The resulting equation after the first step in the solution is: 2v + 4 = 8.
What is an equation?In Mathematics, an equation is sometimes referred to as an expression and it can be defined as a mathematical expression which shows that two (2) or more thing are equal.
In this exercise, you're required to describe the steps that should be taken to find a solution to the given equation by solving for v. Therefore, the appropriate and required steps that should be used include the following:
Step 1: Rearrange the equation by collecting like terms.
(v + v) + 4 = 8
Step 2: Add the like terms together.
2v + 4 = 8
Step 3: Subtract 4 from both sides of the equation.
2v + 4 - 4 = 8 - 4
2v = 4
Step 4: Divide both sides of the equation by 2.
v = 4/2
v = 2.
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Complete Question:
Consider the equation v + 4 + v = 8. What is the resulting equation after the first step in the solution?
v +4 = 8 – v
v +4 = 8
4 + v = 8 – v
2v + 4 = 8
Please help. Find x and y. NEED ASAP
Answer:
x=10
y=5
Step-by-step explanation:
you have to find the length
On a map, 2 inches equals 180 miles. The distance that a family travels is 3.5 inches on the map. Represent the scale as two different ratios. What is the actual distance the family travels?
Answer:
315
Step-by-step explanation:
2/180=3.5/x
2x=630
x=315
Which of the following are characteristics of the graph of the absolute value
parent function?
Check all that apply.
A. It goes through the origin.
B. It is in quadrants I and II.
C. The left half has a slope of 1.
D. It is V-shaped.
Answer: All Are correct
Step-by-step explanation:
Look at graph, the vertex hits the origin, the parent function is on the top half of the graph (quads 1 and 2), both the left and right side have a slope of 1, and it is v shaped!
How many values of x must be excluded in the expression (x+9)(x-5)?
The number of values of x to be excluded is 2.
To find out the values of x that must be excluded in the expression
(x+9)(x-5) as follows:
The value of x is 2.
We are given to find the number of value of x that must be excluded in the expression below:
E = (x+9)(x-5)
We have to exclude those values of x for which the expression E becomes undefined.
Since E is a rational expression, so the becomes undefined only when the denominator becomes 0.
That is,
(x+9)(x-5) = 0
= x+9 = 0 x-5 = 0
= x = -9 x = 5
Therefore, we need to exclude the values x = -9 and x =5.
So, there are two values of x to be excluded from the given expression.
Hence the answer, the number of values of x to be excluded is 2.
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NO LINKS!! Please help me with this symmetry part 2
Functions that are symmetric with respect to the x-axis are those with even degree of y, i.e y², y⁴ etc.
Correct choices are:
x = 1/8y²x = - y² + 9
Answer:
[tex]x=\dfrac{1}{8}y^2[/tex]
[tex]x=-y^2+9[/tex]
Step-by-step explanation:
Functions are symmetric with respect to the x-axis if for every point (a, b) on the graph, there is also a point (a, −b) on the graph:
f(x, y) = f(x, −y)To determine if a graph is symmetric with respect to the x-axis, replace all the y's with (−y). If the resultant expression is equivalent to the original expression, the graph is symmetric with respect to the x-axis.
Therefore, any function that includes the term y² will be symmetric with respect to the x-axis since (-y)² = y².
[tex]\begin{aligned}&\textsf{Given}: \quad& x&=\dfrac{1}{8}y^2\\&\textsf{Replace $y$ for $(-y)$}: \quad& x&=\dfrac{1}{8}(-y)^2\\&\textsf{Simplify}: \quad &x&=\dfrac{1}{8}y^2\\\end{aligned}[/tex]
Therefore, since the resultant expression is equivalent to the original expression, it is symmetric with respect to the x-axis.
[tex]\begin{aligned}&\textsf{Given}: \quad& x&=-y^2+9\\&\textsf{Replace $y$ for $(-y)$}: \quad& x&=-(-y)^2+9\\&\textsf{Simplify}: \quad &x&=-y^2+9\\\end{aligned}[/tex]
Therefore, since the resultant expression is equivalent to the original expression, it is symmetric with respect to the x-axis.
it is given that the rainfall in 2017 of 420mm was 25% more than in 2016. Find the annual rainfall in 2016
The annual rainfall in 2016 is 336 mm.
Let the annual rainfall in 2016 be 100x mm.
Now it is given that rainfall in 2017 is 25% more than rainfall in 2016.
So. rainfall in 2017 is = 100x + 100x*(25/100) = 100x+25x = 125x mm
Also given that the amount of rainfall in 2017 = 420 mm.
According to question the suitable equation is,
125x = 420
x = 420/125
x = 3.36
Hence the rainfall in 2016 is = 100x = 100*3.36 = 336 mm.
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Which expression shows the distance on the number line between -12 and negative one
Answer: (-12,-1)
Step-by-step explanation: Point A=-1 and Point B=-12
:)
The sum of two numbers is 42. The sum of 5 times the 1st number and 9 times the 2nd number is 190. What are the two numbers?
Step-by-step explanation:
x + y = 42
5x + 9y = 190
x = 42 - y
5(42 - y) + 9y = 190
210 - 5y + 9y = 190
210 + 4y = 190
4y = -20
y = -5
x = 42 - y = 42 - -5 = 42 + 5 = 47
A container ship left port last week carrying some goods that weighed a total of 130,980 tons. Today, it stopped in another port to unload. The weight of the goods on the ship is now 91,686 tons. By what percent has the weight of the goods on the ship decreased?
help please annnd thaannks
Answer:
30%
Step-by-step explanation:
130980-91686=39294
39294/130908=0.3
Answer: 168,609 ton
Hi, to answer this question, first we have to calculate the amount of the weight decrease by multiplying the original weight of the goods (240,870) by the percentage decrease in decimal form ( divided by 100)
Mathematically speaking:
240,870 (30/100) =72,261 ton
Finally we have to subtract that value to the original weight:
240,870-72,261 = 168,609 ton
Feel free to ask for more if needed or if you did not understand something.
Step-by-step explanation:
The function f(x) is graphed below. What is true about the graph on the interval from point e to point f?
Answer: It is positive and increasing
Step-by-step explanation:
From point e to f it is clearly going up, and is part of the positive side of the graph.
Factor 3x+11y if the expression cannot be factored
The expression 3x+11y cannot be factorized.
What is factorization?
To factorise an algebraic statement, we first identify the terms' highest common factors before organising the words in the appropriate way. An algebraic expression's factorization is, to put it simply, the process of expansion in reverse. The same way, as the product of their factors, are the algebraic expressions written in algebra. The only difference is that in an algebraic expression, variables and integers are combined to perform mathematical operations like addition or subtraction.
Here the given expression 3x+11y didn't have any common factors.
The given expression has two variables 3x and 11y and they didn"t have any common terms.
Hence the expression 3x+11y cannot be factored.
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3. Use the graph of f(x) below to answer the following questions. Approximate answers are okay.
Answer:
Step-by-step explanation:
f(0) = 4
f(x)=0 when x = 0.75
f(x) =5 when x =3
A{ x ∈ R ║ 3≤x}
14. Reflection: in the line y=x
Rotation: 180 about the origin
The image of the end points X(-3 , 1) and Y(4 , -5) is
X'' = (-1 , 3) and Y'' = (5 , -4).
Given, a line segment with end points X(-3 , 1) and Y(4 , -5)
We have to find the image of the points after the given composition,
Reflection in the line y = x.
Rotation 180° about the origin.
After the reflection the image of the points X and Y be,
X' = (1 , -3) and Y' = (-5 , 4)
Now, after the rotation of the points of 180° about the origin be,
X'' = (-1 , 3) and Y'' = (5 , -4)
Hence, the image of the end points X(-3 , 1) and Y(4 , -5) is
X'' = (-1 , 3) and Y'' = (5 , -4).
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How much money must be deposited today to become $2250 in 20 years at 5.5%
compounded continuously?
The deposit must be $
(Round to the nearest cent as needed.)
The amount of money that must be deposited today is $749 .
In the question ,
it is given that ,
the amount that is need to be made (A) = $2250
time (t) = 20 years
rate percent (r) = 5.5% = 0.055
let the amount that must be deposited today be P .
The amount that is needed to be deposited today at 5.5% compounded continuously can be calculated using the formula .
A = P×[tex]e^{r\times t}[/tex]
Substituting the values , we get
2250 = P × [tex]e^{0.055\times 20}[/tex]
2250 = P × [tex]e^{1.1}[/tex]
P = 2250/ [tex]e^{1.1}[/tex]
P = 748.9599
P ≈ 749
Therefore , The amount of money that must be deposited today is $749 .
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How many ways are there to split the integers 1 through 14 into 7 pairs so that in each pair the
greater number is at least 2 times the lesser number?
The number of ways to split the integers, given the condition and using the Fundamental Counting Theorem, is of:
144.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the total number of outcomes considering all trials is calculated by the multiplication of the factorials as presented as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
Given the condition that the greater number is at least 2 times the lesser number we have that the pairs are composed by one number between 1 and 7 and another number between 8 and 14.
Hence the pairs of each number are built as follows:
For the pair of the number 7, there are only one possible outcome, which is of 14.For the pair of the number 6, there are two possible outcomes, which are of either 12 or 13.For the pair of the number 5, there are three possible outcomes, which are of either 10, 11, and whichever of 12 or 13 is not paired with 6.For the pair of the number 4, there are four possible outcomes, which are of either 8, 9, and the two remaining numbers that are not paired with 5 or 6.For the pair of the number 3, there are three possible outcomes, which are the remaining numbers that are not paired with 4, 5 or 6.For the pair of the number 2, there are two possible outcomes, which are the remaining numbers that are not paired with 3, 4, 5 or 6.For the pair of the number 1, there is one possible outcome, which is the remaining numbers that is not paired with 2,3, 4, 5 or 6.Hence the number of ways to split the numbers is:
2 x 3 x 4 x 3 x 2 = 144.
(the numbers were multiplied because of the Fundamental Counting Theorem).
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Is it possible for a number to be a product of 2, a product of 5,
and a product of 10? Explain.
Answer: Yes
Step-by-step explanation:
Yes, it is because if you multiply 2 and 5, you get 10. 2 and 5 LCM is also 10. If you check 2 and five multiples you see this is also proved true.
2 - 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 ...
5 - 5, 10, 15, 20 ...
describe how to map line p onto line q
Answer:r
Step-by-step explanation:r
If Pam has 40 dollars in her account, how much money does her brother have in his account? Use a tape diagram to
support your answer.
Answer:
[tex] \binom{?}{?} [/tex]
Step-by-step explanation:
$40 Pam use type diagram
$45. bro
Consider triangle XYZ with altitude WZ. What is XZ?
X
W
N
28
21
Y
The value for the side of rectangle XZ is equal 14, using the trigonometric ratios of cosine and sine of angles.
What is trigonometric ratios?The trigonometric ratios concerns the relationship of an angle of a right-angled triangle to ratios of two side lengths. The basic trigonometric ratios includes;
sine, cosine and tangent.
Considering the triangle WYZ, the cosine of angle Y;
cos(Y) = 21/YZ {adjacent/hypotenuse}
YZ = [21/cos(Y)] {cross multiply}
Considering the triangle XYZ, the cosine of angle Y;
cos(Y) = YZ/28
YZ = 28 × cos(Y)
Therefore,
28cos(Y) = [21/cos(Y)]
cos²(Y) = 21/28 {cross multiply}
cos(Y) = √(21/28) {take the square root of both sides}
cos(Y) = 0.8660
Y = cos^(-1)(0.8660) {cross multiply}
Y = 30°
To get the side XZ, considering the triangle XYZ the sine of 30°;
sin30° = XZ/28 {opposite/hypotenuse}
by cross multiplication
XZ = 28 × sin30°
XZ = 14
Therefore, by proper application of the trigonometric ratios of cosine and sine of the angle for the given triangle, the side XZ = 14.
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How long will it take to double your money if you invest in an account that pays 8% interest, compounded continuously
The time that would be taken for the money to double is 9 years.
How long would it take to double the money?Given that a compound interest has to do with the type of interest that is charged both on the principal and on the interest. We know that the principal is the money that was invested.
Let the principal be P and let the time taken be t. Let us now apply the formula;
A = P(1 + r)^n
Where A = 2P and r = 0.08
2P = P(1 + 0.08)^n
2P/P = (1.08)^n
2 = (1.08)^n
ln2 = nln1.08
n = ln2/ln1.08
n = 0.693/0.077
n = 9
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I need the answer and work please.
Answer: you prob fininshed 5,3
Step-by-step explanation:
also this is easy im srry for doing this
The ratio of boys to girls in a class is 5:4. There are 36 students in the class. How many
students are girls?
Answer:
Let the girls be x
then, 5:4 = 5x and 4x
,
total stud.=36 so,
5x+4x=36
9x=36
x=36÷9
hence
x=4
now, boys = 5x=5×4=20
girls= 4x=4×4=16
so there are 16 girls
Use the table below to find d/dx[5f(x)-4x] x=2
The value of derivative of d/dx[5f(x)-4x] at x=2 = 16.
From the table:
At x=2,
f'(x) = 4
f(x) = 4x
= d/dx(5*4x - 4x)
= d/dx(20x - 4x)
= d/dx(16x)
= 16
Therefore the value of derivative of d/dx[5f(x)-4x] at x=2 = 16.
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2009
Evaluate x y for the following values of x and y.
value of x value of y value of xy
1
5
-205
1
67
1
-1
11
.
-1
-7.93
-1
-11
Answer:meh
Step-by-step explanation:good enough
Need help with question
a) The decay formula for the mass of Strontium-90 is m(t) = 75 · [tex]e^{-t /40.395}[/tex].
b) The sample of Strontium-90 has a mass of approximately 13.258 miligrams after 70 days.
c) The sample of Strontium-90 takes a time of approximately 146.405 days.
How to model the mass decay of a sample of Strontium-90
The mass of Strontium-90 decays exponentially in time, whose model is described below:
m(t) = m' · [tex]e^{- t /\tau}[/tex]
Where:
m' - Initial mass of the isotope, in miligrams. m(t) - Current mass of the isotope, in miligrams. τ - Time constant, in days.And the time constant can be estimated by the following formula:
τ = t' / ㏑ 2
Where t' is the half-life of the isotope.
a) If we know that m' = 75 mg and t' = 28 d, then the expression for the mass of the sample is:
τ = 28 / ㏑ 2
τ ≈ 40.395 d
m(t) = 75 · [tex]e^{-t /40.395}[/tex]
b) And the mass of the isotope after 70 days is:
m(70) = 75 · [tex]e^{- 70 / 40.395}[/tex]
m(70) ≈ 13.258 mg
The current mass is approximately 13.258 miligrams.
c) If we know that m(t) = 75 · [tex]e^{-t /40.395}[/tex] and m(t) = 2 mg, then the time needed for the decay is:
75 · [tex]e^{-t /40.395}[/tex] = 2
[tex]e^{-t /40.395}[/tex] = 2 / 75
- t / 40.395 = ㏑ (2 / 75)
t = - 40.395 · ㏑ (2 / 75)
t ≈ 146.405 d
The needed time is approximately 146.405 days.
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IXL Help Fast Please!
The equation of the line d that is parallel to line c is y = -5x + 4.
How to find the equation of a line in slope intercept form?The equation of a line in slope intercept form can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, c has an equation y = -5x + 3. Line d is parallel to line c. Therefore, they have the same slopes. Parallel lines have the same slope.
Hence, let's find the equation of line d passing through (2, -6)
Let's find the y-intercept
-6 = -5(2) + b
-6 = -10 + b
b = -6 + 10
b = 4
Therefore, the equation of the line d is y = -5x + 4
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A restaurant has 33,500 gallon aquarium and a 500 gallon aquarium. How many times greater is the capacity of the larger aquarium than the smaller aquarium?
Answer:
67
Step-by-step explanation:
33,500/500 = 67
To check our work:
67 x 500 = 33,500
Answer:
67 percentStep-by-step explanation:
Women’s heights have a mean of 63.6 in. and a standard deviation of 2.5 inches. The z score corresponding to a woman with a height is 2.56. How tall is the woman?
Answer:
70
Step-by-step explanation:
Had this question too ;)
4.8 is what percent of 12
Answer:40%
Step-by-step explanation:
4.5÷0.9= what is 4.5 divided by 0.9 equal to .explain
Answer: The answer is 5.
Step-by-step explanation:
4.5 ÷ 0.9 = 450/90.
Convert decimal 4.5 to fraction 45/10
Convert decimal 0.9 to fraction 9/10
Divide 450/90
Simply 450/90 = 5
Answer:
5
Step-by-step explanation: