Which Statements about Trapezoids and Rhombuses are true?
A.) Both shapes are 2-dimensional figures.
B.) The first shape has the same number of angles as the second shape.
C.) Both shapes have all sides of equal length.
I need help!!!
Answers
As for A, it is obvious how they are two dimensional. And as for B, if you look at these shapes you'll see that they both have 4 angles.
Option A & B are true about trapezoids and rhombuses.
What are trapezoids and Rhombuses?
A trapezoid is a polygon that has only one pair of parallel sides. These parallel sides are also called parallel bases of trapezoid. The other two sides of trapezoids are non-parallel and called legs of trapezoids.
A rhombus is a special case of a parallelogram. In a rhombus, opposite sides are parallel and the opposite angles are equal. Moreover, all the sides of a rhombus are equal in length, and the diagonals bisect each other at right angles. The rhombus is also called a diamond or rhombus diamond.
Now determine which statement is true about trapezoid and rhombuses
We have given,
Option A: Both shapes are 2-dimensional figures.
This option is true because both trapezoid and rhombuses are a type of quadrilateral and we know quadrilaterals are 2 dimensional figures.
Option B: The first shape has the same number of angles as the second shape.
Yes,this option is true because both the shapes are quadrilateral type and a quadrilateral is a closed polygon containing 4 sides and 4 vertices enclosing 4 angles.
Option C: Both shapes have all sides of equal length.
No,this is not true as rhombus has all sides of equal length but trapezoid has all sides of different length.
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Related Questions
If f(x) = 2x + 2 and g(x) = x3, what is (gºf)(2)?
Answers
Answer:
216
Step-by-step explanation:
(g∘f)(x) = g(f(x))
f(2) = 2·2 +2 = 6
g(f(2)) = g(6) = 6³ = 216
Answer:
216
Step-by-step explanation:
Correct Plato
When solving the proportion x−26=1x+3, Santos first starts by using the Cross Product Property, multiplying the extremes and the means, to get 6=x2+x−6. Then, he subtracts 6 from both sides of the equation 6=x2+x−6 and finds the equation 0=x2+x−12. Part A: What should Santos do next to solve the equation? Part B: What is/are the solution(s) to the proportion? Select one answer for Part A, and select all answers that apply for Part B.
Answers
Answer:
A: factor the equation to (x -3)(x +4) = 0
B: solutions are x=-4, x=3
Step-by-step explanation:
A: Santos has the equation in standard form. Several options for solution are available: graphing (see attached), completing the square, factoring, using the quadratic formula. I find factoring to get to the solution most directly. The other methods work just as well.
To factor the equation, Santos needs to find two factors of -12 that have a sum of +1. Those would be +4 and -3. Putting these numbers into the binomial factors, Santos would have ...
(x +4)(x -3) = 0
__
B: The values of x that make the factors zero are ...
x = -4, x = 3
To solve the equation, Santos should first factor the quadratic equation, then use the Zero Product Property to find the solutions, which are x = 3 and x = -4.
Explanation:For Part A, Santos should factor the quadratic equation x2 + x - 12 = 0. This can be done by finding two numbers that add to 1 (the coefficient of x) and multiply to -12 (the constant term). These numbers are 4 and -3. So the factored form of the equation is (x - 3)(x + 4) = 0.
For Part B, to find the solutions to the proportion, he should use the Zero Product Property which states that if the product of two factors is zero, then at least one of the factors must equal zero. This gives us the solutions x - 3 = 0 and x + 4 = 0. Solving for x in each case provides the solutions: x = 3 and x = -4.
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Can someone let me know if I simplified these equations correctly or at least show me how to do it?
Answers
Answer:
Your work is correct as far as it goes. Now eliminate the terms that are zero.
Step-by-step explanation:
Multiplying anything by zero gives zero. Adding zero is like adding nothing. Zero is called the "additive identity element" because ...
a + 0 = a
Adding zero doesn't change anything. You can (and should) drop the zero if your goal is to simplify the expression.
