What is the value of z in this figure?
The value of z in the figure is 56⁰.
What is an angle?
An angle is a figure in plane geometry that is created by two rays or lines that have a common endpoint. The Latin word "angulus," which means "corner," is the source of the English word "angle." The common endpoint of two rays is known as the vertex, and the two rays are referred to as the sides of an angle.
In the given figure, there are two pairs of vertically opposite angles.
The vertical opposite angle of 124⁰ is y⁰.
The vertical opposite angle of x⁰ is z⁰.
Thus, 124⁰ = y⁰ and x⁰ = z⁰.
The sum of all angles is 360⁰.
Therefore,
124⁰ + x⁰ + y⁰ + z⁰ = 360⁰
Putting y⁰ = 124⁰ and x⁰ = z⁰ in the above equation:
124⁰ + z⁰ + 124⁰ + z⁰ = 360⁰
248⁰ + 2z⁰ = 360⁰
Subtract 248⁰ from both sides:
2z⁰ = 360⁰ - 248⁰
2z⁰ = 112⁰
Divide both sides by 2:
z⁰ = 56⁰
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Simplify: (2+1)2 Responses
Answer:
6
Step-by-step explanation:
Simplifying the expression (2+1)2, we can first perform the operation within the parentheses, which gives us:
(2+1)2 = 3 x 2
Then, we can multiply 3 by 2, which gives us:
3 x 2 = 6
Therefore, the simplified expression for (2+1)2 is 6
A theatre contains 487 seats and the ticket prices for a recent play were $47 for adults and $29 for children. If the total proceeds were $17,525 for a sold-out matinee, how many of each type of ticket were sold?
Answer:
Step-by-step explanation:
Let's use A to represent the number of adult tickets sold and C to represent the number of children tickets sold. We can set up two equations based on the information given:
The total number of tickets sold is the sum of adult and children tickets:
A + C = 487
The total proceeds from ticket sales is the product of the number of tickets and their respective prices:
47A + 29C = 17525
We can use the first equation to solve for one of the variables in terms of the other:
C = 487 - A
Substituting this expression for C into the second equation, we get:
47A + 29(487 - A) = 17525
Simplifying and solving for A:
18A + 14123 = 17525
18A = 3402
A = 189
So 189 adult tickets were sold. Using the equation C = 487 - A, we can find the number of children tickets sold:
C = 487 - 189 = 298
Therefore, 189 adult tickets and 298 children tickets were sold for the matinee.
What is the exponent in the expression 4 to the power of 5?
A. 4
B. 5
C. 9
D. 20
Answer:
B. 5
Step-by-step explanation:
The expression "4 to the power of 5" can be written as 4^5. Here, 4 is the base, and 5 is the exponent. So the exponent in the expression 4 to the power of 5 is option B, 5.
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grams
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5
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6
5
Lena's chocolate bar is 54% cocoa. If the weight of the chocolate bar is 53 grams, how many grams of cocoa does it contain? Round your answer to the nearest
tenth.
7
Q Search
8
9
10
Submit Assignm
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S
Answer:
28.6 grams
Step-by-step explanation:
Percentage of cocoa in the chocolate bar = 54%
Weight of the chocolate = 53 grams
Weight of the cocoa = 54% of 53 = 28.62 grams
Rounding off to nearest tenth = 30 grams
The length of a room is 583 cm. Express the length in metres. *
Your answer
Calculate *
Answer:
5.85m
Step-by-step explanation:
1 meter is 100 centimeters.
583 divided by 100
The ramp is place from a ditch to a main road 2 feet above the ditch if a length of the ramp is 12ft how far away is the bottom of the ramp from the road
Answer:
See My Attached Work For Answer. (POV THIS WAS HARD!!!)
Step-by-step explanation:
use the given conditions to write an equation for the line in point-slope form and slope-intercept form
The equation of the line in point slope form is y + 6 = 3 (x + 3), and the line in slope intercept form is y = 3x + 3.
What is Slope?Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.
We have the points on the line given.
(-3, -6) and (2, 9)
Slope of the line = (9 - -6) / (2 - -3) = 15/5 = 3
Equation of a line in point slope form is,
y - y₁ = m (x - x₁)
where (x₁, y₁) is a point on the line and m is the slope.
