Step-by-step explanation:
The real-world situation that can be represented by 4m+2 is option D, where a music download website has a membership fee of $4 and charges $2 for each download.
Here, "4m" represents the total cost of downloading "m" songs at a cost of $2 per song, and "2" represents the fixed cost of the membership fee. So, the total cost of downloading "m" songs along with the membership fee can be represented by the expression 4m + 2.
Mariam left Riverside, California, driving her motorhome north on Interstate 15 towards Salt Lake City at a
speed of 40 miles per hour. Half an hour later, Porter teft Riverside in his car on the same route as Mariam,
driving 50 miles per hour. Solve the system:
(40-50m
A. for ar to find out how long it will take Porter to
catch up to Mariam.
B. What is the value of y, the number of hours
Mariam will have driven before Porter catches up
to her?
It will take Porter 2 hours to catch up to Mariam.
The answer to part B is y = 2.5 hours.
How to explain the equationdistance = rate x time
d = 40(t + 0.5) (since Mariam started driving half an hour earlier than Porter)
For Porter: distance = rate x time
d = 50t
Since they will meet at the same point, we can set these two equations equal to each other:
40(t + 0.5) = 50t
40t + 20 = 50t
20 = 10t
t = 2
Also, d = 40(t + 0.5)
d = 40(2 + 0.5)
d = 90
So Mariam will have driven 90 miles before Porter catches up to her, which means y = 2.5 (since she drives at a rate of 40 mph and it took 2.5 hours for her to drive 100 miles).
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Is there enough information given to prove
the quadrilateral is a parallelogram?
H
H
Yes, both sets of opposite sides are congruent
Yes, both sets of opposite sides are parallel
O No, opposite sides are different lengths
O No, not enough information given
D) No, there isn't enough information given for this question to determine if it's a parallelogram.
All sides of a parallelogram are equal, but it is not specified in this question if conterminous sides are equal. A parallelogram is a two-dimensional geometric shape with two sides that are comparable.
It's a four-sided polygon (also known as a quadrilateral) with comparable sides that are all the same length. The total of the girding angles of a parallelogram equals 180 degrees.
You must have learned about a variety of 2D shapes and sizes in figures, such as circles, places, blocks, rhombuses, and so on. Each of these categories has unique qualities. A parallelepiped is a three-dimensional shape having faces that are parallelograms.
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There are 10% more boys than girls in a choir. If there are 4 more boys than girls, how many children are there altogether?
Step-by-step explanation:
There are 10% more boys than girls in a choir.
b = 1.1g
If there are 4 more boys than girls,
b = g + 4
Replace b with 1.1g
1.1g = g + 4
1.1g - g = 4
.1g = 40
g = 4/.1
g = 40 girls, then + 4 = 44 boys
StartFraction 27 Over 9 EndFraction = StartFraction 18 Over x EndFraction a. x = 9 c. x = 6 b. x = 18 d. x = 3
The value of the fraction is x = 6 (option c).
In this problem, we are given an equation involving fractions:
27/9 = 18/x
To solve this equation, we can start by simplifying each fraction. Both 27 and 9 are divisible by 9, so we can simplify the left-hand fraction as follows:
3/1 = 18/x
Similarly, we can simplify the right-hand fraction by dividing both the numerator and denominator by 18:
3x = 18
x = 18/3 = 6
Therefore, the answer to this problem is option c. x = 6.
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Match the different types of auxiliary views with their descriptions.
used to represent symmetrical objects
only the details of the inclined surface are projected and
drawn in auxiliary view
a single view projected from the primary auxiliary view to
a plane that is inclined to all three principal planes
a single view projected from a secondary or another tertiary
auxiliary view
secondary auxiliary view
half auxiliary view
partial auxiliary view
tertiary auxiliary view
The correct matching is given below:
Used to represent symmetrical objects: Half auxiliary view
Only the details of the inclined surface are projected and drawn in the auxiliary view: Partial auxiliary view
A single view projected from the primary auxiliary view to a plane that is inclined to all three principal planes: Secondary auxiliary view
A single view projected from a secondary or another tertiary auxiliary view: Tertiary auxiliary view
What is the Half Auxiliary View?The half auxiliary view shows one-half of symmetrical objects while partial auxiliary views focus on inclined surface details.
Secondary auxiliary views offer extra angles by projecting from the primary view to an inclined plane. Tertiary auxiliary views expand on this by projecting from secondary/tertiary views to show details. Auxiliary views clarify technical drawings.
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Which of these descriptions best suits a pyramid?
A.
Pyramids have polygonal faces and a triangular base.
B.
