[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ L(\stackrel{x_1}{1}~,~\stackrel{y_1}{-8})\qquad C(\stackrel{x_2}{9}~,~\stackrel{y_2}{-3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ LC=\sqrt{(~~9 - 1~~)^2 + (~~-3 - (-8)~~)^2} \implies LC=\sqrt{(9 -1)^2 + (-3 +8)^2} \\\\\\ LC=\sqrt{( 8 )^2 + ( 5 )^2} \implies LC=\sqrt{ 64 + 25 } \implies LC=\sqrt{ 89 }\implies LC\approx 9.43[/tex]
Solve each system of equations please show your work! 3x+y-2z=22 x+5y+z=4 x=-3z
The solution of the system of equations are;
⇒ x = - 6 , y = 44 and z = 2
What is substitution method?
To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.
Given that;
The system of the equations are,
3x + y - 2z = 22 .... (i)
x + 5y + z = 4 .... (ii)
x = - 3z .... (iii)
Now,
Solve the equations as;
Substitute x = - 3z in both equations, we get;
⇒ 3x + y - 2z = 22
⇒ 3 × -3z + y - 2z = 22
⇒ - 9z + y - 2z = 22
⇒ - 11z + y = 22 .... (iii)
And, x + 5y + z = 4
- 3z + 5y + z = 4
5y - 2z = 4 ... (iv)
Solve equation (iii) and (iv) we get;
⇒ y = 44 and z = 2
So, x = - 3z
⇒ x = - 3 × 2
⇒ x = - 6
Thus, The solution of the system of equations are;
⇒ x = - 6 , y = 44 and z = 2
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what is the lcm of the rational algebraic equation 6/x+x-3/4=2
The required answer would be (24 -3x - 4x²) / 4x = 0 which is the lcm of the rational algebraic equation 6/x+x-3/4=2.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
The given equation below as:
⇒ 6/x + x - 3/4 = 2
We have to determine the lcm of the rational algebraic equation
⇒ 6/x + x - 3/4 = 2
Rearrange the term of 2 in the equation,
⇒ 6/x + x - 3/4 - 2 = 0
Take LCM in the above equation,
⇒ [tex]\dfrac{6\times4+x\times4x-3\times x -2 \times 4x}{4\times x}[/tex]
⇒ (24 + 4x² -3x - 8x²) / 4x = 0
Combine the likewise terms in the numerator,
⇒ (24 -3x - 4x²) / 4x = 0
Therefore, the required answer would be (24 -3x - 4x²) / 4x = 0.
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ASAP!!!!
PLEASE HELP!!!
When a whole number is multiplied by 10 to the power of 2, how does the placement of the decimal point change?
a) It moves two places to the right.
b) It moves ten places to the right.
c) It moves two places to the left.
d) It moves ten places to the left.
Answer: A) moves two places to the right
Example:
[tex]2.567 * 10^2 = 2.567 * 100 = 256.7[/tex]
The positive exponent over the 10 tells us how many places to move to the right. If the exponent was negative, then we'd move to the left. This only works when the base is 10.
The age of children in kindergarten on the first day of school is uniformly distributed between 5 and5.76 years old. A first time kindergarten child is selected at random. Round answers to 4 decimalplaces if possible.a. The mean of this distribution isb. The standard deviation isC. The probability that the the child will be older than 5 years old?d. The probability that the child will be between 5.4 and 5.6 years old ise. If such a child is at the 53rd percentile, how old is that child?years old.CalculatorScratchwork Area
Given the interval of the distribution as
[tex]5-5.76[/tex]a) To find the mean, we will calculate the mid-value of the interval, this is shown below
[tex]\operatorname{mean}=\frac{5+5.76}{2}=\frac{10.76}{2}=5.38[/tex]Hence, the mean is 5.38
b) To find the standard deviation
[tex]\begin{gathered} SD=\sqrt[]{\frac{(b-a)^2}{12}} \\ b=5.76 \\ a=5 \\ SD=\sqrt[]{\frac{(5.76-5)^2}{12}} \\ =\sqrt[]{\frac{0.76^2}{12}}=0.2194 \end{gathered}[/tex]Hence, the standard deviation is 0.2194
c) The probability that the child will be older than 5 years will be
[tex]P(older\text{ than 5 years)=}\frac{5.76-5}{5.76-5}=\frac{0.76}{0.76}=1.0[/tex]Hence, the probability that the child will be older than 5 years is 1.0
d) The probability that the child age is between 5.4 and 5.6 years old will be
[tex]P(\text{ between 5.4 and 5.6 years old)=}\frac{5.6-5.4}{5.76-5}=\frac{0.2}{0.76}=0.2632[/tex]Hence, the probability that the child age is between 5.4 and 5.6 years old is 0.2632
e) If the child is at the 53rd percentile, the age of the child will be
[tex]\begin{gathered} At\text{ 53rd percentile the age}\Rightarrow5+\frac{53}{100}(5.76-5) \\ =5+0.53(0.76) \\ =5.4028 \end{gathered}[/tex]Hence, at the 53rd percentile, the age of the child is 5.4028 years old
Printer A prints 36 pages every 1.5 minutes. Printer B prints 114 pages every 3 minutes.
Printer C prints 115 pages every 5 minutes. Which printer prints the fastest?
Answer:
Printer B prints the fastest
Using the bankers rule, find the simple interest on 18,000 pesos at 17.25% from Feb.4 to Apr 21 of the same leap year.
From the question
By the bunkers rule
[tex]I=\text{PRT}[/tex]P = 18,000
R = 17.25% = 0.1725
For the time
Since the year is a leap year then
February has 29 days
Hence
From Feb.4 to Apr 21 implies
The number of days left in Feb. = 25
Number of days in March = 31
Number of days for April = 21
Therefore, Total number of days = 25 + 31 + 21 = 77
By Bankers rule, total days for the year will be 360
Hence the interest is
[tex]\begin{gathered} I=18000\times0.1725\times\frac{77}{360} \\ I=18000\times0.1725\times0.2139 \\ I=664.16 \end{gathered}[/tex]Therefore, the interest is 664.16
(2 3/5) Multiply (-2 2/3)
[tex] \frac{13}{5} \times - \frac{8}{3} \\ = - \frac{104}{15} [/tex]
ATTACHED IS THE SOLUTION
Answer:
(-104/15)
Step-by-step explanation:
3 2
2 ------ × -2 -------
5 3
5 × 2 = 10
10 + 3 = 13
3 × -2 = -6
-6 + -2 = -8
13 -8 104
------- × ------- = (-) -------
5 3 15
I hope this helps!
A brick has dimensions of110. cm x 655 cm x 1330 cm.What is the volume of the brick incubic meters?[?] m3Recall that 1 cm =10-2 mGive your rounded answer to the correct number ofsignificant figures.Volume, cubic metersEnter
The dimension of the brick is given 110 cm x 655 cm x 1330 cm.
We know that 1 cm = 10^-2 m.
So, the dimensions of brick in meters will be 1.10 m x 6.55 m x 13.30 m.
The volume of the brick is calculated below:
[tex]\begin{gathered} V=1.10\times6.55\times13.30 \\ =95.8265m^3 \end{gathered}[/tex]Thus, the volume of the brick in cubic meters is 95.8265 m^3.
9. You are working to determine how much paint you will need to paint your perfectly square room. The
length of the wall is 4y+8. The height of each wall in your room is 4y. What is the area of the first wall
The area of the wall whose length is 4y+8 and the height is 4y is 16y^2 + 32y.
How area is calculated?
Area is a phrase used to describe how much room a 2D form or surface occupies. Area is measured in square units, such as cm2 or m2.
The area of a form is computed by dividing its length by its breadth.
It is given that the length of the wall is 4y+8 and height of the wall is 4y.
From this given information, we can conclude that the wall is rectangle.
Formula to calculate the area of rectangle is:
Area of rectangle = length x breadth
Putting the value given in the question:
Area of the wall = (4y+8)(4y)
Area of the wall = 16y^2 + 32y
Therefore, the area of the wall is 16y^2 + 32y
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∠A and \angle B∠B are vertical angles. If m\angle A=(x+12)^{\circ}∠A=(x+12)
∘
and m\angle B=(6x-8)^{\circ}∠B=(6x−8)
∘
, then find the measure of \angle B∠B
Measure of ∠B = 16°
∠A and ∠B are Vertical angles with ∠A = x+12° and ∠B = 6x-8°.
Vertical angles are angles formed between two lines at the intersection of them and are opposite to each other.
Also measures of Vertical angles are equal.
Now to find the measure of ∠B, we need to find x.
