If the equation that models the problem is 3.95m + 8.95b = 47.65, where m is the number of magazines and b is the number of books. The number of books is 4.
How to find the number of books?Given data:
Equation: 3.95m + 8.95b = 47.65
Where:
Magazine, m = 3
Now let find the number of book by using the equation to solve for b
3.95(3) + 8.95b = 47.65
11.85 + 8.95b = 47.65
Collect like terms
8.95b = 35.8
Divide both side by 8.95b
b = 35.8/8.95
b = 4 books
Therefore we can conclude that the number of books is 4.
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The complete question is;
Hugh bought some magazines that cost $3.95 each and some books that cost $8.95 each. He spent a total of $47.65. If Hugh bought 3 magazines, how many books did he buy? The equation that models the problem is 3.95m + 8.95b = 47.65, where m is the number of magazines and b is the number of books.
Please help!! i included a picture as well not sure if it would help !Write the equation of a quadratic function given the transformations given below:
• Opens upwards
●
A = ½
● Horizontal shift right 5
• Vertical shift down 2
The parent function of the quadratic family is f(x) = x2. A transformation of the graph of the parent function is represented by the function g(x) = a(x − h)2 + k, where a ≠ 0.
What is quadratic function?A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero.
A parabola is the shape of a quadratic function's graph. Although the "width" or "steepness" of a parabola can vary as well as its direction of opening, they all share the same fundamental "U" form. The three graphs in the image below are all parabolas.
Regarding a line known as the axis of symmetry, all parabolas are symmetric. The vertex of a parabola is the location where the axis of symmetry of the curve crosses.You are aware that a line is defined by two points. This implies that there is only one line that contains both points if you are given any two points in the plane. Points and quadratic functions both fit this description.There is only one quadratic function f whose graph contains all three points when there are three points in the plane with distinct first coordinates and that are not on a line. This fact is demonstrated by the applet below. Three spots are shown on the graph, and a parabola passes through them all.The text box behind the graph displays the associated function. The function and parabola are updated if any of the points are moved.Using the methods of stretching/shrinking and moving (translation) the parabola y = x2 several quadratic functions can be graphed easily by hand.How do you determine if quadratic equation opens up or down?A quadratic function's graph takes the form of a parabola. The parabola will open upward if the value of the "a" term is positive, and downward if the value is negative
How to shift a function upwards?.A function can be raised by adding outside of it: f (x) + b raises f (x) by b units. The same principles apply for moving a function down, except instead of subtracting a positive integer, f (x) b represents f (x) moved down b units.
Shift Up and Down by Changing the Value of kYou can represent a vertical (up, down) shift of the graph of f(x)=x2 by adding or subtracting a constant, k.
f(x)=x2+k
Right- and down-shift of a functionBy increasing or decreasing the output or the input, you can change the direction of the function's graph to the right, left, up, or down. A function's output can be increased to move the graph up. The graph is shifted downward when a function's output is subtracted from.
Horizontal and vertical shift of a functionThe output has a constant added to it, which causes the vertical shift. For a positive constant, move the graph upward; for a negative constant, move it below. A constant supplied to the input causes a horizontal shift. For a positive constant, move the graph to the left; for a negative one, move it to the right.
Shift left and right by changing the value of hYou can represent a horizontal (left, right) shift of the graph of f(x)=x2 by adding or subtracting a constant, h, to the variable x, before squaring.
f(x)=(x−h)2
If h>0, the graph shifts toward the right and if h<0 , the graph shifts to the left.
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What does the fundamental theorem of algebra state about the equation 2x2+8x+14=0 ?
Answer: The fundamental theorem of algebra states that the equation 2x^2+8x+14=0 has at least one complex root, which means that there are numbers that can be plugged into x that make the equation equal to zero. ✅
PLEASEEEE GIVE BRANLIEST
Step-by-step explanation:
The fundamental theorem of algebra states that for any non-constant polynomial equation with real or complex coefficients, there is at least one complex root (or solution).
