10-2 (2x+1) = 4 (x-2)
x=2
10-2(2x+1)=4(x-2)
10-4x-2=4x-8
10-2=8x-8
8=8x-8
16=8x
2=x
Answer:
X = 2
Step-by-step explanation:
[tex] \sf \: First, solve \: the \: brackets. [/tex]
[tex] \sf \: 10 - 2(2x + 1) = 4(x - 2) \\ \sf10 - 4x - 2 = 4x - 8 \: \: \: \: \: \: \: [/tex]
[tex] \sf \: Combine \: like \: terms .[/tex]
[tex] \sf8 - 4x = 4x - 8[/tex]
[tex] \sf \: Subtract \: 4x \: from \: both \: sides \: to \: remove \: 4x.[/tex]
[tex] \sf \: 8 - 4x - 4x = 4x - 8 - 4x \\ \sf8 - 8x = - 8[/tex]
[tex] \sf \: Subtract \: 8 \: from \: both \: sides \: to \: remove \: 8.[/tex]
[tex] \sf8 - 8 - 8x = - 8 - 8 \\ \sf - 8x = - 16[/tex]
[tex] \sf \: Divide \: both \: sides \: by \: -8.[/tex]
[tex] \sf \: x = 2[/tex]
This question has three parts.
Bruce deposited a certain amount of money in a simple interest bearing savings account.
He neither deposited nor withdrew any money from his account for 4 years.
He kept track of the money in his account by making a graph as shown.
Part A:
What was Bruce’s principle (initial amount deposited)
Part B:
How much interest did Bruce earn after 1 year?
Part C:
What was the interest rate that Bruce’s savings account was earning
Bruce's principle is $140.
The interest that Bruce earned is $9.80
The interest rate that Bruce savings account is 7%.
What is the simple interest?Simple interest is the interest that that is earned a certain amount over a period of time given a principal and the number of years.
Simple interest = amount deposited x time x interest rate.
A graph can be described as a pictorial representation of data. A graph has a y-axis and the x-axis. The y-intercept is a point where the graph touches the y-axis. The y-intercept represents the initial amount that is deposited. The principle is $140.
The slope of the graph represents the rate at which the amount invested increases in value.
Interest Bruce earned after 1 year : change in the slope
149.80 - 140 = $9.80
Interest rate = Interest / (principle x time)
9.80 / (140 x 1) = 0.07 = 7%
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a line contains the (2,2) and is parallel to y=1/2x +1. Write the equation of the line in slope-intercept form
Answer:
y=-2x+6
Step-by-step explanation:
Please see attachment.
Hope this helps!
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The sum of two numbers is thirty one. The first is five less than the second. Find the numbers
Answer:
Step-by-step explanation:
First Number : x - 5
Second Number : x
x + ( x - 5) = 31
2x - 5 = 31
2x = 31 + 5
2x/2 = 36/2
x = 18
Then plugin x= 18 into First numer X - 5
x - 5
18 - 5 = 13
18 + 13 = 31
so .....
First Number is 13
Second number is 18
Complete the proofs on a seperate sheet of paper!
The proof is completed and showed that < 2 ≅ < 3 as required.
How to show that < 2 ≅ < 3Given data
<1 and <2 are linear pair
<1 + <3 = 180 degrees
required to proof <2 ≅ <3
linear pair implies mathematically that the sum of the two angles are 180 degrees, hence we have:
< 1 + < 2 = 180 degrees equation 1
also given that,
< 1 + < 3 = 180 degrees equation 1
equating equation 1 and equation 2 gives
< 1 + < 2 = < 1 + < 3
< 2 = < 3
Hence the required proof
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You thought the balance in your checking account was $68. When your bank statement arrived, you realized that you forgot to record a check. The bank statement listed your balance as $26. What was the amount of the check that you forgot to record?
f(x)=x² + 3
Which answer pairs a possible domain restriction that if placed upon f(x) would impact f¹(x) as shown?
f(x) domain: x ≥ 3
f-¹(x) domain: x ≥ 3
f(x) domain: x≥3
f-¹(x) range: y ≥ 3
f(x) domain: x ≥ 0
f-¹(x) domain: x ≥0
f(x) domain: x ≥ 0
f-¹(x) range: y ≥ 0
The restriction will be f-¹(x) range: y ≥ 0
Domain of a function:
The domain of a function refers to the set of all possible inputs for the function. For example, we get that the domain of f(x) = x² is all real numbers, and the domain of g (x) = 1 / x is all real numbers except for x = 0( as it will make the function indefinite.) Some special functions can also be defined whose domain are limited.
