On solving the provided question, we can say that A dilation is a transformation that yields a different-sized picture with the same general shape as the original.
what is dilation?A dilation in mathematics is a function f from a metric space M to itself that, for any point x, y in M, fulfills the identity d = rd. where r is a positive real integer and d is the separation between x and y. Such extensions are identical in space according to Euclid. Dilation is a transform that modifies an object's size. The process of dilation is used to enlarge or reduce items. The result of this transformation is an image that is a perfect replica of the original shape. However, there is a variation in the shape's size. The initial form ought to be distorted by dilation.
A dilation is a transformation that yields a different-sized picture with the same general shape as the original. The scale factor (also known as the dilation constant) and the dilation center are included in the description of a dilation. A fixed point in the plane around which all points are enlarged or contracted is the center of a dilation.
for example
triangle ABC ≈ triangle A'B'C'
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AB=16 and BC = 22 what does AC equal
Answer:AC is equal to 88
Step-by-step explanation:
C=11
A=8
B=2
Using the calculations for each ingredient:
How much did Hector's homemade sandwich cost?
Hint:
Remember the total cost for the bread is $0.16.
Add the $0.16 and the answers to questions 2, 4, 6, and 7 in order to get the total price for the sandwich.
Hector's homemade sandwich costs $2.00.
The correct option is B.
What is addition?Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.
Given:
The total cost for the bread is $0.16.
And the other ingredients cost $1.84.
And the total cost of Hector's homemade sandwich,
= Total cost for the bread + The cost of the other ingredients.
Total cost of Hector's homemade sandwich,
= $0.16 + $1.84
Total cost of Hector's homemade sandwich,
= $2.00
Therefore, $2.00 is the cost for the sandwich.
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The complete question:
Using the calculations for each ingredient:
How much did Hector's homemade sandwich cost?
Hint:
Remember, the total cost for the bread is $0.16.
And the other ingredients cost $1.84.
A : 1.90
B : 2.00
C : 2.99
D : 1.74
A rectangular piece of metal is 15 in longer than it is wide. Squares with 3 in long are cut from the 4 corners and the flap are folded upward to form an open box. If the volume of the box is 858in^3, what were the original dimensions of the piece of metal?
Note that in the above scenario, the original dimensions of the piece of metal that is rectangular are:
Length: 32 InchesWidth: 15 InchesWhat is the rationale for the above solution?Let x equal the width of the box and x + 15 equal the length of the box.
Subtract 6 (the amount cut out) from both of these to get the following terms: (x+9) and (x-6).
These are the length and width of the box respectively. We also know that the height of the box is 3. Plugging these into the formula for the volume of a box gives you:
3(x+9)(x-6)=858
If the above is expanded, we have:
3x²+9x-162=858
Subtract 858 from both sides to make the quadratic equation equal zero. Plug the a, b and c coefficients into the quadratic formula (or factor) to find x.
3x²+9x-162- 858 = 0
⇒ 3x²+9x -1020= 0
At the stage we solve for x:
3x2+9x−1020 = 0
Factor left side of the equation.
3(x−17)(x+20)=0
Set factors equal to 0.
x−17=0 or x+20=0
x=17 or x=−20
We can't get a negative side, so the answer that makes sense is x =17 recall that the metal is 15 inches longer than its width.
So if the Width is x and the Lenght is x +15
Then Width is 17 while the length is 17 + 15 = 32inces.
Thus the original dimensions of the metal are:
Length: 32 Inches
Width: 15 Inches
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1) Evaluate the integral taking omega is the triangle formed by the x-axis 2y=x and x=2 (6e^(x^2))
2) Find the volue of the solid bounded by the coordinate planes and (1/3)x+(1/2)y+(1/4)z=1
The volume of the solid is 4π([tex]\frac{19}{6}[/tex]) and the integral of the f(x) , the line 2y=x, and x=2 is 3([tex]e^{4}[/tex] -1).
What is integral ?
An integral is a mathematical concept that is used to calculate the area under a curve or the total amount of change in a variable over a certain interval.
1)The first step is to find the intersection of the lines 2y=x and x=2. They will intersect at (2,1).
The second step is to find the intersection of the lines 2y=x and x=0. They will intersect at (0,0).
The third step is to find the integral over the region.
∫∫ (6e^(x^2))dxdy = ∫[0,2] (6e^(x^2))dx ∫[0,x/2] dy = ∫[0,2] (6e^(x^2))dx (x/2) = [3e^(x^2)] at [0,2] = 3e^(4) - 3e^(0) = 3(e^4 -1).
