A perpendicular bisector is a segment which intersects another segment on its midpoint and with a right angle.
First, we have to find the midpoint between X(-9,1) and Y(3,5), as follows
[tex]\begin{gathered} M=(\frac{-9+3}{2},\frac{1+5}{2}) \\ M=(\frac{-6}{2},\frac{6}{2}) \\ M=(-3,3) \end{gathered}[/tex]This means the perpendicular bisector must pass through (-3,3). Now, with the given points we find the slope of XY
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{5-1}{3-(-9)}=\frac{4}{3+9}=\frac{4}{12} \\ m=\frac{1}{3} \end{gathered}[/tex]Then, we apply the rule of perpendicularity to find the slope of the perpendicular bisector.
[tex]\begin{gathered} m_1\cdot m=-1 \\ m_1=\frac{-1}{m} \\ m_1=-\frac{1}{\frac{1}{3}}=-3 \end{gathered}[/tex]Now, we use the slope-point formula to find the equation for the perpendicular bisector.
[tex]y-y_1=m(x-x_1)[/tex]Where we replace the slope -3 and the point (-3,3).
[tex]\begin{gathered} y-3=-3(x-(-3)) \\ y-3=-3x-9 \\ y=-3x-9+3 \\ y=-3x-6 \end{gathered}[/tex]Therefore, the right answer is C.What is the slope of the line through (-4,2) and (3, -3)? Choose 1 answer: А) 7 5 (В 7 5 5 7 1 D 5 7
slope = (change in y)/ change in x
[tex]undefined[/tex]What is the mass of 2 litre of water
Answer: 2 kg
Step-by-step explanation:
Find the exact value by using ahalf-angle formula.[?] --cos 75°
Answer::
[tex]\cos 75\degree=\frac{\sqrt[]{2-\sqrt[]{3}}}{2}[/tex]Explanation:
By the half-angle formula:
[tex]\cos \mleft(\frac{\theta}{2}\mright)=\pm\sqrt[]{\frac{1+\cos\theta}{2}}[/tex]Let θ=150°, therefore:
[tex]\begin{gathered} \cos (\frac{150\degree}{2})=\sqrt[]{\frac{1+\cos150\degree}{2}} \\ \cos (150)\degree=-\cos (180\degree-150\degree)=-\cos 30\degree \\ \implies\cos (\frac{150\degree}{2})=\sqrt[]{\frac{1+\cos150\degree}{2}}=\sqrt[]{\frac{1-\cos30\degree}{2}} \end{gathered}[/tex]Now, cos 30 = √3/2, thus:
[tex]\begin{gathered} =\sqrt[]{\frac{1-\frac{\sqrt[]{3}}{2}}{2}} \\ \text{Multiply both the denominator and numerator by 2} \\ =\sqrt[]{\frac{2-\sqrt[]{3}}{4}} \\ =\frac{\sqrt{2-\sqrt[]{3}}}{\sqrt{4}} \end{gathered}[/tex]The exact value of cos 75° is:
[tex]\cos 75\degree=\frac{\sqrt[]{2-\sqrt[]{3}}}{2}[/tex]Find the x-and y-intercepts.21x + 3y = -63
to find the x intercept, we need to replace y by 0, so we get
[tex]\begin{gathered} 21x+3\cdot0=-63 \\ 21x=-63 \\ x=\frac{-63}{21}=-3 \end{gathered}[/tex]to find the y-intercept we need to replace x by 0
[tex]\begin{gathered} 21\cdot0+3y=-63 \\ 3y=-63 \\ y=\frac{-63}{3}=-21 \end{gathered}[/tex]Determine which set of side measurements could be used to form a triangle. 12, 23, 7 10, 7, 2 8, 3, 11 5, 11, 8
Based on the triangle inequality theorem, the set of side measurements that could be used to form a triangle is: D. 5, 11, 8.
What is the Triangle Inequality Theorem?The triangle inequality theorem states that three set of side measurements, a, b, and c would form a triangle if a + b > c, that is, the sum of any of two sides should be greater than the third side.
