After using 25 square block, a quilt has been prepared by Wei-Min that has an area of 100 square inches. The length of each side of a block is 2 inches by calculating using concept of mensuration.
As per the question statement, Wei-Min makes a square quilt that has an area of 100 square inches and has got 25 square blocks, each the same size. We are supposed to find the length of each side of a block.
Using concept of mensuration,
Area of square quilt = 100 square inches
Number of block used = 25 square blocks
Therefore, area of each block = 100/25 = 4 square inches
As the block is a square, so each side will be equal in length.
Let's assume each side of square be "x" inches
Therefore x^2 = 4
or x = √4
or x = 2 inches
Mensuration: In the field of mathematics known as measurement, length, volume, shape, surface area, and other properties are measured for 2D and 3D objects. In other terms, it is the method of measuring based on mathematical formulas and algebraic equations.To learn more about Mensuration, click on the link given below:
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\left|-c+12\right|=
∣−c+12∣= 14
The value of c from the equation is 2
What is absolute value?The absolute value of a number can be defined as the non -negative value of a number irrespective of its sign.
It is known as the distance of a number from zero without consideration of its sign.
It is also known as the modulus of a number.
It is denoted with the symbol, " | | "
Given the expression;
∣−c+12∣= 14
find the absolute value
c + 12 = 14
collect like terms
c = 14 - 12
c = 2
Thus, the value of c from the equation is 2
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A baby was born every 43 seconds in the UK in 2018 Work out an estimate for the total number of babies born in the UK in 2018. You must show how you get your answer.
Approximately 733395 babies were born in the UK in 2018.
Given,
In the UK in 2018 a baby was born every 43 seconds.
We have to find the total number of babies in the UK in 2018.
A baby in every 43 seconds.
There is 3600 seconds in an hour.
There is 24 hours in a day.
In 2018 there were 365 days.
So, the total number of babies born in 2018 in the UK:
= (Seconds in an hour × hours in a day × total days in 2018) ÷ 43
= (3600 × 24 × 365) ÷ 43
= 31536000 ÷ 43
= 733395.3488
≈ 733395
That is, in the UK in 2018 approximately 733395 babies were born.
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[tex] \rm\int_{0}^{2021} \frac{ \sqrt{x + \sqrt{x + \sqrt{x + \sqrt{x} + \cdots } } } }{1 + \sqrt{x - \sqrt{x - \sqrt{x - \sqrt{x - \cdots} } } } } dx \\ [/tex]
We have the identity
[tex](a + b)^2 = a^2 + 2ab + b^2 = a^2 + ab + b (a + b) \\\\ ~~~~ \implies a + b = \sqrt{a^2 + ab + b (a + b)} \\\\ ~~~~ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{\cdots}}}}[/tex]
assuming [tex]a+b\ge0[/tex].
For the numerator, let [tex]b=1[/tex], so [tex]a\ge-1[/tex], which means
[tex]a^2 + a = x \implies a = \dfrac{-1 + \sqrt{1 + 4x}}2[/tex]
and so
[tex]\sqrt{x + \sqrt{x + \sqrt{x + \sqrt{\cdots}}}} = \dfrac{-1 + \sqrt{1 + 4x}}2 + 1 = \dfrac{1 + \sqrt{1 + 4x}}2[/tex]
For the denominator, let [tex]b=-1[/tex] so that [tex]a\ge1[/tex]. Now
[tex]a^2 - a = x \implies a = \dfrac{1 + \sqrt{1 + 4x}}2[/tex]
so that
[tex]\sqrt{x - \sqrt{x - \sqrt{x - \sqrt{\cdots}}}} = \dfrac{1 + \sqrt{1 + 4x}}2 - 1 = \dfrac{-1 + \sqrt{1 + 4x}}2[/tex]
So, in the integral we can simplify and evaluate it to
[tex]\displaystyle \int_0^{2021} \frac{\sqrt{x + \sqrt{x + \sqrt{x + \sqrt{\cdots}}}}}{1 + \sqrt{x - \sqrt{x - \sqrt{x - \sqrt{\cdots}}}}} \, dx \\\\ ~~~~~~~~ = \int_0^{2021} \frac{\frac{1 + \sqrt{1 + 4x}}2}{1 - \frac{1 - \sqrt{1+4x}}2} \, dx \\\\ ~~~~~~~~ = \int_0^{2021} \frac{1 + \sqrt{1 + 4x}}{1 + \sqrt{1 + 4x}} \, dx \\\\ ~~~~~~~~ = \int_0^{2021} dx = \boxed{2021}[/tex]
Write the given statement as an inequality. a + 4 is positive.
