The value of x is 31/64 or 0.484375 and the value of 61/64 is given by adding the value of 29/64 and 31/64 which is 0.9375.
How to convert a fraction to a decimal?To convert a fraction to a decimal, you need to divide the top number by the bottom number. Here are the steps to follow:
1. Fraction should be written as numerator (top) divided by denominator (bottom).
2. Divide the numerator by the denominator using long division or a calculator.
3. Keep dividing until you get a decimal that terminates or repeats.
a) The given equation is
[tex]\frac{61}{64} = \frac{29}{64} + x[/tex]
[tex]\frac{61}{64} - \frac{29}{64} = x[/tex]
[tex]x = \frac{31}{64}[/tex]
b) Now 31/64 = 0.484375 and given that 29/64 = 0.453125
Hence from the equation 61/64 = 29/64 + 31/64 = 0.453125 + 0.484375
= 0.9375.
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London practices the piano 525 minutes in 3 weeks. Assuming she practices the same amount every week, how many minutes would she practice in 4 weeks?
Answer:
700 minutes
Step-by-step explanation:
First you need to see how much London even practices in one week. So we will divide the total minutes (t) 525 from the total weeks (w) 3:
t / 3 = m
where m equals the amount of minutes London practices in 1 week.
1) rewrite:
t / 3 = m
2) plug in variables:
525 / 3 = m
3) divide:
525 / 3 = 175
Therefore every week, London practices for 175 minutes.
Secondly, we are going to add 1 more week (175) to the total minutes London spent practicing for the 3 weeks (525).
t = m + m
Where t = total minutes altogether (4 weeks) and m equals the minutes of the 3 weeks and the minutes of 1 week.
1) rewrite:
t = m + m
2) plug in:
t = 525 + 175
2) add:
t = 700
Therefore, London would practice 700 minutes in 4 weeks if she practices the same amount every week.
Solve for x round to the nearest tense, if necessary
Using a trigonometric relation we can see that x = 83.7
How to find the value of x?We can see that x is the hypotenuse of the given angle, and we know the measure of the adjacent catehtus to the given angle, then we can use the trigonometric relation:
cos(48°) = 56/hypotenuse
cos(48°) = 56/x
Solving that for x, we will get:
x = 56/cos(48°) = 83.7
That is the value.
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A company's monthly profit, P, from a product is given by P = -x^2+105x-1050, where x is the price of
product in dollars. What is the lowest price of the product, in dollars, that gives a monthly profit of $1550?
Answer:
We are given that the monthly profit, P, from a product is given by the quadratic function:
P = -x^2 + 105x - 1050
To find the lowest price of the product that gives a monthly profit of $1550, we need to solve the equation:
x^2 + 105x - 1050 = 1550Rearranging this equation, we get:
x^2 + 105x - 2600 = 0To solve for x, we can use the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = -1, b = 105, and c = -2600.
Substituting these values, we get:
x = (-105 ± sqrt(105^2 - 4(-1)(-2600))) / 2(-1)
x = (-105 ± sqrt(11025 - 10400)) / (-2)
x = (-105 ± sqrt(625)) / (-2)
We can simplify this expression to:
x = (-105 ± 25) / (-2)
Therefore, the two possible values of x are:
x = (-105 + 25) / (-2) = 40
x = (-105 - 25) / (-2) = 50
Since we are looking for the lowest price that gives a monthly profit of $1550, the answer is $40. Therefore, the lowest price of the product that gives a monthly profit of $1550 is $40.
How many ways can 5 students line up for a picture?
5(98) =___(100-2)
USE THE DISTRIBUTIVE PROPERTY TO FIND EAch product
Answer:
To solve 5(98) =___(100-2) using the distributive property, we can distribute the 5 to both the 100 and the -2:
5(98) = 5(100 - 2)
Now, we can use the distributive property to simplify the right side:
5(98) = 5(100) - 5(2)
Multiplying, we get:
490 = 500 - 10
Simplifying further, we get:
490 = 490
Therefore, the equation is true, and we have verified the distributive property.
Wanda runs a stable. 18 horses currently board at the stable, and 5 of them are bay. What is the probability that a randomly chosen horse will be bay? Write your answer as a fraction or whole number.
Answer:
The probability of choosing a bay horse can be calculated by dividing the number of bay horses by the total number of horses:
Probability of choosing a bay horse = number of bay horses / total number of horses
In this case, we know that there are 5 bay horses and a total of 18 horses:
Probability of choosing a bay horse = 5 / 18
Therefore, the probability of choosing a bay horse is 5/18.
Step-by-step explanation:
Answer:
18/5
Step-by-step explanation:
because a/b equals 18/5
In a classroom survey of twelve students, it was determined that one-half of the students belong to the Chess Club, one-third belong to the Drama Club,
and one-fourth belong to both clubs. How many students are not in either club?
4). 5). 6). 7). 13).
The number of students who belong to neither club is 6 students.
The number of students who are not in either club is 6.
Let's say that there are x students in the classroom.
We know that 1/2 of the students belong to the Chess Club, so 1/2 * x = 6 students belong to the Chess Club.
We also know that 1/3 of the students belong to the Drama Club, so 1/3 * x = 4 students belong to the Drama Club.
Since 1/4 of the students belong to both clubs, then 1/4 * x = 3 students belong to both clubs.
Therefore, the number of students who belong to only one club is 6 - 3 = 3 students.
The number of students who belong to neither club is 6 + 3 - 3 = 6 students.
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PLEASE HELP ME WITH THIS DISCUSSION ASAP!!! 40 POINTS!!
The median is the middle value in a data set when the values are arranged in order, so it would help the real estate agent to set a price that is not too high or too low compared to other similar houses. The student is misrepresenting their performance by reporting the mean as the average, which does not accurately reflect their performance due to the outlier.
What is mean?In statistics, the mean is a measure of central tendency that represents the average value of a set of data. It is calculated by adding up all the values in the data set and dividing the sum by the number of values. The mean is often used to summarize a set of data with a single value that represents the "center" of the data.
Here,
1. For the first situation, the mode would be the most appropriate measure of central tendency because it would tell the supermarket manager which type of lettuce is purchased most often. The mode is the value that appears most frequently in a data set, so it would indicate which type of lettuce is the most popular among customers.
For the second situation, the mean would be the most appropriate measure of central tendency because it would give the average score of all the tests taken during the grading period. The mean is calculated by adding up all the scores and dividing by the number of scores, so it would give a good representation of the student's overall performance.
For the third situation, the median would be the most appropriate measure of central tendency because it would provide a value that is in the middle of the data set, with half of the comparable houses above and half below the selling price.
2. The student is reporting the mean as the average. The mean is calculated by adding up all the grades and dividing by the number of grades, so in this case, the mean would be (97 + 97 + 75 + 70 + 55)/5 = 78.8%. However, this is not an accurate representation of the student's course performance because the mean is sensitive to outliers, which in this case is the low grade of 55%.
If we calculate the median instead, which is the middle value when the grades are arranged in order, we get 77%, which is closer to the actual performance of the student. The median is not affected by outliers, so it provides a better representation of the center of the data set. The student is misrepresenting their performance by reporting the mean as the average, which does not accurately reflect their performance due to the outlier.
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The median is 77%, which is closer to the actual performance of the student.
what is mean?
In statistics, the mean is a measure of central tendency that represents the average value of a set of numbers. It is calculated by adding up all the values in a data set and dividing by the total number of values. The mean is also known as the arithmetic mean or the average. It is commonly used to summarize data and is one of the most widely used measures of central tendency. However, the mean can be sensitive to outliers, which are extreme values that can skew the average and make it less representative of the data set.
The student is reporting the mean as the average. The mean is calculated by adding up all the grades and dividing by the number of grades. In this case, the mean would be:
(97 + 97 + 75 + 70 + 55) / 5 = 78.8%
However, this is not an accurate representation of the student's course performance because the mean is sensitive to outliers, which in this case is the low grade of 55%. If we calculate the median instead, which is the middle value when the grades are arranged in order, we get:
75%, 70%, 55%, 97%, 97%
The median is 77%, which is closer to the actual performance of the student. The median is not affected by outliers, so it provides a better representation of the center of the data set.
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Q22: In a company, the ratio of the number of men to the number of women is 1:3
20% of the men are under the age of 25
80% of the women are under the age of 25
What percentage of all the people in the company are under the age of 25?
A student is making a model of the Great Pyramid of Giza for the school arts festival. The edge length of the right square pyramid is 1.6 meters and its height is 2.4 meters. If the pyramid is to be painted with paint costing $8 per square meter, then, approximately what is the cost of painting the entire surface area of the pyramid, including its square base?.
The cost of painting the entire surface area of the pyramid, including its square base, is approximately $85.44.
What is the cost of painting?
The Great Pyramid of Giza has a square base, so the surface area of the base is simply the area of a square with side length 1.6 meters:
Area of base = (1.6 m)² = 2.56 m²
To find the surface area of the rest of the pyramid, we need to find the area of each of the four triangular faces. Each face is a right triangle with one leg equal to the slant height of the pyramid (which we can find using the Pythagorean theorem) and the other leg equal to half the length of one side of the base.
The slant height can be found using the Pythagorean theorem:
slant height = √((height)² + (1/2 × base)²)
slant height = √((2.4)² + (0.8)²) ≈ 2.53 meters
Then, the area of one triangular face is:
Area of triangular face = (1/2)baseheight
Area of triangular face = (1/2)(1.6 m)(2.53 m) ≈ 2.03 m²
Since there are four triangular faces, the total surface area of the pyramid is:
Total surface area = 4 × (Area of triangular face) + (Area of base)
Total surface area = 4 × (2.03 m²) + 2.56 m²
Total surface area ≈ 10.68 m²
Therefore, the cost of painting the entire surface area of the pyramid at a rate of $8 per square meter is approximately:
Cost = Total surface area × Cost per m²
Cost = 10.68 m² × $8/m²
Cost ≈ $85.44
So, the cost of painting the entire surface area of the pyramid, including its square base, is approximately $85.44.
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HEEELLLLPPP!
Whoever answers right will get brainliest!!!!!!!!!
A hyperbola centered at the origin has vertices at (+/- [tex]\sqrt{7}[/tex] , 0) and foci at (+/- [tex]\sqrt{27}[/tex] , 0). Write the equation of this hyperbola.
The hyperbola equation centered at the origin with the vertices is x²/(t² + 22) - y²/(t² - 27) = 1
How to Solve the Problem?Because the hyperbola is centered at the origin, its standard form equation is:
(x²/a²) - (y²/b²) = 1
Where a denotes the distance between the center and the vertices and b denotes the distance between the center and the co-vertices.
Because the distance between the center and each vertex is √(t² + 72),
We get:
√(t² + 72) = a√(c² - a²) is the distance between the center and each focus, where c is the distance between the center and each focus.
We know that the distance between the center and each focus is √(27),
Thus we can calculate:
√(27 - a²) = √(27 - (t² + 72))
When we simplify, we get:
27 - a² = 27 - t² - 49
a² = t² + 22
When a² is substituted, we get:
(x²/(t² + 22)) - (y²/b²) = 1
Now we must locate b.
Because the distance between the center and each co-vertex is b, we get:
√(a² - 72) = b
√(t² + 22 - 49) = b
√(t² - 27) = b
When b² is substituted, we get:
(x²/(t² + 22)) - (y²/(t² - 27)) = 1
As a result, the hyperbola equation is: x²/(t² + 22) - y²/(t² - 27) = 1
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For circle O, name all the arcs shorter than a semicircle.
A. DBA, DB, DAC, AC, AB
B. BDC, DB, DC, AC, AB, BAC
C. DBA, DB, DC, AC, AB
D. DB, DC, AC, AB
Answer:
C. DBA, DB, DC, AC, AB
Step-by-step explanation:
PLEASE HELP!! ASAP PLEASW
Mr. Wagner was talking to his math class about growth rates and how quickly humans double their weight as babies. As an example, he asked if any of the students knew what they weighed as a newborn. Darren said he weighed 8.25 pounds, Joel said he weighed 8 3 4 pounds, and Rebecca said she was 8 3 8 pounds at birth. Which shows the students from lightest to heaviest weight at birth? Questions
Among the three students the weight of Darren at birth was the lowest with 8.25 pounds.
