Answer:
1- The sum is: 2m + 2n + 7 = 2(m+n) + 7
2- The difference is: 3m - 2
3- The difference is: -2m - 2n + 2 = -2(m+n-1)
Explanation:
Before we begin, remember the following:
+ve * +ve = +ve
-ve * -ve = -ve
+ve * -ve = -ve
-ve * +ve = -ve
Also, remember that, we only add/subtract like terms. There are terms which have the same variable(s) raised to the same degree
Now, let's check the problems:
Problem 1:
Adding two polynomials:
(m + n + 3) + (m + n + 4)
We first start by getting rid of the brackets:
m + n + 3 + m + n + 4
Now, we add like terms:
2m + 2n + 7
As an additional step, we can take 2 as a common factor from the first two terms:
2(m+n) + 7
Problem 2:
Subtracting two polynomials:
(10m - 6) - (7m - 4)
We first start by getting rid of the brackets. Take care of the different signs while doing so:
10m - 6 - 7m + 4
Now, we add/subtract like terms:
3m - 2
Problem 3:
Subtracting two polynomials:
(4m - 5) - (6m - 7 + 2n)
We first start by getting rid of the brackets. Take care of the different signs while doing so:
4m - 5 - 6m + 7 - 2n
Now, we add/subtract like terms:
-2m - 2n + 2
As an additional step, we can take -2 as a common factor from the above expression:
-2(m+n-1)
Hope this helps :)
A cone shaped cup has a radius of 4 inches and a height of 6 inches. Which measurement is the closest to the volume in cubic inches for the cup? Use 3.14 for π.
25.12 in³
12.28 in³
100.48 in³
6.14 in³
maria is planning a triangular garden she wants to build a fence around the garden to keep out the rabbits. the length of one side of the garden is 29 feet. if the angles of this side are 65 and 44 find the length of the fence needed to enclose the garden
Approximately 85.323 feet of fence is needed to enclose the garden.
To find the length of the fence needed to enclose Maria's triangular garden, we can use the Law of Sines since we know one side length and its opposite angle.
The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant:
[tex]\[ \frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)} \][/tex]
Where:
- a, b, c are the side lengths of the triangle.
- A, B, C are the angles of the triangle.
Given that one side length is 29 feet and its opposite angle is 65°, let's denote the other two angles as B and C . Since the sum of angles in a triangle is 180°, we can find angle C as 180° - 65° - 44° = 71°.
Now, we can use the Law of Sines to find the lengths of the other two sides:
[tex]\[ \frac{29}{\sin(65°)} = \frac{b}{\sin(44°)} \][/tex]
Solving for b:
[tex]\[ b = 29 \times \frac{\sin(44°)}{\sin(65°)} \][/tex]
b ≈ [tex]24.438 \text{ feet} \][/tex]
Similarly, we can find the length of side c using the same formula:
[tex]\[ \frac{29}{\sin(65°)} = \frac{c}{\sin(71°)} \][/tex]
[tex]\[ c = 29 \times \frac{\sin(71°)}{\sin(65°)} \][/tex]
c ≈ [tex]31.885 \text{ feet} \][/tex]
Finally, to find the total length of the fence needed, we sum up the lengths of all three sides:
[tex]\[ \text{Total fence length} = 29 + 24.438 + 31.885 \][/tex]
[tex]\[ \text{Total fence length}[/tex] ≈ [tex]85.323 \text{ feet} \][/tex]
So, approximately 85.323 feet of fence is needed to enclose the garden.
(20 Pts) What is the value of h when the function is converted to vertex form? Note: Vertex form is p(x)=a(x−h)^2+k . p(x)=x^2−14x+29
Lindsey’s college will cost her a total of $6,000 a year for the next four years. She is also
foregoing making $26,000 a year at the local mall. However, she will be able to make
about $8,000 a year while going to school. What is her total investment in education?
$24,000
$26,000
$72,000
$96,000
Karam anticipates spending $8,400 a year for the next five years on his college education. He will also forgo making $12,000 a year during this time. How much will he invest in his education?
$42,000
$102,000
$60,000
$12,000
Her total investment in education is $96,000, the correct option is D.
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.
