Question:
The numerator and denominator of a fraction are in the ratio of 3 to 5. If the numerator and denominator are both decreased by 2, the fraction is now equal to [tex]\frac{1}{2}[/tex].
If n = the numerator and d = the denominator, which of the following systems of equations could be used to solve the problem?
5n = 3d and n - 2 = 2d - 4
5n = 3d and 2n - 4 = d - 2
3n = 5d and 2n - 4 = d - 2
Answer:
5n = 3d and 2n – 4 = d – 2
Solution:
Let n be the numerator of the fraction and d be the denominator of the fraction.
Given the numerator and denominator of a fraction are in the ratio of 3 to 5.
This can be written as n : d = 3 : 5.
⇒ [tex]\frac{n}{d}= \frac{3}{5}[/tex] – – – – (1)
Do cross multiplication, we get
⇒ 5n = 3d
When the numerator and denominator are decreased by 2, the fraction is equal to [tex]\frac{1}{2}[/tex].
⇒ [tex]\frac{n-2}{d-2}= \frac{1}{2}[/tex]
Do cross multiplication, we get
⇒ 2(n –2)=1(d – 2)
⇒ 2n – 4 = d – 2
Hence, 5n = 3d and 2n – 4 = d – 2 can be used to solve the problem.
Answer:
5n = 3d and 2n – 4 = d – 2 is the answer
Step-by-step explanation:
9x divided by -2x sqared
Answer:
-9/2x
Step-by-step explanation:
The frequency table shows the number of points scored during 30 Bulldogs
basketball games. On a piece of paper, draw a histogram to represent the
data. Then determine which answer choice matches the histogram you drew
the answer is the that 80-89 is the longer
Step-by-step explanation:
The answer choice that matches the histogram drawn is option C.
What is an histogram?A histogram is used to represent data graphically. The histogram has a y-axis which shows the frequency and an x - axis which shows the class interval. The correct option should match the information provided in the frequency table.
In this case, we have 5 intervals, that means the histogram must have 5 bars, where their height represents the frequency.
Having said that, the first bar must have a height of 4 units, the second one of 9 units, the third one of 5 units, the fourth one of 8 units and the fifth a height of 4 units.
Therefore, the right answer is C., because that's the histogram with the described heights.
To learn more about histograms, please check: brainly.com/question/14473126
#SPJ7
Find domains of the following expressions.
sqrt(2-3x)+sqrt(5-x)
Find the domain by finding where the expression is defined.
Interval Notation:
Interval Notation: ( − ∞ , 2 3 ] (-∞,23]
Set-Builder Notation: { x ∣ ∣ ∣ x ≤ 2 3 }
Answer: (-∞ , 2/3)
Step-by-step explanation:
To find the domain of a radical , we will set the function inside the radical greater than or equal to zero , that is
2 - 3x ≥ 0
2 ≥ 3x
2/3 ≥ x
that is : x ≤ 2/3
Also
5 - x ≥ 0
5 ≥ x
That is : x ≤ 5
Therefore , the domain of the expression is x ≤ 2/3 and x ≤ 5
Identify an equivalent fraction to 8/6. 6/8. 8/3. 4/3. 10/8.
Are two obtuse triangles always, sometimes, or never similar
Answer:
My Answer Is ALWAYS.
Why I Think So:
It's Because As You Said...They Have Obtuse Angle, Which Can Never Change.
Obtuse triangles are sometimes similar if they have congruent angles; however, simply being obtuse does not guarantee similarity. The angles must match exactly among the triangles for them to be considered similar.
Explanation:Two obtuse triangles are sometimes similar but not always.
For two triangles to be similar, they must have exactly the same angle measurements, although the side lengths can differ by a consistent ratio.
In the case of obtuse triangles, they will be similar if they have one obtuse angle that is the same measure in both triangles and their other corresponding angles are also equal.
However, just having obtuse angles is not sufficient for similarity; the angles must be congruent, and in the case of an obtuse triangle, the other two angles must be specifically tailored so that all three angles are congruent to another triangle's angles.