In the case of the equation 2x^2+8x+14=0, the theorem guarantees that this equation has at least one complex root, which means that there are numbers that can be plugged into x that will make the equation equal to zero.
So, the fundamental theorem of algebra guarantees that for the equation 2x^2+8x+14=0, there exists at least one complex solution that makes the equation true. In this case, the solutions are x = -1+i and x = -1-i ✅
Is (5, 0) a solution to the equation y = 3x2 + 5?
By replacing the values of the point in the quadratic equation, we can see that it is not a solution.
Is (5, 0) a solution for the given equation?Here we have the quadratic equation:
y = 3x^2 + 5
And we want to see if the point 3x^2 + 5 is a solution of the quadratic equation.
To check that, we need to replace the values of the point in the equation and see if the equation is true.
We need to replace:
x = 5
y = 0
We will get:
0 = 3*5^2 + 5
0 = 3*25 + 5
0 = 75 + 5
0 = 80
This is a false equation, then (5,0) is not a solution.
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What is a infinitely many solution?
An infinite solution has both sides equal.
What number has an unlimited number of answers?
There are infinitely many possible solutions to some equations. In these equations, the equation is true regardless of the value given to the variable.
If you attempt to solve an equation and it yields a variable or value that is equal to itself, then the equation has an endless number of solutions. 2x and 2x should be combined.
Are all possible solutions parallel?
There are no answers when the lines are parallel, and occasionally the two equations will graph as the same line, in which case there are an endless number of solutions. These kinds of systems are occasionally described using specific words.
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Evaluate the following sin6A-cos6A
On solving the provided question we can say that the value of trigonometry value is - [tex](sin^2x - cos^2x )( 1- sin^2xcos^x)\\[/tex]
what is trigonometry?The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study. The area of mathematics known as exact methods deals with specific trigonometric functions and how they might be used in calculations. There are six popular trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics of triangles, particularly right triangles, is called trigonometry. The study of geometry, however, is the characteristics of all geometric figures.
[tex]sin^6 x - cos^6x\\(sin^3x)^2 - (cos^3x)^2\\(sin x - cosx)(sinx + cosx)(1 + sinx cosx)(1 - sinx cosx)\\(sin^2x - cos^2x )( 1- sin^2xcos^x)\\[/tex]
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3/4 times (15/4-3 1/2) divided bye 1 1/3
Answer:
the awsner is 20 I believe so don't trust me or trust me i don't care
Step-by-step explanation:
I don't know
Answer:
9/64
Step-by-step explanation:
1 3/4 x (15/4-3 1/2) divided by 1 1/3
2 3/4x1/4 divided by 4/3
3 3/16 divided by 4/3
4 3/16x3/4=9/64
A district restaurant manager bought 4 cases of disposable cups for $150 each. Each case contained 3,600 cups. He wants to split the cups equally between 6 restaurants. Which calculation yields the number of cups for each restaurant?.
The district restaurant manager divided 3,600 cups among six restaurants, giving each restaurant 600 number of cups.
The district restaurant manager divided 3,600 cups among six restaurants, giving each restaurant 600 cups. The district restaurant manager purchased four cases of disposable cups, each costing $150 and containing 3,600 cups. He needed to split the cups among six restaurants. To determine how many cups each restaurant would receive, he divided 3,600 by 6. This gave him an answer of 600 cups for each restaurant.
3,600 ÷ 6 = 600 cups
The district restaurant manager divided 3,600 cups among six restaurants, giving each restaurant 600 number of cups.
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2y - 2 = 4x
y = -x + 4
i need the solution please help only have a day to answer it
Answer: x=1,y=3
Step-by-step explanation:
Given,
y - 1 =2x
y = 2x + 1-----(i)
Again,
We have,
y = 2x + 1
Now replacing the value of y from (i)
2x + 1= -x +
or, 2x + x= 3
or,3x= 3
So x=1
Now,
y=2x +1
or, y=2×1+1
so y=
Answer:
x=1, y=3. (1, 3).
Step-by-step explanation:
2y-2=4x
y=-x+4
----------
2y-2=4x implies 2(y-1)=2(2x), so y-1=2x.
