Answer:
(a) k = 4
(b) y = - 2x + 9
Step-by-step explanation:
x2-x1, y2-y1
= 3-2, 3-5
= 1,-2
3,3 + 1,-2 = (4,1)
x=4
The lines below are perpendicular.
the slope of the solid line iS 4, what is the slope of the dashed line?
Answer:
[tex]\frac{-1}{4}[/tex]
Step-by-step explanation:
Perpendicular lines have opposite reciprocal slopes. This means you change the sign and flip the numerator and denominator.
If the original slope is 4, the perpendicular slope is [tex]\frac{-1}{4}[/tex]
Darlene is building a rectangular fence. the length is 8 feet longer than the width. the perimeter of the rectangle is 76 feet. what is the length of the rectangle?
Answer:8 feet
Step-by-step explanation:
Jessica and her friend found some money under the couch. they split the money evenly, each getting $16.32. how much money did they find?
There is two of them each getting $16.32
So take the $16.32 × 2=$32.64
Which two of the following expressions can be simlified by using the Quotient of Powers Property?
Answer:
[tex]\frac{15x^{4}y^{3}}{5x^{3}} \ \ \text{and }\ -10x^{5}\div 2x^{3}y[/tex]
Step-by-step explanation:
the Quotient of Powers Property :
let a be a number where a ≠ 0
[tex]\frac{a^m}{a^n} = a^{m-n}[/tex]
……………………
[tex]\frac{15x^{4}y^{3}}{5x^{3}}[/tex]
[tex]= \frac{3 \times 5x^{3}\times x \times y^{3}}{5x^{3}}[/tex]
[tex]= \frac{3 \times x \times y^{3}}{1}[/tex]
[tex]= 3 x y^{3}[/tex]
=============
[tex]-10x^{5}\div 2x^{3}y[/tex]
[tex]= [-5 \times (2x^{3}) \times x^2] \div [(2x^{3}) \times y][/tex]
[tex]= -5 \times x^2 \div y[/tex]
[tex]= -5 x^2 \div y[/tex]
Does the graph represent a function? Why or why not?
A. No, because it fails the horizontal line test
B. Yes, because it passes the horizontal line test
C. No, because it fails the vertical line test.
•
D. Yes, because it passes the vertical line test.
Answer:
D.
Step-by-step explanation:
Yes, because it passes the vertical line test.
when the product of 15 and 40 is diveded by the sum of 15 and 45 what is the quotient
Answer:
The answer is 10Step-by-step explanation:
First, you have to multiply. 15x4=60. All you need to do is add a zero to that product. You will get 600. Product means the answer to a multiplication problem. That is why you would have to multiply to get your answer. Your answer to that part is 600. 15*40= 600. Then, you would do 45+15= 60. 600/60= 10. Your answer is 10.
Barrett works at an ice cream shop. the function f(x) represents the amount of money in dollars barrett earns per gallon of ice cream, where x is the number of gallons of ice cream he makes. the function g(x) represents the number of gallons of ice cream barrett makes per hour, where x is the number of hours he works. f(x) = 2x2 4 g(x) = the square root of three times x cubed find f(g(x)). f of g of x equals the square root of the quantity 6 times x to the fifth power plus 4 dollars over hour f of g of x equals the square root of the quantity 6 times x to the fifth power plus 4 gallons over hour f(g(x)) = 6x3 4 gallons over hour f(g(x)) = 6x3 4 dollars over hour
Amount of money earned per number of hours of work = [tex]f(g(x)) = 6x^{3} + 4[/tex]
What is a composite function?A composite function is generally a function that is written inside another function. Composition of a function is done by substituting one function into another function. For example, f [g (x)] is the composite function of f (x) and g (x). The composite function f [g (x)] is read as “f of g of x”.To evaluate a composite function f(g(x)) at some x = a, first compute g(a) by substituting x = a in the function g(x). Then substitute g(a) into the function f(x) by substituting x = g(a). In the same way, we can calculate g(f(a)) as well.
