First, let's simplify the expression (4c + 8) + 3c - 2:
(4c + 8) + 3c - 2
= 4c + 3c + 8 - 2 (rearrange terms)
= 7c + 6 (combine like terms)
So the first expression simplifies to 7c + 6.
Next, let's simplify the expression 4c + 2(0.5c + 1):
4c + 2(0.5c + 1)
= 4c + 2(0.5c) + 2(1) (distribute the 2)
= 4c + c + 2 (simplify the parenthesis)
= 5c + 2 (combine like terms)
So the second expression simplifies to 5c + 2.
Now we can compare the two expressions:
7c + 6 vs. 5c + 2
These expressions are not equivalent because they do not have the same coefficients or constants.
100 POINTS NEED HELP ASAP QUESTIONS ARE BELOW
Area of triangle= 24 cm²
Area of sector= 72.243 cm²
Total area= 96.243 cm².
What is triangle?A polygon with three sides and three vertices is called a triangle. It is one of the fundamental geometric forms. Triangle ABC is the designation for a triangle with points A, B, and C. In Euclidean mathematics, any three points that are not collinear produce a distinct triangle and a distinct plane.
What is sector?The portion of a disc enclosed by two radii and an arc is called a circular sector, also known as a circle sector or disc sector. The smaller area is referred to as the minor sector, and the bigger area as the major sector. A sector is referred to as a component of a circle made up of the circular's arc and its two radii.
In this question,
Area of triangle= 1/2 × base × height
= 1/2 × 6 ×8
= 24 cm²
Area of sector = (θ/360°) × πr²
= (82/360) × πr²
Here r=√6²+8²
= 10 cm
Area of sector = (82/360) × π10²
= 0.23 × 314.1
= 72.243 cm²
Total= 24 cm²+72.243 cm²= 96.243 cm².
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Madeleine helps build house with habitat for humanity. After exterior wall is erected she measures to see if it is a square. The height of wall is 9ft. She measures 12 ft along the floor from corner and takes a mark. What should be length of diagonal?
The Iength οf the diagοnaI οf the square exteriοr waII shοuId be 15 feet.
What is Pythagοrean Theοrem?Accοrding tο the Pythagοrean theοrem, the square οf a right triangIe's hypοtenuse (the side οppοsite the right angIe) equaIs the sum οf its οther twο sides' squares.
Outside waII's Iength and width are equaI if it is a square. Let's caII this Iength "x"
Using the Pythagοrean theοrem, we can find the Iength οf the diagοnaI οf the square:
diagοnaI² = height² + width²
Since the height is 9 ft and οne side οf the square is 12 ft, we can write:
diagοnaI² = 9² + 12²
diagοnaI² = 81 + 144
diagοnaI² = 225
Taking the square rοοt οf bοth sides, we get:
diagοnaI = √(225)
diagοnaI = 15 ft
Therefοre, the Iength οf the diagοnaI οf the square exteriοr waII shοuId be 15 feet.
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help True or false.
A poet can include figurative language and context clues to contribute to the overall meaning of a poem.
True
False
The correct answer is true
Answer:
True hope this helps!
Rewrite 1 + 2i in polar form.
A.√5
B.√5∠116.6°
C.[5√∠63.4°]
D.5√∠(63.4°)
1 + 2i in polar form is 5√2∠63.4°.
What is a polar form ?
In mathematics, the polar form is a way of representing complex numbers using their magnitude and angle. A complex number can be represented in the form r(cos θ + i sin θ), where r is the magnitude (or modulus) of the complex number, and θ is its argument (or phase angle). Alternatively, the polar form can be represented in terms of magnitude and angle as r ∠θ, where r is the magnitude and θ is the angle in radians. This form is also known as the exponential form of a complex number. The polar form is useful in calculations involving complex numbers, especially in multiplication and division, where it is often easier to work with the polar form rather than the rectangular form (a + bi).