[tex]a. \quad x_{f}=v_{0}\\\\b. \quad x_{f}=v_{0}t\\\\c. \quad v_{f}^2=v_{0}^2[/tex]
Which expression is a sum of cubes?
Answers
Answer:
-27a³b⁶+ 8a⁹b¹²
Step-by-step explanation:
In the expression above -27 is a perfect cube of -3, 8 is a perfect cube of 2.
The exponents of a and b in both terms in the expression are divisible by 3.
The cube root of x, that is ∛xⁿ=x∧(n/3) where n is an integer.
ANSWER
[tex]- 27 {a}^{3} {b}^{6} + 8 {a}^{9} {b}^{12} [/tex]
EXPLANATION
When we can write an expression in the form
[tex] {(x)}^{3} + {(y)}^{3} [/tex]
then it is a sum of cubes.
To write a given sum as sum of cubes, then the coefficients of the terms should cube be numbers and the exponents of any power should be a multiple of 3.
This tells us that the first option will be the best choice.
[tex] - 27 {a}^{3} {b}^{6} + 8 {a}^{9} {b}^{12} [/tex]
We can rewrite this as:
[tex] { (- 3)}^{3} {a}^{3} {b}^{2 \times 3} + {2}^{3} {a}^{3 \times 3} {b}^{4 \times 3} [/tex]
We apply this property of exponents:
[tex] ({a}^{m} )^{n} = {a}^{mn} [/tex]
This gives us
[tex] {( - 3a {b}^{2}) }^{3} + {(2{a}^{3} {b}^{4} })^{3} [/tex]
Therefore the correct option is A
What is the slope of the line x = 3?
Answers
Answer:
1/3 = .33
THE UNIT RATE IS 1 TO 3
Answer:
infinite slope
Step-by-step explanation:
Note that x=3 is simply a vertical straight line that passes through the point (3,y) for all real values of y
Also recall that the slope of a vertical straight line is undefined (or infinite slope)
hence the slope of x=3 is infinite.
Sue graphed the formula for converting temperatures from Fahrenheit to Celsius. If the temperature is 50 degrees Fahrenheit, what is the temperature in Celsius? 5 degrees Celsius 10 degrees Celsius 15 degrees Celsius 20 degrees Celsius
Answers
For this case, we have by definition that:
[tex]C = (F-32) * \frac {5} {9}[/tex]
If they tell us that the base temperature is 50 degrees Fahrenheit, then we substitute:
[tex]C = (50-32) * \frac {5} {9}\\C = 18 * \frac {5} {9}\\C = 2 * 5\\C = 10[/tex]
Finally, the temperature equals 10 degrees Celsius.
Answer:
10 degrees Celsius
The temperature in Celsius when it is 50 degrees Fahrenheit is 10 degrees Celsius, calculated using the conversion formula Celsius = (Fahrenheit - 32) × 5/9.
Explanation:To convert a temperature from Fahrenheit to Celsius, we use the formula: Celsius = (Fahrenheit - 32) × 5/9. If the temperature is 50 degrees Fahrenheit, we subtract 32 from 50, giving us 18. Then we multiply 18 by 5/9, resulting in 10. Therefore, the temperature in Celsius is 10 degrees Celsius.
Step-by-step conversion:Start with the Fahrenheit temperature: 50°F.Subtract 32 from the Fahrenheit temperature: 50 - 32 = 18.Multiply by 5/9 to convert to Celsius: 18 × 5/9 = 10°C.Thus, when the temperature is 50°F, it is equivalent to 10°C.
Determine the measure of arc CED.
A. 180°
B. 99°
C. 198°
D. 81°
Answers
Answer:
C
Step-by-step explanation:
An angle whose vertex lies on a circle and whose sides are 2 chords of the circle is one half the measure of the intercepted arc.
arc CED is the intercepted arc, hence
arc CED = 2 × 99° = 198°
Answer:
C) 198
Step-by-step explanation:I took the test
A new board game comes with a deck of 20 cards: 5 red, 3 blue, 2 orange, and 10 green.
