[tex]\frac{3n-7}{6}=\frac{2n+5}{3}[/tex] Multiply 3 and 6 on both sides to get rid of the fraction (or cross multiply)
[tex]\frac{3n-7}{6}(3)=\frac{2n+5}{3} (3)[/tex]
[tex]\frac{3n-7}{6}(3)(6)=(2n+5)(6)[/tex]
3(3n - 7) = 6(2n + 5) Distribute/multiply 3 into 3n-7, and 6 into 2n+5
(3)3n - (3)7 = (6)2n + (6)5
9n - 21 = 12n + 30 Subtract 9n on both sides
-21 = 3n + 30 Subtract 30 on both sides
-51 = 3n Divide 3 on both sides
-17 = n
Answer:
n = 17/6 = 2.833
Step-by-step explanation:
Step by step solution :
Step 1 :
5
Simplify —
3
Equation at the end of step 1 :
7 5
(3n - —) - (2n + —) = 0
6 3
Step 2 :
Rewriting the whole as an Equivalent Fraction :
2.1 Adding a fraction to a whole
Rewrite the whole as a fraction using 3 as the denominator :
2n 2n • 3
2n = —— = ——————
1 3
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
2n • 3 + 5 6n + 5
—————————— = ——————
3 3
Equation at the end of step 2 :
7 (6n + 5)
(3n - —) - ———————— = 0
6 3
Step 3 :
7
Simplify —
6
Equation at the end of step 3 :
7 (6n + 5)
(3n - —) - ———————— = 0
6 3
Step 4 :
Rewriting the whole as an Equivalent Fraction :
4.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 6 as the denominator :
3n 3n • 6
3n = —— = ——————
1 6
Adding fractions that have a common denominator :
4.2 Adding up the two equivalent fractions
3n • 6 - (7) 18n - 7
———————————— = ———————
6 6
Equation at the end of step 4 :
(18n - 7) (6n + 5)
————————— - ———————— = 0
6 3
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 6
The right denominator is : 3
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
2 1 0 1
3 1 1 1
Product of all
Prime Factors 6 3 6
Least Common Multiple:
6
Calculating Multipliers :
5.2 Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = 1
Right_M = L.C.M / R_Deno = 2
Making Equivalent Fractions :
5.3 Rewrite the two fractions into equivalent fractions
Two fractions are called equivalent if they have the same numeric value.
For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.
To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.
L. Mult. • L. Num. (18n-7)
—————————————————— = ———————
L.C.M 6
R. Mult. • R. Num. (6n+5) • 2
—————————————————— = ——————————
L.C.M 6
Adding fractions that have a common denominator :
5.4 Adding up the two equivalent fractions
(18n-7) - ((6n+5) • 2) 6n - 17
—————————————————————— = ———————
6 6
Equation at the end of step 5 :
6n - 17
——————— = 0
6
Step 6 :
When a fraction equals zero :
6.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
6n-17
————— • 6 = 0 • 6
6
Now, on the left hand side, the 6 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
6n-17 = 0
Solving a Single Variable Equation :
6.2 Solve : 6n-17 = 0
Add 17 to both sides of the equation :
6n = 17
Divide both sides of the equation by 6:
n = 17/6 = 2.833
One solution was found :
n = 17/6 = 2.833
Simplify the expression 3x(x – 12x) + 3x2 – 2(x – 2)2. Which statements are true about the process and simplified product?
Simplifying the expression requires expanding the brackets, combining like terms, and applying algebraic rules including distribution. The resulting simplified form is – 35x2 + 8x – 8 after properly eliminating unnecessary terms and ensuring the solution is valid.
Explanation:To simplify the expression 3x(x – 12x) + 3x2 – 2(x – 2)2, we need to apply standard algebraic techniques such as distribution, combining like terms, and simplifying polynomial expressions.
Firstly, distribute the 3x across the parentheses: 3x×(x – 12x) becomes 3x2 – 36x2.
Then, expand the square: – 2(x – 2)2 becomes – 2(x2 – 4x + 4).
