The required length of the hypotenuse of the right angle triangle is 23.6 √2.
What is a right angle triangle?A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or anyone angle is a right angle.
Given that,
The legs of the right and triangle are congruent,
And equal to 23.6 yards.
Implies that,
Base = height = 23.6 yards
To find hypotenuse of the triangle, use Pythagoreans theorem,
(Hypotenuse)² = (Base)² + (Height)²
(Hypotenuse)² = (23.6)² + (23.6)²
(Hypotenuse)² = 2 (23.6)²
Hypotenuse = 23.6 √2
The length of the hypotenuse of the right angle triangle is 23.6 √2.
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The factors of the quadratic expression 48x² +38x +5 are (ax + b) and (cx + 1).
A=
B=
C=
Answer:
Step-by-step explanation:
We first rewrite the terms of 48x² +38x + 5 to 48x² + 8x + 30x + 5
We then regroup terms into two proportional parts: (48x² +8x) + (30x + 5)
Factor the expression: 8x(6x + 1) + 5(6x + 1)
We then factor 8x(6x + 1) + 5(6x + 1) to (6x + 1)(8x + 5)
Now that we know (ax + b) and (cx + 1) is (6x + 1)(8x + 5) we just need to apply the numbers to their corresponding letters:
A=8
B=5
C=6
help what is the answer to it
Answer: the first one
Step-by-step explanation:
Answer: should be this V≈549.78
Step-by-step explanation:
a box has 20 chocolate bars with the same ratio as shown above how many dark chocolate bare is in the box
A:3
B:6
C:5
D:4
Answer:
5
Step-by-step explanation:
(20/12)(3)=5
please please PLEASE help
The value of the slope is 1 and the value of the y-intercept is 6.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
The slope of the line will be calculated as,
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = (10 - 6 ) / ( 4-0)
Slope = 4 / 4 = 1
The y-intercept will be calculated as,
y = mx + c
6 = 0 + c
C = 6
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What is true about an image after a dilation?
The pre-image and image have the same shape after dilatation, but they are not the same size.
In the given question, we have to explain what is true about an image after a dilation.
The pre-image and image have the same shape after dilatation, but they are not the same size.
The figure is the same from every perspective. The midpoints of the figure's sides and the dilated shape's midpoint are both unchanged. Lines that are parallel and perpendicular to one another in the figure are identical to those in the dilated figure. The pictures stay the same.
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Evaluate 9-\dfrac{8}S9−
S
8
9, minus, start fraction, 8, divided by, S, end fraction when S=4S=4S, equals, 4
The solution is A = 7
The value of the equation A = 9 - ( 8/S ) when S = 4 is 7
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is given by
The equation A = 9 - ( 8/S )
Now , when S = 4
Substitute the value of S = 4 in the equation , we get
The value of A = 9 - ( 8/S )
The value of A = 9 - ( 8 / 4 )
The value of A = 9 - ( 2 )
The value of A = 7
Therefore , the value of A is 7 when S = 4
Hence , The value of the equation A = 9 - ( 8/S ) when S = 4 is 7
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Given the functions:
f(x) =83 + 8x
8 (x) = V2x
h (x) =7x-9
Evaluate the function h f(x)) for x = 3. Write your answer in exact simplified form. Select "Undefined" if applicable.
The value of the function h(f(x)) for x = 3 is h(f(3)) = 348.
What is a function?
In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
The given function is
[tex]f(x)=x^3+8x\\\\g(x)=\sqrt{2x}\\\\h(x)=7x-9[/tex]
Now we have to find the value of the function h(f(x)),
[tex]h(f(x))=7(f(x)) - 9\\\\h(f(x))=7(x^3+8x)-9\\\\h(f(x))=7x^3+56x-9\\\\$at x = 3, $\\\\h(f(3))=7(3)^3+56(3)-9\\\\h(f(3))=7*27+168-9\\\\h(f(3)) = 348[/tex]
Hence, the value of the function h(f(x)) for x = 3 is h(f(3)) = 348.
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PLEASEHELP 50 POINTS ALGEBRA 2
given list: { 8 9 33 44 57 60 62 64 73 74 77 86 } which list elements will be checked to find the value:
The value of the given elements are: 0.829.
Given:
The given numbers are: 8,9,33,44,57,60,62,64,73,74,77,86
Here, the largest Number is 86 = Xₐ
and the smallest number is 8 = Xₙ
Now,
Range = Xₐ -Xₙ
= 86 - 8
= 78
Therefore,
Coefficient of Range = Xₐ - Xₙ / Xₐ +Xₙ
= 86 - 8 / 86 +8
= 78 / 94
= 0.829
Therefore, the value is 0.829.
