The distance between the points (0, 10) and (–9, 1) is 12.73 units.
Given the following data;
Points ([tex]x_1, x_2[/tex]) = 0, -9
Points ([tex]y_1, y_2[/tex]) = 10, 1
To find the distance between the points;
In Mathematics, the distance between two points on a plane is calculated by using the formula;
[tex]Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2 }[/tex]
Substituting the points into the formula, we have;
[tex]Distance = \sqrt{(0 - [-9])^2 + (10 - 1)^2} \\\\Distance = \sqrt{(0 + 9)^2 + (9)^2}\\\\Distance = \sqrt{9^2 + 9^2}\\\\Distance = \sqrt{81 + 81}\\\\Distance = \sqrt{162}[/tex]
Distance = 12.73 units
Therefore, the distance between the points is 12.73 units.
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How much did Angelo pay for his online purchase
Answer:
Step-by-step explanation:
please include a picture of the question! :)
? Given: All US area codes are three-digit numbers that use the numerals 0 to 9. Step 2: How many area-codes are possible if the first digit can't be zero and no digit can be repeated? Use your keyboard and the keypad to enter your answer. Then click Done.
Explanation:
For the first slot, we have 9 digits to choose from (1 through 9).
Whatever we pick for the first choice, we have 9 choices left for the second slot. Say we picked 2 for the first slot. That means we have {0,1,X,3,4,5,6,7,8,9} to choose from. I used X to indicate we can't pick that digit any more. You'll see there are 9 items in that list.
Then for the third slot, we had 8 choices to pick from
Overall we have 9*9*8 = 81*8 = 648 different area codes possible where the first digit cannot be zero.
Solve by the quadratic formula: 3x^2 - 4x + 1 = 0
Answer:
x = 1/3 and x = 1.
Step-by-step explanation:
3x^2 - 4x + 1 = 0
(3x - 1)(x - 1) = 0
The solutions are when either 3x - 1 = 0 or x - 1 = 0.
3x - 1 = 0
3x = 1
x = 1/3
x - 1 = 0
x = 1
So, x = 1/3 and x = 1.
Hope this helps!
A twelve-foot ladder is leaning against a wall. If the ladder reaches ft high on the wall, what is the angle the ladder forms with the ground to the nearest degree?*
This question is incomplete.
Complete Question
A twelve-foot ladder is leaning against a wall. If the ladder reaches eight ft high on the wall, what is the angle the ladder forms with the ground to the nearest degree?*
Answer:
42°
Step-by-step explanation:
From the question, the diagram that is formed is a right angle triangle.
To solve for this, we would be using the trigonometric function of Sine.
sin θ = Opposite side/ Hypotenuse
From the question, we are told that:
12 foot ladder is leaning against a wall = Hypotenuse
The ladder reaches 8ft high on the wall = Opposite side.
Hence,
sin θ = 8ft/12ft
θ = arc sin (8ft/12ft)
= 41.810314896
Approximately to the nearest degree
θ = 42°
Therefore, the angle the ladder forms with the ground to the nearest degree is 42°
which of the binomials below is a factor of this trinomial? x^2 + 5x - 36 A. x - 5 B. x - 9 C. x + 9 D. x^2 + 5
===============================================
Explanation:
Think of two numbers that multiply to -36 and also add to 5. Put another way: think of two factors of -36 that add to 5.
Those two numbers are 9 and -4 since
9 times -4 = -36
9 plus -4 = 5
So we have x^2 + 5x - 36 factor into (x+9)(x-4)
x+9 is one factor
x-4 is the other factor
-------
Alternatively, you can use a graphing tool to locate the x intercepts, and that will in turn lead to the factorization. Or you could use the quadratic formula to get the job done. Completing the square is yet another tool to use. So there are multiple approaches.
Find mQPR. If mQPS=40,mRPS=8x+7,mQPR=9x+16
compare -1/6 and -2/3
Answer:
-1/6=-0.166
-2/3=-0.66
Step-by-step explanation:
-by looking carefully you will notice that . which number is greater and smaller.
