Rectangle P Q R S has P Q=3 and Q R=4. Points T and V are on side P S such that P T=U S=1
Determine the measure of angle T Q U in degrees and rounded to 1 decimal place
Answers
The measure of angle TQU is 41.1°
What is angle of measure?
The measure of the angle is formed by the two lines or arms having a same vertex.
Solution:
We know that,
PQ² + PT² = QT² -------- By Pythagoras theorem
∴QT = √10
∵ PT + TU + US = 4
∴ TU = 4 - PT - US
TU = 4 - 1 - 1
∴TU = 2
Now, using Pythagoras theorem in triangle PQU
PQ² + PU² = QU²
∴ QU =√ 3² + 3² (∵PU = PT + TU = 1 + 2)
∴ QU = 3
Now using Heron's formula in triangle TQU
Semi-perimeter = (2 + √10 + 3)/2
= 4.08
Area of the triangle = [tex]\sqrt{S(S-TQ)((S-TU)(S-QU)}[/tex]
= [tex]\sqrt{4.08(0.92)(2.08)(1.08)}[/tex]
= 2.903 unit²
Now, we know that
Area of a scalene triangle = ab/2 × sin c
∴ 2.903 = (√10×3/)2 × sin T
∴ sin T = 2.903×2/3√10
sin T = 0.61
∴ ∠T = [tex]sin^{-1}[/tex](0.61)
∴∠T = 93.9°
Using sum of interior angles of a triangle = 180 i.e. (a + b + c =180°)
∠U + ∠T + ∠Q = 180°
∴ ∠Q = 180 - 93.9 - 45
∴∠Q = 41.1°
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The measure of angle TQU is 41.1°
What is angle of measure?
The measure of the angle is formed by the two lines or arms having a same vertex.
We know that,
PQ² + PT² = QT² -------- By Pythagoras theorem
∴QT = √10
∵ PT + TU + US = 4
∴ TU = 4 - PT - US
TU = 4 - 1 - 1
∴TU = 2
Now, using Pythagoras theorem in triangle PQU
PQ² + PU² = QU²
∴ QU =√ 3² + 3² (∵PU = PT + TU = 1 + 2)
∴ QU = 3
Now using Heron's formula in triangle TQU
Semi-perimeter = (2 + √10 + 3)/2
= 4.08
Area of the triangle = 2.903 unit²
Now, we know that
Area of a scalene triangle = ab/2 × sin c
∴ 2.903 = (√10×3/)2 × sin T
∴ sin T = 2.903×2/3√10
sin T = 0.61
∴ ∠T = (0.61)
∴∠T = 93.9°
Using sum of interior angles of a triangle = 180 i.e. (a + b + c =180°)
∠U + ∠T + ∠Q = 180°
∴ ∠Q = 180 - 93.9 - 45
∴∠Q = 41.1°
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Related Questions
Owen paid a landscaping company $108 for an initial lawn treatment,
then $74 per month thereafter.
The function p(t) = 108 + 74t represents the total amount of money he will
have paid after t months.
Find p(12).
Answers
The value of p(12) is $996
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
"Find p(24)" also means "Find the amount of money Owen pays for lawn service after 12 months" as we're given 12 for t. As such, rewrite the given function as p(12) = 108 + 74(12)
p(12) = 108 + 74(12)
p(12) = 108 + 888
p(12) = $996
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An international company has 11,400 employees in one country if this represents 18.6% how many employees does it have in total?
Answers
Answer: about 61290 employees total
Step-by-step explanation:
18.6% is equal to 11400 employees in one country
18.6% of X = 11400
x=11400/0.186
x=61290
Note that the answer is rounded
The data set of the diameters of the metal cylinders manufactured an automatic machine has sample size of n = 25, mean of x = 49.98 mm and std. of S = 0.14 mm. Expected diameter of metal cylinder is mu = 50.00 mm. Can we be 95% confident that machine calibrated properly? {Solution Tips: Yes; if 95% confidence interval includes expected diameter of metal cylinder.}
Answers
95% confidence that machine calibrated properly is (48.536, 51.424).
