^m
For example
4^-2 = 1/4^2 = 1/16. Since 4 • 4 which is the same as 4^2 is 16.
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
Answers
Simple Pythagorean Theorem.....
√(12)²+(5²))
√(169)
B.) 13
what is the squar root of 21
Answers
y = 1/2 x + 2
x = 8
y = __
Answers
y=(1/2)*8+2=8/2+2=4+2=6
x=8
y=8/2 + 2
y = 4 + 2
y = 6
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
Answers
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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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
Answers
x^2 - y^2 = 55
substituting in to it
73 - 55 = 2y^2
18 = 2y^2
y = 3
x^2 - 73 - 9
x = 8
answer is A
Which phrase describes the end behavior of the graph of ƒ(x) = –x5 – 4x4 + 7x2 – 2?
Answers
Is it even or odd? Odd
Is it positive or negative? Negative
Using this we can determine that it is up to the left, and down to the right
Or, for more advanced terms, as x approaches -∞, y approaches ∞, and as x approaches ∞, y approaches -∞
WHAT IS THE BENEFIT OF A "SPACE CUSHION" AROUND YOUR VEHICLE?
Answers
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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