What is weight?
Weight gauges how much gravity is pulling on a body.
The weight formula is provided by -
w = mg
Since weight is a force, it has the same SI unit as a force, which is Newton (N).
The students from lightest to heaviest weight at birth are -
Darren (8.25 pounds) < Joel (8.34 pounds) < Rebecca (8.388 pounds)
This is because 8.25 is less than 8.34, and 8.34 is less than 8.388. In other words, Darren weighed the least at birth, followed by Joel, and then Rebecca weighed the most.
It's important to note that the differences in weight between the students are relatively small, and all three weights are within a narrow range.
However, when comparing weights, even small differences can be significant.
Therefore, the lowest weight was of Darren (8.25 pounds).
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Write the following as an algebraic expression. Simplify if possible.
Subtract 5y−6 from y−3.
Answer:
Algebraic expression:
y - 3 - (5y - 6)
Simplified: -4y + 3
Step-by-step explanation:
"Subtract 5y−6 from y−3" means the 5y-6 is being taken away from the y-3.
y-3 up front and then minus 5y-6. Use parenthesis to keep things organized.
(y-3) - (5y-6)
This is the algebraic expression.
well, tbh, we don't really need the first set of parenthesis.
y-3 - (5y-6)
This is good enough.
Then, to simplify use distributive property. That minus that we wrote in the middle, it has to go to both the 5y and also to the -6.
y-3 - 5y - -6
= y - 3 - 5y + 6
combine like terms
= -4y + 3
Two lines intersect at point P. If the measures of a pair of vertical angles are (3x - 9) and (x + 15)°, determine the value of x.
Sebastian has
x nickels and
y pennies. He has at least 20 coins worth at most $0.65 combined. Solve this system of inequalities graphically and determine one possible solution.
The solution of the inequalities is x = 11 and y = 9.
What is the solution to the inequalities?The value of x nickels is 0.05x dollars, and the value of y pennies is 0.01y dollars.
The total value of Sebastian's coins will be:
0.05x + 0.01y dollars
Writing the given conditions as a system of inequalities:
Sebastian has at least 20 coins: x + y ≥ 20
The total value of Sebastian's coins is at most $0.65: 0.05x + 0.01y ≤ 0.65
Solving the inequalities, we substitute y ≥ 20 - x into the second inequality:
0.05x + 0.01(20 - x) ≤ 0.65
0.05x + 0.2 - 0.01x ≤ 0.65
0.04x + 0.2 ≤ 0.65
0.04x ≤ 0.45
x ≤ 11.25
The largest possible whole number value for x is 11.
Solving for the value of y from the first inequality:
x + y ≥ 20
11 + y ≥ 20
y ≥ 9
The closest possible whole number value for y is 11
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Students are given an IQ test. The data are normally distributed with a mean of 100 and a standard deviation of 12. Sally scores 114 on the test. The test is given to 300 students.
How many students would you expect to score between Sally’s score and the mean?(100-114)
we would expect about 36 students to score between Sally's score and the mean on the IQ test.
What is frequency distribution?
The gathered data is arranged in tables based on frequency distribution. The information could consist of test results, local weather information, volleyball match results, student grades, etc. Data must be presented meaningfully for understanding after data gathering. A frequency distribution graph is a different approach to displaying data that has been represented graphically.
We can use the normal distribution formula to calculate the number of students who would be expected to score between Sally's score and the mean:
z = (x - μ) / σ
where z is the z-score, x is the raw score, μ is the mean, and σ is the standard deviation.
First, we need to calculate the z-score for Sally's score:
z = (114 - 100) / 12 = 1.17
To find the number of students who would be expected to score in this range, we multiply this proportion by the total number of students:
0.1210 x 300 ≈ 36.3
So, we would expect about 36 students to score between Sally's score and the mean on the IQ test.
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I NEED HELP PLEASE!!!!!!!!!!!!!
Examine the following piecewise function.