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Miriam rides her bike around a park. Each lap around the park is 2/3 mi . Maturity rides a total of 3 mi. How many laps around the park does Marion bride write your answer as a whole number of a lab plus a fraction of a lab you can use a model to help . PLEASE HELPPP!!!!
Answer: 4 whole laps plus 1/2 of a lap
Step-by-step explanation:
let x = number of laps
2/3x=3
x=9/2
x=4 1/2
4 whole laps plus 1/2 of a lap
What is the equation of the line which passes thru 1/3 and 2 5?
y = 3x – 2 is the equation of the line which passes through 1/3 and 2 5 with slope.
We can use the slope-intercept form of the equation of a line, which is y = mx + b, where m is the slope and b is the y-intercept. We know one point on the line, which is (1/3, 2.5). We can calculate the slope by calculating the rise (change in y) divided by the run (change in x), which is (2.5 - 0) / (1/3 - 0) = 2.5 / 0.33 = 7.5. Therefore, the equation of the line is y = 7.5x + b. To solve for b, we can substitute in our point, (1/3, 2.5) into the equation. We get 2.5 = 7.5(1/3) + b, or 2.5 = 2.5 + b. Therefore, b = 0, and the equation of the line is y = 7.5x + 0, or y = 7.5x.
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Which expression is equivalent to (64x82y32) for
all positive values of x and y?
A 8x82y32
B 64x4¹y16
C 32x82y32
D 8x4¹y16
Magdalena left out a statement from the proof shown. Which statement is best explained by the alternate exterior angles theorem?
The option which says Angle 2 and Angle 3 are Supplementary is the best statment that describes the Alternate Exterior Angle Theorem.
What is an Exterior Angle?
An Exterior Angle is the angle formed by a polygon's side and an extended neighbouring side; an angle generated by a transversal as it cuts one of two lines and located on the line's outside.
Solution:
Using the Alternate Exterior Angle Property we can say
Adjecent Angle of Angle 2 and Angle 3 are equal
Also, Angle 2 + Adjecent Angle of Angle 2 = 180
So, we can write Angle 2 + Angle 3 = 180
The option which says Angle 2 and Angle 3 are Supplementary is the best statment that describes the Alternate Exterior Angle Theorem.
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Help me with question 5 ( click the image to see the question)
Answer:
1 and 5
Step-by-step explanation:
first category and fifth one up
suppose that a is a 4 x 4 matrix with eigenvalues 1, 2, 3, and 4. is the matrix a - 2i invertible? why or why not?
Yes. The matrix A-2I is invertible because 2 is an eigenvalue for matrix A.
When the matrix (transformation) is applied to some vectors (eigenvectors), the eigenvalues of the matrix are scalars. In other words, if A is a square matrix of order n x n and v is a non-zero column vector of order n x 1, and Av = v (the product of A and v is just a scalar multiple of v), then the scalar (real number) is called an eigenvalue of the matrix A that corresponds to the eigenvector v.
The eigenvalues can be determined by formula,
[tex]|A-\lambda I|=0[/tex]
Where, [tex]\lambda[/tex] = eigenvalues.A square matrix with an inverse is known as an invertible matrix. A square matrix is said to be invertible if and only if the determinant is not equal to zero. In other words, a 2 x 2 matrix is only invertible if its determinant is not zero.
Given,
A is a 4x4 matrix whose eigen values are λ=1,2,3,4
we need to determine that A-2I is invertible or not.
We know that 2 is an eigen value of matrix A, so, if we substitute 2 to find determinant of A-2I, then we will get zero as answer.
So, when determinant of A-2I is zero then the matrix is invertible.
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Describe the end behavior of the function
Answer:
The end behavior of a function f describes the behavior of the graph of the function at the "ends" of the x-axis. In other words, the end behavior of a function describes the trend of the graph if we look to the right end of the x-axis (as x approaches +∞ ) and to the left end of the x-axis (as x approaches −∞ ).
Step-by-step explanation:
umm....I really hope this helps u
Which one is it? Rip i-Ready.
Answer: i-Ready and c
Step-by-step explanation: I hope this helps
the 5 egual members of the terraforming committee of the united martian colonies are randomly chosen from the council of 99 leaders. in how many different ways can this committee be chosen?
The committee can be chosen in 99.98.97.96.95 different ways.
What is a combination?
A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.
Here, we have
Given
The 5 equal members of the terraforming committee of the united martian colonies are randomly chosen from the council of 99 leaders.
We have to find out how many different ways can this committee be chosen.
For this, we concluded that the committee can be chosen in 99.98.97.96.95 different ways.
Hence, the committee can be chosen in 99.98.97.96.95 different ways.