Pyramids have triangular faces and a polygonal base.
C.
Pyramids have triangular faces and a circular base.
D.
Pyramids have polygonal faces and a polygonal base.
E.
Pyramids have curved faces and a polygonal base.
Answer:
The correct option is B. Pyramids have triangular faces and a polygonal base.
Answer:B. Pyramids have triangular faces and a polygonal base.
Step-by-step explanation:
A pyramid is a three-dimensional shape that has a polygonal base and triangular faces that meet at a single point called the apex. Here's how to identify which of the given descriptions best suits a pyramid:
A. Pyramids have polygonal faces and a triangular base.
This description is incorrect because pyramids have a polygonal base, not a triangular base.
B. Pyramids have triangular faces and a polygonal base.
This description is correct because it correctly identifies that pyramids have triangular faces and a polygonal (meaning multi-sided) base.
C. Pyramids have triangular faces and a circular base.
This description is incorrect because pyramids have a polygonal base, not a circular base.
D. Pyramids have polygonal faces and a polygonal base.
This description is partly correct because pyramids do have a polygonal base, but their faces are always triangular.
E. Pyramids have curved faces and a polygonal base.
This description is incorrect because pyramids have flat, triangular faces, not curved faces.
So, in summary, option B, "Pyramids have triangular faces and a polygonal base," is the description that best suits a pyramid.
The product of two numbers is 155952. If one number is 342, find the other
number.
The other number is 456.
Given that the product of two numbers is 155952, one number is 342, we need to find the other number.
So, let the other number be x,
Therefore, x × 342 = 155952
x = 155952 / 342
x = 456
Hence the other number is 456.
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Simplify 13x^-5y^0/5^-3z^-10 Write your answer using only positive exponents.
The simplified expression with only positive exponents is 2197x⁻⁵/z¹⁰.
Now, let's look at the expression you provided: 13x⁻⁵y⁰/5⁻³z⁻¹⁰. We want to simplify this expression by using only positive exponents.
To do this, we can use the following rules:
A negative exponent means we take the reciprocal of the base raised to the positive exponent.
A zero exponent means the base is equal to 1. For example, y⁰ is the same as 1.
When dividing two terms with the same base, we can subtract the exponents.
Now, let's apply these rules to simplify the expression:
13x⁻⁵y⁰/5⁻³z⁻¹⁰
= 13x⁻⁵/5⁻³z⁻¹⁰
= 13(5³/z¹⁰)x⁻⁵
= 2197x⁻⁵/z¹⁰
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decrease £110 by 10%m
Grade
100
95
90
85
80
75
70
65
60
55
5
Which of the following does this situation represent?
10 15 20 25 30 35
Number of Minutes
40 45 50
The statement which this situation represent include the following: D. a relation only.
What is a function?In Mathematics and Geometry, a function is a mathematical equation which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.
This ultimately implies that, all functions are used in mathematics to uniquely map an input variable (domain or independent values) to an output variable (range or dependent values).
Based on the graph shown above, we can reasonably infer and logically deduce that it represents a relation, but it does not represent a function because the input values (domain or independent values) are not uniquely mapped to the output values (range or dependent values).
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Complete Question:
Mrs. Anderton is giving a test in her third-period class. She has decided to record the amount of time that each student takes to finish the test (in minutes) and compare that to the grade each student receives on the test (out of 100). A plot of her results is below.
Which of the following does this situation represent?
A. both a relation and a function
B. a function only
C. neither a relation nor a function
D. a relation only
What is 5+6/7 pls give me an answer now pls
When writing a proof, how do you construct the first statement?
A) By writing the justification for the first statement in the right column.
B) By copying the “prove” statement(s) from the original problem.
C) By writing the next logical statement from the current one.
D) By copying the “given” statement(s) from the original problem.
When writing a proof, you should construct the first statement by copying the “prove” statement(s) from the original problem. The Option B is correct.
How should you construct the first statement in a proof?When constructing the first statement in a proof, it is important to begin with copying the “prove” statement(s) from the original problem. This involves writing the next statement based on the given or previously proven statements.
It is not helpful to write a justification for the first statement in the right column without considering its logical connection to the problem. By beginning with a logically connected statement, the proof can proceed in a clear and organized manner which leads to a valid conclusion.