Substituting a point (-3, -6) and the slope = 3, we get,
y - -6 = 3 (x - -3)
y + 6 = 3 (x + 3), which is the point slope form.
Equation of a line in slope intercept form is,
y = mx + c
where m is the slope and c is the y intercept.
Substituting m = 3 and (x, y) = (2, 9),
9 = (3 × 2) + c
c = 9 - 6 = 3
Equation in slope intercept form becomes,
y = 3x + 3
Hence the point slope form and slope intercept form of the given line are y + 6 = 3 (x + 3) and y = 3x + 3 respectively.
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Joe dreams of being a striker for Bafana Bajora some day. Every day, after school, he takes 100 practice goal kicks from various angles and distances. On the first day he only managed to kick 12 goals. On the second next day be kicked 14 goals, on the third day 16 and on the fourth day 18. If the pattern continues, how long will be huve to practice before he will kick 100 goals?
The number of days it will take for him to kick 100 goals is given as follows:
45 days.
How to define a linear function?The slope-intercept definition of a linear function is presented as follows:
y = mx + b.
In which:
The slope m represents the increase of y per each unit of x.The intercept b represents the value of y when x = 0.The parameters for this problem are given as follows:
m = 2, as each day, the number of goals increased by two.b = 10, as on the first day, he managed to kick 12 goals, hence on the day zero, the amount was of 12 - 2 = 10.Hence the function giving the number of goals on day x is given as follows:
y = 2x + 10.
The number of days for him to score 100 goals is then obtained as follows:
100 = 2x + 10
2x = 90
x = 90/2
x = 45 days.
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A shipping container is in the form of a right rectangular prism, with dimensions of 35 ft by 8 ft by 7 ft 6 inches. How many cubic feet of shipped goods would it hold when it is full? Round your answer to the nearest tenth if necessary.
Answer:
1110
Step-by-step explanation:
¿Cuánto tiempo es necesario para que un capital se duplique a una tasa del 12% simple anual?
On solving the provided question we can say that at a simple 12% annual percentage rate, it would take approximately 6 years for capital to double.
What is percentage?In mathematics, a ratio or number expressed as a percentage of 100 is called a percentage. Also occasionally used are the acronyms "pct.," "pct," and "pc." Nonetheless, the percentage symbol "%" is widely used to represent it. The % quantity is dimensionally empty. Basically, percentages are fractions when the denominator is 100.
The annual rate of return is 12%, so we can calculate:
Time to double = 72 / 12 = 6 years
Therefore, at a simple 12% annual rate, it would take approximately 6 years for capital to double.
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The correct question is -
How long does it take for capital to double at a simple 12% annual rate?
What does it mean to have a skewed distribution? What causes a skew in statistical terms? And how does one deal with skewed data when conducting research? Are there specific types of research questions and types of data where one would expect the data to be skewed?
Please answer in simple terms for someone that is new to statistics
We have discussed what is skewed distribution and how to deal with skewed data as mentioned below.
What is a skewed distribution?
When one tail is longer than the other, the distribution is said to be skewed. The asymmetry of a distribution is defined by skewness. These distributions are asymmetric, in contrast to the well-known normal distribution and its bell-shaped curve. Because the data are not equally distributed on both sides of the distribution peak, the two parts of the distribution are not mirror images.
A) The direction of outliers is revealed by skewness. A distribution curve's tail is longer on the right side when there is a positive skew. As a result, the distribution curve's outliers are more extreme to the right and closer to the mean to the left. Skewness simply conveys the direction of outliers; it does not convey the number of outliers.
B) Lower or upper boundaries on the data frequently cause skewed data. In other words, data with a lower bound are frequently skewed right, whereas data with an upper bound are typically skewed left.
C) One popular method for handling skewed outcome data is to logarithmically transform each observation before conducting the analysis with the resulting values.
D) It is likely that the income distribution curve you plot on a graph will be positively skewed to the right. If the majority of people earn normal earnings and a smaller proportion earn high incomes, then this would happen.
Therefore this is what skewed distribution is and the above mentioned ways are how one deals with skewed data in research.
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Solve: 3|x|+4≥1. Write your solution in interval notation
The solution of the inequality 3|x|+4≥1 in interval notation is {x | -1 ≤ x ≤ 1}.
