Given
Two points (8,6) and (3,−6)
Find
distance between the two points
Explanation
Distance between the two points is given by
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]so , distance between (8,6) and (3,−6) is
[tex]\begin{gathered} d=\sqrt{(3-8)^2+(-6-6)^2} \\ d=\sqrt{25+144} \\ d=\sqrt{169} \\ d=13 \end{gathered}[/tex]Final Answer
Therefore , the distance between these two points is 13
I need help with this Question 5 and Question 6
5) The rate of change from 2000 to 2012 is 0.80
6) The rate of change from 2012 to 2015 is 0.32
From the question, we have
5) Rate of change from 2000 to 2012 = (3.64-2.02)/2.02
=1.62/2.02
=0.80
6) Rate of change from 2012 to 2015 = (3.64-2.45)/3.64
=1.19/3.64
=0.32
Subtraction:
Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.
The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.
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John has 4 different flags that he wants to hang on the wall. How many different wayscan the flags be arranged in a row?
It is given that,
John has 4 different flags that he wants to hang on the wall.
To find the number of different ways can the flags be arranged in a row:
There are 4! ways can the flags be arranged in a row.
That is,
[tex]\begin{gathered} 4!=4\times3\times2\times1 \\ =24 \end{gathered}[/tex]Hence, the answer is 24 different ways.
A bank loaned out $7,500, part of it at the rate of 11% annual interest, and the rest at 14% annual
interest. The total interest earned for both loans was $1,020.00. How much was loaned at each rate?
The 11% annual rate amount is $1000 and 14% annual rate amount is $6500 for total interest $1020.
What is interest?
The financial fee for borrowing money is called interest, and it is typically stated as a percentage, such as an annual percentage rate (APR). For the use of their money, lenders may earn interest, and borrowers may pay interest. For borrowing money or other assets, interest is a cost that must be paid. Principal is the amount borrowed, and interest is calculated as a percentage of principal over a specified period of time.
Here the principal P = $7500
Let us take 11% annual rate part amount as x.
Then remaining is 7500-x.
Now the interest I = PNR/100
=>1020= (x×11×1)/100+((7500-x)×14×1)/100
=> 1020×100=11x+105000-14x
=>102000=105000-3x
=>3x=105000-102000
=>3x=3000
=>x=1000
Now 7500-1000=6500.
Hence $1000 for 11% annual rate and $6500 for 14% annual rate.
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A student is measuring the length of an icicle, y, every hour, x. The icicle is currently 14 inches long and is melting at a rate of 0.9 inches per hour. Find and interpret the slope for this relationship. −0.9; for every additional hour, the length of the icicle decreases by 0.9 inches 0.9; for every additional hour, the length of the icicle increases by 0.9 inches −14; the length of the icicle when the student first measures it 14; the length of the icicle when the student first measures it
The answer is: −0.9; for every additional hour, the length of the icicle decreases by 0.9 inches
Determine whethersecx cotx-cosxsin(-x) cot²xand cotx are equivalent. Justify your answer.
we have the expression
[tex]\frac{secxcot^2x-cosx}{sin(-x)cot^2x}[/tex]Rewrite the given expression
Remember that
sin(-x)=-sin(x)
[tex]\frac{\frac{1}{cosx}\frac{cos^2x}{sin^2x}-cosx}{-sinx\frac{cos^{2}x}{s\imaginaryI n^{2}x}}[/tex]Simplify the expression
[tex]\begin{gathered} \frac{\frac{cosx}{s\imaginaryI n^2x}-cosx}{-\frac{cos^2x}{s\imaginaryI nx}} \\ \\ \frac{\frac{cosx-sin^2xcosx}{sin^2x}}{-\frac{cos^2x}{sinx}} \\ \\ \frac{cosx-s\imaginaryI n^{2}xcosx}{s\imaginaryI n^{2}x}\colon-\frac{cos^{2}x}{s\imaginaryI nx} \\ \\ \frac{sinx(cosx-sin^2xcosx)}{sin^2x(cos^2x)} \\ \\ \frac{(cosx-sin^2xcosx)}{sin^x(cos^2x)} \\ \\ \frac{cosx(1-s\imaginaryI n^2)}{s\imaginaryI nx(cos^2x)} \\ \\ \frac{(1-s\imaginaryI n^2)}{s\imaginaryI nx(cosx)} \\ \\ \frac{cos^2x}{s\imaginaryI nx(cosx)} \\ \\ \frac{cosx}{sinx} \\ \\ cotx \end{gathered}[/tex]therefore
The answer is
yes, the expression is equivalent to cot(x)Assignment: 5.4 Bellwork Wednesday 2/03 Problem iD: PRABRBYC Rose wants to construct a fence around her garden. The garden is circular in shape with a diameter of 9 ft. What is the length of fencing material she will need to fence around the outside her garden?
The garden is described as having a circular shape. The diameter is 9 feet. The length of fencing material needed to fence around the outside of her garden refers to the perimeter or the circumference of the circular garden.
The circumference of a circle is given as;
[tex]\begin{gathered} \text{Cir}=2\pi r \\ r=\frac{\text{diameter}}{2} \\ r=4.5 \\ \text{Cir}=2\times3.14\times4.5 \\ \text{Cir}=28.26 \end{gathered}[/tex]Therefore, Rose would need 28.26 feet of fencing material
The property taxes on a house were $1140. What was the tax rate if the house was valued at $190,000? Follow the problem-solvingprocess and round your answer to the nearest hundredth of a percent, if necessary.
Okay, here we have this:
Considering the provided information we obtain that:
$1140 is x%
$190,000 is 100%
So, here we have the following proportion:
[tex]\frac{190000}{1140}=\frac{100}{x}[/tex]Now, let's solve for x:
[tex]\begin{gathered} x=\frac{1140\cdot100}{190000} \\ x=\frac{114000}{190000} \\ x=\frac{3}{5} \\ x=0.6 \end{gathered}[/tex]Finally we obtain that the tax rate was 0.6%.
which relation is a function A.(2,3),(1,5),(2,7)B.(-1,5),(-2,6),(-3,7)C.(11,9),(11,5),(9,3)D.(3,8),(0,8),(3,-2)
A function can only have one out put value (y) for every input value (x).
A. (2,3) (2,7)
input value 2 has 2 different output values (3 and 7)
It's not a function.
Same case for C and D.
Correct option . B-
Directions - Find the x and y-intercepts for each Standard Form equation. Write your answer as an ordered pair.2x + 4y = 8x - intercept =y - intercept =
We have the following:
[tex]2x+4y=8[/tex]solving for y:
[tex]\begin{gathered} \frac{2}{4}x+\frac{4}{4}y=\frac{8}{4} \\ \frac{1}{2}x+y=2 \\ y=-\frac{1}{2}x+2 \end{gathered}[/tex]now, x- intercept is when y is equal to 0, therefore
[tex]\begin{gathered} 0=-\frac{1}{2}x+2 \\ \frac{1}{2}x=2 \\ x=2\cdot2 \\ x=4 \end{gathered}[/tex]y-intercept is when x is equal to 0, therefore
[tex]\begin{gathered} y=-\frac{1}{2}\cdot0+2 \\ y=2 \end{gathered}[/tex]The answer is:
x - intercept = (4, 0)
y - intercept = (0, 2)
Use the techniques of College Algebra to show how to write an equation for the quadratic graphed below.
x-intercepts: (-3,0) and (1,0). y-intercept: (0,1)
The quadratic equation for the given points x-intercepts: (-3,0) and (1,0). y-intercept: (0,1) is,
f(x) = (-x² - 2x + 3)/3
Given, an equation having
x-intercepts: (-3,0) and (1,0). Also, y-intercept: (0,1)
Now, as we know that the equation is quadratic then, it is clear that the equation will be in the given form :
f(x) = ax² + bx + c
Now, using the given points,
x-intercepts: (-3,0) and (1,0) and y-intercept: (0,1)
we get,
0 = 9a - 3b + c
0 = a + b + c
1 = c
Now, using the value of c, we get
9a - 3b = -1
a + b = -1
On solving the equations, we get
9a - 3b = -1
3a + 3b = -3
On adding both the equations we get,
12a = -4
a = -1/3
Now, using the value of a, we get
-3 - 3b = -1
-2 = 3b
b = -2/3
So, the quadratic equation, be
f(x) = -x²/3 - 2x/3 + 1
On simplifying, we get
f(x) = (-x² - 2x + 3)/3
Hence, the quadratic equation for the given points x-intercepts: (-3,0) and (1,0). y-intercept: (0,1) is,
f(x) = (-x² - 2x + 3)/3
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can someone help with the first problem and show me on a graph
Solution:
The parent graph given was transformed by first shifting it by 3 units to the right, and then shifting 2 units up.