Required calculation -
Amount of money (the earning) per unit x = [tex]f(x) = 2x^{2} + 4[/tex]
Number of gallons of ice cream that Barrett makes per hour, where x is the number of hours he works = [tex]g(x) = \sqrt{3x^{3}}[/tex]
we are to find the composite function [tex]f(g(x))[/tex]
Substituting g(x) into the x of f(x), we find:
[tex]f(g(x)) = 2(\sqrt{3x^{3} } )^{2} + 4\\\\= 2(3x^{3} ) + 4\\= 6 x^{3} + 4[/tex]
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Answer:
f(g(x)) = 6x3 + 4 dollars over hour
Step-by-step explanation:
write a solution system for the inequality 3x-2>10
Answer:
x>4
Step-by-step explanation:
3x - 2 >10 add 2 to both sides
3x > 12 Divide both sides by 3
x >4
Answer:
[tex]x > \bf 4[/tex]
Step-by-step explanation:
To find a solution to this inequality, we have to rearrange this equation to make [tex]x[/tex] its subject:
[tex]3x - 2 > 10[/tex]
⇒ [tex]3x - 2 + 2 > 10 + 2[/tex] [Add 2 to both sides]
⇒ [tex]3x > 12[/tex]
⇒ [tex]\frac{3x}{3} > \frac{12}{3}[/tex] [Divide both sides by 3]
⇒ [tex]x > \bf 4[/tex]
Yu-xi draws a triangle with two angles measuring and . what is the measure, in degrees, of the third angle? 78 79 101 102
Considering the definition of a right triangle and its properties, the value of the third angle of a triangle with two angles measuring 79 degrees and 23 degrees is 78 degrees.
Triangle definitionA triangle is a polygon that is determined by three line segments called sides, or by three non-aligned points called vertices.
In other words, a triangle is a polygon made up of three sides, as well as three vertices and three interior angles.
One of the properties of any triangle is that the sum of the interior angles is equal to 180°.
Missing angle value in this caseIn this case, you know that:
One interior angle measures 79°.Another interior angle measures 23°.The sum of the interior angles is equal to 180°.So the value of the missing angle can be calculated by:
79° + 23° + missing angle = 180°
Solving:
102° + missing angle = 180°
missing angle= 180° - 102°
missing angle= 78°
Finally, the value of the third angle of a triangle with two angles measuring 79 degrees and 23 degrees is 78 degrees.
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Answer:
The answer is 78.
Step-by-step explanation:
Person above is right and I'm also taking the test!!
having trouble with this
Answer:
Step-by-step explanation:
13
-3p+6p
help simplify
Step-by-step explanation:
-3p+6p is 3p
-3 + 6 = 3
So when you simplify the equation you get 3p
A system of equations is shown:
4x = -3y + 17
3x - 4y = -6
What is the solution to this system of equations? (5 points)
(3,2)
(-3,-2)
(-2,-3)
(2,3)
Answer: (2;3).
Step-by-step explanation:
[tex]\displaystyle\\\left \{ {{4x=-3y+17} \atop {3x-4y=-6}} \right. \ \ \ \ \left \{ {{4x+3y=17\ |*4} \atop {3x-4y=-6\ |*3}} \right. \ \ \ \ \left \{ {{16x+12y=68} \atop {9x-12y=-18}} \right. \\Let's\ sum \ up\ these\ equations:\\25x=50\ |:25\\x=2.\\4*2=-3y+17\\8+3y=17\\3y=9\ |:3\\y=3.[/tex]
help me with this question
Answer: A) 23,00
Step-by-step explanation:
A=23,00
B=8,600
C=12,00
D=3,600
Let a_n be the integer obtained by writing all the integers from 1 to n from left to right. For example, a_3 = 123 and a_{11} = 1234567891011. Compute the remainder when a_44 is divided by 45.
