Answer:
m=-2/3 (slope)
b=3 (y-intercept)
Step-by-step explanation:
Slope-intercept form is y=mx+b where the slope is m and the y-intercept is b.
You have 3y+2x=9.
We need to solve this for y to get it into y=mx+b form.
3y+2x=9
Subtract 2x on both sides:
3y =-2x+9
Divide both sides by 3:
[tex]y=\frac{-2}{3}x+\frac{9}{3}[/tex]
[tex]y=\frac{-2}{3}x+3[/tex]
Now compare this to:
y=mx+b
m=-2/3
b=3
Plants are the major source of what biochemical needed in your diet? What specifically is this biochemical used for, and how is it broken down during digestion?
Carbohydrates. Carbohydrates are digested in the mouth, stomach and small intestine. Carbohydrase enzymes break down starch into sugars. The saliva in your mouth contains amylase, which is another starch digesting enzyme.
The owner of a chain of clothing stores is comparing the monthly profit earned in the past year from four different store locations. She calculated the mean and standard deviation of the monthly profit, in dollars, for each location, as shown in the table.
For which store location does 68% of the data lie between $19,371.18 and $22,295.48?
Answer:
Answer choice C, location C
Step-by-step explanation:
If you add or subtract the standard deviation to the monthly profit, then you get $19,371.18 and $22,295.48. This shows that the deviation withholds most of the data given
The store location for which [tex]68%[/tex]% of the data lies between $19,371.18 and $22.295.48 is location C
What is standard deviation?
Standard deviation explains the relation of data with mean.
How to find the location of the data?
For normal distributions, 68% of the data lies under one SD from the mean. Two standard deviations is within 95%, and three standard deviations would take up to 99%.
This implies that on taking (mean + SD) and (mean - SD), 68% of data would cover these two numbers.
Add and subtract SD from the mean to check which location will give $19,371.18 and $22.295.48.
For location A, we have
M-SD=23,124.70-1553.43=21,571.27
M SD = 23,124.70 + 1,553.43 = 24,678.4
For location B, we have
M - SD = 24,842.18 - 1,617.20 = 23,224.98
M + SD = 24, 842.18 + 1,617.20 = 26,459.38
For location C, we have
M - SD = 20,833.33 - 1,462.15 = 19,371.18
M + SD = 20,833.33 + 1,462.15 = 22,295.48
This implies the store location is C
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simplify the expression below
[tex]\sqrt{\dfrac{3}{15x}}=\sqrt{\dfrac{1}{5x}}=\dfrac{1}{\sqrt{5x}}=\dfrac{\sqrt{5x}}{5x}[/tex]
Given the functions f(x) = x^2 - 2x - 4 and g(x) = 2x - 4, at what values of x do f(x) and g(x) intersect?
Answer:
* The values of x are 0 and 4
Step-by-step explanation:
* Lets explain how to solve the problem
- f(x) = x² - 2x - 4 is a quadratic function
- g(x) = 2x - 4
∵ f(x) and g(x) are intersected
∴ They meet each other in a point
- To find this point equate the two functions
∵ f(x) = g(x)
∵ f(x) = x² - 2x - 4
∵ g(x) = 2x - 4
∴ x² - 2x - 4 = 2x - 4 ⇒ subtract 2x from both sides
∴ x² - 4x - 4 = -4
- Add 4 to both sides
∴ x² - 4x = 0
- Take x as a common factor
∴ x(x - 4) = 0
- Equate each factor by 0
∴ x = 0
- OR
∴ x - 4 = 0 ⇒ add 4 to both sides
∴ x = 4
∴ f(x) and g(x) intersected at x = 0 and x = 4
* The values of x are 0 and 4
cos2a=2cos^2a-1 for all of a
true or false?
