Answers
The theorem that verifies that the two right angled triangles are similar is HA.
What are similar triangle?Two triangles are said to be similar if the ratio of their corresponding sides and the corresponding angles are equal.
Analysis:
From the diagrams KL = OQ ( hypotenuse)
∠L is equal to ∠Q which are acute.
so the two triangles are similar in hypotenuse and acute angle which is the HA theorem.
In conclusion, the HA theorem verifies that the two triangles are similar.
Learn more about similar triangles: brainly.com/question/2644832
#SPJ1
Related Questions
How many classrooms would be necessary to hold 1,000,000 inflated balloons? (Assume one balloon is about 1 ft3 and a typical classroom is about 35 ft × 50 ft × 15 ft. Round your answer to the nearest number of classrooms.)
Answers
One balloon = 1 cube ft. Using this value and multiplying it by 1,000,000, we can find how much space all of these would take up. Since 1 times anything is just the unchanged value,
• a million inflated balloons = 1000000 ft^3.
The classroom has dimensions 35, 50, and 15 ft. We can use these values to find the classroom’s volume. The equation for Volume of a rectangular prism: V = lwh, where l is length, w is width, and h is height. Substitute given dimensions into this equation:
• V = 35*50*15 = 26250 ft^3.
now, what times 26250 will equal 1000000? Well, let’s set up an equation and solve for x, the number of classrooms.
• 26,250x = 1,000,000. Divide both sides by 26250 to get x alone:
• x = 38.0952.
Approximately 38 classrooms are necessary to hold 1,000,000 inflated balloons.
Check: when x is 38: 26,250(38) = 997,500 ft^3. When x is 39: 26,250(38) = 1,023,750 ft^3. x = 38 is more accurate.
**(I will note, however, that I’m not sure if you’re instructed to round according to the decimal rules or round UP a whole number because that extra .0952 needs to be included).
To hold 1,000,000 inflated balloons,
38 classrooms are needed.
What is volume?In three-dimensional space,
the amount of space taken by an object is the volume of that object.
The volume of the cubic,
= length x width x height
Given:
The dimensions of the normal classroom are 15 ft × 50 ft × 35 ft.
The volume of the classroom,
= 15 ft by 50 ft by 35 ft.
= 26250 cubic feet.
The number of classrooms,
= 1,000,000 / 26250
Simplifying the fraction,
we get,
= 38.09
≈ 38 to the nearest whole number.
Therefore, 38 classrooms are required.
To learn more about the volume;
https://brainly.com/question/23477586
#SPJ2
Find the height of a trapezium below with are 90cm and parallel sides 6 and 19.
Answers
Answer:
7.2 cm
Step-by-step explanation:
The height of the trapezium can be found by making use of the area formula with known values filled in.
__
solve for heightThe area of a trapezium is given by ...
A = 1/2(b1 +b2)h . . . . b1, b2 are the parallel sides, h is the height
Using the given values, we have ...
90 cm² = 1/2(6 cm +19 cm)h . . . . . . use the known values
(90 cm²)/(12.5 cm) = h = 7.2 cm . . . . divide by the coefficient of h
The height of the trapezium is 7.2 cm.
what is a variable in mathematics?
Answers
Answer:
variable, In algebra, a symbol (usually a letter) standing in for an unknown numerical value in an equation. Commonly used variables include x and y (real-number unknowns), z (complex-number unknowns), t (time), r (radius), and s (arc length).
Answer:
variable, In algebra, a symbol (usually a letter) standing in for an unknown numerical value in an equation. Commonly used variables include x and y (real-number unknowns), z (complex-number unknowns), t (time), r (radius), and s (arc length).
Step-by-step explanation:
In Maths, a variable is an alphabet or term that represents an unknown number or unknown value or unknown quantity. The variables are specially used in the case of algebraic expression or algebra. For example, x+9=4 is a linear equation where x is a variable, where 9 and 4 are constants.
12. Find the solution to the system of equations by
using
substitution.
y = -2x + 13
4x + 8y = 20
A)(-7,-1)
B)(4,5
C)(7,-1)
D)(-3,7)
Answers
Step-by-Step Explanation:
=> y = -2x + 13 (Eq. 1)
=> 4x + 8y = 20 (Eq. 2)
Substitute value of ‘y’ from Eq. 1 in 2 :-
4x + 8y = 20
4x + 8(-2x + 13) = 20
4x + -16x + 104 = 20
-12x + 104 = 20
-12x = 20 - 104
-12x = -84
12x = 84
x = 84/12
=> x = 7
Substitute value of ‘x’ in Eq. 1 :-
y = -2x + 13
y = -2(7) + 13
y = -14 + 13
=> y = -1
Therefore, x = 7, y = -1 which can be written in an ordered pair as (7,-1).
The average profit on each car sold was $2430, correct to the nearest $10. Calculate the lower bound for the total profit. Write down the exact answer.
Answers
The lower bound for the profit is $2425.
What is the lower bound?When a number of rounded off to the nearest $10, it means that the value of the number in the units place, if greater than 5 becomes zero and one is added to the $10 number. If the number is less than 5, there is no change in the $10 number and the units number becomes 0
The possible values of the average profit are 2425, 2426, 2427, 2428, 2429, 2430. 2431. 2432, 2433, 2434
To learn more about profit, please check: https://brainly.com/question/26181966
#SPJ1
rationalize the denominator of the fraction (6)/(4+\sqrt(5))
Answers
The rationalization the denominator of the fraction (6)/(4+\sqrt(5)) is [tex]\dfrac{6(4-\sqrt(5))}{11}[/tex].
How to rationalize a fraction?Suppose the given fraction is [tex]\dfrac{a}{b+c}[/tex]
Then the conjugate of the denominator is given by b - c
Thus, rationalizing the fraction will give us
[tex]\dfrac{a}{b+c} \times \dfrac{b-c}{b-c} = \dfrac{a(b-c)}{b^2 - c^2}[/tex]
The given expression is
[tex]\dfrac{6}{4+\sqrt(5)}\\\\[/tex]
By rationalizing the denominator of the fraction
[tex]\dfrac{6}{4+\sqrt(5)}\times \dfrac{4-\sqrt(5)}{4-\sqrt(5)} \\\\\\\dfrac{6(4-\sqrt(5))}{4^2-(5)}\\\\\\\dfrac{6(4-\sqrt(5))}{11}[/tex]
Thus, the rationalization the denominator of the fraction (6)/(4+\sqrt(5)) is [tex]\dfrac{6(4-\sqrt(5))}{11}[/tex].
Learn more about rationalization here;
https://brainly.com/question/14261303
#SPJ1
Compare 3.5 • 10^4 to standard form
Answers
Answer:
35,000
Step-by-step explanation:
^4 means 4 zeros
10^4 = 10,000
3.5 times 10,000 =
35,000
In which table does yvary directly with x?
Answers
The table in which y varies directly with x is table C.
What is direct variation?
When a variable varies directly with another variable, it means that as one variable increases, the other variable also increases.
The equation that is used to represent direct variation is:
y = kx
Where y is the constant of proportionality
In table c, k is equal to 26
26 x 2 = 54 26 x 3 = 78To learn more about direct variation, please check: https://brainly.com/question/27573249
#SPJ1
Question 9 of 40
Factor this polynomial completely.
6x² + 7x-20
O A. (3x-4)(2x + 5)
OB. (6x- 5)(x+4)
O C. (2x-4)(3x + 5)
OD. (6x-4)(x+5)
Answers
Answer:
6x² + 7x-20
A. (3x-4)(2x + 5)
EGG DROP The physics class is holding an egg drop competition. The formula h= −16t2+h0 can be used to approximate the number of seconds, t, it will take for the eggs to reach height, h, from an initial height of h0 in feet.
Find the time it takes an egg to reach the ground if it is dropped from an initial height of 40 feet. Round to the nearest hundredth, if necessary.
Answers
By solving a quadratic equation we will see that the egg will hit the ground after 1.58 seconds.
How long will take the egg to reach the ground?
Here we know that the initial height of the egg is 40ft, so the equation for the height will be:
[tex]h(t) = -16*t^2 + 40[/tex]
The egg will hit the ground when h(t) = 0, so we need to solve the quadratic equation:
[tex]h(t) = -16*t^2 + 40 = 0\\\\16t^2 = 40\\\\t^2 = 40/16\\\\t = \sqrt{40/16} = 1.58[/tex]
This means that the egg will hit the ground after 1.58 seconds.
