Answers
We need to use the concept of Pythagorean theorem. The value of x in the given triangle is 16.
What is Pythagorean theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this rule, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse, or the side across from the right angle. This theorem can be expressed as the Pythagorean equation, which is an equation connecting the lengths of the sides a, b, and the hypotenuse c: [1]
a^{2}+b^{2}=c^{2},
CalculationSo mark the given triangle as ABC in which B is right angled.
AC=24+x
Mark the height of the given triangle as BD and BD=14.
Now using pythagoras theorem,
(BC)2=(CD)2 + (BD)2
⇒(BC)2=(24)2 + (14)2
∴(BC)2=772
Now after finding BC we need to find AB using pythagoras theorem.
(AD)2 +(BD)2 =(AB)2
⇒(x)2 + (14)2 =(AB)2 - eq1
⇒ (AB)2 + (BC)2 = (24+x)2 - eq2
Substitute eq1 in eq2
⇒(x)2 + (14)2 + (BC)2 =(24+x)2
⇒(x)2 + 576 +772 = 576 + (x)2 + 48x
⇒772=48x
∴x=16.0833
x≈16.
We need to use the concept of Pythagorean theorem. The value of x in the given triangle is 16.
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Related Questions
Is all squares are not parallelogram True or false?
Answers
all squares are parallelogram but all parallelogram are not squares
a chi-square test of independence is used to evaluate the relationship between two variables. if one variable is classified into 3 categories and the other variable is classified into 3 categories, what is the df for the chi-square statistic?
Answers
The df would equal in the chi-square statistic for this test is found as 4.
Define the term chi-square statistic?The discrepancy between the predicted and observed frequencies of the results of a group of events as well as variables is measured by the chi-square (X²) statistic. Chi-square is helpful in examining these variations in category variables, particularly ones that are nominal in character.The formula for the chi-square (X²) statistic is;
(X²) = ∑(O - E)²/E
For the given question-
The link between two variables is being assessed using the chi-square test for independence. Three categories are assigned to the given "A." The second "B" is divided into three categories.The answer to the query is;
We would determine whether two qualities, A and B, under examination are independent or not using the chi-square test.
Taking that as a given, the null hypothesis H0: The two factors are unrelated.
Now, the degrees of freedom in the independence test using chi-square is,
v = (r-1) (s-1) (s-1).
r = 3 and s = 3.
The degree of freedom are;
ν = (r-1) (s-1) = (3-1) (3-1) = 2×4
ν = 4
Consequently, let test statistic be,
(X²) = ∑(O - E)²/E
Consequently, df would equal in the chi-square statistic for this test is found as 4.
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What is this number in standard form? (8×100)+(4×1)+(6×1/100)+(3×1/1,000)
25points
pls helpppppppppppp
Answers
Answer:
804.063 is the answer
Step-by-step explanation:
BRANLIEST
simplify the equation:
×[tex]\frac{(3xy^2)^3×(-4x^2y)}{(2x^2y^2)^2}[/tex]
by the way i dont know why the top has an A with a line on top it should be a multiplication sign; the second picture has what its supposed to like like clearly.
Answers
(3xy^2)^3×(-4x^2y)/(2x^2y^2)^2
= -108x^5y^7/4x^4y^4
= -108xy^3/4
Answer: -27xy^3
A point i reflected in the x-axi followed by the y-axi. The reflected point i (-3, "-4). " What i the original point?
Answers
When the original point is mirrored in the x-axis, it becomes (-3,4).
What is coordinate?The horizontal and vertical distances from the two reference axes are used to define the location of a point on a coordinate plane. The x-value and y-value are often denoted as (x,y). To find the coordinates of a point in a coordinate system, do the inverse. Start at the point and trace a vertical line up or down to the x-axis. There you have your x-coordinate. Then repeat the process, but this time follow a horizontal line to determine the y-coordinate.