D. 5√2∠63.4°
To convert a complex number from rectangular form to polar form, we use the following formulas:
r = √(a^2 + b^2)
θ = tan^-1 (b/a)
Where a and b are the real and imaginary parts of the complex number, respectively.
In this case, a = 1 and b = 2, so:
r = √(1^2 + 2^2) = √5
θ = tan^-1 (2/1) = 63.4°
Therefore, 1 + 2i in polar form is 5√2∠63.4°.
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PLEASE HELP! URGENT AND WORTH 50 POINTS!!!
Answer:
C) 2, 7, 6 can form a triangle.
Step-by-step explanation:
Triangle Inequality TheoremThe triangle inequality theorem states that the sum of any two sides of a triangle is greater than the length of the third side.
To determine which group of given side measures will form a triangle, sum each pair of sides and compare to the third side. If all three inequalities are true, the group will form a triangle.
Given side lengths: 9, 4, 3
⇒ 9 + 4 > 3
⇒ 9 + 3 > 4
⇒ 4 + 3 [tex]\ngtr[/tex] 9
Therefore, this group cannot form a triangle.
Given side lengths: 8, 1, 7
⇒ 8 + 1 > 7
⇒ 8 + 7 > 1
⇒ 1 + 7 [tex]\ngtr[/tex] 8
Therefore, this group cannot form a triangle.
Given side lengths: 2, 7, 6
⇒ 2 + 7 > 6
⇒ 2 + 6 > 7
⇒ 7 + 6 > 2
Therefore, this group can form a triangle.
Given side lengths: 12, 10, 22
⇒ 12 + 10 [tex]\ngtr[/tex] 22
⇒ 12 + 22 > 10
⇒ 10 + 22 > 12
Therefore, this group cannot form a triangle.
Determine the order of the following matrix:
[9 6 -4 8]
The order of the matrix is 2 x 2.
What is a matrix and what is meant by its order?
In the field of mathematics, matrices are rectangular arrangements of numerical values, symbols, or algebraic expressions, organized in rows and columns. Matrices are used in many areas of mathematics and science, as well as in engineering, physics, and computer graphics.
The term 'order' in the context of matrices refers to the dimensions of the matrix, which are determined by the number of rows and columns it contains. It is denoted by m x n, where m is the number of rows and n is the number of columns. To find the order of a matrix, we simply count the number of rows and columns. The order is usually written as a pair of numbers in the form m x n.
Determine the order of the given matrix:
In the given problem, we are asked to find the order of the matrix:
[tex]\begin{pmatrix}9 &6 \\-4 & 8\end{pmatrix}[/tex]
we count the number of rows and columns.
This matrix has 2 rows and 2 columns, so its order is 2 x 2.
Therefore, the order of the matrix is 2 x 2.
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Adrian eats 2/3's of a pack of gum each
day. How many packs of gum will he
have eaten after 7 days?
10 points given!!
Determine o resultado das perguntas a baixo por favor, pra agora
1. {0, 1, 3, 4, 6}; 2. {4, 6}.
Step-by-step explanation:
1. А={0, 1, 2, 3}, B={2, 4, 5, 6}, C={2, 5, 7, 9}; (A∪B)-(B∩C)-?
a) A∪B⇔{0, 1, 2, 3, 4, 5, 6};
b) B∩C⇔{2, 5};
c) (A∪B)-(B∩C)⇒{0, 1, 3, 4, 6}.
2. A={4, 6, 8, 10}, B={4, 6, 8}, C={1, 2, 3, 4, 7}, D={3, 5, 6, 7}; A∩(D∪(B∩C))=?
a) B∩C⇔{4};
b) D∪(B∩C)⇔{3, 4, 5, 6, 7};
c) A∩(D∪(B∩C))⇒{4, 6}.
Need help with the questions
1. Calculating the output when using -6 as the input, we have:
Rule 1: subtract 7 = -13
Rule 2: square the input = 36.
