The measure of the intercepted arc, [tex]\widehat{XY}[/tex], formed by the secants ZW and ZV is 30°
What is a secant of a circle?A secant line is a straight-line which has two points of intersection with a circle.
From a similar question on the internet, the figure consists of an outside angle of 41° formed by two secants and two intercepted consisting of [tex]\widehat{XY}[/tex]and [tex]\widehat{VW}[/tex] which measures 112°
The outside angles of a circle theorem states that the outside angle formed by two secants or two tangent or a combination of a secant and a tangent is the difference of the measure of the difference of the angles of the intercepted arcs divided by two.
Mathematically;
[tex]m\angle z = \dfrac{\widehat{VW} - \widehat{XY}}{2}[/tex]
Where;
The outside angle formed by the secant ZW and ZV, m∠z = 41°
[tex]\widehat{VW}[/tex] = 112°
Which gives;
[tex]41^{\circ}= \dfrac{112^{\circ}- \widehat{XY}}{2}[/tex]
2 × 41° = 112° - [tex]\widehat{XY}[/tex]
82° = 112° - [tex]\widehat{XY}[/tex]
[tex]\widehat{XY}[/tex] = 112° - 82° = 30°
[tex]\widehat{XY}[/tex] = 30°
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Emmett prepared 10 kilograms of dough after working 2 hours. How much dough did Emmett prepare if he worked for 4 hours? Assume the relationship is directly proportional.
The kilograms of dough that Emmett prepare if he worked for 4 hours is 20 kilograms.
What is a proportional relationship?A proportional relationship simply means the relationship that has an equivalent ratio as well as a constant.
In this case, Emmett prepared 10 kilograms of dough after working 2 hours. The kilograms per hour will be:
= 10/2
= 5 kilograms per hour
Therefore, in 4 hours, the kilograms will be:
= Number of hours × 5 kilograms
= 4 × 5
= 20 kilograms
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The greatest temperature ever recorded in the United States occurred at an elevation of 178 feet below sea level. The greatest temperature ever recorded in Africa occurred at an elevation of 545 feet greater than in the United States. At what elevation, in feet, did the greatest temperature in Africa occur?
The greatest temperature in Africa occur is 367 feet.
What are integers?The collection of positive and negative integers is known as an integer. Integers, like whole numbers, do not include the fractional portion.
Zero (0)Positive Integers (Natural numbers)Negative Integers (Additive inverse of Natural Numbers)Given:
The greatest temperature ever recorded in the United States occurred at an elevation of 178 feet below sea level.
Using integers we represent it as (-178) feet.
and, greatest temperature ever recorded in Africa 545 feet greater than in the United States
= -178 + 545
= 367 feet.
Hence, The greatest temperature in Africa occur is 367 feet.
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The mean height of 12 men is 1.70 m, and the mean height of 8 women is 1.60 m. Find:the total height of the 12 men
Answer:
20.4 m
Step-by-step explanation:
mean is calculated as
mean = [tex]\frac{total}{count}[/tex]
given mean height of 12 men is 1.70 m , then
[tex]\frac{total}{12}[/tex] = 1.7 ( multiply both sides by 12 to clear the fraction )
total height = 12 × 1.7 = 20.4 m
which is the correct answer for this ??????
The given system of linear equations has no solution. By solving the equations using substitution method we get (11, 0) where no solution exists.
How many solutions can a system of linear equation can have?
A system of linear equations is usually a set of two linear equations with two variables.
The solution to a system of linear equations is the point at which the lines representing the linear equations intersect.
With linear systems of equations, there are three possible outcomes in terms of number of solutions:
One solutionInfinitely many solutionsNo solutionHow to identify the number of solutions?
Rewrite both equations in slope-intercept form, y = mx + b.
Compare the slopes of the lines, m, and their y-intercepts, b, to determine the number of solutions.
If the two equations have different m-values, then the system has one solution.If the two equations have the same m-value but different b-values, then the system has no solution.If the two equations have both the same m-value and the same b-value, then the system has infinitely many solutions.According to the given question:
Given system of linear equation are: y = -x + 11 and -4x -4y = 44
Rewriting the equations in slope-intercept form
y = -x + 11 ---- 1)-4y = -4x + 44Simplifying further by dividing the equation with -4 on both side
y = x - 11 ------ 2)
Clearly, both the equation have different m-values.