We have given that,
n = 25
mean of x = 49.98 mm
S = 0.14 mm
μ = 50.00 mm
and CI = 95%
from t-table we know that,
t at 95% and n - 1 = 25 - 1 = 24 is 2.064
Therefore 95% of CI means that
(x - 2.064 × S√n, x + 2.064 × S√n)
(49.98 - 2.064 × 0.14√25, 49.98 + 2.064 × 0.14√25)
(49.98 - 2.064 × 0.7, 49.98 + 2.064 × 0.7)
(49.98 - 1.444 , 49.98 + 1.444)
(48.536, 51.424)
Therefore 95% confidence that machine calibrated properly is
(48.536, 51.424).
The 95% confidence interval is a range of values that you can be 95% confident contains the true mean of the population.
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Find the sum
5. 1/4+ 1/28+ 1/70+ ,.....
Answers
The sum is 9/28
What is sum ?
The outcome of adding numbers or quantities mathematically is a summation, often known as a sum. A summation always has an even number of terms in it. There may be just two terms, or there may be 100, 1000, or even a million.
The end result of addition is a sum. For instance, the sum 10, written, is obtained by adding 1, 2, 3, and 4. (1) The sum of the numbers is known as the sum of the addends, or summands occasionally.
1/4 + 1/28 + 1/70 + 1/30 + ............ 1/700
Multiply and divide by 3 in whole series
⇒ 1/3 X [3/4 + 3/28 + 3/70 + 3/130 + ......... 3/700]
⇒1/3 X [1-1/4+1/4-1/7+1/7-1/10+1/10-1/13+..........1/25-1/28]
⇒1/3 x [1 - 1/28]
⇒1/3 * 27/28
⇒ 9 / 28
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Rewrite the following scientific notation numbers into standard form. (Be sure to use commas)
a. 3.23x10 -3
b. 7.45x10 5 =
Answers
Answer:
a. 0.00,323
b. 745,000
Step-by-step explanation:
a) move the decimal 3 places to the left
b) move the decimal 5 places to the right.
help meeeeeeeeeee pleaseee
Answers
For an average intake of 2200 calories per day, the number of acres of land is approximately 2.
How to solve equations?If we are given all a function so in that case, we just need to substitute values given in question and solve for unknown variable that is to be determined.
C(x) is a variable that tells the number of calories consumed daily by a person
x is the number of acres that person own.
C(x) = 270㏑(x+1) +1900
In the given question number of acres ask a person to have who consumed 2200 calories in a day.
Therefore,
C(x)=2200
2200=270㏑(x+1) +1900
2200-1900=270㏑(x+1)
300=270㏑(x+1)
300/270 = ㏑(x+1)
10/9 = ㏑ (x+1)
x+1 = [tex]e^{\frac{10}{9} }[/tex]
x+1 = 3.037
x= 3.037-1
x=2.037
x=2(round off)
Therefore, 2 acres of land a person can consume 2200 calories in a day.
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The local weather forecast has been accurate for 25 of the past 37 days. Based on this fact, what is the relative frequency probability that the
forecast for tomorrow will be accurate?
Answers
The relative frequency probability that the forecast for tomorrow will be accurate = 16/33.
What is probability?
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means.P(A) = Number of accurate days/ Total number of days
Here, the number of accurate days is 25 and total number of days is 37.
Substitute the above values as follows:
P(A) = 25/37
Hence, the relative frequency probability that the forecast for tomorrow will be accurate = 16/33.
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If a polynomial function has integer coefficients, then every rational zero of the function has the form p/q, where p is a factor of the ? and q is a factor of the ?
Answers
If a polynomial function has integer coefficients, the every rational zero of the function has the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
The rational zero theorem says that if a polynomial has integer coefficients then any rational zeros must be of the form p/q where p is the factor of the constant term and q is the factor pf the leading coefficients.