This is shown below:
Therefore, the transformation is a translation of 3 units right and then 2 units up.
Match the figure at the right with the number that represents the sum of the interior angles for that figure.
To calculate the sum of the internal angles of a polygon you have to use the following formula:
[tex](n-2)\cdot180º[/tex]Where "n" is the number of sides of the polygon.
So you have to subtract 2 to the number of sides of the polygon and then multiply the result by 180º to determine the sum of the interior angles.
1) The first polygon has n=4 sides. To calculate the sum of its interior angles you have to do as follows:
[tex]\begin{gathered} (n-2)\cdot180º \\ (4-2)\cdot180º \\ 2\cdot180º=360º \end{gathered}[/tex]2) The second polygon has n=5 sides. The sum of its interior angles can be calculated as:
[tex]\begin{gathered} (n-2)\cdot180º \\ (5-2)\cdot180º \\ 3\cdot180º=540º \end{gathered}[/tex]3) The third polygon has n=6 sides. You can calculate the sum of its interior angles as:
[tex]\begin{gathered} (n-2)\cdot180º \\ (6-2)\cdot180º \\ 4\cdot180º=720º \end{gathered}[/tex]4) The fourth polygon has n=7 sides, so you can calculate the sum of its interior angles as:
[tex]\begin{gathered} (n-2)\cdot180º \\ (7-2)\cdot180º \\ 5\cdot180º=900º \end{gathered}[/tex]on a family trip mr perers travels 130 miles in two hours at this rate how many miles will he travel in 30 minutes?
Answer:
32.5
Step-by-step explanation:
130 miles divided by 120 minutes (2 hours) then take that number and multiply by 30 minutes
Write the expression with a single rational exponent 1/x to the -1 power
Given:
[tex]\frac{1}{x}[/tex]To Determine: The simplified fraction to its rational exponent to the power of -1
Solution
Apply the exponent rule below
[tex]\frac{1}{a^n}=a^{-n}[/tex]Apply the exponent rule above to the given fraction
[tex]\frac{1}{x}=x^{-1}[/tex]Hence, 1/x = x ⁻¹
The worktop is to be covered with square tiles each measuring 4cm by 4cm. How many tiles are needed to cover the worktop.
Answer now.
Answer:
The numbers of tiles is 1900.
Step-by-step explanation:
Firstly, the worktop is 3.04 m^2 or if using conversion that 1m is 100cm, it is 304 cm^2.
Secondly, the surface are of worktop = number of tiles*(side^2).
304 cm^2 = tiles*(3.04cm^2)
Thirdly, solving how many tiles there are, 304 cm^2 / 3.02cm^2
Calculate the given percent of each value.of 2 = 1.84
we have that
2 represents the 100%
Applying proportion, find out how much percentage represents 1.84
100/2=x/1.84
solve for x
x=100*1.84/2
x=92%
the answer is 92%The profit in dollars of running an assembly line that produces custom uniforms each day is given by P(t)=−40t2+960t−4,000
where t represents the number of hours the line is in operation. Determine the number of hours the assembly line should run in order to make a profit of $1,760 per day.
