Your Turn: In the diagram, AB = 12, DX = 2.5, and BX = 5. Find CD. Show all work.
Your Turn: In the diagram, AB = 12, DX = 2.5, and BX = 5. Find CD. Show all work.
Solution:
In ΔABX and ΔCDX,
∠CDX=∠ABX=90°
Also,∠CXD=∠AXB (as shown in figure)
∠DCX=∠BAX, as two angles of the triangle are equal. The third angle is also equal.
So ΔCDX≈ΔABX
Hence, the ratio of sides must be equal.
[tex] \frac{CD}{AB} =\frac{DX}{BX} =\frac{CX}{AX} [/tex]
Now, using,
[tex] \frac{CD}{AB} =\frac{DX}{BX} [/tex]
[tex] \frac{CD}{AB=12} =\frac{DX=2.5}{BX=5} [/tex]
[tex] \frac{CD}{12} =\frac{2.5}{5} [/tex]
Now, To solve for CD, Let us multiply by 12 on both sides
[tex] \frac{12*CD}{12} =\frac{12*2.5}{5} [/tex]
[tex] \frac{1*CD}{1} =\frac{30}{5} [/tex]
[tex] CD =\frac{6}{1} [/tex]
CD=6 Answer
1. What is the constant of variation for the relationship f(x) = 40x?
2. Which equation is the direct variation equation if f(x) varies directly with x and f(x) = -12 when x=6
If f(x) = –x3, g(x) = 3x2 – 1, and h(x) = 2x + 5, what is the degree of [f o g o h](x)?
a-2
b-3
c-5
d-6
Answer:
Option d: 6
Step-by-step explanation:
Find f(g(h(x))).
h(x)=2x+5
g(h(x)) = 3(2x+5)^2 -1 (substitute h(x) in)
f(g(h(x)))= -[3(2x+5)^2 -1]^3 (substitute g(h(x)) in)
Since it asks for the degree of the function, that means we must look for the variable with the highest degree. In this case, after distributing and simplifying out the last equation, we will find that the variable x has the highest degree of x^6, or 6.
Find m<A. Round to the nearest tenth.
A.
49.5°
B.
53.1°
C.
63.4°
D.
66.4°
What is the area of the triangle whose vertices are (0,0), (3,0) and (0,4)?
Suppose that an individual has a body fat percentage of 18.9% and weighs 149 pounds. How many pounds of her weight is made up of fat? Round your answer to the nearest tenth.
Look at the picture below // 99 points // PLEASEE HELPP
What is 59.69 written in expanded form
Final answer:
The expanded form of 59.69 is 50 + 9 + 0.6 + 0.09.
Explanation:
59.69 written in expanded form can be expressed as:
50 + 9 + 0.6 + 0.09
5 * 10 + 9 * 1 + 0.6 * 0.1 + 0.09 * 0.01
5 * 10 + 9 * 1 + 6 * 0.1 + 9 * 0.01
50 + 9 + 0.6 + 0.09
Therefore, the expanded form of 59.69 is 50 + 9 + 0.6 + 0.09.
Final answer:
The number 59.69 written in expanded form is 50 + 9 + 0.6 + 0.09. Each term represents a digit according to its place value, with tens, ones, tenths, and hundredths places accounted for respectively.
Explanation:
Writing the number 59.69 in expanded form means expressing each digit according to its place value. Expanded form is a way of writing numbers to see the math value of individual digits. The number 59.69 would be broken down as follows:
50 + 9 + 0.6 + 0.09
Each term represents a digit in the number: '5' is in the tens place, so it is represented as 50; '9' is in the ones place, so it is simply 9; '6' is in the tenths place, so it is represented as 0.6; '9' is in the hundredths place, so it is represented as 0.09.
When performing calculations, particularly in subjects such as chemistry, scientific notation is often used to express large or tiny numbers efficiently. For example, to enter a number in scientific notation into a calculator, you must know the correct process, which can vary based on the calculator model. Consulting the instructor or the calculator's manual is advisable if there are any doubts.
Furthermore, working with scientific notation involves understanding how to properly write and interpret the exponents, which indicate how many places the decimal point has been moved.
based on the given information ,which statement best explains whether the quadrilateral is a parallelogram
Answer:
the answer is (it cannot be determined from the information given)
Which expression makes the equation true for all values of X? 16 X -16 =4(?)
answer asap, Ill give brainliest, show work
Steve can paint a room three times as fast as Billy. When they work together, Steve and Billy can paint a large room in 4 hours. How many hours would it take Billy to paint it by himself?
I Put 45 Points!!
Use what you have learned from this chapter to make a model boat out of a 10-cm square piece of foil. Test your model boat in a tank of water to see how many pennies it can support before sinking. Compare the performance of your boat with those of your classmates. Suggest several design improvements based on your results. Respond to at least one other students posting giving suggestions on how the model of their boat or yours could be improved to increase buoyancy.
Find the circumstances of the circle
How measuring angles could be useful in thge real world?
NEED HELP ASAP!
simplify the radical expression State any restrictions (n^4 -11n^2 +30) / (n^4 -7n^2 +10)
Please show steps!
