The length of the Hypotenuse is, [tex]\sqrt{5}x[/tex] units.
What is Pythagoras Theorem?
The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.
Let the one leg of a right triangle is twice as long as the other.
Suppose the shorter leg is x.
So the longer leg is 2x.
Let, the hypotenuse is h.
By Pythagoras Theorem,
[tex]x^2 + (2x)^2 = h^2\\x^2 + 4x^2 = h^2\\5x^2 = h^2\\h = \sqrt{5} x[/tex]
Hence, the hypotenuse as a function of the length of the shorter leg, is [tex]\sqrt{5}x[/tex] units.
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40 POINTS AND BRAINLIEST
5.06 mid unit test Algebra 1.
Show all work!
Write the radical below in simplest radical form. Decimals not allowed
√175
2. √5/12
From the procedure, the simplest form of the radical is 5√7.
What is the basic form?A radical can also be called a surd. The surd is an irrational number. We say that it is irrational because it can not be expressed as a terminating decimal.
Now we have to look at the radical √175. We have to think of two numbers that we can multiply to obtain 175 and one of them would be a perfect square.
If we choose the numbers 7 and 25, we can write;
√175 = √7 * √25
Thus we have in the simplest radical form 5√7.
The expression √5/12 is already in the simplest form.
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Solve the equation by identifying the quadratic form. Use a substitute variable(t) and find all real solutions by factoring.
Type your answers from smallest to largest. If an answer is not an integer then type it as a decimal rounded to the nearest hundredth. When typing exponents do not use spaces and use the carrot key ^ (press shift and 6). For example, x cubed can be typed as x^3.
(x^2-1)^2+(x^2-1)-12=0
Step 1. Identify the quadratic form
Let t= Answer
. We now have:
t^2+t-12=0
Step 2. Factor
Factor this and solve for t to get t=Answer
and Answer
Step 3. Solve for x
We have solved for t now we need to use this value for t to help us solve for x. Revisit step 1 to remind you of the relationship between t and x. Type your real solutions (no extraneous) from smallest to largest.
x=___ and ___
The quadratic form of (x² - 1)² + (x² - 1) - 12 = 0 is (x² + 3)(x² - 4) = 0 and the roots are x = ± i√3 Or x = ± 2.
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
Given, (x² - 1)² + (x² - 1) - 12 = 0.
∴ x⁴ - 2x² + 1 + x² - 1 - 12 = 0.
x⁴ - x² - 12 = 0.
x⁴ + 3x² - 4x² - 12 = 0.
x²(x² + 3) - 4(x² + 3) = 0.
(x² + 3)(x² - 4) = 0.
Now (x² + 3) = 0 Or (x² - 4) = 0.
x² = - 3 Or x² = 4.
x = ± √-3 Or x = ± 2.
x = ± i√3 Or x = ± 2.
We can also solve this equation by assuming x² = t and substitute we will get the roots in terms of t and then we'll replace x² again in t.
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Please help me please
The tick marks on the two sides mean those two lengths are the same, which also means the angles opposite them are the same measure. (AKA It's an isosceles triangle.)
Since the two missing angles are equal, we can solve:
28 + x + x = 180
to find that x = 76.
The two angles are 76 degrees.
And since LM = LN, we know LN = 18 in.
To rewrite y(t)=2*sin 4pi t+5*cos 4pi t in the form y(t)=Asin (wt+theta), solve for theta.
I will report if you do not answer
The required standard equation is given as y(t) = 5.39 sin(4πt + 0.379π).
Given that,
To rewrite y(t)=2×sin 4pi t+5×cos 4pi t in the form y(t)=Asin (wt+Ф).
What are trigonometric equations?These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.
Here
We know that.
Asin(α + β) = Asinαcosβ + Acosαsinβ,
Comparing it with the given equation,
Asinα = 5
Acosα = 2
Taking the ratio of the equation,
sinα/cosα = 5/2
tanα = 5/2
α = 0.379π
Now,
Asin0.379π = 5
A = 5 / sin0.379
A = 5.39
Now,
The standard form equation is given as, y(t) = 5.39 sin(4πt + 0.379π) where ω = 4π.
Thus, the required equation is given as y(t) = 5.39 sin(4πt + 0.379π).
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From a sample with n=40, the mean duration of a geyser's eruption is 3.35 minutes and the standard deviation is 0.79 minutes. Using Chebychev's Theorem, determine at least how many of the eruptions lasted between 1.77 and 4.93 minutes.