Rule 3: divide by 3 = 12
Rule 4: divide the input into 3 = -2
Rule 5: write π = -2π
Rule 6: volume of a cube = -216cm³
What is function rule?A function rule is a mathematical expression that describes how to calculate the output value of a function based on its input value. It can be thought of as a set of instructions that tell you what to do with the input value to get the output value.
2. a. True. Speed is the ratio of distance traveled to the time taken to travel that distance. In this case, the distance is fixed at 100 meters, so speed is solely dependent on time. For each value of time, there is only one corresponding value of speed, making it a function.
b. False. While time and distance are related in the formula for speed, time is not a function of distance in this case. Each student's time is independent of the distance they cover, and the same distance is covered by all students (100 meters). Therefore, for any given distance, there are multiple possible values of time, making it not a function.
c. False. The number of students racing is not related to their speed. Each student's speed depends solely on their individual time, which is not affected by the number of other students racing.
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which of these animals can travel at the greatest distance from sea level?
Answer:
Dragonflies
Step-by-step explanation:
They can fly on top of the water, but also, they have the fastest turns per second for their wings.
3 A truck delivered 48 cases of drinks to a gas station. Each case contained 24
drinks. The drinks were placed in rows in the cooler. There were 16 drinks in each
row. Which equation can be used to find r, the number of rows the drinks were
placed in?
€ 48 + 16 + 24 = r
18 x 21 +16=r
Answer: A 48 x 24/16 = r
Step-by-step explanation:
48 x 24 = the total number of drinks
Since there are 16 drinks in each row you want divide to get the number of rows in each drink.
Ex: 48 x 24= 1,152 (total drinks)
16 drinks in a row
1,152/16 = 72
72 rows
(HELP PLEASE)A school track is pictured
below. The straightaway on
each side measures/100 yards.
The curves are semicircles with
diameter 36 yards. What is the
distance, in yards, around the
entire track? Use the button
on your calculator and express
your answer to the nearest
hundredth.
Around [tex]312.57[/tex] yards are required to complete a full lap of the circuit.
What's the easiest way to define distance?The entire movement of an item, independent of direction, is called distance. Regardless of an object's beginning or finishing position, distance may be defined as the amount of ground it has travelled.
Describe a distance example.As a result, distance is indeed a scalar quantity. The whole path an item has taken can be used to define the distance from it. Think about it this way. If a car drives 5 km east, then turns to head north for 8 km, the final distance driven by the automobile must be 13 km.
The circumference of a semicircle with diameter d is [tex](pi/2)d[/tex]. Therefore, the length of each semicircular section is [tex](pi/2) * 36 = 18pi[/tex].
The total distance around the track is the sum of the lengths of the two straight sections and the two semicircular sections.
Distance around track [tex]= 2(100 yards) + 2(18pi yards)[/tex]
[tex]= 200 yards + 36pi yards[/tex]
[tex]= 312.57 yards[/tex] (rounded to two decimal places)
Therefore, the distance around the entire track is approximately [tex]312.57[/tex]yards.
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D) what is the domain and range of the graphed function?
E) Isabel’s competition, who sells books and no other products, charges a shipping fee of $1.99 per book plus a fixed fee of $3 for each order. Let x be the number of books purchased and f(x) be the price of shipping one order of books. Write a function that expresses f(x) and explain the value of f(x) for x = 0.
F) graph the function in part e
G) is your graph discrete or continuous? Explain.
The function that expresses f(x) is f(x) = 1.99x + 3, and its graph is continuous.
What is a Continuous Function?A continuous function is one that doesn't have any sudden or unexpected changes in value. It means that if we make small enough changes to its input, the output will also change by a small amount.
We can express the total cost of an order as a function of the number of books sold, x, using the formula:
f(x) = 1.99x + 3
This function takes the number of books sold, multiplies it by the cost per book ($1.99), and adds a fixed fee of $3.
For example, if we sold 3 books, we can use the function to find the total cost:
f(3) = 1.99(3) + 3 = 9.97
This means that selling 3 books would cost $9.97 in total.
