The equation of the line that passes through (2, -6) and is perpendicular to the given line is y = -x -4
Equation of a lineFrom the question, we are to determine the equation of a line that passes through (2, -6) and it perpendicular to y = x + 4
If two lines are perpendicular, the product of their slope is -1.
That is,
m₁m₂ = -1
First,
We will determine the slope of the line that the equation was given
y = x + 4
Comparing with the slope-intercept form of the equation of a straight line
y = mx + b
Where m is the slope
and b is the y-intercept
By comparison
m = 1
The slope of the line that the equation was given is 1
Thus,
The slope of the line that is perpendicular to this line is -1
From the given information,
The line passes through the point (2, -6)
Using the point-slope form of the equation of a line
y - y₁ = m(x - x₁)
Then,
y - -6 = -1(x - 2)
y + 6 = -x + 2
y = -x + 2 - 6
y= -x -4
Hence, the equation of the described line is y = -x -4
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Answer:
y = -x -4
Step-by-step explanation:
Interest Suppose you deposit $ 2000 in a savings account that pays interest at an annual rate of 4 % . If no money is added or withdrawn from the account, answer the following questions.
d. How many years will it take for the account to contain $ 3000 ?
It will take 10.3 years for the account to contain $3000.
The formula to be used is given as follows :
A(t) = a ( 1 + r )^t (1)
where, A(t) = future value
a = principal amount or amount initially deposited.
r = annual interest rate
t = time
According to the question we have been given that
a = $2000
r = 0.04
A(t) = $3000
putting the required values in equation (1) we get
3000 = 2000(1+0.04)^t
1.5 = (1.04)^t
Taking log both sides we get
log(1.5) = t log(1.04)
0.176 = t *0.017
t = 10.3 years.
Thus it takes 10.3 years for the account to contain $3000.
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pls help me its math gr8
simplify only its in algebra and solution to
1)9+2+9x+2 5)6x2-x1
2)9x2+3x-2
3)8x2+5x+1
4)6x2+x+1
simplify answers to each algebra equation
1) 9x + 13
2) 3x - 16
3) 5x + 17
4) x + 13
The area of mathematics known as algebra aids in the representation of circumstances or problems as mathematical expressions. To create a meaningful mathematical expression, it takes variables like x, y, and z together with mathematical operations like addition, subtraction, multiplication, and division.
on solving the equation we get the solution of algebra as
9x +13
3x-16
5x+17
x+13
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Marie can type 25 labels in 10 mins. How many can
she type
in one hour?
Step-by-step explanation:
her ratio is therefore 25/10, which can be also written as 5/2, because ratios are just a special form of fractions.
to find how many labels she can type in 1 hour, we need to find the rehashing between 10 minutes and 1 hour.
1 hour = 60 minutes.
60 minutes = 6 × 10 minutes.
so, to find the equivalent ratio based on 1 hour, we need to multiply the denominator (bottom part) by 6.
and to keep the ratio value we need to multiply the numerator (top part) by the same number :
25/10 × 6/6 = 150/60
and since the ratio is always telling us how many labels can be typed per unit of time, we see,
she can type 150 labels in 1 hour (60 minutes)
Helpppp plsssss!!!!!!!!!!
y=-2x2+4x+4 And y=4
Two or more expressions with equal sign in between is called as Equation. The value of x is 2 and 0 when y=4 for equation y=-2x2+4x+4.
What is Equation?Two or more expressions with equal sign in between is called as Equation.
The given equation is y=-2x2+4x+4
Where y=4
4=-2x2+4x+4
-2x^2+4x=0
x(-2x+4)=0
x=0 and -2x=-4
x=2
Therefore the value of x is 2 and 0 when y=4 for equation y=-2x2+4x+4.
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Let f(x)=2 x+5 and g(x)=x²-3 x+2 . Perform each function operation, and then find the domain.
