the cost of a broom is $62.50, and the cost of a mop is x + 15 = 62.5 + 15 = $77.50.
Therefore,
a) 1 mop cost $77.50
b) 1 broom cost $62.50
What is the system of equations?
A system of equations is a set of one or more equations involving a number of variables. The solutions to systems of equations are the variable mappings such that all component equations are satisfied in other words, the locations at which all of these equations intersect.
To find the cost of a mop and a broom, we can set up a system of equations using the information given:
Let x be the cost of a broom
Let y be the cost of a mop (which is $15 more than a broom)
From the problem, we know that:
y = x + 15 (since a mop costs $15 more than a broom)
5x + 7y = 855 (since 5 mops and 7 brooms cost a total of $855)
We can substitute the first equation into the second equation:
5x + 7(x + 15) = 855
5x + 7x + 105 = 855
12x = 750
x = 62.5
Hence, the cost of a broom is $62.50, and the cost of a mop is x + 15 = 62.5 + 15 = $77.50.
Therefore,
a) 1 mop cost $77.50
b) 1 broom cost $62.50
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How do you know if it is a linear exponential or quadratic graph?
Linear graphs have the following form: y = mx + b, where m is the slope of the line and b is the y-intercept.
To calculate the slope, you can use the formula m = (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.
Exponential graphs have the following form: y = ab^x, where a and b are constants. To calculate the constants, you can use the formula y = a + b^x, where (x, y) are two points on the graph and a is the y-intercept.
Quadratic graphs have the following form: y = ax^2 + bx + c, where a, b, and c are constants. To calculate the constants, you can use the formula y = ax^2 + bx + c, where (x, y) are two points on the graph and c is the y-intercept.
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a map drawn move to the scale 2 cm : 100 mi. on the map b is 3.5 centimeters from town a and town c is 2 centimeters past town b how many miles apart town a and town b
The distance between town a and b is 175 mi.
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size.
Given that, a map drawn move to the scale 2 cm : 100 mi. on the map town b is 3.5 centimeters from town a and town c is 2 centimeters past town b
Since, 2 cm = 100 mi
1 cm = 50 mi
Therefore, 3.5 cm = 50×3.5 = 175 mi
Hence, the distance between town a and b is 175 mi.
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Forty students are in drama club. 3/8 of the students have a part in the spring play. How many student have a part
Answer:
15
Step-by-step explanation:
-/40 and 3/8 40/5=8 3x5=15
Answer:
15 out of 40 students have a part in the spring play.
Step-by-step explanation:
(3/8) * 40 = 15
What are the like terms in 3x 3 2y and 2 XY x2?
The like terms in 3x (3 - 2y) and 2 (xy + x²) are -6xy and 2xy.
3x (3 - 2y) = 3x * 3 - 3x * 2y = 9x - 6xy2 (xy + x²) = 2 * xy + 2 * x² = 2xy + 2x²What are like terms in math equations?Like terms are terms which have the same variables and exponents. In this case, the like terms are -6xy and 2xy because they both have the same variable (xy) and exponents (1). In algebra, like terms can be added or subtracted to simplify an expression. Like terms are terms which have the same variables and exponents.
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HURRY HURRY WHAT IS THE SOLUTION TO THIS INEQUALITY
6.9
Answer: no question=no answer
Step-by-step explanation:
please help quickly +25pts
X, Y, and Z are collinear. Y is between X and Z.
XY = 12 and XZ = 14
YZ = ___ units
The value of YZ = 2 units.
What are collinear points?The Latin words "col" and "linear" are combined to form the word "colinear." "Col" stands for "together," and "Linear" is a line. Collinear points are hence points that are situated along a single line. Numerous instances of collinearity can be observed in daily life, such as a line of pupils standing together.
Given X, Y, and Z are collinear. Y is between X and Z.
so XY + YZ = XZ
given XY = 12 units and XZ = 14 units
XY + YZ = XZ
12 + YZ = 14
YZ = 14 - 12
YZ = 2 units
Hence measure of YZ is 2 units.
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Is halting problem is solvable or unsolvable?
Therefore , the solution of the given problem of algorithm comes out to be halting problem is unsolvable.
Define algorithm.An algorithm is a process for carrying out a computation or resolving a challenge. Algorithms work as a detailed set of guidelines that lead hardware- or software-based routines through a series of predetermined actions step by step. Algorithms are frequently used in all areas of IT.
Here,
The halting problem, which claims that no program can be created that can anticipate whether or not any other program will halt after a finite number of steps, is an intractable algorithmic challenge.
The inability to solve the stopping problem directly affects software development.
Therefore , the solution of the given problem of algorithm comes out to be halting problem is unsolvable.
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........... I donr know what I'm doing-
Intercept = 1
Equation - y = -(2/5)x + 1
Solve the given differential equation. 3x^2y'' + 6xy' + y = 0
The solution for given differential equation is y = c1e^(-x^3/3) + c2xe^(-x^3/3)
This is a second-order linear differential equation with constant coefficients. To solve this equation, we can use the method of an auxiliary equation, which is 3r^2 + 6r + 1 = 0. This equation has two complex conjugate roots, r = -3 ± i√3. Therefore, the solution of the differential equation is y = c1e^(-x^3/3) + c2xe^(-x^3/3)cos(√3x^2/2) + c3xe^(-x^3/3)sin(√3x^2/2), where c1, c2, and c3 are arbitrary constants.
The method of an auxiliary equation is a popular way to solve second-order linear differential equations with constant coefficients. It involves finding the roots of an auxiliary equation, which is found by setting the coefficient of the second derivative equal to zero.
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Andre and diego were each trying to solve 2x 6=3x-8 describe the first step they each make to the equation
The final answer after solving the given equation could be 14.
What is Linear Equation ?
Linear Equation can be defined as the equation in which the highest degree of the variable is one. Linear equations are generally three types , they are standard form , slope intercept form , point slope form and linear equation is also called as the equation of straight line.
Given,
Given equation,
2x + 6 = 3x -8
separating the value into a similar term:
2x-3x = -8 - 6
subtracting the equation:
-x = -14
remove negative sign:
x = 14
Therefore , the final answer could be 14.
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A group of 36 people from the Nantucket recreation center plans to purchase tickets for a cruise to Permut Bermuda the standard fare for an individual ticket is $1200 the group is informed that because of the size of the group the standard fare will be reduced by 30% with a discount of 30% how much does each member of the Nantucket recreation center have to pay for a cruise ticket show or explain how you got your answer (SOMEONE PLEASE HELP)
The total amount each member of the Nantucket recreation center have to pay after the discount is given by the equation A = $ 840
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total amount for each person after discount be represented as A
Now , the equation will be
The total number of people in the group = 36
The standard fare for each person = $ 1200
So , the total cost of the fare = total number of people x standard fare for each person
Substituting the values in the equation , we get
The total cost of the fare = 1200 x 36
The total cost of the fare = $ 43,200
Now , the discount percentage = 30 %
So , the amount after discount = total cost of the fare - total cost of the fare x discount percentage
Substituting the values in the equation , we get
The amount after discount = 43,200 - ( 30/100 ) x 43,200
The amount after discount = 43200 - 12960
The amount after discount = $ 30,240
Now ,
Total amount for each person after discount A =amount after discount / 36
Total amount for each person after discount A = 30,240 / 36
On simplifying the equation , we get
Total amount for each person after discount A = $ 840
Therefore , the value of A is $ 840
Hence , the amount is $ 840
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Add: (g2 – 4g4 + 5g + 9) + (–3g3 + 3g2 – 6)
Rewrite terms that are subtracted as addition of the opposite.
g2 + (–4g4) + 5g + 9 + (–3g3) + 3g2 + (–6)
Group like terms.
Combine like terms.
Write the resulting polynomial in standard form.
The resulting polynomial in standard form (b) –4g^4 –3g³ +4g² +5g +3
What is standard form of a polynomial?Suppose the considered polynomial is of only one variable.
Then, the standard form of that polynomial is the one in which all the terms with higher exponents are written on left side to those which have lower exponents.
The simplification process is described and partially carried out. We are to finish by combining like terms and writing the result in standard form.
Given
Add: (g² – 4g^4 + 5g + 9) + (–3g³ + 3g² – 6)
Combine Like Terms
g² + (–4g^4) + 5g + 9 + (–3g³) + 3g² + (–6)
The like terms are the g² terms and the constants;
= (1 +3)g² + (–4g^4) +5g +(9 +(–6)) +(–3g³)
= 4g² +(–4g^4) +5g +3 +(–3g³)
Write in Standard Form
In this form, the terms are written in order of decreasing degree.
= –4g^4 –3g³ +4g² +5g +3
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solve please im gonna fail
Answer:
The two little blue boxes are going
Step-by-step explanation:
Lets start with the 0s.
Two zeros is 0. so its
_ _ _ _ 0.
Now we add 2 and 0 which is 2.
_ _ _ 2 0
now we add 6 and 4, which is 10. We have to put the 1 above the 7 and 5 and we are going to put 0 down below
_ _ 0 2 0
now we are going to add 7 +5, but dont forget the 1! Its going to be 13. Put the 3 down below and put the 1 above the 2!
_ 3 0 2 0
Now its 2 + 1 which is 3
your answer is
33020
What are the 3 types of polynomials and how many terms does each one have?
Monomial, binomial, and trinomial expressions are all categorized by the number of terms they include.
A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.
An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
A polynomial with one term is called a monomial. A polynomial having two dissimilar terms is called a binomial. An algebraic expression having three terms is called a trinomial.
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CANN SOEMOEN PLS HELP ME PLS. I DONT KNOW WHAT TO DO AND THIS IS ALREADY A WEEK LATE.
Answer:
y = 72 and x = 36
Step-by-step explanation:
So firstly, the outside angle is 108, right? And the total of all angles in a triangle is 180 degrees. So:
180 - 108 = 72
Then the other angle, angle x, is also 72 degrees. That's because they are supplementary angles.
Now that we know x = 72 degrees. To find the y angle, you add 72 and 72 together. Which is 144.
Then you do 180 - 144. Which is 36. So, x = 72 and y = 36
I hope it helped you!
-35PTS- what theorem can be used to prove these triangles are congruent
Answer:
Neither----------------------------
We see two sides and one angle marked as congruent on both triangles.
The congruent angle is not included.
It means we can neither state it is ASA nor SAA as both of these require two congruent angles.
Please help due in 20 min
5^-1/-9^0
Answer: -0.2 hope this answer helps you good luck
Answer:
-0.2
Step-by-step explanation:
[tex] \frac{ {5}^{ - 1} }{ { - 9}^{0} } = \frac{ \frac{1}{5} }{ - 1} = \frac{1}{5} \times \frac{ - 1}{1} = \frac{ - 1}{5} = - 0.2[/tex]
Choose three true statements about the angles of the figure
1: Z1 and the 55* angle are adjacent
2: mZ1=55* because Z1 and the 55* angle are vertical angles
3: mZ2=125* because Z2 and the 55* angle are supplementary
4: mZ2 cannot be determined from the information
5: mZ1=180*-55*
6: mZ2=180*-55*-45*
Three true statements about the angles of the given figure are,
1. angle 1 and the 55 degree angle are adjacent.
5. angle 1 = 180 degree - 55 degree
6. angle 2 = 180 degree - 55 degree - 45 degree.
How are complementary angles defined?Complementary angles are two angles whose measures add up to 90 degrees. For example, an angle of 45 degrees and an angle of 45 degrees are complementary. When two angles are complementary, they form a right angle. The symbol for complementary angles is ∠A + ∠B = 90°.
What is the difference between acute angles and obtuse angles?Acute angles are angles whose measure is less than 90 degrees. They are sharp angles that are less than a right angle. On the other hand, obtuse angles are angles whose measure is greater than 90 degrees. They are angles that are greater than a right angle and less than 180 degrees. In other words, obtuse angles are angles that are wider than a right angle but less than a straight angle.
Analysing all the statements given in the question,the corrrect options are
Option 1, since angle 1 and 55 degree share the same vertex.
Option 5, since the sum of angle 1 and 55 degree is 180 degrees being supplementary angles.
Option 6, since the sum of all the interior angles of a triangle is 180 degrees.
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What does a 45 45 90 triangle look like?
A 45°-45°-90° triangle looks like Right Angle Triangle.
A 45°−45°−90° triangle is a commonly encountered right triangle whose sides are in the proportion 1:1:√2.
45°−45°−90° triangle is a commonly encountered right triangle whose sides are in the proportion 1:1:√2 . The measures of the sides are x, x, and x√2.
In a 45°−45°−90° triangle, the length of the hypotenuse is √2 times the length of a leg, and the Opposite side to 45 = 1/√2 * Hypotenuse.
The 45-45-90 triangle has three unique properties that make it very special and unlike all the other triangles.
Hence, a 45°−45°−90° triangle is a commonly encountered right triangle whose sides are in the proportion 1:1:√2.
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Could someone please help me?
[tex]\textit{area of the rectangle}\\\\ A=Lw \begin{cases} L=length\\ w=width\\[-0.5em] \hrulefill\\ L=5\\ w=6 \end{cases}\implies A=(5)(6)\qquad \begin{cases} \textit{tripling the sides}\\[-0.5em] \hrulefill\\ L=3\cdot 5\\ w=3\cdot 6 \end{cases} \\\\\\ A=(3\cdot 5)(3\cdot 6)\implies (3\cdot 3)(5)(6)\implies 9(5)(6)\leftarrow \begin{array}{llll} \textit{new area is 9 times}\\ \textit{the old one}\\ \textit{a ratio of 9 : 1} \end{array}[/tex]
A graphical device used for enumerating sample points in a multiple-step experiment is a a. bar chart b. pie chart c. histogram d. None of the other answers is correct.
None of the listed methods are used for enumerating sample points in a multiple-step experiment. So, option D is the correct answer.
Graphical methods are important mathematical tools that are very helpful when it comes to managing a vast amount of data. These also help when we need to visually represent data. These methods help quite a lot since they make it easier to keep track of data and understand it as well.
A bar chart and a histogram are similar tools that are used to represent data by plotting them as rectangular bars. These can be either vertical or horizontal. A pie chart is also a tool that uses a shape for data visualization. In its case, it represents data in the shape of a circle and all categories/data sets have their slices. So, this means that these three are not methods that can be used for enumerating sample points in a multiple-step experiment. Hence, option D is the correct option.
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simplify the equation b^5•b^8
If you are doing a linear regression, what is the slope of the line predicted by the null hypothesis?
The null hypothesis is that the linear regression model does not exist. This essentially means that the value of all the coefficients is equal to zero.
What is the null hypothesis?
The null hypothesis is a common statistical theory that contends that there is no statistical relationship or significance between any two sets of observed data and measured phenomena for any given single observed variable.
Here,
We have to find out the slope of the line predicted by the null hypothesis if we are doing a linear regression.
We concluded that the null hypothesis states that the slope is equal to zero, and the alternative hypothesis states that the slope is not equal to zero.
Hence, the null hypothesis is that the linear regression model does not exist. This essentially means that the value of all the coefficients is equal to zero.
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What is the answer for x+4.5≥5.5
Answer:
B. x ≥ 1
Step-by-step explanation:
i need help with this question
The required slope of the linear equation is -3 which values shown in the table.
What is the slope of the line?The slope of a line is defined as the gradient of the line. It is denoted by m
Slope m = (y₂ - y₁)/(x₂ -x₁ )
The table is given in the question as follows:
x y
-4 -15
-2 9
0 3
2 -3
4 -9
As per the question, we take the given points are (0, 3) and (4, -9).
So we can substitute these values into the formula:
m = (-9 - 3) / (4 - 0)
m = -12 / 4
Apply the division operation, and we get
m = -3
Therefore, the required slope of the linear equation is -3.
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(a) Express tanθ in terms of secθ for θ in Quadrant II (b) Express secθ in terms of sinθ for θ in Quadrant III
a. The trigonometric ratio tanθ = -√(sec²θ - 1)
b. The trigonometric ratio secθ = -1/√(1 - sin²θ)
What are trigonometric ratios?Trigonometric ratios are the following mathematical expressions sinθ, cosθ, tanθ,secθ,cosecθ and cotθ.
a. How to express tanθ in terms of secθ for θ in Quadrant II?Since we want to express tanθ in terms of secθ in the second quadrant,using the trigonometric identity
tan²θ + 1 = sec²θ
Making tanθ subject of the formula, we have that
tan²θ = sec²θ - 1
tanθ = ±√(sec²θ - 1)
Since in Quadrant II, tanθ is negative, we choose the negative answer.
So, tanθ = -√(sec²θ - 1)
b. How to express secθ in terms of sinθ for θ in Quadrant II?Since we want to express tanθ in terms of secθ in the second quadrant,using the trigonometric identity
secθ = 1/cosθ and
sin²θ + cos²θ = 1
Making cosθ subject of the formula, we have that
cos²θ = 1 - sin²θ
cosθ = ±√(1 - sin²θ)
So, secθ = 1/cosθ
= ±1/√(1 - sin²θ)
Since in Quadrant III, secθ is positive, we choose the positive answer.
So, secθ = -1/√(1 - sin²θ)
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How to know if an equation is factorable using discriminate
On solving the provided question we can say that - here in equation we have [tex]y = 160+ 2 *t= > y = 160 + 2X 30 = > y= 160+ 60 = > y = 220 pounds[/tex]
What is equation?An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.
[tex]y = 160+ 2 *t\\y = 160 + 2X 30\\y= 160+ 60\\y = 220 pounds[/tex]
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solve for x. each figure is a parallelogram
9) x = 6
10) x = 1
11) x = 0
12) x = 6
This can be solved from the property of parallelogram.
What is parallelogram?A unique variety of quadrilateral called a parallelogram has both pairs of its opposite sides parallel and equal.
Parallelograms come in 4 different varieties, including 3 unique varieties. The four varieties are rhombuses, parallelograms, squares, and rectangles.
Properties are:
The opposing sides are equally spaced and parallel.Angles on either side are equal.The angles that are consecutive or contiguous are supplementary.All of the angles will be at right angles if any one of them is a right angle.The two diagonals cut across one another.9) As we know, from the property of parallelogram,
SR = TQ and ST = RQ
Now, 4 + 2x = 3x - 2
or, x = 6
10) As we know, from the property of parallelogram,
EF = DC and ED = FC
17x + 1 = 18x
or, x = 1
11) As we know, from the property of parallelogram,
YZ = XW and YX = ZW
2x + 9 = 9
2x = 0
x = 0
12) As we know, from the property of parallelogram,
TU = SV and TS = UV
6 + 2x = 4x - 6
or, 2x = 12
or, x = 6
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Help please radicals
Answer:
5√2
Step-by-step explanation:
Hello!
To simplify the radical, we can identify perfect square factors in the radicand or the number inside the square root.
We know that 50 is 25 times 2, so we can expand the radical like this...
[tex]\sqrt{50[/tex][tex]\sqrt{25*2}[/tex][tex]\sqrt{25} * \sqrt2[/tex]Now we can simplify each radical:
[tex]\sqrt{25} * \sqrt2[/tex][tex]5\sqrt2[/tex]The simplified form is 5√2.
What is the inverse of +5?
The inverse of +5 as calculated is found to be +1 / 5.
To find the inverse of +5 we can simply reciprocate it and the result will be the required answer.
reciprocal of +5 = 1 / 5.
Therefore, the answer is 1 / 5.
The opposite or reciprocal of a number or term in math is known as it's inverse. There are two types of inverse in math, the additive inverse and the multiplicative inverse.
The multiplicative inverse of a number for any n is given as 1/n. It is also called as the reciprocal of a number and 1 is called the multiplicative identity. On the other hand subtraction is the inverse of addition.
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