After the deck is shuffled, the player is to choose the top card and note its color, replace
the card, shuffle the deck again, and then choose the top card again and note its color.
What is the probability that both cards selected are blue?
Answers
Determine whether the two triangles are similar. HELP ASAP! I AM RUNNING OUT OF POINTS!!
Answers
Answer:
ΔKLJ ~ ΔRPQ by AA~
Step-by-step explanation:
Angle angle similarity needs two corresponding angles in two triangles to be same. The two given triangles are similar by: ΔKLJ ~ ΔRPQ by AA~
How to find measure of missing third angle in a triangle?It is a theorem in mathematics that sum of internal angles of a triangle equate to [tex]180^\circ[/tex]
Suppose that two angles are given as [tex]a^\circ[/tex] and [tex]b^\circ[/tex] and let there is one angle missing. Let its measure be [tex]x^\circ[/tex]
Then, by the aforesaid theorem, we get:
[tex]a^\circ + b^\circ + x^\circ = 180^\circ\\\\ \text{Subtracting a + b degrees from both sides} \\\\x^\circ = 180^\circ - (a^\circ + b^\circ)[/tex]
What is Angle-Angle similarity for two triangles?Two triangles are similar if two corresponding angles of them are of same measure. It is because when two pairs of angles are similar, then as the third angle is fixed if two angles are fixed, thus, third angle pair also gets proved to be of same measure. This makes all three angles same and thus, those two triangles are scaled copies of each other. Thus, they're called similar.
For given case, we've got
[tex]m\angle K = m\angle R\\m\angle J = m\angle Q\\[/tex]
Thus, for the rest of the angle pair, we have:
[tex]m\angle L = 180 - (m\angle J + m\angle K) = 180 - (m\angle Q + m\angle R) = m\angle P\\\\m\angle L = m\angle P[/tex]
Thus, given two triangles are similar by angle-angle similarity.
Thus,
The two given triangles are similar by: ΔKLJ ~ ΔRPQ by AA~
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Apple trees cost $ 30 each, and cherry trees cost $ 40 each. Rohan has $ 600 to spend on fruit trees.
a) Let x represent the number of apple trees purchased, and let y represent the number of cherry trees purchased.
b) Write an equation that illustrates the different ways Rohan can purchase apple trees and cherry trees and spend exactly $ 600 .
Equation:
Answers
Answer:
A) Apples: $30x
Cherry: $40y
B) ($30x)+($40y)=600
Which of the following is the correct notation for -48-89
Answers
Answer:
Step-by-step explanation:
Because 48 and 89 have the same sign, that is, the negative sign, their sum takes on that sign:
-48
-89
---------
-137
Does the point “is on the circle shown? Explain.
Answers
Answer:
Option 2: Yes, the distance from (-2,0) to (1,√7) is 4 units
Step-by-step explanation:
The point is:
(1,√7)
If the point lies on the circle, then the distance of point and the center of circle should be equal to the radius of the circle.
The radius can be viewed from the diagram that it is 4 units.
The center is: (-2,0)
Now, distance:
[tex]d = \sqrt{(x_2-x_1)^{2}+ (y_2-y_1)^{2}}\\ d = \sqrt{(-2-1)^{2}+ (0-\sqrt{7} )^{2}}\\ d = \sqrt{(-3)^{2}+ (-\sqrt{7} )^{2}}\\=\sqrt{9+7}\\ =\sqrt{16}\\ =4[/tex]
Hence, option 2 is correct ..
A student's course grade is based on one midterm that counts as 5% of his final grade, one class project that counts as 15% of his final grade, a set of homework assignments that counts as 35% of his final grade, and a final exam that counts as 45% of his final grade. His midterm score is 75, his project score is 93, his homework score is 78, and his final exam score is 70. What is his overall final score? What letter grade did he earn (A, B, C, D, or F)? Assume that a mean of 90 or above is an A, a mean of at least 80 but less than 90 is a B, and so on.