4 f(x)+2 g(x)
The values for 4f(x)+2 g(x) = 2x²- 2x + 24
What are the domain of the function 4f(x)+2 g(x) ?Given : f(x)=2x+5
g(x)=x²-3x+2
Solution:
4f(x) = 8x+20
2g(x) = 2x²-6x+4
4f(x) + 2g(x) = 8x+20 + 2x²-6x+4
4f(x) + 2g(x) = 2x²- 2x + 24
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Use the properties of logarithms to evaluate each expression.
log₄48- 1/2 log₄9
Using the properties of logarithm the value of the expression is [tex]log_{4} 48 - \frac{1}{2}log_{4} 9 = 2[/tex]
A logarithm is the power to which a number must be raised in order to get some other number.
According to the question we have been given the expression as
= [tex]log_{4} 48 - \frac{1}{2}log_{4} 9[/tex]
The properties of logarithm that we are going to use are :
[tex]log(\frac{x}{y} ) = logx - logy[/tex] and [tex]log_{a} a = 1[/tex]
Also we can see that the base are same so we can use the property of logarithm in the given equation and we know that √2304 = 48. Thus replacing 48 by √2304.
Now solving this step by step using the properties of logarithm we get
[tex]=log_{4} \sqrt{2304} - \frac{1}{2} log_{4} 9 \\=\frac{1}{2} log_{4} 2304 - \frac{1}{2} log_{4} 9\\= \frac{1}{2} [log_{4} 2304 - log_{4} 9]\\= \frac{1}{2} [log_{4} (2304/9)]\\= \frac{1}{2} log_{4} 256\\= \frac{1}{2} log_{4} (4^{4} )\\= 2 * log_{4} 4\\= 2*1\\= 2[/tex]
Hence using the properties of logarithm the value of the expression is
[tex]log_{4} 48 - \frac{1}{2}log_{4} 9 = 2[/tex]
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What value of x makes this proportion true?
X4
OA. 6
OB. 20
OC. 9
OD. 5
The value of x is 5 which is option (D) .
A ratio is a mathematical comparison of two numbers. If two given sets of numbers increase or decrease in the same proportion, the proportions are said to be directly proportional to each other.Ratios are indicated by the symbols '::' or '='. Two ratios are said to be proportional if they are equal.For example, the time it takes for a train to travel 50 km/h is equal to the time it takes to travel a distance of 250 km in 5 hours.
It is given that 25/20 = x/4
On simplifying , we get
[tex]\frac{25}{20} =\frac{x}{4} \\\\x=\frac{25\times4}{20} \\\\x=\frac{100}{20} \\\\x=5[/tex]
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The complete question is mention below :
What value of x makes this proportion true? 25/20 = x/4
A.6
B.20
C.9
D.5
Identify all rays and lines in the picture below.
According to this definition given below, we identify all lines and rays as follows, EA, EB, EC, and ED are rays, and ED and BE are, Line.
A line is, it is actually difficult to give a good mathematical definition. Roughly, we can say that a line is an infinitely thin, infinitely long collection of points extending in two opposite directions. When we draw lines in geometry, we use an arrow at each end to show that it extends infinitely.
A line can be named either using two points on the line (for example, AB←→ ) or simply by a letter, usually lowercase (for example, line m ).
A line segment has two endpoints. It contains these endpoints and all the points of the line between them. You can measure the length of a segment, but not of a line.
___
A segment is named by its two endpoints, for example, AB.
A ray is a part of a line that has one endpoint and goes on infinitely in only one direction. You cannot measure the length of a ray.
