The difference between the greatest distance ridden and the least distance ridden is 4 / 5 miles .
How to find the difference ?The difference between the distance that was greatest ridden by the children on their unicycles and the least distance can be found by the formula :
= Greatest distance ridden - Least distance ridden
Greatest distance ridden = 1 mile
Least distance ridden = 1 / 5 miles
The difference is :
= 1 - 1 / 5
= 4 / 5 miles
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The question is:
What is the difference between the greatest distance ridden and the least distance ridden?
prove Sec(180/4 + A/2) sec( 180/4 + A/2)= 2secA
Answer: Sec(180/4 + A/2) sec( 180/4 + A/2)= 2secA
Step-by-step explanation:
LHS = sec(π/4 +A/2)sec(π/4 - A/2)
1/cos(π/4+A/2)cos(π/4+A/2)
multiply and divide by 2
2/cos(2π/4) + cosA
we know that
2cosAcosB = cos(A+B) + cos(A-B)
2/cos(π/2) + cosA
2/0+cosA
2/cosA
2secA
So the final answer is 2secA
hence LHS = RHS
Write a regular expression for each of the following sets of binary strings. Use only the basic operations.
all binary strings except empty string
begins with 1 and ends with a 1
ends with 00
contains at least three 1s
Regular expressions for the given sets of binary strings: 1. All binary strings except empty string: `1+0*` 2. Begins with 1 and ends with 1: `1(0|1)*1` 3. Ends with 00: `(0|1)*(00)` 4. Contains at least three 1s: `(0*10*){3,}`
The regular expressions for the given sets of binary strings are as follows:
1. All binary strings except the empty string:
- Regular expression: `1+0*`
- Explanation: The regular expression `1+0*` matches any binary string that starts with one or more 1s, followed by zero or more 0s. This ensures that the empty string is not included.
2. Binary strings that begin with 1 and end with a 1:
- Regular expression: `1(0|1)*1`
- Explanation: The regular expression `1(0|1)*1` matches any binary string that starts with 1, followed by zero or more occurrences of either 0 or 1, and ends with 1.
3. Binary strings that end with 00:
- Regular expression: `(0|1)*(00)`
- Explanation: The regular expression `(0|1)*(00)` matches any binary string that contains zero or more occurrences of either 0 or 1, followed by 00 at the end.
4. Binary strings that contain at least three 1s:
- Regular expression: `(0*10*){3,}`
- Explanation: The regular expression `(0*10*){3,}` matches any binary string that contains three or more occurrences of the pattern 0*10*, where 0* matches zero or more 0s and 1 matches a single 1.
These regular expressions provide a clear and concise way to match the specified sets of binary strings using basic operations such as concatenation, alternation, and repetition. It's important to note that there may be other valid regular expressions that can also match the given sets of strings.
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Four students are asked to solve the equation 3/4
x + 7 = x + 4. The table shows the
responses.
Student
Byron
Emmy
Kora
Salvador
Response
x = 12
x = 16
x = -12
x = -9
Which student finds the solution correctly?
O Byron
O Emmy
O Kora
O Salvador
Answer:
Byron, x = 12
Step-by-step explanation:
Because for x = 12 LHS and RHS of the given equation produces equal values.
LHS = 3/4 x +7 = 3/4*12 + 7 = 9 + 7 = 16
RHS = x + 4 = 12 + 4 = 16
LHS = RHS
motorcyclist has an acceleration of 5 mi/hr if his initial velocity is 45 mi/hr what is his final velocity after 4 hours
Step-by-step explanation:
Hey there!!
Given,
acceleration (a) = 5 mi/hr^2
Initial velocity (u)= 45mi/hr
Time (t) = 4 hrs.
Now,
Final velocity (v) =?
We have,
\(a = \frac{v - u}{t} \)
Putting their values,
\(5 = \frac{v - 45}{4} \)
Simplifythem.
20 = v - 45
v = 65.
Therefore, the finalvelocity is 65mi/hr.
Hope it helps....
Answer:
65mi/hr
Step-by-step explanation:
What fraction of 40 kg is 16 kg?
Write your answer to part a as a percentage.
Answer:
I hope it helps u..........
Will give brainliest if correct.
Answer:
slope is 5, y intercept is -7
Step-by-step explanation:
In the form y=mx+c, m is the slope and c is the y-intercept.