The graph of this function is continuous, which means that as we move along the x-axis, the y-values change smoothly and without any sudden jumps.
The term "continuous" refers to a function that can take on any value between two given points and can be broken down into infinitely many fractions and decimals.
In contrast, a discrete function can only take on specific values, usually whole numbers or integers.
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Sally opens a savings account with $9,000 that earns 7% interest per year, not compounded How much interest, to the nearest penny, will Sally earn in 7 years?
Answer: Sally will earn $4,830.00 in interest over 7 years.
Step-by-step explanation:
If the interest is not compounded, then Sally will earn simple interest, which can be calculated using the formula:
I = P * r * t
where:
I = the interest earned
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
t = the time period, in years
In this case, we have:
P = $9,000 (the initial deposit)
r = 7% = 0.07 (the annual interest rate)
t = 7 (the number of years)
So, plugging in the values:
I = $9,000 * 0.07 * 7
I = $4,830.00
Therefore, Sally will earn $4,830.00 in interest over 7 years.
The buying and selling rates of US $ I are NRs 119.25 and NRs 119.85 respectively. Rushbu has 300 USD and goes to a bank to exchange her dollars into Nepali currency. Is it sufficient to her to buy a television costing Rs 35,000 after allowing 10% discount and including 13% VAT from the Nepalese rupees which is exchanged with the dollars? Give reason.
Answer:
Rushbu exchanges 300 USD at the buying rate of NRs 119.25, so she will receive:
300 x 119.25 = NRs 35775
After allowing a 10% discount, Rushbu will need to pay:
35000 - (10/100 x 35000) = NRs 31500
Including 13% VAT, Rushbu will need to pay:
31500 + (13/100 x 31500) = NRs 35655
Since Rushbu received NRs 35,775 after exchanging her 300 USD, she will have enough Nepali currency to buy the television, even after accounting for the discount and VAT.
Therefore, Rushbu will have enough money to buy the television, and she will have NRs 120 less than she received from exchanging her 300 USD, but that does not affect her buying capacity in this case.
Math
Practice solving.
1. What is the sum of -5/7 and 3/7?
2. Find the different of 5/12 - 3/4
3. Find the difference of 1/8 - 13/2
4. Find the sim of 2/3 and 1/3
5. Find the difference of 3/4 and 1/3
6. What is 3/5 x 4/6
7. What is -8/9 x 3/4
8. What is 2 2/3 x 4/5
9. What is 3/4 of 120
10. What is 2/3 of 360
11. What is 1/3 of 180
12. Multiply 16/24 by 8/20
13. Multiply 1/7 by 4/1
14. What is 1/5 x 8/1
15. Multiply 4/7 x 6/1
16. Divide 3/8 and 2/5
17. Divide 16/21 and 24/14
18. What is 4/5 divided by 7/10
19. What is -4/15 divided by 8/12
20. What is 4/6 divided by -8
Answer:
1. -2/7
2. 7/6
3. 53/8
4. do u mean sum? if yes then the answer is 1
5. 5/12
6. 2/5
7. -2/3
8.
9.90
10.240
11.60
12. 4/15
13.4/7
14.8/5
15.24/7
16.15/16
17.4/9
18.8/7
19.-2/5
20.-1/12
pls help me with this!!!!!!!!!
Answer:
Supplementary Angles: The angles 1 & 2 are supplementary angles, as, when combined together, their total angle measurement is 180°, or a straight line. Supplementary angles, by definition, is either two angles in which, when combined, the sum is equal to 180°.
Adjacent Angles: The angles 1 & 2 are adjacent angles, as they share a common side and vertex. Vertexes, by definition is the corner point.
Why it is not:
Complementary Angles: Complementary angles suggest that, when two angles are combined together, their total angle measurements is 90°, or it creates a right angle. In this case, the total measurements of the combination of ∠1 & ∠2 is a straight line, or 180°. Therefore, complementary angles is not your answer.