2)To find the volume of this solid, we can use the method of cylindrical shells.
we can find the function of the surface (1/3)x+(1/2)y+(1/4)z=1
by using cylindrical coordinates:
x = rcosθ , y = rsinθ , z = z
and substitute them in the equation (1/3)x+(1/2)y+(1/4)z=1
(1/3)rcosθ+(1/2)rsinθ+(1/4)z=1
(1/3)r(cosθ+2sinθ)+(1/4)z=1
z = 4(1-(1/3)r(cosθ+2sinθ))
V = ∫∫∫ 4(1-(1/3)r(cosθ+2sinθ)) rdrdθdz = 4π ∫[0,3] (1-(1/3)r(cosθ+2sinθ)) r^2 dr = 4π ∫[0,3] (1-r+(2/3)r^2) dr = 4π(3 - (3/2) + (2/3)) = 4π(19/6).
Hence , The volume of the solid is 4π([tex]\frac{19}{6}[/tex]) and the integral of the f(x) , the line 2y=x, and x=2 is 3([tex]e^{4}[/tex] -1).
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At Park Junior High, 10%, or 160, of the students, play a musical instrument. How many students attend the school?
A tape diagram. StartFraction part Over whole EndFraction = StartFraction 10 Over 100 EndFraction = StartFraction 160 Over question mark EndFraction
Which statements are correct? Check all that apply.
The total number of students is < 160.
The total number of students is > 160.
The percent as a part-to-whole ratio is StartFraction 10 Over 100 EndFraction.
The percent as a part-to-whole ratio is StartFraction 160 Over 100 EndFraction
There are 1,600 students in the school.
There are 250 students in the school.
The statements that are correct include the following:
B. The total number of students is > 160.
C. The percent as a part-to-whole ratio is 16/100.
E. There are 1600 students in the school.
What is a percentage?In Mathematics, a percentage can be defined as any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.
For the total number of students, we have:
Total number of students = 10/100 × T = 160
0.1T = 160
T = 160/0.1
T = 1,600 students.
Note: Percentage as a part-to-whole ratio is 10/100.
In conclusion, we can reasonably infer and logically deduce that the total number of students at Park Junior High is equal to 1,600 students.
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Complete Question:
At park junior high 10% or 160 of the students play a musical instrument how many students attended the school?
Which statements are correct? check all that apply.
A.the total number of students is 160
B. The total number of students is > 160.
C.The percent as a part-to-whole ratio is 10/100
D.the percent as a part to whole ratio is 160/100
E.there are 1600 students in the school
F.there are 250 students in the school.
The City of Rock Hill has an approximate population of 70,000. An average of 100 people move in to Rock Hill every month and 150 people move out of Rock Hill each month. The City of Greenville has an approximate population of 61,000. An average of 200 people move into
Greenville every month. In how many months will the populations of
The number of months it will take for both cities to have the same population is; 36 months
How to solve Algebraic Word Problems?We are given;
Current population of city of rock hill = 70000
Rate at which people move into city of rock hill = 100 people per month
Rate at which people move out of city of rock hill = 150 people per month
Net average increase a month = 100 - 150 = -50 people per month
Current population of City of Greenville = 61000
Rate at which people move into City of Greenville = 200 people per month
If the number of months it will take for both cities to have the same population is x, then it means that;
70000 - 50x = 61000 + 200x
Rearrange to get;
200x + 50x = 70000 - 61000
250x = 9000
x = 9000/250
x = 36 months
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Find the center and radius of the circle with the equation:
(x-3)² + (y-1)² = 16
center: (-3,-1)
radius: 4
a.
b. center: (-3,-1)
radius: 16
C.
center: (3, 1)
radius: 4
d. center: (3, 1)
radius: 16
On solving the provided question we can say that in the circle the radius, r = 4 and center, c = -3, -1, so area of the circle will be = [tex]\pi r^2[/tex] = 3.14*4*4 = 50.24 cm sq.
What is circle?Every point in the plane that is a certain distance away from a certain point forms a circle (center). It is, thus, a curve formed by points moving in the plane at a fixed distance from a point. At every angle, it is also rotationally symmetric about the center. A circle is a closed two-dimensional object where every pair of points in the plane are equally spaced out from the "center." A line that goes through the circle creates a specular symmetry line. At every angle, it is also rotationally symmetric about the center.
here,
in the circle
the radius, r = 4
and center, c = -3, -1
area of the circle will be = [tex]\pi r^2[/tex] = 3.14*4*4 = 50.24 cm sq.
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Tornadoes have occurred on every continent except Antarctica. They occur most often between latitudes of 30° and 50°. Write a compound inequality describing the latitude in which tornadoes are not likely to occur.