What is interval notation?An interval on a number line can be represented using interval notation. It is a method of representing subsets of the real number line, in other words. The numbers in between any two particular provided numbers are referred to as an interval. For instance, the interval containing 0, 5, and all values between 0 and 5 is the set of numbers x satisfying 0 x 5.
Given that the inequality is:
3|x|+4≥1
Subtract 4 from both sides of the equation:
3|x| + 4 - 4 ≥ 1 - 4
3 |x| ≥ -3
Divide 3 from both sides of the equation:
|x| ≥ -1
We know that, |x| can be written as x and -x thus,
x ≥ -1
-x ≥ -1 or x ≤ 1
Hence, the solution of the inequality 3|x|+4≥1 in interval notation is {x | -1 ≤ x ≤ 1}.
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if one student is chosen at random, find the probability that the student was not a female and did not earn grade C.Giving a test to a group of students, the table below summarizes the grade earned by gender. Male Female Total А 16 19 35 B 18 6 24 с 17 10 27 Total 51 35 86 If one student is chosen at random, find the probability that the student was not a female and did not earn grade C. Round your answer to four decimal places.
The Probability that the student was not a female and did not earn grade C is 34/59.
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.
Given:
A B C Total
Male 16 18 17 51
Female 19 6 10 35
Total 35 24 27 86
Total number of non-female students who got a A and B : 34
Total number of students who got a A and B: 35+24= 59
So, the probability is
= 34/ 59
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The Spirit Club buys shirts in bulk for $8 each. They mark up the shirts 75% to sell in the school store. At the end of the year, they sell the shirts for 25% off. How much profit does the Spirit Club make on each shirt at the end of the year? Show your work
Write the work down step by step, math involved.
The Spirit Club makes $2.5 profit on each shirt at the end of the year.
What is profit?
Cost price and selling price are better ways to explain profit. Cost price is the actual cost of the good or service, whereas selling price is the price at which it is offered for sale. In this case, the business has made a profit if the selling price of the good is higher than the cost price. Consequently, the profit calculation formula is;
Selling price minus cost price equals profit or gain.
Given that the cost of a shirt for the Spirit Club is $8.
They mark up the shirts 75% to sell in the school store.
The amount that is up on each shirt is $8×75%
= $8×(75/100)
= $8×(3/4)
= $6.
The marked price of each shirt is $8 + $6 = $14.
They sell the shirts for 25% off at the end of the year.
The discount amount is $14×25%
= $14×(25/100)
= $14×(1/4)
= $3.5
The selling price of each shirt at the end of the year is $14 - $3.5 = $10.5.
The profit is Selling price - cost price = $10.5 - $8 = $2.5
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Cuanto costaba un abrigo que , tras experimentar una rebaja del 40% y a continuación una subida del 30% ahora cuesta 56,16€?
Por lo tanto, el precio original del abrigo era de 72€
Para resolver este problema, primero debemos determinar el precio original del abrigo antes de las rebajas.
Sea x el precio original del abrigo.
Después de aplicar la primera rebaja del 40%, el precio del abrigo sería:
x - 0.4x = 0.6x
Luego, tras la subida del 30%, elprecio se incrementaría al 130% del precio anterior:
1.3(0.6x) = 0.78x
Sabemos que este precio final es de 56,16€, por lo que podemos resolver la ecuación:
0.78x = 56.16
x = 72
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Consider the following.
t =
41
6
Terminal point is a term used in mathematics to describe the endpoint of a line segment. It is the point at which the line or curve terminates or comes to an end. It is important to note that a terminal point is not necessarily the same as a vertex or an intersection point; the terminal point is simply the endpoint of the line segment, the point at which it begins and ends.
For example, the terminal points of a line segment that connects the points (3, 5) and (7, 9) are (3, 5) and (7, 9). The line segment does not terminate at any other point.
The reference number is 41, and the given formula is t = 6π.
Therefore, 6π = 41
π = 41/6
π ≈ 6.83
The terminal point is determined by the given formula (r cos θ, r sin θ).
Since r = 1, substitute the values for θ and r into the formula:
(1, cos 6.83, 1, sin 6.83) = (3.5, 2.5)
Therefore, the terminal point determined by the given reference number t = 41 is (3.5, 2.5).
