Answer:
9 units
Step-by-step explanation:
In the points S and T, the y- co ordinate are unchanged. So, the line joining S and T are parallel to x -axis.
So, the distance will be the sum of obsolute value of the x- coordinates.
Distance = I 7I + I - 2I
= 7 + 2
= 9 units
Please help. What is the equation of the line in slope-intercept form?
Answer:
Ray, you need the slope-intercept formula y=mx+b
Step-by-step explanation:
Next you'll need 2 points, any points are fine. Just find two easy ones along the line. I'll just pick Point 1 as P1 = ( 0,4) and point 2 as P2 = (4,0) because they are easy to work with.
next use
point P1 (0,4) in the form (x1,y1)
point P2(4,0) in the form (x2,y2)
slope = m
m = (y2-y1) / (x2-x1)
m = (0-4) / (4-0)
m = -4 / 4
m = -1
now use the point slope with one of the points, to find the slope-intercept form.
y - y1 = m(x -x1)
y - 4 = -1(x-0)
y -4 = -x
y = -x + 4
note:
y = mx +b
y = (-1)x + b is the form. see?
Answer:
y = mx + b
m = slope
b = intercept
From the graphic:
(x₁, y₁) = (0, 4)
(x₂, y₂) = (4, 0)
[tex]\frac{y-y_{1} }{y_{2} -y_{1} } =\frac{x-x_{1} }{x_{2} -x_{1} } \\\\\frac{y-4 }{0 -4} =\frac{x-0 }{4 -0 } \\\\\frac{y-4}{-4} =\frac{x}{4} \\\\(y-4)4=-4x\\\\y-4=-x\\y=-x+4\\[/tex]
Benjamín made 3 times more than Alberto and Carlota 2 times more than Benjamín, so how much is it, help me
Step-by-step explanation:
you are "hiding" some more information (like how much they made together).
without that we cannot calculate the actual values.
all I can do is set up the equations expressing the given relations between the parts of the total :
a = amount Alberto made
b = amount Benjamin made
c = amount Carlota made
b = 3×a
c = 2×b = 2× 3×a = 6×a
that's it.
your see ? now we need something that "ties" all 3 together, an equation of all 3 variables, where we can use the first 2 equations (by substitution) and then solve for the remaining third variable.
and that is missing.
if it is something like "together they made x", then we would have
a + b + c = x
a + 3a + 6a = x
10a = x
a = x/10
b and c we get then from the first 2 equations by simply using the calculated value of a :
b = 3×(x/10) = 3x/10
c = 6×(x/10) = 6x/10 = 3x/5
which of the following best describes how to transform?
Check the picture below.
[tex]\stackrel{parent}{y=x^2}\hspace{5em}y=\stackrel{A}{4}(\stackrel{B}{1}x\stackrel{C}{-2.5})^2\stackrel{D}{-3} \\\\\\ \hspace{7em} \begin{array}{llll} \textit{stretch by }4\cdot 1\implies 4\\\\ \textit{translated by }\frac{2.5}{1}\implies 2.5\textit{ to the right}\\\\ \textit{downwards shift by }3 \end{array}[/tex]
The money collected from selling bacon at a butcher store is given by the function f(x) = 3.55x – 4, where f(x) is the sales revenue in dollars and x is the number of customers visiting the store each day. If {17, 21, 24, 34} customers visited over four days, what is the income from bacon sales each day?
Answer:
See below under "Explanation".
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
Functions
Function NotationStep-by-step explanation:
Step 1: Define
Identify given.
[tex]\displaystyle f(x) = 3.55x - 4[/tex]
[tex]\displaystyle x = \{ 17, 21, 24, 34 \}[/tex]
Step 2: Find Profit
To find the profit the store makes each day, we input the number of customers that visited the store each day into our given function:
For the day that had 17 customers:
[tex]\displaystyle\begin{aligned}f(17) & = 3.55(17) - 4 \\& = 60.35 - 4 \\& = \boxed{56.35} \\\end{aligned}[/tex]
∴ the butcher store made $56.35 when 17 customers visited the store.
For the day that had 21 customers:
[tex]\displaystyle\begin{aligned}f(21) & = 3.55(21) - 4 \\& = 74.55 - 4 \\& = \boxed{70.55} \\\end{aligned}[/tex]
∴ the butcher store made $70.55 when 21 customers visited the store.