A ray is named using its endpoint first, and then any other point on the ray (for example, BA−→− ).
according to this definition, EA EB EC ED are rays, and ED, and BE are Line
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find the coordinates of the point on the curve y=7-3x-2x² where the gradient is 5
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
[tex]y=7-3x-2x^2\implies \cfrac{dy}{dx}=-3-4x\implies \stackrel{\textit{setting the derivative to 5}}{5=-3-4x} \\\\\\ 8=-4x\implies \cfrac{8}{-4}=x\implies \boxed{-2=x} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{when x = -2, what's "y"?}}{y=-7-3(-2)-2(-2)^2}\implies y=-7+6-8\implies \boxed{y=-9} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (-2~~,~~-9)~\hfill[/tex]
pls help in the screen shot
Using proportions, it is found that the conservationist would expect there to be 310 trouts in the lake.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the measures using a rule of three, that can be either direct or inverse, deriving from proportional relationships.
Direct relations, which are the most usual, are when both variable behave similarly(both increase or both decrease), while for inverse relations, they behave differently.
For this problem, we have that from the fact that out of the 26 trout, 13 were tagged, the proportion of tagged trouts is:
p = 13/26 = 0.5.
Hence, if 155 trouts were tagged, the expected amount is given by:
0.5n = 155
n = 155/0.5
n = 155 x 2
n = 310.
The conservationist would expect there to be 310 trouts in the lake.
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WHAT DOES AXIS MEAN ............................
Answer:
An axis is a line with respect to which a curve or figure is drawn, measured, rotated, etc. The most common axes encountered are commonly the mutually perpendicular Cartesian axes in the plane or in space. The plural of "axis" is "axes," pronounced "ax-ees."
Step-by-step explanation:
that
Solve each equation.
log 9- log x+1=6
After solving the given equation log9-log x+1=6, the value of x=(-9log+5)/log.
What is an equation?A mathematical statement made up of two expressions joined by an equal sign is called an equation.An equation is 3x - 5 = 16.We obtain the value of the variable x as x = 7 after solving this equation.So,
Given equation: log9-log x+1=6Then,
log9-logx+1=69log-logx+1=6(9log-logx+1)+(-9log-1)=6+(-9log-1)x=(-9log+5)/logTherefore, after solving the given equation log9-log x+1=6, the value of x=(-9log+5)/log.
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Solve. Check for extraneous solutions. 3 √x=6
No extraneous solution to the equation
The equation given is
3[tex]\sqrt{x}[/tex] = 6
Now we have to find the value of x.
[tex]\sqrt{x}[/tex] = 2
[tex](\sqrt{x} )^{2}[/tex] = [tex]2^{2}[/tex]
x = 4
To find whether it is an extraneous solution or not put the value of x in the given equation.
3[tex]\sqrt{4}[/tex] = 6
3 × 2 = 6
6 = 6
Therefore we get to know that there is no extraneous solution.
x = 4 is the solution of the equation.
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How many real roots does the cubic polynomial equation x³-7 x²+13 x-4=0 have?
The cubic polynomial equation has three real roots. Simplify the expression to a linear factor and a quadratic expression. The linear factor is obtained by taking values for x and substituting in f(x) to get f(x) = 0. If a value of x gives f(p) = 0, then x-p is a linear factor. By algebraic long division, obtain the quadratic equation and solve it to obtain the real roots.
f(x) = x³-7 x²+13 x-4
x = 4,
f(x) = 4³-7 (4)²+13 (4)-4 = 0
Thus, x-4 is a linear factor.
x³-7 x²+13 x-4/ x-4.
(x³-7 x²+13 x-4)/ x-4 = x²-3 x+1
x²-3 x+1 = 0
By quadratic formula: x = (-b±√(b²-4ac))/(2a)
x = (--3±√((-3)²-4(1x1))/(2)
x = (3±√(9-4))/(2)
x = (3±√5)/(2)
x = (3±2.24)/(2)
x = (3+ 2.24)/2 = 2.62
x = (3- 2.24)/2 = 0.38
The real roots are x = 0.38, 2.62 and 4
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Jeff made a 3 out of 7 shots, what was his shooting average.
Answer:
about 42%
Step-by-step explanation:
3/7 = 0.41857... = 42%
What do you notice about the decimal forms of the rates?
Answer: The question is not clear.