Answer:
12
Step-by-step explanation:
[tex]-40t^2+960t-4000=1760 \\ \\ -t^2+24t-100=44 \\ \\ t^2-24t+144=0 \\ \\ (t-12)^2=0 \\ \\ t=12[/tex]
2.8 -2 3/4 -31/8 2.2 from least to greatest
Express the mixed numbers as decimals and compare:
2.8
-2 3/4
-31/8
2.2
-2 3/4 = -(2x4+3 /4)=11/4 = 2.75
- (31
Tommy throws a ball from the balcony of his apartment down to the street. The height of the ball, in meters, is modeled by the function shown in the graph. What's the average rate of change of the height of the ball, in meters per second, while it's in the air?Question options:A) 2∕3B) –2∕3C) –3∕2D) 3∕2
Solution
The average rate of change of the height of the ball is given by
[tex]\frac{f(b)-f(a)}{b-a}[/tex]Here,
[tex]\begin{gathered} a=0 \\ b=10 \\ f(a)=f(0)=15 \\ f(b)=f(10)=0 \end{gathered}[/tex][tex]\begin{gathered} AverageRate=\frac{f(b)-f(a)}{b-a} \\ AverageRate=\frac{0-15}{10-0} \\ AverageRate=\frac{-15}{10} \\ AverageRate=-\frac{3}{2} \end{gathered}[/tex]The average rate is -3/2
Option C
how do you do 0.52 divided by 2?
Given the Division:
[tex]0.52\div2[/tex]You can identify that, in this case, the Dividend is:
[tex]0.52[/tex]And the Divisor is:
[tex]2[/tex]Then, you can rewrite it in this form:
Notice that the Dividend is a Decimal Number. Then, you can follow these steps to solve the Division:
1. Take the first digit of the Dividend. Since it is 0, any number multiplied by zero is zero, you can place 0 at the top. Place 0 under the first digit of the Dividend too.
2. Subtract the numbers:
3. Bring down the next digit. Since it is the first digit after the Decimal Point, you need to write a Decimal Point at the top:
4. Divide the new number by the Divisor.
5. Find a number whose multiplication with the Divisor 2 gives you 5 as the result or a number closer to 5. These would be 2.
6. Place the number 2 at the top and multiply the divisor by it.
7. Place the result below the number 5 and subtract them.
8. Apply the same procedures with the other digits.
Then:
Hence, the answer is:
[tex]=0.26[/tex]You use a garden hose to fill a wading pool. If the water level rises 11 centimeters every 3 minutes and you record the data point of (9,y), what is the value of y? Use slope to justify your answer.
The value of y is 33 cm.
Given:
You use a garden hose to fill a wading pool. If the water level rises 11 centimeters every 3 minutes and you record the data point of (9,y).
points are (3, 11) and (9, y)
3 minutes = 11 cm
divide by 3
1 minute = 11/3 cm
In 9 minutes, the rise will be ,
= 9 * 11/3
= 3*11
y = 33 cm
slope between (3,11) and (9,33)
m = 33 - 11 / 9 - 3
= 22/6
m = 11/3(this is justification).
Therefore the value of y is 33 cm.
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10. Use the Distributive Property to solve the equation 3(x - 6) + 6= 5x - 6.
3(x-6)+6 = 5x-6
Apply distributive property:
3x-18+6= 5x-6
Combine like terms
3x-12 = 5x-6
Move x terms to the right:
3x-5x = -6+12
-2x = 6
divide both sides by -2
x=-3
Can you help me on what 6x equals? (Grade 10, angles)
First we need to find the value of x, we can use the fact that the sum of the interior angles of a quadrilateral is 360°
[tex]6x+6x+9x+9x=360[/tex][tex]\begin{gathered} 30x=360 \\ \end{gathered}[/tex]then we isolate the x
[tex]x=\frac{360}{30}[/tex][tex]x=12[/tex]then for 9x and 6x, we substitute the value of x=12
[tex]6(12)=72[/tex][tex]9(12)=108^{}[/tex]if x =12, therefore, the angle 6x=72° and the 9x=108°
2. Find the area: Upload a picture of your work or type it out here 25 cm 123 cm 21 cm
The area of a triangle is represented by the following expression:
[tex]\begin{gathered} A=\frac{b\cdot h}{2} \\ \text{where,} \\ b=\text{base} \\ h=\text{height} \end{gathered}[/tex]With the information given, we know that base is 21cm and height is 23cm, now we can substitute and calculate the area:
[tex]\begin{gathered} A=\frac{21\cdot23}{2} \\ A=\frac{483}{2} \\ A=241.5cm^2 \end{gathered}[/tex]( 3y + 1 )( 3y - 1 )Determine each product
It is important to know that a Product is the result of a multiplication.