[tex]\bf ~\hspace{10em}\textit{Double Angle Identities}\\\\ sin(2\theta)=2sin(\theta)cos(\theta) ~\hfill cos(2\theta)= \begin{cases} cos^2(\theta)-sin^2(\theta)\\ 1-2sin^2(\theta)\\ \boxed{\bf 2cos^2(\theta)-1} \end{cases} \\\\\\ tan(2\theta)=\cfrac{2tan(\theta)}{1-tan^2(\theta)}[/tex]
well, take a peek at the cos(2θ) identities.
Determine the length of a chord whose central angle is 75° in a circle with a radius of 12 inches.
Answer:
Step-by-step explanation:
length=sqare root of(12^2+12^2-2*12*12*cos(75))=14.6
The length of a chord whose central angle is 75° in a circle with a radius of 12 inches is 14.6 inches.
What is a circle?A circle is the set of all points in the plane that are a fixed distance (the radius) from a fixed point (the center)
What is central angle of a circle?A central angle is an angle with endpoints and located on a circle's circumference and vertex located at the circle's center
How to find the length of the chord?Here, the radius and the chord forms a triangle, whose vertical angle is 75°.We know that for a triangle ABC , we can easily write,[tex]cos A = \frac{b^{2}+c^{2}-a^{2}}{2bc}[/tex], where a, b ,c are the sides opposite to ∠A, ∠B, ∠C respectively.
In triangle, let ∠A = 75°.
∴ We can write, [tex]cos 75 = \frac{b^{2}+c^{2}-a^{2}}{2bc}[/tex].
Here b and c are actually the radius of the circle which is 12 inches.a is actually the chord of the circle.We actually need to find the value of a.So, we can write,
(cos 75)(2 x 12 x 12) = (12)² + (12)² - a²
⇒ a = 14.6
∴ the length of the chord is 14.6 inches.
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In the diagram, the measure of angle 9 is 85°
Which angle must also measure 85°?
Answer:
it is 11 degrees and i did the doom quiz and passt so yeah bye peace
Help I don’t understand how to solve word problems. Answer is not 3/8=21/y
Answer:
[tex]\frac{3}{11}=\frac{21}{y}[/tex]
Step-by-step explanation:
3 boys -> 8 girls -> 11 students
21 boys -> _____ -> y students
This information is lined up for you to solve for your number of students, y:
Looking vertically you could say the proportion is:
[tex]\frac{3}{21}=\frac{11}{y}[/tex]
Looking horizontally you could say the proportion is:
[tex]\frac{3}{11}=\frac{21}{y}[/tex]
There are other ways to write this but this last one I wrote answers your question.
A silversmith combined pure silver that cost $30.48 per ounce with 52 oz of a silver alloy that cost $21.35 per ounce. How many ounces of pure silver were used to make an alloy of silver costing $24.76 per ounce?
oz
To solve for the amount of pure silver in the alloy mixture, use the alloy mixture equation in algebra. After setting up and solving the equation, we find that roughly 22.83 ounces of pure silver are used to produce the desired alloy,
Explanation:This problem can be solved using the alloy mixture equation, which is used to determine how to create a desired mixture by blending two substances of different concentrations. Let's denote the amount of pure silver used as 'x'. So, the equation can be set up as follows:
($30.48 × x + $21.35 × 52) / (x + 52) = $24.76.
After multiplying through by (x + 52) and doing algebra, you will find that x (ounces of pure silver) equals approximately 22.83 ounces.
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The length of a rectangle is 7 yards less than three times the width, and the area of the rectangle is 66 square yards, find the dimensions of the rectangle
Answer:
length = 11
width = 6
Step-by-step explanation:
The area of a rectangle is defined by the following formula:
[tex]A=lw[/tex]
The question content tells us this:
[tex]l=3w-7\\A=66[/tex]
If we plug these into our formula, we can find the dimensions.
[tex]66=w(3w-7)\\66=3w^2-7w\\[/tex]
Once we factor this out, we find that [tex]w=6[/tex] and [tex]w=-\frac{11}{3}[/tex]
Since a side length can't be a negative, our width is 6.
