THe fraction is:
X
----------
2X + 5
Decreases the numerator and denominator by 1, the fraction becomes 3/8.
So now the fraction looks like this:
X-1 3
--------- = -----------
2x +5-1 8
Cross multiplies:
8(x-1) = 3 ( 2x +5 -1)
8x - 8 = 3( 2x + 4)
8x - 8 = 6x + 12 <--- distributive right side
8x - 8 - 6x - 12 = 0 <--- everybody moves left,changing signs, to keep leading coefficient of x term positive
2x - 20 = 0 <-- combines like terms
2x = 20 <--- solves for x
x=10
So the fraction 10/25.
(10-1)/(25-1) = 9/24 = 3/8
The original equivalent value of the fraction is A = 19/43
What is a Fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
Given data ,
Let's start by assigning variables to the numerator and denominator of the original fraction. Let x be the numerator and y be the denominator.
Then we can write:
y = 2x + 5 (since the denominator is five more than twice the numerator)
If both the numerator and denominator are decreased by 7, the new fraction can be written as (x-7)/(y-7), and we know that this is equal to 1/3:
(x-7)/(y-7) = 1/3
To solve for x and y, we can start by cross-multiplying to get:
3(x-7) = y-7
Next, we can substitute the expression for y that we derived earlier:
3(x-7) = 2x + 5 - 7
Simplifying this equation gives:
3x - 21 = 2x - 2
Bringing all the x terms to one side and all the constant terms to the other gives:
x = 19
Now that we know the value of x, we can substitute it back into our expression for y:
y = 2x + 5 = 43
Hence , the original fraction is x/y = 19/43
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The center of a circle lies on the line y = 3x + 1 and is tangent to the x-axis at (−2,0) .
What is the equation of the circle in standard form?
The equation of the circle in standard form is: (x + 2)² + (y - 1)² = 1
What is the equation of the circle?
The general form of the equation of a circle is:
(x - h)² + (y - k)² = r²
Where;
(h, K) is the coordinate of the center of the circle.
r is radius.
To find the equation of the circle in standard form, we need to determine the center and radius of the circle.
Since the center of the circle lies on the line y = 3x + 1 and is tangent to the x-axis at (-2,0), we can determine that the center of the circle is (-2,1) and the radius is 1.
Therefore, the equation of the circle in standard form is:
(x + 2)² + (y - 1)² = 1
How many square feet of outdoor carpet will
we need for this hole?
11 ft
13 ft
2 ft
3 ft
Answer:
39 square feet
Step-by-step explanation:
The outdoor carpet consists of two rectangles.
The area of the rectangle is
[tex]A=\text{Length}\times \text{Width}[/tex]
1st rectangle:
Length = 11 ft
Width = 3 ft
Area [tex]=11\cdot 3=33 \ ft^2[/tex]
2nd rectangle:
Length = 3 ft
Width = 2 ft
Area [tex]=3\cdot 2=6 \ ft^2[/tex]
Total area:
[tex]33+6=39\ ft^2[/tex]
100 POINTS and BRAINLIEST to get both of these answer the third question on my profile :)
Answer:
1. f
2.b
3. d
4. a
5. e
6. g
7. c
Step-by-step explanation:
The parent function is [tex]y = 3 (5)^{x}[/tex].
So,
1. [tex]y = - 3 (5)^{x} + 4[/tex] ≡ f. reflected across x-axis and 4 units up
2. [tex]y = 3 (5)^{x - 4} - 4[/tex] ≡ b. 4 units down and 4 units right.
3. [tex]y = 3 (5)^{x + 4} + 4[/tex] ≡ d. 4 units up and 4 units left.
4. [tex]y = - 3 (5)^{x} - 4[/tex] ≡ a. reflected across x-axis and 4 units down.
5. [tex]y = 3 (5)^{x} - 4[/tex] ≡ e. 4 units down
6. [tex]y = 3 (5)^{x} + 4[/tex] ≡ g. 4 units up.