Step-by-step explanation:
subtract 2 from the hundreths place 724,062.58
The value of subtraction will be equal to 723,862.58.
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
Given that 2 is subtracted from the number 724,062.58. The value of the subtraction is calculated as:-
Subtraction = 724,062.58 - 200
If we write 2 at the hundredth place it will become 200.
Subtraction = 724,062.58 - 200 = 723,862.58
Therefore, the value of subtraction will be equal to 723,862.58.
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The college bookstore is having a back to school sale. T-shirts that usually sale for 34.50 are marked down to 20.7. What percent are they?
The college bookstore is 40 percent off
How to calculate the percent off ?T-shirt are usually on sale for $34.50
The price was marked down to $20.7
The price change is = 34.5 - 20.7
= 13.8
The percent off can be calculated as follows
= 13.8/34.50 × 100
= 0.4 × 100
= 40
Hence the percent off the college bookstore is 40 percent
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Which of the following expressions are equivalent to
The given expression is equivalent to [tex]\frac{l}{m}[/tex]. The correct option is C. None of the above
From the question, we are to determine the expression that is equivalent to the given expression
The given expression is
[tex]- \frac{l}{-m}[/tex]
This expression can be written as
[tex]\frac{-l}{-m}[/tex]
Multiplying the numerator and the denominator by -1
[tex]\frac{-l \times -1 }{-m \times -1 }[/tex]
= [tex]\frac{l}{m}[/tex]
Hence, the given expression is equivalent to [tex]\frac{l}{m}[/tex]. The correct option is C. None of the above
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Use compass and straightedge moves to construct the angle bisector for angle ABC. In other words, create a ray that divides angle ABC into 2 congruent angles.
Answer:
Step-by-step explanation:
Draw a line in the middle of the compass slightly slanted like this /with an on top of the line indicating 2 congruent angles being created.
Find the inverse of each function. Determine if the inverse is a function.
y=2 x-3
The inverse of the function will be y = x/2 + 3/2. Yes, inverse is a function as well.
What is an inverse of a function?Functions that "undo" one another are known as inverse functions. In other words, f(g(x)) = g(f(x)) = x if g(x) is the inverse of f(x). We have a great approach we can use to achieve this given an equation for which we wish to get the inverse.
Not all functions have their opposite. It is simple to see that f(x) will never take on the same value again if f(x) has an inverse. We give this asset a unique name.
If each member of the range corresponds to precisely one element of the domain, a function is said to be one-to-one (f(x)).
Given,
We have a function,
y=2 x-3
Add 3 to each side.
⇒ y + 3 = 2x
Divide by 2 and then either
⇒ x = y/2 + 3/2 or y/2 + 3/2
Just change the labels now, x to y.
⇒ y = x/2 + 3/2
So, the inverse of given function is y = x/2 + 3/2
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help help help guys HELP
Slope can be described as rise/ run, change in the dependent variables relative to the change in the independent variables and Δy / Δx.
How to find the accurate expression of the slope?The slope of a line is a number that describes both the direction and the steepness of the line.
The slope of a line is the change in y coordinate with respect to the change in x coordinate.
Therefore, slopes can be described as follows:
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PLSSS HELP ILL GIVE U 100 POINTS
Evaluate each logarithm.
log₅(-25)
log₅(-25) is undefined
Logarithms are another notation for exponents in mathematics. The logarithm of a number whose base is equal to another number.A logarithm is the reciprocal of a power. For example, if 10² = 100 then log₁₀ 100 = 2. The natural logarithm is called the base e logarithm. The natural logarithm is represented by ln or loge. where 'e' represents Euler's constant, which is approximately equal to 2.71828. For example, the natural logarithm of 78 is written ln 78. The natural logarithm determines how much "e" must be multiplied to get the desired output.Since the logarithmic function y = logₐ(x) is the inverse of the exponential function,
As the base is positive so x must also be positive
The logarithm of the real base of negative numbers is undefined.