The rational zero theorem is used to determine the rational roots of a polynomial function.
Rational Zero Theorem statement:-
The rational zero theorem states that each rational zero(s) of a polynomial wit integer coefficients
f(x) = anxⁿ + an-1xⁿ⁻¹ + ... + a₂x² + a₁x + a₀ is of the form p/q where,
p is a factor of the constant a₀,
q is a factor of the leading coefficient an,
and p and q are relatively prime.
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b) The price of a house increases exponentially over time. A house presently costs $400,000, and it future
value can be modeled by the equation: A = 400,000 (1.04)*, where A is the value of the home after x years.
i) What percent is the house's value going up each year?
ii) What is the value of the home in 15 years?
ii) Assuming the trend continues, when will the value of the home double?
+4
Answers
Answer: The percent that the house's value is going up each year is given by the factor 1.04 - 1, which is 0.04. This represents a 4% increase in the value of the house each year.
ii) To find the value of the home in 15 years, you can substitute x = 15 into the equation to get:
A = 400,000 (1.04)^15
= 400,000 (1.7589)
= 700,356
Therefore, the value of the home in 15 years is $700,356.
iii) To find when the value of the home will double, you can set the value of A equal to 2*400,000 and solve for x:
2*400,000 = 400,000 (1.04)^x
2 = (1.04)^x
x = log(2)/log(1.04)
= 10.67
Therefore, it will take approximately 10.67 years for the value of the home to double, assuming the trend continues.
pls help immediately
Answers
The simplified form of [tex]\sqrt{(2 - \sqrt5)^2} + \sqrt{(2 + \sqrt{5})^2}[/tex] is [tex]\sqrt{9 - 4\sqrt{5}} + \sqrt{9 + 4\sqrt{5}[/tex].
What are surds and indices?We know there are two types of radicals one is surds when the number has been raised by such power that it is greater than zero and less than one,
The other type of radicals are indices where a number is raised to such power that is greater than one.
Given, [tex]\sqrt{(2 - \sqrt5)^2} + \sqrt{(2 + \sqrt{5})^2}[/tex].
= [tex]\sqrt{4 - 4\sqrt{5} + 5}+ \sqrt{4 + 4\sqrt{5} + 5}[/tex].
= [tex]\sqrt{9 - 4\sqrt{5}} + \sqrt{9 + 4\sqrt{5}[/tex].
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what is 2×1+2×
1/
10
+1×
1/
100
+3×
1/
1000
Answers
Answer:
2.213
2×1+2(1÷10)+1(1÷100)+3(1÷1000)
2×1+2×0.1+0.01+3×0.001
2+0.2+0.01+0.003
2.213 #
hope this will help ig
Answer:
2.213
Step-by-step explanation:
2×1+2(1÷10)+1(1÷100)+3(1÷1000)
2×1+2×0.1+0.01+3×0.001
2+0.2+0.01+0.003
2.213
Given the function p(t) in the graph below, identify the intervals over which the function appears to be decreasing.
Answers
The interval of the domain where the function is decreasing are (0, 1) and (3, 4)
How to determine the increasing interval?From the question, we have the graph that represents the given parameters that can be used in our computation
To determine the decreasing interval on the graph, we look for the points where
As the values on the x-axis increaseThe values on the y-axis decreaseThe intervals that represent the above highlights are
From x = 0 to x = 1From x = 3 to x = 4This can be represented as (0, 1) and (3, 4)
Hence, the intervals are (0, 1) and (3, 4)
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Suppose Colleen works two jobs. At job A, Colleen’s monthly earnings can be described by the distribution N(2100, 200) and at job B, her monthly earnings can be described by the distribution N(550, 70). Assuming that her earnings are independent,
1) What is the mean and standard deviation of the TOTAL amount of money she earns in a month? (this will use knowledge from prior units)
2) What is the probability that she earns more than $2750 in a given month?