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How to rewrite without parentheses
-5^3( -9y^3 + 4y^2+3y)
Expanding the product, we can rewrite the expression as follows:
-5³*(-9y³ + 4y² + 3y) = 1,125y³ - 500y² - 375y
How to rewrite the given expression?Here we have the following expression:
-5³*(-9y³ + 4y² + 3y)
To remove the parentheses, we need to expand the product, we know that:
-5³ = -125
Then we can rewrite the expression as:
-125(-9y³ + 4y² + 3y)
Now expand the product, we will get:
-125(-9y³ + 4y² + 3y) = 1,125y³ - 500y² - 375y
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need help will give brainlist
Answer:b
Step-by-step explanation:
can someone please explain this to me briefly, please.
Answer:
468ft²
Step-by-step explanation:
Triangles: 9x12=108 (sides)
TIP: Since there are two of these triangles, you don't need to divide by 2
Rectangles: 12x10=120 (bottom)
9x10=90 (Back)
15x10=150 (top)
108+120+90+150=468ft²
Describe in your own words how to find the break-even point for a profit equation, and explain why that method works. Specifically, what is the condition mentioned in the reading that allows you to find the break-even point from a profit equation?
When a product's profits from sales equal its manufacturing costs, this is called the break-even point.
Since the break-even point is the point at which total costs and total revenues are equal, or "even," in economics, business, and specifically cost accounting.
Therefore, if opportunity costs were paid and capital received the expected return after adjusting for risk, there is no net loss or gain, and one has "broken even."
The break-even point is the point at which total cost and total revenue are equal in the realm of banking and economics.
The amount of units required to cover all costs is determined using the BEP analysis. Fixed and variable costs make up the overall cost in this case.
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A student must answer 3 out of 5 essay questions on a test. In how many different ways can the student select the questions?
The student can select the questions in 10 different ways.
We have,
The student can select any 3 out of the 5 essay questions.
The number of ways to do this can be calculated using the binomial coefficient formula:
C(5, 3) = 5! / (3! x 2!)
= (5 x 4 x 3) / (3 x 2 x 1)
= 10
Therefore, the student can select the questions in 10 different ways.
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the function F is given by f (x) = x^2 - 2x which statement is true about the graph of f
The function does not have any x-intercepts since it is always positive. The graph of f(x) is a U-shaped curve opening upwards, with vertex at (1, 1) and no x-intercepts. Option (b) is the correct answer.
The given function f(x) = x^2 - 2x represents a parabola. The coefficient of x^2 is positive, indicating that the parabola opens upwards. The vertex of the parabola is at (1, 1), obtained by completing the square.
The x-coordinate of the vertex can be found by using the formula -b/2a, where a and b are the coefficients of x^2 and x respectively. The axis of symmetry is a vertical line passing through the vertex, which is x = 1 in this case.
The y-intercept can be found by setting x = 0, which gives f(0) = 0. Option (b) is the correct answer.
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22. How many positive integers less than 1000 a) are divisible by 7? b) are divisible by 7 but not by 11? c) are divisible by both 7 and 11? d) are divisible by either 7 or 11? e) are divisible by exactly one of 7 and 11? f ) are divisible by neither 7 nor 11? g) have distinct digits? h) have distinct digits and are even?
The set of positive integers less than 1000 that are:
a)Divisible by 7 are 142
b)Divisible by 7 but not by 11 are 130
c)Divisible by both 7 and 11 are 12
d)Divisible by either 7 or 11 are 220
e)Divisible by exactly one of 7 and 11 are 220
f)Divisible by neither 7 nor 11 are 780
g)Having distinct digits are 576
h)Having distinct digits and even are 337
We have,
A whole number that is greater than zero is known as positive integer
a)The positive numbers below 1000 that are divisible by 7 are 7, 14, 21, 28,..., 994.
Total terms: 994, divided by 7, plus (n-1)
There are 142 total terms below 1000 that are divisible by 7.
b) The numbers 77, 154, 231, 308, 385, 462, 539, 616, 693, 770, 847, and 924 are all divisible by both 7 and 11.
The total number of integers below 1000 that are divisible by 7 but not 11 therefore equals 142 - (total number of integers divisible by 7 and 11), which means that the total number of integers that fall into this category is 130.
c) The total amount of integers that can be divided by both 7 and 11 equals the total amount of integers that can be divided by 77.
There are 12 total integers below 1000 that can be divided by 77.
d) The total number of integers that can be divided by either 7 or 11 is equal to the sum of the numbers that can be divided by each of those numbers and the number that can be divided by 77.
The total number of integers below 1000 that are divisible by 11 is (11,22,33,...,990). 990 = 11 + (n-1) 11, which equals 90 integers.