For the day that had 24 customers:
[tex]\displaystyle\begin{aligned}f(24) & = 3.55(24) - 4 \\& = 85.2 - 4 \\& = \boxed{81.2} \\\end{aligned}[/tex]
∴ the butcher store made $81.20 when 24 customers visited the store.
For the day that had 34 customers:
[tex]\displaystyle\begin{aligned}f(34) & = 3.55(34) - 4 \\& = 120.7 - 4 \\& = \boxed{116.7} \\\end{aligned}[/tex]
∴ the butcher store made $116.70 when 34 customers visited the store.
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Topic: Algebra I
Taylor buys dog food in bulk at the cost of $1.27 a pound. If he buys $107.95 of dog food, how many pounds will
he be buying?
Answer: 85 lbs
Step-by-step explanation:
$107.95 / $1.27 = 85 pounds of dog food
26. About 1.48 x 108 square kilometers of Earth's surface
is land; the rest, about 3.63 x 108 square kilometers, is
water. If a returning space capsule lands at a random
point on Earth's surface, which of the following is the
best estimate of the probability that the space capsule
will land in water?
F. 80%
G. 71%
H. 65%
J. 41%
K. 29%
Answer:
[tex]P=0.71[/tex] or 71%
Explanation:
[tex]P=\frac{3.63*10^2}{1.48*10^8+3.63*10^8}[/tex]
[tex]=\frac{3.63}{5.11} =0.71[/tex] or 71%
Most phone numbers have seven digits after the area code, where each digit can be 0-9. How many different phone numbers can there be in one area code?
A) 4,782,969
B) 282,475,249
C) 10,000,000
D) 823,543
Answer:
C) 10,000,000
Step-by-step explanation:
Data provided in the question:
- The phone number is of 7 digits
- we have choices from 0-9
meaning 10 number of choices, 0 1 2 3 4 5 6 7 8 9
we have 10 choices out of 10 for each of the 7 blanks
Therefore,
The total number of different phone numbers can there be in one area code that can be formed
= 10 × 10 × 10 × 10 × 10 × 10 × 10
= 10^7
= 10,000,000
Hyla has blocks of clay that are each 4 centimeters by 4 centimeters by 2 centimeters. She needs to cover the bottom of a box with a 2-centimeter tall layer of clay. The bottom of the box is 24 centimeters long and 20 centimeters wide. How many blocks of clay does Hyla need?
The number of blocks of clay needed by Hyla is 30 blocks
What is area?Area is the region bounded by a plane shape.
To calculate the number of blocks of clay needed by Hyla, we find the area of the bottom of the box and divide it by the area of the block.
Formula:
n = LWH/lwh............... Equation 1Where:
n = Number of blocks of clay needed by HylaL = Length of the bottom of the boxW = Width of the bottom of the boxH = Height of the boxl = Length of the bottom of the blockw = Width of the blockh = Height of the block.From the question,
Given:
L = 24 cmW = 20 cmH = 2 cml = 4 cmw = 4 cmh = 2cmSubstitute these values into equation 1
n = (24×20×2)/(4×4×2)n = 30Hence, The number of blocks of clay needed by Hyla is 30 blocks
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Jillian said V25 is irrational because it is a square root. Why is she incorrect?
Answer:
√25
= √( 5 x 5 )
= 5
√25 = 5
5 is an rational number, not an irrational number.
[tex]\rule{50}{1}\large\textsf{\textbf{\underline{Given question:-}}}\rule{50}{1}[/tex]
Jillian said, "√25 is irrational because it's a square root!" Why is
she incorrect?
[tex]\rule{50}{1}\large\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}[/tex]
First let's see if we can simplify √25.
We can, by using either our calculator or our brains.
Anyway, √25=5 (5×5=25)
Now, let's take a look at what irrational numbers are.
[tex]\dagger[/tex] Irrational numbers. This set includes numbers with an infinite
number of digits after the decimal point. Irrational numbers
cannot be expressed as fractions (p/q form)
Can [tex]\LARGE\textbf{5}[/tex] be expressed as a fraction? Sure!
This is how it's done:-
Simply give it a denominator of 1:-[tex]\Large\text{$\displaystyle\frac{5}{1}$}[/tex]
As you can see, 5 is not irrational.
Henceforth, we conclude that [tex]\Large\text{$\sqrt{25}$}[/tex] is not irrational. Good luck with your studies.[tex]\rule{50}{1}\smile\smile\smile\smile\smile\rule{50}{1}[/tex]
please help.... asap
Answer:
GCF is less than 3:
- 12 and 13
GCF is equal to 3:
- 6 and 27
- 12 and 21
- 3 and 6
GCF is greater than 3:
- 4 and 12
- 6 and 18
Step-by-step explanation:
6 and 27 GCF: 3
12 and 13 GCF: 1
4 and 12 GCF: 4
3 and 6 GCF: 3
12 and 21 GCF: 3
6 and 18 GCF: 6
What is the value of this expression?
(23 – 3) + (6 x 9)
Answer:
74
Step-by-step explanation:
(23-3)+(6×9)
(20) +(54)
=74
Why should the writer of this sample paragraph revise words such as fun, happy, and sad? writers should avoid controversial emotions. writers should avoid vague or nonspecific words. writers should focus on their intended topic. writers should avoid sharing personal opinions.
The sentences here are all simple sentences and all begin with the same word.
Why should the paragraph be revised?A paragraph is used to show a complete thought. It is important that a paragraph ought to be presented in complete sentences. However the sentences here are all simple sentences and all begin with the same word.
The reasons pointed out above makes the paragraph appear clumsy and boring to read. The writer should revise the paragraph and introduce a more complex sentence structure as well as the use of pronouns where neccessary.
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Answer:
B
Step-by-step explanation:
edge 22
Find the slope of the LM on the graph
Yoghurts are packed in trays. Each tray holds 12 yoghurts.
What is the smallest number of trays needed to pack 460 yoghurts?
Does anyone know a math equation that equals 14?
Answer: Pretty Simple; an easy equation could be 10 + 4 = 14.
Step-by-step explanation:
A more difficult equation might be (10(8) - 70) + 4 = 14
:)
Answer:
7x2=14
8+6=14
7+7=14
5x2.8=14
28/2=14
140/10=14
100-86=14
81(+-)67= 81-67=14
Determine the exact value for each of the 6 trig functions for the point (-2, 6).
Answer:
Sine: 0.94
Cosine: -0.31
Cotangent: -0.3(infinite)
Cosecant: 1.05
Tangent: -3
Secant: -3.16
Formula for finding the 6 trigonometry functions
To find the sine, you must divide the opposite side by the hypotenuse, because the sine is the ratio or fraction whose angle is opposite to the adjacent angle.To find a cosine, you must divide the adjacent angle by the hypotenuse.When finding a cotangent, you must divide the adjacent angle by the opposite, since the cotangent is also a ratio, but not like a sine.When you are finding a cosecant, you divide the hypotenuse by the opposite angle.You find the tangent by diving the opposite angle by the adjacent angle. It is like finding the cotangent but backwards.Last but not least, the secant. You find the secant by dividing the hypotenuse by the adjacent angle.Finding opposite and adjacent angles
To find the opposite angle, one simple way to determine that is to find the opposite side to that angle you are trying to find. For instance, when finding an angle, one side is 200, the adjacent side is 500. We must divide the opposite angle by the adjacent angle to find the missing angle. 200/500 = 0.4, so the missing angle is 0.4.To find the adjacent angle, that is always the side right next to a given angle.Hope this helps!
Step-by-step explanation:
The six trig functions are
[tex] \sin( \alpha ) = \frac{y}{r} [/tex]
[tex] \cos( \alpha ) = \frac{x}{r} [/tex]
[tex] \tan( \alpha ) = \frac{y}{x} [/tex]
[tex] \csc( \alpha ) = \frac{r}{y} [/tex]
[tex] \sec( \alpha ) = \frac{r}{x} [/tex]
[tex] \cot( \alpha ) = \frac{x}{y} [/tex]
Where
[tex]r = \sqrt{ {x}^{2} + {y}^{2} } [/tex]
[tex]r = \sqrt{ - 2 {}^{2} + {6}^{2} } [/tex]
[tex]r = \sqrt{40} [/tex]
[tex]r = 2 \sqrt{10} [/tex]
So we just plug in -2 for x, 6 for y, and our r value into these functions.
[tex] \sin( \alpha ) = \frac{6}{2 \sqrt{10} } = \frac{3}{ \sqrt{10} } = \frac{3 \sqrt{10} }{10} [/tex]
[tex] \cos( \alpha ) = \frac{ - 2}{2 \sqrt{10} } = \frac{ - 1}{ \sqrt{10} } = \frac{ - \sqrt{10} }{10} [/tex]
[tex] \tan( \alpha ) = \frac{6}{ - 2} = - 3[/tex]
Csc is the reciprocal of sine.