Vertical Angles: Vertical angles suggest that, when there are two angles, they are directly opposite of each other. Vertical angles would share the same angle measurements.
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A cone has a radius of 6 centimeters and a height of 10 centimeters. What is the volume of the cone in cubic centimeters?
centimeters?
A 480π cm³
B 120π cm³
C 360π cm³
D 60π cm³
The volume of the cone in cubic centimeters in terms of π = 120π cm³. That is option B.
How to calculate the volume of a cone?To calculate the volume of a cone, the formula that is to be used;
Volume = 1/3 πr²h
Where;
Height = 10 centimetres
Radius = 6 centimetres
Volume = 1/3 × π × 6²× 10
= 360π/3
= 120π cm³
Therefore the volume of the cone whose dimensions are given = 120π cm³.
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MAKE CONNECTIONS Determine whether triangle XYZ can be a right triangle. Explain.
X (0, 0), Y (2h, 2h), Z (4h, 0)
Slope of XY Select Choice -1, 1, or 0
slope of YZ Select Choice 1, 0, or -1slope of ZX Select Choice -1, 1, or 0because Select Choice 1(1) = 1, 1(-1) = -1, 1(0) = 0, or 0(-1) =0XY Select Choice is or is not
perpendicular to YZ. Therefore, triangle XYZ Select Choice is not or is a right triangle.
Answer: slope of XY is not perpendicular to YZ. Therefore, triangle XYZ is a right triangle.
Step-by-step explanation:
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by (y2 - y1) / (x2 - x1).
Using this formula, we can find the slopes of the three sides of triangle XYZ:
Slope of XY = (2h - 0) / (2h - 0) = 1
Slope of YZ = (0 - 2h) / (4h - 2h) = -h / h = -1
Slope of ZX = (0 - 0) / (4h - 0) = 0
Therefore, the slope of XY is 1, the slope of YZ is -1, and the slope of ZX is 0.
Since the product of the slopes of two perpendicular lines is -1, we can see that the slope of XY and the slope of YZ are negative reciprocals of each other, which means that they are perpendicular. Therefore, triangle XYZ is a right triangle.
Veronica walks dogs in her neighborhood for extra money during the summer. For each dog walk, she earns $5.25. On Monday, she completes 3 walks, and on Tuesday she completes 2 walks. She estimates that in order to save up for a new purse that costs $86, she needs to complete 12 more walks by the end of the week.
Answer:
Veronica is correct
Step-by-step explanation:
On Monday, Veronica earns 3 walks * $5.25 per walk = $15.75.
On Tuesday, Veronica earns 2 walks * $5.25 per walk = $10.50.
So far, Veronica has earned a total of $15.75 + $10.50 = $26.25.
To reach her goal of $86, Veronica needs to earn an additional $86 - $26.25 = $59.75.
Since Veronica earns $5.25 per walk, she needs to complete $59.75 ÷ $5.25 per walk = 11.38 walks.
Since Veronica cannot complete a fraction of a walk, she will need to complete 12 more walks (rounded up from 11.38) by the end of the week.
Write a real-world problem that could be represented by 5x+ 30 ≥ 90.
Answer: If Jamie is selling bags of carrots for $5 each and already has $30 what would he use to calculate how much money he made.
p=6t. what is the value of p when t= 14
Answer:
p=84
Step-by-step explanation:
p=6×14
p=84
answer: p=84
Of the last 20 trains to arrive at Danville Station, 15 were on time. What is the experimental probability that the next train to arrive will be on time?
Write your answer as a fraction or whole number.
P(on time)=
The experimental probability that the next train to arrive at Danville Station will be on time is 3/4 or 0.75.
What is probability?
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.