Answer:
-1/6 is greater than -2/3
Step-by-step explanation:
A circle has a radius of sqrt 45 units and is centered at (-2.4, -4.8) Write the equation of the circle
Answer:
( x+ 2.4) ^2 + ( y+4.8) ^2 = 45
Step-by-step explanation:
The equation of a circle can be written as
( x-h) ^2 + ( y-k) ^2 = r^2
Where ( h,k) is the center and r is the radius
( x-- 2.4) ^2 + ( y--4.8) ^2 = (sqrt45)^2
( x+ 2.4) ^2 + ( y+4.8) ^2 = 45
x: 13, 17, 21, 25 y: 0, 6, 12, 18 is the relationship linear, exponential or neither
━━━━━━━☆☆━━━━━━━
▹ Answer
Linear
▹ Step-by-Step Explanation
As x increases by 4, y increases by 6.
13 + 4 = 17
17 + 4 = 21
21 + 4 = 25
0 + 6 = 6
6 + 6 = 12
12 + 6 = 18
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the Concept of the GRAPHS AND FUNCTIONS.
This here, from the graph we can see that it's a EXPONENTIAL GROWTH.
Thus the relationship is Exponential.
if 1 gallon of water is added to 6 quarts of a mixture of alcohol and water that is 50% alcohol, what percent alcohol is the resulting mixture?
Will mark brainlist
Answer:
The percentage of alcohol in the resulting mixture is 30%
Step-by-step explanation:
The equation given are;
Volume of added water = 1 gallon = 3.79 litres = 4 quarts
Volume of mixture of alcohol = 6 quarts = 5.68 litres
Concentration of the alcohol in 6 quarts = 50%
Given that the mixture of alcohol and water is 50% alcohol and 50% water, we have;
Volume of 100% alcohol in 5.68 liters = 0.5× 5.68 = 2.84 litres = 3 quartz
Total volume of the final solution = 5.68 + 3.78 = 9.46 litres = 10 quarts
Percentage by volume of 100% alcohol in total volume of the resultant solution = 3 quarts/((4 + 6) quarts) × 100 = 3/10 × 100 = 30%
The percentage of alcohol in the resulting mixture = 30%.
What is the value of discontinuity of x^2+8x+4/x^2-x-6? Choices:
Answer:
-2
Step-by-step explanation:
Hello,
First of all, let's check the denominator.
[tex]x^2-x-6 \ \ \text{ *** How to factorise it ...? ***}\\\\\text{*** The product of the roots is -6=-2*3 and their sum is 1 ***}\\\\x^2-x-6=x^2-3x+2x-6=x(x-3)+2(x-3)=(x+2)(x-3)[/tex]
Now, let's see the numerator.
[tex]x^2+8x+4 \ \text{ *** -2 is not a zero as ***}\\\\(-2)^2+8*(-2)+4=4-16+8=-4\\\\\text{*** 3 is not a zero as ***}\\\\3^2+8*3+4=9+24+4=37\\[/tex]
So we cannot factorise the numerator with (x+2) or (x-3)
Then, -2 and 3 are the the discontinuities of the expression.
There is only -2 in the list, this is the correct answer.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Please can someone help it will mean the world
Answer:
The solution is (2,5)
Step-by-step explanation:
The solution to the system of equations is where to the two graphs intersect
The two lines intersect at x=2 and y = 5
The solution is (2,5)
Answer:
Hey there!
The solution for a system of equations (simultaneous equations), is where the two lines intersect.
We see that the lines intersect at (2,5), making (2,5) the solution to the system of equations.
Let me know if this helps :)
A box contains 5 blue, 4 red, and 3 yellow marbles. Two marbles are randomly drawn and not replaced. What is the probability of drawing a blue then a red marble?
Answer:
5/33
Step-by-step explanation:
5/12 * 4/11 = 20/132 = 10/66 = 5/33
Given the coordinates for the function below, which of the following are
coordinates for its inverse?
Gallons Cost, in
of Gas Dollars
1
2
5
15
20
1.25
2.50
6.25
18.75
25.00
The coordinates of the inverse are (1.25, 1) (2.50, 2), (6.25, 5), (18,75, 15) and (25.00, 20)
How to determine the inverse coordinates?The table of values is given as:
Gallons Cost
1 1.25
2 2.50
5 6.25
15 18.75
20 25.00
The inverse of the above table would have the following header
Cost Gallons
When the inverse table is populated, we have:
Cost Gallons
1.25 1
2.50 2
6.25 5
18.75 15
25.00 20
The coordinates are: (1.25, 1) (2.50, 2), (6.25, 5), (18,75, 15) and (25.00, 20)
Hence, the coordinates of the inverse are (1.25, 1) (2.50, 2), (6.25, 5), (18,75, 15) and (25.00, 20)
Read more about coordinates at:
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what is the expression in radical form (2m^2n)^3/2
Answer:
sqrt[(2m^2n)^3]
Step-by-step explanation:
So let's break down the exponent. The top number represents the number of times the term is repeated. The bottom number represents the root to be taken of the final product. With this in mind, let's rewrite this expression.