[tex] \csc( \alpha ) = \frac{ \sqrt{10} }{3} [/tex]
Sec is the reciprocal of cosine
[tex] \sec( \alpha ) = - \sqrt{10} [/tex]
Cot is the reciprocal of tan
[tex] \cot( \alpha ) = - \frac{1}{3} [/tex]
Let x^2+ 6x = 5
What values make an equivalent number sentence after completing the square?
Enter your answers in the boxes.
x² +6x+ ____=_____
Answer:
9
Step-by-step explanation:
For the equation x² - 6x = 5 the coefficient of the term x is -6
(-6/2)2 = 9
The given equation can be written as
x2 - 6x + 9 = 5 + 9
x2 - 6x + 9 = 14
We can write it as
(x - 3)2 = 14
Take square root on both sides.
|x - 3| = √14
We get
x = 3 + √14
In other case,
- x + 3 = √14
x = 3 - √14
Therefore, 9 should be added to both sides of the equation to complete the square (x2 - 6x = 5).
What number should be added to both sides of the equation to complete the square (x2 - 6x = 5)?
Summary:
The number that should be added to both sides of the equation to complete the square (x2 - 6x = 5) is 9.
1. In 2012, the population of a city was 5.63 million. The exponential growth rate was 1.45% per year.
a) Find the exponential growth function.
b) Estimate the population of the city in 2018.
c) When will the population of the city be 10 million?
d) Find the doubling time.
The exponential function is P = 5.63(1.0145)ⁿ. And the population of the city in 2018 is 6.1379 million, the number of the years when the population of the city is 10 million is 40 years, and the doubling time will be 49 years.
What is an exponent?The exponent denotes that the base will rise to a specific level of strength. The base is X, and the power is n.
In 2012, the population of a city was 5.63 million. The exponential growth rate was 1.45% per year.
Then the exponential function will be given as
P = 5.63 (1.0145)ⁿ
Where P is the population (in million) and n is the number of years.
Then the population of the city in 2018 will be
n = 2018 - 2012 = 6
Then we have
P = 5.63 (1.0145)⁶
P = 5.63 x 1.0902
P = 6.1379 million
The number of the years when the population of the city is 10 million.
10 = 5.63 x (1.0145)ⁿ
1.776 = (1.0145)ⁿ
Taking log both sides, then we have
log 1.776 = n x log 1.0145
n = 39.90
n ≅ 40 years
Then the doubling time will be
2 = (1.0145)ⁿ
Taking log on both sides, then we have
log 2 = n x log1.0145
n = 48.1489
n ≅ 49 years
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Dr. Patel plots points J, K, and L in the coordinate plane.
a. What is the distance between points J and K? Show
your work.
The distance between J(-5, -3) and K(1, 5) on the coordinate plane is about 10 units.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Point J is at (-5, -3) while point K is at (1, 5), hence:
[tex]JK=\sqrt{(5-(-3))^2+(1- (-5))^2} =10\ units[/tex]
The distance between J(-5, -3) and K(1, 5) on the coordinate plane is about 10 units.
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How do you show this on a graph?
Simplify (2/3)^3 (1/5 x 2/3)^-3 (1/5)^4
Answer:
[tex](\frac{2}{3})^{3} (\frac{1}{5}.\frac{2}{3} )^{-3} (\frac{1}{5})^{4} =(\frac{2^{3} }{3^{3} }) (\frac{2}{8} )^{-3} (\frac{1^{4}} {5^{4} })[/tex]
[tex]=(\frac{2^{3} }{3^{3} }) (\frac{2^{-3} }{8^{-3} } ) (\frac{1^{4}} {5^{4} })[/tex]
[tex]=\frac{2^{3} .2^{-3}.8^{3}. 1 }{3^{3} .5^{4} }[/tex]
[tex]=\frac{1.8^{3} }{3^{3} .5^{4} }[/tex]
[tex]=\frac{(2^{3}) ^{3} }{3^{3} .5^{4} }[/tex]
[tex]=\frac{2^{9} }{3^{3} .5^{4} }[/tex]
[tex]=\frac{512}{27.625}[/tex]
[tex]=\frac{512}{16875}[/tex]
Below are the supply and demand equations for stereo headphones in a certain market. in these equations, p represents price, d represents demand, and s represents supply. d = startfraction negative 5 over 9 endfraction p 94 s = 3 p minus 160 what is d at the point of equilibrium, to the nearest whole number? a. 151 b. 104 c. 71 d. 54
The value of d at the point of equilibrium, to the nearest whole number is 54
How to determine the value of d at equilibrium?The equations are given as:
[tex]d = \frac{-5}{9}p + 94[/tex]
[tex]s = 3p - 160[/tex]
At the point of equilibrium, d = s.