75% of the eruptions lasted between 1.77 and 4.93 minutes.
Chebyshev's Theorem calculates the proportion of observations that are within a given number of standard deviations of the mean. This theorem is applicable to many different probability distributions. Chebyshev's inequality is another name for Chebyshev's theorem.
According to Chebyshev’s theorem, the proportion of the data lying within k standard deviations of the mean is always at least 1 – 1/k^2, where k>1.
Given
Mean = 3.35
SD = 0.79
Mean – 1*SD = 3.35 – 1*0.79
= 3.35 – 0.79
= 2.56
Mean + 1*SD =3.35 + 1*0.79
= 3.35 + 0.79
= 4.14
Mean – 2*SD =3.35 – 2*0.79
= 3.35 – 1.58
= 1.77
Mean + 2*SD =3.35 + 2*0.79
= 3.35 + 1.58
= 4.93
Here, we have k = 2
For k = 2,
= 1- (1/k2)
= 1- (1/(2)2
= 1- ¼
= ¾
at least ¾ or 75% of all values lie within 2 standard deviations of the mean.
Therefore 75% of the eruptions lasted between 1.77 and 4.93 minutes.
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The function g is defined by the following rule.
g(x) = 5x-1
Complete the function table.
X
-2
1
4
5
X
g(x)
?
?
?
?
?
Step-by-step explanation:
You need to replace x in the equation with x in the table.
question is on image
Answer:
i dont see image..
Step-by-step explanation:
Late assignment. Help ?
The rigid transformation of the pre-image ΔABC, that produces the image ΔDEF is option E as follows;
E. [tex]R_{(90^{\circ},\,(0,\, 0))}[/tex]
What is a rigid transformation?A rigid transformation is one in which the distances between each pair of points on the pre-image is preserved on the image, such that the pre-image and the image have the same size.
The coordinates of the vertices of ΔABC are;
A(-3, -3), B(-1, -4), C(-3, -4)
The coordinates of the vertices of ΔDEF are; D(-3, 3), E(-4, 1), F(-4, 3)
The formula for the rotation of a point (x, y) 90° clockwise about the origin is presented as follows;
Pre-image point [tex]{}[/tex] (Rotation 90° clockwise) Image point after rotation
(x, y) [tex]{}[/tex] ⇒ [tex]{}[/tex] (-y, x)
The points in the image ΔDEF of pre-image triangle ΔABC which corresponds to points on ΔABC are;
Vertex A in triangle ΔABC corresponds to vertex D on triangle ΔDEF
Vertex B in triangle ΔABC corresponds to vertex E on triangle ΔDEF
Vertex C in triangle ΔABC corresponds to vertex F on triangle ΔDEF
The transformation of (x, y) ⇒ (-y, x), (which is the transformation of a 90° clockwise rotation about the origin), on the vertices of ΔABC are;
A(-3, -3) [tex]\underset \longrightarrow {R_{(90^{\circ}, (0, 0)}}[/tex] D(-3, 3)
B(-1, -4) [tex]\underset \longrightarrow {R_{(90^{\circ}, (0, 0)}}[/tex] D(-4, 1)
C(-3, -4) [tex]\underset \longrightarrow {R_{(90^{\circ}, (0, 0)}}[/tex] F(-4, 3)
Therefore, the triangle ΔDEF can be obtained from the triangle ΔABC by a rotation of 90° clockwise about the origin.
The correct option is; E [tex]R_{(90^{\circ}, (0, \,0))}[/tex]
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Tim’ mom filled the ga tank in her SUV and pent $72. 00 for 22. 5 gallon of unleaded gaoline. What i the contant of proportionality that relate the cot in dollar, y, to the number gallon of unleaded gaoline, x?
The constant of proportionality on this case is 3.2
What is constant of proportionality?
The ratio between any two given values that establishes what is referred to as a proportional relationship is the constant of proportionality.
Main body:
Total amount spent by Mom = $ 72
total gallon bought = 22.5
So constant of proportionality can be found by finding value of 1 gallon of gasoline, which can be found by dividing as follows,
Price of 1 gallon = total spent/ total gasoline bought
= 72/22.5
= 3.2
Hence constant of proportionality is 3.2.
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suppose a sample of a radioactive substance weighs 32 mg. One year later, the sample weighs 25.5 mg. What is the half-life of this substance? (round your answer to two decimal places.)