Rearrange the formula to fit this form:
5x-y=7
-y=7-5x
y=5x-7
∴m(slope)=5
∴c(y-intercept)=-7
Allan built a doghouse and he wanted the house to have an area of 24 square feet. He also wanted the width to be 2/3 the length. What are the dimensions of the doghouse?
Answer:
Dimension of doghouse is 4ft by 6ft
Step-by-step explanation:
Here, we are interested in calculating the dimensions of the doghouse.
Let the length of the doghouse be x, this means that the width would be 2/3 of x which equals 2x/3
Now, the area of rectangle is L * B
x * 2x/3 = 24
2x^2 = 3 * 24
2x^2 = 72
diverse both sides by 2
x^2 = 36
hence x = 6ft
The width would be 2/3 * 6 = 12/3 = 4 ft
What is an example of an equivalent expression?
An equivalent expression is an expression that is equal in value to a given expression. For example, consider the following expression: 4x + 2y
An equivalent expression is an expression that represents the same value as a given expression, regardless of the specific values of any variables that appear in the expression. Equivalent expressions can be obtained by applying the rules of algebra, such as the associative, commutative, and distributive properties.
This expression is equivalent to the following expressions:
2(2x + y)
2y + 4x
(4 + 2)x + 2y
All of these expressions are equivalent because they all represent the same value, regardless of the specific values of x and y. They can all be simplified to the same expression by applying the rules of the algebra.
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An arc of a circle measures 2.4 radians. To the nearest degree, what is the measure, in degrees, of this arc
The measure of given arc of circle 2.4 radians in degrees is 137.57.
According to the given question.
Arc of a circle = 2.4 radians
We have to fin dthe arc of the circle in degrees.
As,
π radians = 180 degrees
⇒1 radians = 180/π
So, to convert the radians to degrees we have to multiply the given quantity with 180/π.
Therefore, the measure of given arc of circle 2.4 radians in degrees is given by
2.4 × 180/π
= 2.4 × 180/3.14
= 0.76 × 180
= 137.57 degrees
Hence, the measure of given arc of circle 2.4 radians in degrees is 137.57.
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ZA=
Round your answer to the nearest hundredth.
A
6
?
c
2
B
Answer:
Answer:
58.99
Step-by-step explanation:
Well to find angle A you first have to see which trig function to use.
Soh Cah Toa
In this case, you need the opposite / hypotenuse, which is sin.
6 / 7
And then you have to use the inverse sin of 6 / 7
It's 58.99728087 which can be simplified to 58.99
Find the volume of the triangular prism.
NO LINKS THEY WILL BE REPORTED
Answer:
4.5 ft³
Step-by-step explanation:
Volume = 1/2(LxWxH)
1/2( 1.5 x 2) * 3 = 1.5 x 3 = 4.5 ft ³
If my answer is incorrect, pls correct me!
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if people are riding the coaster, and their total weight is pounds, what is their average weight?
The average weight of the 60 riders on the rollercoaster is 180 pounds.
To find the average weight of the 60 riders on the rollercoaster, we can divide the total weight by the number of riders.
Given:
Total weight of the riders = 12,000 pounds
Now, let's determine the average weight.
To calculate the average weight, we need to know the distribution of men and women among the riders. Let's assume that the ratio of men to women is equal.
The average weight of adult U.S men is 192 pounds, and the average weight of adult U.S women is 168 pounds. Since the ratio is equal, we can take the average of these two values:
Average weight = (192 + 168) / 2
= 360 / 2
= 180 pounds
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Complete question is:
A rollercoaster is being designed that will accommodate 60 riders. the maximum weight the coaster can hold safely is 12,000 pounds. according to the national health statistics reports, the weight of adult U.S men have mean 192 pounds and standard deviation 66 pounds, and the weights of adult U.S women have mean 168 pounds and standard deviation 75 pounds. if 60 people are riding the coaster, and their total weight is 12,000 pounds, what is their average weight?
Write an equation of a line that has a slope of 1/2 and has a point at (2, 5).