Next, we can simplify the expression by combining like terms and further distributing where necessary:
3x2 – 36x2 + 3x2 – 2x2 + 8x – 8Combine like terms:
– 35x2 + 8x – 8Eliminate terms wherever possible and check to see if the simplified expression is reasonable. We are using multiplication, distribution, and combination of like terms to simplify the algebraic expression.
This table shows the length, in inches, of several nails.
Length (in.)
1
2
1
8
3
8
5
16
5
16
5
16
1
2
5
16
3
16
1
8
Create a line plot to display this data.
To create a line plot, hover over each number on the number line. Then click and drag up to plot the data.
A construction of the line plot for the length, in inches, of several nails is shown in the image attached below.
In Mathematics and Statistics, a line plot is a type of graph that is used for the graphical representation of data set above a number line, while using crosses, dots, or any other mathematical symbol.
In this scenario and exercise, we would make use of an online graphing calculator (tool) to graphically represent the given length (in yards) of several nails on a line plot as shown in the image attached below;
Length Frequency
1/2 2
5/16 4
1/8 2
3/8 1
3/16 1
In conclusion, we can reasonably infer and logically deduce that the mode of the data set is equal to 5/16 because it has the highest frequency of 4.
Complete Question;
This table shows the length, in inches, of several nails.
Length (in) 1/2, 5/16, 1/8, 1/2, 3/8, 5/16, 5/16, 3/16, 5/16, 1/8.
Create a line plot to display this data. To create a line plot, hover over each number on the number line. Then click and drag up to plot the data.
kate has 2/3 yards of fabric to make small flags each flag requires 1/6 yards of fabric how many flags cane kate make
Answer:
THE ANSWER IS 7
Step-by-step explanation:
CAUSE UR MOM IS A TRASHIE i'm sorry i meant YO MAMA
Final answer:
Kate can make 4 small flags from 2/3 yards of fabric since each flag requires 1/6 yards of fabric.
Explanation:
Kate has 2/3 yards of fabric and each small flag requires 1/6 yards of fabric. To find out how many flags Kate can make, you divide the total amount of fabric by the amount needed for one flag:
2/3 yards \/ 1/6 yards = 4 flags.
Here's the step-by-step calculation:
First, recall that dividing by a fraction is the same as multiplying by its reciprocal. In this case, the reciprocal of 1/6 is 6/1.
So, multiply 2/3 by the reciprocal of 1/6:
2/3 × 6/1 = 12/3 = 4.
Thus, Kate can make 4 small flags from the fabric she has.
you find a triangle that has an area of 10 sq ft. the height of the triangle is 10 feet. what is the length of the base of the triangle?
Solution:
Given :
Area of triangle = 10 ft² Height of triangle = 10 ftSo, We have to find the Base of Triangle .
Area of triangle = 1/2*b×h, Where represents
B represent Base H represent HeightStep : Substitute those value in Formula;
Area of triangle = 1/2 × b × h
10 = 1/2 × b × 11
20 = 11 × b
b = 20/11
b = 1.81 ft
Therefore, Base of Triangle is 1.81 ft
Final answer:
To find the base of a triangle with an area of 10 sq ft and a height of 10 ft, use the formula 1/2 × base × height. By rearranging the formula and substituting the known values, the base is calculated to be 2 feet.
Explanation:
The question is asking to find the length of the base of a triangle when the area is 10 square feet and the height is 10 feet. The formula for the area of a triangle is 1/2 × base × height. In this case, we know the area (10 sq ft) and the height (10 ft), and we need to solve for the base.
Inserting the known values into the formula gives us:
Area = 1/2 × base × height
10 = 1/2 × base × 10
To solve for the base, we rearrange the formula:
base = 2 × Area / height
base = 2 × 10 / 10
base = 2 feet
Therefore, the length of the base of the triangle is 2 feet.