Answer:
9
Step-by-step explanation:
The 79-digit number of interest can be formulated as a sum of shorter numbers whose remainders can be computed.
Expanded formThe expanded form of the number can be written as ...
a_44 = 01×10^78 +23×10^76 +45×10^74 +67×10^72 +89×10^70 +...
+10×10^68 +11×10^66 +... +43×10^2 +44×10^0
Powers of 10Each number except the last is multiplied by a power of 10. Powers of 10 modulo 45 are ...
10 mod 45 = 10
100 mod 45 = 10
This lets us conclude that any positive power of 10 mod 45 is 10.
Parts of the sumIn short, all of the multiplication by powers of 10 can be collapsed to a single multiplication by 10. Hence, the mod 45 value of a_44 will be ...
a_44 mod 45 = (((01 +23 +45 +67 +89) +10 +11 +12 +... +43)×10 +44) mod 45
= (((01 +23 +45 +67 +89) mod 45 + sum(10 .. 43) mod 45)×10 +44) mod 45
= (((225 mod 45) +(901 mod 45))×10 +44) mod 45
= ((0 +1)×10 +44) mod 45
Final valuea_44 mod 45 = 54 mod 45 = 9
__
Additional comment
The result can be confirmed by a suitable calculator.
__
The sum of the 34 numbers from 10 to 43 is the product of their average value (10+43)/2 = 26.5 and their number, 34. (26.5×34) = 901.
Answer: 9
Step-by-step explanation:
we can manually do this by dividing 1234567891011121314151617181920212223242526272829303132333435363738394041424344
on the calculator. I saw multiple hate comments on the answer above, and I wanted to test it manually - it still is 9.
Two events, a and b, are independent of each other. p(a)= and p(a and b)=. what is p(b) written as a decimal? round to the nearest hundredth, if necessary.
if two occurrences A and B are unrelated to one another. Then, 3/4 or 0.75 is the likelihood of event B.
What is probability?The field of mathematics known as probability studies numerical descriptions of the likelihood of an event occurring or of a statement being true.. The probability of an event is a number between 0 and 1, with 0 generally signifying the event's impossibility and 1 generally signifying its certainty.
What pair of events is referred to as an independent event?These occurrences are referred to as independent events when the occurrence or non-occurrence of one event has no bearing on the occurrence or non-occurrence of any other events.
Figuratively, we have:
If we have the following, two events A and B are said to be independent.
[tex]\mathrm{P}(\mathrm{A} \cap \mathrm{B})=\mathrm{P}(\mathrm{A}) \mathrm{P}(\mathrm{B})[/tex]
Events A and B happen apart from one another. P(A) = 1/6, while P(A and B) = 1/8.
The likelihood of the event B will then be.
[tex]\begin{aligned}&\mathrm{P}(\mathrm{A} \cap \mathrm{B})=\mathrm{P}(\mathrm{A}) \mathrm{P}(\mathrm{B}) \\&\mathrm{P}(\mathrm{B})=\frac{\mathrm{P}(\mathrm{A} \cap \mathrm{B})}{\mathrm{P}(\mathrm{A})} \\&\mathrm{P}(\mathrm{B})=\frac{1 / 8}{1 / 6} \\&\mathrm{P}(\mathrm{B})=\frac{6}{8} \\&\mathrm{P}(\mathrm{B})=\frac{3}{4}=0.75\end{aligned}[/tex]
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I understand that the question you are looking for is:
Two events, A and B, are independent of each other. P(A) = 1/6 and P(A and B) = 1/8. What is P(B) written as a decimal? Round to the nearest hundredth, if necessary.
The area of a circle of radius 10 units is equal to the surface area of a sphere of radius 5 units.
A. True
B.False
Explanation:
The area of the circle with radius 10 is...
A = pi*r^2
A = pi*10^2
A = 100pi
The surface area of the sphere with radius 5 is...
SA = 4pi*r^2
SA = 4pi*5^2
SA = 100pi
Both results are the same, so the claim is true. We can think of surface area as the amount of wrapping paper needed to cover the sphere.
2/13 = 0.153846 In the decimal above, 1 is the first digit in the repeating pattern. What is the 279th digit?
Answer:
F
Step-by-step explanation:
There are 6 digits in the repeating pattern.
279 / 6 = 46.5 remainder 3.
we care about the remainder as this is how many digits in. it is the 3rd digit in so is 3.
If you are playing a game using this spinner, what is the probability of not
landing on yellow or purple?
blue
green
yellow
orange
Your answer should be in the form of a fraction. Type it like this: 15/52.
Answer:
3/4
Step-by-step explanation:
Fraction of total area of the circle each color occupies in the spinner.
purple = 1/8
red = 1/4
orange = 1/8
yellow = 1/8
green = 1/4
blue = 1/8
Landing on yellow or purple: 1/8 + 1/8 = 1/4
Not landing on yellow or purple = 1 - 1/4 = 3/4
Under her cell phone plan, Sarah pays a flat cost of $69 per month and $4 per gigabyte. She wants to keep her bill at $83.80 per month. Write and solve an equation which can be used to determine gg, the number of gigabytes of data Sarah can use while staying within her budget.
Using a linear function, it is found that Sarah can use 3.7 gigabytes while staying within her budget.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Considering the flat cost as the y-intercept and the cost per gigabyte as the slope, the cost of using g gigabytes is:
C(g) = 4g + 69.
She wants to keep her bill at $83.80 per month, hence:
C(g) = 83.80
4g + 69 = 83.80
4g = 14.80
g = 14.80/4
g = 3.7.
Sarah can use 3.7 gigabytes while staying within her budget.
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Answer:
The other person is correct!
Step-by-step explanation:
Yes
i,dk how to do this pls help :)
Given the percentage taken off and the reduced price, the original price of the item is $142.
What was the original price of the item?Given the data in the question;
Percentage off the item = 20%Reduced price of the item = $113.60Original price of the item = ?The original price of the item is at 100%, if the 20% is taken off. The price is now at 80%.
Hence 80% of the original price will give the reduced price.
Let the original price be represented by x
80% × x = $113.60
We solve for x
80/100 × x = $113.60
80x/100 = $113.60
Cross multiply
80x = $11360
x = $11360/80
x = $142
Given the percentage taken off and the reduced price, the original price of the item is $142.
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Expand 10a(2a-7) pls its very urgent
Answer:
[tex]20a^2-70a[/tex]
Step-by-step explanation:
1) Expand by distributing terms.
[tex]10\times2a+10a\times-7[/tex]
2) Take out the constants.
[tex](10\times2)aa+10a\times-7[/tex]
3) Simplify [tex]10\times2[/tex] to [tex]20.[/tex]
[tex]20aa+10a\times7[/tex]
4) Use Product Rule:[tex]x^ax^b=x^{a+b}[/tex].
[tex]20a^2+10a\times-7[/tex]
5) Simplify [tex]10a\times-7[/tex] to [tex]-70a.[/tex]
[tex]20a^2-70a[/tex]
Thank you,
Eddie
Answer:
20a² - 70a
Step-by-step explanation:
(10a)(2a-7)
= 10a*2a + 10a*-7
= 20a² - 70a
Write an equation that represents the line
Use exact. Numbers
Answer soon please
Explanation to :an insurance agent is paid a salary of gh200 and a commission of 3% on all sales over gh2000 per month. if his total income in a particular month was gh530, what was the amount of his sales for that month
GH 13000 is the amount of his sales for that month.
how to find sales of the month?
total income = salary + commission
total income = GH530 (given)
salary = GH200 (given)
Commission is 3% on the sales above Gh2000 (given)
Let sales be x
total income = salary + commission
530 = 200+3%(x-2000)
530-200=0.03(x-2000)
330/.03=x-2000
11000=x-2000
x= 13000
total sales = GH13000
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A right pyramid with a square base has a base edge length of 24 feet and a slant height of 20 feet. a right pyramid with square base has a base edge length of 24 feet and slant height of 20 feet. what is the height of the pyramid?