Answers
1) The mean and the standard deviation of the total amount of money that she earns in a month are of:
Mean: 2650.Standard deviation: 211.9.2) The probability that she earns more than $2750 in a given month is of: 0.3192 = 31.92%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.When two variables are added, the mean is given by the sum of the means, hence:
[tex]\mu = 2100 + 550 = 2650[/tex]
The standard deviation is given by the square root of the sum of the variances, hence:
[tex]\sigma = \sqrt{200^2 + 70^2} = 211.9[/tex]
The probability that she earns more than $2750 in a given month is one subtracted by the p-value of Z = 2750, hence:
Z = (2750 - 2650)/211.9
Z = 0.47
Z = 0.47 has a p-value of 0.6808.
1 - 0.6808 = 0.3192 = 31.92%.
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A 224-inch is cut into two pieces. One piece is three times the length of the other. Find the length of the shorter piece.
Answers
A 60-inch piece is the shorter one. 180 inches long is the longer piece.
Step-by-step explanation:
Let's use the variables L and S to symbolise the longer and shorter pieces of pipe, respectively.Since the pipe will be the sum of L and S, we can create the following equation:L + S = 240
Additionally, we are aware that the longer piece is tri-times the shorter piece, which means:L = 3 S
Replace the first equation with the second equation:L + S = 240 ( 3 S ) + S = 240 \s 4 S = 240 \s S = 60
A 60-inch piece is the shorter one.Replace the following with the lengthier piece's length:L = 3 S L = 3 ( 60 )
L =180
180 inches long is the lengthier piece.Let's give the shorter piece a value.The length is "X." The other piece is three times as big, or three times.When you add them up, you get 4X.To learn more about the lengths of the pieces refer to:
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An international company has 13,500 employees in one country. If this represents 19.6% of the company's employees, how many employees does it have in total?
Round your answer to the nearest whole number.
Answers
The required number of employees does it have in total is 68877.
What is percentage?A percentage is a part of an entire communicated as a number somewhere in the range of 0 and 100 as opposed to as a small portion. Something is all 100%, a big part of it is 50%, none of something is zero percent. To decide a rate, you partition the piece of the entire by the actual entire and duplicate by 100.
According to question:Let total population of the company be X
So,
19.6% of x = 13500
x(19.6/100) = 13500
X = 13500×100/19.6 = 68877 employees
Thus, required number of employees is 68877.
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Bobby and Garnetta thought of four consecutive odd intergers such as five times the sum of the first and the third was 22 greater than the product of 8 and the sum of the second and the fourth. Find the numbers.
Answers
An integer is a whole number x=-11.
What are Integers?The Latin term "Integer," which implies whole or intact, is the source of the English word "integer." A particular category of numbers called integers includes zero, positive numbers, and negative numbers.SymbolThe symbol "Z" stands for an integer.
Z= {……-8,-7,-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8,……}
Example :Let the numbers be x, x + 2, x + 4, x + 6...
5(x+x+4)=8(x+2+x+6)+22
5(2x+4)=8(2x+8)+22
10x+20=16x+64+22
The integers are -11,-9,-7,-5,
10x-16x=64+22-20 -6x=66/-6
x=-11.
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In a recent international sport competition, the top three
countries--Country A, Country B, and Country C-won a total of
129 medals. Country B won 9 more medals than Country C.
Country A won 39 more medals than the total amount won by the
other two. How many medals did each of the top three countries
win?
Answers
The Medals are as follows:
A = 84 medalsB = 27 medalsC = 18 medalsWhat is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
A + B + C = 119
Country B won 9 more than Country C so:
B = C + 9
Also, Country A won 39 more than the other two combined so:
A = B + C + 39
= (C + 9) + C + 39
= 2C + 48
Now we substitute into the equation:
A + B + C = 129
(2C + 48) + (C + 9) + C = 129
4C + 57 = 129
4C = 72
C = 18
So, if B = C + 9 then B = 27
and, A = 2C + 48 = 36+ 48 = 84
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{ (0,5), (9,2), (7,1), (6,3)}, What is the sum of all the elements in the range?
