Answer:
Perimeter of any figure is given by adding up all the side measurements.
So, when a figure is enlarged by a scale factor then we can multiply all the sides with the scale factor to get the new sides measurements and then we can find the perimeter.
Or simply we can find the perimeter of the original figure and then multiply by the scale factor.
In both the methods, the answer will be the same.
We can take an example:
Lets suppose the original figure to be a rectangle with length 5 cm and width 2 cm. The rectangle is enlarged by a scale factor of 6.
The original perimeter is = [tex]2(5+2)[/tex]
= [tex]2(7)=14[/tex] cm
1st method:
Multiply the length by 6 and width by 6 to get new dimensions.
Length becomes: [tex]5\times6=30[/tex]
Width becomes: [tex]2\times6=12[/tex]
Perimeter becomes: [tex]2(30+12)[/tex]
= [tex]2(42)=84[/tex] cm
2nd method:
Simply multiply 6 with the original perimeter.
[tex]14\times6=84[/tex] cm
We can see that in both methods, the perimeter is same.
Sample Response:
To find the perimeter of an enlarged figure, you can multiply the original figure’s perimeter by the scale factor. You could also multiply each dimension of the original figure by the scale factor to find the dimensions of the enlarged figure, and then add to find the perimeter.
Find the values of x,y, and z. The diagram is not to scale.
A. x = 86, y = 94, z = 75
B. x = 86, y = 75, z = 94
C. x = 75, y = 94, z = 86
D. x = 75, y = 86, z = 94
Answer:
b) x=86,y=75,z=94
Step-by-step explanation:
What must be true of the discriminant the soulution to a quadratic equation is a set of 2 different real numbers?
What is the decimal value of the 2 in the hexadecimal number f42ac16?
The decimal value of the 2 in the hexadecimal number f42ac16 is 2.
Explanation:The hexadecimal number f42ac16 can be split into individual digits, where each digit represents a power of 16. Starting from the rightmost digit, the 2 represents the digit in the 16^0 (1) place, which is simply 2. Therefore, the decimal value of the 2 in the hexadecimal number f42ac16 is 2.
Learn more about Hexadecimal Numbers here:https://brainly.com/question/36345940
#SPJ11
A blueprint for a picnic table has a scale of 1:20. The table in the blueprint is 3 in. long. What is the length of the actual picnic table?
A.) 5 feet
B.) 720 feet
C.) 5 inches
D.) 60 feet
Answer:
Option A is correct
5 feet is the length of the actual picnic table
Step-by-step explanation:
Proportion states that two ratios or fractions are equal.
As per the statement:
A blueprint for a picnic table has a scale of 1 : 20.
The table in the blueprint is 3 in. long.
Let x be the length of the actual picnic table.
By definition of proportion;
[tex]\frac{1}{20} = \frac{3}{x}[/tex]
By cross multiply we have;
[tex]x = 20 \cdot 3 = 60[/tex]
⇒x = 60 inches
Use conversion:
1 inches = [tex]\frac{1}{12}[/tex] feet
then;
60 inches = [tex]\frac{60}{12} = 5[/tex] feet
Therefore, the length of the actual picnic table is, 5 feet
PLEASE HELP WILL GIVE BRAINLIEST!!!! The graph shows the function f(x)=2^x
How did early mathematicians define trigonometric functions?
Answer:
There are six trigonometric function, the first three are mainly used and other three are not use often, they are:
Sine (sin)Cosine (cos)Tangent (tan)Cosecant (cosec or csc)Secant (sec)Cotangent (cot)They are mainly the ratio of two side of triangle.i.e.
[tex]Sin x = \dfrac{Perpendicular}{Hypotenuse}[/tex]
[tex]Cos x = \dfrac{Base}{Hypotenuse}[/tex]
[tex]Tan x = \dfrac{Perpendicular}{Base}[/tex]
[tex]Cosec x = \dfrac{Hypotenuse}{Perpendicular}[/tex]
[tex]Sec x = \dfrac{Hypotenuse}{Base}[/tex]
[tex]Cot x = \dfrac{Base}{Perpendicular}[/tex]
On the basis of these ratios there are different relations defined in Trigonometry Chapter.
Answer:
length of chords
Explanation:
In the study of the earth and astronomy, mathematicians developed trigonometric functions as lengths of chords in a circle, not as ratios. The mathematician Ptolemy calculated chord lengths by inscribing regular polygons in a circle. Remarkably, he was able to calculate these lengths to an accuracy of about five decimal places. Ptolemy's table of chords is equivalent to our table of sine values. In this lesson, you will begin to see the relationship between the trigonometric functions and the circle.
Consider the diagram shown where a ladder is leaning against the side of a building. The base of the ladder is 12 ft from the building. How far is the top of the ladder from the ground?(to the nearest ft)
If the area of the parallelogram is 540 in^2 what is the missing height?
in how may ways could mushrooms or olives be included in his toppings?