Here,
The reflected point= (-3,-4)
A point reflected in the x-axis followed by the y-axis,
=(-3,4)
The original point is (-3,4) when point reflected in the x-axis followed by the y-axis.
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Amadou and his children went into a grocery store and he bought $9 worth of apples and bananas. Each apple costs $1 and each banana costs $0.50. He bought 4 times as many apples as bananas. By following the steps below, determine the number of apples, x, and the number of bananas, y, that Amadou bought.
Determine three ways to have 4 times as many apples as bananas
Answers
Answer:
To have 4 times as many apples as bananas, Amadou could have bought 4 apples for every 1 banana, or 8 apples for every 2 bananas, or 16 apples for every 4 bananas.
4 apples : 1 banana
8 apples : 2 bananas
16 apples : 4 bananas
We can use the fact that the total cost of the apples and bananas was $9 to determine the number of apples and bananas that Amadou bought. Since each apple costs $1, Amadou bought 9 apples if he bought no bananas, or 7 apples if he bought 2 bananas, or 5 apples if he bought 4 bananas.
9 apples : 0 bananas
7 apples : 2 bananas
5 apples : 4 bananas
Therefore, the possible combinations of apples and bananas that Amadou could have bought are 9 apples and 0 bananas, 7 apples and 2 bananas, or 5 apples and 4 bananas.
Use the graph of g(x) to complete the table.
Answers
When x=0, g(x)=-2
Remember, because the graph is in quadrant 3 of the coordinate plane, the x-values are negative, and the y-values are also negative for this graph.
write the slope-intercept form of the equation of each line give the slope and y-intercept
Answers
13) y= 3/5 x +2
14) y= x + 2
The picture below shows the Apollo spacecraft that took astronauts to the Moon in 1969. The spacecraft weighed 6.1 million pounds, and its motors produced 7.5 million pounds of thrust.
When the spacecraft returned to Earth, it slowed until a parachute could be opened for a landing at sea. Which of the following best explains how the spacecraft slowed down for a safe landing?
a
The parachute created a downward force to resist the downward force of gravity.
b
The parachute created an upward force to resist the upward force of gravity.
c
The parachute created an upward force to resist the downward force of gravity.
d
The parachute created a downward force to resist the upward force of gravity.
Answers
Since the spacecraft returned to planet Earth and slowed until a parachute could be opened for a landing at sea, a statement which best explains how the spacecraft slowed down for a safe landing is that: C. the parachute created an upward force to resist the downward force of gravity.
What is the force of gravity?In Mathematics, the force of gravity is also referred to weight and it can be defined as the force that is acting on a physical object or body, especially due to the effect of gravity.
What is Newton's Third Law of Motion?Newton's Third Law of Motion states that for every action there is an equal but opposite reaction. This ultimately implies that, in every interaction, there is a pair of forces acting on the two interacting objects such as between a spacecraft and a parachute.
In this context, we can reasonably infer and logically deduce that the parachute would create an upward force in order to resist the downward force of gravity that is acting on it, in accordance with Newton's Third Law of Motion.
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Find the Rate of Change
Answers
Answer:
c 5
Step-by-step explanation:
2=10
1=5
5+5=10
hope this helps by now
Answer:
Blue: 1/5
Step-by-step explanation:
To find the rate of change you use your slope formula which is y2-y1 over x2-x1.
You'd set your equation and you'd get 4-2 over 20-10. You solve and you get 2/10 and because it isn't one of the answer choices you have to simplify it. To simplify it you find the common number they both share and they both share 2 so you divide both by 2. 2 divided by 2 is 1 and 10 divide by 2 is 5. So then the rate of change or slope is 1/5.