Answer:
screenshot shows the answer but: n^2-6/n^2-2
Step-by-step explanation:
n^4-11n^2+30/n^4-7n^2+10
simplify the numerator
rewrite n^4 as (n^2)^2
and let u substititue for all occurences of n^2
u^2-11y+30/n^4-7n^2+10
factor u^2 - 11u+30 using the AC method.
(u-6)(u-5)/n^4-7n^2+10
(n^2-6)(n^2-5)/(n^2-5(n^2-2)
Cancel the common factor, and n^2-6/n^2-2 is your answer.
Excluded values/restrictions are n= -sqrt5 n= -sqrt2, also n= sqrt5 n= sqrt2
laissez faire is the term used to describe a capitalist economy without any regulations
Information about Laissez-faire's economy is given.
What is a Laissez-faire economy?Laissez-faire is a free-market, capitalist economic theory that rejects government interference. The French Physiocrats, who lived in the 18th century, created the laissez-faire ideology. According to proponents of laissez-faire, government involvement in industry and markets hinders economic progress.
Laissez-Faire capitalism allowed businesses to pursue just their financial goals without having to worry about restrictions from the state or taxes. Naturally, this might induce unfavorable externalities and knowledge asymmetries that could enable producers to act badly and get away with it. Laissez-Faire proponents contend that since the market would eliminate such undesirable actors, extensive and expensive regulation is not necessary. However, in practice, negative actors might carry on their operations for a very long time. Without government testing and regulatory oversight to safeguard consumers, for instance, it could not be known if a vitamin manufacturer is putting sawdust in place of herb powder in their capsules.
Therefore, In real world the laissez-faire is a capitalist economy have regulations.
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Which expression can be used to find the number of liters in 15 quarts?
Answer:15 quarts/1 x 0.95 liter/1 quart
Step-by-step explanation:
Write an equation of the line with a slope of 2 that passes through the point (2,0)
Hence, the line with a slope [tex]2[/tex] that passes through the point [tex](2,0)[/tex] is
[tex]y=2x-4[/tex]
What is the line of equation?
The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system.
The numerous points which together form a line in the coordinate axis are represented as a set of variables [tex]x, y[/tex] to form an algebraic equation, which is referred to as an equation of a line.
As we know the line of the slope is
[tex]y=mx+b[/tex]
where [tex]m[/tex] is the slope we have [tex]m = 2.[/tex]
So it would be
[tex]y=2x+b[/tex]
Given the point, [tex](2, 0)[/tex]
Now, we replace [tex]x[/tex] with [tex]2[/tex] and [tex]y[/tex] with [tex]0[/tex].
Now, we solve for [tex]b[/tex].
So,
[tex]0=2(2)+b\\b+4=0\\b=-4[/tex]
Since we get [tex]b = -4[/tex], we replace [tex]b = -4[/tex]
i.e., [tex]2x-4[/tex]
Hence, the line with a slope [tex]2[/tex] that passes through the point [tex](2,0)[/tex] is
[tex]y=2x-4[/tex]
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Round 6541 to the nearest thousand
To round 6541 to the nearest thousand, identify the place value and look at the hundreds place. The answer is 6000.
Rounding 6541 to the nearest thousand:
Identify the place value you are rounding to, which is the nearest thousand.
Look at the hundreds place since we are rounding to the nearest thousand. In 6541, the hundreds digits is 5, so the thousands digit remains 6, and all digits after that become 0. Therefore, 6541 rounded to the nearest thousand is 6000.
Find the value of a in the parallelogram.
Fifty students in the third-grade class listed their hair and eye colors in the table below: Brown hair Blonde hair Total Blue eyes 14 8 22 Brown eyes 16 12 28 30 20 50 Are the events "blonde hair" and "blue eyes" independent?
A) Yes, P(blonde hair) • P(blue eyes) = P(blonde hair ∩ blue eyes)
B) Yes, P(blonde hair) • P(blue eyes) ≠ P(blonde hair ∩ blue eyes)
C) No, P(blonde hair) • P(blue eyes) = P(blonde hair ∩ blue eyes)
D) No, P(blonde hair) • P(blue eyes) ≠ P(blonde hair ∩ blue eyes)
Answer: the answer is D
Step-by-step explanation:
You survey 67 employees, and 30 respond that their job satisfaction is high. What percentage of your employees have high job satisfaction?
Answer:
Percentage of employees have high satifaction of tthe job = 44.78%
Explanation:
In a company there are 67 employees
after survey only 30 employees give the high satisfaction feedback.
So, percentage of employess have high job satisfaction = [tex] \frac{Survey result}{Total employees} *100
[/tex]
= [tex] \frac{30}{67}*100 [/tex]
= 0.44776*100
= 44.78% Final answer
What is the approximate volume of the cone? Use 3.14 for π . 1206 cm³ 2170 cm³ 3260 cm³ 6510 cm³ Outline of cone with a dotted line rising from middle of base to the point. Line is labeled 8 cm. A second dotted line extends horizontally from middle of base to its edge. Line is labeled 12 cm.
The required approximate value volume of the cone is v = 1206 `cm³.
Given that the Height of the cone = 8 m
The Radius of the cone = 12 m
We have to find,The approximate volume of the cone .
What is the volume of a cone?The volume of a cone is equal to one-third of the volume of a cylinder having the same base radius and height.
Where V is the volume, r is the radius and h is the height.
The volume of the cone
[tex]V = \dfrac{1}{3} \pi r^3 h \: \rm unit^3[/tex]
Where, π = 3.14
[tex]V = \dfrac{1}{3} \pi r^3 h \: \rm unit^3\\\\ V = \dfrac{1}{3} \pi (8)^3 (12) \: \rm unit^3[/tex]
V = 1206 cm³
Hence, The required approximate value volume of the cone is v = 1206 `cm³
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Can one angle of a parallelogram be equal to 40° and another one 50°? Justify your reasoning.
In right triangle PQR, P and Q are complementary angles. The value of sin Q is 9/41. What is the value of cos P?
Final answer:
In right triangle PQR, sin Q = 9/41. To find cos P, we need to determine the length of the hypotenuse PR. Once we have PR, we can use the cosine function to find cos P.
Explanation:
In a right triangle, the sine of an angle is the length of the side opposite the angle divided by the length of the hypotenuse. So, in triangle PQR, sin Q = opposite/hypotenuse = PQ/PR = 9/41.
Since angles P and Q are complementary, their sum is 90 degrees. Therefore, angle P = 90 - angle Q.
Now, using the Pythagorean theorem for triangle PQR (PQ^2 + QR^2 = PR^2), we can find PR. Since PQ = 9 and QR = 41, we have: 9^2 + 41^2 = PR^2. Solving for PR gives us PR ≈ 41.297.
Now that we have PR, we can find cos P using the cosine function: cos P = adjacent/hypotenuse = QR/PR = 41/41.297 ≈ 0.993.
In a right triangle, sin Q = 9/41. To find cos P, we can use the identity cos(90 - x) = sin(x). So cos P = sin(Q) = 9/41.
Explanation:In a right triangle, the sine of an angle is equal to the length of the side opposite the angle divided by the hypotenuse. In this case, sin Q = 9/41, which means that the length of the side opposite Q is 9 and the length of the hypotenuse is 41. Since P and Q are complementary angles, P = 90 - Q. Therefore, cos P = cos(90 - Q).
Using the identity cos(90 - x) = sin(x), we can substitute the value of Q to find cos P. cos P = sin(Q) = 9/41.
The histogram represents the distributions of rain amounts in two cities. Which best explains how the histogram is useful for comparing the shapes of the data sets? It is easier to visually compare the means of the data. It is easier to visually compare the standard deviations of the data. It is easier to visually compare the medians of the data. It is easier to visually compare symmetry and skew of the data.
Answer:
It is easier to visually compare symmetry and skew of the data.
Step-by-step explanation:
Given that the histogram represents the distributions of rain amounts in two cities.
Histogram enables us to have a visual idea easily understandable about the pattern of the distribution.
The important points are whether the distribution is symmetrical or right/left skewed.
Mean, median, std deviations cannot be found easily by justing seeing the histograms.
Hence correct answer is
It is easier to visually compare symmetry and skew of the data.
How do you Simplify a4 x a5
The simplification of the given expression by the law of indices will be a⁹.
What is the law of indices?Index (indices) in Maths is the power or exponent which is raised to a number or a variable.
In other words, the mathematics of power or exponent of any number is called indices.
Another example could be 7² = 7³/7 here we divide to obtain power 2.
As per the given expression,
a⁴ × a⁵
By the law of indices that [tex]a^{m} \times a^{n} = a^{m+n}[/tex].
a⁴ × a⁵ = a⁽⁴ ⁺ ⁵⁾ = a⁹
Hence "The simplification of the given expression by the law of indices will be a⁹".
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Pencils sells for 98 cents per dozen. how much more per pencils
The ratio of girls to boys in a classroom is 3:5. Kevin says there must be 8 students in the classroom. Which explains whether Kevin is correct?
Kevin is incorrect because 3:5 may be a simplified ratio.
Kevin is incorrect because 3:5 may be a simplified ratio. Option C is correct.
Given that,
The ratio of girls to boys in a classroom is 3:5. Kevin says there must be 8 students in the classroom. Which explains whether Kevin is correct is to be determined,
The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
Here, the ratio of girls to boys is 3:5, Which implies there are 3 girls over 5 boys in the number, This is the simplified ratio of the girls to boys of the students in the class. So, Kevin says there must be 8 students in the classroom which is right, but Kevin does not explain the proportion in his statement,
Thus, Kevin is incorrect because 3:5 may be a simplified ratio. Option C is correct.
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Write and solve an equation to answer the question. "18 is 32% of what number w"
The value of 32% of 18 is equal to 56.25.
The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that 18 is 32% of the number w. The value of w will be calculated as:-
18 x 32/100 = w
Solve the above equation by mathematical operations to get the value of w,
18 x 32/100 = w
w = 56.25
Therefore, the value of w will be 56.25.
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