Hence the system of equation have one solution.
Now solving by substitution method
Substituting 2) in 1)
x - 11 = -x + 11 (since y = x -11 from 2))
2x = 22
∴ x = 11
Now substituting x = 11 in equation 2) to get the value of y
y = 11 - 11
∴ y = 0
So, the system of equation has no solution at (11, 0).
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Which of the graphs below shows correctly plotted points for the following line? y=2x+3
Answer: The image is for an idea of what you should look for
Step-by-step explanation:
Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. 8(x2 + 2x + 1) = –3 + 8 x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot 8(x2 + 2x + 1) = 3 + 1 8(x2 + 2x) = –3
The steps that Patel could he use to solve the quadratic equation include:
8(x² + 2x) = –3
8(x² + 2x + 1) = –3 + 8
x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot
How to illustrate tye information?It is preferred to solve quadratic equations without the use of the known quadratic formula solver. This can be completing squares and solving for x.
The equation given is:
8x² + 16x + 3 = 0
8(x² + 2x) = -3
Completing squares in the brackets and balancing the equation:
8(x² + 2x + 1) = -3 + 8
Factoring the perfect square will give 8(x + 1)² = 5.
This is illustrated in the options picked for the step.
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Need help please someone
Answer:
16
Step-by-step explanation:
The x's go up by 1 (1, 2, 3, 4, 5)
The y's go up by 4's. 0, 4, 8, 12, 16
There is a rule to find the y's from the x's instead:
times by 4 and minus 4.
y = 4x - 4
y = 4(5) - 4
y = 20 - 4
y = 16
Write the expression in words 2x + 2
Answer:
two times x plus two
Step-by-step explanation:
Determine which integer will make the inequality 4x + 6 < 2x + 12 false.
Answer:
x>=3 make the inequality false
Step-by-step explanation:
4x-2x<12-6
2x<6
x<3
Answer:
Any number higher than 3
Ex. 4, 5, 6, 7, 8, 9, 10, etc
Step-by-step explanation:
4x + 6 < 2x + 12
-2x -2x
---------------------
2x + 6 < 12
-6 -6
------------------
2x < 6
÷2 ÷2
-----------
x < 3
Since x is less than 3, any number higher than 3 will make the inequality false. For Ex. 4
4(4) + 6 < 2(4) + 12
16 + 6 < 8 + 12
22 < 20 (false)
I hope this helps!
a vegetable seller purchased 1 quintal of potatoes at rs 35 per kg and sold at a loss of rs 350. find his rate of selling price and loss percent
Answer:
Selling price = RS 3150
Loss percent = 10%
Step-by-step explanation:
1 quintal = 100kg
Cost price = 35*100
= RS 3500
Loss = RS 350
Selling price = RS 3500-350
Selling price = RS 3500-350 =RS 3150
Loss percent = Loss *100%
Cost Price
= 0.1 *100
= 10%
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Which lists the distances between towns in order from greatest to least?
(picture of problem below)
Answer:
Step-by-step explanation:
the side opposite to greater angle is greater.
72>60>48
AB>AC>BC
A=Afton
B=Badeton
C=Capeton
Write these as normal numbers.
b)
9.6 × 10⁹
Answer:
9600000000
Step-by-step explanation:
9.6 x (10^9)
First, write 10^9 as 1000000000
Multiply by 9.6
= 9600000000.
If the original function is f(x)
What would be the function notation when the function was
Shifted Right 6
The function notation when the function was shifted right 6 is f(x-6).
Given that, the function was shifted right 6 units.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Rule: In function notation, to shift a function left, add inside the function's argument: f(x + b) shifts f(x) b units to the left. Shifting to the right works the same way, f(x - b) shifts f(x) b units to the right.
So, the transformation from the original function to new function is
f(x-6)
Therefore, the function notation when the function was shifted right 6 is f(x-6).
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Ten men working 6 hours a day takes 12 days to complete a job.How long will it take 8 men working 12 hours a day to complete the same job
Answer:
It will take 7.5 days to complete the job.
Step-by-step explanation:
First, find how many total hours the ten men worked to complete the job
10 x 6 = 60 hours a day
12 x 60 = 720 hours total
Now compare that with the 8 men's hours
8 x 12 = 96 hours a day
720 / 96 = 7.5 days
the cost of 2kg carrots is £7 work out the cost of 5kg carrots.
21. An artist created a piece of art with 675 round glass beads. There were
also 179 beads in the shape of a heart. Write a number sentence to
find about how many more round beads there were.
By using subtraction, it can be calculated that there were 496 round beads more than heart shaped beads
What is subtraction?
Suppose, there are two numbers and it is required to find out how much one number is bigger than the other. The operation used for this is subtraction.
The larger number is called minuend and the smaller number is called subtrehend.
Here, subtraction will be used
Number of round glass beads = 675
Number of beads in the shape of heart = 179
Number of more round beads there were = 675 - 179
= 496
There were 496 round beads more than glass beads
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For a field trip 9 students rode in cars and
the rest filled eight buses. How many
students were in each bus if 265 students
were on the trip?
Answer:
32 students were on each bus.
Step-by-step explanation:
First deduct 9 students from the total number: 265 - 9 = 256
Then divide the students among the total number of buses, which is 8: 256/8 = 32
So there are 32 students on each bus.
Hope this helps
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A coin (5 grams), a small parachute (21 grams), and a hammer (710 grams) are all dropped from a height of 10 meters. The coin and the hammer take
about the same amount of time to fall. Which statement describes the time it takes for the parachute to fall? (1 point)
O It takes less time to fall because it has the most surface area.
O It takes the same amount of time to fall because the effect of gravity is the same.
O It takes less time to fall because it has the least mass
O It takes longer to fall because it experiences greater air resistance.
Answer:
the last one= It takes longer to fall because it experiences greater air resistance.
also the reason is the air resistance provides an upthrust to the parachute which takes longer time to fall
Answer: It takes longer to fall because it experiences greater air resistance.
What is 3/4 written in 12 of denominator
Answer: The correct answer in 9/12
Step-by-step explanation:
For 3/4, the numerator is 3 and the denominator is 4
To change the denominator to 12, you must multiply by 3 (12/4=3)
3/4 * 3/3
= (3*3)/(4*3)
= 9/12
3.201 x 10^9 and 4.85 x 10^3
(3.201 x 10^9) * (4.85 x 10^3) =
15524850000000
in scientifc notation
1.552485 x 10^13
Radius of the base of a cylinder is 38 mm and its height is 51 mm. Find the surface area of the cylinder, in terms of pi
The surface area of the cylinder in term of π is 6764πmm^2
What is surface area of a cylinder?A cylinder is a three-dimensional solid that contains two parallel bases connected by a curved surface. The bases are usually circular in shape. The perpendicular distance between the bases is denoted as the height “h” of the cylinder and “r” is the radius of the cylinder.
The total surface area of a cylinder is 2πr(r+h)
Where r is the radius and h is the height of the cylinder
therefore T.S.A= 2×38π(38+51)
T.S.A=76π×89
The total surface area(T.S.A) of the cylinder =6764πmm^2
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What is the quotient of
15y^3+ 28y^2+ 7y-6 / 5y+6?
Answer: The quotient is 3y² + 2y - 1.
Step-by-step explanation:
You can use long division to solve this expression by setting the dividend under the roof and the divisor outside as you would normally do when dividing numbers.
1) Look at the first term of the dividend, 15y³, and the first term of the divisor, 5y. Determine what value multiplied by 5y would give you 15y³. The answer is 3y², and given the number, you multiply it by the WHOLE divisor.
3y²(5y + 6) = 15y³ + 18y² <-- subtract this from the dividend.
2) Continue this process and make sure to drag down the next term for each new value you form after subtracting. Keep in mind of any negative values! When you reach up to -5y, determine what value multiplied by 5y would give you the value of -5y, which would be -1.
3) You should be left with a remainder of 0, leaving you with a quotient of 3y² + 2y - 1.
2, 5, 4, 10, 8, 20 [Hint: It is a combined series: two geometric series. Find common ratio for each by dividing.]
The two combined geometric series is separated and the common ratios are shown
2, 4, 8, - common ratio = 25, 10, 20 - common ratio = 2What is geometric series?The total of a geometric sequence's finite or infinite terms is known as a geometric series.
The ratios of every two successive terms in the series (sum of terms) are equal. this means that
4/2 = 8/4 = 210/5 = 20/10 = 2The common ratio is calculated by dividing the succeeding term (eg 2nd term) by the preceding term (eg 1st term)
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If P= (2, 7) and Q= (2, -3), which could be the coordinates of R if triangle PQR is isosceles?
If P= (2, 7) and Q= (2, -3), then for triangle to be isosceles coordinate of R must be 2
Let coordinates
P = (2, 7) and Q = (2, -3)
PR = QR
(X-2)^2 +(Y-7)^2 = (X-2)^2 + {Y-(-3)}^2
(Y-7) = {Y - (-3)}^2. or y - 7 = ±(Y
or Y^2 - 14Y + 49 = Y^2 + 6Y + 9
20Y = 40
Y=2
coordinates of R if triangle PQR is isosceles ;
Hence any point R on the line Y = 2 will make PQR a isosceles triangle
with PR = QR.
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What is the reason for each step in the solution of the equation?
−6x=−2(x+12)
Drag and drop the reasons into the boxes to correctly complete the table.
Answer:
Given
Distributive Property
Addition Property of Equality
Division Property of Equality
Step-by-step explanation:
Frist you distribute the -2 by multiplying it to everything in the parentheses. Next, you add 2x to both sides of the equation and lastly you divide both sides of the equation by -4
Marco opened a savings account 10years ago. The account earns 5% interest,compounded annually. If the current balance is $400, how much did he deposit initially? Round your answer to the nearest cent.
Answer:
245.57
Step-by-step explanation:
[tex]P\left(1+0.05)^{10}=400 \\ \\ P=\frac{400}{(1.05)^{10}} \\ \\ P \approx 245.57[/tex]
One year, the population of a city was 181,000. Several years later it was 150,230. Find the percent decrease.
The percentage decrease in population is 17%
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply it by 100. percentage . The word per cent means per 100. It is represented by the symbol “%”.
percentage decrease in population= (0riginal population- new population)÷ original population × 100
%decrease in population = (181000 - 150230) ÷ 181000× 100
=( 307770×100)/181000
= 17%
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17%
Step-by-step explanation:
i tried it it worked
Bella fills Her gas tank with 13 1/2 gallons of gas. After driving the car she has 11 4/5 gallons left. How much gas did Bella use?
Answer:
1.7 gallons
Step-by-step explanation:
You would chand the 1/2 and 4/5 into tenths by multiplying 1/2 by 5 getting 5/10 then multiplying 4/5 by 2 to get 8/10 so you would have 13 5/10- 11 8/10 to get 1.7 gallons left.
4. Enrique collected 152 recyclable bottles, and
Latasha collected brecyclable bottles. Write
an expression for the number of bottles they
collected altogether.
The required expression is Total = 152+x .
What is expression ?
Mathematical statements called expressions must contain a minimum of two terms with either numbers, variables, or both, joined by an operator. The four different types of mathematical operators are addition, subtraction, multiplication, and division. For instance, the expression x + y is an expression where x and y are terms with an addition operator between them. Mathematical expressions can be divided into two categories: algebraic expressions, which include both numbers and variables, and numerical expressions, which solely contain numbers.
Here,
The number of bottles Enrique collected = 152
Let us take number of bottles collected by Latasha as x. Then,
Total number of bottles collected by the is ,
=> Total = Number of bottles collected + Number of bottle collected
by Enrique By Latasha.
=> Total = 152+x
Hence the required expression is Total = 152+x.
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Solve.
log3 (2x + 5) = 3
Enter your answer in the box.
X = ?
Answer:
x = 11
Step-by-step explanation:
using the rule of logarithms
[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]
given
[tex]log_{3}[/tex] (2x + 5) = 3 , then
2x + 5 = 3³ = 27 ( subtract 5 from both sides )
2x = 22 ( divide both sides by 2 )
x = 11