Answer:
[tex]x + 3x = 52 \\ 4x = 52 \\ x = 13 \\ y = 3x = 3 \times 13 = 39[/tex]
what is the equation of the line graphed below?
Answer:
2x +3y = 15 or y = -2/3x +5
Step-by-step explanation:
You want the equation of the line with y-intercept 5 and x-intercept 7.5.
EquationThe intercept form equation can be written ...
x/a +y/b = 1
where 'a' is the x-intercept and 'b' is the y-intercept.
The given intercepts of a=7.5 and b=5 mean we can write the equation as ...
x/7.5 +y/5 = 1
Multiplying by 15 gives the standard-form equation ...
2x +3y = 15
Solving for y gives the slope-intercept equation ...
y = -2/3x +5
9. The lengths of the sides of four triangles are given.
Which triangle is a right triangle?
a. 16, 10, 20
b. 10, 10, 10
c. 11, 12, 13
d. 9, 40, 41
Answer:
D
Step-by-step explanation:
9^2 + 40^2 = 41^2
To install the right size heating and cooling syster, you must know how many cubic feet an office building contains. The building is 120 feet wide. 20 feet lugh, and 48 feet long. Find the volume.
Answer:
Mizuki is here to help!
115200 [tex]ft^3[/tex] is the volume of the building.
Step-by-step explanation:
120 x 20 x 48 =
2400 x 48 =
115200
The volume of a sphere is given by the equation V = 1/6(square root of 3.14) x 60^3/2
where S is the surface area of the sphere. Find the volume of a water walking ball, to the nearest cubic meter
(25 points for the answer)
If John save 1/5 of his paycheck how much money would it take him to get to 14,500$ for his holiday trip? He earns $9062.5 each paycheck. (Unrealistic question unless you are under paid severely)
Use multiplication or division ONLY!
The amount of john would save 2900 rs
14500*1/5=2900
How much he earns on paycheck?A paycheck, also spelled paycheque, pay check or pay cheque, is traditionally a paper document issued by an employer to pay an employee for services rendered.a check used to pay an employee the amount of money the employee has earned.A paycheck can be an actual piece of paper (a check) that a person can take to the bank to deposit to their account or exchange for cash. Alternatively, a paycheck can be money a company electronically deposits directly into the employee's bank account.Take a look at how each common payroll interval works: Weekly: Once a week (52 paychecks per year) Biweekly: Once every other week (26 paychecks per year) Semimonthly: Twice per month (24 paychecks per yearTo learn more about paycheck refers to:
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If you are paid $42,000 per year, what is your type of payment?
a.
Commission
b.
Salary
c.
Wage
d.
Pension
Answer:
Hello There!!
Step-by-step explanation:
The answer is=>b.Salary.
hope this helps,have a great day!!
~Pinky~
In the given question, the form of payment is salary.
What is a salary?When someone is paid a certain amount of money for his/her work on a daily, weekly, monthly, or yearly basis is called salary.
Given, I'm getting paid a sum of $42000 per year.
It is not a commission. Because, I'm not getting paid any form of compensation here.
The paid amount is fixed here. Therefore, it is not a wage.
It is not a pension. Because, I'm not getting paid after the retirement.
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Find all the real and complex solutions of the polynomial equation. Be sure to show ALL work (4 points):
The real and complex solutions of the polynomial equation are 2,-3i and 3i
What is Polynomial?Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables
The given polynomial is x³-2x²+9x-18
Factor out x² from x³-2x² which becomes x²(x-2)
Factor out 9 from 9x-18 which becomes 9(x-2)
x³-2x²+9x-18
x²(x-2)+9(x-2)
Factor out common term x-2
( x²+9)(x-2)=0
x²+9=0
x=-3i and 3i
x-2=0
x=2
Hence, the real and complex solutions of the polynomial equation are 2,-3i and 3i
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Find the area of the polygon with the given vertices.
W(-1, 1)
-4
Z(-3,-2)
4
Ay
2
-4
2
X(4,1)
4 x
Y(2,-2)
The area of a polygon with the given vertices is calculated by adding the areas of the individual triangles that make up the polygon.
What is polygon?A polygon is a closed figure in a plane consisting of a set of straight line segments connected end-to-end. The sides of a polygon are all of equal length, and the angles between them are all of equal measure. Polygons are one of the most fundamental shapes in geometry. They include triangles, squares, rectangles, hexagons, and many more.
The area of triangle WXZ is calculated as (1/2) × |XW × ZY|,
where XW is the vector from W to X and ZY is the vector from Z to Y.
In this example,
XW = (3, -2) and ZY = (-2, -4).
Therefore, the area of triangle
WXZ is (1/2) ×|(3, -2) × (-2, -4)| = (1/2) × 14 = 7.
The area of triangle XYA is calculated similarly,
where XY = (2, 3) and YA = (-2, -4).
Therefore, the area of triangle
XYA is (1/2) ×|(2, 3) ×(-2, -4)| = (1/2)× (-14) = -7.
The area of the polygon is calculated by adding the areas of the individual triangles, which in this example is 7 + (-7) = 0. Therefore, the area of the polygon with the given vertices is 0.
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Given the table of values, determine the the constant of proportionality, then write the equation of the proportion.
The constant of proportionality is 9 and equation of the proportion.
is y= 10x.
What is Constant of Proportionality?If the ratio of one variable to the other is constant, then there is a proportional relationship between the two variables. If x and y are in a proportional relationship, then the ratio of y to x is the constant of proportionality.
Given:
As, we know using the Constant of Proportionality
y = kx
or, k = y/x where k is Constant of Proportionality.
Then, from the table we have
k = 90/9
k= 10
Thus, y = kx
or, y= 10x
Hence, the equation of the proportion is y= 10x.
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Help Pls Due In 10 Mins
Answer:
D. Rotate triangle P 90° counter clockwise about point K, and then reflect it across a horizontal line through point K
What is linear equation 8th class?
An equation in which the highest power of the variable is 1 is known as a linear equation. It is also termed a one-degree equation.
There are two types of linear equations, linear equations in one variable and linear equations in two variables. The standard form of a linear equation in one variable is Ax + B = 0. Where x = variable, A = coefficient and B = constant.
The standard form of a linear equation in two variables is Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.
A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always formed in a straight line. That is why it is named a 'linear equation'.
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Which of the following is a factor of 2x^2 3x 5?
The factor of the given expression is -1 and 5/2 first we try to solve given expression as a quadratic equation then we make 2 terms equal to 0.
first, try to understand what is the factor of a quadratic equation.
A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor in mathematics. As an illustration, 3 and 6 are factors of 12 because 12 3 = 4 and 12 6 = 2, respectively. 1, 2, 4, and 12 are the other components that make up 12.
The roots of a quadratic equation are known as a factor. This means if we put the value of x to factor then the quadratic equation will become zero.
2x^2 - 3x - 5 = 2x^2 - (5-2)x - 5
3 can be written as 5-2.
2x^2 - 5x + 2x - 5
x(2x - 5) +1(2x-5)
(2x - 5)(x + 1)
So the factors is 2x - 5 = 0 or x + 1 = 0.
2x - 5 = 0 , x = 5/2.
x + 1 = 0 , x = -1.
Given question is incomplete complete question here:
Which of the following is a factor of 2x^2 - 3x - 5?
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Help asappppp please
Answer:
the answer is a
and the correct answer is letter C
Step-by-step explanation:
I don't know that is the answer
Consider the quadratic function defined by:
f (x) = −3(x −1)(x + 6)
a. State the zeros of the function: ____________________
b. Express this function in standard form by expanding & simplifying.
Answer:
[tex]\implies x = 1 \quad or -6 \\\\\implies f(x) = -3x^2-15x + 18 [/tex]
Step-by-step explanation:
Given :-
A quadratic function is given to us. The function is -3(x-1)(x-6)And we need to find out the zeroes of the quadratic function and we need to express it in Standard form. T
Function :-
[tex]\implies f(x)= -3(x-1)(x+6) [/tex]
So for finding the zeroes equate it with 0 .So that ,[tex]\implies f(x)=0 \\\\\implies -3(x-1)(x+6)=0 \\\\\implies (x - 1 )(x+6) = 0 \\\\\implies x = 1 \quad or \quad -6 [/tex]
Therefore the zeroes are 1 and -6 .
Expressing in Standard form :-
The standard form of a quadratic equation is ,
[tex]\implies ax^2+bx + c = 0 [/tex]
And that of a quadratic function is ,
[tex]\implies f(x) = ax^2+bx + c [/tex]
Simplifying the equation :-
[tex]\implies f(x)= -3(x-1)(x+6)\\\\\implies f(x) = (-3x +3)(x+6) \\\\\implies f(x) = -3x(x+6)+3(x+6)\\\\\implies f(x) = -3x^2 -18x +3x + 18\\\\\implies f(x) = -3x^2-15x + 18 [/tex]
Hence the Standard form of the equation is -3x² - 15x + 18 .
Solve the differential equation by variation of parameters.
y'' − y = cosh x
The general solution is [tex]$$y=c_3 e^x+c_4 e^{-x}+\frac{1}{2} x \sinh x \text {. }$$[/tex]
Consider the following differential equation: y'' − y = cosh x
The given differential equation in the operator form will be: (D^2-1)y=coshx
The auxiliary equation of the corresponding homogeneous equation will be:
m^2-1 = 0
=>m^2=1
=>m=+1,-1
So, the complementary function will be [tex]y_c=c_1 e^x+c_2 e^{-x}.\alpha[/tex]
Now, let [tex]y_1=e^x, y_2=e^{-x}.[/tex]
Compute the Wronskian determinant:
[tex]$$\begin{aligned}W\left(y_1, y_2\right) & =\left|\begin{array}{ll}y_1 & y_2 \\y_1^{\prime} & y_2^{\prime}\end{array}\right| \\& =\left|\begin{array}{ll}e^x & e^{-x} \\e^x & -e^{-x}\end{array}\right| \\& =-e^x e^{-x}-e^x e^{-x} \\& =-2\end{aligned}$$[/tex]
Since the given differential equation is already in the form [tex]$y^{\prime \prime}+P(x) y^{\prime}+Q(x) y=f(x)$[/tex] (that is, the coefficient of y'' is 1 ),
So identify:
f(x)=cosh x
Then, calculate the values of u_1' and u_2', using formulas as follows:
[tex]$$\begin{aligned}u_1^{\prime} & =-\frac{y_2 f(x)}{W} & u_2^{\prime} & =\frac{y_1 f(x)}{W} \\& =-\frac{e^{-x} \cdot \cosh x}{-2} & & =\frac{e^x \cdot \cosh x}{-2} \\& =\frac{e^{-x} \cdot\left(\frac{e^x+e^{-x}}{2}\right)}{2} & \text { and } & =-\frac{e^x \cdot\left(\frac{e^x+e^{-x}}{2}\right)}{2} \\& =\frac{1}{4}\left(1+e^{-2 x}\right) & & =-\frac{1}{4}\left(e^{2 x}+1\right)\end{aligned}$$[/tex]
Integrate on both sides of u_1' and u_2' with respect to ' x', to get:
[tex]$$u_1=\frac{x}{4}-\frac{e^{-2 x}}{8} \text { and } u_2=-\frac{x}{4}-\frac{e^{2 x}}{8} .$$[/tex]
So, the particular solution is,
[tex]$$\begin{aligned}y_p & =u_1 y_1+u_2 y_2 \\& =\left(\frac{x}{4}-\frac{e^{-2 x}}{8}\right) e^x+\left(-\frac{x}{4}-\frac{e^{2 x}}{8}\right) e^{-x} \\& =\frac{1}{4} x\left(e^x-e^{-x}\right)-\frac{1}{8}\left(e^{-x}+e^x\right) \\& =\frac{1}{2} x \sinh x-\frac{1}{8}\left(e^{-x}+e^x\right)\end{aligned}$$[/tex]
Thus, the general solution of the given differential equation is,
[tex]$$\begin{aligned}y & =y_c+y_p \\& =c_1 e^x+c_2 e^{-x}+\frac{1}{2} x \sinh x-\frac{1}{8} e^{-x}-\frac{1}{8} e^x \\& =\left(c_1-\frac{1}{8}\right) e^x+\left(c_2-\frac{1}{8}\right) e^{-x}+\frac{1}{2} x \sinh x \\& =c_3 e^x+c_4 e^{-x}+\frac{1}{2} x \sinh x\end{aligned}$$[/tex]
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Why is there only 180 degrees in a triangle?
A triangle is a three-sided polygon and each of its interior angles must add up to 180°; so each angle can have at most 180°.
A triangle is a three-sided polygon with three interior angles. According to the mathematical rule known as the “sum of interior angles”, the sum of the three interior angles of any triangle must always equal 180 degrees. Therefore, if the three angles of a triangle are A, B, and C, then A + B + C = 180. Since the sum of the three angles must equal 180 degrees, it means that each angle can have at most 180 degrees; none of the angles can be greater than 180 degrees. In other words, the maximum possible value of the angles in a triangle is 180 degrees, so the triangle can have only 180 degrees in total.
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Im doubting my choice on this question can someone help?
Answer: You're correct
Step-by-step explanation:
All values on the dice are < 7, so 6/6 are less.
6/6 simplifies to 1, so that is also correct.
6/6 = 1 = 100%
0/6 is incorrect.
Answer:
You are 100% correct so dw abt it!
Step-by-step explanation:
I'm sorry
Which variation is represented by this situation:
Martha earns $375 when she works 5 hours. How much will she earn
if she works 12 hours? Is it direct variation or inverse variation?
Direct variation is represented by this situation and she earn $900
if she works 12 hours.
What are direct variation and indirect variation?Direct variation describes a relationship whereby one measure directly affects the other when the first one changes. This is completely opposed by inverse variation. Learn the definitions of direct and inverse variations in this article, along with some instances that have been solved.
How do inverse and direct variations differ from one another?When x is not equal to 0, y = kx is the equation that describes the linear function known as direct variation. An equation of the form xy = k, where x is not equal to zero and k is a nonzero real number constant, describes the nonlinear function known as inverse variation.
5 hours = earns $ 375
1 hours = 375/5 = earns $ 75
12 hours = 75 12 = earns $ 900
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For one kindergarten class in his district, a researcher determines which children already can read simple words and which children cannot upon entering kindergarten. The children are followed until third grade, at which point they are tested to determine the grade level at which they are reading. Those children who were reading simple words upon entering kindergarten are found to be reading at a higher level than those who could not read simple words upon entering kindergarten. Fill in the Blank: The researcher _____________________________. Select one: a. can conclude that children should be taught to read in preschool, as there are clear benefits to reading early. b. needs to check the reading level of the children's parents. c. cannot establish a cause-and-effect relationship because the study did not use a random sample of kindergarten students. d. finds these results beneficial, as there may be confounding variables in this study. e. needs to retest in sixth grade or no conclusions can be reached.
The correct answer is that we cannot conclude that being able to read is beneficial for them as there can be various cause and effect relation.
A research is conducted to collect information about a specific topic for the purpose of study. A group of population is asked to fill a survey form or answer questions based on the research topic.
This data is collected and analyzed to get the required result.
Here, in this question kindergarten students are the population from whom data is collected . Here, the conclusion is that having the ability to read and write from before only doesn't means they will have academic intelligence later.
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Please show your work; only #8!
Answer:
x = 0.16
Step-by-step explanation:
Step 3:
Solve the equation for x by finding a , b , and c of the quadratic then applying the quadratic formula.
[tex]x = - \frac{11 - \sqrt{185} }{16}[/tex]
Then, evaluate for x:
x = 0.16259190... which is about,
x = 0.16
Chicken is on sale for $2.29 per lb at the grocery store. If Jerry buys 3 lbs, what would be his final cost including 6% tax?
What is the discriminant of 3x^2 2x 1 0?
The discriminant of quadratic equation 3x^2 + 2x + 1 =0 is -8
We know that the standard form of quadratic equation is ax^2 + bx + c = 0, with a ≠ 0
The discriminant of quadratic equation ax^2 + bx + c = 0 is:
D = b^2 - 4ac
Comparing given quadratic equation 3x^2 + 2x + 1 =0 with ax^2 +bx + c = 0 we get,
a = 3, b = 2 and c = 1
So, the discriminant of given equation would be,
D = b^2 - 4ac
D = 2^2 - 4(3)(1)
D = 4 - 12
D = -8
Therefore, the discriminant is D = -8
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ava has 2 dozen pencles.3/8 of them are sharpened. how many are sharpened? how many are not?
Answer:
3/8 of 24 is 9
9 are sharpened so 24-9=15
15 pencils are not sharpened.
In 1800, the slave population in the United States of America was 893,602. By 1860, the slave population rose to about 1,953,760. How large of a percentage did the slave population increase by from 1800 to 1860?
To find the percentage increase of the slave population from 1800 to 1860, we can use the following formula:
What does math's % mean?
In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).
percentage increase = (new value - original value) / original value x 100
We know that in 1800 the slave population was 893,602 and in 1860 the slave population was 1,953,760. So we can plug in these values into the formula:
percentage increase = (1,953,760 - 893,602) / 893,602 x 100
percentage increase = (1,060,158) / 893,602 x 100
percentage increase = 1.1885 x 100
percentage increase = 118.85
So, the slave population increased by 118.85% from 1800 to 1860.
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How do you solve inequalities in 7th grade?
Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤. To ‘solve’ an inequality means to find a range, or ranges, of values that an unknown x can take and still satisfy the inequality.
Suppose we want to solve the inequality x + 3 > 2.
We can solve this by subtracting 3 from both sides:
x + 3 > 2
x > −1
So the solution is x > −1. This means that any value of x greater than −1 satisfies x + 3 > 2.
Inequalities can be represented on a number line such as that shown in the image attached below. The solid line shows the range of values that x can take. We put an open circle at −1 to show that although the solid line goes from −1, x cannot actually equal −1.
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What must be added to 5x³ 2x² 6x 7 to make the sum X 3x² x 1?
To make the sum X 3x² x 1, you must add -5x³ -2x² -6x -7 to 5x³ 2x² 6x 7.
Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
These expressions are represented with the help of unknown variables, constants and coefficients. The combination of these three (as terms) is said to be an expression. It is to be noted that, unlike the algebraic equation, an algebraic expression has no sides or equal to sign.
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Please help with this question
Answer:
C
Step-by-step explanation:
Start with the vertex. It is the lowest point. It is located at (-2,4)
The axis of symmetry is always the x value when the parabola opens upward or down ward. This parabola opens upward so it is x = - 2.
The answer is C
Mr Hong is a rare coin collector. He recently bought a coin valued at $5400. It has been determined that the coin will increase in value by $30 each month. Mr Hong plans to sell the coin within 5 years. a. name the quantities that stay the same in this problem situation & the quantities that remain constant .
Given: △ACE,BD¯¯¯¯¯∥AE¯¯¯¯¯ Prove: BACB=DECD A triangle with vertices labeled as A, C, and E, with base A E. Sides C A and C E contain midpoints B and D, respectively. A line segment parallel to base A E is drawn from point B to D. Angle C A E is labeled as 4 and angle C E A is labeled as 3. Angle C B D is labeled as 1 and angle C D B is labeled as 2. Drag an expression or phrase to each box to complete the proof. Statement Reason △ACE,BD¯¯¯¯¯∥AE¯¯¯¯¯ Given Response area Corresponding Angles Postulate △ACE∼△BCD Response area CACB=CECD Definition of similar triangles CA=CB+BACE=CD+DE Segment Addition Postulate CB+BACB=CD+DECD Substitution Property of Equality CBCB+BACB=CDCD+DECD Addition of fractions 1+BACB=1+DECD Simplification of fractions Response area Subtraction Property of Equality
For triangle ACE, if BD ∥AE , then BA/CB = DE/CD is proved.
For given triangle ACE,
BD || AE ...............(Given)
∠4 ≅ ∠1 and ∠3 ≅ ∠2 ..............(Corresponding Angles Postulates)
ΔACE ~ ΔBCD .............(Angle-Angle Similarity Postulate)
CA/CB = CE/CD ............(Definition of similar triangles)
CA = CB + BA, CE = CD + DE ..........(Segment Addition Postulate)
(CB + BA)/CB = (CD + DE)/CD ..........(Substitution Property of Equality)
CB/CB + BA/CB = CD/CD + DE/CD .........(Addition of Fractions)
1 + BA/CB = 1 + DE/CD .............(Siplification of fractions)
BA/CB = DE/CD ...............(Subtraction Property of equality)
Hence proved.
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What is an equation of the line that passes through the points (-4, -1) and (6, -1)
Answer:
y = -1
Step-by-step explanation:
y2 - y1 / x2 - x1
-1 - (-1) / 6 - (-4)
0
y = 0x + b
-1 = 0(-4) + b
-1 = 0 + b
-1 = b