Find the area of the following polygon
Answer:
84 m^2
Step-by-step explanation:
We can break the polygon into a rectangle and a triangle
The rectangle at the bottom is 12 by 4
A = 12*4 = 48
The triangle at the top has a base of 12 and a height of (10-4) = 6
A = 1/2 (12) *6 = 36
The total is the sum of the two areas
A = 48+36 =84 m^2
What is the vertex of the parabola
Answer:
(1,-4) the vertex will always be the lowest point
Step-by-step explanation:
lowest point my dude
Answer: (1,-4)
Step-by-step explanation: The vertex is either the highest point or the lowest point on the parabola depending on whether the parabola opens upward or downward.
In this case, since the parabola opens upward, we can see that
the vertex is the lowest point on the parabola which is (1,-4).
The volume of a cube is 85.184 cubic inches. What is the length of each side of the cube?
Answer:
4.4 inches
Step-by-step explanation:
To work out the length of each side of the cube you would need to cube root of the volume as seen below:
[tex] \sqrt[3]{85.184} [/tex]
And this gives the answer 4.4 inches.
Answer:
Volume = Length * Width * Height
A cube has equal length, width, and height values.
[tex]\sqrt[3]{85.184}[/tex] is 4.4
So the length of each side is 4.4 units
Find the surface area of the regular hexagonal prism. Round your answer to the nearest hundredth.
Answer:
860.55 mm²
Step-by-step explanation:
The surface area of an hexagonal prism, also known as an octahedron, is given by the following formula (since we have the apothem):
S= 6*b*(a+h)
where b = is the side of the base, a is the apothem length, and h = the height
S = 6 * 8 * (4√3 + 11) = 48 * 17.92812 = 860.55 sq mm
Could have also have used another formula without the apothem:
S =3 * √3 * b² + 6 * b * h
S = 3 * √3 * 8² + 6 * 8 * 11 = 3√3 * 64 + 528 = 332.55 + 528 = 860.55 sq mm
An electronics company can spend no more than $4,000 on raw materials for circuit boards. The raw materials cost $10 per ounce for copper and $20 per ounce for silver.
To summarize the situation, a worker writes the inequality:
10c + 20s ≤ 4,000, where c is the number of ounces of copper material and s is the number of ounces of silver material.
Which graph's shaded region shows the possible combinations of raw materials the company can buy?
Answer:
Option B is the correct answer.
Step-by-step explanation:
answer this fast
will mark brainlist for sure
answer the question whichever u know
:)
Answer:
[tex]\large\boxed{1.\ 38\ and\ 22}\\\boxed{1'.\ 42\ and\ 30}[/tex]
Step-by-step explanation:
[tex]1.\\x,\ y-the\ numbers\ (x>y)\\\\\text{We have the system of equations:}\\\\\underline{\left\{\begin{array}{ccc}x-y=16\\x+y=60\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad2x=76\qquad\text{divide both sides by 2}\\.\qquad\boxed{x=38}\\\\\text{Put the value of x to the second equation.}\\\\38+y=60\qquad\text{subtract 38 from both sides}\\\boxed{y=22}[/tex]
[tex]1'.\\x-larger\ part\\x-12-smaller\ page\\\\x+(x-12)=72\\x+x-12=72\qquad\text{add 12 to both sides}\\2x=84\qquad\text{divide both sides by 2}\\\boxed{x=42}\\\boxed{x-12=30}[/tex]
Use the elimination method to solve the system of equations
Answer:
D- (3, 1).
Step-by-step explanation: Add the first equation so you can figure out what x equals. Then, plug the value into your next equation in order to find y. Hope this helps. :)
For this case we have the following system of equations:
[tex]2x + 4y = 10\\3x-4y = 5[/tex]
We solve by the method of elimination, then:
We add both equations:
[tex]2x + 3x = 10 + 5\\5x = 15\\x = \frac {15} {5}\\x = 3[/tex]
We find the value of y:
[tex]3 (3) -4y = 5\\9-4y = 5\\9-5 = 4y\\4 = 4y\\y = \frac {4} {4}\\y = 1[/tex]
Answer:
(3,1)
Option D
Find the length of the missing side. The triangle is not drawn to scale. Show your work. (Will give brainliest)
A^2 + b^2 = c^2
C is your hypotenuse or the longest side of the triangle; you plug in your values and solve for the missing side:
15^2 + b^2 = 17^2
225 + b^2 = 289
*-225 on both sides to get b by itself*
B^2 = 64
*to get rid of the ^2; you take the square root*
B = sqrt 64
B= 8 <— final answer
We can use the Pythagorean Theorem to solve for the missing side length (a).