(-x+4)-1=2x
-x+4-1=2x
-x+3=2x
3=2x-(-x)
3=2x+x
3=3x
x=3/3
x=1
y=-1+4=3
Solve the equation -8x < 32
Answer: x < -4
Step-by-step explanation: This is a question of an inequality. Here, everything proceeds like a normal equation that we solve. To obtain the value of x, we will divide 32 by 8.
-8x<32
x<-32/8
x<-4 (On dividing -32 by 8)
This means x can take any value less than -4 i.e. -5,-6,-7,......
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I'm actually really stuck will anyone help
Answer:
Step-by-step explanation:
104 units
2 3/4 is between the whole number_____and_____
Answer: 2 and 3
Step-by-step explanation:
Which trigonometric ratio is used to find the cosine of a right triangle?
Answer: Cosine ratios are exactly the same idea of sine ratios or tangent ratios. The only difference between it and the other two trigonometric ratios is that it is the ratio of the adjacent side to the hypotenuse of a right triangle.
helpppp asap !!!!!!!!!!!
The numeric value for the logarithmic expressions is given as follows:
1. [tex]\log_{6}{\left(\frac{5}{8}\right)} = -0.263[/tex]
2. [tex]\log_6{40} = 2.059[/tex]
3. [tex]\log_6{64} = 2[/tex]
4. [tex]\log_6{125} = 2.694[/tex]
a. [tex]\log_{5}{\left(\frac{11}{30}\right)} = -0.623[/tex]
b. [tex]\log_5{330} = 3.603[/tex]
c. [tex]\log_5{121} = 2.98[/tex]
How to obtain the numeric value for the logarithmic expressions?For the first expression, we have that the logarithm of the quotient is the subtraction of the logarithms, hence:
[tex]\log_{6}{\left(\frac{5}{8}\right)} = \log_6{5} - \log_6{8} = 0.898 - 1.161 = -0.263[/tex]
The same rule is applied for item a, hence:
[tex]\log_{5}{\left(\frac{11}{30}\right)} = \log_5{11} - \log_5{30} = 1.49 - 2.113 = -0.623[/tex]
For the second expression, we apply the logarithm of the product, which is the sum of the logarithms, hence:
[tex]\log_6{40} = \log_6{5 \times 8} = \log_6{5} + \log_6{8} = 0.898 + 1.161 = 2.059[/tex]
For item b, we have that:
[tex]\log_5{330} = \log_5{11 \times 30} = \log_5{11} + \log_5{30} = 1.49 + 2.113 = 3.603[/tex]
For the third expression, we have that the exponent is equals to the base, hence we just take the lower term, as follows:
[tex]\log_6{64} = \log_6{2^6} = 2[/tex]
For the fourth term, we have the rule for the logarithm of an exponent, hence:
[tex]\log_6{125} = \log_6{5^3} = 3\log_6{5} = 3 \times 0.898 = 2.694[/tex]
The same rule is applied for item c, as follows:
[tex]\log_5{121} = \log_5{11^2} = 2\log_5{11} = 2 \times 1.49 = 2.98[/tex]
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Which type of dilation are the given scale factors?
Select Expansion or Contraction to correctly describe the type of dilation for each given scale factor.
Scale Factor Expansion
336
554
0.5
-1.2
O
Contraction
O
O
O
O
ہے
Enlarging or contracting a figure's size is known as dilatation. In other words, a scale factor is used to either enlarge or diminish the image while maintaining similarity between the preimage and the image.
What Is A Dilation ?In line with the illustrations below. A dilation that produces a smaller image is called a reduction (conjure up shrinking), whereas a dilation that produces a larger image is called an enlargement (conjure up stretching).Image reduction occurs when the scale factor is between 0 and 1.An expansion of the image occurs when the scale factor exceeds 1.The center point of the dilation is located, and the distances between this center point and various points on the preimage and the image are measured in order to determine the scale factor for the dilation. According to Math Bits Notebook, we can determine the scale factor by dividing these distances by two.Given that each angle is congruent, each segment is proportional, the slope of each segment is preserved, and the perimeter of the preimage and image have the same scale factor, using dilation scale factors allows us to enlarge or reduce a figure to the desired size.To Learn more About dilatation Refer To:
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Fred borrowed $38,000 for 5 years at an APR of 4%
a) find the monthly payment.
b) What is the total payment?
c) Find the Finance Charge
a) The monthly payment for a loan of $38,000 borrowed by Fred for 5 years at 4% APR is $699.83.
b) The total payment to be made is $41,989.80.
c) The finance charge is $3,989.80.
