Answer:
Step-by-step explanation:
The definitions of rigid-motion transformations need to be precise as they entail more than physical descriptions of motions. They have unique mathematical definitions and are important for understanding and interpreting real-world movements and physical phenomena.
Explanation:The definitions of each rigid-motion transformation, namely slides (translations), flips (reflections), and turns (rotations), need to be more precise because they are not solely about the physical manifestation of the motion. These transformations have distinct mathematical underpinnings. For instance, a translation involves moving the figure along a specified direction and distance in a straight line, without changing the orientation of the figure. A reflection involves 'flipping' the figure over a line of reflection, altering its orientation but not its shape or size. A rotation involves turning the figure around a specified point for a given angle.
Moreover, in both rotational and translational motion - two forms of rigid-body motion, there are accurate variables such as displacement, velocity, and acceleration related to translational motion and the corresponding angular variables in rotational motion. These specific definitions are crucial for the mathematics behind movement and interpreting the world around us. Understanding such concepts can also aid in studying physical phenomena as diverse as a spinning ballet dancer or a rotating planet.
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Quick!! I need help with this question!
1. 60 / 1/8 * 3/4
2. 3/4 * 15
3. 7/8 / 3/4
Which dimensions can create more than one triangle
Answer:
Three angles, measuring 25,65, and 90.
Step-by-step explanation:
Simplify the expression 7√5 - 3√80
A) -5√5
B) -4√75
C) -5
D) 4√-75
Answer:
A.) -5 √5
Step-by-step explanation:
if you solve the problem above, and solve each answer choice, you can ind a match
Hope this helped! ^_^
The expression 7√5 - 3√80 is simplified as negative 5√5. Then the correct option is A.
What is simplification?Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.
The expression is given below.
⇒ 7√5 - 3√80
Then the expression is simplified as
⇒ 7√5 - 3√(16 x 5)
⇒ 7√5 - 3 x 4√5
⇒ 7√5 - 12√5
⇒ -5√5
Then the correct option is A.
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What is the equation of the graph below?
Answer:
Step-by-step explanation:
the equation of the graph : y = sin(x + 90°)
because when : x= 0 : y = sin90° = 1
Answer:
Option A y = sin ( x + 90 )
Step-by-step explanation:
The given graph is the graph of cosine which should be in the form of
y = a cos ( bx + c ) + d
here a = amplitude = [tex]\frac{1-(-1)}{2}[/tex] = [tex]\frac{2}{2}[/tex] = 1
Since period of the wave is 2x or 360°.
we know, period = [tex]\frac{2\pi }{b}[/tex]
[tex]b=\frac{2\pi }{2\pi }[/tex] = 1
Now equation becomes,
y = cos ( x + c ) + d
In this graph there is no horizontal or vertical shift
c = 0 and d = 0
so equation will be y = cos (x)
as we know y = cos (x) = sin ( 90 + x )
Therefore, Option A y = sin ( x + 90 ) is the answer.
Which figure is always a rectangle
Answer:
A rectangle has two pairs of opposite sides parallel, and four right angles. It is also a parallelogram, since it has two pairs of parallel sides. A square has two pairs of parallel sides, four right angles, and all four sides are equal.
Step-by-step explanation:
Please give me brainiest! <:)
Do you need to write a formula to find the perimeter of a polygon?
Answer: No. But there are steps you have to take
Step-by-step explanation: To find the perimeter of a regular polygon, that is a polygon with equal sides. First, write down the length of 1 side and the total number of sides. Then, multiply the 2 numbers together to find the perimeter.
Which equation yields the solutions x=−3 and x=−4?
a)2x2+14x+24=0
b)x2−6x+5=0
c)3x2+30x+48=0
d)−3x2−12x+15=0
Answer:
a) 2x² + 14x + 24 = 0
Step-by-step explanation:
a)
2x² + 14x + 24 = 0
2(x + 4) (x + 3) = 0
x = -4 or x = -3
b)
x² - 6x + 5 = 0
(x - 1)(x - 5) = 0
x = 1 or x = 5
c)
3x² + 30x + 48 = 0
3 (x + 8) (x + 2) = 0
x = -8 or x = -2
d)
-3x² - 12x + 15 = 0
-3 (x + 5) (x - 1) = 0
x = -5 or x = 1
Final answer:
The equation which yields the solutions x=-3 and x=-4 is a. 2x² + 14x + 24 = 0.