The tomatoes will not likely occur in less than 30 and greater than 50 latitude regions.
What is inequality?When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.
Given that Tornadoes have occurred on every continent except Antarctica. They occur most often between latitudes of 30° and 50°.
The region between tomatoes occur is,
30< T < 50
The region in which the tomatoes are not occur is,
T < 30
T > 50
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What is the difference?
−5−6
−11
−1
1
11
The difference between the two numbers -5-6 is -11 Option A
What is the difference?In basic arithmetic, difference implies the addition or two negative numbers or the subtraction of two positive numbers
The two given numbers we are asked to find the difference are -5-6
We can notice that these tow numbers are negative and negative. to this effect, we have to find the sum of the two negative integers to get
-5 + (-6)
This gives us -11
Conclusively the answer is -11
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Need help on this question
Answer:
600 ml
Step-by-step explanation:
let x = amount of water needed
1/6 = 100/x
cross multiply to solve for x:
x = 600
what is the answers to this question
By evaluating the quadratic equation, we will see that the values of the expressions are:
f(-1) + f(4) = 27
f(-1) - f(4) = -35
How to evaluate the given expressions?Here we need to work with the quadratic function:
f(x) = x^2 + 6x + 1
First, we want to find the value of the expression:
f(-1) + f(4)
To get that, we need to evaluate the quadratic equation:
f(-1) = (-1)^2 + 6*(-1) + 1
f(-1) = 1 - 6 + 1 = -4
f(4) = 4^2 + 6*4 + 1
f(4) = 16 + 24 + 1 = 31
Then the first expression is:
f(-1) + f(4) = -4 + 31 = 27
The second expression is:
f(-1) - f(4)
We already know these values, we can replace these to get:
f(-1) - f(4) = -4 - 31 = -35
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The dimensions of a box are 2x + 5 meters, x + 4 meters, and x + 2 meters. The volume of
the box is 2,520 m³. Find the dimensions of the box.
The rectangular box dimensions are 21m ,12m and 10m.
What is volume of the rectangular box?
The area of the base times the height of the rectangular prism equals the volume of the object. As a result, the formula for a rectangular prism's volume is given. A rectangular prism's volume is equal to its length, width, and height in cubic units.
Here the dimensions of a box is 2x+5 , x+4 and x+2 meters and volume of the box is 2520 [tex]m^3[/tex].
Volume of rectangular box = w×h×l [tex]unit^3[/tex]
=> 2520 = (2x+5)(x+4)(x+2)
=> 2520 = [tex](2x^2+13x+20)(x+2)[/tex]
=> 2520 = [tex]2x^3+4x^2+26x+13x^2+20x+40[/tex]
=> [tex]2x^3-16x^2+33x^2-264x+310x-2480=0[/tex]
=> [tex]2x^2(x-8)+33x(x-8)+310(x-8)=0[/tex]
=> [tex](x-8)(2x^2+33x+310)=0[/tex]
Here x-8=0 and [tex]2x^2+33x+310=0[/tex]
Then x=8 and x ∈ R.
Now the dimensions 2x+5=2(8)+5=16+5=21m.
=> x+4 = 8+4=12 m.
=> x+2= 8+2 = 10m.
Hence the rectangular box dimensions are 21m ,12m and 10m.
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The principal wants to share 1,869 pencils between 4 4th grade and 3 third grade classrooms. How many pencils will each classroom get?
On solving the provided question, we can say that = 9227446, depreciation If round at hundredth, then, Number of tree = 9227400.
How can you compute depreciation mathematically?Identify the asset's cost. Get the asset's total depreciable value by deducting the projected salvage value from the asset's purchase price. Determine the asset's useful life. The annual depreciation amount is obtained by dividing the sum of steps (2) and (3) by the figure determined in steps (3).
Depreciation is the practice of deducting the cost of a company asset over a number of years as opposed to just one. There are four primary ways to depreciate assets: linear, twofold declining, sum of the years' digits, and manufacturing units.
As it is given, 1% of left tree is decaying every year.
Number of tree left after 8 years.
A = P{1-R/100}^ = 10M{1-1%/100}^
= 10M *(0.99)^
= 9227446
If round at hundredth, then,
Number of tree = 9227400.
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The equation, A = 5,000(1 + 0.025t) represents the amount of money earned on a savings account with 2.5% annual simple interest. At the end of the investment period, the account balance is $5,875. How many years is the investment period? 1 year 4 years 7 years 9 years
The number of years that is the investment period, given the account balance, is 7 years
How to find the investment period ?You are given the equation, A = 5,000 ( 1 + 0.025t ) where t is the investment period.