NEED HELP!!! Similar triangles
Answers
Examining the triangles, the length of side QT is 2.5
What are similar triangles?This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent
Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions
The solution is worked out using sides SQ and QR, then ST and TU
(12 + QT) / 18 = 12 / 6(QT)
let QT = x
(12 + x) / 18 = 12 / 6x
cross multiplying
6x(12 + x) = 18 * 12
72x + 6x² = 216
6x² + 72x - 216
x = 2.5 OR -14.4
take the positive value x = 2.5
The length of QT is 2.5
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Which value would complete the table to make the relationhip between the two quantitie proportional?
x 1 2 3 4 5
y 26. 8 53. 6 ? 107. 2 134
Answers
The value that would complete the table to make the relationship between the two quantity proportional is 4.
what is quantity proportional?When two quantities are proportional, their relationship is constant for all values and as one quantity rises, the other rises as well.
A proportional relationship exists between two quantities if they can be written in the general form y = kx, where k is the proportionality constant. In other words, the ratio between these amounts never changes. In other words, no matter which pair of the two numbers you divide, you always obtain the same number k.
The value that would complete the table to make the relationship between the two quantity proportional is 4.
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What are vertical and adjacent angles? How do you find the measure of an unknown angle using these relationships? Give an example and show your work.
Answers
Vertical angles are two angles that are opposite each other and share a common vertex. Adjacent angles are two angles that share a common side and vertex.
To find the measure of an unknown angle using these relationships, you can use the vertical angle theorem which states that if two angles are vertical, then they have equal measure. For example, if angle A and angle B are vertical angles, then angle A = angle B.
Example:
Given: Angle A = 40°
Find the measure of angle B
Solution:
Since angle A and angle B are vertical angles, then angle A = angle B
Therefore, the measure of angle B = 40°
What is an angle?An angle is created when two straight lines or rays intersect at the same point. The point where all points converge is known as an angle's vertex. The Latin word angulus, which meaning "corner," is where the term "angle" comes from.
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A Web music store offers two versions of a popular song. The size of the standard version is 2.7 megabytes (MB). The size of the high-quality version is 4.5 MB. Yesterday, there were 1420 downloads of the song, for a total download size of 5436 MB. How many downloads of the high-quality version were there?
Answers
Answer: 890 downloads the high-quality version
Step-by-step explanation:
Let x be the number of downloads of the high-quality version
1420-x be the number of downloads of the standard version
So, we have the equation
4.5x + 2.7(1420-x) = 5436
4.5x + 3834 - 2.7x = 5436
1.8x + 3834 = 5436
Subtract 3834 on both sides
1.8x = 1602
x = 890
£5200 is invested at 2.8% compound interest per annum.
How many years will it take for the investment to exceed £7000?
Answers
It will take 11 years for the investment to exceed £7000 if £5200 is invested over a year at a compound interest rate of 2.8%.
What is meant by compound interest?The addition of interest to the principal of a loan or deposit is known as compound interest, sometimes known as interest on principal and interest. It occurs when interest is reinvested, added to the lent capital instead of being paid out, or the borrower is required to pay it, resulting in the next period's interest being generated on the principal amount plus any accumulated interest.
In contrast to simple interest, which does not compound since past interest is not added to the current period's principal, compound interest allows for the accumulation of interest from prior periods.
We solve this problem by using compound interest.
Given,
£5200 is invested over a year at a compound interest rate of 2.8%.
£7000. 1.028 = 5 200 x 5200 × 1.028¹¹ = 7045.76 2.
So, number of years=11
Therefore, It will take 11 years for the investment to exceed £7000.
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if a stratified random sampling procedure is used, give one example of an effective variable on which to stratify in this survey. explain your reasoning.
Answers
The kids' judgments of the significance of excellent nutrition in the food given may vary based on the students' ages and, consequently, on school level, making this variable an useful one to stratify the survey on.
what is random sampling?Each sample has an equal chance of being picked when using the random sampling sampling approach. It is intended that a sample picked at random will be a fair reflection of the entire population. Two different approaches to sampling exist: Random selection is a key component of probability sampling, which enables you to draw robust statistical conclusions about the entire group. Non-probability sampling incorporates non-random selection based on practicality or other factors, making it simple to gather data.
The student's degree of education is one potential stratification factor. Depending on the kids' ages and, thus, on their academic ability, the students' judgments of the significance of nutritious meals may vary. In contrast to middle school and high school pupils, elementary school children may place different values on the food that is offered.
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if the sum of tow digits is divided by the sum of the digits ,the quotientis 6 and the number is greater by 9 than the number formed by reversing the digits, find the number
Answers
if the sum of two digits is divided by the sum of the digits, the number is 80.
What are digits?Generally, Let the two digits of the number be x and y. The number can be written as 10x + y.
We are given that (x+y)/(x+y) = 6, which means that x + y = 6x + 6y.
Subtracting x + y from both sides, we get 5x = 5y. Therefore, x = y.
We are also given that the number is 9 greater than the number formed by reversing the digits, which means that 10x + y = 9 + 10y + x.
Combining like terms, we get 9x = 8y, or x = 8/9y.
Substituting this expression for x into the equation x = y, we get 8/9y = y, which means that y = 0.
Therefore, the number is 10x + y = 10 * (8/9y) + 0 = 80.
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Use the given information to write and solve a system of linear equations to find the values of x and y.
Answers
Answer:
x=5, y=2 | Equations: 4x+y=22 (or see below) and 12x-5y=50
Step-by-step explanation:
Here's my attempt:
First Equation:
Because triangles ΔSTU and ΔXYZ are congruent, then we can say that:
m∠S = m∠X
m∠T = m∠Y
m∠U = m∠Z
We know that m∠X = 130°, and that m∠X = m∠S, so m∠S = 130°
We also know that the sum of angles in a triangle = 180°
We also know the rest of the angles in ΔSTU: 28° and (4x+y)°
So, we can say that ∠S + ∠T + ∠U = 130+28+4x+y = 180 (we can remove the degree sign)
Now, you can either enter this as it is or simplify it: ❗
130+28+4x+y=180
4x+y+158=180
4x+y=22
Second Equation:
We can do the same thing as for the first equation and get the angles of ΔXYZ:
∠X = 130, ∠Y = 8x-6y, ∠Z = 4x+y
Then, add them and set it to 180:
130+8x-6y+4x+y=180
Simplify:
12x-5y+130=180
12x-5y=50
To solve for x and y:
Now, we have to solve the systems.
Let's start with the first one:
4x+y=22
Isolate y:
y=22-4x (Equation 1)
Then, we plug it into the second equation:
12x-5y=50
12x-5(22-4x)=50
12x-110+20x=50
32x=160
x=5
So we got x, but to find y, we need to plug in x into Equation 1 (where we isolated y
y=22-4x
y=22-4(5)
y=22-20
y=2
We have both our x and y values
That was my attempt, hope it helped!
Determine the equivalent system for the given system of equations.4x − 5y = 23x − y = 8a. 4x − 5y = 213x − 8y = 4b. 4x − 5y = 210x + 3y = 15c. 4x − 5y = 213x − 8y = 26d. 4x − 5y = 27x + 6y = 10
Answers
Answer:
d. 4x − 5y = 27x + 6y = 10
I hope my answer helps you.
suppose that among a population of visitors to an online shopping website, people are estimated to have an odds of 0.25 of making a purchase. what is the (estimated) probability that a randomly chosen person from this population makes a purchase?
Answers
The probability that a randomly chosen person from the given population makes a purchase is [tex]\left(\begin{array}{ccc}p\\1\end{array}\right)[/tex] *0.25.
We can calculate the probability in the following way,
Let the total population of visitors visiting to the online shopping site be P.
The estimated odds of visitors making a purchase on the online shopping website are 0.25
P(E)=0.25 and n=P
We know that the probability mass function is also known as p.m.f. of Binomial Distribution with parameters n and P.
P(X=x) = [tex]\left(\begin{array}{ccc}n\\x\end{array}\right){p^x}[/tex]* [tex](1-p)^{(1-x)}[/tex] ; 0 < p < 1 And x=0,1,2,3,...