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A teacher is creating a test for his Algebra 1 students. The test is made up of multiple-choice and free response questions. Each mutliple-choice question is worth 2 points and each free response question is worth 3 points. If the test has 48 questions and is worth a total of 100 points, which equations can be used to find x, the number of multiple-choice questions and y, the number of free response questions on the test?
(Choose TWO correct answers.)
Answers:
x+y=100
x+y=48
2x+3y=100
2x +3y=48
3x +2y = 48
3x +2y=100
Please answer asap!!
Answer:
The correct equations are 2x +3y=100 and x+y=48. These equations can be used to find the number of multiple-choice and free response questions on the test. The first equation, 2x +3y=100, shows that the total number of points for the multiple-choice questions (2x) plus the total number of points for the free response questions (3y) equals 100. The second equation, x+y=48, shows that the total number of multiple-choice and free response questions on the test is equal to 48. These equations can be solved simultaneously to find the values of x and y.
a two-sided coin is flipped 3 times. what is the probability that the coin will land heads up on the first flip, tails up on the second flip, and tails up on the third flip?
The probability that the coin will land heads up on the first flip, tails up on the second flip, and tails up on the third flip is (1/8).
What is the probability of getting a head in a single coin toss?If we toss a coin, we have two possible outcomes: head or tail. Now:
P(E) = Favourable outcomes / Total outcomes
= 1/2
As per the question, we need heads on the first throw and tails on the next two throws. We know that for independent events:
P(A∩B∩C) = P(A)*P(B)*P(C)
Let A be the event of getting head on the first throw and B and C be events of getting tails on the second and third throws of dice respectively.
P(A) = P(B) = P(C) = 1/2
So, P(A∩B∩C) = (1/2)*(1/2)*(1/2) = 1/8
So, the Required probability is (1/8)
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The temperature on a cold winter day in Minnesota was - 6゚ F. Which following situations could explain how the temperature became - 6゚F?
A) in the morning the temperature was -2゚then the temperature fell 4゚
B) the temperature was 12゚ this temperature fell by 6 ゚as it got dark out
C) the temperature decreased by 4゚ from a high of 2゚earlier in the day
D) at 9 a.m the temperature was - 11゚ by noon the temperature had dropped 5゚
The temperature on a cold winter day in Minnesota was - 6゚ F. the temperature decreased by 4゚ from a high of 2゚ earlier in the day situations could explain how the temperature became - 6゚F.
A physical number known as temperature expresses the concepts of hotness and coolness in numerical form. With a thermometer, temperature is measured. Thermometers are calibrated using a number of temperature scales that have defined distinct reference points and thermometric substances. The most widely used scales are the Kelvin scale (K), which is mostly used for scientific reasons, the Fahrenheit scale (°F), and the Celsius scale (°C), formerly known as centigrade, with the unit symbol °C. In the International System of Units, one of the seven base units is the kelvin (SI).The temperature was -6゚ F. This means that the temperature must have decreased from a higher temperature to reach - 6゚F. This can be explained by option C, the temperature decreased by 4゚ from a high of 2゚ earlier in the day.
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diseases tend to spread according to the exponential growth model. in the early days of aids, the growth factor (i.e. common ratio; growth multiplier) was around 2.1. in 1983, about 1700 people in the u.s. died of aids. if the trend had continued unchecked, how many people would have died from aids in 2006? people
Approximately 1700 Americans died of AIDS in 1983. In 2006, 14,260,633,600 individuals would have perished from AIDS if the trend had remained unchecked.
When a population's per capita growth rate remains constant, regardless of population size, exponential growth occurs, causing the population to grow exponentially as the population increases.
When people in a population reproduce at a certain pace, exponential growth results. After a time of exponential expansion, a population's growth slows or pauses, which is known as logistic growth.
Exponential growth model Growth factor = 2
model y = a(2)^t
a = initial
y = final
Let 1983 as t=0
y = 1700 × (2)^t
In 2006
t = 2006 - 1983
= 23
y = 1700 × (2)^23
= 1700 × (8388608)
= 14,260,633,600 people would have died
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Jim ordered a sports drink
and three slices of pizza for
$8.50. His friend ordered two
sports drinks and two slices
of pizza for $8.00
Answer:$ 16.50
Step-by-step explanation:If you are adding, you do
$8.50+
8.00
------------
16.50
0 plus 0 is nothing.
5 plus 0 is 5.
8 plus 8 is 16.
Your answer is now "16.50" .
Scores on a certain standardized test have a mean of 500, and a standard deviation of 100. How common is a score between 600 and 700? calculate the probability.
the probability is 68‰
For the normal distribution,
The scores on standardized admissions tests are normally distributed with a mean of 500
Mean (μ)=500
standard deviation(σ)=100
The probability that scores lies between 400 and 600 i.e, P(400
For the standard normal distribution curve
Z=(x-μ)/σ
(400-500)/100<(x-μ)/σ<(600-500)/100
-1
For standard normal distribution mean shifted to zero, P(x)dx=1/(sqrt(2pi))e^(-z^2/2)dz.
so the probability would be 68‰
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What is the speed of 150 km in five hours?