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25
Find five consecutive odd integers if the sum of the first three integers is 7 more than
the sum of the last two.
nswer: The numbers are? Please help
Answer:
Step-by-step explanation:
We can represent the 5 consecutive odd integers as:
1. x
2. x + 2
3. x + 4
4. x + 6
5. x + 8
"...the sum of the first three integers", then, is
x + (x + 2) + (x + 4)
That is "the sum of the last two plus 7", which is
(x + 6) + (x + 8) + 7.
The connecting word "is" means there is an equals sign right there. Therefore,
x + (x + 2) + (x + 4) = (x + 6) + (x + 8) + 7 which simplifies down to
3x + 6 = 2x + 21 after we combine like terms.
x = 15. That means the first integer is 15, the next one is 17, the third one is 19, the fourth one is 21, and the fifth one is 23.
a rectangle prism has a base that is 6 centimeters by 11 centimeters and has a height of 5.5 centimeters what is the surface area in square centimeters of the prism
the total area of all four square faces: 4 x 60.5 cm² = 242 cm²
To find the surface area of a rectangular prism, we need to calculate the area of each of its six faces and then add them up.
The two rectangular faces are congruent, so we only need to calculate one of them and multiply by 2.
The area of one rectangular face is:
6 cm x 5.5 cm = 33 cm²
Multiplying by 2 gives us the total area of both rectangular faces:
2 x 33 cm² = 66 cm²
The other four faces are also congruent, so we only need to calculate one of them and multiply by 4.
The area of one of the square faces is:
11 cm x 5.5 cm = 60.5 cm²
Multiplying by 4 gives us the total area of all four square faces:
4 x 60.5 cm² = 242 cm²
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Given f(x) = 3x - 4 and g(x) = x ^ 2 - 3 find (g f) (x) .
A) 9x ^ 2 - 24x + 19
B) 9x ^ 2 + 13
C) 3x^2 - 13
D) 9x ^ 2 - 24x + 13
Answer:
D
Step-by-step explanation:
f(x) = 3x - 4
Substituting f(x) into g(x) gives:
g(f(x)) = (3x - 4)^2 - 3
Expanding the squared term, we get:
g(f(x)) = 9x^2 - 24x + 16 - 3
Simplifying, we get:
g(f(x)) = 9x^2 - 24x + 13
At the Middletown Middle School fun run, teams compete in a relay race. Each person runs 1 2 of a mile, and the race is 2 miles long. How many people are on each team?
One of the lamp posts at a shopping center has a motion detector on it, and the equation (x+16)2 + (y-13)² = 36 describes the boundary within which motion can be sensed. What is the greatest distance, in feet, a person could be from the lamp and be detected? A. 6 ft B. 12 ft C. 36 ft D. 72 ft
The greatest distance, in feet, a person could be from the lamp and be detected is: B. 12 ft
How to find the greatest distance?The equation (x+16)² + (y-13)² = 36 describes a circle with center (-16,13) and radius 6. The motion detector on the lamp post can detect motion within this circle.
To find the greatest distance a person could be from the lamp and still be detected, we need to find the diameter of the circle, which is equal to twice the radius. Therefore, the greatest distance a person could be from the lamp and still be detected is 2(6) = 12 feet.
Therefore, the correct answer is B) 12 ft.
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If a customer uses a discount code that offers a 25% discount and free shipping, the hammer will cost $17.25. There is no sales tax if the customer buys the hammer online. What is the original price of the hammer from the online retailer?
Answer:
$69
Step-by-step explanation:
25% = 0.25
17.25 ÷ 0.25 = 69
69 × 0.25 = 17.25
The original price of the hammer from the online retailer is $23.
What is Percentage?Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.
Percentage is usually denoted by the symbol '%'.
Given that,
Discount percentage = 25%
Amount after the discount = $17.25
We have to find the original price of the hammer.
Let x be the original price of the hammer.
x - 25% of x = 17.25
x - 0.25x = 17.25
0.75x = 17.25
x = $23
Hence the original cost of the hammer is $23.
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In isosceles trapezoid ABCD, AB || CD. If m
To create an entry code you must first choose 2 letters and then 4 single digit numbers how many different entry codes can you create?
Let f(x)=(x-1)^2
Find a domain on which f is one-to-one and non-decreasing.