So here, ∠A = ∠B
⇒ x+12° = 6x-8°
⇒ 6x - x = 12 + 8
⇒ 5x = 20
⇒ x = 4
Hence, ∠B = 6x-8° = 6 x 4 -8 = 16°
So measure of ∠B = 16°
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Use 2 methods to predict the output for an input of 200.
Given a table represents a relation between x and y
As shown, the change of (x) and (y) vary with a constant rate
So, the table represents a linear function
The general equation will be: y = m * x + b
where (m) is the slope, (b) is the value of y when (x=0)
So, from the table, when x = 0 , y = 25
The slope will be as follows:
[tex]m=\frac{30-25}{1-0}=\frac{5}{1}=5[/tex]So, the equation will be:
[tex]y=5x+25[/tex]When the input = 200, x = 200
So, substitute with (x) to find the output (y)
[tex]y=5\cdot200+25=1000+25=1025[/tex]So, the answer will be:
For an input 200, the output is 1025
===================================================
Another method to solve using the arithmetic sequence.
As shown in the table consider (x) represents the number of terms
So, (y) will be an arithmetic sequence
The first term = a = 30
The common difference = d = 35 - 30 = 5
the general rule of the arithmetic sequence is:
[tex]y_{}=a+d(x-1)[/tex]substitute with (a) and (d)
[tex]y=30+5(x-1)[/tex]When x = 200
[tex]y=30+5(200-1)=30+5\cdot199=1025[/tex]So, for an input 200, the output = 1025
Match the terms (picture)
Answer:
Match that i have the step by step explanations
Step-by-step explanation:
A, F, C, D, E, F, B
Robert Key's group medical insurance coverage costs $6,480 a year. His employer, Covington Arts Center, pays 65% of the cost. What is his monthly paycheck deduction for medical insurance?
Answer:
See below
Step-by-step explanation:
Robert pays 35 % in 12 monthly installments
6480 * .35 / 12 = 189 dollars per month
72b384 is a number in which one of its digits is 'b'. if the number is a multiple of 9, what is the numerical value of 'b'?
Answer:
3
Step-by-step explanation:
Hello!
A simple way to find if the number is a multiple of 9 is if the sum of the digits in the number is a multiple of 9, then the number itself is a multiple of 9.
So that means: 7 + 2 + b + 3 + 8 + 4 is a multiple of 9
If we add it up we should get: 24 + b
The multiples of 9 include 9,18,27,36,45,54....., and the closest multiple of 9 to 24 is 27. Therefore, the missing digit should be 3, as 27 - 24 is 3.
The next closest numbers would be 18 and 36, but you would need to add a negative number to get 18, and a two-digit number to get 36.
Ben is a coal miner and spends most of his workday in an underground mine. Which is the most likely depth he is at while doing his job?
Answer:-900 feet. I think this is correct so don't use it unless you think its right
Step-by-step explanation:
It takes 4 oranges to makes 6 ounces of orange juice. What are the two unit rates?
Answer: The second ratio in the proportion is set up as ounces over oranges. The units should be in the same place in proportion to the first ratio.
Step-by-step explanation:
Please help I did help
The scientific notation of the expression is as follows:
(7 × 10⁻⁶) (7 × 10⁻⁶) = 4.9 × 10⁻¹¹(3.76 × 10⁵) + (7.44 × 10⁵) = 1.12 × 10⁶How to solve expression in scientific notation?The proper format for scientific notation is a x 10ᵇ where a is a number or decimal number such that the absolute value of a is greater than or equal to one and less than ten or, 1 ≤ |a| < 10.
Scientific notation is a special way of writing numbers.
The expression can be express in scientific notation as follows:
Therefore,
(7 × 10⁻⁶) (7 × 10⁻⁶)
Hence, we have to multiply the integers and add the exponents as follows:
(7 × 7) × (10⁻⁶. 10⁻⁶)
49 × 10⁻⁶⁻⁶
49 × 10⁻¹²
4.9 × 10⁻¹¹
Hence, the second can be express in scientific notation as follows:
(3.76 × 10⁵) + (7.44 × 10⁵)
(3.76 + 7.44) × 10⁵
11.2 × 10⁵
1.12 × 10⁵⁺¹
1.12 × 10⁶
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From the diagram below, what is the measure of the angle of depression from point A
The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line.
From point A, point B is observed with an angle of 45 down from the top of the tree to the ground.
Thus, the angle of depression is 45°
Amanda and Jeremiah are standing on the same side of a large lake. They are separated by a horizontal distance of 4000 ft. Both Amanda and Jeremiah can see a helicopter that is directly above the horizontal distance between them. Amanda’s angle of elevation to see the helicopter is 60 and Jeremiah’s angle of elevation to see it is 30. 1.What is the distance between Amanda and the helicopter?
Explanation: First of all we need to know if our triangle is a right triangle (has one 90° inner angle) to be able to use the law of sines to calculate the distance between Amanda and the helicopter.
Step 1: Once we know that the sum of all inner angles of a triangle is equal to 180° we can calculate the unknown angle as follows
As we can see above the missing inner angle is 90° which means it is a right triangle.
Step 2: Now we can use the law of sines as follows
once sin (90°) = 1 and sin (30°) = 0.5, let's calculate "x" below
[tex]\begin{gathered} \frac{x}{sin(30)}=\frac{4000}{sin90} \\ x=\frac{4000*0.5}{1} \\ x=2000ft \end{gathered}[/tex]Final answer: As we can see above, the final answer is 2000 ft
Solve the equation for all values of x.
|5x + 8| 8 = 3x
Part A: On the imagePart B: What is the answer of k?
The effect on the graph replacing f(x) by f(x)+k is a vertical shift k units.
According to the graph the resulting function is 2 units higher from the original one. This means k has a value of 2.
Distribution Whole Number Multiple Choice
Distribution of
a(b + c) = ab + ac
Then
36 + 12 is equivalent to
Find composed numbers
36= 3•12
12 = 3•4
THEN ANSWER IS
3• (12 + 4)
Write a sequence of transformations that takes A to A'.
A rotation of 270 degrees about the origin would transform the figure as follows:
Which does not maps the A to A'.
Now, one sequence of transformations that take A to A' is:
1)First, a reflection over the x-axis would transform the figure as follows:
2) We translate the figure 3 units up and 4 units to the right:
Answer: Reflection over the x-axis, translation 3 units up and 4 units to the right.
9. Assessment Practice Diego wants to
find 8+ 9. 2.NSO.2.1
Which doubles fact can help him?
A 5+5=10
B6+6=12
C7+7= 14
D 8+8=16
They can use counters or their fingers, but they can also use doubles facts. If they know 5 + 5 = 10, they know that the sum of 5 + 6 will be one more.
What is meant by addition?One of the four fundamental mathematical operations, along with addition, subtraction, multiplication, and division, is addition.
The sum of 5 + 6.
They can utilize counters or their fingers, but they can even utilize doubles facts. If they understand 5 + 5 = 10, they know that the sum of 5 + 6 will be one more.
Therefore, 5 + 6 = 11.
Estimating other doubles-plus-one facts together, such as 3 + 4, 7 + 8, and 9 + 8.
Repeat the doubles facts so they can use them to solve equations.
They can also use doubles-minus-one facts to enable them solve equations.
Write down 9 + 10 and have your children find the sum.
If they know that 10 + 10 = 20, they know that the sum of 9 + 10 will be one less. Therefore, 9 + 10 = 19.
Practice solving different number sentences together.
Therefore, they can utilize counters or their fingers, but they can even utilize doubles facts. If they understand 5 + 5 = 10, they know that the sum of 5 + 6 will be one more.
Therefore, the correct answer is option A 5 + 5 = 10.
The complete question is:
Which doubles fact helps you solve 5 + 6 = 11? Circle the number sentence.
A 5+5=10
B6+6=12
C7+7= 14
D 8+8=16
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Carefully follow the steps to find the solution to the three equation system.
a. Use equations 2 and 3 and eliminate the by multiplication and addition, creating a new equation with only two variables.
b. Use equations 1 and 2 and eliminate the by multiplication and addition, creating a second equation with only two variables.
c. Use the two new equations, and eliminate the -variable by multiplication and addition, finding the value for the -variable.
d. Substitute -value in the second new equation and find the -value.
e. Substitute the and values into original equation 2 to find the -value
(-2,-5,-3)
(1,4,2)
(-4,1,-2)
(1,2,4)
(2,5,3)
Answer:
The answer is (1,4,2)
Graph 5x + y = 3x + 2(a) Rewrite the equation in slope intercept form. Show your work.(b) Graph the line. If you aren't able to draw on the graph using the technology you have available,then just describe it in words - tell where it is located
Given the Linear Equation:
[tex]5x+y=3x+2[/tex](a) You need to solve for "y", in order to rewrite it in Slope-Intercept Form, because that form is:
[tex]y=mx+b[/tex]Where "m" is the slope of the line and "b" is the y-intercept.