What is the finance charge?The finance charge is the difference between the sum of the monthly payments and the loan amount.
The monthly payments, total payment, and finance charge can be computed using an online finance calculator as follows:
N (# of periods) = 60 months (5 years x 12)
I/Y (Interest per year) = 4%
PV (Present Value) = $38,000
FV (Future Value) = $0
Results:
PMT (Monthly Payments) = $699.83
Sum of all periodic payments (Total Payment) = $41,989.80
Total Interest (Finance Charge) = $3,989.80
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There were 75 runners to start a race. In the first half of the race, 1/3 of them dropped out. In the second half of the race, 2/5 of the remaining runners dropped out. How many runners finished the race?
The triangles below are similar. Identify the
appropriate similarity theorem that justifies the
similarity. Justify your reasoning.
AAA(Angle angle angle) Theorem can be used to prove given triangles as similar.
As we know we have to show all three angles equally.
so we have to show the similarities between T(DNM) and T(DFE) ....
(T Means Triangle.)
(A Means Angle)
As D is a common vertex in both the triangles
SO A(NDM) = A(FDE)................Angle D .......... 1A(DNM) = A(DFE) ------- by Alternative property exterior angles are equal...........2A(NMD)= A(FED) --------- BY Alternative property interior angles are equal .........3by equations 1, 2, and 3 we can conclude that all three angles of T(DFE) = T(DNM)
SO By the AAA rule, we can say that the two Triangles are similar.
Now we can say all the sides of T(DFE) will be in all propositions of T(DNM).
Like DN/DF=DM/DE=NM/FE
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when asked to find the prime factorization of 16 a student writes two times eight explain the student's error
The student's error is that 16 has to be prime factorized as (2)⁴ or 2 × 2 × 2 × 2.
What is Prime factorization?Prime factorization is defined as the method of writing a number as the product of two or more prime numbers.
Prime numbers are numbers which has only two factors, 1 and the number itself.
Given number is 16.
We have to factorize 16 as a product of prime factors.
Student wrote it as,
16 = 2 × 8
The error here is that 8 is not a prime number. We have to again factorize 8 to get the required factored form.
8 = 2 × 4
4 = 2 × 2
So combining all these,
16 = 2 × 2 × 2 × 2
So 16 can be prime factorized as 16 = 2 × 2 × 2 × 2.
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An object is dropped from 40 feet below the tip of the pinnacle atop a 716-ft tall building. The height h of the object after t seconds is given by the equation h=−16t2+676. Find how many seconds pass before the object reaches the ground.
Answer:
Below
Step-by-step explanation:
When it reaches the ground h = 0
h = 0 = -16t^2+676
16t^2 = 676
t^2 = 42.25 t = 6.5 s
The dimensions of a rectangle are 7 in by (x+2)in. Which expression represents its area?
The correct option for the area of rectangle is A: 7(x + 2) sq in.
Define the term rectangle and its area?The characteristics of a rectangle were just as follows:
It has a tight, flat form.There are 4 corners, 4 angles, as well as 4 sides (vertices).There are two dimensions to it: length and width.A rectangle has 90° angles on each side.The opposing sides are parallel and equal.It features two equal-length diagonals.An area is the amount of space a rectangle takes up.By calculating the product of a rectangle's length and breadth, one can get the area of the shape.
So,
Area of a rectangle = Length × Width
Dimension are-
length : 7 inBreadth : (x + 2)inSo,
Area of a rectangle = 7 × (x + 2) sq in..
Thus, the expression represents area of a rectangle is 7 × (x + 2) sq in.