In 1996, Town M had a population of 30,500 people, and it has grown at a rate of 2% every year. In 1996, Town N had 32,500 people and the population has increased by a contrast rate of 600 people each year. In what year were the populations of the two towns approximately equal?
What is 21/16 simplified
Tim Worker estimates his taxable income will be $7,000. He is paid twice a month or 24 times a year. Because Tim has only one source of income, he uses the Tax Tables to estimate how much will be deducted from his pay for withholding.
Answer: finds the tax rate for his income level: 10%
Enters the base amount 29.16
Enters the amount of tax owed: 700
Divides by: 10 =:700
Step-by-step explanation:
I took the test hope this helps
if gold is currently trading at 800.00 /oz and you inherit a gold coin worth 3200.00 how much does the coin weigh
Given: p(e) = 0.42, p(f) = 0.51, and p(e ∪ f) = 0.70 part
a.find p(e ∩ f). part
b.find p(e | f). part
c.find p(f | e). part
d.are the events e and f independent?
Find the real square roots of .0064 and -.0081
Calculate the integral s f · ds, where s is the entire surface of the solid half ball x2 + y2 + z2 ≤ 1, z ≥ 0, and f = (x + 3y5)i + ( y + 10xz)j + (z − xy)k. (let s be oriented by the outward-pointing normal.)
Final answer:
To find the integral of the vector field over the solid half ball, we calculate two surface integrals, one over the flat disk and one over the hemisphere's curved surface, and then sum their contributions.
Explanation:
The student has asked to calculate the surface integral of the vector field f = (x + 3y^5)i + ( y + 10xz)j + (z - xy)k over the upper half of the sphere [tex]x^2 + y^2 + z^2 = 1[/tex], with z ≥ 0. To solve this, we can use the divergence theorem, noting that the divergence of f is ∇ · f, and then integrating that over the volume of the half sphere. We divide the surface S into two parts: the flat circular disk at the bottom (where z = 0) and the curved surface of the half sphere. The flux through the curved surface can be found by integrating over the sphere's surface, while the disk contributes a separate integral. This requires calculating two different surface integrals, and adding their results.
The surface integral [tex]\(\int_{S} \mathbf{f} \cdot d\mathbf{s}\)[/tex] for the given vector field and half-ball surface is [tex]\(2\pi\)[/tex].
To calculate the surface integral [tex]\(\int_{S} \mathbf{f} \cdot d\mathbf{s}\)[/tex] where [tex]\(S\)[/tex] is the entire surface of the solid half-ball [tex]\(x^2 + y^2 + z^2 \leq 1, z \geq 0\) and \(\mathbf{f} = (x + 3y^5)\mathbf{i} + (y + 10xz)\mathbf{j} + (z - xy)\mathbf{k}\)[/tex], we will use the Divergence Theorem.
The Divergence Theorem states that for a vector field [tex]\(\mathbf{f}\)[/tex],
[tex]\[\int_{S} \mathbf{f} \cdot d\mathbf{s} = \int_{V} (\nabla \cdot \mathbf{f}) \, dV\][/tex]
where [tex]\(S\)[/tex] is the boundary surface of the volume [tex]\(V\),[/tex] oriented by the outward-pointing normal.
1. Calculate the Divergence [tex]\(\nabla \cdot \mathbf{f}\)[/tex]:
[tex]\[\nabla \cdot \mathbf{f} = \frac{\partial}{\partial x}(x + 3y^5) + \frac{\partial}{\partial y}(y + 10xz) + \frac{\partial}{\partial z}(z - xy)\][/tex]
Computing each term:
[tex]\[\frac{\partial}{\partial x}(x + 3y^5) = 1\][/tex]
[tex]\[\frac{\partial}{\partial y}(y + 10xz) = 1\][/tex]
[tex]\[\frac{\partial}{\partial z}(z - xy) = 1\][/tex]
So the divergence is:
[tex]\[\nabla \cdot \mathbf{f} = 1 + 1 + 1 = 3\][/tex]
2. Set up the volume integral:
The volume (V) is the solid half-ball defined by [tex]\(x^2 + y^2 + z^2 \leq 1\)[/tex] and [tex]\(z \geq 0\)[/tex].
We will integrate the constant divergence \(3\) over the volume of the half-ball. The volume of a full ball of radius 1 is \(\frac{4}{3} \pi (1^3) = \frac{4}{3} \pi\). Since we have a half-ball, the volume is:
[tex]\[\text{Volume of half-ball} = \frac{1}{2} \cdot \frac{4}{3} \pi = \frac{2}{3} \pi\][/tex]
3. Evaluate the volume integral:
[tex]\[\int_{V} (\nabla \cdot \mathbf{f}) \, dV = \int_{V} 3 \, dV = 3 \int_{V} dV = 3 \cdot \text{Volume of half-ball} = 3 \cdot \frac{2}{3} \pi = 2 \pi\][/tex]
Therefore, the surface integral is:
[tex]\[\int_{S} \mathbf{f} \cdot d\mathbf{s} = 2\pi\][/tex]
So, the final answer is:
[tex]\[\boxed{2\pi}\][/tex]
What are the solutions of 12 – x2 = 0?