So, we have:
[tex]\frac{-5}{9}p + 94 = 3p - 160[/tex]
Multiply through by 9
-5p + 846 = 27p - 1440
Collect like terms
27p + 5p = 1440 + 846
Evaluate the sum
32p = 2286
Divide through by 32
p = 71.4375
Substitute p = 71.4375 in [tex]d = \frac{-5}{9}p + 94[/tex]
[tex]d = \frac{-5}{9} * 71.4375 + 94[/tex]
Evaluate
d = 54.3125
Approximate
d = 54
Hence, the value of d at the point of equilibrium, to the nearest whole number is 54
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Answer:
its d :)
Step-by-step explanation:
Pls help me I think that it is reciprocal trigonometric ratios
Answer:
67.38 degrees
Step-by-step explanation:
this is a right triangle so we can use sohcahtoa
we want to calculate angle A
we know the side opposite to A as well as the hypotenuse. 13 is the hypotenuse because it is opposite the right angle
thus, sin(A) = opposite/hypotenuse = 12/13
arcsin(12/13) = A ≈ 67.38 degrees
In a bag, there are 5 red marbles, 2 blue marbles, and 3 purple marbles. What is the probability of drawing a purple marble?
Answer:
3/10 or 30%
Step-by-step explanation:
Add all of the marbles: 5+2+3=10
Then use a fraction to represent the three purple marbles: 3/10
That porportion is your answer
what is the constant of proportionality in the equation 3y=2x
Answer :The constant of proportionality is K = 2/3
Maria walked 3/4 of a mile. Cody walked 6/10 of a mile. How much farther did Maria walk than Cody?
Answer:
3/20
Step-by-step explanation:
Take the miles that Maria walked and subtract the miles that Cody walked
3/4 - 6/10
Simplify 6/10 by dividing the top and bottom by2
3/4 - 3/5
Get a common denominator of 20
3/4 *5/5 = 15/20
3/5 *4/4 =12/20
15/20 - 12/20
3/20
Answer:
0.15(3/20) miles more than Cody
3/4 = 0.75
6/10 = 0.6
Therefore, Maria walked 0.15(3/20) miles greater than Cody.
Algebra 2 Question
19. If P(x) = 2x^4 - 5x^2 + 3x -9, then P(6) is
A.) -3
B.) 2439
C.) -2421
D. 2421
[tex]\text{Given that,}\\\\P(x) = 2x^4 -5x^2 +3x -9\\\\P(6) = 2\cdot 6^4 -5 \cdot 6^2 +3 \cdot 6 -9 \\\\~~~~~~~=2592-180+18-9\\\\~~~~~~~=2421\\\\\text{Hence the answer is option D.}[/tex]
C/2 + 5 = 1
Answer Please
Answer: c= -8
Step-by-step explanation:
c/2=-4
-8/2=-4
-4 +5=1
What is the vertex of the function f(x) = x2 12x? (–6, –36) (–6, 0) (6, 0) (6, –36)
The function f(x) = x² + 12x is a quadratic function, and the vertex of the function is (-6,-36)
How to determine the vertex of the function?The equation of the function is given as:
f(x) = x² + 12x
Differentiate the function
f'(x) = 2x + 12
Set the function to 0
2x + 12 = 0
Add -12 to both sides
2x = -12
Divide both sides by 2
x = -6
Set x = -6 in the function f(x)
f(-6) = (-6)² + 12(-6)
Evaluate
f(-6) = -36
Hence, the vertex of the function is (-6,-36)
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Answer:
the vertex of the function is (-6,-36)
Step-by-step explanation:
Pls add brainliest pls
help me answer this now.
x + 2x + 6 = 27
3x + 6 = 27
x + 2 = 9
x = 9 - 2
x = 7
2 × 7 = 14
14 + 6 = 20