Answers
Answer:
76.5CStep-by-step explanation:
Apply the weights to the scores and add them up:
5% × midterm + 15% × project + 35% × homework + 45% × final
= 0.05(75) +0.15(93) +0.35(78) +0.45(70)
= 76.5
The student has a solid letter grade of C.
The student's overall final score is 76.5 which is between 70 and 79, the students earned a C.
To calculate the student's overall final score, we can use the following formula:
Final grade = (midterm score * midterm weight) + (project score * project weight) + (homework score * homework weight) + (final exam score * final exam weight)
where midterm weight is the percentage of the final grade that the midterm counts for, project weight is the percentage of the final grade that the project counts for, homework weight is the percentage of the final grade that the homework assignments count for, and final exam weight is the percentage of the final grade that the final exam counts for.
In this case, the midterm weight is 5%, the project weight is 15%, the homework weight is 35%, and the final exam weight is 45%. The student's midterm score is 75, his project score is 93, his homework score is 78, and his final exam score is 70.
Therefore, the student's overall final score is calculated as follows:
Final grade = (75 * 0.05) + (93 * 0.15) + (78 * 0.35) + (70 * 0.45)
Final grade = 3.75 + 13.95 + 27.3 + 31.5
Final grade = 76.5
Therefore, the student's overall final score is 76.5.
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The value of a collector’s item is expected to increase exponentially each year. The item is purchased for $500. After 2 years, the item is worth $551.25. Which equation represents y, the value of the item after x years?y = 500(0.05)xy = 500(1.05)xy = 500(0.1025)xy = 500(1.1025)x
Answers
Answer:
y = 500(1.05)^x.
Step-by-step explanation:
551.25 = 500x^2 where x is the multiplier for each year.
x^2 = 551.25/500
x = 1.05
So the value after x years is 500(1.05)^x.
Answer: [tex]y=500(1.05)^x[/tex]
Step-by-step explanation:
The exponential growth equation is given by :-
[tex]y=A(1+r)^x[/tex] (1)
, where A is the initial value of , r is the rate of growth ( in decimal) and t is the time period ( in years).
Given : The value of a collector’s item is expected to increase exponentially each year.
The item is purchased for $500. After 2 years, the item is worth $551.25.
Put A= 500 ; t= 2 and y= 551.25 in (1), we get
[tex]551.25=500(1+r)^2\\\\\Rightarrow\ (1+r)^2=\dfrac{551.25}{500}\\\\\Rightarrow (1+r)^2=1.1025[/tex]
Taking square root on both sides , we get
[tex]1+r=\sqrt{1.1025}=1.05\\\\\Rightarrow\ r=1.05-1=0.5[/tex]
Now, put A= 500 and r= 0.5 in (1), we get the equation represents y, the value of the item after x years as :
[tex]y=500(1+0.5)^x\\\\\Rightarrow\ y=500(1.05)^x[/tex]
HELPPPP!!!!!!!!!!!!!!!! (10 points) We want to know the probability that a student selected randomly from her class would have an “A” (90 or above) in her class. Find the probability. Explain HOW to find the probability
Answers
Answer:
23 out of 91
around 1/3 of the class
Step-by-step explanation:
the total number of students so around the third part of the class
The cost in dollars to manufacture x pairs of shoes is given by 12,000 + 19x. This month, the manufacturer produced 1000 more pairs of shoes than last month. The average cost per pair dropped by $0.43.
a) Write an expression for the average cost per pair of shoes. Use this expression to write an equation to represent there situation.
b) Solve your equation
c) Are there any mathematical restrictions on the domain? Explain.
d) Determine reasonable domain in the context of the problem. Use your answers to parts I and II to answer the question.
Answers
Answer:
(a) The expression for the average cost per pair of shoes is [tex]A(x)=\frac{12000}{x}+19[/tex] and equation for the situation is [tex]\frac{12000}{x}+19-(\frac{12000}{x+1000}+19)=0.43[/tex].
(b) x=[tex]x\approx 4806[/tex]
(c) The average function is not defined for x=0, so the domain of the function is all real numbers except 0.