The half-life of this substance that weighs 32 mg and one year later, the sample weighs 25.5 mg will be 3.053 year.
What is half-life?The duration it takes for a given quantity to fall to half of its initial value is known as the half-life. The phrase can be used to refer to other types of decay, whether or not they are exponential, but it is most frequently used in connection with atoms going through radioactive decay. The amount of time needed for the reactant concentration to drop to half its initial value is known as the half-life of a reaction.
Here,
The initial weight of radioactive substance=32 mg
The final weight of radioactive substance=25.5 mg
Duration=1 year
The formula,
N(t)=N(0)*1/2^(t/t₁/₂)
25.5=32*1/2^(1/t₁/₂)
half-life, t₁/₂ = 3.053 year
The half-life of this substance, which weighs 32 mg, will be 3.053 years when the sample weighs 25.5 mg.
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The solution to the inequality −17 + 2x ≤ 19 − 4x is x ≤ k for some number k. What is k?
The solution to the inequality −17 + 2x ≤ 19 − 4x is x ≤ k. The value of k is 6.
How to solve inequality?In mathematics, the relationship between two values that are not equal is defined by inequalities.
Therefore, the inequality can be solved as follows:
−17 + 2x ≤ 19 − 4x is x ≤ k .
Let's solve for k
−17 + 2x ≤ 19 − 4x
subtract 2x from both sides of the inequalities
−17 + 2x ≤ 19 − 4x
−17 + 2x - 2x ≤ 19 − 4x - 2x
- 17 ≤ 19 - 6x
Subtract 19 from both sides of the equation
- 17 ≤ 19 - 6x
- 17 - 19 ≤ 19 - 19 - 6x
- 36 ≤ - 6x
divide both sides by -6
- 36 / -6 ≤ - 6x / -6
6 ≥ x
x ≤ 6
Therefore, k = 6
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X=
58
43
71
no bots fr
Answer:
A
Step-by-step explanation:
please help!!!!! i need an answer asap
Answer: (3,2)
Step-by-step explanation:
[tex]7x-7y=7\\\-4x-7y=-26[/tex]
subtract second equation from the first
[tex]11x=33\\x= 3[/tex]
plug x = 3 back into first equation
[tex]7(3) - 7y = 721 - 7y = 7-7y = -14\\y = -2[/tex]
Answer:
x=3 y=2
Step-by-step explanation:
a family is walking toward their home, which is in an apartment building 123 feet tall. they are walking at a rate of 5 ft/sec. how fast is the distance to the top of the building changing when they are 60 feet from the base of the building?
The distance to the top of the building changing when they are 60 feet from the base of the building is 2.19 ft/s.
In the given question we have to find how fast is the distance to the top of the building changing when they are 60 feet from the base of the building.
A family is walking toward their home, which is in an apartment building 123 feet tall.
They are walking at a rate of 5 ft/sec.
So according to the given statement diagram is
In the diagram x represent base and s represent the distance.
Using the Pythagorean theorem to find the value of s.
So the equation should be
[tex]s^2=x^2+(123)^2[/tex]........................(1)
From the question, x=60 feet
Now putting the value
[tex]s^2=(60)^2+(123)^2[/tex]
[tex]s^2[/tex] = 3600+15129
[tex]s^2[/tex] = 18729
s = 136.85
Differentiate equation 1 with respect to t using the power rule then solve the expression for ds/dt
2s ds/dt=2x dx/dt+0
2s ds/dt= 2x dx/dt
Divide by 2s on both side, we get
ds/dt= x/s dx/dt.......................(2)
They are walking at a rate of 5 ft/sec.
So dx/dt=5
Putting the value in the equation 2
ds/dt=60/136.85 ×5
ds/dt=0.438×5
ds/dt=2.19 ft/s
The distance to the top of the building changing when they are 60 feet from the base of the building is 2.19 ft/s.
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Convert meters to centimeters. 4.5 m = X(
I ment middle not high...
Answer:
450 centimeters
Step-by-step explanation:
We know that,
1 meter = 100 centimeters
so 4.5 meters = 4.5*100 centimeters
=450 centimeters
if an examination Nita scored 372 marks if she scored 62% marks find the maximum marks
If Nita scored 62% of the marks then the maximum marks of the examination was 600 .