Answer:
[tex]\mathrm{a + 4 = |+All~real~numbers|}[/tex] (+∞)
Any concerns please notify me, and have a great day!
Solve
X =-2 and y=3
3x to the 2nd power times y minus x
Answer:
38
Step-by-step explanation:
[tex]3x {}^{2} y - x[/tex]
[tex] 3 \times ( - 2) { \\ }^{2} \times 3 - ( - 2)[/tex]
[tex]3 \times 4 \times 3+ 2[/tex]
[tex]36 + 2[/tex]
[tex]38[/tex]
Compare -3.5 and -10/3 using symbols <, >, or =.
A. -3.5 < -10/3
B. -3.5 > -10/3
C. -10/3 = -3.5
D. -10/3 < -3.5
Answer:
[tex]\sf A. \quad -3.5 < -\dfrac{10}{3}[/tex]
Step-by-step explanation:
Convert -3.5 into a fraction:
[tex]\implies \sf -3.5=-\dfrac{35}{10}=-\dfrac{\diagup\!\!\!\!5 \times 7}{\diagup\!\!\!\!5 \times 2}=-\dfrac{7}{2}[/tex]
Rewrite both fractions so that they have the same denominator:
[tex]\implies \sf -\dfrac{7}{2}=-\dfrac{7 \times 3}{2 \times 3}=-\dfrac{21}{6}[/tex]
[tex]\implies \sf -\dfrac{10}{3}=-\dfrac{10 \times 2}{3 \times 2}=-\dfrac{20}{6}[/tex]
[tex]\textsf{As }\: -\dfrac{21}{6} < -\dfrac{20}{6} \textsf{ then}:[/tex]
[tex]\sf \implies -3.5 < -\dfrac{10}{3}[/tex]
5. Gasoline is priced at $3.39 per gallon. Write
an equation to represent the total cost, y, of
purchasing x number of gallons.
Answer:
3.39x=y
Step-by-step explanation:
This is because the 'y' part is supposed to be the answer for how much the gallons of gasoline would be.
The 'x' part of the equation represents how much gallons of gasoline you got and you can treat it as a normal number.
Pretend that x is 2 and so you are to find out how much 2 gallons of gasoline costs and to work this out you would do this: 3.39 x 2.
You just basically treat x as a normal number like so and it would look like:
3.39 x x=3.39x
Find the value of a for which the solutions of the inequality are all real numbers
a(x+3)<5x+15-x
a > 4 for which the solutions of the inequality are all real numbers.
InequalityIt is an expression mathematical that represents a non-equal relationship between a number or another algebraic expression. Therefore, it is common the use following symbols: ≤ (less than or equal to), ≥ (greater than or equal to), < (less than), and > (greater than).
The solutions for inequalities can be given by: a graph in a number line or numbers.
For solving this exercise, it is necessary to find a for the given inequality.
a(x+3) < 5x+15-x
a(x+3) < 4x +15
ax+3a < 4x+15
Subtract 3a from both sides
ax+3a -3a< 4x+15-3a
ax < 4x+15-3a
ax-4x < 15-3a
x(a-4) < 15-3a
[tex]x < \frac{15-3a}{a-4}[/tex]
Like there is a variable a in the denominator, a-4 >0, then a>4.