Explanation:
To find which equation yields the solutions x=-3 and x=-4, we need to determine which equation, when factored, gives these roots. If an equation has roots x = -3 and x = -4, then it can be written in factorized form as:
(x + 3)(x + 4) = 0
Expanding this, we get:
x² + 4x + 3x + 12 = 0
x² + 7x + 12 = 0
Looking at the given options, we notice that none of them exactly match this equation. However, if we multiply our equation by 2, we get:
2x² + 14x + 24 = 0
This matches option (a). Therefore, the correct equation is:
2x² + 14x + 24 = 0
Tara read 3 1/2 pages in 2 1/2 minutes. Which rate is equivalent to Tara’s unit rate
Tara's unit rate of reading is 1.4 pages per minute, which means an equivalent rate is 2.8 pages per 2 minutes.
The question involves calculating an equivalent rate to Tara's unit rate of reading pages per minute. To find Tara's unit rate, we first need to determine how many pages she reads in one minute. Since Tara reads 3 1/2 pages in 2 1/2 minutes, we divide the number of pages by the number of minutes to find the unit rate:
3 1/2 pages / 2 1/2 minutes = 7/2 pages / 5/2 minutes = 7/2 * 2/5 pages per minuteThis simplifies to 7/5 pages per minute or 1.4 pages per minute.To find an equivalent rate, we can multiply both the numerator and the denominator by the same number to get a rate with different terms but the same value. For example, multiplying by 2 would give us:
(7/5) * 2 pages per (1) * 2 minutes = 14/5 pages per 2 minutes = 2.8 pages per 2 minutesTherefore, an equivalent rate to Tara's reading speed would be 2.8 pages per 2 minutes.
The data below represents the scores in a golf tournament. If the mean is 70 with a standard deviation of 4.9, circle all values with a
z-score greater than 0.5
63, 64, 65, 67, 70, 71, 73, 73, 76, 78
To circle all values with a z-score greater than 0.5, calculate the z-score for each value and compare it to 0.5. The values with a z-score greater than 0.5 are 76 and 78.
Explanation:To determine which values have a z-score greater than 0.5, we need to calculate the z-score for each value in the data set. The z-score formula is calculated by subtracting the mean from a value and then dividing by the standard deviation. If the resulting z-score is greater than 0.5, we circle the corresponding value.
For the value 63: z-score = (63 - 70) / 4.9 = -1.43For the value 64: z-score = (64 - 70) / 4.9 = -1.22For the value 65: z-score = (65 - 70) / 4.9 = -1.02For the value 67: z-score = (67 - 70) / 4.9 = -0.61For the value 70: z-score = (70 - 70) / 4.9 = 0For the value 71: z-score = (71 - 70) / 4.9 = 0.2For the value 73: z-score = (73 - 70) / 4.9 = 0.61For the value 73: z-score = (73 - 70) / 4.9 = 0.61For the value 76: z-score = (76 - 70) / 4.9 = 1.22For the value 78: z-score = (78 - 70) / 4.9 = 1.63Based on the calculations, the values with a z-score greater than 0.5 are 76 and 78. Therefore, these two values should be circled.
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To determine the values with z-scores greater than 0.5, calculate the z-score for each value. The values with z-scores greater than 0.5 are 76 and 78.
Explanation:In order to determine which values have z-scores greater than 0.5, we need to calculate the z-score for each value. The z-score formula is:
z = (x - mean) / standard deviation
Let's calculate the z-scores for each value and circle the ones greater than 0.5:
63 has a z-score of -1.4364 has a z-score of -1.2265 has a z-score of -1.0267 has a z-score of -0.6170 has a z-score of 071 has a z-score of 0.273 has a z-score of 0.6173 has a z-score of 0.6176 has a z-score of 1.2278 has a z-score of 1.63Values with z-scores greater than 0.5 are: 76 and 78.
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For a field trip, 29 students rode in cars and the rest filled nine buses. how many students were in each bus if 551 students were on trips?