In the question ,
it is given that,
the number of marks scored by Nita in the examination = 372 marks
percent of marks scored by Nita in the examination = 62% ,
let the maximum marks of the examination = "x" ,
So , according to the questions
372 = 62% of x
372 = 0.62 * x ....because 62% = 0.62
x = 372/0.62
x = 600
Therefore , If Nita scored 62% of the marks then the maximum marks of the examination was 600 .
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2x-y + 2z = 6
3x+2y-z = 4
4x + 3y - 3z = 1
Answer:
Step-by-step explanation:
Write an equation in standard form that has a y-intercept at (0,-3) and also contains the point (4,5)
Answer: Write an equation in standard form that has a y-intercept at (0,-3) and also contains the point (4,5)
Step-by-step explanation:
PLEASE HELP! I WILL NAME YOU THE BRAINLIEST! PLEASE PLEASE PLEASE!
Write the point-slope form of the equation of the line with slope −7/4 that passes through the point (−9, 2).
WORK DOES NOT NEED TO BE SHOWN!
A. y + 2= −7/4(x − 9)
B. y − 9= −7/4(x + 2)
C. y + 9 = −7/4(x − 2)
D. y − 2 = −7/4(x + 9)
Answer: D. Y-2 = -7/4(X+9)
math homework trigonometry pls help
The area of the given triangle is 21.33 cm²
What is Heron's formula?This formula is understood for its simple calculation supporting the length of three sides of a triangle, if the length of three sides are a, b, and c, then its semi-perimeter is. s=a+b+c2. Thus, the area is given by,
A=√s(s−a)(s−b)(s−c)
Given a triangle, with lengths 8 cm, 6 cm and 12 cm
Perimeter = 8+6+12 = 26 cm
Semi perimeter = 26/2 = 13 cm
Area = √s(s−a)(s−b)(s−c)
Area = √13(13-8)(13-6)(13-12)
Area = √455
Area = 21.33 cm²
Hence, The area of the given triangle is 21.33 cm²
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Jerry rolled a fair number cube 24 times. Which of the following is the most reasonable outcome ?
F. Jerry rolled number 6 twelve times.
G. Jerry rolled a 2 or a 4 twelve times.
H.Jerry rolled each number in the cube six times
J. Jerry rolled an odd number twelve times
Answer:
h
Step-by-step explanation:
i did the quize good luck
if the 5-day simple moving average was $54.27, what was the closing price on thursday?
Answer:
The correct answer is D.
Step-by-step explanation:
1. You add all 4 of the given closing prices with answer choice D ($56.24) Getting $271.35
2. Then divide the total of $271.35 by 5. which gives you $54.27.
meaning that your answer is D.
Sorry if this didn't help very much... Would appreciate a 5 star if it did :)
graph the equation. y=-4(x+2)^2-1
Hope this helps you with your question.
Answer:
Step-by-step explanation:
I did it on a graphing app
Write an equation in point slope for the line that passes through the given points
(-4,6), (-2,22)
Answer:
y - 6 = 8(x + 4)
Step-by-step explanation:
The point-slope form is [tex]y-y_{1}=m(x-x_{1})[/tex], where y1 and x1 are any point on the line and m is the slope.
The formula for slope is [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
By plugging in the points we have, we get: [tex]\frac{22-6}{-2-(-4)}=8=m[/tex]
We can use any of the two pairs of points to represent y1 and x1 so if we choose (-4,6), we get:
[tex]y-6=8(x-(-4))\\y-6=8(x+4)[/tex]
Three undefined terms in mathematics: i. Point ii. Line iii. Plane the mathematical term parallel lines explicitly uses the undefined term(s). The mathematical term perpendicular lines explicitly uses the undefined term(s). The mathematical term line segment explicitly uses the undefined term(s).
Three mathematical terms with no definitions: (1) The terms (ii) and (iii) are correct., (2) The term (ii) is correct., (3) The term (i) and (ii) is correct.
What is parallel and perpendicular lines?
The definition of a parallel line is a pair of lines that never cross and always have the same distance between them. Lines that cross at right angles are referred to as perpendicular lines (90 degrees).
(1) The mathematical term parallel lines explicitly uses the undefined term(s).
The terms (ii) and (iii) are correct.
(2) The mathematical term perpendicular lines explicitly uses the undefined term(s)
The term (ii) is correct.
(3) The mathematical term line segment explicitly uses the undefined term(s).
The term (i) and (ii) is correct.
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find the weighted average of the weighted points on the number line. a number line with four weighted points plotted. the point at negative 4 has weight three, the point at negative 2 has weight three, the point at one has weight one, and the point at five as weight three.