The height of the pyramid is [tex]16ft.[/tex]
What does it mean by right pyramid?The centroid of the base sits just above the right pyramid. Oblique pyramids are non-right pyramids. A right pyramid is typically assumed to be a regular pyramid because it has a regular polygon base.
To find the height of the pyramid:
l=the slant height of the right pyramid.
b=the length side of the square base of the right pyramid.
h=the height of the right pyramid.
Pythagorean Theorem: [tex]l^{2} =h^{2} +(\frac{b}{2} )^{2}[/tex]
Solve:h
[tex]h^{2} =l^{2} +(\frac{b}{2} )^{2}[/tex]
[tex]h^{2} =20^{2} -12^{2}[/tex]
[tex]h^{2} =256[/tex]
[tex]h=16ft[/tex]
Therefore, The height of the pyramid is [tex]16ft.[/tex]
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Answer:
The height of the pyramid is 16ft
Step-by-step explanation:
find the discriminant of the following quadratic equation
x^-5x+3=0
The discriminant of the given quadratic equation as in the task content can be evaluated by means of the formula; D = b²-4ac and it's value is; 13.
What is the discriminant of the quadratic equation as given in the task content?According to the task content, it follows that the quadratic equation whose discriminant is to be determined is; x²-5x+3=0.
By comparison with the standard form equation of a quadratic graph which goes thus; ax²+bx +c = 0, in which case, the determinant is given by the expression; b² - 4ac.
We can consequently evaluate the determinant of the quadratic equation in discuss as follows;
Determinant = b² -4ac = (-5)² - (4×1×3) = 25 - 12
Hence, the determinant in this case is; 13.
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How do i solve this with the steps?
Allison is saving money to buy a new phone that costs $600 by selling her graphic designs. She is using an app to manage her sales, but it keeps a fraction of each sale. Her net pay is modeled by the function P(x) = x2 + 18x – 160, where x represents the number of sales. How many sales does Allison to make to earn $600?
Answer:
20
Step-by-step explanation:
x^2+18x-160
If you put this into your calculator or desmos, you will get a parabola. You want to know the value of x when y=600. You can look at the table for the graph or scan to where y = 600. The value of x is 20 at that point.
To check you can plug 20 in for x. When you do that, y = 600.
Choose the best answer from the choices below: the perpendicular bisector of a chord ____.
The perpendicular bisector of a chord passes through the center of a circle.
What is a chord?In geometry, a chord is a straight line segment that connects two points on the circumference of a circle. It is the longest possible segment within the circle.
The perpendicular bisector of a chord is a line that passes through the midpoint of the chord, creating two equal halves, and is perpendicular to the chord.
Notably, for any chord in a circle, its perpendicular bisector always intersects at the center of the circle, making it a significant geometric property.
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(x+3)^0 Rewrite the equation with positive exponents and simplify. x≠-3.
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathsf{(x + 3)^0}[/tex]
[tex]\huge\textbf{Simplifying:}[/tex]
[tex]\mathsf{(x + 3)^0}[/tex]
[tex]\text{Anything raised to the 0 power it automatically equal to 1.}[/tex]
[tex]\huge\text{So, this mean that your answer should be: \boxed{\mathsf 1}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
The total volume of a tree increases 6% each year. what will its volume be after 7 years if its volume is 5 cubic meters now?
Answer:
7.52 m^3
Step-by-step explanation:
This is like compound interest in a banking calculation
Future volume = 5 (1 + .06)^7 = 7.52 m^3