Total integers that may be divided by both 7 and 11 are equal to 142 + 90 - 12 = 220.
e) The total number of integers that may be divided by either 7 or 11 perfectly is equal to 142 + 90 - 12 = 220 numbers.
f) The total number of integers that cannot be divided by either 7 or 11 is 1000 - (The total number of integers that can be divided by either 7 or 11), which is 1000 - 220 = 780 numbers.
g)Distinct digits from 1 to 100 = 100 - Total number of integers below 1000 with distinct digits = 1000 - (non-distinct digits) ( 11,22,33,44,55,66,77,88,99,100),
=> Unique digits from 1 to 100 equal 90.
=> The distinct numerals 101 to 200 equal 100. (101,110,111,112,113,114,115,116,117,118,119,121,122,131,133,141,144,151,155,161,166,171,177,181,188,191,199,200),
=> Unique digits from 101 to 200 are: 100 to 28, 72.
=> Unique numbers between 201 and 1000 = 72 x 8 = 576.
h)Different digits and even values equal to 337
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Can you please help me solve?
The zeros of the polynomial function are x = -1 and x = 5
Finding the zeros of the polynomial functionFrom the question, we have the following parameters that can be used in our computation:
y = x⁴ - 4x³ - 4x² - 4x - 5
To calculate the zeros of the polynomial function, we create a graph of the polynomial
The point where the graph intersect with the x-axis are the zeros of the polynomial function
using the above as a guide, we have the following:
Zeros: x = -1 and x = 5
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The diameter of a cylindrical water tank is 8ft, and its height is 6ft. What is the volume of the tank?
Use the value 3.14 for π, and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
If the diameter of a cylindrical water tank is 8ft, and its height is 6ft, the volume of the water tank is approximately 302 cubic feet.
To find the volume of the cylindrical water tank, we need to use the formula V = πr²h, where r is the radius of the base and h is the height of the cylinder. Since we are given the diameter of the tank, which is 8ft, we can find the radius by dividing it by 2. Thus, the radius of the tank is 4ft. The height is given as 6ft.
Substituting these values into the formula, we get:
V = π(4ft)²(6ft)
V = π(16ft²)(6ft)
V = 96π ft³
Now we can approximate this volume by using the value of π as 3.14 and rounding the answer to the nearest whole number.
V ≈ 96(3.14) = 302.4
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Math Games...
A cat adoption facility takes in an average of 5 cats per day. The facility has to keep their cat occupancy below 200. Currently, the
facility has 165 cats.
If none of their cats get adopted, how many more days, x, can the facility continue to take in cats? Select the inequality that incluc
the largest number of days this facility can continue to take in cats without exceeding its occupancy limit.
OA. x < 30
OB. x<35
OC. x<7
OD.x<40
6x+146<200 will represent the largest number of days this facility can continue to take in cats without exceeding its occupancy.
Here, we have,
Given,
Cat occupancy = below 200
Facility has cats already = 146
Cats per day = 6
Let,
x be the number of days.
Cats per day*number of days + Cats already in facility < Cat occupancy
6*x+146<200
6x+146<200 will represent the largest number of days this facility can continue to take in cats without exceeding its occupancy.
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complete question:
a cat adoption facility takes in an average of 6 cats per day. The facility has to keep their cat occupancy below 200. Currently, the facility has 146 cats. If none of their cats get adopted, how many more days, x, can the facility continue to take cats? select the inequality that includes the largest number of days this facility can continue to take in cats without exceeding its occupancy limit
Determine the first 4 term of the sequence
tn=4(n - 1 )
Answer:
n1=0 n2=4 n3=8 n4=12
Step-by-step explanation:
tn=4(n-1) is the formula to determine the value of the nth term, so all you have to do is plug in what term you want for the variable and solve.
for example
n1=4(1-1)=0
n2=4(2-1)=4
n3=4(3-1)=8
n4=4(4-1)=12
Hope you understand and have a great day.
The pentagonal prism below has a base area of 36 units and a volume of 237.6 units . Find its height.
The height of the pentagonal prism is approximately 2.94 units
The formula for the volume of a pentagonal prism is;
V = (1/2) × base_area × height × (1 + √(5))
where base_area is the area of the base of the prism, height is the height of the prism, and sqrt(5) is the square root of 5.
In this problem, we are given that the base area is 36 units and the volume is 237.6 units. We can use this information to set up an equation and solve for the height;
237.6 = (1/2) × 36 × height × (1 + √(5))
Dividing both sides by (1/2) × 36 × (1 + √(5)), we get;
height = 237.6 / [18 × (1 + √(5))]
Simplifying this expression, we get;
height = 4.8 / (1 + √(5))
Rationalizing the denominator by multiplying both the numerator and denominator by (√(5) - 1), we get;
height = [4.8 × (√(5) - 1)] / [4]
Simplifying further, we get;
height = 1.2 × √(5) - 1)
height = 2.94 units
Therefore, the height is 2.94 units
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Divide √9x² by √18y²
When the expression √9x² is divided by √18y², we get result which is equal to x/2y.