Pythagorean Theorem:
a² + b² = c²
a and b are the legs (shorter sides) of the triangle and c is the hypotenuse (the longer side of the triangle).
1. Substitute in the known values.
a = ?
b = 15
c = 17
a² + 15² = 17²
2. Solve for a.
a² + 15² = 17²
a² + 225 = 289
a² + 225 - 225 = 289 - 225
a² = 64
√a² = √64
a = 8
Hope this helps!
An engineer estimated the weight of a steel beam to be 600 pounds. The actual weight of the beam was 639 pounds. Find the absolute error and the percent error of the engineer's estimate. If necessary, round your answers to the nearest tenth.
Answer:
Absolute error = 39
Percent Error = 6.10%
Step-by-step explanation:
Actual value = 639 pounds
Observed Value = 600 pounds
The formula to find absolute error is:
Absolute Error = Actual value - Observed Value
= 639 - 600
= 39
The formula to find Percent error is:
Percent Error = (Actual value - Observed Value / Actual value)*100
= (639 - 600/639)*100
= 6.10%
Answer:
Absolute error = 39 pounds
Percent error = 6.10%
Step-by-step explanation:
We know that the estimated weight was 600 pounds while the actual weight of the beam was 639 pounds.
So we will find their difference to get the absolute error.
Absolute error = 639 - 600 = 39 pounds
We will use the following formula to find the percent error.
Percent error = (Estimated value - actual value / actual value) * 100
Percent error = 639 - 600 / 600 * 100 = 6.10%
suppose that F(x)=x^3 and G(x)=-2x^3
Answer:
A
Step-by-step explanation:
Given a function f(x) = x^2, we can say:
g(x) = -(x^2) is the reflection of f(x) in the x-axish(x) = ax^2 is a vertical stretch if a > 1 and a vertical compression if 0 < a < 1The negative sign in front says that G(x) is flipped over the x-axis with respect to F(x). Also, the 2 in front tells us that it is a vertical stretch of the function F(x), since a > 1.
Hence, answer choice A is right.
Answer:
it is answer A
Step-by-step explanation:
Ap*x
Find the lateral area and surface area of cone
Answer:
[tex]\large\boxed{L.A.=168\pi\ in^2}\\\boxed{S.A.=232\pi\ in^2}[/tex]
Step-by-step explanation:
The formula of a lateral area of a cone:
[tex]L.A.=\pi rl[/tex]
r - radius
l - slant height
The formula of a surface area of a cone:
[tex]S.A.=\pi r^2+\pi rl[/tex]
We have r= 8in and l = 21in. Substitute:
[tex]L.A.=\pi(8)(21)=168\pi\ in^2[/tex]
[tex]S.A.=\pi(8^2)+168\pi=232\pi\ in^2[/tex]
A jacket is on sale for 70% of the original price. If the discount saves $45, what was the original price of the jacket? What is the sale price?
100 - 70% = 30
0.30 × p (p=45)
0.30 × 45 = 13.5
the sale price is $13.50
Which of the following is an outlier in the set of data below? I think it’s 12 but I’m not so sure.
I think the answer might be 2
because
in the data given above all the numbers are between 12-19 they are all bigger than 10
and then there's 2 which is very far from 12 or any other numbers there and it is also less than 10
which makes more sense for it to be an outlier.