[tex]66=6l\\11=l[/tex]
which expression shows the perimeter of a rug that is 5 yards in length and 3 yards in width? A.2(5x3) B.2(5+3) C , 2(5-3) D.2(5/3)
For this case we have that the rug is rectangular.
By definition, the perimeter of a rectangle is given by:[tex]P = 2a + 2b = 2 (a + b)[/tex]
Where:
a, b: Represent the sides of the rectangle
Substituting according to the data we have:
[tex]P = 2 (5 + 3)[/tex]
Thus, the correct expression is option B.
Answer:
Option B
Simplify remove all perfect squares from inside the square 98
Answer:
[tex]7\sqrt{2}[/tex]
Step-by-step explanation:
We start by factoring 98 and look for a perfect square:
98=7*7*2 = [tex]7^{2} *2[/tex]
This allow us to simplify the radical:
[tex]\sqrt{98} = \sqrt{7^{2}*2 }[/tex]
Finally we have:
[tex]\sqrt{7^{2}*2 } =7\sqrt{2}[/tex]
What is the angle of elevation of the sun if a 45 foot tall flag pole casts a 22 foot long shadow?
Answer:
=63.9°
Step-by-step explanation:
To find the angle of elevation using the shadow of an object, we use the trigonometric ratio Tangent.
Tan∅=opposite/adjacent
Opposite is the height of pole while adjacent is the shadow of the pole.
The tan of the angle of elevation= height of the pole/length of shadow
Tan ∅=45/22
∅= Tan⁻¹(45/22)
=63.9°
Angle of elevation=63.9°
One solution to the problem below is 6.
What is the other solution?
m²-36=0
Answer:
-6
Step-by-step explanation:
[tex]m^2-36=0[/tex]
Adding 36 on both sides gives:
[tex]m^2=36[/tex]
Square rooting both sides:
[tex]m=\pm \sqrt{36}[/tex]
[tex]m=\pm 6[/tex]
So if square -6 , you will get 36 just like when you square 6.
That is [tex](-6)^2=6^2=36[/tex]
Answer:
-6
Step-by-step explanation:
If one solution to the problem m²-36=0 is 6, the other solution is -6.
(m + 6) • (m - 6) = 0
Any solution of term = 0 solves product = 0 as well.
m+6 = 0
m = -6
m-6 = 0
m = 6
Two solutions were found : m = 6 m = -6A 3-digit numeral is formed by selecting digits at random from 2,4,6,7 without repetition. Find the probability that the number formed contains only even digits. P(even digits)
Answer:
3/4.
Step-by-step explanation:
Total number of ways to pick 3 digits from the 4 given digits = 4P3
= 4!/ 1! = 24 ways.
The odd numbers are formed when 7 is the last digit of the 3 digits and this will be in 6 numbers 247, 267, 427, 467, 647 and 627 . So there will be 24 - 6 = 18 even numbers.
So the probability of only even digits = 18/24 = 3/4.
What is the distance between the points (-4, -12) and (-4, 22) in the coordinate plane?
Answer:
34
Step-by-step explanation:
You can use the distance formula to find the distance between any two points in the coordinate plane.
For this problem, you can use a simpler method since both points have the same x-coordinate. Two points than have the same x-coordinate are on the same vertical line. The distance between them is the absolute value of the difference between the y-coordinates.
distance = |-12 - 22| = |-34| = 34
Answer:
34
Step-by-step explanation:
By the distance formula:
[tex]D = \sqrt{[-4-(-4)]^2 + (22-(-12))^2} = \sqrt{34^2} = |34| = 34[/tex]
Which statements describe one of the transformations performed on f(x) = x^2
to create g(x) = 2x^2 +5?
Answer:
vertically stretched by a factor of 2 and moved up 5 units
Step-by-step explanation:
f(x)=x^2
f(x+5) means it moved left 5 units.
f(x-5) means it moved right 5 units.
f(x)+5 means it moved up 5 units.
f(x)-5 means it moved down 5 units.
