Answer:
y = -2x -7
Step-by-step explanation:
y + 5 = -2 (x +1)
y + 5 = -2x -2 . move 5 to the other side by subtracting from both sides.
y = -2x -7
What is the numerator of the simplified sum?
x/x^2 +3x+2 + 3/x+1
Question:
What is the numerator of the simplified sum?
x/x^2 +3x+2 + 3/x+1
Answer & Step-by-step explanation:
The given equation is as follows.
\frac{x}{x^{2}+3x+2} + \frac{3}{x+1}
Taking L.C.M, the equation will become as follows.
\frac{x(x+1)+ 3(x^{2}+3x+2)}{(x^{2}+3x+2)(x+1)} ........ (1)
Factorize the equation x^{2}+3x+2 in the denominator as follows.
x^{2}+3x+2
= x^{2} + 2x + x + 2
= x(x+2) + 1(x + 2)
= (x+1)(x+2) ........ (2)
Put the factors in equation (2) in to equation (1), then the equation will become as follows.
\frac{x(x+1)+ 3(x^{2}+3x+2)}{(x^{2}+3x+2)(x+1)}
= \frac{x^{2}+x +3x^{2}+9x+6)}{(x+1)(x+2)(x+1)}
= \frac{4x^{2}+10x+6}{(x+1)^{2}(x+2)}
Now, factorize the numerator as follows.
\frac{4x^{2}+10x+6}{(x+1)^{2}(x+2)}
= \frac{4x^{2}+4x+6x+6}{(x+1)^{2}(x+2)}
= \frac{4x(x+1) + 6(x+1)}{(x+1)^{2}(x+2)}
= \frac{(4x+6)(x+1)}{(x+1)^{2}(x+2)}
Cancelling (x+1) from both numerator and denominator. Then the equation will be written as follows.
\frac{(4x+6)(x+1)}{(x+1)^{2}(x+2)}
= \frac{(4x+6)}{(x+1)(x+2)}
The numerator of simplified sum is (4x+6).
4x+6
C on Edge 2022
20 characters20 characters20 characters20 characters20 characters20 characters20 characters20 characters
what is 4x-2y=8 and y=2x+1 using substitution
Answer:
No Solution
Step-by-step explanation:
4x-2y=8
y=2x+1
Make the first equation into where it says y=.
-2y=-4x+8
y=2x-4
Substitute either equation into the other as y=.
2x+1=2x-4 or 2x-4=2x+1
Switch terms around so they're with their like terms. Make sure it becomes the opposite when switching.
2x-2x=-1-4 or 2x-2x=4+1
0=-5 0=5
Since x did not come back to equal an answer, this problem is not workable. There is no solution to it. If you were to do it a different way, there still would not be a solution to it.
The graph of the equation is Ax+2y =-2 is the line that passes through (2,-2) what is value A
Answer:
The value of A in the given graph of the equation is 1
That is A=1
Step-by-step explanation:
Given graph of the equation is Ax+2y=-2
Given that the equation of line Ax+2y=-2 passes through the point (2,-2)
Let (x,y) br the point (2,-2)
Therefore we have that
A(2)+2(-2)=-2
2A-4=-2
2A-4+2=-2+2
2A-2=0
2A=2
[tex]A=\frac{2}{2}[/tex]
Therefore A=1
Therefore the value of A in the given graph of the equation is 1
Suppose that the probability that a person will die in the next 20 years is
7.2698%. If this person has a life insurance policy that will pay out $60,00
the beneficiaries of the policy if the person dies in the next 20 years, what is
the premium of the policy? Assume that the administrative costs of the policy
amount to $75.
The premium of the policy is approximately $64,198.32.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
To calculate the premium of the policy, we need to take into account the probability of the person dying in the next 20 years and the payout of the policy.
Let P be the probability of the person dying in the next 20 years, and let A be the administrative costs of the policy.