If you want to learn more about quadratic equations:
https://brainly.com/question/1214333
#SPJ1
Multiply:
(x+y)by (x+y)
a+b by a^2-b^2
(a+5) by (a^2-2a-3)
(a^2-ab+b^3) by (a+b)
Answers
Answer:
Multiply:
[tex](x+y)by (x+y)[/tex]
[tex] : \implies(x + y)(x + y)[/tex]
[tex] : \implies \: x(x + y) + y(x + y)[/tex]
[tex] : \implies {x}^{2} + xy + xy + {y}^{2} [/tex]
[tex] : \implies{x}^{2} + 2xy + {y}^{2} [/tex]
Multiply:
[tex]a+b \: by \: a^2-b^2[/tex]
[tex]: \implies( {a}^{2} + {b}^{2} ) \times (a + b)[/tex]
[tex]: \implies \: {a}^{2} (a + b) - {b}^{2} (a + b)[/tex]
[tex]: \implies \: {a}^{3} + {a}^{2} b - {ab}^{2} - {b}^{3} [/tex]
Multiply:
[tex](a+5) by (a^2-2a-3)[/tex]
[tex]: \implies{(a + 5) \times ( {a}^{2} - 2a - 3) }[/tex]
[tex]: \implies \: a({a}^{2} - 2a - 3) + 5( {a}^{2} - 2a - 3)[/tex]
[tex]: \implies(a \times {a}^{2} - a \times 2a - a \times 3) + (5 \times {a}^{2} - 5 \times 2a - 5 \times 3)[/tex]
[tex]: \implies{a}^{3} - {2a}^{2} - 3a + 5 {a}^{2} - 10a - 15 [/tex]
[tex]: \implies{ {a}^{3} + {3a}^{2} - 13a - 15}[/tex]
Multiply:
[tex](a^2-ab+b^3) by (a+b)[/tex]
[tex]: \implies{(a + b) \times ( {a}^{2} - ab + {b}^{3} )}[/tex]
[tex]: \implies \: a( {a}^{2} - ab + {b}^{3}) + b( {a}^{2} - ab + {b}^{3} ) [/tex]
[tex]: \implies {a}^{3} - {a}^{2} b + a {b}^{3} + {a^2b} - {ab}^{2} + {b}^{4} [/tex]
[tex]: \implies{ {a}^{3}+ab^3 - ab^2+ {b}^{4} }[/tex]
Step-by-step explanation:
[tex] \blue{ \frak{Seolle_{aph.rodite}}}[/tex]
PLEASE HELP!!!!!!!!!! I'll NAME BRAINLIEST!!!!!!
Classify the expression by the number of terms.
5y^2-8+6y^4
Answers
Answer:
5x2-2x+1 The highest exponent is the 2 so this is a 2nd degree trinomial.
Step-by-step explanation: Also pls answer by question
What is the y-intercept for this function?
a
(0, −3)
b
(3, 0)
c
(−9, 0)
d
(0, −9)
Answers
Answer:
d
Step-by-step explanation:
the y- intercept is the point on the y- axis where the graph crosses
the graph crosses the y- axis at point (0, - 9 )
then y- intercept = (0, - 9 )
An auto weighing 2,000 pounds is on a street inclined at 10° with the horizontal. Find the force necessary to prevent the car from rolling down the hill. (Round your answer to the nearest whole number.)
347 pounds
14,397 pounds
2,462 pounds
Answers
Force (F) = WSin(angle)
F = 2000×Sin(10)
Therefore, F = 347lb.
Which equation best models the data y=186-6.2x, y=246-6.2x, y=186-12.4x, y=246-12.4x which one
Answers
The equation that best models the data is (a) y = 186 - 6.2x
How to determine the equation?The data is not provided; so I would give a general guide on how to model a linear equation.
Assume the points on the line are:
(0,186) and (1,179.8)
Start by calculating the slope of the line using:
[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]
This gives
[tex]m = \frac{179.8 - 186}{1 - 0}[/tex]
Evaluate
m = -6.2
The equation is then calculated using:
[tex]y = m(x - x_1) + y_1[/tex]
This gives
y = -6.2(x - 0) + 186
Evaluate
y = -6.2x + 186
Rewrite as:
y = 186 - 6.2x
Hence, the equation that best models the data is (a) y = 186 - 6.2x
Read more about linear equations at:
https://brainly.com/question/14323743
#SPJ1
EASY POINTS
What is the slope-intercept equation of this line?
Answers
Answer:
B
Step-by-step explanation:
The y-intercept is 8
The slope is -2x
Therefore the slope-intercept is y = -2x + 8
need help with this graphing question please
Answers
Step-by-step explanation:
12 . The x-intercept is where a line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis. Thinking about intercepts helps us graph linear equations..
A polynomial function h(x) with integer coefficients has a leading coefficient of 20 and a constant term of 1. According to the Rational Root Theorem, which of the following are possible roots of h(x) ?
Answers
Plus c
what is the transformation
(x,y) (x+5,y -3)
(x -5, y+3)
(x+3 y-5 )
x-3,y +5
Answers
please help! acellus
find the missing side of this right triangle.
30
3
x
x= [?]
Answers
Answer:
The number that belongs in the green box is equal to 909.
General Formulas and Concepts:
Algebra I
Equality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityTrigonometry
[Right Triangles Only] Pythagorean Theorem:
[tex]\displaystyle a^2 + b^2 = c^2[/tex]
Step-by-step explanation:
Step 1: Define
Identify given variables.
a = 30
b = 3
c = x
Step 2: Find x
Let's solve for the general equation that allows us to find the hypotenuse:
[Pythagorean Theorem] Square root both sides [Equality Property]:[tex]\displaystyle \begin{aligned}a^2 + b^2 = c^2 \rightarrow c = \sqrt{a^2 + b^2}\end{aligned}[/tex]
Now that we have the formula to solve for the hypotenuse, let's figure out what x is equal to:
[Equation] Substitute in variables:[tex]\displaystyle \begin{aligned}c & = \sqrt{a^2 + b^2} \\x & = \sqrt{30^2 + 3^2}\end{aligned}[/tex]Evaluate:
[tex]\displaystyle \begin{aligned}c & = \sqrt{a^2 + b^2} \\x & = \sqrt{30^2 + 3^2} \\& = \boxed{ \sqrt{909} } \\\end{aligned}[/tex]
∴ the hypotenuse length x is equal to √909 and the number under the square root, our answer, is equal to 909.
___
Learn more about Trigonometry: https://brainly.com/question/27707750
___
Topic: Trigonometry
What are the domain and range of g(x)= √x-3?
A. D: [3, ∞) and R: [0, ∞)
B. D: [–3, ∞) and R: [0, ∞)
C. D: (–3, ∞) and R: (–∞, 0)
D. D: (3, ∞) and R: (–∞, 0)
Answers
Answer:
I guess, A is the wanted answer, but
A and D together are the really correct answer.
Step-by-step explanation:
if I understand this correctly, then
g(x) = sqrt(x - 3)
the domain of a function is the definition of all valid x (input) values.
the range of a function is the definition of all valid y (result) values.
well, the content (the arguments) of a square root cannot be negative (at least not while dealing with real numbers).
so, the answer options B and D are automatically out, because the domain contains values that would make the arguments of the square root negative.
I guess your teacher wants to focus only on the positive results of the square root, so A is the correct number.
BUT formally, without designated restrictions, a square root has always 2 solutions : a positive and a negative one.
because (-x)² = (x)² = x².
so, I would have to say that the really correct answer is
A + D, because the range contains both, the positive and the negative numbers.
Lila invested 10000 in one of long life insurance company annuity contracts. When issued, the contract was paying a 5 percent rate of return
Answers
The kind of annuity does Lila own is: variable immediate annuity.
What is variable immediate annuity?Variable immediate annuity can be defined as the type of annuity that vary or fluctuate based on the type of investment you choose or pick.
In this type of annuity the payment you will receive will not be fixed reason being that payments that will made to you will always increase or decrease.
Therefore the kind of annuity does Lila own is: variable immediate annuity.
Learn more about variable immediate annuity here:https://brainly.com/question/13644926
#SPJ1
what equation is equivalent to 2^3^x =10
Answers
Answer:
[tex]log_2(10)[/tex]
how to findSimplify the equation using logarithms.
part 1[tex]2^3x=10[/tex]
[tex]log_1_0(2^3x)=log_1_0(10)[/tex]
log rule ⇩
[tex]log_a(x^y)=y*log_a(x)[/tex]
move exponent out of log.