Probability of one randomly chosen visitor making a purchase= P(x=1)
=[tex]\left(\begin{array}{ccc}p\\1\end{array}\right)[/tex] 0.25^1 * 0.75^0
=[tex]\left(\begin{array}{ccc}p\\1\end{array}\right)[/tex]*0.25
Therefore, the Probability of a random visitor making a purchase depends on the value of the population and is equal to [tex]\left(\begin{array}{ccc}p\\1\end{array}\right)[/tex] * 0.25
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which of these is the only meaningful measure of the central location for a categorical variable? a. median b. mean c. mode d. variance
Answers
Variance is the only meaningful measure of the central location for a categorical variable.
Variance is the anticipated squared variation of a random variable from its population mean or sample mean in probability theory and statistics. Variance is a measure of dispersion, or how far apart from the mean a group of data is from one another.
Descriptive statistics, statistical inference, hypothesis testing, the goodness of fit, and Monte Carlo sampling are just a few of the concepts that make use of a variance. In the sciences, where statistical data analysis is widespread, a variance is a crucial tool.
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Which system of equations can be used to determine the values of A and B?
Answers
The system of equations that should be used is the second one:
-15 = 5A
10 = -2A + B
Which system of equations can be used?Here we have the following equation:
[tex]\frac{-15x + 10}{(5x - 2)^2} = \frac{A}{5x - 2} + \frac{B}{(5x - 2)^2}[/tex]
If we multiply and divide the first therm in the right side by (5x - 2) we will get:
[tex]\frac{-15x + 10}{(5x - 2)^2} = \frac{A*(5x - 2)}{(5x - 2)^2} + \frac{B}{(5x - 2)^2}[/tex]
The numerators must be equal, then we can write:
-15x + 10 = A*(5x - 2) + B
-15x + 10 = A*5x - 2A + B
Then we can write two equations, one that has x as a factor and other that does not, these are:
-15 = 5A
10 = -2A + B
That is the system of equations.
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Answer:
B.
Step-by-step explanation:
took unit test
Identify the measure of angle EHF. Please show ur work Bc I have too !!!
Answers
Answer:
153°
Step-by-step explanation:
Angle EHG is a right angle, so it measures 90°.
The measures of angles EHF and FHG add to 90°.
m<EHF + m<FHG = 90°
m<FHG = 27°
m<EHF + 27° = 180°
m<EHF = 153°
Write a proof, that AJKN ALMN (15 points)
K
N
M
I
Answers
Find the end behavior of the function:
f(x) = 2^-xsin3x
Answers
Answer:
The end behavior of the function f(x) = 2^-xsin3x is that it approaches 0 as x approaches positive infinity and approaches infinity as x approaches negative infinity.
Step-by-step explanation:
The end behavior of a function refers to how the function behaves as the input values approach positive infinity or negative infinity.For example, consider the function f(x) = 2^-xsin3x as x approaches positive infinity and negative infinity; its behavior is that it begins to oscillate between 1, -1/2, and 0. The end behavior of the function f(x) = 2^-xsin3x is that it approaches infinity as x approaches positive infinity.The same is true for the function g(x), where the end behavior is to oscillate between 1, -1/2, and 0 with respect to negative infinity.HII EASY MATH PUZZLE
please help!
Best answer get brainliest!
give the value of
1 GREEN SACK
1 RED SACK
ELF MASK
and
CHRISTMAS LIST
Answers
Answer:
Step-by-step explanation:
you get a tutor
" BRAINLY TUTOR "
press that link
Answer:
1 Green Sack = 2
1 Red Sack = 2
1 Elf Mask = 8
1 Christmas List = 5
Step-by-step explanation:
g=Green sack
r= Red sack
e = Elf mask
c = Christmas list
6g+6r=24Divide by 6, g+r=4Assuming that each sack is equal, both sacks equal 24+4*e=36Subtract 4 from both sides, 4*e=32Divide by 4, e=816*16+2c=266256+2c=266Subtract 256 from both sides, 2c=10Divide by 2, c=55+2(8)*8=?5+16*8=?5+128=?133A bank i advertiing the following aving account
Calculate the AER on thi aving account
Answers
For an saving account in a bank, With the given value of the rate 'r' and the compounding period 'n' , The AER on the saving account is given by :
AER = [tex](1+\frac{r}{n})^{n} -1[/tex] .