The concept of triangle similarity falls under the Uniqueness of Solutions which denotes that a triangle is determined by three known elements, but these do not always provide a unique solution.
While often seen in the context of right triangles, such as when applying the Pythagorean Theorem, for obtuse triangles, similarity is determined by angle congruence rather than side lengths.
This implies that if two obtuse triangles have all three angles congruent, they are similar by definition. If not, they are not similar
The yearbook club had a meeting. The meeting had 12 people, which is two-thirds of the club. How many people are in the club?
people
Answer:
18 people
Step-by-step explanation:
a sum expression that equals -3/4
Answer:
2 1/4 - 3 = -3/4 can be a simple equation.
X over 5 equals 15 what does x equal
answer
75
Step-by-step explanation:
x over 5 = 15 is 75
this meanstitute x with 75 is a equation she's both sides equal we can conclude that x = 75 is the correct solution to the equation x over 5=15
A new computer system sells for approximately $2000 and depreciates at the rate of $500 per year.
what are you asking
Step-by-step explanation:
Which numbers are perfect squares? Check all that apply
37:57
1
2
16
18
32
44
94
100
ANSWER: 1, 16, 100 are perfect squares.
STEP-BY-STEP EXPLANATION:
A perfect square is a number that can be expressed as the product of two equal integers.
1 x 1 = 1
4 x 4 = 16
10 x 10 = 100
Answer:
1, 16, 100 (a, c, h)
please mark brainliest
100 Points! What are the classifications of each system?
Drag the answer into the box to match each system.
Answer:
Part 1) Is a inconsistent system
Part 2) Is a consistent independent system
Part 3) Is a consistent dependent system
see the attached figure
Step-by-step explanation:
we know that
If a system has at least one solution, it is said to be consistent .
If a consistent system has exactly one solution, it is independent .
If a consistent system has an infinite number of solutions, it is dependent
If a system not have solution, it is said to be inconsistent
Part 1) we have
[tex]x+5y=-2\\x+5y=4[/tex]
This system of linear equations has two parallel lines (their slopes are equal) with different y-intercept
so
The lines don't intersect
The system has no solution
therefore
Is a inconsistent system
Part 2) we have
[tex]y=3x+4\\-2x+y=4[/tex]
we know that
If two lines have different slopes, then the lines intersect at one point and the system of equations has one solution
In this problem, the lines have different slopes (m=3 and m=2)
so
The lines intersect at one point
The system has one solution
therefore
Is a consistent independent system
Part 3) we have
[tex]3x+y=4[/tex] ----> equation A
[tex]-6x-2y=-8[/tex] ----> equation B
Multiply equation A by -2 both sides
[tex]-2(3x+y)=-2(4)[/tex]
[tex]-6x-2y=-8[/tex] ----> equation C
Compare equation B and equation C
Are identical lines
so
The system has infinity solutions
therefore
Is a consistent dependent system
Answer:
1) inconsient system
2) consient system
3) consient system
olve for x. -3x = -15 x = -45 x = 5 x = -5
Answer:
it 1/4
Step-by-step explanation:
i did the other anwser and it anwsered after i got it wrong
Which expression are equivalent to: -2y -8+4y
Answer: 2y−8
Step-by-step explanation:
1) Simplify step-by-step.
−2y−8+4y
=−2y+−8+4y
2) Combine Like Terms:
=−2y+−8+4y
=(−2y+4y)+(−8)
=2y+−8
Answer:
both A and B
Step-by-step explanation:
The basic price for an annual dental checkup and cleaning is $50. If the dentist finds any cavities in there will be an additional charge of $100 for each cavity tour dentist will have to find. Write an expression to describe the cost of the visit if the dentist finds n cavities
Answer:
100n+50
Step-by-step explanation:
the dentist charges $100 dollars per cavity found. Per indicates multiplication. Since there is an additional fee, we add $50 to the $100n, which will make the expression
$100n+50
is 213 2.3 greater less or equal to
Answer:
2 1/3 > 2.3
Step-by-step explanation:
There are a couple of ways you can compare these numbers. One is to convert 2 1/3 to a decimal fraction. It is the repeating decimal ...
2 1/3 = 2.3333333...
Compared to 2.30, we see that 2 1/3 has a 3 in the hundredths place, where 2.3 has 0. Thus 2 1/3 is greater than 2.3.
__
You can convert them both to improper fractions and then to fractions with a common denominator.
2 1/3 = 7/3 = 70/30
2.3 = 23/10 = 69/30
70/30 > 69/30 . . . . so 2 1/3 > 2.3
Could someone explain to me how to solve this
? I got (-1,2) and it said I was wrong.
never mind found out why, i was supposed to plug in x for one of the equations to find y!
The ordered pair is (–1, –2)
Solution:
Given system of linear equations are
4x –7y = 10 – – – – (1)
3x + 2y = –7 – – – – (2)
To solve this by elimination method.
First multiply equation (1) by 3 and then multiply equation (2) by 4.
(1) × 3 ⇒ 12x –21y = 30 – – – – (3)
(2) × 4 ⇒ 12x + 8y = –28 – – – – (4)
Subtract equation (4) from equation (3), we get
⇒ 12x –21y – (12x + 8y) = 30 – (–28)
⇒ 12x –21y – 12x – 8y = 30 + 28
Combine like terms together.
⇒ 12x – 12x –21y – 8y = 30 + 28
⇒ –29y = 58
Divide both sides by –29, we get
⇒ y = –2
Substitute y = –2 in equation (1), we get
(1) ⇒ 4x –7y = 10
⇒ 4x – 7(–2) = 10
⇒ 4x + 14 = 10
⇒ 4x = 10 – 14
⇒ 4x = –4
Divide both side by 4, we get
⇒ x = –1
Hence the ordered pair for the given system of equations is (–1, –2).
If y varies directly as x and y=8 when x=2, find x=6.
Step-by-step explanation:
X=ky
2=8k
K=4
X=4y
6=4y
Y=1. 5
Answer:
Step-by-step explanation:
y varies directly as x
y ∞ x
y = kx
and y=8 when x=2
8 = 2(k)
8 = 2k
k = 8/2
k = 4
y = 4x
find y when x=6
y = 4(6)
y = 24
can someone help me with this problem please
Answer:
Option C that is [tex]x=4,DF=EG=15[/tex] the right choice.
Step-by-step explanation:
Given,
A rectangle with the measures of its diagonal DF and EG.
Measure of diagonal DF = [tex]5x-5[/tex]
Measure of diagonal EG = [tex]x+11[/tex]
Note:Diagonal length of the rectangle are same.
So DF = EG
[tex]5x-5=x-11[/tex]
Subtracting [tex]x[/tex] and adding [tex]5[/tex] on both sides.
We have,
[tex]5x-x=11+5[/tex]
[tex]4x=16[/tex]
Dividing 4 both sides.
[tex]x=\frac{16}{4}=4[/tex]
So the value of [tex]x[/tex] is [tex]4[/tex].
Now plugging the value of [tex]x=4[/tex],we will find the numeric value of DF and EG.
DF = [tex]5x-5 =5(4)-5=15[/tex]
EG= [tex]x+11=4+11=15[/tex]
Both are equal DF = EG.
So x=[tex]4[/tex] and the length of diagonals are equal, DF = EG = [tex]15[/tex] unit.
PLZ HELP ASAP!
a gallon of latex paint can cover 500 square feet. maria has a rectangular room whose dimensions are 14 feet by 25 feet, with 7-foot ceilings. how many gallon containers of paint does she need to buy to paint two coats on each wall?
Maria needs to purchase three gallons of paint to cover her room walls with two coats, as calculations show she needs slightly more than two gallons.