Then, you get:
[tex]\begin{gathered} y=-5x+3x+2 \\ y=-2x+2 \end{gathered}[/tex]Notice that:
[tex]\begin{gathered} m=-2 \\ b=2 \end{gathered}[/tex](b) You can graph the line by finding the x-intercept and the y-intercept. You already know that the y-intercept is:
[tex]b=2[/tex]Then, in order to find the x-intercept, you need to substitute this value of "y" into the equation and then solve for "x":
[tex]y=0[/tex]Because the value of "y" is zero when the line intersects the x-axis.
Therefore, you get:
[tex]\begin{gathered} y=-2x+2 \\ 0=-2x+2 \\ -2=-2x \\ \\ \frac{-2}{-2}=x \\ \\ x=1 \end{gathered}[/tex]Now you know that the line passes through these points:
[tex](1,0),(0,2)[/tex]Hence, you can graph it.
Therefore, the answers are:
(a) Equation in Slope-Intercept Form:
[tex]y=-2x+2[/tex](b) Graph:
Pam needs 2 yards of blue ribbon she has 0.497 yard she buys 0.91 yard more than she buys 0.4 yard of red ribbon how much more blue ribbon does Pam need?
Total ribbon Pam needs = 2 yards
Total ribbon Pam purchased = 0.497 + 0.91 + 0.40 = 1.807
The amount of ribbon Pam needs is calculated as,
[tex]\begin{gathered} \text{Amount n}eeded\text{ = 2 - 1.807} \\ \text{Amount n}eeded\text{ = }0.193 \end{gathered}[/tex]Thus the amount of ribbon needed is 0.193 yards .
Linh buys $11.23 worth of groceries and pays for them with a $20 bill.List her change using the smallest number of coins and bills?
Given: Linh buys $11.23 worth of groceries and pays for them with a $20 bill.
So, the change will be = 20 - 11.23 = $8.77
I need to know the answer but I need to know how to get it and work it out
Let's start by completing the first table.
The questions gives the depth in two times:
- 2 hours after start -> 64 inches of water
- 4 hours after start -> 48 inches of water
From this, we can identifythe units:
- for time, we will use hours
- for depth, we will use inches
The first given values are:
- for time, 2
- for depth, 64
The second given valuesa are:
- for time, 4
- for depth, 48
So, the table is:
Quantity Name | Time | Depth of Pool
Unit | hour | inch
Given Value 1 | 2 | 64
Given Value 2 | 4 | 48
Now, we need to calculate the slope, which can be done using the given points and the equation:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{48-64}{4-2} \\ m=\frac{-16}{2} \\ m=-8 \end{gathered}[/tex]So, the slope is -8 inches per hour.
The interceptwe the b in the equation:
[tex]y=mx+b[/tex]Where y is the depth and x is the time. So, using the first given values and the slope, we can find b:
[tex]\begin{gathered} 64=-8\cdot2+b \\ 64=-16+b \\ b=64+16 \\ b=80 \end{gathered}[/tex]Thus, the intercept is 80 inches.
So, the formula we have for the pump is:
[tex]y=-8x+80[/tex]Using it, we can answer questions 1 and 2:
1. After 6 hours means x = 6, so:
[tex]\begin{gathered} y=-8\cdot6+80 \\ y=-48+80 \\ y=32 \end{gathered}[/tex]So, y = 32, thus, the depth of the water will be 32 inches.
2. The level 24 inches mean y = 24, so:
[tex]\begin{gathered} 24=-8x+80 \\ 8x=80-24 \\ 8x=56 \\ x=\frac{56}{8} \\ x=7 \end{gathered}[/tex]Thus, x = 7, and the water will be at 24 inches after 7 hours.
In the circle below, the central angle is measured in radians.When rounded to the nearest .01 of a centimeter,the length of arc Sis?? cm?
Length of the given arc
[tex]\begin{gathered} l=r\theta \\ =2\times\frac{\pi}{4} \\ =\frac{\pi}{2} \\ =\frac{22}{14} \\ =1.571 \\ =1.57 \end{gathered}[/tex]So the length of the given arc is 1.57 cm