[tex] \frac{2}{3} x + 5 = 1[/tex]
[tex] \frac{2}{3} x = 1 - 5[/tex]
[tex] \frac{2}{3} x = ( - 4)[/tex]
[tex]x = ( - 4) \div \frac{2}{3} [/tex]
[tex]x = ( - 4) \times \frac{3}{2} [/tex]
[tex]x = \frac{ - 12}{ \: \: \: 2} [/tex]
[tex]x = ( - 6)[/tex]
[tex]∴ \frac{2}{3} \times ( - 6) + 5 = 1[/tex]
Find the range of 4/3-t
Answer:
4/3 is 1.3333333333,so the range of it is that
shondra wants to cut a cloth into 10 squares strips. how wide would each strip get?
To find the width of each strip, divide the total width of the cloth by the number of strips required.
Explanation:To find the width of each strip, we need to divide the total width of the cloth by the number of strips required. Let's assume the width of the cloth is W. So, each strip would get a width of W/10.
Is 9/10 larger than 13/14
Answer:
13/14 is greater
Step-by-step explanation:
Find the lcm for both:
9 x 7 = 63
10 x 7 70
13 x 5 = 65
14 x 5 70
so therefore 13/14 is greater since it has a greater value when finding the lcm
the student council orders 12 sandwhiches for the school dance. each sandwich is 6 feet long cut into sections that are 4 inches long. how many small sandwiches will they have?
1ft = 12inch
The school council will have 216 small sandwiches.
Step-by-step explanation:
Sandwiches ordered = 12
Length of one sandwich = 6 feet
1 foot = 12 inch
6 feet = 12*6 = 72 inches
Length of one sandwich in inches = 72 inches
As one small sandwich is 4 inches,
Number of small sandwiches in one sandwich = [tex]\frac{72}{4}=18[/tex]
One sandwich = 18 small sandwiches
12 sandwiches = 18*12 = 216 small sandwiches
The school council will have 216 small sandwiches.
Keywords: multiplication, division
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A chicken farm produces ideally 600,000 eggs per day. But this total can vary by as many as 5,000 eggs. What is the maximum and minimum expected production at the farm?
Answer:
max.600,000
min.595,000
Step-by-step explanation:
Three numbers form a geometric progression. If the second term is increased by 2, then the progression will become arithmetic and if, after this, the last term is increased by 9, then the progression will again become geometric. Find these three numbers.
The three numbers forming the geometric progression are [tex]4/7, 32/7,[/tex] and [tex]81/7.[/tex] The second term is increased by [tex]2[/tex], then the progression will become arithmetic and if, after this, the last term is increased by [tex]9[/tex], then the progression will again become geometric.
Let's denote the three numbers forming the geometric progression as [tex]a[/tex], [tex]ar[/tex], and [tex]ar^2}[/tex], where a is the first term and [tex]r[/tex] is the common ratio.
If the second term is increased by [tex]2[/tex], then the progression becomes arithmetic. This means:
[tex]ar+2=2ar-a[/tex]
[tex]2=ar-a \\2=a(r-1)[/tex]
If after this, the last term is increased by [tex]9[/tex], then the progression becomes geometric again. This means: [tex]ar^2} +9=(ar+2)r[/tex]
[tex]ar^2} +9=ar^2} +2r \\9=2r \\r=9/2[/tex]
Now, we have found the value of [tex]r[/tex], which is the common ratio. Let's substitute [tex]r=29[/tex] into the equation [tex]2=a(r-1)[/tex] to find the value of a:
[tex]2=a((9/2)-1) \\2=a(9-2/2) \\2=a(7/2) \\a=4/7[/tex]
So, the first term a is [tex]4/7.[/tex]
Now, let's find the second term by substituting [tex]a=4/7[/tex] into the equation [tex]ar+2=2ar-a:\\4/7.9/2+2=2.4/7.9/2-4/7 \\18/7+2=36/7-4/7 \\32/7=32/7[/tex]
This equation is satisfied, so the second term is [tex]32/7.[/tex]
Finally, let's find the third term by multiplying the first term by the common ratio:
[tex]4/7.(9/2)2=7.4/4.1/8=81/7[/tex]
So, the three numbers forming the geometric progression are [tex]4/7, 32/7,[/tex]and [tex]81/7.[/tex]
We used the properties of geometric and arithmetic progressions to set up and solve equations to find the three numbers. First, we found the common ratio r by solving the equations derived from the given conditions. Then, we found the first term a and used it to find the second term. Finally, we found the third term by multiplying the first term by the common ratio squared.
COMPLETE QUESTION:
Three numbers form a geometric progression. If the second term is increased by [tex]2[/tex], then the progression will become arithmetic and if, after this, the last term is increased by [tex]9[/tex], then the progression will again become geometric. Find these three numbers.
The three numbers are 4, 18, and 81.
Let the three numbers forming the geometric progression be [tex]\( a, ar, \)[/tex] and [tex]\( ar^2 \)[/tex], where [tex]\( r \)[/tex] is the common ratio.
Given that increasing the second term by 2 makes it an arithmetic progression, we have:
[tex]\[ar + 2 = a + 2d\][/tex]
where d is the common difference in the arithmetic progression.
Similarly, after increasing the last term by 9, the progression becomes geometric again, so:
[tex]\[ar^2 + 9 = (ar + 2)r\][/tex]
From the first equation, [tex]\( d = (ar - a)/2 \)[/tex], and substituting this into the second equation, we get:
[tex]\[ar^2 + 9 = (ar + 2)r\][/tex]
[tex]\[ar^2 + 9 = ar^2 + 2r\][/tex]
[tex]\[9 = 2r\][/tex]
[tex]\[r = \frac{9}{2}\][/tex]
Substituting [tex]\( r = \frac{9}{2} \)[/tex] into the first equation, we find [tex]\( d = \frac{a}{2} \)[/tex].
Thus, [tex]\( a + 2 = a + \frac{a}{2} \)[/tex], and solving for [tex]\( a \)[/tex], we find [tex]\( a = 4 \)[/tex].
Then, using [tex]\( r = \frac{9}{2} \)[/tex], we find [tex]\( ar = 18 \) and \( ar^2 = 81 \)[/tex].
Therefore, the three numbers are 4, 18, and 81.
One week a company filled 546 boxes with widgets each box held 38 widgets how many widgets did the company pack in boxes that week
Answer:
20748
Step-by-step explanation:
546 times 38
NEED ASAP!!!! BRANELIEST IF ANSWERED CORRECTLY WITH SHOWN WORK.
Carolyn is searching online for tickets to a concert. Two weeks ago, the cost was $30. Now the cost is $39. What is the percent increase? What would be the percent increase if the ticket agent charges an additional $4.50 fee with the new ticket price?
Answer: at new cost increase is 30%
after additional $4.50 fee increase would be 45%
Step-by-step explanation:
use equation
30:100=39:x
30x=3900
x=3900/30
x=130
130-100=30%
39+4.50=43.5
30:100=43.5:x
30x=4350
x=4350/30
x=145
145-100=45%
The increase percent will be 30%
And, The percent increase if the ticket agent charges an additional $4.50 fee with the new ticket price is 45%.
What is mean by Percentage?
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
To Calculate the percent of a number , divide the number by whole number and multiply by 100.
Given that;
The old cost of the tickets = $30
And, New cost of the ticket = $39
Now,
The increase percent is calculate as;
Increase percent = (39 - 30) / 30 x 100
= 9/30 x 100
= 30%
And, When the ticket agent charges an additional $4.50 fee with the new ticket price.
Then, The new cost of the tickets = $39 + $4.50
= $43.50
Thus, The percent increase if the ticket agent charges an additional $4.50 fee with the new ticket price is calculated as;
Increase percent = (43.50 - 30) / 30 x 100
= 13.50/30 x 100
= 45%
Therefore, The increase percent will be 30%.
And, The percent increase if the ticket agent charges an additional $4.50 fee with the new ticket price is 45%.
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Find the equation of the line through the point (6, 9) that has a slope of 4?
A) y = 6x + 4
B) y = 3x + 121
C) y = 4x + 15
D) y = 4x - 15
Answer:
D Y=4x-15
Step-by-step explanation:y=Mx+b
Answe 25 and 26 easy
Answer:
25. rational
26. irrational
Step-by-step explanation:
A rational number is a number that can be written as a fraction. It may have decimals that end or repeating decimals.
An irrational number cannot be written as a fraction. It's decimals continue on and do not repeat.
25.
When you multiply two rational numbers, the product is rational. The square root of 16 is 4, which is rational because it is a whole number. 4/7 is written as a fraction so it is rational.