Answer:
58 students were in each bus
Step-by-step explanation:
First, you'd have to subtract 29 from 551. This gives you 522. Then, you'd simply have to divide 522 by 9. 5 cannot go into 9 so we drag down the 2, 9 can go into 52 5 times. Then, you'll be left with 7, so you bring down the last digit, 2. 9 goes into 72 exactly 8 times.
Here is the picture i'm mostly trying to understand how to solve these type of problems.
[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{25\% of "h"}}{\left( \cfrac{25}{100} \right)h}\implies 0.25h \\\\\\ \stackrel{\textit{Rob spent then}}{\stackrel{\textit{planned hours}}{h}+\stackrel{\textit{extra hours}}{0.25h}}\implies h+0.25h\implies \stackrel{\textit{common factor}}{h(1+0.25)}\implies 1.25h[/tex]
Pencils cost 25p each. Mr smith spends £15 on pencils. Work out the number of pencils he gets.
Answer:
Step-by-step explanation:
HELPPPPP FAST PLEASE
1. what is the excluded value of 2x/ 1-2x
a.0
b.1/2
c.1
2.what are the excluded values of -7/x^2-2x-15
a.0 and 15
b.3 and -5
c.-3 and 5
Answer:
b and c
Step-by-step explanation:
The excluded values are any values of x that make the denominator equal to zero as this would make the rational function undefined.
Equate the denominator to zero and solve for x to obtain excluded values
1
solve 1 - 2x = 0 ⇒ 2x = 1 ⇒ x = [tex]\frac{1}{2}[/tex] → b
2
x² - 2x - 15 = 0 ← in standard form
(x - 5)(x + 3) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
x + 3 = 0 ⇒ x = - 3
Excluded values are x = - 3 and x = 5 → c
Answer:
B and C
Step-by-step explanation:
Describe the transformations to get from image A to A'.
Answer:
A reflection over the y axis and then a reflection over the x axis gets a to a'. Hope this helps!
24 is 0.4 of what number
Answer:
60
Step-by-step explanation:
All you have to do is this:
24 * 2/5 (original equation)
24*5/2 = 60
x 0 4 9 10 y 3 2 7 -1 Graph the relation and its inverse. Use open circles to graph the points of the inverse.
Answer:
Observe the attached image
Step-by-step explanation:
If we have a function f(x), the inverse of the function denoted [tex]f ^{- 1} (x)[/tex] will have as domain the range of f(x) and its rank will be the domain of the function f(x) this means that if f(x) is given by the following ordered pairs:
x: 0, 4, 9, 10; and: 3, 2, 7, -1
(0, 3) (4, 2) (9, 7) (10, -1)
Then [tex]f ^{- 1}(x)[/tex] will have the following ordered pairs
x: 3, 2, 7, -1 and: 0, 4, 9, 10
(3, 0) (2, 4) (7, 9) (-1, 10)
Observe the attached image
The blue dots are the ordered pairs of the relationship
The red open dots are the ordered pairs of the inverse of the relationship
There are 15 printers in one department. If 2/5 are color printers, how many can only print black and white?
Answer:
your answer would be 9 printers
The answer is:
There are a total of 9 black and white printers
Why?To solve the problem, first, we need to calculate how many color printers represents two-fifths of the total printers, then, calculate the number of black and white printers using the total number of printers and the number of color printers.
Calculating how many color printers does the departament have:
[tex]ColorPrinters=TotalPrinters*\frac{2}{5} \\\\ColorPrinters=15*\frac{2}{5}\\\\ColorPrinters=\frac{30}{5}=6[/tex]
Therefore, we have that there are 6 color printers.
Now, calculating the number of black and white printers, we have:
[tex]TotalPrinters=ColorPrinters+BlackAndWhitePrinters\\\\BlackAndWhitePrinters=TotalPrinters-ColorPrinters\\\\BlackAndWhitePrinters=15printers-6printers=9printers[/tex]
Hence, we have that there are a total of 9 black and white printers.
Have a nice day!
pls help ASAP
Explain how to find the relationship between two quantities, x and y, in a table. How can you use the relationship to calculate the missing values in the table?
To find the relationship between two quantities, x and y, in a table, analyze patterns in the changes of the values, determine if the relationship is linear or nonlinear, and then use the identified relationship to calculate missing values. A computer can be useful for plotting data and visualizing the relationship.