One of the transformations we have is that it moved up 5 units.
m(x)=f(x)+5
m(x)=x^2+5
Now there is another transformation.
f(x)=x^2
a*f(x) means it is either being vertically stretched or compressed. a also tells if we have a reflection (if a is negative) or not (if a is positive).
n(x)=2x^2 means it has been vertically stretched by a factor of 2.
Let's put it altogether.
g(x)=2x^2+5
means the parent function has been vertically stretched by a factor of 2 and moved up 5 units
The transformations applied to f(x) to create g(x) involve a vertical stretching by a factor of 2 and a vertical shift upward by 5 units. These modifications result in a parabolic curve that is steeper and shifted upwards compared to the original f(x).
To transform the function [tex]f(x) = x^2[/tex] into [tex]g(x) = 2x^2 + 5,[/tex] several alterations are made.
First, the function is scaled vertically by a factor of 2.
This means that the output values of g(x) are twice as large as those of f(x) for any given input.
This vertical stretching increases the steepness of the parabolic curve.
Secondly, a constant term of 5 is added to g(x).
This shifts the entire graph of the function vertically upward by 5 units, creating an upward shift.
Consequently, g(x) is now centered 5 units above f(x).
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How do I figure this one out whats the answer
Look at the picture
Find the missing angle measure in each triangle. Show your work.
Answer:
see explanation
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Subtract the sum of the 2 given angles from 180 for third angle
∠C = 180° - (50 + 75)° = 180° - 125° = 55°
∠B = 180° - (60 + 30)° = 180° - 90° = 90°
∠A = 180° - (45 + 30)° = 180° - 75° = 105°
The required measure of the angle for the given triangles is given as ∠C = 55°, ∠B = 90° and ∠A = 105°
What is the triangle?The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°
Here,
The sum of the 3 angles in a triangle = 180°
Subtract the sum of the 2 given angles from 180 for the third angle
∠C = 180° - (50 + 75)°
= 180° - 125°
= 55°
Similarly,
∠B = 90°
∠A = 105°
Thus, the required measure of the angle for the given triangles is given as ∠C = 55°, ∠B = 90° and ∠A = 105°
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A pair of shoes costs $30.99 and the sales tax is 5%. Use the formula C = p + rp to find the total cost of the shoes, where C is the total cost, p is the price, and r is the sales tax rate.
Answer:
32.49
Step-by-step explanation:
First you must set up the probably and plug in the variables into the formula. Sthe formula would turn into the equation: C=30.99 (c for cost) + .5 [r for tax] (30.99) c for cost. Then you will solve the equation:
1. C= 30.99+.5(30.99)
2. C= 30.99+ 1.50
3. C= 32.49
Answer:
The total cost of the shoes is $32.5395.
Step-by-step explanation:
The equation that you must use is [tex]C=p+p\times r[/tex]. Keep in mind that percentage number is the number divided by 100 in real numbers. For example, 5% equals 0.05. So, instead of using the term 5%, you must use 0.05.
Now, let's replace the variables in the equation with the data that the problem gives.
[tex]C=p+p\times r[/tex]
[tex]C=(30.99)+(30.99)\times (0.05)[/tex]
[tex]C=30.99+1.5495[/tex]
The term $1.5495 refers to the tax that must be paid for the shoes. The total cost is the sum of the price and the tax.
[tex]C=32.5395[/tex]
Thus, the total cost of the shoes is $32.5395.
A person is standing 40 ft from a light post and can see the top of the light at a 35∘ angle of elevation. The person’s eye level is 5 feet from the ground. What is the height of the lightpost to the nearest foot. The height of the light post is feet.
Answer:
Height of light post = 33 feet
Step-by-step explanation:
We will use the trigonometric ratios to find the height of light post
The given scenario forms a right angled triangle with the right angle with the light post.
The distance between light post and the person is the base.
So, base = b = 40 feet
The height of light post will be the perpendicular
So,
Perpendicular = p = x
Angle = 35°
So,
tan (angle) = p/b
tan 35° = p/40
0.7002 =p/40
0.7002*40 = p
p = 28 feet
Since the persons eye level is 5 feet from the ground, 5 feet will be added to perpendicular for actual height of light post.
