The constant of variation in a direct variation is found by dividing the y-coordinate by the x-coordinate. Using this constant, we can determine the y-value of a point given the x-value. In this case, n = 5.
Explanation:In a direct variation, the ratio of the two variables is constant. This means that the product of the two corresponding coordinates of any two points is always the same.
Given a point (4,20), we can find the constant of variation by dividing the y-coordinate by the x-coordinate, which yields 20/4 = 5. So, the constant of variation (k) is 5.
For the point (1, n), the product of the two coordinates should also yield the same constant of variation. Therefore, 1 * n = 5. Solving for n, we find that n = 5.
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If p(x) = ab^x and r(x) = cd^x, then p(x) * r(x) equals
p(x) * r(x) = ab^x * cd^x
p(x) * r(x) = (a*c)*(b^x*d^x)
p(x)*r(x) = ac(bd)^x
For the last step, I used the rule that (ab)^x = a^x*b^x
Final Answer: ac(bd)^xThe product of two exponential functions p(x) = ab^x and r(x) = cd^x is calculated by following the rules of exponents in mathematics, resulting in p(x) * r(x) = a * c * (bd)^x
Explanation:The student is asking for the product of two exponential functions. If p(x) = ab^x and r(x) = cd^x, their product can be calculated as follows:
Firstly, recognize each function as an exponential. The base of the exponential in p(x) is b, and in r(x) is d. Multiply the two equations together. This can be done because the operations defined for the exponential can be applied when the base of two exponential functions are the same. Substitute p(x) and r(x) back into the equation. We get: p(x) * r(x) = ab^x * cd^x Apply the rules of exponents in math, more specifically the multiplication rule, which states that a^m * a^n = a^(m+n). So, p(x) * r(x) = a * c * (bd)^xLearn more about Multiplication of Exponential Functions here:
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Need help with #1 please it’s algebra!
Answer:
145°
Step-by-step explanation:
The angle is 90°+55°=145°
Answer: 145°
Step-by-step explanation:
The angle of straight lines is always 180°, so I took 180 and subtracted 55 from it, and then 90 to get 35. I got 90 because the x and y axis are perpendicular to each other, and the angle between perpendicular lines is always 90. 35° is the angle of the small un marked section to the left of the circles, so to get the angle of the circle-like line, I did 180-35 to get 145°.
puzzle: the quadratic code 4- 3
Answer:
The answer to 4-3 is 1.
Step-by-step explanation:
The quadratic code '4 - 3' corresponds to the mathematical expression "4 minus 3," which equals 1.
The quadratic equation '4 - 3' is a simple algebraic equation that can be decoded as follows:
Start with the number 4.
Subtract 3 from it.
So, the decoded mathematical expression is:
4 - 3 = 1
The result is 1.
Therefore, the quadratic code '4 - 3' corresponds to the mathematical expression "4 minus 3," which equals 1.
This demonstrates how to decode and interpret a simple algebraic expression, showing that when you subtract 3 from 4, the result is 1.
It's a basic example of performing arithmetic operations on numbers.
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The probable question may be:
Decode the quadratic expression '4 - 3' to reveal the mathematical expression it represents. Provide the complete mathematical expression that corresponds to the given quadratic code.
What is the simplified expression for 4 to the power of negative 3 multiplied by 3 to the power of 4 multiplied by 4 to the power of 2 whole over 3 to the power of 5 multiplied by 4 to the power of negative 2
To simplify the expression, combine the exponents and evaluate the values to get the simplified expression 1/12.
Explanation:To simplify the expression, we can combine the exponents of the same base. Let's break it down step-by-step:
Combine the exponents of 4: (-3+2) = -1Combine the exponents of 3: (4-5) = -1Combine the exponents of 4: (2-2) = 0So, the simplified expression is 4-1 * 3-1 * 40. Any number raised to the power of 0 is equivalent to 1, so the expression can be further simplified to 4-1 * 3-1 * 1. Finally, we can evaluate the values: 4-1 = 1/4, and 3-1 = 1/3.