Explanation:To calculate how many gallons of paint Maria needs, first determine the total area of the walls. Each rectangular wall is 14 feet by 7 feet, with an area of 98 square feet, and each of the longer walls is 25 feet by 7 feet, with an area of 175 square feet. Thus, there are two of each, resulting in a total area of 2(98) + 2(175) = 546 square feet. Since Maria wants to apply two coats of paint, the total area to be painted doubles to 1,092 square feet. Given that one gallon covers 500 square feet, Maria needs 1,092 / 500 = 2.184 gallons. Therefore, Maria should purchase three gallons of paint to have enough for two coats, since paint is only sold by the gallon.
The area of an equilateral triangle is given by A =3^1/2/4s^2. Find the length of the side s of an equilateral triangle with an area of 12^1/2 square inches.
Answer:
The length of the side of an equilateral traingle [tex]s=2\sqrt{2}[/tex] inches
Step-by-step explanation:
Given that the area of an equilateral triangle is given by
[tex]A=3^\frac{1}{2}s^2[/tex]
It can be written as
[tex]a=\frac{\sqrt{3}}{4} s^2[/tex] Square inches (1)
To find the length of the side s os an equilateral triangle
Given that area of an equilateral triangle is [tex]12^\frac{1}{2}[/tex] square inches
It can be written as
[tex]A=12^\frac{1}{2}[/tex]
[tex]A=\sqrt{12}[/tex] square inches
It can be written as
[tex]A=12^\frac{1}{2}[/tex]
[tex]A=\sqrt{12}[/tex] square inches (2)
Now comparing equations (1) and (2) we get
[tex]\frac{\sqrt{3}}{4}s^2=\sqrt{12}[/tex]
[tex]\frac{\sqrt{3}}{4}s^2=\sqrt{4\times 3}[/tex]
Dividing by [tex]\frac{\sqrt{3}}{4}[/tex] on both sides we get
[tex]\frac{\frac{\sqrt{3}}{4}s^2}{\frac{\sqrt{3}}{4}}=\frac{2\sqrt{3}}{\frac{\sqrt{3}}{4}}[/tex]
[tex]\frac{\sqrt{3}}{4}s^2\times\frac{4}{\sqrt{3}}=2\sqrt{3}\times\frac{4}{\sqrt{3}}[/tex]
[tex]s^2=8[/tex]
[tex]s=\sqrt{8}[/tex]
Therefore [tex]s=2\sqrt{2}[/tex] inches
Therefore the length of the side of an equilateral traingle [tex]s=2\sqrt{2}[/tex] inches
is 1.15 a rational number
Answer:
No
Step-by-step explanation:
The given number is 1.15. Here, the digits after the decimal are terminating, so the given number is rational, NOT irrational. Thus, 1.15 is NOT an irrational number.
Coefficient of 5x/6?
Answer:
5
Step-by-step explanation:
The coefficient is the number that is followed by an exponent. In this expression 5 is followed by x, making it a coefficient.
Final answer:
The coefficient of 5x/6 is the numerical factor 5/6, which is the fraction representing the relationship of numbers in front of the variable 'x'.
Explanation:
The coefficient of the term 5x/6 is the numerical factor that is multiplied by the variable 'x'. In this fraction, the numerator is 5 and the denominator is 6. Therefore, the coefficient of the term is 5/6. It is important to separate the coefficient (the number in front of the variable) from the variable itself when doing mathematical operations like addition, subtraction, or algebraic simplification.
The audience thinks 30% of Brandon's jokes are funny. What fraction of Brandons jokes does the audience think are funny?
Answer: 3/10
Step-by-step explanation:
3/10 • 100 = 30%
What is the correct solution
-3(6-r)=6
-18-3r=6
-3r=24
r=-8
Answer:-3(6-r)=6
-18+3r=6
3r=6+18
3r=24
r=24/3
r=8
Step-by-step explanation:
32=27+5x solve for x
Answer:
x = 1
Explanation:
32=27+5x
Simplify both sides of the equation.32=5x+27
Flip the equation.