7. [tex]y = 3 (5)^{x - 4}[/tex] ≡ c. 4 units right. (Answer)
Leila writes 6 pages per day starting on Sunday. She wants to know how many pages she will write by the end of the day on Saturday. Write a multiplication equation to represent the problem.
Answer: 42 pages
Step-by-step explanation: 6 pages x 7 days= 42 pages
PLEASE HELP ASAP with questions 12 and 13
Answer:
12. x = 50
13. m∠M = 34°
Step-by-step explanation:
12.
Since the triangles are congruent, the sides' lengths are proportional. We can set up a ratio and solve for x.
Side JG corresponds to Side KM
Side HG corresponds to Side LM
Now, we can set up a ratio, cross multiply, and solve for x. Shown below:
[tex]\frac{35}{70}=\frac{25}{x}\\35x=70*25\\35x=1750\\x=\frac{1750}{35}\\x=50[/tex]
Thus, the value of x is 50
13.
The triangles are similar, so sides are proportional and angles are not related in the same way. Angles are same for both.
We want the value of Angle M, that angle corresponds to Angle G of the left triangle.
It is given that Angle G = 34, so Angle M would be the same degree measure as well.
Hence,
m∠M = 34°
Please help I gave extra points please it’s super simple to some of you I just don’t know how to do it :(
Answer:
1. The required slope m, for the context is[tex]m = \frac{-25}{3}[/tex]
2. The y-intercept in the context is [tex]P_{2}(d) = y = 100[/tex]
3. The x-intercept of the linear model is [tex]d = x = 12[/tex]
Step-by-step explanation:
Given:
[tex]P_{2}(d) = \frac{-25}{3}\times d + 100[/tex]
Where,
[tex]P_{2}[/tex] is the number of phones.
d is the number of days he has worked that week.
This is a linear model type equation.
Can be represented in the slope intercept form which is equal to
[tex]y = mx + c[/tex]
Where,
m = Slope of the line.
c = y-intercept.
Now if we compare the given model by slope intercept formula we get
[tex]m = \frac{-25}{3}\\\\c = 100[/tex]
So ,the slope in the context of the problem is [tex]m = \frac{-25}{3}[/tex].
and the y intercept in the context of the problem [tex]P_{2}(d) = c = y = 100[/tex]
For finding x-intercept put y = 0
Here,[tex]P_{2}(d) = 0[/tex]
[tex]\therefore 0 = \frac{-25}{3}\times d + 100\\ \therefore \frac{25}{3}\times d = 100\\\therefore d=\frac{300}{25}\\\therefore d=12[/tex]
So, the x intercept of the linear model is [tex]d = x = 12[/tex]
write the first five terms of the sequence using the recursive formula shown:
a1=6 an=4/3a n-1
The first five terms of the sequence are:
6 , 8 , [tex]\frac{32}{3}[/tex] , [tex]\frac{128}{9}[/tex] , [tex]\frac{512}{27}[/tex]
Step-by-step explanation:
The recursive formula of the sequence is
[tex]a_{1}=6[/tex] and [tex]a_{n}=\frac{4}{3}*a_{n-1}[/tex]
To find the first five terms do that:
[tex]a_{1}=6[/tex][tex]a_{2}=\frac{4}{3}*a_{1}[/tex][tex]a_{3}=\frac{4}{3}*a_{2}[/tex][tex]a_{4}=\frac{4}{3}*a_{3}[/tex][tex]a_{5}=\frac{4}{3}*a_{4}[/tex]∵ [tex]a_{1}=6[/tex]
∴ [tex]a_{2}=\frac{4}{3}*6[/tex]
∴ [tex]a_{2}=8[/tex]
∵ [tex]a_{2}=8[/tex]
∴ [tex]a_{3}=\frac{4}{3}*8[/tex]
∴ [tex]a_{3}=\frac{32}{3}[/tex]
∵ [tex]a_{3}=\frac{32}{3}[/tex]
∴ [tex]a_{4}=\frac{4}{3}*\frac{32}{3}[/tex]
∴ [tex]a_{4}=\frac{128}{9}[/tex]
∵ [tex]a_{4}=\frac{128}{9}[/tex]
∴ [tex]a_{5}=\frac{4}{3}*\frac{128}{9}[/tex]
∴ [tex]a_{5}=\frac{512}{27}[/tex]
The first five terms of the sequence are:
6 , 8 , [tex]\frac{32}{3}[/tex] , [tex]\frac{128}{9}[/tex] , [tex]\frac{512}{27}[/tex]
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At a local fitness center, members pay a $12 membership fee and $2 for each aerobics class. Nonmembers pay $4 for each aerobics class. For what number of aerobics classes will the cost for members and nonmembers be the same?