The speed of 150 kilometres in five hours is 30 kilometres per hour.
The speed is calculated by the formula -
Speed = total distance covered ÷ total time taken
The distance covered is 150 kilometres and time taken is five hours.
Keep the values in formula to find the speed -
Speed = 150/5
Performing division on Right Hand Side of the equation to find the speed
Speed = 30 kilometres per hour
Hence, the speed of mentioned data covering the distance 150 kilometres in time duration of five hours is 30 kilometres per hour.
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HOW THE HECK AM I SUPPOSED TO USE X AND Y ON A COORDINATE GRID THAT HAS THE PROPORTIONS OF M=24R
Answer:
To use coordinates on a coordinate grid, you first need to determine the scale of the grid, which is represented by the proportion M=24R. This means that for every 24 units on the grid, the corresponding real-world distance is equal to R units.
Once you have determined the scale of the grid, you can use the coordinates to locate points on the grid. To do this, you will need to know the coordinates of at least one point on the grid, which is known as the origin. The origin is typically represented by the coordinates (0,0).
To find the coordinates of a point on the grid, you can use the following steps:
Locate the point on the grid that you want to find the coordinates for.Measure the distance from the point to the origin, using the grid scale as a guide. This distance is the point's x-coordinate.Measure the distance from the point to the y-axis, using the grid scale as a guide. This distance is the point's y-coordinate.The coordinates of the point will be a pair of numbers in the form (x, y), where x is the point's x-coordinate and y is the point's y-coordinate.
For example, if you wanted to find the coordinates of a point that is 5 units to the right of the origin and 3 units above the y-axis, the coordinates of the point would be (5, 3).
Slope is 1/4 and the y-intercept is 3
Answer:
y=14x−3 .
Step-by-step explanation:
We know that the equation of a line is y=mx+b with m being the slope and b being the y-intercept. We can plug in your slope ( 14 ) and your y-intercept ( −3 ). This simplifies to y=14x−3 .
Find C. Round to the nearest tenth: 18ft, 20ft, and 22ft
The value of C to the nearest tenth, is 70.5.
What is the Law of Cosines?A planar triangle's side's square is equal to the sum of the squares of the other sides minus the product of those sides and the cosine of the angle between them, divided by two.
We have the triangle ABC.
Where c = 22ft, a = 18ft and b = 20ft
Law of Cosines:
c² = a² + b² - 2ab cosC
Substituting the value of a, b and c to the above equation.
22² = 18² + 20² - 2(18)(20) x cosC
484 = 724 - 720 x cosC
Rearranging
-240 = -720 x cosC
Divide both sides by
-7200.3333333333 = cosC
To find the value of C:
C = Arc cos 0.3333333333
Now the value of arc cos from the trigonometric table,
C = 70.52877936753502
Therefore, the C = 70.5 rounded to the nearest tenth.
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Please help!!!!
In the figure, ∆BAT ≅ ∆CAT. Which statement is not true by CPCTC?
∠BCA ≅ ∠BCT
∠ABT ≅ ∠ACT
TB ≅ TC
TA ≅ AT
Based on the CPCTC, the statement that is not true is: A. ∠BCA ≅ ∠BCT.
What is the CPCTC?CPCTC stands for "corresponding parts of congruent triangles are congruent". This simply means that if two triangles are congruent to each other, every of its corresponding angles and corresponding sides are equal or congruent to each other.
In the image given, we are told that ∆BAT ≅ ∆CAT. Thus, this implies that all the corresponding angles are congruent to each other, so also are all their corresponding sides.
Therefore:
∠ABT ≅ ∠ACT∠ATB ≅ ∠ATC∠TAB ≅ ∠TACTA ≅ ATAB ≅ ACBT ≅ CTTherefore, the statement that is not true is:
A. ∠BCA ≅ ∠BCT
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Which theorem proves that the triangles are congruent a asab Sasc SSAD SSS?
The theorem that proves that the triangles are congruent is the Side-Side-Side (SSS) Congruence Theorem.
The Side-Side-Side (SSS) Congruence Theorem states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. This theorem is useful for proving that two triangles are congruent without having to use angles. The SSS Congruence Theorem is a useful tool for solving geometry problems involving triangles. It can be used to find the unknown side length of a triangle given the lengths of the other two sides, or in more complicated proofs involving multiple triangles. This theorem is also helpful in determining the area of a triangle, as the area is proportional to the product of the lengths of the sides.
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