26.
The square root of 2 is an irrational number because its decimals go on and do not repeat. 7 is a whole number so it is rational. Subtracting a irrational number from a rational number gives an irrational number.
what is the value of sin 0 given that (-6, -8) is a point on the terminal side of 0
4/5
3/5
-4/5
-3/5
Answer: I believe it’s -4/5
Step-by-step explanation:
W divided by -1.3 equals -6.2. What does w equal? Hurry 88 pts
Answer:
[tex]w=8.06[/tex]
Step-by-step explanation:
Given statement:
[tex]w[/tex] divided by -1.3 equals -6.2
The above statement can be written mathematically as:
[tex]\frac{w}{-1.3}=-6.2[/tex]
We need to solve for [tex]w[/tex].
Multiplying both sides by -1.3 to remove fraction and isolate [tex]w[/tex] on one side.
[tex]-1.3\times \frac{w}{-1.3}=(-6.2)\times (-1.3)[/tex]
∴ [tex]w=8.06[/tex] [Product of two negatives is a positive]
Answer:
w = 8.06
Step-by-step explanation:
The point (-4,0) is rotated 180 degrees counterclockwise using center (0,0). what are the coordinates of the image?
Answer:
The new coordinate of the image will be (4, 0) when the point (-4,0) is rotated 180 degrees counterclockwise using center (0,0).
i.e. [(-4,0)→(4,0)]
Step-by-step explanation:
The rule for rotation a point 180° counterclockwise about the origin states that when a point (x, y) is rotated 180° counterclockwise about the origin, the new position of the coordinates of point P(x, y) becomes (-x, -y).
Hence,
Rotate (x, y) counterclockwise 180° about the origin: [(x,y)→(-x,-y)]So, when the given point (-4,0) is rotated 180 degrees counterclockwise using center (0,0), the new coordinates of the image will be:
Rotate (-4, 0) counterclockwise 180° about the origin: [(-4,0)→(4,0)]Therefore, the new coordinate of the image will be (4, 0) when the point (-4,0) is rotated 180 degrees counterclockwise using center (0,0).
i.e. [(-4,0)→(4,0)]
Keywords: rotation, origin, image
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Wanni cycled 6 km from her house to the school at a uniform speed, v km/h. If she increased her speed
by 2 km/h, she would arrive at the school 4 minutes earlier. Form a quadratic equation in term of v.
Final answer:
To form the quadratic equation, we consider the original time to cover 6 km at speed v km/h and the new time at speed (v+2) km/h, then equate the difference in time to 4 minutes. Solving for v using a common denominator and simplifying, we obtain the quadratic equation 15v^2 + 30v - 90 = 0.
Explanation:
To form a quadratic equation from the given scenario, we’ll first define the relationship between distance, speed, and time. The time taken to travel 6 km at the original speed v km/h is distance divided by speed, which is 6/v hours. If Wanni increased her speed by 2 km/h, her new speed would be v + 2 km/h, and the new time taken would be 6/(v+2) hours.
We are told that by increasing her speed, Wanni arrives 4 minutes earlier. Since 1 hour is 60 minutes, 4 minutes is 4/60 or 1/15 hours. We can now set up an equation relating the difference between the two times to 1/15 hours:
6/v - 6/(v+2) = 1/15
To solve for v, we first find a common denominator for the fractions on the left side of the equation, which is v(v+2). Multiplying both sides by the common denominator, we get:
6(v+2) - 6v = v(v+2)/15
Expanding the terms and moving everything to one side of the equation, we get our quadratic equation in terms of v:
15v2 + 30v - 90 = 0
a scale factor of 1/3 is used to make a reduction of the original triangle
Answer:
8 units.Step-by-step explanation:
The complete question is
A scale factor of 1/3 is used to make a reduction, as shown in table below.
What is the base of the reduced triangle?
48921According to the given table, the original base is 24. If the given scale factor is applied, the reduced base would be
[tex]\frac{1}{3}24=8[/tex]
Remember that a scale factor is a number that multiples the figure, a scale factor can reduced or amplify a figure.
Therefore, the reduced base is 8 units.
Answer:
8 units
Step-by-step explanation:
Marcos has $24. Yaneliz has 1/6 of the amount of money Marcos has. Write an expression.