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The complete question is-
The dimensions of a rectangle are 7 in by (x+2)in. Which expression represents its area?
A: 7(x + 2) sq in..
B: 7 + (x + 2) sq in..
Camryn is moving 240 miles and will have to pay a travel fee. If she hires movers for 35 hours to pack all of her boxes it will cost $1221, including the travel fee. If she hires movers for only 10 hours to pack boxes, it will cost $546, including the travel fee. What is the hourly rate for the movers? What is the cost per mile? I I I I 19 i
The total cost of the move when hiring movers for 35 hours is $1221, and the total cost of the move when hiring movers for 10 hours is $546.
What is the hourly rate for the movers?Hourly rate for the movers = $54 ($1221 / 35 hours)Cost per mile = $5.11 ($1221 / 240 miles)The hourly rate for the movers is $35 per hour.If Camryn hires the movers for 35 hours to pack all of her boxes, it will cost $1221 including the travel fee.If she hires the movers for only 10 hours to pack boxes, it will cost $546 including the travel fee.This means that the cost per mile to move Camryn's belongings is $5.19. This cost includes the travel fee of the movers, so Camryn is paying $5.19 for every mile that the movers have to travel.This cost does not include the cost of any other services or supplies that the movers may need to complete the move, such as packing materials or fuel.Camryn should take these additional costs into account when deciding how many hours to hire the movers for.The hourly rate for the movers is $35 per hour. This fee includes the cost of the travel fee. The cost per mile is $5.10. This cost takes into account the travel fee, which is included in the total cost.This means that hiring movers for 35 hours will cost $675 more than hiring movers for 10 hours. The difference in cost is due to the travel fee and the number of hours spent packing and loading boxes.The hourly rate for the movers is constant and does not change based on the number of hours hired. This rate is $35 per hour and includes the cost of the travel fee. The cost per mile is determined by dividing the total cost for the move, including the travel fee, by the number of miles being moved. In this case, the cost per mile is $5.10. Overall, the cost of the move depends on the number of hours spent packing and loading boxes, as well as the travel fee. The hourly rate for the movers is the same regardless of the number of hours hired, but the cost per mile is determined by the total cost of the move, including the travel fee.To learn more about cost analysis of hiring movers to help with a move refer to:
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A store buys a jacket for $20.00 and then sells it to customers for 80% more than that. what is the selling price of the ja
Answer: 36
Step-by-step explanation:
80% or 200 is 16
16+20=36
I need help with 27 and 28 does anyone know??
Answer:
[tex]27)x {}^{3} + 3x {}^{2} - 10x - 24 \\ 28)x {}^{3} - 9 {}^{2} + 8x + 60[/tex]
Step-by-step explanation:
Greetings!!
[tex]27)(x - 3)(x + 2)(x + 4)[/tex]
Expand; (x-3)(x+2): x^2-x-6
Apply FOIL method: (a+b) (c+d) = ac+ad+bc+bd
[tex](x - 3)(x + 2) = x.x + x.2 - 3.x - 3.2[/tex]
simplify
[tex]x {}^{2} - x - 6[/tex]
[tex]x {}^{2} - x - 6.(x + 4)[/tex]
distribute parentheses
[tex] = x {}^{2} .x + x {}^{2} .4 - x.x - x.4 - 6.x - 6.4 \\ = x {}^{3} + 4x {}^{2} - x {}^{2} - 6x - 24[/tex]
simplify/ Add similar elements
[tex]x {}^{3} + 3x {}^{2} - 10x - 24[/tex]
Thus, use the same format for question number 28 and you will get the value
[tex]x {}^{3} - 9x {}^{2} + 8x + 60[/tex]
If you have any questions or there is sth unclear tag me on comment box
Hope it helps!!
Help please, I don't understand any of this
The graph solution is in the attached images, for all the systems of inequalities.
What is the graph of a function?
The graph of a function is a visual representation of the relationship between the input values (x-coordinates) and the output values (y-coordinates) of the function. In other words, it is a visual representation of the function's rule.