The experimental probability of the next train to arrive at Danville Station being on time is given by the number of on-time trains divided by the total number of trains that arrived -
experimental probability = number of on-time trains / total number of trains
From the information given, we know that out of the last 20 trains to arrive, 15 were on time. Therefore -
number of on-time trains = 15
total number of trains = 20
Substituting these values into the equation, we get -
experimental probability = 15 / 20
Simplifying the fraction, we get -
experimental probability = 3/4
Therefore, the experimental probability value is obtained to be 3/4 or 0.75.
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PLEASE HELP???!!!!!!!
The quadratic equation on the graph can be written as:
y = x² + 6x + 8
Which function is represented byy the graph?Remember that a quadratic equation whose vertex is (h,k) and the leading coefficient is a, can be written as:
y = a*(x - h)² + k
Here we can see that the vertex is at (-3, -1), replacing that we will get:
y = a*(x + 3)² - 1
Now we can also see that it passes through the point (-2, 0), replacing these values we will get:
0 = a*(-2 + 3)² - 1
0 = a - 1
1 = a
Then the quadratic is:
y = (x + 3)² - 1
Expanding that we get:
y = x² + 6x + 9 - 1
y = x² + 6x + 8
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A superintendent of a school district awarded a total of $5000 in bonuses to the most productive teachers that helped impact student achievement this pat year. The bonuses were awarded in the amount of $500 or $1000. If at least one $500 bonus and at least one $1000 bonus were awarded, what is a total possible number of $500 bonuses awarded?
A total possible number of bonuses awarded is given as follows:
6 bonuses.
How to obtain the total number of bonuses awarded?The total number of bonuses awarded is obtained applying the proportions in the context of the problem.
The total amount of bonuses is of $5,000, and at least one $500 bonus and at least one $1000 bonus were awarded, hence the remaining amount to be awarded is of:
5000 - (500 + 1000) = $3,500.
For an amount of $3,500, a possible division of the bonuses is given as follows:
One bonus of $500.Three bonuses of $1000.Hence a possible number of bonuses is given as follows:
2 + 1 + 3 = 6 bonuses.
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Somebody pls help meee!!
Anybody??
Answer:
85 degrees.
Step-by-step explanation:
These are parallelograms, meaning the opposite sides are parallel. Since they are parallel, that the line EA becomes a transversal and a bisector for the angle CEK. That means the angle 8 and 3 are equivalent and 7 and 4 are equivalent. This is due to Same Side Interior Angles. These are two halves of the big angle. If the halves are equal, so are the angles. Therefore, CEK = CAK.
I thought of a number. Seven times the number decreased by 13 equals 5 times the number increased by 5. What was my number?
answer:
The number is 9
Step-by-step explanation:
9 × 7 = 63
63 - 13 = 50
9×5 = 45
45 + 5 = 50
Steps for solving t|u prove mt=mu
We may conclude after answering the presented question that As a equation result, we have demonstrated that mt = mu when t | u.
How to solve the problem?Make a note of the definition of t | u. It denotes the existence of an integer k such that u = tk.
To get mt = m, substitute u = tk into mt = mu (tk).
Rewrite m(tk) as (mt)k using the associative property of multiplication.
To get mt = (mt)k, substitute (mt)k for m(tk) in the equation mt = mu.
Multiply both sides by mt. If mt is greater than zero, we obtain 1 = k. If mt is zero, we must also have mu = 0, hence the equation holds.
Since 1 Equals k, we get u = tk = t(1) = t.
We get mt = mt by substituting u = t into the original equation mt = mu.
As a result, we have demonstrated that mt = mu when t | u.
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Question is posted on the picture. Plssss help!!!
Step-by-step explanation:
that the answerrrrrrrrr
A store sells water bottles in large and small sizes. There are 24
large water bottles and 18 small water bottles on display in the
store. The manager of the store wants there to be 3 large water
bottles on display for every 2 small water bottles. Should the
manager make any changes to the current display? Explain.
Answer:
Yes, the manager should make changes to the current display. There should be 36 large water bottles and 36 small water bottles, which would be a 3:2 ratio. To achieve this, the manager should add 12 more large water bottles to the display.