Answer:4
Step-by-step explanation: since he has 24
Yaneliz has 24 X 1/6 = 4
Answer: y = 24 x 1/6
Step-by-step explanation:
Hi, to answer this question we have to analyze the information given:
Marcos: $24
Yaneliz: 1/6 of the amount of money Marcos has
So, to write an expression we have to multiply the amount of money Marcos has (24) by 1/6.
Mathematically speaking
Y = 24 x 1/6
Where "y" is the amount of money Yaneliz has.
Solving:
24 x 1/6 = 4
Yaneliz has $4.
Feel free to ask for more if needed or if you did not understand something.
What is the mean of: 3.7,5, 9.2,4,6.1,5,2.6, 4.5.2,5?
A. 4.88
B. 4.5
C. 4
D. 6.6
The mean of 3.7,5, 9.2,4,6.1,5,2.6, 4,5.2,5 is 4.88.
Explanation:Mean is referred in mathematics to as average of the mentioned numbers. Average can be virtually imagined as a center position giving every number equal weight. Average can be calculated by diving the sum of all the numbers by count of total numbers.
For example, 2, and 4 will have average of 3. Average of 2,3,4 will be also 3. This is because [tex]\frac{(2+4)}{2} = 3, and\ also\ \frac{(2+3+4)}{3} = 3[/tex].
So considering the above Question, count of all the above numbers is 10.
Sum = 3.7 + 5 + 9.2 + 4 + 6.1 + 5 + 2.6 + 4 + 5.2 + 5 = 488
Mean = Average = [tex]\frac{Sum}{Count}[/tex]
Mean = [tex]\frac{488}{10}[/tex] = 4.88
Answer:
its 4.88
Step-by-step explanation:
it was on my test
Which ordered pairs match the table?
x 0 1 2 1 3
y 2 2 3 4 1
Help please
(0, 2) , (1, 2) , (2, 3) , (1, 4) , (3, 1)
(0, 2) , (0, 2) , (2, 2) , (2, 3) , (2, 4)
(1, 2) , (1, 1) , (2, 0) , (0, 4) , (2, 1)
(2, 0) , (2, 1) , (3, 2) , (4, 1) , (
A.
(0, 2) , (1,2) , (2,3) , (1,4) , (3,1)
Answer:
A.
(0, 2) , (1,2) , (2,3) , (1,4) , (3,1)
Thats the correct answer.
How do you simplify 21+(n-5)
Answer:
n+16
Step-by-step explanation:
21+(n-5)=21+n-5=n+21-5=n+16
please help me out. find the sum using the number line
Answer
-1
Step-by-step explanation:
6x-2y=10 for y when x=2
Answer: 1
Step-by-step explanation:
6 times 2 minus 2y = 10
first 6x2=12
12-2y=10
minus 12 from each side =0
so now you have;
-2y= -2
divide & you get one!
<33333
15 points. Would the rules for interference work the same for light waves as they do for sound waves? Explain why or why not.
Answer:
Yes, because when waves are at the same place at the same time, the amplitudes of the waves simply add together and this is really all we need to know!
Step-by-step explanation:
The sum of two waves can be less than either wave, alone, and can even be zero. This is called destructive interference.
If we place the waves side-by-side, point them in the same direction and play the same frequency, we will have constructive interference.
factor the polynomial completely x^2-x-20
Answer:
(x − 5) (x + 4)
Step-by-step explanation:
x² − x − 20
Factor using AC method:
1 × -20 = -20
Factors of -20 that add up to -1: -5 and 4
Divide by 1 and reduce: -5/1 and 4/1
(x − 5) (x + 4)
Answer:
[tex]\displaystyle [x + 4][x - 5][/tex]
Step-by-step explanation:
Find two quantities that when differed to −1, they also multiply to −20, and those numbers are 4 and −5.
I am joyous to assist you anytime.
Tell whether each equation has one, zero, or infinitely many solutions.
5(x - 3) +6= 5x - 9
Answer:
Infinitely many solutions
Step-by-step explanation:
the 5x's cancel and -15 + 6 = -9 so -9 equals -9. No matter what value you input for x, the answer is equal.
Answer:
Infinitely many.
Step-by-step explanation:
5(x - 3) +6= 5x - 9
5x - 15 + 6 = 5x - 9
5x - 9 = 5x - 9.