Then the expected value of the payout of the policy is:
E(payout) = P x $60,000
And the expected value of the cost of the policy (including administrative costs) is:
E(cost) = P x premium + A
We want to find the premium of the policy, so we can rearrange this equation to solve for the premium:
premium = (E(cost) - A) / P
Substituting the given values, we get:
P = 0.072698
A = $75
E(payout)
= P x $60,000
= 0.072698 x $60,000
= $4,361.88
Now we need to calculate the expected value of the cost of the policy.
The cost of the policy includes both the payout (if the person dies) and the administrative costs (whether or not the person dies).
So we can write:
E(cost) = E(payout) + A x (1 - P)
where (1 - P) is the probability that the person will not die in the next 20 years.
Substituting the given values, we get:
E(cost) = $4,361.88 + $75 x (1 - 0.072698) = $4,746.88
Finally, we can calculate the premium of the policy:
premium = ($4,746.88 - $75) / 0.072698 = $64,198.32
Therefore,
The premium of the policy is approximately $64,198.32.
Learn more about expressions here:
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hope it helps I just did it
The graph of f(x) is shown. Estimate f(–3).
f(–3) =
The value estimated for f ( -3 ) from the graph is 12.5
Step-by-step explanation:
The function (f) in the graph defines all point sets in plane as (x, f(x)) form. The graph of equation to be the graph of function. I.e. y = f (x). Hence, graph of f is if the special case for graph of equation.
Given x = - 3 and asked to find f (-3). So, we have to see the point of y mapped (meeting point of y) on the point x = -3. In the graph, the point marked on y straight away to x = - 3 is 12.5.
Answer: 12.5
Step-by-step explanation:
it is the same as the g (x) problem. we sub -3 for x and see what the y value is on graph. At -3, y = 12.5
Brainliest? :)
Callie thinks of a number. She adds 6 to the number, multiplied the result by 2, and then subtracts 4. The number she ends up with is 46. what number did callie start with?
Answer:
20
Step-by-step explanation:
Add 4 to 46 = 52
Divide 52 by 2 = 26
Finally, subtract 6 to get 20
Look at attached photo!! Please answer asap!!
Answer:
C 1
Step-by-step explanation:
BC is perpendicular to AB, so has a slope that is the negative reciprocal of that of AB:
BC slope = -1/(AB slope) = -1/-1 = 1
Dilating the triangle has no effect on the slope.
The slope of B'C' is 1.
What is the equation, in slope-intercept form, of the line that is perpendicular to the line
y – 4 = –Two-thirds(x – 6) and passes through the point (−2, −2)?
Answer:
[tex]y=\frac{3}{2}x +1[/tex]
Step-by-step explanation:
We are given;
The equation of a line;
[tex]y-4 = -\frac{2}{3}(x-6)[/tex]
We are required to determine the equation of a line perpendicular to the above line and passing through (-2, -2).
We can get the gradient of a line when given its gradient and a point where it is passing through.In this case;We need to know that the product of gradient of two parallel lines is -1
Therefore, we can get the gradient of the unknown line;m₁× m₂ = -1
Thus;
m₂ = -1 ÷ -2/3
= 3/2
Thus, the gradient is 3/2 and the line passes through (-2,-2)
Thus, to get its equation, we take another point (x,y)
We get;
[tex]\frac{y+2}{x+2}= \frac{3}{2}[/tex]
Then;
[tex]2(y+2)=3(x+2\\2y + 4 = 3x + 6[/tex]
Combining the like terms,
[tex]2y=3x+2[/tex]
In the form of slope-intercept;
[tex]y=\frac{3}{2}x +1[/tex]
what inequality is equivalent to -m is greater than or equal to 15
an example of an equivalent inequality is
5+(-m) is greater than or equal to 20
The diameter of a circle is 18 kilometers. What is the length of a 120° arc?
Final answer:
The length of a 120° arc in a circle with an 18-kilometer diameter is approximately 18.85 kilometers.
Explanation:
The question asks to find the length of a 120° arc, given the diameter of a circle is 18 kilometers. To solve this, we first find the radius of the circle by dividing the diameter by 2, which gives us 9 kilometers.
Knowing the circumference formula is 2πr, we calculate the circumference as 2π(9) or 18π kilometers. Since 360° represents the full circumference, a 120° arc represents one-third of the circle.
Thus, the arc's length is one-third of the circumference: ⅓(18π) = 6π kilometers, which is approximately 18.85 kilometers.
Cora made a scale drawing of the middle school. The scale of the drawing was
7 inches
Could I get more context about the question? If I had more numbers then I could solve it.
3 consecutive integers are such that the when the smallest is multiplied by 3 is 18 more than the largest
Answer: 10 , 11 , 12
Step-by-step explanation:
Let the integers be : x , x + 1 and x + 2
the smallest multiplied by 3 implies 3x
From the first statement
3x = 18 + (x+2)
3x = 18 + x + 2
3x - x = 18 + 2
2x = 20
x = 10
Therefore : the numbers are : 10 , 10 + 1 and 10 + 2
the numbers are : 10 , 11 , 12
Answer:
10,11,12
Step-by-step explanation:
3 consecutive integers...x and x + 1 and x + 2
3x = x + 2 + 18
3x = x + 20
3x - x = 20
2x = 20
x = 20/2
x = 10
x + 1 = 10 + 1 = 11
x + 2 = 10 + 2 = 12
ur numbers are 10, 11, and 12
What is the value of x and y I’m stuck!!!
Answer:
x = 4 and y = 8
Step-by-step explanation:
Using the tangent and cosine ratios in the right triangle and the exact values
tan30° = [tex]\frac{1}{\sqrt{3} }[/tex], cos30° = [tex]\frac{\sqrt{3} }{2}[/tex]
tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{x}{4\sqrt{3} }[/tex] = [tex]\frac{1}{\sqrt{3} }[/tex] ( cross- multiply )
[tex]\sqrt{3}[/tex] x = 4[tex]\sqrt{3}[/tex] ( divide both sides by [tex]\sqrt{3}[/tex] )
x = 4
-------------------------------------------------------------------
cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{4\sqrt{3} }{y}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
[tex]\sqrt{3}[/tex] y = 8[tex]\sqrt{3}[/tex] ( divide both sides by [tex]\sqrt{3}[/tex] )
y = 8
Ed has two dogs the smaller dog weighs 1 1/3 lb the larger dog weighs 1 1/2 times as much as a smaller dog how much does the larger dog weigh
The tables below show four sets of data:
Set A
x
1
2
3
4
5
6
7
8
9
y
10
9
8
7
6
5
4
3
2
Set B
x
1
2
3
4
5
6
7
8
9
y
3
4
5
6
7
8
9
10
11
Set C
x
1
2
3
4
5
6
7
8
9
y
8
6
5
4
3.5
3
2.5
2
2
Set D
x
1
2
3
4
5
6
7
8
9
y
1
2.5
2.5
3
4
5
6
8
9
For which set of data will the scatter plot represent a positive linear association between x and y?
Set A
Set B
Set C
Set D
Answer:
B? sorry if its wrong
Step-by-step explanation:
Answer:
The answer is not set c!
Step-by-step explanation:
g(x) = 5 - 2.7
What is the domain of g?
Answer:
3
Step-by-step explanation:
noah has 4 bags of marbles with the same number in each bag. if there are 536 marbles altogether,how many marbles are in each bag?explain how u know
Answer:
There are 134 marbles in each bag.
Step-by-step explanation:
536/4=134
Answer:536 divided by 4 equals 134 marbles in each bag
Step-by-step explanation:
How to solve -5x(-7xcubed)
-5x(-7x^3)
Because -7x^3 is in parentheses, you add the degrees together:
35x^4
what is an equation that passes the points (4,-1) and (8,5) in fully reduced form
Answer:
y=3x-13
Step-by-step explanation:
1) find slope
5--1/8-4=6/2=3
2) (y--1)=3(x-4)
y+1=3x-12
y=3x-13
Chen’s report will take 8 and one third hours to complete. He has worked for three fifths of the time doing research. How long has he worked?
Answer:
5 Hours
Step-by-step explanation:
Given:
Chen’s report will take 8 and one third hours to complete.
He has worked for three fifths of the time doing research.
Question asked:
How long has he worked = ?
Solution:
Total hour required to complete the report = [tex]8\frac{1}{3}[/tex] = [tex]\frac{25}{3}[/tex]
He has worked of the total hour = [tex]\frac{3}{5}[/tex]
He has worked = three fifth of the total time doing research.
= [tex]\frac{3}{5} \times\frac{25}{3}[/tex]
= [tex]\frac{75}{15}[/tex]
= [tex]5 hours[/tex]
Thus,he has worked 5 hours doing his research.
Line k passes through (2, -3) and (8,1). Which equation represents a line that is parallel to k? A. y = -2/3 x - 5/3 B. y = 2/3 x - 13/3 C. y = 3/2 x - 6 D. y = -3/2 x
Answer: B. y = 2/3 x - 13/3
Step-by-step explanation:
two lines are said to be parallel if they have the same slope.
To find the slope of line K we will use the formula fro calculating slope which is :
m = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]x_{1}[/tex] = 2
[tex]x_{2}[/tex] = 8
[tex]y_{1}[/tex] = -3
[tex]y_{2}[/tex] = 1
substituting into the values into the formula , we have :
m = [tex]\frac{1-(-3)}{8-2}[/tex]
m = [tex]\frac{4}{6}[/tex]
m = [tex]\frac{2}{3}[/tex]
Therefore : the slope of line K = [tex]\frac{2}{3}[/tex] , this means that any line that will be parallel to K must have a gradient of [tex]\frac{2}{3}[/tex].
The only line that has a gradient of [tex]\frac{2}{3}[/tex] is the line y = 2/3x - 13/ 3 ,this means that the line is parallel to Line K
Fraction 45/100 what the decimal
Answer:
.45
Step-by-step explanation:
Answer:
0.45
Step-by-step explanation:
If you divide 45 by 100, the decimal point will move two times to the left because there is two 0's in 100, making it 0.45
What is an equivalent fraction for 5/10
Answer:
1/2
Step-by-step explanation:
5/10, 5 is HALF of ten so 1/2
11. Circle all of the examples that are perfect square. (You must circle all correct responses to receive credit)
2
4
0
8
10
12
14
16
18
120
Good evening ,
Answer:
Circle 0 , 4 , 16
Step-by-step explanation:
→ 0 = 0²
→ 4 = 2²
→ 16 = 4²
:)
5(w-4) in distributive property
Answer:
the answer would be 5w-20 after distribution
Answer: 5w + (-20)
Step-by-step explanation: So let's simplify this problem using the distributive property. The first thing we want to do is change the minus to plus a negative.
Now we can distribute or multiply the 5 by each of the terms inside the set of parentheses.
So we get 5(w) + 5(-4) and this simplifies to 5w + (-20).
x + y = -1 when x = -1
Answer:
-2
Step-by-step explanation:
Answer:
-1+y=-1
y=0
Step-by-step explanation:
cuz you basically add 1 to both sides
Complete the square x squared +18x-64=0
Answer:
x = -9±√145 (= 3.04 or -21.04)
Step-by-step explanation:
x²+18x-64 = 0 (move the constant to the right side, add 64 to both sides)
x²+18x = 64 (divide the x-term by 2, square it, then add it to both sides)
x²+18x + (18/2)²= 64 + (18/2)² (simplify)
x²+18x + 9²= 64 + 9²
x²+18x + 9²= 64 + 81
x²+18x + 9²= 145 (simplify left side using the property (a+b)² = a²+ 2ab+b²)
(x+9)² = 145 (take square root of both sides)
x+9 = ±√145
x = -9±√145 (= 3.04 or -21.04)
The two triangles below are similar. Triangle A B C. Side A B is 4 centimeters and B C is 9 centimeters. Angle A is 104 degrees, B is 50 degrees, C is 26 degrees. Triangle A prime B prime C prime. Side A prime B prime is 2 centimeters and B prime C prime is 4.5 centimeters. Angle A prime is 104 degrees, B prime is 50 degrees, C prime is 26 degrees. What is the ratio of the corresponding side lengths? 4:9 4:2 26:26 4.5:2
Answer:
4 : 2
Step-by-step explanation:
The two triangles Δ ABC and Δ A'B'C' are similar.
Here, ∠ A = ∠ A' = 104°, ∠ B = ∠ B' = 50° and ∠ C = ∠ C' = 26°.
Now, the length of AB and the length of A'B' are 4 cm and 2 cm respectively.
Again, the length of BC and the length of B'C' are 9 cm and 4.5 cm respectively.
Therefore, [tex]\frac{AB}{A'B'} = \frac{BC}{B'C'} = \frac{CA}{C'A'} = \frac{4}{2} = \frac{9}{4.5} = 2[/tex]
Hence, the ratio of the corresponding side lengths is 4 : 2. (Answer)
Answer:
4:2
Step-by-step explanation:
Write the following as an exponential expression?
Answer:
Step-by-step explanation:
recall that for a radical expression, the following apply
[tex]\sqrt[x]{y} = y^{\frac{1}{x} }[/tex]
compare this with our case, we can clearly see that
x = 4 and y = 10,
substituting into the above equation gives:
[tex]\sqrt[4]{10} = 10^{\frac{1}{4} }[/tex]
The expression [tex]$\sqrt[4]{10}[/tex] can be written as an exponent as [tex]$(10)^{\frac{1}{4} }[/tex].
What is the general equation of exponential function? What is the general equation of a quadratic equation?The general equation of a exponential relationship is -
y = Aeˣ
The general equation of a quadratic equation is -
y = ax² + bx + c
Given is the following expression -
[tex]$\sqrt[4]{10}[/tex]
We can write the given expression in the form of exponential expression as -
y = [tex]$(10)^{\frac{1}{4} }[/tex]
Therefore, the expression [tex]$\sqrt[4]{10}[/tex] can be written as an exponent as [tex]$(10)^{\frac{1}{4} }[/tex].
To solve more questions on exponential function, visit the link below-
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What are the domain and range of the function?
f(x)=−35x3
Domain: (−∞, 0)∪ (0, ∞)
Range: (−∞, 0)∪ (0, ∞)
Domain: (−∞, 0)∪ (0, ∞)
Range: (−∞, 0)
Domain: (−∞, 0)∪ (0, ∞)
Range: (0, ∞)
Domain: (−∞, ∞)
Range: (−∞, 0)
The domain and the range of the functions is real numbers. Hence, option A is correct.
We need to determine the domain and range of the function [tex]\bold{f(x)=-35x^3}[/tex].
Let us define the domain and the range of the function:
Domain:
When all the possible values of an independent variable for which we get the real value of a dependent variable then the values of the independent variables is called domain of the function.
Range:
All the possible values of the function is called the range of the function. Range is the sub-set of co-domain.
Now,
For the given function [tex]f(x)=-35x^3[/tex].
No value of x can restrict the above function hence its domain is real number that is [tex](-\infty, +\infty)[/tex].
And, range of the function is also the same [tex](-\infty, +\infty)[/tex].
Thus, the domain and the range of the functions is real numbers. Hence, option A is correct.
To know more about the domain, please refer to the link:
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The domain and range of the cubic function f(x) = -35x^3 are both all real numbers, because there are no restrictions on x and the function's output covers all real values.
Explanation:The function described is f(x) = −35x^3. The domain of a polynomial function, which includes cubic functions like this one, is all real numbers because there are no restrictions on the values that x can take. Therefore, the domain is (−∞, ∞). Since the leading coefficient of the cubic term is negative, the ends of the graph will go towards negative infinity as x goes to positive and negative infinity. Therefore, the range of the function is also all real numbers, which we write as (−∞, ∞).