Find the simple interest per year :
= 5, 000 x 2. 5 %
= $ 125
Then find the number of years as :
= ( Account balance - Opening deposit ) / Annual simple interest
= ( 5, 875 - 5, 000 ) / 125
= 7 years
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Y = - 6x + 4
y = 1/4x - 4
Answer:
x = 1.28, y = -3.68
Step-by-step explanation:
y = -6x + 4
y = 1/4x - 4
-4= -6x - y
4 = 1/4x - y
4= 6x + y
4 = 1/4x - y
8= 6 1/4x
x = 1.28
y = -6(1.28) + 4
y = -7.68 + 4
y = -3.68
find f
f '(t) =20/1+t^2 f(1) = 0
If f '(t) =20/1 + t2 f(1) = 0, f is f(x) = 20tan⁻¹(t) - 5π.
Integrals are the values of the function seen by the process of integration.
The procedure of getting f(x) from F (x) is called integration.
Given f '(t) = 20/ 1 + t2 and f(1) = 0
We know that by definition of the integral of tan⁻¹(x) = 1/1 + t2
f '(t) = 20 / 1 + t2 = 20(1/ 1 + t2)
Integrate on both sides, we get
f(t) = 20tan⁻¹(t) + c
f(1) = 0; f(1) = 20tan⁻¹(1) + c = 0
c = -20(π/4) = -5π.
Therefore, f(x) = 20tan⁻¹(t) -5π.
If f '(t) =20/1 + t2 f(1) = 0, f is f(x) = 20tan⁻¹(t) - 5π.
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Determine whether the equation is exact. If it is exact, find the solution. If it is not, enter NS. (7x2-2xy +2)dx + (29-x2+7)dy = 0 Do not enter an arbitary constant The solution in implicit form is a K = c, where c is an arbitrary constant.
PLEASE HELP, I ATTACHED AN IMAGE OF THE PROBLEM!!!
The correct rule of the transformation is,
⇒ Dilation of 0.5.
What is Translation?A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
We have to given that;
The coordinate of CDE are,
⇒ C (4, - 5), D (3, - 1), E (5, - 3)
And, After transformation the coordinate of image C'D'E' are,
⇒ C' (2, - 2.5) , D' (1.5, - 0.5), E' (2.5, - 1.5)
Now, We have;
⇒ C (4, - 5) = C' (2, - 2.5)
Let a dilation of the points = k
So, We can formulate;
⇒ 4 × k = 2
⇒ k = 2/4
⇒ k = 1/2
⇒k = 0.5
Hence, The correct rule of the transformation is,
⇒ Dilation of 0.5.
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Write 3 numbers that are divisible by 2,
5, and 10.
Answer:
2,4,6,8,0
Step-by-step explanation:
A number is divisible by 2 if it ends in 2, 4, 6, 8 or 0. A number is divisible by 5 if it ends in 5 or 0. A number is divisible by 10 if it ends in a 0.
The question is in the screenshot below. TIA
Answer: 3c+3
Step-by-step explanation:
How do we solve this?
Correct option is E, The roots of Auxiliary equation are √6 and -√6.
The solution of an nth-order differential equation or difference equation depends on an algebraic equation of degree n called the characteristic equation (or auxiliary equation) in mathematics.
The auxiliary equation, however, lacks true roots. Consider the simple harmonic equation y + y = 0, which has solutions and was given that name because of how it relates to the vibration of a musical tone. Y2(t) = cos t and Y1(t) = sin t. r2 + 1 = 0 is the auxiliary equation for the straightforward harmonic equation.
The Auxiliary form of the given equation is m² - 6 = 0
Using identity a² - b² = (a - b) (a + b),
⇒ The equation becomes (m - √6)(m+√6) = 0
⇒ either m = √6 or m = -√6
Hence, The roots of Auxiliary equation are √6 and -√6.
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you mix 1/2 quart of blue paint for every 1/3 quart of red paint to make 5 quart of purple paint. How much blue paint and how much red paint do you use?
The amount of blue paint and red paint that you use will be 3 quarts and 2 quarts, respectively.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
You mix 1/2 quart of blue paint for every 1/3 quart of red paint to make 5 quarts of purple paint.
Let 'x' be the amount of blue paint and 'y' be the amount of red paint. Then the equations are given as,
x / y = (1/2) / (1/3)
x / y = 3/2 ...1
x + y = 5 ...2
From equations 1 and 2, then we have
(3/2) y + y = 5
(5/2) y = 5
y = 2 quart
Then the value of 'x' is given as
x + 2 = 5
x = 3 quart
The amount of blue paint and red paint that you use will be 3 quarts and 2 quarts, respectively.