The graph of a function can take many different forms, depending on the function's rule. Linear functions, for example, will produce a straight line on the graph.
we have the following inequalities:
i)
y > 3x - 17,
y ≤ -4x +11.
ii)
4x - 4y > -40,
-5x + 5y < 10.
iii)
x + 3y ≥ 31,
4x - 2y ≥ -2,.
iv)
5x + y < 3,
5x + y > 37
Hence, the graph solution is in the attached images, for all the systems of inequalities.
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If the length of a rectangle increases 2 times and the width decreses 3 times, then its area decreased by :
a) 66.6%
b) 66.(6)%
c) 33.(3)%
d) 33.3%
e) 30%
The statement which is correct about the Area of the rectangle in discuss as required is that the area decreased by; Choice C; 33.(3)%.
By what percent does the area of the rectangle decrease?As evident in the task content; the length of a rectangle increases 2 times and the width decreses 3 times;
Since the initial length can be said to be; l and the initial width can be said to be; w and Area A = l × w.
However, when the length and width change as described; the area of the rectangle is;
Area = 2l × ( w / 3 )
Area = ( 2/3 ) × lw
On this note, the new Area of the rectangle is two-third the initial area.
On this note, the area of the rectangle has decreased by one-third which is equivalent to; Choice C; 33.(3)%.
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How many children can you predict a family has if the amount spent on groceries per week is $169.47?
Answer: Well for a family of 6 we spend around 200-300$, so a family of 4-5 if older like teens, or 6-7 for young toddlers.
What is the coefficient of the variable in the expression 2 − 5x − 4 8?
So, on solving the provided question, we can say that coefficient of the variable in the expression 2 − 5x − 4 8 is 5
What is the coefficient?A coefficient in mathematics is a polynomial, a series, or the multiplicative coefficient of a particular term in an expression. Typically numeric, however any expression is permitted. The term "parameter" can also refer to the coefficients themselves if they are variables. A number times a variable equals a coefficient. Coefficient examples include: The coefficient is 14 in phrase 14c 14c 14c. The coefficient is 1 for word g. multiplies the variable by this amount. example Given that "z" is a variable and that 6z is the definition of the term, the coefficient is 6. One is the coefficient of the square of x.
here,
coefficient of the variable in the expression 2 − 5x − 4 8 is 5
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Triangle A”B”C” is formed using the translation (x+2, y+0) and the dilation by a scale factor of 1/2 from the origin. Which equation explains the relationship between line AB and line A”B”?
Point A: (-3,3)
Point B: (1,-3)
Point C: (-3,-3)
Answer options:
A) Line A”B” equals Line AB divided by two
B) Line AB equals Line A”B” divided by two
C) Line AB over Line A”B” equals 1/2
D) Line A”B” over Line AB equals two
Triangle ABC is dilated by a scale factor of 1/2, the line A”B” equals Line AB divided by two
What is an equation?An equation is an expression composed of variables and numbers linked together by mathematical operations.
Translation is the movement of a point up, down, left or right in the coordinate plane.
Dilation is the increase or decrease in the size of a figure.
Triangle A”B”C” is formed using the translation (x+2, y+0) and the dilation by a scale factor of 1/2 from the origin.
Since there is a dilation by a scale factor of 1/2, hence:
A"B" = AB * 1/2
A"B" = AB/2
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help pleaseee i can’t get it right
The compositions between functions f(x) = 3 · x - 2 and g(x) = x + 1 are f[g(x)] = 3 · x + 1 and g[f(x)] = 3 · x - 1, respectively.
How to use composition between two functions
Let be f(x) and g(x) functions, there is a composition of the form f[g(x)], when the independent variable of function f is substituted by function g. That is to say:
f ° g(x) = f [g(x)]
First, define functions f(x) and g(x):
f(x) = 3 · x - 2
g(x) = x + 1
Second, perform the required compositions and simplify the expressions:
f[g(x)] = 3 · (x + 1) - 2
f[g(x)] = 3 · x + 1
g[f(x)] = (3 · x - 2) + 1
g[f(x)] = 3 · x - 1
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