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PLEASE HELP AND HURRY
Solve for x: −6 < x − 1 < 9 5 < x < 10 −5 < x < 10 −5 > x > 10 5 > x > −10
Answer:
i want orange juice
Answer:
−5 > x > 10
Step-by-step explanation:
A $25,000 machine depreciates linearly to 0 over a 10 year period. What is the value of the machine after 3 years?
The value of machine after 3 years which costs $25000 will be $17500.
What is the depreciation in value ?
An asset loses value over time as a result of use, damage, or obsolescence. This decline in value is known as depreciation.
The value of a machine is $25000.
The value of the machine after 3 years must be found.
Let y be the machine's price and x be its production time.
We are aware that the line's equation is y = mx + c.
Machine costs $25,000, therefore the point is (0,25000), and when it costs nothing after 10 years, the point becomes (10,0).
Regarding the first point (0 , 25000)
25000 = 0(x) + c
c = 25000
For a second point which is (10,0)
0 = 10(m) + 25000
m = -2500
As a result, y = -2500x + 25000 is the equation.
We know that , we have to find the value of machine after 3 years i.e., x = 3.
So ,
y = - 2500 × 3 + 25000
y = -7500 + 25000
y = $ 17500
Therefore , the value of machine after 3 years which costs $25000 will be $17500.
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The machine after 3 years when depreciates linearly to 0 over a 10 year period is 17500.
What is equation?
An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.
Given:
A $25,000 machine depreciates linearly to 0 over a 10 year period.
According to given question we have
At the time of launch, its cost is $25,000 so the point becomes (0,25000) and after 10 years its cost becomes zero then the point becomes (10,0).
For the first point (0, 25000)
25000 = 0(x) + c
c = 25000
For second point (10,0)
0 = 10(m) + 25000
m = -2500
Thus the equation become y = -2500x + 25000.
When x=3
y = -2500x + 25000
y=-2500*3+25000
y=17500
Therefore, the machine after 3 years when depreciates linearly to 0 over a 10 year period is 17500.
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ill give brainly and 15points
The required solution of the given expression is -9.
What is number line?A straight line with numbers placed at equal intervals or segments along its length. Number line is a straight line with a "zero" point in the middle, with positive and negative numbers listed on either side of zero and going on indefinitely.
Given:
The given expression is
-2-(+7)
According to given question we have
Number line is a line with 0 in the middle, and then increasing positive numbers to the right of the 0 and decreasing negative numbers to the left of the 0. The line is infinite in length and it's not possible to show the whole line, but we will illustrate where on the line 9 and -9 are located.
-2-(+7)
=-2-7
=-9
Therefore, the required solution of the given expression is -9.
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A spinner is divided into five colored sections that are not of equal size: red, blue, green, yellow, and purple. The spinner is spun several times, and the results are recorded below:
Spinner Results
Color Frequency
Red 19
Blue 20
Green 14
Yellow 8
Purple 10
Based on these results, express the probability that the next spin will land on blue or green or purple as a fraction in simplest form.
The probability that the next spin will land on blue or green or purple as a fraction in simplest form is 44/71.
Given that, a spinner is divided into five coloured sections that are not of equal size: red, blue, green, yellow, and purple.
What is probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favourable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.
Probability(Event) = Favorable Outcomes/Total Outcomes = x/n
The spinner results are as follows:
Colour Frequency
Red 19
Blue 20
Green 14
Yellow 8
Purple 10
Total number of outcomes = 19+20+14+8+10=71
The probability of getting blue =20/71
The probability of getting green =14/71
The probability of getting purple =10/71
So, the probability of getting blue or green or purple = 20/71 + 14/71 + 10/71
=44/71
Therefore, the probability that the next spin will land on blue or green or purple as a fraction in simplest form is 44/71.
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I need help with this question for my Precalculus class
If [tex]x[/tex] is positive, then [tex]\tan^{-1}(x)[/tex] is between 0 and π/2, which means [tex]\cos(\tan^{-1}(x))[/tex] is between 1 and 0.
Let [tex]\theta = \tan^{-1}(x)[/tex]. Then [tex]\tan(\theta) = x[/tex], and it follows from the Pythagorean identity that
[tex]\sin^2(\theta) + \cos^2(\theta) = 1 \implies \tan^2(\theta) + 1 = \sec^2(\theta) \\\\ ~~~~ \implies \sec(\theta) = \sqrt{1 + \tan^2(\theta)} \\\\ ~~~~ \implies \cos(\theta) = \dfrac1{\sqrt{1+\tan^2(\theta)}} \\\\ ~~~~ \implies \cos(\tan^{-1}(x)) = \boxed{\dfrac1{\sqrt{1+x^2}}}[/tex]
We took the positive square root when solving for [tex]\sec(\theta)[/tex] because we know [tex]\cos(\theta)[/tex] is non-negative, between 0 and 1.
I am a quadrilateral with no right angles what shape am I
Answer:
a diamond ♦ it as acute angles
A sample of 15 Girl Scouts was selected and their weights (in pounds) were recorded. The results are listed below. Construct a frequency histogram for the data using a class width of 10 and using 95 as the lower limit of the first class.
97 120 137 124 117
108 134 126 123 106
130 110 100 120 140
Frequency Histogram for the data using a class width of 10 and using 95 as the lower limit of the first class.
A histogram is a bar graph type of data representation in this representation the width of the class size is represented by the rectangle shapes reaching a particular height which describes the the number of frequency distribution.
The girls scouted got their weight recorded. The weights of the girls recorded are 97 120 137 124 117 108 134 126 123 106 130 110 100 120 140.
All the weights are measured in pounds.
The histogram is represented in the x axis and the y axis. The weight of the girls is represented on the y axis. The number of girls is represented on the x axis.
Each girl's weight is represented by a different color to understand the graph easily.
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A class has 6 boys and 15 girls. What is the raito of boys to girls
Boys: 2, Girls: 5
There are 6 boys and 15 girls.
If there were 5 boys and 15 girls, the ratio would go to 1 to 3
But this is 6 boys to 15 girls
Final answer: 2:5
Solve for r.
P=q+r+s
In linear equation, The value of the r is a P-q-s.
According to the statement
We have to find that the value of the r .
So, For this purpose, we know that the
The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.
From the given information:
The equation is a :
P=q+r+s
This a type of the linear equation then
P=q+r+s
Now, rearrange the terms
P-q-s = r
Then the value of the r is
r = P-q-s .
So, In linear equation, The value of the r is a P-q-s.
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The number of clients who are being consulted in a firm decreases from week 2 of the month to week 3 of the month in the ratio 4:3. If
280 people were consulted in week 2 of May 2009, how many people were consulted in week 3 of May 2009?
Work Shown:
x = number of people in week 3
280/x = 4/3
280*3 = 4*x
x = 280*3/4
x = 210
The table shows the approximate population and land area for several states. Order the states from least population density (top) to greatest population density (bottom). State Population Land Area (mi2) Arizona 6 . 83 × 10 6 113 , 594 Colorado 5 . 46 × 10 6 103 , 642 Kentucky 4 . 43 × 10 6 39 , 486 Minnesota 5 . 45 × 10 6 79 , 627
States from least population density (top) to greatest population density (bottom) are Colorado Arizona Minnesota Kentucky.
In the problem we are given with some datas
State Population Land Area
Arizona 6 . 83 × [tex]10^{6}[/tex] 113 , 594
Colorado 5 . 46 × [tex]10^{6}[/tex] 103 , 642
Kentucky 4 . 43 × [tex]10^{6}[/tex] 39 , 486
Minnesota 5 . 45 × [tex]10^{6}[/tex] 79 , 627
population density are for
Arizona (6 . 83 × [tex]10^{6}[/tex] )/113594=60.12
Colorado 52.68
Kentucky 112.19
Minnesota 68.44
States from least population density (top) to greatest population density (bottom) are Colorado Arizona Minnesota Kentucky.
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Equation for the line that passes through the points (6,-5) and (-4,1)
Answer: Equation for the line that passes through the points (6,-5) and (-4,1) is equal to 3x+5y+7 = 0.
Step-by-step explanation:
The equation of a line can be written in slope intercept form:
y = mx + b where m is the slope and b is the y-intercept
You can use the two points to find the slope m:
m = (y2 - y1 ) / ( x2 - x1 )
Given that points (6,-5) and (-4,1)
It represents the values are,
x1 = 6
y1 = -5
x2 = -4
y2 = 1
so,
Replace with x1, x2, y1, y2 values in this equation,
we can write,
m=(1-(-5)) / (-4-(6))
m = (1+5) / (-4-6)
m= 6/-10
m = 3/-5
Now you can select either point and substitute the coordinates in the equation to determine b, the y intercept. Let's us (-4, 1):
y= mx + b
so, x = -4 and y = 1 and m = 3/-5
Replace with the values in this equation,
y= mx +b
1 = (-3/5)(-4) + b
1 = (0.6)(4) +b
1 = 2.4 +b
1-2.4 = b
-1.4 = b
b = -1.4
The equation will be:
y = mx +b
substitute m and b values,
Then,
y = (-3/5)x + (-1.4)
y = (-3/5)x -1.4
In standard form, the equation would be transformed as:
y = (-3x-7) / 5
5y = -3x-7
3x+5y = -7
3x+5y+7 = 0
In standard form, the equation would be transformed as: 3x+5y+7 = 0
Therefore,
Equation for the line that passes through the points (6,-5) and (-4,1) is equal to 3x+5y+7 = 0.
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30 points
The school that Jessica goes to is selling tickets to a fall musical. On the first day of ticket sales
the school sold 6 senior citizen tickets and 5 student tickets for a total of $50. The school took in
$44 on the second day by selling 8 senior citizen tickets and 1 student ticket. Find the price of a
senior citizen ticket and the price of a student ticket.
6C+ SS=50
8C+15=44
Answer:
The price of a senior citizen ticket to the fall musical is $6
The price of a student citizen ticket to the fall musical is $4
Step-by-step explanation:
C = the price of a senior citizen ticket to the fall musical
S = the price of a student citizen ticket to the fall musical
Day 1:
6C + 5S = 50
Day 2:
8C + 1S = 44
Manipulate the equations so that they have a common coefficient.
Multiple Day 2's equation by 5.
8C + 1S = 44
40C + 5S = 220
Subtract Day 2's equation from Day 1's
(40C + 5S = 220) - (6C + 5S = 50)
(40C + 5S) - (6C + 5S) = 220 - 50
(40C - 6C) + (5S - 5S) = 220 - 50
34C = 170
C = 5
Substitute C into either equation to solve for S.
Day 1:
6C + 5S = 50
6(5) + 5S = 50
30 + 5S = 50
5S = 50 - 30
5S = 20
S = 4
Day 2:
8C + 1S = 44
8(5) + 1S = 44
40 + 1S = 44
1S = 44 - 40
S = 4
The price of oil recently went from $11.00 to $13.20 per case of 12 quarts. Find the ratio of the increase in price to the original price? What is the ratio in simplified fraction?
Answer:
0.67
Step-by-step explanation:
Original price = $8.10
New price = $13.50
Increase in price = 13.50−8.10=$5.40
Ratio of the increase in price to the original price = 5.40 8.10=0.67
Use the appropriate compound interest formula to compute the balance in the account after the stated period of time $13,000 is invested for 7 years with an APR of 4% and quarterly compounding
Answer:
Step-by-step explanation:
Compound Interest Formula
The Amount A after t years due to a principle P invested at an annual interest rate r compounded n times per year
Compounded Quartely means 4 times per year
A = P(1 + r/n)^nt
A= 13000(1 + 0.04/4)^4(7)
A = 13000(1 + 0.01)^28
A = 13000(1.01)^28
A = 13000(1.321290967)
A = 17176.78|257
A ≈ 17,176.78
The average temperature in the mountains is 62° in April. The average temperature in that same spot is −4° in December. Determine how much warmer this location is in April than in December, and determine which temperature is the farthest away from 0°.
62 − |−4| = 58°, 62° is the farthest from 0°
62 + |−4| = 66°, 62° is the farthest from 0°
62 − |−4| = 58°, −4° is the farthest from 0°
62 + |−4| = 66°, −4° is the farthest from 0°
Answer: 62 + |−4| = 66°, 62° is the farthest from 0°
I believe this is the correct answer.
The one that shows how much warmer this location is in April than in December, and which temperature is the farthest away from 0°. will be B Option 62 - |−4| = 566°, 62° is the farthest from 0°
How are Kelvin, Celsius, and Fahrenheit related?We have got an equation that can relate these three units of measurement of temperature, as given below:
[tex]\dfrac{C}{5} = \dfrac{F - 32}{9} = \dfrac{K - 273}{5}[/tex]
where C represents the measurement of a fixed temperature in celsius, F represents the measurement of that same intensity temperature in fahrenheit, and K represents the measurement of equally intense temperature in kelvin.
Based on the information given, the value of warmer will be;
= 62 - (-4)
= 62 + 4.
= 66
Therefore, the correct option will be option B. 62 - |−4| = 566°, 62° is the farthest from 0°
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Marco bought pens and pencils with his company's name and website address to give away to people at a festival. He bought a total of 300 pens and pencils together and spent $62.50. If pencils cost $0.15 each and pens cost $0.25 each, how many
pens did Marco buy?
Macro bought 175 pens
The number of pens Macro bought can be calculated as follows
let x represent the number of pens bought
let y represent the number of pencils bought
x + y = 300.........equation 1
0.25x + 0.15y= 62.50.........equation 2
From equation 1
x + y= 300
x= 300-y
Substitute 300-y for x in equation 2
0.25(300-y) + 0.15y= 62.50
75 - 0.25y + 0.15y= 62.50
75 - 0.1y= 62.50
-0.1y= 62.50-75
0.1y= 12.5
y= 12.5/0.1
y= 125
Substitute 125 for y in equation 1
x + y= 300
x + 125= 300
x= 300-125
x= 175
Hence Marco bought 175 pens
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3. 0.5b +4=2(b-2) (1 point)
O10
O5
Ono solution
O identity
Answer:
0.5b + 4 = 2(b + 2)
0.5b + 4 = 2b + 4
0.5b - 2b = 4 - 4
-1.5b = 0
b = 0/-1.5
b = 0
5. a) A farmer has 9 1/2 ha (hectares) of land. He needs 1 1/4 ha for each crop. How many different crops can he plant? b) Will all the land be used for planting? Explain your thinking.
Answer:
Step-by-step explanation:
Answer:
a farmer has 9 1/ 2 ha of land . He needs 11/4 ha for each crops
the no of different crop he can plant is ..
Step-by-step explanation:
please help me in my maths question
Zen Have 20 Apples.. his weight is 45kg And have 2 shopping bags; then how many oranges he have
In this problem you have two unknowns: the weight of a bag of apples and the weight of a bag of oranges.
You have one given equation, which allows you to reduce the number of unknowns by one. This means that you will not be able to tell both the weight of the apples and the oranges, but find a line with possible solutions instead.
e.g. apples weigh 6+2x, oranges 7-3x where x is any real number.
You may narrow the problem down by assuming the weights to be non-negative, but to solve for x you need another piece of information that allows you to eliminate the last unknown.
How many multiples of 14 are there in 406?
Answer:29
Step-by-step explanation:14 multiplied by 29=406
Answer:
14 x 29 = 406
Step-by-step explanation:
so I believe it's 29
Which expression is NOT equivalent to 60+20
A 10(6+2)
b 5(12+4)
c2(30+10)
d 10(6+1)