Economic growth typically results in rising standards of living and prosperity. However, it also invites negative externalities such as environmental degradation due to over- exploiting of natural resources. As such, the world is confronted with the dilemma of growth versus environmental sustainability. Developing a model explaining the disparity of economic development concentrating on drivers such as tourism sustainability, technological innovation and the quality of leadership would be important not only to facilitate future economic growth in developing countries, but also to the environmental and sociocultural sustainability which ultimately lead to global sustainable development. The present research objective is to develop and test framework of sustainable development by considering the elements of tourism, technological innovation, and national leadership. This further would facilitate growth, environmental and socio-cultural sustainability. Understanding the integration of these dimensions would enable the building of a Sustainable Development Framework (SDF) that would provide better insight in promoting the SDGS agenda. Ultimately, growth and environmental sustainability can be achieved which will benefit the society, the economy, and nations and of course for future sustainable policy recommendation. Based on the issue above, you are required to propose relevant econometric approaches with the aims to test sustainable development by considering the elements of tourism, technological innovation, and national leadership. Question 1 [10 marks] [CLO2] Based on the scenario above, a. Propose an appropriate model specification based on the scenario above. [4 marks] used in the [4 marks] [2 marks] b. Justify the selection of the dependent and independent variables model. c. Justify the selection of the sample period.
According to the given information, the sample period should be from 2010-2020.
a) Model specification
The model specification based on the scenario above is as follows:
SDF= f(T, TI, NL)
Where: SDF= Sustainable Development Framework
T= Tourism
TI= Technological innovation
NL= National leadership
b) Justification for the selection of the dependent and independent variables model:
Dependent variable: The dependent variable in this model is Sustainable Development Framework (SDF). The model seeks to develop a framework for sustainable development that would facilitate growth, environmental and socio-cultural sustainability.
Independent variables:
The independent variables are tourism sustainability, technological innovation, and quality of leadership. These variables drive economic development. The inclusion of tourism sustainability reflects its importance in the global economy and its potential to drive growth.
The inclusion of technological innovation reflects its potential to enhance productivity and create new industries. The inclusion of national leadership reflects the role of governance in promoting sustainable development and managing negative externalities.
c) Justification for the selection of the sample period:
The sample period should be selected based on the availability of data for the variables of interest. Ideally, the period should be long enough to capture trends and patterns in the data. However, it should not be too long that the data becomes obsolete or no longer relevant.
Additionally, the period should also reflect the context and relevance of the research question. Therefore, the sample period for this study should cover the last decade to capture the trends and patterns in the data and reflect the relevance of the research question.
The sample period should be from 2010-2020.
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The phases of the moon are periodic and repetitive. A new moon occurs when no moon is visible to an observer on Earth. During the first quarter, half of the side of the moon facing the Earth is visible. During a full moon the entire side of the moon is visible. During the last quarter the other half of the side of the moon facing Earth is visible. The U.S. Naval Observatory lists the following dates for phases of the Moon in the year 2008. Date Moon Phase x: Days since Jan. 8 y: The Amount of Moon Visible Jan 8 New 0 0 Jan 15 1st quarter 7 0.5 Jan 22 Full 13 1 Jan 30 Last quarter 22 0.5 Feb 7 New 30 0 Feb 14 1st quarter 37 0.5 Feb 21 Full 44 1 Feb 29 Last quarter 52 0.5 Mar 7 New 59 0 Mar 14 1st quarter 66 0.5 Using the information above, plot the data points and produce a sine regression model for the data. Round a, b, c, and d to the nearest 0.001. a. y = 0.508 sine (0.212 x + 1.529) minus 0.512 b. y = 0.508 sine (0.212 x minus 1.529) + 0.512 c. y = 0.508 sine (0.212 x minus 1.529 + 0.512) d. y = 0.512 sine (1.529 x minus 0.212) + 0.508
The correct sine regression model for the data is y = 0.508 sine (0.212 x + 1.529) minus 0.512.
What is regression?Regression is a statistical technique used to analyze data and identify relationships between variables. It is used to predict the value of a dependent variable based on one or more independent variables. In regression analysis, the relationship between the dependent and independent variables is described using a mathematical equation.
This sine regression model is based on the data given in the question. The model is in the form y = a* sin(bx + c) + d.
The coefficients a, b, c, and d can be determined by fitting the model to the data.
By fitting the model to the data, the coefficients can be determined to be a = 0.508, b = 0.212, c = 1.529, and d = -0.512.
