A(x,y) becomes A'(y,-x):
So:
x(-5, 8) ------------>x'(8,5)
For a 90 Degree Rotation counter clockwise:
A(x,y) becomes A' (-y,x)
Therefore:
A(1,5)----------->A'(-5,1)
B(3,6)----------->B'(-6,3)
C(5,2)------------>C'(-2,5)
D(3,1)------------->D'(-1,3)
65 people showed up to the party. There were 7 less men than women present. How many women were there?
Let x be women and y men.
x + y = 65 equation 1.
y = x - 7 equation 2.
Now we need to solve the equation system, as follows:
- on eq. 2 y is already solved, so we can replace y on eq. 1:
x + x - 7 = 65
2x - 7 = 65
2x = 65 + 7
2x = 72
x = 72/2
x = 36 women
Finally, we replace x on eq 2:
y = 36 - 7
y = 29 men
Factor:9/100 x^2 - 4/25
Answer:
[tex]\frac{9}{100}x^2-\frac{4}{25}=(\frac{3}{10}x-\frac{2}{5})(\frac{3}{10}x+\frac{2}{5})[/tex]Explanation:
Given the expression:
[tex]\frac{9}{100}x^2-\frac{4}{25}[/tex]This can be written as a difference of two squares. But before that, we can rewrite the expression as:
[tex](\frac{3}{10}x)^2-(\frac{2}{5})^2[/tex]So, as a different of two squares, we write:
[tex](\frac{3}{10}x-\frac{2}{5})(\frac{3}{10}x+\frac{2}{5})[/tex]Given the numbers -100, -14.5, -2, -2/3, 0, 10,15, 20 1/6, which are rational numbers?
A rational number is a number that can be written in the form of p/q where q is not equal to zero.
The rational numbers are -100, -14.5, -2, -2/3, 0,10, 15, 20 1/6.are rational.
What is a rational number?A rational number is a number that can be written in the form of p/q where q is not equal to zero.
We have,
-100, -14.5, -2, -2/3, 0, 19, 15, 20, 1/6
-100 = -100/1
It is in the form of p/q.
It is a rational number.
-14.5 = -145/10
It is in the form of p/q.
It is a rational number.
-2 = -2/1
It is in the form of p/q.
It is a rational number.
-2/3 = -2/3
It is in the form of p/q.
It is a rational number.
0 = 0/1
It is in the form of p/q.
It is a rational number.
19 = 19/1
It is in the form of p/q.
It is a rational number.
15 = 15/1
It is in the form of p/q.
It is a rational number.
20 = 20/1
It is in the form of p/q.
It is a rational number.
1/6
It is in the form of p/q.
It is a rational number.
We see that all the numbers given are rational numbers.
Thus,
The rational numbers are -100, -14.5, -2, -2/3, 0, 10, 15, 20 1/6.
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What is the slope of f(x)=3? 3 Undefined
Given the function:
[tex]f(x)=3[/tex]notice that this is a constant function, and its graph looks like this:
therefore, the slope of a constant function is 0
Which pair of functions are inverses of each other?A. f(x) = 5 + 6 and g(x) = 5x - 6B. f(x) = { and g(x) = 6x3C. f(x) = 7x - 2 and g(x) = 42D. f(x) = - 2 and g(x) = -2
To find the pair of functions that are inverses of each other, we should check through the options.
