to solve this question, we need to difine our variables
we have values for end points as
x1 = -8
y1 = 4
x2 = -4
y2 = -8
next we can find the slope of the equation
[tex]\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ \text{slope}=\frac{-8-4}{-4-(-8)} \\ \text{slope}=\frac{-12}{4} \\ \text{slope}=-3 \end{gathered}[/tex]step 2
let's find the mid-point using mid-point formula
[tex]\begin{gathered} md=\frac{x_1+x_2}{2},\frac{y_2+y_1}{2} \\ md=\frac{-8+(-4)}{2},\frac{-8+4}{2} \\ md=-6,-2 \end{gathered}[/tex]mid-point = (-6, -2)
now we know the perpendicular line travels (-6 , -2) and has a slope of -3
equation of a straight line => y = mx + c
we can solve for c to find the equation.
[tex]\begin{gathered} y=mx+c \\ -2=(-3)(-6)+c \\ -2=18+c \\ c=-2-18 \\ c=-20 \end{gathered}[/tex]note: m = slope
c = intercept
the equation of the perpendicular bisector can be written as
y = -3x - 20
[tex]y=-3x-20[/tex]Write in simplest form 0.875:1/4
Hey there!
[tex]0.875:1/4\/\\\textmd{To Simplest form}[/tex]
[tex]0.875[/tex] ÷ [tex]\frac{1}{4}[/tex]
[tex]=3.5[/tex]
Your final answer would be 3.5.
Hope this helps!
The Outsiders
Movie vs. Book Comparison Project
The formula V=4/3 pie r3 gives the volume with radius r. Find the volume of a sphere with radius x+9. Write your answer as standard form.
We will find it as follows:
[tex]V=\frac{4}{3}\pi(x+9)^3\Rightarrow V=\frac{4\pi}{3}(x^3+27x^2+243x+729)^{}[/tex][tex]\Rightarrow V=\frac{4}{3}\pi x^3+36\pi x^2+324x+972[/tex]The volume of such a sphere is given by the expression found.
***
When we have a binomial at the power of a number, of the form:
[tex](a+b)^n[/tex]We use Pascal's triangle to determine the expansion. Pascal's triangle is the following:
Each row can be used to calculate a specific power, in our case the binomial is at the power of three, and we will use the 4rth row to expand, that is:
[tex](a+b)^3=a^3+3a^2b+3ab^2+b^3[/tex]As you can see, the numbers that accompany a & b are the ones found in the 4th row of Pascal's triangle. We also see that the "degree" o the expansion always sums 3, that is a^3 has an overall degree of 3, a^2b has an overall degree of 3, ab^2 has an overall degree of 3 & b^3 has an overall degree of 3.
***
If we, for example, wanted to expand (a + b)^4, we then would have the following:
*We would use the 5th row and get:
[tex](a+b)^4=a^4+4a^3b+6a^2b^2+4ab^3+b^4[/tex][Pascal's triangle expands to infinity. So, you in theory can manually expand any binomial at any power, but for big numbers, it will take a long time]
***
In our case, the binomial was:
[tex](x+9)^3[/tex]And, its respective expansion is:
[tex](x+9)^3=x^3+3x^2(9)+3x(9)^2+9^3[/tex][tex]=x^3+27x^2+243x+729[/tex]As the value of cosx approaches 1 and the value of sinx approaches 0, the value of cotx approaches infinity. True or false?
Recall that:
[tex]\cot \text{ x=}\frac{\cos x}{\sin x}[/tex]Therefore as sin x approaches 0 and cos x approaches 1, the value of cot x approaches infinity.
Answer: True.
If f(x)=x²+5 and g(x)=3x, find (f . g)(x) and (g . f)(x).
(f . g)(x)= ____
(Simplify your answer.)
The value of the functions are;
(f. g)(x) = 9x² + 5
(g . f)(x) = 3x² + 15
What is a function?A function can be defined as a law, rule or expression showing the elaborate relationship between two variables in an expression or equation.
The variables are;
The dependent variableThe independent variableGiven the functions;
f(x)=x²+5g(x)=3xTo determine (f .g)(x), we substitute the value of g(x) as x in the function, we have;
(g)(x) = (3x)² + 5
expand the bracket
(g)(x) = 9x² + 5
To determine (g . f )(x), substitute the value of x as fx)
(g . f)(x) = 3(x² + 5)
expand the bracket
(g . f)(x)= 3x² + 15
Hence, the functions are 9x² + 5 and 3x² + 15
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Which of the following scatterplots do not show a clear relationship and would not have a trend line?
Group of answer choices
The scatterplot that do not show a clear relationship and would not have a trend line is: graph B.
What is a trend line?A trend line is also referred to as a line of best fit and it can be defined as a statistical or analytical tool that is commonly used in conjunction with a scatter plot, in order to determine whether or not there's any association (correlation) between data points.
In Mathematics, there are different types of trend line and these include the following:
Linear trend line.Exponential trend line.Polynomial trend line.Logarithm or Natural logarithm trend line.Power trend line.Moving average trend line.By critically observing the scatter plot (see attachment) which models the data in the given table, we can reasonably and logically deduce that the data points in graph B are scattered around and as such, it does not illustrate a clear relationship (pattern).
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K 370 45° Which equation can be used to find the value of k? 37° - K +45º = 180° 37° + k +45º = 180° 37" + k = 45° 180° 37° -45° - 180°
The sum of angle on a straight line is always 180 degree.
Determine the equation for the angle.
[tex]k+37+45=180[/tex]When twenty is reduced by one-third of a number, the result is 19. Find the number.
Answer:
x = 3
Step-by-step explanation:
When twenty is reduced by one-third of a number, the result is 19. Find the number.
20 - 1/3x = 19
subtract 20 to both sides:
20 - 1/3x - 20 = 19 - 20
-1/3x = -1
multiply both sides by -3:
-3(-1/3x) = -1(-3)
x = 3
An FICA tax of 7.51% and an SDI deduction of 1.2% are charged against
an employee's wages. If her total monthly wages were $1538.46, what
would her paycheck be after FICA and SDI deductions as well as
withholding tax deductions of $245.80?
The employee's paycheck after FICA and SDI deductions as well as
withholding tax deductions is $1158.65.
What is FICA?FICA is a federal payroll tax in the US. It is taken out of every paycheck and stands for the Federal Insurance Contributions Act. Your nine-digit number enables Social Security to precisely record your self-employment or insured wages. You accrue credits for Social Security benefits as you work and pay FICA taxes.
Employee monthly salary= $1538.46FICA calculation= 7.51% of $1538.46= $115.54SDI calculation= 1.2% of $1538.46= $18.47Employee final paycheck= Monthly wage - FICA - SDI - Tax deductions.$1538.46 - $115.54 - $18.47 - $245.80= $1158.65The final monthly paycheck of the employee after deducting all taxes is $1158.65.
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(2a) Multiple Choice: Place the letter of the correct answer on the answer line to the right:
For which of the following values of k will the equation have infinite solutions?
4(4x + 1) = k(8x + 2)
(a) 4
(b) 8
(c) 2
(d) 1
(2b) Using your answer from Part (2a) replace the value you selected in the equation below. Then solve the
equation and show that it will, in fact, yield infinite solutions.
4(4x+1)=k(8x + 2)
For k=2 for infinite solutions.
What is 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. LHS = RHS is a common mathematical formula.
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:
4(4x + 1) = k(8x + 2)
Now, the equation should have infinite solutions
In consider the situation then we must put value of k such that LHS part become Equal to RHS.
Now, take k=2
4(4x + 1) = k(8x + 2)
LHS: 4(4x+1)= 16x+ 4
RHS: 2(8x+ 2)= 16x+ 4
Hence, k=2 for infinite solutions.
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The half-life of silicon-32 is 710 years. If 50 grams is present now, how much will be present in 700 years?(Round your answer to three decimal places.)A) OB) 25.245C) 0.054D) 46.697
In this type of question, we will use the exponential equation
[tex]y=a(b)^x[/tex]Where:
a is the initial amount
b is the factor of growth or decay
Since it is a half-life, then
b = 1/2 = 0.5
Since it is now 50 grams, then
a = 50
Since x is the number of years, then
x = 700
Substitute them in the rule above
[tex]\begin{gathered} y=50(0.5)^{700} \\ y=0 \end{gathered}[/tex]It will be representing 0 grams after 700 years
The answer is A
Which graph represents the following function?
f(x) = |x|.
The graph of the function f (x) = |x| is shown in attached figure.
Hence, Option A is true.
What is mean by Modulus function?
The modulus function is the magnitude or absolute value of a positive or negative number. It is defined as y = |x| or f (x) = |x|
Where, f : R → R and x ∈ R.
This is also called the absolute value function.
Given that;
The modulus function is,
⇒ y = |x|
Now, The modulus function is,
⇒ y = |x|
Since, The function y = |x| is not differentiable at x = 0.
So, It break at point x = 0, and have all positive values of y.
Which is shown in image A.
Thus, The graph of function y = |x| is shown in attached figure.
Therefore, In the images;
⇒ Option A is true.
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Mal works at a photo gallery. He charges $50 for a large photo and $40 for a large frame. Sales tax is 5%. How much total tax will a customer pay on both?
Answer the questions to show how to write and simplify expressions that represent the problem.
1. One way to calculate the total tax is 0.05(50 + 40). Use the order of operations to evaluate this expression. Show your work. (2 points)
2. Use the distributive property to expand 0.05(50 + 40). (2 points)
3. Find the total tax using the expanded expression. Did you get the same answer as you did by evaluating the original expression? (3 points)
4. Which expression, the original expression or the expanded expression, involves finding the total cost first, then calculating the tax on that total? (3 points)
1. Using the order of mathematical operations, the values in brackets are added and multiplied to a product of $4.50 as the total tax.
2. Using the distributive property to expand the expression, 0.05(50 + 40) is 0.05 x 50 + 0.05 x40.
3. The total tax using the expanded expression is $4.50, the same product as when evaluating the original mathematical expression.
4. The original expression involves finding the total cost first before calculating the tax on the total.
What is the order of mathematical operations?The following is the order of mathematical operations:
ParenthesesExponentsMultiplicationDivision Addition Subtraction.1) The original expression, 0.05(50 + 40):
= 0.05 x 90
= 4.5
= $4.50
2) The expanded expression, 0.05(50 + 40)
= 0.05 x 50 + 0.05 x40
= 2.5 + 2.0
= 4.5
= $4.50
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Choose the best estimate for the quotient. - See image inserted
Answer:
≈0.694 or rounded to 0.7
Step-by-step explanation:
4.06/5.85≈0.694
Which equation could be represented by the number line?
An equation which could be represented by the number line is: D. -5 + (-1) = -6.
What is a number line?A number line simply means a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line can be used to compare or determine the difference between two numbers. Additionally, a number line typically increases in numerical value towards the right and decreases in numerical value towards the left.
From the number line shown above, we have:
Distance = -5 + (-1)
Distance = -5 - 1
Distance = -6.
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I dont understand the part "Would this be true if the numbers were-3, 5, -16, and -10?"
Yes, the numbers will be similar.
it will be true if the numbers were -3, 5, -16 and -10
Explanation:
The first list: -3, 5, 16 and -10
Arranging from least to greatest:
-10, -3, 5, 16
Arranging the same numbers from closest to zero to farthest to zero:
Let's use zero as our reference. Then start arranging towards the left and right side of it.
-10, -3, 0, 5, 16
Looking at the above: when we remove 0, we would have same answer as the arrangement from least to greatest:
-10, -3, 5, 16
The second list:
-3, 5, -16, -10
Arranging from least to greatest:
-16, -10, -3, 5
Arranging the same numbers from closest to zero to farthest to zero:
Let's use zero as our reference. Then start arranging towards the left and right side of it.
-16, -10, -3, 0, 5
Looking at the above: when we remove 0, we would have same answer as the arrangement from least to greatest:
-16, -10, -3, 5
Hence, fromt the above: if we arrange the same numbers from least to greatest and from closest to zero to farthest to zero, we would arrive at the same result.
Using the graphs what are the solutions to the following systems
The solution to the system is the intersection of the graphs.
From the problem, the intersection is at (-3, 2)
The answer is (-3, 2)
I need help with this practice problem solving in trigonometry
The secant function is the reciprocal of the cosine function.
We can evaluate trigonometric functions of angles outside the first quadrant using reference angles as we have already done with the sine and cosine functions. The procedure is the same:
Find the reference angle formed by the terminal side of the given angle with the horizontal axis. The trigonometric function values for the original angle will be the same as those for the reference angle, except for the positive or negative sign, which is determined by x– and y-values in the original quadrant. (Figure) shows which functions are positive in which quadrant.
An even function is one in which f(-x) = f(x)
An even function is one in which f(-x) = - f(x)
Cosine and secant are even:
[tex]\begin{gathered} \cos (-t)=\cos (t) \\ \sec (-t)=\sec (t) \end{gathered}[/tex]Therefore from the drop down the correct answer : secant function is EVEN
The half-life of radium is 1690 years. If 50 grams are present now, how much will be present in 800 years?
In order to determine the amount of radium after 800 years, use the following formula:
[tex]N=N_oe^{-\lambda t}[/tex]where,
N: amount of radium after t years = ?
No: initial amount of radium = 50g
λ: decay constant
t = 800
The decay constant is calculated by using the following expression:
[tex]\lambda=\frac{ln2}{t\frac{_1}{2}}=\frac{ln2}{1960}\approx3.5*10^{-4}[/tex]where t1/2 = 1960 is the half-life.
Now, by replacing λ, No and t = 800 you obtain:
[tex]N=50e^{-(3.5*10-4)(800)}\approx37.68g[/tex]Hence, after 800 years there are approximately 37.68g of uranium
Marlene decided to buy 2 bags of apples weighing 3 14 pounds each, instead of 3 bags weighing 2 25 pounds each. Did she end up with more apples or fewer apples by buying the bigger bags?To find the total weight of 2 bags of apples weighing 3 14 pounds, multiply. 2 × 3 14 = To find the total weight of 3 bags weighing 2 25 pounds, multiply. 3 × 2 25 = She ended up purchasing apples by buying the bigger bags.
Answer:
She ended up with fewer apples by buying the bigger bags.
Explanation:
The total weight of 2 bags of apples weighing 314 pounds each is equal to:
2 x 314 = 628 pounds
At the same way, the total weight of 3 bags weighing 223 pounds each is:
3 x 225 = 675 pounds
Since 628 pounds is less than 675 pounds, Marlene ended up with fewer apples by buying the bigger bags
Justin has $7.50 more than Eva, and Emma has $12 less than Justin. Together, they have a total of $63.00. Write an equation to determine how much money each person has.
let j be justin, e for Eva and m for Emma. We get
[tex]\begin{gathered} j+e+m=63 \\ j=e+7.5 \\ m=j-12=e+7.5-12=e-4.5 \end{gathered}[/tex]so we get that, replacing all the variables
[tex]\begin{gathered} e+7.5+e+e-4.5=63 \\ 3e+3=63 \\ 3e=60 \\ e=20 \end{gathered}[/tex]so we get that Eva has $20. therefore Justin has $27.5 and Emma has $15.5
I solved this and think the range is: y>=3.Did I solve correctly?
Notice that
[tex]\begin{gathered} x^2\ge0,x\in\Re \\ \Rightarrow x^2+3\ge3,x\in\Re \\ \Rightarrow f(x)\ge3,x\in\Re \end{gathered}[/tex]Therefore, the range of the function is f(x)>=3, or [3,infinite)
A line passes through the point (-4, 1) and has a slope of -2.
Write an equation in slope-intercept form for this line.
Answer:
y= -2x -7
Step-by-step explanation:
The equation of a line in slope-intercept form is given by y= mx +c.
m= slopec= y-intercept
Given that the slope is -2, we can substitute m= -2 into the equation.
y= -2x +c
The value of c can be found by substituting a point in which the line passes through into the equation. In this case, the point is (-4, 1).
y= -2x +c
When x= -4, y= 1,
1= -2(-4) +c
1= 8 +c
Subtract 8 on both sides:
c= 1 -8
c= -7
Substituting c= -7 into the equation:
y= -2x -7
Optional step:
To check our answer, we can substitute one coordinate and see if the other coordinate is the same as the given coordinate. For example, let's substitute the x-coordinate of -4 into the equation.
y= -2(-4) -7
y= 8 -7
y= 1
Since the y-coordinate is indeed 1, the equation above is correct.
Additional reading:
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Benny had 49 books. He sold
15 at a garage-sale. He used
the money he earned to buy 7
more books. How many books
does Benny have now?
Answer: 41
so he has 49 books and he sold 15 so its 49-15= 34 so he bought 7 more books so its 34+7=41
Step-by-step explanation:
Have great day
Write two decimals that are equivalent to the given decimal 3,200
The two equivalent expression of the decimal 3.200 is 3200/1000 and 3.2
What is defined as the decimals?A decimal is a number with a whole as well as a fractional part. Decimal numbers are between integers as well as represent numeric values for whole plus some fraction of a whole. When we divide a whole in to the smaller parts, we get decimals. A decimal number has two parts: a whole number component and a fractional component. The decimal place value system is identical to the whole number value system for the entire part of a decimal number. However, as we move to the right after the decimal point, we get the fractional part of a decimal number.For the given question, the stated decimal is;
3.200
Removing point will be;
3200/1000 is the equivalent expression.
Divide numerator an denominator by 100 .
32/10 = 3.2 is also the equivalent expression of 3.200.
Thus, the two equivalent expression of the decimal 3.200 is 3200/1000 and 3.2.
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The correct question is-
Write two decimals that are equivalent to the given decimal 3.200
Find the equation of the parabola that has a vertex at (2,0) and a y-intercept of (0,12).Question 19 options:A) y = 3(x + 2)2B) y = (x – 2)2C) y = (x + 2)2D) y = 3(x – 2)2
SOLUTION
Equation of a parabola is given by the equation
[tex]y=a(x-h)^2+k[/tex]Where (h, h) are the coordinates of the vertex.
From the question given, the vertex is (2, 0)
So, h = 2, k = 0.
The y-intercept is given as (0, 12).
So, this means that x = 0 and y = 12
Substituting the values for h, k, x and y into the equation we have
[tex]\begin{gathered} y=a(x-h)^2+k \\ \\ 12=a(0-2)^2+0 \\ \\ 12=a\times-2^2+0 \\ \\ 12=4a \\ \\ a=\frac{12}{4} \\ \\ a=3 \end{gathered}[/tex]Now, let's substitute the value of a into the equation to get equation for the parabola.
This becomes
[tex]\begin{gathered} y=a(x-h)^2+k \\ \\ y=3(x-2)^2+0 \\ \\ y=3(x-2)^2 \\ \\ \end{gathered}[/tex]If a costume designer takes 20 hours to make 16 costumes, at what rate per hour are costumes being made?
Answer:it takes 1 hor 25 minutes to make a costume
Step-by-step explanation:
20 divided by 16 =1.25
Great evening to you all, I need help with this math problem please
AA (or AAA) or Angle-Angle Similarity
If any two angles of a triangle are equal to any two angles of another triangle, then the two triangles are similar to each other.
We do not have 3 angles.
SAS or Side-Angle-Side Similarity
If the two sides of a triangle are in the same proportion of the two sides of another triangle, and the angle inscribed by the two sides in both the triangle are equal, then two triangles are said to be similar.
We have two sides and 1 angle. But, two sides of a triangle are not in the same proportion of the two sides of another triangle
SSS or Side-Side-Side Similarity
If all the three sides of a triangle are in proportion to the three sides of another triangle, then the two triangles are similar.
Letter D
determine if the following sequence is Arithmetic if so what is the common difference -6 -2 2 6
We are given the following series
-6, -2, 2, 6
Common difference = last term - first term
For the first two terms
The common difference is calculated as
Last term - first term
Last term = -2
First term = -6
Common difference = -2 - (-6)
= -2 + 6
common difference = 4
Common difference = 2 - (-2)
common difference = 2 + 2
Common difference = 4
Last two terms
common difference = 6 - 2
Common difference = 4
The common difference for this sequence is 4
The sequence is arithmetic.
Find the result when 60 is increased by 40%.
Given:
The number is 60.
Aim is to find the result when 60 is increased by 40%.
First calculate 40% of 60,
[tex]\frac{40}{100}\times60=24[/tex]Now, add the amount 24 in 60.
[tex]24+60=84[/tex]Answer: 84 is a 40% increase of 60.