[tex]x*log_1_0(2)=log_1_0(10)[/tex]
part 2isolate variable further
[tex]x*log_1_0(2)=log_1_0(10)[/tex]
[tex]x=\frac{log_{10}(10)}{log_{10}(2)}[/tex]
formula for combining logs. ⇩
[tex]\frac {log_b(x)}{log_b(a)}=log_a(x)[/tex]
the result ⇩
[tex]x=log_2(10)[/tex]
What is the median of the data set?
16, 21, 28, 30, 40, 45, 54, 58
A. 58
Β. 35
C. 10
D. 19
Answers
Answer:
I think 10 is the answer it's not sure.
A bag contains 2 red, 5 blue, and 3 green marbles. A marble is chosen at random. What is the probability of NOT choosing a red marble
Answers
Step-by-step explanation:
Number of red = 2Number of blue = 5Number of green = 3total number of marbles = 10probability of not choosing a red marble = 1--choosing a red marble.Because probability is always one(1).
Probability =
[tex]1 - \frac{2}{10} [/tex]
[tex] \frac{8}{10} [/tex]
[tex] \frac{4}{5} [/tex]
Is the probability of not choosing a red marble.
Please help we’re stuck
Answers
Answer:
Divide 12 by -6
Fahari kicks a ball on the ground into the air. One
second after being kicked, the ball reaches its
maximum height of 16 feet above the ground, and
2 seconds after being kicked, the ball is back on the
ground. A quadratic function models the height h(t) ,
in feet, of the ball t seconds after Fahari kicks it.
Which equation defines this relationship?
Answers
The equation that defines the relationship between the height and the time and models the position of the ball in time is the quadratic function y = - 8 · t² + 24 · t.
How to derive a quadratic function for the height of a ball
Quadratic functions are polynomials of grade 2 of the form y = a · t² + b · t + c, where t and y are the time and the height of the ball, in seconds and feet, respectively. To determine the value of the three coefficients we need to know three different points of the form (t, y).
If we know that (t₁, y₁) = (0 s, 0 ft), (t₂, y₂) = (1 s, 16 ft) and (t₃, y₃) = (3 s, 0 ft), then the quadratic function is:
a · 0² + b · 0 + c = 0 (1)
a · 1² + b · 1 + c = 16 (2)
a · 3² + b · 3 + c = 0 (3)
The solution to this system is a = - 8, b = 24, c = 0.
The equation that defines the relationship between the height and the time and models the position of the ball in time is the quadratic function y = - 8 · t² + 24 · t.
To learn more on quadratic functions: https://brainly.com/question/17177510
#SPJ1
Which equation is correct?
O a
52 x 7 = 50+ 2 × 7
Ob
b
52 x 7 = 50 x 7+2
Oc
52 x 7 = 50 x 7+2x7
Od
52 x 7 = 500 ×7+2×7
Answers
Answer:
52 x 7= 50 x 7 + 2 x 7
Step-by-step explanation:
WHAT IS THIS HELP
if u put a bad answer i'll report
Answers
Answer:
C
Step-by-step explanation:
Two negatives cancel out and turn into a positive.
In the expression 11 - ( -3 5/8 ) there are two negative signs. If the parenthesis are removed, the two negative signs cancel out and turn into a positive and we are left with 11 +3 5/8
So the answer is C
Julian calculates the volume of a rectangular prism with the dimensions 3/4ft by 4 feet by 1/2 ft. His work is shown here.
What error did Julian make?
He multiplied the numerators incorrectly.
He multiplied the denominators incorrectly.
He simplified 12/6 incorrectly.
He wrote 4 as a fraction incorrectly.
Answers
Answer:
He multiplied the denominators incorrectly
Step-by-step explanation:
we know that
The volume of a rectangular prism is given by the formula
V=LWH
we have
L=3/4 ft
W=5/1 ft
H=1/2
substitute
V=(3/4)(5/1)(1/2)= 3x5x1= 15
₋₋₋₋₋₋₋₋ ₋₋₋₋ ft³
4x1x2= 8
therefore
He multiplied the denominators incorrectly