Hence, log₅(-25) is undefined
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Can you guys help me with my math homework? I'll be asking more q's after they get answered. THX!!!
Answer:
y = 22.5x
Step-by-step explanation:
Using the scale 1:22.5
then the actual length is y = 22.5x
Answer all of them there on the screenshot
The complete table is shown in the attachment.
1. 4.8 gallons of water
2. 25 mins
3. The constant of proportionality = 1.6
What is a Proportional Relationship?An example of a proportional relationship is the relationship between time taken and the number of gallons of water that fills the tank which is at a constant rate.
Constant rate is the same as constant of proportionality. It is calculated as, k = y/x.
The equation of a proportional relationship is expressed as y = kx.
Using the pair, (0.5, 0.8), find the constant rate/constant of proportionality (k):
k = y/x = 0.8/0.5
k = 1.6 gallon/min
Substitute k = 1.6 into y = kx
y = 1.6x
Fill the table using the equation, y = 1.6x
For 1 min (x):
y = 1.6(1) = 1.6
1.6 gallon
For 3 mins (x):
y = 1.6(3) = 4.8
4.8 gallons
For 40 gallons (y):
40 = 1.6x
40/1.6 = x
x = 25
25 mins.
The complete table is shown in the attachment.
1. 4.8 gallons of water will be in the tank after 3 mins
2. It will take 25 mins to fill the tank with 40 gallons of water.
3. The constant of proportionality = 1.6
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Kelly has 203 fishes she sells 3 how many does Kelly have now
Answer:it’s 200 Oumou
Step-by-step explanation:203-3=200
Castel and Huong each improved their yards by planting grass sod and ornamental grass. They bought their supplies from the same store. Castel spent $144 on 6 ft²
of grass sod and 9 bunches of ornamental grass. Huong spent $151 on 9 ft' of grass sod and 7 bunches of ornamental grass. What is the cost of one ft' of grass sod
and the cost of one bunch of ornamental grass?
The cost of one ft' of grass sod is $ [Select]
and the cost of one bunch of ornamental grass is $ [Select]
The cost of one ft' of grass sod is $9 and the cost of one bunch of ornamental grass is $10.
How to illustrate the information?Based on the information, the appropriate equation will be:
6g + 9y = 144
9g + 7y = 151
where g = grass sod
o = ornamental grass
Multiply equation I by 9
Multiply equation ii by 6
54g + 81y = 1296
54g + 42y = 906
Subtract
39y = 390
y = 390/39
y = 10
From 9g + 7y = 151
9g + 7(10) = 151
9g = 151 - 70
9g = 81
g = 81/9
g = 9
Therefore, the cost of one ft' of grass sod is $9 and the cost of one bunch of ornamental grass is $10.
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convert 3100 fluid ounces to milliliters. round your answer to the nearest whole number
Answer:
91678 milliliters
Step-by-step explanation:
hope this is helpful! stay safe, and have a blessed day! :)
Samantha is following a blueprint to build an addition to her house. The kitchen countertop will be 8.75 feet long. The scale of the blueprint is 1 centimeter = 1.75 feet. What is the length of the countertop on the blueprint?
The length of the countertop on the blueprint is 5 cm.
What is defined as the scale?Scale is a ratio that reflects the relation between the size of a model and the actual dimensions of a figure or object. It aids in the representation of real-world objects on paper with relatively tiny dimensions. Scale is primarily employed in maps as well as blueprints for building construction.For the given question;
The length of kitchen countertop = 8.75 feet.
The scale used in blueprint is 1 centimeter = 1.75 feet.
Thus, use the unitary method.
1.75 feet -----> 1 cm.
Divide both side by 1.75.
1 feet ------>1/1.75 cm
Multiply both side by 8.75.
8.75 feet ---> 8.75/1.75 cm
8.75 feet ------> 5 cm.
Therefore, the the length of a countertop for the blueprint is found as 5 cm.
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