Explanation:To find the relationship between two quantities, x and y, in a table, first, you need to look for a pattern in the way the numbers change. If y changes by a consistent amount when x changes by a set amount, the relationship is likely linear. If the rate of change itself changes, the relationship may be nonlinear. To determine the relationship:
Calculate the differences in y-values and x-values between successive points.Look for a constant ratio or a constant difference to identify a linear relationship.Plot the data to visually inspect the form of the relationship.To fill in missing values:
Use any known relationships (e.g., y = mx + b for linear relationships).If you identify a consistent pattern in the changes of x and y, apply this pattern to estimate the missing values.If the relationship is nonlinear, you may need to estimate the slope at a point or apply a nonlinear model.Use extra information provided to calculate missing x or y values.When calculating these relationships, plotting data using computers can be helpful, especially for identifying linear or nonlinear relationships and for regression analysis in more complex datasets.
Δ ABC is isosceles with m∠B ≅ m∠C. If m∠A = 100°, m∠B = (12x + 4)°, and m∠C = (14x - 2)°, find x.
A) 1
B) 3
C) 5
D) 7
will mark brainliest if correct and give 50 pts.
The answer is B. If angle b is congruent to angle c, then you would write the problem as 12x + 4= 14x-2. X=3. You can check by substituting three for x.
Final answer:
To find the value of x in the isosceles triangle ABC with given angle expressions, we set the expressions for angles B and C equal, leading to a simple equation that yields x = 3.
Explanation:
The question involves finding the value of x in an isosceles triangle where the angles at base B and C are given as algebraic expressions in terms of x. Since triangle ABC is isosceles with angles at B and C being equal, we can set the expressions for m∆B and m∆C equal to each other and solve for x.
Let's set up the equation using the fact that m∆B = m∆C since ∆ ABC is isosceles:
(12x + 4)° = (14x - 2)°
We can then solve for x:
Subtract 12x from both sides: 4° = 2x - 2°
Add 2° to both sides: 6° = 2x
Divide by 2 to solve for x: x = 3
The value of x is therefore 3, which corresponds to answer choice B.
Rewrite the radical expression as an expression with rational exponents.
5 square root of x to the 7th power
Hello!
5 √ x^7
(^7) means smaller 7 exponent
Hope I helped!
~ Destiny ^_^
Final answer:
To rewrite the radical expression 5 square root of x to the 7th power with rational exponents, express it as 5x7/2.
Explanation:
To rewrite the radical expression as an expression with rational exponents, we can use the property that the square root is equivalent to raising to the power of 1/2. Thus, 5√x7 = 5x7/2.
calculate the angle between the longest side and the diagonal of a 577mm by 1000mm rectangle
This should help in the photo
The angle between the longest side and the diagonal of the rectangle is approximately 30 degrees.
What are Trigonometric functions?Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.
To solve this problem, we can use the Pythagorean theorem and trigonometric functions.
First, we can find the length of the diagonal of the rectangle using the Pythagorean theorem:
diagonal² = longest side² + shortest side²
diagonal² = 1000² + 577²
diagonal = √(1000² + 577²)
diagonal = 1162.46 mm (rounded to two decimal places)
Next, we can find the angle between the longest side and the diagonal using the inverse tangent function:
tan(θ) = opposite / adjacent
tan(θ) = 577 / 1000
θ= arctan(577 / 1000)
θ= 29.98
θ ≈ 30 degrees
Therefore, the angle between the longest side and the diagonal of the rectangle is approximately 30 degrees.
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The table shows the relationship between the number of roller coasters written at the fair and the amount spent at the fair graph the data in a scatterplot and describe the trend shown by the graph
Answer:
I believe its C
A scatter plot is just plotting the x and y coordinates on the graph.
x is horizontal (side to side) and y is vertical up and down.
What is the meaning of a scatter plot?
A graph in which the values of two variables are plotted along two axes, the pattern of the resulting points revealing any correlation present.
The trend is just basically a line you guesstimate in the middle of the points that are scattered through the graph.
Describe it by saying whether it is positive or negative.
Therefore option C is correct.
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Which of the following is not an idea from the enlightenment?
Answer:
The answer is B.