The weighted average of the weighted points on the number line is -0.2.
A weighted average refers to the average of a data set that considers certain numbers as more important. Weighted averages are commonly used in statistical analysis, stock portfolios and teacher grading averages. In order to determine the weighted average of the weight points on the number line:
Determine the sum of weight value of each number. Weight value sum = (-4*3) + (-2*3) + (1*1) + (5*3) = -12 – 6 + 1 + 15 = -2 Determine the sum of weight points. Sum of weights = 3 + 3 + 1 + 3 = 10.Divide the sum of weight value by weight value sum. Weighted average = -2/10 = -0.2Hence, the average weight is -0.2.
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Which of these are equivalent to -11/-4? Choose ALL that apply.
-11 / 4
11 / (-4)
-11 / (-4)
-11/4
11/-4
-11/-4
The equivalent fraction for the given fraction -11/-4 is -11/(-4) and -11/-4.
Fraction.
Fraction means a number expressed as a quotient, in which a numerator is divided by a denominator.
Given,
Here we have the fraction -11/-4.
Now, we have to find the equivalent fraction of this fraction.
In order to find the equivalent fraction, we have to identify that the given term is reduceable or not.
If it is reduceable, then we have to simplify it to get the equivalent fraction.
But here the given fraction -11/-4 is not reduceable.
So, the next thing we have to do is to find the sign equivalent value for this one.
In the given fraction both the numerator and the denominator are in negative sign.
So, the equivalent fraction, must have both positive or both negative one.
Therefore, the equivalent fraction are -11/(-4) and -11/-4.
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Which of the following is an equivalent form of the compound inequality −22 > −5x − 7 ≥ −33? flvs
Isolating the variable x we will get the simplified inequality (which is equivalent to the given one)
3 < x ≤ 5.2
How to get an equivalent inequality?Sadly, the options are not given, so we can get a trivial equivalent inequality which is the one where the variable x is isolated, and it gives the solution set for the inequality.
So let's isolate the variable:
-22 > -5x - 7 ≥ −33
First, we can add 7 everywhere, so we get:
-22 + 7 > -5x - 7 + 7 ≥ −33 + 7
-15 > -5x ≥ −26
Now we can divide everywhere by -5, because it is a negative number, it changes the direction of the symbols.
-15/-5 < -5x/-5 ≤ -26/-5
3 < x ≤ 5.2
That is the equivalent inequality, and the solution set is:
(3, 5.2]
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1. Choose the correct answer.
Which theorem or postulate could be used to prove the congruence of the pair of triangles?
Answer:
(d) HA
Step-by-step explanation:
You have two right triangles with the hypotenuse and one angle marked as congruent. You want to know the applicable theorem for claiming the triangles are congruent.
Right triangle congruenceWhen two triangles are known to be right triangles, the known angle is opposite the longest side (hypotenuse), and the two legs are the sides that form that known angle. Hence, some special theorems can be invoked for right triangles:
LA — leg, angle; equivalent to ASA
LL — leg, leg; equivalent to SAS
HA — hypotenuse, angle; equivalent to AAS
HL — hypotenuse, leg; no equivalent for non-right triangles
ApplicationThe given triangles have the hypotenuse (H) and an acute angle (A) marked, so the HA theorem can be used to prove congruence.
__
Additional comment
The HL condition described above refers two two consecutive sides and the angle not between them (SSA). This set of descriptors will create a unique triangle if and only if the angle is opposite the longest side. In general, that will not be the case, but it is guaranteed to be the case for a right triangle.
Hi! I can’t figure out m<4 and m<5. Can anyone help me?
The measure of angle 4 is 35 degrees and the measure of angle 5 is 81 degrees
The sum of angles on a straight line is equal to 180 degrees
Then the equation will be
∠3 + 81 +∠4 = 180 degrees
Substitute the value of ∠3 in the equation
64 + 81 + ∠4 = 180
145 + ∠4 = 180
∠4 = 180 - 145
∠4 = 35 degrees
The sum of interior angles of the triangle is 180 degrees
∠4 + ∠5 + 64 = 180
Substitute the values in the equation
35 + ∠5 + 64 = 180
∠5 + 99 = 180
∠5 = 180 - 99
∠5 = 81 degrees
Hence, the measure of angle 4 is 35 degrees and the measure of angle 5 is 81 degrees
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