(d) The reasonable domain is all natural numbers.
Step-by-step explanation:
The cost in dollars to manufacture x pairs of shoes is given by
[tex]C(x)=12000+19x[/tex]
where, x is the pairs of shoes.
(a)
The expression for the average cost per pair of shoes.
[tex]A(x)=\frac{C(x)}{x}[/tex]
[tex]A(x)=\frac{12000+19x}{x}[/tex]
[tex]A(x)=\frac{12000}{x}+19[/tex]
This month, the manufacturer produced 1000 more pairs of shoes than last month. The average cost per pair dropped by $0.43.
[tex]A(x)-A(x+1000)=0.43[/tex]
[tex]\frac{12000}{x}+19-(\frac{12000}{x+1000}+19)=0.43[/tex]
Therefore the expression for the average cost per pair of shoes is [tex]A(x)=\frac{12000}{x}+19[/tex] and equation for the situation is [tex]\frac{12000}{x}+19-(\frac{12000}{x+1000}+19)=0.43[/tex].
(b)
On solving the above equation we get
[tex]\frac{12000}{x}-\frac{12000}{x+1000}=0.43[/tex]
[tex]\frac{12000000}{x^2 + 1000 x} = 0.43[/tex]
[tex]12000000=0.43(x^2 + 1000 x)[/tex]
[tex]12000000=0.43x^2 + 430x[/tex]
[tex]0=0.43x^2 + 430x-12000000[/tex]
Using graphing calculator we get
[tex]x\approx -5806.31,4806.31[/tex]
The pair of shoe can not be native and decimal value.
[tex]x\approx 4806[/tex]
Therefore the solution is [tex]x\approx 4806[/tex].
(c)
The average cost function is
[tex]A(x)=\frac{12000}{x}+19[/tex]
The function is not defined if the denominator is 0.
The above function is not defined for x=0, so the domain of the function is all real numbers except 0.
(d)
In the average function x represents the number of pair of shoe.
It means the value of x must be a positive integer.
Since the average function is not defined for x=0, So the reasonable domain of average function is
Domain={x : x∈Z⁺, x≠0}
Domain=N
Therefore the reasonable domain is all natural numbers.
Safari Adventure Theme Park is a selfguided theme park in which people drive through a park filled with African wildlife. They are given a map and a written guide to the wildlife of the park. They charge $20.00 per car plus $2.00 per person in the car. The number of people per car can be represented by the random variable X which has a mean value μX = 3.2, and a variance σ2x = 1.4. What is the mean of the total amount of money per car that is collected entering the park?
Answers
Answer:
$26.40
Step-by-step explanation:
For a linear function, the mean of the function is the function of the mean:
20 + 2.00·μX = 20 + 2.00·3.2 = 20 + 6.40 = 26.40 . . . . dollars
The mean total amount collected per car entering the Safari Adventure Theme Park is $26.40.
The mean of the total amount of money collected per car entering the park can be calculated by finding the expected value of the total amount, considering the price per car and per person. In this case, the mean total amount collected per car = price per car + (mean number of people per car) * price per person. Substituting the given values: 20 + 3.2 * 2 = $26.40.
What is this (pic provided) written as a single log?
Answers
Answer:
Step-by-step explanation:
when logs are added, they can be multiplied to produce a simplified log.
log_5(4*7) + log_5(2)
log_5(4*7*2)
log_5(56)
A recent study claimed that half of all college students "drink to get drunk" at least once in a while. Believing that the true proportion is much lower, the College Alcohol Study interviews an SRS of 14,941 college students about their drinking habits and finds that 7,352 of them occasionally "drink to get drunk". What type of statistical inference is this?
Answers
Answer: Hypothesis testing
Step-by-step explanation:
In statistics , Hypothesis testing is a general procedure to check the results of a experiment or a survey to confirm that they have actual and valid results.
Given claim : A recent study claimed that half of all college students "drink to get drunk" at least once in a while. By believing that the true proportion is much lower, the College Alcohol Study interviews an SRS of 14,941 college students about their drinking habits and finds that 7,352 of them occasionally "drink to get drunk".
Here the College Alcohol Study is just testing the results of the survey .
Hence, this is is s a type of Hypothesis testing.
If f(x) = 2x - 3 and g(x) = Radical over x-8,
what is (fºg)(24)?
Answers
Answer:
5
Step-by-step explanation:
Plug in 24 for x in your g(x) equation.
[tex]g(24)=\sqrt{24-8} \\g(24)=\sqrt{16} \\g(24)=4[/tex]
Next, plug in your g(x) value, 4, to your f(x) equation for x.
[tex]f(4)=2(4)-3\\f(4)=8-3\\f(4)=5[/tex]
Drag the tiles to the boxes to form correct pairs.
Multiply the sets of numbers and match them with their products.
Answers
Answer:
[tex](-\frac{3}{4})(\frac{7}{8})[/tex] ↔ [tex]-\frac{21}{32}[/tex]
[tex](\frac{2}{3})(-4)(9)[/tex] ↔ [tex]-24[/tex]
[tex](\frac{5}{16})(-2)(-4)(-\frac{4}{5})[/tex] ↔ [tex]-2[/tex]
[tex](2\frac{3}{5})(\frac{7}{9})[/tex] ↔ [tex]\frac{91}{45}[/tex]
Step-by-step explanation:
The first expression is
[tex](-\frac{3}{4})(\frac{7}{8})[/tex]
On simplification we get
[tex]-\frac{3\times 7}{4\times 8}[/tex]
[tex]-\frac{21}{32}[/tex]
Therefore the product of [tex](-\frac{3}{4})(\frac{7}{8})[/tex] is [tex]-\frac{21}{32}[/tex].
The second expression is
[tex](\frac{2}{3})(-4)(9)[/tex]
On simplification we get
[tex](\frac{2}{3})(-36)[/tex]
[tex]-\frac{72}{3}[/tex]
[tex]-24[/tex]
Therefore, the product of [tex](\frac{2}{3})(-4)(9)[/tex] is [tex]-24[/tex].
Similarly,
[tex](\frac{5}{16})(-2)(-4)(-\frac{4}{5})\Rightarrow (\frac{5}{16})(8)(-\frac{4}{5})=(\frac{5}{2})(-\frac{4}{5})=-2[/tex]
[tex](2\frac{3}{5})(\frac{7}{9})=(\frac{13}{5})(\frac{7}{9})=\frac{91}{45}[/tex]
The sets of numbers are:
(-7)(-1.2) <-> 8.4
(-2 1/2)(-2) <-> 5
(2.5)(-2)<->-5
(7) (-1.2) <-> -8.4
The given expressions involve multiplication and follow the product rule of signs. According to this rule, the product of two numbers with the same sign is positive, while the product of two numbers with different signs is negative.
(-7)(-1.2) = 8.4: Both numbers have the same sign (negative * negative), so the product is positive. The result is 8.4.
(-2 1/2)(-2) = (-5/2)(-2) = 5: Again, both numbers are negative, so the product is positive. The calculation involves multiplying mixed numbers, where -2 1/2 is equivalent to -5/2. The result is 5.
(2.5)(-2) = -5: The numbers have different signs (positive * negative), so the product is negative. The result is -5.
(7)(-1.2) = -8.4: Once more, the numbers have different signs (positive * negative), leading to a negative product. The result is -8.4.
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Y – 4 = 20 A. The difference between a number and 4 is 20. B. The product of a number and 4 is 20. C. A number combined with 4 is 20. D. The quotient of a number and 4 is 20.
Answers
Answer:
A
Step-by-step explanation:
Subtraction means "difference". The only choice there that has the word "difference" in it is choice A.
myra's stamp collection consisted of 120 stamps in october. By the following march, her collection had grown to 138 stamps. By how much did her collection increase between october and march
Answers
Answer:
18 stamp increase
15 % increase
Step-by-step explanation:
To find the increase in number , we take the number of stamps in march and subtract the stamps in october
128-120 = 18
To find the percent increase, we take the number of stamps that we gained over the original amount of stamps * 100%
percent increase = 18/120 * 100%
.15 * 100%
15% increase
Myra's stamp collection increased by 18 stamps from October to the following March. This is calculated by subtracting the number of stamps she had in October (120 stamps) from the number she had in March (138 stamps).
To find out by how much Myra's stamp collection has increased between October and March, you simply need to subtract the number of stamps she had in October from the number she had in March. She had 120 stamps in October, and by March, she had 138 stamps.
To calculate the increase, we'll use the following steps:
Take the number of stamps in March: 138 stamps.Subtract the number of stamps she had in October: 120 stamps.The difference will give us the increased number of stamps.Doing the math:
138 stamps (in March) - 120 stamps (in October) = 18 stamps
So, Myra's collection increased by 18 stamps between October and March.
Which of the following points lies on the circle whose center is at the origin and whose radius is 10?
Answers
Answer:
C.(5 sqrt(2), 5 sqrt(2)
Step-by-step explanation:
The point which lie on the circle is :
[tex](5\sqrt{2},5\sqrt{2})[/tex]
Step-by-step explanation:It is given that the circle is centered at origin and has a radius of 10 units.
We know that if (h, k) represents the coordinate of the center of circle and r is the radius of the circle then the equation of circle is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Here we have:
[tex]h=0\ ,\ k=0\ and\ r=10[/tex]
Hence, the equation of circle is given by:
[tex](x-0)^2+(y-0)^2=10^2\\\\i.e.\\\\x^2+y^2=100------------(1)[/tex]
If we substitute the given point into the equation of the circle and it makes the equation true then the point lie on the circle and if it doesn't make the equation true then the point do not lie on the circle.
a)
[tex](\sqrt{10},0)[/tex]
i.e.
[tex]x=\sqrt{10}\ and\ y=0[/tex]
i.e. we put these points in the equation(1)
[tex](\sqrt{10})^2+(0)^2=100\\\\i.e.\\\\10=100[/tex]
which is a false statement .
Hence, this point do not lie on the circle.
b)
[tex](0,2\sqrt{5})[/tex]
i.e.
[tex]x=0\ and\ y=2\sqrt{5}[/tex]
i.e. we put these points in the equation(1)
[tex](0)^2+(2\sqrt{5})^2=100\\\\i.e.\\\\20=100[/tex]
which is a false statement .
Hence, this point do not lie on the circle.
c)
[tex](5\sqrt{2},5\sqrt{2})[/tex]
i.e.
[tex]x=5\sqrt{2}\ and\ y=5\sqrt{2}[/tex]
i.e. we put these points in the equation(1)
[tex](5\sqrt{2})^2+(5\sqrt{2})^2=100\\\\i.e.\\\\50
+50=100\\\\i.e.\\\\100=100[/tex]
which is a true statement .
Hence, this point lie on the circle.
Find the product. 8y 3(-3y 2)
Answers
For this case we must find the product of the following expression:
[tex]8y ^ 3 (-3y ^ 2) =[/tex]
We have to by law of signs of multiplication:
[tex]+ * - = -[/tex]
Also, by definition of multiplication of powers of the same base, we put the same base and add the exponents, then the expression is rewritten as:
[tex]-24y ^ {3 + 2} =\\-24y ^ 5[/tex]
Answer:
[tex]-24y ^ 5[/tex]
Answer:
The Answer is -24y^5
Step-by-step explanation:
We know this because multiplying 8 by -3 = -24
Then we have to combine the exponents and we get 5.
Hope I helped. I used a website called mathwa3 to help, the 3 stands for a y.
Have a great day!!!
the vertex of this parabola is at (5,5). when the x-value is 6, the y-value is -1. what is the coefficient of the squared in the parabola's equations
Answers
Answer: OPTION D.
Step-by-step explanation:
The vertex form of a quadratic function is:
[tex]y= a(x - h)^2 + k[/tex]
Where (h, k) is the vertex of the parabola and "a" is the coefficient of the squared in the parabola's equation.