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the graph below represents a linear function. which of the following equations models the linear graph above? please answer and explain why you chose the answer. i will mark you brainliest
D. Y= 4/3 (x)+4
The first step i did was finding C for the standard form equation of a linear function which is:
y=mx+c
Finding C is easy because C is simply the y-intercept(The point that crosses the y axis) which we can see from the graph is 4.
That allowed me to isolate possible answers of B and D because they contain a C which is equal to 4.
To determine which equation it was, i substituted an X coordinate to see if i got the correct Y coordinate from the graph.
Lets try B first and substitute the coordinate -3:
3/4 ×(-3)+4=1.75
As we see thats incorrect because the coordinate on the graph is (-3;0).
So we can conclude it is not b, however lets try D.
4/3 (-3)+4=0.
We see that this equation gives us the correct answer.
So therefore the correct equation is D
4/3 (x)+4
The graph of linear equation is always a straight line ?
Yes, the graph of linear equation is always a straight line.
What is a linear equation?Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.
Consider the equation y = mx + c to define a linear function with a straight line as its graph.
We are aware that the rate of change, m, for a linear function is constant. On the graph, shifting by 1 always causes you to go up by m as shown in attached image.
The graph thus resembles a staircase. It is a straight line because it always rises in equal-sized steps.
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of Write the equation of this line in slope-intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form.
We want to get the equation on the graphed line.
The equation of the line is: y = 8*x - 9
Then the line is something like:
y = 8*x + b
To find the value of b, we can use one of the two points we got above.
The point (0, -9) means that when x = 0, y is equal to -9, then we can write:
-9 = 8*0 + b
-9 = b
Finally, the equation of the line is:
y = 8*x - 9
What is graphed line?When displaying information that changes over time, a line graph, also referred to as a line chart or a line plot, is frequently used.It can be visualized using a series of points connected by straight lines. The "x-axis" and the "y-axis" are two of its axes. An informational change over time is graphically represented by a line graph. It is a graph that was created by connecting points with line segments. An informational change over time is graphically represented by a line graph. It is a graph that was created by connecting points with line segments. A line graph, also referred to as a line plot or a line chart, is a graph in which individual data points are connected by lines.To learn more about line plot refer to:
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if AT= 4x-7 and CT = -x + 13, solv e for x
Answer to this math question
By means of relationship between powers and roots and algebra properties we conclude that radical expression ∛y · [2 · y · ∛(8 · y²) - ∛(y⁵) - 4∛(8 · y²)] is equivalent to 2 · y · ∛(8 · y⁵) - ∛(y⁶) - 4 ∛(8 · y³).
How to simplify a polynomial-like radical expression
In this problem we find a polynomial-like radical expression that must be simplified by algebra properties and by taking advantage of relationship between powers and roots. First, write the entire expression:
∛y · [2 · y · ∛(8 · y²) - ∛(y⁵) - 4∛(8 · y²)]
Second, apply distributive property:
2 · y · ∛(8 · y²) · ∛y - ∛(y⁵) · ∛y - 4∛(8 · y²) · ∛y
Third, use relationship between roots and powers:
2 · ∛(y³) · ∛(8 · y²) · ∛y - ∛(y⁵) · ∛y - 4∛(8 · y²) · ∛y
Fourth, apply multiplication of roots and multiplication of powers of equal base:
2 · y · ∛(8 · y⁵) - ∛(y⁶) - 4 ∛(8 · y³)
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Please help me with this!
yall better help me this is 45 points for one question if ya get it right u get brainliest too.(:
The value of B, the area of the base, is 1,540 m^2.
What is value?Value is the relative worth, merit, or importance of something. It can refer to an intangible concept such as a person's principles or a tangible object such as a rare coin. Values vary widely across cultures, societies, and individuals, and can even vary within the same individual over time. Value is often used to describe the worth of something in terms of its usefulness, beauty, or desirability. Value can also refer to the moral or ethical standards of a person or group.
The area of the base can be found by using the formula A = V/h where A is the area of the base, V is the volume, and h is the height. In this case, A = 26,214 / 17 = 1,540 m^2. Therefore, the value of B, the area of the base, is 1,540 m^2.
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Jon bought a pizza as shown write an equation to find the cost per slice c
The equation to find the cost per slice is c=x/n where x is the total prize of pizza and n is the total no. of slices.
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
If x is the total price of pizza( which is $20 in this case) and if all the slices are equally cut, then the cost of each slice would be total price divided by total slices.
Hence, the equation is c= x/n
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