Final answer:
The costs for members and nonmembers of a local fitness center will be the same after attending 6 aerobics classes. Members have an initial $12 membership fee plus $2 per class, while nonmembers pay $4 per class.
Explanation:
To find the number of aerobics classes for which the cost for members and nonmembers will be the same, we need to set up an equation that compares the two cost structures. For members, the cost is a $12 membership fee plus $2 per class, which we can express as Cm = 12 + 2n, where Cm is the cost for members and n is the number of classes. For nonmembers, the cost is $4 per class, so we can express that as Cnm = 4n, where Cnm is the cost for nonmembers.To find the number of classes where costs are the same, we set Cm equal to Cnm:
Subtract 2n from both sides: 12 = 2n
Divide both sides by 2: n = 6
Therefore, the costs for members and nonmembers will be the same when they attend 6 aerobics classes.
Using data for the population in the state of Alabama calculate the percent change in population growth to the nearest thousandth place from 2004 to 2005
Answer:Can You please like this I want to rank up
Step-by-step explanation:
Press the Heart
P.S. Please
expand (3x+7)(3x-7) =
Answer:
[tex]9 {x}^{2} - 49[/tex]
Step-by-step explanation:
Do FOIL, first outside inside last
3x × 3x = 9x^2
3x × -7 = -21x
7 × 3x = 21x
7 × -7 = -49
[tex]9 {x}^{2} - 21x + 21x - 49 \: midde \: cancels \: each \: other \: out[/tex]
So it would just be 9x^2 - 49
(3x + 7)(3x - 7) =
= 9x² + 21x - 21x - 49
= 9x² - 49
Find the standard form of the equation of the parabola with a focus at (0, -3) and a directrix at y = 3. (5 points)
y^2 = -12x
y^2 = -3x
y = negative x^2 divided by 12
y = negative x^2 divided by 3
Answer:
From given option , the equation of parabola is y = negative x² divided by 12
Step-by-step explanation:
Given as for parabola :
The focus is at (0 , - 3)
The directrix equation is y = 3
Now, equation of parabola parallel to y-axis is
( x - h )² = 4 p ( y - k )
where focus is ( h , k+p ) and directrix equation is y = k - p
So, from equation
h = 0 and k + p = - 3
And y = k - p i.e k - p = 3
Now solving ( k + p ) + ( k - p ) = - 3 + 3
or, 2 k = 0 ∴ k = 0
Put the value of k , k + p = - 3
So, 0 + p = - 3 ∴ p = - 3
Now equation of parabola with h = 0 , k = 0 , p = - 3
( x - h )² = 4 p ( y - k )
I.e ( x - 0 )² = 4 × ( - 3 ) ( y - 0 )
Or, x² = - 12 y is the equation of parabola
Hence From given option , the equation of parabola is y = negative x² divided by 12 Answer
Determine whether the sequence 7, 21, 35, 49 is geometric. If so, find its common
ratio.
Answer:
a. no
b. yes, common ratio of 14
c. yes, common ratio of 2
Answer:
B
Step-by-step explanation:
Answer:
a. no
Step-by-step explanation:
The sequence is arithmetic. It has a common difference of 14.