(2m^2n)^3/2
= [(2m^2n)^3]^1/2
Notice we have 3 of the (2m^2n) terms, but they are all under the 2nd root (aka a square root).
So now, we'll rewrite this into the radical form.
sqrt[(2m^2n)^3]
I hope this helps.
Cheers.
Alicia Keys's new album As I Am is climbing the charts, and the manager of Tip Top Tunes expects to sell a lot of copies. Because she has limited shelf space, she can't put out all her copies of the CD at once. On Monday morning, she stocked the display with 40 copies. By the end of the day, some of the copies had been sold. On Tuesday morning, she counted the number of copies left and then added that many more to the shelf. In other words, she doubled the number that was left in the display. At the end of the day, she discovered that she had sold the exact same number of copies as had been sold on Monday. On Wednesday morning, the manager decided to triple the number of copies that had been left in the case after Tuesday. Amazingly, she sold the same number of copies on Wednesday as she had on each of the first two days! But this time, at the end of the day the display case was empty. How many copies of the As I Am CD did she sell each day?
Answer:
About 4.44
Step-by-step explanation:
Let x represent the unknown amount of CD's sold each day. Thus, the linear equation is formed:
40-x = 2x + 3 (2x) Next collect like terms by adding x to both sides.
40-x+x= x + 2x + 3 (2x)
40 = 3x + 3 (2x)
40 = 3x + 6x
40= 9x
40/9 = 9x/9
x= 4.44
Note: 2x represents doubling up the sales amount, which was left.
3x represents tripling the sales amount left.
Can an absolute value function also be a polynomial function? Why or why not?
Answer:
For this case a polynomial is defined with the following expression:
[tex] p(x) =\sum_{i=1}^n a_i x^i[/tex]For all x on the domain considered and n is finite
And by definition the absolute value function is defined as:
[tex] |x|= x, x \geq 0[/tex]
[tex] |x| =-x , x<0[/tex]
If we use the function [tex] f(x) =|x|[/tex] we see that is impossible to obtain the general expression of a polynomial since we can't obtain the form |x| and since we don't satisfy the definition the answer would be:
An absolute value function CANNOT be considered as a polynomial function
Step-by-step explanation:
For this case a polynomial is defined with the following expression:
[tex] p(x) =\sum_{i=1}^n a_i x^i[/tex]For all x on the domain considered and n is finite
And by definition the absolute value function is defined as:
[tex] |x|= x, x \geq 0[/tex]
[tex] |x| =-x , x<0[/tex]
If we use the function [tex] f(x) =|x|[/tex] we see that is impossible to obtain the general expression of a polynomial since we can't obtain the form |x| and since we don't satisfy the definition the answer would be:
An absolute value function CANNOT be considered as a polynomial function
If an object is propelled upward from a height of 72 feet at an initial velocity of 90 feet per second, then its height h after t seconds is given by the equation h = − 16 t 2 + 90 t + 72 . After how many seconds does the object hit the ground?
Answer:
6.34 seconds.
Step-by-step explanation:
The object will hit the ground when h = 0.
-16t^2 + 90t + 72 = 0
8t^2 - 45t - 36 = 0
We can then use the quadratic formula to solve.
[please ignore the A-hat; that is a bug]
[tex]\frac{45±\sqrt{45^2 - 4 * 8 * -36} }{2 * 8}[/tex]
= [tex]\frac{45±\sqrt{2025 + 1152} }{16}[/tex]
= [tex]\frac{45±\sqrt{3177} }{16}[/tex]
= [tex]\frac{45±56.36488268}{16}[/tex]
(45 - 56.36488268) / 16 = -0.7103051678
(45 + 56.36488268) / 16 = 6.335305168
Since the time cannot be negative, the object will hit the ground after about 6.34 seconds.
Hope this helps!