Therefore, the correct sine regression model for the data is y = 0.508 sine (0.212 x + 1.529) minus 0.512.
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Alyssa’s extended family is staying at the lake house this weekend for a family reunion. She is in charge of making homemade pancakes for the entire group. The pancake mix requires 2 cups of flour for every 10 pancakes.
1. Write a ratio to show the relationship between the number of cups of flour and the number of pancakes made.
2. Determine the value of the ratio.
3. Use the value of the ratio to fill in the following two multiplicative comparison statements.
a. The number of pancakes made is ________ times the amount of cups of flour needed.
b. The amount of cups of flour needed is ________ of the number of pancakes made.
4. If Alyssa has to make 70 pancakes, how many cups of flour will she have to use?
Answer:
1. 2:10 or 1:5
2. 20%
3a. 5
3b. 1/5
4. 14 cups. If you multiply the ratio by 7 to get 70 total pancakes, the other value will be 14.
2:10 * 7 = 14:70
Which of the following shows the true solution to the logarithmic equation solved below? log Subscript 2 Baseline (x) = log Subscript 2 Baseline (x 7) = 3. Log Subscript 2 Baseline left-bracket x (x 7) right-bracket = 3. X (x 7) = 2 cubed. X squared 7 x minus 8 = 0. (x 8) (x 1) = 0. X = negative 8, 1 x = negative 8 x = 1 x = 1 and x = negative 8 x = 1 and x = 8.
The value which shows the true solution to the given logarithmic equation is 1.
What is the domain and range of the function?The domain of a function is defined as the set of all the possible input values that are valid for the given function.
The range of a function is defined as the set of all the possible output values that are valid for the given function.
The given logarithmic equation is,
\(\rm log_{2} (x) + log_{2} (x +7) = 3.\)
Use the addition property of log in the above expression.
\(\rm log_{2} (x \times (x +7) )= 3.\\ (x \times (x +7) ) = 2^{3} \\x \times (x +7) = 8\\x^{2} +7x-8=0\)
Solve the quadratic equation we get,
\((x+8)(x-1)=0\)
x = -8, 1
Here, the logarithmic function is defined only for positive real numbers as its input.
Thus, the value which shows the true solution to the logarithmic equation solved above is 1.
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Answer:X=1
Step-by-step explanation:b on edge
On a piece of paper, graph y= see pic
Answer:
a
Step-by-step explanation:
assuming theyre asking you to graph y = (x-2)(x+3) -cant see the signs in your photo
the x-intercepts would be 2 and -3 , so option a!
On a coordinate plane, parallelogram R S T U is shown. Point R is at (1, 1), point S is at (7, 0), point T is at (10, 4), and point U is at (4, 5). If line segment RU is considered the base of parallelogram RSTU, what is the corresponding height of the parallelogram? 4. 5 units 5. 4 units 9. 0 units 10. 8 units.
The height of a parallelogram can be found using the formula: Height = Distance between the base and the opposite side.
Let's find the distance between line segment RU and the opposite side ST first. We can use the distance formula to find the distance between two points.DR = √(x2 − x1)² + (y2 − y1)²
Where (x1, y1) is the first point, (x2, y2) is the second point, and DR is the distance between them.Distance between R and TDT = √(10 - 1)² + (4 - 1)²
= √9² + 3²
= √81 + 9
= √90
Since line segment RU is parallel to ST, the distance from R to ST is the same as the distance from U to ST.Height of parallelogram RSTUH = DT = √90Answer: 8 units.
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a boy owns 8 pairs of pants, 5 shirts, 3 ties and 6 jackets. how many different outfits can he wear to school if he must wear one of each item?
The boy can wear 720 different outfits to school if he must wear one of each item, we need to find the number of combinations of one pair of pants, one shirt, one tie, and one jacket. The number of different combinations of pants he can wear is 8.
The number of different combinations of shirts he can wear is 5.
The number of different combinations of ties he can wear is 3.
The number of different combinations of jackets he can wear is 6.
To find the total number of different outfits, we multiply the number of combinations of each item:
8 * 5 * 3 * 6 = 8 * 90 = 720
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what is 1.92 ÷ 32 ???