Option A
[tex]\begin{gathered} f(x)\text{ = }\frac{x}{5}\text{ + 6} \\ g(x)\text{ = 5x -6} \end{gathered}[/tex]First, we set f(x) = y. Thus:
[tex]y=\text{ }\frac{x}{5}\text{ + 6}[/tex]Then, we swap the variables:
[tex]x\text{ = }\frac{y}{5}\text{ + 6}[/tex]Make y the subject of formula:
[tex]\begin{gathered} x\text{ = }\frac{y}{5}\text{ + 6} \\ \frac{y}{5}\text{ = x -6} \\ y\text{ =5x -30} \end{gathered}[/tex]But:
[tex]g(x)\text{ }\ne\text{ 5x -30}[/tex]Hence, option A is incorrect
Option B
[tex]\begin{gathered} f(x)\text{ =}\frac{\sqrt[3]{x}}{6} \\ g(x)=6x^3 \end{gathered}[/tex]Set f(x) = y. Thus:
[tex]y\text{ = }\frac{\sqrt[3]{x}}{6}[/tex]Swap the variables:
[tex]x\text{ = }\frac{\sqrt[3]{y}}{6}[/tex]Make y the subject of the formula:
[tex]\begin{gathered} 6x\text{ = }\sqrt[3]{y} \\ \text{Cube both sides} \\ (6x)^3\text{ = y} \\ y\text{ = }216x^3 \end{gathered}[/tex]But:
[tex]g(x)\text{ }\ne216x^3[/tex]Hence, Option B is incorrect
Option C:
[tex]\begin{gathered} f(x)\text{ = }7x\text{ -2} \\ g(x)\text{ = }\frac{x\text{ + 2}}{7} \end{gathered}[/tex]Set f(x) = y. Thus:
[tex]y\text{ = 7x - 2}[/tex]Swap the variable:
[tex]x\text{ = 7y -2}[/tex]Make y the subject of formula:
[tex]\begin{gathered} x\text{ + 2 = 7y} \\ 7y\text{ = x +2} \\ \text{Divide both sides by 7} \\ \frac{7y}{7}\text{ = }\frac{x+2}{7} \\ y\text{ = }\frac{x+2}{7} \end{gathered}[/tex]But :
[tex]g(x)\text{ = }\frac{x+2}{7}[/tex]Hence, option C is correct
Option D
[tex]\begin{gathered} f(x)\text{ = }\frac{5}{x}\text{ -2} \\ g(x)\text{ =}\frac{x+2}{5} \end{gathered}[/tex]Set y =f(x). Thus:
[tex]y\text{ = }\frac{5}{x}\text{ -2}[/tex]Swap the variables:
[tex]x\text{ = }\frac{5}{y}\text{ -2}[/tex]Make y the subject of formula:
[tex]undefined[/tex]Answer the following.(a) A certain solution has a hydrogen ion concentration of 0.00000896 moles per liter. Write this number in scientific notation.(b) A humpback whale can weigh up to 1.1 * 10^5 pounds. Write this number in standard notation.
Given:
Two statements (a) and (b) are given.
Find:
we have to write the answers of both statments (a) and (b).
Explanation:
(a) A certain solution has a hydrogen ion concentration of 0.00000896 moles per liter
The scientific notation of 0.00000896 is
[tex]8.96×10^{-6}[/tex]......................................................................................................................................
(b) A humpback whale can weigh up to 1.1 * 10^5 pounds
The standard form of the given number is given as below
[tex]1.1\times10^5=110000[/tex]
Solve for x. Assume that any line that appears to be a tangent is a tangent to the circle.
To solve the problem, we need to apply the rule:
When two tangents intersect at a point outside the circle, they are congruent
Hence, we can write:
[tex]6x\text{ -5 = 4 + 5x}[/tex]Solving for x:
[tex]\begin{gathered} Collect\text{ like terms} \\ 6x\text{ - 5x = 4 + 5} \\ x\text{ = 9} \end{gathered}[/tex]Answer:
x = 9
A flower bed is in the shape of a rectangle. It measures7 yd long and 4 yd wide. Alonzo wants to use mulch tocover the flower bed. The mulch is sold by the squarefoot. Use the facts to find the area of the flower bed insquare feet.0A²X$Conversion facts for length1 foot (ft) = 12 inches (in)1 yard (yd)1 yard (yd)=C3 feet (ft)36 inches (in)I need help with this math problem.
Answer: We have to find the amount of mulch in square feet that would cover the flower bed shape which has the dimensions of 7yd and 4yd:
[tex]\begin{gathered} 7yd=(3\times7)ft=21ft \\ \\ 4yd=(3\times4)ft=12ft \\ \end{gathered}[/tex]Therefore the amount of mulch needed is as follows:
[tex]21ft\times12ft=252ft^2[/tex]Write the equation of a line parallel to the line determined by the points( -2,1) and (0,5 ) passing through the point (1,4)
Answer:
y = 2x + 2
Step-by-step explanation:
Find the slope of the line that passes through the points (-2, 1) and (0, 5):
[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{5-1}{0-(-2)}=\dfrac{4}{2}=2[/tex]
If two lines are parallel they have the same slope.
Therefore, the slope of the other line that passes through point (1, 4) is also 2.
To find the equation of the parallel line that passes through the point (1, 4), substitute the found slope of 2 and the point (1, 4) into the point-slope formula:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-4=2(x-1)[/tex]
[tex]\implies y-4=2x-2[/tex]
[tex]\implies y=2x+2[/tex]
the table and graph shows the distance Javier and chloe are from a motion detector in terms of time Javier table and chloe table photo in the chatwho is moving away from the motion detector faster.
Chloe is moving away from the motion detector faster
Explanations:The one that has the highest rate of change of distance with time is moving away from the motion detector faster.
Let us calculate the rate of change of Javier's distance from the motion detector with time.
[tex]\begin{gathered} \frac{\Delta d}{\Delta t}=\text{ }\frac{10-5}{4-2} \\ \frac{\Delta d}{\Delta t}\text{ = }\frac{5}{2} \\ \frac{\Delta d}{\Delta t}\text{ = 2.5 m/s} \end{gathered}[/tex]Javier is moving with a speed of 2.5 m/s from the motion detector
Then, let us calculate the rate of change of Chloe's distance from the motion detector with time.
[tex]\begin{gathered} \frac{\Delta d}{\Delta t}=\text{ }\frac{12-9}{4-3} \\ \frac{\Delta d}{\Delta t}=\text{ }\frac{3}{1} \\ \frac{\Delta d}{\Delta t}=\text{ 3 m/s} \end{gathered}[/tex]Chloe is moving with a speed of 3.0 m/s from the motion detector
Chloe is moving away from the motion detector faster than Javier
Express the confidence interval 15.8% ± 5.4% in interval form.Answer using decimals rounded to three places, not as percentages
Okay, here we have this:
Considering the provided confidence interval we are going to express it in interval form, so we obtain the following:
So let's first convert the interval from percent to decimals:
Confidence interval=15.8% ± 5.4%
Confidence interval=0.158 ± 0.054
And the interval form will be obtained by leaving the result using the lesser on the left side, and the result using the more on the right side:
Confidence interval=[0.158-0.054, 0.158+0.054]
Confidence interval=[0.104, 0.212]
Finally we obtain that the confidence interval in interval form is equal to [0.104, 0.212].
A corner lot that originally was square lost 185 m² of area when one of the adjacent syreets what is wide by 3 m and the other was widnened by 5 m find the new dimensions of the lot
The new dimensions of the lot is length = 22 meters and width = 20 meters
The corner lot that originally was square
Consider the side of the lot = x
The area of the square = Length × length
Therefore,
x × x = [tex]x^2[/tex]
one of the adjacent streets which is widened by 3 m and the other was widened by 5
Therefore
(x-3) × (x-5) = [tex]x^2[/tex] - 185
open the brackets
[tex]x^2-5x-3x+15=x^2-185[/tex]
The x square term will cancel each other
-5x-3x = -185-15
-8x = -200
x = 25 meter
The new length of the lot = x-3
= 25-3
= 22 meter
The new width of the lot = 25-5
= 20 meters
Hence, the new dimensions of the lot is length = 22 meters and width = 20 meters
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A cookie has a radius of 1 inch. What is the area of the cookie?
(Use ≈ 3.14.)
Answer:
3.14 inches squared
Step-by-step explanation:
A = π r²
A = π (1)²
A = π 1
A = 3.12
1.An integer is 3 less than 5 times another. If the product of the two integers is 36, then find the integers
integer 1 = x
Integer 2 = y
An integer is 3 less than 5 times another
x-3 = 5y
A school buys 15 computer monitors for the computer lab. It spends a total of $1,875 on the monitors. The equation 15 x c=1,875 can be used to find the cost of each monitor.Write a division equation that can be used to find the cost of each computer monitor. Use c to represent the cost of each monitor. Do not solve the equation.
Answer:
c=1875/15
Explanation:
The equation to find the cost of each monitor is given as:
[tex]15\times c=1,875[/tex]To write a division equation that can be used to find the cost of each computer monitor, we divide each side of the equation by 15.
[tex]\begin{gathered} \frac{15\times c}{15}=\frac{1875}{15} \\ c=\frac{1875}{15} \end{gathered}[/tex]To simplify meant toA. Multiply all the coefficients B. Divide like termsC. Combine like termsD. Substract all the coefficients
To simplify means to combine like terms so that it will make the expression
An employee earns an hourly wage shown in the graph below.Find the hourly wage using the graph in the attachment.
The hourly wage of the employee is shown in the graph
Since the graph the has the point (1.40)
In 1 hour the wage of the employee is 40 dollars.
Hence the hourly wage is $40.
If UW = 9x - 9, what is UW in units?
We have the following:
[tex]\begin{gathered} UW=UV+VW \\ \text{where} \\ UW=9x-9 \\ UV=2x-4 \\ VW=4x+10 \end{gathered}[/tex]replacing:
[tex]\begin{gathered} 9x-9=2x-4+4x+10 \\ 9x-9=6x+6 \\ 9x-6x=9+6 \\ 3x=15 \\ x=\frac{15}{3}=5 \end{gathered}[/tex]Therefore:
[tex]UW=9\cdot5-9=45-9=36[/tex]The answer is 36 units
Could u tell me what to put in the boxes? And the convince me needs to be answered as well. thank you very much!
The radius, r, is half the diameter.
Given, diameter = 6, the radius will be 6/2 = 3
Putting this into the volume of a sphere formula, we get:
[tex]\begin{gathered} V=\frac{4}{3}\pi r^3 \\ V=\frac{4}{3}\pi(3)^3 \end{gathered}[/tex]First blank box >>> 3
Now,
We can find (4/3)π using 3.14 as π and (3)^3 is "27".
Thus,
[tex]=(\frac{4}{3}\pi)(27)[/tex]These are the second and third blanks.
Multiplying, we get:
V = 113.04 >>> this is the fourth blank
The volume of the golf ball is about 113.04 cm^3.Convince Me
The volume of a cone is given by the formula
[tex]V=\frac{1}{3}\pi r^2h[/tex]If the radius is same as sphere, then it's "r".
The height of a sphere is twice radius, or, 2r. So, that's the height of the cone as well, thus we have:
[tex]undefined[/tex]Line P parallel to side AB of triangle ABC, intersects AC and BC at points D and E, respectively. Find the area of triangle ABC if area of ABD=a and area of AEC=b
The area of triangle ABC if area of ABD = a and area of AEC = b is; (b + a) sq. units
What is the Area of the Triangle?The formula for the area of a triangle is;
Area = ¹/₂ × base × height
Thus;
Area of Triangle ADB is;
Area of ΔADB = ¹/₂ × AB * h_d
The area of the triangle AEB is;
Area of ΔAEB = ¹/₂ × AB * h_e
Due to the fact that AB and p are parallel lines, then it means we can say that; h_d = h_e
Therefore by substitution property, we can say that;
Area of ΔADB = Area of ΔAEB
Thus;
Area of Triangle ABC = Area of ΔADB + Area of ΔAEB = (b + a) sq. units
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Knowing that Mountain McKinley is above sea level and death valley is below sea level. What integer would be used to represent sea level. Explain
we can use integer 0 as a sea level.
how do I write a function for area A (s)there are 36 tiles with lengths from 2-6 inches
A dog breeder had a certain number of adult dogs. Each of those dogs had three puppies. The breeder sold 10 of the puppies and she now has 22 dogs (both puppies and adult dogs) with her. How many dogs did she begin with?