Step-by-step explanation:
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Find 4 1/5 - 7 2/3
28 2/15
28 3/10
32 1/5
323/5
Answer:
Final answer is [tex]=3\frac{7}{15}[/tex].
Step-by-step explanation:
[tex]4\ \frac{1}{5}-7\ \frac{2}{3}[/tex]
[tex]=\frac{4\cdot5+1}{5}-\frac{7\cdot3+2}{3}[/tex]
[tex]=\frac{20+1}{5}-\frac{21+2}{3}[/tex]
[tex]=\frac{21}{5}-\frac{23}{3}[/tex]
[tex]=\frac{21}{5}\cdot\frac{3}{3}-\frac{23}{3}\cdot\frac{5}{5}[/tex]
[tex]=\frac{63}{15}-\frac{115}{15}[/tex]
[tex]=-\frac{52}{15}[/tex]
[tex]=-3\frac{7}{15}[/tex]
Hence final answer is [tex]=3\frac{7}{15}[/tex].
How do you find the area of a circle?
(I’m in 7th grade)
Answer:
A =πr^2
Step-by-step explanation:
Answer: The formula for the area of a circle is pi times the radius, squared (A = π r²)
Step-by-step explanation:
Four friends have dinner and bill comes to 85.78. They leave an 18 percent tip. What is the total amount of their bill.
Answer:
$15.44
Step-by-step explanation:
Answer:
about 101.22
Step-by-step explanation:
Determine the projection of u=1.6i+3.3j in the v=-2.1i-0.5j direction
The projection of [tex]\vec u[/tex] onto [tex]\vec v[/tex] is
[tex]\mathrm{proj}_{\vec v}(\vec u)=\dfrac{\vec u\cdot\vec v}{\vec v\cdot\vec v}\vec v[/tex]
We have
[tex]\vec u\cdot\vec v=1.6\cdot(-2.1)+3.3\cdot(-0.5)=-5.01[/tex]
[tex]\vec v\cdot\vec v=\|\vec v\|^2=(-2.1)^2+(-0.5)^2=4.66[/tex]
[tex]\implies\mathrm{proj}_{\vec v}(\vec u)=\dfrac{-5.01}{4.66}\vec v\approx2.26\,\vec\imath+0.54\,\vec\jmath[/tex]
Answer:
answer is B i think on edg. 2.3i+0.5j
Step-by-step explanation:
just took the test
two lenghts are in the ratio 7:8. if the first lenght is 273m, what amount is the second lenght
Answer:
312 m
Step-by-step explanation:
Write and solve an equation of ratios:
7 273 m
----- = ------------
8 x
Then 7x = 8(273 m) = 2184 m
and x = 2184 m / 7 = 312 m
The second length in the given ratio of 7:8, when the first length is 273m, is calculated to be 312m.
Explanation:The given question is about ratios, particularly the ratio between two lengths, where one of them is given as 273 meters and the ratio is 7:8. The ratio tells us that for every 7 units of the first length, there are 8 units of the second length. To calculate the second length, first find the value of one ratio unit by dividing the given length by its ratio (273m / 7), then multiply your result by 8.
Steps:
1. 273m / 7 = 39m (This is one ratio unit)
2. 39m * 8 = 312m (This is the second length).
Therefore, the length of the second line is 312 m.
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What is the slope of the line (7,6) and (3,2)
Answer:
1
Step-by-step explanation:
Answer:
slope = 1
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (7, 6) and (x₂, y₂ ) = (3, 2)
m = [tex]\frac{2-6}{3-7}[/tex] = [tex]\frac{-4}{-4}[/tex] = 1
A rectangular sheep pen measures 5 m long and 9 m wide. The perimeter of the cow pen is double the perimeter of the sheep pen what is the perimeter of the cow pen?
Answer:
56m
Step-by-step explanation:
First calculate the perimeter of the sheep pen.
The perimeter is all the side lengths added together.
The rectangle has two sides that are 5m long and two sides that are 9m long.
5 + 5 + 9 + 9 = 28m
Now that you know the perimeter of the sheep pen you can double it by multiplying by 2 to find tha perimeter of the cow pen.
28 * 2 = 56m
Answer:
56
Step-by-step explanation:
5×2 +9×2=28
28 × 2 =56