7 + 14 = 21
21 + 14 = 35
35 + 14 = 49
A geometric series has a common ratio (multiplication). For example:
7 × 3 = 21
21 × 3 = 63
63 × 3 = 189
In a group 120 children there are teice as many boys as girls. How many girls are there?
Answer:
40 girls 80 boys
Step-by-step explanation:
80/2=40
40+80=120
Answer:
80 girls
Step-by-step explanation:
120/3 = 40.
40 x 2 = 80
Quick question what’s 2ab+3b+7b+3a•3a•b+4b-8ab•8ab+5a•5a•b-12ab?
Answer:
14b - 10ab + 34a²b - 64a²b²
Step-by-step explanation:
We have to simplify the expression
2ab + 3b + 7b + 3a × 3a × b + 4b - 8ab × 8ab + 5a × 5a × b - 12ab
= 2ab + 3b + 7b + 9a²b + 4b - 64a²b² + 25a²b - 12ab
{Since (3a × 3a × b) = 9a²b, (8ab × 8ab) = 64a²b² and (5a × 5a × b) = 25a²b}
= 2ab + 10b + 9a²b + 4b - 64a²b² + 25a²b - 12ab
= 14b - 10ab + 34a²b - 64a²b² (Answer)
what is 1 5/8 divided by 5 1/7
Answer: 91/288
Step-by-step explanation: To divide mixed numbers, first write the mixed numbers as improper fractions.
We can do this by multiplying the denominator by the whole number and then adding the numerator. Then, we put our new numerator over our old denominator.
So here, we can write 1 and 5/8 as the improper fraction 13/8 and we can write 5 and 1/7 as the improper fraction 36/7.
So here, we have 13/8 ÷ 36/7.
Dividing by a fraction is the same as multiplying by the reciprocal of that fraction.
So here, 13/8 ÷ 36/7 is the same as 13/8 × 7/36.
So now we are simply multiplying fractions and we do this by multiplying across the numerators and multiply across the denominators.
[tex]\frac{13}{8} x \frac{7}{36} = \frac{91}{288}[/tex]
So now we have 91/288 which is in lowest terms.
This means that 1 and 5/8 divided by 5 and 1/7 is 91/288.
1. Find the slope of a line passing through (56, 67) and (-12, -50)
Answer:
117/78
Step-by-step explanation:
(-50-67)/(-12-56)=-117/-78=117/78
gets brainilist!!!!!!!what is the absoulute value of -4.5 and what is the absoulute value of 1
Answer:
The absolute value of a number is its distance from zero on the number line. For example, -7 is 7 units away from zero, so its absolute value would be 7
|-4|=4
|1|=1
Step-by-step explanation:
the absolute value of - 4.5 = | - 4.5 | = + 4.5
the absolute value of 1 = | 1 | = + 1
Could someone help me please:(
Answer:
Domain: -∞ < x < +∞
Range : 2 ≤ f(x) < +∞
Step-by-step explanation:
See the graph attached to this question.
The two arrow shows the graph of a function y = f(x).
Now, the value of x varies from +∞ to -∞.
So, the domain of the function is -∞ < x < +∞
Again from the graph the range of the function i.e. values of y varies from 2 to +∞ and including 2.
Therefore, the range of the function is 2 ≤ f(x) < +∞ (Answer)
Complete each geometric sequence.
A) 1/7, ___, 9/7, 27/7, ___
B) 24, 12, 6, ___, ___
Answer:
Step-by-step explanation:
A) 1/7, 3/7, 9/7, 27/7,81/7
Explanation: actually in it we simply multiply the nominator with 3.
B) 24,12,6,3,1.5
Explanation: In this we simply half the value or we can say that divided by 2.