Find the inverse of f restricted to this domain
The domain where fx) is 1-to-1 is x ≥1 , and the inverse there is:
f⁻¹(x) = √x + 1
How to find the domain where the function is 1-to-1?Here we have the quadratic function:
f(x) = (x - 1)^2
If we look from the vertex to the right (or the left, is the same) we will have an one to one function.
Here the vertex is at x = 1
f(1) = (1 - 1)^2 = 0
Then for x ≥1 we have an one to one function.
Noe let's find the inverse, if the inverse is f⁻¹(x), then we must have that:
f( f⁻¹(x) ) = x
Solving that:
(f⁻¹(x) - 1)^2 = x
(f⁻¹(x) - 1) = √x (here we only take the positive square root)
f⁻¹(x) = √x + 1
That is the inverse.
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Write one complete sentence to interpret the solution of the graph below.
The interpretation of the solution of the graph can be: the solution (6, 64) on the graph represents that after 6 minutes, there are 64 gallons of water.
How to Interpret the Solution of a Graph?The solution to a system that is plotted on a graph is the coordinates of the point interception of the graph.
Therefore, the solution (6, 64) represents a point on the graph of a relationship between time in minutes (represented by the x-axis) and water in gallons (represented by the y-axis).
The solution tells us that at 6 minutes, the water level is 64 gallons. In other words, (6, 64) on the graph, represents the amount of water in the tank over time.
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How do we factorise 6x squared minus 4xy
I will rate your answer 5 stars if correct and a thanks
To factorize 6x²2 - 4xy, we can factor out the greatest common factor (GCF), which is 2x:
6x²2 - 4xy = 2x(3x - 2y)
What is factorization?
Factorization is the process of finding two or more expressions that, when multiplied together, produce a given expression. In other words, it is the process of breaking down a mathematical expression into simpler factors.
For example, consider the expression x²2 - 4x - 21. We can factorize it by finding two expressions that, when multiplied together, give us x²2 - 4x - 21. One way to do this is to factor the expression into (x - 7)(x + 3):
x²2 - 4x - 21 = (x - 7)(x + 3)
This is an example of factorization, where the expression on the left-hand side has been broken down into the simpler factors on the right-hand side.
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The point A ( 3 , − 2 ) is reflected over the point ( 4 , 0 ) and its image is point B . What are the coordinates of point B ?
The coordinates of point B are (1,2).
How to find Reflection of a point?
When a point is reflected across the X-axis, the x-coordinates remain the same. But the Y-coordinates are transformed into their opposite signs. Therefore, the reflection of the point (x, y) across X-axis is (x, -y).
The reflected point will be equidistant from the point over which it is reflected as the original point and in the same line as the original point and the reflected point.
Find the difference between the x and y values of the given points and add that value (distance) to the reflection point.
x-values: 4-3 = 1 y-values: 0-(-2) = 2
Add to reflection point x: 4-3 = 1 y: 0 -(-2)= 2
Hence, The coordinates of point B are (1,2).
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To prepare for his mountain biking trip, Rhyan bought four tire patches. Rhyan paid using a gift card that had $22.20 on it. After the sale, Rhyan’s gift card had $1.90 remaining. Which equations could you use to find the price of one tire patch? Select all that apply. 4x – 1.9 = 22.2 4x – 22.2 = 1.9 4x + 1.9 = 22.2 4x + 22.2 = –1.9 22.2 – 4x = 1.9
The equations used to calculate the cost of a single tire patch are 22.2 - 4x = 1.9 and 4x + 1.9 + 22.2.
what is equation ?The statistic is said to be in its simplistic definition when divided into its smallest equivalent portion. How to further find the most basic form. Identify common factors in the denominator and the numerator. Verify a fractional integer to verify if it qualifies as a prime number. A remark having two quadrilateral and an identical sign in the middle is called an equation in mathematics. The general form of any issue contains the degrees of all the components in descending order. The basic form of a system of equations is an x + b = 0. The general form of a linear function with two variables is an x + b y + c = 0. (or something similar). Mathematics can be categorized as identity or conditional equations. An identity stands true regardless of the value given to the variables.
given
equations 4x + 1.9 + 22.2
22.2 - 4x = 1.9
It should all total up to $22.20 if you use the undetermined cost of the four tire patches as x, or $1.90 if you're deducting it.
The equations used to calculate the cost of a single tire patch are 22.2 - 4x = 1.9 and 4x + 1.9 + 22.2.
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