Range of a function:
The range of a function refers to the complete set of all possible resulting values of the dependent variable, after we have substituted the domain.
So, the restriction will be f-¹(x) range: y ≥ 0 as x² will always be positive.
Therefore, the restriction will be f-¹(x) range: y ≥ 0.
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suppose that Angle Hik and Angle LIJ are verticle angles. find their measures if the following conditions apply. Question 2...
=========================================================
Explanation:
Vertical angles are always congruent.
Set the two expressions equal to one another and solve for x.
6x - 6 = 3(x+6)
6x - 6 = 3x + 18
6x - 3x = 18 + 6
3x = 24
x = 24/3
x = 8
Then use this x value to find each angle
angle HIK = 6x - 6 = 6*8 - 6 = 42angle LIJ = 3(x+6) = 3*(8+6) = 42Both angles are 42 degrees each to confirm the answer.
Find the coordinates of the midpoint of a segment with the given endpoints. A(2,14), C(0,5)
The coordinates of the midpoint of a segment with the given endpoints will be (1, 9.5).
What is the mid-point of the line segment?Let AB be the line segment and C be the mid-point of line segment AB. Let the coordinate of point A (x₁, y₁), the coordinate of point B (x₂, y₂), and the coordinate of the mid-point (x, y).
Then the coordinate of the mid-point of the line segment is given as,
(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]
The endpoints are A(2, 14) and C(0, 5).
Then the coordinates of the midpoint of a segment with the given endpoints will be
(x, y) = [(2 + 0) / 2, (14 + 5) / 2]
(x, y) = (2/2, 19/2)
(x, y) = (1, 9.5)
The coordinates of the midpoint of a segment with the given endpoints will be (1, 9.5).
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A storage tank will have a circular base of radius r and a height of r . The tank can be either cylindrical or hemispherical (half a sphere).
a. Write and simplify an expression for the ratio of the volume of the hemispherical tank to its surface area (including the base). For a sphere, V=4/3πr³ and SA=4πr²
The ratio of the volume of the hemispherical tank to its surface area is, V/A = 2r/9.
What is meant by TSA?A three-dimensional object's total surface area exists the whole area of all of its external surfaces.
Let r be the radius of the circle and h be the height
To find volume of the hemispherical tank and its surface area.
Here,
TSA = Total Surface Area
CSA = Curved Surface Area
Volume of a hemisphere (V) = (2/3) πr³
TSA of the hemispherical tank(A) = CSA of the tank + CSA of the base.
TSA(A) = 2πr² + πr² = 3πr²
The ratio of the volume of the hemispherical tank to its surface area is,
V/A = (2/3)πr³ / 3πr²
V/A = 2r/9
Therefore, the ratio of the volume of the hemispherical tank to its surface area is, V/A = 2r/9.
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Recycled CDs, Incorporated, offers a choice of 5 used CDs for $29, with each additional CD costing $. Write a cost function for purchasing 5 or more CDs. What will the cost of buying CDs be? Let x represent the number of CDs over 5.
The cost function will be of the form f(x) = x + 29.
What is a function ?A function have a set of dependent variable for the given or specified independent variable.
According to the given question Recycled CDs, Incorporated, offers a choice of 5 used CDs for 29 dollars with each additional CD costing a dollar.
We have to write a function for purchasing 5 or more CDs where x represents the no. of CDs over 5.
Let f(x) represents the cost of CDs.
∴ f(x) = x + 29.
Here the constant 29 dollars represents the cost of 5 CDs and x represents no. of CD's over 5.Put x = 0 and the cost for 5 CDs will be 29 and for any more value of x we will get our desire result.
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A certain state uses the following progressive
tax rate for calculating individual income tax:
Income
Progressive
Range ($)
Tax Rate
0 - 10,000
3%
10,001 - 50,000
5%
50,001 - 100,000
5.5%
Calculate the state income tax owed on a $50,000
per year salary.
tax = $[?]
Round your answer to the nearest whole dollar amount.
Answer: 52
Step-by-step explanation: it might not be it. GOD BLESS.
PLEASE PLEASE HELP QUICK
Which relation is displayed in the graph?
Answer:
First option A
Step-by-step explanation:
Solved this by looking at the points of the graph from left to right. (-3,-2) is the first being the furthest left then so on.
Given the formula for an exponential function, is it possible to determine whether the function grows or decays exponentially just by looking at the formula?
yes, actually it is possible. The mathematical expression f(x)=exp or ex denotes the exponential function.
What is meant exponential function?The mathematical expression f(x)=exp or ex denotes the exponential function. The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, though it can be extended to the complex numbers or adapted to other mathematical objects like matrices or Lie algebras. When the input variable x appears as an exponent in the formula f(x) = axe, an exponential function is indicated. The exponential curve is influenced by both the exponential function and the value of x.
One of the key mathematical operations is the exponential function (though it would have to admit that the linear function ranks even higher in importance). We allow the exponent to be the independent variable to create an exponential function. The formula f(x)=2x is a straightforward example.
Hence, yes, actually it is possible.
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What is the vertex of y=|x|-5 ?
a. (5,0)
b. (-5,0)
c. (0,5)
d. (0,-5)
Answer: The answer is D
Step-by-step explanation:
Write an explicit and a recursive formula for each sequence. -5,-3.5,-2,-0.5,1, . . . . . .
The formula for an arithmetic series -5,-3.5,-2,-0.5,1, is An = A1 + (n-1)d
What is arithmetic series ?
See the pattern
-5-(-3.5)= -1.5
-3.5-(-2)= -1.5
The formula for an arithmetic series -5,-3.5,-2,-0.5,1, is An = A1 + (n-1)d
An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.
Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.
An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.
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If there are ten marbles in a bag (those marbles being two yellow, three pink, and five blue) and two are randomly drawn, what is the probability of drawing two yellow marbles if the first one isn't put back before the second draw? please help T^T
Answer:
the answer is 2 upon 10 ndnznnznznzjzjzj
bonjour pouvez-vous m’aidez avec se devoir svp?
Lors des soldes, Rami, qui accompagne sa mère et s'ennuie un peu, compare trois étiquettes pour passer le temps:
n°1-valeurs: 120 €
soldé: 105 €
n°2-Robe rouge: 45 euros
soldé: -30%
n°3-soldes: 25 € - 12,50 €
1. Quel est le plus fort pourcentage de remise?
2. Est-ce que la plus forte remise en euros est la plus forte en pourcentage?
merci d’avance
Answer:
Step-by-step explanation:
Theresa purchased 10 rakes and 15 shovels for $595. brett purchased 8 rakes and 20 shovels for $676. assume the rakes are all priced the same, and all shovels are priced the same.
The price of a rake and a shovel is $22 and $25 respectively.
Let's assume the price of a rake is x and the cost of a shovel is y.
Now, Theresa purchased 10 rakes and 15 shovels for $595.
10x + 15y = $595 -------------------(1)
Taking 5 common out from each side of the equation,
5( 2x + 3y) = 5( 119)
2x + 3y = 119 ------------------(2)
Brett purchased 8 rakes and 20 shovels for $676.
8x + 20y = $676 ------------------(3)
Multiply equation (2) by 4 and subtract from equation (3),
8x + 20y - ( 8x + 12y ) = 676 - 476
8x + 20y - 8x - 12y = 200
8y = 200
y = $25
Therefore,
10x + 15y = 595
10x + 15(25) = 595
10x + 375 = 595
10x = 595 - 375
10x = 220
x = $22
Hence, the price of a rake and shovel is $22 and $25 respectively.
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which equation describes a line of symmetry for the figure shown? y=0 y=-x y =x x=0
Answer:
The last option: x = 0
Step-by-step explanation:
The line of symmetry for a figure is a straight line that divides the figure into two congruent figures
The vertical line passing along the y axis is the line of symmetry and since it passes through all y values where x = 0, the equation is x = 0
Write each logarithmic expression as a single logarithm. 7 log p + 2log q
The given lograthimic expression 7log p + 2logq can be written as log(p^7q^2).
According to the given question.
We have a lograthimic expression.
7log p + 2logq
As we know that, a logarithmic expression is an expression that involves the logarithm of an expression containing a variable.
Also according to the product and power rule we know that
log(mn) = logm + logn
log(x^y) = ylogx
Therefore, the given lograthimic expression 7log p + 2logq can be written as
7log p + 2logq
= log p^7 + log q^2
= log(p^7q^2)
Hence, the given lograthimic expression 7log p + 2logq can be written as log(p^7q^2) as log(p^7q^2).
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What is the y -value of the focus of the parabola?
Answer:
8136366271773737i228882ywhw
g(t) = t^2 + 4t
h(t) = 2t
Find (g/t) (-6)
The value of h(g(t))(-6) is 24.
What is function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Functions are ubiquitous in mathematics and are essential for formulating physical relationships in the sciences.
An example of this would be y=x².
If you put in anything for x, you get one output for y. We would say that y is a function of x since x is the input value.
Given:
g(t) = t² + 4t
h(t) = 2t
h(g(t))
=h( t² + 4t)
=2( t² + 4t)
And, h(g(t)) (-6)
=2( (-6)² + 4(-6))
=2(36-24)
=2*12
=24
Hence, the value of the function is 24.
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Find the distance from the line to the given point.
x=4,(-2,5)
The distance from the line x=4 to the given point (-2,5) is 6 units .
Distance formula from line to point :
The distance from the line ax+by+c=0 to the point (u,v) is given by the formula
[tex]distance=\frac{|au+bv+c|}{\sqrt{a^{2} +b^{2} } }[/tex]
In the given question
the equation of the line is [tex]x=4[/tex]
taking all the terms to Left side we get
[tex]x-4=0[/tex]
[tex]1.x+0.y-4=0[/tex]
given the points (-2,5)
From above values we the values as a=1 , b=0 , c=-4 , u=-2 , v=5 .
Substituting the values in the distance formula we get
[tex]d=\frac{|1*(-2)+0*(5)-4|}{\sqrt{1^{2} +0^{2} } }[/tex]
[tex]=\frac{|-2+0-4|}{1} \\ \\ =|-6|\\ \\ =6[/tex]
Therefore , the distance from the line x=4 to the given point (-2,5) is 6 units.
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Use the following information to complete parts I, II, and III.
Part I: Use scientific notation to estimate the number of hours in one year.
Part II: Use scientific notation to calculate the exact number of hours in one year.
Part III: In two or more complete sentences, compare your answers to parts I and II. In your comparison, discuss similarities and differences in your answers.
I) There are 8.76* 10³ hours in 1 year.
II) The exact number of hours in one year is 8.76582*10³ hours.
What is scientific notation?Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.
Given:
1 hour=3600 seconds
1 year = 31556952 seconds.
Now,
I) Use scientific notation to estimate the number of hours in one year.
1 day = 24 hours
1 year = 365 days
So, number of hours in one year is given by,
=24*365
=8760
=8.76* 10³
So, there are 8.76* 10³ hours in 1 year.
II) 1 year = 31556952 seconds.
1 hour = 3600 seconds
In one year the number of hour is given by,
=31556952/3600
=8765.82
=8.76582*10³
So, the exact number of hours in one year is 8.76582*10³ hours.
III)
The exact numbers of hours using 365 days is 8760 which is written as in scientific notation but using the given data we get hours.
Comparing these answers the first one has only 3 significant figures and the second answer has six significant figures.
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Alex and ben share £520 in the ratio 1: 3 what fraction of the £520 does ben receive
Ben will receive £390
How to calculate the fraction that will be received ?
Alex and Ben share £520
They share this money in the ratio 1:3
The fraction of this amount that Ben will receive can be calculated as follows
1 + 3
= 4x
4x= 520
x= 520/4
x= 130
Ben Fraction= 130 × 3
= 390
Hence Ben's fraction of the money is £390
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Use the table below to find the cumulative frequency of the class "less then 30.5?"
Set both given equations equal to zero, then combine them into one standard form equation. x + 6 = 0 and y - 3 = 4 x + 6 = 0 → y - 3 = 4 → Combined equation
The standard form of the given equation is; x + (-y) = -5
How to write a linear combined equation in standard form?
We are given the equations;
x + 6 = 0 -----(1)
y - 3 = 4 -----(2)
Add 4 to both sides of equation 2 to get;
y - 3 + 4 = 0
y + 1 = 0 -----(3)
Put y + 1 for 0 in eq 1 to get;
x + 6 = y + 1
The standard form of an equation is expressed in the form;
Ax + By = C
Thus;
x + 6 = y + 1 can be rewritten as;
x + (-y) = 1 - 6
x + (-y) = -5
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A certain species of fish costs $3.49 each. You can spend at most $45: How many of this type of fish can you buy for your aquarium?
HELP ASP WILL GET SHOW UR WORK!! BRAINILEsT AND 10 points
Answer:
x=4
Step-by-step explanation:
Answer:
x=4
Step-by-step explanation:
2x-2=6
Okay, first we need to create the inverse of this equation.
The inverse of subtraction is addition.
2(x)-2=6
2x = 6+2
Now, we solve the right-hand side.
2x = 8
Then, divide both sides by the greatest common factor.
We get x by itself.
2x = 8
/2 /2
x = 4