Determine m angle F by using the figure
Answer:
The measure of angle F is m∠F=130°
Step-by-step explanation:
step 1
Find the measure of angle E
we know that
An isosceles triangle has two equal sides and two equal interior angles
In this problem
DF=EF ----> given problem
so
Triangle DEF is an isosceles triangle
m∠D=m∠E
we have
m∠D=25°
substitute
m∠E=25°
step 2
Find the measure of angle F
we know that
The sum of the measures of the interior angles in a triangle must be equal to 180 degrees
so
m∠D+m∠E+m∠F=180°
substitute the values
25°+25°+m∠F=180°
50°+m∠F=180°
m∠F=180°-50°
m∠F=130°
if 25% of next month's rent is $174.25 what is the total next month's rent
Answer:
$697
Step-by-step explanation:
25% × 4 = 100%
174.25 × 4 = 697
Answer:
174.25
Step-by-step explanation:
174.25 × 4 = 697
697 × 0.25 = 174.25
Answer: 174.25
Write the slope intercept form of the equation of the line through the given points and slope 1,1 and slope of -3/5
Slope is already given in the question so we only need to solve for the y-intercept.
Slope intercept form: y = mx + b
m = slope
b = y-intercept
-3/5 = -0.6
1 = -0.6(1) + b
1 = -0.6 + b
1 + 0.6 = -0.6 + b + 0.6
1.6 = b
Now, write in slope-intercept form.
y = -3/5x - 1.6
______
Best of Luck,
Wolfyy :)
County fair charges 1.25 per ticket for rides. Tom bought 25 ride tickets and spent a total of $43.75 total for rides and admission. The price of admission is the same for everyone. Use y to represent total cost and x for the number of tickets.
Define variables
Write linear equation to determine the cost for rides tickets and admission
Answer:
The linear equation is 1.25x + 0.5x = y
Step-by-step explanation:
1. Let's review the data given to us for solving the question:
Price of ride ticket at country fair = US$ 1.25
Total spent by Tom for rides and admission= US$ 43.75
Number of ride tickets bought by Tom = 25
Price of admission is the same for everyone
Total cost = y
Number of tickets = x
2. Let's find out the cost of the admission:
Total cost of ride tickets + Total cost of admission = Total cost of rides tickets and admission
Replacing with real values:
1.25 * 25 + Cost of admission * 25 = 43.75
31.25 + 25 * Cost of admission = 43.75
25 * Cost of admission = 43.75 - 31.25 (Subtracting 31.25 at both sides)
25 * Cost of admission = 12.50
Cost of admission = 12.50/25 (Dividing by 25 at both sides)
Cost of admission = 0.50
3. Let's write a linear equation to determine the cost for rides tickets and admission:
Total cost of ride tickets + Total cost of admission = Total cost of rides tickets and admission
Total cost = y
Number of tickets = x
1.25x + 0.5x = y
Tom planted 1/2 of an 8-ft by 9-ft garden with vegetables. He planted tomatoes in 1/3 of the vegetable garden and corn in the rest . What is the area planted in corn
Answer:
Corn was planted in 24 sq.ft. of the vegetable garden.
Step-by-step explanation:
Length of garden = 9 ft
width of garden = 8 ft
Hence we will first find the total area of garden.
Total area of garden = length × width = [tex]8 \times 9 = 72ft^2[/tex]
He planted 1/2 of the garden with vegetables.
Hence.
Area of Vegetables garden = [tex]\frac{1}{2}\times \textrm{Total Area of Garden} = \frac{1}{2}\times 72 = 36ft^2[/tex]
He planted tomatoes in 1/3 of the vegetable garden and corn in the rest
Area in which tomatoes was planted = [tex]\frac{1}{3}\times \textrm{Area of Vegetables Garden} = \frac{1}{3}\times 36 = 12ft^2[/tex]
Hence Area in which corn were planted = Area of Vegetables garden - Area in which tomatoes was planted = [tex]36ft^2-12ft^2=24ft^2[/tex]
Hence Area of vegetable garden in which corn was planted is 24 sq.ft.
BC is parallel to DE.what is the length of CE?