Hope this helps
Need help with b and c
Answer:
Step-by-step explanation:
the formula is:
[tex]a_n = \frac{n+1}{n+2}[/tex]
[tex]a_100 = \frac{101}{103}[\tex]
Answer:
see explanation
Step-by-step explanation:
We note that for each term, the numerator increases by 1 and the denominator increases by 1 from the previous term, that is
term 1 = [tex]\frac{1+1}{1+2}[/tex] = [tex]\frac{2}{3}[/tex]
term 2 = [tex]\frac{2+1}{2+2}[/tex] = [tex]\frac{3}{4}[/tex]
term 3 = [tex]\frac{3+1}{3+2}[/tex] = [tex]\frac{4}{5}[/tex]
-----------------------------------------------------------------------------
term 100 = [tex]\frac{100+1}{100+2}[/tex] = [tex]\frac{101}{102}[/tex]
If we let n be the term value, then the n th term is
[tex]a_{n}[/tex] = [tex]\frac{n+1}{n+2}[/tex]
Match the description to the best example so that all terms have a matching example.
1. A set of decimal fractions
2. A set of whole numbers
3. A set of integers
4. A set of natural numbers
5. A set of rational numbers
here are the options
{3,4,5}
{¼,½, ¾ }
{0.1, 0.2, 0.3}
{0,1,2,3 }
{-2, -1, 0, +1}
Answer: 1. A- (0.1 0.2 0.3)
2.a-(3,4,5)
3.A-(-2,-1,0,+1)
4.a-(0123)
5.a-( 1/4 1/2 3/4
Step-by-step explanation:
I'm sorry you had to wait a whole year to get your answer :)
The exercise involves matching the terms decimal fractions, whole numbers, integers, natural numbers, and rational numbers to their respective sets of numbers. The correct matches are: decimal fractions {0.1, 0.2, 0.3}, whole numbers {0,1,2,3}, integers {-2, -1, 0, +1}, natural numbers {3,4,5}, and rational numbers {1/4,1/2, 3/4}.
Explanation:The goal here is to
match
the given
description
or term to the given sets of numbers according to their properties. Let's start.
A set of decimal fractions would be {0.1, 0.2, 0.3} as these are fractions written in decimal format. A set of whole numbers would be {0,1,2,3}. Whole numbers include all natural numbers and zero. A set of integers would be {-2, -1, 0, +1}. Integers are numbers that do not have fractional or decimal parts and they include both positive and negative numbers, and the number zero. A set of natural numbers would be {3,4,5} as these are numbers naturally counted starting from 1. Finally, a set of rational numbers would be {1/4,1/2, 3/4}. Rational numbers are numbers that can be expressed as fractions or ratios.So, we have successfully made a
matching
for each description.
Learn more about matching here:https://brainly.com/question/36757679
#SPJ2
Type the correct answer in the box. Round your answer to the nearest hundredth.
Scarlett is trying to find the height of a dam. She stands 90 meters away from the dam and records the angle of elevation to the top of the dam to be 26º.
Scarlett's height is 1.65 meters, so the height of the dam is meters.
Answer:
top question is not correct
Step-by-step explanation:
Answer:
what
Step-by-step explanation:
___ cosb =1/2 sin(a+b)+sin(a-b)?
Answer:
That would be sina.
Step-by-step explanation:
sin(a+b) = sinacosb + cosasinb
sin(a-b) = sinacosb - cosasinb
Adding we get sin(a+b) + sin(a-b) = 2sinaccosb
so sinacosb = 1/2sin(a+b) + sin(a-b)
Answer:
sina
Step-by-step explanation:
We have
sin(a+b) = sina cosb + cosa sinb ---------------------eqn 1
sin(a-b) = sina cosb - cosa sinb ---------------------eqn 2
eqn 1 + eqn 2
sin(a+b) + sin(a-b) = sina cosb + cosa sinb + sina cosb - cosa sinb
sin(a+b) + sin(a-b) = 2sina cosb
[tex]sina\times cosb =\frac{1}{2}(sin(a+b) + sin(a-b))[/tex]
So answer is sina
125.663 in terms of pi
Just divide by pi, so it would be about 39.999(Pi)
Identify the following as exponential or linear and growth or decay
This would be linear growth because the y values are increasing, but not at an exponential rate.
