A pair of parallel lines divide a parallelogram as shown in the diagram into three regions with the same area. If one of the three regions is an equilateral triangle with perimeter $1$, then what is the perimeter of the original parallelogram?
Answers
The perimeter of the original parallelogram is 22/9 * √3
What is the perimeter of the original parallelogram?The vertices of the parallelogram are A, B, C, and D, with AB parallel to CD and AD parallel to BC.
The parallel lines intersect the sides of the parallelogram at E, F, G, and H.
The side length of the equilateral triangle is s.
The three regions have the same area, hence, the area of each region is 1/3 of the total area of the parallelogram.
Let's the area of the parallelogram as A.
The area of the equilateral triangle is (s²√3)/4
This area is one-third of A
(s²√3)/4 = A/3
s² = 4A/(3√3)
Considering the whole parallelogram;
AB is parallel to CD, hence, triangle AEF is similar to triangle BGF
Also, AD is parallel to BC, hence, triangle ADE is similar to triangle BCF.
AE/EB = BF/FG AD/DE
AE/EB = BC/CF
Expressing AE, BF, AD, and BC in terms of s:
AE = s/3 (perimeter of the equilateral triangle is 1)
EB = 2s/3
BF = 2s/3
FG = s/3
AD = (2s + 2EB)/3
AD = (2s + 4s/3)/3
AD = 10s/9
DE = (2s + 2AE)/3
DE = (2s + 2s/3)/3
DE = 8s/9
BC = (2s + 2FG)/3
BC = (2s + s/3)/3
BC = 7s/9
CF = (2s + 2BF)/3
CF = (2s + 4s/3)/3
CF = 10s/9
Now we can find the perimeter of the parallelogram:
Perimeter = 2(AB + AD)
Perimeter = 2(EB + BC)
Perimeter = 2(2s/3 + 7s/9)
Perimeter = 4s/3 + 14s/9
Perimeter = (22s/9)
Substituting s² = 4A/(3√3) from the earlier equation, we get:
Perimeter = (22/9)√3
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Related Questions
A rocket is launched from the top of an 88-foot cliff with an initial velocity of 100 ft/sec. a. Use the vertical motion formula h(t) = -16t2 + vt + c to write an equation that represents the height of the rocket with respect to time. b. Determine how long the rocket will take to hit the ground at the base of the cliff (h = 0) after it is launched. Round to the nearest hundredth of a second.
Answers
Answer:17
Step-by-step explanation:
i took the test
In theâ U.S., shoe sizes are defined differently for men andâ women, but inâ Europe, both genders use the same shoe size scale. The accompanying histogram shows the European shoe sizes of 269 male and female collegeâ students, converted from their reported U.S. shoe sizes.âa) Describe the shape.âb) How many modes does the histogramâ have? What might explainâ that?
Answers
a) The shape of the histogram appears to be roughly symmetric and bimodal.
b) The histogram appears to have two modes, explanation is given below.
c) D option is correct.
a) The shape of the histogram appears to be roughly symmetric and bimodal.
b) The histogram appears to have two modes, which may be due to the fact that the data includes both male and female students. The two modes may correspond to the average shoe sizes for men and women, respectively.
c) D option is correct. The distribution has two modes from 38 to 40 and from 44 to 46. This may be due to having data for both men and women. The lower mode might be for women and the upper for men.
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____ The given question is incomplete, the complete question is given below:
In the U.S., shoe sizes are defined differently for men and women, but in Europe, both genders use the same shoe size scale. The accompanying histogram shows the European shoe sizes of 269 male and female college students, converted from their reported U.S. shoe sizes.
a) Describe the shape.
view the histogram (The distribution is roughly symmetric and bimodal.)
b) How many modes does the histogram have? What might explain that?
c) Choose the correct answer below.
A. The distribution is multimodal, with modes from 38 to 40, from 44 to 46, and from 48 to 50. This may be due to having data for both men and women. The first two modes might be for women and the third for men.
B. The distribution has one mode from 44 to 46. This is due to the students having roughly the same mean shoe size.
C. The distribution has one mode from 38 to 40. This is due to the students having roughly the same mean shoe size.
D. The distribution has two modes from 38 to 40 and from 44 to 46. This may be due to having data for both men and women. The lower mode might be for women and the upper for men.
E. The distribution has two modes from 34 to 36 and from 44 to 46. This may be due to having data for both men and women. The lower mode might be for women and the upper for men.
F. The distribution is multimodal, with modes from 34 to 36, from 40 to 42, and from 43 to 50. This may be due to having data for both men and women. The first two modes might be for men and the third for women
G. The distribution does not have any modes, because it is uniform i Shoe Sizes Count.
Function w is a nonlinear function. Which representation could represent function w?
Answers
A representation that could represent function w (nonlinear function) is: D. table D.
What is a linear function?In Mathematics, a linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.
This ultimately implies that, a linear function has the same slope and it is typically used for uniquely mapping an input variable to an output variable, which both increases simultaneously.
Therefore, table D represents a non-linear function because the slope is not constant and the common difference is not constant between successive data points.
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Alice purchased a dress for $23.95, a necklace for $10.95, and a pair of
earrings for $6.79. What was the total amount of her purchase including 5%
tax?
Answers
Answer:
$43.77
Step-by-step explanation:
The total price without tax is $41.69. To add tax, we take 5% of this total (which ends up being $2.08) and add it to the total. This makes the final price $43.77.
Reflect the triangle over the y-axis and find the coordinate of the image of point K.
K’(2, 1)
K’(–2, 1)
K’(–2, –1)
K’(2, –1)
Answers
K'(-2, 1) is the coordinate of the image of point K, found by multiplying the original x-coordinate of the point K (2) by -1. To reflect the triangle over the y-axis, the x-coordinate of each point is multiplied by -1.
What is triangle?Triangle is a three-sided geometric shape which has three angles and three sides. The three sides of a triangle are typically referred to as the base, the height, and the hypotenuse. A triangle can be classified as either right, obtuse, or acute depending on the measure of its angles. Right triangles have one right angle, obtuse triangles have one obtuse angle, and acute triangles have three acute angles.
The coordinate of the image of point K is K’(-2, 1). This means that the x-coordinate of the point is -2 and the y-coordinate of the point is 1. This can be found by multiplying the original x-coordinate of the point K (2) by -1. The y-coordinate of point K remains the same, so the y-coordinate of the image of point K is 1.
Therefore, the coordinate of the image of point K is K’(-2, 1).
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Kingsley knows that 1 inch is about 2.54 centimeters.He wants to write an equation he can use to convert any given length in inche (I) to centimeters (c)
Answers
The equation of conversion between the length y inches to centimeters is y inches = 2.54y centimeters.
What is the relation between inches and centimeters?Both the inches and centimeters are units of length, where the inch is an ES unit and the centimeter is a CGS unit. They are connected by the relation, 1 inch equals 2.54 centimeters.
Let, the length is y inches.
It is known that 1 inch = 2.54 centimeters. So, convert the y inches to centimeters.
y inches = y×1 inch
= y×2.54 centimeters
= 2.54y centimeters
Therefore, the obtained answer is y inches = 2.54y centimeters, where y is the length of an object.
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Find the value of each variable using the properties of a parallelogram
Answers
The value of x is 10.
What is Parallelogram?Parallelogram is a type of polygon with four sides, four angles and four vertices. It is a type of Quadrilateral.
Opposite sides are parallel, and the opposite sides and opposite angles are equal.
Parallelogram has the property that the consecutive or adjacent angles of a parallelogram are supplementary.
That is, they sum up to 180°.
Here, (6x)° and (12x)° are supplementary.
6x + 12x = 180
18x = 180
x = 10
Hence the value of x is 10.
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In the year 2002, a company made $6.5 million in profit. For each consecutive year after that, their profit increased by 5%. How much would the company's profit be in the year 2004, to the nearest tenth of a million dollars?
Answers
7.2 million is the company's profit be in the year 2004.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
To find the company's profit in the year 2004
We have to first calculate its profit in the year 2003.
We know that its profit in 2002 was $6.5 million, so we can use the formula:
Profit in 2003 = profit in 2002 + (5% of profit in 2002)
= $6.5 + (0.05 x $6.5 )
= $6.825 million
Now, to find the profit in 2004, we use the same formula:
profit in 2004 = profit in 2003 + (5% of profit in 2003)
= $6.825 + (0.05 x $6.825 )
= $7.16625 million
profit in 2004=$7.2 million
Hence, 7.2 million is the company's profit be in the year 2004.
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10, 110, 210, 310, …
find a^30
Answers
The 30th term value is 2900.
What is an arithmetic sequence?A series of integers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.
Given:
A sequence,
10, 110, 210, 310, …
To find the common difference:
110 - 10 = 100
So, d = 100
Remember that,
aₙ= a₁ + (n-1)d
aₙ=a₁+(n−1)d
So,
aₙ = 10 +(n−1)100.
a₃₀ = 10 + (30 - 1)100
a₃₀ = 10 + 29(100)
a₃₀ = 10 + 2900
a₃₀ = 2910.
Therefore, a₃₀ = 2910.
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“Find the length of a side of an equilateral triangle of area 10.2 m^2”
Answers
The length of the equilateral triangle = 4.8m
Given that,
The area of the equilateral triangle = 10.2 m²
The formula for the area of an equilateral triangle = [tex]\sqrt{3} /4 a^{2}[/tex]
Therefore,
[tex]\sqrt{3} /4 a^{2}[/tex] = 10.2
[tex]a^{2}[/tex] = 10.2 × [tex]4/\sqrt{3}[/tex]
[tex]a^{2}[/tex] = 10.2 × 4/ 1.732
[tex]a[/tex] = 4.85
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Follow the given steps to subtract mixed numbers with different denominators: Step 1– Convert the mixed numbers into improper fractions. Step 2– Find the common multiple of both the denominators. Step 3– Convert the fractions as common denominators.
Answers
The steps for subtracting mixed numbers are the transformation of improper fractions, subtraction of denominator, then subtracting numerator, making it the smallest term, and reverse.
Finding the difference between two mixed numbers is required when subtracting mixed numbers. The steps for subtracting mixed numbers are as follows:
Step 1: Transform the mixed values into improper fractions in step 1. To achieve this, divide the total by the denominator, then add the numerator. The new numerator is the outcome, and it is positioned above the denominator.
Step 2: Identify a common denominator in step two. You must identify a common denominator to subtract fractions with various numerators.
Step 3: Subtract the fractions in step three. Subtract the numerators from the fractions while maintaining the same denominator.
Step 4: Make the outcome simpler. Simplify the outcome if you can by breaking the fraction down into its smallest terms. 13/4 in this instance may be expressed as 3 1/4.
Step 5: Reverse the incorrect fraction to a mixed number in step 5. Divide the numerator by the denominator to return the improper fraction to a mixed number. The full number serves as the numerator, and the remainder serves as the quotient.
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The question is -
How to Subtract mixed numbers?
solve please i need help am failing class will give brainliest for the
correct answer
Answers
Answer:
9 a3 b8
Step-by-step explanation:
109 a11 b16 - 100 a8 b8
A line passes through the coordinates (0,1) and 4,3). What is the y-intercept for the line in slope-intercept form
Answers
The equation of the line is y = ( 1/2 )x + 1 and the y intercept is b = 1
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( 0 , 1 )
Let the second point be Q ( 4 , 3 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 3 - 1 ) / ( 4 - 0 )
Slope m = 2/4
Slope m = 1/2
Now , the equation of line is y - y₁ = m ( x - x₁ )
y - 1 = ( 1/2 ) ( x - 0 )
y - 1 = ( 1/2 )x
Adding 1 on both sides , we get
y = ( 1/2 )x + 1
Hence , the equation of line is y = ( 1/2 )x + 1
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pls helppppp its math and its pretty hard
A maintenance worker needs to wax a restaurant floor shaped like the image shown. A six-sided figure. There is a horizontal base of 35 feet then another horizontal base below it of 20 feet. The longest side is to the right and is 40 feet. The top is 30 feet. There is a perpendicular from the vertex of the top to the first base of 35 that is labeled 15 feet. If the wax cost $1.38 a square foot, how much will the wax cost to cover the floor? $1,224.75 $1,569.75 $2,104.50 $2,449.50
Answers
If the wax cost $1.38 a square foot, the cost of wax to cover the area of the floor is $1,569.75.
The correct option is B.
What is the total area of the floor?The total area of the floor is calculated from the shape of the floor.
The floor is made up of a trapezoid and a rectangle.
The area of a trapezoid can be calculated as:
A = (a + b)/2 * h
where
a and b are the lengths of the bases and h is the height.
The trapezoid has a height of 15 feet and bases of 35 feet and (20 - 20) or 10 feet. So its area is:
A = (35 + 10)/2 * 15
A = 337.5 square feet
The rectangle has a base of 20 feet and a height of 40 feet. So its area is:
A =20 * 40
A = 800 square feet
The total area of the figure is the sum of the areas of the trapezoid and triangle:
A = 337.5 + 800
A = 1137.5 square feet
Finally, to find the cost of the wax, we multiply the area by the cost per square foot:
Cost = 1137.5 * $1.38
Cost = $1569.75
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Question
Andre calculated the volume of a cylinder. Andre said, “I found the area of a circular cross section and multiplied it by the cylinder’s height.”
Do you agree with Andre's strategy? Explain your reasoning.
Answers
Yes, I agree with Andre's strategy for calculating the volume of a cylinder.
The volume of a cylinder is equal to the area of the base (which is a circle) multiplied by the cylinder's height. This formula is expressed as follows:
Volume = r2h, where r is the radius of the circular base and h is the cylinder's height.
We can use the following formula to calculate the area of the circular base:
Area = r2
So, if we multiply the area of the circular base by the cylinder's height, we get:
Volume = r2h is the formula for calculating the volume of a cylinder.
As a result, Andre's strategy of calculating the volume of a cylinder by finding the area of a circular cross section and multiplying it by the height of the cylinder is valid and correct.
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The diagram shows a tennis ball, centre O, resting on a flat surface PQR. A ruler, PTS, rests on the ball at T. PT = 20 cm and ZTPQ = 30°. Calculate the radius of the tennis ball correct to the nearest millimetre. P 20 30°
Answers
The radius of the ball which is the each of the smaller balls is R = 2r.
What is volume of circle?The formula for the volume of a sphere is V = 4/3 π r³, where V = volume and r = radius. The radius of a sphere is half its diameter. So, to calculate the surface area of a sphere given the diameter of the sphere, you can first calculate the radius, then the volume.
We can use the following formula to get the volume of a sphere whose radius is "r": A sphere's volume is equal to 4/3r³.
here, we have,
Given,
A steel ball which is melted down to make eight smaller identical balls.
If the radius of the original steel ball was 20 cm:
Let the spherical ball's radius be R.
And with r being the radius of 8 similar balls,
According to the inquiry,
Volume of 8 similar balls = the volume of a larger sphere
3/4πR³ = 8 × 3/4πr³
R³ = 8r³
R = 2r
Hence, The radius of the ball which is the each of the smaller balls is R = 2r.
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Find the values of x and y. SHOW YOUR WORK!
Answers
⇒ 75° and (4x+9)° are co-interior angles which means when they are added they give 180°
[tex]75+(4x+9)=180\\4x=180-75-9\\4x=96\\\frac{4x}{4} =\frac{96}{4} \\x=24[/tex]
this simply means that x=24°
75° and 3y are corresponding angles, corresponding angels are equal.
this means that :
[tex]3y=75\\\frac{3y}{3} =\frac{75}{3} \\y=25[/tex]
this means that y=25°
goodluck
eric reads an article that says 15 out of 25 adults use their computer everyday. He collects data from a random sample of adults. Out of 1,270 adults, estimate the number of adults who use their computer every day. Please show your work!
Answers
The number of people that read their computer everyday out of 1270 surveyed adults using the given fraction is; 762 people
How to solve fraction problems?Wea re told that eric reads an article that says 15 out of 25 adults use their computer everyday. Thus, fraction of those that read their computer everyday = 15/25
Now, to find the number of people that read their computer everyday out of 1270 surveyed adults using the article fraction is;
15/25 * 1270 = 762 people
This represents the number of people that read their computer everyday
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Answer:
Step-by-step explanation:(:;44(()6)!
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Charlie is saving money to buy an everlasting gobstopper. He estimates that he will need $13.50. However, he forgot about the added
sales tax. The actual price of his gobstopper is $15.25. What is Charlie's percent error? (ROUND TO THE NEAREST TENTH)
Answers
The percentage error of Charlie is given by the equation A = 13 %
What is Percentage?A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %
The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.
Percentage change is the difference between the measured value and the true value , as a percentage of the true value
Percentage change =( (| Measured Value - True Value |) / True Value ) x 100
Given data ,
Let the percentage error of the gobstopper be A
Now , the initial price of the gobstopper = $ 13.50
The final price of the gobstopper = $ 15.25
Now , the equation will be
The percentage error A = ( final price - initial price / initial price ) x 100
The percentage error A = [ ( 15.25 - 13.50 ) / 13.50 ] x 100
The percentage error A = ( 1.75 / 13.50 ) x 100
The percentage error A = 0.1296 x 100
The percentage error A = 12.96 %
The percentage error A = 13 %
Hence , the percentage error is 13 %
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the measure of the larger angle is 12 less than 3 times the measure of the smaller angle
Answers
Answer:
Let x be the measure of the smaller angle. Then the measure of the larger angle is 3x - 12.
We can write this as an equation:
larger angle = 3 * smaller angle - 12 or 3x - 12 = larger angle.
Alternatively, we can write it as:
smaller angle + larger angle = 180 (since they form a straight line)
Substituting larger angle with 3x - 12, we get:
x + 3x - 12 = 180
Simplifying:
4x - 12 = 180
4x = 192
x = 48
Therefore, the measure of the smaller angle is 48 degrees, and the measure of the larger angle is 3(48) - 12 = 132 degrees.
The measure of the larger angle is 12 less than 3 times the measure of the smaller angle x = 48
What is angle?An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’ meaning “corner.”
Angles can mean is an acute angle.
Let smaller angle = x
Larger angle = 3x - 12
x & (3x - 12) are supplementary
So, x + 3x - 12 = 180°
4x - 12 = 180
4x = 180 +12
4x = 192
x = 192/4
⇒ x = 48°
Hence, the measure of the larger angle is 12 less than 3 times the measure of the smaller angle x = 48
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CROWN PLEASE HELP ME (ALSO PLEASE SEPARATE IT)
Answers
Answer: WVZ=84 XVW=84 IFH= 14 EFG= 58
Step-by-step explanation:
9x-15=5x+29- do 9-5 to get 4x then 29+5 to get 44 then divide 44 by 4
6x+25=2x+3- do 6-2 to get 4x then 3-25 to get -22 then divide -22 by 4
The question is in the picture.
Answers
Answer:
x = 3 , y = 8
Step-by-step explanation:
Consider the figure to be a parallelogram.
• opposite sides of a parallelogram are congruent
then
8x = 5x + 9 ( subtract 5x from both sides )
3x = 9 ( divide both sides by 3 )
x = 3
and
7y - 16 = 5y ( subtract 5y from both sides )
2y - 16 = 0 ( add 16 to both sides )
2y = 16 ( divide both sides by 2 )
y = 8
Every morning, a deli offers a “commuter special” in which customers can select a pastry, beverage, and a copy of one of the local papers and pay $1.00. Their options are listed in the table.
Commuter Special
Pastry
Beverage
Paper
Donut
Coffee
The Times
Brownie
Milk
The Herald
Muffin
Tea
Scone
Orange Juice
Croissant
Last Tuesday, the deli did not have any muffins. How did that affect the number of possible combinations?
It decreased the number of combinations by 1.
It decreased the number of combinations by 4.
It decreased the number of combinations by 8.
It decreased the number of combinations by 10.
Answers
the correlation coefficient will always take values
Answers
The correlation coefficient can take values between -1 and 1, inclusive. A correlation coefficient of -1 indicates negative correlation and 1 indicates positive correlation.
A correlation coefficient of -1 indicates a perfect negative correlation, meaning that as the values of one variable increase, the values of the other variable decrease. A correlation coefficient of 1 indicates a perfect positive correlation, meaning that as the values of one variable increase, the values of the other variable also increase.
A correlation coefficient of 0 indicates no correlation, meaning that there is no relationship between the two variables. Correlation coefficients can take any value between -1 and 1, inclusive, including fractional and decimal values.
Positive values indicate positive correlation, negative values indicate negative correlation, and values close to 0 indicate little or no correlation. The magnitude of the correlation coefficient indicates the strength of the relationship between the two variables.
The closer the coefficient is to 1 or -1, the stronger the relationship between the variables.
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how many pattern block triangles would create 3 hexagons
Answers
If you draw all the diagonals of a normal hexagon, there are 3*6=18 possible triangles; however, three of those are identical (the equilateral triangles), leaving us with 18-3=15 triangle possibilities.
In terms of geometry, a hexagon is a closed, six-sided polygon in two dimensions. A hexagon has six angles and six vertices. Hexa and gonio both denote the number six. A hexagon can be found in the shapes of a honeycomb, a football, a pencil face, and floor tiles. a standard hexagonal 2D geometric polygon with six equal-length sides and six equal-sized angles. All of the lines are closed, and there are no curving edges. A regular hexagon has 720 degrees of internal angles. Additionally, these shapes have six rotating and six reflective symmetries.
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Graph the equation x + 4y - 3 = 0
Answers
The graph of the function is attached below.
What is the Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Given a function x +4y -3 = 0
To graph the equation x + 4y - 3 = 0, we need to find at least two points that satisfy the equation and plot them on a coordinate plane. To do this, we can use the intercept method.
First, we can find the x-intercept by setting y = 0 in the equation and solving for x:
x + 4(0) - 3 = 0
x = 3
So the x-intercept is (3, 0).
Next, we can find the y-intercept by setting x = 0 in the equation and solving for y:
0 + 4y - 3 = 0
4y = 3
y = 3/4
So the y-intercept is (0, 3/4).
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When a number is increased by ten, the result is
three times the number. What is the number?
Answers
Answer:
used to works by in BBC FDA's in BBC FDA's keep that u now u now u now how to be successful so do it.
Step-by-step explanation:
no exception
The regular price on a pair of jeans is $54. The store advertises a back to school sale at 40% of the regular price of the jeans. Two weeks later, the store advertises a sale at an additional 20% off the sale price of the jeans. Two friends decided to purchase the jeans. Shannon says these jeans are now 60% of the regular price. Mary disagrees because she figures that the total discount is less than 60%. What is the cost of the jeans at the 40% off back-to-school sale. What is the cost of the jeans during the additional 20% off sale.
Answers
Answer:
See explanation
Step-by-step explanation:
40% of the original $54 is $21.60, therefore the pants are $21.60 off of their original price. This makes the pants $32.40.
20% of the new $32.40 is $6.48, therefore the pants are $6.48 off of the 40%-off price. This makes the pants $25.92 for their final price.
Number of terms: 8 - 4c
Answers
The Number of terms in the expression 8 - 4c is 2.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Terms are added or subtracted to make a polynomial. They're composed of variables and constants all in multiplication.
We are given an expression as;
8 - 4c
Here c is the variable.
The first one is 8 and the second one is 4c
Therefore, number of terms are 2
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The volume of a cylindrical concrete pillar is approximately 12,042 cubic centimeters. The diameter of the pillar is 10 centimeters.
What is the height of the pillar? Use π ≈3.14 .
Answers
The height of the cylindrical concrete pillar is approximately 153.2 centimeters.
What is the volume of a right circular cylinder?Suppose that the radius of considered right circular cylinder be 'r' units.
And let its height be 'h' units.
Then, its volume is given as;
[tex]V = \pi r^2 h \: \rm unit^3[/tex]
Right circular cylinder is the cylinder in which the line joining center of top circle of the cylinder to the center of the base circle of the cylinder is perpendicular to the surface of its base, and to the top.
We are given that;
Diameter of pillar= 10cm
Volume = 12,042 cubic centimeters
Now,
First, we need to find the radius of the pillar. The diameter of the pillar is given as 10 centimeters, so the radius is half of that:
r = 10/2 = 5 centimeters
Now we can substitute the given volume and radius into the formula and solve for the height:
12,042 = π(5)^2h
Divide both sides by π(5)^2:
h = 12,042 / (π(5)^2)
h ≈ 153.2 centimeters (rounded to one decimal place)
Therefore, by the given volume the answer will be 153.2 centimeters.
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