The set of side of measurements 5, 11, 8 will form a triangle because:
5 + 11 > 8 ⇒ 16 > 8
5 + 8 > 11 ⇒ 13 > 11
8 + 11 > 5 ⇒ 19 > 8
The other set of side of measurements do not conform to this criterion set by the triangle inequality theorem, therefore, the only set of side measurements that will form a triangle is: D. 5, 11, 8.
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Answer:
D.
5, 11, 8
Step-by-step explanation:
Given the polynomial expression 3x2 + 3bx - 6x - 6b, factor completely.
(3x-6)(x - b)
(x-2)(x + b)
3(x-2)(x + b)
3(x + 2)(x + b)
The factors of the given polynomial is 3(x-2)(x+b). Therefore, option C is the correct answer.
The given polynomial expression is 3x² + 3bx - 6x - 6b.
What are factors of polynomial?The factors are the polynomials which are multiplied to produce the original polynomial.
The factors of given polynomial can be find using grouping method, that is
(3x² + 3bx) - 6x - 6b
=3x(x+b)-6(x+b)
=(x+b)(3x-6)
=3(x-2)(x+b)
The factors of the given polynomial is 3(x-2)(x+b). Therefore, option C is the correct answer.
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Find the domain and range of the function represented by the graph.
543
domain: -4 ≤ x ≤ 2.
O domain: -4 < x <2.
O domain: -4 ≤ x ≤ 4.
O domain: -4 <
2
range: -4 Sy≤4
range: -4
range: -4 Sy≤2
x < 4. range: -4
Answer:
c
Step-by-step explanation:
c
5 A salesman sold $1,500 worth of
merchandise and received $75 in
commission for the sale.What percent of the sale was commission
Answer:20%
Step-by-step explanation:
1500/75=20(%)
Create an example of a difference of
polynomials and explain how to simplify
your expression.
(9x² + 8x) - (2x²+ 3x) = 7x² + 5x .
By simplifying we get x( 7x + 5) .
What is polynomial ?Polynomials are algebraic expressions with variables and coefficients. Variables are also known as indeterminates. For polynomial expressions, we can perform arithmetic operations such as addition, subtraction, multiplication, and positive integer exponents, but not division by variable.The variables and exponents of polynomials do not change when they are subtracted. Only their coefficients are subject to change. This ensures that the difference has variables and exponents that are already classified as polynomials. As a result, the difference is always a polynomial.Consider two polynomials,
(9x² + 8x) and (2x² + 3x)
The difference of polynomials is,
(9x² + 8x) - (2x²+ 3x)
9x² + 8x - 2x²+ 3x
= 7x² + 8x - 3x
= 7x² + 5x
Simplifying we get ,
taking x common,
= x( 7x + 5) .
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11 ^ (5/16) + 4 ^ (1/16)
Answer:
3.20611579...
Step-by-step explanation:
does anyone mind helping me?
For the given expression √25 = ∛125. As, 5 is equal to 5.
What is termed as the square root and cube root?Square root: To discover the square root of such a number, look for a number that, when multiplied by itself, yields the original number.For the given question;
Square root of 25 i.e, √25
To identify the square root of 25, determine the number because when multiplied by itself yields 25. The square root of 25 is thus 5.
Cube root: To locate the cube root of a number, look for a number so when multiplied on its own twice yields the original number. In other words.To find the cube root of 125, determine the number that when multiplied on its own twice yields 125.
The cube root of 125 is thus 5, because 5×5×5 = 125.
The radical sign with such a small three (named the index) above and on the left is the symbol for cube root.
Thus, both the values are equal.
√25 = ∛125.
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Question 6 is the target pls helo
Answer:
80°Step-by-step explanation:
the angles in a triangle add up to 180
2x + 3x + 4x = 180
(combine like terms)
9x = 180
(divide both sides by 9 to find out what x is)
x = 20
so now we know
(2x)° = 40°
(3x)° = 60°
(4x)° = 80°
What is the measure of the largest angle in the triangle shown above?
80°Write the equation in standard form for the circle passing through (2,3) centered at the origin
Given
coordinates (2, 3) and centre points (0,0)
Find
Equation of a circle
Explanation
As we know the standard equation for a circle with centre (h , k ) and r is a radius
[tex](x-h)^2+(y-k)^2=r^2[/tex]since, center is (0 , 0) , the equation becomes
[tex]x^2+y^2=r^2[/tex]Now, we find the value of radius , it is can find by using the pythagoras theorem,
[tex]r^2=2^2+3^2=4+9=13[/tex]so,
[tex]x^2+y^2=13[/tex]Final Answer
The equation for a circle passing through (2, 3) is
[tex]x^2+y^2=13[/tex]I dint know the answers to this and its SUPER important I get it right.