What is the total perimeter of this figure? Express your answer in feet.
Answer:
i need to see the figure
Step-by-step explanation:
Answer:
i cant get the figure to go thru
Step-by-step explanation:
What is the sine cosine and tangent of 120 degrees
The sin of 120 is the square root of 3 over 2.
The cos of 120 is -1/2
The tan of 120 is negative square root of 3
Which statement about these rectangles is true ?
the answer for this question is the dilation is reduction
The statement which is true about these rectangles is:
The dilation is an enlargement.
Step-by-step explanation:Dilation Transformation--
It is the translation which changes the size of the original figure.The shape of the figure is conserved.Also, in dilation either the size increases (i.e. the figure enlarges) or it decreases( i.e. the figure reduces).Also, in a polygon if there is a dilation then there is a scalar multiplication in each of the sides of the polygon.If the scalar multiple is greater than 1 then there is a enlargement.and if the scalar multiple is less than 1 but greater than 0 then there is a reduction.Here we see that each of the sides of the original figure is multiplied by "1.5" to obtain a larger rectangle.
This means that the dilation is a enlargement.
( since the scalar is strictly greater than one )
The function y=3.75 + 1.5(x-1) can be used to determine cost in dollars for a taxi ride of x miles. What is the rate of change of the cost in dollars with respect to the number of miles?
Answer:
1.5 dollars/miles
Step-by-step explanation:
Given function [tex]y=3.75 + 1.5(x-1)[/tex] can be used to determine cost in dollars for a taxi ride of x miles.
Now we need to find about what is the rate of change of the cost in dollars with respect to the number of miles.
First we need to rewrite [tex]y=3.75 + 1.5(x-1)[/tex] in y=mx+b form
[tex]y=3.75 + 1.5(x-1)[/tex]
[tex]y=3.75 + 1.5x-1.5[/tex]
[tex]y=2.25 + 1.5x[/tex]
[tex]y=1.5x + 2.25[/tex]
comparing with y=mx+b, we get m=1.5
Hence rate of change of the cost in dollars with respect to the number of miles is 1.5.
Find the limit of the function by using direct substitution. limit as x approaches zero of quantity x squared minus two.
Answer:
[tex]\lim_{x \to 0}\ x^2 -2 = -2[/tex]
Step-by-step explanation:
We have the following limit
[tex]\lim_{x \to 0}\ x^2 -2[/tex]
To solve this limit using direct substitution to substitute the value that tends x into f(x) and simplify.
In this case x tends to zero, then we substitute x = 0 in the function and simplify
[tex]\lim_{x \to 0}\ x^2 -2= (0)^2 -2= -2[/tex]
Therefore
[tex]\lim_{x \to 0}\ x^2 -2 = -2[/tex]
When x approaches 0 then f(x) it tends to -2
(17 points)
Determine if line AB is tangent to the circle
1. If AB is tangent to the circle, then
[tex]18^2=(2\cdot7.2)^2+10.8^2[/tex]
We have
[tex]18^2=324[/tex]
[tex](2\cdot7.2)^2+10.8^2=324[/tex]
so AB is indeed tangent to the circle.
2. The unlabeled leg is another radius of the circle so it has length 8. Then if AB is tangent to the circle,
[tex](10+8)^2=8^2+15^2[/tex]
but we have
[tex](10+8)^2=324[/tex]
[tex]8^2+15^2=289[/tex]
so that cannot be a right triangle and AB is not tangent to the circle.
Answer #6 and tell the steps of how u did it
Answer:
3131x+1
Step-by-step explanation:
Make equation simple
5x times 5x times 5x times 5x times 5x +x+1
Solve
5 times 5 times 5 times 5 times 5 = 3125
x times x times x times x times x times x = 5x
3125+5x=3130x
Now you might be thinking you cant add x but here your can because it is just broken apart
now add x+1
3131x+1