Height of light post = 28+5 = 33 feet ..
A house was valued at $120,000 in the year 1992. The value appreciated to $160,000 by the year 2007.
Use the compund interest formula S=P(1+r)t to answer the following questions.
A) What was the annual growth rate between 1992 and 2007?
r = ______ Round the growth rate to 4 decimal places.
B) What is the correct answer to part A written in percentage form?
r =___ %.
C) Assume that the house value continues to grow by the same percentage. What will the value equal in the year 2010 ?
value = $ ____ Round to the nearest thousand dollars
Answer:
A) 0.0194
B) 1.94%
C) $ 170,000
Step-by-step explanation:
Value of house in 1992 = P = $ 120,000
Value of house in 2007 = S = $ 160,000
Time difference from 1992 to 2007 = 15 years
Part A)
The formula of compound interest is:
[tex]S=P(1+r)^{t}[/tex]
P is the original amount i.e. $ 120,000
t is the time in years which is 15 years
S is the amount after t years which is $ 160,000
r is the annual growth rate
Using the values, we get:
[tex]160000=120000(1+r)^{15}\\\\\frac{160000}{120000}=(1+r)^{15}\\\\ \frac{4}{3}=(1+r)^{15}\\\\(\frac{4}{3} )^{\frac{1}{15}}=1+r\\\\ r=(\frac{4}{3} )^{\frac{1}{15}}-1\\\\ r=0.0194[/tex]
Thus, the annual growth rate is 0.0194
Part B)
In order to convert a decimal to percentage, simply multiply the decimal by 100.
So, 0.0194 in percentage would be 1.94%
Part C)
We have to find the value of house in 2010 i.e. after 18 years. So t =18
Using the values in the formula, we get:
[tex]S=120000(1+0.0194)^{18}\\\\ S=169584[/tex]
Rounded to nearest thousand dollars, the value of the house would be $ 170,000
I live - Villal
Use the distributive property to simplify this
expression:-2(3x+x-5)
1. Using order of operations, combine like terms
in the parentheses:
-2(4x + 5)
2. Distribute -2 to each term in the
parentheses:
What is the simplified algebraic expression?
O 4x-5
08x-5
O 8x + 10
O 8x - 10
-2(4x + 5)
Answer:
-8x+10
Step-by-step explanation:
The expression is: -2(3x+x-5)
Step 1: Using order of operations, combine like terms
-2(4x-5)
Step 2: Distribute -2 to each term in the parentheses:
-8x+10
Hence, the simplified expression is:
-8x+10
Answer:
-8x+10
Step-by-step explanation:
on edge
Cathy's customer base is 2/3 residential and 1/3 business. If she has 350 residential customers, how many total customers does she have?
Answer:
Step-by-step explanation:
In your quilt shop,you make and sell quilts. You like to have a total of 26 yards of royal blue fabric in stock at the beginning of each month. Today your inventory includes 4 pieces of this fabric that are each 22 1/2 inches long and 3 pieces that are each 33 inches long. You must purchase this fabric in 3 yard long pieces. To replenish your stock,how many pieces do you need to buy?
Answer:
7 pieces
Step-by-step explanation:
Stock that must be available at the beginning of each month = 26 yards
Since,
1 yard = 36 inches
26 yards = 26 x 36 = 936 inches
This means 936 inches of fabric must be available at beginning of each month.
Current Inventory:
4 pieces that are each 22 1/2 (or 22.5) inches long. So total length of these fabrics = 4 x 22.5 = 90 inches
3 pieces that each 33 inches long. So total length of these fabrics = 3 x 33 = 99 inches
Therefore, the total length of current inventory = 90 + 99 = 189 inches.
Length of fabric needed more:
Length of fabric that must be bought more = 936 - 189 = 747 inches
It is given that the fabric must be bought in pieces are the 3 yards long. 3 yards is equal to 108 inches.