A. The corresponding angles of triangles are coungrent (YES)
B. The triangles have the same shape (YES)
C. The triangles have the same size (YES)
D. The corresponding sides of the triangles are congruent (YES)
Determine the average rate of change for 3x²-3x+1 over the interval [-5, 5].
Answer: The average rate of change is −3.
Step-by-step explanation:
The average rate of change f(x) on the interval [a,b] is (f(b)−f(a))/(b−a)
a=−5 , b=5, f(x)=3x2−3x+1.
(f(b)-f(a))/(b-a)= (1-3(5)+3(5)^2-(1-3(-5)+3(-5)^2)) / (5-(-5)) = -3
Kali just started a new sales floor job to save for college. She earns 15.75 plus a flat fee of 50 . She wants to earn between 200 and 400 . The following inequality represents her earning potential
200 ≤ 15.75x + 50 ≤ 400 Solve the inequality PLEASE HELP ASAP
!!
Kali will have to work a minimum of 10 hours and a maximum of 22 hours to earn between 200 and 400. The inequality representing the solution will be 9 ≤ 15.75x ≤ 22.
In the question, it is stated that Kali earns $15.75 and a flat fee 0f 50. She wants to maintain her earnings between 200 and 400. Potential earning will be 'x'. The equation representing the earnings is 200 ≤ 15.75x + 50 ≤ 400. We will have to solve the inequality and find out the value for x.
=> 200 ≤ 15.75x + 50 ≤ 400
Subtracting 50 from the equation,
=> 150 ≤ 15.75x ≤ 350
Dividing the equation by 15.75
=> 9.52 ≤ x ≤ 22.22
So, here x lies between 9.52 and 22.22. After rounding off we get range 10 and 22.
Hence, the solution for the inequality is 9.52 ≤ x ≤ 22.22
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In 2016, there were 35,867 burger restaurants worldwide, with 13,232 of them located in a country. Determine the percent of burger restaurants in that country in 2016Approximately what percent ?
we have that
35,867 ------> represents 100%
Applying proportion
Find out how much percentage represents 13,232
100/35,867=x/13,232
solve for x
x=(100/35,867)*13,232
x=36.89% ------> 37%
Sherry has 40% as much money as Anna. Anna has $80?
Sherry has $112.
bo
Answer: Sherry has $112
P(6,23), Q (13,28)
Distance=?
Midpoint=?
Answer:
Step-by-step explanation:
distance between the two points:
[tex]\sqrt{ (x_2-x_1)^{2} +(y_2-y_1)^2[/tex]
[tex]\sqrt[/tex](13-6)²+(28-23)²
√(7)²+(5)²
√49+25
√74
distance: 8.6cm
midpoint=
[tex](\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2} )[/tex]
(6+3/2,23+28/2)
(19/2,51/2)
(9.5,25.5)
Which equation is the equation of the line, in point-slope form, that has a slope of 2 and passes through the point (-8, 1)?
Oy-8 -2(x-1)
Oy-1=2(2-8)
Oy-1=2(x+8)
Oy-8=2(x+1)
The slope of 2 and passes through the point (-8,1) : y-1 = 2(x+8)
what is slope ?
The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
The standard equation of a line in point slope form is expressed as;
so ,
y-y0 = m(x-x0)
m is the slope
(x0, y0) is the point
Given
Slope m = 5 (assumed value)
Point (-8,1)
Substitute the given data's into the formula
y -1 = 5(x-(-8))
y-1 = 5(x+8)
Hence the required equation is y-1 = 5(x+8)
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Which expression shows 42+6 rewritten as a product of the greatest common factor and sum of two numbers with no common factor?