Therefore:
\(\frac{1.92}{32}=0.06\)
What is the simplified form of the expression? HELP ASAP
Answer:
\(360\)
Step-by-step explanation:
\( \frac{5(14 - 2)^{2} }{2} = \frac{5 {(12)}^{2} }{2} = \frac{5(144)}{2} \\ \\ \frac{720}{2} = 360\)
Answer:
The answer is option (d) 360.
Step-by-step explanation:
Solution :\(\implies{\tt{\dfrac{5(14 - 2)^{2} }{2}}}\)
\(\implies{\tt{\dfrac{5(12)^{2} }{2}}}\)
\(\implies{\tt{\dfrac{5(12 \times 12) }{2}}}\)
\(\implies{\tt{\dfrac{5(144) }{2}}}\)
\(\implies{\tt{\dfrac{5 \times 144 }{2}}}\)
\(\implies{\tt{\dfrac{5 \times \cancel{144}}{ \cancel{2}}}}\)
\(\implies{\tt{5 \times 72}}\)
\(\implies{\tt{360}}\)
\(\dag{\underline{\boxed{\sf{\red{360}}}}}\)
Hence, the answer is 360.
\(\rule{300}{1.5}\)
Learn More :✧ BODMAS :
↝ BODMAS rule is an acronym used to remember the order of operations to be followed while solving expressions in mathematics.
It stands for :-
⠀ ⇝ B - Brackets,
⠀ ⇝ O - Order of powers or roots,
⠀ ⇝ D - Division,
⠀ ⇝ M - Multiplication
⠀ ⇝ A - Addition
⠀ ⇝ S - Subtraction.
↝ It means that expressions having multiple operators need to be simplified from left to right in this order only.
✧ BODMAS RULE :
↝ First, we solve brackets, then powers or roots,then division or multiplication (whatever comes first from the left side of the expression), and then at last subtraction or addition.
⠀ ↠ Addition (+)
⠀ ↠ Subtraction (-)
⠀ ↠ Multiplication (×)
⠀ ↠ Division (÷)
⠀ ↠ Brackets ( )
\(\rule{300}{1.5}\)
Please find ‘?’ Please help me out
Answer:
? = 16
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan ? = opp side / adj
tan ? = 13 / 46
Taking the inverse tan of each side
tan ^ -1 ( tan ? ) = tan ^-1 ( 13/46)
? = 15.78075
To the nearest degree
? = 16
12. A certain sum of money is divided among 2 boys and 3 girls. One boy gets 27 and the other boy gets 3/14. The balance is divided equally among the 3 girls. Find the shere of each girl
The share of each girl is 1/6.
Given that, certain sum of money is divided among 2 boys and 3 girls.
One boy gets 2/7 and the other boy gets 3/14
Total amount of money boys gets = 2/7+3/14
= (4+3)/14
= 7/14
= 1/2
Remaining money = 1-1/2
= 1/2
The balance is divided equally among the 3 girls.
Let the amount of money each girl gets be x.
Now, 3x=1/2
x=1/6
Therefore, the share of each girl is 1/6.
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"Your question is incomplete, probably the complete question/missing part is:"
A certain sum of money is divided among 2 boys and 3 girls. One boy gets 2/7 and the other boy gets 3/14 the balance is divided equally among the 3 girls . Find the share of each girl.
4. A rectangle is a four-sided flat shape where every interior angle is a right angle.
Therefore, opposite sides are parallel and consecutive sides are perpendicular.
Rae is drawing rectangle PQRS on a coordinate plane. The rectangle has
coordinates P(-1,2), Q(2,4), R(x, y), and S(3,-4).
Answer:
coordinates of R(x,y) is R(6,-2).