So, I have to buy pieces that are each 108 inches long and I need to complete 747 inches in total.
Therefore, the number of pieces that I need to buy = [tex]\frac{747}{108}=6.9[/tex]
Since, the pieces cannot be bought in fraction, I need to buy 7 complete pieces to replenish my stock.
You need to purchase 7 pieces of 3-yard fabric.
To determine how many pieces of fabric you need to buy, follow these steps:
Calculate your current inventory:4 pieces at [tex]22 \frac{1}{2}[/tex] inches each:Therefore, you need to purchase 7 pieces of fabric to replenish your stock.
If y varies directly as x, and y = 2 when x = 8, then the constant of variation is :1/4 1/8 4 8
Answer:
1/4
Step-by-step explanation:
y varies directly as x means you should translate this as y=kx.
y varies indirectly as x means you should translate this as y=k/x.
Anyways we had directly, so the equation is of the form y=kx for any point (x,y) where k is the constant.
We are given y=kx and that this equation should satisfy (x,y)=(8,2).
So let's plug in 8 for x and 2 for y giving us
2=k*8
Divide both sides by 8:
2/8=k
Simplify:
1/4=k
So k is a constant, that constant, the never changing number, for the point (x,y) is 1/4.
That means the equation is y=1/4 *x. The 1/4 is the constant of variation, also called the constant of proportionality.
The constant of variation, in this case, is found to be 1/4 using the formula y = kx.
The constant of variation in this case is 1/4.
Given that y varies directly as x and y = 2 when x = 8, we can use the formula y = kx to find the constant of variation.
By substituting the values y = 2 and x = 8 into the formula, we get 2 = k * 8, which simplifies to k = 1/4.
If f(x) = x + 4 and g(x) = x, what is (gºf)(-3)?
(gºf) means solve f(x) first, then use that for g(x)
In the equation for f(x) replace x with -3:
f(x) = x +4 = -3 +4 = 1
Now replace the x in the equation for g(x) with 1
g(x) = x = 1
The length of a rectangle is three times its width.
If the perimeter of the rectangle is 40 in, find its area.
Answer:
75 in^2
Step-by-step explanation:
L = 3W here. Also, P = 2W + 2L = 40 in here. Subbing 3W for L, we get
2W + 2(3W) = 40, or
2W + 6W = 40, or 8W = 40. Thus, W = 5 in and L = 15 in
and the area is W*L, or 5(15) in^2, or 75 in^2
The width of the rectangle is 5 inches and the length is 15 inches. Therefore, the area of this rectangle is 75 square inches.
Explanation:Let's indicate the width of the rectangle as 'w'. Given the length is three times the width, it would be represented as '3w'. The perimeter of any rectangle is calculated as 2*(length + width). Therefore, 2*(w + 3w) = 40. Solving this, we get 'w' as 5 inches and, therefore, the length as 15 inches.
The area of a rectangle is calculated by multiplying the length and width. Therefore, the area of this rectangle would be length * width = 15*5 = 75 square inches.
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What are the solutions of the following system
Answer:
(-6, 312), (6, 312)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}10x^2-y=48\\2y=16x^2+48&\text{subtracy}\ 16x^2\ \text{from both sides}\end{array}\right\\\\\left\{\begin{array}{ccc}10x^2-y=48\\-16x^2+2y=48&\text{divide both sides by 2}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}10x^2-y=48\\-8x^2+y=24\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad2x^2=72\qquad\text{divide both sides by 2}\\.\qquad x^2=36\to x=\pm\sqrt{36}\\.\qquad x=\pm6\\\\\text{Put the values of}\ x\ \text{to the second equation}[/tex]
[tex]2y=16(\pm6)^2+48\\\\2y=16(36)+48\\2y=576+48\\2y=624\qquad\text{divide both sides by 2}\\y=312[/tex]
What is the equation of the following line? Be sure to scroll down first to see
all answer options.