Pam works as an office administrator. She spends $7500 of her income on personal expenses each year. If this represents 18% of her salary, how much money does Pam earn in one year? Round your answer to the nearest whole dollar.
Answer: Pam earns $41,667 in one year.
Step-by-step explanation:
Hi, to answer this question we have to write an equation:
Pam's salary (x) multiplied by the percentage represented by expenses (18%) in decimal form (divided by 100) must be equal to $7500.
Mathematically speaking:
x (18/100) = 7500
Solving for x:
x (0.18) = 7500
x = 7500/0.18
x = 41,667
Pam earns $41,667 in one year.
Feel free to ask for more if needed or if you did not understand something.
A science club is raising money by selling t-shirts. The cost of producing the t-shirts is a one time 550 dollar design and set up fee plus 12
dollars per shirt. If they sell the t-shirts for $17.50 each, what is the minimum number of t-shirts the club can order and still make a profit?
Answer: not sure
Step-by-step explanation:
8 7 12 7 11
10 7 12
Find:
a)the median
b) the range
c)the mode
Answer:
a) Median: 9
b) Range: 5
c) Mode: 7
Step-by-step explanation:
The median is the number in the middle.
First, you put the numbers in order: 7, 7, 7, 8, 10, 11, 12, 12
The middle of this is 8 and 10, so you plus them and divide by to 2, then it gives 9, so the median is 9.
To find the range, you minus the highest number and the lowest number, 12-7=5.
Mode is the most occurring and repetitive number, in this case, 7, because it is written 3 times.
Hope this helps!!!
Answer:
[tex]\boxed{\mathrm {Median = 9}}[/tex]
[tex]\boxed{\mathrm{Range = 5}}[/tex]
[tex]\boxed{\mathrm{Mode = 7}}[/tex]
Step-by-step explanation:
The observations are:
8,7,12,7,11,10,7,12
In ascending order:
=> 7,7,7,8,10,11,12,12
A) Median => Middlemost no.
Median = 8,10
=> [tex]\frac{8+10}{2}[/tex]
=> [tex]\frac{18}{2}[/tex]
Median = 9
B) Range = Highest No. = Lowest No.
RANGE = 12-7
Range = 5
C) Mode => frequently occurring number
Mode = 7
Jennifer invested $302 in a simple interest account. The account earns 3.3%/year how much will Jennifer have in her account in 10 months??
Answer: $310.31
Step-by-step explanation:
Invested amount (P) = $302
Interest rate (r) = 3.3% per year
Period = 10 months
Recall, simple interest formula :
A = P(1 + rt) where ; A = final amount
Interest = 3.3% = 3.3/ 100 = 0.033
A = $302 ( 1 + 0.033(10/12))
A = $302 (1 + 0.033(0.8333333))
A = $302 ( 1 + 0.0275)
A = $302 ( 1. 0275)
A = $310.305
A = $310.31
ASAP! PLEASE help me with this question! I am really stuckk...
Answer:
8 pi cm^2
Step-by-step explanation:
To answer this question, what we need firstly is the name of the cross section that results from slicing a sphere into half.
The cross section that results is called a hemisphere, which is half the size of the sphere.
But before we can calculate the area of the new cross section, we will need the radius of the original shape.
This is obtainable from the volume of the shape.
Mathematically;
Volume of a sphere = 4/3 * pi * r^3
32/3 * pi = 4/3 * pi * r^3
We can take off pi/3 from both sides so we are left with;
32 = 4r^3
Divide through by 4
r^3 = 8
r is the cube root of 8 = 2 cm
Now we find the area of the hemisphere
Mathematically, the area of a hemisphere is 2 * pi * r^2
using the value of r = 2 cm given above, we have
Hemisphere area = 2 * pi * 2^2 = 8pi cm^2
Find the values for which the statement is true and mark them on the number line: |x|=x
Answer:
x ≥ 0
Step-by-step explanation:
The absolute value of something will always be the same number if the number is positive. Therefore, the values of x which make this true are x ≥ 0.
Which statements about the hyperbola are true? Check
all that apply.
There is a vertex at (-3, 6).
The center of the hyperbola is at (-3,5).
There is a vertex at (-5,5).
The transverse axis is vertical.
The directrices are horizontal lines
Answer:
Options (1), (2), (4) and (5) are correct.
Step-by-step explanation:
Characteristics of the given hyperbola,
1). Vertex of the given hyperbola are at (-3, 6) and (-3, 4).
2). Since center of a hyperbola is the center of a line joining vertices of the hyperbola,
Center of the given parabola will be,
[tex](\frac{-3-3}{2},\frac{6+4}{2})[/tex] ⇒ (-3, 5)
3). Vertical line joining the foci of the hyperbola is the transverse axis.
4). A line perpendicular to the transverse axis and passing through the center will be the conjugate axis.
5). Directrices of a horizontal hyperbola are the horizontal lines.
Therefore, Options (1), (2), (4) and (5) are correct.
Answer:
check photo. <3
Step-by-step explanation:
solve the equation 2/3x-2=7
Answer: x = 27/2
Step-by-step explanation:
2/3x-2=7
2/3x=9
2/3x=27/3
2/3x(3/2)=27/3(3/2)
x=81/6
x=27/2
Answer: x = 27/2
Step-by-step explanation: In this equation, our first step is to isolate the x term by adding 2 to both sides.
On the left, -2 and +2 cancel out and were left
with 2/3x and on the right, 7 + 2 simplifies 9.
So we have 2/3x = 9.
In order to get x by itself, since it's being multiplied by a fraction,
we multiply both sides of the equation by the reciprocal of that fraction.
The reciprocal of a fraction is just that fraction
flipped so the reciprocal of 2/3 is 3/2.
So we have (3/2)(2/3x) = 9(3/2).
On the left, the 2's cancel and the 3's cancel.
On the right, 9(3/2) is 27/2.
So x = 27/2
the scale on the map is 1 cm represents 40 km . the actual straight line distance between 2 cities is about 320 km what is the map distance between these 2 cities
Answer:
8cm
Step-by-step explanation:
the ratio of cm to km is 1 cm on the map equals 40 km. or 1/40 so you have to find what is x/320 using the ratio of 1/40 you gt that x equals 8
The freezing point of water is
0
∘
C
0
∘
C0, degrees, start text, C, end text. Scientists use positive numbers to show temperatures above the freezing point of water and negative numbers to show temperatures below the freezing point of water.
Jess stores her bacteria samples at
4
∘
C
4
∘
C4, degrees, start text, C, end text.
What does
4
∘
C
4
∘
C4, degrees, start text, C, end text mean in this situation?
Step-by-step explanation:
the freezing point of water is 0⁰c...
0⁰c is as positive value but this is also considered as also in negative so it is not fixed but after a experiment it shows that 0⁰c ⁷
Answer:
Mia's iced coffee is 4^\circ\text{C}4
∘
C4, degrees, start text, C, end text below the freezing point of water.
Step-by-step explanation:
Band uniforms cost 45 dollars each how many can i buy for 1000 dollars
Answer:
22
Step-by-step explanation:
Answer:
22 band uniforms
Step-by-step explanation:
Each band uniform costs $45, and you have $1000. We want to find how many band uniforms you can purchase.
Therefore, we can divide 1000 (total money) by 45 (cost of one band uniform)
1000/45
Divide
22.2222222
0.2222... , or a part, of a uniform cannot be purchased, so we must round down to the nearest whole number.
22
22 band uniforms can be purchased.
Two factory plants are making TV panels. Yesterday, Plant A produced 5000 fewer panels than Plant B did. Five percent of the panels from Plant A and 2% of the panels from Plant B were defective. How many panels did Plant B produce, if the two plants together produced 450 defective panels
Answer:
10,000 panels
Step-by-step explanation:
A TV panel is being produced by two factory plants
Plant A produced 5000 fewer panels than plant B
Let a represent the number of panels produced by plant A and b represent the number of panels produced by plant B
a= b-5000............equation 1
5% of the panels from plant A were defective
= 5/100
= 0.05
2% of the panels from plant B were defective
= 2/100
= 0.02
The total defective panels of both plants is 450
0.05a + 0.02b= 450..............equation 2
Substitute b-5000 for a in equation 2
0.05(b-5000) + 0.02b= 450
0.05b - 250 + 0.02b= 450
Collect the like terms
0.05b+0.02b= 450+250
0.07b= 700
Divide both side by the coefficient of b which is 0.07
0.07 b/0.07= 700/0.07
b= 10,000
Hence plant B produced 10,000 panels