A. x = and x =
B. x = and x =
C. x = and x =
D. x = 6 and x = –6
The solution of the expression are,
⇒ x = 3.5 and x = - 3.5
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 12 - x² = 0
Now, We can simplify as;
⇒ 12 - x² = 0
⇒ 12 = x²
⇒ x = √12
⇒ x = ± 3.5
⇒ x = 3.5 and x = - 3.5
Thus, The solution of the expression are,
⇒ x = 3.5 and x = - 3.5
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ3
One side of a rectangle is five times as long as the other side. If the perimeter is 72 meters, what is the length of the shorter side?
PLEASE HELP!!
A music store orders wooden drumsticks that weigh 96 grams per pair. The total weight of the box of drumsticks is 782 grams. How many pairs of drumsticks are in the box if the empty box weighs 206 grams?
_______ pairs?
Answer: 6 Drumsticks
Step-by-step explanation:
what is the volume of the 3d shape created by rotating the square with side lengths of 14cm
130.8996939 rounded to the nearest hundredth
caleb and his classmates are making felt dog toys for a local animal shelter. how much red and yellow felt does his teacher need to buy so 20 students can each make a toy?
felt needed for each toy
1/8 sheet of white
3/8 sheet of red
5/8 sheet of yellow
1 1/8 sheets of black
Answer:
C ) 8 sheets of red and 13 sheets of yellow felt
Step-by-step explanation:
Final answer:
Caleb's teacher needs to purchase 7.5 sheets of red felt and 12.5 sheets of yellow felt so that each of the 20 students can make a dog toy.
Explanation:
To calculate the amount of red and yellow felt Caleb's teacher needs to buy for 20 students to each make a dog toy, we can multiply the amount of felt needed for one toy by the total number of students.
Red felt needed: 3/8 sheet per toy
Yellow felt needed: 5/8 sheet per toy
For red felt:
3/8 sheet x 20 students = 60/8 sheets
To simplify this, we divide 60 by 8, which equals 7.5 sheets. So, the teacher needs to buy 7.5 sheets of red felt.
For yellow felt:
5/8 sheet x 20 students = 100/8 sheets
After simplifying, 100 divided by 8 equals 12.5 sheets. Therefore, the teacher needs to acquire 12.5 sheets of yellow felt.
The center of a circle is at the origin. An endpoint of a diameter of the circle is at (-3, -4). How long is the diameter of the circle? 5, 10, or 25?
What are the direction indices for a vector that passes from point 34 1 12 to point 14 12 1 in a cubic unit cell? please indicate negative directions by a "-" sign before the integer and omit spaces between numbers?
The direction indices for a vector passing from point (34, 1, 12) to point (14, 12, 1) are calculated by subtracting the coordinates of the starting point from the ending point, resulting in the indices [-20 11 -11].
Explanation:The student asked for the direction indices of a vector passing from point (34, 1, 12) to point (14, 12, 1) in a cubic unit cell. To determine the direction indices, we need to subtract the coordinates of the initial point from the coordinates of the final point. The resulting vector ∆r will have components ∆x, ∆y, and ∆z as follows:
∆x = 14 - 34 = -20∆y = 12 - 1 = 11∆z = 1 - 12 = -11Therefore, the direction indices for the vector are written without spaces and with negative signs for negative directions. In this case, the direction indices would be [-20 11 -11].
Learn more about direction indices here:https://brainly.com/question/1420586
#SPJ3
Compare 0.3 and 0.8 using >,=,or <. Draw a model or number line to support your solutions
Jamel swam 92 meters in 4 minutes. Andre swam 105 meters in 5 minutes. Who is ther faster swimmer? Provide very clear evidence to support your answer.
A circle has a radius of 26.85 inches what is the circumference of this circle
If Lewis's house increases in value by 3% each year over two decades, he could still lose money when he sells the house if _____.
Select the best answer from the choices provided.
a) interest rates on mortgages fell 3% over the same time
b) his repair and maintenance costs were more than 3% a year
c) homes in other areas of town lost more than 3% of their value
d) his down payment was significantly more than 3% of the house value
The correct answer is:
b) his repair and maintenance costs were more than 3% a year
Explanation:
Lewis's house increases in value by 3% each year. However, if he spends more than 3% of the value of his home each year in repairs and maintenance, when he sells the home, he will not be making money; he will in fact lose money, compared to what he's spent the last two decades.
Which expression is equivalent to (xy)z?
Answer:
C is the correct answer.
Step-by-step explanation:
Took the test.
x(yz)
a parallelogram with congruent diagonals is a _____.