We know that the vertex of this parabola is at (5,5) and we also know that when the x-value is 6, the y-value is -1.
Then we can substitute values into [tex]f (x) = a(x - h)^2 + k[/tex] and solve for "a". This is:
[tex]-1= a(6- 5)^2 + 5\\\\-1=a+5\\\\-1-5=a\\\\a=-6[/tex]
Answer:
D
Step-by-step explanation:
Bubble wrap sells in sheets, and each sheet has 1 million individual spherical bubbles, each with a diameter of 0.01 m. What is the total volume of air contained in the bubbles of one sheet of bubble wrap? Round to the nearest tenth.
Answers
Answer: The total volume of air contained in the bubbles of one sheet of bubble wrap is about 0.5 cubic meters.
Step-by-step explanation:
Volume of sphere :-
[tex]V=\dfrac{4}{3}\pi r^3[/tex], where r is the radius of the sphere.
Given : Diameter of the bubble = 0.01 m
Then Radius of the bubble = [tex]\dfrac{0.01}{2}=0.005\ m[/tex]
Volume of each bubble:-
[tex]V=\dfrac{4}{3}(3.14) (0.005)^3[/tex]
Also, Number of bubbles in each sheet = 1,000,000
Then , the total volume of air contained in the bubbles of one sheet of bubble wrap will be :-
[tex]\dfrac{4}{3}(3.14) (0.005)^3\times1,000,000=0.52333333\approx0.5\ \text{cubic meters} [/tex]
Hence, the total volume of air contained in the bubbles of one sheet of bubble wrap is about 0.5 cubic meters.
Evaluate the expression
5⋅x3x2\dfrac{5\cdot x^3}{x^2}
x
2
5⋅x
3
start fraction, 5, dot, x, start superscript, 3, end superscript, divided by, x, start superscript, 2, end superscript, end fraction
for
x=2x=2
x=2
x, equals, 2
Answers
The simplified expression for [tex]\((5 \cdot x^3) / (x^2)\) is \(5 \cdot x\).[/tex]
When x = 2, the result is [tex]\(5 \times 2 = 10.[/tex]
The answer is 10.
To evaluate the expression[tex]\((5 \cdot x^3) / (x^2)\) for \(x = 2\),[/tex] we first need to simplify the given expression.
Given:
[tex]\[ \dfrac{5 \cdot x^3}{x^2} \][/tex]
Simplifying, we divide the powers of x :
[tex]\[ x^3 / x^2 = x^{3-2} = x^1 = x. \][/tex]
So the expression simplifies to:
[tex]\[ 5 \cdot x. \][/tex]
Now substitute x = 2 :
[tex]\[ 5 \cdot 2 = 10[/tex]
Thus, the value of [tex]\((5 \cdot x^3) / (x^2)\) when \(x = 2\)[/tex] is: 10.
Question : Evaluate the expression [tex]\[ \dfrac{5 \cdot x^3}{x^2} \][/tex]for x = 2. start fraction, 5, dot, x, cubed, divided by, x, squared, end fraction for x=2x=2x, equals, 2.
What ia the measure of x?
Answers
Answer:
58
Step-by-step explanation:
Rule: the exterior angle = the sum of the two angles that do not share a side with the exterior angle. Put in much simpler terms <DAB = <B + <C
Solution
<C + <B = <DAB
<C + 56 = 114 Subtract 56 from both sides
<C +56-56 = 114-56 Combine
<C = 58
x = 58
A pair of angles which share a common side and vertex is called
Answers
Answer: Adjacent Angles
A pair of angles which share a common side and vertex is called adjacent angles.
What is an angle measure?When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.
Given:
A pair of angles which share a common side and vertex.
If two angles share a side and a vertex, they are said to be adjacent in geometry.
In other words, adjacent angles do not overlap and are placed precisely next to one another.
Therefore, the right definition is adjacent angles.
To learn more about the angle measure;
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