To simplify the expression √9x²/√18y², we need to first simplify the square roots in the numerator and denominator.
√9x² = √(3²)(x²) = 3x
√18y² = √(2²)(3²)(y²) = 2(3y)
So, √9x²/√18y² can be written as:
(3x)/(2(3y))
We can simplify this expression by canceling out the common factor of 3 in the numerator and denominator:
(3x)/(2(3y)) = (x)/(2y)
Therefore, the simplified expression of √9x²/√18y² is x/2y.
In conclusion, the expression √9x²/√18y² can be simplified to x/2y by factoring out the common factors from the numerator and denominator, and then canceling out the common factor of 3.
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The triangle above has the following measures.
s = 29 m
r= 63 m
Find the m/Q.
Round to the nearest tenth and include correct units.
Show all your work.
The value of m∠Q as shown in the right-angled triangle below is 62.59°.
The Formula used is:
m∠Q = cos⁻¹(s/r)........................ (1)
Where:
s = 29 m
r = 63 m
Now, Substitute these values into equation 1
m∠Q = cos⁻¹(29/63)
m∠Q = cos⁻¹(0.46)
m∠Q = 62.59°
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Scientific notation 5.5x10^7 divided by 3.25x10^-3
Refer to image if necessary
The quotient written in scientific notation is:
[tex]1.69*10^{10}[/tex]
How to take the quotient in scientific notation?To do so, we can separate the quotients between the powers of 10 and the rational numbers, then we can rewrite the quotient as follows:
[tex]\frac{5.5*10^7}{3.25*10^{-3}} = \frac{5.5}{3.25}*\frac{10^7}{10^{-3}}[/tex]
Now solve these two:
[tex]\frac{5.5}{3.25}*\frac{10^7}{10^{-3}} = 1.69*10^{7 - (-3)} = 1.69*10^{10}[/tex]
That is the quotient between two numbers in scientific notation, expressed in scientific notation.
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Find missing probability
The value of missing probability is,
⇒ P (A or B) = 131/200
We have to given that;
P (A) = 9/20
P (B) = 1/4
P (A and B) = 9/200
Now, We know that;
P (A or B) = P (A) + P (B) - P (A and B)
P (A or B) = 9/20 + 1/4 - 9/200
P (A or B) = 9/20 + 5/20 - 9/200
P (A or B) = 14/20 - 9/200
P (A or B) = 140/200 - 9/200
P (A or B) = 131/200
Thus, The value of missing probability is,
⇒ P (A or B) = 131/200
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find the vertex of y=4x^2+4x-15
Answer:
[tex]\left(-\dfrac{1}{2},\:-16\right)[/tex]
Step-by-step explanation:
The general equation of a parabola in polynomial form is
y = ax² + bx + c
where a, b, c are constants
If a is > 0, the parabola opens upward and the vertex is a minimum
If a < 0, the the parabola opens downward and the vertex is a maximum
The vertex x value is given by the points
[tex]x_v = -b/2a\\[/tex]
The given parabola equation is
y = 4x² + 4x - 15
Since we have a = 4, b = 4
[tex]x_v = -b/2a = -{\dfrac{4}{2\cdot 4} = - \dfrac{4}{8} = - \dfrac{1}{2}[/tex]
To find the y value of the vertex, [tex]y_v[/tex] , plug this value into the parabola equation and solve for y
[tex]y_v=4\left(-\dfrac{1}{2}\right)^2+4\left(-\dfrac{1}{2}\right)-15\\\\= 4 \cdot \dfrac{1}{4} -2 - 15\\\\= 1 - 2 - 15\\\\= -16[/tex]
So the vertex is at [tex]\left(-\dfrac{1}{2},\:-16\right)[/tex] and is a minimum
Which statement shows how the product of (x + 7)2 demonstrates the closure property of multiplication?
x2 + 14x + 49 is a polynomial
x2 + 14x + 49 may or may not be a polynomial
x2 + 49 is a polynomial
x2 + 49 may or may not be a polynomial
Answer:
A
Step-by-step explanation:
x2 + 14x + 49 is a polynomial, and since it is the product of (x + 7)2, it demonstrates the closure property of multiplication because multiplying two polynomials results in another polynomial. Therefore, the statement that shows how the product of (x + 7)2 demonstrates the closure property of multiplication is: "x2 + 14x + 49 is a polynomial."