We are given that;
Total= $6,000
At local mall=$26,000
Now,
To find the total investment in education, we need to consider both the direct costs and the opportunity costs of going to college. The direct costs are the expenses that Lindsey has to pay for her education, such as tuition, fees, books, etc. The opportunity costs are the income that Lindsey could have earned if she did not go to college, such as working at the local mall.
The direct costs of going to college are $6,000 a year for four years, which is $24,000 in total.
The opportunity costs of going to college are $26,000 a year minus $8,000 a year for four years, which is $18,000 a year or $72,000 in total. This is because Lindsey could have earned $26,000 a year at the mall, but she is only earning $8,000 a year while going to school.
The total investment in education is the sum of the direct costs and the opportunity costs, which is
$24,000 + $72,000
= $96,000.
Therefore, by algebra the answer will be $96,000.
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You have a camera with a 16 mp resolution. how many pixels are represented by that resolution? 16 16 million 16,000 16 billion
SOLVE FOR X PLEASE :D
Which property is demonstrated below
Find a positive angle less than one revolution around the unit circle that is co-terminal with the given angle: 52pi/5
At the beginning of the spelling bee there were 60 participants. One-third of the participants were eliminated during the first round. One-fourth of the remaining participants were eliminate during the second round. One-sixth of the remaining participants were eliminated during the third round. How many participants were still cmpeting at the beginning of the fourth round?
By subtracting the eliminated participants in each round from the original number, it is determined that 25 participants were still competing at the beginning of the fourth round.
To find out how many participants were still competing at the beginning of the fourth round of the spelling bee, we need to perform some calculations based on the given percentages of participants eliminated in each round.
In the first round, one-third of the 60 participants were eliminated. This is 60 / 3 = 20 participants eliminated. So, 60 - 20 = 40 participants remained after the first round.In the second round, one-fourth of the remaining participants were eliminated. This is 40 / 4 = 10 participants eliminated. So, 40 - 10 = 30 participants remained after the second round.In the third round, one-sixth of the remaining participants were eliminated. This is 30 / 6 = 5 participants eliminated. So, 30 - 5 = 25 participants remained.Therefore, 25 participants were still competing at the beginning of the fourth round.
A sphere is dilated by a scale factor of 1.5 to create a new sphere. How does the volume of the new sphere compare with the volume of the original sphere?
A)
The volume of the new sphere is 1.5 times the volume of the original sphere.
B)
The volume of the new sphere is 3.0 times the volume of the original sphere.
C)
The volume of the new sphere is 1.52 times the volume of the original sphere.
D)
The volume of the new sphere is 1.53 times the volume of the original sphere.
Answer: D
Step-by-step explanation:
bracelet costs $8. Simone is also buying a necklace for her mother for $18. She believes that her total will be $98. Which expression could be used to estimate the reasonableness of Simone’s total? 8 × $8 + $10 8 × $8 + $18 10 × $8 + $20 10 × $10 + $10
A regular decagon is mapped onto itsslf everytime it is rotated by how many degrees
Answer:
36° is correct.
Step-by-step explanation:
The degree of rotational symmetry is equal to 360° divided by the number of sides of a regular polygon
360° ÷ 10 = 36°
Answer:
A regular decagon is mapped onto itself every time it is rotated by 36°
Step-by-step explanation:
A regular decagon means a polygon with 10 sides and all sides are equal.
Refer the given figure, if we rotate by 36° we will get same decagon.
So a regular decagon is mapped onto itself every time it is rotated by 36°
A tour group charges a flat price for a tour of up to 20 people. The cost per person varies inversely with the number of people. If five people pay 135 each, what must 15 people pay per person.
Miss Monett gave 1 cup of red paint to each of her 20 students how many quarts of red paint does she give out
Answer: 5 Quarts
Hope this helped :>
Is it possible to take a cross section of a tetrahedron and get an octagon? Why or why not?
A.) Yes, because an octagon has eight sides, which is twice the number of faces on a tetrahedron.
B.) Yes, because a tetrahedron is symmetric about its center.
C.) No, because the only cross section that can result from a tetrahedron is a triangle.