Which statements are true?
Select all that apply.
The statements that are true include the following:
A. the function is increasing over the interval -8 ≤ x ≤ -2.
B. the function is constant over the interval -2 ≤ x ≤ 2.
A. the function is decreasing over the interval 3 ≤ x ≤ 7.
What is a piecewise-defined function?In Mathematics, a piecewise-defined function can be defined as a type of function that is defined by two (2) or more mathematical expressions over a specific domain.
Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains. By critically observing the graph of the given piecewise-defined function, we can reasonably infer and logically deduce that it is constant over the interval -2 ≤ x ≤ 2, increasing over the interval -8 ≤ x ≤ -2, and decreasing over the interval 3 ≤ x ≤ 7.
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What is 86/100 simplified
Answer:43/50
Step-by-step explanation:
you must divide both the numerator and denominator by 2
86/100 can be simplified to 43/50 by dividing both the numerator and denominator by 2, which is the greatest common factor. 86/100 can also be written as 0.86 or 86%.
+
P
8
2. Find the interest earned on a $25,000 deposit for 2 years at 4.7%
2
interest, compounded continuously?
(25000) (4.7
25,000
P
P(25,000) (47)
+-117500
= 117
com
or
Interest earned on $25,000 when it is compounded annually for 2 years at the rate of 4.7% is $2,405.23.
What is compounding interest?Compound interest is the term for interest that is earned on interest.
This may be shown using simple math: if you start with $100 and it earns 5% interest every year, you will have $105 at the end of the first year.
At the end of the second year, you will have $110.25.
So, we know that:
Principal amount = $25000
Interest rate = 4.7%
Time = 2 years
Compounded annually
Then, using the compounding calculator:
(Refer to the graph attached below)
The amount after 2 years will be $27,405.23.
Interest in this is:
$27,405.23 - $25,000
$2,405.23
Therefore, interest earned on $25,000 when it is compounded annually for 2 years at the rate of 4.7% is $2,405.23.
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Correct question:
Find the interest earned on a $25,000 deposit for 2 years at 4.7% interest, compounded annually.
Dwane uses 2/6 of a jar of tomato sauce for his pasta. He uses the rest to make pizza. On paper, complete the number bond to show the fraction of a jar of tomato sauce used for pasta and for pizza.
Answer:
Step-by-step explanation:
if he uses 2/6 for his pasta, he should use 2/6 on his pizza (assumption) therefore, he should have used 4/6 of his tomato sauce jar
e) Write a proof to show AABC~ ACFD.
f) What is the longest cart that can pass through the second doorway?
Explain.
Some of the factory's products are long fragile rods that are carried through
the door by hand. The first door is 72 inches west of the start of the second
door. Assume the rod has zero width and BA = 13 in.
The longest cart that can pass through the second doorway is 85 inches or less in length.
e) To demonstrate that AABC~ACFD, we want to show that they have the very shape and that their comparing sides are corresponding.
To start with, we can see that point An is normal to the two triangles. Moreover, point BAC is harmonious to point FDC in light of the fact that they are both right points.
Additionally, point ABC is consistent to point ACF on the grounds that they are substitute inside points framed by the cross-over AC converging equal lines Stomach muscle and FD.
Then, we want to show that the relating sides are corresponding. We can begin by contrasting Stomach muscle and FD. We are given that Stomach muscle = 13 inches, and we can see that FD is the flat distance between the two entryways.
How about we call this distance x. Then, at that point, we can set up an extent:
Stomach muscle/FD = 13/x
To find the length of AC, we can utilize the Pythagorean Hypothesis. We know that BC = Cd = 60 inches, so:
[tex]AC^2 = AB^2 + BC^2[/tex]
[tex]AC^2 = 169 + 3600[/tex]
[tex]AC^2 = 3779[/tex]
[tex]AC = \sqrt{(3779)[/tex]
Presently, we can set up another extent:
AC/CF = Stomach muscle/FD
Subbing the qualities we viewed as before, we get:
[tex]\sqrt{(3779)}/CF = 13/x[/tex]
Increasing the two sides by x, we get:
[tex]x * \sqrt{(3779)}/CF = 13[/tex]
Addressing for CF, we get:
[tex]CF = x * \sqrt{(3779)}/13[/tex]
Thus, we have shown that AABC~ACFD on the grounds that they have similar shape and their comparing sides are relative.
f) The longest truck that can go through the subsequent entryway is a truck whose length is equivalent to or not exactly the level distance between the two entryways. This is on the grounds that the entryways are lined up with one another, so the main limitation on the length of the truck is the level distance between the two entryways.
