A proportion looks like this:
[tex]a\div b = c\div d[/tex]
It means that the quantity a,b,c and d are in the same proportion: the ratio between a and b is the same ratio between c and d.
They are particularly useful in situation when you have an example given, and you want to extrapolate the relationship for another couple.
For example, you can think of the following problem: "Five apples cost 2 dollars. How much will 8 apples cost?"
You can build the proportion
[tex]5\div 2 = 8\div x[/tex]
And then solve it for x:
[tex]\dfrac{5}{2}=\dfrac{8}{x} \iff 5x=16 \iff x = \dfrac{16}{5} = 3.2[/tex]
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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If Bradley has 4 times as many dimes as nickels and they have a combined value of 315 cents, how many of each coin does he have?
d=4n
315=5n+10d
315=5n+40n
315=45n
315/45=n
7=n
d=4n
d=4(7)
d=28
28 dimes and 7 nickels
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]
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]
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
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
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]
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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!!!!!!!!!!!!!!!!!!!!!
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.
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
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]
What number divided by -3 gives 12 as the result?
A)-36
B)-4
C)4
D)36
Answer:
-36
Step-by-step explanation:
We don't need one, do we? It's just simple math.
An equation is formed of two equal expressions. The number which when divided by -3 gives 12 as the result is -36. The correct option is A.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let the number be represented by x.
Given that the number when divided by -3 gives 12 as the result. The given situation can be written in the form of an equation as,
x/-3 = 12
Solving the equation to get the value of x,
x/-3 = 12
x = 12 × -3
x = -36
Hence, the number which when divided by -3 gives 12 as the result is -36.
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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:
WILL MARK BRAINLIEST!!!! PLEASE HELP!!!!
X is 3
Refer to picture
Your yard is in a shape of a trapezoid
Answer:
1725
Step-by-step explanation:
50+65=115 divided by 2 =57.5 57.5*30H= 1725
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
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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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
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.
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
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
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°.
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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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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i NEEEED HELP PLEASE COMMENT IF U WILL HELP ME. ITS AN ALGEBRA QUESTION Enter your answer and show all the steps that you use to solve this problem in the space provided.
f(x)=9x3+2x2−5x+4and g(x)=5x3−7x+4.what is f(x)−g(x)?
Show all of your steps and write your final answer in factored form.
PLEASE HELP FAST 20 PTS
f(x)= 9x^3+ 2x^2 -5x+ 4
g(x)= 5x^3 -7x+ 4
f(x) - g(x)
= (9x^3+ 2x^2 -5x+ 4) - (5x^3 -7x+ 4)
= 9x^3+ 2x^2 -5x+ 4 -5x^3+ 7x -4
= (9x^3 -5x^3)+ 2x^2+ (7x -5x)+ (4-4) (combine like terms)
= 4x^3+ 2x^2+ 2x
= 2x* (2x^2+ x+ 1)
The final answer is 2x* (2x^2+ x+ 1).
The final answer in factored form is 2x(x² + x + 1).
f(x) = 9x³ + 2x² - 5x + 4
g(x) = 5x³ - 7x + 4
To find f(x) - g(x) ,, we subtract g(x) from f(x) term by term.
Subtract the like terms from f(x) and g(x):f(x) - g(x) = (9x³ + 2x² - 5x + 4) - (5x³ - 7x + 4) = 4x³ + 2x² + 2x
The final answer in factored form is 2x(x² + x + 1).
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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Layla wants to build a wooden box with a volume of 454545 cubic centimeters. She started with a width of 3\text{ cm}3 cm3, space, c, m and a height of 3\text{ cm}3 cm3, space, c, m.
How long should Layla make the box?
Answer:
91,125
Step-by-step explanation:
V=Bh
V=l*w*h
V=45*45*45
V=2,025 *45
V=91,125
Answer:
50,505 cm
Step-by-step explanation:
In order to calculate this you just have to calculate the length necessary to create a wooden box with the volume of 454545 cubic centimeters, and now you just have to calculate since you have the base of the area, measuring 3 cm by 3 cm, that would be 9 square centimeters, so you just have to divide the desired volume by 9 square centimeters:
454545/9=50,505 cm
So the length of the wooden box should be 50,505 cm in order to have a 454545 cubic centimeters wooden box.
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.
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.