D.) No, because the number of sides on the resulting shape cannot exceed the number of faces on the solid.
Answer: D.) No, because the number of sides on the resulting shape cannot exceed the number of faces on the solid.
Option (D) No, it is not possible to take a cross section of a tetrahedron and get an octagon because the number of sides on the resulting shape cannot exceed the number of faces on the solid. A tetrahedron, having only four faces, cannot have a cross section with eight sides like an octagon.
The question asks if it is possible to take a cross section of a tetrahedron and get an octagon. A tetrahedron is composed of four triangular faces, six edges, and four vertices. It is the simplest of all the ordinary convex polyhedra and the only one with fewer than 5 faces. The provided options suggest various reasons why an octagon could or could not result from a cross section of a tetrahedron. The correct answer is D: No, because the number of sides on the resulting shape cannot exceed the number of faces on the solid.
A cross section that intersects a solid will typically not have more sides than the number of faces of the solid itself. Since a tetrahedron has only four faces, any cross-section made through it cannot naturally have more than four sides, thus it cannot result in an octagon, which has eight sides. The concept of symmetry or the fact that an octagon has twice as many sides as a tetrahedron does not relate to the possibility of such a cross section.
1. Ki’von has a sink that is shaped like a half-sphere. The sink has a diameter of 20 inches. One day, his sink clogged. He has to use one of two different cups to scoop the water out of the sink. The sink is completely full when Ki’von begins scooping. (a) What is the exact volume of the sink? Show your work. (3 points) (b) One conical cup has a diameter of 8 in. and a height of 6 in. How many cups of water must Ki’von scoop out of the sink with this cup to empty it? Round the number of scoops to the nearest whole number. Show your work. (6 points) (c) One cylindrical cup has a diameter of 4 in. and a height of 6 in. How many cups of water must he scoop out of the sink with this cup to empty it? Round the number of scoops to the nearest whole number. Show your work. (6 points)
how do i graph and shade this linear inequality?
4x + 5y < 20
x - 2y <6
Describe one way that concepts about similarity could be used in real life
Answer with explanation:
Uses of Similarity in Real Life:
1. When you will look,at the technology, personal Computers or Laptops produced by the same company,they all appear Similar.
2. When you will look at the bricks,which are used on the walls,on the roads, whether it is in the shape of a cube, Three dimensional Pentagon,or Hexagon,all of them are Similar.
→Similarity is also used for creating Electrical equipment ,Bulbs,Tube light,fans of different kinds.
So, There are Thousand of places on earth in which Concept of Similarity is used by Humans.Just Wrote few of them.
ILL GIVE BRAINLIST TO FIRST PERSON!!! Which of these is a primary economic activity? A) tourism B) farming C) healthcare D) construction
divide. and simplify 4/7÷8/3
Question 2: A circular picture is 8 inches in diameter. Part A What is the area of the picture in square inches? A. 4π square inches B. 8π square inches C. 16π square inches D. 32π square inches Part B A frame that is 2 inches wide surrounds the picture. What is the total area of the picture and the frame in square inches? A. 4π square inches B. 12π square inches C. 36π square inches D. 40π square inches
really important please answer correctly
find the geometric mean of the pair of numbers 36 and 4
The geometric mean of the pair of numbers 36 and 4 is calculated by getting the square root of the product of the two numbers, which gives us the geometric mean as 12.
Explanation:To find the geometric mean of the pair of numbers 36 and 4, we use the formula for the geometric mean of two positive numbers, which is the square root of the product of the two numbers.
When we multiply 36 and 4 we get 144. So, the geometric mean of 36 and 4 is the square root of 144, which equals 12.
Therefore, the geometric mean of the numbers 36 and 4 is 12.
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Find the two numbers whose sum is 29 and whose difference is 15
What is the value of x?
sin(x+22)°=cos(2x−7)°
Remember to show all of you work for credit!
Given cosx=1213 and sinx=513 .
What is ratio for tan x ?
leave answer as a fraction in simplest form
Remember to show all of you work for credit!
Q1: Given sin(x+22)° = cos(2x−7)°
Using the concept of Right triangles and Trigonometric ratios, we can use a formula given as follows :-
If, sin(A) = cos(B). Then we must have A + B = 90 degrees.
We have sin(x+22)° = cos(2x−7)°
Then it must be true that (x+22)° + (2x−7)° = 90 degrees.
(x + 22) + (2x - 7) = 90
3x + 15 = 90
3x + 15 - 15 = 90 - 15
3x = 75
[tex] \frac{3x}{3} =\frac{75}{3} \\\\x = 25 \;degrees [/tex]
Hence, x = 25 degrees is the final answer.
Q2: Given cos(x) = 1213 and sin(x) = 513.
It says to find ratio of tan(x).
Using the concepts of Trigonometric ratios, We can the formula that relates all three functions i.e. sin(x), cos(x), and tan(x).
tan(x) = [tex] \frac{sin(x)}{cos(x)} [/tex]
We can plug the given values in the formula.
[tex] tan(x) = \frac{513}{1213} [/tex] is the final answer.
WHAT IS 2 400 000 written as a standard form?
write 4bc/16b in simplest form
7. Simplify the product using the distributive property.
(5h - 3)(3h + 7)
(A). 15h^2 - 44h + 21
(B). 15h^2 - 26h - 21
(C). 15h^2 + 44h + 21
(D). 15h^2 + 26h - 21
8. Simplify the product using a table. ***I will add a picture of the table***
(5h + 4)(3h + 6)
(A). 15h^2 + 42h + 24
(B). 15h^2 - 42h + 24
(C). 15h^2 + 18h - 24
(D). 15h^2 - 18h - 24
9. Simplify using a table. ***I will also add a picture of this table***
(-4m + 6)(3m + 2)
(A). -12m^2 + 10m + 12
(B). -12m^2 - 10m - 12
(C). -12m^2 + 26m + 12
(D). -12m^2 - 26m - 12
10. Simplify the product using FOIL.
(4x - 4)(3x - 4)
(A). 12x^2 - 28x + 16
(B). 12x^2 - 4x - 16
(C). 12x^2 + 4x - 16
(D). 12x^2 + 28x + 16
11. A cylinder has a radius of 4x + 2 and a height of 5x + 4. Which polynomial in standard form best describes the total volume of the cylinder? Use the formula V= πr^2h for the volume of a cylinder.
(A). 80πx^3 + 144πx^2 + 84πx + 16π
(B). 20πx^2 + 26πx + 8π
(C). 80πx^3 + 144πx^2 + 84πx - 16π
(D). 400πx^4 + 1040πx^3 + 996πx^2 + 416πx + 64π
12. A sphere had a radius of 2x + 5. Which polynomial in standard form best describes the total surface area of the sphere? Use the formula S= 4πr^2 for surface area of a sphere.
(A). 16πx^2 + 80πx + 100π
(B). 16πx^2 + 40πx + 100π
(C). 100πx^2 + 80πx + 16π
(D). 100πx^2 + 100π
What is the product of 5the square root of 3. • 4the square root of 15.? Simplify if possible. 60the square root of 5. 20the square root of 5. 60the square root of 15. 20the square root of 15.
twice the measure of an angle's complement less 6 is equal to 124 find the measure of the angle
Answer
you work it out the same way the first guy did, except instead of
2 (180-x) - 6 = 124, it's
2(90-x) -6 = 124.
the first guy divided by the supplement instead of the complement.
Step-by-step explanation:
To find the measure of the angle, you can use the equation 2(90 - x) - 6 = 124, where x represents the angle. By solving for x, you can determine that the measure of the angle is 25 degrees.
Explanation:To find the measure of the angle, we can use the information provided in the question. Let's let the measure of the angle be x degrees. The complement of the angle can be found by subtracting the measure of the angle from 90 degrees, since the sum of an angle and its complement is always 90 degrees. Therefore, the complement of the angle is 90 - x degrees.
According to the given equation, twice the measure of the angle's complement less 6 is equal to 124. We can write this as 2(90 - x) - 6 = 124. Now we can solve for x:
2(90 - x) - 6 = 124
180 - 2x - 6 = 124
-2x + 174 = 124
-2x = -50
x = 25
Therefore, the measure of the angle is 25 degrees.
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Please help me I have 2 questions.