We are given that the main entryway is 72 inches west of the beginning of the subsequent entryway, and we know that BA = 13 inches. In this way, the flat distance between the two entryways is:
FD = 72 + BA = 85 inches
Subsequently, the longest truck that can go through the subsequent entryway is a truck that is 85 inches or less long.
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What would the answer be?
The length of the arc CD is 14.13 centimeters.
How to find the length of CD?Remember that for an arc defined by an angle a in a circle of radius R, the length of the arc is given by:
L = (a/360°)*2*pi*R
Where pi = 3.14
Here the angle is a = 45°
And R = 18cm, so we can replace that in the formula above to find the length.
L = (45°/360°)*2*3.14*18cm = 14.13cm
That is the length of the arc CD.
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Suppose that a macroeconomic variable is defined by a quadratic function, Q(x) = x^2 − 6x + 7.
a.) Find x and y intercepts as well as the vertex point of Q(x).
b.) Sketch the graph of this quadratic equation.
Part a: x intercepts are (4.414, 0) and (1.586,0) and y intercept = (0, 7).
Part b: From the graph, vertex = (3, -2).
Explain about the quadratic function:In mathematics, a quadratic equation is a second-degree polynomial with the conventional form ax² + bx + c = 0, where a, b, and c are mathematical coefficients and a 0. Second degree refers to an equation where at least one term has been raised to a power of two. The value of the variable x in a quadratic equation is unknown, so we must discover the answer.
Given quadratic function for the macroeconomic variable
Q(x) = x² − 6x + 7.
Part a: x and y intercept:
x-intercept occurs when the function becomes zero.
Put Q(x) = 0
0 = x² − 6x + 7.
Find the factors:
x² − 6x + 7 = 0
a = 1 , b = -6 , c = 7 using the quadratic formula.
x = [-b ± √(b² - 4ac)]/ 2a
x = [6 ± √(36 - 4*1*7)]/ 2*1
x = 3 ± √2
Now,
x = 3 + √2
x = 4.414
and x = 3 - √2 = 1.586
Thus, x intercepts are (4.414, 0) and (1.586,0)
Y-intercept, when x = 0
Q(x) = 0² − 6(0) + 7.
Q(x) = 7
y intercept = (0, 7)
Part b: using the graphing tool, draw the graph of the given quadratic function.
Mark the points (4.414, 0), (1.586,0), and (0, 7).
From the graph, vertex = (3, -2).
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I need help with the first question of this problem.
Answer:
Step-by-step explanation:
hello, it seems this is problematic im sorry but I'm not sure if you could put a better picture.
Find the equation of the straight line passing through the point (0, 2) which is perpendicular to the line y = 1/4x + 5.
Answer:
The given line has a slope of 1/4. The slope of any line perpendicular to this line will have a slope equal to the negative reciprocal of 1/4, which is -4.
We are also given that the line passes through the point (0, 2). Using point-slope form, we can write the equation of the line as:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is the point (0, 2). Substituting the values, we get:
y - 2 = -4(x - 0)
Simplifying, we get:
y - 2 = -4x
Adding 2 to both sides, we get the final equation of the line:
y = -4x + 2
Therefore, the equation of the straight line passing through the point (0, 2) which is perpendicular to the line y = 1/4x + 5 is y = -4x + 2.
The radius of a circle is 19 m. Find its area to the nearest whole number
Answer:
7.07cm
Step-by-step explanation:
A cylinder with a radius of 4 cm and a height of 6-cm is inside of a
sphere with a radius of 10 cm. How much space is inside the sphere,
but outside the cylinder? Round to the nearest tenth if necessary. Use 3.14 for π.