We can enter any real value of x and both sides will be equal so there are infinitely many solutions.
how do i find the volume of these similar solids? round to the nearest tenth HELP
Answer:
The volume of the larger solid is [tex]592.6\ mm^3[/tex]
Step-by-step explanation:
The question is
If these solids are similar, find the volume of the larger solid
step 1
Find the scale factor
we know that
If two solids are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor
Let
x ----> the height of the larger solid in mm
y ----> the height of the smaller solid in mm
z ---> the scale factor
[tex]z=\frac{x}{y}[/tex]
we have
[tex]x=4\ mm\\y=3\ mm[/tex]
substitute
[tex]z=\frac{4}{3}[/tex] ---> scale factor
step 2
Find the volume of the larger solid
we know that
If two solids are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube
Let
x ----> the volume of the larger solid in cubic millimeters
y ----> the volume of the smaller solid in in cubic millimeters
z ---> the scale factor
[tex]z^3=\frac{x}{y}[/tex]
we have
[tex]z=\frac{4}{3}[/tex]
[tex]y=250\ mm^3[/tex]
substitute the values
[tex](\frac{4}{3})^3=\frac{x}{250}[/tex]
solve for x
[tex](\frac{64}{27})=\frac{x}{250}[/tex]
[tex]x=250(\frac{64}{27})[/tex]
[tex]x=592.6\ mm^3[/tex]
What are the steps for solving, 7,542÷3
Answer:
2514
Step-by-step explanation:
Do the long division and you'll find the answer.
Answer 20 points pls
The sum of slopes b and c is 0
This statement is NOT always true
Step-by-step explanation:
(1) According to the graph, line a and b are parallel to each other. This, therefore, means that they have the same slope/gradient.
(2) Line c however, is perpendicular to both lines a and b. The slope of two lines that are perpendicular to each other is always the negative inverse of the slope of the other. This means that the product of their slopes will become -1.
An example is that if the slope of a line is 2, then a line perpendicular to it will have a slop of – ½
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Answer:
The sum of the slopes of line b and line c is 0
Step-by-step explanation:
Verify each statement
case a) The sum of the slopes of line b and line c is 0
we know that
Line b and line c are perpendicular lines
If two lines are perpendicular, then their slopes are opposite reciprocal
If the slope of line c is n
then the slope of line b is -1/n
[tex]-\frac{1}{n}+n=0[/tex]
Solve for n
[tex]n^{2}=1[/tex]
[tex]n=\pm1[/tex]
That means -----> This statement is true only when the slopes of the perpendicular lines are 1 and -1
therefore
NOT always true
case b) Line a and line b have the same slope
This statement is always true, because the lines are parallel
Remember that
If two lines are parallel, then the lines have the same slope
case c) The product of the slopes of line a and line c is -1
This statement is always true, because the lines are perpendicular
Remember that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
case d) The product of the slopes of line c and line b is -1
This statement is always true, because the lines are perpendicular
Remember that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
Find k, the constant of proportionality, for the data in this table. Then write an equation for the relationship.
They equation needs to be in the form y=kx
K=
Equation:
Answer:
[tex]k=\frac{32}{5}[/tex], [tex]y=\frac{32}{5}x[/tex]
[tex]k=6.4[/tex], [tex]y=6.4x[/tex]
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]
Find the value of the constant of proportionality k
take any ordered pair from the data
For x=25, y=160
[tex]k=\frac{y}{x}[/tex]
substitute the values of x and y
[tex]k=\frac{160}{25}[/tex]
simplify
[tex]k=\frac{32}{5}[/tex]
The linear equation is equal to
[tex]y=\frac{32}{5}x[/tex]
or
[tex]y=6.4x[/tex]
find the exact values of sin 2θ and cos 2θ for sin θ= 5/11 on the interval 0° ≤ θ ≤ 90°
pls help asap!
Answer:
Below in bold.
Step-by-step explanation:
sin ^2x + cos ^2 x = 1, so
cos^2x = 1 - (5/11)^2 = 96/121
cos x = √96/11
= 4√6/11.
sin 2x = 2 sinx cosx = 2 * 5/11 * 4√6/11.
= 40√6/121.
cos2x = 2cos^2 x - 1
= 2 * 96/121 - 1
= 192/121 - 121/121
= 71/121.
8(19-17) number- number
Answer:
16
Step-by-step explanation:
8(19-17)=8(2)=16