What Is the Annual Equivalent Rate (AER)?The interest rate on a savings account or investment product with multiple compounding periods is known as the annual equivalent rate (AER). The next interest payment will be based on the marginally higher account amount, and AER is computed under the presumption that any interest paid is included in the balance of the principle payment.
What are Advantages and Disadvantages of the AER?The main benefit of AER is that it takes compounding effects into account, making it the real rate of interest.
Unfortunately, the AER is typically not mentioned when investors are comparing various investment possibilities. Investors are required to perform the calculations themselves.
n= compounding periods.
r= rate
Annual Equivalent Rate (AER) = [tex](1+\frac{r}{n})^{n} -1[/tex]
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Find all points of intersections of the graphs of the equation
p(x)=(2x+3)(x-5)
Answers
Answer:
The equation intersects the x or y axis a total ot three times:
(-1.5,0), (5,0), and (-15,0).
Step-by-step explanation:
I will assume that the "all points of intersection" refers to the intersection of the line with the x and y axes. One can find those points by either a mathematical or graphing approach.
1) MathematicalWe and to find all points that have a zero for either the x or y coordinate: (0,y) and (x,0)
(x,0): Solve p(x)=(2x+3)(x-5) for p(x) = 0:
0=(2x+3)(x-5)
(2x+3)=0 and (x-5)=0
(2x+3)=0
2x=-3
x= - 1.5 (-1.5,0)
and
(x-5)=0
X=5 (5,0)
The two points marking the intersection with the x axis are (-1.5,0) and (5,0).
--
(0,y): Solve p(x)=(2x+3)(x-5) for p(x) for x=0:
p(x) = (2x+3)(x-5)
p(x) = (2*0+3)(0-5)
p(x) = (3)*(-5)
p(x) = -15 (-15,0)
The equation crosses the y axis at one point: (-15,0).
2. Graphing
See the attached graph. The points of intersection can be located, as shown. They match the values obtained mathematically, but a free graphing utility (DESMOS) makes graphing a pleasant chore.
find the area of the region enclosed by the curves y = x and 4x + y2 = 12.
Answers
On integrating we will find that the area enclosed by the curves given is 64 / 3.
First we will plot a graph ,
The graph for x = y will be a straight line passing through the origin and the graph for 4x + y2 = 12 will be a parabola.
Integration of 4x + y2 = 12
= ∫4/2x² + y² dx = C
= 2x² + y² x - C
On putting the value of x and y we get ,
the area as 64 / 3.
In integration we generally add various parts to form one single object. It is a mathematical concept and comes under the branch of calculus.
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Please help!!!
Find measure QR.
Answers
Answer:
QR = 20
Step-by-step explanation:
You want the measure of side QR of isosceles triangle PQR with congruent sides PQ and QR marked 5x and 3x+8, respectively.
Congruent sidesThe sides of the isosceles triangle are congruent, so we have ...
PQ = QR
5x = 3x +8
2x = 8 . . . . . . . subtract 3x
x = 4 . . . . . . . divide by 2
QR = 3x +8 = 3(4) +8 = 20 . . . . . . find the length of QR
The measure of QR is 20 units.
__
Additional comment
You will recognize that the segment QS is both the altitude and median of the triangle. That means the triangle is isosceles, so symmetrical about QS.
If you need a formal proof, you can observe that QS is congruent to itself, so the two right triangles are congruent by LL (or SAS).