Answer:
Option B [tex]2\frac{2}{3}\ units[/tex]
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
In this problem
Triangles ABC and ADE are similar by AA Similarity Theorem
so
[tex]\frac{AB}{AD}=\frac{AC}{AE}[/tex]
substitute the given values
[tex]\frac{3}{3+2}=\frac{4}{AE}[/tex]
Solve for AE
[tex]\frac{3}{5}=\frac{4}{AE}[/tex]
[tex]AE=5(4)/3[/tex]
[tex]AE=\frac{20}{3}\ units[/tex]
Find the length of CE
[tex]AE=AC+CE\\CE=AE-AC[/tex]
substitute the values
[tex]CE=\frac{20}{3}-4[/tex]
[tex]CE=\frac{8}{3}\ units[/tex]
Convert to mixed number
[tex]\frac{8}{3}\ units=\frac{6}{3}+\frac{2}{3}=2\frac{2}{3}\ units[/tex]
Help!! Please!!
Basketball star Mumford (a six foot senior forward) places a mirror on the ground x ft. from the base of a basketball goal. He walks backward four feet until he can see the top of the goal, which he knows is 10 feet tall. Determine the how far the mirror is from the basketball goal. Justify your answer.
Step-by-step explanation:
x=10+4=14
14+14=28
the answer is 28 fts
Answer:
The answer is 6.67 feet, approximately.Step-by-step explanation:
The image attached shows the context that the problems refered.
Notice that two acute angles from those triangles are congruent, just because their complement are also congruent.
[tex]\angle AOB \cong \angle COD[/tex]
[tex]\angle AOB= \angle COD=90\° - a[/tex]
Remember that the tangent function is defined as
[tex]tan(\theta)=\frac{Opposite \ Leg}{Adjacent \ Leg}[/tex]
Replacing each equiavlence, we have
[tex]tan(90-a)=\frac{6}{4}=\frac{10}{x}[/tex]
Then, we solve for [tex]x[/tex]
[tex]\frac{6}{4} =\frac{10}{x}\\ x=\frac{40}{6}\\ x \approx 6.67 ft[/tex]
Thereofre, the answer is 6.67 feet, approximately.
a group of adults plus a child attend a movie tickets cost $9 for adults and $6 for children the total for the movie is $78 write an equation to find the number of adults in the group
You are given a circle of radius 12. What is the segment area of an arc that is 90 degrees?
Answer:
The segment area [tex]= 113.09\ unit^2[/tex]
Step-by-step explanation:
Area of the segment = [tex]\frac{(\theta)}{360} \times \pi r^2[/tex],where [tex]\theta[/tex] is the angle.
We can also say that [tex]90\ degrees[/tex] is covered with one segment and we have total [tex]4[/tex] segments (quadrants),so area of the circle divided by [tex]4[/tex] will give us the segement area of the arc.
So area [tex]\frac{\pi r^2 }{4} =\frac{\pi(12)^2}{4} = 113.09\ units^2[/tex]
So the area of the segment [tex]= 113.09 \ units^2[/tex]
The quotient of 5 times a number and 2
Answer:
Let x be the number
5 times a number:
5x
The quotient of the number and 2.
5x / 2
Final answer:
The 'quotient of 5 times a number and 2' can be expressed as '5x/2', where 'x' is the unknown number. Important mathematical concepts, such as order of operations, exponents, and percentages, influence how we calculate and understand such expressions.
Explanation:
The statement 'The quotient of 5 times a number and 2' represents a mathematical expression, where you are asked to first multiply a number by 5 and then divide that product by 2. To elucidate, let us assume the unknown number is represented by 'x'. So we multiply 5 by 'x' to get '5x', and then we divide that by 2 to get the final expression, which is '5x/2'. In this case, we are dealing with division, which is opposite to multiplication, and it's important to follow the correct order of operations when solving mathematical problems.
what is w in 10+15(w-2)=40
Answer:
w=4
Step-by-step explanation:
10+15(w-2)=40
distribute the 15
10+15w-30=40
combine like terms
-20 + 15w = 40
15w=60
w=4