You have the following expression given in the exercise:
[tex]\mleft(3y+1\mright)\mleft(3y-1\mright)[/tex]Notice that it is the multiplication of two Binomials and it has this form:
[tex](a+b)(a-b)[/tex]By definition:
[tex](a+b)(a-b)=a^2-b^2[/tex]This is called "Difference of two squares".
You can identify that, in this case:
[tex]\begin{gathered} a=3y \\ b=1 \end{gathered}[/tex]Therefore, you get:
[tex]\mleft(3y+1\mright)\mleft(3y-1\mright)=(3y)^2-(1)^2=9y^2-1[/tex]The answer is:
[tex]9y^2-1[/tex](-3,-5) (-6,10)Find the slope
Weare asked to find the slope of the segment that joins the points (-3, -5) and (-6, 10) on the plane.
We used the formula for the slope:
slope = (y2 - y1) / (x2 - x1)
which in our case gives:
slope = (10 - -5) / (-6 - -3) = 15 / -3 = -5
The slope is -5.
A realtor wanted to determine if there was a relationship between the size (in 100 square feet) of a new custom-built home and the price (in thousands of dollars) of the home.
Size, x Price, y
26 235
27 273
41 387
29 253
33 295
34 335
36 395
45 475
22 203
a) Determine the Person Correlation Coefficient.
b) Test whether there is a relation between size and price.
c) Draw the scatter diagram
d) Determine the Least Square line.
e) If a new custom-built home is of a size 3700 square feet what would be its price.
¬¬
The graphs , solutions and table are attached below and check out the calculation part just by scrolling down.
What is statistics ?In the field of applied mathematics known as statistics, gathering, describing, analyzing, and drawing conclusions from numerical data are important tasks. Probability theory, linear algebra, and differential and integral calculus are the main mathematical foundations of statistics.
Calculationsee the graphs and table attached below
a ) The cluster (points) shows upward direction and nearly to linear form. So it is positive Correlation.)
b ) calculation part for this part has been attached in pictures below since it was not possible to write here .
the regression line of y on x is =
Y = 11.5355X - 58.7667
c ) r^2 = 58313.22 / 62507.5556 = 0.9328
It is high correlation, So the regression equation is good fit to the given data. 93% of the total variation in y occurs because of the variation in their x.
d ) H0: Slope of Regression Coefficient is Zero
H1: Slope of Regression coefficient is not Zero.
calculation part in pictures attached .
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what is (15+ -7) (-4)
Answer:
-32
Explanation:
Given the expression:
[tex]\mleft(15+-7\mright)(-4)[/tex]We can rewrite this as:
[tex]\begin{gathered} (15-7)(-4) \\ =8\times-4 \\ =-32 \end{gathered}[/tex]Which list shows the numbers below in order from least to greatest?5.78, -5.9, 58%, 23-5.9, 23. 5.78, 58%2.-5.9, 58%, 5.78-5.9, 23. 58%, 5.7858%, 23. 5.78, -5,9o
The numbers in the alternatives are the same, so we have to see which is the lowest to start with.
There are two negative ones: -5.9 and -23/4. Dividing the second one we have:
[tex]-\frac{23}{4}=-5.75[/tex]We can see that -5.9 is lower than -5.75. So we have only two alternatives left.
58% is equivalent of 58/100, so:
[tex]\frac{58}{100}=0.58[/tex]So 58% = 0.58, which is lower than 5.78.
So we have the order, from least to greatest:
-5.9, -23/4, 58%, 5.78.
This corresponds to the third alternative.
What is the missing length?Area of shaded region = 184 mm^2.p = ___ milimeters.
The formula to calculate the area of a triangle is
[tex]A=\frac{p\cdot b}{2}[/tex]in our case we have p is the height of the triangle, and b is the base of the triangle
A=184 mm^2
b=16mm
we substitute the data given
[tex]184=\frac{p\cdot16}{2}[/tex]then we isolate the p
[tex]p=\frac{184\cdot2}{16}[/tex][tex]p=23[/tex]