Therefore, the simplified expression is (1/4) * (1/3) = 1/12.
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The expression [tex]\(\frac{4^{-3} \times 3^4 \times 4^2}{3^5 \times 4^{-2}}\)[/tex] simplifies to [tex]\(\frac{4}{3}\).[/tex]
To simplify the expression [tex]\(\frac{4^{-3} \times 3^4 \times 4^2}{3^5 \times 4^{-2}}\)[/tex], follow these steps:
Combine the exponents for the similar bases using the exponent rules.For the base 4: [tex]\(4^{-3 + 2} \times 4^{2} \times 4^{2}\)[/tex]Combine into: [tex]\(4^{-3 + 2 + (-(-2))} = 4^1\)[/tex]For the base 3: [tex]\(3^4 / 3^5 = 3^{4-5} = 3^{-1}\)[/tex]Simplify the expression: [tex]\(\frac{4}{3}\)[/tex]So the simplified expression is [tex]\(\frac{4}{3}\)[/tex] .
Corrected question:
What is the simplified expression for [tex]\(\frac{4^{-3} \times 3^4 \times 4^2}{3^5 \times 4^{-2}}\)[/tex]
Solve for r.
r16≥8
r≥2
r≤2
r≥128
r≤128
The equation doesn't provide enough context to definitively solve for 'r'. Given the original equation r16 ≥ 8, r shouldn't be less than 1 if only integer values are accepted.
Explanation:In Mathematics, the original equation provided here, 'r16 ≥ 8', seems to indicate that a value 'r' is being multiplied by 16 and the product should be greater than or equal to 8. To solve for 'r', you would normally divide both sides of the equation by 16. However, each sub-question provided 'r ≥ 2', 'r ≤ 2', 'r ≥ 128', and 'r ≤ 128', indicates different potential solutions for 'r'. Without the proper context or further information it is difficult to properly solve for 'r'. Given the original equation, if only integer values are allowed, 'r' should not be less than 1 to maintain the inequality. Further clarification on the nature of 'r' and the context of the question is highly recommended.
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!!!!!!!!!!!!!!!!!!!!!
ANSWER
A. (x+4)
EXPLANATION
The given binomial is
[tex] {x}^{2} + 12x + 32[/tex]
Split the middle term:
[tex] {x}^{2} + 8x + 4x + 32[/tex]
Factor;
[tex]x(x + 8) + 4( x + 8)[/tex]
Factor further;
[tex](x + 8)(x + 4)[/tex]
Therefore
[tex](x + 4)[/tex]
is a factor.
Find the value of x if A,B,and C are collinear points and B is between A and C. AB=3x, BC=2x-7, AC=2x+35
Answer:
x = 14
Step-by-step explanation:
3x+2x-7=2x+35
then solve for x
Answer:
x = 14
Step-by-step explanation:
We are given that A, B and C are collinear points and B is in between A and C.
The length from A to B is [tex] 3 x [/tex], length from B to C is [tex] 2x - 7 [/tex] and AC is [tex] 2 x + 35 [/tex].
We are to find the value of x.
[tex] A B + B C = A C [/tex]
[tex] 3 x + 2 x - 7 = 2 x + 3 5 [/tex]
[tex] 3 x + 2 x - 2 x = 3 5 + 7 [/tex]
[tex] 3 x = 4 2 [/tex]
[tex] x = \frac { 4 2 } { 3 } [/tex]
x = 14
An animal shelter has a total of 275 animals composed of dogs and cats. The number of cats is 5 more than one half of the number of dogs. How many dogs are in the shelter?
Answer: There are 180 dogs in the shelter.
Step-by-step explanation:
Let be "c" the number of cats in the shelter and "d" the number of dogs in the shelter.
You know that the total number of dogs and cats in the animal shelter is 275. Then you can express this with:
[tex]d+c=275[/tex]
If the number of cats is 5 more than one half of the number of dogs, you can express it with:
[tex]c=\frac{d}{2}+5[/tex]
Then, substitute [tex]c=\frac{d}{2}+5[/tex] into [tex]d+c=275[/tex] and solve for "d" to calculate the number of dogs that are in the shelter. Then:
[tex]d+c=275\\\\d+\frac{d}{2}+5=275\\\\d+\frac{d}{2}=275-5\\\\\frac{2d+d}{2}=270\\\\\frac{3d}{2}=270\\\\3d=270*2\\\\d=\frac{540}{3}\\\\d=180[/tex]
PLEASE. HELP. ME I WILL GIVE BRAINLIEST I NEED TO ANSWER ALL OF THESE AND EXPLAIN THEM
Donna buys some fabrics to make place meta. She needs 1/5 yards of each fabrics. She has 9 different types of fabrics to make her design. Use the following equation. Write the number in the box to make the statement true.
Answer:
9/5 = 9 x 1/ 5
Answer:
9/5 = 9 * 1/5
Step-by-step explanation:
Angles A and B are complementary. Angles A has a measure of (3x+30). Angle B has a measure of 36. What is the value of x?
Answer:
2
Step-by-step explanation:
3(2)+30=36
a different lake currently has an area of 240 square km but is shrinking each year by 6% from the previous year's area. How much area will the lake have after 13 years?
The answer is:
[tex]A(13)=107.37Km^{2}[/tex]
Why?We can calculate the area of the lake after 13 years using the following equation:
[tex]A(t)=A(initial)(1-ShrinkingRate)^{t}[/tex]
Where,
A(t), is the area after t time (years)
A(Initial), is the initial area
Shrinking Rate, is the rafe of shrinking and it's 6% or 0.06.
t, is the time
So, substituting we have:
[tex]A(13)=240(1-0.06)^{13}=240*0.447=107.37Km^{2}[/tex]
So, the are after 13 years will be:
[tex]A(13)=107.37Km^{2}[/tex]
Have a nice day!
50 POINTS PLEASE HELP ME IM RUNNING OUT OF TIME!!!!!!!!!
Given the vertices of ∆ABC are A (2,-5), B (-4,6) and C (3,1), find the vertices following each of the transformations FROM THE ORIGINAL vertices:
Rx = 3 T<3,-6> r(90◦, o)
Answer:
Step-by-step explanation:
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Bill is going to order new jerseys for his baseball team. The jerseys will have the team logo printed on the front.
"Print It" will charge $21.50 each for the jerseys.
Using n for the number of jerseys ordered and c for the total cost in dollars, write an equation to show the total cost of the jerseys from "Print It."
Answer:
Equation: $21.50•n=c
Lines a is perpendicular to line b . Which statement about lines a and b is true ?
Answer:
The product of the slopes of line a and line is -1.
Perpendicular lines a and b intersect at a right angle, or 90 degrees. This is independent of whether they are increasing or decreasing, or their steepness on a graph.
Explanation:The statement about lines a and b that is true when they are perpendicular is that they form a 90-degree angle with each other. The concept of perpendicularity in geometry refers to lines, planes, or surfaces that intersect at a right angle.
Terms like increasing or decreasing line or the steepness of a line do not apply here as they pertain to the slope of the line in the context of a graph, which is distinct from the concept of perpendicularity.
For example, saying line A is a decreasing line while line B is an increasing line, does not describe their perpendicular relationship. Instead, they intersect or meet at a right angle (90 degrees), proving their perpendicular nature.
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In a week tracey earns $12.45 less than twice the amount Kayla earns. Tracy earns $102.45 write and solve an algebraic equation to show how to find the amount that Kayla earns
Answer:
Step-by-step explanation:
Tracey Earns in week= $102.45
Tracy=2x-12.45
102.45=2x-12.45
2x= 102.45+12.45
2x=114.90
x= 114.90/2
x=$57.45
Kayla earns 57.45 dollars
The equation is n = (102.45 + 12.45) x 2.
And Kayla earns $229.8.
What is an equation?Two algebraic expressions having same value and symbol '=' in between are called as an equation.
Given:
In a week, Tracey earns $12.45 less than twice the amount Kayla earns. Tracy earns $102.45.
Let n be the amount Kayla earns.
Then,
Kayla earns,
n = (102.45 + 12.45) x 2
n = $229.8
Therefore, Kayla earns $229.8.
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A bakery used 2 cups of flour to make a full size cake If they wanted to make cake that was 0.4 the size how many cups of flour would they need.
Answer:
0.8 cup(s)
Step-by-step explanation:
2 x 0.4 = 0.8
Answer:
0.8
Step-by-step explanation:
So to get this answer you had to mulyiply the 2 cups of flour by the size you want which is 0.4 . 2(0.4)=0.8
how do you solve for the indicated variable. 8x+4y=12;y
Answer:
x=1
Step-by-step explanation:
8x+4y=12y
-4y -4y
8x=8y
x=1
Find the value of the angle x in the triangle below
Answer:
[tex]\large\boxed{x=53^o}[/tex]
Step-by-step explanation:
We know: the sum of the measures of the angles of the triangle is equal to 180 °.
Therefore e have the equation:
[tex]x+45^o+82^o=180^o[/tex]
[tex]x+127^o=180^o[/tex] subtract 127° from both sides
[tex]x=53°[/tex]
Help plz show work plz
Answer: c) 286.5 in²
Step-by-step explanation:
S.A.= 2π r · h
= 2π (7.3/2) · 12.5
= 2π (3.65) (12.5)
= 286.5
the student council at Madison Middle School has five sixth graders 5 7 grade and 5 eight graders. 1 student council member will be selected at random to represent the school at a conference what is the probability that the selected student council member will be in the 7th grade
5/15 or 1/3 would be the correct answer
what are x, y, and z? Simplest radical form.
Answer:
x=5, y=22.36, z=11.18
Step-by-step explanation:
Use mean extremes
10^2=sqrt(20x)
Solving x = 5
for y:
y=sqrt(20(20+5))=22.36
for z:
z=sqrt(5(20+5))=11.18
WILL MARK BRAINLIEST!!!! PLEASE HELP!!!!
X is 3
Refer to picture
If 4b-1=b, then 24b= ?
Answer:
Step-by-step explanation:
4b-1=b
3b-1=0
3b=1
b=1/3
24b=
24(1/3)=
8
Equations are expression separated by an equal sign. The value of 24b if 4b-1 = b is 8
Equation and expressionEquations are expression separated by an equal sign
Given the expresion
4b - 1 = b
Find the value of "b"
4b - b = 1
3b = 1
b = 1/3
Determine the value of 24b
24b = 24(1/3)
24b = 8
Hence the value of 24b if 4b-1 = b is 8
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If 30% of the students in Mrs.Rutherfords class like chocolate ice cream, then how many students are in Mrs. Rutherford’s class if six like chocolate ice cream
Answer: 20
Step-by-step explanation:
6/30 = 0.2
0.2 times 100 = 20
Final answer:
After setting up a proportion and solving the equation 0.30x = 6, we find that there are 20 students in Mrs. Rutherford's class.
Explanation:
To determine how many students are in Mrs. Rutherford's class when 30% like chocolate ice cream and we know that 6 students like chocolate ice cream, we can set up a proportion where 30% (or 0.30) of the total number of students (which we will call x) is equal to 6. Therefore, the equation to find x is 0.30x = 6.
To solve for x, we divide both sides of the equation by 0.30:
0.30x = 6
x = 6 / 0.30
x = 20
So, there are 20 students in Mrs. Rutherford's class.
Rewrite this polynomial in terms of its simplest factors using the appropriate method: x3 + x2 − 6x.
Answer: GCF = x
Step-by-step explanation:
x(x^3/x + x^2/x + -6x/x)
x(x^2 + -6)
x(x - 2)(x + 3)
Answer:
x(x + 3)(x - 2)
Step-by-step explanation:
Factor out x from each term
= x(x² + x - 6)
To factor the quadratic
Consider the factors of the constant term (- 6) which sum to give the coefficient of the x - term (+ 1)
The factors are + 3 and - 2, since
+ 3 × - 2 = - 6 and + 3 - 2 = + 1, hence
x² + x - 6 = (x + 3)(x - 2)
---------------------------------------
x³ + x² - 6x = x(x + 3)(x - 2) ← in factored form
find the equation to a circle with a radius of 10 and a center at (-1, 7)
Answer:
[tex]\large\boxed{(x+1)^2+(y-7)^2=100}[/tex]
Step-by-step explanation:
The equation of a circle in standard form:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
We have the center (-1, 7) and the radius r = 10. Substitute:
[tex](x-(-1))^2+(y-7)^2=10^2\\\\(x+1)^2+(y-7)^2=100[/tex]
a line passing through the origin intersects the point -8 -5 what is the slope of the line
To find the slope of a line passing through the origin and a point, use the formula slope = (y2 - y1)/(x2 - x1). For a line passing through origin and the point (-8,-5), the slope is 5/8.
Explanation:The topic at hand revolves around the concept of slope and the algebra of straight lines. The slope is calculated by finding the change in y (vertical axis) over the change in x (horizontal axis). To find the slope of a line passing through the origin and the point (-8,-5), use the formula slope = (y2 - y1)/(x2 - x1).
In this case, the origin is point (0,0) and the given point is (-8,-5). So to find the slope, we substitute these values into the slope formula: slope = (-5 - 0)/(-8 - 0) = 5/8. Therefore, the slope of the line passing through the origin and the point (-8,-5) is 5/8.
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The slope of the line is 5/8.
Explanation:The slope of a line, denoted by m, represents the rate of change between the vertical and horizontal components of two points on the line.
To find the slope of a line passing through the origin and intersecting the point (-8, -5), we can use the slope formula. The slope formula is given by: m = (y2 - y1) / (x2 - x1).
Plugging in the values from the given point gives: m = (-5 - 0) / (-8 - 0)
= -5 / -8
= 5/8.
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Find the sum.
Homework: 9.4 arithmetic series
Answer:
Step-by-step explanation:
a1 = 3(1) - 7 = - 4
a2 = 3(2) - 7 = -1
d = a2 - a1
d = -1 - (-4)
d = -1 + 4
d = 3
a60 = 3(60) - 7
a60 = 180 - 7
a60 = 173
n = 60
Sum = (a1 + a60) * n / 2
Sum = (-4 + 173) * 60/2
Sum = (169)*30
Sum = 5070
==================
Just to check, we'll use the second summation formula
d = 3
n = 60
a1 = -4
Sum = (2*a1 + (n - 1)*d )*n / 2
Sum = (2*(-4) + (60 -1)*3)* 60/2
Sum = (-8 + 59*3) * 30
Sum = (177 - 8)*30
Sum = 169 * 30
Sum = 5070
Same answer.
An account earns simple interest.
$2000 at 3.5% for 4 years
a. Find the interest earned.
$280
b. Find the balance of the account.
$
Answer:
$2280
Step-by-step explanation:
I see you've already found part a, which is to find the amount of interest earned. The next part is easy, to find the balance of the account after four years, just add the interest you've found back to the principal (the original size of the account or loan). $2000 + $280 equals $2280.
The interest earned on the account is $280. The balance of the account after 4 years is $2280.
Explanation:To find the interest earned on the account, we use the formula for simple interest:
I = PRT
where:
I is the interest P is the principal amount (the initial amount of money) R is the rate of interest T is the time in years
Substituting the given values:
I = $2000 * 3.5/100 * 4 = $280
To find the balance of the account, we add the interest earned to the principal:
Balance = P + I = $2000 + $280 = $2280
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