Answer:
7(1 + 6)
Step-by-step explanation:
in the diagram below AD||EH I=54 and FBC=44. find CGH
Given,
angle I = 54 degrees
angle FBC = 44 degrees
Recall, the sum of the angles in a triangle is 180 degrees. This means that for triangle BIC,
angle B + angle I + angle BCI = 180 degrees
54 + 44 + angle BCI = 180
angle BCI + 98 = 180
angle BCI = 180 - 98 = 82(sum of angles in a triangle)
Since lines AD and EH are parallel,
angle BCI and angle FGI are corresponding angles(They have similar positions and lie on the same side of the transversal, CI)
Thus,
angle FGI = 82(corresponding angles)
angle CGH and angle
angle CGH and angle FGI are vertically opposite angles. Vertically opposite angles are equal. Thus,
angle CGH = 82 degrees
The reason is 'vertically opposite angles'
The mean height of an adult giraffe is 19 feet. Suppose that the distribution is normally distributed with standard deviation 0.9 feet. Let X be the height of a randomly selected adult giraffe. Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N(19,0.9)b. What is the median giraffe height? 19 ft.c. What is the Z-score for a giraffe that is 22 foot tall? d. What is the probability that a randomly selected giraffe will be shorter than 18.9 feet tall? e. What is the probability that a randomly selected giraffe will be between 19.6 and 20.1 feet tall? f. The 70th percentile for the height of giraffes is ft.
I am stuck on the graphing portion of this question, would it be formatted like A or like B?
To determine which option is a representation of the graph we need to make the numer line analysis; to make it we need to notice that the functions has zeros at the points:
[tex]\begin{gathered} x=2 \\ x=4 \\ x=-3 \\ x=0 \end{gathered}[/tex]once we know this we divide the number line in the following intervals:
now we need check the sign of the function in each interval, to do this we choose a value in them.
For the first interval let's take x=-4, then we have:
[tex]\begin{gathered} f(-4)=-(-4)^3(-4-2)^2(-4-4)(-4+3) \\ f(-4)=-(-64)(36)(-8)(-1) \\ f(-4)=(64)(36)(8) \\ f(-4)=18432 \end{gathered}[/tex]From the last expression we notice that the value of the function is positive at this point. Hence the firts interval have positive values for the function.
For the second interval let's take x=-1, then we have:
[tex]\begin{gathered} f(-1)=-(-1)^3(-1-2)^2(-1-4)(-1+3) \\ f(-1)=-(-1)(9)(-5)(2) \\ f(-1)=-90 \end{gathered}[/tex]From the result we conclude that the function is negative in this interval.
For the third interval, let's take x=1, we have:
[tex]\begin{gathered} f(1)=-(1)^3(1-2)^2(1-4)(1+3) \\ f(1)=-(1)(1)(-3)(-4) \\ f(1)=12 \end{gathered}[/tex]From the result we conclude that the function is positive in this interval.
For the fourth interval, let's take x=3. then we have:
[tex]\begin{gathered} f(3)=-(3)^3(3-2)^2(3-4)(3+3) \\ f(3)=-(27)(1)(-1)(6) \\ f(3)=162 \end{gathered}[/tex]Then the function is positive in this interval.
Finally, for the fifth interval let's take x=5, then we have:
[tex]\begin{gathered} f(5)=-(5)^3(5-2)^2(5-4)(5+3) \\ f(5)=-(125)(9)(1)(8) \\ f(1)=-9000 \end{gathered}[/tex]Then the function is negative in the last interval.
Hence the line analysis is:
The y-intercept of the function happens when x=0, then we have that:
[tex]\begin{gathered} f(0)=-(0)^3(0-2)^2(0-4)(0+3) \\ f(0)=0 \end{gathered}[/tex]Therefore the y-intercept of the function is 0.
Once we know the information from the line analysis and the y-intercept of the function we conclude that the sketch of the graph is option B.
Two graphs of the function (with different values for the y-axis) are shown below:
This graphs confirm that option B is an approximate sketch of the graph.
The Organic Produce Stand sells bundles of tomatoes ($8) and bunches of green beans ($5). If
yesterday's total sales were $464 and people bought 3 times as many tomato bundles as green bean
bunches, how many bundles of tomatoes were sold?
Therefore, number of bundles of tomatoes which was sold as selling price are: 225.5
What is selling price or sale?
In mathematics, the term selling price can be explained with the help of profit which states, as the amount which is on the commodity and in the form of standard price called selling price. For the profit, the amount of the commodity can be designed by the shopkeeper which is bigger amount as per the cost price.
According to the question, the organic producer sells bundle of tomatoes as the selling price of $8 and the bunches of green beans as $5.
Total sales amount is: $464
In this, people bought three times more tomatoes as green bean bunches.
Let us assume tomatoes be 'x' and green beans be 'y'
3x + y = $464
x + y = $13
⇒ 2x = 451
⇒ x = 225.5 dollars
Therefore, number of bundles of tomatoes which was sold as selling price are: 225.5 dollars
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A science class is going on a field trip to a museum. The school hires vans to take the students to the museum. Each van can hold a maximum 11 people including
passengers and driver
If there are a total of 30 students going on the field trip, which inequality represents the number of vans, V. that will be needed?
Answer: 3 Vans are needed.
Step-by-step explanation:
There are 30 students so already you need 3 vans, if you only have 2 vans, you will be leaving behind 10 students so regardless you need a 3rd van. with 3 vans you can hold 33 people. 30 students+ 3 drivers=33 people.
The inequality that represents the number of vans for the given case is V ≤ 30/11.
What is linear inequality?Linear inequality refers to the relation between a linear algebraic expression to some known value that contains inequality sign.
Unlike a linear equation it can have a range of values inside an interval.
Suppose the number of vans be V.
The number of students for each van is 11.
And, the total number of students is 30.
Now, the inequality for the number of vans can be written as,
11V ≤ 30
⇒ V ≤ 30/11
Hence, the inequality for the number of vans is given as V ≤ 30/11.
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Why is a third-degree polynomial function with a negative leading coefficient not appropriate for modeling non-negative real-world phenomena over a long period of time?
Given:
A third-degree polynomial function with a negative leading coefficient not appropriate for modeling non-negative real-world phenomena over a long period of time.
Explanation:
Because a third-degree polynomial function with a negative leading coefficient is always going to turn negative as the independent variable increases.
That is, the end behavior of the graph will always be negative on the right.
Final Answer:
Because a third-degree polynomial function with a negative leading coefficient is always going to turn negative as the independent variable increases.
That is, the end behavior of the graph will always be negative on the right.
You are an apprentice plumber for Pointer Plumbing. You are earning an annual salary of $21,060. You are married and claim 3 allowances. What amount in withheld from your weekly pay for federal income tax?
If you are an apprentice plumber earning an annual salary of $21,060, and you lay claim to 3 allowances, the amount that will be withheld from your weekly pay for federal income tax is: $7.
How much will be witheld from your weekly pay?To obtain the correct amount to be paid, we need to use the table provided by the IRS. First note that there are 52 weeks in a year, so we need to divide your annual earnings by the total number of weeks in a year.
So, 21060/52 = $405
When we look at the table to see the chart for a person who has a weekly wage of 400 - 410, and lays claim to three allowances, we will see that the right amount that such an individual is meant to pay is $7.
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Fluff and Fold charges $2.25 for each load of laundry. Draw the graph of the proportional relationship between the two quantities, where x is the number of loads of laundry and y is the total cost
The graph of the proportional relationship between the two quantities is attached below.
It is given that the company Fluff and Fold charges $2.25 for each load of laundry.We are also given that "x" is the number of loads of laundry and "y" is the total cost.From the above data, we see that the cost will be as high as the number of loads."y" is directly proportional to "x".To remove the proportionality and make it an equation, we need a constant that represents the cost of a single load.y = 2.25xWe can easily plot this equation on the graph.The graph is attached below.To learn more about equations, visit :
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Define a variable, set up an inequality, and solve. Only algebraic solutions are accepted. “Mikayla has three savings accounts that she distributes her money into each paycheck. If she wishes to put at least $80 into each account this paycheck, how much money must she make?”
Solution:
Note that Mikayla has three savings accounts that she distributes her money into each paycheck. Now, let us denote by x the money in the accounts, thus if she wishes to put at least $80 into each account this paycheck, this means that the total amount of money must be greater than or equal to 3(80). This is equivalent to say:
[tex]3(80)\leq x[/tex]this is equivalent to:
[tex]240\leq x\text{ }[/tex]so that, we can conclude that the correct answer is:
[tex]x\ge240[/tex]