Answers
Answer:
11
Step-by-step explanation:
The range is the set of outputs, or the second element in each ordered pair.
The sum of these values is [tex]5+2+1+3=11[/tex].
how do i find x? please help me, I tried everything :(
Answers
We are given an isosceles triangle because two sides are marked congruent, and therefore, the base angles opposite those sides are congruent. First we need to calculate the angles of the triangle using the Isosceles Triangle Theorem.
We are given a 110° angle with a ray that forms a straight line. Straight lines measure 180° by definition. So, we can calculate the vertex angle in the triangle by creating this equation:
110+x=180
110 degrees plus x creates a 180 degree line. Now, solve for x:
x=70
We have our first angle in the triangle, and we know a triangle must sum up to 180°. We also know the triangle is isosceles, and so the two base angles are congruent. We can create another equation to find all angles in the triangle:
70+2x=180
Remember, we have one angle and because the two base angles are congruent, we can denote them with the same variable and multiply by 2 because the angles will add to each other twice. Solve for x:
2x=110
x=55
So, we now have all there angles and can solve for “x.” Like we did before, a straight line forms one of the rays of the angle. So, we can create the equation:
55+x=180
55° plus x° sums up to 180. Now, solve for “x:”
x=125
The four models each show two parallel lines cut by a transversal and some angle measures formed by the
intersection of the lines.
What are the values of angle measures a and b in model 4?
Move the correct answer to each box. Each answer may be used more than once. Not all answers will be used.
19° 71° 90° 109° 180° 119°
The value of a is _____, and the value of b is _____.
Answers
The value of a is 71°, and the value of b is 109°.
What is a parallel line?A parallel lines is defined as those type of line that are equidistant to each other which are on the same plane and they doesn't meet each other till infinity.
When two parallel lines are being intersected by another line called the transverse line, the following relationship is bound to occur such as;
Corresponding angles, Alternate Interior Angles, Alternate Interior Angles, Alternate Exterior Angles and Consecutive Interior Angles.From model 4, the pair of alternate exterior angles are equal in measure. That is 71° = angle opposite b°.
That is 180 - 71 = 109°
Also in model 4, the pair of alternate interior angles are equal in measure. a = 71°.
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one number is six less than a second number. Four times the first is 2 more than 6 times the second. Finde the numbers
Answers
The numbers are -19 and -13 by the given conditions.
How to solve word problems?
It's actually fairly easy to solve word problems using a tried-and-true step-by-step approach. Aloud to yourself, read the issue.
Make a Drawing.Consider: "What am I trying to find?”List the items that have been provided.Locate the key phrases.Solve.Verify your work.Let the two numbers be x and y
One number is six less than a second number: x = y - 6 ⇒ i
Four times the first is 2 more than 6 times the second: 4x = 6y + 2 ⇒ ii
Substitute the value of x in (ii)
4(y-6) = 6y + 2
4y - 24 = 6y + 2
2y = -26
y = -13
Now substitute the value of y in (i);
x = -13 - 6
x = -19
Hence, the numbers are -19 and -13 by the given conditions.
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Write answer using listing method
Answers
Using listing method the elements in the set are +2 and -2.
What is listing method ?
The listing approach involves writing the members of the set as a list, with commas separating the items and curly brackets enclosing the list. The rule or condition that may be used to determine if an object can belong to the set is specified when using the rule method for sets.
The members of a set are listed using this technique, with commas used to separate them and curly braces used to enclose the list. The four distinct seasons, for instance, can all be written as "Summer, Autumn, Spring, and Winter." The list's elements can be in any order, so don't worry.
We are given the set [tex]\left\{x \mid x^2=4\right\}[/tex]
all such x such that the perfect square is 4. Now, we have
[tex]$x^2=4 \Rightarrow x=\pm 2$[/tex]
Therefore, the elements in the set are +2 and -2.