5x+27=32
Subtract 27 from both sides.5x+27−27=32−27
5x=5
Divide both sides by 5.5x/5 = 5/5
x = 1
Answer:
x=1
Step-by-step explanation:
1) subtract
32-27=27-27 +5x
2) 5 = 5x
3) divide by 5
4) x = 1
The point slope form of the equation of the line that passes through -5,-1 and 10,-7 is y+7= -2/5(x-10). What is the standard form of this equation
2x + 5y = -15 is the standard form of equation
Solution:
Given that,
The point slope form of the equation of the line that passes through (-5, -1) and (10, -7) is given by:
[tex]y + 7 = \frac{-2}{5}(x-10)[/tex]
We have to write the standard form of the equation
The standard form of an equation is Ax + By = C
In this kind of equation, x and y are variables and A, B, and C are integers
Let us convert the given equation into standard form
[tex]y + 7 = \frac{-2}{5}(x-10)\\\\\text{Simplify the right hand side of equation }\\\\y + 7 = \frac{-2x}{5}+\frac{20}{5}\\\\y + 7 = \frac{-2x +20}{5}\\\\5(y+7) = -2x + 20\\\\\text{Simplify the left hand side of equation }\\\\5y + 35 = -2x + 20\\\\\text{Move the variables to left side of equation and constants to right side }\\\\2x + 5y = 20 - 35\\\\2x + 5y = -15[/tex]
Thus the standard form of equation is found
please help urgent !!!!
Answer:
50
Step-by-step explanation:
Will someone please help me
Answer:
[tex]4.53 \times 10^{- 1}[/tex]
Step-by-step explanation:
We have to divide [tex]1.6 \times 10^{- 10}[/tex] by [tex]3.53 \times 10^{- 10}[/tex] and we have to write the answer in scientific notation.
Now, [tex](1.6 \times 10^{- 10}) \div (3.53 \times 10^{- 10})[/tex]
= [tex](\frac{1.6}{10^{- 10}})\div (\frac{3.53}{10^{- 10}})[/tex] {Since using the property of exponent [tex]x^{- a} = \frac{1}{x^{a} }[/tex] }
= [tex](\frac{1.6}{10^{- 10}}) \times (\frac{10^{- 10}}{3.53} )[/tex]
{Since we know the mathematical operation [tex]\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}[/tex] }
= [tex]\frac{1.6}{3.53}[/tex]
= 0.45325
= [tex]4.53 \times 10^{- 1}[/tex] (Answer) {Rounded the coefficient to two decimal places}
Write an inequality that represents the verbal expression.
All real numbers less than 74.
{x < 74; x ∈ R}
Solution:
Given verbal expression is all real numbers less than 74.
R represents the set of all real numbers.
To write the verbal expression into inequality.
Let us assume that the set of all real numbers which is less than 74 are x.
So, all real numbers less than 74 means x < 74 and
x belongs to real numbers.
Therefore, the inequality is {x < 74; x ∈ R}.
For the function f(x) = 3(x − 1)2 + 2, identify the vertex, domain, and range.
a- The vertex is (1, 2), the domain is all real numbers, and the range is y ≥ 2.
b- The vertex is (1, 2), the domain is all real numbers, and the range is y ≤ 2.
c- The vertex is (−1, 2), the domain is all real numbers, and the range is y ≥ 2.
d- The vertex is (−1, 2), the domain is all real numbers, and the range is y ≤ 2.
See picture reply for solution steps.
Final answer:
The vertex of the function f(x) = 3(x − 1)² + 2 is (1, 2), the domain is all real numbers, and the range is y ≥ 2, Option A is correct in the given options.
Explanation:
The vertex of the function f(x) = 3(x − 1)² + 2 is (1, 2), because the vertex form of a quadratic function is given by f(x) = a(x − h)² + k, where (h, k) is the vertex. In this case, a = 3, h = 1, and k = 2. The domain of the function is all real numbers, because there are no restrictions on x. The range of the function is y ≥ 2, because the minimum value of the function is 2 (occurring at the vertex) and y can be any value greater than or equal to 2.