Step-by-step explanation:
A. we know that
The rectangle has coordinates P (-1,2), Q(2,4), R(x,y) and S(3,-4)
using a graph tool
see the attached figure
Step 1
Find the slope of the line PS
the slope is equal to
m=(y2-y1)/(x2-x1)
mPS=(-4-2)/(3+1)=-6/4=-3/2
Step 2
Find the equation of the line QR
we know that
PS and QR are parallel lines
so
their slopes are the same
mQR=-3/2
with mQR and the point Q(2,4) find the equation of the line
y-y1=m*(x-x1)
y-4=(-3/2)*(x-2)
y=(-3/2)*x+3+4--------> y=7-(3/2)*x
Step 3
Find the equation of the line SR
we know that
SR and QR are perpendicular lines
so
the product of their slopes is equal to minus one
mSR*mQR=-1
mSR=2/3
with mSR and the point S(3,-4) find the equation of the line SR
y-y1=m*(x-x1)
y+4=(2/3)*(x-3)
y=(2/3)*x-2-4---------> y=-6+(2/3)*x
Step 4
Find the intersection of the lines QR and SR
we know that
the intersection of the lines QR and SR is the point R
y=7-(3/2)*x------> equation 1
y=-6+(2/3)*x------> equation 2
equate equation 1 and equation 2
7-(3/2)*x=-6+(2/3)*x
7+6=(2/3)*x+(3/2)*x
13=(2/3)*x+(3/2)*x
Multiply by 6 both sides
6*13=4*x+9*x
13*x=6*13
x=6
find the value of y
y=-6+(2/3)*x------> y=-6+(2/3)*6---------> y=-6+4
y=-2
therefore, the coordinates of point R are (6,-2)
Prove that (36^5-6^9)(38^9-38^8) is divisible by 30 and 37
Answer:
(36^5-6^9)(38^9-38^8) is divisible by both 2, 3, and 37, and hence it is divisible by 30 and 37.
Step-by-step explanation:
To prove that (36^5-6^9)(38^9-38^8) is divisible by 30, we need to show that it is divisible by both 2 and 3.
To prove that it is divisible by 2, we note that (36^5-6^9) is even, since it contains at least one factor of 2. We also note that (38^9-38^8) is even, since it can be factored as 38^8(38-1), and 38-1 is even. Therefore, their product is even and divisible by 2.
To prove that it is divisible by 3, we note that (36^5-6^9) is divisible by 3, since the sum of its digits is 3+6+5+6+9 = 29, which is divisible by 3. We also note that (38^9-38^8) is divisible by 3, since the sum of its digits is 3+8+9 = 20, which is divisible by 3. Therefore, their product is divisible by 3.
To prove that (36^5-6^9)(38^9-38^8) is divisible by 37, we can use Fermat's Little Theorem, which states that if p is a prime number and a is an integer not divisible by p, then a^(p-1) is congruent to 1 mod p. Since 37 is a prime number and 6 is not divisible by 37, we have:
6^36 ≡ 1 (mod 37)
Therefore, we can rewrite the expression as:
(36^5-6^9)(38^9-38^8) ≡ (36^5-6^9)(1-38) (mod 37)
Simplifying further, we get:
(36^5-6^9)(1-38) ≡ (1-6^9)(1-38) (mod 37)
= (1-531441)(1-38)
= (531440)(-37)
Since 531440 is divisible by 37, we have shown that (36^5-6^9)(38^9-38^8) is divisible by 37.
Therefore, we have proved that (36^5-6^9)(38^9-38^8) is divisible by both 2, 3, and 37, and hence it is divisible by 30 and 37.
Given x=-3, y=6, and z=-4
-15+(-x)+y=
x = -3 , y = 6 , z = -4
Take Given equation :
⇒-15 + (-x) + y = 0
substitute values of x and y
⇒-15 + [- ( -3)] + 6
⇒-15 + (3) + 6
⇒-15 + 9
⇒-6
Hence, value of -15 + (-x) + y = - 6
Please help me :)
ty ty
Answer:
the slope is stepper and the line is shifted up
Point T is on line segment SU. Given TU = x - 1, SU = 3x - 7, and ST = x + 7, determine the numerical length of TU
According to the solving the lenght of line segment is TU = 12.
how the addition of line segments is done?An portion of a line with two endpoints is referred to as a line segment. A line segment, unlike a line, has a definite length.
according to the given information:Because T is on the line segment SU. so, addition of ST and TU must be equal to SU
SU = ST + TU..........(1)
SU = 3x -7
TU = x -1
ST = x + 7
Substituting these values into equation (1)
3x-7 = x +7 + x -1
3x -7 = 2x + 6
x = 13
For the numerical length of TU
TU = x - 1
TU = 13 - 1
TU = 12
The numerical value of tu is 12
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what’s the difference between the area of the larger circle and the area of the smaller circle? in pi
Answer:
105 pi m^2
Step-by-step explanation:
radius squared - radius squared =
(16+3)^2 - 16^2 =
19^2 - 16^2 =
361-256= 105