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19. The amount of money in a savings account increases from $ 250 to $ 270 in one month. If the percent increase is the same for every month, how much money will be in the account at the end of the next month?
(A) $ 291.60
(B) $ 295
(C) $ 289.60
(D) $ 300
Answers
Answer:
the answer will be the options A
Will give brainliest!!!
What is the value of x?
Use the provided picture
Answers
Answer: C
Step-by-step explanation:
pythagorean theorem : a^2 + b^2 = c^2
8^2 + 8^2 = x^2
64 + 64 = x^2
128 = x^2
x = sqrt(128) square root both sides
x = 8sqrt(2) simplified
Answer: c, [tex]8\sqrt{2}[/tex]
Step-by-step explanation:
Since this is a right triangle, we will use the Pythagorean theorem to help us solve for x.
Theorem:
a² + b² = c²
Substitue values:
8² + 8² = c²
To the power of 2:
64 + 64 = c²
Addition:
128 = c²
Square root both sides of the equation:
[tex]\sqrt{128}[/tex] = c
Reflexive property and breaking up 128 into two factors:
c = [tex]\sqrt{64*2}[/tex]
Square root of 64:
c = 8[tex]\sqrt{2}[/tex]
So, x = 8[tex]\sqrt{2}[/tex]
A retirement account is opened with an initial deposit of $6,500 and earns 9.11% interest compounded monthly. What will the account be worth in 45 years?
Answers
Answer: $385,993.09
Step-by-step explanation:
Initial Amount: 6500
Rate: 0.0911 comp. monthly
Time: 45 years
Answer: 385,993.09
A substance grows exponentially, and its weight doubles every 3 hours. Suppose it weighs 2 pounds at noon. After how many hours will it weigh 9 pounds? (Do not simplify result)
Answers
The substance will weigh 9 pounds after 4.5123 hours.
Here it is given that every 3 hours the weight of the substance doubles.
At 12 noon it weighed 2 pounds. Hence we will consider the initial weight to be 2.
Let the weight after x hours be w(x)
Here it doubles in 3 hours, hence the growth rate is 100%
Since the growth rate is given, the equation for the growth rate will be
w(x) = w₀.eˣ
where x = no. of 3-hour spans.
Here
w₀ = 2
and w(x) is given 9
Hence,
2eˣ = 9
or, e²ˣ = 9/2
Taking log on both sides we get
loge²ˣ = ln(9/2)
or, 2xloge = ln(9/2)
Since loge = 1 we get
2x = log(9/2)
or, x = 1.5041
Hence they will become 9 pounds after
3 X 1.5041 hours
= 4.5123 hours
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Which equation is equivalent to the given equation?
x² - 6x = 8
Answers
Answer:
(x-3)^2=17
Step-by-step explanation:
i took dis test b4
Find the value of x.
Answers
The triangles are similar triangles. Then the value of the variable 'x' will be 6.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
Similar triangles are shown below.
We know that the ratio of the corresponding sides of similar triangles remains constant. Then the equation is given as,
(6x - 1) / 15 = 14 / 6
Simplify the equation, then we have
(6x - 1) / 15 = 14 / 6
(6x - 1) / 5 = 7
6x - 1 = 35
6x = 36
x = 6
The triangles are comparable triangles. Then, at that point, the worth of the variable 'x' will be 6.
More about the triangle link is given below.
https://brainly.com/question/25813512
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6) Tyger and Newton have a long jump
competition. Tyger jumps 20% further than
Newton. If Newton jumps 475 cm, how far
does Tyger jump?
★need help solving this problem
Answers
475 times 1.20 equals 570
ANS: Tyger jumps 570 cm
Which type of information could best be displayed on a two-way frequency table? Select all that apply.
A the number of library books, by genre, borrowed by children and adults during the summer
B the amount of rainfall each week during a year
c the number of daylight hours each day for a month
D the number and type of meals students choose in a lunchroom
Answers
Answer: B C and D
Step-by-step explanation: