Simplified form of the expression 4m+5−3m:
m + 5
Expression : Degree of m is 1 , so the expression is linear.
Given , that expression: 4m+5−3m
Now to simplify the expression,
⇒ 4m + 5 − 3m
Combine like terms,
⇒ (4m - 3m) + 5
⇒ m + 5
Thus the simplified form is m + 5 .
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The number of baseball cards in Neil's collection is 80 percent of the number in Larry's collection. If Neil has 80 fewer baseball cards than Larry, how many do they have altogether
The problem involves setting up an equation based on the given situation to solve for the number of baseball cards Neil and Larry have. By solving the equation, you find that Larry has 400 cards and Neil has 320 cards. So, they have 720 baseball cards together.
Explanation:This is a problem of percentages and of algebra. First, you know that the number of cards Neil has is 80% of what Larry has. This can be set up as an algebraic equation, where N represents Neil’s cards and L represents Larry’s cards: N = 0.8L. You also know that Neil has 80 fewer cards than Larry, which provides a second equation: N = L - 80.
Because both expressions equal N, you can set them equal to each other to solve for L. This leads to 0.8L = L - 80. Solve this equation for L, and you get L = 400. Substituting this into the equation N = 0.8L, you find that N = 320. Therefore, Neil and Larry have 720 baseball cards altogether.
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A rectangle has a length of ∛81 and a width of 3 2/3 inches. Find the area of the rectangle.
A.3 2/3 power inches squared
B.3 8/3 power inches squared
C.9 inches squared
D. 9 2/3 power inches squared
A motorcycle with an initial value of $14,000 is decreasing in value at a rate of 3% each year. At this rate, approximately what will the value of the motorcycle be in 9 years?
A) 14,000
B) 10,000
C) 9,800
D) 550
The value of the motorcycle after 9 years, with a depreciation rate of 3% per year, will be approximately $9,800. This answer has been calculated using the formula for percent decrease applied to the initial value of the motorcycle.
Explanation:This question revolves around the concept of percent decrease, a fundamental topic in mathematics. To estimate the value of the motorcycle after nine years, we need to apply the percent decrease continuously for these years.
The formula is: Final Value = Initial Value * (1 - rate of decrease)number of years
So in this case, the final value will be: $14,000 * (1 - 0.03)^9.
Calculating that gives us approximately $9,855, so the closest answer would be option C, $9,800.
Therefore after 9 years, the motorcycle will have depreciated to around $9,800 in value given a yearly depreciation rate of 3%.
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Calculate the hypotenuse
The manager at a restaurant keeps track of the number of calzones and slices sold each day and the total money received. On Sunday, a total of 59 calzones and slices were sold, and the money collected was $456. If calzones are sold for $9 and slices are sold for $6, how many calzones and slices were sold?
Write two ratios that are equivalent to 3:11
Consider the following sets.
U = {all real number points on a number line}
A = {solutions to the inequality 3x + 4 ≥ 13}
B = {solutions to the inequality x + 3 ≤ 4}
For which values of x is A ⋃ B = Ø?
a 2 < x < 3
b 2 ≤ x ≤ 3
c x ≤ 2 and x ≥ 3
d x < 2 and x > 3
Answer:
A. 2 < x < 3
Step-by-step explanation:
The values of x which A ⋃ B = Ø is:
A. 2 < x < 3This refers to the grouping of data which can be graphically represented on a Venn diagram.
With this in mind, we have a set of data which makes use of a general set that contains:
Therefore, the values of x to which A ⋃ B = Ø is:
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Marla is looking for a new car. She has test-driven two cars but can only purchase one. The probability that she will purchase car A is 0.52, and the probability that she will purchase car B is 0.38. What is the probability that she will not purchase either car A or car B?
Answer: The required probability is 0.10.
Step-by-step explanation: Given that Marla is looking for a new car. She has test-driven two cars A and B but can only purchase one.
We are to find the probability that she will not purchase either car A or car B.
Let, 'C' denotes the event that Marla will purchase car A and 'D' denotes the event that Marla will purchase car 'B'.
Then, according to the given information, we have
[tex]P(A)=0.52,~~~P(B)=0.38.[/tex]
Since Marla cannot purchase both the cars, so the events A and B are disjoint.
That is,
[tex]A\cap B=\phi~~~~~\Rightarrow P(A\cap B)=0.[/tex]
Therefore, the probability that Marla will purchase either car A or car B is given by
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)=0.52+0.38-0=0.90.[/tex]
Hence, the probability that she will not purchase either car A or car B will be
[tex]P^\prime(A\cup B)=1-P(A\cup B)=0-0.90=0.10.[/tex]
Thus, the required probability is 0.10.
find the area of a regular hexagon if a side is 20cm
Area = 1039.23 square units
Round answer as needed. See picture for equation
Simplify the expression.
a. square root 6
b. square root 12
c. 9 square root 12
d. 9 square root 6
The expression is d) [tex]9 \sqrt{6}[/tex]
To simplify the given expressions involving square roots, follow these steps:
a. Square root 6
Since 6 is not a perfect square and has no perfect square factors, [tex]\sqrt{6} i[/tex]s already in its simplest form.
b. Square root 12
Break down 12 into its prime factors: 12 = [tex]2 \times 2 \times 3[/tex]. Therefore,[tex]\sqrt{12}[/tex]can be simplified as follows:
[tex]\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}[/tex]
c. 9 square root 12
We already know that [tex]\sqrt{12} = 2\sqrt{3},[/tex] so we substitute it into the expression:
[tex]9 \sqrt{12} = 9 \times 2\sqrt{3} = 18\sqrt{3}[/tex]
d. 9 square root 6
Since [tex]\sqrt{6[/tex]} is already in its simplest form, the expression remains:
[tex]9 \sqrt{6}[/tex]
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Mountain officials want to know the length of a new ski lift from A to C , as shown in the figure below. They measure angle DAC to be 32° . They then move 960 feet to point B and measure angle DBC to be 18° . What is the length of the new ski lift from A to C ? Round your answer to the nearest tenth of a foot.
Knowing if trigonometry knowledge we can say that the distance will be 305.4 ft.
So knowing how sine and tangent work we can write the equals as:
[tex]sin (32) = CD / 960\\CD = 508.72[/tex]
[tex]tan (32) = 508.72 / AD\\AD = 814.13[/tex]
To calculate the distance, we will decrease the two values found, like this:
[tex]814.13 - 508.72 = 305.4 ft[/tex]
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The quotient of 13 ÷ 24 is a decimal number. Which digit in the quotient is overlined?
1
4
5
6
13/24 = 0.5416666
since 6 keeps repeating that would be the number that has the line over it.
A man travelled 3/8 of his journey by a rail 1/4 by a taxi 1/8 by and the remaining 2km on foot what is the length of his total journey?
simplify the expression.
cos^2(pi/2-x)/sqrt1-sin^2(x)
a. tan(x)
b. cos(x)tan(x)
c. cos(x)cot(x)
d. sin(x)tan(x)
The graph below shows the price, y, in dollars, of different amounts of pounds of almonds, x: A graph titled Almond Prices shows Number of Pounds on x axis and Price in dollars on y axis. The scale on the x axis shows numbers from 0 to 12 at increments of 2, and the scale on the y axis shows numbers from 0 to 84 at increments of 14. A straight line joins the ordered pairs 0, 0 and 12, 84 Which equation best represents the relationship between x and y? y = 7x y = x + 7 y = 14x y = x + 14
Answer:
my brain has exceeded the limit of cofusion
Step-by-step explanation:
A quadrilateral has two consecutive angles that measure 90° each. Which of the following quadrilaterals could have this property?
i. square
ii. rectangle
iii. parallelogram
iv. kite
v. rhombus
vi. trapezoid
A.
i, ii
B.
i, ii, iii
C.
i, ii, iii, iv
D.
i, ii, iii, v, vi
Final answer:
A square, rectangle, and certain cases of rhombuses and trapezoids can have two consecutive right angles, while typically a parallelogram and kite do not unless they are special cases of the rectangle or square respectively.
Explanation:
In the context of quadrilaterals with two consecutive right angles, it's important to recognize that certain quadrilaterals have this property by definition. A square and a rectangle both have four right angles, which means they certainly have at least two consecutive right angles.
A parallelogram typically does not have right angles, but a rectangle is a special type of parallelogram with right angles, so it fits this description. A kite generally does not have right angles unless specifically constructed to do so, which is not typical.
A rhombus can have right angles, making it a square, so it fits the criteria too. A trapezoid can also have a pair of consecutive right angles when it is a right trapezoid.
Therefore, the list of quadrilaterals that might have two consecutive right angles is not only the square and the rectangle but extends to include the rhombus and trapezoid as well.
Given these definitions, the correct answer to the question would be:
D. i, ii, iii, v, vi
Final answer:
The quadrilaterals that can have two consecutive angles measuring 90° each are squares, rectangles, and certain parallelograms (when they are squares or rectangles). Therefore, the correct answer to the question is B. This includes a square (i), a rectangle (ii), and some parallelograms (iii).
Explanation:
If a quadrilateral has two consecutive angles measuring 90° each, it could be any of the shapes that inherently contain right angles by definition. These shapes are a square, a rectangle, and certain types of parallelograms, specifically rectangles and squares. Both a square and a rectangle always have four right angles, which makes them valid answers. A rhombus or a general parallelogram may also have right angles, but only in specific cases, such as when a rhombus is also a square. Thus, kites and trapezoids do not necessarily fit this criterion as they do not always have consecutive right angles. Therefore, the correct answer is B, which includes a square, a rectangle, and some parallelograms.
A system of equations is shown below: x + 3y = 5 (equation 1) 7x − 8y = 6 (equation 2) A student wants to prove that if equation 2 is kept unchanged and equation 1 is replaced with the sum of equation 1 and a multiple of equation 2, the solution to the new system of equations is the same as the solution to the original system of equations. If equation 2 is multiplied by 1, which of the following steps should the student use for the proof?
Answer:
The correct answer is B. Show that the solution to the system of equations 8x − 5y = 11 and 7x − 8y = 6 is the same as the solution to the given system of equations"
Step-by-step explanation:
Solve: 3x-15/2=4x
................
The required solution of the expression is x = -3.
Given that,
To determine the solution of the equation 3x-15/2=4x.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
What are functions?Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
Simplification of 3x-15/2=4x.
3x - 15 = 8x
5x = -15
x = -3
Thus, the required solution of the expression is x = -3.
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The graph shows the distance, y, in miles, of a moving motorboat from an island for a certain amount of time, x, in hours:
A graph titled Distance Vs Time is shown with Time in hours labeled on x axis and Distance from Island in miles labeled on y axis. The scale on the x axis shows the numbers 1, 2, 3, 4, 5, 6, 7, and the scale on the y axis shows the numbers 0, 25, 50, 75, 100, 125, 150, 175, 200, 225. The graph shows a straight line joining the ordered pairs 0, 25, and 1, 75, and 2, 125, and 3, 175, and 4,225.
What is the speed of the motorboat?
225 miles per hour
25 miles per hour
75 miles per hour
50 miles per hour
the graph is showing for every 1 hour the boat is 50 miles further away
so the speed of the boat is 50 miles per hour
The speed of the boat is 50 miles per hour.
We have given that,
The graph shows the distance, y, in miles, of a moving motorboat from an island for a certain amount of time, x, in hours
A graph titled Distance Vs Time is shown with Time in hours labeled on the x-axis and Distance from Island in miles labeled on the y-axis. The scale on the x-axis shows the numbers 1, 2, 3, 4, 5, 6, 7, and the scale on the y-axis shows the numbers 0, 25, 50, 75, 100, 125, 150, 175, 200, 225. The graph shows a straight line joining the ordered pairs 0, 25, and 1, 75, and 2, 125, and 3, 175, and 4,225.
We have to determine the speed of the motorboat.
What is the speed?The speed of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time it is thus a scalar quantity.
The graph is showing for every 1 hour the boat is 50 miles further away
1hour=50 miles from the graph
So the speed of the boat is 50 miles per hour.
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Suppose that F(x) = x^2 and G(x) = 2/3x^2. Which statement best compares the graph of G(x) with the graph of F(x)?
A.) the graph of G(x) is the graph of F(x) compressed vertically.
B.) the graph of G(x) is the graph of F(x) stretched vertically and flipped over the x-axis.
C.) the graph of G(x) is the graph of F(x) stretched vertically.
D.) the graph of G(x) is the graph of F(x) compressed vertically and flipped over the x-axis
Answer:
The statement which best compares the function F(x) and G(x) is that the graph of G(x) is the graph of F(x) stretched vertically.
Step-by-step explanation:
Since the difference between the two functions is in the coefficent which multiplies the square function, 1 and 2/3 respectively in F(x) and G(x). So, as the coefficient are positive and is minor for G(x) than for F(x), the values for G(x) will be smaller and thus the graph of G(x) would be below the graph of F(x). Therefore the graph for G(x) is it compressed vertically respect to F(x). The explanation here is ore understandable by looking at the illustration attached.
A 50 foot ramp makes an angle of 4.9° with the horizontal. to meet new accessibility guidelines, a new ramp must be built so it makes an angle of 2.7° with the horizontal as shown below. what is the length of the new ramp?
Four letters to different insureds are prepared along with accompanying envelopes. the letters are put into the envelopes randomly. calculate the probability that at least one letter ends up in its accompanying envelope.
Final answer:
The probability that at least one of four randomly distributed letters ends up in its correct envelope is 62.5%. This calculation uses the complementary approach, subtracting the probability of no matches (9/24) from 1.
Explanation:
The question asks about the probability that at least one letter ends up in its accompanying envelope when four letters are randomly put into four envelopes.
To solve this, we employ the principle of complementary probability, which suggests that the probability of at least one match is 1 minus the probability of no letters matching their envelopes.
Calculating the probability of no matches directly can be complex due to numerous possible permutations, so using the complementary approach is more efficient.
We can calculate the total permutations of the four letters being distributed into four envelopes as 4!, which equals 24.
To find the probability of no letters matching their envelopes (a derangement of 4 items), we use a specific formula or recognition of known patterns, resulting in 9 derangements. Thus, the probability of no matches is 9/24.
The probability of at least one letter matching its corresponding envelope is then 1 - (9/24), which simplifies to 15/24 or 5/8. Therefore, the probability is 0.625 or 62.5%.
The city planning committee is discussing making a bike path extension in its city park. They have a $5050 budget for the proposed project. The cost to construct the path is $2.20 per foot. The path would be a straight line from the fountain to the large oak tree. In the right triangle formed, the height is 880 ft and the base is 2112 ft. How much will the path cost? Will this work with the city planning budget?
Final answer:
After using the Pythagorean theorem to calculate the length of the bike path as approximately 2287 feet, and multiplying by the cost of $2.20 per foot, the total comes to $5031.40. This total cost fits within the city planning budget of $5050.
Explanation:
The city planning committee needs to determine if their $5050 budget is sufficient for the bike path extension, with construction costs at $2.20 per foot. To calculate the cost of the bike path, we first must find the length of the path, which will be the hypotenuse in a right triangle formed by the height (880 ft) and the base (2112 ft). Applying the Pythagorean theorem (a² + b² = c²), where a is the height and b is the base, the length of the path (c) can be calculated as follows:
c = √(880² + 2112²) = √(774400 + 4456444) = √5230844 ≈ 2287 ft.
Now, we can determine the total cost by multiplying the length of the path by the cost per foot:
Total Cost = 2287 ft × $2.20/ft = $5031.40
Thus, the total cost for constructing the path would be $5031.40, which is within the city planning budget of $5050.
Which statements about the graph of the function f(x) = 2x2 – x – 6 are true? Check all that apply.
The domain of the function is .
The range of the function is all real numbers.
The vertex of the function is .
The function has two x-intercepts.
The function is increasing over the interval (, ∞).
we have
[tex] f(x) = 2x^{2}- x -6 [/tex]
using a graph tool
see the attached figure
we know that
1) the domain of the function is all real numbers-------> interval (-∞,∞)
2) The range of the function is the interval [-6.125,∞)
3) The vertex of the function is the point (0.25,-6.125)
4) The function has two x-intercepts-----> ( -1.5,0) and (2,0)
5) The function is increasing over the interval (0.25,∞) and decreasing over the interval (-∞,0.25)
Line m passes through the point (4,1) and has a slope of -1/3. what is the equation of line m in standard form
Help me with this please
Mr. Carr has to buy each of his 24 students a flash drive. Each flash drive costs $12. How much will he spend?
Answer:
Step-by-step explanation:
$228
Among the contestants in a competition are 3636 women and 2525 men. if 5 winners are randomly? selected, find the probability that they are all? men? round to five decimal places.
Which graph shows the solution set for -1.1x+ 6.4> -1.3