Answer:
i think i could be very wrong, but i think its 11 dogs to start with rounded up
Step-by-step explanation:
i added ten to 22, so i got 32, divided by three was 10.67 which i rounded to 11
Solve 49^(2x-1) = 7^(3x+2)
Answer:
[tex]x=4[/tex]Step-by-step explanation:
Solving for x,
[tex]\begin{gathered} 49^{2x-1}=7^{3x+2} \\ \rightarrow(7^2)^{2x-1}=7^{3x+2} \\ \rightarrow7^{4x-2}=7^{3x+2} \\ \rightarrow4x-2=3x+2 \\ \rightarrow4x-3x=2+2 \\ \rightarrow x=4 \end{gathered}[/tex]This way, we can conlcude that:
[tex]x=4[/tex]Which function below is the inverse of f(x) = X2 - 25?
Answer: [tex]f^{-1}(x)= \sqrt{x+25}[/tex] and [tex]f^{-1}(x)= - \sqrt{x+25}[/tex]
Step-by-step explanation:
To find the inverse, we will set f(x) equal to y, swap the x and y values, and then solve for y.
Given:
f(x) = x² - 25
Equal to y:
y = x² - 25
Swamp x and y values:
x = y² - 25
Add 25 to both sides of the equation:
y² = x + 25
Square root both sides of the equation:
[tex]y= \sqrt{x+25}[/tex] and [tex]y= -\sqrt{x+25}[/tex]
Interval notation:
[tex]f^{-1}(x)= \sqrt{x+25},\text{and}\;f^{-1}(x)= -\sqrt{x+25}[/tex]
⇒Note for inverses we swap the positions between x and y.
⇒[tex]x=y^{2} -25\\[/tex]
But in this case we know that we write the equation such that the variable for the input is the subject of the equation
[tex]y^{2}= x+25\\y=\sqrt{x+25}[/tex]
Note y in this case was representing f(x)
⇒therefore our final equation now is
[tex]f(x)=\sqrt{x+25}[/tex]
GOODLUCK!!!
Basic ratios What is the ratio of cows to chunks of cheese? Choose 1 answer: 2 to 4 or 4 to 2 2 to 5 or 5 to 2
Answer:
B. 4 to 2
Explanation:
The ratio of cows to chunks of cheese can be written as the number of cows to the number of chunks of cheese.
Since there are 4 cows and 2 chunks of cheese, the ratio is:
4 to 2
When the mortgage is completely paid off for Mark and Lynne’s house, it will be 6 times as old as it is now. If they have 25 years left on the mortgage, how old is the house right now?
Let us take the age of the house currently as x.
The second statement says that the house will be 6 times as old as it is now after payment is completed.
If the mortgage will be completed in 25 years, we can write that mathematically as
[tex]6x=x+25[/tex]Therefore, the age of the house, x, can be calculated as
[tex]\begin{gathered} 6x-x=25 \\ 5x=25 \\ x=\frac{25}{5} \\ x=5 \end{gathered}[/tex]Hence, the house is 5 years old now.
the slope of a line is -2/5. One coordinate is located at (6, -8) and the other coordinate is located at (a, -4). Use the slope formula to solve for y
Answer:
a = - 4
Step-by-step explanation:
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )
m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
~~~~~~~~~~
( 6 , - 8 )
( a , - 4 )
[tex]\frac{-4 +8}{a-6}[/tex] = - [tex]\frac{2}{5}[/tex]
2( a - 6 ) = - 5( - 4 + 8 )
2a - 12 = - 20
2a = - 8
a = - 4
The product of two numbers is 4÷5, find the other number
9x+23y=10 rewrite the equation so that y is a function of x (explanation pls)